diff --git a/archive/Kenzo-1/Demo.cl b/archive/Kenzo-1/Demo.cl
deleted file mode 100644
index 9cada96..0000000
--- a/archive/Kenzo-1/Demo.cl
+++ /dev/null
@@ -1,100 +0,0 @@
-;;; DEMO DEMO DEMO DEMO DEMO DEMO DEMO DEMO DEMO DEMO DEMO
-;;; DEMO DEMO DEMO DEMO DEMO DEMO DEMO DEMO DEMO DEMO DEMO
-;;; DEMO DEMO DEMO DEMO DEMO DEMO DEMO DEMO DEMO DEMO DEMO
-
-(IN-PACKAGE :USER)
-
-(DEFVAR *STATEMENT*)
-
-;; C = comment
-(DEFUN C (string)
-  (terpri)
-  (dotimes (i 50) (princ "-"))
-  (princ "<Comment>")
-;  (dotimes (i 31) (princ "-"))
-;  (terpri)
-  (princ string)
-;  (terpri)
-  (dotimes (i 50) (princ "-"))
-  (values))
-
-;; R = read
-(DEFMACRO R (statement)
-  (declare (special *statement*))
-  (setf *statement* statement)
-  `(progn
-     (terpri)
-     (dotimes (i 50) (princ "-"))
-     (princ "<Lisp Statement>")
-;     (dotimes (i 29) (princ "-"))
-;     (terpri)
-     (pprint ',statement)
-     (terpri) ; (terpri)
-     (dotimes (i 50) (princ "-"))
-     (values)))
-
-(DEFUN STRIP-INITIAL-SPACES (st)
-  (let ((st2 (make-string (- (length st) (count #\Newline st)))))
-    (declare (type string st2))
-    (do ((i 0 (1+ i))
-         (j 0 (1+ j)))
-        ((= i (length st)))
-      (let ((char (aref st i)))
-        (when (char= char #\newline)
-          (incf i))
-        (setf (aref st2 j) char)))
-    st2))
-
-(DEFMACRO R2 (dstatement)
-  (declare (special *statement* *dstatement*))
-  (setf *dstatement* dstatement)
-  (setf *statement* (read-from-string dstatement))
-  `(progn
-     (terpri)
-      (dotimes (i 50) (princ "-"))
-      (princ "<Lisp Statement>")
-      ;  (dotimes (i 31) (princ "-"))
-      ;  (terpri)
-      (princ (strip-initial-spaces *dstatement*))
-      ;  (terpri)
-      (dotimes (i 50) (princ "-"))
-      (values)))
-
-;; E = EXECUTE
-(DEFUN E ()
-  (declare (special *statement*))
-  (terpri)
-  (dotimes (i 50) (princ "-"))
-  (princ "<Result>")
-;  (dotimes (i 32) (princ "-"))
-  (terpri) ; (terpri)
-  (prin1 (eval *statement*))
-  (terpri) ; (terpri)
-  (dotimes (i 50) (princ "-"))
-  (values))
-
-(DEFUN EE ()
-  (declare (special *statement*))
-  (terpri)
-  (dotimes (i 10) (princ "-"))
-  (princ " Error ")
-  (dotimes (i 33) (princ "-"))
-  (terpri) (terpri)
-  (restart-case
-      (handler-bind ((error
-                         #'(lambda (condition)
-                             (format t "Type-error: ~S~&"
-                               (class-name (class-of condition)))
-                             (apply #'format t
-                                    (simple-condition-format-control condition)
-                                    (simple-condition-format-arguments condition))
-                             (invoke-restart 'my-restart))))
-                  (eval *statement*))
-    (my-restart () (values)))
-  (terpri) (terpri)
-  (dotimes (i 50) (princ "-"))
-  (values))
-
-(DEFMACRO M (statement)
-  (eval statement)
-  '(values ))
\ No newline at end of file
diff --git a/archive/Kenzo-1/How-to-Compile-Kenzo-with-Acl8.txt b/archive/Kenzo-1/How-to-Compile-Kenzo-with-Acl8.txt
deleted file mode 100644
index 944977e..0000000
--- a/archive/Kenzo-1/How-to-Compile-Kenzo-with-Acl8.txt
+++ /dev/null
@@ -1,214 +0,0 @@
-;;;
-;;; [[ Comments added to the listing.]]
-;;;
-
-
-International Allegro CL Free Express Edition
-8.0 [Windows] (Dec 27, 2006 16:11)
-Copyright (C) 1985-2006, Franz Inc., Oakland, CA, USA.  All Rights Reserved.
-
-This development copy of Allegro CL is licensed to:
-   Trial User
-
-CG version 1.81.2.23 / IDE version 1.80.2.21
-Loaded options from C:\Documents and Settings\Fourier\Mes documents\allegro-prefs.cl.
-
-;; Optimization settings: safety 1, space 1, speed 1, debug 2.
-;; For a complete description of all compiler switches given the current
-;; optimization settings evaluate (EXPLAIN-COMPILER-SETTINGS).
-;;;
-;;; [[ Don't forget to define the standard package "COMMON-LISP-USER"
-;;; [[   before starting.
-;;; [[ Cf Tools > IDE 1 > Initial Package := COMMON-LISP-USER
-;;;
-CL-USER(1): (load "cat-init")
-; Loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-Acl8\cat-init.cl
-
- FILE  1: macros
- FILE  2: various
- FILE  3: classes
- FILE  4: combinations
- FILE  5: chain-complexes
- FILE  6: chcm-elementary-op
- FILE  7: effective-homology
- FILE  8: homology-groups
- FILE  9: searching-homology
- FILE 10: cones
- FILE 11: tensor-products
- FILE 12: coalgebras
- FILE 13: cobar
- FILE 14: algebras
- FILE 15: bar
- FILE 16: simplicial-sets
- FILE 17: simplicial-mrphs
- FILE 18: delta
- FILE 19: special-smsts
- FILE 20: suspensions
- FILE 21: disk-pasting
- FILE 22: cartesian-products
- FILE 23: eilenberg-zilber
- FILE 24: kan
- FILE 25: simplicial-groups
- FILE 26: fibrations
- FILE 27: loop-spaces
- FILE 28: ls-twisted-products
- FILE 29: lp-space-efhm
- FILE 30: classifying-spaces
- FILE 31: k-pi-n
- FILE 32: serre
- FILE 33: cs-twisted-products
- FILE 34: cl-space-efhm
- FILE 35: whitehead
- FILE 36: smith
-T
-CL-USER(2): (compile-files)
-
-*CMBN-CONTROL*  = T
-
-;;; Compiling file macros.cl
-;;; Writing fasl file macros.fasl
-;;; Fasl write complete
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-Acl8\macros.fasl
-;;; Compiling file various.cl
-;;; Writing fasl file various.fasl
-;;; Fasl write complete
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-Acl8\various.fasl
-;;; Compiling file classes.cl
-;;; Writing fasl file classes.fasl
-;;; Fasl write complete
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-Acl8\classes.fasl
-;;; Compiling file combinations.cl
-;;; Writing fasl file combinations.fasl
-;;; Fasl write complete
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-Acl8\combinations.fasl
-;;; Compiling file chain-complexes.cl
-;;; Writing fasl file chain-complexes.fasl
-;;; Fasl write complete
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-Acl8\chain-complexes.fasl
-;;; Compiling file chcm-elementary-op.cl
-;;; Writing fasl file chcm-elementary-op.fasl
-;;; Fasl write complete
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-Acl8\chcm-elementary-op.fasl
-;;; Compiling file effective-homology.cl
-;;; Writing fasl file effective-homology.fasl
-;;; Fasl write complete
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-Acl8\effective-homology.fasl
-;;; Compiling file homology-groups.cl
-;;; Writing fasl file homology-groups.fasl
-;;; Fasl write complete
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-Acl8\homology-groups.fasl
-;;; Compiling file searching-homology.cl
-;;; Writing fasl file searching-homology.fasl
-;;; Fasl write complete
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-Acl8\searching-homology.fasl
-;;; Compiling file cones.cl
-;;; Writing fasl file cones.fasl
-;;; Fasl write complete
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-Acl8\cones.fasl
-;;; Compiling file tensor-products.cl
-;;; Writing fasl file tensor-products.fasl
-;;; Fasl write complete
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-Acl8\tensor-products.fasl
-;;; Compiling file coalgebras.cl
-;;; Writing fasl file coalgebras.fasl
-;;; Fasl write complete
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-Acl8\coalgebras.fasl
-;;; Compiling file cobar.cl
-;;; Writing fasl file cobar.fasl
-;;; Fasl write complete
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-Acl8\cobar.fasl
-;;; Compiling file algebras.cl
-;;; Writing fasl file algebras.fasl
-;;; Fasl write complete
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-Acl8\algebras.fasl
-;;; Compiling file bar.cl
-;;; Writing fasl file bar.fasl
-;;; Fasl write complete
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-Acl8\bar.fasl
-;;; Compiling file simplicial-sets.cl
-;;; Writing fasl file simplicial-sets.fasl
-;;; Fasl write complete
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-Acl8\simplicial-sets.fasl
-;;; Compiling file simplicial-mrphs.cl
-;;; Writing fasl file simplicial-mrphs.fasl
-;;; Fasl write complete
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-Acl8\simplicial-mrphs.fasl
-;;; Compiling file delta.cl
-;;; Writing fasl file delta.fasl
-;;; Fasl write complete
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-Acl8\delta.fasl
-;;; Compiling file special-smsts.cl
-;;; Writing fasl file special-smsts.fasl
-;;; Fasl write complete
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-Acl8\special-smsts.fasl
-;;; Compiling file suspensions.cl
-;;; Writing fasl file suspensions.fasl
-;;; Fasl write complete
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-Acl8\suspensions.fasl
-;;; Compiling file disk-pasting.cl
-;;; Writing fasl file disk-pasting.fasl
-;;; Fasl write complete
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-Acl8\disk-pasting.fasl
-;;; Compiling file cartesian-products.cl
-;;; Writing fasl file cartesian-products.fasl
-;;; Fasl write complete
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-Acl8\cartesian-products.fasl
-;;; Compiling file eilenberg-zilber.cl
-;;; Writing fasl file eilenberg-zilber.fasl
-;;; Fasl write complete
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-Acl8\eilenberg-zilber.fasl
-;;; Compiling file kan.cl
-;;; Writing fasl file kan.fasl
-;;; Fasl write complete
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-Acl8\kan.fasl
-;;; Compiling file simplicial-groups.cl
-;;; Writing fasl file simplicial-groups.fasl
-;;; Fasl write complete
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-Acl8\simplicial-groups.fasl
-;;; Compiling file fibrations.cl
-;;; Writing fasl file fibrations.fasl
-;;; Fasl write complete
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-Acl8\fibrations.fasl
-;;; Compiling file loop-spaces.cl
-;;; Writing fasl file loop-spaces.fasl
-;;; Fasl write complete
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-Acl8\loop-spaces.fasl
-;;; Compiling file ls-twisted-products.cl
-;;; Writing fasl file ls-twisted-products.fasl
-;;; Fasl write complete
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-Acl8\ls-twisted-products.fasl
-;;; Compiling file lp-space-efhm.cl
-;;; Writing fasl file lp-space-efhm.fasl
-;;; Fasl write complete
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-Acl8\lp-space-efhm.fasl
-;;; Compiling file classifying-spaces.cl
-;;; Writing fasl file classifying-spaces.fasl
-;;; Fasl write complete
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-Acl8\classifying-spaces.fasl
-;;; Compiling file k-pi-n.cl
-;;; Writing fasl file k-pi-n.fasl
-;;; Fasl write complete
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-Acl8\k-pi-n.fasl
-;;; Compiling file serre.cl
-;;; Writing fasl file serre.fasl
-;;; Fasl write complete
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-Acl8\serre.fasl
-;;; Compiling file cs-twisted-products.cl
-;;; Writing fasl file cs-twisted-products.fasl
-;;; Fasl write complete
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-Acl8\cs-twisted-products.fasl
-;;; Compiling file cl-space-efhm.cl
-;;; Writing fasl file cl-space-efhm.fasl
-;;; Fasl write complete
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-Acl8\cl-space-efhm.fasl
-;;; Compiling file whitehead.cl
-;;; Writing fasl file whitehead.fasl
-;;; Fasl write complete
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-Acl8\whitehead.fasl
-;;; Compiling file smith.cl
-;;; Writing fasl file smith.fasl
-;;; Fasl write complete
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-Acl8\smith.fasl
-("macros" "various" "classes" "combinations" "chain-complexes" "chcm-elementary-op"
- "effective-homology" "homology-groups" "searching-homology" "cones" ...)
-CL-USER(3): (exit)
\ No newline at end of file
diff --git a/archive/Kenzo-1/How-to-Compile-Kenzo-with-CLisp.txt b/archive/Kenzo-1/How-to-Compile-Kenzo-with-CLisp.txt
deleted file mode 100644
index 0b0c175..0000000
--- a/archive/Kenzo-1/How-to-Compile-Kenzo-with-CLisp.txt
+++ /dev/null
@@ -1,257 +0,0 @@
-c:\Documents and Settings\Francis\AA\Kenzo\Kenzo-1.1-CLisp>CLisp
-
-  i i i i i i i       ooooo    o        ooooooo   ooooo   ooooo
-  I I I I I I I      8     8   8           8     8     o  8    8
-  I  \ `+' /  I      8         8           8     8        8    8
-   \  `-+-'  /       8         8           8      ooooo   8oooo
-    `-__|__-'        8         8           8           8  8
-        |            8     o   8           8     o     8  8
-  ------+------       ooooo    8oooooo  ooo8ooo   ooooo   8
-
-Copyright (c) Bruno Haible, Michael Stoll 1992, 1993
-Copyright (c) Bruno Haible, Marcus Daniels 1994-1997
-Copyright (c) Bruno Haible, Pierpaolo Bernardi, Sam Steingold 1998
-Copyright (c) Bruno Haible, Sam Steingold 1999-2000
-Copyright (c) Sam Steingold, Bruno Haible 2001-2006
-
-[1]> (load "cat-init")
-
-;; Loading file C:\DOCUME~1\Francis\AA\Kenzo\Kenzo-1.1-CLisp\cat-init.cl ...
- FILE  1: macros
- FILE  2: various
- FILE  3: classes
- FILE  4: combinations
- FILE  5: chain-complexes
- FILE  6: chcm-elementary-op
- FILE  7: effective-homology
- FILE  8: homology-groups
- FILE  9: searching-homology
- FILE 10: cones
- FILE 11: tensor-products
- FILE 12: coalgebras
- FILE 13: cobar
- FILE 14: algebras
- FILE 15: bar
- FILE 16: simplicial-sets
- FILE 17: simplicial-mrphs
- FILE 18: delta
- FILE 19: special-smsts
- FILE 20: suspensions
- FILE 21: disk-pasting
- FILE 22: cartesian-products
- FILE 23: eilenberg-zilber
- FILE 24: kan
- FILE 25: simplicial-groups
- FILE 26: fibrations
- FILE 27: loop-spaces
- FILE 28: ls-twisted-products
- FILE 29: lp-space-efhm
- FILE 30: classifying-spaces
- FILE 31: k-pi-n
- FILE 32: serre
- FILE 33: cs-twisted-products
- FILE 34: cl-space-efhm
- FILE 35: whitehead
- FILE 36: smith
-;; Loaded file C:\DOCUME~1\Francis\AA\Kenzo\Kenzo-1.1-CLisp\cat-init.cl
-T
-[2]> (compile-files)
-
-*CMBN-CONTROL*  = T
-
-;; Compiling file C:\DOCUME~1\Francis\AA\Kenzo\Kenzo-1.1-CLisp\macros.cl ...
-;; Wrote file C:\DOCUME~1\Francis\AA\Kenzo\Kenzo-1.1-CLisp\macros.fas
-0 errors, 0 warnings
-;; Loading file macros.fas ...
-;; Loaded file macros.fas
-;; Compiling file C:\DOCUME~1\Francis\AA\Kenzo\Kenzo-1.1-CLisp\various.cl ...
-;; Wrote file C:\DOCUME~1\Francis\AA\Kenzo\Kenzo-1.1-CLisp\various.fas
-0 errors, 0 warnings
-;; Loading file various.fas ...
-;; Loaded file various.fas
-;; Compiling file C:\DOCUME~1\Francis\AA\Kenzo\Kenzo-1.1-CLisp\classes.cl ...
-;; Wrote file C:\DOCUME~1\Francis\AA\Kenzo\Kenzo-1.1-CLisp\classes.fas
-
-;;;
-;;; [[ Do not take account of this warning.
-;;; [[ For coherence, these functions are defined in later files.
-;;;
-
-The following functions were used but not defined:
- CMBN-PRINT RESULT-PRINT BICN-PRINT TNPR-PRINT ALLP-PRINT ABAR-PRINT
- ABSM-PRINT CRPR-PRINT LOOP-PRINT GBAR-PRINT
-0 errors, 0 warnings
-;; Loading file classes.fas ...
-;; Loaded file classes.fas
-;; Compiling file C:\DOCUME~1\Francis\AA\Kenzo\Kenzo-1.1-CLisp\combinations.cl ...
-;; Wrote file C:\DOCUME~1\Francis\AA\Kenzo\Kenzo-1.1-CLisp\combinations.fas
-0 errors, 0 warnings
-;; Loading file combinations.fas ...
-;; Loaded file combinations.fas
-;; Compiling file C:\DOCUME~1\Francis\AA\Kenzo\Kenzo-1.1-CLisp\chain-complexes.cl ...
-;; Wrote file C:\DOCUME~1\Francis\AA\Kenzo\Kenzo-1.1-CLisp\chain-complexes.fas
-0 errors, 0 warnings
-;; Loading file chain-complexes.fas ...
-;; Loaded file chain-complexes.fas
-;; Compiling file C:\DOCUME~1\Francis\AA\Kenzo\Kenzo-1.1-CLisp\chcm-elementary-op.cl ...
-;; Wrote file C:\DOCUME~1\Francis\AA\Kenzo\Kenzo-1.1-CLisp\chcm-elementary-op.fas
-0 errors, 0 warnings
-;; Loading file chcm-elementary-op.fas ...
-;; Loaded file chcm-elementary-op.fas
-;; Compiling file C:\DOCUME~1\Francis\AA\Kenzo\Kenzo-1.1-CLisp\effective-homology.cl ...
-;; Wrote file C:\DOCUME~1\Francis\AA\Kenzo\Kenzo-1.1-CLisp\effective-homology.fas
-0 errors, 0 warnings
-;; Loading file effective-homology.fas ...
-;; Loaded file effective-homology.fas
-;; Compiling file C:\DOCUME~1\Francis\AA\Kenzo\Kenzo-1.1-CLisp\homology-groups.cl ...
-;; Wrote file C:\DOCUME~1\Francis\AA\Kenzo\Kenzo-1.1-CLisp\homology-groups.fas
-0 errors, 0 warnings
-;; Loading file homology-groups.fas ...
-;; Loaded file homology-groups.fas
-;; Compiling file C:\DOCUME~1\Francis\AA\Kenzo\Kenzo-1.1-CLisp\searching-homology.cl ...
-;; Wrote file C:\DOCUME~1\Francis\AA\Kenzo\Kenzo-1.1-CLisp\searching-homology.fas
-0 errors, 0 warnings
-;; Loading file searching-homology.fas ...
-;; Loaded file searching-homology.fas
-;; Compiling file C:\DOCUME~1\Francis\AA\Kenzo\Kenzo-1.1-CLisp\cones.cl ...
-;; Wrote file C:\DOCUME~1\Francis\AA\Kenzo\Kenzo-1.1-CLisp\cones.fas
-0 errors, 0 warnings
-;; Loading file cones.fas ...
-;; Loaded file cones.fas
-;; Compiling file C:\DOCUME~1\Francis\AA\Kenzo\Kenzo-1.1-CLisp\tensor-products.cl ...
-;; Wrote file C:\DOCUME~1\Francis\AA\Kenzo\Kenzo-1.1-CLisp\tensor-products.fas
-0 errors, 0 warnings
-;; Loading file tensor-products.fas ...
-;; Loaded file tensor-products.fas
-;; Compiling file C:\DOCUME~1\Francis\AA\Kenzo\Kenzo-1.1-CLisp\coalgebras.cl ...
-;; Wrote file C:\DOCUME~1\Francis\AA\Kenzo\Kenzo-1.1-CLisp\coalgebras.fas
-0 errors, 0 warnings
-;; Loading file coalgebras.fas ...
-;; Loaded file coalgebras.fas
-;; Compiling file C:\DOCUME~1\Francis\AA\Kenzo\Kenzo-1.1-CLisp\cobar.cl ...
-;; Wrote file C:\DOCUME~1\Francis\AA\Kenzo\Kenzo-1.1-CLisp\cobar.fas
-0 errors, 0 warnings
-;; Loading file cobar.fas ...
-;; Loaded file cobar.fas
-;; Compiling file C:\DOCUME~1\Francis\AA\Kenzo\Kenzo-1.1-CLisp\algebras.cl ...
-;; Wrote file C:\DOCUME~1\Francis\AA\Kenzo\Kenzo-1.1-CLisp\algebras.fas
-0 errors, 0 warnings
-;; Loading file algebras.fas ...
-;; Loaded file algebras.fas
-;; Compiling file C:\DOCUME~1\Francis\AA\Kenzo\Kenzo-1.1-CLisp\bar.cl ...
-;; Wrote file C:\DOCUME~1\Francis\AA\Kenzo\Kenzo-1.1-CLisp\bar.fas
-0 errors, 0 warnings
-;; Loading file bar.fas ...
-;; Loaded file bar.fas
-;; Compiling file C:\DOCUME~1\Francis\AA\Kenzo\Kenzo-1.1-CLisp\simplicial-sets.cl ...
-;; Wrote file C:\DOCUME~1\Francis\AA\Kenzo\Kenzo-1.1-CLisp\simplicial-sets.fas
-0 errors, 0 warnings
-;; Loading file simplicial-sets.fas ...
-;; Loaded file simplicial-sets.fas
-;; Compiling file C:\DOCUME~1\Francis\AA\Kenzo\Kenzo-1.1-CLisp\simplicial-mrphs.cl ...
-;; Wrote file C:\DOCUME~1\Francis\AA\Kenzo\Kenzo-1.1-CLisp\simplicial-mrphs.fas
-0 errors, 0 warnings
-;; Loading file simplicial-mrphs.fas ...
-;; Loaded file simplicial-mrphs.fas
-;; Compiling file C:\DOCUME~1\Francis\AA\Kenzo\Kenzo-1.1-CLisp\delta.cl ...
-;; Wrote file C:\DOCUME~1\Francis\AA\Kenzo\Kenzo-1.1-CLisp\delta.fas
-0 errors, 0 warnings
-;; Loading file delta.fas ...
-;; Loaded file delta.fas
-;; Compiling file C:\DOCUME~1\Francis\AA\Kenzo\Kenzo-1.1-CLisp\special-smsts.cl ...
-;; Wrote file C:\DOCUME~1\Francis\AA\Kenzo\Kenzo-1.1-CLisp\special-smsts.fas
-0 errors, 0 warnings
-;; Loading file special-smsts.fas ...
-;; Loaded file special-smsts.fas
-;; Compiling file C:\DOCUME~1\Francis\AA\Kenzo\Kenzo-1.1-CLisp\suspensions.cl ...
-;; Wrote file C:\DOCUME~1\Francis\AA\Kenzo\Kenzo-1.1-CLisp\suspensions.fas
-0 errors, 0 warnings
-;; Loading file suspensions.fas ...
-;; Loaded file suspensions.fas
-;; Compiling file C:\DOCUME~1\Francis\AA\Kenzo\Kenzo-1.1-CLisp\disk-pasting.cl ...
-;; Wrote file C:\DOCUME~1\Francis\AA\Kenzo\Kenzo-1.1-CLisp\disk-pasting.fas
-0 errors, 0 warnings
-;; Loading file disk-pasting.fas ...
-;; Loaded file disk-pasting.fas
-;; Compiling file C:\DOCUME~1\Francis\AA\Kenzo\Kenzo-1.1-CLisp\cartesian-products.cl ...
-;; Wrote file C:\DOCUME~1\Francis\AA\Kenzo\Kenzo-1.1-CLisp\cartesian-products.fas
-0 errors, 0 warnings
-;; Loading file cartesian-products.fas ...
-;; Loaded file cartesian-products.fas
-;; Compiling file C:\DOCUME~1\Francis\AA\Kenzo\Kenzo-1.1-CLisp\eilenberg-zilber.cl ...
-;; Wrote file C:\DOCUME~1\Francis\AA\Kenzo\Kenzo-1.1-CLisp\eilenberg-zilber.fas
-0 errors, 0 warnings
-;; Loading file eilenberg-zilber.fas ...
-;; Loaded file eilenberg-zilber.fas
-;; Compiling file C:\DOCUME~1\Francis\AA\Kenzo\Kenzo-1.1-CLisp\kan.cl ...
-;; Wrote file C:\DOCUME~1\Francis\AA\Kenzo\Kenzo-1.1-CLisp\kan.fas
-0 errors, 0 warnings
-;; Loading file kan.fas ...
-;; Loaded file kan.fas
-;; Compiling file C:\DOCUME~1\Francis\AA\Kenzo\Kenzo-1.1-CLisp\simplicial-groups.cl ...
-;; Wrote file C:\DOCUME~1\Francis\AA\Kenzo\Kenzo-1.1-CLisp\simplicial-groups.fas
-0 errors, 0 warnings
-;; Loading file simplicial-groups.fas ...
-;; Loaded file simplicial-groups.fas
-;; Compiling file C:\DOCUME~1\Francis\AA\Kenzo\Kenzo-1.1-CLisp\fibrations.cl ...
-;; Wrote file C:\DOCUME~1\Francis\AA\Kenzo\Kenzo-1.1-CLisp\fibrations.fas
-0 errors, 0 warnings
-;; Loading file fibrations.fas ...
-;; Loaded file fibrations.fas
-;; Compiling file C:\DOCUME~1\Francis\AA\Kenzo\Kenzo-1.1-CLisp\loop-spaces.cl ...
-;; Wrote file C:\DOCUME~1\Francis\AA\Kenzo\Kenzo-1.1-CLisp\loop-spaces.fas
-0 errors, 0 warnings
-;; Loading file loop-spaces.fas ...
-;; Loaded file loop-spaces.fas
-;; Compiling file C:\DOCUME~1\Francis\AA\Kenzo\Kenzo-1.1-CLisp\ls-twisted-products.cl ...
-;; Wrote file C:\DOCUME~1\Francis\AA\Kenzo\Kenzo-1.1-CLisp\ls-twisted-products.fas
-0 errors, 0 warnings
-;; Loading file ls-twisted-products.fas ...
-;; Loaded file ls-twisted-products.fas
-;; Compiling file C:\DOCUME~1\Francis\AA\Kenzo\Kenzo-1.1-CLisp\lp-space-efhm.cl ...
-;; Wrote file C:\DOCUME~1\Francis\AA\Kenzo\Kenzo-1.1-CLisp\lp-space-efhm.fas
-0 errors, 0 warnings
-;; Loading file lp-space-efhm.fas ...
-;; Loaded file lp-space-efhm.fas
-;; Compiling file C:\DOCUME~1\Francis\AA\Kenzo\Kenzo-1.1-CLisp\classifying-spaces.cl ...
-;; Wrote file C:\DOCUME~1\Francis\AA\Kenzo\Kenzo-1.1-CLisp\classifying-spaces.fas
-0 errors, 0 warnings
-;; Loading file classifying-spaces.fas ...
-;; Loaded file classifying-spaces.fas
-;; Compiling file C:\DOCUME~1\Francis\AA\Kenzo\Kenzo-1.1-CLisp\k-pi-n.cl ...
-;; Wrote file C:\DOCUME~1\Francis\AA\Kenzo\Kenzo-1.1-CLisp\k-pi-n.fas
-0 errors, 0 warnings
-;; Loading file k-pi-n.fas ...
-;; Loaded file k-pi-n.fas
-;; Compiling file C:\DOCUME~1\Francis\AA\Kenzo\Kenzo-1.1-CLisp\serre.cl ...
-;; Wrote file C:\DOCUME~1\Francis\AA\Kenzo\Kenzo-1.1-CLisp\serre.fas
-0 errors, 0 warnings
-;; Loading file serre.fas ...
-;; Loaded file serre.fas
-;; Compiling file C:\DOCUME~1\Francis\AA\Kenzo\Kenzo-1.1-CLisp\cs-twisted-products.cl ...
-;; Wrote file C:\DOCUME~1\Francis\AA\Kenzo\Kenzo-1.1-CLisp\cs-twisted-products.fas
-0 errors, 0 warnings
-;; Loading file cs-twisted-products.fas ...
-;; Loaded file cs-twisted-products.fas
-;; Compiling file C:\DOCUME~1\Francis\AA\Kenzo\Kenzo-1.1-CLisp\cl-space-efhm.cl ...
-;; Wrote file C:\DOCUME~1\Francis\AA\Kenzo\Kenzo-1.1-CLisp\cl-space-efhm.fas
-0 errors, 0 warnings
-;; Loading file cl-space-efhm.fas ...
-;; Loaded file cl-space-efhm.fas
-;; Compiling file C:\DOCUME~1\Francis\AA\Kenzo\Kenzo-1.1-CLisp\whitehead.cl ...
-;; Wrote file C:\DOCUME~1\Francis\AA\Kenzo\Kenzo-1.1-CLisp\whitehead.fas
-0 errors, 0 warnings
-;; Loading file whitehead.fas ...
-;; Loaded file whitehead.fas
-;; Compiling file C:\DOCUME~1\Francis\AA\Kenzo\Kenzo-1.1-CLisp\smith.cl ...
-;; Wrote file C:\DOCUME~1\Francis\AA\Kenzo\Kenzo-1.1-CLisp\smith.fas
-0 errors, 0 warnings
-;; Loading file smith.fas ...
-;; Loaded file smith.fas
-("macros" "various" "classes" "combinations" "chain-complexes" "chcm-elementary-op" "effective-homology"
- "homology-groups" "searching-homology" "cones" ...)
-[3]> (exit)
-
-Bye.
-
-C:\DOCUME~1\Francis\AA\Kenzo\Kenzo-1.1-CLisp>
diff --git a/archive/Kenzo-1/How-to-Compile-Kenzo-with-LispWorks.txt b/archive/Kenzo-1/How-to-Compile-Kenzo-with-LispWorks.txt
deleted file mode 100644
index e14beb8..0000000
--- a/archive/Kenzo-1/How-to-Compile-Kenzo-with-LispWorks.txt
+++ /dev/null
@@ -1,1338 +0,0 @@
-;;;
-;;; [[ Loading the initialization file.
-;;; [[ Do not forget the extension ".cl" not guessed by LispWorks.
-;;; 
-
-CL-USER 1 > (load "cat-init.cl")
-; Loading text file C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-LispWorks\cat-init.cl
-
- FILE  1: macros
- FILE  2: various
- FILE  3: classes
- FILE  4: combinations
- FILE  5: chain-complexes
- FILE  6: chcm-elementary-op
- FILE  7: effective-homology
- FILE  8: homology-groups
- FILE  9: searching-homology
- FILE 10: cones
- FILE 11: tensor-products
- FILE 12: coalgebras
- FILE 13: cobar
- FILE 14: algebras
- FILE 15: bar
- FILE 16: simplicial-sets
- FILE 17: simplicial-mrphs
- FILE 18: delta
- FILE 19: special-smsts
- FILE 20: suspensions
- FILE 21: disk-pasting
- FILE 22: cartesian-products
- FILE 23: eilenberg-zilber
- FILE 24: kan
- FILE 25: simplicial-groups
- FILE 26: fibrations
- FILE 27: loop-spaces
- FILE 28: ls-twisted-products
- FILE 29: lp-space-efhm
- FILE 30: classifying-spaces
- FILE 31: k-pi-n
- FILE 32: serre
- FILE 33: cs-twisted-products
- FILE 34: cl-space-efhm
- FILE 35: whitehead
- FILE 36: smith
-#P"C:/Docume~1/Francis/AA/Kenzo/Kenzo-1.1-LispWorks/cat-init.cl"
-
-;;;
-;;; [[ Compiling the Kenzo files.
-;;; [[ Compiling will be stopped by LispWorks because
-;;; [[   a claimed error; which is not one!
-;;; [[   see below how to bypass.
-;;; [[ Find "***" with your editor.
-;;;
-
-CL-USER 2 > (compile-files)
-
-*CMBN-CONTROL*  = T
-
-;;; Compiling file macros.cl ...
-;;; Safety = 1, Speed = 3, Space = 0, Float = 1, Interruptible = 0
-;;; Compilation speed = 1, Debug = 0, Fixnum safety = 3
-;;; Source level debugging is off 
-;;; Source file recording is  on 
-;;; Cross referencing is on
-; (TOP-LEVEL-FORM 1)
-; (TOP-LEVEL-FORM 2)
-; (TOP-LEVEL-FORM 3)
-; -1-EXPT-N
-; -1-EXPT-N+1
-; -1-EXPT-N-1
-; 2-EXP
-; MASK
-; BINOMIAL-P-Q
-; LEXICO
-; TERM
-; -TERM
-; CFFC
-; -CFFC
-; GNRT
-; -GNRT
-; WITH-TERM
-; WITH--TERM
-; WITH-CMBN
-; TERM-CMBN
-; CMBN-NON-ZERO-P
-; CMBN-ZERO-P
-; CONTROL
-; CONTROLN
-; (DEFVAR *WRONG-CMBN*)
-; CMPR
-; CMPR3
-; BASIS
-; BASIS3
-; DFFR
-; ?
-; MAKE-RSLT
-; RSLT-GNRT
-; RSLT-VALUE
-; RSLT-CLNM
-; RSLT-RNTM
-; I-CMPS
-; I-ADD
-; I-SBTR
-; BCC
-; TCC
-; F
-; G
-; H
-; LBCC
-; RBCC
-; LF
-; LG
-; LH
-; RF
-; RG
-; RH
-; BASELIG
-; BASECOL
-; BCNB
-; BCNC
-; BCND
-; WITH-BICN
-; TNPR
-; WITH-TNPR
-; CPRD
-; CBGN
-; CDEGR
-; CGNRT
-; -CDEGR
-; -CGNRT
-; WITH-CBGN
-; WITH--CBGN
-; WITH-ALLP
-; GNRT-ALLP-TNPR
-; APRD
-; BRGN
-; BDEGR
-; BGNRT
-; -BDEGR
-; -BGNRT
-; WITH-BRGN
-; WITH--BRGN
-; WITH-ABAR
-; WITH-GBAR
-; ABSM
-; WITH-ABSM
-; DEGENERATE-P
-; NON-DEGENERATE-P
-; BSPN
-; BNDR
-; DGNL
-; FACE
-; D
-; MAKE-GMSM-FACES-INFO
-; INFO-GMSM
-; INFO-FACES
-; INFO-FACE-I
-; INFO-BNDR
-; CRPR
-; CRPR2
-; CRPR4
-; ABSM1
-; ABSM2
-; WITH-CRPR
-; WITH-CRPR-2
-; WITH-CRPR-4
-; EILENBERG-ZILBER
-; KFLL
-; KFLL4
-; GRML
-; GRIN
-; BUILD-AB-SMGR
-; POWR
-; PGMSM
-; EXPN
-; WITH-POWR
-; WITH-APOWR
-; APOWR
-; APDGOP
-; APGMSM
-; APEXPN
-; LINE-NUMBER
-; COLUMN-NUMBER
-; LINE-OP-5
-; COLUMN-OP-5
-; LINE-SWAP-5
-; COLUMN-SWAP-5
-; LINE-MINUS-5
-; COLUMN-MINUS-5
-; GNRT-NAME
-; (TOP-LEVEL-FORM 4)
-; Loading fasl file C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-LispWorks\macros.ofasl
-;;; Compiling file various.cl ...
-;;; Safety = 1, Speed = 3, Space = 0, Float = 1, Interruptible = 0
-;;; Compilation speed = 1, Debug = 0, Fixnum safety = 3
-;;; Source level debugging is off 
-;;; Source file recording is  on 
-;;; Cross referencing is on
-; (TOP-LEVEL-FORM 1)
-; (TOP-LEVEL-FORM 2)
-; (TOP-LEVEL-FORM 3)
-; (DEFCONSTANT +EMPTY-LIST+)
-; (DEFCONSTANT +F-EMPTY-VECTOR+)
-; (DEFCONSTANT +S-EMPTY-VECTOR+)
-; (DEFCONSTANT +TRUE+)
-; (DEFCONSTANT +FALSE+)
-; (DEFCONSTANT +2-EXP+)
-; (DEFCONSTANT +MASK+)
-; BINOMIAL-N-P
-; (TOP-LEVEL-FORM 4)
-; (TOP-LEVEL-FORM 5)
-; <A-B<
-; <A-B>
-; >A-B<
-; >A-B>
-; V<A-B>
-; SRANDOM
-; CLOCK
-; DONE
-; (TOP-LEVEL-FORM 6)
-; Loading fasl file C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-LispWorks\various.ofasl
-;;; Compiling file classes.cl ...
-;;; Safety = 1, Speed = 3, Space = 0, Float = 1, Interruptible = 0
-;;; Compilation speed = 1, Debug = 0, Fixnum safety = 3
-;;; Source level debugging is off 
-;;; Source file recording is  on 
-;;; Cross referencing is on
-; (TOP-LEVEL-FORM 1)
-; (TOP-LEVEL-FORM 2)
-; (TOP-LEVEL-FORM 3)
-; (DEFTYPE ANY)
-; (SUBFUNCTION (DEFSETF CMBN-LIST) (DEFSTRUCT CMBN))
-; (SUBFUNCTION (DEFSETF CMBN-DEGR) (DEFSTRUCT CMBN))
-; (SUBFUNCTION MAKE-CMBN (DEFSTRUCT CMBN))
-; (SUBFUNCTION MAKE-CMBN (DEFSTRUCT CMBN))
-; CFFC-P
-; (DEFTYPE CFFC)
-; (DEFTYPE GNRT)
-; (DEFTYPE CMPR)
-; (DEFTYPE CMPRF)
-; TERM-P
-; (DEFTYPE TERM)
-; ICMBN-P
-; (DEFTYPE ICMBN)
-; (DEFTYPE BASIS)
-; (DEFTYPE INTR-MRPH)
-; (DEFCLASS CHAIN-COMPLEX)
-; (DEFCLASS MORPHISM)
-; (DEFCLASS HOMOTOPY-EQUIVALENCE)
-; (DEFVAR *IDNM-COUNTER*)
-; (TOP-LEVEL-FORM 4)
-
-;;;
-;;; [[ Do not take account of these warnings.
-;;; [[ These classes are mutually recursive
-;;; [[   and redefinitions are necessary.
-;;;
-
-;;;*** Warning in (DEFCLASS CHAIN-COMPLEX): (DEFCLASS CHAIN-COMPLEX) defined more than once in C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-LispWorks\classes.cl.
-; (DEFCLASS CHAIN-COMPLEX)
-; (DEFTYPE STRT)
-;;;*** Warning in (DEFCLASS MORPHISM): (DEFCLASS MORPHISM) defined more than once in C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-LispWorks\classes.cl.
-; (DEFCLASS MORPHISM)
-; (SUBFUNCTION (DEFSETF RESULT-RNTM) (DEFSTRUCT RESULT))
-; (SUBFUNCTION (DEFSETF RESULT-CLNM) (DEFSTRUCT RESULT))
-; (SUBFUNCTION (DEFSETF RESULT-VALUE) (DEFSTRUCT RESULT))
-; (SUBFUNCTION (DEFSETF RESULT-GNRT) (DEFSTRUCT RESULT))
-; (SUBFUNCTION MAKE-RESULT (DEFSTRUCT RESULT))
-; (SUBFUNCTION MAKE-RESULT (DEFSTRUCT RESULT))
-; (DEFCLASS REDUCTION)
-;;;*** Warning in (DEFCLASS HOMOTOPY-EQUIVALENCE): (DEFCLASS HOMOTOPY-EQUIVALENCE) defined more than once in C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-LispWorks\classes.cl.
-; (DEFCLASS HOMOTOPY-EQUIVALENCE)
-; (SUBFUNCTION (DEFSETF UPLIG) (DEFSTRUCT MATRICE))
-; (SUBFUNCTION (DEFSETF LEFTCOL) (DEFSTRUCT MATRICE))
-; (SUBFUNCTION MAKE-MATRICE (DEFSTRUCT MATRICE))
-; (SUBFUNCTION MAKE-MATRICE (DEFSTRUCT MATRICE))
-; (SUBFUNCTION (DEFSETF UP) (DEFSTRUCT T-MAT))
-; (SUBFUNCTION (DEFSETF LEFT) (DEFSTRUCT T-MAT))
-; (SUBFUNCTION (DEFSETF ICOL) (DEFSTRUCT T-MAT))
-; (SUBFUNCTION (DEFSETF ILIG) (DEFSTRUCT T-MAT))
-; (SUBFUNCTION (DEFSETF VAL) (DEFSTRUCT T-MAT))
-; (SUBFUNCTION MAKE-T-MAT (DEFSTRUCT T-MAT))
-; (SUBFUNCTION MAKE-T-MAT (DEFSTRUCT T-MAT))
-; (SUBFUNCTION (DEFSETF IBICN) (DEFSTRUCT BICN))
-; (SUBFUNCTION (DEFSETF BCNX) (DEFSTRUCT BICN))
-; (SUBFUNCTION MAKE-BICN (DEFSTRUCT BICN))
-; (SUBFUNCTION MAKE-BICN (DEFSTRUCT BICN))
-; (SUBFUNCTION (DEFSETF GNRT2) (DEFSTRUCT TNPR))
-; (SUBFUNCTION (DEFSETF DEGR2) (DEFSTRUCT TNPR))
-; (SUBFUNCTION (DEFSETF GNRT1) (DEFSTRUCT TNPR))
-; (SUBFUNCTION (DEFSETF DEGR1) (DEFSTRUCT TNPR))
-; (SUBFUNCTION MAKE-TNPR (DEFSTRUCT TNPR))
-; (SUBFUNCTION MAKE-TNPR (DEFSTRUCT TNPR))
-; (DEFCLASS COALGEBRA)
-; CBGN-P
-; (DEFTYPE CBGN)
-; IALLP-P
-; (DEFTYPE IALLP)
-; (SUBFUNCTION (DEFSETF ALLP-LIST) (DEFSTRUCT ALLP))
-; (SUBFUNCTION MAKE-ALLP (DEFSTRUCT ALLP))
-; (SUBFUNCTION MAKE-ALLP (DEFSTRUCT ALLP))
-; (DEFCLASS ALGEBRA)
-; (DEFCLASS HOPF-ALGEBRA)
-; BRGN-P
-; (DEFTYPE BRGN)
-; IABAR-P
-; (DEFTYPE IABAR)
-; (SUBFUNCTION (DEFSETF ABAR-LIST) (DEFSTRUCT ABAR))
-; (SUBFUNCTION MAKE-ABAR (DEFSTRUCT ABAR))
-; (SUBFUNCTION MAKE-ABAR (DEFSTRUCT ABAR))
-; (DEFTYPE DGOP)
-; (DEFTYPE GMSM)
-; (DEFTYPE DLOP)
-; (SUBFUNCTION (DEFSETF GMSM) (DEFSTRUCT ABSM))
-; (SUBFUNCTION (DEFSETF DGOP) (DEFSTRUCT ABSM))
-; (SUBFUNCTION MAKE-ABSM (DEFSTRUCT ABSM))
-; (SUBFUNCTION MAKE-ABSM (DEFSTRUCT ABSM))
-; (DEFTYPE FACE)
-; (DEFTYPE FACE*)
-; (DEFCLASS SIMPLICIAL-SET)
-; (DEFTYPE SINTR)
-; (DEFCLASS SIMPLICIAL-MRPH)
-; SOFT-DLOP-P
-; (DEFTYPE SOFT-DLOP)
-; (SUBFUNCTION (DEFSETF GMSM2) (DEFSTRUCT CRPR))
-; (SUBFUNCTION (DEFSETF DGOP2) (DEFSTRUCT CRPR))
-; (SUBFUNCTION (DEFSETF GMSM1) (DEFSTRUCT CRPR))
-; (SUBFUNCTION (DEFSETF DGOP1) (DEFSTRUCT CRPR))
-; (SUBFUNCTION MAKE-CRPR (DEFSTRUCT CRPR))
-; (SUBFUNCTION MAKE-CRPR (DEFSTRUCT CRPR))
-; (DEFTYPE KFLL)
-; (DEFCLASS KAN)
-; FIBRATION-P
-; (DEFTYPE FIBRATION)
-; (DEFCLASS SIMPLICIAL-GROUP)
-; (DEFCLASS AB-SIMPLICIAL-GROUP)
-; EXPN-P
-; (DEFTYPE EXPN)
-; POWR-P
-; (DEFTYPE POWR)
-; APOWR-P
-; (DEFTYPE APOWR)
-; ILOOP-P
-; (DEFTYPE ILOOP)
-; (SUBFUNCTION (DEFSETF LOOP-LIST) (DEFSTRUCT LOOP))
-; (SUBFUNCTION MAKE-LOOP (DEFSTRUCT LOOP))
-; (SUBFUNCTION MAKE-LOOP (DEFSTRUCT LOOP))
-; (SUBFUNCTION (DEFSETF GBAR-LIST) (DEFSTRUCT GBAR))
-; (SUBFUNCTION (DEFSETF GBAR-DMNS) (DEFSTRUCT GBAR))
-; (SUBFUNCTION MAKE-GBAR (DEFSTRUCT GBAR))
-; (SUBFUNCTION MAKE-GBAR (DEFSTRUCT GBAR))
-; (TOP-LEVEL-FORM 5)
-; Loading fasl file C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-LispWorks\classes.ofasl
-Warning: (DEFCLASS CHAIN-COMPLEX) defined more than once in C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-LispWorks\classes.cl.
-Warning: (DEFCLASS MORPHISM) defined more than once in C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-LispWorks\classes.cl.
-Warning: (DEFCLASS HOMOTOPY-EQUIVALENCE) defined more than once in C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-LispWorks\classes.cl.
-
-;;; ***
-;;; [[ Defining (METHOD PRINT-OBJECT (LOOP T))
-;;; [[   is not at all an error.
-;;; [[ LispWorks complains for Loop being an identifier
-;;; [[   of the Common-Lisp Package and is afraid we damage the system!
-;;; [[ The loops here are the loops of Algebraic Topology
-;;; [[   not the iterated loops of standard programming !!!
-;;;
-
-Error: Defining (METHOD PRINT-OBJECT (LOOP T)) visible from packages COMMON-LISP, CLOS.
-  1 (continue) Define it anyway.
-  2 Discard the new method.
-  3 Try loading classes.ofasl again.
-  4 Give up loading classes.ofasl.
-  5 Try loading another file instead of classes.ofasl.
-  6 (abort) Return to level 0.
-  7 Return to top loop level 0.
-
-Type :b for backtrace, :c <option number> to proceed,  or :? for other options
-
-;;;
-;;; [[ To bypass this claimed "error", answer ":c 1".
-;;;
-
-CL-USER 3 : 1 > :c 1
-;;; Compiling file combinations.cl ...
-;;; Safety = 1, Speed = 3, Space = 0, Float = 1, Interruptible = 0
-;;; Compilation speed = 1, Debug = 0, Fixnum safety = 3
-;;; Source level debugging is off 
-;;; Source file recording is  on 
-;;; Cross referencing is on
-; (TOP-LEVEL-FORM 1)
-; (TOP-LEVEL-FORM 2)
-; (TOP-LEVEL-FORM 3)
-; CMBN-PRINT
-; MAPLEXICO
-; S-CMPR
-; F-CMPR
-; L-CMPR
-; CMBN
-; CHECK-CMBN
-; ZERO-CMBN
-; ZERO-INTR-DFFR
-; (DEFCONSTANT +ZERO-NEGATIVE-CMBN+)
-; CMBN-OPPS
-; N-CMBN
-; 2CMBN-ADD
-; 2CMBN-SBTR
-; 2N-2CMBN
-; CMBN-CMBN
-; NTERM-ADD
-; NCMBN-ADD
-; DSTR-ADD-TERM-TO-CMBN
-; (TOP-LEVEL-FORM 4)
-; Loading fasl file C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-LispWorks\combinations.ofasl
-;;; Compiling file chain-complexes.cl ...
-;;; Safety = 1, Speed = 3, Space = 0, Float = 1, Interruptible = 0
-;;; Compilation speed = 1, Debug = 0, Fixnum safety = 3
-;;; Source level debugging is off 
-;;; Source file recording is  on 
-;;; Cross referencing is on
-; (TOP-LEVEL-FORM 1)
-; (TOP-LEVEL-FORM 2)
-; (TOP-LEVEL-FORM 3)
-; (DEFVAR *LIST-LIST*)
-; CAT-INIT
-; HOW-MANY-OBJECTS
-; ALL-OBJECTS
-; KD
-; K
-; KD2
-; (DEFVAR *CHCM-LIST*)
-; (TOP-LEVEL-FORM 4)
-; (TOP-LEVEL-FORM 5)
-; (METHOD PRINT-OBJECT (CHAIN-COMPLEX T))
-; CHCM
-; (METHOD PRINT-KEYCONS ((EQL :RSLT) T T))
-; (DEFPARAMETER +MAXIMAL-DIMENSION+)
-; (DEFVAR *MRPH-LIST*)
-; (TOP-LEVEL-FORM 6)
-; (TOP-LEVEL-FORM 7)
-; (METHOD ?2 (MORPHISM T))
-; (METHOD ?2 (CHAIN-COMPLEX T))
-; (METHOD ?3 (MORPHISM T T))
-; (METHOD ?3 (CHAIN-COMPLEX T T))
-; (METHOD PRINT-OBJECT (MORPHISM T))
-; MRPH
-;;;*** Warning in BUILD-CHCM: Eliminating a test of a variable with a declared type : BASIS [type BASIS]
-; BUILD-CHCM
-; BASIS2
-; BUILD-MRPH
-; (DEFVAR *START-STACK*)
-; (DEFPARAMETER +TOO-MUCH-TIME+)
-; MRPH-GNRT
-; MRPH-CMBN
-; DO-CONTROL
-; (DEFVAR *FUTURE-DISPLAY*)
-; (DEFVAR *TIME-INTERVAL*)
-;;;*** Warning in GNRT-?: symbol-macro MDEGR is bound but not referenced
-; GNRT-?
-; CMBN-?
-; (TOP-LEVEL-FORM 8)
-; Loading fasl file C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-LispWorks\chain-complexes.ofasl
-;;; Compiling file chcm-elementary-op.cl ...
-;;; Safety = 1, Speed = 3, Space = 0, Float = 1, Interruptible = 0
-;;; Compilation speed = 1, Debug = 0, Fixnum safety = 3
-;;; Source level debugging is off 
-;;; Source file recording is  on 
-;;; Cross referencing is on
-; (TOP-LEVEL-FORM 1)
-; (TOP-LEVEL-FORM 2)
-; (TOP-LEVEL-FORM 3)
-; Z-CHCM
-; ZERO-MRPH
-; IDNT-MRPH
-; OPPS
-; (METHOD CMPS (CHAIN-COMPLEX CHAIN-COMPLEX))
-; (METHOD CMPS (CHAIN-COMPLEX MORPHISM))
-; (METHOD CMPS (MORPHISM CHAIN-COMPLEX))
-; (METHOD CMPS (MORPHISM MORPHISM))
-; N-MRPH-INTR
-; N-MRPH
-; (METHOD ADD (MORPHISM MORPHISM))
-; (METHOD SBTR (MORPHISM MORPHISM))
-; CHANGE-SORC-TRGT
-; DSTR-CHANGE-SORC-TRGT
-; (METHOD ADD (CHAIN-COMPLEX MORPHISM))
-; (TOP-LEVEL-FORM 4)
-; Loading fasl file C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-LispWorks\chcm-elementary-op.ofasl
-;;; Compiling file effective-homology.cl ...
-;;; Safety = 1, Speed = 3, Space = 0, Float = 1, Interruptible = 0
-;;; Compilation speed = 1, Debug = 0, Fixnum safety = 3
-;;; Source level debugging is off 
-;;; Source file recording is  on 
-;;; Cross referencing is on
-; (TOP-LEVEL-FORM 1)
-; (TOP-LEVEL-FORM 2)
-; (TOP-LEVEL-FORM 3)
-; (DEFVAR *RDCT-LIST*)
-; (TOP-LEVEL-FORM 4)
-; (TOP-LEVEL-FORM 5)
-; (METHOD PRINT-OBJECT (REDUCTION STREAM))
-; RDCT
-; BUILD-RDCT
-; TRIVIAL-RDCT
-; (DEFVAR *HMEQ-LIST*)
-; (TOP-LEVEL-FORM 6)
-; (TOP-LEVEL-FORM 7)
-; (METHOD BUILD-HMEQ ((EQL :LRDCT) T))
-; (METHOD PRINT-OBJECT (HOMOTOPY-EQUIVALENCE STREAM))
-; (METHOD HMEQ (INTEGER))
-; (METHOD BUILD-HMEQ ((EQL :LF) T))
-; TRIVIAL-HMEQ
-; (DEFVAR *TDD*)
-; (DEFVAR *BDD*)
-; (DEFVAR *ID-FG*)
-; (DEFVAR *ID-GF-DH-HD*)
-; (DEFVAR *HH*)
-; (DEFVAR *FH*)
-; (DEFVAR *HG*)
-; (DEFVAR *DF-FD*)
-; (DEFVAR *DG-GD*)
-; PRE-CHECK-RDCT
-; (DEFVAR *TC*)
-; (DEFVAR *BC*)
-; CHECK-RDCT
-; (METHOD CMPS (REDUCTION REDUCTION))
-; (METHOD ADD (REDUCTION MORPHISM))
-; BASIC-PERTURBATION-LEMMA
-; EASY-PERTURBATION-LEMMA
-;;;*** Warning in SPECIAL-BPL: symbol-macro OLD-BCC is bound but not referenced
-; SPECIAL-BPL
-; SPECIAL-BPL-2
-; BPL-*-SIGMA
-; (METHOD ADD (HOMOTOPY-EQUIVALENCE MORPHISM))
-; (TOP-LEVEL-FORM 8)
-; Loading fasl file C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-LispWorks\effective-homology.ofasl
-;;; Compiling file homology-groups.cl ...
-;;; Safety = 1, Speed = 3, Space = 0, Float = 1, Interruptible = 0
-;;; Compilation speed = 1, Debug = 0, Fixnum safety = 3
-;;; Source level debugging is off 
-;;; Source file recording is  on 
-;;; Cross referencing is on
-; (TOP-LEVEL-FORM 1)
-; (TOP-LEVEL-FORM 2)
-; (TOP-LEVEL-FORM 3)
-; CREER-MATRICE
-; CHERCHER-HOR
-; CHERCHER-VER
-; INSERER-TERME
-; SUPPRIMER-TERME
-; MAJ-TERME
-; MAJ-LIGNE
-; MAJ-COLONNE
-; MAJ-MATRICE
-; DISP-P
-; DISP-LIGNE
-; DISP-COLONNE
-; NLIG
-; NCOL
-; DISP-MATRICE
-; (METHOD PRINT-OBJECT (MATRICE T))
-; DISP-MATRICE-COLONNES
-; TERME
-; MAT-ALEAT
-; OP-ELEM
-; PEIGNE-VER
-; PEIGNE-HOR
-; OP-LIG
-; OP-COL
-; OP-LIG-N
-; OP-COL-N
-; N-LIG
-; N-COL
-; COPIER-MATRICE
-; RESTE
-; DIVISEUR
-; MAJ-PEIGNE-VER
-; MAJ-PEIGNE-HOR
-; IDENTITE
-; INIT-PEIGNE-VER
-; INIT-PEIGNE-HOR
-; DISP-PEIGNE
-; TERME-MINIMAL-MATRICE
-; TUER-LIGNE
-; TUER-COLONNE
-; PIVOT
-; PIVOT-PARALLELE
-; GENERATEUR-TORSION-H*
-; TERMINER-H*
-; RESTE-MINIMAL-LIGNE
-; RESTE-MINIMAL-COLONNE
-; HOMOLOGIE
-; CHCM-MAT
-; CHCM-HOMOLOGY
-; CHCM-HOMOLOGY-GEN
-; (TOP-LEVEL-FORM 4)
-; Loading fasl file C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-LispWorks\homology-groups.ofasl
-;;; Compiling file searching-homology.cl ...
-;;; Safety = 1, Speed = 3, Space = 0, Float = 1, Interruptible = 0
-;;; Compilation speed = 1, Debug = 0, Fixnum safety = 3
-;;; Source level debugging is off 
-;;; Source file recording is  on 
-;;; Cross referencing is on
-; (TOP-LEVEL-FORM 1)
-; (TOP-LEVEL-FORM 2)
-; (TOP-LEVEL-FORM 3)
-; ECHCM
-; (METHOD HOMOLOGY (CHAIN-COMPLEX T))
-; (DEFGENERIC SEARCH-EFHM)
-; (METHOD SEARCH-EFHM (T T))
-; (METHOD SLOT-UNBOUND (T CHAIN-COMPLEX (EQL (QUOTE EFHM))))
-; (TOP-LEVEL-FORM 4)
-; Loading fasl file C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-LispWorks\searching-homology.ofasl
-;;; Compiling file cones.cl ...
-;;; Safety = 1, Speed = 3, Space = 0, Float = 1, Interruptible = 0
-;;; Compilation speed = 1, Debug = 0, Fixnum safety = 3
-;;; Source level debugging is off 
-;;; Source file recording is  on 
-;;; Cross referencing is on
-; (TOP-LEVEL-FORM 1)
-; (TOP-LEVEL-FORM 2)
-; (TOP-LEVEL-FORM 3)
-; DISPATCH-BICN-CMBN
-; BICN-CMBN-CMBNB
-; BICN-CMBN-CMBNC
-; BICN-CMBN-CMBND
-; MAKE-BICN-CMBN
-; BICN-PRINT
-; BICONE-CMPR
-; BICONE-BASIS
-; BICONE-INTR-DFFR
-; BICONE
-; (METHOD CMPS (HOMOTOPY-EQUIVALENCE HOMOTOPY-EQUIVALENCE))
-; (TOP-LEVEL-FORM 4)
-; Loading fasl file C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-LispWorks\cones.ofasl
-;;; Compiling file tensor-products.cl ...
-;;; Safety = 1, Speed = 3, Space = 0, Float = 1, Interruptible = 0
-;;; Compilation speed = 1, Debug = 0, Fixnum safety = 3
-;;; Source level debugging is off 
-;;; Source file recording is  on 
-;;; Cross referencing is on
-; (TOP-LEVEL-FORM 1)
-; (TOP-LEVEL-FORM 2)
-; (TOP-LEVEL-FORM 3)
-; (DEFVAR *TNPR-WITH-DEGREES*)
-; TNPR-PRINT
-; 2CMBN-TNPR
-; TNSR-PRDC-CMPR
-; TNSR-PRDC-BASIS
-; TNSR-PRDC-INTR-DFFR
-; (METHOD TNSR-PRDC (CHAIN-COMPLEX CHAIN-COMPLEX))
-; TNSR-PRDC-INTR
-; (METHOD TNSR-PRDC (MORPHISM MORPHISM))
-;;;*** Warning in (METHOD TNSR-PRDC (REDUCTION REDUCTION)): symbol-macro TCC2 is bound but not referenced
-;;;*** Warning in (METHOD TNSR-PRDC (REDUCTION REDUCTION)): symbol-macro BCC2 is bound but not referenced
-;;;*** Warning in (METHOD TNSR-PRDC (REDUCTION REDUCTION)): symbol-macro BCC1 is bound but not referenced
-; (METHOD TNSR-PRDC (REDUCTION REDUCTION))
-; (METHOD TNSR-PRDC (HOMOTOPY-EQUIVALENCE HOMOTOPY-EQUIVALENCE))
-; (METHOD SEARCH-EFHM (T (EQL (QUOTE TNSR-PRDC))))
-; (TOP-LEVEL-FORM 4)
-; Loading fasl file C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-LispWorks\tensor-products.ofasl
-;;; Compiling file coalgebras.cl ...
-;;; Safety = 1, Speed = 3, Space = 0, Float = 1, Interruptible = 0
-;;; Compilation speed = 1, Debug = 0, Fixnum safety = 3
-;;; Source level debugging is off 
-;;; Source file recording is  on 
-;;; Cross referencing is on
-; (TOP-LEVEL-FORM 1)
-; (TOP-LEVEL-FORM 2)
-; (TOP-LEVEL-FORM 3)
-; (DEFVAR *CLGB-LIST*)
-; (TOP-LEVEL-FORM 4)
-; (TOP-LEVEL-FORM 5)
-; (METHOD PRINT-OBJECT (COALGEBRA T))
-; CLGB
-; BUILD-CLGB
-; CHANGE-CHCM-TO-CLGB
-; (TOP-LEVEL-FORM 6)
-; Loading fasl file C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-LispWorks\coalgebras.ofasl
-;;; Compiling file cobar.cl ...
-;;; Safety = 1, Speed = 3, Space = 0, Float = 1, Interruptible = 0
-;;; Compilation speed = 1, Debug = 0, Fixnum safety = 3
-;;; Source level debugging is off 
-;;; Source file recording is  on 
-;;; Cross referencing is on
-; (TOP-LEVEL-FORM 1)
-; (TOP-LEVEL-FORM 2)
-; (TOP-LEVEL-FORM 3)
-; ALLP
-; (DEFCONSTANT +NULL-ALLP+)
-; ALLP-PRINT
-; COBAR-CMPR
-; COBAR-BASIS-LENGTH
-; COBAR-BASIS
-; COBAR-INTR-VRTC-DFFR
-; (METHOD VRTC-COBAR (CHAIN-COMPLEX))
-; COBAR-INTR-HRZN-DFFR
-; COBAR-HRZN-DFFR
-; COBAR-INTR-DFFR
-; (METHOD COBAR (COALGEBRA))
-; CMBN-ALLP-CMBN-TNPR
-; NCMBN-COBAR
-; MRPH-VRTC-COBAR-INTR
-; (METHOD VRTC-COBAR (MORPHISM))
-;;;*** Warning in HMTP-VRTC-COBAR-INTR: Eliminating a test of a variable with a declared type : SIGN [type FIXNUM]
-;;;*** Warning in HMTP-VRTC-COBAR-INTR: Eliminating a test of a variable with a declared type : SIGN [type FIXNUM]
-; HMTP-VRTC-COBAR-INTR
-; HMTP-VRTC-COBAR
-; (METHOD VRTC-COBAR (REDUCTION))
-; (METHOD VRTC-COBAR (HOMOTOPY-EQUIVALENCE))
-; (METHOD COBAR (HOMOTOPY-EQUIVALENCE))
-; (TOP-LEVEL-FORM 4)
-; Loading fasl file C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-LispWorks\cobar.ofasl
-;;; Compiling file algebras.cl ...
-;;; Safety = 1, Speed = 3, Space = 0, Float = 1, Interruptible = 0
-;;; Compilation speed = 1, Debug = 0, Fixnum safety = 3
-;;; Source level debugging is off 
-;;; Source file recording is  on 
-;;; Cross referencing is on
-; (TOP-LEVEL-FORM 1)
-; (TOP-LEVEL-FORM 2)
-; (TOP-LEVEL-FORM 3)
-; (DEFVAR *ALGB-LIST*)
-; (TOP-LEVEL-FORM 4)
-; (TOP-LEVEL-FORM 5)
-; (METHOD PRINT-OBJECT (ALGEBRA T))
-; ALGB
-; BUILD-ALGB
-; CHANGE-CHCM-TO-ALGB
-; (DEFVAR *HOPF-LIST*)
-; (TOP-LEVEL-FORM 6)
-; (TOP-LEVEL-FORM 7)
-; (METHOD PRINT-OBJECT (HOPF-ALGEBRA T))
-; HOPF
-; (TOP-LEVEL-FORM 8)
-; Loading fasl file C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-LispWorks\algebras.ofasl
-;;; Compiling file bar.cl ...
-;;; Safety = 1, Speed = 3, Space = 0, Float = 1, Interruptible = 0
-;;; Compilation speed = 1, Debug = 0, Fixnum safety = 3
-;;; Source level debugging is off 
-;;; Source file recording is  on 
-;;; Cross referencing is on
-; (TOP-LEVEL-FORM 1)
-; (TOP-LEVEL-FORM 2)
-; (TOP-LEVEL-FORM 3)
-; ABAR
-; (DEFCONSTANT +NULL-ABAR+)
-; ABAR-PRINT
-; BAR-CMPR
-; BAR-BASIS-LENGTH
-; BAR-BASIS
-; BAR-INTR-VRTC-DFFR
-; (METHOD VRTC-BAR (CHAIN-COMPLEX))
-; BAR-INTR-HRZN-DFFR
-; BAR-HRZN-DFFR
-; BAR-INTR-DFFR
-; (METHOD BAR (ALGEBRA))
-; CMBN-ABAR-CMBN-TNPR
-; NCMBN-BAR
-; MRPH-VRTC-BAR-INTR
-; (METHOD VRTC-BAR (MORPHISM))
-; HMTP-VRTC-BAR-INTR
-; HMTP-VRTC-BAR
-; (METHOD VRTC-BAR (REDUCTION))
-; (METHOD VRTC-BAR (HOMOTOPY-EQUIVALENCE))
-; (METHOD BAR (HOMOTOPY-EQUIVALENCE))
-; (TOP-LEVEL-FORM 4)
-; Loading fasl file C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-LispWorks\bar.ofasl
-;;; Compiling file simplicial-sets.cl ...
-;;; Safety = 1, Speed = 3, Space = 0, Float = 1, Interruptible = 0
-;;; Compilation speed = 1, Debug = 0, Fixnum safety = 3
-;;; Source level debugging is off 
-;;; Source file recording is  on 
-;;; Cross referencing is on
-; (TOP-LEVEL-FORM 1)
-; (TOP-LEVEL-FORM 2)
-; (TOP-LEVEL-FORM 3)
-; (DEFVAR *SMST-LIST*)
-; (TOP-LEVEL-FORM 4)
-; (TOP-LEVEL-FORM 5)
-; DGOP-EXT-INT
-; DGOP-INT-EXT
-; HYPHENIZE-LIST
-; ABSM-PRINT
-; FACE4
-; (METHOD PRINT-OBJECT (SIMPLICIAL-SET T))
-; SMST
-;;;*** Warning in BUILD-SMST: Eliminating a test of a variable with a declared type : FACE [type FACE]
-; BUILD-SMST
-; A-BASIS2
-; INTR-DIAGONAL
-; FACE-BNDR
-; FACE*-BNDR
-; A-CMPR3
-; BSPN-P
-; DLOP-EXT-INT
-; DLOP-INT-EXT
-; 1DGOP*DGOP
-; DGOP*DGOP
-; REMOVE-BIT
-; DGOP/DGOP
-; 1DLOP-DGOP
-; A-FACE4
-; 1DGNR
-; NDGNR
-; NFACE
-; CHECK-FACES
-; CHECK-SMST
-; (TOP-LEVEL-FORM 6)
-; Loading fasl file C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-LispWorks\simplicial-sets.ofasl
-;;; Compiling file simplicial-mrphs.cl ...
-;;; Safety = 1, Speed = 3, Space = 0, Float = 1, Interruptible = 0
-;;; Compilation speed = 1, Debug = 0, Fixnum safety = 3
-;;; Source level debugging is off 
-;;; Source file recording is  on 
-;;; Cross referencing is on
-; (TOP-LEVEL-FORM 1)
-; (TOP-LEVEL-FORM 2)
-; (TOP-LEVEL-FORM 3)
-; (DEFVAR *SMMR-LIST*)
-; (TOP-LEVEL-FORM 4)
-; (TOP-LEVEL-FORM 5)
-; (METHOD ?3 (SIMPLICIAL-MRPH T T))
-; (METHOD PRINT-OBJECT (SIMPLICIAL-MRPH T))
-; SMMR
-; SINTR-INTR
-; BUILD-SMMR
-; TW-A-SINTR3
-; (TOP-LEVEL-FORM 6)
-; Loading fasl file C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-LispWorks\simplicial-mrphs.ofasl
-;;; Compiling file delta.cl ...
-;;; Safety = 1, Speed = 3, Space = 0, Float = 1, Interruptible = 0
-;;; Compilation speed = 1, Debug = 0, Fixnum safety = 3
-;;; Source level debugging is off 
-;;; Source file recording is  on 
-;;; Cross referencing is on
-; (TOP-LEVEL-FORM 1)
-; (TOP-LEVEL-FORM 2)
-; (TOP-LEVEL-FORM 3)
-; (METHOD PRINT-KEYCONS ((EQL :DELT) T T))
-; SOFT-DELTA-CMPR
-; DELTA-FACE
-; SOFT-DELTA-FACE
-; DELTA-BNDR
-; SOFT-DELTA-BNDR
-; DELTA-DGNL
-; SOFT-DELTA-DGNL
-; DELTA-INFINITY
-; SOFT-DELTA-INFINITY
-; DELTA-N-BASIS
-; SOFT-DELTA-N-BASIS
-; DELTA
-; SOFT-DELTA
-; DELTAB-CMPR
-; DELTAB-BNDR
-; DELTAB2-FACE
-; DELTAB2-DGNL
-; DELTAB2-BNDR
-; DELTAB
-; DELTAB2
-; (TOP-LEVEL-FORM 4)
-; Loading fasl file C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-LispWorks\delta.ofasl
-;;; Compiling file special-smsts.cl ...
-;;; Safety = 1, Speed = 3, Space = 0, Float = 1, Interruptible = 0
-;;; Compilation speed = 1, Debug = 0, Fixnum safety = 3
-;;; Source level debugging is off 
-;;; Source file recording is  on 
-;;; Cross referencing is on
-; (TOP-LEVEL-FORM 1)
-; (TOP-LEVEL-FORM 2)
-; (TOP-LEVEL-FORM 3)
-; FINITE-SS-PRE-TABLE
-; FINITE-SS-PRE-TABLE-TABLE
-; FINITE-SS-FIND-GMSM
-; FINITE-SS-FINISH-TABLE
-; FINITE-SS-FINISH-LINE
-; FINITE-SS-FINISH-ENTRY
-; FINITE-SS-TABLE
-; FINITE-SS-BASIS
-; FINITE-SS-FACE
-; FINITE-SS-INTR-BNDR
-; BUILD-FINITE-SS
-; SPHERE-CMPR
-; SPHERE-BASIS
-; SPHERE-FACE
-; SPHERE
-; SPHERE-WEDGE-BASIS
-; SPHERE-WEDGE-FACE
-; SPHERE-WEDGE
-; MOORE-CMPR
-; MOORE-BASIS
-; MOORE-FACE
-; MOORE-INTR-BNDR
-; MOORE
-; R-PROJ-SPACE-CMPR
-; R-PROJ-SPACE-BASIS
-; R-PROJ-SPACE-FACE
-; R-PROJ-SPACE-INTR-BNDR
-; R-PROJ-SPACE
-; (TOP-LEVEL-FORM 4)
-; Loading fasl file C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-LispWorks\special-smsts.ofasl
-;;; Compiling file suspensions.cl ...
-;;; Safety = 1, Speed = 3, Space = 0, Float = 1, Interruptible = 0
-;;; Compilation speed = 1, Debug = 0, Fixnum safety = 3
-;;; Source level debugging is off 
-;;; Source file recording is  on 
-;;; Cross referencing is on
-; (TOP-LEVEL-FORM 1)
-; (TOP-LEVEL-FORM 2)
-; (TOP-LEVEL-FORM 3)
-; SUSPENSION-CMPR
-; SUSPENSION-BASIS
-; SUSPENSION-INTR-DFFR
-; SUSPENSION
-; (METHOD SUSPENSION-1 (CHAIN-COMPLEX))
-; SUSPENSION-INTR-CPRD
-; (METHOD SUSPENSION-1 (COALGEBRA))
-; SUSPENSION-FACE
-; (METHOD SUSPENSION-1 (SIMPLICIAL-SET))
-; SUSPENSION-INTR
-; (METHOD SUSPENSION-1 (MORPHISM))
-; (METHOD SUSPENSION-1 (REDUCTION))
-; (METHOD SUSPENSION-1 (HOMOTOPY-EQUIVALENCE))
-; (METHOD SEARCH-EFHM (T (EQL (QUOTE SUSPENSION))))
-; (TOP-LEVEL-FORM 4)
-; Loading fasl file C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-LispWorks\suspensions.ofasl
-;;; Compiling file disk-pasting.cl ...
-;;; Safety = 1, Speed = 3, Space = 0, Float = 1, Interruptible = 0
-;;; Compilation speed = 1, Debug = 0, Fixnum safety = 3
-;;; Source level debugging is off 
-;;; Source file recording is  on 
-;;; Cross referencing is on
-; (TOP-LEVEL-FORM 1)
-; (TOP-LEVEL-FORM 2)
-; (TOP-LEVEL-FORM 3)
-; DISK-PASTING-CMPR
-; DISK-PASTING-BASIS
-; DISK-PASTING-INTR-DFFR
-; CHCM-DISK-PASTING
-; DISK-PASTING-FACE
-; DISK-PASTING
-; MRPH-DISK-PASTING-INTR
-; MRPH-DISK-PASTING
-; HMEQ-DISK-PASTING
-; (METHOD SEARCH-EFHM (T (EQL (QUOTE DISK-PASTING))))
-; (TOP-LEVEL-FORM 4)
-; Loading fasl file C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-LispWorks\disk-pasting.ofasl
-;;; Compiling file cartesian-products.cl ...
-;;; Safety = 1, Speed = 3, Space = 0, Float = 1, Interruptible = 0
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-;;; Source level debugging is off 
-;;; Source file recording is  on 
-;;; Cross referencing is on
-; (TOP-LEVEL-FORM 1)
-; (TOP-LEVEL-FORM 2)
-; (TOP-LEVEL-FORM 3)
-; CRPR-PRINT
-; EXTRACT-COMMON-DGOP
-; 2ABSM-ACRPR
-; CRTS-PRDC-CMPR
-; CRTS-PRDC-BASIS
-; CRTS-PRDC-FACE
-; CRTS-PRDC-FACE*
-; CRTS-PRDC
-; (TOP-LEVEL-FORM 4)
-; Loading fasl file C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-LispWorks\cartesian-products.ofasl
-;;; Compiling file eilenberg-zilber.cl ...
-;;; Safety = 1, Speed = 3, Space = 0, Float = 1, Interruptible = 0
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-;;; Source level debugging is off 
-;;; Source file recording is  on 
-;;; Cross referencing is on
-; (TOP-LEVEL-FORM 1)
-; (TOP-LEVEL-FORM 2)
-; (TOP-LEVEL-FORM 3)
-; SHUFFLE-SIGN
-; INTR-EML
-; EML
-; INTR-PHI
-; INTR-PHI-2
-; PHI
-; INTR-AW
-; AW
-; EZ
-; LEFT-CRTS-PRDC-EFHM
-; (METHOD SEARCH-EFHM (T (EQL (QUOTE CRTS-PRDC))))
-; (TOP-LEVEL-FORM 4)
-; Loading fasl file C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-LispWorks\eilenberg-zilber.ofasl
-;;; Compiling file kan.cl ...
-;;; Safety = 1, Speed = 3, Space = 0, Float = 1, Interruptible = 0
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-;;; Source level debugging is off 
-;;; Source file recording is  on 
-;;; Cross referencing is on
-; (TOP-LEVEL-FORM 1)
-; (TOP-LEVEL-FORM 2)
-; (TOP-LEVEL-FORM 3)
-; (DEFVAR *KAN-LIST*)
-; (TOP-LEVEL-FORM 4)
-; (TOP-LEVEL-FORM 5)
-; KAN
-; (METHOD PRINT-OBJECT (KAN T))
-; SMST-KAN
-; CHECK-HAT
-; CHECK-KAN
-; (TOP-LEVEL-FORM 6)
-; Loading fasl file C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-LispWorks\kan.ofasl
-;;; Compiling file simplicial-groups.cl ...
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-;;; Source level debugging is off 
-;;; Source file recording is  on 
-;;; Cross referencing is on
-; (TOP-LEVEL-FORM 1)
-; (TOP-LEVEL-FORM 2)
-; (TOP-LEVEL-FORM 3)
-; (DEFVAR *SMGR-LIST*)
-; (TOP-LEVEL-FORM 4)
-; (TOP-LEVEL-FORM 5)
-; SMGR
-; (METHOD PRINT-OBJECT (SIMPLICIAL-GROUP T))
-; (METHOD PRINT-OBJECT (AB-SIMPLICIAL-GROUP T))
-; BUILD-SMGR
-; A-GRML4
-; A-GRIN4
-; (METHOD SLOT-UNBOUND (T SIMPLICIAL-GROUP (EQL (QUOTE KFLL))))
-; SMGR-KFLL-INTR
-; SMGR-KFLL
-; (METHOD SLOT-UNBOUND (T SIMPLICIAL-GROUP (EQL (QUOTE APRD))))
-; SMGR-APRD
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-;;; Compiling file fibrations.cl ...
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-;;; Cross referencing is on
-; (TOP-LEVEL-FORM 1)
-; (TOP-LEVEL-FORM 2)
-; (TOP-LEVEL-FORM 3)
-; FIBRATION-TOTAL-FACE
-; FIBRATION-TOTAL
-; FIBRATION-KFLL
-; (TOP-LEVEL-FORM 4)
-; Loading fasl file C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-LispWorks\fibrations.ofasl
-;;; Compiling file loop-spaces.cl ...
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-;;; Source level debugging is off 
-;;; Source file recording is  on 
-;;; Cross referencing is on
-; (TOP-LEVEL-FORM 1)
-; (TOP-LEVEL-FORM 2)
-; (TOP-LEVEL-FORM 3)
-; (DEFCONSTANT +NULL-LOOP+)
-; NORMALIZE-LOOP
-; UNNORMALIZE-LOOP
-; LOOP3
-;;;*** Warning in LOOP-PRINT: Eliminating a test of a variable with a declared type : STREAM [type STREAM]
-; LOOP-PRINT
-; APOWR-NILOOP
-; LOOP-SPACE-CMPR
-; APOWR-FACE4
-; APOWR-LASTFACE4
-; LOOP-SPACE-FACE
-; LOOP-SPACE-FACE*
-; LOOP-SPACE-GRIN-SINTR
-; LOOP-SPACE-GRML-SINTR
-; LOOP-SPACE
-; GDELTAB
-; (TOP-LEVEL-FORM 4)
-; Loading fasl file C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-LispWorks\loop-spaces.ofasl
-;;; Compiling file ls-twisted-products.cl ...
-;;; Safety = 1, Speed = 3, Space = 0, Float = 1, Interruptible = 0
-;;; Compilation speed = 1, Debug = 0, Fixnum safety = 3
-;;; Source level debugging is off 
-;;; Source file recording is  on 
-;;; Cross referencing is on
-; (TOP-LEVEL-FORM 1)
-; (TOP-LEVEL-FORM 2)
-; (TOP-LEVEL-FORM 3)
-; ABSM-LOOPABSM
-; TWISTED-CRTS-PRDC-FACE
-; TWISTED-CRTS-PRDC
-; DTAU-D-INTR
-; DTAU-D
-; SZCZARBA
-; TWISTED-TNSR-PRDC
-; POP-FIRST-ABSM
-; CRTS-CONTRACTION-INTR
-; CRTS-CONTRACTION
-; TNPR-CONTRACTION
-; (TOP-LEVEL-FORM 4)
-; Loading fasl file C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-LispWorks\ls-twisted-products.ofasl
-;;; Compiling file lp-space-efhm.cl ...
-;;; Safety = 1, Speed = 3, Space = 0, Float = 1, Interruptible = 0
-;;; Compilation speed = 1, Debug = 0, Fixnum safety = 3
-;;; Source level debugging is off 
-;;; Source file recording is  on 
-;;; Cross referencing is on
-; (TOP-LEVEL-FORM 1)
-; (TOP-LEVEL-FORM 2)
-; (TOP-LEVEL-FORM 3)
-; LS-HAT-U-U
-; LS-HAT-LEFT-PERTURBATION-INTR
-; LS-HAT-LEFT-PERTURBATION
-; LS-HAT-T-U
-; LS-HAT-RIGHT-PERTURBATION
-; LS-HAT-U-T
-; LS-LEFT-HMEQ-HAT
-; LS-PRE-LEFT-HMEQ-LEFT-REDUCTION-INTR-F
-; LS-PRE-LEFT-HMEQ-LEFT-REDUCTION-F
-; LS-LEFT-HMEQ-LEFT-REDUCTION-G-INTR
-; LS-LEFT-HMEQ-LEFT-REDUCTION-G
-; LS-PRE-LEFT-HMEQ-LEFT-REDUCTION-H-INTR
-; LS-PRE-LEFT-HMEQ-LEFT-REDUCTION-H
-; LS-PRE-LEFT-HMEQ-LEFT-REDUCTION
-; LS-LEFT-HMEQ-LEFT-REDUCTION
-; LS-PRE-LEFT-HMEQ-RIGHT-REDUCTION-INTR-F
-; LS-PRE-LEFT-HMEQ-RIGHT-REDUCTION-F
-; LS-PRE-LEFT-HMEQ-RIGHT-REDUCTION-INTR-G
-; LS-PRE-LEFT-HMEQ-RIGHT-REDUCTION-G
-; LS-PRE-LEFT-HMEQ-RIGHT-REDUCTION-H
-; LS-PRE-LEFT-HMEQ-RIGHT-REDUCTION
-; LS-LEFT-HMEQ-RIGHT-REDUCTION
-; LS-LEFT-HMEQ
-; LOOP-SPACE-EFHM
-; (METHOD SEARCH-EFHM (T (EQL (QUOTE LOOP-SPACE))))
-; (TOP-LEVEL-FORM 4)
-; Loading fasl file C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-LispWorks\lp-space-efhm.ofasl
-;;; Compiling file classifying-spaces.cl ...
-;;; Safety = 1, Speed = 3, Space = 0, Float = 1, Interruptible = 0
-;;; Compilation speed = 1, Debug = 0, Fixnum safety = 3
-;;; Source level debugging is off 
-;;; Source file recording is  on 
-;;; Cross referencing is on
-; (TOP-LEVEL-FORM 1)
-; (TOP-LEVEL-FORM 2)
-; (TOP-LEVEL-FORM 3)
-; (DEFCONSTANT +NULL-GBAR+)
-; GBAR-PRINT
-; NORMALIZE-GBAR
-; UNNORMALIZE-GBAR
-; GBAR
-; CLASSIFYING-SPACE-CMPR
-; CLASSIFYING-SPACE-BASIS
-; CLASSIFYING-SPACE-FACE
-; (METHOD CLASSIFYING-SPACE (SIMPLICIAL-GROUP))
-; CLASSIFYING-SPACE-GRML-SINTR
-; CLASSIFYING-SPACE-GRIN-SINTR
-; (METHOD CLASSIFYING-SPACE (AB-SIMPLICIAL-GROUP))
-; (TOP-LEVEL-FORM 4)
-; Loading fasl file C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-LispWorks\classifying-spaces.ofasl
-;;; Compiling file k-pi-n.cl ...
-;;; Safety = 1, Speed = 3, Space = 0, Float = 1, Interruptible = 0
-;;; Compilation speed = 1, Debug = 0, Fixnum safety = 3
-;;; Source level debugging is off 
-;;; Source file recording is  on 
-;;; Cross referencing is on
-; (TOP-LEVEL-FORM 1)
-; (TOP-LEVEL-FORM 2)
-; (TOP-LEVEL-FORM 3)
-; K-Z-1-CMPR
-; K-Z-1-FACE
-; Z-ABSM-BAR
-; Z-BAR-ABSM
-; K-Z-1-GRML
-; K-Z-1-GRIN
-; K-Z-1
-; K-Z
-; CIRCLE-CMPR
-; CIRCLE-BASIS
-; CIRCLE
-; KZ1-RDCT-F-INTR
-; KZ1-RDCT-F
-; KZ1-RDCT-G-INTR
-; KZ1-RDCT-G
-; KZ1-RDCT-H-INTR
-; KZ1-RDCT-H
-; KZ1-RDCT
-; KZ1-EFHM
-; (METHOD SEARCH-EFHM (T (EQL (QUOTE K-Z-1))))
-; K-Z2-1-GRML-INTR
-; K-Z2-1-GRML
-; K-Z2-1-GRIN-INTR
-; K-Z2-1-GRIN
-; K-Z2-1
-; K-Z2
-; Z2-ABSM-BAR
-; Z2-BAR-ABSM
-; HOPF-FIBRATION-SINTR
-; HOPF-FIBRATION
-; Z-FUNDAMENTAL-GMSM
-; INTERESTING-FACES
-; GMSM-COCYCLE
-; Z-COCYCLE-GBAR
-; Z-COCYCLE-GBAR-HEAD
-; Z2-FUNDAMENTAL-GMSM
-; Z2-COCYCLE-GBAR
-; Z2-COCYCLE-GBAR-HEAD
-; K-Z-FUNDAMENTAL-CLASS
-; K-Z2-FUNDAMENTAL-CLASS
-; (TOP-LEVEL-FORM 4)
-; Loading fasl file C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-LispWorks\k-pi-n.ofasl
-;;; Compiling file serre.cl ...
-;;; Safety = 1, Speed = 3, Space = 0, Float = 1, Interruptible = 0
-;;; Compilation speed = 1, Debug = 0, Fixnum safety = 3
-;;; Source level debugging is off 
-;;; Source file recording is  on 
-;;; Cross referencing is on
-; (TOP-LEVEL-FORM 1)
-; (TOP-LEVEL-FORM 2)
-; (TOP-LEVEL-FORM 3)
-; FIBRATION-DTAU-D-INTR
-; FIBRATION-DTAU-D
-; BROWN-REDUCTION
-; LEFT-SERRE-EFHM
-; RIGHT-SERRE-EFHM
-; FIBRATION-TOTAL-EFHM
-; (METHOD SEARCH-EFHM (T (EQL (QUOTE FIBRATION-TOTAL))))
-; (TOP-LEVEL-FORM 4)
-; Loading fasl file C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-LispWorks\serre.ofasl
-;;; Compiling file cs-twisted-products.cl ...
-;;; Safety = 1, Speed = 3, Space = 0, Float = 1, Interruptible = 0
-;;; Compilation speed = 1, Debug = 0, Fixnum safety = 3
-;;; Source level debugging is off 
-;;; Source file recording is  on 
-;;; Cross referencing is on
-; (TOP-LEVEL-FORM 1)
-; (TOP-LEVEL-FORM 2)
-; (TOP-LEVEL-FORM 3)
-; SMGR-FIBRATION-SINTR
-; SMGR-FIBRATION
-; SMGR-CRTS-CONTRACTION-INTR
-; SMGR-CRTS-CONTRACTION
-; SMGR-TNPR-CONTRACTION
-; (TOP-LEVEL-FORM 4)
-; Loading fasl file C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-LispWorks\cs-twisted-products.ofasl
-;;; Compiling file cl-space-efhm.cl ...
-;;; Safety = 1, Speed = 3, Space = 0, Float = 1, Interruptible = 0
-;;; Compilation speed = 1, Debug = 0, Fixnum safety = 3
-;;; Source level debugging is off 
-;;; Source file recording is  on 
-;;; Cross referencing is on
-; (TOP-LEVEL-FORM 1)
-; (TOP-LEVEL-FORM 2)
-; (TOP-LEVEL-FORM 3)
-; CS-HAT-U-U
-; CS-HAT-RIGHT-PERTURBATION-INTR
-; CS-HAT-RIGHT-PERTURBATION
-; CS-HAT-U-T
-; CS-HAT-LEFT-PERTURBATION
-; CS-HAT-T-U
-; CS-LEFT-HMEQ-HAT
-; CS-PRE-LEFT-HMEQ-LEFT-REDUCTION-INTR-F
-; CS-PRE-LEFT-HMEQ-LEFT-REDUCTION-F
-; CS-PRE-LEFT-HMEQ-LEFT-REDUCTION-INTR-G
-; CS-PRE-LEFT-HMEQ-LEFT-REDUCTION-G
-; CS-PRE-LEFT-HMEQ-LEFT-REDUCTION-INTR-H
-; CS-PRE-LEFT-HMEQ-LEFT-REDUCTION-H
-; CS-PRE-LEFT-HMEQ-LEFT-REDUCTION
-; CS-LEFT-HMEQ-LEFT-REDUCTION
-; CS-PRE-LEFT-HMEQ-RIGHT-REDUCTION-INTR-F
-; CS-PRE-LEFT-HMEQ-RIGHT-REDUCTION-F
-; CS-PRE-LEFT-HMEQ-RIGHT-REDUCTION-INTR-G
-; CS-PRE-LEFT-HMEQ-RIGHT-REDUCTION-G
-; CS-PRE-LEFT-HMEQ-RIGHT-REDUCTION-H
-; CS-PRE-LEFT-HMEQ-RIGHT-REDUCTION
-; CS-LEFT-HMEQ-RIGHT-REDUCTION
-; CS-LEFT-HMEQ
-; CLASSIFYING-SPACE-EFHM
-; (METHOD SEARCH-EFHM (T (EQL (QUOTE CLASSIFYING-SPACE))))
-; (TOP-LEVEL-FORM 4)
-; Loading fasl file C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-LispWorks\cl-space-efhm.ofasl
-;;; Compiling file whitehead.cl ...
-;;; Safety = 1, Speed = 3, Space = 0, Float = 1, Interruptible = 0
-;;; Compilation speed = 1, Debug = 0, Fixnum safety = 3
-;;; Source level debugging is off 
-;;; Source file recording is  on 
-;;; Cross referencing is on
-; (TOP-LEVEL-FORM 1)
-; (TOP-LEVEL-FORM 2)
-; (TOP-LEVEL-FORM 3)
-; Z-WWHITEHEAD-SINTR
-; Z-WHITEHEAD-SINTR
-; Z-WHITEHEAD
-; Z2-WWHITEHEAD-SINTR
-; Z2-WHITEHEAD-SINTR
-; Z2-WHITEHEAD
-; (TOP-LEVEL-FORM 4)
-; Loading fasl file C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-LispWorks\whitehead.ofasl
-;;; Compiling file smith.cl ...
-;;; Safety = 1, Speed = 3, Space = 0, Float = 1, Interruptible = 0
-;;; Compilation speed = 1, Debug = 0, Fixnum safety = 3
-;;; Source level debugging is off 
-;;; Source file recording is  on 
-;;; Cross referencing is on
-; (TOP-LEVEL-FORM 1)
-; (TOP-LEVEL-FORM 2)
-; (TOP-LEVEL-FORM 3)
-; (DEFTYPE MATRIX)
-; RANDOM-MATRIX
-; IDNT-MTRX
-; COPY-MTRX
-; LEFT-SUBMATRIX
-; MTRX-PRDC
-; CHCM-MTRX
-; LINE-OP
-; COLUMN-OP
-; LINE-SWAP
-; COLUMN-SWAP
-; LINE-MINUS
-; COLUMN-MINUS
-; MINIMAL-TERM
-; MINIMAL-REST-1
-; MINIMAL-REST-2
-;;;*** Warning in MINIMAL-TERM-TOP-LEFT: Declared type (ARRAY FIXNUM (* *)) and value type LIST are disjoint.
-; MINIMAL-TERM-TOP-LEFT
-; PIVOTT
-; LIST-SMITH
-; SMITH
-; (TOP-LEVEL-FORM 4)
-; (DEFCONSTANT +GNRTS-PCKG+)
-; GNRT-NAME-BASIS
-; ECHCM-KILL-EPI-F-INTR
-; ECHCM-KILL-EPI-G-INTR
-; ECHCM-KILL-EPI-H-INTR
-;;;*** Warning in ECHCM-WITHOUT-EPI: symbol-macro ORGN is bound but not referenced
-; ECHCM-WITHOUT-EPI
-; ECHCM-KILL-EPI
-; KILL-EPI
-; KILL-EPIS
-; CHML-CLSS-INTR
-; CHML-CLSS
-; (TOP-LEVEL-FORM 5)
-; Loading fasl file C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-LispWorks\smith.ofasl
-("macros" "various" "classes" "combinations" "chain-complexes" "chcm-elementary-op" "effective-homology" "homology-groups" "searching-homology" "cones" ...)
-
-CL-USER 4 > (quit)
\ No newline at end of file
diff --git a/archive/Kenzo-1/How-to-Use-Kenzo-with-Acl8.txt b/archive/Kenzo-1/How-to-Use-Kenzo-with-Acl8.txt
deleted file mode 100644
index d3c99af..0000000
--- a/archive/Kenzo-1/How-to-Use-Kenzo-with-Acl8.txt
+++ /dev/null
@@ -1,350 +0,0 @@
-;;;
-;;; [[ Comments added to the listing.]]
-;;;
-
-
-International Allegro CL Free Express Edition
-8.0 [Windows] (Dec 27, 2006 16:11)
-Copyright (C) 1985-2006, Franz Inc., Oakland, CA, USA.  All Rights Reserved.
-
-This development copy of Allegro CL is licensed to:
-   Trial User
-
-CG version 1.81.2.23 / IDE version 1.80.2.21
-Loaded options from C:\Documents and Settings\Fourier\Mes documents\allegro-prefs.cl.
-
-;; Optimization settings: safety 1, space 1, speed 1, debug 2.
-;; For a complete description of all compiler switches given the current
-;; optimization settings evaluate (EXPLAIN-COMPILER-SETTINGS).
-;;;
-;;; [[ Don't forget to define the standard package "COMMON-LISP-USER"
-;;; [[   before starting.
-;;; [[ Cf Tools > IDE 1 > Initial Package := COMMON-LISP-USER
-;;;
-;;; [[ You must anyway load the "cat-init" file
-;;;
-CL-USER(1): (load "cat-init")
-; Loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-Acl8\cat-init.cl
-
- FILE  1: macros
- FILE  2: various
- FILE  3: classes
- FILE  4: combinations
- FILE  5: chain-complexes
- FILE  6: chcm-elementary-op
- FILE  7: effective-homology
- FILE  8: homology-groups
- FILE  9: searching-homology
- FILE 10: cones
- FILE 11: tensor-products
- FILE 12: coalgebras
- FILE 13: cobar
- FILE 14: algebras
- FILE 15: bar
- FILE 16: simplicial-sets
- FILE 17: simplicial-mrphs
- FILE 18: delta
- FILE 19: special-smsts
- FILE 20: suspensions
- FILE 21: disk-pasting
- FILE 22: cartesian-products
- FILE 23: eilenberg-zilber
- FILE 24: kan
- FILE 25: simplicial-groups
- FILE 26: fibrations
- FILE 27: loop-spaces
- FILE 28: ls-twisted-products
- FILE 29: lp-space-efhm
- FILE 30: classifying-spaces
- FILE 31: k-pi-n
- FILE 32: serre
- FILE 33: cs-twisted-products
- FILE 34: cl-space-efhm
- FILE 35: whitehead
- FILE 36: smith
-T
-;;;
-;;; [[ Then the Kenzo function "load-cfiles" load the *compiled* files.
-;;; [[ The Kenzo function "load-sfiles" would load the *source* files
-;;; [[   and later the code is interpreted (much slower).
-;;;
-CL-USER(2): (load-cfiles)
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-Acl8\macros.fasl
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-Acl8\various.fasl
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-Acl8\classes.fasl
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-Acl8\combinations.fasl
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-Acl8\chain-complexes.fasl
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-Acl8\chcm-elementary-op.fasl
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-Acl8\effective-homology.fasl
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-Acl8\homology-groups.fasl
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-Acl8\searching-homology.fasl
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-Acl8\cones.fasl
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-Acl8\tensor-products.fasl
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-Acl8\coalgebras.fasl
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-Acl8\cobar.fasl
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-Acl8\algebras.fasl
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-Acl8\bar.fasl
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-Acl8\simplicial-sets.fasl
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-Acl8\simplicial-mrphs.fasl
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-Acl8\delta.fasl
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-Acl8\special-smsts.fasl
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-Acl8\suspensions.fasl
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-Acl8\disk-pasting.fasl
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-Acl8\cartesian-products.fasl
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-Acl8\eilenberg-zilber.fasl
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-Acl8\kan.fasl
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-Acl8\simplicial-groups.fasl
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-Acl8\fibrations.fasl
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-Acl8\loop-spaces.fasl
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-Acl8\ls-twisted-products.fasl
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-Acl8\lp-space-efhm.fasl
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-Acl8\classifying-spaces.fasl
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-Acl8\k-pi-n.fasl
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-Acl8\serre.fasl
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-Acl8\cs-twisted-products.fasl
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-Acl8\cl-space-efhm.fasl
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-Acl8\whitehead.fasl
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-Acl8\smith.fasl
-("macros" "various" "classes" "combinations" "chain-complexes" "chcm-elementary-op"
- "effective-homology" "homology-groups" "searching-homology" "cones" ...)
-;;;
-;;; [[ Now Kenzo is ready.
-;;; [[ For example the computing time
-;;; [[   for the homology group H_7(\Omega^2 S^3).
-;;;
-CL-USER(3): (time (homology (loop-space (sphere 3) 2) 7))
-
-Computing boundary-matrix in dimension 7.
-Rank of the source-module : 13.
-
-
-;; Clock -> 2007-02-05, 14h 48m 1s.
-Computing the boundary of the generator 1 (dimension 7) :
-<<AlLp[7 <<AlLp[2 S3][2 S3][2 S3][2 S3]>>]>> 
-End of computing.
-
-
-;; Clock -> 2007-02-05, 14h 48m 8s.
-Computing the boundary of the generator 2 (dimension 7) :
-<<AlLp[1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][5 <<AlLp[2 S3][2 S3][2 S3]>>]>> 
-End of computing.
-
-
-;; Clock -> 2007-02-05, 14h 48m 8s.
-Computing the boundary of the generator 3 (dimension 7) :
-<<AlLp[1 <<AlLp[2 S3]>>][3 <<AlLp[2 S3][2 S3]>>][3 <<AlLp[2 S3][2 S3]>>]>> 
-End of computing.
-
-
-;; Clock -> 2007-02-05, 14h 48m 8s.
-Computing the boundary of the generator 4 (dimension 7) :
-<<AlLp[1 <<AlLp[2 S3]>>][5 <<AlLp[2 S3][2 S3][2 S3]>>][1 <<AlLp[2 S3]>>]>> 
-End of computing.
-
-
-;; Clock -> 2007-02-05, 14h 48m 8s.
-Computing the boundary of the generator 5 (dimension 7) :
-<<AlLp[3 <<AlLp[2 S3][2 S3]>>][1 <<AlLp[2 S3]>>][3 <<AlLp[2 S3][2 S3]>>]>> 
-End of computing.
-
-
-;; Clock -> 2007-02-05, 14h 48m 8s.
-Computing the boundary of the generator 6 (dimension 7) :
-<<AlLp[3 <<AlLp[2 S3][2 S3]>>][3 <<AlLp[2 S3][2 S3]>>][1 <<AlLp[2 S3]>>]>> 
-End of computing.
-
-
-;; Clock -> 2007-02-05, 14h 48m 8s.
-Computing the boundary of the generator 7 (dimension 7) :
-<<AlLp[5 <<AlLp[2 S3][2 S3][2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>]>> 
-End of computing.
-
-
-;; Clock -> 2007-02-05, 14h 48m 8s.
-Computing the boundary of the generator 8 (dimension 7) :
-<<AlLp[1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][3 <<AlLp[2 S3][2 S3]>>]>> 
-End of computing.
-
-
-;; Clock -> 2007-02-05, 14h 48m 8s.
-Computing the boundary of the generator 9 (dimension 7) :
-<<AlLp[1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][3 <<AlLp[2 S3][2 S3]>>][1 <<AlLp[2 S3]>>]>> 
-End of computing.
-
-
-;; Clock -> 2007-02-05, 14h 48m 8s.
-Computing the boundary of the generator 10 (dimension 7) :
-<<AlLp[1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][3 <<AlLp[2 S3][2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>]>> 
-End of computing.
-
-
-;; Clock -> 2007-02-05, 14h 48m 8s.
-Computing the boundary of the generator 11 (dimension 7) :
-<<AlLp[1 <<AlLp[2 S3]>>][3 <<AlLp[2 S3][2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>]>> 
-End of computing.
-
-
-;; Clock -> 2007-02-05, 14h 48m 8s.
-Computing the boundary of the generator 12 (dimension 7) :
-<<AlLp[3 <<AlLp[2 S3][2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>]>> 
-End of computing.
-
-
-;; Clock -> 2007-02-05, 14h 48m 8s.
-Computing the boundary of the generator 13 (dimension 7) :
-<<AlLp[1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>]>> 
-End of computing.
-
-
-Computing boundary-matrix in dimension 8.
-Rank of the source-module : 21.
-
-
-;; Clock -> 2007-02-05, 14h 48m 8s.
-Computing the boundary of the generator 1 (dimension 8) :
-<<AlLp[1 <<AlLp[2 S3]>>][7 <<AlLp[2 S3][2 S3][2 S3][2 S3]>>]>> 
-End of computing.
-
-
-;; Clock -> 2007-02-05, 14h 48m 9s.
-Computing the boundary of the generator 2 (dimension 8) :
-<<AlLp[3 <<AlLp[2 S3][2 S3]>>][5 <<AlLp[2 S3][2 S3][2 S3]>>]>> 
-End of computing.
-
-
-;; Clock -> 2007-02-05, 14h 48m 9s.
-Computing the boundary of the generator 3 (dimension 8) :
-<<AlLp[5 <<AlLp[2 S3][2 S3][2 S3]>>][3 <<AlLp[2 S3][2 S3]>>]>> 
-End of computing.
-
-
-;; Clock -> 2007-02-05, 14h 48m 9s.
-Computing the boundary of the generator 4 (dimension 8) :
-<<AlLp[7 <<AlLp[2 S3][2 S3][2 S3][2 S3]>>][1 <<AlLp[2 S3]>>]>> 
-End of computing.
-
-
-;; Clock -> 2007-02-05, 14h 48m 9s.
-Computing the boundary of the generator 5 (dimension 8) :
-<<AlLp[1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][5 <<AlLp[2 S3][2 S3][2 S3]>>]>> 
-End of computing.
-
-
-;; Clock -> 2007-02-05, 14h 48m 10s.
-Computing the boundary of the generator 6 (dimension 8) :
-<<AlLp[1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][3 <<AlLp[2 S3][2 S3]>>][3 <<AlLp[2 S3][2 S3]>>]>> 
-End of computing.
-
-
-;; Clock -> 2007-02-05, 14h 48m 10s.
-Computing the boundary of the generator 7 (dimension 8) :
-<<AlLp[1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][5 <<AlLp[2 S3][2 S3][2 S3]>>][1 <<AlLp[2 S3]>>]>> 
-End of computing.
-
-
-;; Clock -> 2007-02-05, 14h 48m 10s.
-Computing the boundary of the generator 8 (dimension 8) :
-<<AlLp[1 <<AlLp[2 S3]>>][3 <<AlLp[2 S3][2 S3]>>][1 <<AlLp[2 S3]>>][3 <<AlLp[2 S3][2 S3]>>]>> 
-End of computing.
-
-
-;; Clock -> 2007-02-05, 14h 48m 10s.
-Computing the boundary of the generator 9 (dimension 8) :
-<<AlLp[1 <<AlLp[2 S3]>>][3 <<AlLp[2 S3][2 S3]>>][3 <<AlLp[2 S3][2 S3]>>][1 <<AlLp[2 S3]>>]>> 
-End of computing.
-
-
-;; Clock -> 2007-02-05, 14h 48m 10s.
-Computing the boundary of the generator 10 (dimension 8) :
-<<AlLp[1 <<AlLp[2 S3]>>][5 <<AlLp[2 S3][2 S3][2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>]>> 
-End of computing.
-
-
-;; Clock -> 2007-02-05, 14h 48m 10s.
-Computing the boundary of the generator 11 (dimension 8) :
-<<AlLp[3 <<AlLp[2 S3][2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][3 <<AlLp[2 S3][2 S3]>>]>> 
-End of computing.
-
-
-;; Clock -> 2007-02-05, 14h 48m 10s.
-Computing the boundary of the generator 12 (dimension 8) :
-<<AlLp[3 <<AlLp[2 S3][2 S3]>>][1 <<AlLp[2 S3]>>][3 <<AlLp[2 S3][2 S3]>>][1 <<AlLp[2 S3]>>]>> 
-End of computing.
-
-
-;; Clock -> 2007-02-05, 14h 48m 10s.
-Computing the boundary of the generator 13 (dimension 8) :
-<<AlLp[3 <<AlLp[2 S3][2 S3]>>][3 <<AlLp[2 S3][2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>]>> 
-End of computing.
-
-
-;; Clock -> 2007-02-05, 14h 48m 10s.
-Computing the boundary of the generator 14 (dimension 8) :
-<<AlLp[5 <<AlLp[2 S3][2 S3][2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>]>> 
-End of computing.
-
-
-;; Clock -> 2007-02-05, 14h 48m 11s.
-Computing the boundary of the generator 15 (dimension 8) :
-<<AlLp[1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][3 <<AlLp[2 S3][2 S3]>>]>> 
-End of computing.
-
-
-;; Clock -> 2007-02-05, 14h 48m 12s.
-Computing the boundary of the generator 16 (dimension 8) :
-<<AlLp[1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][3 <<AlLp[2 S3][2 S3]>>][1 <<AlLp[2 S3]>>]>> 
-End of computing.
-
-
-;; Clock -> 2007-02-05, 14h 48m 12s.
-Computing the boundary of the generator 17 (dimension 8) :
-<<AlLp[1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][3 <<AlLp[2 S3][2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>]>> 
-End of computing.
-
-
-;; Clock -> 2007-02-05, 14h 48m 12s.
-Computing the boundary of the generator 18 (dimension 8) :
-<<AlLp[1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][3 <<AlLp[2 S3][2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>]>> 
-End of computing.
-
-
-;; Clock -> 2007-02-05, 14h 48m 12s.
-Computing the boundary of the generator 19 (dimension 8) :
-<<AlLp[1 <<AlLp[2 S3]>>][3 <<AlLp[2 S3][2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>]>> 
-End of computing.
-
-
-;; Clock -> 2007-02-05, 14h 48m 12s.
-Computing the boundary of the generator 20 (dimension 8) :
-<<AlLp[3 <<AlLp[2 S3][2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>]>> 
-End of computing.
-
-
-;; Clock -> 2007-02-05, 14h 48m 12s.
-Computing the boundary of the generator 21 (dimension 8) :
-<<AlLp[1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>]>> 
-End of computing.
-
-
-
-
-Homology in dimension 7 :
-
-
-Component Z/2Z
-
-Component Z/2Z
-
-
----done---
-
-;; Clock -> 2007-02-05, 14h 48m 13s.
-
-; cpu time (non-gc) 7,633 msec user, 421 msec system
-; cpu time (gc)     3,293 msec user, 40 msec system
-; cpu time (total)  10,926 msec user, 461 msec system
-; real time  11,497 msec
-; space allocation:
-;  3,324,666 cons cells, 94,505,896 other bytes, 0 static bytes
-NIL
-CL-USER(4): (exit)
\ No newline at end of file
diff --git a/archive/Kenzo-1/How-to-Use-Kenzo-with-CLisp.txt b/archive/Kenzo-1/How-to-Use-Kenzo-with-CLisp.txt
deleted file mode 100644
index cb496fd..0000000
--- a/archive/Kenzo-1/How-to-Use-Kenzo-with-CLisp.txt
+++ /dev/null
@@ -1,386 +0,0 @@
-;;;
-;;; [[ Added comments.
-;;;
-c:\Documents and Settings\Francis\AA\Kenzo\Kenzo-1.1-CLisp>clisp
-
-  i i i i i i i       ooooo    o        ooooooo   ooooo   ooooo
-  I I I I I I I      8     8   8           8     8     o  8    8
-  I  \ `+' /  I      8         8           8     8        8    8
-   \  `-+-'  /       8         8           8      ooooo   8oooo
-    `-__|__-'        8         8           8           8  8
-        |            8     o   8           8     o     8  8
-  ------+------       ooooo    8oooooo  ooo8ooo   ooooo   8
-
-Copyright (c) Bruno Haible, Michael Stoll 1992, 1993
-Copyright (c) Bruno Haible, Marcus Daniels 1994-1997
-Copyright (c) Bruno Haible, Pierpaolo Bernardi, Sam Steingold 1998
-Copyright (c) Bruno Haible, Sam Steingold 1999-2000
-Copyright (c) Sam Steingold, Bruno Haible 2001-2006
-;;;
-;;; [[ You must anyway load the "cat-init" file
-;;;
-[1]> (load "cat-init")
-
-;; Loading file C:\DOCUME~1\Francis\AA\Kenzo\Kenzo-1.1-CLisp\cat-init.cl ...
- FILE  1: macros
- FILE  2: various
- FILE  3: classes
- FILE  4: combinations
- FILE  5: chain-complexes
- FILE  6: chcm-elementary-op
- FILE  7: effective-homology
- FILE  8: homology-groups
- FILE  9: searching-homology
- FILE 10: cones
- FILE 11: tensor-products
- FILE 12: coalgebras
- FILE 13: cobar
- FILE 14: algebras
- FILE 15: bar
- FILE 16: simplicial-sets
- FILE 17: simplicial-mrphs
- FILE 18: delta
- FILE 19: special-smsts
- FILE 20: suspensions
- FILE 21: disk-pasting
- FILE 22: cartesian-products
- FILE 23: eilenberg-zilber
- FILE 24: kan
- FILE 25: simplicial-groups
- FILE 26: fibrations
- FILE 27: loop-spaces
- FILE 28: ls-twisted-products
- FILE 29: lp-space-efhm
- FILE 30: classifying-spaces
- FILE 31: k-pi-n
- FILE 32: serre
- FILE 33: cs-twisted-products
- FILE 34: cl-space-efhm
- FILE 35: whitehead
- FILE 36: smith
-;; Loaded file C:\DOCUME~1\Francis\AA\Kenzo\Kenzo-1.1-CLisp\cat-init.cl
-T
-;;;
-;;; [[ Then the Kenzo function "load-cfiles" load the *compiled* files.
-;;; [[ The Kenzo function "load-sfiles" would load the *source* files
-;;; [[   and later the code is interpreted (much slower).
-;;;
-[2]> (load-cfiles)
-
-;; Loading file macros.fas ...
-;; Loaded file macros.fas
-;; Loading file various.fas ...
-;; Loaded file various.fas
-;; Loading file classes.fas ...
-;; Loaded file classes.fas
-;; Loading file combinations.fas ...
-;; Loaded file combinations.fas
-;; Loading file chain-complexes.fas ...
-;; Loaded file chain-complexes.fas
-;; Loading file chcm-elementary-op.fas ...
-;; Loaded file chcm-elementary-op.fas
-;; Loading file effective-homology.fas ...
-;; Loaded file effective-homology.fas
-;; Loading file homology-groups.fas ...
-;; Loaded file homology-groups.fas
-;; Loading file searching-homology.fas ...
-;; Loaded file searching-homology.fas
-;; Loading file cones.fas ...
-;; Loaded file cones.fas
-;; Loading file tensor-products.fas ...
-;; Loaded file tensor-products.fas
-;; Loading file coalgebras.fas ...
-;; Loaded file coalgebras.fas
-;; Loading file cobar.fas ...
-;; Loaded file cobar.fas
-;; Loading file algebras.fas ...
-;; Loaded file algebras.fas
-;; Loading file bar.fas ...
-;; Loaded file bar.fas
-;; Loading file simplicial-sets.fas ...
-;; Loaded file simplicial-sets.fas
-;; Loading file simplicial-mrphs.fas ...
-;; Loaded file simplicial-mrphs.fas
-;; Loading file delta.fas ...
-;; Loaded file delta.fas
-;; Loading file special-smsts.fas ...
-;; Loaded file special-smsts.fas
-;; Loading file suspensions.fas ...
-;; Loaded file suspensions.fas
-;; Loading file disk-pasting.fas ...
-;; Loaded file disk-pasting.fas
-;; Loading file cartesian-products.fas ...
-;; Loaded file cartesian-products.fas
-;; Loading file eilenberg-zilber.fas ...
-;; Loaded file eilenberg-zilber.fas
-;; Loading file kan.fas ...
-;; Loaded file kan.fas
-;; Loading file simplicial-groups.fas ...
-;; Loaded file simplicial-groups.fas
-;; Loading file fibrations.fas ...
-;; Loaded file fibrations.fas
-;; Loading file loop-spaces.fas ...
-;; Loaded file loop-spaces.fas
-;; Loading file ls-twisted-products.fas ...
-;; Loaded file ls-twisted-products.fas
-;; Loading file lp-space-efhm.fas ...
-;; Loaded file lp-space-efhm.fas
-;; Loading file classifying-spaces.fas ...
-;; Loaded file classifying-spaces.fas
-;; Loading file k-pi-n.fas ...
-;; Loaded file k-pi-n.fas
-;; Loading file serre.fas ...
-;; Loaded file serre.fas
-;; Loading file cs-twisted-products.fas ...
-;; Loaded file cs-twisted-products.fas
-;; Loading file cl-space-efhm.fas ...
-;; Loaded file cl-space-efhm.fas
-;; Loading file whitehead.fas ...
-;; Loaded file whitehead.fas
-;; Loading file smith.fas ...
-;; Loaded file smith.fas
-("macros" "various" "classes" "combinations" "chain-complexes" "chcm-elementary-op" "effective-homology"
- "homology-groups" "searching-homology" "cones" ...)
-;;;
-;;; [[ Now Kenzo is ready.
-;;; [[ For example the computing time
-;;; [[   for the homology group H_7(\Omega^2 S^3).
-;;;
-[3]> (time (homology (loop-space (sphere 3) 2) 7))
-
-Computing boundary-matrix in dimension 7.
-Rank of the source-module : 13.
-
-
-;; Clock -> 2007-02-05, 15h 55m 4s.
-Computing the boundary of the generator 1 (dimension 7) :
-<<AlLp[7 <<AlLp[2 S3][2 S3][2 S3][2 S3]>>]>> 
-End of computing.
-
-
-;; Clock -> 2007-02-05, 15h 55m 15s.
-Computing the boundary of the generator 2 (dimension 7) :
-<<AlLp[1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][5 <<AlLp[2 S3][2 S3][2 S3]>>]>> 
-End of computing.
-
-
-;; Clock -> 2007-02-05, 15h 55m 15s.
-Computing the boundary of the generator 3 (dimension 7) :
-<<AlLp[1 <<AlLp[2 S3]>>][3 <<AlLp[2 S3][2 S3]>>][3 <<AlLp[2 S3][2 S3]>>]>> 
-End of computing.
-
-
-;; Clock -> 2007-02-05, 15h 55m 16s.
-Computing the boundary of the generator 4 (dimension 7) :
-<<AlLp[1 <<AlLp[2 S3]>>][5 <<AlLp[2 S3][2 S3][2 S3]>>][1 <<AlLp[2 S3]>>]>> 
-End of computing.
-
-
-;; Clock -> 2007-02-05, 15h 55m 16s.
-Computing the boundary of the generator 5 (dimension 7) :
-<<AlLp[3 <<AlLp[2 S3][2 S3]>>][1 <<AlLp[2 S3]>>][3 <<AlLp[2 S3][2 S3]>>]>> 
-End of computing.
-
-
-;; Clock -> 2007-02-05, 15h 55m 16s.
-Computing the boundary of the generator 6 (dimension 7) :
-<<AlLp[3 <<AlLp[2 S3][2 S3]>>][3 <<AlLp[2 S3][2 S3]>>][1 <<AlLp[2 S3]>>]>> 
-End of computing.
-
-
-;; Clock -> 2007-02-05, 15h 55m 16s.
-Computing the boundary of the generator 7 (dimension 7) :
-<<AlLp[5 <<AlLp[2 S3][2 S3][2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>]>> 
-End of computing.
-
-
-;; Clock -> 2007-02-05, 15h 55m 16s.
-Computing the boundary of the generator 8 (dimension 7) :
-<<AlLp[1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][3 <<AlLp[2 S3][2 S3]>>]>> 
-End of computing.
-
-
-;; Clock -> 2007-02-05, 15h 55m 16s.
-Computing the boundary of the generator 9 (dimension 7) :
-<<AlLp[1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][3 <<AlLp[2 S3][2 S3]>>][1 <<AlLp[2 S3]>>]>> 
-End of computing.
-
-
-;; Clock -> 2007-02-05, 15h 55m 16s.
-Computing the boundary of the generator 10 (dimension 7) :
-<<AlLp[1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][3 <<AlLp[2 S3][2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>]>> 
-End of computing.
-
-
-;; Clock -> 2007-02-05, 15h 55m 16s.
-Computing the boundary of the generator 11 (dimension 7) :
-<<AlLp[1 <<AlLp[2 S3]>>][3 <<AlLp[2 S3][2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>]>> 
-End of computing.
-
-
-;; Clock -> 2007-02-05, 15h 55m 17s.
-Computing the boundary of the generator 12 (dimension 7) :
-<<AlLp[3 <<AlLp[2 S3][2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>]>> 
-End of computing.
-
-
-;; Clock -> 2007-02-05, 15h 55m 17s.
-Computing the boundary of the generator 13 (dimension 7) :
-<<AlLp[1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>]>> 
-End of computing.
-
-
-Computing boundary-matrix in dimension 8.
-Rank of the source-module : 21.
-
-
-;; Clock -> 2007-02-05, 15h 55m 17s.
-Computing the boundary of the generator 1 (dimension 8) :
-<<AlLp[1 <<AlLp[2 S3]>>][7 <<AlLp[2 S3][2 S3][2 S3][2 S3]>>]>> 
-End of computing.
-
-
-;; Clock -> 2007-02-05, 15h 55m 18s.
-Computing the boundary of the generator 2 (dimension 8) :
-<<AlLp[3 <<AlLp[2 S3][2 S3]>>][5 <<AlLp[2 S3][2 S3][2 S3]>>]>> 
-End of computing.
-
-
-;; Clock -> 2007-02-05, 15h 55m 18s.
-Computing the boundary of the generator 3 (dimension 8) :
-<<AlLp[5 <<AlLp[2 S3][2 S3][2 S3]>>][3 <<AlLp[2 S3][2 S3]>>]>> 
-End of computing.
-
-
-;; Clock -> 2007-02-05, 15h 55m 19s.
-Computing the boundary of the generator 4 (dimension 8) :
-<<AlLp[7 <<AlLp[2 S3][2 S3][2 S3][2 S3]>>][1 <<AlLp[2 S3]>>]>> 
-End of computing.
-
-
-;; Clock -> 2007-02-05, 15h 55m 20s.
-Computing the boundary of the generator 5 (dimension 8) :
-<<AlLp[1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][5 <<AlLp[2 S3][2 S3][2 S3]>>]>> 
-End of computing.
-
-
-;; Clock -> 2007-02-05, 15h 55m 20s.
-Computing the boundary of the generator 6 (dimension 8) :
-<<AlLp[1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][3 <<AlLp[2 S3][2 S3]>>][3 <<AlLp[2 S3][2 S3]>>]>> 
-End of computing.
-
-
-;; Clock -> 2007-02-05, 15h 55m 21s.
-Computing the boundary of the generator 7 (dimension 8) :
-<<AlLp[1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][5 <<AlLp[2 S3][2 S3][2 S3]>>][1 <<AlLp[2 S3]>>]>> 
-End of computing.
-
-
-;; Clock -> 2007-02-05, 15h 55m 21s.
-Computing the boundary of the generator 8 (dimension 8) :
-<<AlLp[1 <<AlLp[2 S3]>>][3 <<AlLp[2 S3][2 S3]>>][1 <<AlLp[2 S3]>>][3 <<AlLp[2 S3][2 S3]>>]>> 
-End of computing.
-
-
-;; Clock -> 2007-02-05, 15h 55m 21s.
-Computing the boundary of the generator 9 (dimension 8) :
-<<AlLp[1 <<AlLp[2 S3]>>][3 <<AlLp[2 S3][2 S3]>>][3 <<AlLp[2 S3][2 S3]>>][1 <<AlLp[2 S3]>>]>> 
-End of computing.
-
-
-;; Clock -> 2007-02-05, 15h 55m 21s.
-Computing the boundary of the generator 10 (dimension 8) :
-<<AlLp[1 <<AlLp[2 S3]>>][5 <<AlLp[2 S3][2 S3][2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>]>> 
-End of computing.
-
-
-;; Clock -> 2007-02-05, 15h 55m 22s.
-Computing the boundary of the generator 11 (dimension 8) :
-<<AlLp[3 <<AlLp[2 S3][2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][3 <<AlLp[2 S3][2 S3]>>]>> 
-End of computing.
-
-
-;; Clock -> 2007-02-05, 15h 55m 22s.
-Computing the boundary of the generator 12 (dimension 8) :
-<<AlLp[3 <<AlLp[2 S3][2 S3]>>][1 <<AlLp[2 S3]>>][3 <<AlLp[2 S3][2 S3]>>][1 <<AlLp[2 S3]>>]>> 
-End of computing.
-
-
-;; Clock -> 2007-02-05, 15h 55m 22s.
-Computing the boundary of the generator 13 (dimension 8) :
-<<AlLp[3 <<AlLp[2 S3][2 S3]>>][3 <<AlLp[2 S3][2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>]>> 
-End of computing.
-
-
-;; Clock -> 2007-02-05, 15h 55m 22s.
-Computing the boundary of the generator 14 (dimension 8) :
-<<AlLp[5 <<AlLp[2 S3][2 S3][2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>]>> 
-End of computing.
-
-
-;; Clock -> 2007-02-05, 15h 55m 23s.
-Computing the boundary of the generator 15 (dimension 8) :
-<<AlLp[1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][3 <<AlLp[2 S3][2 S3]>>]>> 
-End of computing.
-
-
-;; Clock -> 2007-02-05, 15h 55m 23s.
-Computing the boundary of the generator 16 (dimension 8) :
-<<AlLp[1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][3 <<AlLp[2 S3][2 S3]>>][1 <<AlLp[2 S3]>>]>> 
-End of computing.
-
-
-;; Clock -> 2007-02-05, 15h 55m 24s.
-Computing the boundary of the generator 17 (dimension 8) :
-<<AlLp[1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][3 <<AlLp[2 S3][2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>]>> 
-End of computing.
-
-
-;; Clock -> 2007-02-05, 15h 55m 24s.
-Computing the boundary of the generator 18 (dimension 8) :
-<<AlLp[1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][3 <<AlLp[2 S3][2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>]>> 
-End of computing.
-
-
-;; Clock -> 2007-02-05, 15h 55m 24s.
-Computing the boundary of the generator 19 (dimension 8) :
-<<AlLp[1 <<AlLp[2 S3]>>][3 <<AlLp[2 S3][2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>]>> 
-End of computing.
-
-
-;; Clock -> 2007-02-05, 15h 55m 25s.
-Computing the boundary of the generator 20 (dimension 8) :
-<<AlLp[3 <<AlLp[2 S3][2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>]>> 
-End of computing.
-
-
-;; Clock -> 2007-02-05, 15h 55m 25s.
-Computing the boundary of the generator 21 (dimension 8) :
-<<AlLp[1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>]>> 
-End of computing.
-
-
-
-
-Homology in dimension 7 :
-
-
-Component Z/2Z
-
-Component Z/2Z
-
-
----done---
-
-;; Clock -> 2007-02-05, 15h 55m 25s.
-
-Real time: 21.330671 sec.
-Run time: 21.310644 sec.
-Space: 256716896 Bytes
-GC: 256, GC time: 3.8255007 sec.
-NIL
-[4]> (exit)
-
-Bye.
-
-C:\DOCUME~1\Francis\AA\Kenzo\Kenzo-1.1-CLisp>
diff --git a/archive/Kenzo-1/How-to-Use-Kenzo-with-LispWorks.txt b/archive/Kenzo-1/How-to-Use-Kenzo-with-LispWorks.txt
deleted file mode 100644
index 64f58c8..0000000
--- a/archive/Kenzo-1/How-to-Use-Kenzo-with-LispWorks.txt
+++ /dev/null
@@ -1,365 +0,0 @@
-;;;
-;;; [[ Loading the initialization file.
-;;; [[ Do not forget the extension ".cl" not guessed by LispWorks.
-;;; 
-
-CL-USER 1 > (load "cat-init.cl")
-; Loading text file C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-LispWorks\cat-init.cl
-
- FILE  1: macros
- FILE  2: various
- FILE  3: classes
- FILE  4: combinations
- FILE  5: chain-complexes
- FILE  6: chcm-elementary-op
- FILE  7: effective-homology
- FILE  8: homology-groups
- FILE  9: searching-homology
- FILE 10: cones
- FILE 11: tensor-products
- FILE 12: coalgebras
- FILE 13: cobar
- FILE 14: algebras
- FILE 15: bar
- FILE 16: simplicial-sets
- FILE 17: simplicial-mrphs
- FILE 18: delta
- FILE 19: special-smsts
- FILE 20: suspensions
- FILE 21: disk-pasting
- FILE 22: cartesian-products
- FILE 23: eilenberg-zilber
- FILE 24: kan
- FILE 25: simplicial-groups
- FILE 26: fibrations
- FILE 27: loop-spaces
- FILE 28: ls-twisted-products
- FILE 29: lp-space-efhm
- FILE 30: classifying-spaces
- FILE 31: k-pi-n
- FILE 32: serre
- FILE 33: cs-twisted-products
- FILE 34: cl-space-efhm
- FILE 35: whitehead
- FILE 36: smith
-#P"C:/Docume~1/Francis/AA/Kenzo/Kenzo-1.1-LispWorks/cat-init.cl"
-
-CL-USER 2 > (load-cfiles)
-; Loading fasl file C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-LispWorks\macros.ofasl
-; Loading fasl file C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-LispWorks\various.ofasl
-; Loading fasl file C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-LispWorks\classes.ofasl
-
-;;;
-;;; [[ Do not take account of these warnings.
-;;; [[ These classes are mutually recursive
-;;; [[   and redefinitions are necessary.
-;;;
-
-Warning: (DEFCLASS CHAIN-COMPLEX) defined more than once in C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-LispWorks\classes.cl.
-Warning: (DEFCLASS MORPHISM) defined more than once in C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-LispWorks\classes.cl.
-Warning: (DEFCLASS HOMOTOPY-EQUIVALENCE) defined more than once in C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-LispWorks\classes.cl.
-
-;;;
-;;; [[ Defining (METHOD PRINT-OBJECT (LOOP T))
-;;; [[   is not at all an error.
-;;; [[ LispWorks complains for Loop being an identifier
-;;; [[   of the Common-Lisp Package and is afraid we damage the system!
-;;; [[ The loops here are the loops of Algebraic Topology
-;;; [[   not the iterated loops of standard programming !!!
-;;;
-
-Error: Defining (METHOD PRINT-OBJECT (LOOP T)) visible from packages COMMON-LISP, CLOS.
-  1 (continue) Define it anyway.
-  2 Discard the new method.
-  3 Try loading classes.ofasl again.
-  4 Give up loading classes.ofasl.
-  5 Try loading another file instead of classes.ofasl.
-  6 (abort) Return to level 0.
-  7 Return to top loop level 0.
-
-Type :b for backtrace, :c <option number> to proceed,  or :? for other options
-
-;;;
-;;; [[ To bypass this claimed "error", answer ":c 1".
-;;;
-
-CL-USER 3 : 1 > :c 1
-; Loading fasl file C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-LispWorks\combinations.ofasl
-; Loading fasl file C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-LispWorks\chain-complexes.ofasl
-; Loading fasl file C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-LispWorks\chcm-elementary-op.ofasl
-; Loading fasl file C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-LispWorks\effective-homology.ofasl
-; Loading fasl file C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-LispWorks\homology-groups.ofasl
-; Loading fasl file C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-LispWorks\searching-homology.ofasl
-; Loading fasl file C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-LispWorks\cones.ofasl
-; Loading fasl file C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-LispWorks\tensor-products.ofasl
-; Loading fasl file C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-LispWorks\coalgebras.ofasl
-; Loading fasl file C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-LispWorks\cobar.ofasl
-; Loading fasl file C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-LispWorks\algebras.ofasl
-; Loading fasl file C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-LispWorks\bar.ofasl
-; Loading fasl file C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-LispWorks\simplicial-sets.ofasl
-; Loading fasl file C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-LispWorks\simplicial-mrphs.ofasl
-; Loading fasl file C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-LispWorks\delta.ofasl
-; Loading fasl file C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-LispWorks\special-smsts.ofasl
-; Loading fasl file C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-LispWorks\suspensions.ofasl
-; Loading fasl file C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-LispWorks\disk-pasting.ofasl
-; Loading fasl file C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-LispWorks\cartesian-products.ofasl
-; Loading fasl file C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-LispWorks\eilenberg-zilber.ofasl
-; Loading fasl file C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-LispWorks\kan.ofasl
-; Loading fasl file C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-LispWorks\simplicial-groups.ofasl
-; Loading fasl file C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-LispWorks\fibrations.ofasl
-; Loading fasl file C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-LispWorks\loop-spaces.ofasl
-; Loading fasl file C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-LispWorks\ls-twisted-products.ofasl
-; Loading fasl file C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-LispWorks\lp-space-efhm.ofasl
-; Loading fasl file C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-LispWorks\classifying-spaces.ofasl
-; Loading fasl file C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-LispWorks\k-pi-n.ofasl
-; Loading fasl file C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-LispWorks\serre.ofasl
-; Loading fasl file C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-LispWorks\cs-twisted-products.ofasl
-; Loading fasl file C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-LispWorks\cl-space-efhm.ofasl
-; Loading fasl file C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-LispWorks\whitehead.ofasl
-; Loading fasl file C:\Docume~1\Francis\AA\Kenzo\Kenzo-1.1-LispWorks\smith.ofasl
-("macros" "various" "classes" "combinations" "chain-complexes" "chcm-elementary-op" "effective-homology" "homology-groups" "searching-homology" "cones" ...)
-
-;;;
-;;; [[ Now Kenzo is ready.
-;;; [[ For example the computing time
-;;; [[   for the homology group H_7(\Omega^2 S^3).
-;;;
-
-CL-USER 4 > (time (homology (loop-space (sphere 3) 2) 7))
-Timing the evaluation of (HOMOLOGY (LOOP-SPACE (SPHERE 3) 2) 7)
-
-Computing boundary-matrix in dimension 7.
-Rank of the source-module : 13.
-
-
-;; Clock -> 2007-02-05, 16h 4m 5s.
-Computing the boundary of the generator 1 (dimension 7) :
-<<AlLp[7 <<AlLp[2 S3][2 S3][2 S3][2 S3]>>]>> 
-End of computing.
-
-
-;; Clock -> 2007-02-05, 16h 4m 8s.
-Computing the boundary of the generator 2 (dimension 7) :
-<<AlLp[1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][5 <<AlLp[2 S3][2 S3][2 S3]>>]>> 
-End of computing.
-
-
-;; Clock -> 2007-02-05, 16h 4m 8s.
-Computing the boundary of the generator 3 (dimension 7) :
-<<AlLp[1 <<AlLp[2 S3]>>][3 <<AlLp[2 S3][2 S3]>>][3 <<AlLp[2 S3][2 S3]>>]>> 
-End of computing.
-
-
-;; Clock -> 2007-02-05, 16h 4m 8s.
-Computing the boundary of the generator 4 (dimension 7) :
-<<AlLp[1 <<AlLp[2 S3]>>][5 <<AlLp[2 S3][2 S3][2 S3]>>][1 <<AlLp[2 S3]>>]>> 
-End of computing.
-
-
-;; Clock -> 2007-02-05, 16h 4m 8s.
-Computing the boundary of the generator 5 (dimension 7) :
-<<AlLp[3 <<AlLp[2 S3][2 S3]>>][1 <<AlLp[2 S3]>>][3 <<AlLp[2 S3][2 S3]>>]>> 
-End of computing.
-
-
-;; Clock -> 2007-02-05, 16h 4m 8s.
-Computing the boundary of the generator 6 (dimension 7) :
-<<AlLp[3 <<AlLp[2 S3][2 S3]>>][3 <<AlLp[2 S3][2 S3]>>][1 <<AlLp[2 S3]>>]>> 
-End of computing.
-
-
-;; Clock -> 2007-02-05, 16h 4m 8s.
-Computing the boundary of the generator 7 (dimension 7) :
-<<AlLp[5 <<AlLp[2 S3][2 S3][2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>]>> 
-End of computing.
-
-
-;; Clock -> 2007-02-05, 16h 4m 8s.
-Computing the boundary of the generator 8 (dimension 7) :
-<<AlLp[1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][3 <<AlLp[2 S3][2 S3]>>]>> 
-End of computing.
-
-
-;; Clock -> 2007-02-05, 16h 4m 8s.
-Computing the boundary of the generator 9 (dimension 7) :
-<<AlLp[1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][3 <<AlLp[2 S3][2 S3]>>][1 <<AlLp[2 S3]>>]>> 
-End of computing.
-
-
-;; Clock -> 2007-02-05, 16h 4m 8s.
-Computing the boundary of the generator 10 (dimension 7) :
-<<AlLp[1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][3 <<AlLp[2 S3][2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>]>> 
-End of computing.
-
-
-;; Clock -> 2007-02-05, 16h 4m 8s.
-Computing the boundary of the generator 11 (dimension 7) :
-<<AlLp[1 <<AlLp[2 S3]>>][3 <<AlLp[2 S3][2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>]>> 
-End of computing.
-
-
-;; Clock -> 2007-02-05, 16h 4m 8s.
-Computing the boundary of the generator 12 (dimension 7) :
-<<AlLp[3 <<AlLp[2 S3][2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>]>> 
-End of computing.
-
-
-;; Clock -> 2007-02-05, 16h 4m 8s.
-Computing the boundary of the generator 13 (dimension 7) :
-<<AlLp[1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>]>> 
-End of computing.
-
-
-Computing boundary-matrix in dimension 8.
-Rank of the source-module : 21.
-
-
-;; Clock -> 2007-02-05, 16h 4m 8s.
-Computing the boundary of the generator 1 (dimension 8) :
-<<AlLp[1 <<AlLp[2 S3]>>][7 <<AlLp[2 S3][2 S3][2 S3][2 S3]>>]>> 
-End of computing.
-
-
-;; Clock -> 2007-02-05, 16h 4m 9s.
-Computing the boundary of the generator 2 (dimension 8) :
-<<AlLp[3 <<AlLp[2 S3][2 S3]>>][5 <<AlLp[2 S3][2 S3][2 S3]>>]>> 
-End of computing.
-
-
-;; Clock -> 2007-02-05, 16h 4m 9s.
-Computing the boundary of the generator 3 (dimension 8) :
-<<AlLp[5 <<AlLp[2 S3][2 S3][2 S3]>>][3 <<AlLp[2 S3][2 S3]>>]>> 
-End of computing.
-
-
-;; Clock -> 2007-02-05, 16h 4m 9s.
-Computing the boundary of the generator 4 (dimension 8) :
-<<AlLp[7 <<AlLp[2 S3][2 S3][2 S3][2 S3]>>][1 <<AlLp[2 S3]>>]>> 
-End of computing.
-
-
-;; Clock -> 2007-02-05, 16h 4m 9s.
-Computing the boundary of the generator 5 (dimension 8) :
-<<AlLp[1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][5 <<AlLp[2 S3][2 S3][2 S3]>>]>> 
-End of computing.
-
-
-;; Clock -> 2007-02-05, 16h 4m 9s.
-Computing the boundary of the generator 6 (dimension 8) :
-<<AlLp[1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][3 <<AlLp[2 S3][2 S3]>>][3 <<AlLp[2 S3][2 S3]>>]>> 
-End of computing.
-
-
-;; Clock -> 2007-02-05, 16h 4m 10s.
-Computing the boundary of the generator 7 (dimension 8) :
-<<AlLp[1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][5 <<AlLp[2 S3][2 S3][2 S3]>>][1 <<AlLp[2 S3]>>]>> 
-End of computing.
-
-
-;; Clock -> 2007-02-05, 16h 4m 10s.
-Computing the boundary of the generator 8 (dimension 8) :
-<<AlLp[1 <<AlLp[2 S3]>>][3 <<AlLp[2 S3][2 S3]>>][1 <<AlLp[2 S3]>>][3 <<AlLp[2 S3][2 S3]>>]>> 
-End of computing.
-
-
-;; Clock -> 2007-02-05, 16h 4m 10s.
-Computing the boundary of the generator 9 (dimension 8) :
-<<AlLp[1 <<AlLp[2 S3]>>][3 <<AlLp[2 S3][2 S3]>>][3 <<AlLp[2 S3][2 S3]>>][1 <<AlLp[2 S3]>>]>> 
-End of computing.
-
-
-;; Clock -> 2007-02-05, 16h 4m 10s.
-Computing the boundary of the generator 10 (dimension 8) :
-<<AlLp[1 <<AlLp[2 S3]>>][5 <<AlLp[2 S3][2 S3][2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>]>> 
-End of computing.
-
-
-;; Clock -> 2007-02-05, 16h 4m 10s.
-Computing the boundary of the generator 11 (dimension 8) :
-<<AlLp[3 <<AlLp[2 S3][2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][3 <<AlLp[2 S3][2 S3]>>]>> 
-End of computing.
-
-
-;; Clock -> 2007-02-05, 16h 4m 10s.
-Computing the boundary of the generator 12 (dimension 8) :
-<<AlLp[3 <<AlLp[2 S3][2 S3]>>][1 <<AlLp[2 S3]>>][3 <<AlLp[2 S3][2 S3]>>][1 <<AlLp[2 S3]>>]>> 
-End of computing.
-
-
-;; Clock -> 2007-02-05, 16h 4m 10s.
-Computing the boundary of the generator 13 (dimension 8) :
-<<AlLp[3 <<AlLp[2 S3][2 S3]>>][3 <<AlLp[2 S3][2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>]>> 
-End of computing.
-
-
-;; Clock -> 2007-02-05, 16h 4m 10s.
-Computing the boundary of the generator 14 (dimension 8) :
-<<AlLp[5 <<AlLp[2 S3][2 S3][2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>]>> 
-End of computing.
-
-
-;; Clock -> 2007-02-05, 16h 4m 10s.
-Computing the boundary of the generator 15 (dimension 8) :
-<<AlLp[1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][3 <<AlLp[2 S3][2 S3]>>]>> 
-End of computing.
-
-
-;; Clock -> 2007-02-05, 16h 4m 11s.
-Computing the boundary of the generator 16 (dimension 8) :
-<<AlLp[1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][3 <<AlLp[2 S3][2 S3]>>][1 <<AlLp[2 S3]>>]>> 
-End of computing.
-
-
-;; Clock -> 2007-02-05, 16h 4m 11s.
-Computing the boundary of the generator 17 (dimension 8) :
-<<AlLp[1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][3 <<AlLp[2 S3][2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>]>> 
-End of computing.
-
-
-;; Clock -> 2007-02-05, 16h 4m 11s.
-Computing the boundary of the generator 18 (dimension 8) :
-<<AlLp[1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][3 <<AlLp[2 S3][2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>]>> 
-End of computing.
-
-
-;; Clock -> 2007-02-05, 16h 4m 11s.
-Computing the boundary of the generator 19 (dimension 8) :
-<<AlLp[1 <<AlLp[2 S3]>>][3 <<AlLp[2 S3][2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>]>> 
-End of computing.
-
-
-;; Clock -> 2007-02-05, 16h 4m 11s.
-Computing the boundary of the generator 20 (dimension 8) :
-<<AlLp[3 <<AlLp[2 S3][2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>]>> 
-End of computing.
-
-
-;; Clock -> 2007-02-05, 16h 4m 11s.
-Computing the boundary of the generator 21 (dimension 8) :
-<<AlLp[1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>]>> 
-End of computing.
-
-
-
-
-Homology in dimension 7 :
-
-
-Component Z/2Z
-
-Component Z/2Z
-
-
----done---
-
-;; Clock -> 2007-02-05, 16h 4m 11s.
-
-
-User time    =        6.088
-System time  =        0.050
-Elapsed time =        6.139
-Allocation   = 123378148 bytes
-0 Page faults
-NIL
-
-CL-USER 5 > (exit)
\ No newline at end of file
diff --git a/archive/Kenzo-1/Kenzo-Doc.pdf b/archive/Kenzo-1/Kenzo-Doc.pdf
deleted file mode 100644
index d274fa9..0000000
Binary files a/archive/Kenzo-1/Kenzo-Doc.pdf and /dev/null differ
diff --git a/archive/Kenzo-1/Test.cl b/archive/Kenzo-1/Test.cl
deleted file mode 100644
index b7959e2..0000000
--- a/archive/Kenzo-1/Test.cl
+++ /dev/null
@@ -1,39 +0,0 @@
-;;;  TEST  TEST  TEST  TEST  TEST  TEST  TEST  TEST  TEST  TEST  TEST  TEST
-;;;  TEST  TEST  TEST  TEST  TEST  TEST  TEST  TEST  TEST  TEST  TEST  TEST
-;;;  TEST  TEST  TEST  TEST  TEST  TEST  TEST  TEST  TEST  TEST  TEST  TEST
-
-(kenzo-version)
-
-(time (progn
-
-        (cat-init)
-        (setf s3 (sphere 3))
-        (homology s3 3)
-        (setf os3 (loop-space s3))
-        (homology os3 4)
-        (setf o2s3 (loop-space os3))
-        (homology o2s3 5)
-        (homology (loop-space (moore 2 4) 2) 7)
-
-        (homology (k-z2 2) 3 8)
-        
-        (homology (k-z2 3) 3 8)
-        
-        (setf s3 (sphere 3))
-        (homology s3 3)
-        (setf ch3 (chml-clss s3 3))
-        (setf f3 (z-whitehead s3 ch3))
-        (setf x4 (fibration-total f3))
-        (homology x4 4)
-        (setf ch4 (chml-clss x4 4))
-        (setf f4 (z2-whitehead x4 ch4))
-        (setf x5 (fibration-total f4))
-        (homology x5 5)
-        (setf ch5 (chml-clss x5 5))
-        (setf f5 (z-whitehead x5 ch5))
-        (setf x6 (fibration-total f5))
-
-))
-
-(time (homology o2s3 7))
-(time (homology x6 6))
\ No newline at end of file
diff --git a/archive/Kenzo-1/algebras.cl b/archive/Kenzo-1/algebras.cl
deleted file mode 100644
index 962fd6e..0000000
--- a/archive/Kenzo-1/algebras.cl
+++ /dev/null
@@ -1,98 +0,0 @@
-;;;  ALGEBRAS  ALGEBRAS  ALGEBRAS  ALGEBRAS  ALGEBRAS  ALGEBRAS
-;;;  ALGEBRAS  ALGEBRAS  ALGEBRAS  ALGEBRAS  ALGEBRAS  ALGEBRAS
-;;;  ALGEBRAS  ALGEBRAS  ALGEBRAS  ALGEBRAS  ALGEBRAS  ALGEBRAS
-
-(IN-PACKAGE "COMMON-LISP-USER")
-
-(PROVIDE "algebras")
-
-(DEFVAR *ALGB-LIST*)
-(SETF *ALGB-LIST* +empty-list+)
-(PUSHNEW '*ALGB-LIST* *list-list*)
-
-#+clisp(eval-when (:compile-toplevel :load-toplevel :execute)
-         (setf (ext:package-lock :clos) nil))
-(DEFMETHOD PRINT-OBJECT ((algb algebra) stream)
- (the algebra
-   (progn
-      (format stream "[K~D Algebra]" (idnm algb))
-      algb)))
-#+clisp(eval-when (:compile-toplevel :load-toplevel :execute)
-         (setf (ext:package-lock :clos) t))
-
-(DEFUN ALGB (idnm)
-   (declare (fixnum idnm))
-   (the (or algebra null)
-      (find idnm *algb-list* :key #'idnm)))
-
-(DEFUN BUILD-ALGB
-    (&key cmpr basis bsgn intr-dffr dffr-strt intr-aprd aprd-strt orgn)
-   (declare
-      (type cmprf cmpr)
-      (type intr-mrph intr-dffr intr-aprd)
-      (type basis basis)
-      (type gnrt bsgn)
-      (type strt dffr-strt aprd-strt)
-      (list orgn))
-   (the algebra
-      (progn
-         (let ((already (find orgn *algb-list* :key #'orgn :test #'equal)))
-            (declare (type (or null algebra) already))
-            (when already
-               (return-from build-algb already)))
-         (let* ((rslt (build-chcm :cmpr cmpr :basis basis :bsgn bsgn
-                        :intr-dffr intr-dffr :strt dffr-strt
-                        :orgn orgn))
-		;; to be done before change-class
-		(rslt-rslt (tnsr-prdc rslt rslt)))
-            (declare (type chain-complex rslt rslt-rslt))
-            (change-class rslt 'algebra)  
-            (setf (slot-value rslt 'aprd)
-                  (build-mrph :sorc rslt-rslt :trgt rslt :degr 0
-                        :intr intr-aprd :strt aprd-strt
-                        :orgn `(algebra-product ,rslt)))
-               (push rslt *algb-list*)
-               rslt))))
-
-(DEFUN CHANGE-CHCM-TO-ALGB (chcm &key intr-aprd aprd-strt orgn)
-   (declare
-      (type chain-complex chcm)
-      (type intr-mrph intr-aprd)
-      (type strt aprd-strt)
-      (list orgn))
-   (the algebra
-     (let ((chcm-chcm (tnsr-prdc chcm chcm)))
-       (declare (type chain-complex chcm-chcm))
-       (change-class chcm 'algebra)
-       (setf orgn (list (orgn chcm) 'then orgn))
-       (let ((already (find orgn *algb-list* :key #'orgn :test #'equal)))
-	 (declare (type (or null algebra) already))
-	 (when already
-               (return-from change-chcm-to-algb already)))
-       (setf (slot-value chcm 'aprd) (build-mrph
-				      :sorc chcm-chcm :trgt chcm
-				      :degr 0
-				      :intr intr-aprd :strt aprd-strt
-				      :orgn orgn))
-       (push chcm *algb-list*)
-       chcm)))
-
-(DEFVAR *HOPF-LIST*)
-(SETF *HOPF-LIST* +empty-list+)
-(PUSHNEW '*HOPF-LIST* *list-list*)
-
-#+clisp(eval-when (:compile-toplevel :load-toplevel :execute)
-         (setf (ext:package-lock :clos) nil))
-(DEFMETHOD PRINT-OBJECT ((hopf hopf-algebra) stream)
- (the hopf-algebra
-   (progn
-      (format stream "[K~D Hopf-Algebra]" (idnm hopf))
-      hopf)))
-#+clisp(eval-when (:compile-toplevel :load-toplevel :execute)
-         (setf (ext:package-lock :clos) t))
-
-(DEFUN HOPF (idnm)
-   (declare (fixnum idnm))
-   (the (or hopf-algebra null)
-      (find idnm *hopf-list* :key #'idnm)))
-
diff --git a/archive/Kenzo-1/bar.cl b/archive/Kenzo-1/bar.cl
deleted file mode 100644
index 13fd789..0000000
--- a/archive/Kenzo-1/bar.cl
+++ /dev/null
@@ -1,719 +0,0 @@
-;;;  BAR  BAR  BAR  BAR  BAR  BAR  BAR  BAR  BAR
-;;;  BAR  BAR  BAR  BAR  BAR  BAR  BAR  BAR  BAR
-;;;  BAR  BAR  BAR  BAR  BAR  BAR  BAR  BAR  BAR
-
-;;;
-;;;  MAC-LANE signs (p. 306)
-;;;
-
-(IN-PACKAGE "COMMON-LISP-USER")
-
-(PROVIDE "bar")
-
-(DEFUN ABAR (&rest list)
-  (when (= 1 (length list))
-    (setf list (first list)))
-  (unless (evenp (length list))
-    (error "In ABAR, the length list should be even."))
-  (the abar
-    (let ((rslt +empty-list+))
-      (declare (list rslt))
-      (do ((mark list (cddr mark)))
-          ((endp mark))
-        (declare (list mark))
-        (push (brgn (car mark) (cadr mark)) rslt))
-        (make-abar :list rslt))))
-#|
-()
-(abar )
-(abar '(2 a 3 b))
-(abar 2 'a 3 'b)
-(abar 2 'a 3))  ;; error
-|#
-
-(DEFCONSTANT +NULL-ABAR+ (make-abar :list +empty-list+))
-
-
-;;; -[CLISP
-#|
-(DEFMETHOD PRINT-KEYCONS ((car (eql :abar)) cdr stream)
-   (declare
-      (list cdr)
-      (stream stream))
-   (the abar
-      (progn
-         (format stream "<<Abar")
-         (dolist (brgn cdr)
-            (declare (type brgn brgn))
-            (with-brgn (degr gnrt) brgn
-               (format stream "[~D ~A]" degr gnrt)))
-         (format stream ">>")
-         (cons car cdr))))
-|#
-;;;    CLISP]-
-;;; +[CLISP
-(DEFUN ABAR-PRINT (abar stream depth)
-  (declare
-   (type abar abar) (stream stream)
-   (ignore depth))
-  (the abar
-    (progn
-      (format stream "<<Abar")
-      (dolist (brgn (abar-list abar))
-        (declare (type brgn brgn))
-        (with-brgn (degr gnrt) brgn
-                   (format stream "[~D ~A]" degr gnrt)))
-      (format stream ">>")
-      abar)))
-;;; CLISP]+
-
-
-
-(DEFUN BAR-CMPR (cmpr)
-  (declare (type cmprf cmpr))
-  (flet ((rslt (abar1 abar2)
-               (declare (type abar abar1 abar2))
-               (the cmpr
-                 (let ((list1 (abar-list abar1))
-                       (list2 (abar-list abar2)))
-                   (declare (list list1 list2))
-                   (lexico
-                    (f-cmpr (length list1) (length list2))
-                    (maplexico
-                     #'(lambda (brgn1 brgn2)
-                         (lexico
-                          (f-cmpr (bdegr brgn1) (bdegr brgn2))
-                          (funcall cmpr (bgnrt brgn1) (bgnrt brgn2))))
-                     list1 list2))))))
-    (the cmprf #'rslt)))
-
-#|
-  (setf r (bar-cmpr #'s-cmpr))
-  (funcall r (abar) (abar))
-  (funcall r (abar 3 'a) (abar))
-  (funcall r (abar 3 'a) (abar 2 'a 1 'b))
-  (funcall r (abar 3 'a) (abar 3 'b))
-  (funcall r (abar 3 'a) (abar 3 'a)))
-|#
-
-(DEFUN BAR-BASIS-LENGTH (basis degr length)
-  (declare
-   (type basis basis)
-   (fixnum degr length))
-  (the list
-    (progn
-      (when (= 1 length)
-        (return-from bar-basis-length
-          (mapcar
-              #'(lambda (item)
-                  (declare (type gnrt item))
-                  (list (brgn degr item)))
-            (funcall basis (1- degr)))))
-      (when (< degr 4)
-        (return-from bar-basis-length +empty-list+))
-      (mapcan
-          #'(lambda (degr1)
-              (declare (fixnum degr1))
-              (let ((list1 (funcall basis (1- degr1)))
-                    (list2 (bar-basis-length
-                            basis (- degr degr1) (1- length))))
-                (declare (list list1 list2))
-                (mapcan
-                    #'(lambda (item1)
-                        (declare (type gnrt item1))
-                        (mapcar
-                            #'(lambda (item2)
-                                (declare (type iabar item2))
-                                (cons (brgn degr1 item1) item2))
-                          list2))
-                  list1)))
-        (>a-b< 1 (1- degr))))))
-
-#|
-()
-(setf basis #'(lambda (degr)
-                (list degr)))
-(bar-basis-length basis 2 1)
-(bar-basis-length basis 2 2)
-(bar-basis-length basis 3 1)
-(bar-basis-length basis 3 2)
-(bar-basis-length basis 4 1)
-(bar-basis-length basis 4 2)
-(bar-basis-length basis 4 3)
-(bar-basis-length basis 4 4)
-(bar-basis-length basis 8 1)
-(bar-basis-length basis 8 2)
-(bar-basis-length basis 8 3)
-(bar-basis-length basis 8 4)
-(bar-basis-length basis 8 5)
-(bar-basis-length basis 8 6)
-(bar-basis-length basis 8 11))
-|#
-
-(DEFUN BAR-BASIS (basis)
-  (declare (type basis basis))
-  (the basis
-    (progn
-      (when (eq :locally-effective basis)
-        (return-from bar-basis :locally-effective))
-      (flet
-          ((rslt (degr)
-                 (declare (fixnum degr))
-                 (cond ((zerop degr) (list +null-abar+))
-                       ((< degr 2) +empty-list+)
-                       (t
-                        (mapcan
-                            #'(lambda (length)
-                                (declare (fixnum length))
-                                (mapcar
-                                    #'(lambda (iabar)
-                                        (declare (type iabar iabar))
-                                        (make-abar :list iabar))
-                                  (bar-basis-length basis degr length)))
-                          (>a-b> 0 (floor degr 2)))))))
-        #'rslt))))
-
-#|
-()
-(setf basis #'(lambda (degr)
-                (list degr)))
-(setf r (bar-basis basis))
-(funcall r 0)
-(funcall r 1)
-(funcall r 2)
-(dotimes (i 7)
-  (print (funcall r i)))
-(bar-basis :locally-effective))
-|#
-
-(DEFUN BAR-INTR-VRTC-DFFR (dffr)
-   (declare (type morphism dffr))
-   (labels ((rslt (degr iabar)
-               ;; the argument iabar is an internal algebraic bar,
-               ;;     without the keyword :abar
-               ;; rslt returns an internal combination
-               ;;     without the keyword :cmbn, without degree
-               (declare
-                  (fixnum degr)
-                  (type iabar iabar))
-	       (progn
-		 (unless iabar
-		   (return-from rslt +empty-list+))
-		 (let ((brgn1 (first iabar))
-		       (rest2 (rest iabar)))
-		   (declare
-		     (type brgn brgn1)
-		     (type iabar rest2))
-		   (with-brgn (degr1 gnrt1) brgn1
-                (let ((d-gnrt1 (cmbn-list (gnrt-? dffr (1- degr1) gnrt1)))
-                      (d-rest2 (rslt (- degr degr1) rest2))
-                      (degr1-1 (1- degr1))
-                      (rest-sign (-1-expt-n degr1)))
-                  (declare
-                   (type icmbn d-gnrt1 d-rest2)
-                   (fixnum degr1-1 rest-sign))
-		     (nconc
-		       (mapcar
-			 #'(lambda (term)
-			     (declare (type term term))
-			     (with-term (cffc gnrt) term
-			       (term (- cffc)
-				     (cons (brgn degr1-1 gnrt) rest2))))
-			 d-gnrt1)
-		       (mapcar
-			 #'(lambda (term)
-			     (with-term (cffc gnrt) term
-			       (term (* rest-sign cffc)
-				     (cons brgn1 gnrt))))
-			 d-rest2))))))))
-	(the intr-mrph
-	  #'(lambda (degr abar)
-	      (declare
-	        (fixnum degr)
-		(type abar abar))
-              (make-cmbn
-	        :degr (1- degr)
-		:list (mapcar
-		        #'(lambda (term)
-			    (with-term (cffc iabar) term
-			      (term cffc (make-abar :list iabar))))
-			(rslt degr (abar-list abar))))))))
-
-#|
-  (setf d (soft-delta-infinity))
-  (setf r (bar-intr-vrtc-dffr (dffr d)))
-  (funcall r 0 (abar))
-  (funcall r 3 (abar 3 (d 7)))
-  (funcall r 5 (abar 3 (d 7) 2 (d 3)))
-  (funcall r 5 (abar 2 (d 3) 3 (d 7))))
-|#
-
-(DEFMETHOD VRTC-BAR ((chcm chain-complex))
-   (the chain-complex
-      (with-slots (cmpr basis dffr) chcm
-         (declare
-            (type cmprf cmpr)
-            (type basis basis)
-            (type morphism dffr))
-         (build-chcm
-            :cmpr (bar-cmpr cmpr)
-            :basis (bar-basis basis)
-            :bsgn +null-abar+
-            :intr-dffr (bar-intr-vrtc-dffr dffr)
-            :strt :gnrt
-            :orgn `(vrtc-bar ,chcm)))))
-
-#|
-  (cat-init)
-  (setf v (vrtc-bar (soft-delta-infinity)))
-  (defun random-abar (length)
-     (let ((rslt nil))
-        (dotimes (i length)
-           (let* ((gmsm (random (mask 7)))
-                  (dmns (1- (logcount gmsm))))
-              (when (plusp dmns)
-                 (push (brgn (1+ dmns) (d gmsm)) rslt))))
-        (make-abar :list rslt)))
-  (dotimes (i 10) (print (random-abar 5)))
-  (dotimes (i 10)
-     (let ((abar (random-abar 3)))
-        (print abar)
-        (print (? v (apply #'+ (mapcar #'car (abar-list abar))) abar))
-        (print (? v (? v (apply #'+ (mapcar #'car (abar-list abar))) abar)))))
-|#
-
-(DEFUN BAR-INTR-HRZN-DFFR (aprd)
-   (declare (type morphism aprd))
-   (labels ((rslt (degr iabar)
-               (declare
-                  (fixnum degr)
-                  (type iabar iabar))
-               (the icmbn
-                  (progn
-                     (unless (cdr iabar)
-                        (return-from rslt +empty-list+))
-                     (let ((brgn1 (first iabar))
-			   (brgn2 (second iabar))
-			   (rest1 (rest iabar))
-			   (rest2 (cddr iabar)))
-                        (declare
-                           (type brgn brgn1 brgn2)
-                           (type iabar rest1 rest2))
-                        (with-brgn (degr1 gnrt1) brgn1
-			(with-brgn (degr2 gnrt2) brgn2
-                           (let ((sign (-1-expt-n degr1))
-				 (aprd-brgn1-brgn2 (gnrt-? aprd (+ degr1 degr2 -2)
-							   (tnpr (1- degr1) gnrt1
-								 (1- degr2) gnrt2)))
-				 (aprd-rest1 (rslt (- degr degr1) rest1)))				  
-			     (declare
-			      (type icmbn aprd-brgn1-brgn2 aprd-rest1))
-			     (with-cmbn (degr12 icmbn12) aprd-brgn1-brgn2
-			       (incf degr12)
-			       (nconc
-			        (mapcar
-				 #'(lambda (term2)
-				     (declare (type term term2))
-				     (with-term (cffc2 iabar2) term2
-				       (term (* sign cffc2) (cons brgn1 iabar2))))
-				  aprd-rest1)
-				(mapcar
-				  #'(lambda (term1)
-				      (declare (type term term1))
-				      (with-term (cffc1 gnrt12) term1
-					(term (* sign cffc1) (cons (brgn degr12 gnrt12) rest2))))
-				  icmbn12)))))))))))
-      (the intr-mrph
-         #'(lambda (degr abar)
-              (declare
-                 (fixnum degr)
-                 (type abar abar))
-              (the cmbn
-                 (make-cmbn :degr (1- degr)
-                    :list (mapcar #'(lambda (term)
-                                       (declare (type term term))
-                                       (with-term (cffc iabar) term
-                                          (term cffc (make-abar :list iabar))))
-                             (rslt degr (abar-list abar)))))))))
-
-#|
-  (setf k (k-z-1))
-  (setf r (bar-intr-hrzn-dffr (aprd k)))
-  (funcall r 0 (abar ))
-  (funcall r 3 (abar 3 '(2 3)))
-  (funcall r 6 (abar 3 '(2 3) 3 '(-2 -3)))
-  (funcall r 9 (abar 3 '(2 3) 3 '(-2 -3) 3 '(2 3)))
-  (funcall r 11 (abar 3 '(2 3) 3 '(-2 -3) 2 '(-2) 3 '(-2 -3))))
-|#
-
-(DEFUN BAR-HRZN-DFFR (algb)
-   (declare (type algebra algb))
-   (the morphism
-      (with-slots (aprd) algb
-         (declare (type morphism aprd))
-         (build-mrph
-            :sorc (vrtc-bar algb) :trgt (vrtc-bar algb) :degr -1
-            :intr (bar-intr-hrzn-dffr aprd) :strt :gnrt
-            :orgn `(bar-hrzn-dffr ,algb)))))
-
-#|
-  (cat-init)
-  (setf h (bar-hrzn-dffr (k-z-1)))
-  (defun random-abar (tot-degr~ max-degr)
-    (do ((rslt nil)
-         (cum-degr 0 (+ cum-degr degr 1))
-         (degr))
-        ((>= cum-degr tot-degr~) (make-abar :list rslt))
-       (setf degr (1+ (random max-degr)))
-       (push (brgn (1+ degr)
-                   (let ((list (make-list degr)))
-                     (mapl
-                       #'(lambda (sublist)
-                           (setf (car sublist) (- (random 21) 10)))
-                       list)
-                     list))
-             rslt)))
-  (dotimes (i 10) (print (random-abar 10 5)))
-  (setf abar (random-abar 10 5))
-  (? h (apply #'+ (mapcar #'car (abar-list abar))) abar)
-  (? h (? h (apply #'+ (mapcar #'car (abar-list abar))) abar))
-  (dotimes (i 10)
-     (let ((abar (random-abar 10 3)))
-        (print abar)
-        (print (? h (apply #'+ (mapcar #'car (abar-list abar))) abar))
-        (print (? h (? h (apply #'+ (mapcar #'car (abar-list abar))) abar)))))
-|#
-
-(DEFUN BAR-INTR-DFFR (vrtc-dffr hrzn-dffr)
-   (declare (type morphism vrtc-dffr hrzn-dffr))
-   (flet ((rslt (degr abar)
-             (declare
-                (fixnum degr)
-                (type abar abar))
-             (make-cmbn :degr (1- degr)
-                :list (append       ;;; and not nconc, otherwise a terrible bug, when the
-                                    ;;;   first result is stored in memory...
-                         (cmbn-list (gnrt-? hrzn-dffr degr abar))
-                         (cmbn-list (gnrt-? vrtc-dffr degr abar))))))
-      (the intr-mrph #'rslt)))
-
-(DEFMETHOD BAR ((algebra algebra))
-   (let ((vrtc-bar (vrtc-bar algebra))
-         (bar-hrzn-dffr (bar-hrzn-dffr algebra)))
-     (declare (type chain-complex vrtc-bar)
-              (type morphism bar-hrzn-dffr))
-      (the chain-complex
-	 (let ((rslt (build-chcm
-		      :cmpr (cmpr vrtc-bar)
-		      :basis (basis vrtc-bar)
-		      :bsgn +null-abar+
-		      :intr-dffr (bar-intr-dffr (dffr vrtc-bar) bar-hrzn-dffr)
-		      :strt :gnrt
-		      :orgn `(add ,vrtc-bar ,bar-hrzn-dffr))))
-	   (declare (type chain-complex rslt))
-	   (setf (slot-value rslt 'grmd) (grmd vrtc-bar))
-	   rslt))))
-
-#|
-  (cat-init)
-  (setf b (bar (k-z-1)))   
-  (defun random-abar (tot-degr~ max-degr)
-    (do ((rslt nil)
-         (cum-degr 0 (+ cum-degr degr 1))
-         (degr))
-        ((>= cum-degr tot-degr~) (make-abar :list rslt))
-       (setf degr (1+ (random max-degr)))
-       (push (brgn (1+ degr)
-                   (let ((list (make-list degr)))
-                     (mapl
-                       #'(lambda (sublist)
-                           (setf (car sublist) (- (random 21) 10)))
-                       list)
-                     list))
-             rslt)))
-  (setf abar (random-abar 10 3))
-  (? b (apply #'+ (mapcar #'car (abar-list abar))) abar)
-  (? b (? b (apply #'+ (mapcar #'car (abar-list abar))) abar))
-  (dotimes (i 10)
-     (let ((abar (random-abar 10 3)))
-        (print abar)
-        (print (? b (apply #'+ (mapcar #'car (abar-list abar))) abar))
-        (print (? b (? b (apply #'+ (mapcar #'car (abar-list abar))) abar)))))
-|#
-
-(DEFUN CMBN-ABAR-CMBN-TNPR (cmbn abar-cmbn)
-   (declare (type cmbn cmbn abar-cmbn))
-   (the cmbn
-      (with-cmbn (degr1 list1) cmbn
-         (incf degr1)     ;; because abar organization
-      (with-cmbn (degrr listr) abar-cmbn
-         (make-cmbn
-            :degr (+ degr1 degrr)
-            :list
-            (mapcan
-               #'(lambda (term1)
-                    (declare (type term term1))
-                    (with-term (cffc1 gnrt1) term1
-                       (let ((brgn1 (brgn degr1 gnrt1)))
-                          (declare (type brgn brgn1))
-                          (mapcar
-                             #'(lambda (termr)
-                                  (declare (type term termr))
-                                  (with-term (cffcr abarr) termr
-                                     (term (* cffc1 cffcr)
-                                        (make-abar
-                                           :list (cons brgn1 (abar-list abarr))))))
-                             listr))))
-               list1))))))
-
-(DEFUN NCMBN-BAR (cmbn-list)
-   (declare (list cmbn-list))
-   (the cmbn
-      (progn
-         (unless cmbn-list
-            (return-from ncmbn-bar (cmbn 0 1 +null-abar+)))
-         (cmbn-abar-cmbn-tnpr
-            (first cmbn-list)
-            (ncmbn-bar (rest cmbn-list))))))
-#|
-  (ncmbn-bar nil)
-  (ncmbn-bar (list (cmbn 3 2 'a 3 'b)))
-  (ncmbn-bar (list (cmbn 1 2 'a 3 'b) (cmbn 2 4 'c 5 'd)))
-  (ncmbn-bar (list (cmbn 1 2 'a 3 'b) (cmbn 1 4 'c 5 'd) (cmbn 1 6 'e 7 'f))))
-|#
-
-(DEFUN MRPH-VRTC-BAR-INTR (mrph)
-   (declare (type morphism mrph))
-   (flet ((rslt (degr abar)
-             (declare
-                (ignore degr)
-                (type abar abar))
-             (the cmbn
-                (ncmbn-bar
-                   (mapcar #'(lambda (brgn)
-                                (declare (type brgn brgn))
-                                (with-brgn (degr gnrt) brgn
-                                   (gnrt-? mrph (1- degr) gnrt)))
-                      (abar-list abar))))))
-      (the intr-mrph #'rslt)))
-
-#|
-  (setf cc (build-chcm :cmpr #'f-cmpr :strt :cmbn))
-  (setf m (build-mrph :sorc cc :trgt cc :degr 0 :intr
-            #'(lambda (degr gnrt) (cmbn degr 2 gnrt 3 (1+ gnrt)))
-            :strt :gnrt :orgn '(test)))
-  (setf r (mrph-vrtc-bar-intr m))
-  (funcall r 4 (abar 2 3 2 4))
-|#
-
-(DEFMETHOD VRTC-BAR ((mrph morphism))
-   (the morphism
-      (if (eq (first (orgn mrph)) 'idnt-mrph)
-         (idnt-mrph (vrtc-bar (sorc mrph)))
-         (build-mrph
-            :sorc (vrtc-bar (sorc mrph))
-            :trgt (vrtc-bar (trgt mrph))
-            :degr 0
-            :intr (mrph-vrtc-bar-intr mrph)
-            :strt :gnrt
-            :orgn `(vrtc-bar ,mrph)))))
-
-#|
-  (cat-init)
-  (setf f (aw (soft-delta-infinity) (soft-delta-infinity)))
-  (setf cf (vrtc-bar f))
-  (? cf 6 (abar 3 (crpr 0 (d 7) 0 (d 7)) 3 (crpr 0 (d 56) 0 (d 56))))
-|#
-
-(DEFUN HMTP-VRTC-BAR-INTR (h gf)
-   (declare (type morphism h gf))
-   (labels ((rslt (degr iabar)
-	      (declare
-	       (fixnum degr)
-	       (type iabar iabar))
-	      (unless iabar
-		(return-from rslt +empty-list+))
-	      (let ((brgn1 (first iabar))
-		    (rest2 (rest iabar)))
-		(declare
-		 (type brgn brgn1)
-		 (list rest2))
-		(with-brgn (degr1 gnrt1) brgn1
-		  (let ((h-gnrt1 (cmbn-list (gnrt-? h (1- degr1) gnrt1)))
-			(h-rest2 (rslt (- degr degr1) rest2))
-			(degr1+1 (1+ degr1))
-			(rest-sign (-1-expt-n degr1))
-			(gf-gnrt1 (cmbn-list (gnrt-? gf (1- degr1) gnrt1))))
-		    (declare
-		      (fixnum degr1+1 rest-sign)
-		      (type icmbn h-gnrt1 h-rest2 gf-gnrt1))
-		    (nconc
-		     (mapcan
-		      #'(lambda (term1)
-			  (declare (type term term1))
-			  (with-term (cffc1 gnrt11) term1
-			    (mapcar
-			     #'(lambda (term2)
-				 (declare (type term term2))
-				 (with-term (cffc2 iabar2) term2
-				   (term (* rest-sign cffc1 cffc2)
-					 (cons (brgn degr1 gnrt11) iabar2))))
-			     h-rest2)))
-		      gf-gnrt1)
-		     (mapcar
-		      #'(lambda (term1)
-			  (declare (type term term1))
-			  (with-term (cffc1 gnrt11) term1
-			    (term (- cffc1)
-				  (cons (brgn degr1+1 gnrt11) rest2))))
-		      h-gnrt1)))))))
-	   (the intr-mrph
-	      #'(lambda (degr abar)
-		  (declare
-		    (fixnum degr)
-		    (type abar abar))
-		  (make-cmbn
-		   :degr (1+ degr)
-		   :list (mapcar
-			  #'(lambda (term)
-			      (declare (type term term))
-			      (with-term (cffc iabar) term
-				(declare
-				   (fixnum cffc)
-				   (type iabar iabar))
-				(term cffc (make-abar :list iabar))))
-			  (rslt degr (abar-list abar))))))))
-
-#|
-  (cat-init)
-  (setf ez (ez (delta-infinity) (delta-infinity)))
-  (setf h (h ez) gf (cmps (g ez) (f ez)))
-  (setf r (hmtp-vrtc-bar-intr h gf))
-  (funcall r 3 (abar 3 (crpr 0 7 0 7)))
-  (funcall r 9 (abar 3 (crpr 0 7 0 7) 3 (crpr 0 14 0 14) 3 (crpr 0 14 0 14)))
-|#
-
-(DEFUN HMTP-VRTC-BAR (h gf)
-   (declare (type morphism h gf))
-   (unless (and (= +1 (degr h))
-                (= +0 (degr gf)))
-      (error "In HMTP-VRTC-BAR, the morphism degrees are not the right ones."))
-   (unless (and (eq (sorc h) (trgt h))
-                (eq (trgt h) (sorc gf))
-                (eq (sorc gf) (trgt gf)))
-      (error "In HMTP-VRTC-BAR, fg-h sources and targets are not the same."))
-   (the morphism
-      (if (eq (first (orgn h)) 'zero-mrph)
-         (zero-mrph (vrtc-bar (sorc h)))
-         (build-mrph
-            :sorc (vrtc-bar (sorc h)) :trgt (vrtc-bar (sorc h)) :degr +1
-            :intr (hmtp-vrtc-bar-intr h gf)
-            :strt :gnrt
-            :orgn `(hmtp-vrtc-bar ,h ,gf)))))
-
-(DEFMETHOD VRTC-BAR ((rdct reduction))
-   (the reduction
-      (if (eq (first (orgn rdct)) 'trivial-rdct)
-         (trivial-rdct (vrtc-bar (bcc rdct)))
-         (with-slots (f g h) rdct
-            (build-rdct
-               :f (vrtc-bar f)
-               :g (vrtc-bar g)
-               :h (hmtp-vrtc-bar h (cmps g f))
-               :orgn `(vrtc-bar ,rdct))))))
-
-#|
-  (cat-init)
-  (setf tcc (build-chcm
-               :cmpr #'s-cmpr
-               :basis #'(lambda (degr) '(a b c d))
-               :bsgn 'd
-               :intr-dffr #'(lambda (degr gnrt)
-                               (ecase gnrt
-                                  (a (cmbn (1- degr) 1 'b 1 'd))
-                                  ((b d) (cmbn (1- degr)))
-                                  (c (cmbn (1- degr) 1 'd))))
-               :strt :gnrt
-               :orgn '(tcc)))
-  (setf bcc (build-chcm
-               :cmpr #'s-cmpr
-               :basis #'(lambda (degr) '(c d))
-               :bsgn 'd
-               :intr-dffr #'(lambda (degr gnrt)
-                               (ecase gnrt
-                                  (d (cmbn (1- degr)))
-                                  (c (cmbn (1- degr) 1 'd))))
-               :strt :gnrt
-               :orgn '(bcc)))
-  (setf f (build-mrph :sorc tcc :trgt bcc :degr 0
-             :intr #'(lambda (degr gnrt)
-                        (ecase gnrt
-                           (a (cmbn degr 1 'c 1 'd))
-                           (b (cmbn degr))
-                           ((c d) (cmbn degr 1 gnrt))))
-             :strt :gnrt :orgn '(f)))
-  (setf g (build-mrph :sorc bcc :trgt tcc :degr 0
-             :intr #'identity :strt :cmbn :orgn '(g)))
-  (setf h (build-mrph :sorc tcc :trgt tcc :degr +1
-             :intr #'(lambda (degr gnrt)
-                        (ecase gnrt
-                           ((a b) (cmbn (1+ degr) 1 'a -1 'b -1 'c -1 'd))
-                           ((c d) (cmbn (1+ degr)))))
-             :strt :gnrt :orgn '(h)))
-  (setf rdct (build-rdct :f f :g g :h h :orgn '(rdct)))
-  (tcc rdct 3 'a)
-  (g rdct (f rdct 3 'a))
-  (h rdct 3 'a)
-  (setf bar (vrtc-bar rdct))
-  (pre-check-rdct bar)
-  (defun aleat-tc ()
-     (do ((tdegr 0 (+ tdegr degr))
-          (degr (+ 2 (random 3)) (+ 2 (random 3)))
-          (gnrt (intern (coerce (vector (code-char (+ 65 (random 4)))) 'string))
-                (intern (coerce (vector (code-char (+ 65 (random 4)))) 'string)))
-          (rslt nil (cons (brgn degr gnrt) rslt)))
-         ((> tdegr 10) (setf *tc* (cmbn tdegr 1 (make-abar :list rslt))))))
-  (aleat-tc)
-  (defun aleat-bc ()
-     (do ((tdegr 0 (+ tdegr degr))
-          (degr (+ 2 (random 3)) (+ 2 (random 3)))
-          (gnrt (intern (coerce (vector (code-char (+ 67 (random 2)))) 'string))
-                (intern (coerce (vector (code-char (+ 67 (random 2)))) 'string)))
-          (rslt nil (cons (brgn degr gnrt) rslt)))
-         ((> tdegr 10) (setf *bc* (cmbn tdegr 1 (make-abar :list rslt))))))
-  (aleat-bc)
-  (defun c ()
-     (aleat-tc)
-     (aleat-bc)
-     (check-rdct))
-  (loop (c))  ;; degrees >= 15 is possible => error.
-|#
-
-(DEFMETHOD VRTC-BAR ((hmeq homotopy-equivalence))
-   (the homotopy-equivalence
-      (if (eq (first (orgn hmeq)) 'trivial-hmeq)
-         (trivial-hmeq (vrtc-bar (lbcc hmeq)))
-         (with-slots (lrdct rrdct) hmeq
-            (build-hmeq 
-               :lrdct (vrtc-bar lrdct)
-               :rrdct (vrtc-bar rrdct)
-               :orgn `(vrtc-bar ,hmeq))))))
-
-(DEFMETHOD BAR ((hmeq homotopy-equivalence))
-   (unless (typep (lbcc hmeq) 'algebra)
-      (error "In (BAR HMEQ), the LBCC should be a algebra."))
-   (the homotopy-equivalence
-      (if (eq (first (orgn hmeq)) 'trivial-hmeq)
-         (trivial-hmeq (bar (lbcc hmeq)))
-         (add (vrtc-bar hmeq) (bar-hrzn-dffr (lbcc hmeq))))))
-
-#|
-  (cat-init)
-  (setf h (efhm (k-z-1)))
-  (setf b (bar h))
-  (inspect b)
-  (homology (rbcc b) 0 11)
-|#
-
-  
-
diff --git a/archive/Kenzo-1/bicones.cl b/archive/Kenzo-1/bicones.cl
deleted file mode 100644
index 257d7f3..0000000
--- a/archive/Kenzo-1/bicones.cl
+++ /dev/null
@@ -1,444 +0,0 @@
-;;;  BICONES  BICONES  BICONES  BICONES  BICONES  BICONES  BICONES  BICONES
-;;;  BICONES  BICONES  BICONES  BICONES  BICONES  BICONES  BICONES  BICONES
-;;;  BICONES  BICONES  BICONES  BICONES  BICONES  BICONES  BICONES  BICONES
-
-(IN-PACKAGE "COMMON-LISP-USER")
-
-(PROVIDE "bicones")
-
-(DEFUN DISPATCH-BICN-CMBN (cmbn)
-   (declare (type cmbn cmbn))
-   (the (values cmbn cmbn cmbn)
-      (with-cmbn (degr list) cmbn
-         (let ((listb +empty-list+)
-               (listc +empty-list+)
-               (listd +empty-list+))
-            (declare (list listb listc listd))
-            (dolist (term list)
-               (declare (type term term))
-               (with-term (cffc bicn) term
-                  (with-bicn (bcnx ibicn) bicn
-                     (ecase bcnx
-                        (:bcnb (push (term cffc ibicn) listb))
-                        (:bcnc (push (term cffc ibicn) listc))
-                        (:bcnd (push (term cffc ibicn) listd))))))
-            (values
-               (make-cmbn :degr degr :list (nreverse listb))
-               (make-cmbn :degr (1+ degr) :list (nreverse listc))
-               (make-cmbn :degr degr :list (nreverse listd)))))))
-
-#|
-()
-(dispatch-bicn-cmbn (cmbn 3 3 (bcnb 'b1) 4 (bcnb 'b2) 33 (bcnc 'c) 333 (bcnd 'd)))
-|#
-
-
-(DEFUN BICN-CMBN-CMBNB (cmbn)
-  (declare (type cmbn cmbn))
-  (the cmbn
-    (with-cmbn (degr list) cmbn
-      (make-cmbn :degr degr
-                 :list (do ((rslt +empty-list+)
-                            (mark list (cdr mark)))
-                           ((endp mark) (nreverse rslt))
-                         (declare (list rslt mark))
-                         (with--term (cffc bicn) mark
-                         (with-bicn (bcnx gnrtB) bicn
-                                    (if (eq bcnx :bcnB)
-                                        (push (term cffc gnrtB) rslt)
-                                      (return (nreverse rslt))))))))))
-
-(DEFUN BICN-CMBN-CMBNC (cmbn)
-   (declare (type cmbn cmbn))
-   (the cmbn
-      (with-cmbn (degr list) cmbn
-         (make-cmbn :degr (1+ degr)
-            :list (do ((rslt +empty-list+)
-                       (mark (member :bcnc list
-                                     ;; Correction 1-1-2
-                                     :key #'(lambda (term)
-                                              (declare (type term term))
-                                              (bcnx (gnrt term))))
-                             (cdr mark)))
-                      ((endp mark) (nreverse rslt))
-                     (declare (list rslt mark))
-                     (with--term (cffc bicn) mark
-                     (with-bicn (bcnx gnrtC) bicn
-                        (if (eq bcnx :bcnC)
-                           (push (term cffc gnrtC) rslt)
-                           (return (nreverse rslt))))))))))
-
-
-(DEFUN BICN-CMBN-CMBND (cmbn)
-  (declare (type cmbn cmbn))
-  (the cmbn
-    (with-cmbn (degr list) cmbn
-      (make-cmbn :degr degr
-                 :list (mapcar
-                           #'(lambda (term)
-                               (declare (type term term))
-                               (with-term (cffc bicn) term
-                                          (term cffc (ibicn bicn))))
-                         (member :bcnd list
-                                 :key #'(lambda (term)
-                                          (declare (type term term))
-                                          (the keyword (bcnx (gnrt term))))))))))
-
-#|
-()
-(bicn-cmbn-cmbnb (cmbn 3 1 (bcnb 'a) 2 (bcnc 'b)))
-(bicn-cmbn-cmbnb (cmbn 3 2 (bcnc 'b)))
-(bicn-cmbn-cmbnc (cmbn 3 1 (bcnb 'a) 2 (bcnc 'b) 3 (bcnd 'c)))
-(bicn-cmbn-cmbnc (cmbn 3 1 (bcnb 'a) 3 (bcnd 'c)))
-(bicn-cmbn-cmbnd (cmbn 3 1 (bcnb 'a) 2 (bcnc 'b) 3 (bcnd 'c)))
-(bicn-cmbn-cmbnd (cmbn 3 2 (bcnb 'b)))
-|#
-
-(DEFUN MAKE-BICN-CMBN (cmbnb cmbnc cmbnd)
-   (declare (type cmbn cmbnb cmbnc cmbnd))
-   (the cmbn
-      (with-cmbn (degrb listb) cmbnb
-      (with-cmbn (degrc listc) cmbnc
-      (with-cmbn (degrd listd) cmbnd
-         (unless (= degrb (1- degrc) degrd)
-            (error "In MAKE-BICN-CMBN, the degrees are not coherent."))
-         (make-cmbn :degr degrb
-            :list (nconc
-                     (mapcar #'(lambda (termb)
-                                  (declare (type term termb))
-                                  (with-term (cffc gnrtb) termb
-                                     (term cffc (bcnb gnrtb))))
-                        listb)
-                     (mapcar #'(lambda (termc)
-                                  (declare (type term termc))
-                                  (with-term (cffc gnrtc) termc
-                                     (term cffc (bcnc gnrtc))))
-                        listc)
-                     (mapcar #'(lambda (termd)
-                                  (declare (type term termd))
-                                  (with-term (cffc gnrtd) termd
-                                     (term cffc (bcnd gnrtd))))
-                        listd))))))))
-
-#|
-()
-(multiple-value-call #'make-bicn-cmbn 
-  (dispatch-bicn-cmbn (cmbn 3 3 (bcnb 'b1) 4 (bcnb 'b2) 33 (bcnc 'c) 333 (bcnd 'd))))
-|#
-
-(DEFUN BICN-PRINT (bicn stream depth)
-  (declare
-   (type bicn bicn) (stream stream)
-   (ignore depth))
-  (the bicn
-    (with-bicn (bcnx ibicn) bicn
-               ;; Correction 1-1-2
-               (format stream "<Bcn~A ~A>"
-                 ;; Correction 1-1-3
-                 (ecase bcnx (:bcnb #\B) (:bcnc #\C) (:bcnd #\D))
-                 ibicn)
-               bicn)))
-
-#|
-()
-(bcnb 'a)
-(bcnc 'b)
-(bcnd 'c)
-|#
-
-(DEFUN BICONE-CMPR (cmprb cmprc cmprd)
-   (declare (type cmprf cmprb cmprc cmprd))
-   (flet ((rslt (bicn1 bicn2)
-             (declare (type bicn bicn1 bicn2))
-             (let ((bcnx1 (bcnx bicn1)))
-                (declare (type (member :bcnb :bcnc :bcnd) bcnx1))
-                (lexico
-                   (s-cmpr bcnx1 (bcnx bicn2))
-                   (case bcnx1
-                      (:bcnb (funcall cmprb (ibicn bicn1) (ibicn bicn2)))
-                      (:bcnc (funcall cmprc (ibicn bicn1) (ibicn bicn2)))
-                      (:bcnd (funcall cmprd (ibicn bicn1) (ibicn bicn2))))))))
-      (the cmprf #'rslt)))
-
-#|
-()
-(setf r (bicone-cmpr #'f-cmpr #'f-cmpr #'f-cmpr))
-(funcall r (bcnb 1) (bcnc 0))
-(funcall r (bcnb 1) (bcnb 2))
-|#
-
-(DEFUN BICONE-BASIS (basisb basisc basisd)
-   (declare (type basis basisb basisc basisd))
-   (the basis
-      (if (or (eq :locally-effective basisb)
-              (eq :locally-effective basisc)
-              (eq :locally-effective basisd))
-         :locally-effective
-         (flet ((rslt (degr)
-                   (declare (fixnum degr))
-                   (append
-                      (mapcar #'(lambda (item)
-                                   (declare (type gnrt item))
-                                   (bcnb item))
-                         (funcall basisb degr))
-                      (mapcar #'(lambda (item)
-                                   (declare (type gnrt item))
-                                   (bcnc item))
-                         (funcall basisc (1+ degr)))
-                      (mapcar #'(lambda (item)
-                                   (declare (type gnrt item))
-                                   (bcnd item))
-                         (funcall basisd degr)))))
-            (the basis #'rslt)))))
-
-#|
-()
-(bicone-basis :locally-effective :locally-effective :locally-effective)
-(setf b #'(lambda (degr) (mapcar #'(lambda (item) (cons degr item)) (<a-b> 0 degr))))
-(setf r (bicone-basis b b b))
-(funcall r 3)
-|#
-
-(DEFUN BICONE-INTR-DFFR (cmprc dffrb dffrc dffrd f1 f2)
-   (declare
-      (type cmprf cmprc)
-      (type morphism dffrb dffrc dffrd f1 f2))
-   (flet ((rslt (cmbn)
-             (declare (type cmbn cmbn))
-             (the cmbn
-                (multiple-value-bind (cmbnb cmbnc cmbnd) (dispatch-bicn-cmbn cmbn)
-                   (declare (type cmbn cmbnb cmbnc cmbnd))
-                   (let ((dffrb (cmbn-? dffrb cmbnb))
-                         (dffrc (cmbn-? dffrc cmbnc))
-                         (dffrd (cmbn-? dffrd cmbnd))
-                         (f1 (cmbn-? f1 cmbnb))
-                         (f2 (cmbn-? f2 cmbnd)))
-                      (declare (type cmbn dffrb dffrc dffrd f1 f2))
-                      (let ((cmbnc (2cmbn-sbtr cmprc (2cmbn-add cmprc f1 f2) dffrc)))
-                         (declare (type cmbn cmbnc))
-                         (make-bicn-cmbn dffrb cmbnc dffrd)))))))
-      (the intr-mrph #'rslt)))
-                      
-(DEFUN BICONE (rdct1 rdct2)
-   (declare (type reduction rdct1 rdct2))
-   (the chain-complex
-      (with-slots ((tcc1 tcc) (bcc1 bcc) (f1 f)) rdct1
-         (declare
-            (type chain-complex tcc1 bcc1)
-            (type morphism f1))
-      (with-slots ((tcc2 tcc) (bcc2 bcc) (f2 f)) rdct2
-         (declare
-            (type chain-complex tcc2 bcc2)
-            (type morphism f2))
-         (unless (eq bcc1 bcc2)
-            (error "In BICONE, both reductions have different BCC's."))
-         (let ((rslt (build-chcm
-                        :cmpr (bicone-cmpr (cmpr tcc1) (cmpr bcc1) (cmpr tcc2))
-                        :basis (bicone-basis (basis tcc1) (basis bcc1) (basis tcc2))
-                        :bsgn :undefined
-                        :intr-dffr (bicone-intr-dffr (cmpr bcc1)
-                                      (dffr tcc1) (dffr bcc1) (dffr tcc2)
-                                      f1 f2)
-                        :strt :cmbn
-                        :orgn `(bicone ,rdct1 ,rdct2))))
-            (declare (type chain-complex rslt))
-            ; (slot-makunbound rslt 'bsgn)
-            rslt)))))
-
-#|
-()
-(cat-init)
-(progn
-  (defun cdelta (dmns)
-    (build-chcm
-     :cmpr #'l-cmpr
-     :basis #'(lambda (n)
-                (mapcar #'dlop-int-ext (funcall (delta-n-basis dmns) n)))
-     :bsgn '(0)
-     :intr-dffr #'(lambda (degr gmsm)
-                    (make-cmbn
-                     :degr (1- degr)
-                     :list (do ((rslt +empty-list+
-                                      (cons (cons sign (append
-                                                        (subseq gmsm 0 nark)
-                                                        (subseq gmsm (1+ nark))))
-                                            rslt))
-                                (sign 1 (- sign))
-                                (nark 0 (1+ nark)))
-                               ((> nark degr) rslt))))                                           
-     :strt :gnrt
-     :orgn `(locally effective version of C_* delta ,dmns)))
-  (defun make-f (tdmns bdmns)
-    (build-mrph
-     :sorc (cdelta tdmns) :trgt (cdelta bdmns) :degr 0
-     :intr #'(lambda (degr gmsm)
-               (let ((pos (position-if #'(lambda (vertex) (>= vertex bdmns)) gmsm)))
-                 (if pos
-                     (if (< pos degr)
-                         (zero-cmbn degr)
-                       (cmbn degr 1 (nconc (butlast gmsm) (list bdmns))))
-                   (cmbn degr 1 gmsm))))
-     :strt :gnrt
-     :orgn `(projection delta ,tdmns => delta ,bdmns)))
-  (defun make-g (tdmns bdmns)
-    (build-mrph
-     :sorc (cdelta bdmns) :trgt (cdelta tdmns) :degr 0
-     :intr #'identity
-     :strt :cmbn
-     :orgn `(injection delta ,bdmns => delta ,tdmns)))
-  (defun make-h (tdmns bdmns)
-    (build-mrph
-     :sorc (cdelta tdmns) :trgt (cdelta tdmns) :degr +1
-     :intr #'(lambda (degr gmsm)
-               (let ((pos (position-if #'(lambda (vertex) (>= vertex bdmns)) gmsm)))
-                 (if pos
-                     (if (member bdmns gmsm)
-                         (zero-cmbn (1+ degr))
-                       (cmbn (1+ degr) (-1-expt-n pos)
-                             (append (subseq gmsm 0 pos) (list bdmns) (subseq gmsm pos))))
-                   (zero-cmbn (1+ degr)))))
-     :strt :gnrt
-     :orgn `(homotopy for delta ,tdmns => ,bdmns)))
-  (defun make-rdct (tdmns bdmns)
-    (setf rdct (build-rdct
-                :f (make-f tdmns bdmns)
-                :g (make-g tdmns bdmns)
-                :h (make-h tdmns bdmns)
-                :orgn `(reduction delta ,tdmns ,bdmns)))))
-(setf b (bicone (make-rdct 3 2) (make-rdct 4 2)))
-(basis b 1)
-(? b (cmbn 1 3 (bcnb '(0 3)) 4 (bcnc '(0 1 2)) 5 (bcnd '(0 4))))
-|#
-
-(DEFMETHOD CMPS ((hmeq1 homotopy-equivalence) (hmeq2 homotopy-equivalence) &optional dummy)
-   (declare (ignore dummy))
-   (the homotopy-equivalence
-      (progn
-         (when (eq 'trivial-hmeq (orgn hmeq2))
-            (return-from cmps hmeq1))
-         (with-slots ((cc-A lbcc) (cc-B tcc) (cc-C rbcc)
-                      (f1 lf) (g1 lg) (h1 lh) (f2 rf) (g2 rg) (h2 rh)) hmeq1
-            (declare
-               (type chain-complex cc-A cc-B cc-C)
-               (type morphism f1 g1 h1 f2 g2 h2))
-         (with-slots ((cc-C2 lbcc) (cc-D tcc) (cc-E rbcc)
-                      (f3 lf) (g3 lg) (h3 lh) (f4 rf) (g4 rg) (h4 rh)) hmeq2
-            (declare
-               (type chain-complex cc-C2 cc-D cc-E)
-               (type morphism f3 g3 h3 f4 g4 h4))
-            (unless (eq (grmd cc-C) (grmd cc-C2))
-               (error "In (CMPS HMEQ HMEQ), both hmeq's may not be composed."))
-            (let ((bicone (bicone (rrdct hmeq1) (lrdct hmeq2)))
-                  (cmpr-B (cmpr cc-B))
-                  (cmpr-D (cmpr cc-D)))
-               (declare (type chain-complex bicone))
-               (let ((lf (build-mrph
-                            :sorc bicone :trgt cc-A :degr 0
-                            :intr #'(lambda (cmbn)
-                                       (declare (type cmbn cmbn))
-                                       (cmbn-? f1 (bicn-cmbn-cmbnB cmbn)))
-                            :strt :cmbn
-                            :orgn `(cmps ,hmeq1 ,hmeq2 lf)))
-                     (lg (build-mrph
-                            :sorc cc-A :trgt bicone :degr 0
-                            :intr #'(lambda (cmbn)
-                                       (declare (type cmbn cmbn))
-                                       (let* ((cmbnB (cmbn-? g1 cmbn))
-                                              (cmbnC (zero-cmbn (1+ (cmbn-degr cmbn))))
-                                              (cmbnD (cmbn-? g3 (cmbn-? f2 (cmbn-opps cmbnB)))))
-                                          (declare (type cmbn cmbnB cmbnC cmbnD))
-                                          (make-bicn-cmbn cmbnB cmbnC cmbnD)))
-                            :strt :cmbn
-                            :orgn `(cmps ,hmeq1 ,hmeq2 lg)))
-                     (lh (build-mrph
-                            :sorc bicone :trgt bicone :degr +1
-                            :intr #'(lambda (cmbn)
-                                       (declare (type cmbn cmbn))
-                                       (multiple-value-bind (cmbnB cmbnC cmbnD) 
-                                           (dispatch-bicn-cmbn cmbn)
-                                          (declare (type cmbn cmbnB cmbnC cmbnD))
-                                          (setf cmbnB (cmbn-? h1 cmbnB))
-                                          (let ((cmbnC (zero-cmbn (1+ (cmbn-degr cmbnC))))
-                                                (cmbnD1 (cmbn-? g3 (cmbn-? f2 cmbnB)))
-                                                (cmbnD2 (cmbn-? g3 cmbnC))  ;; let, not let*
-                                                (cmbnD3 (cmbn-? h3 cmbnD)))
-                                             (declare (type cmbn cmbnC cmbnD1 cmbnD2 cmbnD3))
-                                             (make-bicn-cmbn
-                                                cmbnB
-                                                cmbnC
-                                                (2cmbn-sbtr cmpr-D
-                                                   (2cmbn-add cmpr-D cmbnD2 cmbnD3)
-                                                   cmbnD1)))))
-                            :strt :cmbn
-                            :orgn `(cmps ,hmeq1 ,hmeq2 lh)))
-                     (rf (build-mrph
-                            :sorc bicone :trgt cc-E :degr 0
-                            :intr #'(lambda (cmbn)
-                                       (declare (type cmbn cmbn))
-                                       (cmbn-? f4 (bicn-cmbn-cmbnD cmbn)))
-                            :strt :cmbn
-                            :orgn `(cmps ,hmeq1 ,hmeq2 rf)))
-                     (rg (build-mrph
-                            :sorc cc-E :trgt bicone :degr 0
-                            :intr #'(lambda (cmbn)
-                                       (declare (type cmbn cmbn))
-                                       (let* ((cmbnD (cmbn-? g4 cmbn))
-                                              (cmbnC (zero-cmbn (1+ (cmbn-degr cmbn))))
-                                              (cmbnB (cmbn-? g2 (cmbn-? f3 (cmbn-opps cmbnD)))))
-                                          (declare (type cmbn cmbnD cmbnC cmbnB))
-                                          (make-bicn-cmbn cmbnB cmbnC cmbnD)))
-                            :strt :cmbn
-                            :orgn `(cmps ,hmeq1 ,hmeq2 rg)))
-                     (rh (build-mrph
-                            :sorc bicone :trgt bicone :degr +1
-                            :intr #'(lambda (cmbn)
-                                       (declare (type cmbn cmbn))
-                                       (multiple-value-bind (cmbnB cmbnC cmbnD) 
-                                           (dispatch-bicn-cmbn cmbn)
-                                          (declare (type cmbn cmbnB cmbnC cmbnD))
-                                          (setf cmbnD (cmbn-? h4 cmbnD))
-                                          (let ((cmbnC (zero-cmbn (1+ (cmbn-degr cmbnC))))
-                                                (cmbnB1 (cmbn-? g2 (cmbn-? f3 cmbnD)))
-                                                (cmbnB2 (cmbn-? g2 cmbnC))  ;; let, not let*
-                                                (cmbnB3 (cmbn-? h2 cmbnB)))
-                                             (declare (type cmbn cmbnC cmbnB1 cmbnB2 cmbnB3))
-                                             (make-bicn-cmbn
-                                                (2cmbn-sbtr cmpr-B
-                                                   (2cmbn-add cmpr-B cmbnB2 cmbnB3)
-                                                   cmbnB1)
-                                                cmbnC
-                                                cmbnD))))
-                            :strt :cmbn
-                            :orgn `(cmps ,hmeq1 ,hmeq2 rh))))
-                  (declare
-                     (type morphism lf lg lh rf rg rh))
-                  (build-hmeq :lf lf :lg lg :lh lh :rf rf :rg rg :rh rh
-                     :orgn `(cmps ,hmeq1 ,hmeq2)))))))))
-   
-#|
-()
-(cat-init)
-(setf c (build-chcm
-         :cmpr #'s-cmpr
-         :basis #'(lambda (dmns) '(a))
-         :bsgn 'a
-         :intr-dffr #'zero-intr-dffr
-         :strt :cmbn
-         :orgn '(c)))
-(setf h1 (trivial-hmeq c))
-(setf h2 (cmps h1 h1))
-(pre-check-rdct (lrdct h2))
-(setf *tc* (cmbn 3 1 (bcnB 'a) 10 (bcnC 'a) 100 (bcnD 'a)))
-(setf *bc* (cmbn 3 1 'a))
-(check-rdct)
-(pre-check-rdct (rrdct h2))
-(check-rdct)
-(setf h3 (cmps h2 h2))
-(setf *tc* (cmbn 3 1 (bcnB (bcnB 'a)) 10 (bcnB (bcnC 'a)) 100 (bcnB (bcnD 'a))
-                 1000 (bcnC 'a)
-                 10000 (bcnD (bcnB 'a)) 5234 (bcnD (bcnC 'a)) 223 (bcnD (bcnD 'a))))
-(pre-check-rdct (lrdct h3))
-(check-rdct)
-(pre-check-rdct (rrdct h3))
-(check-rdct)
-|#
diff --git a/archive/Kenzo-1/cartesian-products.cl b/archive/Kenzo-1/cartesian-products.cl
deleted file mode 100644
index f3e7552..0000000
--- a/archive/Kenzo-1/cartesian-products.cl
+++ /dev/null
@@ -1,326 +0,0 @@
-;;;  CARTESIAN-PRODUCTS  CARTESIAN-PRODUCTS  CARTESIAN-PRODUCTS  CARTESIAN-PRODUCTS
-;;;  CARTESIAN-PRODUCTS  CARTESIAN-PRODUCTS  CARTESIAN-PRODUCTS  CARTESIAN-PRODUCTS
-;;;  CARTESIAN-PRODUCTS  CARTESIAN-PRODUCTS  CARTESIAN-PRODUCTS  CARTESIAN-PRODUCTS
-
-(IN-PACKAGE "COMMON-LISP-USER")
-
-(PROVIDE "cartesian-products")
-
-
-(DEFUN CRPR-PRINT (crpr stream depth)
-  (declare
-   (type crpr crpr)
-   (stream stream)
-   (ignore depth))
-  (with-crpr (dgop1 gmsm1 dgop2 gmsm2) crpr
-             (format stream "<CrPr ~A ~A ~A ~A>"
-               (hyphenize-list (dgop-int-ext dgop1)) gmsm1
-               (hyphenize-list (dgop-int-ext dgop2)) gmsm2)
-             crpr))
-
-
-(DEFUN EXTRACT-COMMON-DGOP (dgop1 dgop2)
-   (declare (fixnum dgop1 dgop2))
-   (let ((dgop (logand dgop1 dgop2)))
-      (declare (fixnum dgop))
-      (do ((indx (1- (integer-length dgop)) (1- indx)))
-          ((minusp indx))
-         (declare (fixnum indx))
-         (when (logbitp indx dgop)
-            (setf dgop1 (remove-bit dgop1 indx)
-                  dgop2 (remove-bit dgop2 indx))))
-      (values dgop dgop1 dgop2)))
-
-#|
-  (dotimes (i 100)
-     (dotimes (j 100)
-        (multiple-value-bind (dgop dgop1 dgop2) (extract-common-dgop i j)
-           (unless (and (= i (dgop*dgop dgop dgop1))
-                        (= j (dgop*dgop dgop dgop2)))
-              (error "i = ~D, j = ~D, dgop = ~D, dgop1 = ~D, dgop2 = ~D"
-                 i j dgop dgop1 dgop2)))))
-|#
-
-(DEFUN 2ABSM-ACRPR (absm1 absm2)
-   (declare (type absm absm1 absm2))
-   (the absm
-      (with-absm (dgop1 gmsm1) absm1
-      (with-absm (dgop2 gmsm2) absm2
-         (multiple-value-bind (dgop dgop11 dgop22) (extract-common-dgop dgop1 dgop2)
-            (declare (fixnum dgop dgop11 dgop22))
-            (absm dgop
-               (crpr dgop11 gmsm1 dgop22 gmsm2)))))))
-
-#|
-  (2absm-acrpr (absm 5 'a) (absm 3 'b))
-|#
-
-
-#|
-(DEFUN CRTS-PRDC-CMPR (cmpr1 cmpr2)
-   (declare (type cmprf cmpr1 cmpr2))
-   (flet ((rslt (crpr1 crpr2)
-             (declare (type crpr crpr1 crpr2))
-             (the cmpr
-                (let ((left-cons-1 (cadr crpr1))
-                      (left-cons-2 (cadr crpr2)))
-                   (declare (cons left-cons-1 left-cons-2))
-                   (lexico
-                      (f-cmpr (car left-cons-1) (car left-cons-2))
-                      (let ((right-cons-1 (cddr crpr1))
-                            (right-cons-2 (cddr crpr2)))
-                         (declare (cons right-cons-1 right-cons-2))
-                         (lexico
-                            (f-cmpr (car right-cons-1) (car right-cons-2))
-                            (funcall cmpr1 (cdr left-cons-1) (cdr left-cons-2))
-                            (funcall cmpr2 (cdr right-cons-1) (cdr right-cons-2)))))))))
-     (the cmprf #'rslt)))
-|#
-
-(DEFUN CRTS-PRDC-CMPR (cmpr1 cmpr2)
-   (declare (type cmprf cmpr1 cmpr2))
-   (flet ((rslt (crpr1 crpr2)
-             (declare (type crpr crpr1 crpr2))
-             (the cmpr
-               (lexico
-                (f-cmpr (dgop1 crpr1) (dgop1 crpr2))
-                (f-cmpr (dgop2 crpr1) (dgop2 crpr2))
-                (funcall cmpr1 (gmsm1 crpr1) (gmsm1 crpr2))
-                (funcall cmpr2 (gmsm2 crpr1) (gmsm2 crpr2))))))
-     (the cmprf #'rslt)))
-
-
-#|
-()
-(setf c (cmpr (delta-infinity)))
-(setf rslt (crts-prdc-cmpr c c))
-(funcall rslt (crpr 0 3 0 3) (crpr 1 1 0 3))
-(funcall rslt (crpr 4 3 0 7) (crpr 3 1 0 7))
-(funcall rslt (crpr 0 3 0 3) (crpr 0 3 1 1))
-(funcall rslt (crpr 0 3 0 3) (crpr 0 5 0 3))
-(funcall rslt (crpr 0 3 0 3) (crpr 0 3 0 5))
-(funcall rslt (crpr 0 3 0 3) (crpr 0 3 0 3)))
-|#
-           
-(DEFUN CRTS-PRDC-BASIS (basis1 basis2)
-   (declare (type basis basis1 basis2))
-   (when (or (eq basis1 :locally-effective)
-             (eq basis2 :locally-effective))
-      (return-from crts-prdc-basis :locally-effective))
-   (flet ((rslt (dmns)
-             (declare (fixnum dmns))
-             (the list
-                (progn
-                   (when (minusp dmns)
-                      (return-from rslt +empty-list+))
-                   (let ((array1 (make-array (1+ dmns)))
-                         (array2 (make-array (1+ dmns)))
-                         (rslt +empty-list+)
-                         (mask (mask dmns)))
-                      (declare
-                         (simple-vector array1 array2)
-                         (list rslt)
-                         (fixnum mask))
-                      (dotimes (i (1+ dmns))
-                         (setf (svref array1 i) (funcall basis1 i)
-                               (svref array2 i) (funcall basis2 i)))
-                      (do ((dgop1 mask (1- dgop1)))
-                          ((minusp dgop1))
-                         (declare (fixnum dgop1))
-                         (let ((dmns1 (- dmns (logcount dgop1))))
-                            (declare (fixnum dmns1))
-                            (do ((dgop2 mask (1- dgop2)))
-                                ((minusp dgop2))
-                               (declare (fixnum dgop2))
-                               (unless (plusp (logand dgop1 dgop2))
-                                  (setf rslt
-                                        (nconc
-                                           (mapcan
-                                              #'(lambda (item1)
-                                                   (declare (type gmsm item1))
-                                                   (mapcar
-                                                      #'(lambda (item2)
-                                                           (declare (type gmsm item2))
-                                                           (crpr dgop1 item1 dgop2 item2))
-                                                      (svref array2 (- dmns (logcount dgop2)))))
-                                              (svref array1 dmns1))
-                                           rslt))))))
-                      rslt)))))
-          (the basis #'rslt)))
-
-#|
-  (setf b (basis (delta 1)))
-  (setf r (crts-prdc-basis b b))
-  (funcall r 0)
-  (funcall r 1)
-  (funcall r 2)
-  (funcall r 3)
-  (setf d3 (basis (delta 3)))
-  (setf r (crts-prdc-basis d3 d3))
-  (time (dotimes (i 7)
-           (print (length (funcall r i)))))
-  (setf s3 (basis (sphere 3)))
-  (setf p (crts-prdc-basis s3 s3))
-  (dotimes (i 8)
-     (print (funcall p i)))
-|#
-
-(DEFUN CRTS-PRDC-FACE (face1 face2)
-   (declare (type face face1 face2))
-   (flet ((rslt (indx dmns crpr)
-             (declare
-                (fixnum indx dmns)
-                (type crpr crpr))
-             (with-crpr (dgop1 gmsm1 dgop2 gmsm2) crpr
-                (multiple-value-bind (dgop1 del1) (1dlop-dgop indx dgop1)
-                   (declare
-                      (fixnum dgop1)
-                      (type (or null fixnum) del1))
-                (multiple-value-bind (dgop2 del2) (1dlop-dgop indx dgop2)
-                   (declare
-                      (fixnum dgop2)
-                      (type (or null fixnum) del2))
-                   (when del1
-                      (let ((absm1 (funcall face1 del1 (- dmns (logcount dgop1)) gmsm1)))
-                         (declare (type absm absm1))
-                         (setf dgop1 (dgop*dgop dgop1 (dgop absm1))
-                               gmsm1 (gmsm absm1))))
-                   (when del2
-                      (let ((absm2 (funcall face2 del2 (- dmns (logcount dgop2)) gmsm2)))
-                         (declare (type absm absm2))
-                         (setf dgop2 (dgop*dgop dgop2 (dgop absm2))
-                               gmsm2 (gmsm absm2))))
-                   (multiple-value-bind (dgop dgop1 dgop2) (extract-common-dgop dgop1 dgop2)
-                            (declare (fixnum dgop dgop1 dgop2))
-                            (absm dgop (crpr dgop1 gmsm1 dgop2 gmsm2))))))))
-         (the face #'rslt)))
-
-#|
-  (setf d2 (delta 2))
-  (setf b2 (basis d2))
-  (setf f2 (face d2))
-  (setf b (crts-prdc-basis b2 b2))
-  (setf r (crts-prdc-face f2 f2))
-  (dotimes (i 5)
-     (unless (zerop i)
-        (dolist (item (funcall b i))
-           (dotimes (j (1+ i))
-              (format t "~%del-~D ~A = ~A"
-                 j item (funcall r j i item))))))
-|#
-
-(DEFUN CRTS-PRDC-FACE* (face1 face2)
-   (declare (type face face1 face2))
-   (flet ((rslt (indx dmns crpr)
-             (declare
-                (fixnum indx dmns)
-                (type crpr crpr))
-             (with-crpr (dgop1 gmsm1 dgop2 gmsm2) crpr
-                (multiple-value-bind (dgop1 del1) (1dlop-dgop indx dgop1)
-                   (declare
-                      (fixnum dgop1)
-                      (type (or null fixnum) del1))
-                (multiple-value-bind (dgop2 del2) (1dlop-dgop indx dgop2)
-                   (declare
-                      (fixnum dgop2)
-                      (type (or null fixnum) del2))
-                   (when del1
-                      (let ((absm1 (funcall face1 del1 (- dmns (logcount dgop1)) gmsm1)))
-                         (declare (type absm absm1))
-                         (setf dgop1 (dgop*dgop dgop1 (dgop absm1))
-                               gmsm1 (gmsm absm1))))
-                   (when del2
-                      (let ((absm2 (funcall face2 del2 (- dmns (logcount dgop2)) gmsm2)))
-                         (declare (type absm absm2))
-                         (setf dgop2 (dgop*dgop dgop2 (dgop absm2))
-                               gmsm2 (gmsm absm2))))
-                   (if (plusp (logand dgop1 dgop2))
-                      :degenerate
-                      (crpr dgop1 gmsm1 dgop2 gmsm2)))))))
-         (the intr-mrph #'rslt)))
-
-#|
-  (setf d2 (delta 2))
-  (setf b2 (basis d2))
-  (setf f2 (face d2))
-  (setf b (crts-prdc-basis b2 b2))
-  (setf r (crts-prdc-face* f2 f2))
-  (dotimes (i 5)
-     (unless (zerop i)
-        (dolist (item (coerce (funcall b i) 'list))
-           (dotimes (j (1+ i))
-              (format t "~%del-~D ~A = ~A"
-                 j item (funcall r j i item))))))
-  (setf s3 (sphere 3))
-  (setf b3 (basis s3))
-  (setf f3 (face s3))
-  (setf b (crts-prdc-basis b3 b3))
-  (setf r (crts-prdc-face* f3 f3))
-  (dotimes (i 7)
-     (unless (zerop i)
-        (dolist (item (coerce (funcall b i) 'list))
-           (dotimes (j (1+ i))
-              (format t "~%del-~D ~A = ~A"
-                 j item (funcall r j i item))))))
-|#
-
-(DEFUN CRTS-PRDC (smst1 smst2)
-   (declare (type simplicial-set smst1 smst2))
-   (with-slots ((cmpr1 cmpr) (basis1 basis) (face1 face) (bspn1 bsgn)) smst1
-      (declare
-         (type cmprf cmpr1)
-         (type basis basis1)
-         (type face face1))
-   (with-slots ((cmpr2 cmpr) (basis2 basis) (face2 face) (bspn2 bsgn)) smst2
-      (declare
-         (type cmprf cmpr2)
-         (type basis basis2)
-         (type face face2))
-      (the simplicial-set
-         (build-smst
-            :cmpr (crts-prdc-cmpr cmpr1 cmpr2)
-            :basis (crts-prdc-basis basis1 basis2)
-            :bspn (crpr 0 bspn1 0 bspn2)
-            :face (crts-prdc-face face1 face2)
-            :face* (crts-prdc-face* face1 face2)
-            :orgn `(crts-prdc ,smst1 ,smst2))))))
-
-#|
-  (setf p (crts-prdc (delta 3) (delta 3)))
-  (? p 0 (crpr 0 1 0 2))
-  (? p 1 (crpr 0 3 0 3))
-  (? p 2 (crpr 0 7 0 7))
-  (? p 3 (crpr 0 15 0 15))
-  (? p 4 (crpr 1 15 2 15))
-|#
-
-#|
-  ;; For comparison with EAT.
-  ;; In CAT.
-  (setf s5 (sphere 5))
-  (setf p (crts-prdc s5 s5))
-  (setf b (basis p))
-  (setf d (bndr p))
-  (setf basis (funcall b 10))
-  (length basis)
-  (setf c (make-cmbn :degr 10 :list (mapcar #'(lambda (item)
-                                                (term (1+ (random 5)) item))
-                                      basis)))
-  (setf +too-much-time+ -1)
-  (cmbn-? d (cmbn-? d c))
-  (time (dotimes (i 5) (cmbn-? d (cmbn-? d c))))
-|#
-
-#|
-  ;; In EAT.
-  (setf s5 (sphere 5))
-  (setf p (cpr-2ss s5 s5))
-  (setf d (cc-d (ss-cc p)))
-  (setf basis (sbs p 10))
-  (length basis)
-  (setf c (make-cmb :dgr 10 :lst (mapcar #'(lambda (item)
-                                                (mnm (1+ (random 5)) item))
-                                     basis)))
-  (??? d (??? d c))
-  (time (dotimes (i 5) (??? d (??? d c))))
-|#
diff --git a/archive/Kenzo-1/cat-init.cl b/archive/Kenzo-1/cat-init.cl
deleted file mode 100644
index a5a7564..0000000
--- a/archive/Kenzo-1/cat-init.cl
+++ /dev/null
@@ -1,86 +0,0 @@
-;;;  FILES  FILES  FILES  FILES  FILES  FILES  FILES  FILES  FILES  FILES
-;;;  FILES  FILES  FILES  FILES  FILES  FILES  FILES  FILES  FILES  FILES
-;;;  FILES  FILES  FILES  FILES  FILES  FILES  FILES  FILES  FILES  FILES
-
-(IN-PACKAGE "COMMON-LISP-USER")
-
-(DEFUN KENZO-VERSION ()
-  (format t "~%*** Kenzo-Version 1.1.7 ***~2%")
-  (values))
-
-(PROCLAIM '(OPTIMIZE (speed 3) (safety 1) (space 0) (debug 0)))
-
-(DEFCONSTANT +FILE-LIST+
-    '("macros"
-      "various"
-      "classes"
-      "combinations"
-      "chain-complexes"
-      "chcm-elementary-op"
-      "effective-homology"
-      "homology-groups"
-      "searching-homology"
-      "cones"
-      "bicones"
-      "tensor-products"
-      "coalgebras"
-      "cobar"
-      "algebras"
-      "bar"
-      "simplicial-sets"
-     "simplicial-mrphs"
-      "delta"
-      "special-smsts"
-      "suspensions"
-      "disk-pasting"
-     "cartesian-products"
-      "eilenberg-zilber"
-      "kan"
-      "simplicial-groups"
-     "fibrations"
-      "loop-spaces"
-      "ls-twisted-products"
-      "lp-space-efhm"
-      "classifying-spaces"
-      "k-pi-n"
-      "serre"
-      "cs-twisted-products"
-      "cl-space-efhm"
-      "whitehead"
-      "smith"
-      ))
-
-(DO ((i 1 (1+ i))
-     (mark +file-list+ (cdr mark)))
-    ((endp mark) (terpri))
-   (format t "~% FILE ~2D: ~A" i (car mark)))
-
-(DEFCONSTANT +SOURCE-EXTENSION+
-  #+(or allegro clisp lispworks) "cl"
-  #-(or allegro clisp lispworks)
-    (error "Not an Allegro or CLisp or LispWorks environment."))
-
-(DEFCONSTANT +COMPILED-EXTENSION+ 
-    #+allegro "fasl"
-    #+clisp "fas"
-    #+lispworks "ofasl")
-
-(DEFUN LOAD-SFILES ()
-   (mapc #'(lambda (file-name)
-             (load (concatenate 'string file-name "." +source-extension+)))
-    +file-list+))
-
-(DEFVAR *CMBN-CONTROL*)
-(SETF *CMBN-CONTROL* T)
-
-(DEFUN COMPILE-FILES ()
-  (format t "~%*CMBN-CONTROL*  = ~A~2%" *cmbn-control*)
-  (mapc #'(lambda (file-name)
-            (compile-file (concatenate 'string file-name "." +source-extension+))
-            (load (concatenate 'string file-name "." +compiled-extension+)))
-    +file-list+))
-
-(DEFUN LOAD-CFILES ()
-   (mapc #'(lambda (file-name)
-             (load (concatenate 'string file-name "." +compiled-extension+)))
-    +file-list+))
diff --git a/archive/Kenzo-1/chain-complexes.cl b/archive/Kenzo-1/chain-complexes.cl
deleted file mode 100644
index 588a7d3..0000000
--- a/archive/Kenzo-1/chain-complexes.cl
+++ /dev/null
@@ -1,605 +0,0 @@
-;;;  CHAIN-COMPLEXES  CHAIN-COMPLEXES  CHAIN-COMPLEXES  CHAIN-COMPLEXES
-;;;  CHAIN-COMPLEXES  CHAIN-COMPLEXES  CHAIN-COMPLEXES  CHAIN-COMPLEXES
-;;;  CHAIN-COMPLEXES  CHAIN-COMPLEXES  CHAIN-COMPLEXES  CHAIN-COMPLEXES
-
-(IN-PACKAGE "COMMON-LISP-USER")
-
-(PROVIDE "chain-complexes")
-
-(DEFVAR *LIST-LIST* +empty-list+)
-
-(DEFUN CAT-INIT ()
-  (declare (special *idnm-counter* *results-n* *results-cmlt-tm*))
-  (setf *idnm-counter* 0 *results-n* 0 *results-cmlt-tm* 0.0)
-  (map nil #'(lambda (listname)
-               (declare (symbol listname))
-               (setf (symbol-value listname) +empty-list+))
-    *list-list*)
-  (done))
-
-(DEFUN HOW-MANY-OBJECTS ()
-   (mapc #'(lambda (symbol)
-              (declare (type (or string symbol) symbol))
-              (let ((length (length (eval symbol))))
-                 (declare (fixnum length))
-                 (setf symbol (symbol-name symbol))
-                 (setf symbol (subseq symbol 1 (- (length symbol) 6)))
-                 (format t "~%~6D ~As" length symbol)))
-      *list-list*)
-   (done))
-
-(DEFUN ALL-OBJECTS ()
-  (let ((object-list
-	 (sort (delete-duplicates
-		  (mapcan #'(lambda (symbol)
-			      (copy-list (eval symbol)))
-			  *list-list*)
-		  :test #'eq)
-	       #'< :key #'idnm)))
-    (declare (list object-list))
-    (dolist (item object-list)
-      (format t "~%~A = ~A" item (orgn item))))
-  (done))
-
-(DEFUN KD (idnm)
-  (declare (fixnum idnm))
-  (dolist (list *list-list*)
-    (let ((found (find idnm (eval list) :key #'idnm)))
-      (when found
-	(format t "~%Object: ~A
-~3TOrigin: ~A~2%" found (orgn found))
-	(return-from kd (values))))))
-
-(DEFUN K (idnm)
-  (declare (fixnum idnm))
-  (dolist (list *list-list*)
-    (let ((found (find idnm (eval list) :key #'idnm)))
-      (when found
-	(return-from k found)))))
-
-(DEFUN KD2 (idnm)
-  (declare (fixnum idnm))
-  (let ((k-list (k idnm)))
-    (declare (list k-list))
-    (unless k-list
-      (return-from kd2 nil))
-    (setf k-list (list k-list))
-    (do ((idnm (1- idnm) (1- idnm)))
-	((zerop idnm))
-      (declare (fixnum idnm))
-      (let ((found (find-if
-		     #'(lambda (item)
-			 (declare (type (or chain-complex morphism) item))
-			 (member (k idnm) (orgn item)))
-		     k-list)))
-	(declare (type (or null chain-complex morphism) found))
-	(when found
-	  (push (k idnm) k-list))))
-    (mapc #'kd (nreverse (mapcar #'idnm k-list)))))
-    
-
-(DEFVAR *CHCM-LIST*)
-(SETF *CHCM-LIST* +empty-list+)
-(PUSHNEW '*CHCM-LIST* *list-list*)
-
-#+clisp(eval-when (:compile-toplevel :load-toplevel :execute)
-         (setf (ext:package-lock :clos) nil))
-(DEFMETHOD PRINT-OBJECT ((chcm chain-complex) stream)
- (the chain-complex
-   (progn
-      (format stream "[K~D Chain-Complex]" (idnm chcm))
-      chcm)))
-#+clisp(eval-when (:compile-toplevel :load-toplevel :execute)
-         (setf (ext:package-lock :clos) t))
-
-(DEFUN CHCM (idnm)
-   (declare (fixnum idnm))
-   (the (or chain-complex null)
-      (find idnm *chcm-list* :key #'idnm)))
-
-(DEFUN RESULT-PRINT (result stream depth)
-  (declare
-   (type result result) (stream stream)
-   (ignore depth))
-    (format stream "~%<Rslt>
-~4TGNRT-> ~A
-~3TVALUE-> ~A
-~4TCLNM-> ~6D
-~4TRNTM-> ~11,3F"
-    (result-gnrt result) (result-value result)
-    (result-clnm result) (result-rntm result))
-  result)
-  
-
-#|
-()
-(make-result :gnrt 'a :value '(a a) :clnm 23 :rntm 2.345)
-|#
-
-(DEFPARAMETER +MAXIMAL-DIMENSION+ 15)
-
-(DEFVAR *MRPH-LIST*)
-(SETF *MRPH-LIST* +empty-list+)
-(PUSHNEW '*MRPH-LIST* *list-list*)
-
-(DEFMETHOD ?2 ((mrph morphism) cmbn)
-   (declare (type cmbn cmbn))
-   (the cmbn
-      (cmbn-? mrph cmbn)))
-
-(DEFMETHOD ?2 ((chcm chain-complex) cmbn)
-   (declare
-      (type cmbn cmbn))
-   (the cmbn
-      (cmbn-? (dffr1 chcm) cmbn)))
-
-(DEFMETHOD ?3 ((mrph morphism) degr gnrt)
-   (declare
-      (fixnum degr)
-      (type gnrt gnrt))
-   (the cmbn
-      (gnrt-? mrph degr gnrt)))
-
-(DEFMETHOD ?3 ((chcm chain-complex) degr gnrt)
-   (declare
-      (fixnum degr)
-      (type gnrt gnrt))
-   (gnrt-? (dffr1 chcm) degr gnrt))
-
-#+clisp(eval-when (:compile-toplevel :load-toplevel :execute)
-         (setf (ext:package-lock :clos) nil))
-(DEFMETHOD PRINT-OBJECT ((mrph morphism) stream)
-   (the morphism
-      (progn
-	(if (eq (first (orgn (trgt mrph))) 'z-chcm)
-	    (format stream "[K~D Cohomology-Class on K~D of degree ~D]"
-		    (idnm mrph) (idnm (sorc mrph)) (- (degr mrph)))
-	  (format stream "[K~D Morphism (degree ~D): K~D -> K~D]"
-		  (idnm mrph) (degr mrph)
-		  (idnm (sorc mrph)) (idnm (trgt mrph))))
-         mrph)))
-#+clisp(eval-when (:compile-toplevel :load-toplevel :execute)
-         (setf (ext:package-lock :clos) t))
-
-(DEFUN MRPH (n)
-   (declare (fixnum n))
-   (the (or morphism null)
-      (find n *mrph-list* :key #'idnm)))
-
-(DEFUN BUILD-CHCM (&key cmpr basis bsgn intr-dffr strt orgn)
-   (declare
-      (type cmprf cmpr)
-      (type basis basis)
-      (type gnrt bsgn)
-      (type intr-mrph intr-dffr)
-      (type strt strt)
-      (type list orgn))
-   (the chain-complex
-      (progn
-         (let ((already (find orgn *chcm-list* :test #'equal :key #'orgn)))
-            (declare (type (or chain-complex null) already))
-            (when already
-               (return-from build-chcm already)))
-         (unless basis
-            (setf basis :locally-effective))
-         (let ((chcm (make-instance 'chain-complex
-                        :cmpr cmpr
-                        :basis basis
-                        :bsgn bsgn
-                        :orgn orgn)))
-            (declare (type chain-complex chcm))
-            (setf (slot-value chcm 'dffr)
-                  (build-mrph
-                     :sorc chcm :trgt chcm :degr -1
-                     :intr intr-dffr :strt strt
-                     :orgn `(dffr ,chcm)))
-            (setf (slot-value chcm 'grmd) chcm)
-            (push chcm *chcm-list*)
-            chcm))))
-
-(DEFUN BASIS2 (object n)         ;;;
-   (declare
-      (type t object)
-      (fixnum n))
-   (the list
-      (with-slots (basis) object
-         (declare (type basis basis))
-         (when (eq :locally-effective basis)
-            (error "The object ~A is locally-effective." object))
-         (funcall basis n))))
-
-(DEFUN BUILD-MRPH (&key sorc trgt degr intr strt orgn)
-   (declare
-      (type chain-complex sorc trgt)
-      (fixnum degr)
-      (type intr-mrph intr)
-      (type strt strt)
-      (list orgn))
-   (the morphism
-      (progn
-         (let ((already (find orgn *mrph-list* :test #'equal :key #'orgn)))
-            (declare (type (or morphism null) already))
-            (when already
-               (return-from build-mrph already)))
-         (let ((mrph (make-instance 'morphism
-                        :sorc sorc :trgt trgt :degr degr
-                        :intr intr :strt strt
-                        :orgn orgn)))
-            (declare (type morphism mrph))
-            (setf (slot-value mrph 'rslts)
-                  (ecase strt
-                     (:gnrt (map 'simple-vector
-                               ;; (vector (vector result))
-                               #'(lambda (dummy)
-                                    (declare (ignore dummy))
-                                    (make-array 0
-                                       :adjustable t
-                                       :fill-pointer 0))
-                               (make-list +maximal-dimension+)))
-                     (:cmbn nil)))
-            (push mrph *mrph-list*)
-            mrph))))
-
-;;; FUNCTIONS
-
-(DEFVAR *START-STACK* +empty-list+)
-
-(DEFPARAMETER +TOO-MUCH-TIME+ -1)
-
-(DEFVAR *RESULTS-MAX* (expt 10 5))
-
-(DEFVAR *RESULTS-COEF* 3.0)
-(DEFVAR *RESULTS-CMLT-TM* 0.0)
-(DEFVAR *RESULTS-N* 0)
-
-(DEFVAR *RESULTS-VERBOSE* t)
-
-(DEFUN NRESULTS ()
-  (the fixnum
-    (let ((nrslts 0))
-      (declare (fixnum nrslts))
-      (dolist (item *mrph-list*)
-        (declare (type morphism item))
-        (when (eq :gnrt (strt item))
-          (map nil
-            #'(lambda (drslt)
-                (declare (vector drslt))
-                (incf nrslts (length drslt)))
-            (rslts item))))
-      nrslts)))
-
-(DEFUN TIME-LIST ()
-  (the list
-    (let ((time-list +empty-list+))
-      (declare (list time-list))
-      (dolist (item *mrph-list*)
-        (declare (type morphism item))
-        (when (eq :gnrt (strt item))
-          (map nil #'(lambda (drslt)
-                       (declare (vector drslt))
-                       (map nil #'(lambda (rslt)
-                                    (declare (type result rslt))
-                                    (let ((rntm (result-rntm rslt)))
-                                      (declare (integer rntm))
-                                      (when (plusp rntm)
-                                        (push rntm time-list))))
-                         drslt))
-            (rslts item))))
-      (sort time-list #'>))))
-
-(DEFUN CLEAN-RESULTS (&optional (results-coef *results-coef*))
-  (declare
-   (single-float results-coef)
-   (special *results-coef* *results-cmlt-tm* *results-n* *results-verbose*))
-  (the (values )
-    (let ((cut (* results-coef (/ *results-cmlt-tm* *results-n*))))
-      (declare (single-float cut))
-      (setf *results-n* 0 *results-cmlt-tm* 0.0)
-      (dolist (item *mrph-list*)
-        (declare (type morphism item))
-        (when (eq :gnrt (strt item))
-            (let ((rslts (rslts item)))
-              (declare (vector rslts))
-              (dotimes (i +maximal-dimension+)
-                (declare (fixnum i))
-                (let ((rslts-i (aref rslts i))
-                      (output (make-array 0 :adjustable t :fill-pointer 0)))
-                  (declare (vector rslts-i output))
-                  (map nil
-                    #'(lambda (rslt)
-                        (declare (type result rslt))
-                        (let ((rntm (result-rntm rslt)))
-                          (declare (single-float rntm))
-                          (when (> rntm cut)
-                            (incf *results-n*)
-                            (incf *results-cmlt-tm* rntm)
-                            (vector-push-extend rslt output))))
-                    rslts-i)
-                  (setf (aref rslts i) output))))))
-      (when *results-verbose*
-        (format t "~%*CR* -- Cut = ~A -- N = ~A" cut *results-n*)))))
-
-
-
-
-(DEFUN MRPH-GNRT (cmpr2 intr degr gnrt memory &optional (left -1) (right (fill-pointer memory)))
-  (declare
-     (type intr-mrph intr)
-     ;; (function (fixnum gnrt) cmbn)
-     (type cmprf cmpr2)
-     (fixnum degr left right)
-     (type gnrt gnrt)
-   (vector memory)
-   (special *results-n*)
-   (fixnum *results-n*))
-   ;; (vector result)
-   (the (values cmbn fixnum)
-      ;;; cmbn = image of the generator
-      ;;; fixnum = index "exact" or just "lower" of the maybe stored result
-      (loop
-        (when (= right (1+ left))            ;; the result for gnrt is not available
-          (push (get-internal-run-time) *start-stack*)
-          (let ((value (funcall intr degr gnrt))
-                (runtime (- (get-internal-run-time) (pop *start-stack*))))
-            (declare
-             (type cmbn value)
-             (integer runtime))
-            (if (> runtime +too-much-time+)
-                ;;; the condition deciding whether
-                ;;;   storing must happen
-                (let ((old-length (vector-push-extend nil memory)))
-                  (declare (fixnum old-length))
-                  (replace memory memory
-                           :start1 (1+ right) :end1 (1+ old-length)
-                           :start2 right :end2 old-length)
-                  (setf (aref memory right)
-                    (make-result
-                     :gnrt gnrt :value value
-                     :clnm 1
-                     :rntm (let ((rntm
-                                  (float
-                                   (/ runtime internal-time-units-per-second))))
-                             (declare (single-float rntm))
-                             (incf *results-cmlt-tm* rntm)
-                             rntm)))                     
-                  (mapl #'(lambda (mark)
-                            (declare (cons mark))
-                            (incf (car mark) runtime))
-                    *start-stack*)
-                  (when (> (incf *results-n*) *results-max*)
-                    (clean-results))
-                  (return (values value right)))
-              (return (values value left)))))
-        (let ((middle (truncate (+ right left) 2)))
-            (declare (fixnum middle))
-            (ecase (funcall cmpr2 gnrt (result-gnrt (aref memory middle)))
-               (:equal (let ((rslt (aref memory middle)))
-			  (declare (type cons rslt))
-			  (incf (result-clnm rslt))
-			  (return (values (result-value rslt) middle))))
-               (:less (setf right middle))
-              (:greater (setf left middle)))))))
-
-	   
-(DEFUN MRPH-CMBN (scmpr2 tcmpr2 intr cmbn memory)
-   (declare
-      (type intr-mrph intr)
-      ;; (function (fixnum gnrt) cmbn)
-      (type cmprf scmpr2 tcmpr2)
-      (type cmbn cmbn)                    ;;; cmbn is a non-zero one
-      (vector memory))
-      ;; (vector result)
-   (the cmbn
-      (with-cmbn (degr list) cmbn
-         (let ((n-cmbn-list +empty-list+))
-            (declare (list n-cmbn-list))
-            (do ((mark list (cdr mark))
-                 (left -1))
-                ((endp mark))
-               (declare (list mark))
-               (multiple-value-bind (rslt new-left)
-                                    (mrph-gnrt scmpr2 intr degr (-gnrt mark) memory left)
-                  (setf left new-left)
-                  (push (cons (-cffc mark) rslt) n-cmbn-list)))
-	    (cmbn-cmbn tcmpr2 n-cmbn-list)))))
-
-(DEFUN DO-CONTROL (cmpr cmbn)
-   (declare
-      (type cmprf cmpr)
-      (type cmbn cmbn))
-   (let ((list (cmbn-list cmbn)))
-      (declare (list list))
-      (do ((mark1 (rest list) (cdr mark1))
-	   (mark2 list mark1))
-	  ((endp mark1))
-	 (declare (list mark1 mark2))
-	 (unless (eq :less (funcall cmpr (-gnrt mark2) (-gnrt mark1)))
-	    (setf *wrong-cmbn* cmbn)
-	    (error "In the combination located by *WRONG-CMBN*, the generators:~@
-                    ~A and ~A are in a wrong order." (cdar mark2) (cdar mark1)))))
-   cmbn)
-
-#|
-  (do-control #'s-cmpr (cmbn 0 1 'a 1 'b -1 'c))
-  (do-control #'s-cmpr (cmbn 0 1 'b 1 'b -1 'c))
-  (do-control #'s-cmpr (cmbn 0 1 'a 1 'b -1 'b))
-  (setf *cmbn-control* nil)
-  (control #'s-cmpr (cmbn 0 1 'a 1 'b -1 'b))
-  (setf *cmbn-control* t)
-  (control #'s-cmpr (cmbn 0 1 'a 1 'b -1 'b))
-|#
-
-#|
-(DEFVAR *PROFILER-STACK*)
-(SETF *PROFILER-STACK* +empty-list+)
-
-(DEFUN PROFILER-INIT ()
-   (mapc #'(lambda (mrph)
-              (declare (type morphism mrph))
-              (setf (wrtm mrph) 0))
-      *mrph-list*))
-
-(DEFUN PROFILER-ON ()
-   (push (get-internal-run-time) *profiler-stack*))
-
-(DEFUN PROFILER-OFF (mrph)
-   (declare (type morphism mrph))
-   (let ((time-spent 
-          (- (get-internal-run-time) (pop *profiler-stack*))))
-      (declare (integer time-spent))
-      (mapl #'(lambda (mark)
-                 (declare (cons mark))
-                 (incf (car mark) time-spent))
-         *profiler-stack*)
-      (incf (wrtm mrph) time-spent)))
-|#
-
-(DEFVAR *FUTURE-DISPLAY* nil)
-
-(DEFVAR *TIME-INTERVAL* 60000)
-
-(DEFUN GNRT-? (mrph degr gnrt)
-   (declare
-      (type morphism mrph)
-      (fixnum degr)
-      (type gnrt gnrt))
-   (the cmbn
-      (progn
-;;         (profiler-on)
-         (when (and *future-display*
-                    (> (get-internal-run-time) *future-display*))
-            (format t "~%GNRT-?
-~3T~A  ORGN = ~A
-~3TDEGR = ~D
-~3TGNRT = ~A"
-               mrph (orgn mrph) degr gnrt)
-            (setf *future-display* (+ (get-internal-run-time) *time-interval*)))
-         (with-slots (sorc (mdegr degr) intr strt ?-clnm) mrph
-            (declare
-               (type chain-complex sorc)
-               (fixnum mdegr ?-clnm)
-               (type intr-mrph intr)
-               (type strt strt))
-         (with-slots ((scmpr cmpr)) sorc
-            (declare (type cmprf scmpr))
-            (control (slot-value (slot-value mrph 'trgt) 'cmpr)
-               (progn
-                  (incf ?-clnm)
-                  (prog1
-                     (ecase strt
-                        (:gnrt
-                         (mrph-gnrt scmpr intr
-                            degr gnrt (svref (rslts mrph) degr)))
-                        (:cmbn
-                         (funcall intr (term-cmbn degr 1 gnrt))))
-;;                     (profiler-off mrph)
-                     ))))))))
-
-#|
-()
-(cat-init)
-(setf cc (build-chcm :cmpr #'f-cmpr
-                     :basis :locally-effective
-                     :bsgn 0
-                     :intr-dffr #'(lambda (cmbn)
-                                    (cmbn (1- (cmbn-degr cmbn))))
-                     :strt :cmbn
-                     :orgn '(Z of Z)))
-(setf cc (build-chcm :cmpr #'f-cmpr
-                     :basis :locally-effective
-                     :bsgn 0
-                     :intr-dffr #'(lambda (cmbn)
-                                    (cmbn (1- (cmbn-degr cmbn))))
-                     :strt :cmbn
-                     :orgn '(Z of Z)))
-(setf ff (build-mrph :sorc cc :trgt cc :degr 0
-                     :intr #'(lambda (degr n) (cmbn degr 1 n))
-                     :strt :gnrt :orgn '(test)))
-(setf ff (build-mrph :sorc cc :trgt cc :degr 0
-                     :intr #'(lambda (degr n) (cmbn degr 1 n))
-                     :strt :gnrt :orgn '(test)))
-(dotimes (i 20)
-  (let ((n (- (random 50) 50)))
-    (format t "~%~D   ~D" n (gnrt-? ff 0 n))))
-(setf +too-much-time+ -1)
-(dotimes (i 20)
-  (let ((n (- (random 50) 50)))
-    (format t "~%~D   ~D" n (gnrt-? ff 0 n))))
-(setf +too-much-time+ 50)
-|#
-
-(DEFUN CMBN-? (mrph cmbn)
-   (declare
-      (type morphism mrph)
-      (type cmbn cmbn))
-   (the cmbn
-      (progn
-;;         (profiler-on)
-         (when (and *future-display*
-                    (> (get-internal-run-time) *future-display*))
-            (format t "~%CMBN-?
-~3T~A  ORGN = ~A
-~3TCMBN = ~A"
-               mrph (orgn mrph) cmbn)
-            (setf *future-display* (+ (get-internal-run-time) *time-interval*)))
-         (with-slots (sorc trgt degr intr strt ???-clnm) mrph
-            (declare
-               (type chain-complex sorc trgt)
-               (fixnum degr ???-clnm)
-               (type intr-mrph intr)
-               (type strt strt))
-         (with-slots ((scmpr cmpr)) sorc
-            (declare (type cmprf scmpr))
-         (with-slots ((tcmpr cmpr)) trgt
-            (declare (type cmprf tcmpr))
-            (control tcmpr
-               (progn
-                  (controln scmpr cmbn)
-                  (incf ???-clnm)
-                  (when (eq strt :cmbn)
-                     (return-from cmbn-? (funcall intr cmbn)))
-                  (prog1
-                     (if (cmbn-zero-p cmbn)
-                        (zero-cmbn (+ (cmbn-degr cmbn) degr))
-                        (mrph-cmbn scmpr tcmpr intr
-                           cmbn (svref (rslts mrph) (cmbn-degr cmbn))))
-;;                     (profiler-off mrph)
-                     )))))))))
-
-#|
-()
-(cat-init)
-(setf cc (build-chcm :cmpr #'f-cmpr
-                     :basis :locally-effective
-                     :bsgn 0
-                     :intr-dffr #'(lambda (cmbn)
-                                    (cmbn (1- (cmbn-degr cmbn))))
-                     :strt :cmbn
-                     :orgn '(Z of Z)))
-(setf *n* 10)
-(defun ff (degr i)
-  (do ((*2n* (ash *n* 1))
-       (rslt +empty-list+
-             (cons (cons (let ((cffc (- (random *2n*) *n*)))
-                           (if (minusp cffc) cffc (1+ cffc)))
-                         (decf gnrt (1+ (random *n*))))
-                   rslt))
-       (gnrt i)
-       (k 0 (1+ k)))
-      ((= k *n*)
-       (make-cmbn
-        :degr 0
-        :list rslt))))
-(ff 0 20)
-(compile 'ff)
-(setf mrph (build-mrph :sorc cc :trgt cc :degr 0
-                       :intr #'ff :strt :gnrt :orgn '(test)))
-(cmbn-? mrph (cmbn 0 1 100))
-(cmbn-? mrph *)
-(cmbn-? mrph *)
-(cmbn-? mrph *)
-(cmbn-? mrph *)
-(cmbn-? mrph *)
-(time (cmbn-? mrph *))
-(inspect mrph)
-|#
diff --git a/archive/Kenzo-1/chcm-elementary-op.cl b/archive/Kenzo-1/chcm-elementary-op.cl
deleted file mode 100644
index e5f8932..0000000
--- a/archive/Kenzo-1/chcm-elementary-op.cl
+++ /dev/null
@@ -1,463 +0,0 @@
-;;;  CHCM-ELEMENTARY-OP  CHCM-ELEMENTARY-OP  CHCM-ELEMENTARY-OP  CHCM-ELEMENTARY-OP
-;;;  CHCM-ELEMENTARY-OP  CHCM-ELEMENTARY-OP  CHCM-ELEMENTARY-OP  CHCM-ELEMENTARY-OP
-;;;  CHCM-ELEMENTARY-OP  CHCM-ELEMENTARY-OP  CHCM-ELEMENTARY-OP  CHCM-ELEMENTARY-OP
-
-(IN-PACKAGE "COMMON-LISP-USER")
-
-(PROVIDE "chcm-elementary-op")
-
-(DEFUN Z-CHCM ()
-   (the chain-complex
-      (build-chcm
-         :cmpr #'(lambda (gnrt1 gnrt2)
-                    (declare (ignore gnrt1 gnrt2))
-                    (the cmpr :equal))
-         :basis #'(lambda (n)
-                     (declare (type fixnum n))
-                     (the list
-                        (if (zerop n)
-                           (list :Z-gnrt)
-                           +empty-list+)))
-         :bsgn :Z-gnrt
-         :intr-dffr #'zero-intr-dffr
-         :strt :cmbn
-         :orgn '(Z-chcm))))
-
-(DEFUN ZERO-MRPH (chcm1 &optional (chcm2 chcm1) (degr 0))
-   (declare (type chain-complex chcm1 chcm2)
-            (type fixnum degr))
-   (the morphism
-      (build-mrph
-         :sorc chcm1 :trgt chcm2 :degr degr
-         :intr #'(lambda (cmbn)
-                    (declare (type cmbn cmbn))
-                    (zero-cmbn (+ (cmbn-degr cmbn) degr)))
-         :strt :cmbn
-         :orgn `(zero-mrph ,chcm1 ,chcm2 ,degr))))
-
-#|
-  (cat-init)
-  (setf z (zero-mrph (Z-chcm) (Z-chcm) 2))
-  (gnrt-? z 0 :z-gnrt)
-  (cmbn-? z (cmbn 3))
-  (setf z2 (zero-mrph (Z-chcm) (Z-chcm) 2))
-  (eq z z2)
-  (setf z3 (zero-mrph (Z-chcm) (Z-chcm) 3))
-  (gnrt-? z3 0 :z-gnrt)
-  (eq z z3))
-|#    
-
-
-
-(DEFUN IDNT-MRPH (chcm)
-   (declare (type chain-complex chcm))
-   (the morphism
-      (build-mrph
-         :sorc chcm :trgt chcm :degr 0
-         :intr #'identity
-         :strt :cmbn
-         :orgn `(idnt-mrph ,chcm))))
-
-#|
-  (setf zi (idnt-mrph (Z-chcm)))
-  (gnrt-? zi 0 :z-gnrt)
-  (setf zi2 (idnt-mrph (Z-chcm)))
-  (eq zi zi2))
-|#
-
-(DEFUN OPPS (mrph)
-   (declare (type morphism mrph))
-   (the morphism
-      (with-slots (sorc trgt degr) mrph
-         (build-mrph
-            :sorc sorc :trgt trgt :degr degr
-            :intr #'(lambda (cmbn)
-                       (declare (type cmbn cmbn))
-                       (cmbn-opps (cmbn-? mrph cmbn)))
-            :strt :cmbn
-            :orgn `(opps ,mrph)))))
-
-#|
-  (cat-init)
-  (setf -zi (opps (idnt-mrph (Z-chcm))))
-  (gnrt-? -zi 0 :z-gnrt)
-  (setf -zi2 (opps (idnt-mrph (Z-chcm))))
-  (eq -zi -zi2))
-|#
-
-(DEFMETHOD CMPS ((chcm1 chain-complex) (chcm2 chain-complex) &optional strt)
-   (declare (type (or strt null) strt))
-   (the morphism
-      (cmps (dffr chcm1) (dffr chcm2) strt)))
-
-(DEFMETHOD CMPS ((chcm1 chain-complex) (mrph2 morphism) &optional strt)
-   (declare (type (or strt null) strt))
-   (the morphism
-      (cmps (dffr chcm1) mrph2 strt)))
-
-(DEFMETHOD CMPS ((mrph1 morphism) (chcm2 chain-complex) &optional strt)
-   (declare (type (or strt null) strt))
-   (the morphism
-      (cmps mrph1 (dffr chcm2) strt)))
-
-(DEFMETHOD CMPS ((mrph1 morphism) (mrph2 morphism) &optional strt)
-   (declare (type (or strt null) strt))
-   (the morphism
-      (with-slots ((sorc1 sorc) (trgt1 trgt) (degr1 degr) (strt1 strt)) mrph1
-         (declare
-            (type chain-complex sorc1 trgt1)
-            (fixnum degr1)
-            (type strt strt1))
-      (with-slots ((sorc2 sorc) (trgt2 trgt) (degr2 degr) (strt2 strt)) mrph2
-         (declare
-            (type chain-complex sorc2 trgt2)
-            (fixnum degr2)
-            (type strt strt2))
-         (unless (eq (grmd sorc1) (grmd trgt2))
-            (error "In 2MRPH-CMPS, the morphisms ~A and ~A may not be composed (cf source and target)."
-               mrph1 mrph2))
-         (unless strt
-            (setf strt (if (and (eq strt1 :gnrt)
-                                (eq strt2 :gnrt))
-                          :gnrt
-                          :cmbn)))
-         (when (or (eq (first (orgn mrph1)) 'zero-mrph)
-                   (eq (first (orgn mrph2)) 'zero-mrph))
-            (return-from cmps
-               (zero-mrph sorc2 trgt1 (+ degr1 degr2))))
-         (when (eq (first (orgn mrph1)) 'idnt-mrph)
-            (return-from cmps mrph2))
-         (when (eq (first (orgn mrph2)) 'idnt-mrph)
-            (return-from cmps mrph1))
-         (ecase strt
-            (:cmbn (build-mrph
-                      :sorc sorc2 :trgt trgt1 :degr (+ degr1 degr2)
-                      :intr #'(lambda (cmbn)
-                                 (declare (type cmbn cmbn))
-                                 (the cmbn
-                                    (cmbn-? mrph1 (cmbn-? mrph2 cmbn))))
-                      :strt :cmbn :orgn `(2mrph-cmps ,mrph1 ,mrph2 ,strt)))
-            (:gnrt (build-mrph
-                      :sorc sorc2 :trgt trgt1 :degr (+ degr1 degr2)
-                      :intr #'(lambda (degr gnrt)
-                                 (declare
-                                    (type fixnum degr)
-                                    (type gnrt gnrt))
-                                 (the cmbn
-                                    (cmbn-? mrph1 (gnrt-? mrph2 degr gnrt))))
-                      :strt :gnrt :orgn `(2mrph-cmps ,mrph1 ,mrph2 ,strt))))))))
-  
-#|
-  (cat-init)
-  (setf cc (build-chcm :cmpr #'f-cmpr
-                       :basis :locally-effective
-                       :bsgn 0
-                       :intr-dffr #'(lambda (cmbn)
-                                       (cmbn (1- (cmbn-degr cmbn))))
-                       :strt :cmbn
-                       :orgn '(Z of Z)))
-  (setf *n* 5)
-  (defun ff (degr i)
-     (do ((*2n* (ash *n* 1))
-          (rslt +empty-list+
-                (cons (cons (let ((cffc (- (random *2n*) *n*)))
-                               (if (minusp cffc) cffc (1+ cffc)))
-                            (decf gnrt (1+ (random *n*))))
-                      rslt))
-          (gnrt i)
-          (k 0 (1+ k)))
-         ((= k *n*)
-          (make-cmbn
-             :degr 0
-             :list rslt))))
-  (setf mrph (build-mrph :sorc cc :trgt cc :degr 0
-			 :intr #'ff :strt :gnrt :orgn '(test)))
-  (setf mrph2 (2mrph-cmps mrph mrph :gnrt))
-  (gnrt-? mrph2 0 0) 
-  (dotimes (i 5)
-     (print (gnrt-? mrph2 0 i)))
-  (setf mrph (build-mrph :sorc cc :trgt cc :degr 0
-			 :intr #'ff :strt :gnrt :orgn '(test)))
-  (setf mrph3 (cmps mrph mrph :cmbn))
-  (gnrt-? mrph3 0 0) 
-  (dotimes (i 5)
-     (print (gnrt-? mrph3 0 i)))
-  (setf mrph33 (cmps mrph mrph :cmbn))
-  (eq mrph3 mrph33))
-|# 
-
-(DEFUN N-MRPH-INTR (n mrph)
-  (declare
-    (fixnum n)
-    (type morphism mrph))
-  (flet ((rslt (cmbn)
-	   (declare (type cmbn cmbn))
-	   (n-cmbn n (cmbn-? mrph cmbn))))
-     (the intr-mrph #'rslt)))
-
-(DEFUN N-MRPH (n mrph)
-  (declare
-    (fixnum n)
-    (type morphism mrph))
-  (the morphism
-    (with-slots (sorc trgt degr) mrph
-      (declare
-        (type chain-complex sorc trgt)
-	(fixnum degr))
-      (build-mrph
-        :sorc sorc :trgt trgt :degr degr
-	:intr (n-mrph-intr n mrph) :strt :cmbn
-	:orgn `(n-mrph ,n ,mrph)))))
-
-#|
-  (setf s3 (sphere 3))
-  (setf ch3 (chml-clss s3 3))
-  (setf 2ch3 (n-mrph 2 ch3))
-  (setf f3 (z-whitehead s3 2ch3))
-  (setf x (fibration-total f3))
-  (homology x 0 10)
-  (setf k (k-z 3))
-  (setf ch3 (chml-clss k 3))
-  (setf 2ch3 (n-mrph 2 ch3))
-  (setf f3 (z-whitehead k 2ch3))
-  (setf x (fibration-total f3))
-  (homology x 0 10)
-|#  
-
-(DEFMETHOD ADD ((mrph1 morphism) (mrph2 morphism) &optional strt)
-   (declare (type (or null strt) strt))
-   (the morphism
-      (with-slots ((sorc1 sorc) (trgt1 trgt) (degr1 degr) (strt1 strt)) mrph1
-         (declare
-            (type chain-complex sorc1 trgt1)
-            (fixnum degr1)
-            (type strt strt1))
-      (with-slots ((sorc2 sorc) (trgt2 trgt) (degr2 degr) (strt2 strt)) mrph2
-         (declare
-            (type chain-complex sorc2 trgt2)
-            (fixnum degr2)
-            (type strt strt2))
-         (unless (and (eq (grmd sorc1) (grmd sorc2))
-                      (eq (grmd trgt1) (grmd trgt2))
-                      (= degr1 degr2))
-            (error "In 2MRPH-ADD, ~A and ~A may not be added." mrph1 mrph2))
-         (when (eq (first (orgn mrph1)) 'zero-mrph)
-            (return-from add mrph2))
-         (when (eq (first (orgn mrph2)) 'zero-mrph)
-            (return-from add mrph1))
-         (unless strt
-            (setf strt
-                  (if (and (eq strt1 :gnrt)
-                           (eq strt2 :gnrt))
-                     :gnrt
-                     :cmbn)))
-         (when (or (eq (first (orgn mrph1)) 'idnt-mrph)
-                   (eq (first (orgn mrph2)) 'idnt-mrph))
-            (setf strt :cmbn))
-         (let ((cmpr (cmpr trgt1)))
-            (declare (type cmprf cmpr))
-            (ecase strt
-               (:gnrt (build-mrph
-                         :sorc sorc1 :trgt trgt1 :degr degr1
-                         :intr #'(lambda (degr gnrt)
-                                    (declare (type fixnum degr) (type gnrt gnrt))
-                                    (2cmbn-add cmpr
-                                       (gnrt-? mrph1 degr gnrt)
-                                       (gnrt-? mrph2 degr gnrt)))
-                         :strt :gnrt
-                         :orgn `(2mrph-add ,mrph1 ,mrph2 ,strt)))
-               (:cmbn (build-mrph
-                         :sorc sorc1 :trgt trgt1 :degr degr1
-                         :intr #'(lambda (cmbn)
-                                    (declare (type cmbn cmbn))
-                                    (2cmbn-add cmpr
-                                       (cmbn-? mrph1 cmbn)
-                                       (cmbn-? mrph2 cmbn)))
-                         :strt :cmbn
-                         :orgn `(2mrph-add ,mrph1 ,mrph2 ,strt)))))))))
-
-#|
-  (cat-init)
-  (setf cc (build-chcm :cmpr #'f-cmpr
-                       :basis :locally-effective
-                       :bsgn 0
-                       :intr-dffr #'(lambda (cmbn)
-                                       (cmbn (1- (cmbn-degr cmbn))))
-                       :strt :cmbn
-                       :orgn '(Z of Z)))
-  (setf *n* 10)
-  (defun ff (degr i)
-     (do ((*2n* (ash *n* 1))
-          (rslt +empty-list+
-                (cons (cons (let ((cffc (- (random *2n*) *n*)))
-                               (if (minusp cffc) cffc (1+ cffc)))
-                            (decf gnrt (1+ (random *n*))))
-                      rslt))
-          (gnrt i)
-          (k 0 (1+ k)))
-         ((= k *n*)
-          (make-cmbn
-             :degr 0
-             :list rslt))))
-  (setf mrph1 (build-mrph :sorc cc :trgt cc :degr 0
-                          :intr #'ff :strt :gnrt :orgn '(test)))
-  (setf mrph2 (build-mrph :sorc cc :trgt cc :degr 0
-                          :intr #'ff :strt :gnrt :orgn '(test2)))
-  (setf mrph3 (add mrph1 mrph2 :gnrt))
-  (setf +too-much-time+ -1)
-  (gnrt-? mrph1 0 0)
-  (gnrt-? mrph2 0 0)
-  (gnrt-? mrph3 0 0)
-  (setf mrph4 (add mrph1 mrph2 :cmbn))
-  (gnrt-? mrph4 0 0)
-  (setf mrph44 (add mrph1 mrph2 :cmbn))
-  (eq mrph4 mrph44))
-|#
-
-(DEFMETHOD SBTR ((mrph1 morphism) (mrph2 morphism) &optional strt)
-   (declare (type (or null strt) strt))
-   (the morphism
-      (with-slots ((sorc1 sorc) (trgt1 trgt) (degr1 degr) (strt1 strt)) mrph1
-         (declare
-            (type chain-complex sorc1 trgt1)
-            (fixnum degr1)
-            (type strt strt1))
-      (with-slots ((sorc2 sorc) (trgt2 trgt) (degr2 degr) (strt2 strt)) mrph2
-         (declare
-            (type chain-complex sorc2 trgt2)
-            (fixnum degr2)
-            (type strt strt2))
-         (unless (and (eq (grmd sorc1) (grmd sorc2))
-                      (eq (grmd trgt1) (grmd trgt2))
-                      (= degr1 degr2))
-            (error "In 2MRPH-SBTR, ~A and ~A may not be subtracteded." mrph1 mrph2))
-         (when (eq (first (orgn mrph1)) 'zero-mrph)
-            (return-from sbtr mrph2))
-         (when (eq (first (orgn mrph2)) 'zero-mrph)
-            (return-from sbtr mrph1))
-         (unless strt
-            (setf strt
-                  (if (and (eq strt1 :gnrt)
-                           (eq strt2 :gnrt))
-                     :gnrt
-                     :cmbn)))
-         (when (or (eq (first (orgn mrph1)) 'idnt-mrph)
-                   (eq (first (orgn mrph2)) 'idnt-mrph))
-            (setf strt :cmbn))
-         (let ((cmpr (cmpr trgt1)))
-            (declare (type cmprf cmpr))
-            (ecase strt
-               (:gnrt (build-mrph
-                         :sorc sorc1 :trgt trgt1 :degr degr1
-                         :intr #'(lambda (degr gnrt)
-                                    (declare (type fixnum degr) (type gnrt gnrt))
-                                    (2cmbn-sbtr cmpr
-                                       (gnrt-? mrph1 degr gnrt)
-                                       (gnrt-? mrph2 degr gnrt)))
-                         :strt :gnrt
-                         :orgn `(2mrph-sbtr ,mrph1 ,mrph2 ,strt)))
-               (:cmbn (build-mrph
-                         :sorc sorc1 :trgt trgt1 :degr degr1
-                         :intr #'(lambda (cmbn)
-                                    (declare (type cmbn cmbn))
-                                    (2cmbn-sbtr cmpr
-                                       (cmbn-? mrph1 cmbn)
-                                       (cmbn-? mrph2 cmbn)))
-                         :strt :cmbn
-                         :orgn `(2mrph-sbtr ,mrph1 ,mrph2 ,strt)))))))))
-
-#|
-()
-(cat-init)
-(setf cc (build-chcm :cmpr #'f-cmpr
-                     :basis :locally-effective
-                     :bsgn 0
-                     :intr-dffr #'(lambda (cmbn)
-                                    (cmbn (1- (cmbn-degr cmbn))))
-                     :strt :cmbn
-                     :orgn '(Z of Z)))
-(setf *n* 10)
-(defun ff (degr i)
-  (do ((*2n* (ash *n* 1))
-       (rslt +empty-list+
-             (cons (cons (let ((cffc (- (random *2n*) *n*)))
-                           (if (minusp cffc) cffc (1+ cffc)))
-                         (decf gnrt (1+ (random *n*))))
-                   rslt))
-       (gnrt i)
-       (k 0 (1+ k)))
-      ((= k *n*)
-       (make-cmbn
-        :degr 0
-        :list rslt))))
-(setf mrph1 (build-mrph :sorc cc :trgt cc :degr 0
-                        :intr #'ff :strt :gnrt :orgn '(test)))
-(setf mrph2 (build-mrph :sorc cc :trgt cc :degr 0
-                        :intr #'ff :strt :gnrt :orgn '(test2)))
-(setf mrph3 (sbtr mrph1 mrph2 :gnrt))
-(setf +too-much-time+ -1)
-(gnrt-? mrph1 0 0)
-(gnrt-? mrph2 0 0)
-(gnrt-? mrph3 0 0)
-(setf mrph4 (sbtr mrph1 mrph2 :cmbn))
-(gnrt-? mrph4 0 0)
-(setf mrph44 (sbtr mrph1 mrph2 :cmbn))
-(eq mrph4 mrph44))
-|#
-
-(DEFUN CHANGE-SORC-TRGT (mrph &key new-sorc new-trgt)
-   (declare
-      (type morphism mrph)
-      (type (or null chain-complex) new-sorc new-trgt))
-   (the morphism
-      (with-slots (sorc trgt degr intr strt) mrph
-         (build-mrph
-            :sorc (or new-sorc sorc)
-            :trgt (or new-trgt trgt)
-            :degr degr
-            :intr intr
-            :strt strt
-            :orgn `(change-sorc-trgt ,mrph ,new-sorc ,new-trgt)))))
-
-(DEFUN DSTR-CHANGE-SORC-TRGT (mrph &key new-sorc new-trgt)
-   (declare
-      (type morphism mrph)
-      (type (or null chain-complex) new-sorc new-trgt))
-   (the morphism
-      (with-slots (sorc trgt) mrph
-         (when new-sorc 
-            (setf sorc new-sorc))
-         (when new-trgt
-            (setf trgt new-trgt))
-         mrph)))
-
-(DEFMETHOD ADD ((chcm chain-complex) (perturbation morphism) &optional strt)
-   (declare (type (or strt null) strt))
-   (the chain-complex
-      (with-slots (cmpr basis bsgn dffr) chcm
-         (declare
-            (type cmprf cmpr)
-            (type basis basis)
-            (type morphism dffr))
-      (with-slots (sorc trgt degr) perturbation
-         (declare
-            (type chain-complex sorc trgt)
-            (fixnum degr))
-         (unless (and (eq (grmd sorc) (grmd chcm))
-                      (eq (grmd trgt) (grmd chcm))
-                      (= degr -1))
-            (error "In (METHOD ADD CHAIN-COMPLEX MORPHISM), the data are not coherent."))
-         (let ((new-dffr (add dffr perturbation strt)))
-            (declare (type intr-mrph new-dffr))
-            (let ((new-chcm (build-chcm
-                               :cmpr cmpr
-                               :basis basis
-                               :intr-dffr (intr new-dffr)
-                               :strt (strt new-dffr)
-                               :orgn  `(add ,chcm ,perturbation))))
-	      (declare (type chain-complex new-chcm))
-	      (if (slot-boundp chcm 'bsgn)
-		 (setf (slot-value new-chcm 'bsgn) bsgn)
-		 (slot-makunbound new-chcm 'bsgn))
-	      (setf (slot-value new-chcm 'grmd) (grmd chcm))
-	      new-chcm))))))
\ No newline at end of file
diff --git a/archive/Kenzo-1/cl-space-efhm.cl b/archive/Kenzo-1/cl-space-efhm.cl
deleted file mode 100644
index c77a9f1..0000000
--- a/archive/Kenzo-1/cl-space-efhm.cl
+++ /dev/null
@@ -1,875 +0,0 @@
-;;;  CL-SPACE-EFHM  CL-SPACE-EFHM  CL-SPACE-EFHM  CL-SPACE-EFHM
-;;;  CL-SPACE-EFHM  CL-SPACE-EFHM  CL-SPACE-EFHM  CL-SPACE-EFHM
-;;;  CL-SPACE-EFHM  CL-SPACE-EFHM  CL-SPACE-EFHM  CL-SPACE-EFHM
-
-(IN-PACKAGE "COMMON-LISP-USER")
-
-(provide "cl-space-efhm")
-
-(DEFUN CS-HAT-U-U (smgr
-		     &aux (bar (bar smgr))
-		          (cl-space (classifying-space smgr))
-			  (clsp-tnsr-smgr (tnsr-prdc cl-space smgr)))
-  (declare
-    (type simplicial-group smgr)
-    (type chain-complex bar clsp-tnsr-smgr)
-    (type simplicial-set cl-space))
-  (the chain-complex
-     (tnsr-prdc clsp-tnsr-smgr bar)))
-
-(DEFUN CS-HAT-RIGHT-PERTURBATION-INTR (smgr)
-  (declare (type simplicial-group smgr))
-  (let ((aprd (aprd smgr)))
-    (flet ((rslt (degr tnpr)
-	     (declare
-	       (fixnum degr)
-	       (type tnpr tnpr))
-	     (with-tnpr (degr1 tnpr1 degr2 abar2) tnpr
-	       (when (zerop degr2)
-		 (return-from rslt (zero-cmbn (1- degr))))
-	       (with-tnpr (degr11 gbar11 degr12 gmsm12) tnpr1
-		 (let ((sign (-1-expt-n degr1))
-		       (brgn21 (first (abar-list abar2)))
-		       (bar22 (make-abar :list (rest (abar-list abar2)))))
-		   (declare
-		     (fixnum sign)
-		     (type brgn brgn21)
-		     (type abar bar22))
-		   (with-brgn (degr21 gmsm21) brgn21
-		   (let ((degr22 (- degr2 degr21)))
-		     (declare (fixnum degr22))
-		     (decf degr21) ;; = dmns(gmsm21)
-		     (let ((aprd (gnrt-? aprd (+ degr12 degr21)
-					 (tnpr degr12 gmsm12 degr21 gmsm21))))
-		       (declare (type cmbn aprd))
-		       (with-cmbn (degr12+21 list) aprd
-			 (make-cmbn :degr (1- degr)
-			   :list
-			   (mapcar
-			     #'(lambda (term)
-				 (declare (type term term))
-				 (with-term (cffc gmsm) term
-				   (term (* sign cffc)
-					 (tnpr (+ degr1 degr21)
-					       (tnpr degr11 gbar11 degr12+21 gmsm)
-					       degr22 bar22))))
-			     list)))))))))))
-	  (the intr-mrph #'rslt))))
-
-(DEFUN CS-HAT-RIGHT-PERTURBATION (smgr
-				    &aux (hat-u-u (cs-hat-u-u smgr)))
-  (declare
-    (type simplicial-group smgr)
-    (type chain-complex hat-u-u))
-  (the morphism
-     (build-mrph
-        :sorc hat-u-u
-	:trgt hat-u-u
-	:degr -1
-	:intr (cs-hat-right-perturbation-intr smgr)
-	:strt :gnrt
-	:orgn `(cs-hat-right-perturbation ,smgr))))
-
-(DEFUN CS-HAT-U-T (smgr
-		     &aux (hat-u-u (cs-hat-u-u smgr))
-		          (hat-right-perturbation
-			    (cs-hat-right-perturbation smgr)))
-  (declare
-    (type simplicial-group smgr)
-    (type chain-complex hat-u-u)
-    (type morphism hat-right-perturbation))
-  (the chain-complex
-    (progn
-      (setf (slot-value hat-right-perturbation 'sorc) hat-u-u
-	    (slot-value hat-right-perturbation 'trgt) hat-u-u)
-      ;; cf lp-space-efhm.lisp
-      (add hat-u-u hat-right-perturbation))))
-
-#|
-  (cat-init)
-  (setf c (cs-hat-u-t (k-z-1)))
-  (defun random-abar (tot-degr~ max-degr)
-    (do ((rslt nil)
-         (cum-degr 0 (+ cum-degr degr 1))
-         (degr))
-        ((>= cum-degr tot-degr~) (make-abar :list rslt))
-       (setf degr (1+ (random max-degr)))
-       (push (brgn (1+ degr)
-                   (let ((list (make-list degr)))
-                     (mapl
-                       #'(lambda (sublist)
-                           (setf (car sublist) (- (random 21) 10)))
-                       list)
-                     list))
-             rslt)))
-  (dotimes (i 5) (print (random-abar 8 4)))
-  (setf abar (random-abar 8 4))
-  (setf abar-degr (apply #'+ (mapcar #'car (abar-list abar))))
-  (setf gnrt (tnpr 5 (tnpr 3 (gbar 3 0 '(1 2) 0 '(3) 0 '()) 2 '(4 5))
-                   abar-degr abar))
-  (? c (+ 5 abar-degr) gnrt)
-  (? c *)
-  (dotimes (i 10)
-    (let ((abar (random-abar 8 4)))
-      (setf abar-degr (apply #'+ (mapcar #'car (abar-list abar))))
-      (setf gnrt (tnpr 5 (tnpr 3 (gbar 3 0 '(1 2) 0 '(3) 0 '()) 2 '(4 5))
-                       abar-degr abar))
-      (unless (>= abar-degr 10)
-         (print (? c (+ 5 abar-degr) gnrt))
-         (print (? c (? c (+ 5 abar-degr) gnrt))))))
-  (dotimes (i 10)
-    (let ((abar (random-abar 8 4)))
-      (setf abar-degr (apply #'+ (mapcar #'car (abar-list abar))))
-      (setf gnrt (tnpr 6 (tnpr 3 (gbar 3 0 '(1 2) 0 '(3) 0 '()) 3 '(4 5 6))
-                       abar-degr abar))
-      (unless (>= abar-degr 9)
-         (print (? c (+ 6 abar-degr) gnrt))
-         (print (? c (? c (+ 6 abar-degr) gnrt))))))
-  (dotimes (i 10)
-    (let ((abar (random-abar 8 4)))
-      (setf abar-degr (apply #'+ (mapcar #'car (abar-list abar))))
-      (setf gnrt (tnpr 5 (tnpr 2 (gbar 2 0 '(3) 0 '()) 3 '(4 5 6))
-	   	     abar-degr abar))
-      (unless (>= abar-degr 10)
-        (print (? c (+ 5 abar-degr) gnrt))
-        (print (? c (? c (+ 5 abar-degr) gnrt))))))
-  (dotimes (i 10)
-    (let ((abar (random-abar 8 4)))
-      (setf abar-degr (apply #'+ (mapcar #'car (abar-list abar))))
-      (setf gnrt (tnpr 4 (tnpr 2 (gbar 2 0 '(3) 0 '()) 2 '(4 5))
-                       abar-degr abar))
-      (unless (>= abar-degr 11)
-         (print (? c (+ 4 abar-degr) gnrt))
-         (print (? c (? c (+ 4 abar-degr) gnrt))))))
-|#
-
-(DEFUN CS-HAT-LEFT-PERTURBATION (smgr
-			       &aux (fibration (smgr-fibration smgr))
-			            (bar (bar smgr))
-			            (hat-u-t (cs-hat-u-t smgr)))
-  (declare
-    (type simplicial-group smgr)
-    (type fibration fibration)
-    (type chain-complex bar hat-u-t))
-  (the morphism
-    (multiple-value-bind (brown bottom-perturbation)
-			 (brown-reduction fibration)
-      (declare
-        (ignore brown)
-	(type morphism bottom-perturbation))
-      (let ((rslt (tnsr-prdc bottom-perturbation (idnt-mrph bar))))
-	(declare (type morphism rslt))
-	(setf (slot-value rslt 'sorc) hat-u-t
-	      (slot-value rslt 'trgt) hat-u-t)
-	rslt))))
-
-(DEFUN CS-HAT-T-U (smgr
-		    &aux (bar (bar smgr))
-		         (fibration (smgr-fibration smgr))
-		         (brown (brown-reduction fibration))
-		         (twisted-tnsr-prdc (bcc brown))
-		         (hat-u-u (cs-hat-u-u smgr)))
-  (declare
-    (type simplicial-group smgr)
-    (type chain-complex bar twisted-tnsr-prdc hat-u-u)
-    (type fibration fibration)
-    (type reduction brown))
-  (the chain-complex
-    (let ((rslt (tnsr-prdc twisted-tnsr-prdc bar)))
-      (declare (type chain-complex rslt))
-      (setf (slot-value rslt 'grmd) hat-u-u)
-      rslt)))
-
-#|
-  (cat-init)
-  (setf c (cs-hat-t-u (k-z-1)))
-  (defun random-abar (tot-degr~ max-degr)
-    (do ((rslt nil)
-         (cum-degr 0 (+ cum-degr degr 1))
-         (degr))
-        ((>= cum-degr tot-degr~) (make-abar :list rslt))
-       (setf degr (1+ (random max-degr)))
-       (push (brgn (1+ degr)
-                   (let ((list (make-list degr)))
-                     (mapl
-                       #'(lambda (sublist)
-                           (setf (car sublist) (- (random 21) 10)))
-                       list)
-                     list))
-             rslt)))
-  (dotimes (i 5) (print (random-abar 8 4)))
-  (setf abar (random-abar 8 4))
-  (setf abar-degr (apply #'+ (mapcar #'car (abar-list abar))))
-  (setf gnrt (tnpr 5 (tnpr 3 (gbar 3 0 '(1 2) 0 '(3) 0 '()) 2 '(4 5))
-                   abar-degr abar))
-  (? c (+ 5 abar-degr) gnrt)
-  (? c *)
-  (dotimes (i 10)
-    (let ((abar (random-abar 8 4)))
-      (setf abar-degr (apply #'+ (mapcar #'car (abar-list abar))))
-      (setf gnrt (tnpr 5 (tnpr 3 (gbar 3 0 '(1 2) 0 '(3) 0 '()) 2 '(4 5))
-                       abar-degr abar))
-      (unless (>= abar-degr 10)
-         (print (? c (+ 5 abar-degr) gnrt))
-         (print (? c (? c (+ 5 abar-degr) gnrt))))))
-  (dotimes (i 10)
-    (let ((abar (random-abar 8 4)))
-      (setf abar-degr (apply #'+ (mapcar #'car (abar-list abar))))
-      (setf gnrt (tnpr 6 (tnpr 3 (gbar 3 0 '(1 2) 0 '(3) 0 '()) 3 '(4 5 6))
-                       abar-degr abar))
-      (unless (>= abar-degr 9)
-         (print (? c (+ 6 abar-degr) gnrt))
-         (print (? c (? c (+ 6 abar-degr) gnrt))))))
-  (dotimes (i 10)
-    (let ((abar (random-abar 8 4)))
-      (setf abar-degr (apply #'+ (mapcar #'car (abar-list abar))))
-      (setf gnrt (tnpr 5 (tnpr 2 (gbar 2 0 '(3) 0 '()) 3 '(4 5 6))
-	   	     abar-degr abar))
-      (unless (>= abar-degr 10)
-        (print (? c (+ 5 abar-degr) gnrt))
-        (print (? c (? c (+ 5 abar-degr) gnrt))))))
-  (dotimes (i 10)
-    (let ((abar (random-abar 8 4)))
-      (setf abar-degr (apply #'+ (mapcar #'car (abar-list abar))))
-      (setf gnrt (tnpr 4 (tnpr 2 (gbar 2 0 '(3) 0 '()) 2 '(4 5))
-                       abar-degr abar))
-      (unless (>= abar-degr 11)
-         (print (? c (+ 4 abar-degr) gnrt))
-         (print (? c (? c (+ 4 abar-degr) gnrt))))))
-|#
-
-(DEFUN CS-LEFT-HMEQ-HAT (smgr
-			   &aux (hat-t-u (cs-hat-t-u smgr))
-			        (hat-right-perturbation
-				  (cs-hat-right-perturbation smgr)))
-  (declare
-    (type simplicial-group smgr)
-    (type chain-complex hat-t-u)
-    (type morphism hat-right-perturbation))
-  (the chain-complex
-    (add hat-t-u hat-right-perturbation)))
-
-#|
-  (cat-init)
-  (setf c (cs-left-hmeq-hat (k-z-1)))
-  (defun random-abar (tot-degr~ max-degr)
-    (do ((rslt nil)
-         (cum-degr 0 (+ cum-degr degr 1))
-         (degr))
-        ((>= cum-degr tot-degr~) (make-abar :list rslt))
-       (setf degr (1+ (random max-degr)))
-       (push (brgn (1+ degr)
-                   (let ((list (make-list degr)))
-                     (mapl
-                       #'(lambda (sublist)
-                           (setf (car sublist) (- (random 21) 10)))
-                       list)
-                     list))
-             rslt)))
-   (dotimes (i 10)
-    (let ((abar (random-abar 8 4)))
-      (setf abar-degr (apply #'+ (mapcar #'car (abar-list abar))))
-      (setf gnrt (tnpr 5 (tnpr 3 (gbar 3 0 '(1 2) 0 '(3) 0 '()) 2 '(4 5))
-                       abar-degr abar))
-      (unless (>= abar-degr 10)
-         (print (? c (+ 5 abar-degr) gnrt))
-         (print (? c (? c (+ 5 abar-degr) gnrt))))))
-  (dotimes (i 10)
-    (let ((abar (random-abar 8 4)))
-      (setf abar-degr (apply #'+ (mapcar #'car (abar-list abar))))
-      (setf gnrt (tnpr 6 (tnpr 3 (gbar 3 0 '(1 2) 0 '(3) 0 '()) 3 '(4 5 6))
-                       abar-degr abar))
-      (unless (>= abar-degr 9)
-         (print (? c (+ 6 abar-degr) gnrt))
-         (print (? c (? c (+ 6 abar-degr) gnrt))))))
-  (dotimes (i 10)
-    (let ((abar (random-abar 8 4)))
-      (setf abar-degr (apply #'+ (mapcar #'car (abar-list abar))))
-      (setf gnrt (tnpr 5 (tnpr 2 (gbar 2 0 '(3) 0 '()) 3 '(4 5 6))
-	   	     abar-degr abar))
-      (unless (>= abar-degr 10)
-        (print (? c (+ 5 abar-degr) gnrt))
-        (print (? c (? c (+ 5 abar-degr) gnrt))))))
-  (dotimes (i 10)
-    (let ((abar (random-abar 8 4)))
-      (setf abar-degr (apply #'+ (mapcar #'car (abar-list abar))))
-      (setf gnrt (tnpr 4 (tnpr 2 (gbar 2 0 '(3) 0 '()) 2 '(4 5))
-                       abar-degr abar))
-      (unless (>= abar-degr 11)
-         (print (? c (+ 4 abar-degr) gnrt))
-         (print (? c (? c (+ 4 abar-degr) gnrt))))))
-|#
-
-(DEFUN CS-PRE-LEFT-HMEQ-LEFT-REDUCTION-INTR-F (cmbn)
-  (declare (type cmbn cmbn))
-  (the cmbn
-    (with-cmbn (degr list) cmbn
-      (make-cmbn
-        :degr degr
-	:list (mapcar
-	        #'(lambda (term)
-		    (declare (type term term))
-		    (with-term (cffc tnpr) term
-		      (term cffc (gnrt1 (gnrt1 tnpr)))))		    
-	        (member-if	       
-		  #'(lambda (term)
-		      (declare (type term term))
-		      (with-term (cffc tnpr) term
-			(declare (ignore cffc))
-		      (with-tnpr (degr1 tnpr1 degr2 abar2) tnpr
-			(declare (ignore degr1 abar2))
-			(and (zerop degr2) (zerop (degr2 tnpr1))))))
-		  list))))))
-
-#|
-  (cs-pre-left-hmeq-left-reduction-intr-f
-    (cmbn 6 100 (tnpr 4 (tnpr 2 'a 2 'b) 2 'c)
-            10  (tnpr 6 (tnpr 2 'a 4 'b) 0 'c)
-            50  (tnpr 6 (tnpr 6 'a 0 'b) 0 'c)
-            1   (tnpr 6 (tnpr 6 'aa 0 'b) 0 'c)))
-|#
-
-(DEFUN CS-PRE-LEFT-HMEQ-LEFT-REDUCTION-F (smgr
-					   &aux (hat-u-t (cs-hat-u-t smgr))
-					        (classifying-space (classifying-space smgr)))
-  (declare
-    (type simplicial-group smgr)
-    (type chain-complex hat-u-t)
-    (type simplicial-set classifying-space))
-  (the morphism
-    (build-mrph
-      :sorc hat-u-t
-      :trgt classifying-space
-      :degr 0
-      :intr #'cs-pre-left-hmeq-left-reduction-intr-f
-      :strt :cmbn
-      :orgn `(cs-pre-left-hmeq-left-reduction-f ,smgr))))
-
-(DEFUN CS-PRE-LEFT-HMEQ-LEFT-REDUCTION-INTR-G (idnt)
-  (declare (type gmsm idnt))
-  (flet ((rslt (cmbn)
-	   (declare (type cmbn cmbn))
-	   (the cmbn
-	     (with-cmbn (degr list) cmbn
-	       (make-cmbn
-		 :degr degr
-		 :list (mapcar
-			 #'(lambda (term)
-			     (declare (type term term))
-			     (with-term (cffc gbar) term
-			       (term cffc
-				     (tnpr degr
-					   (tnpr degr gbar 0 idnt)
-					   0 +null-abar+))))
-			 list))))))
-     (the intr-mrph #'rslt)))
-
-#|
-  (setf g (cs-pre-left-hmeq-left-reduction-intr-g '()))
-  (funcall g (cmbn 3 14 (gbar 3 0 'a 1 'b 0 '())))
-|#
-
-(DEFUN CS-PRE-LEFT-HMEQ-LEFT-REDUCTION-G (smgr
-					   &aux (hat-u-t (cs-hat-u-t smgr))
-					        (classifying-space (classifying-space smgr)))
-  (declare
-    (type simplicial-group smgr)
-    (type chain-complex hat-u-t)
-    (type simplicial-set classifying-space))
-  (the morphism
-    (build-mrph
-      :sorc classifying-space
-      :trgt hat-u-t
-      :degr 0
-      :intr (cs-pre-left-hmeq-left-reduction-intr-g (bspn smgr))
-      :strt :cmbn
-      :orgn `(cs-pre-left-hmeq-left-reduction-g ,smgr))))
-
-(DEFUN CS-PRE-LEFT-HMEQ-LEFT-REDUCTION-INTR-H (cmpr idnt)
-  (declare (type gmsm idnt))
-  (flet ((rslt (cmbn)
-	   (declare (type cmbn cmbn))
-	   (the cmbn
-	     (with-cmbn (degr list) cmbn
-	       (do ((rslt (zero-cmbn (1+ degr)))
-		    (mark list (cdr mark)))
-		   ((endp mark) rslt)
-		   (declare
-		     (type cmbn rslt)
-		     (list mark))
-		  (let ((term (car mark)))
-		    (declare (type term term))
-		    (with-term (cffc tnpr) term
-		    (with-tnpr (degr1 tnpr1 degr2 abar2) tnpr
-		      (declare (ignore degr1))
-		    (with-tnpr (degr11 gbar11 degr12 gmsm12) tnpr1
-		      (unless (zerop degr12)
-			(dstr-add-term-to-cmbn
-			  cmpr
-			  (if (evenp degr11) cffc (- cffc))
-			  (tnpr degr11
-				(tnpr degr11 gbar11 0 idnt)
-				(+ 1 degr12 degr2)
-				(make-abar
-				 :list
-				 (cons (brgn (1+ degr12)
-					     gmsm12)
-				       (abar-list abar2))))
-			  rslt)))))))))))
-     (the intr-mrph #'rslt)))
-
-(DEFUN CS-PRE-LEFT-HMEQ-LEFT-REDUCTION-H (smgr
-					   &aux (hat-u-t (cs-hat-u-t smgr)))
-  (declare
-    (type simplicial-group smgr)
-    (type chain-complex hat-u-t))
-  (the morphism
-    (build-mrph
-      :sorc hat-u-t
-      :trgt hat-u-t
-      :degr +1
-      :intr (cs-pre-left-hmeq-left-reduction-intr-h (cmpr hat-u-t) (bspn smgr))
-      :strt :cmbn
-      :orgn `(cs-pre-left-hmeq-left-reduction-h ,smgr))))
-
-
-
-(DEFUN CS-PRE-LEFT-HMEQ-LEFT-REDUCTION (smgr)
-  (declare (type simplicial-group smgr))
-  (the reduction
-    (build-rdct
-      :f (cs-pre-left-hmeq-left-reduction-f smgr)
-      :g (cs-pre-left-hmeq-left-reduction-g smgr)
-      :h (cs-pre-left-hmeq-left-reduction-h smgr)
-      :orgn `(cs-pre-left-hmeq-left-reduction ,smgr))))
-
-#|
-  (cat-init)
-  (defun random-abar (tot-degr~ max-degr)
-    (do ((rslt nil)
-         (cum-degr 0 (+ cum-degr degr 1))
-         (degr))
-        ((>= cum-degr tot-degr~) (make-abar :list rslt))
-       (setf degr (1+ (random max-degr)))
-       (push (brgn (1+ degr)
-                   (let ((list (make-list degr)))
-                     (mapl
-                       #'(lambda (sublist)
-                           (setf (car sublist) (- (random 21) 10)))
-                       list)
-                     list))
-             rslt)))
-  (setf rdct (cs-pre-left-hmeq-left-reduction (k-z-1)))
-  (pre-check-rdct rdct)
-  (setf *tc* (cmbn 0 1 (tnpr 0 (tnpr 0 +null-gbar+ 0 '()) 0 +null-abar+))
-        *bc* (cmbn 0 1 +null-gbar+))
-  (check-rdct)
-  (setf *tc* (cmbn 1 1 (tnpr 1 (tnpr 0 +null-gbar+ 1 '(13)) 0 +null-abar+)))
-  (check-rdct)
-  (dotimes (i 10)
-    (let ((abar (random-abar 8 4)))
-      (setf abar-degr (apply #'+ (mapcar #'car (abar-list abar))))
-      (setf gnrt (tnpr 5 (tnpr 3 (gbar 3 0 '(1 2) 0 '(3) 0 '()) 2 '(4 5))
-                       abar-degr abar))
-      (setf gbar (gbar 2 0 '(1) 0 '()))
-      (unless (>= abar-degr 9)
-        (setf *tc* (cmbn (+ 5 abar-degr) 1 gnrt)
-              *bc* (cmbn 2 1 gbar))
-        (check-rdct))))
-  (dotimes (i 10)
-    (let ((abar (random-abar 6 4)))
-      (setf abar-degr (apply #'+ (mapcar #'car (abar-list abar))))
-      (setf gnrt (tnpr 6 (tnpr 3 (gbar 3 0 '(1 2) 0 '(3) 0 '()) 3 '(4 5 6))
-                       abar-degr abar))
-      (setf gbar (gbar 3 0 '(1 2) 1 '() 0 '()))
-      (unless (>= abar-degr 8)
-        (setf *tc* (cmbn (+ 6 abar-degr) 1 gnrt)
-              *bc* (cmbn 3 1 gbar))
-        (check-rdct))))
-  (dotimes (i 10)
-    (let ((abar (random-abar 6 4)))
-      (setf abar-degr (apply #'+ (mapcar #'car (abar-list abar))))
-      (setf gnrt (tnpr 5 (tnpr 2 (gbar 2 0 '(3) 0 '()) 3 '(4 5 6))
-	   	     abar-degr abar))
-      (setf gbar (gbar 4 0 '(1 2 3) 0 '(4 5) 0 '(6) 0 '()))
-      (unless (>= abar-degr 9)
-        (setf *tc* (cmbn (+ 5 abar-degr) 1 gnrt))
-        (setf *bc* (cmbn 4 1 gbar))
-        (check-rdct))))
-  (dotimes (i 10)
-    (let ((abar (random-abar 6 4)))
-      (setf abar-degr (apply #'+ (mapcar #'car (abar-list abar))))
-      (setf gnrt (tnpr 4 (tnpr 2 (gbar 2 0 '(3) 0 '()) 2 '(4 5))
-                       abar-degr abar))
-      (setf gbar (gbar 5 8 '(1 2 3) 0 '(4 5 6) 0 '(7 8) 0 '(9) 0 '()))
-      (unless (>= abar-degr 10)
-         (setf *tc* (cmbn (+ 4 abar-degr) 1 gnrt))
-         (setf *bc* (cmbn 5 1 gbar))
-         (check-rdct))))
-|#
-
-(DEFUN CS-LEFT-HMEQ-LEFT-REDUCTION (smgr
-				     &aux (pre-left-hmeq-left-reduction
-					     (cs-pre-left-hmeq-left-reduction smgr))
-				          (hat-left-perturbation
-					     (cs-hat-left-perturbation smgr)))
-  (declare
-    (type simplicial-group smgr)
-    (type reduction pre-left-hmeq-left-reduction)
-    (type morphism hat-left-perturbation))
-  (the reduction
-    (progn
-      (dstr-change-sorc-trgt hat-left-perturbation
-	:new-sorc (tcc pre-left-hmeq-left-reduction)
-	:new-trgt (tcc pre-left-hmeq-left-reduction))
-      (let ((rslt (special-bpl-2 pre-left-hmeq-left-reduction
-				 hat-left-perturbation)))
-	(declare (type reduction rslt))
-	(with-slots (tcc f g h) rslt
-	  (setf tcc (cs-left-hmeq-hat smgr)
-		(slot-value f 'sorc) tcc
-		(slot-value g 'trgt) tcc
-		(slot-value h 'sorc) tcc
-		(slot-value h 'trgt) tcc))
-	rslt))))
-	
-
-#|
-  (cat-init)
-  (defun random-abar (tot-degr~ max-degr)
-    (do ((rslt nil)
-         (cum-degr 0 (+ cum-degr degr 1))
-         (degr))
-        ((>= cum-degr tot-degr~) (make-abar :list rslt))
-       (setf degr (1+ (random max-degr)))
-       (push (brgn (1+ degr)
-                   (let ((list (make-list degr)))
-                     (mapl
-                       #'(lambda (sublist)
-                           (setf (car sublist) (- (random 21) 10)))
-                       list)
-                     list))
-             rslt)))
-  (setf rdct (cs-left-hmeq-left-reduction (k-z-1)))
-  (pre-check-rdct rdct)
-  (setf *tc* (cmbn 0 1 (tnpr 0 (tnpr 0 +null-gbar+ 0 '()) 0 +null-abar+))
-        *bc* (cmbn 0 1 +null-gbar+))
-  (check-rdct)
-  (setf *tc* (cmbn 1 1 (tnpr 1 (tnpr 0 +null-gbar+ 1 '(13)) 0 +null-abar+)))
-  (check-rdct)
-  (dotimes (i 10)
-    (let ((abar (random-abar 8 4)))
-      (setf abar-degr (apply #'+ (mapcar #'car (abar-list abar))))
-      (setf gnrt (tnpr 5 (tnpr 3 (gbar 3 0 '(1 2) 0 '(3) 0 '()) 2 '(4 5))
-                       abar-degr abar))
-      (setf gbar (gbar 2 0 '(1) 0 '()))
-      (unless (>= abar-degr 9)
-        (setf *tc* (cmbn (+ 5 abar-degr) 1 gnrt)
-              *bc* (cmbn 2 1 gbar))
-        (check-rdct))))
-  (dotimes (i 10)
-    (let ((abar (random-abar 6 4)))
-      (setf abar-degr (apply #'+ (mapcar #'car (abar-list abar))))
-      (setf gnrt (tnpr 6 (tnpr 3 (gbar 3 0 '(1 2) 0 '(3) 0 '()) 3 '(4 5 6))
-                       abar-degr abar))
-      (setf gbar (gbar 3 0 '(1 2) 1 '() 0 '()))
-      (unless (>= abar-degr 8)
-        (setf *tc* (cmbn (+ 6 abar-degr) 1 gnrt)
-              *bc* (cmbn 3 1 gbar))
-        (check-rdct))))
-  (dotimes (i 10)
-    (let ((abar (random-abar 6 4)))
-      (setf abar-degr (apply #'+ (mapcar #'car (abar-list abar))))
-      (setf gnrt (tnpr 5 (tnpr 2 (gbar 2 0 '(3) 0 '()) 3 '(4 5 6))
-	   	     abar-degr abar))
-      (setf gbar (gbar 4 0 '(1 2 3) 0 '(4 5) 0 '(6) 0 '()))
-      (unless (>= abar-degr 9)
-        (setf *tc* (cmbn (+ 5 abar-degr) 1 gnrt))
-        (setf *bc* (cmbn 4 1 gbar))
-        (check-rdct))))
-  (dotimes (i 10)
-    (let ((abar (random-abar 6 4)))
-      (setf abar-degr (apply #'+ (mapcar #'car (abar-list abar))))
-      (setf gnrt (tnpr 4 (tnpr 2 (gbar 2 0 '(3) 0 '()) 2 '(4 5))
-                       abar-degr abar))
-      (setf gbar (gbar 5 8 '(1 2 3) 0 '(4 5 6) 0 '(7 8) 0 '(9) 0 '()))
-      (unless (>= abar-degr 10)
-         (setf *tc* (cmbn (+ 4 abar-degr) 1 gnrt))
-         (setf *bc* (cmbn 5 1 gbar))
-         (check-rdct))))
-|#
-
-(DEFUN CS-PRE-LEFT-HMEQ-RIGHT-REDUCTION-INTR-F (cmbn)
-  (declare (type cmbn cmbn))
-  (the cmbn
-     (with-cmbn (degr list) cmbn
-     (let ((rslt +empty-list+))
-       (declare (list rslt))
-       (do ((mark list (cdr mark)))
-	   ((endp mark))
-	   (declare (list mark))
-	  (with--term (cffc tnpr) mark
-	  (with-tnpr (degr1 nil nil abar2) tnpr
-	    (if (zerop degr1)
-	       (push (term cffc abar2) rslt)
-	       (return)))))
-       (make-cmbn :degr degr
-		  :list (nreverse rslt))))))
-
-#|
-  (cs-pre-left-hmeq-right-reduction-intr-f
-    (cmbn 4 2 (tnpr 0 (tnpr 0 +null-gbar+ 0 'i)
-                    4 (abar 2 'a 2 'b))
-            3 (tnpr 0 (tnpr 0 +null-gbar+ 0 'i)
-                    4 (abar 2 'a 2 'c))
-            5 (tnpr 1 (tnpr 0 +null-gbar+ 1 'a)
-                    3 (abar 1 'a 2 'b))))
-|#
-
-(DEFUN CS-PRE-LEFT-HMEQ-RIGHT-REDUCTION-F (smgr
-					     &aux (hat-t-u (cs-hat-t-u smgr))
-					          (bar (bar smgr)))
-  (declare
-    (type simplicial-group smgr)
-    (type chain-complex hat-t-u bar))
-  (the morphism
-    (build-mrph
-      :sorc hat-t-u :trgt bar :degr 0
-      :intr #'cs-pre-left-hmeq-right-reduction-intr-f
-      :strt :cmbn
-      :orgn `(cs-pre-left-hmeq-right-reduction-f ,smgr))))
-
-(DEFUN CS-PRE-LEFT-HMEQ-RIGHT-REDUCTION-INTR-G (idnt)
-  (declare (type gmsm idnt))
-  (flet ((rslt (cmbn)
-	   (declare (type cmbn cmbn))
-	   (the cmbn
-	     (with-cmbn (degr list) cmbn
-	     (let ((bsgn (tnpr 0 +null-gbar+ 0 idnt)))
-	       (declare (type tnpr bsgn))
-	       (make-cmbn :degr degr
-		 :list (mapcar
-			 #'(lambda (term)
-			     (declare (type term term))
-			     (with-term (cffc abar) term
-			       (term cffc
-				     (tnpr 0 bsgn
-					   degr abar))))
-			 list)))))))
-    (the intr-mrph #'rslt)))
-
-#|
-  (setf g (cs-pre-left-hmeq-right-reduction-intr-g 'i))
-  (funcall g (cmbn 3 2 (abar 1 'a 2 'b)))
-|#
-
-(DEFUN CS-PRE-LEFT-HMEQ-RIGHT-REDUCTION-G (smgr
-					    &aux (hat-t-u (cs-hat-t-u smgr))
-					         (bar (bar smgr))
-						 (idnt (bspn smgr)))
-  (declare
-    (type simplicial-group smgr)
-    (type chain-complex hat-t-u bar)
-    (type gmsm idnt))
-  (the morphism
-    (build-mrph
-      :sorc bar :trgt hat-t-u :degr 0
-      :intr (cs-pre-left-hmeq-right-reduction-intr-g idnt)
-      :strt :cmbn
-      :orgn `(cs-pre-left-hmeq-right-reduction-g ,smgr))))
-
-(DEFUN CS-PRE-LEFT-HMEQ-RIGHT-REDUCTION-H (smgr
-					    &aux (bar (bar smgr))
-					         (tnpr-contraction
-						   (smgr-tnpr-contraction smgr)))
-  (declare
-    (type simplicial-group smgr)
-    (type chain-complex bar)
-    (type morphism tnpr-contraction))
-  (the morphism
-    (tnsr-prdc tnpr-contraction (idnt-mrph bar))))
-
-(DEFUN CS-PRE-LEFT-HMEQ-RIGHT-REDUCTION (smgr)
-  (declare (type simplicial-group smgr))
-  (the reduction
-    (build-rdct
-      :f (cs-pre-left-hmeq-right-reduction-f smgr)
-      :g (cs-pre-left-hmeq-right-reduction-g smgr)
-      :h (cs-pre-left-hmeq-right-reduction-h smgr)
-      :orgn `(cs-pre-left-hmeq-right-reduction ,smgr))))
-
-#|
-  (cat-init)
-  (defun random-abar (tot-degr~ max-degr)
-    (do ((rslt nil)
-         (cum-degr 0 (+ cum-degr degr 1))
-         (degr))
-        ((>= cum-degr tot-degr~) (make-abar :list rslt))
-       (setf degr (1+ (random max-degr)))
-       (push (brgn (1+ degr)
-                   (let ((list (make-list degr)))
-                     (mapl
-                       #'(lambda (sublist)
-                           (setf (car sublist) (- (random 21) 10)))
-                       list)
-                     list))
-             rslt)))
-  (setf rdct (cs-pre-left-hmeq-right-reduction (k-z-1)))
-  (pre-check-rdct rdct)
-  (setf *tc* (cmbn 0 1 (tnpr 0 (tnpr 0 +null-gbar+ 0 '()) 0 +null-abar+))
-        *bc* (cmbn 0 1 +null-abar+))
-  (check-rdct)
-  (setf *tc* (cmbn 1 1 (tnpr 1 (tnpr 0 +null-gbar+ 1 '(13)) 0 +null-abar+)))
-  (check-rdct)
-  (dotimes (i 10)
-    (let ((abar (random-abar 8 4)))
-      (setf abar-degr (apply #'+ (mapcar #'car (abar-list abar))))
-      (setf gnrt (tnpr 5 (tnpr 3 (gbar 3 0 '(1 2) 0 '(3) 0 '()) 2 '(4 5))
-                       abar-degr abar))
-      (unless (>= abar-degr 9)
-        (setf *tc* (cmbn (+ 5 abar-degr) 1 gnrt)
-              *bc* (cmbn abar-degr 1 abar))
-        (check-rdct))))
-  (dotimes (i 10)
-    (let ((abar (random-abar 6 4)))
-      (setf abar-degr (apply #'+ (mapcar #'car (abar-list abar))))
-      (setf gnrt (tnpr 6 (tnpr 3 (gbar 3 0 '(1 2) 0 '(3) 0 '()) 3 '(4 5 6))
-                       abar-degr abar))
-      (unless (>= abar-degr 8)
-        (setf *tc* (cmbn (+ 6 abar-degr) 1 gnrt)
-              *bc* (cmbn abar-degr 1 abar))
-        (check-rdct))))
-  (dotimes (i 10)
-    (let ((abar (random-abar 6 4)))
-      (setf abar-degr (apply #'+ (mapcar #'car (abar-list abar))))
-      (setf gnrt (tnpr 5 (tnpr 2 (gbar 2 0 '(3) 0 '()) 3 '(4 5 6))
-	   	     abar-degr abar))
-      (unless (>= abar-degr 9)
-        (setf *tc* (cmbn (+ 5 abar-degr) 1 gnrt))
-        (setf *bc* (cmbn abar-degr 1 abar))
-        (check-rdct))))
-  (dotimes (i 10)
-    (let ((abar (random-abar 6 4)))
-      (setf abar-degr (apply #'+ (mapcar #'car (abar-list abar))))
-      (setf gnrt (tnpr 4 (tnpr 2 (gbar 2 0 '(3) 0 '()) 2 '(4 5))
-                       abar-degr abar))
-      (unless (>= abar-degr 10)
-         (setf *tc* (cmbn (+ 4 abar-degr) 1 gnrt))
-         (setf *bc* (cmbn abar-degr 1 abar))
-         (check-rdct))))
-|#
-
-(DEFUN CS-LEFT-HMEQ-RIGHT-REDUCTION (smgr
-				      &aux (pre-reduction
-					     (cs-pre-left-hmeq-right-reduction smgr))
-				           (perturbation
-					     (cs-hat-right-perturbation smgr)))
-  (declare
-    (type simplicial-group smgr)
-    (type reduction pre-reduction)
-    (type morphism perturbation))
-  (the reduction
-    (progn
-      (setf (slot-value perturbation 'sorc) (tcc pre-reduction)
-	    (slot-value perturbation 'trgt) (tcc pre-reduction))
-      (special-bpl-2 pre-reduction perturbation))))
-
-#|
-  (cat-init)
-  (defun random-abar (tot-degr~ max-degr)
-    (do ((rslt nil)
-         (cum-degr 0 (+ cum-degr degr 1))
-         (degr))
-        ((>= cum-degr tot-degr~) (make-abar :list rslt))
-       (setf degr (1+ (random max-degr)))
-       (push (brgn (1+ degr)
-                   (let ((list (make-list degr)))
-                     (mapl
-                       #'(lambda (sublist)
-                           (setf (car sublist) (- (random 21) 10)))
-                       list)
-                     list))
-             rslt)))
-  (setf rdct (cs-left-hmeq-right-reduction (k-z-1)))
-  (pre-check-rdct rdct)
-  (setf *tc* (cmbn 0 1 (tnpr 0 (tnpr 0 +null-gbar+ 0 '()) 0 +null-abar+))
-        *bc* (cmbn 0 1 +null-abar+))
-  (check-rdct)
-  (setf *tc* (cmbn 1 1 (tnpr 1 (tnpr 0 +null-gbar+ 1 '(13)) 0 +null-abar+)))
-  (check-rdct)
-  (dotimes (i 10)
-    (let ((abar (random-abar 4 2)))
-      (setf abar-degr (apply #'+ (mapcar #'car (abar-list abar))))
-      (setf gnrt (tnpr 3 (tnpr 2 (gbar 2 0 '(3) 0 '()) 1 '(4))
-                       abar-degr abar))
-      (unless (>= abar-degr 9)
-        (setf *tc* (cmbn (+ 3 abar-degr) 1 gnrt)
-              *bc* (cmbn abar-degr 1 abar))
-        (check-rdct))))
-  (dotimes (i 10)
-    (let ((abar (random-abar 3 1)))
-      (setf abar-degr (apply #'+ (mapcar #'car (abar-list abar))))
-      (setf gnrt (tnpr 4 (tnpr 2 (gbar 2 0 '(3) 0 '()) 2 '(5 6))
-                       abar-degr abar))
-      (unless (>= abar-degr 8)
-        (setf *tc* (cmbn (+ 4 abar-degr) 1 gnrt)
-              *bc* (cmbn abar-degr 1 abar))
-        (check-rdct))))
-  (dotimes (i 10)
-    (let ((abar (random-abar 3 1)))
-      (setf abar-degr (apply #'+ (mapcar #'car (abar-list abar))))
-      (setf gnrt (tnpr 5 (tnpr 3 (gbar 3 0 '(1 2) 1 '() 0 '()) 2 '(5 6))
-	   	     abar-degr abar))
-      (unless (>= abar-degr 9)
-        (setf *tc* (cmbn (+ 5 abar-degr) 1 gnrt))
-        (setf *bc* (cmbn abar-degr 1 abar))
-        (check-rdct))))
-  (dotimes (i 10)
-    (let ((abar (random-abar 6 4)))
-      (setf abar-degr (apply #'+ (mapcar #'car (abar-list abar))))
-      (setf gnrt (tnpr 4 (tnpr 2 (gbar 2 0 '(3) 0 '()) 2 '(4 5))
-                       abar-degr abar))
-      (unless (>= abar-degr 10)
-         (setf *tc* (cmbn (+ 4 abar-degr) 1 gnrt))
-         (setf *bc* (cmbn abar-degr 1 abar))
-         (check-rdct))))
-|#
-
-(DEFUN CS-LEFT-HMEQ (smgr)
-  (declare (type simplicial-group smgr))
-  (the homotopy-equivalence
-    (build-hmeq
-      :lrdct (cs-left-hmeq-left-reduction smgr)
-      :rrdct (cs-left-hmeq-right-reduction smgr)
-      :orgn `(cs-left-hmeq ,smgr))))
-
-#|
-  (cat-init)
-  (setf h (cs-left-hmeq (k-z-1)))
-  (setf abar (abar 2 '(2) 3 '(3 4)))
-  (rg h 5 abar)
-  (lf h *)
-  (lg h *)
-  (rf h *)
-|#
-
-(DEFUN CLASSIFYING-SPACE-EFHM (smgr)
-  (declare (type simplicial-group smgr))
-  (let ((left-hmeq (cs-left-hmeq smgr))
-	(right-hmeq (bar (efhm smgr))))
-    (declare (type homotopy-equivalence left-hmeq right-hmeq))
-    (cmps left-hmeq right-hmeq)))
-
-(DEFMETHOD SEARCH-EFHM (classifying-space (orgn (eql 'classifying-space)))
-  (declare (type simplicial-set classifying-space))
-  (classifying-space-efhm (second (orgn classifying-space))))
-
-#|
-  (cat-init)
-  (setf k (k-z-1))
-  (homology k 0 10)
-  (setf bk (classifying-space k))
-  (homology bk 0 10)
-  (setf obk (loop-space bk))
-  (homology obk 0 6)
-|#
\ No newline at end of file
diff --git a/archive/Kenzo-1/classes.cl b/archive/Kenzo-1/classes.cl
deleted file mode 100644
index f7c041c..0000000
--- a/archive/Kenzo-1/classes.cl
+++ /dev/null
@@ -1,514 +0,0 @@
-;;;  CLASSES  CLASSES  CLASSES  CLASSES  CLASSES  CLASSES  CLASSES
-;;;  CLASSES  CLASSES  CLASSES  CLASSES  CLASSES  CLASSES  CLASSES
-;;;  CLASSES  CLASSES  CLASSES  CLASSES  CLASSES  CLASSES  CLASSES
-
-(IN-PACKAGE "COMMON-LISP-USER")
-
-(PROVIDE "classes")
-
-;;;
-;;; VARIOUS
-;;;
-
-(DEFTYPE ANY () t)
-
-;;; 
-;;;  COMBINATIONS
-;;;
-
-(DEFSTRUCT (CMBN (:print-function cmbn-print))
-  (degr #+allegro :type #+allegro fixnum)
-  (list #+allegro :type #+allegro list))
-
-;; CFFC = CoeFFiCient
-(DEFUN CFFC-P (object)
-   (declare (type any object))
-   (the boolean
-      (and (typep object 'fixnum)
-           (/= 0 object))))
-
-(DEFTYPE CFFC () '(satisfies cffc-p))
-
-;; GNRT = GeNeRaTor
-(DEFTYPE GNRT () 'any)
-
-;; CMPR = CoMPaRison
-(DEFTYPE CMPR () '(member :less :equal :greater))
-
-;; CMPRF = CoMPaRison Function
-(DEFTYPE CMPRF () 'function)
-               ;; (function (gnrt gnrt) cmpr)
-
-(DEFUN TERM-P (object)
-   (declare (type any object))
-   (the boolean
-      (and (consp object)
-           (typep (car object) 'cffc)
-           (typep (cdr object) 'gnrt))))
-
-(DEFTYPE TERM () '(satisfies term-p))
-
-;; ICMBN = Internal-CoMBiNation
-(DEFUN ICMBN-P (object)
-   ;; ICMBN = Internal CoMBiNation,
-   ;;   without the keyword and the degree
-   (declare (type any object))
-   (the boolean
-      (and (listp object)
-           (every #'term-p object))))
-
-(DEFTYPE ICMBN () '(satisfies icmbn-p))
-
-#|
-;; CMBN = CoMBiNation
-(DEFUN CMBN-P (object)
-   (declare (type any object))
-   (the boolean
-      (and (consp object)
-           (eql (car object) :cmbn)
-           (consp (cdr object))
-           (typep (second object) 'fixnum)
-           (typep (cddr object) 'icmbn))))
-
-(DEFTYPE CMBN () '(satisfies cmbn-p))
-|#
-
-(DEFTYPE BASIS () '(or function (eql :locally-effective)))
-                   ;; (function (degr) (list gnrt))
-
-;; INTR-MRPH = INTeRnal-MoRPHism
-(DEFTYPE INTR-MRPH () 'function)
-               ;; (or (function (degr gnrt) cmbn)  ;; if :gnrt strategy
-               ;;     (function (cmbn) (cmbn))     ;; if :cmbn strategy
-
-;;;
-;;;  CHAIN-COMPLEXES
-;;;
-
-#+allegro
-(DEFVAR REDEFINITION-WARNINGS-SAVED)
-
-#+allegro
-(eval-when (:compile-toplevel :load-toplevel :execute)
-  (setf redefinition-warnings-saved
-    excl::*redefinition-warnings*
-    *redefinition-warnings* nil))
-
-(DEFCLASS CHAIN-COMPLEX () ())  ;; will be redefined later.
-
-(DEFCLASS MORPHISM () ())  ;; will be redefined later.
-
-(DEFCLASS HOMOTOPY-EQUIVALENCE () ())  ;;  will be redefined later
-
-;;  IDNM = IDentification NuMber
-(DEFVAR *IDNM-COUNTER*)
-(SETF *IDNM-COUNTER* 0)
-
-(DEFCLASS CHAIN-COMPLEX ()
-    ((cmpr :type cmprf :initarg :cmpr :reader cmpr1)
-     (basis :type basis :initarg :basis :reader basis1)
-     ;; BaSe GeNerator
-     (bsgn :type gnrt :initarg :bsgn :reader bsgn)
-     ;; DiFFeRential
-     (dffr :type morphism :initarg :dffr :reader dffr1)
-     ;; GRound MoDule
-     (grmd :type chain-complex :initarg :grmd :reader grmd)
-     ;; EFfective HoMology
-     (efhm :type homotopy-equivalence :initarg :efhm :accessor efhm)
-     ;; IDentification NuMber
-     (idnm :type fixnum :initform (incf *idnm-counter*) :reader idnm)
-     ;; ORiGiN
-     (orgn :type list :initarg :orgn :reader orgn)))
-
-;; STRT = STRaTegy
-(DEFTYPE STRT () '(member :gnrt :cmbn))
-
-
-(DEFCLASS MORPHISM ()
-     ;; SOuRCe
-    ((sorc :type chain-complex :initarg :sorc :reader sorc)
-     ;; TaRGeT
-     (trgt :type chain-complex :initarg :trgt :reader trgt)
-     ;; DEGRee
-     (degr :type fixnum :initarg :degr :reader degr)
-     ;; INTeRnal
-     (intr :type intr-mrph :initarg :intr :reader intr)
-     ;; STRaTegy
-     (strt :type strt :initarg :strt :reader strt)
-;;     ;; WoRk-TiMe
-;;     (wrtm :type integer :initform 0 :accessor wrtm)
-     ;; CaLl NuMber
-     (???-clnm :type fixnum :initform 0 :accessor ???-clnm)
-     (?-clnm :type fixnum :initform 0 :accessor ?-clnm)
-     ;; ReSuLTS
-     (rslts :type simple-vector
-        ;; (vector (vector result))
-        :reader rslts)
-     ;; IDentification NuMber
-     (idnm :type fixnum :initform (incf *idnm-counter*) :reader idnm)
-     ;; ORiGiN
-     (orgn :type list :initarg :orgn :reader orgn)))
-
-(DEFSTRUCT (RESULT (:print-function result-print))
-  (gnrt #+allegro :type #+allegro gnrt)
-  (value #+allegro :type #+allegro cmbn)
-  (clnm #+allegro :type #+allegro fixnum)
-  (rntm #+allegro :type #+allegro single-float))
-
-;;;
-;;;  EFFECTIVE HOMOLOGY
-;;;
-
-(DEFCLASS REDUCTION ()
-     ;; Top Chain Complex
-    ((tcc :type chain-complex :initarg :tcc :reader tcc1)
-     ;; Bottom Chain Complex
-     (bcc :type chain-complex :initarg :bcc :reader bcc1)
-     (f :type morphism :initarg :f :reader f1)
-     (g :type morphism :initarg :g :reader g1)
-     (h :type morphism :initarg :h :reader h1)
-     ;; IDentification NuMber
-     (idnm :type fixnum :initform (incf *idnm-counter*) :reader idnm)
-     ;; ORiGiN
-     (orgn :type list :initarg :orgn :reader orgn)))
-
-(DEFCLASS HOMOTOPY-EQUIVALENCE ()
-     ;; Left Bottom Chain Complex
-    ((lbcc :type chain-complex :initarg :lbcc :reader lbcc1)
-     ;; Top Chain Complex
-     (tcc  :type chain-complex :initarg :tcc  :reader tcc1)
-     ;; Bottom Right Chain Complex
-     (rbcc :type chain-complex :initarg :rbcc :reader rbcc1)
-     ;; Left f
-     (lf   :type morphism      :initarg :lf   :reader lf1)
-     ;; Left g
-     (lg   :type morphism      :initarg :lg   :reader lg1)
-     ;; Left h
-     (lh   :type morphism      :initarg :lh   :reader lh1)
-     ;; Right f
-     (rf   :type morphism      :initarg :rf   :reader rf1)
-     ;; Right g
-     (rg   :type morphism      :initarg :rg   :reader rg1)
-     ;; Right h
-     (rh   :type morphism      :initarg :rh   :reader rh1)
-     ;; Left ReDuCTion
-     (lrdct :type reduction    :initarg :lrdct :reader lrdct)
-     ;; Right ReDuCTion
-     (rrdct :type reduction    :initarg :rrdct :reader rrdct)
-     ;; IDentification NuMber
-     (idnm :type fixnum :initform (incf *idnm-counter*) :reader idnm)
-     ;; ORiGiN
-     (orgn :type list          :initarg :orgn :reader orgn)))
-
-#+allegro
-(eval-when (:compile-toplevel :load-toplevel :execute)
-  (setf excl::*redefinition-warnings*
-    redefinition-warnings-saved))
-
-;;;
-;;;  HOMOLOGY-GROUPS
-;;;
-
-
-(DEFSTRUCT (matrice (:conc-name nil))
-  leftcol uplig)
-
-(DEFSTRUCT (t-mat (:conc-name nil))
-  val ilig icol left up)
-
-
-;;;
-;;;  CONES
-;;;
-
-(DEFSTRUCT (CONE (:conc-name nil) (:print-function cone-print))
-  (conx #+allegro :type #+allegro (member 0 1))
-  (icon #+allegro :type #+allegro gnrt))
-
-(DEFSTRUCT (BICN (:conc-name nil) (:print-function bicn-print))
-  (bcnx #+allegro :type #+allegro (member :bcnb :bcnc :bcnd))
-  (ibicn #+allegro :type #+allegro gnrt))
-
-
-;;;
-;;;  TENSOR-PRODUCTS
-;;;
-
-
-(DEFSTRUCT (TNPR (:conc-name nil) (:print-function tnpr-print))
-  degr1 gnrt1 degr2 gnrt2)
-
-
-
-;;;
-;;;  COALGEBRAS
-;;;
-
-(DEFCLASS COALGEBRA (chain-complex)
-    ((cprd :type morphism :initarg :cprd :reader cprd1)))   ;; coproduct
-
-;;;
-;;;  COBAR
-;;;
-
-;; CBGN CoBar-GeNerator
-(DEFUN CBGN-P (object)
-   ;; CBGN = CoBar GeNerator
-   (declare (type any object))
-   (the boolean
-      (and (consp object)
-           (typep (car object) 'fixnum)      ;; degree *in* the cobar
-           (typep (cdr object) 'gnrt))))
-
-(DEFTYPE CBGN () '(satisfies cbgn-p))
-
-;; IALLP = Internal-ALgebraic LooP
-(DEFUN IALLP-P (object)
-   (declare (type any object))
-   (the boolean
-      (and (listp object)
-           (every #'cbgn-p object))))
-
-(DEFTYPE IALLP () '(satisfies iallp-p))
-
-(DEFSTRUCT (ALLP (:print-function allp-print))
-  (list #+allegro :type #+allegro iallp))
-
-;;;
-;;;  ALGEBRAS
-;;;
-
-(DEFCLASS ALGEBRA (chain-complex)
-    ((aprd :type morphism :initarg :aprd :reader aprd1)))   ;; product
-
-(DEFCLASS HOPF-ALGEBRA (coalgebra algebra)
-  ())
-
-;;;
-;;;  BAR
-;;;
-
-;; BRGN BaR-GeNerator
-(DEFUN BRGN-P (object)
-   ;; BRGN = BaR GeNerator
-   (declare (type any object))
-   (the boolean
-      (and (consp object)
-           (typep (car object) 'fixnum)      ;; degree *in* the bar
-           (typep (cdr object) 'gnrt))))
-
-(DEFTYPE BRGN () '(satisfies brgn-p))
-
-;; IABAR = Internal-ALgebraic LooP
-(DEFUN IABAR-P (object)
-   (declare (type any object))
-   (the boolean
-      (and (listp object)
-           (every #'brgn-p object))))
-
-(DEFTYPE IABAR () '(satisfies iabar-p))
-
-;; ABAR = ALgebraic BAR
-
-
-#|
-(DEFUN ABAR-P (object)
-   (declare (type any object))
-   (the boolean
-      (and (consp object)
-           (eq :abar (car object))
-           (typep (cdr object) 'iabar))))
-
-(DEFTYPE ABAR () '(satisfies abar-p))
-|#
-
-(DEFSTRUCT (ABAR (:print-function abar-print))
-  (list #+allegro :type #+allegro list))
-
-;;;
-;;;  SIMPLICIAL SETS
-;;;
-
-;;  DGOP = DeGeneray OPerator
-(DEFTYPE DGOP () `(integer 0 ,most-positive-fixnum))
-
-;; GMSM = GeoMetric SiMplex
-(DEFTYPE GMSM () 'gnrt)
-
-;;  DLOP = DeL OPerator
-(DEFTYPE DLOP () 'dgop) 
-
-#|
-;; IABSM = Internal ABstract SiMplex
-(DEFUN IABSM-P (object)
-  (declare (type any object))
-  (the boolean
-     (and (consp object)
-	  (typep (car object) 'dgop)
-	  (typep (cdr object) 'gmsm))))	   
-
-(DEFTYPE IABSM () '(satisfies iabsm-p))
-|#
-
-(DEFSTRUCT (ABSM (:conc-name nil) (:print-function absm-print))
-  (dgop #+allegro :type #+allegro dgop)
-  (gmsm #+allegro :type #+allegro gmsm))
-
-
-#|
-()
-(absm-p 1)
-(absm-p '(1))
-(absm-p '(:absm nil))  ;; printer-error
-(absm-p '(:absm 5 . a))
-(absm-p '(:absm -5 . a)) ;; printer-error
-|#
-
-
-(DEFTYPE FACE () 'function)
-            ;;   (function (indx dmns gmsm) absm)
-
-(DEFTYPE FACE* () 'function)
-            ;;    (function (indx dmns gmsm) (or gmsm (eql :degenerate)))
-
-(DEFCLASS SIMPLICIAL-SET (coalgebra)
-    ((face :type face :initarg :face :reader face1)))
-
-
-;;;
-;;;  SIMPLICIAL-MRPHS
-;;;
-
-(DEFTYPE SINTR () 'function)
-               ;; (function (dmns gmsm) absm)
-
-(DEFCLASS SIMPLICIAL-MRPH (morphism)
-  ((sintr :type sintr :initarg :sintr :reader sintr)))
-
-
-;;;
-;;;  SPECIAL-SMSTS
-;;;
-
-;;  DLOP = DeL OPerator
-(DEFUN SOFT-DLOP-P (object)
-   (declare (type any object))
-   (the boolean
-      (and (consp object)
-           (eq :delt (car object))
-           (typep (cdr object) 'dgop))))
-
-(DEFTYPE SOFT-DLOP () '(satisfies soft-dlop-p))
-
-;;;
-;;;  CARTESIAN PRODUCTS
-;;;
-
-
-(DEFSTRUCT (CRPR (:print-function crpr-print) (:conc-name nil))
-  (dgop1 #+allegro :type #+allegro dgop)
-  (gmsm1 #+allegro :type #+allegro gmsm)
-  (dgop2 #+allegro :type #+allegro dgop)
-  (gmsm2 #+allegro :type #+allegro gmsm))
-
-;;;;
-;;;;  KAN
-;;;;
-
-(DEFTYPE KFLL () 'function)
-              ;; (function (indx dmns (list absm)) absm)
-
-(DEFCLASS KAN (simplicial-set)
-  ((kfll :type kfll :initarg :kfll :reader kfll1)))
-
-;;;
-;;;  FIBRATIONS
-;;;
-
-(DEFUN FIBRATION-P (object)
-  (declare (type any object))
-  (the boolean
-     (and (typep object 'simplicial-mrph)
-	  (= -1 (degr object)))))
-
-(DEFTYPE FIBRATION ()
-  '(satisfies fibration-p))
-
-(DEFCLASS SIMPLICIAL-GROUP (kan hopf-algebra)
-   ((grml :type simplicial-mrph :initarg :grml :reader grml1)
-    (grin :type simplicial-mrph :initarg :grin :reader grin1)))
-
-(DEFCLASS AB-SIMPLICIAL-GROUP (simplicial-group) ())
-
-
-;;;
-;;;  LOOP SPACES
-;;;
-
-;;  EXPN = EXPoNent
-(DEFUN EXPN-P (object)
-   (declare (type any object))
-   (the boolean
-      (typep object '(and fixnum
-                          (not (eql 0))))))
-
-(DEFTYPE EXPN () '(satisfies expn-p))
-
-;;  POWR = POWeR
-(DEFUN POWR-P (object)
-   (declare (type any object))
-   (the boolean
-      (and (consp object)
-           (typep (car object) 'gmsm)
-           (typep (cdr object) 'expn))))
-
-(DEFTYPE POWR () '(satisfies powr-p))
-
-;;  APOWR = Abstract POWeR
-(DEFUN APOWR-P (object)
-   (declare (type any object))
-   (the boolean
-      (and (consp object)
-           (typep (car object) 'dgop)
-           (typep (cdr object) 'powr))))
-
-(DEFTYPE APOWR () '(satisfies apowr-p))
-
-;;  ILOOP = Internal LOOP
-(DEFUN ILOOP-P (object)
-   (declare (type any object))
-   (the boolean
-      (and (listp object)
-           (every #'apowr-p object))))
-
-(DEFTYPE ILOOP () '(satisfies iloop-p))
-
-
-#+allegro
-(eval-when (:compile-toplevel :load-toplevel :execute)
-     (setf excl:*enable-package-locked-errors* nil))
-#+clisp(eval-when (:compile-toplevel :load-toplevel :execute)
-         (setf (ext:package-lock :common-lisp) nil))
-
-(DEFSTRUCT (LOOP (:print-function loop-print))
-  (list #+allegro :type #+allegro iloop))
-                  
-#+allegro
-(eval-when (:compile-toplevel :load-toplevel :execute)
-     (setf excl:*enable-package-locked-errors* t))
-#+clisp(eval-when (:compile-toplevel :load-toplevel :execute)
-         (setf (ext:package-lock :common-lisp) t))
-
-
-
-;;;
-;;;  CLASSIFYING-SPACES
-;;;
-
-;;  GBAR Geometrical BAR
-;;  (:gbar dmns absm_(m-1) ... absm_1)
-
-(DEFSTRUCT (GBAR (:print-function gbar-print))
-  (dmns #+allegro :type #+allegro fixnum)
-  (list #+allegro :type #+allegro list))
-
diff --git a/archive/Kenzo-1/classifying-spaces.cl b/archive/Kenzo-1/classifying-spaces.cl
deleted file mode 100644
index b743f86..0000000
--- a/archive/Kenzo-1/classifying-spaces.cl
+++ /dev/null
@@ -1,392 +0,0 @@
-;;;  CLASSIFYING-SPACES  CLASSIFYING-SPACES  CLASSIFYING-SPACES
-;;;  CLASSIFYING-SPACES  CLASSIFYING-SPACES  CLASSIFYING-SPACES
-;;;  CLASSIFYING-SPACES  CLASSIFYING-SPACES  CLASSIFYING-SPACES
-
-(IN-PACKAGE "COMMON-LISP-USER")
-
-(provide "classifying-spaces")
-
-(DEFCONSTANT +NULL-GBAR+ (make-gbar :dmns 0 :list +empty-list+))
-
-(DEFUN GBAR-PRINT (gbar stream depth)
-  (declare
-   (type gbar gbar) (stream stream)
-   (ignore depth))
-  (the gbar
-    (progn
-      (princ "<<GBar" stream)
-      (dolist (absm (gbar-list gbar))
-        (declare (type absm absm))
-        (with-absm (dgop gmsm) absm
-                   (format stream "<~A ~A>"
-                     (hyphenize-list (dgop-int-ext dgop))
-                     gmsm)))
-      (princ ">>" stream)
-      gbar)))
-
-;;; NIGBAR = non-normalized igbar (with dimension)
-
-(DEFUN NORMALIZE-GBAR (nigbar)
-  (declare (list nigbar))
-  (the absm
-    (let ((dmns (first nigbar))
-          (igbar (rest nigbar)))
-      (declare
-       (fixnum dmns)
-       (list igbar))
-      (when (zerop dmns)
-        (return-from normalize-gbar (absm 0 +null-gbar+)))
-      (do ((mark igbar (cdr mark))
-           (indx (1- dmns) (1- indx))
-           (2-indx (2-exp (1- dmns)) (ash 2-indx -1))
-           (mask (mask (1- dmns)) (ash mask -1))
-           (and-dgops -1 (logand and-dgops (dgop (car mark))))
-           ;; r = result
-           (r-dgop 0)
-           (r-absm-list +empty-list+))
-          ((endp mark)
-           (absm r-dgop
-                 (make-gbar
-                  :dmns (- dmns (logcount r-dgop))
-                  :list (nreverse r-absm-list))))	   
-        (declare
-         (list mark r-absm-list)
-         (fixnum indx 2-indx mask and-dgops r-dgop))
-        (when (zerop and-dgops)
-	    (return-from normalize-gbar
-	      (absm r-dgop
-		    (make-gbar
-		     :dmns (- dmns (logcount r-dgop))
-		     :list (nreconc r-absm-list mark)))))
-	  (let ((absm (car mark)))
-	    (with-absm (dgop gmsm) absm
-	      (declare (ignore gmsm))
-	      (if (and (= dgop mask)
-		       (logbitp indx and-dgops))
-		 (progn
-		   (incf r-dgop 2-indx)
-		   (mapl
-		    #'(lambda (sublist)
-			(declare (list sublist))
-			(setf (car sublist)
-			      (let ((absm (car sublist)))
-				(declare (type absm absm))
-				(with-absm (dgop gmsm) absm
-				  (absm (multiple-value-bind (q r)
-							     (floor dgop 2-indx)
-					  (declare (fixnum q r))
-					  (+ (ash (1- q) (1- indx)) r))
-					gmsm)))))
-		    r-absm-list))
-		 (push absm r-absm-list))))))))
-
-#|
-()
-(normalize-gbar (list 0))
-(normalize-gbar (list 1 (absm 0 'i)))
-(normalize-gbar (list 2 (absm 1 'i) (absm 0 'i)))
-(normalize-gbar (list 2 (absm 0 'a) (absm 0 'i)))
-(normalize-gbar (list 4 (absm 0 'a) (absm 0 'b) (absm 0 'c) (absm 0 'i)))
-(normalize-gbar (list 4 (absm 7 'i) (absm 3 'i) (absm 1 'i) (absm 0 'i)))
-(normalize-gbar (list 4 (absm 0 'a) (absm 3 'i) (absm 0 'c) (absm 0 'i)))
-(normalize-gbar (list 4 (absm 1 'a) (absm 3 'i) (absm 0 'c) (absm 0 'i)))
-(normalize-gbar (list 4 (absm 2 'a) (absm 3 'i) (absm 0 'c) (absm 0 'i)))
-(normalize-gbar (list 4 (absm 4 'a) (absm 3 'i) (absm 0 'c) (absm 0 'i)))
-(normalize-gbar (list 4 (absm 3 'a) (absm 3 'i) (absm 0 'c) (absm 0 'i)))
-(normalize-gbar (list 4 (absm 5 'a) (absm 3 'i) (absm 0 'c) (absm 0 'i)))
-(normalize-gbar (list 4 (absm 6 'a) (absm 3 'i) (absm 0 'c) (absm 0 'i)))
-(normalize-gbar (list 4 (absm 1 'a) (absm 3 'i) (absm 1 'i) (absm 0 'i)))
-|#
-
-(DEFUN UNNORMALIZE-GBAR (absm idnt)
-  (declare
-     (type absm absm)
-     (type gmsm idnt))
-  (the list ;; igbar
-    (with-absm (dgop gbar) absm
-    (with-gbar (dmns list) gbar
-      (setf list (reverse list))
-      (do ((dgop2 dgop (ash dgop2 -1))
-	   (indx 0 (1+ indx))
-	   (2-indx 1 (ash 2-indx 1))
-	   (dgop3 0)
-	   (rslt +empty-list+))
-	  ((zerop dgop2)
-	   (cons (+ dmns (logcount dgop))
-		 (nreconc
-		  (mapcar
-		   #'(lambda (absm)
-		       (declare (type absm absm))
-		       (ndgnr dgop3 absm))
-		   list)
-		  rslt)))
-	  (declare
-	    (list rslt)
-	    (fixnum dgop2 2-indx dgop3))
-	 (if (oddp dgop2)
-	    (progn
-	      (push (absm (mask indx) idnt) rslt)
-	      (incf dgop3 2-indx))
-	    (push (ndgnr dgop3 (pop list)) rslt)))))))
-
-#|
-()
-(unnormalize-gbar (absm 1 +null-gbar+) 'i)
-(unnormalize-gbar (absm 15 +null-gbar+) 'i)
-(normalize-gbar (unnormalize-gbar (absm 15 +null-gbar+) 'i))
-(unnormalize-gbar
- (absm 0 (make-gbar :dmns 4
-                    :list (list (absm 0 'a) (absm 0 'b)
-                                (absm 0 'c) (absm 0 'i)))) 'i)
-(normalize-gbar
- (unnormalize-gbar
-  (absm 0 (make-gbar :dmns 4
-                     :list (list (absm 0 'a) (absm 0 'b)
-                                 (absm 0 'c) (absm 0 'i)))) 'i))
-(unnormalize-gbar
- (absm 5 (make-gbar :dmns 4
-                    :list (list (absm 0 'a) (absm 0 'b)
-                                (absm 0 'c) (absm 0 'i)))) 'i)
-(normalize-gbar
- (unnormalize-gbar
-  (absm 5 (make-gbar :dmns 4
-                     :list (list (absm 0 'a) (absm 0 'b)
-                                 (absm 0 'c) (absm 0 'i)))) 'i))
-(unnormalize-gbar
- (absm 9 (make-gbar :dmns 4
-                    :list (list (absm 0 'a) (absm 0 'b)
-                                (absm 0 'c) (absm 0 'i)))) 'i)
-(normalize-gbar
- (unnormalize-gbar
-  (absm 9 (make-gbar :dmns 4
-                     :list (list (absm 0 'a) (absm 0 'b)
-                                 (absm 0 'c) (absm 0 'i)))) 'i))
-|#
-
-(DEFUN GBAR (dmns &rest rest)
-  (the gbar
-    (progn
-      (unless (= (+ dmns dmns) (length rest))
-        (error "In GBAR, the argument list has a wrong length."))
-      (make-gbar :dmns dmns
-                 :list (do ((mark rest (cddr mark))
-                            (rslt +empty-list+
-                                  (cons (absm (car mark) (cadr mark))
-                                        rslt)))
-                           ((endp mark) (nreverse rslt))
-                         (declare (list mark rslt)))))))
-
-#|
-()
-(gbar 0)
-(gbar 1)
-(gbar 2 1 'a 2 'b)
-|#
-
-(DEFUN CLASSIFYING-SPACE-CMPR (cmpr)
-  (declare (type cmprf cmpr))
-  (flet ((rslt (gbar1 gbar2)
-	   (declare (type gbar gbar1 gbar2))
-	   (maplexico
-	    #'(lambda (absm1 absm2)
-		(declare (type absm absm1 absm2))
-		(a-cmpr3 cmpr absm1 absm2))
-	    (gbar-list gbar1) (gbar-list gbar2))))
-     (the cmprf #'rslt)))
-
-#|
-  (setf cmpr (classifying-space-cmpr 's-cmpr))
-  (funcall cmpr (gbar 2 0 'a 0 'a) (gbar 2 1 'a 0 'a))
-  (funcall cmpr (gbar 2 0 'a 0 'a) (gbar 2 0 'b 0 'a))
-  (funcall cmpr (gbar 2 0 'a 0 'a) (gbar 2 0 'a 0 'a))
-|#
-
-(DEFUN CLASSIFYING-SPACE-BASIS (basis)
-  (declare (type basis basis))
-  (when (eq basis :locally-effective)
-    (return-from classifying-space-basis :locally-effective))
-  (let ((crts-basis :locally-effective)  ;; to be redefined
-        (idnt (first (funcall basis 0))))
-    (declare
-     (type basis crts-basis)
-     (type gmsm idnt))
-    (labels
-        ((rslt (dmns)
-               (declare (fixnum dmns))
-               (when (minusp dmns)
-                 (return-from rslt +empty-list+))
-               (when (zerop dmns)
-                 (return-from rslt (list +null-gbar+)))
-               (let ((basis-1 (funcall crts-basis (1- dmns))))
-                 (declare (list basis-1))
-                 (nreverse
-                  (mapcar  ;; xxx bug
-                      #'(lambda (crpr)
-                          (declare (type crpr crpr))
-                          (with-crpr
-                           (absm1 absm2) crpr
-                           (make-gbar
-                            :dmns dmns
-                            :list (cons absm1
-                                        (rest (unnormalize-gbar absm2 idnt))))))
-                    (member-if  ;; xxx bug
-                     #'(lambda (dgop)
-                         (declare (fixnum dgop))
-                         (< dgop (mask (1- dmns))))
-                     (reverse basis-1)
-                     :key #'dgop1))))))
-;;;                  :key #'caadr))))))
-      (setf crts-basis (crts-prdc-basis basis #'rslt))
-      (the basis #'rslt))))
-
-#|
-()
-(cat-init)
-(setf k (k-z2-1))
-(setf b (classifying-space-basis (basis k)))
-(funcall b 0)
-(funcall b 1)
-(dotimes (i 5) (print (funcall b i)))
-|#
-
-(DEFUN CLASSIFYING-SPACE-FACE (face sintr-grml)
-  (declare
-     (type face face)
-     (type sintr sintr-grml))
-  (flet ((rslt (indx dmns gbar)
-	   (declare
-	     (fixnum indx dmns)
-	     (type gbar gbar))
-	   (when (= indx dmns)
-	     (return-from rslt
-	       (normalize-gbar (cons (1- dmns) (rest (gbar-list gbar))))))
-	   (do ((mark (gbar-list gbar) (cdr mark))
-		(dmns2 (1- dmns) (1- dmns2))
-		(rslt +empty-list+
-		      (cons (a-face4 face indx dmns2 (car mark))
-			    rslt)))
-	       ((= dmns2 indx)
-		(if (zerop indx)
-		   (normalize-gbar (cons (1- dmns) (nreverse rslt)))
-		   (normalize-gbar
-		    (cons (1- dmns)
-			  (nreconc
-			    rslt
-			    (cons (a-grml4 sintr-grml (1- indx)
-					   (second mark)
-					   (a-face4 face indx indx (first mark)))
-				  (nthcdr 2 mark))))))))))
-     (the face #'rslt)))
-
-#|
-  (setf om (loop-space (moore 2 2)))
-  (setf face (classifying-space-face (face om) (sintr (grml om))))
-  (setf gbar (gbar 4 0 (loop3 3 'm2 1 4 'n3 1)
-                     0 (loop3 0 'n3 1)
-                     0 (loop3 0 'm2 1)
-                     0 +null-loop+))
-  (dotimes (i 5)
-    (print (funcall face i 4 gbar)))
-|#
-
-(DEFMETHOD CLASSIFYING-SPACE ((smgr simplicial-group))
-  (the simplicial-set
-     (build-smst :cmpr (classifying-space-cmpr (cmpr smgr))
-		 :basis (classifying-space-basis (basis smgr))
-		 :bspn +null-gbar+
-		 :face (classifying-space-face (face smgr) (sintr (grml smgr)))
-		 :orgn `(classifying-space ,smgr))))
-
-#|
-  (cat-init)
-  (setf c (classifying-space (k-z2-1)))
-  (orgn c)
-  (first (basis c 4))
-  (? c 4 (first (basis c 4)))
-  (? c *)
-  (cprd c 4 ***)
-  (dotimes (i 5)
-    (print (face c i 4 (first (basis c 4)))))
-|#
-
-(DEFUN CLASSIFYING-SPACE-GRML-SINTR (idnt sintr-grml)
-  (declare
-    (type gmsm idnt)
-    (type sintr sintr-grml))
-  (flet ((rslt (dmns crpr)
-	   (declare
-	     (fixnum dmns)
-	     (type crpr crpr))
-	   (with-crpr (absm1 absm2) crpr
-	   (let ((absm-list-1 (rest (unnormalize-gbar absm1 idnt)))
-		 (absm-list-2 (rest (unnormalize-gbar absm2 idnt))))
-	     (declare (list absm-list-1 absm-list-2))
-	     (normalize-gbar
-	       (cons dmns
-		 (mapcar
-		   #'(lambda (absm1 absm2)
-		       (declare (type absm absm1 absm2))
-		       (decf dmns) ;; !!
-		       (a-grml4 sintr-grml dmns absm1 absm2))
-		   absm-list-1 absm-list-2)))))))
-    (the sintr #'rslt)))
-
-#|
-  (setf grml (classifying-space-grml-sintr '() (sintr (grml (k-z-1)))))
-  (funcall grml 3 (crpr 0 (gbar 3 0 '(1 2) 0 '(3) 0 '())
-                        0 (gbar 3 0 '(-1 -2) 0 '(-3) 0 '())))
-  (funcall grml 3 (crpr 0 (gbar 3 0 '(1 2) 0 '(3) 0 '())
-                        4 (gbar 2 0 '(-3) 0 '())))
-  (funcall grml 3 (crpr 0 (gbar 3 0 '(1 2) 0 '(3) 0 '())
-                        1 (gbar 2 0 '(-3) 0 '())))
-|#
-
-
-(DEFUN CLASSIFYING-SPACE-GRIN-SINTR (sintr-grin)
-  (declare (type sintr sintr-grin))
-  (flet ((rslt (dmns gbar)
-	   (declare
-	     (fixnum dmns)
-	     (type gbar gbar))
-	   (absm 0
-	     (make-gbar
-	       :dmns dmns
-	       :list (mapcar
-		       #'(lambda (absm)
-			   (declare (type absm absm))
-			   (a-grin4 sintr-grin dmns absm))
-		       (gbar-list gbar))))))
-    (the sintr #'rslt)))
-
-#|
-  (setf grin (classifying-space-grin-sintr (sintr (grin (k-z-1)))))
-  (funcall grin 3 (gbar 3 0 '(1 2) 1 '() 0 '()))
-|#
-
-(DEFMETHOD CLASSIFYING-SPACE ((smgr ab-simplicial-group))
-  (the ab-simplicial-group
-     (change-class 
-       (build-smgr :cmpr (classifying-space-cmpr (cmpr smgr))
-		   :basis (classifying-space-basis (basis smgr))
-		   :bspn +null-gbar+
-		   :face (classifying-space-face (face smgr) (sintr (grml smgr)))
-		   :sintr-grml (classifying-space-grml-sintr
-				 (bspn smgr)
-				 (sintr (grml smgr)))
-		   :sintr-grin (classifying-space-grin-sintr
-				 (sintr (grin smgr)))
-		   :orgn `(classifying-space ,smgr))
-       'ab-simplicial-group)))
-
-#|
-  (setf k-z-1 (k-z-1))
-  (setf k-z-2 (classifying-space k-z-1))
-  (setf k-z-3 (classifying-space k-z-2))
-  (homology k-z-3 0 10)
-  (setf k-z2-1 (k-z2-1))
-  (setf k-z2-2 (classifying-space k-z2-1))
-  (setf k-z2-3 (classifying-space k-z2-2))
-  (setf k-z2-4 (classifying-space k-z2-3))
-  (setf k-z2-5 (classifying-space k-z2-4))
-  (homology k-z2-5 0 7)
-|#
diff --git a/archive/Kenzo-1/coalgebras.cl b/archive/Kenzo-1/coalgebras.cl
deleted file mode 100644
index 03e2e57..0000000
--- a/archive/Kenzo-1/coalgebras.cl
+++ /dev/null
@@ -1,76 +0,0 @@
-;;;  COALGEBRAS  COALGEBRAS  COALGEBRAS  COALGEBRAS  COALGEBRAS  COALGEBRAS
-;;;  COALGEBRAS  COALGEBRAS  COALGEBRAS  COALGEBRAS  COALGEBRAS  COALGEBRAS
-;;;  COALGEBRAS  COALGEBRAS  COALGEBRAS  COALGEBRAS  COALGEBRAS  COALGEBRAS
-
-(IN-PACKAGE "COMMON-LISP-USER")
-
-(PROVIDE "coalgebras")
-
-(DEFVAR *CLGB-LIST*)
-(SETF *CLGB-LIST* +empty-list+)
-(PUSHNEW '*CLGB-LIST* *list-list*)
-
-#+clisp(eval-when (:compile-toplevel :load-toplevel :execute)
-         (setf (ext:package-lock :clos) nil))
-(DEFMETHOD PRINT-OBJECT ((clgb coalgebra) stream)
- (the coalgebra
-   (progn
-      (format stream "[K~D Coalgebra]" (idnm clgb))
-      clgb)))
-#+clisp(eval-when (:compile-toplevel :load-toplevel :execute)
-         (setf (ext:package-lock :clos) t))
-
-(DEFUN CLGB (idnm)
-   (declare (fixnum idnm))
-   (the (or coalgebra null)
-      (find idnm *clgb-list* :key #'idnm)))
-
-(DEFUN BUILD-CLGB
-    (&key cmpr basis bsgn intr-dffr dffr-strt intr-cprd cprd-strt orgn)
-   (declare
-      (type cmprf cmpr)
-      (type intr-mrph intr-dffr intr-cprd)
-      (type basis basis)
-      (type gnrt bsgn)
-      (type strt dffr-strt cprd-strt)
-      (list orgn))
-   (the coalgebra
-      (progn
-         (let ((already (find orgn *clgb-list* :key #'orgn :test #'equal)))
-            (declare (type (or null coalgebra) already))
-            (when already
-               (return-from build-clgb already)))
-         (let ((rslt (build-chcm :cmpr cmpr :basis basis :bsgn bsgn
-                        :intr-dffr intr-dffr :strt dffr-strt
-                        :orgn orgn)))
-            (declare (type chain-complex rslt))
-            (change-class rslt 'coalgebra)
-            (setf (slot-value rslt 'cprd)
-                  (build-mrph :sorc rslt :trgt (tnsr-prdc rslt rslt) :degr 0
-                        :intr intr-cprd :strt cprd-strt
-                        :orgn `(coalgebra-coproduct ,rslt)))
-               (push rslt *clgb-list*)
-               rslt))))
-
-(DEFUN CHANGE-CHCM-TO-CLGB (chcm &key intr-cprd cprd-strt orgn)
-   (declare
-      (type chain-complex chcm)
-      (type intr-mrph intr-cprd)
-      (type strt cprd-strt)
-      (list orgn))
-   (the coalgebra
-      (progn
-         (change-class chcm 'coalgebra)
-         (setf orgn (list (orgn chcm) 'then orgn))
-         (let ((already (find orgn *clgb-list* :key #'orgn :test #'equal)))
-            (declare (type (or null coalgebra) already))
-            (when already
-               (return-from change-chcm-to-clgb already)))
-         (setf (slot-value chcm 'cprd) (build-mrph
-                                          :sorc chcm :trgt (tnsr-prdc chcm chcm)
-                                          :degr 0
-                                          :intr intr-cprd :strt cprd-strt
-                                          :orgn orgn))
-         (push chcm *clgb-list*)
-         chcm)))
-
diff --git a/archive/Kenzo-1/cobar.cl b/archive/Kenzo-1/cobar.cl
deleted file mode 100644
index 7447efd..0000000
--- a/archive/Kenzo-1/cobar.cl
+++ /dev/null
@@ -1,708 +0,0 @@
-;;;  COBAR  COBAR  COBAR  COBAR  COBAR  COBAR  COBAR  COBAR  COBAR
-;;;  COBAR  COBAR  COBAR  COBAR  COBAR  COBAR  COBAR  COBAR  COBAR
-;;;  COBAR  COBAR  COBAR  COBAR  COBAR  COBAR  COBAR  COBAR  COBAR
-
-(IN-PACKAGE "COMMON-LISP-USER")
-
-(PROVIDE "cobar")
-
-(DEFUN ALLP (&rest list)
-  (when (= 1 (length list))
-    (setf list (first list)))
-  (unless (evenp (length list))
-    (error "In ALLP, the length list should be even."))
-  (the allp
-    (let ((rslt +empty-list+))
-      (declare (list rslt))
-      (do ((mark list (cddr mark)))
-          ((endp mark))
-        (declare (list mark))
-        (push (cbgn (car mark) (cadr mark)) rslt))
-      (make-allp :list (nreverse rslt)))))
-
-#|
-()
-(allp )
-(allp '(2 a 3 b))
-(allp 2 'a 3 'b)
-(allp 2 'a 3))  ;; error
-|#
-
-(DEFCONSTANT +NULL-ALLP+ (make-allp :list +empty-list+))
-
-(DEFUN ALLP-PRINT (allp stream depth)
-  (declare
-   (type allp allp) (stream stream)
-   (ignore depth))
-  (the allp
-    (progn
-      (format stream "<<AlLp")
-      (dolist (cbgn (allp-list allp))
-        (declare (type cbgn cbgn))
-        (with-cbgn (degr gnrt) cbgn
-                   (format stream "[~D ~A]" degr gnrt)))
-      (format stream ">>")
-      allp)))
-            
-(DEFUN COBAR-CMPR (cmpr)
-  (declare (type cmprf cmpr))
-  (flet ((rslt (allp1 allp2)
-               (declare (type allp allp1 allp2))
-               (the cmpr
-                 (let ((list1 (allp-list allp1))
-                       (list2 (allp-list allp2)))
-                   (declare (type iallp list1 list2))
-                   (lexico
-                    (f-cmpr (length list1) (length list2))
-                    (maplexico
-                     #'(lambda (cbgn1 cbgn2)
-                         (lexico
-                          (f-cmpr (cdegr cbgn1) (cdegr cbgn2))
-                          (funcall cmpr (cgnrt cbgn1) (cgnrt cbgn2))))
-                     list1 list2))))))
-    (the cmprf #'rslt)))
-
-#|
-  (setf r (cobar-cmpr #'s-cmpr))
-  (funcall r (allp) (allp))
-  (funcall r (allp 3 'a) (allp))
-  (funcall r (allp 3 'a) (allp 2 'a 1 'b))
-  (funcall r (allp 3 'a) (allp 3 'b))
-  (funcall r (allp 3 'a) (allp 3 'a)))
-|#
-
-(DEFUN COBAR-BASIS-LENGTH (basis degr length)
-   (declare
-      (type basis basis)
-      (fixnum degr length))
-   (the list
-      (progn
-	(when (= 1 length)
-	      (return-from cobar-basis-length
-			   (mapcar
-			    #'(lambda (item)
-				(declare (type gnrt item))
-				(list (cbgn degr item)))
-			    (funcall basis (1+ degr)))))                                         
-	(mapcan
-	 #'(lambda (degr1)
-	     (declare (fixnum degr1))
-	     (let ((list1 (funcall basis (1+ degr1)))
-		   (list2 (cobar-basis-length
-			    basis (- degr degr1) (1- length))))
-	       (declare (list list1 list2))
-	       (mapcan
-		#'(lambda (item1)
-		    (declare (type gnrt item1))
-		    (mapcar
-		     #'(lambda (item2)
-			 (declare (type iallp item2))
-			 (cons (cbgn degr1 item1) item2))
-		     list2))
-		list1)))
-	 (>a-b< 0 degr)))))
-
-#|
-  (setf basis #'(lambda (degr)
-                   (list degr)))
-  (cobar-basis-length basis 1 1)
-  (cobar-basis-length basis 2 1)
-  (cobar-basis-length basis 2 2)
-  (cobar-basis-length basis 3 1)
-  (cobar-basis-length basis 3 2)
-  (cobar-basis-length basis 3 3)
-|#
-
-(DEFUN COBAR-BASIS (basis)
-   (declare (type basis basis))
-   (the basis
-      (progn
-	(when (eq :locally-effective basis)
-	  (return-from cobar-basis :locally-effective))
-	(flet ((rslt (degr)
-		     (declare (fixnum degr))
-		     (cond ((minusp degr) +empty-list+)
-			   ((zerop degr) (list +null-allp+))
-			   (t
-			    (mapcan
-			     #'(lambda (length)
-				 (declare (fixnum length))
-				 (mapcar
-				  #'(lambda (iallp)
-                                      (declare (type iallp iallp))
-                                      (make-allp :list iallp))
-				  (cobar-basis-length basis degr length)))
-			     (>a-b> 0 degr))))))
-	      #'rslt))))
-   
-#| The following version of the COBAR-BASIS function is
-   not correctly compiled with ACL-Unix, probably
-   because the too complicated (but natural and correct)
-   structure of closures. This version works on ACL-PC.
-(DEFUN COBAR-BASIS (basis)
-   (declare
-      (type basis basis))
-   ;; if the coalgebra is effective, it is assumed simply-connected :
-   ;;   (length (funcall basis 0))  ==>  1
-   ;;   (length (funcall basis 1))  ==>  0
-   (the basis
-      (progn
-         (when (eq :locally-effective basis)
-            (return-from cobar-basis :locally-effecive))
-         (labels ((rslt (degr length)
-                     (declare (fixnum degr length))
-                     (when (= 1 length)
-                        (return-from rslt
-                           (mapcar
-                              #'(lambda (item)
-                                   (declare (type gnrt item))
-                                   (list (cbgn degr item)))
-                              (funcall basis (1+ degr)))))                                         
-                     (mapcan
-                        #'(lambda (degr1)
-                             (declare (fixnum degr1))
-                             (let ((list1 (funcall basis (1+ degr1)))
-                                   (list2 (rslt (- degr degr1) (1- length))))
-                                (declare (list list1 lis2))
-                                (mapcan
-                                   #'(lambda (item1)
-                                        (declare (type gnrt item1))
-                                        (mapcar
-                                           #'(lambda (item2)
-                                                (declare (type iallp item2))
-                                                (cons (cbgn degr1 item1) item2))
-                                           list2))
-                                   list1)))
-                        (>a-b< 0 degr))))
-            #'(lambda (degr)
-                 (declare (fixnum degr))
-                 (if (zerop degr)
-                    (list (make-allp :list +empty-list+))
-                    (mapcan
-                       #'(lambda (length)
-                            (declare (fixnum length))
-                            (mapcar
-                               #'(lambda (iallp)
-                                    (declare (type iallp iallp))
-                                    (make-allp :list iallp))
-                               (rslt degr length)))
-                       (>a-b> 0 degr))))))))
-|#
-
-#|
-  (setf basis #'(lambda (degr)
-                   (list degr)))
-  (setf r (cobar-basis basis))
-  (funcall r 0)
-  (funcall r 1)
-  (funcall r 2)
-  (dotimes (i 7)
-     (print (funcall r i)))
-  (cobar-basis :locally-effective)
-|#
-
-(DEFUN COBAR-INTR-VRTC-DFFR (dffr)
-   (declare (type morphism dffr))
-   (labels ((rslt (degr iallp)
-               ;; the argument iallp is an internal algebraic loop,
-               ;;     without the keyword :allp
-               ;; rslt returns an internal combination
-               ;;     without the keyword :cmbn, without degree
-               (declare
-                  (fixnum degr)
-                  (type iallp iallp))
-               (the icmbn
-                  (progn
-                     (unless iallp
-                        (return-from rslt +empty-list+))
-                     (let ((cbgn1 (first iallp))
-                           (rest (rest iallp)))
-                        (declare
-                           (type cbgn cbgn1)
-                           (type iallp rest))
-                        (with-cbgn (degr1 gnrt1) cbgn1
-                           (let ((d-gnrt1 (cmbn-list (gnrt-? dffr (1+ degr1) gnrt1)))
-                                 (d-rest (rslt (- degr degr1) rest))
-                                 (degr1-1 (1- degr1))
-                                 (first-sign (-1-expt-n-1 (length rest)))
-                                 (rest-sign (-1-expt-n degr1)))
-                              (declare
-                                 (type icmbn d-gnrt1 d-rest)
-                                 (fixnum degr1-1 rest-sign))
-                              (nconc
-                                 (mapcar
-                                    #'(lambda (term)
-                                         (with-term (cffc gnrt) term
-                                            (term (* first-sign cffc)
-                                               (cons (cbgn degr1-1 gnrt) rest))))
-                                    d-gnrt1)
-                                 (mapcar
-                                    #'(lambda (term)
-                                         (with-term (cffc gnrt) term
-                                            (term (* rest-sign cffc)
-                                               (cons cbgn1 gnrt))))
-                                    d-rest)))))))))
-      (the intr-mrph
-         #'(lambda (degr allp)
-              (make-cmbn
-                 :degr (1- degr)
-                 :list (mapcar
-                          #'(lambda (term)
-                               (with-term (cffc iallp) term
-                                  (term cffc (make-allp :list iallp))))
-                          (rslt degr (allp-list allp))))))))
-         
-
-#|
-(setf d (soft-delta-infinity))
-(setf r (cobar-intr-vrtc-dffr (dffr d)))
-(funcall r 0 (allp))
-(funcall r 3 (allp 3 (d 15)))
-(funcall r 5 (allp 3 (d (mask 5)) 2 (d (mask 4))))
-(funcall r 5 (allp 2 (d (mask 4)) 3 (d (mask 5)))))
-|#
-
-(DEFMETHOD VRTC-COBAR ((chcm chain-complex))
-   (the chain-complex
-      (with-slots (cmpr basis dffr) chcm
-         (declare
-            (type cmprf cmpr)
-            (type basis basis)
-            (type morphism dffr))
-         (build-chcm
-            :cmpr (cobar-cmpr cmpr)
-            :basis (cobar-basis basis)
-            :bsgn +null-allp+
-            :intr-dffr (cobar-intr-vrtc-dffr dffr)
-            :strt :gnrt
-            :orgn `(vrtc-cobar ,chcm)))))
-
-#|
-  (cat-init)
-  (setf v (vrtc-cobar (soft-delta-infinity)))
-  (defun random-allp (length)
-     (let ((rslt nil))
-        (dotimes (i length)
-           (let* ((gmsm (random (mask 9)))
-                  (dmns (1- (logcount gmsm))))
-              (when (plusp dmns)
-                 (push (cbgn (1- dmns) (d gmsm)) rslt))))
-        (make-allp :list rslt)))
-  (dotimes (i 10) (print (random-allp 5)))
-  (dotimes (i 10)
-     (let ((allp (random-allp 3)))
-        (print allp)
-        (print (? v (apply #'+ (mapcar #'car (allp-list allp))) allp))
-        (print (? v (? v (apply #'+ (mapcar #'car (allp-list allp))) allp)))))
-|#
-
-(DEFUN COBAR-INTR-HRZN-DFFR (cprd)
-   (declare (type morphism cprd))
-   (labels ((rslt (degr iallp)
-               (declare
-                  (fixnum degr)
-                  (type iallp iallp))
-               (the icmbn
-                  (progn
-                     (unless iallp
-                        (return-from rslt +empty-list+))
-                     (let ((cbgn1 (first iallp))
-                           (rest (rest iallp)))
-                        (declare
-                           (type cbgn cbgn1)
-                           (type iallp rest))
-                        (with-cbgn (degr1 gnrt1) cbgn1
-                           (let ((cprd-gnrt1 (cmbn-list (gnrt-? cprd (1+ degr1) gnrt1)))
-                                 (cprd-rest (rslt (- degr degr1) rest))
-                                 (sign (-1-expt-n-1 (length rest))))
-                              (declare
-                                 (type icmbn cprd-gnrt1 cprd-rest)
-                                 (fixnum sign))
-                              (setf cprd-gnrt1 (rest (butlast cprd-gnrt1)))  ;;; because \bar{A}
-                              (nconc
-                                 (mapcar
-                                    #'(lambda (term1)
-                                         (declare (type term term1))
-                                         (with-term (nil tnpr) term1  ;;; cffc is in fact 1
-                                            (with-tnpr (degr1 gnrt1 degr2 gnrt2) tnpr
-                                               (term sign              ;;; (* cffc sign)
-                                                  (cons (cbgn (1- degr1) gnrt1)
-                                                     (cons (cbgn (1- degr2) gnrt2)
-                                                        rest))))))
-                                    cprd-gnrt1)
-                                 (mapcar
-                                    #'(lambda (term2)
-                                         (declare (type term term2))
-                                         (with-term (cffc allp2) term2
-                                            (term cffc
-                                               (cons cbgn1 allp2))))
-                                    cprd-rest)))))))))
-      (the intr-mrph
-         #'(lambda (degr allp)
-              (declare
-                 (fixnum degr)
-                 (type allp allp))
-              (the cmbn
-                 (make-cmbn :degr (1- degr)
-                    :list (mapcar #'(lambda (term)
-                                       (declare (type term term))
-                                       (with-term (cffc iallp) term
-                                          (term cffc (make-allp :list iallp))))
-                             (rslt degr (allp-list allp)))))))))
-
-#|
-  (setf d (soft-delta-infinity))
-  (setf r (cobar-intr-hrzn-dffr (cprd d)))
-  (funcall r 0 (allp))
-  (funcall r 3 (allp 3 (d (mask 5))))
-  (funcall r 5 (allp 3 (d (mask 5)) 2 (d (mask 4))))
-  (funcall r 5 (allp 2 (d (mask 4)) 3 (d (mask 5))))
-|#
-
-(DEFUN COBAR-HRZN-DFFR (clgb)
-   (declare (type coalgebra clgb))
-   (the morphism
-      (with-slots (cprd) clgb
-         (declare (type morphism cprd))
-         (build-mrph
-            :sorc (vrtc-cobar clgb) :trgt (vrtc-cobar clgb) :degr -1
-            :intr (cobar-intr-hrzn-dffr cprd) :strt :gnrt
-            :orgn `(cobar-hrzn-dffr ,clgb)))))
-
-#|
-  (cat-init)
-  (setf h (cobar-hrzn-dffr (soft-delta-infinity)))
-  (defun random-allp (length)
-     (let ((rslt nil))
-        (dotimes (i length)
-           (let* ((gmsm (random (mask 9)))
-                  (dmns (1- (logcount gmsm))))
-              (when (plusp dmns)
-                 (push (cbgn (1- dmns) (d gmsm)) rslt))))
-        (make-allp :list rslt)))
-  (dotimes (i 10) (print (random-allp 5)))
-  (setf allp (random-allp 4))
-  (? h (apply #'+ (mapcar #'car (allp-list allp))) allp)
-  (? h (? h (apply #'+ (mapcar #'car (allp-list allp))) allp))
-  (dotimes (i 10)
-     (let ((allp (random-allp 3)))
-        (print allp)
-        (print (? h (apply #'+ (mapcar #'car (allp-list allp))) allp))
-        (print (? h (? h (apply #'+ (mapcar #'car (allp-list allp))) allp)))))
-|#
-
-(DEFUN COBAR-INTR-DFFR (vrtc-dffr hrzn-dffr)
-   (declare (type morphism vrtc-dffr hrzn-dffr))
-   (flet ((rslt (degr allp)
-             (declare
-                (fixnum degr)
-                (type allp allp))
-             (make-cmbn :degr (1- degr)
-                :list (append       ;;; and not nconc, otherwise a terrible bug, when the
-                                    ;;;   first result is stored in memory...
-                         (cmbn-list (gnrt-? vrtc-dffr degr allp))
-                         (cmbn-list (gnrt-? hrzn-dffr degr allp))))))
-      (the intr-mrph #'rslt)))
-
-(DEFMETHOD COBAR ((coalgebra coalgebra))
-   (let ((vrtc-cobar (vrtc-cobar coalgebra))
-         (cobar-hrzn-dffr (cobar-hrzn-dffr coalgebra)))
-     (declare (type chain-complex vrtc-cobar)
-              (type morphism cobar-hrzn-dffr))
-      (the chain-complex
-	 (let ((rslt (build-chcm
-		      :cmpr (cmpr vrtc-cobar)
-		      :basis (basis vrtc-cobar)
-		      :bsgn +null-allp+
-		      :intr-dffr (cobar-intr-dffr (dffr vrtc-cobar) cobar-hrzn-dffr)
-		      :strt :gnrt
-		      :orgn `(add ,vrtc-cobar ,cobar-hrzn-dffr))))
-	   (declare (type chain-complex rslt))
-	   (setf (slot-value rslt 'grmd) (grmd vrtc-cobar))
-	   rslt))))
-
-#|
-  (cat-init)
-  (setf c (cobar (deltab)))   
-  (defun random-allp (length)
-     (let ((rslt nil))
-        (dotimes (i length)
-           (let* ((gmsm (random (mask 9)))
-                  (dmns (1- (logcount gmsm))))
-              (when (plusp dmns)
-                 (push (cbgn (1- dmns) gmsm) rslt))))
-        (make-allp :list rslt)))
-  (dotimes (i 10) (print (random-allp 5)))
-  (setf allp (random-allp 4))
-  (? c (apply #'+ (mapcar #'car (allp-list allp))) allp)
-  (? c (? c (apply #'+ (mapcar #'car (allp-list allp))) allp))
-  (dotimes (i 10)
-     (let ((allp (random-allp 3)))
-        (print allp)
-        (print (? c (apply #'+ (mapcar #'car (allp-list allp))) allp))
-        (print (? c (? c (apply #'+ (mapcar #'car (allp-list allp))) allp)))))
-|#
-
-(DEFUN CMBN-ALLP-CMBN-TNPR (cmbn allp-cmbn)
-   (declare (type cmbn cmbn allp-cmbn))
-   (the cmbn
-      (with-cmbn (degr1 list1) cmbn
-         (decf degr1)     ;; because allp organization
-      (with-cmbn (degrr listr) allp-cmbn
-         (make-cmbn
-            :degr (+ degr1 degrr)
-            :list
-            (mapcan
-               #'(lambda (term1)
-                    (declare (type term term1))
-                    (with-term (cffc1 gnrt1) term1
-                       (let ((cbgn1 (cbgn degr1 gnrt1)))
-                          (declare (type cbgn cbgn1))
-                          (mapcar
-                             #'(lambda (termr)
-                                  (declare (type term termr))
-                                  (with-term (cffcr allpr) termr
-                                     (term (* cffc1 cffcr)
-                                        (make-allp
-                                           :list (cons cbgn1 (allp-list allpr))))))
-                             listr))))
-               list1))))))
-
-(DEFUN NCMBN-COBAR (cmbn-list)
-   (declare (list cmbn-list))
-   (the cmbn
-      (progn
-         (unless cmbn-list
-            (return-from ncmbn-cobar (cmbn 0 1 +null-allp+)))
-         (cmbn-allp-cmbn-tnpr
-            (first cmbn-list)
-            (ncmbn-cobar (rest cmbn-list))))))
-#|
-  (ncmbn-cobar nil)
-  (ncmbn-cobar (list (cmbn 3 2 'a 3 'b)))
-  (ncmbn-cobar (list (cmbn 1 2 'a 3 'b) (cmbn 2 4 'c 5 'd)))
-  (ncmbn-cobar (list (cmbn 1 2 'a 3 'b) (cmbn 1 4 'c 5 'd) (cmbn 1 6 'e 7 'f)))
-|#
-
-(DEFUN MRPH-VRTC-COBAR-INTR (mrph)
-  (declare (type morphism mrph))
-  (flet ((rslt (degr allp)
-               (declare
-                (ignore degr)
-                (type allp allp))
-               (the cmbn
-                 (ncmbn-cobar
-                   (mapcar #'(lambda (cbgn)
-                                (declare (type cbgn cbgn))
-                                (with-cbgn (degr gnrt) cbgn
-                                   (gnrt-? mrph (1+ degr) gnrt)))
-                      (allp-list allp))))))
-      (the intr-mrph #'rslt)))
-
-#|
-  (setf cc (build-chcm :cmpr #'f-cmpr :strt :cmbn))
-  (setf m (build-mrph :sorc cc :trgt cc :degr 0 :intr
-            #'(lambda (degr gnrt) (cmbn degr 2 gnrt 3 (1+ gnrt)))
-            :strt :gnrt :orgn '(test)))
-  (setf r (mrph-vrtc-cobar-intr m))
-  (funcall r 4 (allp 2 3 2 4))
-|#
-
-(DEFMETHOD VRTC-COBAR ((mrph morphism))
-   (the morphism
-      (if (eq (first (orgn mrph)) 'idnt-mrph)
-         (idnt-mrph (vrtc-cobar (sorc mrph)))
-         (build-mrph
-            :sorc (vrtc-cobar (sorc mrph))
-            :trgt (vrtc-cobar (trgt mrph))
-            :degr 0
-            :intr (mrph-vrtc-cobar-intr mrph)
-            :strt :gnrt
-            :orgn `(vrtc-cobar ,mrph)))))
-
-#|
-  (cat-init)
-  (setf f (aw (soft-delta-infinity) (soft-delta-infinity)))
-  (setf cf (vrtc-cobar f))
-  (? cf 2 (allp 1 (crpr 0 (d 7) 0 (d 7)) 1 (crpr 0 (d 56) 0 (d 56))))
-|#
-
-(DEFUN HMTP-VRTC-COBAR-INTR (h gf)
-   (declare (type morphism h gf))
-   (flet ((rslt (degr allp)
-             (declare
-                (fixnum degr)
-                (type allp allp))
-             (let* ((cbgn-list (reverse (allp-list allp)))
-                    (rslt (list nil))
-                    (sign (oddp (apply #'+ (mapcar #'car cbgn-list))))  ;; nil = -1 ;; t = +1
-                    (gfgf-tail (term-cmbn 0 1 +null-allp+)))
-                (declare
-                   (list cbgn-list rslt)
-                   (fixnum sign)
-                   (type cmbn gfgf-tail))
-                (unless cbgn-list
-                   (return-from rslt (zero-cmbn 1)))
-                (loop
-                   (let ((cbgn (car cbgn-list)))
-                      (declare (type cbgn cbgn))
-                      (with-cbgn (degr gnrt) cbgn
-                         (when (evenp degr)
-                            (setf sign (not sign)))
-                         (incf degr)
-                         (let ((h-gnrt (gnrt-? h degr gnrt)))
-                            (declare (type cmbn h-gnrt))
-                            (let ((hgfgf (cmbn-list (cmbn-allp-cmbn-tnpr h-gnrt gfgf-tail))))
-                               (declare (type cmbn hgfgf))
-                               (when sign
-                                  (mapc #'(lambda (term)
-                                             (declare (type term term))
-                                             (setf (cffc term) (- (cffc term))))
-                                     hgfgf))
-                               (setf cbgn-list (rest cbgn-list))
-                               (let ((head (reverse cbgn-list)))
-                                  (declare (list head))
-                                  (mapc #'(lambda (term)
-                                             (setf (allp-list (gnrt term))
-                                                   (append head (allp-list (gnrt term)))))
-                                     hgfgf))
-                               (nconc rslt hgfgf)))
-                         (unless cbgn-list (return))
-                         (setf gfgf-tail
-                               (cmbn-allp-cmbn-tnpr
-                                  (gnrt-? gf degr gnrt) gfgf-tail)))))
-                (make-cmbn
-                   :degr (1+ degr)
-                   :list (rest rslt)))))
-      (the intr-mrph #'rslt)))
-
-#|
-  (require "special-smsts")
-  (require "eilenberg-zilber")
-  (cat-init)
-  (setf ez (ez (delta-infinity) (delta-infinity)))
-  (setf h (h ez) gf (cmps (g ez) (f ez)))
-  (setf r (hmtp-vrtc-cobar-intr h gf))
-  (funcall r 3 (allp 1 (crpr 0 7 0 7) 1 (crpr 0 14 0 14) 1 (crpr 0 14 0 14)))
-|#
-
-(DEFUN HMTP-VRTC-COBAR (h gf)
-   (declare (type morphism h gf))
-   (unless (and (= +1 (degr h))
-                (= +0 (degr gf)))
-      (error "In HMTP-VRTC-COBAR, the morphism degrees are not the right ones."))
-   (unless (and (eq (sorc h) (trgt h))
-                (eq (trgt h) (sorc gf))
-                (eq (sorc gf) (trgt gf)))
-      (error "In HMTP-VRTC-COBAR, fg-h sources and targets are not the same."))
-   (the morphism
-      (if (eq (first (orgn h)) 'zero-mrph)
-         (zero-mrph (vrtc-cobar (sorc h)))
-         (build-mrph
-            :sorc (vrtc-cobar (sorc h)) :trgt (vrtc-cobar (sorc h)) :degr +1
-            :intr (hmtp-vrtc-cobar-intr h gf)
-            :strt :gnrt
-            :orgn `(hmtp-vrtc-cobar ,h ,gf)))))
-
-(DEFMETHOD VRTC-COBAR ((rdct reduction))
-   (the reduction
-      (if (eq (first (orgn rdct)) 'trivial-rdct)
-         (trivial-rdct (vrtc-cobar (bcc rdct)))
-         (with-slots (f g h) rdct
-            (build-rdct
-               :f (vrtc-cobar f)
-               :g (vrtc-cobar g)
-               :h (hmtp-vrtc-cobar h (cmps g f))
-               :orgn `(vrtc-cobar ,rdct))))))
-
-#|
-  (cat-init)
-  (setf tcc (build-chcm
-               :cmpr #'s-cmpr
-               :basis #'(lambda (degr) '(a b c d))
-               :bsgn 'd
-               :intr-dffr #'(lambda (degr gnrt)
-                               (ecase gnrt
-                                  (a (cmbn (1- degr) 1 'b 1 'd))
-                                  ((b d) (cmbn (1- degr)))
-                                  (c (cmbn (1- degr) 1 'd))))
-               :strt :gnrt
-               :orgn '(tcc)))
-  (setf bcc (build-chcm
-               :cmpr #'s-cmpr
-               :basis #'(lambda (degr) '(c d))
-               :bsgn 'd
-               :intr-dffr #'(lambda (degr gnrt)
-                               (ecase gnrt
-                                  (d (cmbn (1- degr)))
-                                  (c (cmbn (1- degr) 1 'd))))
-               :strt :gnrt
-               :orgn '(bcc)))
-  (setf f (build-mrph :sorc tcc :trgt bcc :degr 0
-             :intr #'(lambda (degr gnrt)
-                        (ecase gnrt
-                           (a (cmbn degr 1 'c 1 'd))
-                           (b (cmbn degr))
-                           ((c d) (cmbn degr 1 gnrt))))
-             :strt :gnrt :orgn '(f)))
-  (setf g (build-mrph :sorc bcc :trgt tcc :degr 0
-             :intr #'identity :strt :cmbn :orgn '(g)))
-  (setf h (build-mrph :sorc tcc :trgt tcc :degr +1
-             :intr #'(lambda (degr gnrt)
-                        (ecase gnrt
-                           ((a b) (cmbn (1+ degr) 1 'a -1 'b -1 'c -1 'd))
-                           ((c d) (cmbn (1+ degr)))))
-             :strt :gnrt :orgn '(h)))
-  (setf rdct (build-rdct :f f :g g :h h :orgn '(rdct)))
-  (tcc rdct 3 'a)
-  (g rdct (f rdct 3 'a))
-  (h rdct 3 'a)
-  (setf cobar (vrtc-cobar rdct))
-  (pre-check-rdct cobar)
-  (defun aleat-tc ()
-     (do ((tdegr 0 (+ tdegr degr))
-          (degr (1+ (random 4)) (1+ (random 4)))
-          (gnrt (intern (coerce (vector (+ 65 (random 4))) 'string))
-                (intern (coerce (vector (+ 65 (random 4))) 'string)))
-          (rslt nil (cons (cbgn degr gnrt) rslt)))
-         ((> tdegr 10) (setf *tc* (cmbn tdegr 1 (make-allp :list rslt))))))
-  (aleat-tc)
-  (defun aleat-bc ()
-     (do ((tdegr 0 (+ tdegr degr))
-          (degr (1+ (random 4)) (1+ (random 4)))
-          (gnrt (intern (coerce (vector (+ 67 (random 2))) 'string))
-                (intern (coerce (vector (+ 67 (random 2))) 'string)))
-          (rslt nil (cons (cbgn degr gnrt) rslt)))
-         ((> tdegr 10) (setf *bc* (cmbn tdegr 1 (make-allp :list rslt))))))
-  (aleat-bc)
-  (defun c ()
-     (aleat-tc)
-     (aleat-bc)
-     (check-rdct))
-  (loop (c))  ;; degrees >= 15 is possible => error.
-|#
-
-(DEFMETHOD VRTC-COBAR ((hmeq homotopy-equivalence))
-   (the homotopy-equivalence
-      (if (eq (first (orgn hmeq)) 'trivial-hmeq)
-         (trivial-hmeq (vrtc-cobar (lbcc hmeq)))
-         (with-slots (lrdct rrdct) hmeq
-            (build-hmeq 
-               :lrdct (vrtc-cobar lrdct)
-               :rrdct (vrtc-cobar rrdct)
-               :orgn `(vrtc-cobar ,hmeq))))))
-
-(DEFMETHOD COBAR ((hmeq homotopy-equivalence))
-   (unless (typep (lbcc hmeq) 'coalgebra)
-      (error "In (COBAR HMEQ), the LBCC should be a coalgebra."))
-   (the homotopy-equivalence
-      (if (eq (first (orgn hmeq)) 'trivial-hmeq)
-         (trivial-hmeq (cobar (lbcc hmeq)))
-         (add (vrtc-cobar hmeq) (cobar-hrzn-dffr (lbcc hmeq))))))
-
-#|
-  (cat-init)
-  (setf h (left-hmeq (sphere 3)))
-  (setf c (cobar h))
-  (inspect c)
-|#
\ No newline at end of file
diff --git a/archive/Kenzo-1/combinations.cl b/archive/Kenzo-1/combinations.cl
deleted file mode 100644
index 285dd66..0000000
--- a/archive/Kenzo-1/combinations.cl
+++ /dev/null
@@ -1,674 +0,0 @@
-;;;  COMBINATIONS  COMBINATIONS  COMBINATIONS  COMBINATIONS  COMBINATIONS
-;;;  COMBINATIONS  COMBINATIONS  COMBINATIONS  COMBINATIONS  COMBINATIONS
-;;;  COMBINATIONS  COMBINATIONS  COMBINATIONS  COMBINATIONS  COMBINATIONS
-
-(IN-PACKAGE "COMMON-LISP-USER")
-
-(provide "combinations")
-
-;;;;
-;;;;  COMPARISONS.
-;;;;
-
-
-(DEFUN CMBN-PRINT (cmbn stream depth)
-  (declare
-   (type cmbn cmbn) (stream stream)
-   (ignore depth))
-  (the cmbn
-    (with-cmbn (degr list) cmbn
-               (format stream "~%~70@{-~}{CMBN ~D}" degr)
-               (do ((mark list (cdr mark))
-                    (nth 0 (1+ nth)))
-                   ((endp mark))
-                 (declare
-                  (list mark)
-                  (fixnum nth))
-                 (when (and *print-length* (= nth *print-length*))
-                   (format stream "~%... ...")
-                   (return))
-                 (format stream "~%<~D * ~A>" (-cffc mark) (-gnrt mark)))
-               (format stream "~%~78@{-~}~%" t)
-               cmbn)))
-
-
-(DEFUN MAPLEXICO (cmpr list1 list2)
-   (declare
-      (type cmprf cmpr)
-      (list list1 list2))
-   (the boolean
-      (do ((mark1 list1 (cdr mark1))
-           (mark2 list2 (cdr mark2)))
-          (nil)
-         (declare (list mark1 mark2))
-         (unless mark1
-            (return-from maplexico
-               (if mark2 :less :equal)))
-         (unless mark2
-            (return-from maplexico :greater))
-         (case (funcall cmpr (car mark1) (car mark2))
-            (:less (return-from maplexico :less))
-            (:greater (return-from maplexico :greater))))))
-
-#|
-  (maplexico #'f-cmpr '(1 2 3) '(1 3))
-  (maplexico #'f-cmpr '(1 2 3) '(1 1))
-  (maplexico #'f-cmpr '(1 1) '(1 1 0))
-  (maplexico #'f-cmpr '(1 1 0) '(1 1))
-  (maplexico #'f-cmpr '(1 1) '(1 1))
-  (maplexico #'f-cmpr nil nil)
-|#
-
-(DEFUN S-CMPR (symbol1 symbol2)
-   (declare (symbol symbol1 symbol2))
-   (the cmpr
-      (if (#+aclpc acl:whole-string<
-          #-aclpc string< symbol1 symbol2)
-         :less
-         (if (#+aclpc acl:whole-string=
-              #-aclpc string= symbol1 symbol2)
-            :equal
-            :greater))))
-
-(DEFUN F-CMPR (n1 n2)
-   (declare (fixnum n1 n2))
-   (the cmpr
-      (if (< n1 n2)
-         :less
-         (if (= n1 n2)
-            :equal
-            :greater))))
-
-(DEFUN L-CMPR (list1 list2)
-  (declare (list list1 list2))
-  (unless list1
-    (return-from l-cmpr (if list2 :less :equal)))
-  (unless list2
-    (return-from l-cmpr :greater))
-  (if (symbolp (first list1))
-      (if (symbolp (first list2))
-          (lexico
-           (s-cmpr (first list1) (first list2))
-           (l-cmpr (rest list1) (rest list2)))
-        :greater)
-    (if (symbolp (first list2))
-        :less
-      (lexico
-       (f-cmpr (first list1) (first list2))
-       (l-cmpr (rest list1) (rest list2))))))
-
-#|
-  (s-cmpr 'a 'b)
-  (s-cmpr 'b 'b)
-  (s-cmpr 'c 'b)
-  (f-cmpr 1 2)
-  (f-cmpr 2 2)
-  (f-cmpr 3 2)
-  (l-cmpr nil nil)
-  (l-cmpr nil '(1))
-  (l-cmpr '(1) nil)
-  (l-cmpr '(a) '(a))
-  (l-cmpr '(a) '(1))
-  (l-cmpr '(1) '(a))
-  (l-cmpr '(1) '(1))
-  (l-cmpr '(1 a) '(1 1))
-  (l-cmpr '(1 a) '(1 a b)))
-|# 
-
-
-;;;;
-;;;;  COMBINATIONS
-;;;;
-
-
-#|
-(DEFUN CMBN (degr &rest rest)
-   (declare (fixnum degr))
-   (the cmbn
-      (let ((rslt (list degr :cmbn)))
-	(do ((mark rest (cddr mark)))
-	    ((endp mark) (nreverse rslt))
-	   (declare (list mark))
-	   (push (term (car mark) (cadr mark)) rslt)))))
-|#
-
-(DEFUN CMBN (degr &rest rest)
-   (declare (fixnum degr))
-   (the cmbn
-     (make-cmbn :degr degr
-                :list (do ((rslt +empty-list+
-                                 (cons (term (car mark) (cadr mark)) rslt))
-                           (mark rest (cddr mark)))
-                          ((endp mark) (nreverse rslt))
-                        (declare (list rslt mark))))))
-
-
-#|
-  (cmbn 2)
-  (cmbn 2 2 'a)
-  (cmbn 2 'a)
-  (cmbn 2 2 'a -3 'b))
-  (term-cmbn 3 -5 'a)
-|#
-
-#+allegro
-(setf *print-pretty* nil)
-
-
-(DEFUN CHECK-CMBN (chcm cmbn)
-  (declare
-    (type chain-complex chcm)
-    (type cmbn cmbn))
-  (the boolean
-    (do ((cmpr (cmpr chcm))
-	 (mark2 (cmbn-list cmbn) mark1)
-	 (mark1 (rest (cmbn-list cmbn)) (cdr mark1)))
-	((endp mark1) t)
-	(declare
-	  (type cmprf cmpr)
-	  (list mark1 mark2))
-      (unless (eq :less (funcall cmpr (-gnrt mark2) (-gnrt mark1)))
-	(error "In CHECK-CMBN, bad order; the generator:~@
-                ~A~@
-                is not less than the generator:~@
-                ~A."
-	       (-gnrt mark2) (-gnrt mark1))))))
-
-(DEFUN ZERO-CMBN (degr)
-   (declare (fixnum degr))
-   (the cmbn
-      (make-cmbn
-       :degr degr
-       :list +empty-list+)))
-
-#|
-  (zero-cmbn 3))
-|#  
-
-(DEFUN ZERO-INTR-DFFR (cmbn)
-   (declare (type cmbn cmbn))
-   (the cmbn (zero-cmbn (1- (cmbn-degr cmbn)))))
-
-#|
-  (zero-intr-dffr (cmbn 2))
-|#
-
-(DEFCONSTANT +ZERO-NEGATIVE-CMBN+
-   (make-cmbn :degr -1 :list +empty-list+))
-
-#|
-  (cmbn-non-zero-p (cmbn 0))
-  (cmbn-non-zero-p (cmbn 0 1 'a)))
-  (cmbn-zero-p (cmbn 0))
-  (cmbn-zero-p (cmbn 0 1 'a)))
-|#
-
-(DEFUN CMBN-OPPS (cmbn)
-   (declare (type cmbn cmbn))
-   (the cmbn
-      (with-cmbn (degr list) cmbn
-         (make-cmbn
-            :degr degr
-            :list (mapcar #'(lambda (term)
-                               (declare (type term term))
-                               (with-term (cffc gnrt) term
-                                  (term (- cffc) gnrt)))
-                     list)))))
-
-#|
-  (setf c (cmbn 0 1 'a -2 'b))
-  (cmbn-opps c)
-  (symbol-value 'c))
-|#
-
-(DEFUN N-CMBN (n cmbn)
-   ;; n is assumed non-zero
-   (declare
-      (fixnum n)
-      (type cmbn cmbn))
-   (the cmbn
-      (if (= n 1)
-         cmbn
-         (with-cmbn (degr list) cmbn
-            (make-cmbn
-               :degr degr
-               :list (mapcar #'(lambda (term)
-                                  (declare (type term term))
-                                  (with-term (cffc gnrt) term
-                                     (term (* n cffc) gnrt)))
-                        list))))))
-
-#|
-  (setf c (cmbn 2 3 'a))
-  (setf c2 (n-cmbn 1 c))
-  (eq c c2)
-  (n-cmbn -1 c)
-  (n-cmbn -3 c))
-|#
-
-(DEFUN 2CMBN-ADD (cmpr cmbn1 cmbn2)
-   (declare
-      (type cmprf cmpr)
-      (type cmbn cmbn1 cmbn2))
-   (the cmbn
-      (with-cmbn (degr1 list1) cmbn1
-      (with-cmbn (degr2 list2) cmbn2
-         (unless (= degr1 degr2)
-            (error "In ADD, the combination arguments have different degrees ~D and ~D."
-               degr1 degr2))
-         (unless list1
-            (return-from 2cmbn-add cmbn2))
-         (unless list2
-            (return-from 2cmbn-add cmbn1))
-         (let ((pre-rslt +empty-list+)
-               (mark1 list1)
-               (mark2 list2))
-            (declare (list pre-rslt mark1 mark2))
-            (with--term (cffc1 gnrt1) mark1
-            (with--term (cffc2 gnrt2) mark2
-               (tagbody
-                  :begin
-                  (ecase (funcall cmpr gnrt1 gnrt2)
-                     (:equal
-                      (let ((cffc (+ cffc1 cffc2)))
-                         (declare (fixnum cffc))
-                         (unless (zerop cffc)
-                            (push (term cffc gnrt1) pre-rslt))
-                         (setf mark1 (cdr mark1)
-                               mark2 (cdr mark2))
-                         (unless mark1 (go :cmbn1-is-finished))
-                         (unless mark2 (go :cmbn2-is-finished))
-                         (setf cffc1 (-cffc mark1)
-                               gnrt1 (-gnrt mark1)
-                               cffc2 (-cffc mark2)
-                               gnrt2 (-gnrt mark2))
-                         (go :begin)))
-                     (:less
-                      (push (-term mark1) pre-rslt)
-                      (setf mark1 (cdr mark1))
-                      (unless mark1 (go :cmbn1-is-finished))
-                      (setf cffc1 (-cffc mark1)
-                            gnrt1 (-gnrt mark1))
-                      (go :begin))
-                     (:greater
-                      (push (-term mark2) pre-rslt)
-                      (setf mark2 (cdr mark2))
-                      (unless mark2 (go :cmbn2-is-finished))
-                      (setf cffc2 (-cffc mark2)
-                            gnrt2 (-gnrt mark2))
-                      (go :begin)))
-                  :cmbn1-is-finished
-                  (setf pre-rslt (nreconc pre-rslt mark2))
-                  (go :exit)
-                  :cmbn2-is-finished
-                  (setf pre-rslt (nreconc pre-rslt mark1))
-                  :exit))
-            (make-cmbn :degr degr1 :list pre-rslt)))))))
-
-#|
-  (2cmbn-add #'s-cmpr (cmbn 0) (cmbn 1))
-  (2cmbn-add #'s-cmpr (cmbn 0) (cmbn 0))
-  (2cmbn-add #'s-cmpr (cmbn 0 1 'a) (cmbn 0))
-  (2cmbn-add #'s-cmpr (cmbn 0 1 'a) (cmbn 0 2 'a))
-  (2cmbn-add #'s-cmpr (cmbn 0 1 'a) (cmbn 0 -1 'a))
-  (2cmbn-add #'s-cmpr (cmbn 0 1 'a) (cmbn 0 2 'b))
-  (2cmbn-add #'s-cmpr (cmbn 0 2 'b) (cmbn 0 1 'a))
-  (2cmbn-add #'s-cmpr (cmbn 0 1 'a -2 'b) (cmbn 0 2 'b))
-  (2cmbn-add #'s-cmpr (cmbn 0 2 'b) (cmbn 0 1 'a 3 'c)))
-|#
-
-(DEFUN 2CMBN-SBTR (cmpr cmbn1 cmbn2)
-   (declare
-      (type cmprf cmpr)
-      (type cmbn cmbn1 cmbn2))
-   (the cmbn
-      (with-cmbn (degr1 list1) cmbn1
-      (with-cmbn (degr2 list2) cmbn2
-         (unless (= degr1 degr2)
-            (error "In SBTR, the combination arguments have different degrees ~D and ~D."
-               degr1 degr2))
-         (unless list1
-            (return-from 2cmbn-sbtr (cmbn-opps cmbn2)))
-         (unless list2
-            (return-from 2cmbn-sbtr cmbn1))
-         (let ((pre-rslt +empty-list+)
-               (mark1 list1)
-               (mark2 list2))
-            (declare (list pre-rslt mark1 mark2))
-            (with--term (cffc1 gnrt1) mark1
-            (with--term (cffc2 gnrt2) mark2
-               (tagbody
-                  :begin
-                  (ecase (funcall cmpr gnrt1 gnrt2)
-                     (:equal
-                      (let ((cffc (- cffc1 cffc2)))
-                         (declare (fixnum cffc))
-                         (unless (zerop cffc)
-                            (push (term cffc gnrt1) pre-rslt))
-                                                  (unless mark1 (go :cmbn1-is-finished))
-                         (setf mark1 (cdr mark1)
-                               mark2 (cdr mark2))
-                         (unless mark1 (go :cmbn1-is-finished))
-                         (unless mark2 (go :cmbn2-is-finished))
-                         (setf cffc1 (-cffc mark1)
-                               gnrt1 (-gnrt mark1)
-                               cffc2 (-cffc mark2)
-                               gnrt2 (-gnrt mark2))
-                         (go :begin)))
-                     (:less
-                      (push (-term mark1) pre-rslt)
-                      (setf mark1 (cdr mark1))
-                      (unless mark1 (go :cmbn1-is-finished))
-                      (setf cffc1 (-cffc mark1)
-                            gnrt1 (-gnrt mark1))
-                      (go :begin))
-                     (:greater
-                      (push (term (- cffc2) gnrt2) pre-rslt)
-                      (setf mark2 (cdr mark2))
-                      (unless mark2 (go :cmbn2-is-finished))
-                      (setf cffc2 (-cffc mark2)
-                            gnrt2 (-gnrt mark2))
-                      (go :begin)))
-                  :cmbn1-is-finished
-                  (setf pre-rslt
-                        (nreconc pre-rslt
-                           (mapcar #'(lambda (term)
-                                        (declare (cons term))
-                                        (with-term (cffc gnrt) term
-                                           (term (- cffc) gnrt)))
-                              mark2)))
-                  (go :exit)
-                  :cmbn2-is-finished
-                  (setf pre-rslt (nreconc pre-rslt mark1))
-                  :exit))
-            (make-cmbn
-               :degr degr1
-               :list pre-rslt)))))))
-
-#|
-  (2cmbn-sbtr #'s-cmpr (cmbn 0) (cmbn 1))
-  (2cmbn-sbtr #'s-cmpr (cmbn 0) (cmbn 0))
-  (2cmbn-sbtr #'s-cmpr (cmbn 0) (cmbn 0 1 'a))
-  (2cmbn-sbtr #'s-cmpr (cmbn 0 2 'b) (cmbn 0))
-  (2cmbn-sbtr #'s-cmpr (cmbn 0 3 'b) (cmbn 0 3 'b))
-  (2cmbn-sbtr #'s-cmpr (cmbn 0 3 'b) (cmbn 0 4 'b))
-  (2cmbn-sbtr #'s-cmpr
-    (cmbn 0 1 'a 2 'c  2 'd       3 'g)
-    (cmbn 0      1 'c -2 'd 4 'f -3 'g 4 'h))
-  (2cmbn-sbtr #'s-cmpr
-    (cmbn 0      1 'c -2 'd 4 'f -3 'g 4 'h)
-    (cmbn 0 1 'a 2 'c  2 'd       3 'g))
-  (2cmbn-sbtr #'s-cmpr
-    (cmbn 0      1 'c -2 'd 4 'f -3 'g)
-    (cmbn 0 1 'a 2 'c  2 'd       3 'g))
-  (2cmbn-sbtr #'s-cmpr
-    (cmbn 0 1 'b 2 'a)
-    (cmbn 0 1 'a 1 'b)))  ;;; !!!
-  (2cmbn-sbtr #'s-cmpr
-    (cmbn 0 1 'b 2 'c)
-    (cmbn 0 1 'a 1 'b)))
-|#
-
-(DEFUN 2N-2CMBN (cmpr n1 cmbn1 n2 cmbn2)
-   ;; n1 * cmbn1 + n2 * cmbn2
-   ;; combinations may be null but not n1 and n2
-   (declare
-      (type cmprf cmpr)
-      (fixnum n1 n2)
-      (type cmbn cmbn1 cmbn2))
-   (the cmbn
-      (with-cmbn (degr1 list1) cmbn1
-      (with-cmbn (degr2 list2) cmbn2
-         (unless (= degr1 degr2)
-            (error "In 2N-2CMBN, the combination arguments have different degrees ~D and ~D."
-               degr1 degr2))
-         (unless list1
-            (return-from 2n-2cmbn (n-cmbn n2 cmbn2)))
-         (unless list2
-            (return-from 2n-2cmbn (n-cmbn n1 cmbn1)))
-         (let ((pre-rslt +empty-list+)
-               (mark1 list1)
-               (mark2 list2))
-            (declare (list pre-rslt mark1 mark2))
-            (with--term (cffc1 gnrt1) mark1
-            (with--term (cffc2 gnrt2) mark2
-               (setf cffc1 (* n1 cffc1)
-                     cffc2 (* n2 cffc2))
-               (tagbody
-                  :begin
-                  (ecase (funcall cmpr gnrt1 gnrt2)
-                     (:equal
-                      (let ((cffc (+ cffc1 cffc2)))
-                         (declare (fixnum cffc))
-                         (unless (zerop cffc)
-                            (push (term cffc gnrt1) pre-rslt))
-                         (setf mark1 (cdr mark1)
-                               mark2 (cdr mark2))
-                         (unless mark1 (go :cmbn1-is-finished))
-                         (unless mark2 (go :cmbn2-is-finished))
-                         (setf cffc1 (* n1 (-cffc mark1))
-                               gnrt1 (-gnrt mark1)
-                               cffc2 (* n2 (-cffc mark2))
-                               gnrt2 (-gnrt mark2))
-                         (go :begin)))
-                     (:less
-                      (push (term cffc1 gnrt1) pre-rslt)
-                      (setf mark1 (cdr mark1))
-                      (unless mark1 (go :cmbn1-is-finished))
-                      (setf cffc1 (* n1 (-cffc mark1))
-                            gnrt1 (-gnrt mark1))
-                      (go :begin))
-                     (:greater
-                      (push (term cffc2 gnrt2) pre-rslt)
-                      (setf mark2 (cdr mark2))
-                      (unless mark2 (go :cmbn2-is-finished))
-                      (setf cffc2 (* n2 (-cffc mark2))
-                            gnrt2 (-gnrt mark2))
-                      (go :begin)))
-                  :cmbn1-is-finished
-                  (setf pre-rslt
-                        (nreconc pre-rslt
-                           (if (= 1 n2)
-                              mark2
-                              (mapcar #'(lambda (term)
-                                           (declare (cons term))
-                                           (with-term (cffc gnrt) term
-                                              (term (* n2 cffc) gnrt)))
-                                 mark2))))
-                  (go :exit)
-                  :cmbn2-is-finished
-                  (setf pre-rslt
-                        (nreconc pre-rslt
-                           (if (= 1 n1)
-                              mark1
-                              (mapcar #'(lambda (term)
-                                           (declare (cons term))
-                                           (with-term (cffc gnrt) term
-                                              (term (* n1 cffc) gnrt)))
-                                 mark1))))
-                  :exit))
-            (make-cmbn
-               :degr degr1
-               :list pre-rslt)))))))
-
-#|
-  (2n-2cmbn #'s-cmpr 3 (cmbn 0) 4 (cmbn 1))
-  (2n-2cmbn #'s-cmpr 3 (cmbn 0) 4 (cmbn 0))
-  (2n-2cmbn #'s-cmpr 3 (cmbn 0 1 'a) 4 (cmbn 0))
-  (2n-2cmbn #'s-cmpr 3 (cmbn 0  1 'a 2 'b 3 'c     )
-                     1 (cmbn 0 -3 'a 2 'b      4 'd))
-  (2n-2cmbn #'s-cmpr 3 (cmbn 0 -3 'a 2 'b     4 'd)
-                     1 (cmbn 0  1 'a 2 'b 3 'c    ))
-  (2n-2cmbn #'s-cmpr 1 (cmbn 0  1 'a 2 'b 3 'c     )
-                     1 (cmbn 0 -3 'a 2 'b      4 'd))
-  (2n-2cmbn #'s-cmpr 1 (cmbn 0 -3 'a 2 'b     4 'd)
-                     1 (cmbn 0  1 'a 2 'b 3 'c    ))
-  (2n-2cmbn #'s-cmpr 1 (cmbn 0 -3 'a 2 'b     4 'd)
-                     3 (cmbn 0  1 'a 2 'b 3 'c    )))
-|#
-
-(DEFUN CMBN-CMBN (cmpr n-cmbn-list)
-  ;; n-cmbn-list = list of (cons n cmbn)
-  ;;               non-empty-list
-  ;;            every n is non-null
-  (declare
-     (type cmprf cmpr)
-     (list n-cmbn-list))
-  (unless (rest n-cmbn-list)
-     (return-from cmbn-cmbn
-	(n-cmbn (caar n-cmbn-list) (cdar n-cmbn-list))))
-  (unless (cddr n-cmbn-list)
-     (return-from cmbn-cmbn
-	(2n-2cmbn cmpr
-		  (caar n-cmbn-list) (cdar n-cmbn-list)
-		  (caadr n-cmbn-list) (cdadr n-cmbn-list))))
-  (the cmbn
-     (let ((new-rslt +empty-list+))
-        (declare (list new-rslt))
-	(do ((mark1 (rest n-cmbn-list) (cddr mark1))
-	     (mark2 n-cmbn-list (cdr mark1)))
-	    ((endp mark2))
-	   (declare (list mark1 mark2))
-	   (when (endp mark1)
-	      (push (n-cmbn (caar mark2) (cdar mark2)) new-rslt)
-	      (return))
-	   (push (2n-2cmbn cmpr
-			   (caar mark2) (cdar mark2)
-			   (caar mark1) (cdar mark1))
-		 new-rslt))
-	(let ((old-rslt +empty-list+))
-	  (declare (list old-rslt))
-	  (loop
-	   (unless (rest new-rslt)
-	      (return-from cmbn-cmbn (first new-rslt)))
-	   (setf old-rslt new-rslt
-		 new-rslt +empty-list+)
-	   (do ((mark1 (rest old-rslt) (cddr mark1))
-		(mark2 old-rslt (cdr mark1)))
-	       ((endp mark2))
-	      (declare (list mark1 mark2))
-	      (when (endp mark1)
-		 (push (car mark2) new-rslt)
-		 (return))
-	      (push (2cmbn-add cmpr (car mark2) (car mark1))
-		    new-rslt)))))))
-
-#|
-  (setf cons (cons 3 (cmbn 0 4 'a)))
-  (cmbn-cmbn #'s-cmpr (make-list 5 :initial-element cons))
-  (dotimes (i 10)
-     (print
-       (cffc (first (cmbn-list
-          (cmbn-cmbn #'s-cmpr (make-list (1+ i) :initial-element cons))))))))
-|#
-
-(DEFUN NTERM-ADD (cmpr degr &rest rest)
-   (declare
-      (type cmprf cmpr)
-      (fixnum degr)
-      (list rest))
-      ;; (list term)
-   (unless rest
-      (return-from nterm-add (zero-cmbn degr)))
-   (the cmbn
-      (let ((rslt (list (first rest))))
-         (declare (list rslt))
-         (dolist (term (rest rest))
-            (declare (type term term))
-            (with-term  (cffc gnrt) term
-               (do ((mark1 rslt (cdr mark1))
-                    (mark2 nil mark1))
-                   ((endp mark1) (setf (cdr mark2) (list term)))
-                  (ecase (funcall cmpr gnrt (-gnrt mark1))
-                     (:less
-                      (if mark2
-                         (push term (cdr mark2))
-                         (push term rslt))
-                      (return))                     
-                     (:equal
-                      (incf (-cffc mark1) cffc)
-                      (return))                     
-                     (:greater )))))
-         (make-cmbn
-            :degr degr
-            :list (delete 0 rslt :key #'car)))))
-
-#|
-  (nterm-add #'s-cmpr 11)
-  (nterm-add #'s-cmpr 11 (term 1 'a))
-  (nterm-add #'s-cmpr 11 (term 1 'a) (term 2 'b))
-  (nterm-add #'s-cmpr 11 (term 1 'b) (term 2 'a) (term 3 'aa)
-                         (term -2 'aa) (term -2 'a) (term 4 'aab)
-                         (term 5 'c))
-|#
-
-(DEFUN NCMBN-ADD (cmpr cmbn &rest rest)
-   (declare
-      (type cmprf cmpr)
-      (type cmbn cmbn))
-   (the cmbn
-      (cmbn-cmbn cmpr (mapcar #'(lambda (cmbn)
-                                   (declare (type cmbn cmbn))
-                                   (cons 1 cmbn))
-                         (cons cmbn rest)))))
-
-#|
-  (setf c (cmbn 3 4 'a))
-  (ncmbn-add #'s-cmpr c c c c c)
-|#
-
-(DEFUN DSTR-ADD-TERM-TO-CMBN (cmpr cffc gnrt cmbn)
-   (declare
-      (type cmprf cmpr)
-      (fixnum cffc)  ;; non-zero
-      (type gnrt gnrt)
-      (type cmbn cmbn))
-   (the cmbn
-      (let ((list (cmbn-list cmbn)))
-         (declare (list list))
-         (unless list
-            (push (term cffc gnrt) (cmbn-list cmbn))
-            (return-from dstr-add-term-to-cmbn cmbn))
-         (do ((mark2 nil mark1)
-              (mark1 list (cdr mark1)))
-             ((endp mark1) (setf (cdr mark2) (list (term cffc gnrt))))
-            (declare (list mark1 mark2))
-            (ecase (funcall cmpr gnrt (-gnrt mark1))
-               (:less
-                (if mark2
-                   (push (term cffc gnrt) (cdr mark2))
-                   (push (term cffc gnrt) (cmbn-list cmbn)))
-                (return))
-               (:equal
-                (let ((new-cffc (+ cffc (-cffc mark1))))
-                   (declare (fixnum new-cffc))
-                   (if (zerop new-cffc)
-                      (if mark2
-                         (pop (cdr mark2))
-                         (pop (cmbn-list cmbn)))
-                      (setf (-cffc mark1) new-cffc))
-                   (return)))
-               (:greater)))
-         cmbn)))
-
-#|
-()
-(setf c (zero-cmbn 10))
-(dstr-add-term-to-cmbn #'s-cmpr 3 'f c)
-(eq * c)
-(dstr-add-term-to-cmbn #'s-cmpr 3 'g c)
-(eq * c)
-(dstr-add-term-to-cmbn #'s-cmpr 3 'a c)
-(eq * c)
-(dstr-add-term-to-cmbn #'s-cmpr 3 'd c)
-(eq * c)
-(dstr-add-term-to-cmbn #'s-cmpr -3 'd c)
-(eq * c)
-(dstr-add-term-to-cmbn #'s-cmpr -2 'a c)
-(dstr-add-term-to-cmbn #'s-cmpr -1 'a c)
-(eq * c)
-(dstr-add-term-to-cmbn #'s-cmpr -3 'g c)
-(eq * c)
-(dstr-add-term-to-cmbn #'s-cmpr -3 'f c)
-(eq * c))
-|#
diff --git a/archive/Kenzo-1/cones.cl b/archive/Kenzo-1/cones.cl
deleted file mode 100644
index 1de1743..0000000
--- a/archive/Kenzo-1/cones.cl
+++ /dev/null
@@ -1,368 +0,0 @@
-;;;  CONES  CONES  CONES  CONES  CONES  CONES  CONES  CONES  CONES  CONES
-;;;  CONES  CONES  CONES  CONES  CONES  CONES  CONES  CONES  CONES  CONES
-;;;  CONES  CONES  CONES  CONES  CONES  CONES  CONES  CONES  CONES  CONES
-
-(IN-PACKAGE "COMMON-LISP-USER")
-
-(PROVIDE "cones")
-
-(DEFUN CONE-PRINT (cone stream depth)
-  (declare
-   (type cone cone)
-   (stream stream)
-   (ignore depth))
-  (the cone
-    (with-cone (conx icon) cone
-      (format stream "<CONE ~D" conx)
-      (do ((mark icon))
-          ((not (typep mark 'cone))
-           (format stream " ~A>" mark))
-        (declare (type gnrt icon))
-        (with-cone (conx icon) mark
-          (format stream "-~D" conx)
-          (setf mark icon)))
-      cone)))
-
-#|
-()
-(con0 'a)
-(con1 'a)
-(con0 (con0 'a))
-(con0 (con1 'a))
-(con1 (con0 'a))
-(con1 (con1 'a))
-(con0 (con1 (con0 (con1 'a))))
-|#
-
-(DEFUN CONE-CMPR (cmpr0 cmpr1)
-  (declare (type cmprf cmpr0 cmpr1))
-  (the cmprf
-    (flet ((rslt (gnrt1 gnrt2)
-             (declare (type cone gnrt1 gnrt2))
-             (the cmpr
-               (let ((ind1 (conx gnrt1))
-                     (ind2 (conx gnrt2))
-                     (gnrt11 (icon gnrt1))
-                     (gnrt22 (icon gnrt2)))
-                 (declare
-                  (fixnum ind1 ind2)
-                  (type gnrt gnrt11 gnrt22))
-                 (ecase ind1
-                   (0 (ecase ind2
-                        (0 (funcall cmpr0 gnrt11 gnrt22))
-                        (1 :less)))
-                   (1 (ecase ind2
-                        (0 :greater)
-                        (1 (funcall cmpr1 gnrt11 gnrt22)))))))))
-      (declare (ftype (function (cone cone) cmpr) rslt))
-      #'rslt)))
-
-#|
-()
-(setf cmpr (cone-cmpr #'s-cmpr #'f-cmpr))
-(funcall cmpr (con0 'a) (con0 'b))
-(funcall cmpr (con0 'b) (con0 'b))
-(funcall cmpr (con0 'b) (con0 'a))
-(funcall cmpr (con0 'b) (con1 '2))
-(funcall cmpr (con1 '2) (con0 'b))
-(funcall cmpr (con1 '1) (con1 '2))
-(funcall cmpr (con1 '2) (con1 '2))
-(funcall cmpr (con1 '2) (con1 '1))
-|#
-
-(DEFUN CONE-BASIS (basis0 basis1)
-  (declare (type basis basis0 basis1))
-  (the basis
-    (progn
-      (when (or (eq basis0 :locally-effective)
-                (eq basis1 :locally-effective))
-        (return-from cone-basis :locally-effective))
-      (flet ((rslt (degr)
-               (declare (type fixnum degr))
-               (the list
-                 (append
-                  (mapcar #'(lambda (item) (con0 item))
-                    (funcall basis0 degr))
-                  (mapcar #'(lambda (item) (con1 item))
-                    (funcall basis1 (1- degr)))))))
-        (declare (ftype (function (fixnum) list) rslt))
-        #'rslt))))
-
-#|
-()
-(setf basis (cone-basis
-             #'(lambda (n) (list n))
-             #'(lambda (n) (list n))))
-(funcall basis 4)
-|#
-
-(DEFUN TERM-CON0 (term)
-  (declare (type term term))
-  (the term
-    (term (cffc term)
-          (con0 (gnrt term)))))
-(DEFUN TERM-CON1 (term)
-  (declare (type term term))
-  (the term
-    (term (cffc term)
-          (con1 (gnrt term)))))
-(DEFUN TERM-UNCON (term)
-  (declare (type term term))
-  (the term
-    (term (cffc term) (icon (gnrt term)))))
-
-#|
-()
-(term-con0 (term 2 'a))
-(term-con1 (term 2 'a))
-(term-uncon (term 2 (con0 'a)))
-|#
-
-(DEFUN CMBN-CON0 (cmbn)
-  (declare (type cmbn cmbn))
-  (the cmbn
-    (make-cmbn
-     :degr (cmbn-degr cmbn)
-     :list (mapcar #'term-con0 (cmbn-list cmbn)))))
-
-(DEFUN CMBN-CON1 (cmbn)
-  (declare (type cmbn cmbn))
-  (the cmbn
-    (make-cmbn
-     :degr (cmbn-degr cmbn)
-     :list (mapcar #'term-con1 (cmbn-list cmbn)))))
-
-#|
-()
-(cmbn-con0 (cmbn 3 1 'a 2 'b))
-(cmbn-con1 (cmbn 3 1 'a 2 'b))
-|#
-
-(DEFUN CONE-CMBN-SPLIT (cmbn)
-  (declare (type cmbn cmbn))
-  (the (values cmbn cmbn)
-    (with-cmbn (degr list) cmbn
-      (let ((list0 +empty-list+)
-            (list1 +empty-list+))
-        (declare (type list list0 list1))
-        (do ((mark list (cdr mark)))
-            ((endp mark)
-             (setf list0 (nreverse list0)
-                   list1 +empty-list+))
-          (declare (type list mark))
-          (when (eql 1 (conx (cdar mark)))
-            (setf list0 (nreverse list0)
-              list1 (mapcar #'term-uncon mark))
-            (return))
-          (push (term-uncon (car mark)) list0))
-        (values (make-cmbn :degr degr :list list0)
-                (make-cmbn :degr (1- degr) :list list1))))))
-
-#|
-()
-(cone-cmbn-split
- (cmbn 3 4 (con0 'a) 5 (con1 'b)))
-(cone-cmbn-split (cmbn 3 4 (con0 'a)))
-(cone-cmbn-split (cmbn 3 4 (con1 'a)))
-|#
-
-(DEFUN CONE-2CMBN-APPEND (cmbn0 cmbn1)
-  (declare (type cmbn cmbn0 cmbn1))
-  (the cmbn
-    (make-cmbn
-     :degr (cmbn-degr cmbn0)
-     :list (append (mapcar #'term-con0 (cmbn-list cmbn0))
-                   (mapcar #'term-con1 (cmbn-list cmbn1))))))
-
-#|
-()
-(cone-2cmbn-append (cmbn 3 4 'a) (cmbn 2 5 'b))
-|#
- 
-(DEFUN CONE-2MRPH-DIAG-IMPL (mrph0 mrph1)
-  (declare (type morphism mrph0 mrph1))
-  (the intr-mrph
-    (flet ((rslt (cmbn)
-                 (declare (type cmbn cmbn))
-                 (the cmbn
-                   (multiple-value-bind (cmbn0 cmbn1)
-                       (cone-cmbn-split cmbn)
-                     (declare (type cmbn cmbn0 cmbn1))
-                     (cone-2cmbn-append (? mrph0 cmbn0)
-                                        (? mrph1 cmbn1))))))
-      #'rslt)))
-
-#|
-()
-(setf mrph (dffr (delta 4)))
-(setf rslt (cone-2mrph-diag-impl mrph mrph))
-(funcall rslt (cmbn 3 4 (con0 15) 5 (con1 7)))
-|#
- 
-(DEFUN CONE-3MRPH-TRIANGLE-IMPL (cmpr0 mrph0 mrph1 phi)
-  (declare (ignore cmpr0) (type morphism mrph0 mrph1 phi))
-  (the intr-mrph
-    (flet ((rslt (degr gnrt)
-             (declare (type fixnum degr) (type gnrt gnrt))
-               (the cmbn
-                 (ecase (conx gnrt)
-                   (0 (cmbn-con0 (? mrph0 degr (icon gnrt))))
-                   (1
-                    (let ((gnrt (icon gnrt)))
-                      (declare (type gnrt gnrt))
-                      (cone-2cmbn-append
-                       (? phi (1- degr) gnrt)
-                       (? mrph1 (1- degr) gnrt))))))))
-      #'rslt)))
-
-#|
-()
-(setf rslt (cone-3mrph-triangle-impl #'f-cmpr
-                                     (dffr (delta 4))
-                                     (dffr (delta 4))
-                                     (idnt-mrph (delta 4))))
-(funcall rslt 4 (con0 '31))
-(funcall rslt 5 (con1 '31))
-(funcall rslt 4 (con1 '15))
-; (funcall rslt (cmbn 4 1 (con0 '31) 1 (con1 '15)))
-|#
-
-(DEFUN CONE (mrph)
-  (declare (type morphism mrph))
-  (the chain-complex
-    (let ((chcm0 (trgt mrph))
-          (chcm1 (sorc mrph)))
-      (declare (type chain-complex chcm0 chcm1))
-      (build-chcm
-       :cmpr (cone-cmpr (cmpr chcm0) (cmpr chcm1))
-       :basis (cone-basis (basis chcm0) (basis chcm1))
-       :bsgn (con0 (bsgn chcm0))
-       :intr-dffr (cone-3mrph-triangle-impl (cmpr chcm0)
-                                            (dffr chcm0)
-                                            (n-mrph -1 (dffr chcm1))
-                                            mrph)
-       :strt :gnrt
-       :orgn `(cone ,mrph)))))
-
-#|
-()
-(cat-init)
-(setf k (k-z 1))
-(setf u (idnt-mrph k))
-(setf c (cone u))
-(setf *tc* (cmbn 4 1 (con0 '(1 2 3 4))))
-(? c 4 (con0 '(1 2 3 4)))
-(? c *tc*)
-|#
-
-
-#|
-()
-(setf cone (cone (idnt-mrph (delta 4))))
-(? cone (cmbn 4 1 (con0 '31) -1 (con1 '15)))
-(? cone *)
-|#
-
-
-(DEFUN CONE-2MRPH-DIAG (sorc-cone trgt-cone mrph0 mrph1)
-  (declare
-   (type chain-complex sorc-cone trgt-cone)
-   (type morphism mrph0 mrph1))
-  (the morphism
-    (progn
-      (unless (= (degr mrph0) (degr mrph1))
-        (error "Non-coherent degrees in CONE-2MRPH-DIAG."))
-      (build-mrph
-       :sorc sorc-cone
-       :trgt trgt-cone
-       :degr (degr mrph0)
-       :intr (cone-2mrph-diag-impl mrph0 mrph1)
-       :strt :cmbn
-       :orgn `(cone-2mrph-diag ,sorc-cone ,trgt-cone ,mrph0 ,mrph1)))))
-
-#|
-()
-(setf idnt (idnt-mrph (delta 4)))
-(setf cone (cone idnt))
-(setf ff (cone-2mrph-diag cone cone idnt idnt))
-(? ff (cmbn 4 1 (con0 '31) 10 (con1 '15)))
-|#
-
-(DEFUN CONE-3MRPH-TRIANGLE (sorc-cone trgt-cone mrph0 mrph1 phi)
-  (declare
-   (type chain-complex sorc-cone trgt-cone)
-   (type morphism mrph0 mrph1 phi))
-  (the morphism
-    (progn
-      (unless (= (degr mrph0) (degr mrph1))
-        (error "Non-coherent degrees in CONE-3MRPH-TRIANGLE."))
-      (unless (= (1+ (degr mrph0)) (degr phi))
-        (error "Non-coherent-degrees in CONE-3MRPH-TRIANGLE."))
-      (build-mrph
-       :sorc sorc-cone
-       :trgt trgt-cone
-       :degr (degr mrph0)
-       :intr (cone-3mrph-triangle-impl
-              (cmpr (trgt phi))
-              mrph0 mrph1 phi)
-       :strt :gnrt
-       :orgn `(cone-3mrph-triangle ,sorc-cone ,trgt-cone
-                                    ,mrph0 ,mrph1 ,phi)))))
-
-#|
-()
-(cat-init)
-(setf d (delta 4))
-(setf df (dffr (delta 4)))
-(setf n (idnt-mrph d))
-(setf c (cone n))
-(setf z (sbtr (dffr c)
-              (cone-3mrph-triangle c c df (n-mrph -1 df) n)))
-(? z 0 (con0 '1))
-(? z 1 (con1 '1))
-(? z 1 (con0 '3))
-(? z 2 (con1 '3))
-(? z 4 (con0 '31))
-(? z 5 (con1 '31))
-|#
-
-
-(DEFUN CONE-EFHM (cone)
-  (declare (type chain-complex cone))
-  (the homotopy-equivalence
-    (let* ((phi (second (orgn cone)))
-           (chcm0 (trgt phi)) (chcm1 (sorc phi))
-           (efhm0 (efhm chcm0)) (efhm1 (efhm chcm1))
-           (lf0 (lf efhm0)) (lg0 (lg efhm0)) (lh0 (lh efhm0))
-           (rf0 (rf efhm0)) (rg0 (rg efhm0)) (rh0 (rh efhm0))
-           (lf1 (lf efhm1)) (lg1 (lg efhm1)) (lh1 (lh efhm1))
-           (rf1 (rf efhm1)) (rg1 (rg efhm1)) (rh1 (rh efhm1))
-           (hphi (cmps lg0 (cmps phi lf1)))
-           (ephi (cmps rf0 (cmps hphi rg1)))
-           (hcone (cone hphi))
-           (econe (cone ephi))
-           (LF (cone-2mrph-diag hcone cone lf0 lf1))
-           (LG (cone-2mrph-diag cone hcone lg0 lg1))
-           (LH (cone-2mrph-diag hcone hcone lh0 (n-mrph -1 lh1)))
-           (RF (cone-3mrph-triangle hcone econe rf0 rf1
-                 (cmps rf0 (cmps hphi rh1))))
-           (RG (cone-3mrph-triangle econe hcone rg0 rg1
-                 (n-mrph -1 (cmps rh0 (cmps hphi rg1)))))
-           (RH (cone-3mrph-triangle hcone hcone rh0 (n-mrph -1 rh1)
-                 (cmps rh0 (cmps hphi rh1)))))
-      (declare
-       (type chain-complex chcm0 chcm1 hcone econe)
-       (type morphism phi lf0 lg0 lh0 rf0 rg0 rh0 lf1 lg1 lh1 rf1 rg1 rh1
-                      hphi ephi LF LG LH RF RG RH))
-      (build-hmeq
-       :lrdct (build-rdct :f LF :g LG :h LH
-                          :orgn `(cone-efhm ,cone lrdct))
-       :rrdct (build-rdct :f RF :g RG :h RH
-                          :orgn `(cone-efhm ,cone rrdct))
-       :orgn `(cone-efhm ,cone)))))
-
-(DEFMETHOD SEARCH-EFHM (chcm (orgn (eql 'cone)))
-  (declare (type chain-complex chcm))
-  (the homotopy-equivalence
-    (cone-efhm chcm)))
-
diff --git a/archive/Kenzo-1/cs-twisted-products.cl b/archive/Kenzo-1/cs-twisted-products.cl
deleted file mode 100644
index f9d9773..0000000
--- a/archive/Kenzo-1/cs-twisted-products.cl
+++ /dev/null
@@ -1,146 +0,0 @@
-;;;  CS-TWISTED-PRODUCTS  CS-TWISTED-PRODUCTS  CS-TWISTED-PRODUCTS
-;;;  CS-TWISTED-PRODUCTS  CS-TWISTED-PRODUCTS  CS-TWISTED-PRODUCTS
-;;;  CS-TWISTED-PRODUCTS  CS-TWISTED-PRODUCTS  CS-TWISTED-PRODUCTS
-
-(IN-PACKAGE "COMMON-LISP-USER")
-
-(PROVIDE "cs-twisted-products")
-
-(DEFUN SMGR-FIBRATION-SINTR (dmns gbar)
-  (declare
-    (ignore dmns)
-    (type gbar gbar))
-  (the absm
-    (first (gbar-list gbar))))
-
-(DEFUN SMGR-FIBRATION (smgr)
-  (declare (type simplicial-group smgr))
-  (the fibration
-    (build-smmr
-      :sorc (classifying-space smgr)
-      :trgt smgr
-      :degr -1
-      :sintr #'smgr-fibration-sintr
-      :orgn `(simplicial-group-fibration ,smgr))))
-
-#|
-  (setf k1 (k-z-1))
-  (setf tw (smgr-fibration k1))
-  (setf k2 (sorc tw))
-  (setf tt (fibration-total tw))
-  (setf gmsm (crpr 0 (gbar 4 0 '(10 11 12) 0 '(20 21) 0 '(30) 0 '())
-                   0 '(2 4 6 8)))
-  (dotimes (i 5)
-    (print (face tt i 4 gmsm)))
-  (setf br (brown-reduction tw))
-  (setf tw-pr (bcc br))
-  (? tw-pr 4 (tnpr 4 (gbar 4 0 '(1 10 100) 0 '(1000 10000)
-                             0 '(100000) 0 '())
-                   0 '()))
-|#
-
-(DEFUN SMGR-CRTS-CONTRACTION-INTR (idnt)
-  (declare
-    (type gmsm idnt))
-  (flet ((rslt (degr crpr
-		     &aux (degr+1 (1+ degr)))
-	   (declare
-	    (fixnum degr degr+1)
-	    (type crpr crpr))
-	   (the cmbn
-	     (with-crpr (absm1 absm2) crpr
-	       (if (= (dgop absm2) (mask degr))
-		 (zero-cmbn degr+1)
-		 (term-cmbn degr+1
-		   (-1-expt-n+1 degr)
-		   (crpr 0 (make-gbar
-			    :dmns degr+1
-			    :list (cons absm2
-					(rest (unnormalize-gbar absm1 idnt))))
-			 (mask degr+1) idnt)))))))
-     (the intr-mrph #'rslt)))
-
-(DEFUN SMGR-CRTS-CONTRACTION (smgr)
-  (declare (type simplicial-group smgr))
-  (the morphism
-    (build-mrph
-      :sorc (fibration-total (smgr-fibration smgr))
-      :trgt (fibration-total (smgr-fibration smgr))
-      :degr +1
-      :intr (smgr-crts-contraction-intr (bspn smgr))
-      :strt :gnrt
-      :orgn `(smgr-crts-contraction ,smgr))))
-
-#|
-  (cat-init)
-  (setf chi (smgr-crts-contraction (k-z-1)))
-  (setf rdct (build-rdct :f (zero-mrph (sorc chi) (z-chcm))
-                         :g (zero-mrph (z-chcm) (sorc chi))
-                         :h chi))
-  (pre-check-rdct rdct)
-  (setf *tc* (cmbn 0 1 (crpr 0 +null-gbar+ 0 '())))
-  (setf *bc* (cmbn 0 1 :z-gnrt))
-  (check-rdct)
-  (setf *tc* (cmbn 1 1 (crpr 1 +null-gbar+ 0 '(1))))
-  (check-rdct)
-  (setf *tc* (cmbn 4 1 (crpr 0 (gbar 4 0 '(10 11 12) 0 '(20 21) 0 '(30) 0 '())
-                             0 '(2 4 6 8))))
-  (check-rdct)
-  (setf *tc* (cmbn 3 1 (crpr 0 (gbar 3 0 '(10 11) 0 '(20) 0 '())
-                             0 '(2 4 6))))
-  (check-rdct)
-|#
-
-(DEFUN SMGR-TNPR-CONTRACTION (smgr
-			        &aux (fibration (smgr-fibration smgr))
-				     (brown (brown-reduction fibration))
-				     (f (f brown))
-				     (g (g brown))
-				     (chi (smgr-crts-contraction smgr)))
-  (declare
-    (type simplicial-group smgr)
-    (type fibration fibration)
-    (type reduction brown)
-    (type morphism f g chi))
-  (the morphism
-    (i-cmps f chi g)))
-
-#|
-  (cat-init)
-  (setf chi (smgr-tnpr-contraction (k-z-1)))
-  (setf rdct (build-rdct :f (zero-mrph (sorc chi) (z-chcm))
-                         :g (zero-mrph (z-chcm) (sorc chi))
-                         :h chi))
-  (pre-check-rdct rdct)
-  (setf *tc* (cmbn 0 1 (tnpr 0 +null-gbar+ 0 '())))
-  (setf *bc* (cmbn 0 1 :z-gnrt))
-  (check-rdct)
-  (setf *tc* (cmbn 1 1 (tnpr 0 +null-gbar+ 1 '(1))))
-  (check-rdct)
-  (setf *tc* (cmbn 3 1 (tnpr 0 +null-gbar+ 3 '(1 10 100))))
-  (? chi *tc*)
-  (check-rdct)
-  (setf *tc* (cmbn 3 1 (tnpr 2 (gbar 2 0 '(1) 0 '()) 1 '(10))))
-  (? chi *tc*)
-  (check-rdct)
-  (setf *tc* (cmbn 3 1 (tnpr 3 (gbar 3 0 '(1 10) 0 '(100) 0 '()) 0 '())))
-  (? chi *tc*)
-  (check-rdct)
-  (setf *tc* (cmbn 4 1 (tnpr 0 +null-gbar+ 4 '(1 10 100 1000))))
-  (? chi *tc*)
-  (check-rdct)
-  (setf *tc* (cmbn 4 1 (tnpr 2 (gbar 2 0 '(1) 0 '()) 2 '(10 100))))
-  (? chi *tc*)
-  (check-rdct)
-  (setf *tc* (cmbn 4 1 (tnpr 3 (gbar 3 0 '(1 10) 0 '(100) 0 '())
-                             1 '(1000))))
-  (? chi *tc*)
-  (check-rdct)
-  (setf *tc* (cmbn 4 1 (tnpr 4 (gbar 4 0 '(1 10 100)
-                                       0 '(1000 10000)
-                                       0 '(100000)
-                                       0 '())
-                              0 '())))
-  (? chi *tc*)
-  (check-rdct)
-|#
\ No newline at end of file
diff --git a/archive/Kenzo-1/delta.cl b/archive/Kenzo-1/delta.cl
deleted file mode 100644
index f41f954..0000000
--- a/archive/Kenzo-1/delta.cl
+++ /dev/null
@@ -1,417 +0,0 @@
-;;;  DELTA  DELTA  DELTA  DELTA  DELTA  DELTA  DELTA  DELTA  DELTA
-;;;  DELTA  DELTA  DELTA  DELTA  DELTA  DELTA  DELTA  DELTA  DELTA
-;;;  DELTA  DELTA  DELTA  DELTA  DELTA  DELTA  DELTA  DELTA  DELTA
-
-(IN-PACKAGE "COMMON-LISP-USER")
-
-(PROVIDE "delta")
-
-(DEFMETHOD PRINT-KEYCONS ((car (eql :delt)) cdr stream)
-   (format stream "~A" (hyphenize-list (dlop-int-ext cdr)))
-   (cons car cdr))
-
-(DEFUN SOFT-DELTA-CMPR (gmsm1 gmsm2)
-   (f-cmpr (cdr gmsm1) (cdr gmsm2)))
-
-#|
-()
-(soft-delta-cmpr (d 12) (d 23))
-|#
-   
-(DEFUN DELTA-FACE (indx dmns gmsm)
-   (declare
-      (fixnum indx gmsm)
-      (ignore dmns))
-   (the absm
-      (do ((pmark 1 (ash pmark 1))
-           (bmark indx)
-           (gmsm2 gmsm (ash gmsm2 -1)))
-          (nil)
-         (declare (fixnum pmark bmark gmsm2))
-         (when (oddp gmsm2)
-            (when (minusp (decf bmark))
-               (return-from delta-face (absm 0 (logxor gmsm pmark))))))))
-
-(DEFUN SOFT-DELTA-FACE (indx dmns gmsm)
-   (declare
-      (fixnum indx dmns)
-      (type soft-dlop gmsm))
-   (absm 0 (d (gmsm (delta-face indx dmns (cdr gmsm))))))
-
-#|
-()
-(dotimes (i 4)
-  (print (dlop-int-ext (gmsm (delta-face i 3 (dlop-ext-int '(0 1 2 3)))))))
-(dotimes (i 4)
-  (print (dlop-int-ext (gmsm (delta-face i 3 (dlop-ext-int '(0 2 4 6))))))))
-(dotimes (i 4)
-  (print (soft-delta-face i 3 (d (mask 4)))))
-(dotimes (i 4)
-  (print (soft-delta-face i 3 (d (dlop-ext-int '(0 2 4 6))))))
-|#
-
-(DEFUN DELTA-BNDR (dmns gmsm)
-   (declare (fixnum dmns gmsm))
-   (the cmbn
-      (if (zerop dmns)
-         +zero-negative-cmbn+
-         (make-cmbn
-            :degr (1- dmns)
-            :list (do ((rslt +empty-list+)
-                      (gmsm2 gmsm (ash gmsm2 -1))
-                      (pmark 1 (ash pmark +1))
-                      (sign 1))
-                     ((zerop gmsm2) rslt)
-                    (declare
-                       (list rslt)
-                       (fixnum gmsm2 pmark sign))
-                    (when (oddp gmsm2)
-                       (push (term sign (logxor gmsm pmark)) rslt)
-                       (setf sign (- sign))))))))
-
-(DEFUN SOFT-DELTA-BNDR (dmns gmsm)
-   (declare
-      (fixnum dmns)
-      (type soft-dlop gmsm))
-   (make-cmbn
-      :degr (1- dmns)
-      :list (mapcar #'(lambda (term)
-                         (with-term (cffc gmsm) term
-                            (term cffc (d gmsm))))
-               (cmbn-list (delta-bndr dmns (cdr gmsm))))))
-
-#|
-()
-(delta-bndr 0 4)
-(delta-bndr 1 3)
-(delta-bndr 1 5)
-(delta-bndr 1 10)
-(delta-bndr 5 63)
-(soft-delta-bndr 5 (d (mask 6)))
-|#
-
-
-(DEFUN DELTA-DGNL (dmns gmsm)
-   (declare (fixnum dmns gmsm))
-   (the cmbn
-      (make-cmbn
-         :degr dmns
-         :list (do ((rslt +empty-list+)
-                    (ldegr dmns)
-                    (indx (1- (integer-length gmsm)) (1- indx)))
-                   ((minusp indx))
-                  (declare
-                     (list rslt)
-                     (fixnum indx))
-                  (when (logbitp indx gmsm)
-                     (push (term 1 (tnpr
-                                    ldegr (logand gmsm (mask (1+ indx)))
-                                    (- dmns ldegr) (logandc2 gmsm (mask indx))))
-                        rslt)
-                     (when (minusp (decf ldegr))
-                        (return rslt)))))))
-
-(DEFUN SOFT-DELTA-DGNL (dmns gmsm)
-   (declare
-      (fixnum dmns)
-      (type soft-dlop gmsm))
-   (make-cmbn :degr dmns
-      :list (mapcar
-               #'(lambda (term)
-                    (with-term (cffc tnpr) term
-                       (with-tnpr (degr1 gmsm1 degr2 gmsm2) tnpr
-                          (term cffc
-                             (tnpr degr1 (d gmsm1) degr2 (d gmsm2))))))
-               (cmbn-list (delta-dgnl dmns (cdr gmsm))))))
-
-#|
-()
-(delta-dgnl 3 15)
-(delta-dgnl 3 170)
-(soft-delta-dgnl 3 (d (dlop-ext-int '(1 3 5 7))))
-(delta-dgnl 0 64)
-|#
-                                        
-(DEFUN DELTA-INFINITY ()
-   (the simplicial-set
-      (build-smst
-         :cmpr #'f-cmpr
-         :basis :locally-effective
-         :bspn 1
-         :face #'delta-face
-         :intr-dgnl #'delta-dgnl
-         :dgnl-strt :gnrt
-         :intr-bndr #'delta-bndr
-         :bndr-strt :gnrt
-         :orgn '(delta-infinity))))
-
-#|
-()
-(cmpr (delta-infinity) 2 4)
-(cmpr (delta-infinity) 4 4)
-(cmpr (delta-infinity) 8 4)
-(basis (delta-infinity) 1)   ;;; => error
-(face (delta-infinity) 1 2 21)
-(cprd (delta-infinity) 3 15)
-(dgnl (delta-infinity) 3 15)
-(? (delta-infinity) 2 21)
-|#
-
-(DEFUN SOFT-DELTA-INFINITY ()
-   (the simplicial-set
-      (build-smst
-         :cmpr #'soft-delta-cmpr
-         :basis :locally-effective
-         :bspn (d 1)
-         :face #'soft-delta-face
-         :intr-dgnl #'soft-delta-dgnl :dgnl-strt :gnrt
-         :intr-bndr #'soft-delta-bndr :bndr-strt :gnrt
-         :orgn '(soft-delta-infinity))))
-
-#|
-()
-(cat-init)
-(cmpr (soft-delta-infinity) (d 2) (d 4))
-(face (soft-delta-infinity) 1 2 (d (dlop-ext-int '(1 3 5))))
-(cprd (soft-delta-infinity) 3 (d 15))
-(dgnl (soft-delta-infinity) 3 (d 15))
-(? (soft-delta-infinity) 2 (d (dlop-ext-int '(0 2 4))))
-|#
-
-(DEFUN DELTA-N-BASIS (n)
-   (declare (fixnum n))
-  (flet ((rslt (dmns)
-               (declare (fixnum dmns))
-             (when (> dmns n)
-                (return-from rslt +empty-list+))
-             (setf dmns (1+ dmns))
-             (do ((rslt +empty-list+)
-                  (count (binomial-n-p (1+ n) dmns))
-                  (gmsm (mask (1+ n)) (1- gmsm)))
-                 ((zerop count) rslt)
-                (when (= (logcount gmsm) dmns)
-                   (push gmsm rslt)
-                   (decf count)))))
-      (the basis #'rslt)))
-
-(DEFUN SOFT-DELTA-N-BASIS (n)
-   (declare (fixnum n))
-   (flet ((rslt (dmns)
-             (when (> dmns n)
-                (return-from rslt +empty-list+))
-             (setf dmns (1+ dmns))
-             (do ((rslt +empty-list+)
-                  (count (binomial-n-p (1+ n) dmns))
-                  (gmsm (mask (1+ n)) (1- gmsm)))
-                 ((zerop count) rslt)
-                (when (= (logcount gmsm) dmns)
-                   (push (d gmsm) rslt)
-                   (decf count)))))
-      (the basis #'rslt)))
-      
-
-#|
-()
-(setf basis (delta-n-basis 3))
-(setf soft-basis (soft-delta-n-basis 3))
-(dotimes (i 5)
-  (print (funcall basis i)))
-(dotimes (i 5)
-  (print (funcall soft-basis i)))
-|#   
-
-(DEFUN DELTA (dmns)
-   (declare (fixnum dmns))
-   (the simplicial-set
-      (build-smst
-         :cmpr #'f-cmpr
-         :basis (delta-n-basis dmns)
-         :bspn 1
-         :face #'delta-face
-         :intr-dgnl #'delta-dgnl
-         :dgnl-strt :gnrt
-         :intr-bndr #'delta-bndr
-         :bndr-strt :gnrt
-         :orgn `(delta ,dmns))))
-
-#|
-()
-(cat-init)
-(setf d3 (delta 3))
-(cmpr d3 2 4)
-(cmpr d3 4 4)
-(cmpr d3 8 4)
-(basis d3 1)
-(dgnl d3 3 15)
-(face d3 1 2 21)
-(? d3 2 13)
-(setf d (delta-infinity))
-(basis d)
-(setf d (delta-infinity)))
-|#
-
-(DEFUN SOFT-DELTA (dmns)
-   (declare (fixnum dmns))
-   (the simplicial-set
-      (build-smst
-         :cmpr #'soft-delta-cmpr
-         :basis (soft-delta-n-basis dmns)
-         :bspn (d 1)
-         :face #'soft-delta-face
-         :intr-dgnl #'soft-delta-dgnl :dgnl-strt :gnrt
-         :intr-bndr #'soft-delta-bndr :bndr-strt :gnrt
-         :orgn `(soft-delta ,dmns))))
-      
-#|
-()
-(cat-init)
-(setf d3 (soft-delta 3))
-(cmpr d3 (d 2) (d 4))
-(basis d3 1)
-(dgnl d3 3 (d 15))
-(face d3 1 2 (d 21))
-(? d3 2 (d 13))
-|#
-
-#| For comparison with EAT.
-   In 
-  (setf delta (delta-infinity))
-  (setf d (bndr delta))
-  (setf s14 (mask 15))
-  (cmbn-? d (gnrt-? d 14 s14))
-  (defun t1 (n)
-     (time (dotimes (i n) (cmbn-? d (gnrt-? d 14 s14)))))
-  (compile 't1)
-  (t1 500)
-  (setf +too-much-time+ -1)
-  (t1 500)
-|#
-#|
-  In EAT:
-  (setf delta *delta*)
-  (setf d (cc-d (ss-cc delta)))
-  (setf s14 (<a-b> 0 14))
-  (??? d (? d 14 s14))
-  (defun t1 (n)
-     (time (dotimes (i n) (??? d (? d 14 s14)))))
-  (compile 't1)
-  (t1 500)
-|#
-
-(DEFUN DELTAB-CMPR (gmsm1 gmsm2)
-   (declare (fixnum gmsm1 gmsm2))
-   (if (= 1 (logcount gmsm1))
-      :equal
-      (f-cmpr gmsm1 gmsm2)))
-
-(DEFUN DELTAB-BNDR (dmns gmsm)
-   (declare (fixnum dmns gmsm))
-   (the cmbn
-      (if (< dmns 2)
-         (zero-cmbn (1- dmns))
-         (make-cmbn
-            :degr (1- dmns)
-            :list (do ((rslt +empty-list+)
-                      (gmsm2 gmsm (ash gmsm2 -1))
-                      (pmark 1 (ash pmark +1))
-                      (sign 1))
-                     ((zerop gmsm2) rslt)
-                    (declare
-                       (list rslt)
-                       (fixnum gmsm2 pmark sign))
-                    (when (oddp gmsm2)
-                       (push (term sign (logxor gmsm pmark)) rslt)
-                       (setf sign (- sign))))))))
-
-(DEFUN DELTAB2-FACE (indx dmns gmsm)
-   (declare
-      (fixnum indx dmns gmsm))
-   (the absm
-      (progn
-	(when (= 2 dmns)
-	   (return-from deltab2-face (absm 1 1)))
-	(do ((pmark 1 (ash pmark 1))
-	     (bmark indx)
-	     (gmsm2 gmsm (ash gmsm2 -1)))
-	    (nil)
-	    (declare (fixnum pmark bmark gmsm2))
-	    (when (oddp gmsm2)
-		  (when (minusp (decf bmark))
-			(return-from deltab2-face (absm 0 (logxor gmsm pmark)))))))))
-
-(DEFUN DELTAB2-DGNL (dmns gmsm)
-  (declare (fixnum dmns gmsm))
-  (the cmbn
-    (make-cmbn
-     :degr dmns
-     :list (if (zerop dmns)
-               (list (term 1 (tnpr 0 gmsm 0 gmsm)))
-             (do ((rslt +empty-list+)
-                  (ldegr dmns)
-                  (indx (1- (integer-length gmsm)) (1- indx)))
-                 ((minusp indx))
-               (declare (list rslt) (fixnum indx))
-               (when (logbitp indx gmsm)
-                 (push (term 1 (tnpr
-                                ldegr (logand gmsm (mask (1+ indx)))
-                                (- dmns ldegr) (logandc2 gmsm (mask indx))))
-                       rslt)
-                 (when (minusp (decf ldegr))
-                   (setf rslt (delete 1 rslt :key #'caaddr))
-                   (setf (gnrt1 (gnrt (first rslt)))
-                     (setf (gnrt2 (gnrt (car (last rslt))))
-                       1))				    
-                   (return (delete 1 rslt :key #'cadddr)))))))))
-
-#|
-()
-(dotimes (i 7)
-  (print (deltab2-dgnl i (mask (1+ i)))))
-|#
-  
-
-(DEFUN DELTAB2-BNDR (dmns gmsm)
-   (declare (fixnum dmns gmsm))
-   (the cmbn
-      (if (< dmns 3)
-         (zero-cmbn (1- dmns))
-         (make-cmbn
-            :degr (1- dmns)
-            :list (do ((rslt +empty-list+)
-                      (gmsm2 gmsm (ash gmsm2 -1))
-                      (pmark 1 (ash pmark +1))
-                      (sign 1))
-                     ((zerop gmsm2) rslt)
-                    (declare
-                       (list rslt)
-                       (fixnum gmsm2 pmark sign))
-                    (when (oddp gmsm2)
-                       (push (term sign (logxor gmsm pmark)) rslt)
-                       (setf sign (- sign))))))))
-
-#|
-  (deltab-bndr 1 5)
-  (deltab-bndr 3 15)
-|#
-
-(DEFUN DELTAB ()
-  (the simplicial-set
-   (build-smst
-      :cmpr #'deltab-cmpr
-      :basis :locally-effective
-      :bspn 1
-      :face #'delta-face
-      :intr-dgnl #'delta-dgnl
-      :dgnl-strt :gnrt
-      :orgn '(deltab))))
-
-(DEFUN DELTAB2 ()
-  (the simplicial-set
-     (build-smst
-      :cmpr #'f-cmpr
-      :basis :locally-effective
-      :bspn 1
-      :face #'deltab2-face
-      :intr-dgnl #'deltab2-dgnl
-      :dgnl-strt :gnrt
-      :orgn '(deltab2))))
diff --git a/archive/Kenzo-1/disk-pasting.cl b/archive/Kenzo-1/disk-pasting.cl
deleted file mode 100644
index a70ad56..0000000
--- a/archive/Kenzo-1/disk-pasting.cl
+++ /dev/null
@@ -1,396 +0,0 @@
-;;;  DISK-PASTING  DISK-PASTING  DISK-PASTING  DISK-PASTING
-;;;  DISK-PASTING  DISK-PASTING  DISK-PASTING  DISK-PASTING
-;;;  DISK-PASTING  DISK-PASTING  DISK-PASTING  DISK-PASTING
-
-(IN-PACKAGE "COMMON-LISP-USER")
-
-(provide "disk-pasting")
-
-(DEFUN DISK-PASTING-CMPR (cmpr new)
-  (declare
-    (type cmprf cmpr)
-    (symbol new))
-  (flet ((rslt (gnrt1 gnrt2)
-	   (declare (type gnrt gnrt1 gnrt2))
-	   (if (eq gnrt1 new)
-	       (if (eq gnrt2 new)
-		   :equal
-		 :less)
-	     (if (eq gnrt2 new)
-		 :greater
-	       (funcall cmpr gnrt1 gnrt2)))))
-    (the cmprf #'rslt)))
-
-#|
-  (setf c (delta 3))
-  (setf cmpr (disk-pasting-cmpr (cmpr c) 'new))
-  (funcall cmpr 'new 'new)
-  (funcall cmpr 'new 5)
-  (funcall cmpr 5 'new)
-  (funcall cmpr 5 5)
-  (funcall cmpr 5 6)
-  (funcall cmpr 6 5)
-|#
-
-(DEFUN DISK-PASTING-BASIS (basis dmns new)
-  (declare
-    (type basis basis)
-    (fixnum dmns)
-    (symbol new))
-  (flet ((rslt (degr)
-	   (declare (fixnum degr))
-	   (if (= degr dmns)
-	       (cons new (funcall basis dmns))
-	     (funcall basis degr))))
-    (the basis #'rslt)))
-
-#|
-  (setf c (delta 3))
-  (setf basis (disk-pasting-basis (basis c) 3 'new))
-  (funcall basis 3)
-  (funcall basis 2)
-|#
-
-(DEFUN DISK-PASTING-INTR-DFFR (old-dffr degr new bndr)
-  (declare
-    (type morphism old-dffr)
-    (fixnum degr)
-    (symbol new)
-    (type cmbn bndr))
-  (when (cmbn-non-zero-p (cmbn-? old-dffr bndr))
-    (error "In CHCM-DISK-PASTING, the given boundary has a non-null boundary."))
-  (let ((cmpr (cmpr (trgt old-dffr))))
-    (declare (type cmprf cmpr))
-    (flet ((rslt (cmbn)
-	     (declare (type cmbn cmbn))
-	     (with-cmbn (degr2 list) cmbn
-	       (unless (= degr degr2)
-		 (return-from rslt
-		   (cmbn-? old-dffr cmbn)))
-	       (unless list
-		 (return-from rslt
-		   (zero-cmbn (1- degr))))
-	       (unless (eq (-gnrt list) new)
-		 (return-from rslt
-		   (cmbn-? old-dffr cmbn)))
-	       (2cmbn-add cmpr
-		 (n-cmbn (-cffc list) bndr)
-		 (cmbn-? old-dffr
-			 (make-cmbn :degr degr
-				    :list (rest list)))))))
-      (the intr-mrph #'rslt))))
-
-#|
-  (cat-init)
-  (setf c (delta 3))
-  (setf intr (disk-pasting-intr-dffr (dffr c) 3 'new (cmbn 2 1 7)))
-  (setf intr (disk-pasting-intr-dffr (dffr c) 3 'new (? c 3 15)))
-  (funcall intr (cmbn 2 1 7))
-  (funcall intr (cmbn 3))
-  (funcall intr (cmbn 3 1 15))
-  (funcall intr (cmbn 3 1 'new 1 15))
-  (funcall intr (cmbn 3 1 'new -1 15))
-  (funcall intr (cmbn 3 -1 'new 1 15))
-  (funcall intr (cmbn 3 -1 'new -1 15))
-|#
- 
-(DEFUN CHCM-DISK-PASTING (chcm dmns new bndr)
-  (declare
-    (type chain-complex chcm)
-    (fixnum dmns)
-    (symbol new)
-    (type cmbn bndr))
-  (the chain-complex
-    (with-slots (cmpr basis dffr) chcm
-      (declare
-       (type cmprf cmpr)
-       (type basis basis)
-       (type morphism dffr))
-      (let ((rslt (build-chcm
-		   :cmpr (disk-pasting-cmpr cmpr new)
-		   :basis (disk-pasting-basis basis dmns new)
-		   :intr-dffr (disk-pasting-intr-dffr dffr dmns new bndr)
-		   :strt :cmbn
-		   :orgn `(chcm-disk-pasting ,chcm ,dmns ,new ,bndr))))
-	(declare (type chain-complex rslt))
-	(when (slot-boundp chcm 'bsgn)
-	  (setf (slot-value rslt 'bsgn) (slot-value chcm 'bsgn)))
-	rslt))))
-
-#|
-  (setf c (delta 3))
-  (setf s3 (chcm-disk-pasting c 3 'new (? c 3 15)))
-  (homology s3 0 5))
-|#
-
-(DEFUN DISK-PASTING-FACE (cmpr face dmns new faces)
-  (declare
-    (type cmprf cmpr)
-    (type face face)
-    (fixnum dmns)
-    (symbol new)
-    (list faces))
-  (unless (= (1+ dmns) (length faces))
-    (error "In DISK-PASTING, non-coherent arguments."))
-  (mapl #'(lambda (mark)
-	    (declare (list mark))
-	    (unless (typep (car mark) 'absm)
-	      (setf (car mark) (absm 0 (car mark)))))
-	faces)
-  (flet ((rslt (indx dmns2 gmsm)
-	   (declare
-	     (fixnum indx dmns2)
-	     (type gmsm gmsm))
-	   (unless (= dmns dmns2)
-	     (return-from rslt
-	       (funcall face indx dmns2 gmsm)))
-	   (if (eq gmsm new)
-	       (nth indx faces)
-	     (funcall face indx dmns gmsm))))
-    (unless (check-faces cmpr #'rslt dmns new)
-      (error "The new simplicial-set is not constructed."))
-    (the face #'rslt)))
-
-#|
-  (cat-init)
-  (setf c (delta 3))
-  (setf face (disk-pasting-face (cmpr c) (face c)
-                3 'new (list 14 (absm 0 13) 11 7)))
-  (funcall face 0 2 7)
-  (funcall face 0 3 15)
-  (dotimes (i 4) (print (funcall face i 3 'new)))
-|#
-
-(DEFUN DISK-PASTING (smst dmns new faces)
-  (declare
-    (type simplicial-set smst)
-    (fixnum dmns)
-    (symbol new)
-    (list faces))
-  (the simplicial-set
-    (with-slots (cmpr basis bsgn face dffr) smst
-      (declare
-       (type cmprf cmpr)
-       (type basis basis)
-       (type gmsm bsgn)
-       (type face face)
-       (type morphism dffr))
-      (let ((new-face (disk-pasting-face (cmpr smst) face
-					 dmns new faces))
-	    (new-bndr (zero-cmbn (1- dmns))))
-	(declare
-	  (type face new-face)
-	  (type cmbn new-bndr))
-	(do ((mark faces (cdr mark))
-	     (sign 1 (- sign)))
-	    ((endp mark))
-	    (declare
-	      (list mark)
-	      (fixnum sign))
-	  (let ((absm (car mark)))
-	    (declare (type absm absm))
-	    (with-absm (dgop gmsm) absm
-	      (unless (plusp dgop)
-		(dstr-add-term-to-cmbn cmpr sign gmsm new-bndr)))))
-	(build-smst
-	 :cmpr (disk-pasting-cmpr cmpr new)
-	 :basis (disk-pasting-basis basis dmns new)
-	 :bspn bsgn
-	 :face new-face
-	 :intr-bndr (disk-pasting-intr-dffr dffr dmns new new-bndr)
-	 :bndr-strt :cmbn
-	 :orgn `(disk-pasting ,smst ,dmns ,new ,faces))))))
-
-#|
-  (setf d2 (delta 2))
-  (setf s2 (disk-pasting d2 2 'new '(6 5 3)))
-  (homology s2 0 4)
-  (setf s2xs2 (crts-prdc s2 s2))
-  (homology s2xs2 0 6)
-|#
-
-(DEFUN MRPH-DISK-PASTING-INTR (mrph trgt-cmpr dmns new new-im)
-  (declare
-    (type morphism mrph)
-    (type cmprf trgt-cmpr)
-    (fixnum dmns)
-    (symbol new)
-    (type cmbn new-im))
-  (let ((mrph-degr (degr mrph)))
-    (declare (fixnum mrph-degr))
-    (flet ((rslt (cmbn)
-	     (declare (type cmbn cmbn))
-	     (with-cmbn (degr list) cmbn
-	       (unless (= degr dmns)
-		 (return-from rslt
-		   (cmbn-? mrph cmbn)))
-	       (unless list
-		 (return-from rslt
-		   (zero-cmbn (+ degr mrph-degr))))
-	       (unless (eq new (-gnrt list))
-		 (return-from rslt
-		   (cmbn-? mrph cmbn)))
-	       (2cmbn-add trgt-cmpr
-		 (n-cmbn (-cffc list) new-im)
-		 (cmbn-? mrph
-			 (make-cmbn :degr degr
-				    :list (rest list)))))))
-      (the intr-mrph #'rslt))))
-
-#|
-  (setf m (idnt-mrph (delta 3)))
-  (setf intr
-        (mrph-disk-pasting-intr m (cmpr (delta 3))
-                                3 'new (cmbn 3 -1 15)))
-  (funcall intr (cmbn 2 3 7))
-  (funcall intr (cmbn 3))
-  (funcall intr (cmbn 3 4 15))
-  (funcall intr (cmbn 3 1 'new 1 15))
-  (funcall intr (cmbn 3 -1 'new 1 15))
-|#
-
-(DEFUN MRPH-DISK-PASTING (mrph new-sorc new-trgt dmns new new-im)
-  (declare
-    (type morphism mrph)
-    (type chain-complex new-sorc new-trgt)
-    (fixnum dmns)
-    (symbol new)
-    (type cmbn new-im))
-  (the morphism
-    (build-mrph
-      :sorc new-sorc :trgt new-trgt :degr (degr mrph)
-      :intr (mrph-disk-pasting-intr mrph (cmpr new-trgt)
-				    dmns new new-im)
-      :strt :cmbn
-      :orgn `(mrph-disk-pasting ,mrph ,new-sorc ,new-trgt
-				,dmns ,new ,new-im))))
-
-#|
-  (setf d (delta 3))
-  (setf m (idnt-mrph d))
-  (setf sorc (chcm-disk-pasting d 3 'new (? d 3 15)))
-  (setf nm (mrph-disk-pasting m sorc sorc 3 'new (cmbn 3 1 'new)))
-  (? nm (cmbn 3 2 'new 3 15))
-|#
-
-(DEFUN HMEQ-DISK-PASTING (hmeq dmns new bndr &key new-lbcc)
-  (declare
-    (type homotopy-equivalence hmeq)
-    (fixnum dmns)
-    (symbol new)
-    (type cmbn bndr)
-    (type (or null chain-complex) new-lbcc))
-  (let* ((lg (lg hmeq))
-	 (rf (rf hmeq))
-	 (rh (rh hmeq))
-	 (t-bndr (cmbn-? lg bndr))
-	 (rb-bndr (cmbn-? rf t-bndr))
-	 (new-lbcc (or new-lbcc
-		       (chcm-disk-pasting (lbcc hmeq)
-					  dmns new bndr)))
-	 (new-tcc (chcm-disk-pasting (tcc hmeq)
-				      dmns new t-bndr))
-	 (new-rbcc (chcm-disk-pasting (rbcc hmeq)
-				      dmns new rb-bndr))
-	 (1+dmns (1+ dmns)))
-    (declare
-      (type morphism lg rf rh)
-      (type cmbn t-bndr rb-bndr)
-      (type chain-complex new-lbcc new-tcc new-rbcc)
-      (fixnum 1+dmns))
-    (build-hmeq
-      :lrdct (build-rdct
-	       :f (mrph-disk-pasting (lf hmeq) new-tcc new-lbcc
-				     dmns new (cmbn dmns 1 new))
-	       :g (mrph-disk-pasting lg new-lbcc new-tcc
-				     dmns new (cmbn dmns 1 new))
-	       :h (mrph-disk-pasting (lh hmeq) new-tcc new-tcc
-				     dmns new (zero-cmbn 1+dmns)))
-      :rrdct (build-rdct
-	       :f (mrph-disk-pasting rf new-tcc new-rbcc
-				     dmns new (cmbn dmns 1 new))
-	       :g (mrph-disk-pasting (rg hmeq) new-rbcc new-tcc
-				     dmns new
-				     (make-cmbn
-				      :degr dmns
-				      :list (cons (term 1 new)
-						  (cmbn-list
-						   (cmbn-opps
-						    (cmbn-? rh t-bndr))))))
-	       :h (mrph-disk-pasting rh new-tcc new-tcc
-				     dmns new (zero-cmbn 1+dmns)))
-      :orgn `(hmeq-disk-pasting ,hmeq ,dmns ,new ,bndr))))
-				     
-#|
-(cat-init)
-(setf tcc
-      (build-chcm
-       :cmpr #'s-cmpr
-       :basis #'(lambda (degr)
-		  (case degr
-			(0 (list 'a))
-			(1 (list 'b))
-			(otherwise nil)))
-       :intr-dffr #'(lambda (degr gnrt)
-		      (if (= 1 degr)
-			  (cmbn 0 1 'a)
-			(zero-cmbn (1- degr))))
-       :strt :gnrt
-       :orgn '(z-z)))
-(setf bcc
-      (build-chcm
-       :cmpr #'s-cmpr
-       :basis #'(lambda (degr) nil)
-       :intr-dffr #'(lambda (degr gnrt) (error "Impossible."))
-       :strt :gnrt
-       :orgn '(zero)))
-(setf rh (build-mrph
-	  :sorc tcc :trgt tcc :degr +1
-	  :intr #'(lambda (degr gnrt)
-		    (if (zerop degr)
-			(cmbn 1 1 'b)
-		      (zero-cmbn 2)))
-	  :strt :gnrt
-	  :orgn '(rh)))
-(setf hmeq (build-hmeq
-	    :lrdct (trivial-rdct tcc)
-	    :rrdct (build-rdct
-		    :f (zero-mrph tcc bcc 0)
-		    :g (zero-mrph bcc tcc 0)
-		    :h rh
-		    :orgn '(rrdct))))
-(setf nhmeq (hmeq-disk-pasting hmeq 1 'new (cmbn 0 1 'a)))
-(pre-check-rdct (lrdct nhmeq))
-(setf *tc* (cmbn 0 1 'a))
-(setf *bc* *tc*)
-(check-rdct)
-(setf *tc* (cmbn 1 1 'new 10 'b))
-(setf *bc* *tc*)
-(check-rdct)
-(pre-check-rdct (rrdct nhmeq))
-(setf *bc* (zero-cmbn 0))
-(check-rdct)
-(setf *tc* (cmbn 0 1 'a))
-(check-rdct)
-|#
-
-(DEFMETHOD SEARCH-EFHM (smst (orgn (eql 'disk-pasting)))
-  (declare (type simplicial-set smst))
-  (the homotopy-equivalence
-    (destructuring-bind (old-smst dmns new faces) (rest (orgn smst))
-			(declare
-			  (type simplicial-set old-smst)
-			  (fixnum dmns)
-			  (symbol new)
-			  (ignore faces))
-      (hmeq-disk-pasting (efhm old-smst)
-			 dmns new (? smst dmns new)
-			 :new-lbcc smst))))
-
-#|
-(cat-init)
-(setf d (delta 2))
-(setf s2 (disk-pasting d 2 'new '(6 5
-  3)))
-(homology s2 0 4)
-|#
diff --git a/archive/Kenzo-1/effective-homology.cl b/archive/Kenzo-1/effective-homology.cl
deleted file mode 100644
index b3b2346..0000000
--- a/archive/Kenzo-1/effective-homology.cl
+++ /dev/null
@@ -1,576 +0,0 @@
-;;;  EFFECTIVE-HOMOLOGY  EFFECTIVE-HOMOLOGY  EFFECTIVE-HOMOLOGY
-;;;  EFFECTIVE-HOMOLOGY  EFFECTIVE-HOMOLOGY  EFFECTIVE-HOMOLOGY
-;;;  EFFECTIVE-HOMOLOGY  EFFECTIVE-HOMOLOGY  EFFECTIVE-HOMOLOGY
-
-(IN-PACKAGE "COMMON-LISP-USER")
-
-(PROVIDE "effective-homology")
-
-;;;
-;;;  REDUCTIONS
-;;;
-
-(DEFVAR *RDCT-LIST*)
-(SETF *RDCT-LIST* +empty-list+)
-(PUSHNEW '*RDCT-LIST* *list-list*)
-
-#+clisp(eval-when (:compile-toplevel :load-toplevel :execute)
-         (setf (ext:package-lock :clos) nil))
-(DEFMETHOD PRINT-OBJECT ((rdct reduction) (stream stream))
- (the reduction
-   (progn
-      (format stream "[K~D Reduction K~D => K~D]"
-	      (idnm rdct) (idnm (tcc rdct)) (idnm (bcc rdct)))
-     rdct)))
-#+clisp(eval-when (:compile-toplevel :load-toplevel :execute)
-         (setf (ext:package-lock :clos) t))
-
-(DEFUN RDCT (n)
-   (declare (fixnum n))
-   (the (or null reduction)
-      (find n *rdct-list* :key #'idnm)))
-
-(DEFUN BUILD-RDCT (&key f g h orgn)
-   (declare
-      (type morphism f g h)
-      (list orgn))
-   (the reduction
-      (progn
-         (unless orgn
-            (setf orgn `(build-rdct ,f ,g ,h)))
-         (let ((already (find orgn *rdct-list* :test #'equal :key #'orgn)))
-            (declare (type (or reduction null) already))
-            (when already
-               (return-from build-rdct already)))
-         (with-slots ((fsorc sorc) (ftrgt trgt) (fdegr degr)) f
-            (declare
-               (type chain-complex fsorc ftrgt)
-               (fixnum fdegr))
-         (with-slots ((gsorc sorc) (gtrgt trgt) (gdegr degr)) g
-            (declare
-               (type chain-complex gsorc gtrgt)
-               (fixnum gdegr))
-         (with-slots ((hsorc sorc) (htrgt trgt) (hdegr degr)) h
-            (declare
-               (type chain-complex hsorc htrgt)
-               (fixnum hdegr))
-            (unless (and (eq gsorc ftrgt)
-                         (eq fsorc gtrgt)
-                         (eq hsorc fsorc)
-                         (eq htrgt fsorc)
-                         (zerop fdegr)
-                         (zerop gdegr)
-                         (= +1 hdegr))
-               (error "In BUILD-RDCT, the data are non coherent."))
-            (let ((rdct (make-instance 'reduction
-                           :tcc fsorc :bcc ftrgt
-                           :f f :g g :h h
-                           :orgn orgn)))
-               (declare (type reduction rdct))
-               (push rdct *rdct-list*)
-               rdct)))))))
-
-(DEFUN TRIVIAL-RDCT (chcm)
-  (declare (type chain-complex chcm))
-   (build-rdct
-    :f (idnt-mrph chcm)
-    :g (idnt-mrph chcm)
-    :h (zero-mrph chcm chcm +1) 
-    :orgn `(trivial-rdct ,chcm)))
-
-;;;
-;;;  HOMOTOPY-EQUIVALENCES
-;;;
-
-(DEFVAR *HMEQ-LIST*)
-(SETF *HMEQ-LIST* +empty-list+)
-(PUSHNEW '*HMEQ-LIST* *list-list*)
-
-(DEFMETHOD BUILD-HMEQ ((keyword1 (eql :lrdct)) lrdct &key rrdct orgn)
-   (declare
-      (type reduction lrdct rrdct)
-      (list orgn))
-   (the homotopy-equivalence
-      (progn
-         (with-slots ((lf f) (lg g) (lh h) (ltcc tcc) (lbcc bcc)) lrdct
-            (declare
-               (type morphism lf lg lh)
-               (type chain-complex ltcc lbcc))
-         (with-slots ((rf f) (rg g) (rh h) (rtcc tcc) (rbcc bcc)) rrdct
-            (declare
-               (type morphism rf rg rh)
-               (type chain-complex rtcc rbcc))         
-            (unless (eq ltcc rtcc)
-               (error "In BUILD-HMEQ (version from rdct), the tcc's are not the same."))
-            (unless orgn
-               (setf orgn `(build-hmeq ,lrdct ,rrdct)))
-            (let ((already (find orgn *hmeq-list* :test #'equal :key #'orgn)))
-               (declare (type (or homotopy-equivalence null) already))
-               (when already
-                  (return-from build-hmeq already)))
-            (let ((hmeq (make-instance 'homotopy-equivalence
-                           :lbcc lbcc :tcc ltcc :rbcc rbcc
-                           :lf lf :lg lg :lh lh
-                           :rf rf :rg rg :rh rh
-                           :lrdct lrdct :rrdct rrdct
-                           :orgn orgn)))
-               (declare (type homotopy-equivalence hmeq))
-               (push hmeq *hmeq-list*)
-               hmeq))))))
-#|
-  (cat-init)
-  (progn ;;;; reused in another test
-   (defun cdelta (dmns)
-     (build-chcm
-        :cmpr #'l-cmpr
-        :basis :locally-effective
-        :bsgn '(0)
-        :intr-dffr #'(lambda (degr gmsm)
-                        (make-cmbn
-                           :degr (1- degr)
-                           :list (do ((rslt +empty-list+
-                                           (cons (cons sign (append
-                                                               (subseq gmsm 0 nark)
-                                                               (subseq gmsm (1+ nark))))
-                                                 rslt))
-                                     (sign 1 (- sign))
-                                     (nark 0 (1+ nark)))
-                                    ((> nark degr) rslt))))                                           
-        :strt :gnrt
-        :orgn `(locally effective version of C_* delta ,dmns)))
-   (defun make-f (tdmns bdmns)
-     (build-mrph
-        :sorc (cdelta tdmns) :trgt (cdelta bdmns) :degr 0
-        :intr #'(lambda (degr gmsm)
-                   (let ((pos (position-if #'(lambda (vertex) (>= vertex bdmns)) gmsm)))
-                      (if pos
-                         (if (< pos degr)
-                            (zero-cmbn degr)
-                            (cmbn degr 1 (nconc (butlast gmsm) (list bdmns))))
-                         (cmbn degr 1 gmsm))))
-        :strt :gnrt
-        :orgn `(projection delta ,tdmns => delta ,bdmns)))
-   (defun make-g (tdmns bdmns)
-     (build-mrph
-        :sorc (cdelta bdmns) :trgt (cdelta tdmns) :degr 0
-        :intr #'identity
-        :strt :cmbn
-        :orgn `(injection delta ,bdmns => delta ,tdmns)))
-   (defun make-h (tdmns bdmns)
-     (build-mrph
-        :sorc (cdelta tdmns) :trgt (cdelta tdmns) :degr +1
-        :intr #'(lambda (degr gmsm)
-                   (let ((pos (position-if #'(lambda (vertex) (>= vertex bdmns)) gmsm)))
-                      (if pos
-                         (if (member bdmns gmsm)
-                            (zero-cmbn (1+ degr))
-                            (cmbn (1+ degr) (-1-expt-n pos)
-                               (append (subseq gmsm 0 pos) (list bdmns) (subseq gmsm pos))))
-                         (zero-cmbn (1+ degr)))))
-        :strt :gnrt
-        :orgn `(homotopy for delta ,tdmns => ,bdmns)))
-   (defun make-rdct (tdmns bdmns)
-       (setf rdct (build-rdct
-                    :f (make-f tdmns bdmns)
-                    :g (make-g tdmns bdmns)
-                    :h (make-h tdmns bdmns)
-                    :orgn `(reduction delta ,tdmns ,bdmns)))))
-  (setf rdct (make-rdct 6 3))
-  (setf f (f rdct) g (g rdct) h (h rdct)
-        tcc (tcc rdct) bcc (bcc rdct))
-  (setf dh (cmps (dffr tcc) h))
-  (setf hd (cmps h (dffr tcc)))
-  (setf gf (cmps g f))
-  (setf id-gf-dh-hd (i-sbtr (idnt-mrph tcc) gf dh hd))
-  (setf c (cmbn 2 1 '(0 1 2) 10 '(1 2 3) 100 '(1 2 4) 1000 '(2 3 4)))
-  (cmbn-? id-gf-dh-hd c)
-|#                                   
-
-#+clisp(eval-when (:compile-toplevel :load-toplevel :execute)
-         (setf (ext:package-lock :clos) nil))
-(DEFMETHOD PRINT-OBJECT ((hmeq homotopy-equivalence) (stream stream))
- (the homotopy-equivalence
-   (progn
-      (format stream "[K~D Homotopy-Equivalence K~D <= K~D => K~D]"
-	      (idnm hmeq)
-	      (idnm (lbcc hmeq)) (idnm (tcc hmeq)) (idnm (rbcc hmeq)))
-     hmeq)))
-#+clisp(eval-when (:compile-toplevel :load-toplevel :execute)
-         (setf (ext:package-lock :clos) t))
-
-
-(DEFMETHOD HMEQ ((n integer))
-   (declare (fixnum n))
-   (the (or homotopy-equivalence null)
-      (find n *hmeq-list* :key #'idnm)))
-
-(DEFMETHOD BUILD-HMEQ ((keyword1 (eql :lf)) lf &key lg lh rf rg rh orgn)
-   (declare
-      (type morphism lf lg lh rf rg rh)
-      (list orgn))
-   (the homotopy-equivalence
-      (progn
-         (unless orgn
-            (setf orgn `(build-hmeq ,lf ,lg ,lh ,rf ,rg ,rh)))
-         (let ((already (find orgn *hmeq-list* :test #'equal :key #'orgn)))
-            (declare (type (or null homotopy-equivalence) already))
-            (when already
-               (return-from build-hmeq already)))
-         (build-hmeq
-          :lrdct (build-rdct :f lf :g lg :h lh :orgn `(build-hmeq ,lf ,lg ,lh ,rf ,rg ,rh lrdct))
-          :rrdct (build-rdct :f rf :g rg :h rh :orgn `(build-hmeq ,lf ,lg ,lh ,rf ,rg ,rh rrdct))
-          :orgn orgn))))
-
-(DEFUN TRIVIAL-HMEQ (chcm)
-   (declare (type chain-complex chcm))
-   (build-hmeq
-      :lrdct (trivial-rdct chcm)
-      :rrdct (trivial-rdct chcm)
-      :orgn `(trivial-hmeq ,chcm)))
-
-#|
-  (cat-init)
-  (setf cc (cdelta 5))
-  (setf hmeq (trivial-hmeq cc))
-|# 
-
-;; Functions.
-
-(DEFVAR *TDD*)
-(DEFVAR *BDD*)
-(DEFVAR *ID-FG*)
-(DEFVAR *ID-GF-DH-HD*)
-(DEFVAR *HH*)
-(DEFVAR *FH*)
-(DEFVAR *HG*)
-(DEFVAR *DF-FD*)
-(DEFVAR *DG-GD*)
-
-(DEFUN PRE-CHECK-RDCT (rdct)
-   (declare (type reduction rdct))
-   (with-slots (bcc tcc f g h) rdct
-      (declare
-         (type chain-complex bcc tcc)
-         (type morphism f g h))
-      (setf *tdd* (cmps tcc tcc)
-            *bdd* (cmps bcc bcc)
-            *df-fd* (sbtr
-                       (cmps bcc f)
-                       (cmps f tcc))
-            *dg-gd* (sbtr
-                       (cmps tcc g)
-                       (cmps g bcc))
-            *id-fg* (sbtr (idnt-mrph bcc) (cmps f g))
-            *id-gf-dh-hd* (i-sbtr (idnt-mrph tcc)
-                             (cmps g f)
-                             (cmps tcc h)
-                             (cmps h tcc))
-            *hh* (cmps h h)
-            *fh* (cmps f h)
-            *hg* (cmps h g)))
-   (done))
-
-(DEFVAR *TC*)
-(DEFVAR *BC*)
-
-(DEFUN CHECK-RDCT ()
-  (dolist (cmbn '(*tc* *bc*))
-    (declare (type symbol cmbn))
-    (format t "~%~A => ~A" cmbn (eval cmbn)))
-  (dolist (phi '(*tdd* *bdd* *df-fd* *dg-gd* *id-fg* *id-gf-dh-hd*
-		       *hh* *fh* *hg*))
-    (declare (type symbol phi))
-    (format t "~%Checking ~A = 0" phi)
-    (format t "~%Result: ")
-    (princ (cmbn-? (eval phi)
-              (if (member phi '(*bdd* *dg-gd* *id-fg* *dg-gd* *hg*))
-                 *bc* *tc*)))
-    (read-line))
-  (done))
-
-#|
-  (setf rdct (make-rdct 6 3))        ;;; defined in a previous test
-  (pre-check-rdct rdct)
-  (setf *tc* (cmbn 2 1 '(0 1 2) 10 '(1 2 3) 100 '(1 2 4) 1000 '(2 3 4)))
-  (setf *bc* (cmbn 3 4 '(0 1 2 3)))  
-  (check-rdct))
-|#                                   
-
-(DEFMETHOD CMPS ((brdct reduction) (trdct reduction) &optional dummy)
-  (declare (ignore dummy))
-  (when (eq (first (orgn brdct)) 'trivial-rdct)
-     (return-from cmps trdct))
-  (when (eq (first (orgn trdct)) 'trivial-rdct)
-     (return-from cmps brdct))
-  (with-slots ((tf f) (tg g) (th h)) trdct
-    (declare (type morphism tf tg th))
-  (with-slots ((bf f) (bg g) (bh h)) brdct
-    (declare (type morphism bf bg bh))
-    (build-rdct
-       :f (cmps bf tf)
-       :g (cmps tg bg)
-       :h (add th (i-cmps tg bh tf))
-       :orgn `(cmps ,brdct ,trdct)))))
-
-#|
-  (setf trdct (make-rdct 6 4))
-  (setf brdct (make-rdct 4 3))
-  (setf rdct (cmps brdct trdct))
-  (pre-check-rdct rdct)
-  (setf *tcc* (cmbn 2 1 '(0 1 2) 10 '(1 2 3) 100 '(1 2 4)
-                      100 '(1 3 5) 10 '(1 4 5) 1 '(3 4 5))
-        *bcc* (cmbn 2 1 '(0 1 3)))
-  (check-rdct))
-|#
-
-;
-; BASIC PERTURBATION LEMMA.
-;
-
-(DEFMETHOD ADD ((rdct reduction) (perturbation morphism) &optional dummy)
-   (declare (type null dummy))
-   (when dummy
-      (error "Why a third argument in (ADD REDUCTION MORPHISM)?"))
-   (when (eq (grmd (tcc rdct)) (grmd (sorc perturbation)))
-      (return-from add
-         (basic-perturbation-lemma rdct perturbation)))
-   (when (eq (grmd (bcc rdct)) (grmd (sorc perturbation)))
-      (return-from add
-         (easy-perturbation-lemma rdct perturbation)))
-   (error "In (METHOD ADD REDUCTION MORPHISM),~@
-           the data do not sound like coherent."))
-
-(DEFUN BASIC-PERTURBATION-LEMMA (reduction top-perturbation)
-   (declare
-      (type reduction reduction)
-      (type morphism top-perturbation))
-   (the (values reduction morphism)
-      (with-slots ((old-tcc tcc) (old-bcc bcc)
-                   (old-f f) (old-g g) (old-h h)) reduction
-         (declare
-            (type chain-complex old-tcc old-bcc)
-            (type morphism old-f old-g old-h))
-         (when (eq (first (orgn top-perturbation)) 'zero-mrph)
-            (return-from basic-perturbation-lemma
-               (values reduction (zero-mrph old-bcc))))
-         (when (eq (first (orgn (h reduction))) 'zero-mrph)
-            (return-from basic-perturbation-lemma
-               (values
-                  (trivial-rdct (add old-tcc top-perturbation))
-                  (i-cmps old-f top-perturbation old-g))))      
-         (let* ((sigma (bpl-*-sigma old-h top-perturbation))
-                (new-f (cmps old-f 
-                          (sbtr (idnt-mrph old-tcc)
-                             (i-cmps
-                                top-perturbation
-                                sigma
-                                old-h))))
-                (new-g (cmps sigma old-g))
-                (new-h (cmps sigma old-h))
-                (bottom-perturbation (i-cmps
-                                        old-f
-                                        top-perturbation
-                                        new-g))
-                (new-tcc (add old-tcc top-perturbation))
-                (new-bcc (add old-bcc bottom-perturbation)))
-            (declare
-               (type chain-complex new-tcc new-bcc)
-               (type morphism sigma new-f new-g new-h bottom-perturbation))
-            (setf new-f (dstr-change-sorc-trgt new-f :new-sorc new-tcc :new-trgt new-bcc)
-                  new-g (dstr-change-sorc-trgt new-g :new-sorc new-bcc :new-trgt new-tcc)
-                  new-h (dstr-change-sorc-trgt new-h :new-sorc new-tcc :new-trgt new-tcc))
-            (values
-               (build-rdct :f new-f :g new-g :h new-h
-                  :orgn `(basic-perturbation-lemma ,reduction ,top-perturbation))
-               bottom-perturbation)))))
-
-(DEFUN EASY-PERTURBATION-LEMMA (reduction bottom-perturbation)
-   (declare
-      (type reduction reduction)
-      (type morphism bottom-perturbation))
-   (the (values reduction morphism)
-      (with-slots ((old-tcc tcc) (old-bcc bcc)
-                   (old-f f) (old-g g) (old-h h)) reduction
-         (declare
-            (type chain-complex old-tcc old-bcc)
-            (type morphism old-f old-g old-h))
-         (when (eq 'zero-mrph (first (orgn bottom-perturbation)))
-            (return-from easy-perturbation-lemma
-               (values reduction (zero-mrph old-tcc))))
-	 (when (eq 'trivial-rdct (first (orgn reduction)))
-	    (return-from easy-perturbation-lemma
-	       (trivial-rdct (add (bcc reduction) bottom-perturbation))))
-         (let ((top-perturbation (i-cmps old-g bottom-perturbation old-f)))
-            (declare (type morphism top-perturbation))
-            (let ((new-bcc (add old-bcc bottom-perturbation))
-                  (new-tcc (add old-tcc top-perturbation)))
-               (declare (type chain-complex new-bcc new-tcc))
-               (values
-                  (build-rdct
-                     :f (dstr-change-sorc-trgt old-f :new-sorc new-tcc :new-trgt new-bcc)
-                     :g (dstr-change-sorc-trgt old-g :new-sorc new-bcc :new-trgt new-tcc)
-                     :h (dstr-change-sorc-trgt old-h :new-sorc new-tcc :new-trgt new-tcc)
-                     :orgn `(easy-perturbation-lemma ,reduction ,bottom-perturbation))
-                  top-perturbation))))))
-
-(DEFUN SPECIAL-BPL (reduction top-perturbation)
-   (declare
-      (type reduction reduction)
-      (type morphism top-perturbation))
-   (when (eq (first (orgn top-perturbation)) 'zero-mrph)
-      (return-from special-bpl reduction))
-   (the reduction
-      (with-slots ((old-tcc tcc) (old-bcc bcc)
-                   (old-f f) (old-g g) (old-h h)) reduction
-         (declare
-            (type chain-complex old-tcc old-bcc)
-            (type morphism old-f old-g old-h))
-         (let* ((sigma (bpl-*-sigma old-h top-perturbation))
-                (new-f (cmps old-f 
-                          (sbtr (idnt-mrph old-tcc)
-                             (i-cmps
-                                top-perturbation
-                                sigma
-                                old-h))))
-                (new-h (cmps sigma old-h))
-                (new-tcc (add old-tcc top-perturbation)))
-            (declare
-               (type chain-complex new-tcc)
-               (type morphism sigma new-f new-h))
-            (setf new-f (dstr-change-sorc-trgt new-f :new-sorc new-tcc)
-                  old-g (dstr-change-sorc-trgt old-g :new-trgt new-tcc)
-                  new-h (dstr-change-sorc-trgt new-h :new-sorc new-tcc :new-trgt new-tcc))
-            (build-rdct :f new-f :g old-g :h new-h
-               :orgn `(special-bpl ,reduction ,top-perturbation))))))
-
-(DEFUN SPECIAL-BPL-2 (reduction top-perturbation)
-   (declare
-      (type reduction reduction)
-      (type morphism top-perturbation))
-   (the reduction
-      (with-slots ((old-tcc tcc) (old-bcc bcc)
-                   (old-f f) (old-g g) (old-h h)) reduction
-         (declare
-            (type chain-complex old-tcc old-bcc)
-            (type morphism old-f old-g old-h))
-         (when (eq (first (orgn top-perturbation)) 'zero-mrph)
-            (return-from special-bpl-2
-               (values reduction (zero-mrph old-bcc))))
-         (when (eq (first (orgn (h reduction))) 'zero-mrph)
-            (return-from special-bpl-2
-               (values
-                  (trivial-rdct (add old-tcc top-perturbation))
-                  (i-cmps old-f top-perturbation old-g))))      
-         (let* ((sigma (bpl-*-sigma old-h top-perturbation))
-                (new-g (cmps sigma old-g))
-                (new-h (cmps sigma old-h))
-                (new-tcc (add old-tcc top-perturbation)))
-            (declare
-               (type chain-complex new-tcc)
-               (type morphism sigma new-g new-h))
-            (setf old-f (dstr-change-sorc-trgt old-f :new-sorc new-tcc)
-		  new-g (dstr-change-sorc-trgt new-g :new-trgt new-tcc)
-                  new-h (dstr-change-sorc-trgt new-h :new-sorc new-tcc :new-trgt new-tcc))
-            (values
-               (build-rdct :f old-f :g new-g :h new-h
-                  :orgn `(special-bpl-2 ,reduction ,top-perturbation)))))))
-
-(DEFUN BPL-*-sigma (homotopy perturbation)
-   (declare (type morphism homotopy perturbation))
-   (the morphism
-      (let ((cmpr (cmpr (sorc perturbation)))
-            (h-delta (cmps homotopy perturbation)))
-         (declare
-            (type cmprf cmpr)
-            (type morphism h-delta))
-         (flet
-            ((sigma-* (degr gnrt)
-                (declare
-                   (fixnum degr)
-                   (type gnrt gnrt))
-                (do ((rslt (zero-cmbn degr) (2cmbn-add cmpr rslt iterated))
-                     (iterated (term-cmbn degr 1 gnrt) (cmbn-opps (cmbn-? h-delta iterated))))
-                    ((cmbn-zero-p iterated) rslt)
-                   (declare (type cmbn rslt iterated)))))
-            (build-mrph
-               :sorc (sorc homotopy) :trgt (sorc homotopy) :degr 0
-               :intr #'sigma-*
-               :strt :gnrt
-               :orgn `(bpl-*-sigma ,homotopy ,perturbation))))))
-     
-#|
-  (cat-init)
-  (setf rdct (make-rdct 6 3))
-  (setf perturb (zero-mrph (cdelta 6) (cdelta 6) -1))
-  (setf new-rdct (add rdct perturb))
-  (pre-check-rdct new-rdct)
-  (setf *tc* (cmbn 2 3 '(0 1 2))
-        *bc* (cmbn 3 4 '(0 1 2 3)))
-  (check-rdct))
-|#
-
-#|
-  (cat-init)
-  (setf rdct (make-rdct 6 3))
-  (setf perturb (opps (dffr (tcc rdct))))
-  (setf new-rdct (add rdct perturb))
-  (pre-check-rdct new-rdct)
-  (setf *tc* (cmbn 2 3 '(0 1 2))
-        *bc* (cmbn 3 4 '(0 1 2 3)))
-  (check-rdct))
-|#
-
-#|  ;; an absurd reduction ; just to test bpl-*-sigma
-  (cat-init)
-  (setf tcc (build-chcm
-               :cmpr #'l-cmpr
-               :basis :locally-effective
-               :bsgn '(0)
-               :intr-dffr #'(lambda (degr gnrt)
-                               (cmbn (1- degr) 1 gnrt))
-               :strt :gnrt
-               :orgn '(test1)))
-  (setf rdct (trivial-rdct tcc))
-  (setf (slot-value rdct 'h)
-        (build-mrph
-           :sorc tcc :trgt tcc :degr +1
-           :intr #'(lambda (degr gnrt)
-                      (cmbn (1+ degr) 1 gnrt))
-           :strt :gnrt
-           :orgn '(test2)))
-  (setf perturb
-        (build-mrph
-           :sorc tcc :trgt tcc :degr -1
-           :intr #'(lambda (degr gnrt)
-                      (if (zerop (first gnrt))
-                         (zero-cmbn (1- degr))   
-                         (cmbn (1- degr) 1 (list (1- (first gnrt)) (1+ (second gnrt))))))
-           :strt :gnrt
-           :orgn '(test3)))
-  (setf new-rdct (add rdct perturb))
-  (gnrt-? (dffr (tcc new-rdct)) 3 '(3 5))
-  (gnrt-? (dffr (bcc new-rdct)) 3 '(3 5))
-|#
-
-(DEFMETHOD ADD ((hmeq homotopy-equivalence) (lb-perturbation morphism) &optional dummy)
-   (declare (ignore dummy))
-   (the homotopy-equivalence
-      (with-slots (lrdct rrdct) hmeq
-         (declare (type reduction lrdct rrdct))
-         (multiple-value-bind (new-lrdct top-perturbation)
-                              (add lrdct lb-perturbation)
-            (declare
-               (type reduction new-lrdct)
-               (type morphism lb-perturbation))
-            (build-hmeq
-               :lrdct new-lrdct
-               :rrdct (add rrdct top-perturbation)
-               :orgn `(add ,hmeq ,lb-perturbation))))))
-                        
-#|
-  (cat-init)
-  (setf hmeq (trivial-hmeq (cdelta 4)))
-  (add (lrdct hmeq) (opps (dffr (cdelta 4))))
-  (setf hmeq (add hmeq (opps (dffr (cdelta 4)))))
-  (gnrt-? (dffr (rbcc hmeq)) 3 '(0 1 2 3)))
-|#
diff --git a/archive/Kenzo-1/eilenberg-zilber.cl b/archive/Kenzo-1/eilenberg-zilber.cl
deleted file mode 100644
index c888713..0000000
--- a/archive/Kenzo-1/eilenberg-zilber.cl
+++ /dev/null
@@ -1,480 +0,0 @@
-;;;  EILENBERG-ZILBER  EILENBERG-ZILBER  EILENBERG-ZILBER
-;;;  EILENBERG-ZILBER  EILENBERG-ZILBER  EILENBERG-ZILBER
-;;;  EILENBERG-ZILBER  EILENBERG-ZILBER  EILENBERG-ZILBER
-
-(IN-PACKAGE "COMMON-LISP-USER")
-
-(PROVIDE "eilenberg-zilber")
-
-(DEFUN SHUFFLE-SIGN (dgop)
-   (declare (fixnum dgop))
-   (the fixnum
-      (do ((rslt +1)
-           (bit-position (- (integer-length dgop) 2) (1- bit-position))
-           (factor -1))
-          ((minusp bit-position) rslt)
-         (declare (fixnum rslt bit-position factor))
-         (if (logbitp bit-position dgop)
-            (setf factor (- factor))
-            (setf rslt (* rslt factor))))))
-
-#|
-  (dotimes (i 30)
-     (format t "~%~A => ~@D" (hyphenize-list (dlop-int-ext i)) (shuffle-sign i)))
-|#       
-
-(DEFUN INTR-EML (cmbn)
-   (declare (type cmbn cmbn))
-   (when (cmbn-zero-p cmbn)
-      (return-from intr-eml cmbn))
-   (the cmbn
-      (with-cmbn (degr list) cmbn
-         (let* ((limits (make-array (+ degr 2)))
-                (rslt (list nil))
-                (rslt-mark rslt)
-                (mask (mask degr)))
-            (declare
-               (simple-vector limits)
-               (list rslt rslt-mark)
-               (fixnum mask))
-            (do ((mark list (member i mark
-                               :test #'<
-                               :key #'(lambda (term)
-                                         (declare (type term term))
-                                         (degr1 (gnrt term)))))
-                 (i 0 (1+ i)))
-                ((> i degr) (setf (svref limits i) nil))
-               (declare
-                  (list mark)
-                  (fixnum i))
-               (setf (svref limits i) mark))
-            (dotimes (dgop1 (1+ mask))
-               (declare (fixnum dgop1))
-               (let* ((i (- degr (logcount dgop1)))
-                      (dgop2 (- mask dgop1))
-                      (sign (shuffle-sign dgop2)))
-                  (declare (fixnum i dgop2 sign))
-                  (do ((mark (svref limits i) (cdr mark))
-                       (stop (svref limits (1+ i))))
-                      ((eq mark stop))
-                     (declare (list mark stop))
-                     (with--term (cffc tnpr) mark
-                        (setf rslt-mark
-                              (setf (cdr rslt-mark)
-                                    (list (term
-                                             (* sign cffc)
-                                             (crpr
-                                                dgop1 (gnrt1 tnpr)
-                                                dgop2 (gnrt2 tnpr))))))))))
-            (make-cmbn
-               :degr degr
-               :list (rest rslt))))))
-
-#|
-  (intr-eml (cmbn 3 1 (tnpr 0 'a 3 'b) 2 (tnpr 2 'a 1 'b) 3 (tnpr 2 'aa 1 'bb) 4 (tnpr 3 'a 0 'b)))
-  (intr-eml (cmbn 3 1 (tnpr 1 'c 2 'd) 10 (tnpr 2 'a 1 'b)))
-  (intr-eml (cmbn 3 10 (tnpr 1 'c 2 'd) 1 (tnpr 2 'a 1 'b) 100 (tnpr 2 'aa 1 'bb)))
-  (intr-eml (cmbn 3 10 (tnpr 1 'c 2 'd) 100 (tnpr 1 'cc 2 'dd) 1 (tnpr 2 'a 1 'b)))
-|#
-                                                    
-(DEFUN EML (smst1 smst2)
-   (build-mrph
-      :sorc (tnsr-prdc smst1 smst2)
-      :trgt (crts-prdc smst1 smst2)
-      :degr 0
-      :intr #'intr-eml
-      :strt :cmbn
-      :orgn `(eml ,smst1 ,smst2)))
-
-#|
-  (cat-init)
-  (setf d (delta-infinity))
-  (setf eml (eml d d))
-  (? eml (cmbn 3 1 (tnpr 0 1 3 30) 10 (tnpr 1 3 2 28) 100 (tnpr 2 7 1 24) 1000 (tnpr 3 15 0 16)))
-|#
-
-(DEFUN INTR-PHI (smst1 smst2
-                   &aux (crts-prdc (crts-prdc smst1 smst2))
-                        (cmpr (cmpr crts-prdc))
-                        (face1 (face smst1))
-                        (face2 (face smst2)))
-  (declare
-     (type simplicial-set smst1 smst2 crts-prdc)
-     (type cmprf cmpr)
-     (type face face1 face2))
-   (flet ((rslt (cmbn)
-             (declare (type cmbn cmbn))
-                (when (cmbn-zero-p cmbn)
-                (return-from rslt (zero-cmbn (1+ (cmbn-degr cmbn)))))
-             (the cmbn
-                (let* ((n (cmbn-degr cmbn))
-                       (n+1 (1+ n))
-                       (array-pq (make-array (list (1+ n+1) (1+ n+1)))))
-                   (declare
-                      (fixnum n n+1)
-                      (simple-array array-pq))
-                   (do ((i 1 (1+ i)))
-                       ((> i n+1))
-                      (declare (fixnum i))
-                      (do ((p i (1+ p))
-                           (q n+1 (1- q)))
-                          ((> p n+1))
-                         (declare (fixnum p q))
-                        (setf (aref array-pq p q) (zero-cmbn i))))
-                   (dolist (term (cmbn-list cmbn))
-                      (declare (type term term))
-                      (with-term (cffc crpr) term
-                         (let ((absm1 (absm1 crpr))
-                               (absm2 (absm2 crpr)))
-                            (declare (type absm absm1 absm2))
-                            (do ((n-alpha n (1- n-alpha))
-                                 (left-d absm1 (a-face4 face1 n-alpha n-alpha left-d)))
-                                ((zerop n-alpha))
-                               (declare
-                                  (fixnum n-alpha)
-                                  (type absm left-d))
-                               (do ((beta 0 (1+ beta))
-                                    (i n-alpha (1- i))  ;; pseudo-degree
-                                    (sign (-1-expt-n n-alpha) (- sign))
-                                    (right-d absm2
-                                       (a-face4 face2 (1- i) dim-right-d right-d))
-                                    (dim-right-d n (1- dim-right-d)))
-                                   ((= beta n-alpha))
-                                  (declare
-                                     (fixnum beta i sign dim-right-d)
-                                     (type absm right-d))
-                                  (let ((absm1 (1dgnr (1- i) left-d)))
-                                     (declare (type absm absm1))
-                                     (with-absm (dgop1 gmsm1) absm1
-                                     (with-absm (dgop2 gmsm2) right-d
-                                        (or (> (integer-length dgop1) i)
-                                            (> (integer-length dgop2) i)
-                                            (plusp (logand dgop1 dgop2))
-                                            (dstr-add-term-to-cmbn
-                                               cmpr
-                                               (* sign cffc)
-                                               (crpr dgop1 gmsm1 dgop2 gmsm2)
-                                             (aref array-pq (1+ n-alpha) (- n beta))))))))))))
-                  ;;                 array-pq)))  ;; in case of debugging
-                  (intr-phi-2 array-pq cmpr)
-               ))))
-      (the intr-mrph #'rslt)))
-
-#|
-()
-(setf d (delta-infinity))
-(setf rslt (intr-phi d d))
-(funcall rslt (cmbn 3 1 (crpr 0 15 0 15)))
-|#
-
-#|
-
-(DEFUN INTR-PHI-22 (array-pq cmpr)
-   (declare
-      (type (simple-array cmbn (* *)) array-pq)
-      (type cmprf cmpr))
-;   (format t "  -22-  ")
-   (the cmbn
-      (let* ((n+1 (1- (array-dimension array-pq 0)))
-             (n (1- n+1)))
-         (declare (fixnum n n+1))
-         (flet ((step-i (i)
-                   (declare (fixnum i))
-                 (do ((p (1+ i) (1+ p))
-                      (p-1 i p)
-                      (q n+1 q-1)
-                      (q-1 n (1- q-1))
-                      (sign t (not sign))
-                      (ibit (2-exp i)))
-                     ((> p n+1))
-                    (declare
-                       (fixnum p p-1 q q-1 ibit)
-                       (type boolean sign))
-                    (setf (aref array-pq p q)
-                          (2cmbn-add cmpr
-                             (aref array-pq p q)
-                             (make-cmbn
-                                :degr (1+ i)
-                                :list (nconc
-                                         (mapcar
-                                            #'(lambda (term)
-                                                 (declare (type term term))
-                                                 (with-term (cffc crpr) term
-                                                    (with-crpr (dgop1 gmsm1 dgop2 gmsm2) crpr
-                                                       (term cffc (crpr
-                                                                     dgop1 gmsm1
-                                                                     (+ ibit dgop2) gmsm2)))))
-                                            (cmbn-list (aref array-pq p q-1)))
-                                         (let ((list (cmbn-list (aref array-pq p-1 q))))
-                                            (declare (list lst))
-                                            (unless sign
-                                               (dolist (term list)
-                                                  (declare (type term term))
-                                                  (setf (cffc term) (- (cffc term)))))
-                                            (dolist (term list)
-                                               (declare (type term term))
-                                               (incf (dgop1 (gnrt term)) ibit))
-                                           list))))))))
-            (do ((i 1 (1+ i)))
-                ((= i n+1))
-               (declare (type fixnum i))
-               (step-i i))
-            (aref array-pq n+1 n+1)))))
-|#
-
-(DEFUN INTR-PHI-2 (array-pq cmpr)
-   (declare
-      (type (simple-array cmbn (* *)) array-pq)
-      (type cmprf cmpr))
-;   (format t "  -2-  ")
-   (the cmbn
-      (let* ((n+1 (1- (array-dimension array-pq 0)))
-             (n (1- n+1))
-             (cmbn-list +empty-list+))
-         (declare
-            (fixnum n n+1)
-            (list cmbn-list))
-         (do ((i 1 (1+ i))
-              (cmbn-i (list nil) (list nil))
-              (mask (mask n) (ash mask -1)))
-             ((= i n+1))
-            (declare
-               (fixnum i mask)
-               (list cmbn-i))
-            (let ((cmbn-i-tail cmbn-i))
-               (declare (list cmbn-i-tail))
-               (do ((dgop1 0 (1+ dgop1)))
-                   ((> dgop1 mask)
-                    (push (make-cmbn
-                             :degr n+1
-                             :list (rest cmbn-i)) 
-                       cmbn-list))
-                  (declare (fixnum dgop1))
-                  (let ((p (- n+1 (logcount dgop1)))
-                        (dgop2 (- mask dgop1)))
-                     (declare (fixnum p dgop2))
-                     (unless (= p i)
-                        (let ((q (- (+ n+1 i) p))
-                              (sign (shuffle-sign dgop2))
-                              (dgop1-ashed (ash dgop1 i))
-                              (dgop2-ashed (ash dgop2 i)))
-                           (declare (fixnum q sign dgop1-ashed dgop2-ashed))
-                           (dolist (term (cmbn-list (aref array-pq p q)))
-                              (declare (type term term))
-                              (with-term (cffc crpr) term
-                                 (with-crpr (dgop1 gmsm1 dgop2 gmsm2) crpr
-                                    (setf cmbn-i-tail
-                                          (setf (cdr cmbn-i-tail)
-                                                (list (term (* sign cffc)
-                                                         (crpr
-                                                            (+ dgop1 dgop1-ashed) gmsm1
-                                                            (+ dgop2 dgop2-ashed) 
-                                                            gmsm2))))))))))))))
-         (if cmbn-list
-            (apply #'ncmbn-add cmpr cmbn-list)
-            (zero-cmbn n+1)))))
-
-#|
-  (setf d (delta-infinity))
-  (setf rslt (intr-phi d d))
-  (funcall rslt (cmbn 3 1 (crpr 0 15 0 15)))
-  (funcall rslt (cmbn 2 1 (crpr 0 7 0 7)))
-  (funcall rslt (cmbn 1 1 (crpr 0 3 0 3)))
-  (funcall rslt (cmbn 0 1 (crpr 0 1 0 1)))
-|#
-
-(DEFUN PHI (smst1 smst2)
-   (declare (type simplicial-set smst1 smst2))
-   (the morphism
-      (build-mrph
-         :sorc (crts-prdc smst1 smst2)
-         :trgt (crts-prdc smst1 smst2)
-         :degr +1
-         :intr (intr-phi smst1 smst2)
-         :strt :cmbn
-         :orgn `(phi ,smst1 ,smst2))))
-
-#|
-  (setf phi (phi (delta-infinity) (delta-infinity)))
-  (? phi 3 (crpr 0 15 0 15))
-|#
-
-#|  ;; Comparison with EAT.
-    ;; In Kenzo.
-  (cat-init)
-  (setf s (sphere 5))
-  (setf p (crts-prdc s s))
-  (setf b (basis p 8))
-  (setf c (make-cmbn :degr 8
-             :list (mapcar #'(lambda (item)
-                                (term (1+ (random 5)) item))
-                      b)))
-  (setf phi (phi s s))
-  (time (? phi c)))
-|#
-
-#|  ;; in EAT
-  (setf s (sphere 5))
-  (setf p (cpr-2ss s s))
-  (setf b (sbs p 8))
-  (setf c (make-cmb :dgr 8
-             :lst (mapcar #'(lambda (item)
-                               (mnm (1+ (random 5)) item))
-                     b)))
-  (setf phi (phi s s))
-  (time (??? phi c))
-|#
-
-(DEFUN INTR-AW (face1 face2)
-   (declare (type face face1 face2))
-   (flet ((rslt (dmns crpr)
-           (declare
-              (fixnum dmns)
-              (type crpr crpr))
-           (the cmbn
-              (let ((absm1 (absm1 crpr))
-                    (absm2 (absm2 crpr))
-                    (rslt +empty-list+)
-                    (del-0-s +empty-list+))
-                 (declare
-                    (type absm absm1 absm2)
-                    (list rslt del-0-s))
-                 (do ((face absm2 (a-face4 face2 0 dmns2 face))
-                      (dmns2 dmns (1- dmns2)))
-                     ((zerop dmns2) (push face del-0-s))
-                    (declare
-                       (type absm face)
-                       (fixnum dmns))
-                    (push face del-0-s))
-                 (do ((face absm1 (a-face4 face1 dmns1 dmns1 face))
-                      (dmns1 dmns (1- dmns1))
-                      (dmns2 0 (1+ dmns2))
-                      (mark del-0-s (cdr mark)))
-                     ((zerop dmns1)
-                      (unless (degenerate-p absm2)
-                         (push
-                            (term 1
-                               (tnpr 0 (gmsm face) dmns (gmsm absm2)))
-                            rslt)))
-                    (declare
-                       (type absm face)
-                       (fixnum dmns1 dmns2)
-                       (list mark))
-                    (unless (or (degenerate-p face)
-                                (degenerate-p (car mark)))
-                       (push
-                          (term 1
-                             (tnpr dmns1 (gmsm face) dmns2 (gmsm (car mark))))
-                          rslt)))
-                 (make-cmbn
-                    :degr dmns
-                    :list rslt)))))
-      (the intr-mrph #'rslt)))
-
-#|
-  (setf r (intr-aw #'delta-face #'delta-face))
-  (funcall r 3 (crpr 0 15 0 15))
-  (setf s (sphere 3))
-  (setf f (face s))
-  (setf r (intr-aw f f))
-  (funcall r 3 (crpr 0 's3 0 's3))
-|#
-
-(DEFUN AW (smst1 smst2
-             &aux (crts-prdc (crts-prdc smst1 smst2))
-                  (tnsr-prdc (tnsr-prdc smst1 smst2))
-                  (face1 (face smst1))
-                  (face2 (face smst2)))
-   (declare
-      (type simplicial-set smst1 smst2)
-      (type face face1 face2))
-   (the morphism
-      (build-mrph
-         :sorc crts-prdc
-         :trgt tnsr-prdc
-         :degr 0
-         :intr (intr-aw face1 face2)
-         :strt :gnrt
-         :orgn `(aw ,smst1 ,smst2))))
-
-#|
-  (setf aw (aw (delta-infinity) (delta-infinity)))
-  (? aw (cmbn 3 1 (crpr 0 15 0 30) -1 (crpr 0 23 0 29)))
-|#
-
-(DEFUN EZ (smst1 smst2)
-   (declare (type simplicial-set smst1 smst2))
-   (the reduction
-      (build-rdct
-         :f (aw smst1 smst2)
-         :g (eml smst1 smst2)
-         :h (phi smst1 smst2)
-         :orgn `(eilenberg-zilber ,smst1 ,smst2))))
-
-#|
-(setf ez (ez (delta-infinity) (delta-infinity)))
-(setf *bc* (cmbn 3 1 (tnpr 0 1 3 30)
-             10 (tnpr 1 96 2 896)
-             100 (tnpr 2 7168 1 3)
-             1000 (tnpr 3 15 0 4096)))
-(setf *tc* (cmbn 3 1 (crpr 0 15 0 480)
-             100 (crpr 0 15 5 96)
-             10 (crpr 6 3 0 480)
-             1000 (crpr 6 3 1 224)))
-(pre-check-rdct ez)
-(check-rdct)
-|#
-
-
-#|
-  ;; Comparison EAT.
-  ;; In Kenzo.
-  (cat-init)
-  (setf s (sphere 5))
-  (setf ez (ez s s))
-  (setf b (basis (tcc ez) 8))
-  (setf c (make-cmbn :degr 8
-             :list (mapcar #'(lambda (item)
-                                (term (1+ (random 5)) item))
-                      b)))
-  (pre-check-rdct ez)
-  (setf +too-much-time+ -1)
-  (time (? *id-gf-dh-hd* c))
-  (time (? *id-gf-dh-hd* c))
-|#
-
-#|
-  ;; in EAT
-  (setf s (sphere 5))
-  (setf ez (ez s s))
-  (setf b (cbs (rdc-tcc ez) 8))
-  (setf c (make-cmb :dgr 8
-           :lst (mapcar #'(lambda (item)
-                             (mnm (1+ (random 5)) item))
-                   b)))
-  (verif-rdc ez)
-  (time (??? *id-gf-dh-hd* c))
-  (time (??? *id-gf-dh-hd* c))
-|#
-
-(DEFUN LEFT-CRTS-PRDC-EFHM (smst1 smst2)
-  (declare (type simplicial-set smst1 smst2))
-  (the homotopy-equivalence
-     (build-hmeq
-       :lrdct (trivial-rdct (crts-prdc smst1 smst2))
-       :rrdct (ez smst1 smst2))))
-
-(DEFMETHOD SEARCH-EFHM (smst (orgn (eql 'crts-prdc)))
-  (declare (type simplicial-set smst))
-  (the homotopy-equivalence
-    (cmps
-      (left-crts-prdc-efhm (second (orgn smst)) (third (orgn smst)))
-      (tnsr-prdc (efhm (second (orgn smst)))
-		 (efhm (third (orgn smst)))))))
-
-#|
-  (cat-init)
-  (setf k (k-z 2))
-  (setf k2 (crts-prdc k k))
-  (homology k2 0 10)
-|#
\ No newline at end of file
diff --git a/archive/Kenzo-1/fibrations.cl b/archive/Kenzo-1/fibrations.cl
deleted file mode 100644
index ca968b1..0000000
--- a/archive/Kenzo-1/fibrations.cl
+++ /dev/null
@@ -1,185 +0,0 @@
-;;;  FIBRATIONS  FIBRATIONS  FIBRATIONS  FIBRATIONS  FIBRATIONS
-;;;  FIBRATIONS  FIBRATIONS  FIBRATIONS  FIBRATIONS  FIBRATIONS
-;;;  FIBRATIONS  FIBRATIONS  FIBRATIONS  FIBRATIONS  FIBRATIONS
-
-(IN-PACKAGE "COMMON-LISP-USER")
-
-(PROVIDE "fibrations")
-
-(DEFUN FIBRATION-TOTAL-FACE (fibration
-		     &aux (base (sorc fibration))
-		          (bface (face base))
-		          (fibr (trgt fibration))
-			  (fbspn (bspn fibr))
-			  (fface (face fibr))
-			  (grml (grml fibr))
-			  (sintr-grml (sintr grml))
-			  (totl (crts-prdc base fibr))
-			  (uface (face totl))
-			  (sintr-twist (sintr fibration)))			  
-  (declare
-     (type fibration fibration)
-     (type simplicial-mrph grml)
-     (type simplicial-set base totl)
-     (type simplicial-group fibr)
-     (type gmsm fbspn)
-     (type face bface fface uface)
-     (type sintr sintr-grml sintr-twist))
-  (flet ((rslt (indx dmns crpr)
-	    (declare
-	       (fixnum indx dmns)
-	       (type crpr crpr))
-	    (the absm
-	       (progn
-		 (when (< indx dmns)
-		    (return-from rslt
-		       (funcall uface indx dmns crpr)))
-		 (with-crpr (b-absm f-absm) crpr
-		    (let ((deln-b
-			   (a-face4 bface dmns dmns
-				     b-absm))
-			  (deln-f
-			   (a-face4 fface dmns dmns
-				     f-absm))
-			  (tau-b
-			   (tw-a-sintr3 sintr-twist dmns
-					b-absm fbspn)))
-		      (declare
-		         ( type absm deln-b deln-f tau-b))
-		      (2absm-acrpr
-		        deln-b
-		        (a-grml4 sintr-grml (1- dmns)
-				 tau-b deln-f))))))))
-	(the face #'rslt)))
-
-#|
-  (cat-init)
-  (setf h (hopf 1))
-  (setf sf (serre-face h))
-  (funcall sf 0 2 (crpr 0 's2 0 '(2 4)))
-  (funcall sf 1 2 (crpr 0 's2 0 '(2 4)))
-  (funcall sf 2 2 (crpr 0 's2 0 '(2 4)))
-  (funcall sf 3 3 (crpr 1 's2 2 '(2 4)))
-|#
-
-(DEFUN FIBRATION-TOTAL (fibration
-			  &aux (base (sorc fibration))
-			       (fibre (trgt fibration))
-			       (untwisted-prdc
-				  (crts-prdc base fibre)))
-  (declare (type fibration fibration))
-  (the simplicial-set
-     (let ((rslt (build-smst
-                    :cmpr (cmpr untwisted-prdc)
-		    :basis (basis untwisted-prdc)
-		    :bspn (bspn untwisted-prdc)
-		    :face (fibration-total-face fibration)
-		    :orgn `(fibration-total ,fibration))))
-       (declare (type simplicial-set rslt))
-       (setf (slot-value rslt 'grmd) untwisted-prdc) 
-       (when (and (typep base 'kan)
-		  (typep fibre 'kan))
-	  (change-class rslt 'kan)
-	  (setf (slot-value rslt 'kfll)
-		(fibration-kfll fibration)))
-       rslt)))
-
-#|
-  (cat-init)
-  (setf s2 (sphere 2))
-  (setf k (k-z-1))
-  (setf tw (build-smmr
-             :sorc s2
-	     :trgt k
-	     :degr -1
-	     :sintr #'(lambda (dmns gmsm)
-			(absm 0 (list 1)))
-	     :orgn '(s2-tw-kz1)))
-  (setf e (fibration-total tw))
-  (homology e 2)
-  (homology e 0 8)
-  (cat-init)
-  (setf s2 (sphere 2))
-  (setf k (k-z2-1))
-  (setf tw (build-smmr
-             :sorc s2
-	     :trgt k
-	     :degr -1
-	     :sintr #'(lambda (dmns gmsm)
-			(absm 0 1))
-	     :orgn '(s2-tw-kz2)))
-  (setf e (fibration-total tw))
-  (homology e 2)
-  (homology e 0 8)
-|#
-		 
-(DEFUN FIBRATION-KFLL (twist
-		        &aux (sintr-twist (sintr twist))
-			     (base (sorc twist))
-			     (fibre (trgt twist))
-			     (fbspn (bspn fibre))
-			     (bkfll (kfll base))
-			     (fkfll (kfll fibre))
-			     (sintr-grml (sintr (grml fibre)))
-			     (sintr-grin (sintr (grin fibre))))
-  (declare
-     (type fibration twist)
-     (type kan base fibre)
-     (type gmsm fbspn)
-     (type kfll bkfll fkfll)
-     (type sintr sintr-grml sintr-grin))
-  (flet ((rslt (indx dmns hat)
-	   (declare
-	      (fixnum indx dmns)
-	      (list hat))
-	   (let (bhat fhat)
-	     (declare (type list bhat fhat))
-	     (do ((mark hat (cdr mark)))
-		 ((endp mark))
-		(declare (list mark))
-		(let ((absm (car mark)))
-		  (declare (type absm absm))
-		  (with-absm (dgop crpr) absm
-		  (with-crpr (dgop1 gmsm1 dgop2 gmsm2) crpr
-		     (push (absm (dgop*dgop dgop dgop1) gmsm1) bhat)
-		     (push (absm (dgop*dgop dgop dgop2) gmsm2) fhat)))))
-	     (setf bhat (nreverse bhat))
-	     (let ((bkfll (funcall bkfll indx dmns bhat)))
-	       (declare (type absm bkfll))
-	       (when (< indx dmns)
-		 (setf (first fhat)
-		       (a-grml4 sintr-grml (1- dmns)
-				(a-grin4 sintr-grin (1- dmns)
-					 (tw-a-sintr3 sintr-twist dmns bkfll fbspn))
-				(first fhat))))
-	       (setf fhat (nreverse fhat))
-	       (let ((fkfll (funcall fkfll indx dmns fhat)))
-		 (declare (type absm fkfll))
-		 (2absm-acrpr bkfll fkfll))))))
-	(the kfll #'rslt)))
-
-#|
-  (cat-init)
-  (load "r-proj-space")
-  (setf tw (kdivide-z2-twist opr opr-chml-clss))
-  (setf pr-4 (fibration-total tw))
-  (setf absm (absm 0 (crpr 0 (loop3 0 5 2) 0 4)))
-  (setf hat (mapcar #'(lambda (i) (face pr-4 i 4 absm))
-                    (<a-b> 0 4)))
-  (dotimes (i 5)
-    (print (kfll pr-4 i 4 (remove (nth i hat) hat)))
-    (check-kan pr-4 i 4 (remove (nth i hat) hat)))
-|#
-
-#|
-  (cat-init)
-  (setf os3-fibration os3-fibration)
-  (setf total (fibration-total os3-fibration))
-  (setf absm (absm 1 (crpr 0 (loop3 1 's3 1 2 's3 -2)
-				   0 '(-2 1 1))))
-  (setf hat (mapcar #'(lambda (i) (face total i 4 absm))
-                    '(0 1 2 3 4)))
-  (dotimes (i 5)
-    (print (kfll total i 4 (remove (nth i hat) hat)))
-    (check-kan total i 4 (remove (nth i hat) hat)))
-|#
\ No newline at end of file
diff --git a/archive/Kenzo-1/homology-groups.cl b/archive/Kenzo-1/homology-groups.cl
deleted file mode 100644
index 130b178..0000000
--- a/archive/Kenzo-1/homology-groups.cl
+++ /dev/null
@@ -1,673 +0,0 @@
-;;  HOMOLOGY-GROUPS  HOMOLOGY-GROUPS  HOMOLOGY-GROUPS  HOMOLOGY-GROUPS
-;;  HOMOLOGY-GROUPS  HOMOLOGY-GROUPS  HOMOLOGY-GROUPS  HOMOLOGY-GROUPS
-;;  HOMOLOGY-GROUPS  HOMOLOGY-GROUPS  HOMOLOGY-GROUPS  HOMOLOGY-GROUPS
-
-(IN-PACKAGE "COMMON-LISP-USER")
-
-(provide "homology-groups")
-
-;;
-;;  Computing ordinary homology-groups. 
-;;  
-
-
-;; Functions.
-
-(defun creer-matrice (n1 n2)
-   (let ((mat (make-matrice
-                 :leftcol (make-array (1+ n1))
-                 :uplig (make-array (1+ n2)))))
-      (setf (baselig mat 0) (make-t-mat :ilig 0 :icol 0))
-      (setf (basecol mat 0) (baselig mat 0))
-      (do ((i 1 (1+ i)))
-         ((> i n1))
-         (setf (baselig mat i)
-            (make-t-mat :ilig i :icol 0 :up (baselig mat (1- i))))
-         (setf (left (baselig mat i)) (baselig mat i)))
-      (do ((j 1 (1+ j)))
-         ((> j n2))
-         (setf (basecol mat j)
-            (make-t-mat :ilig 0 :icol j :left (basecol mat (1- j))))
-         (setf (up (basecol mat j)) (basecol mat j)))
-      (setf (up (baselig mat 0)) (baselig mat n1))
-      (setf (left (basecol mat 0)) (basecol mat n2))
-      mat))
-
-(defun chercher-hor (p ic)
-   (do ((p2 p p1)
-        (p1 (left p) (left p1)))
-        ((<= (icol p1) ic) p2)))
-
-(defun chercher-ver (p il)
-   (do ((p2 p p1)
-        (p1 (up p) (up p1)))
-       ((<= (ilig p1) il) p2)))
-
-(defun inserer-terme (pl pc val)
-   (setf (left pl) (make-t-mat :val val
-                               :ilig (ilig pl)
-                               :icol (icol pc)
-                               :left (left pl)
-                               :up (up pc))
-         (up pc) (left pl)))
-
-(defun supprimer-terme (pl pc)
-   (setf (left pl) (left (left pl))
-         (up pc) (up (up pc))))
-
-(defun maj-terme (pl pc val)
-  (if (= val 0)
-      (if (eq (left pl) (up pc)) (supprimer-terme pl pc))
-      (if (eq (left pl) (up pc))
-          (setf (val (left pl)) val)
-          (inserer-terme pl pc val))))
-
-(defun maj-ligne (mat il liste)
-   (let ((ptl (baselig mat il)))
-        (mapcar
-           #'(lambda (elem)
-                (maj-terme (chercher-hor ptl (first elem))
-                           (chercher-ver (basecol mat (first elem)) il)
-                           (second elem)))
-           liste)
-        ptl))
-
-(defun maj-colonne (mat ic liste)
-   (let ((ptc (basecol mat ic)))
-        (mapcar
-           #'(lambda (elem)
-                (maj-terme (chercher-hor (baselig mat (first elem)) ic)
-			   (chercher-ver ptc (first elem))
-                           (second elem)))
-           liste)
-        ptc))
-
-(defun maj-matrice (mat liste)
-  (mapcar
-     #'(lambda (elem) (apply #'maj-ligne mat elem))
-     liste)
-  mat)
-
-(defun disp-p (p)
-   `((,(ilig p) ,(icol p) ,(val p))
-     (,(ilig (left p)) ,(icol (left p)) ,(val (left p)))
-     (,(ilig (up p)) ,(icol (up p)) ,(val (up p)))))
-
-(defun disp-ligne (mat il)
-   (terpri)
-   (princ "L")
-   (princ il)
-   (princ "=")
-   (mapcar
-      #'(lambda (elem)
-           (princ "(")
-           (princ (first elem))
-           (princ ":")
-           (princ (second elem))
-           (princ ")"))
-      (let ((ptl (baselig mat il))
-            (res '()))
-         (do ((pl (left ptl) (left pl)))
-             ((eq pl ptl))
-            (push (list (icol pl) (val pl)) res))
-         res))
-  (values ))
-
-(defun disp-colonne (mat ic)
-   (terpri)
-   (princ "C")
-   (princ ic)
-   (princ "=")
-   (mapcar
-      #'(lambda (elem)
-           (princ "(")
-           (princ (first elem))
-           (princ ":")
-           (princ (second elem))
-           (princ ")"))
-      (let ((ptc (basecol mat ic))
-            (res '()))
-         (do ((pc (up ptc) (up pc)))
-             ((eq pc ptc))
-            (push (list (ilig pc) (val pc)) res))
-         res))
-   (values ))
-
-(defun nlig (mat) (1- (array-dimension (leftcol mat) 0)))
-(defun ncol (mat) (1- (array-dimension (uplig mat) 0)))
-
-(defun disp-matrice (mat)
-   (let ((nlig (nlig mat)))
-      (do ((i 1 (1+ i)))
-          ((> i nlig))
-          (disp-ligne mat i)))
-   (done))
-
-#+clisp(eval-when (:compile-toplevel :load-toplevel :execute)
-         (setf (ext:package-lock :clos) nil))
-(DEFMETHOD PRINT-OBJECT ((mtrx matrice) stream)
-  (declare (stream stream))
-  (the matrice (progn
-    (let ((nlig (nlig mtrx))
-	  (ncol (ncol mtrx)))
-      (declare (fixnum nlig ncol))
-      (format stream "~%========== MATRIX ~D lines + ~D columns ====="
-	      nlig ncol)
-      (do ((ilig 1 (1+ ilig)))
-	  ((> ilig nlig))
-	  (declare (fixnum ilig))
-	(format stream "~%L~D=" ilig)
-	(dolist (item (let ((baselig (baselig mtrx ilig)))
-			(declare (type t-mat baselig))
-			(do ((rslt +empty-list+ (cons t-mat rslt))
-			     (t-mat (left baselig) (left t-mat)))
-			    ((eq t-mat baselig) rslt)
-			    (declare
-			      (list rslt)
-			      (type t-mat t-mat)))))
-	   (declare (type t-mat item))
-	   (format stream "[C~D=~D]" (icol item) (val item))))
-      (format stream "~%========== END-MATRIX"))
-                 mtrx)))
-#+clisp(eval-when (:compile-toplevel :load-toplevel :execute)
-         (setf (ext:package-lock :clos) t))
-
-
-(defun disp-matrice-colonnes (mat)
-   (let ((ncol (ncol mat)))
-      (do ((i 1 (1+ i)))
-          ((> i ncol))
-          (disp-colonne mat i)))
-   (done))
-
-(defun terme (mat i j)
-   (let ((p (left (chercher-hor (baselig mat i) j))))
-        (if (= j (icol p))
-            (val (left p))
-            nil)))
-
-(defun mat-aleat (n1 n2 dens x)
-   (let ((mat (creer-matrice n1 n2))
-         (n (truncate (* dens n1 n2)))
-         (2x (* 2 x))
-         (res nil))
-      (dotimes (i n)
-         (let* ((il (1+ (random n1)))
-                (ic (1+ (random n2)))
-                (val (let ((pval (- (random 2x) x)))
-                        (if (minusp pval)
-                            pval
-                            (1+ pval))))
-                (elem (member il res
-                         :test #'(lambda (x y) (eql x (first y))))))
-            (if elem
-                (push (list ic val) (cadar elem))
-                (push (list il (list (list ic val))) res))))
-      (maj-matrice mat res)))
-
-(defun op-elem (pl pc alpha)
-   (if (eq (left pl) (up pc))
-       (if (= alpha (val (left pl)))
-           (supprimer-terme pl pc)
-           (decf (val (left pl)) alpha))
-       (inserer-terme pl pc (- alpha))))
-
-(defun peigne-ver (mat ptl il)
-       (if (< il (ilig ptl))
-           (do ((res nil (cons (chercher-ver pl il)
-                               res))
-                (pl (left ptl) (left pl)))
-               ((eq pl ptl) (nreverse res)))
-           (do ((res nil (cons (chercher-ver (basecol mat (icol pl)) il)
-                               res))
-                (pl (left ptl) (left pl)))
-               ((eq pl ptl) (nreverse res)))))
-
-(defun peigne-hor (mat ptc ic)
-       (if (< ic (icol ptc))
-           (do ((res nil (cons (chercher-hor pc ic)
-                               res))
-                (pc (up ptc) (up pc)))
-               ((eq pc ptc) (nreverse res)))
-           (do ((res nil (cons (chercher-hor (baselig mat (ilig pc)) ic)
-                               res))
-                (pc (up ptc) (up pc)))
-               ((eq pc ptc) (nreverse res)))))
-
-(defun op-lig (ptl1 ptl2 peigne lambda)
-  (do ((pl1 (left ptl1) (left pl1))
-       (pp peigne (rest pp))
-       (pl2 ptl2))
-      ((endp pp) ptl2)
-    (setf pl2 (chercher-hor pl2 (icol pl1)))
-    (op-elem pl2 (first pp) (* lambda (val pl1)))))
-
-(defun op-col (ptc1 ptc2 peigne lambda)
-  (do ((pc1 (up ptc1) (up pc1))
-       (pp peigne (rest pp))
-       (pc2 ptc2))
-      ((endp pp) ptc2)
-    (setf pc2 (chercher-ver pc2 (ilig pc1)))
-    (op-elem (first pp) pc2 (* lambda (val pc1)))))
-
-(defun op-lig-n (mat l1 l2 lambda)
-  (op-lig (baselig mat l1)
-          (baselig mat l2)
-          (peigne-ver mat (baselig mat l1) l2)
-          lambda))
-
-(defun op-col-n (mat c1 c2 lambda)
-  (op-col (basecol mat c1)
-          (basecol mat c2)
-          (peigne-hor mat (basecol mat c1) c2)
-          lambda))
-
-(defun n-lig (mat)
-  (1- (array-dimension (leftcol mat) 0)))
-
-(defun n-col (mat)
-  (1- (array-dimension (uplig mat) 0)))
-
-(defun copier-matrice (mat)
-  (let ((mat2 (creer-matrice (n-lig mat) (n-col mat))))
-    (do ((i 1 (1+ i)))
-        ((> i (n-lig mat)) mat2)
-      (do ((ptl1 (baselig mat i))
-           (pl1 (left (baselig mat i)) (left pl1))
-           (pl2 (baselig mat2 i) (left pl2)))
-          ((eq pl1 ptl1))
-        (inserer-terme pl2 (basecol mat2 (icol pl1)) (val pl1))))))
-
-(defun reste (a b)
-  (second (multiple-value-list (round a b))))
-
-(defun diviseur (a b)
-  (round a b))
-
-(defun maj-peigne-ver (peigne il)
-  (do ((pp peigne (rest pp)))
-      ((endp pp) peigne)
-    (setf (first pp) (chercher-ver (first pp) il))))
-
-(defun maj-peigne-hor (peigne ic)
-  (do ((pp peigne (rest pp)))
-      ((endp pp) peigne)
-    (setf (first pp) (chercher-hor (first pp) ic))))
-
-(defun identite (n)
-  (let ((mat (creer-matrice n n)))
-    (do ((ptl (baselig mat n) (up ptl))
-         (ptc (basecol mat n) (left ptc)))
-        ((eq ptl ptc))
-      (inserer-terme ptl ptc 1))
-    mat))
-
-(defun init-peigne-ver (mat ptl)
-  (do ((res nil (cons (basecol mat (icol pl))
-                      res))
-       (pl (left ptl) (left pl)))
-      ((eq pl ptl) (nreverse res))))
-
-(defun init-peigne-hor (mat ptc)
-  (do ((res nil (cons (baselig mat (ilig pc))
-                      res))
-       (pc (up ptc) (up pc)))
-      ((eq pc ptc) (nreverse res))))
-
-(defun disp-peigne (peigne)
-  (mapcar #'(lambda (elem) (first (disp-p elem)))
-          peigne))
-
-(defun terme-minimal-matrice (mat)
-  (catch '?
-    (do* ((fin (baselig mat 0))
-          (ptl (up fin) (up ptl)))
-         ((eq ptl fin) (throw '? nil))
-      (if (not (eq ptl (left ptl)))
-          (let* ((pmin (left ptl))
-                 (min (abs (val pmin))))
-            (if (= min 1) (throw '? pmin))
-            (do ((ptl ptl (up ptl)))
-                ((eq ptl fin) (throw '? pmin))
-              (do ((pl (left ptl) (left pl)))
-                  ((eq pl ptl))
-                (let ((val (abs (val pl))))
-                  (when (< val min)
-                    (if (= val 1) (throw '? pl))
-                    (setq pmin pl min val))))))))))
-
-(defun tuer-ligne (mat il)
-  (let* ((ptl (baselig mat il))
-         (peigne (peigne-ver mat ptl il)))
-    (do ((pp peigne (rest pp)))
-        ((endp pp))
-      (supprimer-terme ptl (first pp)))
-    (setf (up (chercher-ver (baselig mat 0) il)) (up ptl)))
-  mat)
-
-(defun tuer-colonne (mat ic)
-  (let* ((ptc (basecol mat ic))
-         (peigne (peigne-hor mat ptc ic)))
-    (do ((pp peigne (rest pp)))
-        ((endp pp))
-      (supprimer-terme (first pp) ptc))
-    (setf (left (chercher-hor (basecol mat 0) ic)) (left ptc)))
-  mat)
-
-(defun pivot (mat p)
-  (let* ((div (val p))
-         (ptl (baselig mat (ilig p)))
-         (ptc (basecol mat (icol p)))
-         (peigne (init-peigne-ver mat ptl))
-         (peigne2 '*non-defini*))
-    (do ((pc (up ptc) (up pc)))
-        ((eq pc ptc))
-      (maj-peigne-ver peigne (ilig pc))
-      (if (eq pc p)
-          (setf peigne2 (copy-list peigne))
-          (op-lig ptl
-                  (baselig mat (ilig pc))
-                  peigne
-                  (truncate (val pc) div))))
-    (do ((pp peigne2 (rest pp)))
-        ((endp pp))
-      (supprimer-terme ptl (first pp)))
-    (setf (left (chercher-hor (basecol mat 0) (icol p))) (left ptc))
-    (setf (up   (chercher-ver (baselig mat 0) (ilig p))) (up   ptl))
-    (list (ilig p) (icol p) (val p))))
-
-(defun pivot-parallele (M N p)
-  (let* ((div (val p))
-         (ic (icol p))
-         (ptl (baselig M (ilig p)))
-         (ptc (basecol N ic))
-         (peigne (init-peigne-hor N ptc))
-         (peigne2 '*non-defini*))
-    (do ((pl (left ptl) (left pl)))
-        ((eq pl ptl))
-      (maj-peigne-hor peigne (icol pl))
-      (if (eq pl p)
-          (setf peigne2 (copy-list peigne))
-          (op-col ptc
-                  (basecol N (icol pl))
-                  peigne
-                  (truncate (val pl) div))))
-    (do ((pp peigne2 (rest pp)))
-        ((endp pp))
-      (supprimer-terme (first pp) ptc))
-    (setf (left (chercher-hor (basecol N 0) ic)) (left ptc))))
-
-(defun generateur-torsion-H* (B N p)
-  (let ((tab (make-array (1+ (n-lig B)) :initial-element 0))
-        (ptcN (basecol N (icol p))))
-    (do ((pcN (up ptcN) (up pcN)))
-        ((eq pcN ptcN))
-      (let ((facteur (truncate (val pcN) (val p)))
-            (ptcB (basecol B (ilig pcN))))
-        (do ((pcB (up ptcB) (up pcB)))
-            ((eq pcB ptcB))
-          (incf (aref tab (ilig pcB)) (* (val pcB) facteur)))))
-    (cons (abs (val p))
-          (let ((res '()))
-            (do ((ind (n-lig B) (1- ind)))
-                ((zerop ind) res)
-              (if (/= 0 (aref tab ind))
-                  (push (cons (aref tab ind) ind) res)))))))
-
-(defun terminer-H* (B)
-  (let ((res '())
-        (fin (basecol B 0)))
-    (do ((ptc (left fin) (left ptc)))
-        ((eq ptc fin) res)
-      (push (cons 0
-                  (do ((pc (up ptc) (up pc))
-                       (res '() (cons (cons (val pc) (ilig pc)) res)))
-                      ((eq pc ptc) res)))
-            res))))
-
-(defun reste-minimal-ligne (mat p)
-  (block ?
-    (let ((div (val p))
-          (ptl (baselig mat (ilig p))))
-      (do ((pl (left ptl) (left pl)))
-          ((eq pl ptl) (return-from ? nil))
-        (let ((val (reste (val pl) div)))
-          (if (/= 0 val)
-              (if (= 1 val)
-                  (return-from ? pl)
-                  (let ((pmin pl)
-                        (min val))
-                    (do ((pl (left pl) (left pl)))
-                        ((eq pl ptl) (return-from ? pmin))
-                      (let ((val (reste (val pl) div)))
-                        (if (and (/= 0 val) (< val min))
-                            (if (= 1 val)
-                                (return-from ? pl)
-                                (setf pmin pl min val)))))))))))))
-
-(defun reste-minimal-colonne (mat p)
-  (block ?
-    (let ((div (val p))
-          (ptc (basecol mat (icol p))))
-      (do ((pc (up ptc) (up pc)))
-          ((eq pc ptc) (return-from ? nil))
-        (let ((val (reste (val pc) div)))
-          (if (/= 0 val)
-              (if (= 1 val)
-                  (return-from ? pc)
-                  (let ((pmin pc)
-                        (min val))
-                    (do ((pc (up pc) (up pc)))
-                        ((eq pc ptc) (return-from ? pmin))
-                      (let ((val (reste (val pc) div)))
-                        (if (and (/= 0 val) (< val min))
-                            (if (= 1 val)
-                                (return-from ? pc)
-                                (setf pmin pc min val)))))))))))))
-
-
-
-(defun homologie (M N)
-  (prog ((B (identite (n-col M)))
-         (res nil)
-         (p1) (p2) (div))
-    depart1
-      (setf p1 (terme-minimal-matrice M))
-    loop1
-      (if (null p1)
-          (go depart2)
-          (if (= 1 (abs (val p1)))
-              (go pivot1)
-              (progn (setf p2 (reste-minimal-colonne M p1))
-                     (if (null p2)
-                         (progn (setf p2 (reste-minimal-ligne M p1))
-                                (if (null p2)
-                                    (go pivot1)
-                                    (go op-col1)))
-                         (go op-lig1)))))
-    op-lig1
-      (op-lig-n M (ilig p1) (ilig p2) (diviseur (val p2) (val p1)))
-      (setf p1 p2)
-      (go loop1)
-    op-col1
-      (setf div (diviseur (val p2) (val p1)))
-      (op-col-n M (icol p1) (icol p2) div)
-      (op-col-n B (icol p1) (icol p2) div)
-      (op-lig-n N (icol p2) (icol p1) (- div))
-      (setf p1 p2)
-      (go loop1)
-    pivot1
-      (tuer-ligne N (icol p1))
-      (pivot-parallele M B p1)
-      (pivot M p1)
-      (go depart1)
-
-    depart2
-      (setf p1 (terme-minimal-matrice N))
-    loop2
-      (if (null p1)
-          (go depart3)
-          (if (= 1 (abs (val p1)))
-              (go pivot2)
-              (progn (setf p2 (reste-minimal-ligne N p1))
-                     (if (null p2)
-                         (progn (setf p2 (reste-minimal-colonne N p1))
-                                (if (null p2)
-                                    (go pivot2-torsion)
-                                    (go op-lig2)))
-                         (go op-col2)))))
-    op-lig2
-      (setf div (diviseur (val p2) (val p1)))
-      (op-col-n B (ilig p2) (ilig p1) (- div))
-      (op-lig-n N (ilig p1) (ilig p2) div)
-      (setf p1 p2)
-      (go loop2)
-    op-col2
-      (op-col-n N (icol p1) (icol p2) (diviseur (val p2) (val p1)))
-      (setf p1 p2)
-      (go loop2)
-    pivot2-torsion
-      (setf res (cons (generateur-torsion-H* B N p1) res))
-    pivot2
-      (tuer-colonne B (ilig p1))
-      (pivot N p1)
-      (go depart2)
-
-    depart3
-      (return (append res (terminer-H* B)))))
-
-(DEFVAR *HOMOLOGY-VERBOSE* t)
-
-(DEFUN CHCM-MAT (chcm n)
-  (declare
-   (type chain-complex chcm)
-   (fixnum n))
-  (when (eq (basis chcm) :locally-effective)
-    (error "CHCMC-MAT cannot work with a LOCALLY-EFFECTIVE chain complex."))
-  (let ((sorc (basis chcm n))
-        (trgt (basis chcm (1- n)))
-        (cmpr (cmpr chcm)))
-    (declare
-     (list sorc trgt)
-     (type cmprf cmpr))
-    (format t "~%Computing boundary-matrix in dimension ~D.
-Rank of the source-module : ~D.~2%"
-      n (length sorc))
-    (let ((sorcl (length sorc))
-          (mat (creer-matrice (length trgt) (length sorc)))
-          (test #'(lambda (gnrt1 gnrt2)
-                    (eq (funcall cmpr gnrt1 gnrt2) :equal))))
-      (declare
-       (fixnum sorcl)
-       (type matrice mat)
-       (function test))
-      (do ((i 1 (1+ i))
-           (mark sorc (cdr mark)))
-          ((endp mark))
-        (declare
-         (fixnum i)
-         (list mark))
-        (when *homology-verbose*
-          (clock)
-          (format t "Computing the boundary of the generator ~D/~D (dimension ~D) :"
-            i sorcl n)
-          (print (car mark)))
-          (maj-colonne mat i
-             (mapcar #'(lambda (term)
-                          (declare (type term term))
-                          (list
-                             (1+ (position (gnrt term) trgt :test test))
-                             (cffc term)))
-               (cmbn-list (? chcm n (car mark)))))
-        (when *homology-verbose*
-          (format t "~%End of computing.~2%")))
-       mat)))
-
-#|
-()
-(setf d (delta 3))
-(chcm-mat d 2)
-(chcm-mat d 3)
-(chcm-mat d 4)
-|#
-
-(defun chcm-homology (cc n)
-  (declare (type chain-complex cc) (type fixnum n))
-  (let ((rsl (homologie (chcm-mat cc n) (chcm-mat cc (1+ n)))))
-    (declare (type list rsl))    
-    (format t "~3%Homology in dimension ~D :~%" n)
-    (dolist (item rsl)
-      (declare (type list item))
-      (format t "~2%Component Z")
-      (unless (zerop (first item)) 
-	(format t "/~DZ" (first item)))))
-  (terpri) (terpri)
-  (done))
-
-#|
-()
-(setf d (sphere 3))
-(chcm-homology d 2)
-(chcm-homology d 3)
-(chcm-homology d 4)
-|#
-
-(defun chcm-homology-gen (cc n)
-  (declare (type chain-complex cc) (type fixnum n))
-  (let ((src (cons :unused (basis cc n)))
-        (rsl (homologie (chcm-mat cc n) (chcm-mat cc (1+ n)))))
-    (declare (type list src rsl))
-    (format t "~3%Homology in dimension ~D :~%" n)
-    (dolist (item rsl)
-      (declare (type list item))
-      (format t "~%Component Z")
-      (unless (zerop (first item)) 
-        (format t "/~DZ" (first item))))
-    (terpri) (terpri)
-    (setf rsl (mapcar #'cdr rsl))
-    (setf rsl (mapcar #'(lambda (item)
-                          (declare (type list item))
-                          (mapcar #'(lambda (term)
-                                      (declare (type term term))
-                                      (term (car term) (nth (cdr term) src)))
-                            item))
-                rsl))
-    (setf rsl (mapcar #'(lambda (item)
-                          (declare (type list item))
-                          (make-cmbn :degr n :list item))
-                rsl))
-    rsl))    
-    
-#|
-()
-(setf d (sphere 3))
-(chcm-homology-gen d 2)
-(chcm-homology-gen d 3)
-(chcm-homology-gen d 4)
-
-|#
-
-(defun chcm-homology-gen-old (cc n)
-  (declare (type chain-complex cc) (type fixnum n))
-  (let ((src (cons :unused (basis cc n)))
-        (rsl (homologie (chcm-mat cc n) (chcm-mat cc (1+ n)))))
-    (declare (type list src rsl))
-    (format t "~3%Homology in dimension ~D :~%" n)
-    (dolist (item rsl)
-      (declare (type list item))
-      (format t "~2%Component Z")
-      (unless (zerop (first item)) 
-	(format t "/~DZ" (first item)))
-      (format t "~2%Generator :")
-      (dolist (item2 (rest item))
-	(declare (type cons item2))
-	(format t "~%~D~6T*  ~S" (car item2) (nth (cdr item2) src)))))
-  (done))
-
-#|
-()
-(setf d (sphere 3))
-(chcm-homology-gen-old d 2)
-(chcm-homology-gen-old d 3)
-(chcm-homology-gen-old d 4)
-|#
diff --git a/archive/Kenzo-1/k-pi-n.cl b/archive/Kenzo-1/k-pi-n.cl
deleted file mode 100644
index 852f624..0000000
--- a/archive/Kenzo-1/k-pi-n.cl
+++ /dev/null
@@ -1,1071 +0,0 @@
-;;;  K-PI-1  K-PI-1  K-PI-1  K-PI-1  K-PI-1  K-PI-1  K-PI-1
-;;;  K-PI-1  K-PI-1  K-PI-1  K-PI-1  K-PI-1  K-PI-1  K-PI-1
-;;;  K-PI-1  K-PI-1  K-PI-1  K-PI-1  K-PI-1  K-PI-1  K-PI-1
-
-(IN-PACKAGE "COMMON-LISP-USER")
-
-(PROVIDE "k-pi-1")
-
-(DEFUN K-Z-1-CMPR (gnrt1 gnrt2)
-   (declare (list gnrt1 gnrt2))
-   (the cmpr
-   (do ((mark1 gnrt1 (cdr mark1))
-	(mark2 gnrt2 (cdr mark2)))
-       ((endp mark1) :equal)
-       (case (f-cmpr (car mark1) (car mark2))
-	  (:equal)
-	  (:less (return-from k-z-1-cmpr :less))
-	  (:greater (return-from k-z-1-cmpr :greater))))))
-
-#|
-  (k-z-1-cmpr '(1 1 2) '(1 2 2))
-  (k-z-1-cmpr '(1 1 2) '(1 1 2))
-  (k-z-1-cmpr '(1 1 2) '(1 1 -1))
-|#
-
-(DEFUN K-Z-1-FACE (indx dmns gmsm)
-   (declare
-      (fixnum indx dmns)
-      (list gmsm))
-   (the absm
-   (cond ((zerop indx) (absm 0 (rest gmsm)))
-	 ((= indx dmns) (absm 0 (butlast gmsm)))
-	 (t
-	  (do ((rslt +empty-list+ (cons (car mark) rslt))
-	       (mark gmsm (cdr mark))
-	       (i 1 (1+ i)))
-	      ((= i indx) (let ((new-k (+ (car mark) (cadr mark))))
-			    (declare (fixnum new-k))
-			    (if (zerop new-k)
-			       (absm (2-exp (1- indx)) (nreconc rslt (cddr mark)))
-			       (absm 0 (nreconc rslt (cons new-k (cddr mark)))))))
-	     (declare
-	        (list rslt mark)
-		(fixnum i)))))))
-
-#|
-  (k-z-1-face 0 1 '(3))
-  (k-z-1-face 1 1 '(3))
-  (k-z-1-face 0 3 '(1 2 3))
-  (k-z-1-face 1 3 '(1 2 3))
-  (k-z-1-face 2 3 '(1 2 3))
-  (k-z-1-face 2 3 '(1 2 -2))
-  (k-z-1-face 3 3 '(1 2 3))
-|#
-
-(DEFUN Z-ABSM-BAR (absm)
-  (declare (type absm absm))
-  (the list
-    (with-absm (dgop bar1) absm
-      (do ((dgop dgop (ash dgop -1))
-	   (rslt +empty-list+))
-	  ((and (zerop dgop) (endp bar1)) (nreverse rslt))
-	  (declare
-	     (fixnum dgop)
-	     (list rslt))
-	  (push (if (oddp dgop)
-		    0
-		  (pop bar1))
-		rslt)))))
-
-#|
-  (z-absm-bar (absm 0 '()))
-  (z-absm-bar (absm 1 '()))
-  (z-absm-bar (absm 0 '(2)))
-  (dotimes (i 8)
-    (print (z-absm-bar (absm i '(3 6)))))
-|#
-
-(DEFUN Z-BAR-ABSM (bar)
-  (declare (list bar))
-  (the absm
-     (do ((rslt-dgop 0)
-	  (rslt-bar +empty-list+)
-	  (mark bar (cdr mark))
-	  (bark 1 (+ bark bark)))
-	 ((endp mark) (absm rslt-dgop (nreverse rslt-bar)))
-	(declare
-	   (fixnum rslt-dgop bark)
-	   (list rslt-bar mark))
-	(let ((k-i (car mark)))
-	  (declare (fixnum k-i))
-	  (if (zerop k-i)
-	     (incf rslt-dgop bark)
-	     (push k-i rslt-bar))))))
-
-#|
-  (z-bar-absm (z-absm-bar (absm 0 '())))
-  (z-bar-absm (z-absm-bar (absm 1 '())))
-  (z-bar-absm (z-absm-bar (absm 0 '(2))))
-  (dotimes (i 8)
-    (print (z-bar-absm (z-absm-bar (absm i '(3 6))))))
-|#
-
-(DEFUN K-Z-1-GRML (dmns crpr)
-   (declare
-      (fixnum dmns)
-      (type crpr crpr))
-   (the absm
-      (with-crpr (dgop1 bar1 dgop2 bar2) crpr
-	 (do ((indx 1 (1+ indx))
-	      (dgop1 dgop1 (ash dgop1 -1))
-	      (dgop2 dgop2 (ash dgop2 -1))
-	      (bark 1 (ash bark +1))
-	      (rslt-dgop 0)
-	      (rslt-bar +empty-list+))
-	     ((> indx dmns) (absm rslt-dgop (nreverse rslt-bar)))
-	     (declare
-	        (fixnum indx dgop1 dgop2 bark rslt-dgop)
-		(list rslt-bar))
-	     (let ((item (if (evenp dgop1)
-			     (if (evenp dgop2)
-				 (+ (pop bar1) (pop bar2))
-			       (pop bar1))
-			   (if (evenp dgop2)
-			       (pop bar2)
-			     0))))
-	       (declare (fixnum item))
-	       (if (zerop item)
-		   (incf rslt-dgop bark)
-		 (push item rslt-bar)))))))
-
-#|
-  (k-z-1-grml 0 (crpr 0 nil 0 nil))
-  (k-z-1-grml 1 (crpr 0 '(3) 0 '(4)))
-  (k-z-1-grml 1 (crpr 0 '(3) 0 '(-3)))
-  (k-z-1-grml 1 (crpr 0 '(3) 1 '()))
-  (k-z-1-grml 1 (crpr 1 '() 0 '(3)))
-  (k-z-1-grml 1 (crpr 1 '() 1 '()))
-  (k-z-1-grml 5 (crpr 24 '(2 2 3) 20 '(-2 2 4)))
-|#
-
-(DEFUN K-Z-1-GRIN (dmns bar)
-  (declare
-     (ignore dmns)
-     (list bar))
-  (the absm
-     (absm 0 (mapcar #'- bar))))
-
-#|
-  (k-z-1-grin 3 '(2 3 -4))
-  (setf gmsm '(2 3 -4))
-  (k-z-1-grml 3 (crpr 0 gmsm 0 (gmsm (k-z-1-grin 3 gmsm))))
-|#
-
-#|
-(DEFUN K-Z-1-KFLL (indx dmns hat)
-  (declare
-     (fixnum indx dmns)
-     (list hat))
-  (the absm
-     (cond ((= 1 dmns)
-	    (absm 1 +empty-list+))
-	   ((zerop indx)
-	    (let ((del-1 (first hat))
-		  (del-2 (second hat)))
-	      (declare (type absm del-1 del-2))
-	      (with-absm (dgop1 bar1) del-1
-	      (with-absm (dgop2 bar2) del-2
-		 (let ((bar01 (if (oddp dgop2)
-				 0
-				 (first bar2)))
-		       (bar02 (if (oddp dgop1)
-				 0
-				 (first bar1))))
-		   (declare (fixnum bar01 bar02))
-		   (let ((bar12 (- bar02 bar01)))
-		     (declare (fixnum bar02))
-		     (if (zerop bar01)
-			(1dgnr 0 del-1)
-		        (if (zerop bar12)
-			   (1gnr 1 del-1)
-			   (let (del-01 (k-z-1-face 0 (1- dmns)
-						    del-1))
-			     (declare (type absm del-01))
-			     (with-absm (dgop01 gmsm01) del-01
-				(absm (* 4 dgop01)
-				      (cons bar01
-					    (cons bar02 gmsm01)))))))))))))
-	   ((= 1 indx)
-	    (let ((del-0 (first hat))
-		  (del-2 (second hat)))
-	      (declare (type absm del-0 del-2))
-	      (with-absm (dgop0 gmsm0) del-0
-	      (with-absm (dgop2 gmsm2) del-2
-		 (if (oddp dgop2 )))))))))
-
-|#
-
-(DEFUN K-Z-1 ()
-  (the ab-simplicial-group
-     (build-ab-smgr
-        :cmpr #'k-z-1-cmpr
-	:basis :locally-effective
-	:bspn +empty-list+
-	:face #'k-z-1-face
-	:sintr-grml #'k-z-1-grml
-	:sintr-grin #'k-z-1-grin
-	:orgn '(k-z-1))))
-
-#|
-  (setf k (k-z-1))
-  (defun aleat-list (max length)
-     (let ((rslt nil)
-           (2max (+ max max)))
-        (dotimes (i length)
-           (push (let ((k (- (random 2max) max)))
-                    (if (zerop k)
-                       max
-                       k))
-              rslt))
-        rslt))
-  (? k (? k 14 (aleat-list 200 14)))
-  (setf zero? (add (idnt-mrph k) (grin k)))
-  (? zero? 14 (aleat-list 200 14))
-|#
-
-(DEFUN K-Z (n)
-   (declare (fixnum n))
-   (the ab-simplicial-group
-      (if (= n 1)
-         (k-z-1)
-         (classifying-space (k-z (1- n))))))
-
-(DEFUN CIRCLE-CMPR (gnrt1 gnrt2)
-   (declare (ignore gnrt1 gnrt2))
-   (the cmpr :equal))
-
-(DEFUN CIRCLE-BASIS (dmns)
-   (declare (fixnum dmns))
-   (the list
-      (case dmns
-	 (0 '(*))
-	 (1 '(s1))
-	 (otherwise +empty-list+))))
-
-(DEFUN CIRCLE ()
-   (the chain-complex
-      (build-chcm
-         :cmpr #'circle-cmpr
-	 :basis #'circle-basis
-	 :bsgn '*
-	 :intr-dffr #'zero-intr-dffr
-	 :strt :cmbn
-	 :orgn '(circle))))
-
-#|
-  (setf c (circle))
-  (cmpr c '* '*)
-  (basis c 1)
-  (? c 1 's1)
-|#
-
-(DEFUN KZ1-RDCT-F-INTR (cmbn)
-  (declare (type cmbn cmbn))
-  (the cmbn
-     (with-cmbn (degr list) cmbn
-	(case degr
-	   (0 (if list
-		 (term-cmbn 0 (-cffc list) '*)
-		 (zero-cmbn 0)))
-	   (1 (let ((rslt
-		     (apply #'+
-			(mapcar
-			 #'(lambda (term)
-			     (declare (type term term))
-			     (with-term (cffc gnrt) term
-					(the fixnum (* cffc
-						       (first gnrt)))))
-			 list))))
-		(if (zerop rslt)
-		    (zero-cmbn 1)
-		  (term-cmbn 1 rslt 's1))))
-	   (otherwise (zero-cmbn degr))))))
-
-#|
-  (kz1-rdct-f-intr (cmbn 0))
-  (kz1-rdct-f-intr (cmbn 0 4 '()))
-  (kz1-rdct-f-intr (cmbn 1))
-  (kz1-rdct-f-intr (cmbn 1 4 '(3)))
-  (kz1-rdct-f-intr (cmbn 1 4 '(3) 5 '(2)))
-  (kz1-rdct-f-intr (cmbn 1 4 '(3) -3 '(4)))
-  (kz1-rdct-f-intr (cmbn -3))
-|#
-
-(DEFUN KZ1-RDCT-F ()
-  (the morphism
-     (build-mrph
-        :sorc (k-z-1)
-	:trgt (circle)
-	:degr 0
-	:intr #'kz1-rdct-f-intr
-	:strt :cmbn
-	:orgn '(kz1-rdct-f))))
-
-(DEFUN KZ1-RDCT-G-INTR (cmbn)
-  (declare (type cmbn cmbn))
-  (the cmbn
-     (with-cmbn (degr list) cmbn
-	(if list
-	    (ecase degr
-	       (0 (term-cmbn 0 (-cffc list) +empty-list+))
-	       (1 (term-cmbn 1 (-cffc list) (list 1))))
-	  (zero-cmbn degr)))))
-
-(DEFUN KZ1-RDCT-G ()
-  (the morphism
-     (build-mrph
-        :sorc (circle)
-	:trgt (k-z-1)
-	:degr 0
-	:intr #'kz1-rdct-g-intr
-	:strt :cmbn
-	:orgn '(kz1-rdct-g))))
-
-(DEFUN KZ1-RDCT-H-INTR (dmns bar)
-  (declare
-     (fixnum dmns)
-     (list bar))
-  (the cmbn
-     (progn
-       (when (zerop dmns)
-	  (return-from kz1-rdct-h-intr (zero-cmbn +1)))
-       (let ((k1 (first bar))
-	     (tail (rest bar)))
-	 (declare
-	    (fixnum k1)
-	    (list tail))
-	 (if (plusp k1)
-	    (do ((rslt +empty-list+
-		       (cons (term -1
-				   (cons 1 (cons i tail)))
-			     rslt))
-		 (i (1- k1) (1- i)))
-		((zerop i) (make-cmbn :degr (1+ dmns)
-				      :list rslt))
-	       (declare
-		  (list rslt)
-		  (fixnum i)))
-	    (do ((rslt +empty-list+
-		       (cons (term +1
-				   (cons 1 (cons i tail)))
-			     rslt))
-		 (i -1 (1- i)))
-		((< i k1) (make-cmbn :degr (1+ dmns)
-				     :list rslt))))))))
-
-#|
-  (kz1-rdct-h-intr 0 nil)
-  (kz1-rdct-h-intr 1 '(-4))
-  (kz1-rdct-h-intr 1 '(-1))
-  (kz1-rdct-h-intr 1 '(1))
-  (kz1-rdct-h-intr 1 '(4))
-  (kz1-rdct-h-intr 3 '(-4 3 5))
-  (kz1-rdct-h-intr 3 '(-1 3 -1))
-  (kz1-rdct-h-intr 3 '(1 2 2))
-  (kz1-rdct-h-intr 3 '(4 3 5))
-|#
-
-(DEFUN KZ1-RDCT-H ()
-  (the morphism
-     (build-mrph
-        :sorc (k-z-1)
-	:trgt (k-z-1)
-	:degr +1
-	:intr #'kz1-rdct-h-intr
-	:strt :gnrt
-	:orgn '(kz1-rdct-h))))
-
-(DEFUN KZ1-RDCT ()
-  (the reduction
-     (build-rdct
-        :f (kz1-rdct-f)
-	:g (kz1-rdct-g)
-	:h (kz1-rdct-h)
-	:orgn '(kz1-rdct))))
-
-#|
-  (pre-check-rdct (kz1-rdct))
-  (setf *tc* (cmbn 0 1 '()))
-  (setf *bc* (cmbn 0 1 '*))
-  (check-rdct)
-  (setf *tc* (cmbn 1 1 '(-4) 10 '(-1) 100 '(1) 1000 '(5)))
-  (setf *bc* (cmbn 1 1 's1))
-  (check-rdct)
-  (setf *tc* (cmbn 2 1 '(-4 2) 10 '(-1 3) 100 '(1 -4) 1000 '(5 5)))
-  (check-rdct)
-  (setf *tc* (cmbn 3 1 '(-4 -4 5) 10 '(-1 2 1)
-                     100 '(1 4 2) 1000 '(5 1 -1)))
-  (check-rdct)
-|#
-
-(DEFUN KZ1-EFHM ()
-  (the homotopy-equivalence
-     (build-hmeq
-        :lrdct (trivial-rdct (k-z-1))
-	:rrdct (kz1-rdct)
-	:orgn '(kz1-efhm))))
-
-(DEFMETHOD SEARCH-EFHM (k-z-1 (orgn (eql 'k-z-1)))
-  (declare (ignore k-z-1))
-  (kz1-efhm))
-
-#|
-  (cat-init)
-  (homology (k-z-1) 1)
-|#
-
-(DEFUN K-Z2-1-GRML-INTR (dmns crpr)
-  (declare
-     (fixnum dmns)
-     (type crpr crpr))
-  (the absm
-     (with-crpr (dgop1 gmsm1 dgop2 gmsm2) crpr
-	(declare (ignore gmsm1 gmsm2))
-	(let ((dgop (- (mask dmns) (logxor dgop1 dgop2))))
-	  (declare (fixnum dgop))
-	  (absm dgop (- dmns (logcount dgop)))))))
-
-(DEFUN K-Z2-1-GRML ()
-  (the simplicial-mrph
-     (build-smmr
-        :sorc (crts-prdc (r-proj-space) (r-proj-space))
-	:trgt (r-proj-space)
-	:degr 0
-	:sintr #'k-z2-1-grml-intr
-	:orgn '(k-z2-1-grml))))
-
-(DEFUN K-Z2-1-GRIN-INTR (dmns gmsm)
-  (declare
-     (ignore dmns)
-     (fixnum gmsm))
-  (the absm
-     (absm 0 gmsm)))
-
-(DEFUN K-Z2-1-GRIN ()
-  (the simplicial-mrph
-     (build-smmr
-        :sorc (r-proj-space)
-	:trgt (r-proj-space)
-	:degr 0
-	:sintr #'k-z2-1-grin-intr
-	:intr #'identity
-	:strt :cmbn
-	:orgn '(k-z2-1-grin))))
-
-(DEFUN K-Z2-1 ()
-  (the ab-simplicial-group
-     (let ((rslt (r-proj-space)))
-       (declare (type simplicial-set rslt))
-       (change-class rslt 'ab-simplicial-group)
-       (setf (slot-value rslt 'grml)
-	     (k-z2-1-grml)
-	     (slot-value rslt 'grin)
-	     (k-z2-1-grin))
-       (pushnew rslt *smgr-list*)
-       rslt)))
-
-#|
-  (setf k (k-z2-1))
-  (homology k 0 4)
-|#
-
-(DEFUN K-Z2 (n)
-   (declare (fixnum n))
-   (the ab-simplicial-group
-      (if (= n 1)
-         (k-z2-1)
-         (classifying-space (k-z2 (1- n))))))
-
-#|
-  (setf k3 (k-z2 3))
-  (homology k3 7)
-|#
-
-(DEFUN Z2-ABSM-BAR (absm)
-  (declare (type absm absm))
-  (the list
-     (with-absm (dgop gmsm) absm
-       (do ((bmark (1- (+ (logcount dgop) gmsm)) (1- bmark))
-	    (rslt +empty-list+
-		  (cons (if (logbitp bmark dgop)
-			    0 1)
-			rslt)))
-	   ((minusp bmark) rslt)
-	  (declare
-	     (fixnum bmark)
-	     (list rslt))))))
-
-(DEFUN Z2-BAR-ABSM (bar)
-  (declare (list bar))
-  (the absm
-     (do ((dgop 0)
-	  (2-pwr 1 (+ 2-pwr 2-pwr))
-	  (gmsm 0)
-	  (mark bar (cdr mark)))
-	 ((endp mark) (absm dgop gmsm))
-	(declare
-	   (fixnum dgop 2-pwr gmsm)
-	   (list mark))
-	(if (zerop (car mark))
-	   (incf dgop 2-pwr)
-	   (incf gmsm)))))
-
-#|
-  (dotimes (i 8)    ;;; not really legal
-  (dotimes (j 8)
-    (print (z2-bar-absm (z2-absm-bar (absm i j))))))
-|#
-
-
-(DEFUN HOPF-FIBRATION-SINTR (n)
-  (declare (fixnum n))
-  (flet ((rslt (dmns gmsm)
-	   (declare (ignore dmns gmsm))
-	   (if (zerop n)
-	      (absm 1 +empty-list+)
-	      (absm 0 (list n)))))
-     (the sintr #'rslt)))
-
-(DEFUN HOPF-FIBRATION (n)
-  (declare (fixnum n))
-  (the simplicial-mrph
-     (build-smmr
-        :sorc (sphere 2)
-	:trgt (k-z-1)
-	:degr -1
-	:sintr (hopf-fibration-sintr n)
-	:orgn `(hopf-fibration ,n))))
-
-(DEFUN Z-FUNDAMENTAL-GMSM (dmns pi-elm)   ;;; pi-elm not equal to 0
-   (declare (fixnum dmns pi-elm))
-   (the gmsm
-      (if (= 1 dmns)
-         (list pi-elm)
-         (let ((bspn (if (= 2 dmns) +empty-list+ +null-gbar+)))
-            (declare (type gmsm bspn))
-            (make-gbar :dmns dmns
-               :list (cons (absm 0 (z-fundamental-gmsm (1- dmns) pi-elm))
-                        (mapcar
-                           #'(lambda (k)
-                                (declare (fixnum k))
-                                (absm (mask k) bspn))
-                           (nreverse (<a-b> 0 (- dmns 2))))))))))
-
-#|
-  (z-fundamental-gmsm 1 33)
-  (z-fundamental-gmsm 2 33)
-  (z-fundamental-gmsm 3 33)
-  (z-fundamental-gmsm 4 33)
-|#
-
-(DEFUN INTERESTING-FACES (face small-dmns high-dmns gmsm)
-  (declare
-    (type face face)
-    (fixnum small-dmns high-dmns)
-    (type gmsm gmsm))
-  (the list
-    (let ((max (mask high-dmns)))
-      (declare (fixnum max))
-      (if (= small-dmns high-dmns)
-	 (list (cons max (absm 0 gmsm)))
-	 (do ((prev-list (interesting-faces face (1+ small-dmns) high-dmns gmsm))
-	      (k (1- max) (1- k))
-	      (rslt +empty-list+)
-	      (count (binomial-n-p high-dmns small-dmns)))
-	     ((zerop count) rslt)
-	     (declare
-	       (list prev-list rslt)
-	       (fixnum k count))
-	    (when (= small-dmns (logcount k))
-	      (decf count)
-	      (do ((i 0 (1+ i)))
-	          ((not (logbitp i k))
-		   (push (cons k
-			       (a-face4 face
-					(- small-dmns -1
-					   (if (= i (integer-length k)) (1+ i) i))
-					(1+ small-dmns)
-					(cdr (assoc (+ k (2-exp i)) prev-list))))
-			 rslt)))))))))
-
-#|
-  (setf d (delta 14))
-  (setf f (face d))
-  (do ((i 5 (1- i)))
-      ((minusp i))
-    (print (interesting-faces f i 5 (mask 6))))
-|#     
-
-(DEFUN GMSM-COCYCLE (face small-dmns high-dmns gmsm chml-clss)
-  (declare
-    (type face face)
-    (fixnum small-dmns high-dmns)
-    (type gmsm gmsm)
-    (type morphism chml-clss))
-  (the list
-    (let ((int-faces (interesting-faces face small-dmns high-dmns gmsm)))
-      (declare (list int-faces))
-      (mapc
-        #'(lambda (cons)
-	    (declare (cons cons))
-	    (setf (cdr cons)
-		  (let ((absm (cdr cons)))
-		    (declare (type absm absm))
-		    (with-absm (dgop gmsm2) absm
-		      (if (plusp dgop)
-			 0
-			(let ((cmbn-list (cmbn-list (gnrt-? chml-clss
-						 small-dmns gmsm2))))
-			  (declare (list cmbn-list))
-			  (if cmbn-list
-			      (-cffc cmbn-list)
-			    0)))))))
-        int-faces)
-      int-faces)))
-
-#|
-  (cat-init)
-  (setf d (delta 10))
-  (setf chml-clss
-    (build-mrph :sorc d :trgt (z-chcm) :degr -2
-                :intr #'(lambda (dmns gmsm)
-                          (term-cmbn 0 gmsm :gnrt-z))
-                :strt :gnrt
-                :orgn '(essai-1)))
-  (gmsm-cocycle (face d) 2 4 31 chml-clss)
-  (setf chml-clss
-    (build-mrph :sorc d :trgt (z-chcm) :degr -1
-                :intr #'(lambda (dmns gmsm)
-                          (term-cmbn 0 gmsm :gnrt-z))
-                :strt :gnrt
-                :orgn '(essai-2)))
-  (gmsm-cocycle (face d) 1 4 31 chml-clss)
-|#
-
-(DEFUN Z-COCYCLE-GBAR (n dmns cocycle)
-  ;; cocycle \in Z^n(\Delta^{dmns}, \pi) with \pi = Z
-  (declare
-    (fixnum n dmns)
-    (list cocycle))
-  (the absm
-    (cond ((= n 1)
-	   (z-bar-absm (nreverse (mapcar #'cdr cocycle))))
-	  ((= n dmns)
-	   (let ((value (cdr (first cocycle))))
-	     (declare (fixnum value))
-	     (if (zerop value)
-		(absm (mask dmns) +null-gbar+)
-	        (absm 0 (z-fundamental-gmsm dmns value)))))
-	  (t
-	   (let ((cocycle1 +empty-list+)
-		 (cocycle2 +empty-list+))
-	     (declare (list cocycle1 cocycle2))
-	     (dolist (cons cocycle)
-	       (declare (cons cons))
-	       (if (evenp (car cons))
-		  (push (cons (ash (car cons) -1) (cdr cons))
-			cocycle1)
-		  (push (cons (ash (car cons) -1) (cdr cons))
-			cocycle2)))
-	     (setf cocycle1 (nreverse cocycle1)
-		   cocycle2 (nreverse cocycle2))
-	     (mapc
-	       #'(lambda (cons)
-		   (declare (cons cons))
-		   (when (evenp (car cons))
-		     (decf (cdr cons)
-			   (cdr (assoc (1+ (car cons)) cocycle1)))))
-	       cocycle2)
-	     (let ((head-absm (z-cocycle-gbar (1- n) (1- dmns) cocycle2))
-		   (tail-absm (z-cocycle-gbar n (1- dmns) cocycle1)))
-	       (declare (type absm head-absm tail-absm))
-	       (normalize-gbar
-		 (cons dmns
-		       (cons head-absm
-			     (rest (unnormalize-gbar tail-absm
-				     (if (= n 2) () +null-gbar+))))))))))))
-
-#|
-  (cat-init)
-  (setf d (delta 10))
-  (setf chml-clss
-    (build-mrph :sorc d :trgt (z-chcm) :degr -1
-                :intr #'(lambda (dmns gmsm)
-                          (term-cmbn 0 gmsm :gnrt-z))
-                :strt :gnrt
-                :orgn '(essai-1)))
-  (gmsm-cocycle (face d) 1 4 31 chml-clss)
-  (z-cocycle-gbar 1 4 *)
-  (setf chml-clss
-    (build-mrph :sorc d :trgt (z-chcm) :degr -2
-                :intr #'(lambda (dmns gmsm)
-                          (term-cmbn 0 gmsm :gnrt-z))
-                :strt :gnrt
-                :orgn '(essai-2)))
-  (gmsm-cocycle (face d) 2 2 7 chml-clss)
-  (z-cocycle-gbar 2 2 *)
-  (gmsm-cocycle (face d) 2 2 0 chml-clss) ;; normally illegal
-  (z-cocycle-gbar 2 2 *)
-  (gmsm-cocycle (face d) 2 3 15 chml-clss)
-  (z-cocycle-gbar 2 3 *)
-  (gmsm-cocycle (face d) 2 4 31 chml-clss)
-  (z-cocycle-gbar 2 4 *)
-  (setf chml-clss
-    (build-mrph :sorc d :trgt (z-chcm) :degr -3
-                :intr #'(lambda (dmns gmsm)
-                          (term-cmbn 0 gmsm :gnrt-z))
-                :strt :gnrt
-                :orgn '(essai-3)))
-  (gmsm-cocycle (face d) 3 4 31 chml-clss)
-  (z-cocycle-gbar 3 4 *)
-  (setf chml-clss
-    (build-mrph :sorc d :trgt (z-chcm) :degr -3
-                :intr #'(lambda (dmns gmsm)
-                          (zero-cmbn 0))
-                :strt :gnrt
-                :orgn '(essai-33)))
-  (gmsm-cocycle (face d) 3 4 31 chml-clss)
-  (z-cocycle-gbar 3 4 *)
-|#
-
-(DEFUN Z-COCYCLE-GBAR-HEAD (n dmns cocycle)
-  ;; cocycle \in Z^n(\Delta^{dmns}, \pi) with \pi = Z
-  (declare
-    (fixnum n dmns)
-    (list cocycle))
-  (the absm
-    (cond ((= n 1)
-	   (error "In Z-COCYCLE-GBAR-HEAD, this point should not have been reached."))
-	   ; (z-bar-absm (nreverse (mapcar #'cdr cocycle))))
-	  ((= n dmns)
-	   (let ((value (cdr (first cocycle))))
-	     (declare (fixnum value))
-	     (if (zerop value)
-		(if (= n 2)
-		   (absm 1 +empty-list+)
-		   (absm (mask (1- dmns)) +null-gbar+))
-	       (absm 0 (z-fundamental-gmsm (1- dmns) value)))))
-	  (t
-	   (let ((cocycle1 +empty-list+)
-		 (cocycle2 +empty-list+))
-	     (declare (list cocycle1 cocycle2))
-	     (dolist (cons cocycle)
-	       (declare (cons cons))
-	       (if (evenp (car cons))
-		  (push (cons (ash (car cons) -1) (cdr cons))
-			cocycle1)
-		  (push (cons (ash (car cons) -1) (cdr cons))
-			cocycle2)))
-	     (setf cocycle1 (nreverse cocycle1)
-		   cocycle2 (nreverse cocycle2))
-	     (mapc
-	       #'(lambda (cons)
-		   (declare (cons cons))
-		   (when (evenp (car cons))
-		     (decf (cdr cons)
-			   (cdr (assoc (1+ (car cons)) cocycle1)))))
-	       cocycle2)
-	     (z-cocycle-gbar (1- n) (1- dmns) cocycle2))))))
-
-#|
-  (cat-init)
-  (setf d (delta 10))
-  (setf chml-clss
-    (build-mrph :sorc d :trgt (z-chcm) :degr -1
-                :intr #'(lambda (dmns gmsm)
-                          (term-cmbn 0 gmsm :gnrt-z))
-                :strt :gnrt
-                :orgn '(essai-1)))
-  (gmsm-cocycle (face d) 1 4 31 chml-clss)
-  (z-cocycle-gbar 1 4 *)
-  (z-cocycle-gbar-head 1 4 **)
-  (setf chml-clss
-    (build-mrph :sorc d :trgt (z-chcm) :degr -2
-                :intr #'(lambda (dmns gmsm)
-                          (term-cmbn 0 gmsm :gnrt-z))
-                :strt :gnrt
-                :orgn '(essai-2)))
-  (gmsm-cocycle (face d) 2 2 7 chml-clss)
-  (z-cocycle-gbar 2 2 *)
-  (z-cocycle-gbar-head 2 2 **)
-  (gmsm-cocycle (face d) 2 2 0 chml-clss) ;; normally illegal
-  (z-cocycle-gbar 2 2 *)
-  (z-cocycle-gbar-head 2 2 **)
-  (gmsm-cocycle (face d) 2 3 15 chml-clss)
-  (z-cocycle-gbar 2 3 *)
-  (z-cocycle-gbar-head 2 3 **)
-  (gmsm-cocycle (face d) 2 4 31 chml-clss)
-  (z-cocycle-gbar 2 4 *)
-  (z-cocycle-gbar-head 2 4 **)
-  (setf chml-clss
-    (build-mrph :sorc d :trgt (z-chcm) :degr -3
-                :intr #'(lambda (dmns gmsm)
-                          (term-cmbn 0 gmsm :gnrt-z))
-                :strt :gnrt
-                :orgn '(essai-3)))
-  (gmsm-cocycle (face d) 3 4 31 chml-clss)
-  (z-cocycle-gbar 3 4 *)
-  (z-cocycle-gbar-head 3 4 **)
-  (setf chml-clss
-    (build-mrph :sorc d :trgt (z-chcm) :degr -3
-                :intr #'(lambda (dmns gmsm)
-                          (zero-cmbn 0))
-                :strt :gnrt
-                :orgn '(essai-33)))
-  (gmsm-cocycle (face d) 3 4 31 chml-clss)
-  (z-cocycle-gbar 3 4 *)
-  (z-cocycle-gbar-head 3 4 **)
-|#
-
-(DEFUN Z2-FUNDAMENTAL-GMSM (dmns pi-elm)  ;; pi-elm not "equal" to 0, therefore 1.
-   (declare (fixnum dmns pi-elm))
-   (the gmsm
-      (if (= 1 dmns)
-         1
-         (let ((bspn (if (= 2 dmns) 0 +null-gbar+)))
-            (declare (type gmsm bspn))
-            (make-gbar :dmns dmns
-               :list (cons (absm 0 (Z2-fundamental-gmsm (1- dmns) pi-elm))
-                        (mapcar
-                           #'(lambda (k)
-                                (declare (fixnum k))
-                                (absm (mask k) bspn))
-                           (nreverse (<a-b> 0 (- dmns 2))))))))))
-
-#|
-  (Z2-fundamental-gmsm 1 1)
-  (Z2-fundamental-gmsm 2 1)
-  (Z2-fundamental-gmsm 3 1)
-  (Z2-fundamental-gmsm 4 1)
-|#    
-
-(DEFUN Z2-COCYCLE-GBAR (n dmns cocycle)
-  ;; cocycle \in Z^n(\Delta^{dmns}, \pi) with \pi = Z/2Z
-  (declare
-    (fixnum n dmns)
-    (list cocycle))
-  (the absm
-    (progn
-      (mapc
-        #'(lambda (cons)
-	    (declare (cons cons))
-	    (setf (cdr cons)
-		  (if (evenp (cdr cons)) 0 1)))
-        cocycle)
-      (cond ((= n 1)
-	     (z2-bar-absm (nreverse (mapcar #'cdr cocycle))))
-	    ((= n dmns)
-	     (let ((value (cdr (first cocycle))))
-	       (declare (fixnum value))
-	       (if (zerop value)
-		   (absm (mask dmns) +null-gbar+)
-		 (absm 0 (z2-fundamental-gmsm dmns value)))))
-	    (t
-	     (let ((cocycle1 +empty-list+)
-		   (cocycle2 +empty-list+))
-	       (declare (list cocycle1 cocycle2))
-	       (dolist (cons cocycle)
-		 (declare (cons cons))
-		 (if (evenp (car cons))
-		     (push (cons (ash (car cons) -1) (cdr cons))
-			   cocycle1)
-		   (push (cons (ash (car cons) -1) (cdr cons))
-			 cocycle2)))
-	       (setf cocycle1 (nreverse cocycle1)
-		     cocycle2 (nreverse cocycle2))
-	       (mapc
-		#'(lambda (cons)
-		    (declare (cons cons))
-		    (when (evenp (car cons))
-			  (setf (cdr cons)
-				(mod (- (cdr cons)
-					(cdr (assoc (1+ (car cons)) cocycle1)))
-				     2))))
-		cocycle2)
-	       (let ((head-absm (z2-cocycle-gbar (1- n) (1- dmns) cocycle2))
-		     (tail-absm (z2-cocycle-gbar n (1- dmns) cocycle1)))
-		 (declare (type absm head-absm tail-absm))
-		 (normalize-gbar
-		  (cons dmns
-			(cons head-absm
-			      (rest (unnormalize-gbar tail-absm
-						      (if (= n 2) 0 +null-gbar+)))))))))))))
-
-#|
-  (cat-init)
-  (setf d (delta 10))
-  (setf chml-clss
-    (build-mrph :sorc d :trgt (z-chcm) :degr -1
-                :intr #'(lambda (dmns gmsm)
-                          (term-cmbn 0 (mod gmsm 2) :gnrt-z))
-                :strt :gnrt
-                :orgn '(essai-1)))
-  (gmsm-cocycle (face d) 1 4 31 chml-clss)
-  (z2-cocycle-gbar 1 4 *)
-  (setf chml-clss
-    (build-mrph :sorc d :trgt (z-chcm) :degr -2
-                :intr #'(lambda (dmns gmsm)
-                          (term-cmbn 0 (mod gmsm 2) :gnrt-z))
-                :strt :gnrt
-                :orgn '(essai-2)))
-  (gmsm-cocycle (face d) 2 2 7 chml-clss)
-  (z2-cocycle-gbar 2 2 *)
-  (gmsm-cocycle (face d) 2 2 0 chml-clss) ;; normally illegal
-  (z2-cocycle-gbar 2 2 *)
-  (gmsm-cocycle (face d) 2 3 15 chml-clss)
-  (z2-cocycle-gbar 2 3 *)
-  (gmsm-cocycle (face d) 2 4 31 chml-clss)
-  (z2-cocycle-gbar 2 4 *)
-  (setf chml-clss
-    (build-mrph :sorc d :trgt (z-chcm) :degr -3
-                :intr #'(lambda (dmns gmsm)
-                          (term-cmbn 0 (mod gmsm 2) :gnrt-z))
-                :strt :gnrt
-                :orgn '(essai-3)))
-  (gmsm-cocycle (face d) 3 4 31 chml-clss)
-  (z2-cocycle-gbar 3 4 *)
-|#
-
-(DEFUN Z2-COCYCLE-GBAR-HEAD (n dmns cocycle)
-  ;; cocycle \in Z^n(\Delta^{dmns}, \pi) with \pi = Z/2Z
-  (declare
-    (fixnum n dmns)
-    (list cocycle))
-  (the absm
-    (progn
-      (mapc
-        #'(lambda (cons)
-	    (setf (cdr cons)
-		  (if (evenp (cdr cons)) 0 1)))
-        cocycle)
-      (cond ((= n 1)
-	     (error "In Z2-COCYCLE-GBAR-HEAD, this point should not have been reached."))
-		 ; (z2-bar-absm (nreverse (mapcar #'cdr cocycle))))
-	    ((= n dmns)
-	     (let ((value (cdr (first cocycle))))
-	       (declare (fixnum value))
-	       (if (zerop value)
-		   (if (= n 2)
-		       (absm 1 0)
-		     (absm (mask (1- dmns)) +null-gbar+))
-		 (absm 0 (z2-fundamental-gmsm (1- dmns) value)))))
-	    (t
-	     (let ((cocycle1 +empty-list+)
-		   (cocycle2 +empty-list+))
-	       (declare (list cocycle1 cocycle2))
-	       (dolist (cons cocycle)
-		 (declare (cons cons))
-		 (if (evenp (car cons))
-		     (push (cons (ash (car cons) -1) (cdr cons))
-			   cocycle1)
-		   (push (cons (ash (car cons) -1) (cdr cons))
-			 cocycle2)))
-	       (setf cocycle1 (nreverse cocycle1)
-		     cocycle2 (nreverse cocycle2))
-	       (mapc
-		#'(lambda (cons)
-		    (declare (cons cons))
-		    (when (evenp (car cons))
-			  (setf (cdr cons)
-				(mod (- (cdr cons)
-					(cdr (assoc (1+ (car cons)) cocycle1)))
-				     2))))
-		cocycle2)
-	       (z2-cocycle-gbar (1- n) (1- dmns) cocycle2)))))))
-
-#|
-  (cat-init)
-  (setf d (delta 10))
-  (setf chml-clss
-    (build-mrph :sorc d :trgt (z-chcm) :degr -1
-                :intr #'(lambda (dmns gmsm)
-                          (term-cmbn 0 (mod gmsm 2) :gnrt-z))
-                :strt :gnrt
-                :orgn '(essai-1)))
-  (gmsm-cocycle (face d) 1 4 31 chml-clss)
-  (z2-cocycle-gbar 1 4 *)
-  (z2-cocycle-gbar-head 1 4 **)
-  (setf chml-clss
-    (build-mrph :sorc d :trgt (z-chcm) :degr -2
-                :intr #'(lambda (dmns gmsm)
-                          (term-cmbn 0 (mod gmsm 2) :gnrt-z))
-                :strt :gnrt
-                :orgn '(essai-2)))
-  (gmsm-cocycle (face d) 2 2 7 chml-clss)
-  (z2-cocycle-gbar 2 2 *)
-  (z2-cocycle-gbar-head 2 2 **)
-  (gmsm-cocycle (face d) 2 2 0 chml-clss) ;; normally illegal
-  (z2-cocycle-gbar 2 2 *)
-  (z2-cocycle-gbar-head 2 2 **)
-  (gmsm-cocycle (face d) 2 3 15 chml-clss)
-  (z2-cocycle-gbar 2 3 *)
-  (z2-cocycle-gbar-head 2 3 **)
-  (gmsm-cocycle (face d) 2 4 31 chml-clss)
-  (z2-cocycle-gbar 2 4 *)
-  (z2-cocycle-gbar-head 2 4 **)
-  (setf chml-clss
-    (build-mrph :sorc d :trgt (z-chcm) :degr -3
-                :intr #'(lambda (dmns gmsm)
-                          (term-cmbn 0 (mod gmsm 2) :gnrt-z))
-                :strt :gnrt
-                :orgn '(essai-3)))
-  (gmsm-cocycle (face d) 3 4 31 chml-clss)
-  (z2-cocycle-gbar 3 4 *)
-  (z2-cocycle-gbar-head 3 4 **)
-|#
-
-(DEFUN K-Z-FUNDAMENTAL-CLASS (n)
-  (declare (fixnum n))
-  (the morphism
-    (build-mrph
-      :sorc (k-z n) :trgt (z-chcm) :degr (- n)
-      :intr #'(lambda (dmns gmsm)
-		(declare
-		  (fixnum dmns)
-		  (type gmsm gmsm))
-		(if (= dmns n)
-		   (do ((gmsm gmsm (gmsm (first (gbar-list gmsm))))
-			(dmns dmns (1- dmns)))
-		       ((= 1 dmns)
-			(term-cmbn 0 (first gmsm) :z-gnrt))
-		       (declare
-			 (type gmsm gmsm)
-			 (fixnum dmns)))
-		  (zero-cmbn (- dmns n))))
-      :strt :gnrt
-      :orgn `(k-z-fundamental-class ,n))))
-
-#|
-  (cat-init)
-  (setf c1 (k-z-fundamental-class 1))
-  (? c1 1 '(34))
-  (? c1 2 '(34 45))
-  (setf c3 (k-z-fundamental-class 3))
-  (? c3 3 (z-fundamental-gmsm 3 45))
-|#
-
-(DEFUN K-Z2-FUNDAMENTAL-CLASS (n)
-  (declare (fixnum n))
-  (the morphism
-    (build-mrph
-      :sorc (k-z2 n) :trgt (z-chcm) :degr (- n)
-      :intr #'(lambda (dmns gmsm)
-		(declare
-		  (fixnum dmns)
-		  (ignore gmsm))
-		(if (= dmns n)
-		   (term-cmbn 0 1 :z-gnrt)
-		  (zero-cmbn (- dmns n))))
-      :strt :gnrt
-      :orgn `(k-z2-fundamental-class ,n))))
-
-#|
-  (cat-init)
-  (setf c1 (k-z2-fundamental-class 1))
-  (? c1 1 1)
-  (? c1 2 2)
-  (setf c3 (k-z2-fundamental-class 3))
-  (? c3 3 (z2-fundamental-gmsm 3 1))
-|#
-
diff --git a/archive/Kenzo-1/kan.cl b/archive/Kenzo-1/kan.cl
deleted file mode 100644
index 5d82a75..0000000
--- a/archive/Kenzo-1/kan.cl
+++ /dev/null
@@ -1,198 +0,0 @@
-;;;  KAN  KAN  KAN  KAN  KAN  KAN  KAN  KAN  KAN  KAN  KAN  KAN
-;;;  KAN  KAN  KAN  KAN  KAN  KAN  KAN  KAN  KAN  KAN  KAN  KAN
-;;;  KAN  KAN  KAN  KAN  KAN  KAN  KAN  KAN  KAN  KAN  KAN  KAN
-
-(IN-PACKAGE "COMMON-LISP-USER")
-
-(provide "kan")
-
-(DEFVAR *KAN-LIST*)
-(SETF *KAN-LIST* +empty-list+)
-(PUSHNEW '*KAN-LIST* *list-list*)
-
-(DEFUN KAN (idnm)
-  (declare (fixnum idnm))
-  (the (or null simplicial-group)
-     (find idnm *kan-list* :key #'idnm)))
-
-#+clisp(eval-when (:compile-toplevel :load-toplevel :execute)
-         (setf (ext:package-lock :clos) nil))
-(DEFMETHOD PRINT-OBJECT ((kan kan) stream)
-  (the kan
-     (progn
-       (format stream "[K~D Kan-Simplicial-Set]" (idnm kan))
-       kan)))
-#+clisp(eval-when (:compile-toplevel :load-toplevel :execute)
-         (setf (ext:package-lock :clos) t))
-
-(DEFUN SMST-KAN (smst kfll)
-  (declare
-     (type simplicial-set smst)
-     (type kfll kfll))
-  (the kan
-     (progn
-       (change-class smst 'kan)
-       (setf (slot-value smst 'kfll) kfll)
-       (pushnew smst *kan-list*)
-       smst)))
-
-#|
-  (setf d (delta-infinity))
-  (defun vertex-i (absm i)
-     (with-absm (dgop gmsm) absm
-       (let ((dgop (nreverse (dgop-int-ext dgop)))
-             (gmsm (dlop-int-ext gmsm)))
-         (do ((dgop-mark dgop)
-              (gmsm-mark gmsm)
-              (ii 0 (1+ ii)))
-             ((= i ii) (car gmsm-mark))
-            (if (and dgop-mark
-                     (= ii (car dgop-mark)))
-               (pop dgop-mark)
-               (pop gmsm-mark))))))
-  (vertex-i (absm 0 1) 0)
-  (vertex-i (absm 1 1) 0)
-  (vertex-i (absm 1 1) 1)
-  (vertex-i (absm 0 3) 0)
-  (vertex-i (absm 0 3) 1)
-  (vertex-i (absm 3 1) 0)
-  (vertex-i (absm 3 1) 1)
-  (vertex-i (absm 3 1) 2)
-  (vertex-i (absm 1 3) 0)
-  (vertex-i (absm 1 3) 1)
-  (vertex-i (absm 1 3) 2)
-  (vertex-i (absm 2 3) 0)
-  (vertex-i (absm 2 3) 1)
-  (vertex-i (absm 2 3) 2)
-  (vertex-i (absm 0 7) 0)
-  (vertex-i (absm 0 7) 1)
-  (vertex-i (absm 0 7) 2)
-  (defun absm-int-ext (absm)
-     (with-absm (dgop gmsm) absm
-        (do ((dgop (nreverse (dgop-int-ext dgop)))
-             (gmsm (rest (dlop-int-ext gmsm)))
-             (i 0 (1+ i))
-             (rslt (list (first (dlop-int-ext gmsm)))))
-            ((and (endp dgop) (endp gmsm)) (nreverse rslt))
-           (if dgop
-              (if (= i (car dgop))
-                 (progn
-                   (pop dgop)
-                   (push (first rslt) rslt))
-                 (push (pop gmsm) rslt))
-              (return (nreconc rslt gmsm))))))
-  (defun absm-ext-int (vlist)
-     (do ((dgop nil)
-          (gmsm (list (first vlist)))
-          (mark (rest vlist) (cdr mark))
-          (idgop 0 (1+ idgop)))
-         ((endp mark) (absm (dgop-ext-int dgop)
-                            (dgop-ext-int gmsm)))
-        (if (= (first gmsm) (car mark))
-           (push idgop dgop)
-           (push (car mark) gmsm))))
-  (absm-ext-int '(0 0 0 1 2 3 3 3))
-  (absm-ext-int '(0 1 1 1 2))
-  (absm-int-ext (absm-ext-int '(0 0 0 1 2 3 3 3)))
-  (absm-int-ext (absm-ext-int '(0 1 1 1 2)))
-  (defun dkfll (indx dmns hat)
-     (cond ((= 1 dmns)
-            (absm 1 (gmsm (first hat))))
-           ((= 0 indx)
-            (let ((del-1 (absm-int-ext (first hat)))
-                  (del-2 (absm-int-ext (second hat))))
-              (absm-ext-int
-                 (cons (first del-1)
-                       (cons (second del-2) (rest del-1))))))
-           ((= 1 indx)
-            (let ((del-0 (absm-int-ext (first hat)))
-                  (del-2 (absm-int-ext (second hat))))
-              (absm-ext-int
-                 (cons (first del-2) del-0))))
-           (t
-            (let ((del-0 (absm-int-ext (first hat)))
-                  (del-1 (absm-int-ext (second hat))))
-              (absm-ext-int
-                 (cons (first del-1) del-0))))))
-  (smst-kan d #'dkfll)
-  (kfll d 0 1 (list (absm 0 1)))
-  (kfll d 0 2 (list (absm 0 5) (absm 0 3)))
-  (kfll d 1 2 (list (absm 0 6) (absm 0 3)))
-  (kfll d 2 2 (list (absm 0 6) (absm 0 5)))
-  (kfll d 0 2 (list (absm 0 3) (absm 0 3)))
-  (kfll d 1 2 (list (absm 1 2) (absm 0 3)))
-|#
-
-(DEFUN CHECK-HAT (kan indx dmns hat)
-  (declare
-     (type kan kan)
-     (fixnum indx dmns)  ;;; dmns like in (funcall kfll ...)
-     (list hat))
-  (assert (= dmns (length hat)))
-  (setf hat
-	(append (subseq hat 0 indx)
-		(list :hole)
-		(nthcdr indx hat)))
-  (do ((cmpr (cmpr kan))
-       (j 0 (1+ j)))
-      ((> j dmns) t)
-      (declare
-         (type cmprf cmpr)
-	 (fixnum j))
-     (unless (= j indx)
-       (let ((del-j (nth j hat)))
-	 (declare (type absm del-j))
-	 (do ((i j (1+ i)))
-	     ((= i dmns))
-	     (declare (fixnum i))
-	    (unless (= i (1- indx))
-	      (let ((del-i-del-j (face kan i (1- dmns) del-j))
-		    (del-j-del-i+1 (face kan j (1- dmns)
-					 (nth (1+ i) hat))))
-		(declare (type absm del-i-del-j del-j-del-i+1))
-		(assert (eq :equal
-			    (a-cmpr3 cmpr del-i-del-j del-j-del-i+1))))))))))
-
-#|
-  (setf od (gdeltab))
-  (setf s (loop3 0 31 2))
-  (setf faces (mapcar #'(lambda (indx) (face od indx 3 s))
-                      '(0 1 2 3)))
-  (delete (nth 1 faces) faces)
-  (check-hat od 1 3 faces)
-  (setf (nth 2 faces) (nth 1 faces))
-  (check-hat od 1 3 faces)
-|#
-
-
-(DEFUN CHECK-KAN (kan indx dmns hat)
-  (declare
-     (type kan kan)
-     (fixnum indx dmns)
-     (list hat))
-  (the (values)
-     (let ((rslt (kfll kan indx dmns hat))
-	   (cmpr (cmpr kan))
-	   (face (face kan)))
-       (declare
-	  (type absm rslt)
-	  (type cmprf cmpr)
-	  (type face face))
-       (check-hat kan indx dmns hat)
-       (do ((i 0 (1+ i)))
-	   ((> i dmns))
-	  (declare (fixnum i))
-	  (unless (= i indx)
-	    (let ((x-i (pop hat))
-		  (del-i-rslt (a-face4 face i dmns rslt)))
-	      (declare (type absm x-i del-i-rslt))
-	      (with-absm (dgop1 gmsm1) x-i
-	      (with-absm (dgop2 gmsm2) del-i-rslt
-		 (unless (and (= dgop1 dgop2)
-			      (eq (funcall cmpr gmsm1 gmsm2) :equal))
-		    (error "Wrong result:~@
-                            Fill = ~A~@
-                            Del-~D(Fill) = ~A~@
-                            Hat-~D = ~A"
-		       rslt i del-i-rslt i x-i)))))))
-       (done))))
\ No newline at end of file
diff --git a/archive/Kenzo-1/loop-spaces.cl b/archive/Kenzo-1/loop-spaces.cl
deleted file mode 100644
index 202d308..0000000
--- a/archive/Kenzo-1/loop-spaces.cl
+++ /dev/null
@@ -1,611 +0,0 @@
-;;;  LOOP-SPACES  LOOP-SPACES  LOOP-SPACES  LOOP-SPACES  LOOP-SPACES  LOOP-SPACES
-;;;  LOOP-SPACES  LOOP-SPACES  LOOP-SPACES  LOOP-SPACES  LOOP-SPACES  LOOP-SPACES
-;;;  LOOP-SPACES  LOOP-SPACES  LOOP-SPACES  LOOP-SPACES  LOOP-SPACES  LOOP-SPACES
-
-(IN-PACKAGE "COMMON-LISP-USER")
-
-(PROVIDE "loop-spaces")
-
-(DEFCONSTANT +NULL-LOOP+ (make-loop :list +empty-list+))
-
-;;; NILOOP = non-normalized iloop; a common dgop is possible.
-
-(DEFUN NORMALIZE-LOOP (dmns niloop)
-   (declare (list niloop))      
-   (the absm
-      (progn
-         (unless niloop
-            (return-from normalize-loop
-               (absm (mask dmns) +null-loop+)))
-         (let ((dgop (apply #'logand (mapcar #'car niloop))))
-            (declare (fixnum dgop))
-            (if (zerop dgop)
-               (absm 0 (make-loop :list niloop))
-               (absm dgop
-                  (make-loop
-                     :list (mapcar #'(lambda (apowr)
-                                        (cons
-                                           (dgop/dgop (apdgop apowr) dgop)
-                                           (cdr apowr)))
-                              niloop))))))))
-
-#|
-  (normalize-loop 4 +empty-list+)
-  (normalize-loop 4 '((1 a . 1)))
-  (normalize-loop 4 '((1 a . 1) (3 b . 1) (5 b . 1)))
-|#
-
-(DEFUN UNNORMALIZE-LOOP (absm)
-  (declare (type absm absm))
-  (the iloop
-     (with-absm (dgop loop) absm
-        (mapcar #'(lambda (apowr)
-		    (declare (type apowr apowr))
-		    (cons (dgop*dgop dgop (car apowr))
-			  (cdr apowr)))
-		(loop-list loop)))))
-
-#|
-  (unnormalize-loop (absm 1 (loop3 2 'a 3)))
-|#
-
-(DEFUN LOOP3 (&rest list)
-  (when (and (= 1 (length list))
-             (listp (first list)))
-    (setf list (first list)))
-  (unless (zerop (mod (length list) 3))
-    (error "In LOOP3, 3 should divide the list length."))
-  (flet ((fixnumpp (object)
-                   (unless (typep object 'fixnum)
-                     (error "In LOOP3, ~A should be a fixnum." object))
-                   object))
-    (do ((rslt +empty-list+ (cons (apowr
-                                   (fixnumpp (car mark))
-                                   (cadr mark)
-                                   (fixnumpp (caddr mark)))
-                                  rslt))
-         (mark list (cdddr mark)))
-        ((endp mark) (make-loop :list (nreverse rslt)))
-      (declare (list rslt mark)))))
-
-#|
-()
-(loop3 nil)
-(loop3 '(1 a 2 3 b -2))
-(loop3 '(1 a 2 3 b b))
-(loop3 '(1 a 2 3 b))
-(loop3 1 'a 2 3 'b 4)
-(loop3 1 'a 2 3 'b)
-|#
-
-(DEFUN LOOP-PRINT (loop stream depth)
-  (declare
-   (type loop loop) (stream stream)
-   (ignore depth))
-  (the loop
-    (progn
-      (format stream "<<Loop")
-      (dolist (apowr (loop-list loop))
-        (declare (type apowr apowr))
-        (with-apowr (dgop gmsm expn) apowr
-                    (format stream "[")
-                    (unless (zerop dgop)
-                      (format stream "~A " (hyphenize-list (dgop-int-ext dgop))))
-                    (format stream "~A" gmsm)
-                    (unless (= 1 expn)
-                      (format stream "\\~D" expn))
-                    (format stream "]")))
-      (format stream ">>")
-      loop)))
-
-#|
-  (loop3 nil)
-  (loop3 '(0 a 2))
-  (loop3 '(1 a 2))
-  (loop3 '(3 a 2 5 b -1 6 c 4))
-  (loop3 '(7 a 1 11 b 1 13 c 1 14 d 1))
-  (loop3 '(7 a 1 11 b 1 13 c 1 7 d 1))
-  (loop3 '(0 a 1 0 b 2 0 c -1 1 d 1))
-|#
-
-(DEFUN APOWR-NILOOP (cmpr apowr niloop)
-   (declare
-      (type cmprf cmpr)
-      (type apowr apowr)
-      (type iloop niloop))
-   (the iloop
-      (progn
-         (unless niloop
-            (return-from apowr-niloop
-               (list apowr)))
-         (let ((apowr2 (first niloop)))
-            (declare (type apowr apowr2))
-            (with-apowr (dgop2 gmsm2 expn2) apowr2
-               (unless (and (= (apdgop apowr) dgop2)
-                            (eq :equal (funcall cmpr (apgmsm apowr) gmsm2)))
-                  (return-from apowr-niloop
-                     (cons apowr niloop)))
-               (incf expn2 (apexpn apowr))
-               (if (zerop expn2)
-                  (rest niloop)
-                  (cons (apowr dgop2 gmsm2 expn2) (rest niloop))))))))
-
-#|
-  (apowr-niloop #'s-cmpr '(0 a . 1) +empty-list+)
-  (apowr-niloop #'s-cmpr '(0 a . 1) '((1 a . 1)))
-  (apowr-niloop #'s-cmpr '(0 a . 1) '((0 b . 1)))
-  (apowr-niloop #'s-cmpr '(0 a . 1) '((0 a . 1) (0 b . 1)))
-  (apowr-niloop #'s-cmpr '(0 a . 1) '((0 a . -1) (0 b . 1)))
-|#
-
-(DEFUN LOOP-SPACE-CMPR (cmpr)
-   (declare (type cmprf cmpr))
-   (flet ((2apowr-cmpr (apowr1 apowr2)
-           (declare (type apowr apowr1 apowr2))
-           (lexico
-              (f-cmpr (apdgop apowr1) (apdgop apowr2))
-              (funcall cmpr (apgmsm apowr1) (apgmsm apowr2))
-              (f-cmpr (apexpn apowr1) (apexpn apowr2)))))
-      (flet ((rslt (loop1 loop2)
-              (declare (type loop loop1 loop2))
-              (maplexico #'2apowr-cmpr (loop-list loop1) (loop-list loop2))))
-         (the cmprf #'rslt))))
-
-#|
-  (setf cmpr (loop-space-cmpr #'s-cmpr))
-  (funcall cmpr (loop3 '(1 a 2)) (loop3 '(1 a -1)))
-  (funcall cmpr (loop3 '(3 b 4 1 a 2)) (loop3 '(3 b 4 1 a -1)))
-|#
-
-(DEFUN APOWR-FACE4 (face indx dmns apowr)
-   ;; dmns = dimension in the loop-space
-   (declare
-      (type face face)
-      (type apowr apowr))
-   (with-apowr (dgop gmsm expn) apowr
-      (let ((face (a-face4 face indx (1+ dmns) (absm dgop gmsm))))
-         (declare (type absm face))
-         (with-absm (dgop gmsm) face
-            (if (logbitp (1- dmns) dgop)
-               nil
-               (apowr dgop gmsm expn))))))
-
-#|
-  (setf face (face (delta-infinity)))
-  (apowr-face4 face 3 4 (apowr 1 31 5))
-  (setf face (face (sphere 5)))
-  (apowr-face4 face 2 5 (apowr 1 's5 4))
-  (apowr-face4 face 2 5 (apowr 2 's5 4))
-|#
-
-(DEFUN APOWR-LASTFACE4 (cmpr face dmns apowr)
-   ;; indx =dmns
-   (declare
-      (type cmprf cmpr)
-      (type face face)
-      (fixnum dmns)
-      (type apowr apowr))
-   (the list
-      (with-apowr (dgop gmsm expn) apowr
-         (let ((absm (absm dgop gmsm)))
-            (declare (type absm absm))
-            (let ((face-n (a-face4 face dmns (1+ dmns) absm))
-                  (face-n+1 (a-face4 face (1+ dmns) (1+ dmns) absm)))
-               (declare (type absm face-n face-n+1))
-               (with-absm (dgop1 gmsm1) face-n
-               (with-absm (dgop2 gmsm2) face-n+1
-                  (if (logbitp (1- dmns) dgop1)
-                     (if (logbitp (1- dmns) dgop2)
-                        (return-from apowr-lastface4 +empty-list+)
-                        (return-from apowr-lastface4
-                           (list (apowr dgop2 gmsm2 (- expn)))))
-                     (when (logbitp (1- dmns) dgop2)
-                        (return-from apowr-lastface4
-                           (list (apowr dgop1 gmsm1 expn)))))
-                  (when (and (= dgop1 dgop2)
-                             (eq :equal (funcall cmpr gmsm1 gmsm2)))
-                     (return-from apowr-lastface4 +empty-list+))
-                  (case expn
-                     (+1 (list (apowr dgop2 gmsm2 -1) (apowr dgop1 gmsm1 +1)))
-                     (-1 (list (apowr dgop1 gmsm1 -1) (apowr dgop2 gmsm2 +1)))
-                     (otherwise
-                        (if (plusp expn)
-                           (do ((rslt +empty-list+ (cons apowr2 (cons apowr1 rslt)))
-                                (apowr1 (apowr dgop1 gmsm1 +1))
-                                (apowr2 (apowr dgop2 gmsm2 -1))
-                                (nark expn (1- nark)))
-                               ((zerop nark) rslt)
-                              (declare
-                                 (list rslt)
-                                 (type apowr apowr1 apowr2)))
-                              (do ((rslt +empty-list+ (cons apowr1 (cons apowr2 rslt)))
-                                   (apowr1 (apowr dgop1 gmsm1 -1))
-                                   (apowr2 (apowr dgop2 gmsm2 +1))
-                                   (nark expn (1+ nark)))
-                                  ((zerop nark) rslt)
-                                 (declare
-                                    (list rslt)
-                                    (type apowr apowr1 apowr2)))))))))))))
-
-#|
-  (setf cmpr #'f-cmpr face (face (delta-infinity)))
-  (apowr-lastface4 cmpr face 4 (apowr 0 63 1))
-  (apowr-lastface4 cmpr face 4 (apowr 0 63 -1))
-  (apowr-lastface4 cmpr face 4 (apowr 0 63 3))
-  (apowr-lastface4 cmpr face 4 (apowr 0 63 -3))
-  (apowr-lastface4 cmpr face 4 (apowr 8 31 1))
-  (setf face #'(lambda (indx dmns gmsm)  ;  dmns = 5
-                  (case indx
-                     (5 (absm 8 'a))
-                     (4 (absm 8 'a)))))
-  (setf cmpr #'s-cmpr)
-  (apowr-lastface4 cmpr face 4 (apowr 0 'a 2))
-  (setf face #'(lambda (indx dmns gmsm)  ;  dmns = 5
-                  (case indx
-                     (5 (absm 1 'a))
-                     (4 (absm 8 'a)))))
-  (apowr-lastface4 cmpr face 4 (apowr 0 'a 2))
-  (setf face #'(lambda (indx dmns gmsm)  ;  dmns = 5
-                  (case indx
-                     (5 (absm 1 'a))
-                     (4 (absm 1 'a)))))
-  (apowr-lastface4 cmpr face 4 (apowr 0 'a 2))
-|#
-                                   
-(DEFUN LOOP-SPACE-FACE (cmpr face)
-   (declare
-      (type cmprf cmpr)
-      (type face face))
-   (flet ((rslt (indx dmns loop)
-             (declare
-                (fixnum indx dmns)
-                (type loop loop))
-             (the absm
-                (let ((rslt +empty-list+))
-                   (declare (type iloop rslt))
-                   (if (< indx dmns)
-                      (dolist (apowr (loop-list loop))
-                         (declare (type apowr apowr))
-                         (let ((lface (apowr-face4 face indx dmns apowr)))
-                            (declare (type (or null apowr) lface))
-                            (when lface (setf rslt (apowr-niloop cmpr lface rslt)))))
-                      (dolist (apowr (loop-list loop))
-                         (declare (type apowr apowr))
-                         (let ((lface (apowr-lastface4 cmpr face dmns apowr)))
-                            (declare (list lface))
-                            (dolist (apowr lface)
-                               (declare (type apowr apowr))
-                               (setf rslt (apowr-niloop cmpr apowr rslt))))))
-                   (normalize-loop (1- dmns) (nreverse rslt))))))
-      (the face #'rslt)))
-
-#|
-  (setf cmpr #'f-cmpr
-        face (face (delta-infinity)))
-  (setf rslt (loop-space-face cmpr face))
-  (funcall rslt 2 4 (loop3 '(0 63 3 1 31 -3)))
-  (funcall rslt 2 4 (loop3 '(0 63 3 0 63 -3)))
-  (funcall rslt 4 4 (loop3 '(0 63 3 0 63 -3)))
-  (funcall rslt 4 4 (loop3 '(0 63 3)))
-|#
-
-(DEFUN LOOP-SPACE-FACE* (cmpr face)
-   (declare
-      (type cmprf cmpr)
-      (type face face))
-   (flet ((rslt (indx dmns loop)
-             (declare
-                (fixnum indx dmns)
-                (type loop loop))
-             (the (or loop (eql :degenerate))
-                (let ((rslt +empty-list+))
-                   (declare (type iloop rslt))
-                   (if (< indx dmns)
-                      (dolist (apowr (loop-list loop))
-                         (declare (type apowr apowr))
-                         (let ((lface (apowr-face4 face indx dmns apowr)))
-                            (declare (type (or null apowr) lface))
-                            (when lface (setf rslt (apowr-niloop cmpr lface rslt)))))
-                      (dolist (apowr (loop-list loop))
-                         (declare (type apowr apowr))
-                         (let ((lface (apowr-lastface4 cmpr face dmns apowr)))
-                            (declare (list lface))
-                            (dolist (apowr lface)
-                               (declare (type apowr apowr))
-                               (setf rslt (apowr-niloop cmpr apowr rslt))))))
-                   (if (zerop (apply #'logand (mapcar #'car rslt)))
-                      (make-loop :list (nreverse rslt))
-                      :degenerate)))))
-      (the face* #'rslt)))
-
-(DEFUN LOOP-SPACE-GRIN-SINTR (dmns loop)
-  (declare
-     (ignore dmns)
-     (type loop loop))
-  (the absm
-     (absm 0 (make-loop
-	      :list (mapcar #'(lambda (apowr)
-				(declare (type apowr apowr))
-				(with-apowr (dgop gmsm expn) apowr
-					    (apowr dgop gmsm (- expn))))
-			    (reverse (loop-list loop)))))))
-
-#|
-  (loop-space-grin-sintr 5 (loop3 0 'a 2 3 'b -3))
-|#
-
-(DEFUN LOOP-SPACE-GRML-SINTR (cmpr)
-  (declare (type cmprf cmpr))
-  (flet ((rslt (dmns crpr)
-	    (declare
-	       (fixnum dmns)
-	       (type crpr crpr))
-	    (the absm
-	       (with-crpr (absm1 absm2) crpr
-	         (let ((niloop1 (nreverse (unnormalize-loop absm1)))
-		       (niloop2 (unnormalize-loop absm2)))
-		   (declare (type iloop niloop1 niloop2))
-		   (loop
-		    (unless niloop1 (return))
-		    (unless niloop2 (return))
-		    (let ((apowr1 (first niloop1))
-			  (apowr2 (first niloop2)))
-		      (declare (type apowr apowr1 apowr2))
-		      (with-apowr (dgop1 gmsm1 expn1) apowr1
-		      (with-apowr (dgop2 gmsm2 expn2) apowr2
-		         (unless (and (= dgop1 dgop2)
-				      (eq :equal (funcall cmpr gmsm1 gmsm2)))
-			    (return))
-			 (incf expn1 expn2)
-			 (cond ((zerop expn1)
-				(pop niloop1)
-				(pop niloop2))
-			       (t
-				(pop niloop1)
-				(setf niloop2
-				      (cons (apowr dgop2 gmsm2 expn1)
-					    (rest niloop2)))
-				(return)))))))
-		   (normalize-loop dmns
-				   (nreconc niloop1 niloop2)))))))
-     (the sintr #'rslt)))
-
-#|
-  (setf cmpr #'s-cmpr)
-  (setf ml (loop-space-grml-sintr cmpr))
-  (funcall ml 2 (crpr 3 (loop3) 0 (loop3 0 'a 2)))
-  (funcall ml 2 (crpr 0 (loop3 0 'a 2) 3 (loop3)))
-  (funcall ml 2 (crpr 0 (loop3 0 'a 2) 0 (loop3 0 'a -2)))
-  (funcall ml 2 (crpr 0 (loop3 0 'a 2) 0 (loop3 0 'a -3)))
-  (funcall ml 2 (crpr 0 (loop3 0 'a 2) 0 (loop3 0 'b -3)))
-  (funcall ml 2 (crpr 0 (loop3 0 'a 2 0 'b -3)
-                      0 (loop3 0 'b +3 0 'a -2)))
-|#
-
-(DEFUN LOOP-SPACE (smst &optional (n 1))
-   (declare
-      (type simplicial-set smst)
-      (fixnum n))   
-   (the simplicial-group
-      (if (= n 1)
-         (with-slots (cmpr face) smst
-            (declare
-               (type cmprf cmpr)
-	       (type face face))
-	    (build-smgr
-	       :cmpr (loop-space-cmpr cmpr)
-	       :basis :locally-effective
-	       :bspn +null-loop+
-	       :face (loop-space-face cmpr face)
-	       :face* (loop-space-face* cmpr face)
-	       :sintr-grml (loop-space-grml-sintr cmpr)
-	       :sintr-grin #'loop-space-grin-sintr
-	       :orgn `(loop-space ,smst)))
-	(loop-space (loop-space smst) (1- n)))))
-
-(DEFUN GDELTAB ()
-   (loop-space (deltab)))
-
-#|
-  (cat-init)
-  (setf g (gdeltab))
-  (cmpr g (loop3 0 3 2) (loop3 0 3 2))
-  (cmpr g (loop3 0 3 2) (loop3 0 3 3))
-  (cmpr g (loop3 0 3 2) (loop3 0 5 2))
-  (cmpr g (loop3 0 5 2) (loop3 0 3 2))
-  (face g 3 3 (loop3 12 7 3))
-  (face g 3 3 (loop3 5 7 3))
-  (face g 3 3 (loop3 6 7 3 5 7 3 3 7 3))
-  (face g 4 4 (absm 4 (loop3 6 7 3 5 7 3 3 7 3)))
-  (check-faces (cmpr g) (face g) 3 (loop3 6 7 -3 5 7 -3 3 7 -3))
-  (setf dd (cmps g g))
-  (? dd 3 (loop3 6 7 3 5 7 3 3 7 3))
-  (grml g 2 (crpr 0 (loop3 0 15 3) 0 (loop3 0 15 4)))
-  (grin g 2 (loop3 0 15 -2))
-  (setf rslt (loop3 0 31 1))
-  (setf hat (mapcar #'(lambda (i) (face g i 3 rslt))
-                    (<a-b> 0 3)))
-  (dotimes (i 4)
-    (print (kfll g i 3 (remove (nth i hat) hat :test #'equal)))
-    (check-kan g i 3 (remove (nth i hat) hat :test #'equal)))
-
-  (setf g (loop-space (sphere 2)))
-  (setf rslt (loop3 3 's2 2 5 's2 -2 6 's2 2))
-  (setf hat (mapcar #'(lambda (i) (face g i 3 rslt))
-                    (<a-b> 0 3)))
-  (dotimes (i 4)
-    (print (kfll g i 3 (remove (nth i hat) hat :test #'equal)))
-    (check-kan g i 3 (remove (nth i hat) hat :test #'equal)))
-
-  (setf g (loop-space (sphere 3) 2))
-  (setf x (first (basis (echcm g) 4)))
-  (setf efhm (efhm g))
-  (setf x (lf efhm (rg efhm 4 x)))
-  (setf rslt (gnrt (first (cmbn-list x))))
-  (setf hat (mapcar #'(lambda (i) (face g i 4 rslt))
-                    (<a-b> 0 4)))
-  (dotimes (i 5)
-    (print (kfll g i 4 (remove (nth i hat) hat :test #'equal)))
-    (check-kan g i 4 (remove (nth i hat) hat :test #'equal)))
-
-  (setf rslt (gnrt (third (cmbn-list x))))
-  (setf hat (mapcar #'(lambda (i) (face g i 4 rslt))
-                    (<a-b> 0 4)))
-  (dotimes (i 5)
-    (print (kfll g i 4 (remove (nth i hat) hat :test #'equal)))
-    (check-kan g i 4 (remove (nth i hat) hat :test #'equal)))
-
-  (setf g (loop-space (sphere 3) 2))
-  (setf efhm (efhm g))
-  (setf echcm (rbcc efhm))
-  (setf basis (basis echcm 4))
-  (setf cmbn (cmbn 4 1 (first basis) 10 (second basis)
-                     100 (third basis)))
-  (setf cmbn2 (lf efhm (rg efhm cmbn)))
-  (setf loop-list (mapcar #'cdr (cmbn-list cmbn2)))
-  (dolist (loop loop-list)
-    (setf hat (mapcar #'(lambda (i) (face g i 4 loop))
-                      (<a-b> 0 4)))
-    (dotimes (i 5)
-      (print (kfll g i 4 (remove (nth i hat) hat)))
-      (check-kan g i 4 (remove (nth i hat) hat))))
-|#
-
-#|
-  (cat-init)
-  (setf p (r-proj-space 3))
-  (setf op (loop-space p))
-  (defun random-apowr (dmns max-expn)
-     (loop
-        (let* ((dgop (random (2-exp (1- dmns))))
-               (gmsm (- dmns (logcount dgop))))
-           (unless (< 0 gmsm 3)
-              (return-from random-apowr
-                 (apowr dgop gmsm (srandom max-expn)))))))
-  (dotimes (i 15) (print (random-apowr 8 3)))
-  (defun random-niloop (dmns max-expn length)
-     (mapcar #'(lambda (dummy)
-                  (random-apowr (1+ dmns) max-expn))
-        (make-list length)))
-  (dotimes (i 20)
-     (print (normalize-loop 7 (random-niloop 7 3 3))))
-  (defun random-loop-cmbn (cmpr degr max-cffc max-expn loop-length cmbn-length)
-     (do ((rslt +empty-list+ (cons term rslt))
-          (i cmbn-length (1- i))
-          (term))
-         ((zerop i)
-          (apply #'nterm-add cmpr degr rslt))
-        (setf term
-              (term (srandom max-cffc)
-                 (make-loop :list (random-niloop degr max-expn loop-length))))))
-  (setf cmpr (cmpr op))
-  (setf +too-much-time+ -1)
-  (setf c (random-loop-cmbn cmpr 8 10 4 4 100))
-  (time (? op (? op c)))
-  (time (? op (? op c)))
-|#
-  
-#|  ;; in EAT.
-  (DEFUN PR-INFINITY-EQS (gsm1 gsm2)
-     (declare (fixnum gsm1 gsm2))
-     t)
-
-  (DEFUN PR-INFINITY-BASIS (k)
-     (declare (fixnum k))
-     (flet ((rslt (dmns)
-               (declare (fixnum dmns))
-               (if (< 0 dmns k)
-                  empty-list
-                  (list dmns))))
-        (the basis #'rslt)))
-
-  (DEFUN PR-INFINITY-GDL (k)
-     (declare (fixnum k))
-     (flet ((rslt (indx dmns gsm)
-             (declare (fixnum indx dmns gsm))
-             (if (<= dmns k)
-                (asm (nreverse (<a-b< 0 (1- dmns))) 0)
-                (if (or (zerop indx)
-                        (= indx dmns))
-                   (asm nil (1- dmns))
-                   (if (= dmns (1+ k))
-                      (asm (nreverse (<a-b< 0 (1- dmns))) 0)
-                      (asm (list (1- indx)) (- dmns 2)))))))
-        (the function #'rslt)))
-
-  (DEFUN PR-INFINITY (&optional (k 1))
-     (declare (fixnum k))
-     (build-ss
-         :eqs #'pr-infinity-eqs
-         :sbs (pr-infinity-basis k)
-         :bsp 0
-         :gdl (pr-infinity-gdl k)
-         :org `(pr-infinity ,k)))
-
-  (setf p (pr-infinity))
-  (sbs p 4)
-  (dotimes (i 5)
-     (print (gdl p i 4 4)))
-  (setf cc (ss-cc p))
-  (dotimes (i 5)
-     (print (d-? cc i i)))
-  (setf dd (cmp-mrp (cc-d cc) (cc-d cc)))
-  (dotimes (i 6)
-     (print (? dd i i)))
-  (setf p (pr-infinity 3))
-  (dotimes (i 7)
-     (print (sbs p i)))
-  (dotimes (i 5)
-     (print (gdl p i 4 4)))
-  (setf d (cc-d (ss-cc p)))
-  (dotimes (i 7)
-     (print (? d i i)))
-  (setf dd (cmp-mrp d d))
-  (dotimes (i 7)
-     (print (? dd i i)))
-
-  (setf p (pr-infinity 3))
-  (setf op (loop-space p))
-  (defun srandom (max)
-     (let ((rslt (- (random (+ max max)) max)))
-        (if (zerop rslt)
-           max
-           rslt)))
-  (dotimes (i 20) (print (srandom 3)))
-  (DEFUN DGOP-INT-EXT (dop)
-     (declare (fixnum dop))
-     (the list
-        (do ((dop dop (ash dop -1))
-             (rslt empty-list)
-             (bmark 0 (1+ bmark)))
-            ((zerop dop) rslt)
-           (declare
-              (fixnum dop bmark)
-              (list rslt))
-           (when (oddp dop)
-              (push bmark rslt)))))
-  (defun random-apowr (dmns max-expn)
-     (let ((dgop (dgop-int-ext (* 2 (random (2-exp (1- dmns)))))))
-        (pwr (asm dgop (- 8 (length dgop))) (srandom max-expn))))
-  (dotimes (i 5) (print (random-apowr 8 3)))
-  (defun random-niloop (dmns max-expn length)
-     (mapcar #'(lambda (dummy)
-                  (random-apowr (1+ dmns) max-expn))
-        (make-list length)))
-  (dotimes (i 20)
-     (print (normalize-loop 7 (make-strloop :lst (random-niloop 7 3 3)))))
-  (defun random-loop-cmbn (degr max-cffc max-expn loop-length cmbn-length)
-     (do ((rslt empty-list (cons mnm rslt))
-          (i cmbn-length (1- i))
-          (term))
-         ((zerop i)
-          (make-cmb :dgr degr :lst rslt))
-        (setf mnm
-              (mnm (srandom max-cffc)
-                 (make-strloop :lst (random-niloop degr max-expn loop-length))))))
-  (setf d (cc-d (ss-cc op)))
-  (setf c (random-loop-cmbn 8 10 4 4 100))
-  (time (??? d (??? d c)))
-  (time (??? d (??? d c)))
-|#
-
diff --git a/archive/Kenzo-1/lp-space-efhm.cl b/archive/Kenzo-1/lp-space-efhm.cl
deleted file mode 100644
index fdb787b..0000000
--- a/archive/Kenzo-1/lp-space-efhm.cl
+++ /dev/null
@@ -1,664 +0,0 @@
-;;;  LP-SPACE-EFHM  LP-SPACE-EFHM  LP-SPACE-EFHM  LP-SPACE-EFHM
-;;;  LP-SPACE-EFHM  LP-SPACE-EFHM  LP-SPACE-EFHM  LP-SPACE-EFHM
-;;;  LP-SPACE-EFHM  LP-SPACE-EFHM  LP-SPACE-EFHM  LP-SPACE-EFHM
-
-(IN-PACKAGE "COMMON-LISP-USER")
-
-(PROVIDE "lp-space-efhm")
-
-(DEFUN LS-HAT-U-U (space
-                  &aux (cobar (cobar space))
-                       (loop-space (loop-space space))
-                       (spac-tnsr-lpsp (tnsr-prdc space loop-space)))
-   (declare
-      (type simplicial-set space)
-      (type chain-complex cobar spac-tnsr-lpsp)
-      (type simplicial-group loop-space))
-   (the chain-complex
-      (tnsr-prdc cobar spac-tnsr-lpsp)))
-
-(DEFUN LS-HAT-LEFT-PERTURBATION-INTR (space)
-   (declare (type simplicial-set space))
-   (let ((cprd (dgnl space)))
-      (flet ((rslt (degr tnpr)
-                (declare
-                   (fixnum degr)
-                   (type tnpr tnpr))
-                (with-tnpr (degr1 allp1 nil tnpr2) tnpr
-                (with-tnpr (degr21 gmsm21 degr22 loop22) tnpr2
-                   (let ((cprd (cmbn-list (gnrt-? cprd degr21 gmsm21))))
-                      (declare (list cprd))
-                      (setf cprd (rest cprd))    ;;; because \bar{A}
-                      (make-cmbn :degr (1- degr)
-                         :list
-                         (mapcar
-                            #'(lambda (term)
-                                 (declare (type term term))
-                                 (with-term (cffc tnpr21) term
-                                 (with-tnpr (degr211 gmsm211 degr212 gmsm212) tnpr21
-                                    (decf degr211)
-                                    (term cffc
-                                       (tnpr
-                                          (+ degr1 degr211)
-                                          (make-allp
-                                             :list (append
-                                                      (allp-list allp1)
-                                                      (list (cbgn degr211 gmsm211))))
-                                          (+ degr212 degr22)
-                                          (tnpr degr212 gmsm212 degr22 loop22))))))
-                            cprd)))))))
-         (the intr-mrph #'rslt))))
-
-(DEFUN LS-HAT-LEFT-PERTURBATION (space)
-   (declare (type simplicial-set space))
-   (the morphism
-      (let ((ls-hat-u-u (ls-hat-u-u space)))
-         (build-mrph
-            :sorc ls-hat-u-u
-            :trgt ls-hat-u-u
-            :degr -1
-            :intr (ls-hat-left-perturbation-intr space)
-            :strt :gnrt
-            :orgn `(ls-hat-left-perturbation ,space)))))
-
-(DEFUN LS-HAT-T-U (space
-                  &aux (ls-hat-u-u (ls-hat-u-u space))
-                       (ls-hat-left-perturbation
-                          (ls-hat-left-perturbation space)))
-   (declare
-      (type simplicial-set space)
-      (type chain-complex ls-hat-u-u)
-      (type morphism ls-hat-left-perturbation))
-   (the chain-complex
-      (progn
-         (setf (slot-value ls-hat-left-perturbation 'sorc) ls-hat-u-u
-               (slot-value ls-hat-left-perturbation 'trgt) ls-hat-u-u)
-         ;; because maybe these slots have been modified when constructing
-         ;;   the ls-left-hmeq-right-reduction
-         (add ls-hat-u-u ls-hat-left-perturbation))))
-
-#|
-  (cat-init)
-  (setf c (ls-hat-t-u (deltab)))
-  (defun random-allp (length)
-     (let ((rslt nil))
-        (dotimes (i length)
-           (let* ((gmsm (random (mask 9)))
-                  (dmns (1- (logcount gmsm))))
-              (when (plusp dmns)
-                 (push (cbgn (1- dmns) gmsm) rslt))))
-        (make-allp :list rslt)))
-  (dotimes (i 10) (print (random-allp 5)))
-  (setf allp (random-allp 4))  ;; the degree could be too big
-                               ;; then redo
-  (setf allp-degr (apply #'+ (mapcar #'car (allp-list allp))))
-  (setf gnrt (tnpr allp-degr allp 4 (tnpr 2 7 2 (loop3 0 15 2))))
-  (? c (+ 4 allp-degr) gnrt)
-  (? c *)
-  (dotimes (i 10)
-     (let ((allp (random-allp 3)))
-        (setf allp-degr (apply #'+ (mapcar #'car (allp-list allp))))
-        (setf gnrt (tnpr allp-degr allp 4 (tnpr 2 7 2 (loop3 0 15 2))))
-        (unless (>= allp-degr 11)
-           (print (? c (+ 4 allp-degr) gnrt))
-           (print (? c (? c (+ 4 allp-degr) gnrt))))))
-  (dotimes (i 20)
-     (let ((allp (random-allp 3)))
-        (setf allp-degr (apply #'+ (mapcar #'car (allp-list allp))))
-        (setf gnrt (tnpr allp-degr allp 5 (tnpr 3 15 2 (loop3 0 15 2))))
-        (unless (>= allp-degr 10)
-           (print (? c (+ 5 allp-degr) gnrt))
-           (print (? c (? c (+ 5 allp-degr) gnrt))))))
-  (dotimes (i 20)
-     (let ((allp (random-allp 3)))
-        (setf allp-degr (apply #'+ (mapcar #'car (allp-list allp))))
-        (setf gnrt (tnpr allp-degr allp 5 (tnpr 2 7 3 (loop3 0 31 2))))
-        (unless (>= allp-degr 10)
-           (print (? c (+ 5 allp-degr) gnrt))
-           (print (? c (? c (+ 5 allp-degr) gnrt))))))
-|#
-
-(DEFUN LS-HAT-RIGHT-PERTURBATION (space
-                                 &aux (cobar (cobar space))
-                                      (ls-hat-t-u (ls-hat-t-u space)))
-   (declare
-      (type simplicial-set space)
-      (type chain-complex cobar ls-hat-t-u))
-   (the morphism
-      (multiple-value-bind (szczarba bottom-perturbation)
-                           (szczarba space)
-         (declare
-            (ignore szczarba)
-            (type morphism bottom-perturbation))
-         (let ((rslt (tnsr-prdc (idnt-mrph cobar) bottom-perturbation)))
-	    (declare (type morphism rslt))
-            (setf (slot-value rslt 'sorc) ls-hat-t-u
-                  (slot-value rslt 'trgt) ls-hat-t-u)
-            rslt))))
-
-(DEFUN LS-HAT-U-T (space
-                  &aux (cobar (cobar space))
-                       (twisted-tnsr-prdc (twisted-tnsr-prdc space))
-                       (ls-hat-u-u (ls-hat-u-u space)))
-   (declare
-      (type simplicial-set space)
-      (type chain-complex cobar twisted-tnsr-prdc ls-hat-u-u))
-   (the chain-complex
-      (let ((rslt (tnsr-prdc cobar twisted-tnsr-prdc)))
-         (declare (type chain-complex rslt))
-         (setf (slot-value rslt 'grmd) ls-hat-u-u)
-         rslt)))
-
-#|
-  (cat-init)
-  (setf c (ls-hat-u-t (deltab)))
-  (defun random-allp (length)
-     (let ((rslt nil))
-        (dotimes (i length)
-           (let* ((gmsm (random (mask 9)))
-                  (dmns (1- (logcount gmsm))))
-              (when (plusp dmns)
-                 (push (cbgn (1- dmns) gmsm) rslt))))
-        (make-allp :list rslt)))
-  (dotimes (i 10) (print (random-allp 5)))
-  (setf allp (random-allp 3))
-  (setf allp-degr (apply #'+ (mapcar #'car (allp-list allp))))
-  (setf gnrt (tnpr allp-degr allp 4 (tnpr 2 7 2 (loop3 0 15 2))))
-  (? c (+ 4 allp-degr) gnrt)
-  (? c *)
-  (dotimes (i 10)
-     (let ((allp (random-allp 3)))
-        (setf allp-degr (apply #'+ (mapcar #'car (allp-list allp))))
-        (setf gnrt (tnpr allp-degr allp 4 (tnpr 2 7 2 (loop3 0 15 2))))
-        (unless (>= allp-degr 11)
-           (print (? c (+ 4 allp-degr) gnrt))
-           (print (? c (? c (+ 4 allp-degr) gnrt))))))
-  (dotimes (i 20)
-     (let ((allp (random-allp 3)))
-        (setf allp-degr (apply #'+ (mapcar #'car (allp-list allp))))
-        (setf gnrt (tnpr allp-degr allp 5 (tnpr 3 15 2 (loop3 0 15 2))))
-        (unless (>= allp-degr 10)
-           (print (? c (+ 5 allp-degr) gnrt))
-           (print (? c (? c (+ 5 allp-degr) gnrt))))))
-  (dotimes (i 20)
-     (let ((allp (random-allp 3)))
-        (setf allp-degr (apply #'+ (mapcar #'car (allp-list allp))))
-        (setf gnrt (tnpr allp-degr allp 5 (tnpr 2 7 3 (loop3 0 31 2))))
-        (unless (>= allp-degr 10)
-           (print (? c (+ 5 allp-degr) gnrt))
-           (print (? c (? c (+ 5 allp-degr) gnrt))))))
-|#
-
-(DEFUN LS-LEFT-HMEQ-HAT (space
-                    &aux
-                    (ls-hat-u-t (ls-hat-u-t space))
-                    (ls-hat-left-perturbation
-                       (ls-hat-left-perturbation space)))
-   (declare
-      (type simplicial-set space)
-      (type chain-complex ls-hat-u-t)
-      (type morphism ls-hat-left-perturbation))
-   (the chain-complex
-      (add ls-hat-u-t ls-hat-left-perturbation)))
-
-#|
-  (cat-init)
-  (setf c (ls-left-hmeq-hat (deltab)))
-  (defun random-allp (length)
-     (let ((rslt nil))
-        (dotimes (i length)
-           (let* ((gmsm (random (mask 9)))
-                  (dmns (1- (logcount gmsm))))
-              (when (plusp dmns)
-                 (push (cbgn (1- dmns) gmsm) rslt))))
-        (make-allp :list rslt)))
-  (dotimes (i 10) (print (random-allp 5)))
-  (setf allp (random-allp 3))
-  (setf allp-degr (apply #'+ (mapcar #'car (allp-list allp))))
-  (setf gnrt (tnpr allp-degr allp 4 (tnpr 2 7 2 (loop3 0 15 2))))
-  (? c (+ 4 allp-degr) gnrt)
-  (? c *)
-  (dotimes (i 10)
-     (let ((allp (random-allp 3)))
-        (setf allp-degr (apply #'+ (mapcar #'car (allp-list allp))))
-        (setf gnrt (tnpr allp-degr allp 4 (tnpr 2 7 2 (loop3 0 15 2))))
-        (unless (>= allp-degr 11)
-           (print (? c (+ 4 allp-degr) gnrt))
-           (print (? c (? c (+ 4 allp-degr) gnrt))))))
-  (dotimes (i 20)
-     (let ((allp (random-allp 3)))
-        (setf allp-degr (apply #'+ (mapcar #'car (allp-list allp))))
-        (setf gnrt (tnpr allp-degr allp 5 (tnpr 3 15 2 (loop3 0 15 2))))
-        (unless (>= allp-degr 10)
-           (print (? c (+ 5 allp-degr) gnrt))
-           (print (? c (? c (+ 5 allp-degr) gnrt))))))
-  (dotimes (i 20)
-     (let ((allp (random-allp 3)))
-        (setf allp-degr (apply #'+ (mapcar #'car (allp-list allp))))
-        (setf gnrt (tnpr allp-degr allp 5 (tnpr 2 7 3 (loop3 0 31 2))))
-        (unless (>= allp-degr 10)
-           (print (? c (+ 5 allp-degr) gnrt))
-           (print (? c (? c (+ 5 allp-degr) gnrt))))))
-|#
-
-(DEFUN LS-PRE-LEFT-HMEQ-LEFT-REDUCTION-INTR-F (cmbn)
-   (declare (type cmbn cmbn))
-   (the cmbn
-      (let ((rslt +empty-list+))
-         (declare (list rslt))
-         (dolist (term (cmbn-list cmbn))
-            (declare (type term term))
-            (with-term (cffc tnpr) term
-            (with-tnpr (degr1 nil nil tnpr2) tnpr
-               (if (zerop degr1)
-                  (with-tnpr (degr21 nil nil loop22) tnpr2
-                     (if (zerop degr21)
-                        (push (term cffc loop22) rslt)
-                        (return)))
-                  (return)))))
-         (make-cmbn :degr (cmbn-degr cmbn)
-            :list (nreverse rslt)))))
-
-#|
-  (ls-pre-left-hmeq-left-reduction-intr-f
-    (cmbn 6 100 (tnpr 0 'a 6 (tnpr 0 'b 6 'c))
-            50 (tnpr 0 'a 6 (tnpr 0 'b 6 'cc))
-            10 (tnpr 0 'a 6 (tnpr 2 'b 4 'c))
-            1 (tnpr 2 'a 4 (tnpr 2 'b 2 'cc))))            
-|#
-
-(DEFUN LS-PRE-LEFT-HMEQ-LEFT-REDUCTION-F (space
-                                         &aux (ls-hat-t-u (ls-hat-t-u space))
-                                              (loop-space (loop-space space)))
-   (declare
-      (type simplicial-set space loop-space)
-      (type chain-complex ls-hat-t-u))      
-   (the morphism
-      (build-mrph  
-         :sorc ls-hat-t-u
-         :trgt loop-space
-         :degr 0
-         :intr #'ls-pre-left-hmeq-left-reduction-intr-f
-         :strt :cmbn
-         :orgn `(ls-pre-left-hmeq-left-reduction-f ,space))))
-
-(DEFUN LS-LEFT-HMEQ-LEFT-REDUCTION-G-INTR (bspn)
-   (declare (type gmsm bspn))
-   (flet ((rslt (cmbn)
-             (declare (type cmbn cmbn))
-             (the cmbn
-                (with-cmbn (degr list) cmbn
-                   (make-cmbn :degr degr
-                      :list (mapcar
-                               #'(lambda (term)
-                                    (declare (type term term))
-                                    (with-term (cffc loop) term
-                                       (term cffc
-                                          (tnpr
-                                             0 +null-allp+
-                                             degr (tnpr 0 bspn degr loop)))))
-                               list))))))
-      (the intr-mrph #'rslt)))
-
-#|
-  (setf r (ls-left-hmeq-left-reduction-g-intr '*))
-  (funcall r (cmbn 3 4 'loop))
-|#
-
-(DEFUN LS-LEFT-HMEQ-LEFT-REDUCTION-G (space
-                                     &aux (bspn (bspn space))
-                                          (ls-hat-t-u (ls-hat-t-u space))
-                                          (loop-space (loop-space space)))
-   (declare
-      (type simplicial-set space loop-space)
-      (type gmsm bspn)
-      (type chain-complex ls-hat-t-u))      
-   (the morphism
-      (build-mrph  
-         :sorc loop-space
-         :trgt ls-hat-t-u
-         :degr 0
-         :intr (ls-left-hmeq-left-reduction-g-intr bspn)
-         :strt :cmbn
-         :orgn `(ls-left-hmeq-left-reduction-g ,space))))
-
-(DEFUN LS-PRE-LEFT-HMEQ-LEFT-REDUCTION-H-INTR
-    (space
-     &aux (ls-hat-t-u (ls-hat-t-u space))
-          (cmpr (cmpr ls-hat-t-u)))
-  (declare
-   (type simplicial-set space)
-   (type chain-complex ls-hat-t-u)
-   (type cmprf cmpr))
-  (flet ((rslt (cmbn)
-           (declare (type cmbn cmbn))
-           (the cmbn
-             (with-cmbn (degr list) cmbn
-               (let ((rslt (zero-cmbn (1+ degr))))
-                 (declare (type cmbn rslt))
-                 (dolist (term list)
-                   (declare (type term term))
-                   (with-term (cffc tnpr) term
-                   (with-tnpr (degr1 allp1 degr2 tnpr2) tnpr
-                     (unless (zerop degr1)
-                       (with-tnpr (degr21 nil degr22 loop22) tnpr2
-                         (when (zerop degr21)
-                           (setf allp1 (allp-list allp1)) ;;;+++
-                           (let ((last-cbgn (car (last allp1))))
-                             (declare (type cbgn last-cbgn))
-                             (with-cbgn (degrl gmsml) last-cbgn
-                               (dstr-add-term-to-cmbn cmpr
-                                 cffc (tnpr (- degr1 degrl)
-                                            (make-allp :list (butlast allp1))
-                                            (+ degr2 degrl 1)
-                                            (tnpr (1+ degrl) gmsml
-                                                  degr22 loop22))
-                                 rslt)))))))))
-                 rslt)))))
-      (the intr-mrph #'rslt)))
-
-#|
-  (setf r (ls-pre-left-hmeq-left-reduction-h-intr (deltab)))
-  (setf *tnpr-with-degrees* t)
-  (funcall r (cmbn 10 1 (tnpr 3 (allp 2 'a 1 'b) 7 (tnpr 5 'c 2 'd)) 
-                      1 (tnpr 7 (allp 2 'a 5 'b) 3 (tnpr 0 '* 3 'c))
-                      10 (tnpr 8 (allp 4 'aa 4 'bb) 2 (tnpr 0 '* 2 'cc))))
-  (funcall r (cmbn 10 1 (tnpr 3 (allp 2 'a 1 'b) 7 (tnpr 5 'c 2 'd)) 
-                      1 (tnpr 7 (allp 4 'a 3 'b) 3 (tnpr 0 '* 3 'c))
-                      10 (tnpr 8 (allp 3 'aa 5 'bb) 2 (tnpr 0 '* 2 'cc))))
-  (setf *tnpr-with-degrees* nil)
-|#
-
-(DEFUN LS-PRE-LEFT-HMEQ-LEFT-REDUCTION-H (space
-                                     &aux (ls-hat-t-u (ls-hat-t-u space)))
-   (declare
-      (type simplicial-set space)
-      (type chain-complex ls-hat-t-u))      
-   (the morphism
-      (build-mrph
-         :sorc ls-hat-t-u
-         :trgt ls-hat-t-u
-         :degr +1
-         :intr (ls-pre-left-hmeq-left-reduction-h-intr space)
-         :strt :cmbn
-         :orgn `(ls-pre-left-hmeq-left-reduction-h ,space))))
-
-(DEFUN LS-PRE-LEFT-HMEQ-LEFT-REDUCTION (space)
-   (declare (type simplicial-set space))
-   (the reduction
-      (build-rdct
-         :f (ls-pre-left-hmeq-left-reduction-f space)
-         :g (ls-left-hmeq-left-reduction-g space)
-         :h (ls-pre-left-hmeq-left-reduction-h space)
-         :orgn `(ls-pre-left-hmeq-left-reduction ,space))))
-
-#|
-  (cat-init)
-  (setf rdct (ls-pre-left-hmeq-left-reduction (deltab)))
-  (pre-check-rdct rdct)
-  (defun random-allp (length)
-     (let ((rslt nil))
-        (dotimes (i length)
-           (let* ((gmsm (random (mask 9)))
-                  (dmns (1- (logcount gmsm))))
-              (when (plusp dmns)
-                 (push (cbgn (1- dmns) gmsm) rslt))))
-        (make-allp :list rslt)))
-  (setf allp (random-allp 3))
-  (setf allp-degr (apply #'+ (mapcar #'car (allp-list allp))))
-  (setf gnrt (tnpr allp-degr allp 4 (tnpr 2 7 2 (loop3 0 15 2))))
-  (setf *tc* (cmbn (+ 4 allp-degr) 1 gnrt))
-  (setf *bc* (cmbn 2 1 (loop3 0 15 2)))
-  (check-rdct)
-  (setf gnrt (tnpr allp-degr allp 4 (tnpr 0 1 4 (loop3 0 (mask 6) 2))))
-  (setf *tc* (cmbn (+ 4 allp-degr) 1 gnrt))
-  (check-rdct)
-  (setf *bc* (cmbn 0 1 (bspn (bcc rdct)))
-  (setf *tc* (cmbn 0 1 (bsgn (tcc rdct)))
-  (check-rdct)
-|#
-
-(DEFUN LS-LEFT-HMEQ-LEFT-REDUCTION (space
-                                   &aux (ls-pre-left-hmeq-left-reduction
-                                           (ls-pre-left-hmeq-left-reduction space))
-                                        (ls-hat-right-perturbation
-                                           (ls-hat-right-perturbation space)))			            
-   (declare
-      (type simplicial-set space)
-      (type reduction ls-pre-left-hmeq-left-reduction)
-      (type morphism ls-hat-right-perturbation))
-   (the reduction
-      (progn
-	 (dstr-change-sorc-trgt ls-hat-right-perturbation
-	    :new-sorc (tcc ls-pre-left-hmeq-left-reduction)
-	    :new-trgt (tcc ls-pre-left-hmeq-left-reduction))
-         (let ((rslt (special-bpl ls-pre-left-hmeq-left-reduction
-                        ls-hat-right-perturbation)))
-            (declare (type reduction rslt))
-            (with-slots (tcc f g h) rslt
-               (setf tcc (ls-left-hmeq-hat space)
-                     (slot-value f 'sorc) tcc
-                     (slot-value g 'trgt) tcc
-                     (slot-value h 'sorc) tcc
-                     (slot-value h 'trgt) tcc)
-               rslt)))))
-
-#|
-  (cat-init)
-  (setf rdct (ls-left-hmeq-left-reduction (deltab2)))
-  (pre-check-rdct rdct)
-  (defun a (d1 d2 d3)
-     (setf *tc* (cmbn (+ d1 d2 d3)
-                 1 (tnpr d1 (allp d1 (mask (+ d1 2)))
-                         (+ d2 d3)
-                      (tnpr d2 (mask (1+ d2))
-                            d3 (loop3 0 (mask (+ d3 2)) 1))))
-           *bc* (cmbn d3 1
-                  (loop3 0 (mask (+ d3 2)) -1)))
-      (check-rdct))
-  (a 1 0 1)
-  (a 1 1 1)  ;; error because 3 does not exist in deltab2
-  (a 1 2 1)
-  (a 2 2 1)
-|#
-
-
-;;; -[CLISP
-#|
-(DEFUN LS-PRE-LEFT-HMEQ-RIGHT-REDUCTION-INTR-F (cmbn)
-   (declare (type cmbn cmbn))
-   (the cmbn
-      (with-cmbn (degr list) cmbn
-         (let ((tail (member 0 list :test #'= :key #'cadddr)))
-            (make-cmbn :degr degr
-               :list (mapcar
-                        #'(lambda (term)
-                             (declare (type term term))
-                             (with-term (cffc tnpr) term
-                                (term cffc (gnrt1 tnpr))))
-                        tail))))))
-|#
-;;;   LISP]-
-;;; +[CLISP
-(DEFUN LS-PRE-LEFT-HMEQ-RIGHT-REDUCTION-INTR-F (cmbn)
-  (declare (type cmbn cmbn))
-  (the cmbn
-    (with-cmbn (degr list) cmbn
-      (let ((tail (member 0 list
-                          :key #'(lambda (term)
-                                   (declare (type term term))
-                                   (degr2 (gnrt term))))))
-        (make-cmbn :degr degr
-                   :list (mapcar
-                             #'(lambda (term)
-                                 (declare (type term term))
-                                 (with-term (cffc tnpr) term
-                                            (term cffc (gnrt1 tnpr))))
-                           tail))))))
-;;;   CLISP]+
-
-#|
-()
-(ls-pre-left-hmeq-right-reduction-intr-f
- (cmbn 3 12 (tnpr 2 'a 1 'b) 14 (tnpr 3 'aa 0 '*))))
-|#
-
-(DEFUN LS-PRE-LEFT-HMEQ-RIGHT-REDUCTION-F (space
-                                          &aux (ls-hat-u-t (ls-hat-u-t space))
-                                               (cobar (cobar space)))
-   (declare
-      (type simplicial-set space)
-      (type chain-complex ls-hat-u-t cobar))
-   (the morphism
-      (build-mrph
-         :sorc ls-hat-u-t :trgt cobar :degr 0
-         :intr #'ls-pre-left-hmeq-right-reduction-intr-f
-         :strt :cmbn
-         :orgn `(ls-pre-left-hmeq-right-reduction-f ,space))))
-
-(DEFUN LS-PRE-LEFT-HMEQ-RIGHT-REDUCTION-INTR-G (bspn)
-   (declare (type gmsm bspn))
-   (flet ((rslt (cmbn)
-             (declare (type cmbn cmbn))
-             (the cmbn
-                (with-cmbn (degr list) cmbn
-                   (let ((bsgn (tnpr 0 bspn 0 +null-loop+)))
-                      (declare (type tnpr bsgn))
-                      (make-cmbn :degr degr
-                         :list (mapcar
-                                  #'(lambda (term)
-                                       (declare (type term term))
-                                       (with-term (cffc gnrt) term
-                                          (term cffc (tnpr degr gnrt 0 bsgn))))
-                                  list)))))))
-      (the intr-mrph #'rslt)))
-
-#|
-  (setf r (ls-pre-left-hmeq-right-reduction-intr-g '*))
-  (funcall r (cmbn 3 4 'a))
-|#
-
-(DEFUN LS-PRE-LEFT-HMEQ-RIGHT-REDUCTION-G (space
-                                          &aux (ls-hat-u-t (ls-hat-u-t space))
-                                               (cobar (cobar space))
-                                               (bspn (bspn space)))
-   (declare
-      (type simplicial-set space)
-      (type chain-complex ls-hat-u-t cobar)
-      (type gmsm bspn))
-   (the morphism
-      (build-mrph
-         :sorc cobar :trgt ls-hat-u-t :degr 0
-         :intr (ls-pre-left-hmeq-right-reduction-intr-g bspn)
-         :strt :cmbn
-         :orgn `(ls-pre-left-hmeq-right-reduction-g ,space))))
-
-(DEFUN LS-PRE-LEFT-HMEQ-RIGHT-REDUCTION-H (space
-                                          &aux (cobar (cobar space))
-                                               (tnpr-contraction (tnpr-contraction space)))
-   (declare
-      (type simplicial-set space)
-      (type chain-complex cobar)
-      (type morphism tnpr-contraction))
-   (the morphism
-      (tnsr-prdc (idnt-mrph cobar) tnpr-contraction)))
-
-(DEFUN LS-PRE-LEFT-HMEQ-RIGHT-REDUCTION (space)
-   (declare (type simplicial-set space))
-   (the reduction
-      (build-rdct
-         :f (ls-pre-left-hmeq-right-reduction-f space)
-         :g (ls-pre-left-hmeq-right-reduction-g space)
-         :h (ls-pre-left-hmeq-right-reduction-h space)
-         :orgn `(ls-pre-left-hmeq-right-reduction ,space))))
-
-#|
-  (cat-init)
-  (setf r (ls-pre-left-hmeq-right-reduction (deltab2)))
-  (pre-check-rdct r)
-  (setf *tc* (cmbn 0 1 (bsgn (tcc r))))
-  (setf *bc* (cmbn 0 1 (bsgn (bcc r))))
-  (check-rdct)
-  (setf *tc* (cmbn 3 1 (tnpr 3 (allp 3 (mask 5)) 0 (tnpr 0 1 0 +null-loop+))))
-  (setf *bc* (cmbn 3 1 (allp 1 7 2 15)))
-  (check-rdct)
-  (setf *tc* (cmbn 6 1 (tnpr 3 (allp 1 7 2 15) 3 (tnpr 2 7 1 (loop3 0 7 2)))))
-  (check-rdct)
-  (setf *tc* (cmbn 6 1 (tnpr 3 (allp 1 7 2 15) 3 (tnpr 0 1 3 (loop3 0 (mask 5) 2)))))
-  (check-rdct)
-|#
-
-(DEFUN LS-LEFT-HMEQ-RIGHT-REDUCTION (space
-                                    &aux (pre-reduction
-                                            (ls-pre-left-hmeq-right-reduction space))
-                                         (perturbation
-                                            (ls-hat-left-perturbation space)))                                    
-   (declare
-     (type simplicial-set space)
-     (type reduction pre-reduction)
-     (type morphism perturbation))
-   (the reduction
-      (progn
-         (setf (slot-value perturbation 'sorc) (tcc pre-reduction)
-               (slot-value perturbation 'trgt) (tcc pre-reduction))
-         (special-bpl pre-reduction perturbation))))
-
-#|
-  (cat-init)
-  (setf r (ls-left-hmeq-right-reduction (deltab2)))
-  (pre-check-rdct r)
-  (setf *tc* (cmbn 0 1 (bsgn (tcc r))))
-  (setf *bc* (cmbn 0 1 (bsgn (bcc r))))
-  (check-rdct)
-  (setf *tc* (cmbn 3 1 (tnpr 3 (allp 3 (mask 5)) 0 (tnpr 0 1 0 +null-loop+))))
-  (setf *bc* (cmbn 3 1 (allp 1 7 2 15)))
-  (check-rdct)
-  (setf *tc* (cmbn 6 1 (tnpr 3 (allp 1 7 2 15) 3 (tnpr 2 7 1 (loop3 0 7 2)))))
-  (check-rdct)
-  (setf *tc* (cmbn 6 1 (tnpr 3 (allp 1 7 2 15) 3 (tnpr 0 1 3 (loop3 0 (mask 5) 2)))))
-  (check-rdct)
-|#
-
-(DEFUN LS-LEFT-HMEQ (space)
-   (declare (type simplicial-set space))
-   (the homotopy-equivalence
-      (build-hmeq 
-         :lrdct (ls-left-hmeq-left-reduction space)
-         :rrdct (ls-left-hmeq-right-reduction space)
-         :orgn `(ls-left-hmeq ,space))))
-
-#|
-  (cat-init)
-  (setf h (ls-left-hmeq (deltab2)))
-  (setf loop (loop3 0 (mask 5) 2))
-  (lg h 3 loop)
-  (rf h *)
-  (rg h *)
-  (lf h *)
-  (setf allp (allp 2 (mask 4) 3 (mask 5)))
-  (rg h 5 allp)
-  (lf h *)
-  (lg h *)
-  (rf h *)  ;; = allp, but why ?
-|#
-
-(DEFUN LOOP-SPACE-EFHM (space)
-  (declare (type simplicial-set space))
-  (let ((ls-left-hmeq (ls-left-hmeq space))
-	(right-hmeq (cobar (efhm space))))
-    (declare (type homotopy-equivalence ls-left-hmeq right-hmeq))
-    (cmps ls-left-hmeq right-hmeq)))
-
-(DEFMETHOD SEARCH-EFHM (loop-space (orgn (eql 'loop-space)))
-  (declare (type simplicial-set loop-space))
-  (loop-space-efhm (second (orgn loop-space))))
-
-#|
-  (cat-init)
-  (setf l (loop-space (sphere 2)))
-  (homology l 6)
-  (setf oos3 (loop-space (loop-space (sphere 3))))
-  (homology oos3 3)
-  (setf ooos4 (loop-space (loop-space (loop-space (sphere 4)))))
-  (homology ooos4 2)
-|#
diff --git a/archive/Kenzo-1/ls-twisted-products.cl b/archive/Kenzo-1/ls-twisted-products.cl
deleted file mode 100644
index 8833561..0000000
--- a/archive/Kenzo-1/ls-twisted-products.cl
+++ /dev/null
@@ -1,524 +0,0 @@
-;;;  LS-TWISTED-PRODUCTS  LS-TWISTED-PRODUCTS  LS-TWISTED-PRODUCTS
-;;;  LS-TWISTED-PRODUCTS  LS-TWISTED-PRODUCTS  LS-TWISTED-PRODUCTS
-;;;  LS-TWISTED-PRODUCTS  LS-TWISTED-PRODUCTS  LS-TWISTED-PRODUCTS
-
-(IN-PACKAGE "COMMON-LISP-USER")
-
-(PROVIDE "ls-twisted-products")
-
-;; ABSM-LOOPABSM is the "twisted" product of ABSM, a simplex of the base
-;;   space of dimension DMNS by LOOP-ABSM, a simplex of the corresponding
-;;   loop-space, of dimension (1- DMNS). The returned object is
-;;   a loop-absm of dimension (1- DMNS).
-
-(DEFUN ABSM-LOOPABSM (cmpr dmns absm loop-absm)
-   (declare
-      (type cmprf cmpr)
-      (fixnum dmns)  ;; dimension of ABSM
-      (type absm absm loop-absm))
-   (the absm
-      (with-absm (dgop1 gmsm1) absm
-         (when (logbitp (1- dmns) dgop1)
-            (return-from absm-loopabsm loop-absm))                  
-         (with-absm (dgop2 loop2) loop-absm
-            (let ((iloop2 (loop-list loop2)))
-               (declare (list iloop2))
-               (unless iloop2
-                  (return-from absm-loopabsm
-                     (absm dgop1 (make-loop :list (list (apowr 0 gmsm1 +1))))))
-               (let ((apowr (first iloop2)))
-                  (declare (type apowr apowr))
-                  (with-apowr (dgop22 gmsm2 expn2) apowr
-                     (if (and (= dgop1 (dgop*dgop dgop2 dgop22))
-                              (eq :equal (funcall cmpr gmsm1 gmsm2)))
-                        ;; the absm is eaten by the first component of the loop
-                        (if (= -1 expn2)
-                           ;; the first item of the loop disappears.
-                           (let ((iloop2-rest (rest iloop2)))
-                              (if iloop2-rest
-                                 (let ((loop-rest (normalize-loop (1- dmns) iloop2-rest)))
-                                    (declare (type absm loop-rest))
-                                    (absm (dgop*dgop dgop2 (dgop loop-rest)) (gmsm loop-rest)))
-                                 (absm (mask (1- dmns)) +null-loop+)))
-                           ;; the exponent of the first item is increased by 1
-                           (absm dgop2 (make-loop :list (cons (apowr dgop22 gmsm2 (1+ expn2))
-                                                           (rest iloop2)))))
-                        ;; a concatenation must be done
-                        (multiple-value-bind (dgop dgop1 dgop2) (extract-common-dgop dgop1 dgop2)
-                           (declare (fixnum dgop dgop1 dgop2))
-                           (absm dgop
-                              (make-loop
-                                 :list (cons (apowr dgop1 gmsm1 +1)
-                                          (if (zerop dgop2)
-                                             iloop2
-                                             (mapcar #'(lambda (apowr)
-                                                          (declare (type apowr apowr))
-                                                          (cons (dgop*dgop dgop2 (apdgop apowr))
-                                                             (cdr apowr)))
-                                                iloop2))))))))))))))
-
-#|
-()
-(setf cmpr (cmpr (deltab)))
-(absm-loopabsm cmpr 3 (absm 4 7) (absm 7 +null-loop+))
-(absm-loopabsm cmpr 3 (absm 0 15) (absm 7 +null-loop+))
-(absm-loopabsm cmpr 3 (absm 2 7) (absm 2 (loop3 0 7 4)))
-(absm-loopabsm cmpr 3 (absm 2 7) (absm 2 (loop3 0 7 4 1 12 -1)))
-(absm-loopabsm cmpr 3 (absm 2 7) (absm 2 (loop3 0 7 -1)))
-(absm-loopabsm cmpr 3 (absm 2 7) (absm 2 (loop3 0 7 -1 1 12 -1)))
-(absm-loopabsm cmpr 3 (absm 2 7) (absm 2 (loop3 0 7 4)))
-(absm-loopabsm cmpr 3 (absm 2 7) (absm 0 (loop3 2 7 4 1 14 -1)))
-(absm-loopabsm cmpr 3 (absm 2 7) (absm 0 (loop3 2 7 -1)))  ;; in principle illegal but works
-(absm-loopabsm cmpr 3 (absm 2 7) (absm 0 (loop3 2 7 -1 1 14 -1)))
-(absm-loopabsm cmpr 3 (absm 2 7) (absm 0 (loop3 0 15 -1 1 14 -1)))
-(absm-loopabsm cmpr 3 (absm 0 15) (absm 2 (loop3 0 7 -1 0 14 -1)))
-(absm-loopabsm cmpr 3 (absm 2 7) (absm 2 (loop3 0 28 -1 0 14 -1)))
-|#
-
-(DEFUN TWISTED-CRTS-PRDC-FACE (cmpr space-face loop-space-face non-twisted-face)
-  (declare
-   (type cmprf cmpr)
-   (type face space-face loop-space-face non-twisted-face))
-  (flet ((rslt (indx dmns crpr)
-               (declare
-                (fixnum indx dmns)
-                (type crpr crpr))
-               (the absm
-                 (progn
-                   (unless (= indx dmns)
-                     (return-from rslt
-                       (funcall non-twisted-face indx dmns crpr)))
-                   (with-crpr (absm1 absm2) crpr
-                              (let ((face1 (a-face4 space-face dmns dmns absm1))
-                                    (face2 (a-face4 loop-space-face dmns dmns absm2)))
-                                (declare (type absm face1 face2))
-                                (setf face2 (absm-loopabsm cmpr dmns absm1 face2))
-                                (2absm-acrpr face1 face2)))))))
-      (the face #'rslt)))
-
-(DEFUN TWISTED-CRTS-PRDC (space
-                            &aux (loop-space (loop-space space))
-                                 (crts-prdc (crts-prdc space loop-space)))
-   (declare (type simplicial-set space loop-space crts-prdc))
-   (the simplicial-set
-      (with-slots ((space-cmpr cmpr) (space-face face)) space
-         (declare
-            (type cmprf space-cmpr)
-            (type face space-face))
-      (with-slots ((loop-space-face face)) loop-space
-         (declare (type face loop-space-face))
-      (with-slots ((crts-prdc-cmpr cmpr) basis bsgn (crts-prdc-face face)) crts-prdc
-        (declare
-         (type cmprf crts-prdc-cmpr)
-         (type basis basis)
-         (type face crts-prdc-face)
-         (type gmsm bsgn))
-        (let ((rslt (build-smst
-                        :cmpr crts-prdc-cmpr
-                        :basis basis
-                        :bspn bsgn
-                        :face (twisted-crts-prdc-face
-                                 space-cmpr space-face loop-space-face crts-prdc-face)
-                        :orgn `(twisted-crts-prdc ,space))))
-            (setf (slot-value rslt 'grmd) crts-prdc)
-            rslt))))))
-
-#|
-  (setf p (r-proj-space 3))
-  (setf tw (twisted-crts-prdc p))
-  (defun random-apowr (dmns max-expn)
-     (loop
-        (let* ((dgop (random (2-exp (1- dmns))))
-               (gmsm (- dmns (logcount dgop))))
-           (unless (< 0 gmsm 3)
-              (return-from random-apowr
-                 (apowr dgop gmsm (srandom max-expn)))))))
-  (defun random-niloop (dmns max-expn length)
-     (mapcar #'(lambda (dummy)
-                  (random-apowr (1+ dmns) max-expn))
-        (make-list length)))
-  (defun random-crpr (dmns max-expn length)
-     (loop
-        (let ((loop (normalize-loop dmns (random-niloop dmns max-expn length)))
-              (dgop (random (2-exp dmns))))
-           (let ((absm (2absm-acrpr (absm dgop (- dmns (logcount dgop))) loop)))
-              (when (and (zerop (dgop absm))
-                         (not (< (gmsm1 (gmsm absm)) 3)))
-                 (return (gmsm absm)))))))
-  (setf cmpr (cmpr tw))
-  (defun random-cmbn (degr max-cffc max-expn loop-length cmbn-length)
-     (apply #'nterm-add cmpr degr
-        (mapcar #'(lambda (dummy)
-                     (term (srandom max-cffc) (random-crpr degr max-expn loop-length)))
-           (make-list cmbn-length))))
-  (setf c (random-cmbn 8 10 4 4 100))
-  (time (? tw (? tw c)))
-  (time (? tw (? tw c)))
-|#
-
-(DEFUN DTAU-D-INTR (crts-prdc-cmpr crts-prdc-face twisted-crts-prdc-face)
-   (declare
-      (type cmprf crts-prdc-cmpr)
-      (type face crts-prdc-face twisted-crts-prdc-face))
-   (flet ((rslt (dmns crpr)
-                (declare
-                 (fixnum dmns)
-                 (type crpr crpr))
-             (when (zerop dmns)
-                (return-from rslt +zero-negative-cmbn+))
-             (the cmbn
-                (let ((dmns-1 (1- dmns)))
-                   (declare (fixnum dmns-1))
-                   (when (logbitp dmns-1 (dgop1 crpr))
-                      (return-from rslt (zero-cmbn dmns-1)))
-                   (let ((face-tau (funcall twisted-crts-prdc-face dmns dmns crpr))
-                         (face (funcall crts-prdc-face dmns dmns crpr))
-                         (sign (-1-expt-n dmns)))
-                      (declare
-                         (type absm face-tau face)
-                         (fixnum sign))
-                      (with-absm (dgop-tau gmsm-tau) face-tau
-                      (with-absm (dgop gmsm) face
-                         (if (plusp dgop-tau)
-                            (if (plusp dgop)
-                               (zero-cmbn dmns-1)
-                               (term-cmbn dmns-1 (- sign) gmsm))
-                            (if (plusp dgop)
-                               (term-cmbn dmns-1 sign gmsm-tau)
-                               (ecase (funcall crts-prdc-cmpr gmsm-tau gmsm)
-                                  (:less
-                                   (cmbn dmns-1 sign gmsm-tau (- sign) gmsm))
-                                  (:greater
-                                   (cmbn dmns-1 (- sign) gmsm sign gmsm-tau))
-                                  (:equal
-                                   (error "Surprise in DTAU-D-INTR.~@
-                                           Crpr = ~A~@
-                                           D-tau = ~A~@
-                                           D = ~A"
-                                      crpr gmsm-tau gmsm))))))))))))
-      (the intr-mrph #'rslt)))
-
-#|
-  (setf d (deltab))
-  (setf p (crts-prdc d (loop-space d)))
-  (setf tw (twisted-crts-prdc d))
-  (setf crts-prdc-cmpr (cmpr p)
-        crts-prdc-face (face p)
-        twisted-crts-prdc-face (face tw))
-  (setf delta (dtau-d-intr crts-prdc-cmpr crts-prdc-face twisted-crts-prdc-face))
-  (funcall delta 3 (crpr 0 15 0 (loop3 0 (- 2048 64) 1)))
-  (funcall delta 5 (crpr 10 15 5 (loop3 0 (- 2048 64) 1)))
-  (funcall delta 5 (crpr 5 15 10 (loop3 0 (- 2048 64) 1)))
-|#
-
-(DEFUN DTAU-D (space
-                 &aux (loop-space (loop-space space))
-                      (crts-prdc (crts-prdc space loop-space))
-                      (crts-prdc-cmpr (cmpr crts-prdc))
-                      (crts-prdc-face (face crts-prdc))
-                      (twisted-crts-prdc (twisted-crts-prdc space))
-                      (twisted-crts-prdc-face (face twisted-crts-prdc)))
-   (declare
-      (type simplicial-set space loop-space crts-prdc twisted-crts-prdc)
-      (type cmprf crts-prdc-cmpr)
-      (type face crts-prdc-face twisted-crts-prdc-face))
-   (the morphism
-      (build-mrph
-         :sorc crts-prdc :trgt crts-prdc :degr -1
-         :intr (dtau-d-intr crts-prdc-cmpr crts-prdc-face twisted-crts-prdc-face)
-         :strt :gnrt
-         :orgn `(dtau-d ,space))))
-
-(DEFUN SZCZARBA (space
-                   &aux (loop-space (loop-space space))
-                        (twisted-crts-prdc (twisted-crts-prdc space))
-                        (ez (ez space loop-space))
-                        (dtau-d (dtau-d space)))
-  (declare
-   (type simplicial-set space loop-space twisted-crts-prdc)
-   (type reduction ez)
-   (type morphism dtau-d))
-  (the (values reduction morphism)
-    (multiple-value-bind (szczarba bottom-perturbation)
-        (add ez dtau-d)
-      (with-slots (tcc f g h) szczarba
-            (setf tcc twisted-crts-prdc
-                  (slot-value f 'sorc) twisted-crts-prdc
-                  (slot-value g 'trgt) twisted-crts-prdc
-                  (slot-value h 'sorc) twisted-crts-prdc
-                  (slot-value h 'trgt) twisted-crts-prdc))
-         (values szczarba bottom-perturbation))))
- 
-#|
-  (cat-init)
-  (setf rdct (szczarba (deltab)))
-  (pre-check-rdct rdct)
-  (setf *tc* (cmbn 2 1 (crpr 0 7 0 (loop3 0 (- 512 32) 1)))
-        *bc* (cmbn 2 1 (tnpr 0 1 2 (loop3 0 (- 512 32) 1))
-                     10 (tnpr 1 (- 4096 1024) 1 (loop3 0 7 1))
-                     100 (tnpr 2 7 0 (loop3 0 (- 4096 1024) 1))))
-  (check-rdct) 
-  (setf bcc (bcc rdct))
-  (time (? bcc 5 (tnpr 5 (mask 6) 0 +null-loop+)))
-  (time (? bcc 6 (tnpr 6 (mask 7) 0 +null-loop+)))
-|#
-
-(DEFUN TWISTED-TNSR-PRDC (space
-                            &aux (szczarba (szczarba space)))
-   (declare
-      (type simplicial-set space)
-      (type reduction szczarba))
-   (the chain-complex
-      (bcc szczarba)))
-
-;;;
-;;;  The important contraction.
-;;;
-
-(DEFUN POP-FIRST-ABSM (dmns iloop)
-   (declare (type iloop iloop))
-   (the (values (member -1 0 1) (or nil absm) absm)
-      (progn
-         (unless iloop
-            (return-from pop-first-absm
-               (values 0 nil iloop)))
-         (let ((apowr (first iloop))
-               (niloop-rest (rest iloop)))
-            (declare
-               (type apowr apowr)
-               (type iloop niloop-rest))
-            (with-apowr (dgop gmsm expn) apowr
-               (let ((popped-absm (absm dgop gmsm)))
-                  (declare (type absm popped-absm))
-                  (cond ((< expn -1)
-                         (values -1 popped-absm
-                            (absm 0
-                               (make-loop
-                                  :list (cons (apowr dgop gmsm (1+ expn)) niloop-rest)))))
-                        ((> expn +1)
-                         (values +1 popped-absm
-                            (absm 0
-                               (make-loop
-                                  :list (cons (apowr dgop gmsm (1- expn)) niloop-rest)))))
-                        (t
-                           (values expn popped-absm
-                              (normalize-loop dmns niloop-rest))))))))))
-
-#|
-()
-(pop-first-absm 4 (cdr +null-loop+))
-(pop-first-absm 4 (cdr (loop3 0 'a -2)))
-(pop-first-absm 4 (cdr (loop3 0 'a +2)))
-(pop-first-absm 4 (cdr (loop3 0 'a -1)))
-(pop-first-absm 4 (cdr (loop3 0 'a +1)))
-(pop-first-absm 4 (cdr (loop3 1 'a -2 2 'b 3)))
-(pop-first-absm 4 (cdr (loop3 0 'a +2 2 'b -3)))
-(pop-first-absm 4 (cdr (loop3 1 'a -1 2 'b 3)))
-(pop-first-absm 4 (cdr (loop3 0 'a +1 2 'b 5)))
-(pop-first-absm 4 (cdr (loop3 2 'a -1 1 'b 3)))
-(pop-first-absm 4 (cdr (loop3 2 'a +1 1 'b 3)))
-|#
-
-(DEFUN CRTS-CONTRACTION-INTR (base-cmpr base-bspn base-face crts-cmpr)
-   (declare
-      (type cmprf base-cmpr crts-cmpr)
-      (type gmsm base-bspn)
-      (type face base-face))
-   
-   (flet ((rslt (n crpr)
-             (declare
-                (fixnum n)
-                (type crpr crpr))
-             (the cmbn
-                (let ((n+1 (1+ n)))
-                   (declare (fixnum n+1))
- (labels (
-  (hh (x-n g-n)
-     (declare (type absm x-n g-n))
-     (if (bspn-p base-cmpr base-bspn n x-n)
-        (if (degenerate-p g-n)
-           (zero-cmbn n+1)
-           (h-hat (loop-list (gmsm g-n))))
-        (if (degenerate-p g-n)
-           (h-tilde (1dgnr n x-n) g-n)
-           (2cmbn-add crts-cmpr (h-hat (loop-list (gmsm g-n)))
-              (h-tilde (1dgnr n x-n) g-n)))))
-  (h-tilde (x-n+1 g-n)
-     (declare (type absm x-n+1 g-n))
-     (when (bspn-p base-cmpr base-bspn n+1 x-n+1)
-        (return-from h-tilde
-           (zero-cmbn n+1)))
-     (do ((i n (1- i))
-          (dgop 0 (+ dgop (2-exp i)))
-          (sign (-1-expt-n+1 n) (- sign))
-          (del-i x-n+1  (a-face4 base-face i (1+ i) del-i))
-          (rslt (zero-cmbn n+1)))
-         ((minusp i) rslt)
-        (declare
-           (fixnum i dgop sign)
-           (type absm del-i)
-           (type cmbn rslt))
-        (let ((absm1 (ndgnr dgop del-i))
-              (loop-absm2 (1dgnr i g-n)))
-           (declare (type absm absm1 loop-absm2))
-           (unless (plusp (logand (dgop absm1) (dgop loop-absm2)))
-             (dstr-add-term-to-cmbn
-                 crts-cmpr
-                 sign (crpr absm1 loop-absm2)
-                 rslt)))))
-  (h-hat (g-n)
-     (declare (type iloop g-n))  ;;; ***
-     (multiple-value-bind (expn y-n+1 gp-n) (pop-first-absm n g-n)
-        (declare
-           (fixnum expn)
-           (type absm y-n+1)
-           (type loop gp-n))  ;;; ***
-        (ecase expn
-           (0 (zero-cmbn (1+ n)))
-           (+1
-            (let ((h-tildes (2cmbn-sbtr crts-cmpr
-                               (h-tilde y-n+1 gp-n)
-                               (h-tilde
-                                  (1dgnr n (a-face4 base-face (1+ n) (1+ n) y-n+1))
-                                  (absm 0 (make-loop :list g-n))))))
-               (declare (type cmbn h-tildes))
-               (if (degenerate-p gp-n)
-                  h-tildes 
-                  (2cmbn-add crts-cmpr (h-hat (loop-list (gmsm gp-n))) h-tildes))))
-           (-1
-            (let ((next-x-n (a-face4 base-face (1+ n) (1+ n) y-n+1))
-                  (h-tilde (h-tilde y-n+1 (absm 0 (make-loop :list g-n)))))
-               (declare
-                  (type absm next-x-n)
-                  (type cmbn h-tilde))
-               (if (zerop (logand (dgop next-x-n) (dgop gp-n)))
-                  (2cmbn-sbtr crts-cmpr
-                     (hh next-x-n gp-n) h-tilde)
-                  (cmbn-opps h-tilde))))))))
-    
-    (with-crpr (absm1 loop-absm2) crpr
-       (hh absm1 loop-absm2)))))))
-    
-    (the intr-mrph #'rslt)))
-
-#|
-()
-(cat-init)
-(setf delta (deltab))
-(setf tw (twisted-crts-prdc delta))
-(setf d (bndr tw))
-(setf base-cmpr (cmpr delta)
-  base-bspn (bspn delta)
-  base-face (face delta)
-  crts-cmpr (cmpr tw))
-(setf r (crts-contraction-intr base-cmpr base-bspn base-face crts-cmpr))
-(setf h (build-mrph :sorc tw :trgt tw :degr +1
-                    :intr r :strt :gnrt :orgn `(crts-contraction ,delta)))
-(setf z (i-sbtr (idnt-mrph tw) (cmps d h) (cmps h d)))
-(? z 0 (crpr 0 1 0 +null-loop+))
-(funcall r 0 (crpr 0 1 0 (loop3 0 96 1)))
-(? z 0 (crpr 0 1 0 (loop3 0 96 1)))
-(? z 0 (crpr 0 1 0 (loop3 0 96 1 0 (+ 256 128) 1)))
-(? z 0 (crpr 0 1 0 (loop3 0 96 1 0 (+ 256 128) 1 0 (+ 512 1024) 1)))
-(? z 0 (crpr 0 1 0 (loop3 0 96 2)))
-(? z 1 (crpr 0 3 0 (loop3 0 (+ 32 64 128) 1)))
-(? z 2 (crpr 0 7 0 (loop3 0 (+ 32 64 128 256) 1)))
-(? z 3 (crpr 2 7 1 (loop3 2 (+ 32 64 128) 2 4 (+ 32 64 128) -2)))
-(? z 3 (crpr 2 7 4 (loop3 2 (+ 32 64 128) 2 1 (+ 32 64 128) -2)))
-(? z 3 (crpr 2 7 1 (loop3 2 (+ 32 64 128) -2 4 (+ 32 64 128) 2)))
-(? z 3 (crpr 2 7 4 (loop3 2 (+ 32 64 128) -2 1 (+ 32 64 128) 2)))
-(? z 3 (crpr 1 7 2 (loop3 2 (+ 32 64 128) 2 4 (+ 32 64 128) -2)))
-(? z 3 (crpr 4 7 2 (loop3 2 (+ 32 64 128) 2 1 (+ 32 64 128) -2)))
-(? z 3 (crpr 1 7 2 (loop3 2 (+ 32 64 128) -2 4 (+ 32 64 128) 2)))
-(? z 3 (crpr 4 7 2 (loop3 2 (+ 32 64 128) -2 1 (+ 32 64 128) 2)))
-|#
- 
-
-#|
-  (cat-init)
-  (setf p (r-proj-space 3))
-  (setf tw (twisted-crts-prdc p))
-  (setf r (crts-contraction-intr (cmpr p) (bspn p) (face p) (cmpr tw)))
-  (defun random-apowr (dmns max-expn)
-     (loop
-        (let* ((dgop (random (2-exp (1- dmns))))
-               (gmsm (- dmns (logcount dgop))))
-           (unless (< 0 gmsm 3)
-              (return-from random-apowr
-                 (apowr dgop gmsm (srandom max-expn)))))))
-  (defun random-niloop (dmns max-expn length)
-     (mapcar #'(lambda (dummy)
-                  (random-apowr (1+ dmns) max-expn))
-        (make-list length)))
-  (defun random-crpr (dmns max-expn length)
-     (loop
-        (let ((loop (normalize-loop dmns (random-niloop dmns max-expn length)))
-              (dgop (random (2-exp dmns))))
-           (let ((absm (2absm-acrpr (absm dgop (- dmns (logcount dgop))) loop)))
-              (when (and (zerop (dgop absm))
-                         (not (< (gmsm1 (gmsm absm)) 3)))
-                 (return (gmsm absm)))))))
-  (setf cmpr (cmpr tw))
-  (defun random-cmbn (degr max-cffc max-expn loop-length cmbn-length)
-     (apply #'nterm-add cmpr degr
-        (mapcar #'(lambda (dummy)
-                     (term (srandom max-cffc) (random-crpr degr max-expn loop-length)))
-           (make-list cmbn-length))))
-  (setf h (build-mrph :sorc tw :trgt tw :degr +1
-             :intr r :strt :gnrt :orgn `(crts-contraction ,p)))
-  (setf d (bndr tw))
-  (setf z (i-sbtr (idnt-mrph tw) (cmps h d) (cmps d h)))
-  (setf c (random-cmbn 5 10 2 2 1))
-  (? z c)
-  (setf c (random-cmbn 6 10 3 3 3))
-  (? z c)
-  (setf c (random-cmbn 7 10 4 4 6))
-  (? z c)
-  (setf c (random-cmbn 8 10 4 4 20))
-  (? z c)
-  (? h c)
-  (? d *)
-  (length *)
-|#
-
-(DEFUN CRTS-CONTRACTION (space
-                           &aux (twisted-crts-prdc (twisted-crts-prdc space)))
-   (declare (type simplicial-set space twisted-crts-prdc))
-   (the morphism
-      (build-mrph
-         :sorc twisted-crts-prdc :trgt twisted-crts-prdc :degr +1
-         :intr (crts-contraction-intr (cmpr space) (bspn space) (face space)
-                  (cmpr twisted-crts-prdc))
-         :strt :gnrt
-         :orgn `(crts-contraction ,space))))
-
-#|
-  (setf h (crts-contraction (deltab)))
-  (setf d (bndr (twisted-crts-prdc (deltab))))
-  (setf z (i-sbtr (idnt-mrph (sorc d)) (cmps d h) (cmps h d)))
-  (? z 3 (crpr 4 7 2 (loop3 2 (+ 32 64 128) -2 1 (+ 32 64 128) 2)))
-|#
-
-(DEFUN TNPR-CONTRACTION (space
-                           &aux
-                           (szczarba (szczarba space))
-                           (f (f szczarba))
-                           (g (g szczarba))
-                           (crts-contraction (crts-contraction space)))
-   (declare
-      (type simplicial-set space)
-      (type reduction szczarba)
-      (type morphism f g crts-contraction))
-   (the morphism
-      (i-cmps f crts-contraction g)))
-
-#|
-  (cat-init)
-  (setf delta (deltab))
-  (setf sz (szczarba (deltab)))
-  (setf tw (bcc sz))
-  (setf h (tnpr-contraction delta))
-  (setf z (i-sbtr (idnt-mrph tw) (cmps tw h) (cmps h tw)))
-  (time (? z 3 (tnpr 0 1 3 (loop3 0 (mask 5) 2 0 (* 32 (mask 5)) -1))))
-  (? h 4 (tnpr 0 1 0 (loop3 0 (mask 6) 1)))
-|#
diff --git a/archive/Kenzo-1/macros.cl b/archive/Kenzo-1/macros.cl
deleted file mode 100644
index 7548121..0000000
--- a/archive/Kenzo-1/macros.cl
+++ /dev/null
@@ -1,886 +0,0 @@
-;;;  MACROS  MACROS  MACROS  MACROS  MACROS  MACROS  MACROS
-;;;  MACROS  MACROS  MACROS  MACROS  MACROS  MACROS  MACROS
-;;;  MACROS  MACROS  MACROS  MACROS  MACROS  MACROS  MACROS
-
-(IN-PACKAGE "COMMON-LISP-USER")
-
-(PROVIDE "macros")
-
-;;;
-;;;  VARIOUS
-;;;
-
-(DEFMACRO -1-EXPT-N (n)
-  `(the fixnum (if (evenp (the fixnum ,n)) 1 -1)))
-
-(DEFMACRO -1-EXPT-N+1 (n)
-  `(the fixnum (if (evenp (the fixnum ,n)) -1 1)))
-
-(DEFMACRO -1-EXPT-N-1 (n)
-  `(-1-expt-n+1 ,n))
-
-#|
-()
-(-1-expt-n 5)
-(-1-expt-n 6)
-(-1-expt-n+1 5)
-(-1-expt-n+1 6)
-(-1-expt-n-1 5)
-(-1-expt-n-1 6)
-|#
-
-(DEFMACRO 2-EXP (n)
-   `(aref +2-exp+ ,n))
-
-(DEFMACRO MASK (n)
-   `(aref +mask+ ,n))
-
-(DEFMACRO BINOMIAL-P-Q (p q)
-  `(binomial-n-p (+ ,p ,q) ,p))
-
-;;;
-;;;  COMBINATIONS
-;;;
-
-(DEFMACRO LEXICO (&rest rest)
-   (unless (cdr rest)
-      (return-from lexico (first rest)))
-   (let ((vrslt (gensym)))
-      `(let ((,vrslt ,(first rest)))
-          (declare (type cmpr ,vrslt))
-          (if (eq ,vrslt :equal)
-             (lexico ,@(rest rest))
-             ,vrslt))))
-
-#|
-()
-(let ((*print-level* nil))
-  (declare (special
-            #+aclpc allegro:*top-print-level*
-            #-aclpc *print-level*))
-  (pprint (macroexpand-1
-           '(lexico
-             comparison1
-             comparison2
-             comparison3
-             comparison4))))
-|#
-
-(DEFMACRO TERM (cffc gnrt)
-  `(cons ,cffc ,gnrt))
-
-(DEFMACRO -TERM (mark)
-   `(car ,mark))
-
-(DEFMACRO CFFC (term)
-   `(car ,term))
-
-(DEFMACRO -CFFC (mark)
-   `(caar ,mark))
-
-(DEFMACRO GNRT (term)
-  `(cdr ,term))
-
-(DEFMACRO -GNRT (mark)
-   `(cdar ,mark))
-
-(DEFMACRO WITH-TERM ((cffc gnrt) term . body)
-   `(let (,@(if cffc `((,cffc (cffc ,term))) nil)
-          ,@(if gnrt `((,gnrt (gnrt ,term))) nil))
-       (declare
-          (fixnum ,@(if cffc `(,cffc) nil))
-          (type gnrt ,@(if gnrt `(,gnrt) nil)))
-       ,@body))
-
-#|
-  (macroexpand-1 '(with-term (cffc gnrt) term
-                     (statement-1)
-                     (statement-2)))
-  (macroexpand-1 '(with-term (nil gnrt) term
-                     (statement-1)
-                     (statement-2)))
-|#
-
-(DEFMACRO WITH--TERM ((cffc gnrt) mark . body)
-   `(let ((,cffc (-cffc ,mark))
-          (,gnrt (-gnrt ,mark)))
-       (declare
-          (fixnum ,cffc)
-          (type gnrt ,gnrt))
-       ,@body))
-
-#|
-  (macroexpand-1 '(with--term (cffc gnrt) mark
-                     (statement-1)
-                     (statement-2)))
-|#
-
-
-(DEFMACRO WITH-CMBN ((degr list) cmbn . body)
-   `(let ((,degr (cmbn-degr ,cmbn))
-          (,list (cmbn-list ,cmbn)))
-       (declare
-          (fixnum ,degr)
-          (list ,list))
-       ,@body))
-
-#|
-  (macroexpand-1 '(with-cmbn (degr list) cmbn
-                     (statement-1)
-                     (statement-2)))
-|#
-
-
-(DEFMACRO TERM-CMBN (degr cffc gnrt)
-  `(make-cmbn :degr ,degr
-              :list (list (term ,cffc ,gnrt))))
-
-
-(DEFMACRO CMBN-NON-ZERO-P (cmbn)
-   `(cmbn-list ,cmbn)) 
-
-(DEFMACRO CMBN-ZERO-P (cmbn)
-  `(null (cmbn-list ,cmbn)))
-
-(DEFMACRO CONTROL (cmpr cmbn)
-   (if *cmbn-control*
-      `(do-control ,cmpr ,cmbn)
-      cmbn))
-
-(DEFMACRO CONTROLN (cmpr cmbn)
-   (if *cmbn-control*
-      `(do-control ,cmpr ,cmbn)
-      nil))
-
-(DEFVAR *WRONG-CMBN*)
-
-
-;;;
-;;;  CHAIN-COMPLEXES
-;;;
-
-(DEFMACRO CMPR (&rest rest)
-   (ecase (length rest)
-      (1 `(cmpr1 ,@rest))
-      (3 `(cmpr3 ,@rest))))
-
-(DEFMACRO CMPR3 (object item1 item2)
-   `(funcall (cmpr1 ,object) ,item1 ,item2))
-
-#|
-  (macroexpand '(cmpr chcm))
-  (macroexpand '(cmpr chcm item1 item2))
-|#
-
-(DEFMACRO BASIS (&rest rest)
-   (ecase (length rest)
-      (1 `(basis1 ,@rest))
-      (2 `(basis2 ,@rest))
-      (3 `(basis3 ,@rest))))
-
-(DEFMACRO BASIS3 (smst dmns keyword)
-  (declare (ignore keyword))  
-  `(a-basis2 (basis ,smst) ,dmns))
-
-(DEFMACRO DFFR (&rest rest)
-   (ecase (length rest)
-      (1 `(dffr1 ,@rest))
-      ((2 3) `(? (dffr1 ,(first rest)) ,@(rest rest)))))
-
-#|
-  (macroexpand '(dffr chcm))
-  (macroexpand '(dffr chcm cmbn))
-  (macroexpand '(dffr chcm degr gnrt))
-|#
-
-(DEFMACRO ? (&rest rest)
-   (ecase (length rest)
-      (2 `(?2 ,@rest))
-      (3 `(?3 ,@rest))))
-
-;;;
-;;;  CHCM-ELEMENTARY-OP
-;;;
-
-(DEFMACRO I-CMPS (mrph1 &rest rest)
-   (if rest
-      `(cmps ,mrph1 (i-cmps ,@rest))
-      mrph1))
-
-#|
-  (macroexpand '(i-cmps m1))
-  (macroexpand '(i-cmps m1 m2))
-  (macroexpand '(i-cmps m1 m2 m3))
-|#
-
-(DEFMACRO I-ADD (mrph1 &rest rest)
-   (if rest
-      `(add ,mrph1 (i-add ,@rest))
-      mrph1))
-
-#|
-  (macroexpand '(i-add m1))
-  (macroexpand '(i-add m1 m2))
-  (macroexpand '(i-add m1 m2 m3))
-|#
-
-(DEFMACRO I-SBTR (mrph1 mrph2 &rest rest)
-   `(sbtr ,mrph1 (i-add ,mrph2 ,@rest)))
-   
-#|
-  (macroexpand '(i-sbtr m1 m2))
-  (macroexpand '(i-sbtr m1 m2 m3))
-|#
-
-;;;
-;;;  EFFECTIVE HOMOLOGY
-;;;
-
-(DEFMACRO BCC (&rest rest)
-   (case (length rest)
-      (1 `(bcc1 ,@rest))
-      (otherwise
-         `(? (bcc1 ,(first rest)) ,@(rest rest)))))
-
-(DEFMACRO TCC (&rest rest)
-   (case (length rest)
-      (1 `(tcc1 ,@rest))
-      (otherwise
-         `(? (tcc1 ,(first rest)) ,@(rest rest)))))
-
-(DEFMACRO F (&rest rest)
-   (case (length rest)
-      (1 `(f1 ,@rest))
-      (otherwise
-         `(? (f1 ,(first rest)) ,@(rest rest)))))
-
-#|
-  (macroexpand '(f rdct))
-  (macroexpand '(f rdct cmbn))
-  (macroexpand '(f rdct degr gnrt))
-|#
-
-(DEFMACRO G (&rest rest)
-   (case (length rest)
-      (1 `(g1 ,@rest))
-      (otherwise
-         `(? (g1 ,(first rest)) ,@(rest rest)))))
-
-(DEFMACRO H (&rest rest)
-   (case (length rest)
-      (1 `(h1 ,@rest))
-      (otherwise
-         `(? (h1 ,(first rest)) ,@(rest rest)))))
-
-(DEFMACRO LBCC (&rest rest)
-   (case (length rest)
-      (1 `(lbcc1 ,@rest))
-      (otherwise
-         `(? (lbcc1 ,(first rest)) ,@(rest rest)))))
-
-(DEFMACRO RBCC (&rest rest)
-   (case (length rest)
-      (1 `(rbcc1 ,@rest))
-      (otherwise
-         `(? (rbcc1 ,(first rest)) ,@(rest rest)))))
-
-(DEFMACRO LF (&rest rest)
-   (case (length rest)
-      (1 `(lf1 ,@rest))
-      (otherwise
-         `(? (lf1 ,(first rest)) ,@(rest rest)))))
-
-(DEFMACRO LG (&rest rest)
-   (case (length rest)
-      (1 `(lg1 ,@rest))
-      (otherwise
-         `(? (lg1 ,(first rest)) ,@(rest rest)))))
-
-(DEFMACRO LH (&rest rest)
-   (case (length rest)
-      (1 `(lh1 ,@rest))
-      (otherwise
-         `(? (lh1 ,(first rest)) ,@(rest rest)))))
-
-(DEFMACRO RF (&rest rest)
-   (case (length rest)
-      (1 `(rf1 ,@rest))
-      (otherwise
-         `(? (rf1 ,(first rest)) ,@(rest rest)))))
-
-(DEFMACRO RG (&rest rest)
-   (case (length rest)
-      (1 `(rg1 ,@rest))
-      (otherwise
-         `(? (rg1 ,(first rest)) ,@(rest rest)))))
-
-(DEFMACRO RH (&rest rest)
-   (case (length rest)
-      (1 `(rh1 ,@rest))
-      (otherwise
-         `(? (rh1 ,(first rest)) ,@(rest rest)))))
-
-
-;;;
-;;;  HOMOLOGY-GROUPS
-;;;
-
-(DEFMACRO BASELIG (mat n)
-  `(aref (leftcol ,mat) ,n))
-
-(DEFMACRO BASECOL (mat n)
-  `(aref (uplig ,mat) ,n))
-
-;;;
-;;;  CONES
-;;;
-
-(DEFMACRO CON0 (gnrt)
-  `(make-cone :conx 0 :icon ,gnrt))
-
-(DEFMACRO CON1 (gnrt)
-  `(make-cone :conx 1 :icon ,gnrt))
-
-(DEFMACRO WITH-CONE ((conx icon) cone . body)
-  (let ((scone (gensym)))
-    (declare (symbol scone))
-    `(let ((,scone ,cone))
-       (declare (type cone ,scone))
-       (let ((,conx (conx ,scone))
-             (,icon (icon ,scone)))
-         (declare (type (member 0 1) ,conx) (type gnrt ,icon))
-         ,@body))))
-
-(DEFMACRO BCNB (gnrt)
-  `(make-bicn :bcnx :bcnb :ibicn ,gnrt))
-
-(DEFMACRO BCNC (gnrt)
-  `(make-bicn :bcnx :bcnc :ibicn ,gnrt))
-
-(DEFMACRO BCND (gnrt)
-  `(make-bicn :bcnx :bcnd :ibicn ,gnrt))
-
-(DEFMACRO WITH-BICN ((bcnx ibicn) bicn . body)
-   `(let ((,bcnx (bcnx ,bicn))
-          (,ibicn (ibicn ,bicn)))
-       (declare
-          (type (member :bcnb :bcnc :bcnd) ,bcnx)
-          (type gnrt ,ibicn))
-       ,@body))
-
-
-;;;
-;;;  TENSOR PRODUCTS
-;;;
-
-#|
-(DEFMACRO TNPR (degr1 gnrt1 degr2 gnrt2)
-   `(cons :tnpr (cons (cons ,degr1 ,gnrt1) (cons ,degr2 ,gnrt2))))
-
-(DEFMACRO DEGR1 (tnpr)
-   `(caadr ,tnpr))
-
-(DEFMACRO GNRT1 (tnpr)
-   `(cdadr ,tnpr))
-
-(DEFMACRO DEGR2 (tnpr)
-   `(caddr ,tnpr))
-
-(DEFMACRO GNRT2 (tnpr)
-   `(cdddr ,tnpr))
-|#
-(DEFMACRO TNPR (degr1 gnrt1 degr2 gnrt2)
-  `(make-tnpr :degr1 ,degr1 :gnrt1 ,gnrt1
-              :degr2 ,degr2 :gnrt2 ,gnrt2))
-
-
-(DEFMACRO WITH-TNPR ((degr1 gnrt1 degr2 gnrt2) tnpr . body)
-   `(let (,@(if degr1 `((,degr1 (degr1 ,tnpr))) nil)
-          ,@(if gnrt1 `((,gnrt1 (gnrt1 ,tnpr))) nil)
-          ,@(if degr2 `((,degr2 (degr2 ,tnpr))) nil)
-          ,@(if gnrt2 `((,gnrt2 (gnrt2 ,tnpr))) nil))
-       (declare
-          (fixnum ,@(if degr1 `(,degr1) nil) ,@(if degr2 `(,degr2) nil))
-          (type gnrt ,@(if gnrt1 `(,gnrt1) nil) ,@(if gnrt2 `(,gnrt2) nil)))
-       ,@body))
-
-#|
-  (macroexpand '(tnpr 1 a 2 b))
-            1 (tnpr 2 'a 4 (tnpr 2 'b 2 'c))
-  (macroexpand-1 '(with-tnpr (degr1 gnrt1 degr2 gnrt2) tnpr
-                    (statement-1)
-                    (statement-2)))
-  (macroexpand-1 '(with-tnpr (nil gnrt1 degr2 gnrt2) tnpr
-                    (statement-1)
-                    (statement-2)))
-|#
-
-;;;
-;;;  COALGEBRAS
-;;;
-
-(DEFMACRO CPRD (&rest rest)
-   (case (length rest)
-      (1 `(cprd1 ,@rest))
-      ((2 3) `(? (cprd1 ,(first rest)) ,@(rest rest)))))
-
-;;;
-;;;  COBAR
-;;;
-
-(DEFMACRO CBGN (degr gnrt)
-   `(cons ,degr ,gnrt))
-
-(DEFMACRO CDEGR (cbgn)
-   `(car ,cbgn))
-
-(DEFMACRO CGNRT (cbgn)
-   `(cdr ,cbgn))
-
-(DEFMACRO -CDEGR (cbgn)
-   `(caar ,cbgn))
-
-(DEFMACRO -CGNRT (cbgn)
-   `(cdar ,cbgn))
-
-(DEFMACRO WITH-CBGN ((cdegr cgnrt) cbgn . body)
-   `(let ((,cdegr (cdegr ,cbgn))
-          (,cgnrt (cgnrt ,cbgn)))
-       (declare
-          (fixnum ,cdegr)
-          (type gnrt ,cgnrt))
-       ,@body))
-
-(DEFMACRO WITH--CBGN ((cdegr cgnrt) cbgn . body)
-   `(let ((,cdegr (-cdegr ,cbgn))
-          (,cgnrt (-cgnrt ,cbgn)))
-       (declare
-          (fixnum ,cdegr)
-          (type gnrt ,cgnrt))
-       ,@body))
-
-(DEFMACRO WITH-ALLP ((list) allp . body)
-   `(let ((,list (allp-list ,allp)))
-       (declare (list ,list))
-       ,@body))
-
-(DEFMACRO GNRT-ALLP-TNPR (degr gnrt allp)
-   `(make-allp :list (cons (cbgn (1- ,degr) ,gnrt) ,allp)))
-
-
-;;;
-;;;  ALGEBRAS
-;;;
-
-(DEFMACRO APRD (&rest rest)
-   (case (length rest)
-      (1 `(aprd1 ,@rest))
-      ((2 3) `(? (aprd1 ,(first rest)) ,@(rest rest)))))
-
-;;;
-;;;  BAR
-;;;
-
-(DEFMACRO BRGN (degr gnrt)
-   `(cons ,degr ,gnrt))
-
-(DEFMACRO BDEGR (brgn)
-   `(car ,brgn))
-
-(DEFMACRO BGNRT (brgn)
-   `(cdr ,brgn))
-
-(DEFMACRO -BDEGR (brgn)
-   `(caar ,brgn))
-
-(DEFMACRO -BGNRT (brgn)
-   `(cdar ,brgn))
-
-(DEFMACRO WITH-BRGN ((bdegr bgnrt) brgn . body)
-   `(let ((,bdegr (bdegr ,brgn))
-          (,bgnrt (bgnrt ,brgn)))
-       (declare
-          (fixnum ,bdegr)
-          (type gnrt ,bgnrt))
-       ,@body))
-
-(DEFMACRO WITH--BRGN ((bdegr bgnrt) brgn . body)
-   `(let ((,bdegr (-bdegr ,brgn))
-          (,bgnrt (-bgnrt ,brgn)))
-       (declare
-          (fixnum ,bdegr)
-          (type gnrt ,bgnrt))
-       ,@body))
-
-
-#|
-(DEFMACRO MAKE-ABAR (&key list)
-   `(cons :abar ,list))
-
-(DEFMACRO ABAR-LIST (abar)
-   `(cdr ,abar))
-|#
-
-(DEFMACRO WITH-ABAR ((list) abar . body)
-   `(let ((,list (abar-list ,abar)))
-       (declare (list ,list))
-       ,@body))
-
-
-#|
-(DEFMACRO MAKE-GBAR (&key dmns list)
-   `(cons :gbar (cons ,dmns ,list)))
-
-(DEFMACRO GBAR-DMNS (gbar)
-   `(cadr ,gbar))
-
-(DEFMACRO GBAR-LIST (gbar)
-   `(cddr ,gbar))
-|#
-
-
-(DEFMACRO WITH-GBAR ((dmns list) gbar . body)
-  `(let ((,dmns (gbar-dmns ,gbar))
-         (,list (gbar-list ,gbar)))
-     (declare
-      (fixnum ,dmns)
-      (list ,list))
-     ,@body))
-
-#|
-(DEFMACRO GNRT-GBAR-TNPR (degr gnrt gbar)
-   `(make-gbar :list (cons (brgn (1- ,degr) ,gnrt) ,gbar)))
-|#
-
-
-;;;
-;;;  SIMPLICIAL SETS
-;;;
-
-
-#|
-(DEFMACRO ABSM (dgop gmsm)
-   `(cons :absm (cons ,dgop ,gmsm)))
-
-(DEFMACRO DGOP (absm)
-   `(cadr ,absm))
-
-(DEFMACRO GMSM (absm)
-  `(cddr ,absm))
-|#
-
-(DEFMACRO ABSM (dgop gmsm)
-  `(make-absm :dgop ,dgop :gmsm ,gmsm))
-
-
-(DEFMACRO WITH-ABSM ((dgop-var gmsm-var) absm . body)
-  (let ((sabsm (gensym)))
-    `(let ((,sabsm ,absm))
-       (declare (type absm ,sabsm))
-       (let ((,dgop-var (dgop ,sabsm))
-             (,gmsm-var (gmsm ,sabsm)))
-         (declare
-          (fixnum ,dgop-var)
-          (type gmsm ,gmsm-var))
-       ,@body))))
-
-(DEFMACRO DEGENERATE-P (absm)
-   `(plusp (dgop ,absm)))
-
-(DEFMACRO NON-DEGENERATE-P (absm)
-   `(zerop (dgop ,absm)))
-
-(DEFMACRO BSPN (smst)
-   `(bsgn ,smst))
-
-(DEFMACRO BNDR (&rest rest)
-   `(dffr ,@rest))
-
-(DEFMACRO DGNL (&rest rest)
-   `(cprd ,@rest))
-
-(DEFMACRO FACE (&rest rest)
-   (ecase (length rest)
-      (1 `(face1 ,@rest))
-      (4 `(face4 ,@rest))))
-
-;;;
-;;;  DELTA
-;;;
-
-(DEFMACRO D (igmsm)
-   `(cons :delt ,igmsm))
-
-;;;
-;;;  SPECIAL-SMSTS
-;;;
-
-;;; GMSM-FACES-INFO = (gmsm (simple-vector absm) . bndr)
-;;;                         faces
-       
-(DEFMACRO MAKE-GMSM-FACES-INFO (&key gmsm faces bndr)
-   `(cons ,gmsm (cons ,faces ,bndr)))
-
-(DEFMACRO INFO-GMSM (gmsm-faces-info)
-   `(car ,gmsm-faces-info))
-
-(DEFMACRO INFO-FACES (gmsm-faces-info)
-   `(cadr ,gmsm-faces-info))
-
-(DEFMACRO INFO-FACE-I (gmsm-faces-info i)
-   `(svref (cadr ,gmsm-faces-info) ,i))
-
-(DEFMACRO INFO-BNDR (gmsm-faces-info)
-   `(cddr ,gmsm-faces-info))
-
-;;;
-;;;  CARTESIAN PRODUCTS
-;;;
-
-#|
-(DEFMACRO CRPR (&rest rest)
-   (ecase (length rest)
-      (2 `(cons :crpr (cons (cdr ,(first rest)) (cdr ,(second rest)))))
-      (4 `(cons :crpr (cons
-                         (cons ,(first rest) ,(second rest))
-                       (cons ,(third rest) ,(fourth rest)))))))
-|#
-(DEFMACRO CRPR (&rest rest)
-  (ecase (length rest)
-    (2 `(crpr2 ,@rest))
-    (4 `(crpr4 ,@rest))))
-
-(DEFMACRO CRPR2 (absm1 absm2)
-  `(crpr4 (dgop ,absm1) (gmsm ,absm1) (dgop ,absm2) (gmsm ,absm2)))
-
-(DEFMACRO CRPR4 (dgop1 gmsm1 dgop2 gmsm2)
-  `(make-crpr :dgop1 ,dgop1 :gmsm1 ,gmsm1
-              :dgop2 ,dgop2 :gmsm2 ,gmsm2))
-
-#|
-()
-(crpr (absm 3 'a) (absm 4 'b))
-(crpr 3 'a 4 'b)
-|#
-
-#|
-()
-(macroexpand '(crpr absm1 absm2))
-(macroexpand '(crpr dgop1 gmsm1 dgop2 gmsm2))
-|#
-
-#|
-(DEFMACRO DGOP1 (crpr)
-   `(caadr ,crpr))
-
-(DEFMACRO GMSM1 (crpr)
-   `(cdadr ,crpr))
-
-(DEFMACRO DGOP2 (crpr)
-   `(caddr ,crpr))
-
-(DEFMACRO GMSM2 (crpr)
-   `(cdddr ,crpr))
-
-(DEFMACRO ABSM1 (crpr)
-   `(cons :absm (cadr ,crpr)))
-
-(DEFMACRO ABSM2 (crpr)
-   `(cons :absm (cddr ,crpr)))
-|#
-(DEFMACRO ABSM1 (crpr)
-  `(absm (dgop1 ,crpr) (gmsm1 ,crpr)))
-
-(DEFMACRO ABSM2 (crpr)
-  `(absm (dgop2 ,crpr) (gmsm2 ,crpr)))
-
-
-
-#|
-()
-(setf c (crpr 1 'a 2 'b))
-(dgop1 c)
-(gmsm1 c)
-(dgop2 c)
-(gmsm2 c)
-(absm1 c)
-(absm2 c)
-|#
-
-(DEFMACRO WITH-CRPR (&rest rest)
-   (ecase (length (first rest))
-      (2 `(with-crpr-2 ,@rest))
-      (4 `(with-crpr-4 ,@rest))))
-
-
-#|
-(DEFMACRO WITH-CRPR-2 ((absm1 absm2) crpr . body)
-   `(let ((,absm1 (cons :absm (cadr ,crpr)))
-          (,absm2 (cons :absm (cddr ,crpr))))
-       (declare (type absm ,absm1 ,absm2))
-       ,@body))
-|#
-
-(DEFMACRO WITH-CRPR-2 ((absm1 absm2) crpr . body)
-  `(let ((,absm1 (absm (dgop1 ,crpr) (gmsm1 ,crpr)))
-         (,absm2 (absm (dgop2 ,crpr) (gmsm2 ,crpr))))
-     (declare (type absm ,absm1 ,absm2))
-     ,@body)) 
-  
-#|
-()
-(with-crpr (absm1 absm2) (crpr 3 'a 4 'b) (list absm1 absm2))
-|#
-
-(DEFMACRO WITH-CRPR-4 ((dgop1 gmsm1 dgop2 gmsm2) crpr . body)
-   `(let ((,dgop1 (dgop1 ,crpr))
-          (,gmsm1 (gmsm1 ,crpr))
-          (,dgop2 (dgop2 ,crpr))
-          (,gmsm2 (gmsm2 ,crpr)))
-       (declare
-          (fixnum ,dgop1 ,dgop2)
-          (type gmsm ,gmsm1 ,gmsm2))
-       ,@body))
-
-#|
-()
-(macroexpand-1
- (macroexpand-1 '(with-crpr (dgop1 gmsm1 dgop2 gmsm2) crpr
-                            (statement-1)
-                            (statement-2))))
-  (macroexpand-1
-  (macroexpand-1 '(with-crpr (absm1 absm2) crpr
-                     (statement-1)
-                     (statement-2))))
-|#
-
-;;;
-;;;  EILENBERG-ZILBER
-;;;
-
-(DEFMACRO EILENBERG-ZILBER (&rest rest)
-   `(ez ,@rest))
-
-;;;
-;;;  KAN
-;;;
-
-(DEFMACRO KFLL (&rest rest)
-  (ecase (length rest)
-     (1 `(kfll1 ,@rest))
-     (4 `(kfll4 ,@rest))))
-
-(DEFMACRO KFLL4 (kan indx dmns hat)
-  `(funcall (kfll1 ,kan) ,indx ,dmns ,hat))
-
-
-;;;
-;;;  SIMPLICIAL-GROUP
-;;;
-
-(DEFMACRO GRML (smgr &rest rest)
-   (ecase (length rest)
-      (0 `(grml1 ,smgr))
-      ((1 2) `(? (grml1 ,smgr) ,@rest))))
-
-(DEFMACRO GRIN (smgr &rest rest)
-   (case (length rest)
-      (0 `(grin1 ,smgr))
-     (otherwise `(? (grin1 ,smgr) ,@rest))))
-
-(DEFMACRO BUILD-AB-SMGR (&rest rest)
-  `(change-class (build-smgr ,@rest) 'ab-simplicial-group))
-
-;;;
-;;;  LOOP SPACES
-;;;
-
-(DEFMACRO POWR (gmsm expn)
-   `(cons ,gmsm ,expn))
-
-(DEFMACRO PGMSM (powr)
-   `(car ,powr))
-
-(DEFMACRO EXPN (powr)
-   `(cdr ,powr))
-
-(DEFMACRO WITH-POWR ((gmsm expn) powr . body)
-   `(let ((,gmsm (car ,powr))
-          (,expn (cdr ,powr)))
-       (declare
-          (type gmsm ,gmsm)
-          (fixnum expn))
-       ,@body))
-
-(DEFMACRO WITH-APOWR ((dgop gmsm expn) apowr . body)
-   `(let ((,dgop (apdgop ,apowr))
-          (,gmsm (cadr ,apowr))
-          (,expn (cddr ,apowr)))
-       (declare
-          (fixnum ,dgop ,expn)
-          (type gmsm ,gmsm))
-       ,@body))
-
-(DEFMACRO APOWR (dgop gmsm expn)
-   `(cons ,dgop (cons ,gmsm ,expn)))
-   
-(DEFMACRO APDGOP (apowr)
-   `(car ,apowr))
-
-
-(DEFMACRO APGMSM (apowr)
-   `(cadr ,apowr))
-
-(DEFMACRO APEXPN (apowr)
-   `(cddr ,apowr))
-
-;;;
-;;;  SMITH
-;;;
-
-(DEFMACRO LINE-NUMBER (mtrx)
-  `(first (array-dimensions ,mtrx)))
-
-(DEFMACRO COLUMN-NUMBER (mtrx)
-  `(second (array-dimensions ,mtrx)))
-
-(DEFMACRO LINE-OP-5 (mtrx-list begin lambda line1 line2)
-  (let ((slambda (gensym)))
-    `(let ((,slambda ,lambda))
-       (column-op (first ,mtrx-list) 0 (- ,slambda) ,line2 ,line1)
-       (line-op (second ,mtrx-list) 0 ,slambda ,line1 ,line2)
-       (line-op (third ,mtrx-list) ,begin ,slambda ,line1 ,line2))))
-
-(DEFMACRO COLUMN-OP-5 (mtrx-list begin lambda column1 column2)
-  (let ((slambda (gensym)))
-    `(let ((,slambda ,lambda))
-       (column-op (third ,mtrx-list) ,begin ,slambda ,column1 ,column2)
-       (column-op (fourth ,mtrx-list) 0 ,slambda ,column1 ,column2)
-       (line-op (fifth ,mtrx-list) 0 (- ,slambda) ,column2 ,column1))))
-
-(DEFMACRO LINE-SWAP-5 (mtrx-list begin line1 line2)
-  `(progn
-     (column-swap (first ,mtrx-list) 0 ,line1 ,line2)
-     (line-swap (second ,mtrx-list) 0 ,line1 ,line2)
-     (line-swap (third ,mtrx-list) ,begin ,line1 ,line2)))
-
-(DEFMACRO COLUMN-SWAP-5 (mtrx-list begin column1 column2)
-  `(progn
-     (column-swap (third ,mtrx-list) ,begin ,column1 ,column2)
-     (column-swap (fourth ,mtrx-list) 0 ,column1 ,column2)
-     (line-swap (fifth ,mtrx-list) 0 ,column1 ,column2)))
-
-(DEFMACRO LINE-MINUS-5 (mtrx-list begin line)
-  `(progn
-     (column-minus (first ,mtrx-list) 0 ,line)
-     (line-minus (second ,mtrx-list) 0 ,line)
-     (line-minus (third ,mtrx-list) ,begin ,line)))
-
-(DEFMACRO COLUMN-MINUS-5 (mtrx-list begin column)
-  `(progn
-     (column-minus (third ,mtrx-list) ,begin ,column)
-     (column-minus (fourth ,mtrx-list) 0 ,column)
-     (line-minus (fifth ,mtrx-list) 0 ,column)))
-
-(DEFMACRO GNRT-NAME (i)
-  `(intern (format nil "GN-~D" ,i) +gnrts-pckg+))
diff --git a/archive/Kenzo-1/searching-homology.cl b/archive/Kenzo-1/searching-homology.cl
deleted file mode 100644
index fe30039..0000000
--- a/archive/Kenzo-1/searching-homology.cl
+++ /dev/null
@@ -1,42 +0,0 @@
-;;;  SEARCHING-HOMOLOGY  SEARCHING-HOMOLOGY  SEARCHING-HOMOLOGY
-;;;  SEARCHING-HOMOLOGY  SEARCHING-HOMOLOGY  SEARCHING-HOMOLOGY
-;;;  SEARCHING-HOMOLOGY  SEARCHING-HOMOLOGY  SEARCHING-HOMOLOGY
-
-(IN-PACKAGE "COMMON-LISP-USER")
-
-(PROVIDE "searching-homology")
-
-(DEFUN ECHCM (chcm)
-   (rbcc (efhm chcm)))
-
-(DEFMETHOD HOMOLOGY ((chcm chain-complex) degr1 &optional (degr2 (1+ degr1)))
-   (declare (fixnum degr1 degr2))
-   (do ((degr degr1 (1+ degr)))
-       ((>= degr degr2))
-      (declare (fixnum degr))
-      (chcm-homology (echcm chcm) degr)
-      (terpri) (clock) (terpri)))
-
-(DEFGENERIC SEARCH-EFHM (chcm orgn))
-
-(DEFMETHOD SEARCH-EFHM (chcm orgn)
-  (declare (ignore chcm orgn))
-  nil)
-
-(DEFMETHOD SLOT-UNBOUND (class (chcm chain-complex) (slot-name (eql 'efhm)))
-   (declare (ignore class))
-   (the homotopy-equivalence
-     (let ((efhm (search-efhm chcm (first (orgn chcm)))))
-       (setf (efhm chcm)
-	     (or efhm
-		 (when (functionp (basis chcm))
-		       (trivial-hmeq chcm))
-		 (error "I don't know how to determine ~
-                         the effective homology of:~@
-                         ~A (Origin: ~A)." chcm (orgn chcm)))))))
-
-#|
-  (cat-init)
-  (setf d (delta 3))
-  (homology d 0)
-|#
diff --git a/archive/Kenzo-1/serre.cl b/archive/Kenzo-1/serre.cl
deleted file mode 100644
index 8f14014..0000000
--- a/archive/Kenzo-1/serre.cl
+++ /dev/null
@@ -1,286 +0,0 @@
-;;;  SERRE  SERRE  SERRE  SERRE  SERRE  SERRE  SERRE  SERRE  SERRE
-;;;  SERRE  SERRE  SERRE  SERRE  SERRE  SERRE  SERRE  SERRE  SERRE
-;;;  SERRE  SERRE  SERRE  SERRE  SERRE  SERRE  SERRE  SERRE  SERRE
-
-(IN-PACKAGE "COMMON-LISP-USER")
-
-(PROVIDE "serre")
-
-(DEFUN FIBRATION-DTAU-D-INTR
-  (fibration &aux (base (sorc fibration))
-	          (bface (face base))
-	          (fibre (trgt fibration))
-		  (fface (face fibre))
-		  (sintr-grml (sintr (grml fibre)))
-		  (fbspn (bspn fibre))
-		  (sintr-twist (sintr fibration))
-		  (total (fibration-total fibration))
-		  (total-cmpr (cmpr total)))
-  (declare
-     (type fibration fibration)
-     (type simplicial-set base total)
-     (type face bface fface)
-     (type simplicial-group fibre)
-     (type gmsm fbspn)
-     (type sintr sintr-grml sintr-twist)
-     (type cmprf total-cmpr))
-  (flet ((rslt (dmns crpr
-                     &aux (dmns-1 (1- dmns)))
-               (declare
-                (fixnum dmns dmns-1)
-                (type crpr crpr))
-               (unless (plusp dmns)
-                 (return-from rslt
-                   (zero-cmbn dmns-1)))
-               (with-crpr (b-absm f-absm) crpr
-                 (let ((tau-b
-                        (tw-a-sintr3 sintr-twist dmns
-                                     b-absm fbspn)))
-                   (declare (type absm tau-b))
-                   (when (= (dgop tau-b) (mask dmns-1))
-                     (return-from rslt
-                       (zero-cmbn dmns-1)))
-                   (let ((deln-b
-                          (a-face4 bface dmns dmns
-                                   b-absm))
-                         (deln-f
-                          (a-face4 fface dmns dmns
-                                   f-absm)))
-                     (declare
-                      (type absm deln-b deln-f tau-b))
-                     (let ((acrpr1 (2absm-acrpr deln-b deln-f))
-                           (acrpr2 
-                            (2absm-acrpr
-                             deln-b
-                             (a-grml4 sintr-grml (1- dmns)
-                                      tau-b deln-f))))
-                       (declare (type absm acrpr1 acrpr2))
-		      (with-absm (dgop1 crpr1) acrpr1
-		      (with-absm (dgop2 crpr2) acrpr2
-			 (if (zerop dgop1)
-			    (if (zerop dgop2)
-			       (dstr-add-term-to-cmbn
-				  total-cmpr
-				  (-1-expt-n+1 dmns) crpr1
-				  (term-cmbn dmns-1
-					     (-1-expt-n dmns)
-					     crpr2))
-			       (term-cmbn dmns-1
-					  (-1-expt-n+1 dmns)
-					  crpr1))
-			    (if (zerop dgop2)
-			       (term-cmbn dmns-1
-					  (-1-expt-n dmns)
-					  crpr2)
-			       (zero-cmbn dmns-1)))))))))))
-	(the intr-mrph #'rslt)))
-
-#|
-  (cat-init)
-  (setf s2 (sphere 2))
-  (setf k (k-z2-1))
-  (setf tw (build-smmr
-             :sorc s2
-	     :trgt k
-	     :degr -1
-	     :sintr #'(lambda (dmns gmsm)
-			(absm 0 1))
-	     :orgn '(s2-tw-kz2)))
-  (setf dt-d (fibration-dtau-d-intr tw))
-  (funcall dt-d 0 (crpr 0 '* 0 0))
-  (funcall dt-d 3 (crpr 4 's2 0 3))
-  (funcall dt-d 3 (crpr 2 's2 0 3))
-  (funcall dt-d 3 (crpr 2 's2 5 1))
-  (funcall dt-d 2 (crpr 0 's2 0 2))
-  (cat-init)
-  (setf s2 (sphere 2))
-  (setf k (k-z-1))
-  (setf tw (build-smmr
-             :sorc s2
-	     :trgt k
-	     :degr -1
-	     :sintr #'(lambda (dmns gmsm)
-			(absm 0 (list 1)))
-	     :orgn '(s2-tw-kz)))
-  (setf dt-d (fibration-dtau-d-intr tw))
-  (funcall dt-d 0 (crpr 0 '* 0 nil))
-  (funcall dt-d 3 (crpr 4 's2 0 '(2 3 4)))
-  (funcall dt-d 3 (crpr 2 's2 0 '(2 3 4)))
-  (funcall dt-d 3 (crpr 2 's2 5 '(5)))
-  (funcall dt-d 2 (crpr 0 's2 0 '(3 -2)))
-|#
-
-(DEFUN FIBRATION-DTAU-D (fibration
-			   &aux (base (sorc fibration))
-			        (fibre (trgt fibration))
-				(utotal (crts-prdc base fibre)))
-  (declare (type fibration fibration))
-  (the morphism
-     (build-mrph
-        :sorc utotal
-	:trgt utotal
-	:degr -1
-	:intr (fibration-dtau-d-intr fibration)
-	:strt :gnrt
-	:orgn `(fibration-dtau-d ,fibration))))
-
-#|
-  (cat-init)
-  (setf s2 (sphere 2))
-  (setf k (k-z-1))
-  (setf tw (build-smmr
-             :sorc s2
-	     :trgt k
-	     :degr -1
-	     :sintr #'(lambda (dmns gmsm)
-			(absm 0 (list 1)))
-	     :orgn '(s2-tw-kz)))
-  (setf dt-d (fibration-dtau-d tw))
-  (? dt-d 0 (crpr 0 '* 0 nil))
-  (? dt-d 3 (crpr 4 's2 0 '(2 3 4)))
-  (? dt-d 3 (crpr 2 's2 0 '(2 3 4)))
-  (? dt-d 3 (crpr 2 's2 5 '(5)))
-  (? dt-d 2 (crpr 0 's2 0 '(3 -2)))
-|#
-
-(DEFUN BROWN-REDUCTION (fibration
-		        &aux (base (sorc fibration))
-			      (fibre (trgt fibration))
-			      (total (fibration-total fibration))
-			      (ez (eilenberg-zilber base fibre))
-			      (t-perturbation (fibration-dtau-d fibration)))
-  (declare
-     (type fibration fibration)
-     (type simplicial-set base fibre total)
-     (type reduction ez)
-     (type morphism t-perturbation))
-  (the (values reduction morphism)
-     (multiple-value-bind (rslt b-perturbation) (add ez t-perturbation)
-	(declare
-	   (type reduction rslt)
-	   (type morphism b-perturbation))
-        (with-slots (f g h tcc) rslt
-	   (setf tcc total)
-	   (dstr-change-sorc-trgt f :new-sorc total)
-	   (dstr-change-sorc-trgt g :new-trgt total)
-	   (dstr-change-sorc-trgt h :new-sorc total :new-trgt total)
-	   (values rslt b-perturbation)))))
-
-#|
-  (cat-init)
-  (setf s2 (sphere 2))
-  (setf k (k-z2-1))
-  (setf tw (build-smmr
-             :sorc s2
-	     :trgt k
-	     :degr -1
-	     :sintr #'(lambda (dmns gmsm)
-			(absm 0 1))
-	     :orgn '(s2-tw-kz2)))
-  (setf brown (brown-reduction tw))
-  (setf tcc (tcc brown) bcc (bcc brown))
-  (homology bcc 3)
-  (homology tcc 1 8)
-  (homology bcc 1 8)
-  (cat-init)
-  (setf s2 (sphere 2))
-  (setf k (k-z-1))
-  (setf tw (build-smmr
-             :sorc s2
-	     :trgt k
-	     :degr -1
-	     :sintr #'(lambda (dmns gmsm)
-			(absm 0 (list 1)))
-	     :orgn '(s2-tw-kz1)))
-  (setf brown (brown-reduction tw))
-  (homology (tcc brown) 1 5)
-  (homology (bcc brown) 1 5)
-|#
-
-(DEFUN LEFT-SERRE-EFHM (fibration)
-  (declare (type fibration fibration))
-  (the homotopy-equivalence
-     (build-hmeq
-        :lrdct (trivial-rdct (fibration-total fibration))
-	:rrdct (brown-reduction fibration))))
-
-(DEFUN RIGHT-SERRE-EFHM (fibration
-			   &aux (base (sorc fibration))
-			        (fibre (trgt fibration))
-				(base-efhm (efhm base))
-				(fibre-efhm (efhm fibre))
-				(uprdc-efhm (tnsr-prdc base-efhm fibre-efhm)))
-  (declare
-     (type fibration fibration)
-     (type simplicial-set base fibre)
-     (type homotopy-equivalence base-efhm fibre-efhm uprdc-efhm))
-  (the homotopy-equivalence
-     (multiple-value-bind (brown b-perturbation) (brown-reduction fibration)
-	(declare
-	   (type reduction brown)
-	   (type morphism b-perturbation))
-	(let ((rslt (add uprdc-efhm b-perturbation)))
-	  (declare (type homotopy-equivalence rslt))
-	  (with-slots (lbcc lf lg lrdct) rslt
-	     (declare
-	        (type chain-complex lbcc)
-		(type morphism lf lg)
-		(type reduction lrdct))
-	     (setf lbcc (bcc brown))
-	     (dstr-change-sorc-trgt lf :new-trgt lbcc)
-	     (dstr-change-sorc-trgt lg :new-sorc lbcc)
-	     (with-slots (bcc f g) lrdct
-		(declare
-		   (type chain-complex bcc)
-		   (type morphism f g))
-		(setf bcc lbcc)
-		(dstr-change-sorc-trgt f :new-trgt lbcc)
-		(dstr-change-sorc-trgt g :new-sorc lbcc)))
-	  rslt))))
-
-#|
-  (cat-init)
-  (setf s2 (sphere 2))
-  (setf k (k-z-1))
-  (setf tw (build-smmr
-             :sorc s2
-	     :trgt k
-	     :degr -1
-	     :sintr #'(lambda (dmns gmsm)
-			(absm 0 (list 1)))
-	     :orgn '(s2-tw-kz1)))
-  (setf rh (right-serre-efhm tw))
-  (setf rbcc (rbcc rh))
-  (homology rbcc 0 5)  
-|#
-
-(DEFUN FIBRATION-TOTAL-EFHM (fibration)
-  (declare (type fibration fibration))
-  (the homotopy-equivalence
-       (cmps (left-serre-efhm fibration)
-	     (right-serre-efhm fibration))))
-
-(DEFMETHOD SEARCH-EFHM (smst (orgn (eql 'fibration-total)))
-  (declare
-     (type simplicial-set smst))
-  (the homotopy-equivalence
-     (fibration-total-efhm (second (orgn smst)))))
-
-#|
-  (cat-init)
-  (setf s2 (sphere 2))
-  (setf k (k-z-1))
-  (setf tw (build-smmr
-             :sorc s2
-	     :trgt k
-	     :degr -1
-	     :sintr #'(lambda (dmns gmsm)
-			(absm 0 (list 2)))
-	     :orgn '(s2-tw-kz1)))
-  (setf p3r (fibration-total tw))
-  (homology p3r 1 )
-|#
-
-
-     
-  
\ No newline at end of file
diff --git a/archive/Kenzo-1/simplicial-groups.cl b/archive/Kenzo-1/simplicial-groups.cl
deleted file mode 100644
index 0108335..0000000
--- a/archive/Kenzo-1/simplicial-groups.cl
+++ /dev/null
@@ -1,198 +0,0 @@
-;;;  SIMPLICIAL-GROUPS  SIMPLICIAL-GROUPS  SIMPLICIAL-GROUPS
-;;;  SIMPLICIAL-GROUPS  SIMPLICIAL-GROUPS  SIMPLICIAL-GROUPS
-;;;  SIMPLICIAL-GROUPS  SIMPLICIAL-GROUPS  SIMPLICIAL-GROUPS
-
-(IN-PACKAGE "COMMON-LISP-USER")
-
-(PROVIDE "simplicial-groups")
-
-(DEFVAR *SMGR-LIST*)
-(SETF *SMGR-LIST* +empty-list+)
-(PUSHNEW '*SMGR-LIST* *list-list*)
-
-(DEFUN SMGR (idnm)
-  (declare (fixnum idnm))
-  (the (or null simplicial-group)
-     (find idnm *smgr-list* :key #'idnm)))
-
-#+clisp(eval-when (:compile-toplevel :load-toplevel :execute)
-         (setf (ext:package-lock :clos) nil))
-(DEFMETHOD PRINT-OBJECT ((smgr simplicial-group) stream)
-  (the simplicial-group
-     (progn
-       (format stream "[K~D Simplicial-Group]" (idnm smgr))
-       smgr)))
-#+clisp(eval-when (:compile-toplevel :load-toplevel :execute)
-         (setf (ext:package-lock :clos) t))
-
-#+clisp(eval-when (:compile-toplevel :load-toplevel :execute)
-         (setf (ext:package-lock :clos) nil))
-(DEFMETHOD PRINT-OBJECT ((smgr ab-simplicial-group) stream)
-  (the simplicial-group
-     (progn
-       (format stream "[K~D Abelian-Simplicial-Group]" (idnm smgr))
-       smgr)))
-#+clisp(eval-when (:compile-toplevel :load-toplevel :execute)
-         (setf (ext:package-lock :clos) t))
-
-
-(DEFUN BUILD-SMGR
-  (&key cmpr basis bspn
-	face face* intr-bndr bndr-strt
-	intr-dgnl dgnl-strt
-	sintr-grml sintr-grin
-	orgn)
-   (declare
-      (type cmprf cmpr)
-      (type basis basis)
-      (type gmsm bspn)
-      (type face face)
-      (type (or null face*) face*)
-      (type (or intr-mrph null) intr-bndr intr-dgnl)
-      (type (or strt null) bndr-strt dgnl-strt)
-      (type sintr sintr-grml sintr-grin)
-      (list orgn))
-   (let ((already (find orgn *smgr-list* :test #'equal :key #'orgn)))
-      (declare (type (or simplicial-group null) already))
-      (when already
-         (return-from build-smgr already)))
-   (let ((rslt (build-smst
-		:cmpr cmpr :basis basis :bspn bspn
-		:face face :face* face* :intr-bndr intr-bndr
-		:bndr-strt bndr-strt :intr-dgnl intr-dgnl
-		:dgnl-strt dgnl-strt :orgn orgn)))
-     (declare (type simplicial-set rslt))
-     (change-class rslt 'simplicial-group)
-     (setf (slot-value rslt 'grml)
-	   (build-smmr
-	      :sorc (crts-prdc rslt rslt) :trgt rslt :degr 0
-	      :sintr sintr-grml :orgn `(group-multiplication ,rslt))
-	   (slot-value rslt 'grin)
-	   (build-smmr
-	      :sorc rslt :trgt rslt :degr 0
-	      :sintr sintr-grin :orgn `(group-inversion ,rslt)))
-     (push rslt *smgr-list*)
-     rslt))
-
-(DEFUN A-GRML4 (sintr-grml dmns absm1 absm2)
-  (declare
-     (fixnum dmns)
-     (type absm absm1 absm2))
-  (the absm
-     (let ((acrpr (2absm-acrpr absm1 absm2)))
-       (declare (type absm acrpr))
-       (with-absm (dgop crpr) acrpr
-          (ndgnr dgop
-		 (funcall sintr-grml
-			  (- dmns (logcount dgop))
-			  crpr))))))
-
-(DEFUN A-GRIN4 (sintr-grin dmns absm)
-  (declare
-     (type sintr sintr-grin)
-     (fixnum dmns)
-     (type absm absm))
-  (the absm
-     (with-absm (dgop gmsm) absm
-	(absm dgop
-	      (gmsm
-	       (funcall sintr-grin (- dmns (logcount dgop)) gmsm))))))
-
-(DEFMETHOD SLOT-UNBOUND (class (smgr simplicial-group)
-			       (name (eql 'kfll)))
-  (declare (ignore class))
-  (the kfll
-     (progn
-       (push smgr *kan-list*)
-       (setf (slot-value smgr 'kfll) (smgr-kfll smgr)))))
-
-(DEFUN SMGR-KFLL-INTR (face sintr-grml sintr-grin)
-  (flet ((rslt (indx dmns hat
-		     &aux (dmns-1 (1- dmns)))
-	    (declare
-	       (fixnum indx dmns dmns-1)
-	       (list hat))
-	    (the absm
-	      (let ((rslt (absm 0 nil)))
-		(declare (type absm rslt))
-		(when (plusp indx)
-		   (setf rslt (1dgnr 0 (pop hat)))
-		   (do ((i 1 (1+ i)))
-		       ((= i indx))
-		      (declare (fixnum i))
-		      (setf rslt
-			    (a-grml4
-			     sintr-grml dmns
-			     rslt
-			     (1dgnr i
-				    (a-grml4
-				     sintr-grml dmns-1
-				     (a-grin4
-				      sintr-grin dmns-1
-				      (a-face4 face
-					i dmns rslt))
-				     (pop hat)))))))
-		(when (< indx dmns)
-		  (setf hat (reverse hat))
-                  (when (zerop indx) 
-		  (setf rslt (1dgnr dmns-1 (pop hat))))
-		  (do ((i (if (zerop indx)
-			      dmns-1
-			      dmns)
-			  (1- i)))
-		      ((endp hat) rslt)
-		     (declare
-		        (type absm rslt)
-			(fixnum i))
-		     (setf rslt
-			   (a-grml4
-			    sintr-grml dmns
-			    rslt
-			    (1dgnr (1- i)
-				   (a-grml4
-				    sintr-grml dmns-1
-				    (a-grin4
-				     sintr-grin dmns-1
-				     (a-face4
-				      face
-				      i dmns rslt))
-				    (pop hat)))))))
-		rslt))))
-     (the kfll #'rslt)))
-
-(DEFUN SMGR-KFLL (smgr)
-  (declare (type simplicial-group smgr))
-  (with-slots (face grml grin) smgr
-     (declare
-        (type face face)
-	(type simplicial-mrph grml grin))
-     (smgr-kfll-intr face (sintr grml) (sintr grin))))
-
-#|
-  (cat-init)
-  (setf k (k-z-1))
-  (setf rslt '(1 10 100))
-  (setf hat (mapcar #'(lambda (i) (face k i 3 rslt)) (<a-b> 0 3)))
-  (dotimes (i 4)
-    (check-kan k i 3 (remove (nth i hat) hat :test #'equal)))
-|#
-
-(DEFMETHOD SLOT-UNBOUND (class (smgr simplicial-group)
-			       (name (eql 'aprd)))
-  (declare (ignore class))
-  (the morphism
-     (progn
-       (push smgr *hopf-list*)
-       (setf (slot-value smgr 'aprd) (smgr-aprd smgr)))))
-
-(DEFUN SMGR-APRD (smgr)
-  (declare (type simplicial-group smgr))
-  (the morphism
-    (let ((eml (eml smgr smgr))
-	  (grml (grml smgr)))
-      (declare
-        (type morphism eml)
-	(type simplicial-mrph grml))
-      (cmps grml eml))))
-
-       
\ No newline at end of file
diff --git a/archive/Kenzo-1/simplicial-mrphs.cl b/archive/Kenzo-1/simplicial-mrphs.cl
deleted file mode 100644
index 9646bdb..0000000
--- a/archive/Kenzo-1/simplicial-mrphs.cl
+++ /dev/null
@@ -1,162 +0,0 @@
-;;;  SIMPLICIAL-MRPHS  SIMPLICIAL-MRPHS  SIMPLICIAL-MRPHS
-;;;  SIMPLICIAL-MRPHS  SIMPLICIAL-MRPHS  SIMPLICIAL-MRPHS
-;;;  SIMPLICIAL-MRPHS  SIMPLICIAL-MRPHS  SIMPLICIAL-MRPHS
-
-(IN-PACKAGE "COMMON-LISP-USER")
-
-(PROVIDE "simplicial-mrphs")
-
-(DEFVAR *SMMR-LIST*)
-(SETF *SMMR-LIST* +empty-list+)
-(PUSHNEW '*SMMR-LIST* *LIST-LIST*)
-
-(DEFMETHOD ?3 ((smmr simplicial-mrph) dmns absm-or-gmsm)
-  (declare
-     (fixnum dmns)
-     (type (or absm gmsm) absm-or-gmsm))
-  (typecase absm-or-gmsm
-     (absm
-      (with-absm (dgop gmsm) absm-or-gmsm
-         (let ((gmsm-smmr (funcall (sintr smmr)
-			     (- dmns (logcount dgop)) gmsm)))
-	   (declare (type absm gmsm-smmr))
-	   (ndgnr dgop gmsm-smmr))))
-     (otherwise
-      (funcall (sintr smmr) dmns absm-or-gmsm))))  
-
-#+clisp(eval-when (:compile-toplevel :load-toplevel :execute)
-         (setf (ext:package-lock :clos) nil))
-(DEFMETHOD PRINT-OBJECT ((smmr simplicial-mrph) stream)
-  (the simplicial-mrph
-     (progn
-       (if (= -1 (degr smmr))
-	   (format stream "[K~D Fibration K~D -> K~D]"
-		   (idnm smmr) (idnm (sorc smmr)) (idnm (trgt smmr)))
-	 (format stream "[K~D Simplicial-Morphism K~D -> K~D]"
-		 (idnm smmr) (idnm (sorc smmr)) (idnm (trgt smmr))))
-       smmr)))
-#+clisp(eval-when (:compile-toplevel :load-toplevel :execute)
-         (setf (ext:package-lock :clos) t))
-
-
-(DEFUN SMMR (idnm)
-  (declare (fixnum idnm))
-  (the (or null simplicial-mrph)
-     (find idnm *smmr-list* :key #'idnm)))
-
-(DEFUN SINTR-INTR (sintr)
-   (declare (type sintr sintr))
-   (flet ((rslt (dmns gmsm)
-	     (declare
-	        (fixnum dmns)
-		(type gmsm gmsm))
-	     (when (minusp dmns)
-		(return-from rslt (zero-cmbn dmns)))
-	     (let ((rslt (funcall sintr dmns gmsm)))
-	        (declare (type absm rslt))
-		(if (degenerate-p rslt)
-		   (zero-cmbn dmns)
-		   (term-cmbn dmns 1 (gmsm rslt))))))
-       (the intr-mrph #'rslt)))
-
-(DEFUN BUILD-SMMR (&key sorc trgt degr sintr intr strt orgn)
-   (declare
-      (type simplicial-set sorc trgt)
-      (fixnum degr)
-      (type sintr sintr)
-      (type (or intr-mrph null) intr)
-      (type (or strt null) strt)
-      (list orgn))
-   (the simplicial-mrph
-      (progn
-	 (let ((already (find orgn *smmr-list* :test #'equal :key #'orgn)))
-	    (declare (type (or simplicial-mrph null) already))
-	    (when already
-	       (return-from build-smmr already)))
-	 (if (zerop degr)
-	     (if intr
-		 (unless strt
-			 (error "In BUILD-SMMR, an intr is given but not its strt"))
-	       (setf strt :gnrt
-		     intr (sintr-intr sintr)))
-	   (setf intr nil strt :gnrt))
-	 (let ((rslt (build-mrph
-		        :sorc sorc :trgt trgt :degr degr
-			:intr intr :strt strt
-			:orgn orgn)))
-	   (declare (type morphism rslt))
-	   (change-class rslt 'simplicial-mrph)
-	   (setf (slot-value rslt 'sintr) sintr)
-	   (push rslt *smmr-list*)
-	   rslt))))
-
-#|
-  (setf d (delta 3))
-  (setf m (build-smmr
-            :sorc d :trgt d :degr 0
-            :sintr #'(lambda (dmns gmsm)
-                        (absm 0 gmsm))
-            :orgn '(identity delta-3)))
-  (setf m2 (build-smmr
-            :sorc d :trgt d :degr 0
-            :sintr #'(lambda (dmns gmsm)
-                       (absm (mask dmns) 1))
-            :orgn '(null delta-3)))
-  (? m2 2 7)
-;;  (s? m2 2 7)
-|#
-
-#|  ????                 
-(DEFUN IA-SINTR3 (sintr dmns iabsm)
-  (declare
-     (type sintr sintr)
-     (fixnum dmns)
-     (type iabsm iabsm))
-  (the absm
-     (with-iabsm (dgop gmsm) iabsm
-	(ndgnr dgop (funcall sintr (- dmns (logcount dgop)) gmsm)))))
-
-(DEFUN A-SINTR3 (sintr dmns absm)
-  (declare
-   (type sintr sintr)
-   (fixnum dmns)
-   (type absm absm))
-  (the absm
-     (with-absm (dgop gmsm) absm
-       (ndgnr dgop (funcall sintr (- dmns (logcount dgop)) gmsm)))))
-|# ;;; ????
-
-
-(DEFUN TW-A-SINTR3 (sintr dmns absm bspn)
-  (declare
-   (type sintr sintr)
-   (fixnum dmns)
-   (type absm absm)
-   (type gmsm bspn))
-  (the absm
-    (with-absm (dgop gmsm) absm
-      (let ((dmns-1 (1- dmns)))
-        (declare (fixnum dmns-1))
-        (if (logbitp dmns-1 dgop)
-          (absm (mask dmns-1) bspn)
-          (ndgnr dgop (funcall sintr
-                        (- dmns (logcount dgop))
-                        gmsm)))))))
-
-#|
-(DEFUN TW-IA-SINTR3 (sintr dmns iabsm bspn)
-  (declare
-     (type sintr sintr)
-     (fixnum dmns)
-     (type iabsm iabsm)
-     (type gmsm bspn))
-  (the absm
-     (with-iabsm (dgop gmsm) iabsm
-	(let ((dmns-1 (1- dmns)))
-	  (declare (fixnum dmns-1))
-	  (if (logbitp dmns-1 dgop)
-	     (absm (mask dmns-1) bspn)
-	     (ndgnr dgop (funcall sintr
-			    (- dmns (logcount dgop))
-                           gmsm)))))))
-|#
diff --git a/archive/Kenzo-1/simplicial-sets.cl b/archive/Kenzo-1/simplicial-sets.cl
deleted file mode 100644
index 5f7c6b6..0000000
--- a/archive/Kenzo-1/simplicial-sets.cl
+++ /dev/null
@@ -1,659 +0,0 @@
-;;;  SIMPLICIAL-SETS  SIMPLICIAL-SETS  SIMPLICIAL-SETS
-;;;  SIMPLICIAL-SETS  SIMPLICIAL-SETS  SIMPLICIAL-SETS
-;;;  SIMPLICIAL-SETS  SIMPLICIAL-SETS  SIMPLICIAL-SETS
-
-(IN-PACKAGE "COMMON-LISP-USER")
-
-(PROVIDE "simplicial-sets")
-
-
-(DEFVAR *SMST-LIST*)
-(SETF *SMST-LIST* +empty-list+)
-(PUSHNEW '*SMST-LIST* *list-list*)
-
-(DEFUN DGOP-EXT-INT (ext-dgop)
-   (declare (list ext-dgop))
-          ;; (list fixnum)
-   (when ext-dgop   
-      (unless (apply #'> ext-dgop)
-         (error "In DGOP-EXT-INT, the external dgop ~A is not decreasing." ext-dgop)))
-   (the fixnum
-      (apply #'logxor (mapcar
-                         #'(lambda (item)
-                              (declare (fixnum item))
-                              (the fixnum (2-exp item)))
-                         ext-dgop))))
-
-#|
-(dgop-ext-int '())
-(dgop-ext-int '(2 2))
-(dgop-ext-int '(4 0))
-|#
-
-(DEFUN DGOP-INT-EXT (dgop)
-   (declare (fixnum dgop))
-   (unless (typep dgop 'dgop)
-      (error "In DXOP-INT-EXT, ~A is not a dxop." dgop))
-   (the list
-      (do ((dgop dgop (ash dgop -1))
-           (rslt +empty-list+)
-           (bmark 0 (1+ bmark)))
-          ((zerop dgop) rslt)
-         (declare
-            (fixnum dgop bmark)
-            (list rslt))
-         (when (oddp dgop)
-            (push bmark rslt)))))
-
-#|
-  (dgop-int-ext 0)
-  (dgop-int-ext 4)
-  (dgop-int-ext 63)
-  (dotimes (i 33)
-     (print (dgop-ext-int (dgop-int-ext i)))))
-|#
-
-(DEFUN HYPHENIZE-LIST (list)
-   (declare (list list))
-   (if list
-      (format nil "~D~{-~D~}" (first list) (rest list))
-      (format nil "-")))
-
-#|
-  (hyphenize-list '())
-  (hyphenize-list '(3))
-  (hyphenize-list '(5 3 1)))
-|#
-
-(DEFUN ABSM-PRINT (absm stream depth)
-  (declare
-   (type absm absm)
-   (type stream stream)
-   (ignore depth))
-  (format stream
-      "<AbSm ~A ~A>"
-      (hyphenize-list (dgop-int-ext (dgop absm)))
-      (gmsm absm))
-  absm)
-
-(DEFUN FACE4 (smst indx dmns gmsm-or-absm)
-   (if (typep gmsm-or-absm 'absm)
-      (a-face4 (face1 smst) indx dmns gmsm-or-absm)
-      (funcall (face1 smst) indx dmns gmsm-or-absm)))
-
-#+clisp(eval-when (:compile-toplevel :load-toplevel :execute)
-         (setf (ext:package-lock :clos) nil))
-(DEFMETHOD PRINT-OBJECT ((smst simplicial-set) stream)
-   (the simplicial-set
-      (progn
-         (format stream "[K~D Simplicial-Set]" (idnm smst))
-        smst)))
-#+clisp(eval-when (:compile-toplevel :load-toplevel :execute)
-         (setf (ext:package-lock :clos) t))
-
-
-(DEFUN SMST (n)
-   (declare (fixnum n))
-   (the (or simplicial-set null)
-      (find n *smst-list* :key #'idnm)))
-
-(DEFUN BUILD-SMST
-    (&key cmpr basis bspn face face* intr-bndr bndr-strt
-	  intr-dgnl dgnl-strt orgn)
-   (declare
-      (type cmprf cmpr)
-      (type basis basis)
-      (type gmsm bspn)
-      (type face face)
-      (type (or null face*) face*)
-      (type (or intr-mrph null) intr-bndr intr-dgnl)
-         (type (or strt null) bndr-strt dgnl-strt)
-      (list orgn))
-   (let ((already (find orgn *smst-list* :test #'equal :key #'orgn)))
-      (declare (type (or simplicial-set null) already))
-      (when already
-         (return-from build-smst already)))
-   (if intr-bndr
-      (unless bndr-strt
-            (error "In BUILD-SMST, an intr-bndr is given but not its strategy."))
-      (cond (face*
-                (setf bndr-strt :gnrt
-                      intr-bndr (face*-bndr cmpr face*)))
-            (face
-               (setf bndr-strt :gnrt
-                     intr-bndr (face-bndr cmpr face)))))
-   (if intr-dgnl
-      (unless dgnl-strt
-            (error "In BUILD-SMST, an intr-dgnl is given but not its strategy."))
-      (setf dgnl-strt :gnrt
-            intr-dgnl (intr-diagonal face)))
-   (the simplicial-set
-      (let ((rslt (build-chcm :cmpr cmpr :basis basis :bsgn bspn
-                     :intr-dffr intr-bndr
-                        :strt bndr-strt :orgn orgn)))
-         (change-chcm-to-clgb rslt
-          :intr-cprd intr-dgnl :cprd-strt dgnl-strt)
-         (setf (slot-value (dgnl rslt) 'orgn)
-               `(diagonal ,rslt))
-         (change-class rslt 'simplicial-set)
-         (setf (slot-value rslt 'face) face)
-         (push rslt *smst-list*)
-         rslt)))
-
-(DEFUN A-BASIS2 (basis dmns)
-  (declare
-     (type basis basis)
-     (fixnum dmns))
-  (the list
-    (let ((basis-array (make-array (1+ dmns) :element-type 'list)))
-      (declare (type (vector list) basis-array))
-      (dotimes (i (1+ dmns))
-	(declare (fixnum i))
-	(setf (aref basis-array i) (funcall basis i)))
-      (do ((dgop (mask dmns) (1- dgop))
-	   (rslt +empty-list+
-		 (nconc (mapcar
-			 #'(lambda (gmsm)
-			     (declare (type gmsm gmsm))
-			     (absm dgop gmsm))
-			 (aref basis-array (- dmns (logcount dgop))))
-			rslt)))
-	  ((minusp dgop) rslt)))))
-
-#|
-(setf m (moore 2 2))
-(dotimes (i 4)
-  (print (basis m i :dgnr)))
-|#
-
-(DEFUN INTR-DIAGONAL (face)
-  (declare (type face face))
-  (flet ((rslt (dmns gmsm)
-               (declare
-                (fixnum dmns)
-                (type gmsm gmsm))
-               (the cmbn
-                 (let ((del-0-s +empty-list+)
-                       (rslt +empty-list+))
-                   (declare (list del-0-s rslt))
-                   (do ((dmns dmns (1- dmns))
-                        (absm (absm 0 gmsm) (a-face4 face 0 dmns absm)))
-                       ((zerop dmns) (push absm del-0-s))
-                     (declare (fixnum dmns) (type absm absm))
-                     (push absm del-0-s))
-                   (do ((ldmns dmns (1- ldmns))
-                        (rdmns 0 (1+ rdmns))
-                        (absm (absm 0 gmsm) (a-face4 face ldmns ldmns absm))
-                        (mark-del-0 del-0-s (cdr mark-del-0)))
-                       ((zerop ldmns)
-                        (push (term 1 (tnpr 0 (gmsm absm) dmns gmsm))
-                              rslt))
-                     (declare
-                      (fixnum ldmns rdmns)
-                      (type gmsm gmsm)
-                      (list mark-del-0))
-                     (unless (or (plusp (dgop absm))
-                                 (plusp (dgop (car mark-del-0))))
-                       (push (term 1 (tnpr ldmns (gmsm absm)
-                                           rdmns (gmsm (car mark-del-0))))
-                             rslt)))
-                   (make-cmbn :degr dmns :list rslt)))))
-    (the intr-mrph #'rslt)))
-
-#|
-()
-(setf cmpr #'f-cmpr
-      face #'delta-face)
-(setf diag (intr-diagonal face))
-(funcall diag 4 (mask 5))
-(funcall diag 0 4)
-(setf cmpr #'s-cmpr
-      face (sphere-face 4))
-(setf diag (intr-diagonal face))
-(funcall diag 4 's4)
-(funcall diag 0 '*)
-(setf s4 (sphere 4))
-(dgnl s4 4 's4)
-|#                 
-
-(DEFUN FACE-BNDR (cmpr face)
-   (declare
-      (type cmprf cmpr)
-      (type face face))
-   (flet ((rslt (dmns gmsm)
-             (declare
-                (fixnum dmns)
-                (type gmsm gmsm))
-             (the cmbn
-                (progn
-                   (when (zerop dmns)
-                      (return-from rslt +zero-negative-cmbn+))
-                   (let ((pre-rslt +empty-list+))
-                      (declare (list pre-rslt))
-                             ;; (list (cons cffc face))
-                      (dotimes (indx (1+ dmns))
-                         (declare (fixnum indx))
-                         (let ((face (funcall face indx dmns gmsm)))
-                            (declare (type absm face))
-                            (unless (degenerate-p face)
-                               (push (term (-1-expt-n indx) (gmsm face))
-                                  pre-rslt))))
-                      (apply #'nterm-add cmpr (1- dmns) pre-rslt))))))
-      (the intr-mrph #'rslt)))
-
-#|
-  (setf face #'(lambda (indx dmns gmsm)
-                  (absm 0 (append
-                             (subseq gmsm 0 indx)
-                             (subseq gmsm (1+ indx))))))
-  (setf bndr (face-bndr #'l-cmpr face))
-  (funcall bndr 0 '(a))
-  (funcall bndr 1 '(a b))
-  (funcall bndr 2 '(a b c))
-  (funcall bndr 3 '(a b c d))
-  (funcall bndr 3 '(d c b a))
-  (funcall bndr 1 '(a a))
-  (funcall bndr 2 '(a a a))
-  (funcall bndr 3 '(a a a a))
-  (setf face #'(lambda (index dmns gmsm)
-                  (absm (dgop-ext-int (nreverse (<a-b< 0 (1- dmns)))) 'a)))
-  (setf bndr (face-bndr #'s-cmpr face))
-  (funcall bndr 1 '(a b))
-  (funcall bndr 2 '(a b c)))
-|#
-
-(DEFUN FACE*-BNDR (cmpr face*)
-   (declare
-      (type cmprf cmpr)
-      (type face* face*))
-   (flet ((rslt (dmns gmsm)
-             (declare
-                (fixnum dmns)
-                (type gmsm gmsm))
-             (the cmbn
-                (progn
-                   (when (zerop dmns)
-                      (return-from rslt +zero-negative-cmbn+))
-                   (let ((pre-rslt +empty-list+))
-                      (declare (list pre-rslt))
-                             ;; (list (list gmsm fixnum))
-                      (dotimes (indx (1+ dmns))
-                         (declare (fixnum indx))
-                         (let ((face (funcall face* indx dmns gmsm)))
-                            (declare (type (or gmsm (eql :degenerate)) face))
-                            (unless (eq face :degenerate)
-                               (push (term (-1-expt-n indx) face) pre-rslt))))
-                      (apply #'nterm-add cmpr (1- dmns) pre-rslt))))))
-      (the intr-mrph #'rslt)))
-
-#|
-  (setf face* 
-        #'(lambda (indx dmns gmsm)
-             (if (and (= dmns 3) (evenp indx))
-                'm2
-                :degenerate)))
-  (setf bndr (face*-bndr #'s-cmpr face*))
-  (funcall bndr 3 'm3)
-  (funcall bndr 2 'm2)
-  (funcall bndr 0 '*)
-  (setf face* 
-        #'(lambda (indx dmns gmsm)
-             (if (and (= dmns 3) (< indx 2))
-                'm2
-                :degenerate)))
-  (setf bndr (face*-bndr #'s-cmpr face*))
-  (funcall bndr 3 'm3)
-  (funcall bndr 2 'm2)
-  (funcall bndr 0 '*))
-|#
-
-(DEFUN A-CMPR3 (cmpr absm1 absm2)
-   (declare
-      (type cmprf cmpr)
-      (type absm absm1 absm2))
-   (the cmpr
-      (with-absm (dgop1 gmsm1) absm1
-      (with-absm (dgop2 gmsm2) absm2
-         (lexico
-            (f-cmpr dgop1 dgop2)
-            (funcall cmpr gmsm1 gmsm2))))))
-
-#|
-  (a-cmpr3 #'s-cmpr (absm 0 'a) (absm 1 'b))
-  (a-cmpr3 #'s-cmpr (absm 2 'a) (absm 1 'b))
-  (a-cmpr3 #'s-cmpr (absm 1 'a) (absm 1 'b))
-  (a-cmpr3 #'s-cmpr (absm 1 'c) (absm 1 'b))
-  (a-cmpr3 #'s-cmpr (absm 1 'a) (absm 1 'a))
-|#
-
-(DEFUN BSPN-P (cmpr bspn dmns absm)
-   ;; this function makes sense only in the simplicial context
-   ;; so that the basg (= base-generator) is called bspn (= base-point)
-   (declare
-      (type gmsm bspn)
-      (fixnum dmns)
-      (type absm absm))
-   (the boolean
-      (with-absm (dgop gmsm) absm
-         (and (= dgop (mask dmns))
-              (eq :equal (funcall cmpr bspn gmsm))))))
-
-#|
-  (setf d (delta-infinity))
-  (setf cmpr (cmpr d))
-  (bspn-p cmpr 1 5 (absm (mask 5) 1))
-  (bspn-p cmpr 1 5 (absm (mask 5) 2))
-  (bspn-p cmpr 1 5 (absm (mask 4) 3))
-|#
-
-(DEFUN DLOP-EXT-INT (ext-dlop)
-   (declare (list ext-dlop))
-          ;; (list fixnum)
-   (when ext-dlop   
-      (unless (apply #'< ext-dlop)
-         (error "In DLOP-EXT-INT, the external dlop ~A is not increasing." ext-dlop)))
-   (the fixnum
-      (apply #'logxor
-         (mapcar #'(lambda (item)
-                      (declare (fixnum item))
-                      (the fixnum (2-exp item)))
-            ext-dlop))))
-#|
-  (dlop-ext-int '())
-  (dlop-ext-int '(2 2))
-  (dlop-ext-int '(0 4)))
-|#
-
-(DEFUN DLOP-INT-EXT (dlop)
-   (declare (fixnum dlop))
-   (the list
-      (nreverse (dgop-int-ext dlop))))
-
-#|
-  (dlop-int-ext 0)
-  (dlop-int-ext 4)
-  (dlop-int-ext 63)
-  (dotimes (i 33)
-     (print (dlop-ext-int (dlop-int-ext i)))))
-|#
-
-(DEFUN 1DGOP*DGOP (1dgop dgop)
-   (declare (fixnum 1dgop dgop))
-   ;; 1dgop is an ordinary integer
-   ;; dgop is a bit string
-   (the fixnum
-      (let ((share (ash -1 1dgop)))
-         (declare (fixnum share))
-         (logxor
-            (ash (logand share dgop) 1)
-            (2-exp 1dgop)
-            (logandc1 share dgop)))))
-      
-#|
-  (dotimes (i 20)
-     (dotimes (j 5)
-       (format t "~% (~D) o ~A = ~A"
-                 j (dgop-int-ext i) (dgop-int-ext (1dgop*dgop j i))))))
-|#
-
-(DEFUN DGOP*DGOP (dgop1 dgop2)
-   (declare (type fixnum dgop1 dgop2))
-   (let ((dgop 0)
-         (bmark 0))
-      (declare (fixnum dgop bmark))
-      (loop
-         (when (zerop dgop1)
-            (return-from dgop*dgop
-               (logxor dgop (ash dgop2 bmark))))
-         (when (zerop dgop2)
-            (return-from dgop*dgop
-               (logxor dgop (ash dgop1 bmark))))
-         (cond ((evenp dgop1)
-                (when (oddp dgop2)
-                   (incf dgop (2-exp bmark)))
-                (setf dgop2 (ash dgop2 -1)))
-               (t
-                  (incf dgop (2-exp bmark))))
-         (setf dgop1 (ash dgop1 -1))
-         (incf bmark))))
-
-#|
-  (dotimes (i 10)
-     (dotimes (j 10)
-        (format t "~%~A o ~A = ~A"
-                  (dgop-int-ext i) (dgop-int-ext j)
-                  (dgop-int-ext (dgop*dgop i j))))))
-|#
-
-(DEFUN REMOVE-BIT (n indx)
-   (declare (fixnum n indx))
-   (the fixnum
-      (let ((cut (2-exp indx)))
-         (multiple-value-bind (quotient remainder) (truncate n cut)
-            (declare (fixnum quotient remainder))
-            (+ (ash (ash quotient -1) indx) remainder)))))
-
-#|
-  (remove-bit 107 3)  ;; 51
-|#
-
-(DEFUN DGOP/DGOP (dgop1 dgop2)
-   (declare (fixnum dgop1 dgop2))
-   (the fixnum
-      (do ((indx (1- (integer-length dgop2)) (1- indx)))
-          ((minusp indx) dgop1)
-         (declare (fixnum indx))
-         (when (logbitp indx dgop2)
-            (setf dgop1 (remove-bit dgop1 indx))))))
-
-#|
-  (dgop/dgop 67 0)
-  (dgop/dgop 68 4)
-  (dgop/dgop 31 5)
-|#      
-
-(DEFUN 1DLOP-DGOP (1dlop dgop)
-   (declare (fixnum 1dlop dgop))
-   ;; 1dlop is an ordinary fixnum
-   ;; dgop is a bit string
-   (the (values fixnum (or fixnum null))
-      (progn
-         (when (logbitp 1dlop dgop)
-            (let ((share (ash -1 1dlop)))
-               (declare (fixnum share))
-               (return-from 1dlop-dgop
-                  (values
-                     (logxor
-                        (logand share (ash dgop -1))
-                        (logandc1 share dgop))
-                     nil))))
-         (when (and (plusp 1dlop)
-                    (logbitp (1- 1dlop) dgop))
-            (let ((share (ash -1 1dlop)))   ;;;
-               (declare (fixnum share))
-	       (setf share (ash share -1))  ;;; because of the compiler bug
-               (return-from 1dlop-dgop
-                  (values
-                     (logxor
-                        (logand share (ash dgop -1))
-                        (logandc1 share dgop))
-                     nil))))
-         (let ((share (ash -1 1dlop)))
-            (declare (fixnum share))
-            (let ((right (logandc1 share dgop)))
-               (declare (fixnum right))
-               (values
-                  (logxor right (logand share (ash dgop -1)))
-                  (- 1dlop (logcount right))))))))
-
-#|
-  (dotimes (i 5)
-     (dotimes (j 17)
-        (multiple-value-bind (dgop 1dlop) (1dlop-dgop i j)
-           (format t "~% del-~D o ~A = ~A o del-~A"
-                     i (dgop-int-ext j) (dgop-int-ext dgop) 1dlop)))))
-|#
-
-
-(DEFUN A-FACE4 (face indx dmns absm) 
-  (declare
-   (type face face)
-   (fixnum indx dmns)
-   (type absm absm))
-  (the absm
-    (with-absm (dgop gmsm) absm
-      (multiple-value-bind (dgop2 1dlop) (1dlop-dgop indx dgop)
-        (declare (fixnum dgop2)
-                 #-lispworks (type (or fixnum nil) 1dlop))
-                 ;; Bug LispWorks if this or-type defined
-        (unless 1dlop
-          (return-from a-face4 (absm dgop2 gmsm)))
-        (locally (declare (fixnum 1dlop))
-          (let ((gmsm-face (funcall face 1dlop (- dmns (logcount dgop)) gmsm)))
-            (declare (type absm gmsm-face))
-            (with-absm (dgop3 gmsm3) gmsm-face
-              (absm (dgop*dgop dgop2 dgop3) gmsm3))))))))
-#|
-()
-(require "special-smsts")
-(let ((simp (dlop-ext-int '(0 1 2 3 4 5 6))))
-   (dotimes (i 5)
-      (dotimes (j 17)
-         (let ((face (a-face4 (face (delta-infinity))
-                        i (+ 6 (logcount j)) (absm j simp))))
-            (format t "~%del-~D o ~A (0 1 2 3 4 5 6) = ~A ~A"
-                      i (dgop-int-ext j)
-                      (dgop-int-ext (dgop face))
-                      (dlop-int-ext (gmsm face)))))))
-|#
-
-(DEFUN 1DGNR (indx absm)
-   (declare
-      (fixnum indx)
-      (type absm absm))
-   (the absm
-      (with-absm (dgop gmsm) absm
-         (absm (1dgop*dgop indx dgop) gmsm))))
-
-#|
-  (1dgnr 2 (absm 17 'a))
-|#
-
-(DEFUN NDGNR (dgop absm)
-   (declare
-      (fixnum dgop)
-      (type absm absm))
-   (the absm
-      (with-absm (dgop2 gmsm) absm
-         (absm (dgop*dgop dgop dgop2) gmsm))))
-
-#|
-  (ndgnr 2 (absm 17 'a))
-|#
-
-
-(DEFUN NFACE (face dlop dmns gmsm)
-  (declare
-     (type face face)
-     (type dlop dlop)
-     (fixnum dmns)
-     (type gmsm gmsm))
-  (do* ((gmsm gmsm)
-	(dmns dmns)
-	(dgop 0)
-	(dlop dlop (- dlop (2-exp bark)))
-	(bark (1- (integer-length dlop))
-	      (1- (integer-length dlop))))
-       ((zerop dlop) (absm dgop gmsm))
-      (declare
-         (type gmsm gmsm)
-	 (fixnum dgop dlop bark))
-      (multiple-value-bind (dgop2 indx) (1dlop-dgop bark dgop)
-	 (declare
-	    (fixnum dgop2)
-	    (type (or null fixnum) indx))
-	 (if indx
-	    (locally (declare (fixnum indx))
-	       (let ((new-absm (funcall face indx dmns gmsm)))
-		  (declare (type absm new-absm))
-		  (with-absm (dgop3 gmsm2) new-absm
-		     (setf gmsm gmsm2
-			   dmns (- dmns 1
-				   (logcount dgop3))
-			   dgop (dgop*dgop dgop2 dgop3)))))
-  	     (setf dgop dgop2)))))
-
-#|
-  (setf f (face (delta-infinity)))
-  (dotimes (dlop 31)
-    (print (dlop-int-ext (gmsm (nface f dlop 4 31)))))
-  (setf p (r-proj-space))
-  (setf f (face p))
-  (dotimes (dlop 31)
-    (format t "~%~A ~A"
-       (hyphenize-list (dlop-int-ext dlop))
-       (nface f dlop 4 4)))
-|#
-
-(DEFUN CHECK-FACES (cmpr face dmns gmsm)
-   (declare
-      (type cmprf cmpr)
-      (type face face)
-      (fixnum dmns)
-      (type gmsm gmsm))
-   (the boolean
-      (progn      
-         (when (> dmns 1)
-            (let ((dmns-1 (1- dmns)))
-               (declare (fixnum dmns-1))
-               (dotimes (i dmns)
-                  (declare (fixnum i))
-                  (dotimes (j (1+ i))
-                     (declare (fixnum j))
-                     (let ((rslt1 (a-face4 face i dmns-1 (funcall face j dmns gmsm)))
-                           (rslt2 (a-face4 face j dmns-1 (funcall face (1+ i) dmns gmsm))))
-                        (declare (type absm rslt1 rslt2))
-                        (unless (eq (a-cmpr3 cmpr rslt1 rslt2) :equal)
-                           (cerror "CHECK-FACES will return NIL."
-                              "Noncoherent boundary operators detected by CHECK-FACES :~@
-                               Simplex => ~A~@
-                               del_~D o del_~D => ~A~@
-                               del_~D o del_~D => ~A"
-                              gmsm i j rslt1 j (1+ i) rslt2)
-                              (return-from check-faces nil)))))))
-         t)))
-
-#|
-  (setf d (delta-infinity))
-  (check-faces #'f-cmpr (face d) 4 31)
-|#
-
-(DEFUN CHECK-SMST (smst dmns1 &optional (dmns2 (1+ dmns1)))
-   (declare
-      (type simplicial-set smst)
-      (fixnum dmns1 dmns2))
-   (with-slots (cmpr basis face) smst
-      (declare
-         (type cmprf cmpr)
-         (type face face))
-   (when (eq basis :locally-effective)
-      (error "In CHECK-SMST, the locally-effective simplicial-set ~A~@
-              cannot be checked." smst))
-      (do ((rslt t)
-           (dmns dmns1 (1+ dmns)))
-          ((>= dmns dmns2) rslt)
-         (declare
-            (type boolean rslt)
-            (fixnum dmns))
-         (format t "~%Checking the ~D-simplices..." dmns)
-         (dolist (gmsm (funcall basis dmns))
-            (declare (type gmsm gmsm))
-            (unless (check-faces cmpr face dmns gmsm)
-               (setf rslt nil))))))
-
-#|
-  (check-smst (delta-infinity) 5)
-  (check-smst (delta 3) 2)
-  (check-smst (delta 3) 2 4)
-|#
-
diff --git a/archive/Kenzo-1/smith.cl b/archive/Kenzo-1/smith.cl
deleted file mode 100644
index 7c4af86..0000000
--- a/archive/Kenzo-1/smith.cl
+++ /dev/null
@@ -1,1106 +0,0 @@
-;;;  SMITH  SMITH  SMITH  SMITH  SMITH  SMITH  SMITH  SMITH
-;;;  SMITH  SMITH  SMITH  SMITH  SMITH  SMITH  SMITH  SMITH
-;;;  SMITH  SMITH  SMITH  SMITH  SMITH  SMITH  SMITH  SMITH
-
-(IN-PACKAGE "COMMON-LISP-USER")
-
-(PROVIDE "smith")
-
-(DEFTYPE MATRIX () '(array fixnum (* *)))
-
-
-(DEFUN RANDOM-MATRIX (line-n column-n max)
-  (declare (fixnum line-n column-n max))
-  (the matrix
-    (let ((rslt (make-array (list line-n column-n)
-			    :element-type 'fixnum))
-	  (2max+1 (+ max max 1)))
-      (declare
-        (type matrix rslt)
-	(fixnum 2max+1))
-      (dotimes (i line-n)
-	(declare (fixnum i))
-	(dotimes (j column-n)
-	  (declare (fixnum j))
-	  (setf (aref rslt i j)
-		(- (random 2max+1) max))))
-      rslt)))
-
-#|
-  (random-matrix 2 3 10)
-|#
-
-(DEFUN IDNT-MTRX (n)
-  (declare (fixnum n))
-  (the matrix
-    (let ((rslt (if (zerop n)
-                    (make-array '(0 0)
-                                :element-type 'fixnum)
-                  (make-array (list n n)
-                              :element-type 'fixnum
-                              :initial-element 0))))
-      (declare (type matrix rslt))
-      (dotimes (i n)
-	(declare (fixnum i))
-	(setf (aref rslt i i) 1))
-      rslt)))
-
-#|
-()
-(idnt-mtrx 3)
-|#
-
-(DEFUN COPY-MTRX (mtrx)
-  (declare (type matrix mtrx))
-  (the matrix
-    (let ((line-n (line-number mtrx))
-	  (column-n (column-number mtrx)))
-      (declare (fixnum line-n column-n))
-      (let ((rslt (make-array (list line-n column-n)
-			      :element-type 'fixnum)))
-	(declare (type matrix rslt))
-	(dotimes (il line-n)
-	  (declare (fixnum il))
-	(dotimes (ic column-n)
-	  (declare (fixnum ic))
-	  (setf (aref rslt il ic) (aref mtrx il ic))))
-	rslt))))
-
-#|
-(setf m (random-matrix 3 4 10))
-(equalp m (copy-mtrx m))
-|#
-
-(DEFUN LEFT-SUBMATRIX (mtrx k)
-  (declare (type matrix mtrx))
-  (the matrix
-    (let ((line-n (line-number mtrx))
-	  (column-n (column-number mtrx)))
-      (declare (fixnum line-n column-n))
-      (assert (<= k column-n))
-      (let ((rslt (make-array (list line-n k)
-			      :element-type 'fixnum)))
-	(declare (type matrix rslt))
-	(dotimes (il line-n)
-	  (declare (fixnum il))
-	(dotimes (ic k)
-	  (declare (fixnum ic))
-	  (setf (aref rslt il ic) (aref mtrx il ic))))
-	rslt))))
-
-#|
-(setf m (random-matrix 3 4 10))
-(left-submatrix m 2)
-|#
-
-(DEFUN MTRX-PRDC (mtrx1 mtrx2)
-  (declare (type matrix mtrx1 mtrx2))
-  (the matrix
-    (let ((rslt-line-n (line-number mtrx1))
-	  (mtrx1-column-n (column-number mtrx1))
-	  (mtrx2-line-n (line-number mtrx2))
-	  (rslt-column-n (column-number mtrx2)))
-      (declare (fixnum rslt-line-n mtrx1-column-n
-		       mtrx2-line-n rslt-column-n))
-      (unless (= mtrx1-column-n mtrx2-line-n)
-	(error "In MTRX-PRDC, bad line or column number."))
-      (let ((rslt (make-array (list rslt-line-n rslt-column-n)
-			      :element-type 'fixnum)))
-	(declare (type matrix rslt))
-	(dotimes (il rslt-line-n)
-	  (declare (fixnum il))
-	(dotimes (ic rslt-column-n)
-	  (declare (fixnum ic))
-	  (do ((k 0 (1+ k))
-	       (sum 0 (+ sum
-			 (* (aref mtrx1 il k) (aref mtrx2 k ic)))))
-	      ((= k mtrx1-column-n) (setf (aref rslt il ic) sum)))))
-	rslt))))
-
-#|
-(setf m1 (random-matrix 2 3 10))
-(setf m2 (random-matrix 3 2 10))
-(mtrx-prdc m1 m2)
-(mtrx-prdc m2 m1)
-|#
-
-(DEFUN CHCM-MTRX (chcm degr)
-  (declare
-   (type chain-complex chcm)
-   (fixnum degr))
-  (the matrix
-    (let ((cmpr (cmpr1 chcm))
-          (dffr (dffr chcm))
-          (sbasis (basis chcm degr))
-          (tbasis (basis chcm (1- degr))))
-      (declare
-       (type cmprf cmpr)
-       (type morphism dffr)
-       (list sbasis tbasis))
-      (let ((srank (length sbasis))
-            (trank (length tbasis)))
-        (declare (fixnum srank trank))
-        (let ((rslt (make-array (list trank srank)
-                                :element-type 'fixnum
-                                :initial-element 0)))
-          (declare (type matrix rslt))
-          (do ((j 0 (1+ j))
-               (mark sbasis (cdr mark)))
-              ((endp mark))
-            (declare
-             (fixnum j)
-             (list mark))
-            (let ((cmbn (gnrt-? dffr degr (car mark))))
-              (declare (type cmbn cmbn))
-              (do ((mark1 (cmbn-list cmbn) (cdr mark1))
-                   (mark2 tbasis)
-                   (i 0))
-                  ((endp mark1))
-                (declare
-                 (list mark1 mark2)
-                 (fixnum i))
-                (with--term (cffc gnrt) mark1
-                            (loop
-                              (cond ((eq :equal (funcall cmpr gnrt (car mark2)))
-                                     (setf (aref rslt i j) cffc)
-                                     (incf i)
-                                     (pop mark2)
-                                     (return))
-                                    (t (incf i)
-                                       (pop mark2))))))))
-          rslt)))))
-
-#|
-()
-(setf d (delta 5))
-(chcm-mtrx d 3)
-(setf m (moore 2 2))
-(dotimes (i 5)
-  (print (chcm-mtrx m i)))
-(dotimes (i 6)
-  (print (array-dimensions (chcm-mtrx m i))))
-|#
-
-(DEFUN LINE-OP (mtrx begin lambda line1 line2)
-  ;; line2 := line2 + lambda * line1
-  (declare
-    (type matrix mtrx)
-    (fixnum begin lambda line1 line2))
-  (the matrix
-  (progn
-  (do ((column-number (column-number mtrx))
-       (j begin (1+ j)))
-      ((= j column-number))
-      (declare (fixnum column-number j))
-    (incf (aref mtrx line2 j)
-	  (* lambda (aref mtrx line1 j))))
-  mtrx)))
-	
-#|
-(setf m (random-matrix 3 4 10))
-(line-op m 1 3 2 0)
-|#
-
-;; mtrx-list = (P P^-1 M Q Q^-1)
-
-#|
-(setf p (idnt-mtrx 4) p-1 (idnt-mtrx 4)
-      m (random-matrix 4 5 10)
-      q (idnt-mtrx 5) q-1 (idnt-mtrx 5))
-(setf list (list p p-1 m q q-1))
-(setf t1 (mtrx-prdc p (mtrx-prdc m q-1)))
-(line-op-5 list 0 3 1 3)
-(equalp t1 (mtrx-prdc p (mtrx-prdc m q-1)))
-(mtrx-prdc p p-1)
-|#
-
-(DEFUN COLUMN-OP (mtrx begin lambda column1 column2)
-  (declare
-    (type matrix mtrx)
-    (fixnum begin lambda column1 column2))
-  (the matrix
-  (progn
-  (do ((line-number (line-number mtrx))
-       (i begin (1+ i)))
-      ((= i line-number))
-      (declare (fixnum line-number i))
-    (incf (aref mtrx i column2)
-	  (* lambda (aref mtrx i column1))))
-  mtrx)))
-	
-#|
-(setf m (random-matrix 3 4 10))
-(column-op m 1 3 2 0)
-|#
-
-#|
-(setf p (idnt-mtrx 4) p-1 (idnt-mtrx 4)
-      m (random-matrix 4 5 10)
-      q (idnt-mtrx 5) q-1 (idnt-mtrx 5))
-(setf list (list p p-1 m q q-1))
-(setf t1 (mtrx-prdc p (mtrx-prdc m q-1)))
-(column-op-5 list 0 3 1 3)
-(equalp t1 (mtrx-prdc p (mtrx-prdc m q-1)))
-(mtrx-prdc p p-1)
-(mtrx-prdc q q-1)
-|#
-
-
-(DEFUN LINE-SWAP (mtrx begin line1 line2)
-  (declare
-    (type matrix mtrx)
-    (fixnum begin line1 line2))
-  (the matrix
-  (progn
-  (do ((column-number (column-number mtrx))
-       (j begin (1+ j)))       
-      ((= j column-number))
-      (declare (fixnum column-number j))
-    (rotatef (aref mtrx line1 j) (aref mtrx line2 j)))
-  mtrx)))
-
-#|
-(setf m (random-matrix 3 4 10))
-(line-swap m 1 0 2)
-|#
-
-#|
-(setf p (idnt-mtrx 4) p-1 (idnt-mtrx 4)
-      m (random-matrix 4 5 10)
-      q (idnt-mtrx 5) q-1 (idnt-mtrx 5))
-(setf list (list p p-1 m q q-1))
-(setf t1 (mtrx-prdc p (mtrx-prdc m q-1)))
-(line-swap-5 list 0 1 3)
-(equalp t1 (mtrx-prdc p (mtrx-prdc m q-1)))
-(mtrx-prdc p p-1)
-(mtrx-prdc q q-1)
-|#
-
-(DEFUN COLUMN-SWAP (mtrx begin column1 column2)
-  (declare
-    (type matrix mtrx)
-    (fixnum begin column1 column2))
-  (the matrix (progn
-  (do ((line-number (line-number mtrx))
-       (i begin (1+ i)))       
-      ((= i line-number))
-      (declare (fixnum line-number i))
-    (rotatef (aref mtrx i column1) (aref mtrx i column2)))
-  mtrx)))
-
-#|
-(setf m (random-matrix 3 4 10))
-(column-swap m 1 0 2)
-|#
-
-#|
-(setf p (idnt-mtrx 4) p-1 (idnt-mtrx 4)
-      m (random-matrix 4 5 10)
-      q (idnt-mtrx 5) q-1 (idnt-mtrx 5))
-(setf list (list p p-1 m q q-1))
-(setf t1 (mtrx-prdc p (mtrx-prdc m q-1)))
-(column-swap-5 list 0 1 3)
-(equalp t1 (mtrx-prdc p (mtrx-prdc m q-1)))
-(mtrx-prdc p p-1)
-(mtrx-prdc q q-1)
-|#
-
-(DEFUN LINE-MINUS (mtrx begin line)
-  (declare
-    (type matrix mtrx)
-    (fixnum begin line))
-  (the matrix (progn
-  (do ((column-number (column-number mtrx))
-       (j begin (1+ j)))
-      ((= j column-number))
-      (declare (fixnum column-number j))
-    (setf (aref mtrx line j) (- (aref mtrx line j))))
-  mtrx)))
-
-(DEFUN COLUMN-MINUS (mtrx begin column)
-  (declare
-    (type matrix mtrx)
-    (fixnum begin column))
-  (the matrix (progn
-  (do ((line-number (line-number mtrx))
-       (i begin (1+ i)))
-      ((= i line-number))
-      (declare (fixnum line-number i))
-    (setf (aref mtrx i column) (- (aref mtrx i column))))
-  mtrx)))
-
-#|
-(setf m (random-matrix 3 4 10))
-(line-minus m 1 2)
-(column-minus m 1 2)
-|#
-
-#|
-(setf p (idnt-mtrx 4) p-1 (idnt-mtrx 4)
-      m (random-matrix 4 5 10)
-      q (idnt-mtrx 5) q-1 (idnt-mtrx 5))
-(setf list (list p p-1 m q q-1))
-(setf t1 (mtrx-prdc p (mtrx-prdc m q-1)))
-(line-minus-5 list 0 3)
-(equalp t1 (mtrx-prdc p (mtrx-prdc m q-1)))
-(mtrx-prdc p p-1)
-(mtrx-prdc q q-1)
-(column-minus-5 list 0 2)
-(equalp t1 (mtrx-prdc p (mtrx-prdc m q-1)))
-(mtrx-prdc p p-1)
-(mtrx-prdc q q-1)
-|#
-
-(DEFUN MINIMAL-TERM (matrix begin)
-  (declare
-    (type matrix matrix)
-    (fixnum begin))
-  (the (values fixnum fixnum fixnum)
-  (do ((line-number (line-number matrix))
-       (column-number (column-number matrix))
-       (min 0)
-       (min-il -1)
-       (min-ic -1)
-       (il begin (1+ il)))
-      ((= il line-number) (values min min-il min-ic))
-      (declare (fixnum line-number column-number
-		       min min-il min-ic il))
-      (do ((ic begin (1+ ic)))
-          ((= ic column-number))
-         (declare (fixnum ic))
-         (let ((term (abs (aref matrix il ic))))
-	   (declare (fixnum term))
-            (when (= term 1)
-               (return-from minimal-term (values 1 il ic)))
-            (when (plusp term)
-               (when (or (< term min)
-                         (zerop min))               
-                  (setf min term
-                        min-il il
-                        min-ic ic))))))))
-
-#|
-(setf m (random-matrix 4 5 10))
-(minimal-term m 1)
-|#
-
-(DEFUN MINIMAL-REST-1 (matrix begin)
-  (declare
-    (type matrix matrix)
-    (fixnum begin))
-  (the (values fixnum fixnum fixnum)
-   (let ((line-number (line-number matrix))
-	 (column-number (column-number matrix))
-	 (corner (aref matrix begin begin))
-         (min 0)
-         (min-il -1)
-         (min-ic -1))
-      (declare (fixnum corner min min-il min-ic))
-      (do ((ic (1+ begin) (1+ ic)))
-          ((= ic column-number))
-         (declare (fixnum ic))
-         (let ((term (abs (second (multiple-value-list (round (aref matrix begin ic) 
-                                                          corner))))))
-            (declare (fixnum term))
-            (when (= term 1)
-               (return-from minimal-rest-1 (values 1 begin ic)))
-            (when (plusp term)
-               (when (or (< term min)
-                         (zerop min))               
-                  (setf min term
-                        min-il begin
-                        min-ic ic)))))
-      (do ((il (1+ begin) (1+ il)))
-          ((= il line-number))
-         (declare (fixnum il))
-         (let ((term (abs (second (multiple-value-list (round (aref matrix il begin)
-                                                          corner))))))
-            (declare (fixnum term))
-            (when (= term 1)
-               (return-from minimal-rest-1 (values 1 il begin)))
-            (when (plusp term)
-               (when (or (< term min)
-                         (zerop min))               
-                  (setf min term
-                        min-il il
-                        min-ic begin)))))
-      (values min min-il min-ic))))
-
-#|
-(setf m (random-matrix 4 5 10))
-(minimal-rest-1 m 1)
-|#
-
-(DEFUN MINIMAL-REST-2 (matrix begin)
-  (declare
-    (type matrix matrix)
-    (fixnum begin))
-  (the (values fixnum fixnum fixnum)
-   (let ((line-number (line-number matrix))
-	 (column-number (column-number matrix))		      
-	 (corner (aref matrix begin begin))
-         (min 0)
-         (min-il  -1)
-         (min-ic -1))
-      (declare (fixnum corner min min-il min-ic))
-      (do ((il (1+ begin) (1+ il)))
-          ((= il line-number))
-         (declare (fixnum il))
-         (do ((ic (1+ begin) (1+ ic)))
-             ((= ic column-number))
-            (declare (fixnum il))
-            (let ((term (abs (second (multiple-value-list (round (aref matrix il ic)
-                                                             corner))))))
-               (declare (fixnum term))
-               (when (= 1 term)
-                  (return-from minimal-rest-2 (values 1 il ic)))
-               (when (plusp term)
-                  (when (or (< term min)
-                            (zerop min))
-                     (setf min term
-                           min-il il
-                           min-ic ic))))))
-      (values min min-il min-ic))))
-
-#|
-(setf m (random-matrix 4 5 10))
-(minimal-rest-2 m 1)
-|#
-
-(DEFUN MINIMAL-TERM-TOP-LEFT (mtrx-list begin il ic)
-   (declare
-     (list mtrx-list)
-     (fixnum begin il ic))
-   (the matrix (progn
-   (when (< begin il)
-      (line-swap-5 mtrx-list begin begin il))
-   (when (< begin ic)
-      (column-swap-5 mtrx-list begin begin ic))
-   (when (minusp (aref (third mtrx-list) begin begin))
-      (line-minus-5 mtrx-list begin begin))
-   mtrx-list)))
-
-#|
-(setf p (idnt-mtrx 4) p-1 (idnt-mtrx 4)
-      m (random-matrix 4 5 10)
-      q (idnt-mtrx 5) q-1 (idnt-mtrx 5))
-(setf list (list p p-1 m q q-1))
-(setf t1 (mtrx-prdc p (mtrx-prdc m q-1)))
-(minimal-term-top-left list 0 1 3)
-(equalp t1 (mtrx-prdc p (mtrx-prdc m q-1)))
-(mtrx-prdc p p-1)
-(mtrx-prdc q q-1))
-|#
-
-(DEFUN PIVOTT (mtrx-list begin)
-  (declare
-    (list mtrx-list)
-    (fixnum begin))
-  (the list (progn
-  (let ((line-number (line-number (third mtrx-list)))
-	(column-number (column-number (third mtrx-list)))
-	(corner (aref (third mtrx-list) begin begin)))
-    (declare (fixnum line-number column-number corner))
-    (do ((il (1+ begin) (1+ il)))
-	((= il line-number))
-	(declare (fixnum il))
-      (line-op-5 mtrx-list begin
-		 (- (round (aref (third mtrx-list) il begin) corner))
-		 begin il))
-    (do ((ic (1+ begin) (1+ ic)))
-	((= ic column-number))
-	(declare (fixnum ic))
-      (column-op-5 mtrx-list begin
-		   (- (round (aref (third mtrx-list) begin ic) corner))
-		   begin ic)))
-  mtrx-list)))
-
-#|
-(setf p (idnt-mtrx 4) p-1 (idnt-mtrx 4)
-      m (random-matrix 4 5 10)
-      q (idnt-mtrx 5) q-1 (idnt-mtrx 5))
-(setf (aref m 0 0) -1)
-(setf list (list p p-1 m q q-1))
-(setf t1 (mtrx-prdc p (mtrx-prdc m q-1)))
-(pivott list 0)
-(equalp t1 (mtrx-prdc p (mtrx-prdc m q-1)))
-(mtrx-prdc p p-1)
-(mtrx-prdc q q-1)
-|#
-
-(DEFUN LIST-SMITH (mtrx-list)
-  (declare (list mtrx-list))
-  (the list (progn
-  (let ((matrix (third mtrx-list))
-	(begin 0))
-    (declare
-      (type matrix matrix)
-      (fixnum begin))
-   (loop
-      (multiple-value-bind (term il ic) (minimal-term matrix begin)
-	(declare (fixnum term il ic))
-        ;; (format t "~%*BEGIN* = ~D ; MIN = ~D." begin term)
-	(when (zerop term)
-	  (return-from list-smith mtrx-list))
-	(minimal-term-top-left mtrx-list begin il ic))
-      (loop
-       (multiple-value-bind (term il ic) (minimal-rest-1 matrix begin)
-	 (declare (fixnum term il ic))
-	 (cond ((zerop term)
-		(pivott mtrx-list begin)
-		(multiple-value-bind (term il ic) (minimal-rest-2 matrix begin)
-		  (declare
-		    (fixnum term il)
-		    (ignore ic))
-		  (if (zerop term)
-		      (return)
-		    (line-op-5 mtrx-list begin 1 il begin))))
-	       ((= il begin)
-		(column-op-5 mtrx-list begin
-			     (- (round (aref matrix begin ic)
-				       (aref matrix begin begin)))
-			     begin ic)
-		(column-swap-5 mtrx-list begin begin ic)
-		(when (minusp (aref matrix begin begin))
-                      (column-minus-5 mtrx-list begin begin)))
-	       (t
-		(line-op-5 mtrx-list begin
-			   (- (round (aref matrix il begin)
-				     (aref matrix begin begin)))
-			    begin il)
-		(line-swap-5 mtrx-list begin begin il)
-		(when (minusp (aref matrix begin begin))
-		      (column-minus-5 mtrx-list begin begin))))))
-      ;; (Format t "~%  Finally the diagonal term is ~D." (aref matrix begin begin))
-      (incf begin)))
-  mtrx-list)))
-
-#|
-(setf p (idnt-mtrx 4) p-1 (idnt-mtrx 4)
-      m (random-matrix 4 5 10)
-      q (idnt-mtrx 5) q-1 (idnt-mtrx 5))
-(setf list (list p p-1 m q q-1))
-(setf t1 (mtrx-prdc p (mtrx-prdc m q-1)))
-(third (list-smith list))
-(equalp t1 (mtrx-prdc p (mtrx-prdc m q-1)))
-(mtrx-prdc p p-1)
-(mtrx-prdc q q-1)
-|#
-
-(DEFUN SMITH (matrix)
-  (declare (type matrix matrix))
-  (the list
-  (let ((line-n (line-number matrix))
-	(column-n (column-number matrix)))
-    (declare (fixnum line-n column-n))
-    (list-smith
-     (list (idnt-mtrx line-n) (idnt-mtrx line-n)
-	   matrix
-	   (idnt-mtrx column-n) (idnt-mtrx column-n))))))
-
-
-;;; ECHCM -> The same without the first epimorphism
-;;;
-;;; epi: C_f <- C_{f+1}
-;;  rank(C_f) = n
-;;  rank(C_{f+1}) = m
-;;  f = first
-
-(eval-when (:compile-toplevel :load-toplevel :execute)
-  (UNLESS (FIND-PACKAGE "GNRTS")
-    (make-package "GNRTS"))
-  (DEFCONSTANT +GNRTS-PCKG+
-    (find-package "GNRTS")))
-
-(DEFUN GNRT-NAME-BASIS (n)
-  (declare (fixnum n))
-  (the list
-  (do ((i (1- n) (1- i))
-       (rslt +empty-list+ (cons (gnrt-name i) rslt)))
-      ((minusp i) rslt)
-      (declare
-        (fixnum i)
-	(list rslt)))))
-
-#|
-(gnrt-name 4)
-(gnrt-name-basis 4)
-|#
-
-(DEFUN ECHCM-KILL-EPI-F-INTR (cmpr first n m f+1-basis mtrx-list)
-  (declare
-    (type cmprf cmpr)
-    (fixnum first n m)
-    (list f+1-basis mtrx-list))
-  (let ((f+1 (1+ first))
-	(m-n (- m n))
-	(q-1 (fifth mtrx-list)))
-    (declare
-      (fixnum f+1 m-n)
-      (type matrix q-1))
-    (flet ((rslt (cmbn)
-	     (declare (type cmbn cmbn))
-	     (with-cmbn (degr list) cmbn
-	       (when (= degr first)
-		 (return-from rslt (zero-cmbn degr)))
-	       (unless (= degr f+1)
-		 (return-from rslt cmbn))
-                 (let ((rslt-cffcs (make-array m-n :element-type 'fixnum
-                                               :initial-element 0)))
-                   (declare (type (array fixnum *) rslt-cffcs))
-                   (do ((cmbn-mark list (cdr cmbn-mark))
-                        (basis-mark f+1-basis)
-                        (ic 0))
-                       ((endp cmbn-mark))
-                     (declare
-                      (list cmbn-mark basis-mark)
-                      (fixnum ic))
-                     (with--term (cffc gnrt) cmbn-mark
-                                 (loop (when (eq :equal (funcall cmpr gnrt (car basis-mark)))
-                                         (return))
-                                       (pop basis-mark)
-                                       (incf ic))
-                                 (dotimes (il m-n)
-                                   (incf (aref rslt-cffcs il)
-                                         (* cffc (aref q-1 (+ n il) ic))))
-                                 (pop basis-mark)
-                                 (incf ic)))
-                   (do ((term-list +empty-list+)
-                        (il (1- m-n) (1- il)))
-                       ((minusp il) (make-cmbn :degr degr
-                                               :list term-list))
-                     (declare
-                      (list term-list)
-                      (fixnum il))
-                     (let ((cffc (aref rslt-cffcs il)))
-                       (declare (fixnum cffc))
-                       (unless (zerop cffc)
-                         (push (term cffc (gnrt-name il)) term-list))))))))
-      (the intr-mrph #'rslt))))
-	      
-#|
-()
-(setf q-1 (random-matrix 5 5 10))
-(setf f (echcm-kill-epi-f-intr #'s-cmpr 2 2 5 '(a b c d e)
-		      (list 0 0 0 0 q-1)))
-(funcall f (cmbn 2 1 'a))
-(funcall f (cmbn 4 1 'a))
-(funcall f (cmbn 3 1 'a 10 'b 100 'c 1000 'd 10000 'e))
-|#
-
-(DEFUN ECHCM-KILL-EPI-G-INTR (first n m f+1-basis mtrx-list)
-  (declare
-   (fixnum first n m)
-   (list f+1-basis mtrx-list))
-  (let ((f+1 (1+ first))
-        (m-n (- m n))
-        (q (fourth mtrx-list)))
-    (declare
-     (fixnum f+1 m-n)
-     (type matrix q))
-    (flet ((rslt (cmbn)
-                 (declare (type cmbn cmbn))
-                 (with-cmbn (degr list) cmbn
-                            (unless (= degr f+1)
-                              (return-from rslt cmbn))
-                            (let ((rslt-cffcs (make-array m :element-type 'fixnum
-                                                          :initial-element 0)))
-                              (declare (type (array fixnum *) rslt-cffcs))
-                              (do ((cmbn-mark list (cdr cmbn-mark))
-                                   (basis-mark (gnrt-name-basis m-n))
-                                   (ic 0))
-                                  ((endp cmbn-mark))
-                                (declare
-                                 (list cmbn-mark basis-mark)
-                                 (fixnum ic))
-                                (with--term (cffc gnrt) cmbn-mark
-                                            (loop (when (eq :equal (s-cmpr gnrt (car basis-mark)))
-                                                    (return))
-                                                  (pop basis-mark)
-                                                  (incf ic))
-                                            (dotimes (il m)
-                                              (incf (aref rslt-cffcs il)
-                                                    (* cffc (aref q il (+ n ic)))))
-                                            (pop basis-mark)
-                                            (incf ic)))
-                              (do ((term-list +empty-list+)
-                                   (il (1- m) (1- il)))
-                                  ((minusp il) (make-cmbn :degr degr
-                                                          :list term-list))
-                                (declare
-                                 (list term-list)
-                                 (fixnum il))
-                                (let ((cffc (aref rslt-cffcs il)))
-                                  (declare (fixnum cffc))
-                                  (unless (zerop cffc)
-                                    (push (term cffc (nth il f+1-basis)) term-list))))))))
-      (the intr-mrph #'rslt))))
-    
-#|
-()
-(setf q (random-matrix 5 5 10))
-(setf g (echcm-kill-epi-g-intr 2 2 5 '(a b c d e)
-		      (list 0 0 0 q 0)))
-(funcall g (cmbn 2))
-(funcall g (cmbn 4 1 'a))
-(funcall g (cmbn 3 1 :gn-0 10 :gn-1 100 :gn-2))
-|#
-
-(DEFUN ECHCM-KILL-EPI-H-INTR (cmpr first n m f-basis f+1-basis mtrx-list)
-  (declare
-   (type cmprf cmpr)
-   (fixnum first n m)
-   (list f-basis f+1-basis mtrx-list))
-  (let ((lqxp-1 (mtrx-prdc (left-submatrix (fourth mtrx-list) n)
-                           (second mtrx-list))))
-    (declare (type matrix lqxp-1))
-    (flet ((rslt (cmbn)
-                 (declare (type cmbn cmbn))
-                 (with-cmbn (degr list) cmbn
-                            (unless (= degr first)
-                              (return-from rslt (zero-cmbn (1+ degr))))
-                            (let ((rslt-cffcs (make-array m :element-type 'fixnum
-                                                          :initial-element 0)))
-                              (declare (type (array fixnum *) rslt-cffcs))
-                              (do ((cmbn-mark list (cdr cmbn-mark))
-                                   (basis-mark f-basis)
-                                   (ic 0))
-                                  ((endp cmbn-mark))
-                                (declare
-                                 (list cmbn-mark basis-mark)
-                                 (fixnum ic))
-                                (with--term (cffc gnrt) cmbn-mark
-                                            (loop (when (eq :equal (funcall cmpr gnrt (car basis-mark)))
-                                                    (return))
-                                                  (pop basis-mark)
-                                                  (incf ic))
-                                            (dotimes (il m)
-                                              (incf (aref rslt-cffcs il)
-                                                    (* cffc (aref lqxp-1 il ic))))
-                                            (pop basis-mark)
-                                            (incf ic)))
-                              (do ((term-list +empty-list+)
-                                   (il (1- m) (1- il)))
-                                  ((minusp il) (make-cmbn :degr (1+ degr)
-                                                          :list term-list))
-                                (declare
-                                 (list term-list)
-                                 (fixnum il))
-                                (let ((cffc (aref rslt-cffcs il)))
-                                  (declare (fixnum cffc))
-                                  (unless (zerop cffc)
-                                    (push (term cffc (nth il f+1-basis)) term-list))))))))
-      (the intr-mrph #'rslt))))
-	      
-#|
-()
-(setf p-1 (random-matrix 2 2 10))
-(setf q (random-matrix 5 5 10))
-(setf h (echcm-kill-epi-h-intr #'s-cmpr 2 2 5 '(a b) '(a b c d e)
-		      (list 0 p-1 0 q 0)))
-(funcall h (cmbn 2 1 'a 1000 'b))
-(funcall h (cmbn 4 1 'a))
-|#
-
-(DEFUN ECHCM-WITHOUT-EPI (echcm first n m intr-f)
-  (declare
-    (type chain-complex echcm)
-    (fixnum first n m)
-    (type intr-mrph intr-f))
-  (the chain-complex
-  (with-slots (cmpr basis dffr orgn) echcm
-    (declare
-      (type cmprf cmpr)
-      (type basis basis)
-      (type morphism dffr)
-      (list orgn))
-    (build-chcm
-     :cmpr #'(lambda (gnrt1 gnrt2)
-	       (if (and (symbolp gnrt1)
-			(eq (symbol-package gnrt1)
-			    +gnrts-pckg+))
-		   (s-cmpr gnrt1 gnrt2)
-		 (funcall cmpr gnrt1 gnrt2)))
-     :basis #'(lambda (degr)
-		(declare (fixnum degr))
-		(cond ((= degr first)
-		       +empty-list+)
-		      ((= degr (1+ first))
-		       (gnrt-name-basis (- m n)))
-		      (t
-		       (funcall basis degr))))
-     :intr-dffr #'(lambda (cmbn)
-		    (declare (type cmbn cmbn))
-		    (case (- (cmbn-degr cmbn) first)
-		      (1 (zero-cmbn first))
-		      (2 (funcall intr-f
-			   (cmbn-? dffr cmbn)))
-		      (otherwise
-		         (cmbn-? dffr cmbn))))
-     :strt :cmbn
-     :orgn `(echcm-without-epi ,echcm)))))
-
-(DEFUN ECHCM-KILL-EPI (echcm first)
-  (declare
-    (type chain-complex echcm)
-    (fixnum first))
-  (the reduction
-  (with-slots (cmpr basis) echcm
-    (declare
-      (type cmprf cmpr)
-      (type basis basis))
-    (assert (not (eq basis :locally-effective)))
-    (let* ((f-basis (funcall basis first))
-	   (f+1-basis (funcall basis (1+ first)))
-	   (mtrx-list (smith (chcm-mtrx echcm (1+ first))))
-	   (smith (third mtrx-list))
-	   (m (column-number smith))
-	   (n (line-number smith))
-	   (intr-f (echcm-kill-epi-f-intr cmpr first n m
-				    f+1-basis
-				    mtrx-list))
-	   (intr-g (echcm-kill-epi-g-intr first n m f+1-basis mtrx-list))
-	   (intr-h (echcm-kill-epi-h-intr cmpr first n m
-				    f-basis f+1-basis
-				    mtrx-list))
-	   (echcm2 (echcm-without-epi echcm first n m intr-f)))				      
-      (declare
-        (list mtrx-list)
-	(type matrix smith)
-	(fixnum m n)
-	(type intr-mrph intr-f intr-g intr-h)
-	(type chain-complex echcm2))
-      (assert (dotimes (i n +true+)
-		(unless (= 1 (aref smith i i))
-		  (return +false+))))
-      (build-rdct
-       :f (build-mrph
-	    :sorc echcm :trgt echcm2 :degr 0
-	    :intr intr-f :strt :cmbn
-	    :orgn `(echcm-kill-epi-f ,echcm))
-       :g (build-mrph
-	    :sorc echcm2 :trgt echcm :degr 0
-	    :intr intr-g :strt :cmbn
-	    :orgn `(echcm-kill-epi-g ,echcm))
-       :h (build-mrph
-	    :sorc echcm :trgt echcm :degr +1
-	    :intr intr-h :strt :cmbn
-	    :orgn `(echcm-kill-epi-h ,echcm))
-       :orgn `(echcm-kill-epi ,echcm))))))
-
-#|
-(cat-init)
-(setf s3 (sphere 3))
-(setf s3-chml-clss (chml-clss 's3))
-(setf s3-fibration (z-whitehead s3 3 s3-chml-clss))
-(setf s3-4 (fibration-total s3-fibration))
-(setf ecc (echcm s3-4))
-(setf rdct (echcm-kill-epi ecc 2))
-(pre-check-rdct rdct)
-(setf *tc* (cmbn 0 1 (bsgn ecc))
-      *bc* *tc*)
-(check-rdct)
-(setf *tc* (cmbn 2 1 (first (basis ecc 2))))
-(check-rdct)
-(setf *tc* (cmbn 3 1 (first (basis ecc 3))))
-(check-rdct)
-(setf *tc* (cmbn 4 1 (first (basis ecc 4)))
-      *bc* *tc*)
-(check-rdct)
-(setf s3-4-chml-clss (chml-clss 's3-4))
-(setf s3-4-fibration (z2-whitehead s3-4 4 s3-4-chml-clss))
-(setf s3-5 (fibration-total s3-4-fibration))
-(setf ecc (echcm s3-5))
-(dotimes (i 7)
-  (format t "~%DIM = ~D ; LENGTH = ~D" i (length (basis ecc i))))
-(setf rdct1 (echcm-kill-epi ecc 2))
-(setf rdct2 (echcm-kill-epi (bcc rdct1) 3))
-(setf rdct3 (echcm-kill-epi (bcc rdct2) 4))
-(setf rdct12 (cmps rdct2 rdct1))
-(setf rdct123 (cmps rdct3 rdct12))
-(pre-check-rdct rdct123)
-(setf *tc* (cmbn 0 1 (bsgn ecc)) *bc* *tc*)
-(check-rdct)
-(setf *tc* (cmbn 2 1 (first (basis ecc 2))))
-(check-rdct)
-(let ((b3 (basis ecc 3)))
-  (setf *tc* (cmbn 3 1 (first b3) 10 (second b3))))
-(check-rdct)
-(let ((b4 (basis ecc 4)))
-  (setf *tc* (cmbn 4 1 (first b4) 10 (second b4))))
-(check-rdct)
-(let ((b5 (basis ecc 5)))
-  (setf *tc* (cmbn 5 1 (first b5)
-		     10 (second b5)
-		     100 (third b5)
-		     1000 (fourth b5))))
-(check-rdct)
-(let ((b6 (basis ecc 6)))
-  (setf *tc* (cmbn 6 1 (first b6)
-		     10 (second b6)
-		     100 (third b6)
-		     1000 (fourth b6)
-		     10000 (fifth b6)
-		     100000 (sixth b6)
-		     1000000 (seventh b6))))
-(check-rdct)
-|#
- 
-(DEFUN KILL-EPI (chcm first)
-  (declare
-    (type chain-complex chcm)
-    (fixnum first))
-  (the homotopy-equivalence
-    (let ((efhm (efhm chcm))
-	  (echcm (echcm chcm)))
-      (declare
-        (type homotopy-equivalence efhm)
-	(type chain-complex echcm))
-      (let ((last-rdct (echcm-kill-epi echcm first)))
-	(declare (type reduction last-rdct))
-	(setf (slot-value chcm 'efhm)
-	      (build-hmeq
-	        :lrdct (lrdct efhm)
-	        :rrdct (cmps last-rdct (rrdct efhm))
-	        :orgn `(kill-epi ,chcm ,first)))))))
-
-(DEFUN KILL-EPIS (chcm first end)
-  (declare
-    (type chain-complex chcm)
-    (fixnum first end))
-  (the homotopy-equivalence (progn
-    (do ((indx first (1+ indx)))
-	((= indx end))
-        (declare (fixnum indx))
-      (kill-epi chcm indx))
-    (efhm chcm))))
-
-#|
-(cat-init)
-(setf s3 (sphere 3))
-(setf s3-chml-clss (chml-clss 's3))
-(setf s3-fibration (z-whitehead s3 3 s3-chml-clss))
-(setf s3-4 (fibration-total s3-fibration))
-(setf s3-4-chml-clss (chml-clss 's3-4))
-(setf s3-4-fibration (z2-whitehead s3-4 4 s3-4-chml-clss))
-(setf s3-5 (fibration-total s3-4-fibration))
-(time (homology s3-5 6))
-(kill-epis s3-5 2 5)
-(homology s3-5 0 7)
-
-(cat-init)
-(setf s3 (sphere 3))
-(setf s3-chml-clss (chml-clss 's3))
-(setf s3-fibration (z-whitehead s3 3 s3-chml-clss))
-(setf s3-4 (fibration-total s3-fibration))
-(kill-epi s3-4 2)
-(setf s3-4-chml-clss (chml-clss 's3-4))
-(setf s3-4-fibration (z2-whitehead s3-4 4 s3-4-chml-clss))
-(setf s3-5 (fibration-total s3-4-fibration))
-(time (homology s3-5 6))
-|#
-
-(DEFUN CHML-CLSS-INTR (chcm first)
-  (declare
-    (type chain-complex chcm)
-    (fixnum first))
-  (let* ((echcm (echcm chcm))
-	 (cmpr (cmpr echcm))
-	 (basis (basis echcm))
-	 (f-basis (funcall basis first))
-	 (mtrx-list (smith (chcm-mtrx echcm (1+ first))))
-	 (p-1 (second mtrx-list))
-	 (smith (third mtrx-list))
-	 (n (line-number smith))
-	 (m (column-number smith))
-         (diag-indx (dotimes (indx (min n m)
-			       (if (> n m)
-				   m
-				 (error "In CHML-CLSS, the cohomology-ring ~@
-                                      is null.")))
-		      (declare (fixnum indx))
-		      (unless (= 1 (aref smith indx indx))
-			(return indx)))))
-    (declare
-      (type chain-complex echcm)
-      (type cmprf cmpr)
-      (type basis basis)
-      (fixnum n m diag-indx)
-      (list f-basis mtrx-list)
-      (type matrix p-1 smith))
-    (flet ((rslt (cmbn)
-	     (declare (type cmbn cmbn))
-	     (with-cmbn (degr list) cmbn
-	       (unless (= degr first)
-		 (return-from rslt (zero-cmbn (- degr first))))
-	       (do ((rslt 0)
-		    (bmark f-basis)
-		    (ic 0)
-		    (cmark list (cdr cmark)))
-		   ((endp cmark)
-		    (if (zerop rslt)
-			(zero-cmbn 0)
-		      (term-cmbn 0 rslt :z-gnrt)))
-		   (declare
-		     (fixnum rslt)
-		     (list bmark cmark))
-		 (with--term (cffc gnrt) cmark
-		   (loop
-		    (when (eq :equal (funcall cmpr gnrt (car bmark)))
-		      (return))
-		    (pop bmark)
-		    (incf ic))
-		   (incf rslt (* cffc (aref p-1 diag-indx ic)))
-		   (pop bmark)
-		   (incf ic))))))
-      (the intr-mrph #'rslt))))
-
-#|
-(cat-init)
-(setf s3 (sphere 3))
-(setf c (chml-clss-intr s3 3))
-(funcall c (cmbn 3 5 's3))
-(setf s3-chml-clss (chml-clss 's3))
-(setf s3-fibration (z-whitehead s3 3 s3-chml-clss))
-(setf s3-4 (fibration-total s3-fibration))
-(kill-epi s3-4 2)
-(setf c (chml-clss-intr s3-4 4))
-(funcall c (cmbn 4 5 (first (basis (echcm s3-4) 4))))
-(setf s3-4-chml-clss (chml-clss 's3-4))
-(setf s3-4-fibration (z2-whitehead s3-4 4 s3-4-chml-clss))
-(setf s3-5 (fibration-total s3-4-fibration))
-(kill-epis s3-5 3 5)
-(setf c (chml-clss-intr s3-5 5))
-(let ((b5 (basis (echcm s3-5) 5)))
-  (funcall c (cmbn 5 1 (first b5) 10 (second b5))))
-|#
-
-(DEFUN CHML-CLSS (chcm first)
-  (declare
-    (type chain-complex chcm)
-    (fixnum first))
-  (the morphism
-    (build-mrph
-      :sorc (echcm chcm) :trgt (z-chcm) :degr (- first)
-      :intr (chml-clss-intr chcm first)
-      :strt :cmbn
-      :orgn `(chml-clss ,chcm ,first))))
-
-#|
-(cat-init)
-(setf s3 (sphere 3))
-(setf s3-chml-clss (chml-clss s3 3))
-(setf s3-fibration (z-whitehead s3 3 s3-chml-clss))
-(setf s3-4 (fibration-total s3-fibration))
-(homology s3-4 0 6)
-(kill-epi s3-4 2)
-(setf s3-4-chml-clss (chml-clss s3-4 4))
-(setf s3-4-fibration (z2-whitehead s3-4 4 s3-4-chml-clss))
-(setf s3-5 (fibration-total s3-4-fibration))
-(homology s3-5 0 6)
-(kill-epis s3-5 3 5)
-(setf s3-5-chml-clss (chml-clss s3-5 5))
-(setf s3-5-fibration (z2-whitehead s3-5 5 s3-5-chml-clss))
-(setf s3-6 (fibration-total s3-5-fibration))
-(homology s3-6 0 7)
-|#
diff --git a/archive/Kenzo-1/special-smsts.cl b/archive/Kenzo-1/special-smsts.cl
deleted file mode 100644
index 45d5eeb..0000000
--- a/archive/Kenzo-1/special-smsts.cl
+++ /dev/null
@@ -1,688 +0,0 @@
-;;;  SPECIAL-SMSTS  SPECIAL-SMSTS  SPECIAL-SMSTS  SPECIAL-SMSTS  SPECIAL-SMSTS
-;;;  SPECIAL-SMSTS  SPECIAL-SMSTS  SPECIAL-SMSTS  SPECIAL-SMSTS  SPECIAL-SMSTS
-;;;  SPECIAL-SMSTS  SPECIAL-SMSTS  SPECIAL-SMSTS  SPECIAL-SMSTS  SPECIAL-SMSTS
-
-(IN-PACKAGE "COMMON-LISP-USER")
-
-(PROVIDE "special-smsts")
-
-;;; GMSM-FACES-INFO = (gmsm (simple-vector absm) . bndr)
-;;;                         faces
-
-(DEFUN FINITE-SS-PRE-TABLE (list)
-   (declare (list list))
-   (the list
-      (let ((pre-rslt +empty-list+)
-            (dmns-mark nil)
-            (gmsm-mark nil))
-         (declare (list pre-rslt dmns-mark gmsm-mark))
-         (dolist (item list)
-            (declare (type (or fixnum symbol list) item))
-            (cond ((typep item 'fixnum)
-                   (let ((found (assoc item pre-rslt)))
-                      (declare (list found))
-                      (setf dmns-mark 
-                            (or found
-                                (car (push (list item) pre-rslt)))
-                            gmsm-mark nil)))
-                  ((symbolp item)
-                   (when (assoc item (cdr dmns-mark))
-                      (error "In BUILD-FINITE-SS, the symbol ~A is present two times."
-                         item))
-                   (setf gmsm-mark (car (push (list item) (cdr dmns-mark)))))
-                  ((listp item)
-                   (unless gmsm-mark
-                      (error "In BUILD-FINITE-SS, the face list ~A~@
-                              is not after a symbol." item))
-                   (nconc gmsm-mark item)
-                   (setf gmsm-mark nil))
-                  (t
-                     (error "In BUILD-FINITE-SS, the argument ~A does not make sense." item))))         
-         (do ((mark1 pre-rslt (cdr mark1)))
-             ((endp mark1))
-             (declare (list mark1))
-            (do ((mark2 (rest mark1) (cdr mark2)))
-                ((endp mark2))
-               (declare (list mark2))
-               (let ((inter (intersection (cdar mark1) (cdar mark2) :key #'first)))
-                  (declare (list inter))
-                  (when inter
-                     (error "In BUILD-FINITE-SS, the symbol ~A is present two times."
-                        (caar inter))))))
-         pre-rslt)))
-
-#|
-  (setf p (finite-ss-pre-table '(0 v0 v1 v2)))
-  (finite-ss-pre-table '(0 v0 v0 v2))
-  (setf p (finite-ss-pre-table '(0 v0 v1 1 e0 e1 e2)))
-  (finite-ss-pre-table '(0 v0 v1 1 e0 e1 v1))
-  (setf p (finite-ss-pre-table '(0 v0 (v0 v0))))
-  (setf p (finite-ss-pre-table '(0 v0 v1 v2 0 v3)))
-  (finite-ss-pre-table '(0 v0 (v0 v0) (v1 v1)))
-  (finite-ss-pre-table '(0 (v0 v0) (v1 v1)))
-  (finite-ss-pre-table '(0 v0 (v0 v0) #(1 2))))
-|#
-
-(DEFUN FINITE-SS-PRE-TABLE-TABLE (pre-table)
-   (declare (list pre-table))
-   (let* ((maxdim (1+ (apply #'max (mapcar #'first pre-table))))
-          (table (make-array maxdim :initial-element +empty-list+)))
-      (declare
-         (fixnum maxdim)
-         (simple-vector table))
-      (dolist (item pre-table)
-         (declare (list item))
-         (setf (svref table (first item))
-               (sort (rest item) #'string< :key #'first)))
-      table))
-
-#|
-  (setf p (finite-ss-pre-table-table
-             (finite-ss-pre-table '(2 v0 (e1 e2) v1 1 e0 e1 e2)))))
-|#
-
-(DEFUN FINITE-SS-FIND-GMSM (table gmsm dmns &optional (max-dmns (1+ dmns)))
-   (declare
-      (type gmsm gmsm)
-      (fixnum dmns max-dmns))
-   (do ((dmns dmns (1+ dmns)))
-       ((>= dmns max-dmns) nil)
-      (declare (fixnum dmns))
-      (let ((found (find gmsm (svref table dmns) :test #'eq :key #'car)))
-         (declare (type (or cons null) found))
-         (when found
-            (return-from finite-ss-find-gmsm dmns)))))
- 
-(DEFUN FINITE-SS-FINISH-TABLE (table bspn)
-   (declare (simple-vector table))
-   (dotimes (dmns (length table))
-      (declare (fixnum dmns))
-      (finite-ss-finish-line table dmns bspn))
-   table)
-
-(DEFUN FINITE-SS-FINISH-LINE (table dmns bspn)
-   (declare
-      (simple-vector table)
-      (fixnum dmns))
-   (setf (svref table dmns)
-         (mapcar
-            #'(lambda (entry)
-                 (finite-ss-finish-entry table entry dmns bspn))
-            (svref table dmns))))
-
-(DEFUN FINITE-SS-FINISH-ENTRY (table entry dmns bspn)
-   (declare
-      (simple-vector table)
-      (list entry)
-      (fixnum dmns)
-      (symbol bspn))
-   (let ((simplex (first entry))
-         (faces (rest entry)))
-      (declare
-         (symbol simplex)
-         (list faces))
-      (when (zerop dmns)
-         (return-from finite-ss-finish-entry
-            (make-gmsm-faces-info
-               :gmsm simplex :faces +s-empty-vector+
-               :bndr +zero-negative-cmbn+)))
-      (setf faces (nconc faces (make-list (1+ (- dmns (length faces)))
-                                  :initial-element bspn)))
-      (let ((rslt (make-gmsm-faces-info :gmsm simplex)))
-         (declare (cons rslt))
-         (flet ((process-face (face)
-                 (declare (type (or symbol list) face))
-                 (when (symbolp face)
-                    (setf face (list face)))
-                 (let* ((gmsm2 (car (last face)))
-                        (dgop-ext (nbutlast face))
-                        (dmns2 (finite-ss-find-gmsm table gmsm2 0 dmns)))
-                    (declare
-                       (symbol gmsm2)
-                       (list dgop-ext)
-                       (type (or fixnum null) dmns2))
-                    (unless dmns2
-                       (error "In BUILD-FINITE-SS, the face ~A is absent." gmsm2))
-                    (when (zerop (length dgop-ext))
-                       (setf dgop-ext (nreverse (<a-b< dmns2 (1- dmns)))))
-                    (unless (= (+ (length dgop-ext) dmns2 1) dmns)
-                       (error "In BUILD-FINITE-SS, the face ~A has a wrong dimension."
-                          (append dgop-ext (list gmsm2))))
-                    (absm (dgop-ext-int dgop-ext) gmsm2))))
-            (setf (info-faces rslt)
-                  (map 'simple-vector #'process-face faces))
-            (setf (info-bndr rslt)
-                  (apply #'nterm-add #'s-cmpr (1- dmns)
-                     (do ((rslt +empty-list+)
-                          (faces (info-faces rslt))
-                          (indx dmns (1- indx)))
-                         ((minusp indx) rslt)
-                        (declare
-                           (list rslt)
-                           (simple-vector faces)
-                           (fixnum indx))
-                        (let ((face (svref faces indx)))
-                           (declare (type absm face))
-                           (unless (degenerate-p face)
-                              (push (term (-1-expt-n indx) (gmsm face))
-                                 rslt))))))
-            rslt))))
-
-(DEFUN FINITE-SS-TABLE (list)
-   (declare (list list))
-   (setf list (cons 0 list))
-   (let* ((bspn (second list))
-          (pre-table (finite-ss-pre-table list))
-          (table (finite-ss-pre-table-table pre-table)))
-      (declare
-         (symbol bspn)
-         (list pre-table)
-         (simple-vector table))
-      ;; (vector (vector gmsm-faces-info))
-      (finite-ss-finish-table table bspn)))
-
-#|
-  (finite-ss-table '(*))
-  (finite-ss-table '(a b))
-  (finite-ss-table '(a b 1 c (b a)))
-  (finite-ss-table '(* 2 s2 3 s3))
-  (finite-ss-table '(s0 s1 s2 1 s01 (s1 s0) s02 (s2 s0) s12 (s2 s1) 2 s012 (s12 s02 s01)))
-  (finite-ss-table '(* 4 s4 ((2 1 0 *))))
-  (finite-ss-table '(* 4 s4 ((1 1 0 *))))
-  (finite-ss-table '(* 1 s (t)))
-  (finite-ss-table '(* 4 s4 ((1 0 *)))))
-|#
-
-(DEFUN FINITE-SS-BASIS (table)
-   (declare (simple-vector table))
-   (flet ((rslt (dmns)
-             (declare (fixnum dmns))
-             (the list
-                (if (< -1 dmns (length table))
-                   (mapcar #'car (svref table dmns))
-                   +empty-list+))))
-      #'rslt))
-
-(DEFUN FINITE-SS-FACE (ind-smst table)
-   (declare
-      (symbol ind-smst)
-      (simple-vector table))
-   (flet ((rslt (indx dmns gmsm)
-           (declare
-              (fixnum indx dmns)
-              (symbol gmsm))
-           (let ((found (find gmsm (svref table dmns) :key #'car)))
-              (unless found
-                 (error "In the finite simplicial set ~A,~@
-                         the simplex ~A is absent in dimension ~D." (eval ind-smst) gmsm dmns))
-              (svref (info-faces found) indx))))
-      #'rslt))
-
-(DEFUN FINITE-SS-INTR-BNDR (ind-smst table)
-   (declare
-      (symbol ind-smst)
-      (simple-vector table))
-   (flet ((rslt (dmns gmsm)
-           (declare
-              (fixnum dmns)
-              (symbol gmsm))
-           (let ((found (find gmsm (svref table dmns) :key #'car)))
-              (unless found
-                 (error "In the finite simplicial set ~A,~@
-                         the simplex ~A is absent in dimension ~D." (eval ind-smst) gmsm dmns))
-              (info-bndr found))))
-      #'rslt))
-
-(DEFUN BUILD-FINITE-SS (list)
-   (declare (list list))
-   (let ((bspn (first list))
-         (table (finite-ss-table list))
-         (ind-smst (gensym)))
-      (declare
-         (symbol bspn ind-smst)
-         (simple-vector table))
-      ;;  (vector (vector gmsm-faces-info))
-      (let ((rslt (build-smst
-                     :cmpr #'s-cmpr
-                     :basis (finite-ss-basis table)
-                     :bspn bspn
-                     :face (finite-ss-face ind-smst table)
-                     :intr-bndr (finite-ss-intr-bndr ind-smst table)
-                     :bndr-strt :gnrt
-                     :orgn `(build-finite-ss ,list))))
-         (setf (symbol-value ind-smst) rslt)
-         (unless (check-smst rslt 0 (length table))
-            (pop *smst-list*)
-            (pop *chcm-list*)
-            (pop *mrph-list*)
-            (return-from build-finite-ss nil))
-         rslt)))
-
-#|
-()
-(cat-init)
-(setf tr (build-finite-ss '(s0 s1 s2
-                               1 s01 (s1 s0) s02 (s2 s0) s12 (s2 s1)
-                               2 s012 (s12 s02 s01))))
-(cmpr tr 's01 's02)
-(basis tr 2)
-(bspn tr)
-(face tr 1 2 's012)
-(? tr 2 's012)
-(? tr *)
-(inspect tr)
-(mapcar #'(lambda (s) (length (eval s))) *list-list*)
-(setf tr (build-finite-ss '(s0 s1 s2
-                               1 s01 (s1 s1) s02 (s2 s0) s12 (s2 s1)
-                               2 s012 (s12 s02 s01))))
-(mapcar #'(lambda (s) (length (eval s))) *list-list*))
-|#
-
-(DEFUN SPHERE-CMPR (gmsm1 gmsm2)
-   (declare (ignore gmsm1 gmsm2))
-   (the cmpr :equal))
-
-(DEFUN SPHERE-BASIS (dmns)
-   (declare (fixnum dmns))
-   (let ((fund-gmsm (intern (format nil "S~D" dmns))))
-      (declare (symbol fund-gmsm))
-      (flet ((rslt (dmns2)
-                (declare (fixnum dmns2))
-                (cond ((zerop dmns2)
-                       (list '*))
-                      ((= dmns2 dmns)
-                       (list fund-gmsm))
-                      (t
-                         +empty-list+))))
-         (the basis #'rslt))))
-
-(DEFUN SPHERE-FACE (dmns)
-   (declare (fixnum dmns))
-   (let ((face (absm (mask (1- dmns)) '*)))
-      (declare (type absm face))
-      (flet ((rslt (indx dmns2 gmsm)
-                (declare (ignore indx dmns2 gmsm))
-                (the absm face)))
-         #'rslt)))
-
-(DEFUN SPHERE (dmns)
-   (declare (fixnum dmns))
-   (unless (plusp dmns)
-      (error "In SPHERE, the dimension ~D should be positive." dmns))
-   (unless (< dmns +maximal-dimension+)
-      (error "In SPHERE, the dimension ~D should be < ~D."
-         dmns +maximal-dimension+))
-   (the simplicial-set
-      (let ((rslt (build-smst
-                     :cmpr #'sphere-cmpr
-                     :basis (sphere-basis dmns)
-                     :bspn '*
-                     :face (sphere-face dmns)
-                     :intr-bndr #'zero-intr-dffr
-                     :bndr-strt :cmbn
-                     :orgn `(sphere ,dmns))))
-         (declare (type simplicial-set rslt))
-         (setf (slot-value (bndr rslt) 'orgn)
-               `(zero-mrph ,rslt ,rslt -1))
-         rslt)))
-
-#|
-  (cat-init)
-  (setf s3 (sphere 3))
-  (funcall (cmpr s3) 's3 's3)
-  (dotimes (i 5)
-     (print (funcall (basis s3) i)))
-  (mapcar #'(lambda (i) (funcall (face s3) i 3 's3)) (<a-b> 0 3))
-  (? s3 3 's3)
-  (smst (idnm s3))
-  (chcm (idnm s3))
-  (setf d (bndr s3))
-  (add d d))
-|#
-
-(DEFUN SPHERE-WEDGE-BASIS (dmns-list)
-   (declare (list dmns-list))
-   (flet ((rslt (dmns)
-             (declare (fixnum dmns))
-             (when (zerop dmns)
-                (return-from rslt '(*)))
-             (do ((i (count dmns dmns-list) (1- i))
-                  (basis +empty-list+
-                         (cons (intern (format nil "S~D-~D" dmns i))
-                               basis)))
-                 ((zerop i) basis)
-                (declare
-                   (fixnum i)
-                   (list basis)))))
-      (the basis #'rslt)))
-
-(DEFUN SPHERE-WEDGE-FACE (indx dmns gmsm)
-   (declare
-      (ignore indx gmsm)
-      (fixnum dmns))
-   (the absm
-      (absm (mask (1- dmns)) '*)))
-
-(DEFUN SPHERE-WEDGE (&rest dmns-list)
-   (declare (list dmns-list))
-   (the simplicial-set
-      (let ((rslt (build-smst
-                     :cmpr #'s-cmpr
-                     :basis (sphere-wedge-basis dmns-list)
-                     :face #'sphere-wedge-face
-                     :intr-bndr #'zero-intr-dffr
-                     :bndr-strt :cmbn
-                     :orgn `(sphere-wedge ,@dmns-list))))
-         (declare (type simplicial-set rslt))
-         (setf (slot-value (bndr rslt) 'orgn)
-               `(zero-mrph ,rslt ,rslt -1))
-         rslt)))
-
-#|
-  (cat-init)
-  (setf w (sphere-wedge 3 2 3))
-  (funcall (cmpr w) 's3-1 's3-2)
-  (dotimes (i 5) (print (funcall (basis w) i)))
-  (funcall (face w) 2 3 's3-1)
-  (gnrt-? (bndr w) 3 's3-2))
-|#
-
-(DEFUN MOORE-CMPR (gmsm1 gmsm2)
-   (declare (ignore gmsm1 gmsm2))
-   (the cmpr :equal))
-
-(DEFUN MOORE-BASIS (dmns)
-   (declare (fixnum dmns))
-   (let ((lgmsm1 (list (intern (format nil "M~D" dmns))))
-         (lgmsm2 (list (intern (format nil "N~D" (1+ dmns))))))
-      (declare (list lgmsm1 lgmsm2))
-      (flet ((rslt (dmns2)
-                (declare (fixnum dmns2))
-                (cond ((zerop dmns2) '(*))
-                      ((= dmns dmns2) lgmsm1)
-                      ((= (1+ dmns) dmns2) lgmsm2)
-                      (t +empty-list+))))
-         (the basis #'rslt))))
-
-(DEFUN MOORE-FACE (pii dmns)
-   (declare (fixnum pii dmns))
-   (let ((face (absm 0 (intern (format nil "M~D" dmns))))
-         (bspn1 (absm (mask (1- dmns)) '*))
-         (bspn2 (absm (mask dmns) '*))
-         (2pii (ash pii 1)))
-      (declare
-         (type absm face)
-         (type absm bspn1 bspn2)
-         (fixnum 2pii))
-      (flet ((rslt (indx dmns2 gmsm)
-                (declare
-                   (fixnum indx dmns2)
-                   (ignore gmsm))
-                (the absm
-                   (if (= dmns dmns2)
-                      bspn1
-                      (if (oddp indx)
-                         bspn2
-                         (if (< indx 2pii)
-                            face
-                            bspn2))))))
-         (the face #'rslt))))
-
-(DEFUN MOORE-INTR-BNDR (pii dmns)
-   (declare (fixnum pii dmns))
-   (let ((1+dmns (1+ dmns))
-         (gmsm1 (intern (format nil "M~D" dmns))))
-      (declare
-         (fixnum 1+dmns)
-         (type symbol gmsm1))
-      (flet ((rslt (cmbn)
-                (declare
-                   (type cmbn cmbn))
-                (with-cmbn (degr list) cmbn
-                   (unless list
-                      (return-from rslt (zero-cmbn (1- (cmbn-degr cmbn)))))
-                   (if (= degr 1+dmns)
-                      (term-cmbn dmns (* (cffc (first list)) pii) gmsm1)
-                      (zero-cmbn (1- (cmbn-degr cmbn)))))))
-         (the intr-mrph #'rslt))))
-
-(DEFUN MOORE (pii dmns)
-   (declare (fixnum pii dmns))
-   (the simplicial-set
-      (build-smst
-         :cmpr #'moore-cmpr
-         :basis (moore-basis dmns)
-         :face (moore-face pii dmns)
-         :intr-bndr (moore-intr-bndr pii dmns)
-         :bndr-strt :cmbn
-         :orgn `(moore ,pii ,dmns))))
-
-#|
-  (cat-init)
-  (setf m4 (moore 2 4))
-  (cmpr m4 'n5 'n5)
-  (dotimes (i 7)
-     (print (basis m4 i)))
-  (mapcar #'(lambda (i) (face m4 i 5 'n5)) (<a-b> 0 5))
-  (? m4 4 'm4)
-  (? m4 5 'n5))
-|#
-
-(DEFUN R-PROJ-SPACE-CMPR (gmsm1 gmsm2)
-   (declare (ignore gmsm1 gmsm2))
-   (the cmpr :equal))
-
-(DEFUN R-PROJ-SPACE-BASIS (k l)
-  (declare (fixnum k) (type (or (eql :infinity) fixnum) l))
-  (the basis
-    (progn
-      (when (eq l :infinity)
-        (setf l most-positive-fixnum))
-      (flet
-          ((rslt (dmns)
-                 (declare (fixnum dmns))
-                 (the list
-                   (if (or (minusp dmns)
-                           (< 0 dmns k)
-                           (>= dmns l))
-                       +empty-list+
-                     (list dmns)))))
-        (the basis #'rslt)))))
-
-#|
-()
-(setf b (r-proj-space-basis 1 :infinity))
-(dotimes (i 5) (print (funcall b i)))
-(setf b (r-proj-space-basis 1 5))
-(dotimes (i 8) (print (funcall b i)))
-(setf b (r-proj-space-basis 3 :infinity))
-(dotimes (i 5) (print (funcall b i)))
-(setf b (r-proj-space-basis 3 6))
-(dotimes (i 10) (print (funcall b i)))
-|#
-
-(DEFUN R-PROJ-SPACE-FACE (k)
-   (declare (fixnum k))
-   (flet ((rslt (indx dmns gmsm)
-           (declare
-	      (fixnum indx dmns)
-	      (ignore gmsm))
-           (if (<= dmns k)
-              (absm (mask (1- dmns)) 0)
-              (if (or (zerop indx)
-                      (= indx dmns))
-                 (absm 0 (1- dmns))
-                 (if (= dmns (1+ k))
-                    (absm (mask (1- dmns)) 0)
-                    (absm (2-exp (1- indx)) (- dmns 2)))))))
-      (the face #'rslt)))
-
-(DEFUN R-PROJ-SPACE-INTR-BNDR (k)
-   (declare (fixnum k))
-   (flet ((rslt (cmbn)
-           (declare (type cmbn cmbn))
-           (with-cmbn (degr list) cmbn
-              (unless list
-                 (return-from rslt (zero-cmbn (1- degr))))
-              (if (<= degr k)
-                 (zero-cmbn (1- degr))
-                 (if (evenp degr)
-                    (make-cmbn
-                       :degr (1- degr)
-                       :list (list (term (* 2 (-cffc list)) (1- degr))))
-                    (zero-cmbn (1- degr)))))))
-      (the intr-mrph #'rslt)))
-
-(DEFUN R-PROJ-SPACE (&optional (l :infinity) (k 1))
-  (declare (fixnum k) (type (or fixnum (eql :infinity))))
-  (assert
-   (and (typep k 'fixnum)
-        (plusp k)
-        (or (eq l :infinity)
-            (and (typep l 'fixnum)
-                 (<= k l)))))    
-  (the simplicial-set
-    (build-smst
-     :cmpr #'R-proj-space-cmpr
-     :basis (R-proj-space-basis k l)
-     :bspn 0
-     :face (R-proj-space-face k)
-     :intr-bndr (R-proj-space-intr-bndr k)
-     :bndr-strt :cmbn
-     :orgn `(R-proj-space ,k ,l))))
-
-#|
-()
-(cat-init)
-(setf p (R-proj-space))
-(basis p 4)
-(dotimes (i 5)
-  (print (face p i 4 4)))
-(dotimes (i 5)
-  (print (? p i i)))
-(setf dd (cmps p p))
-(dotimes (i 6)
-  (print (? dd i i)))
-(setf p (R-proj-space 3))
-(dotimes (i 7)
-  (print (basis p i)))
-(dotimes (i 5)
-  (print (face p i 4 4)))
-(dotimes (i 7)
-  (print (? p i i)))
-(setf dd (cmps p p))
-(dotimes (i 7)
-  (print (? dd i i)))
-|#
-
-;;; Constructing a small simplicial subset
-;;; from a combination of simplices.
-
-(DEFUN CMBN-GMSMS (cmbn)
-  (declare (type cmbn cmbn))
-  (the list
-    ;; Returns a list made of:
-    ;;   the degree of the combination;
-    ;;   the list of simplex generators of the combinations.
-    (cons (cmbn-degr cmbn) (mapcar #'cdr (cmbn-list cmbn)))))
-
-#|
-()
-|#
-
-(DEFUN GMSMS-SUBSMST (smst gmsms
-                           &aux
-                           (dmns (typecase gmsms
-                                   (cmbn (cmbn-degr gmsms))
-                                   (otherwise (first gmsms))))
-                           (cmpr= #'(lambda (gmsm1 gmsm2)
-                                      (declare (type gmsm gmsm1 gmsm2))
-                                      (the boolean
-                                        (eq (cmpr smst gmsm1 gmsm2) :equal)))))                           
-  (declare
-   (type simplicial-set smst)
-   (type (or cmbn list) gmsms)
-   (fixnum dmns)
-   (type (function (gmsm gmsm) boolean) cmpr=))
-  (when (typep gmsms 'cmbn)
-    (setf gmsms (cmbn-gmsms gmsms)))
-  (the (values simplicial-set morphism)
-    (let ((prslt (make-array (1+ dmns) :initial-element +empty-list+)))
-      (declare (type simple-vector prslt))
-      (setf (svref prslt dmns) (rest gmsms))
-      (do ((d dmns (1- d)))
-          ((zerop d))
-        (declare (fixnum d))
-        (dolist (gmsm (svref prslt d))
-          (declare (type gmsm gmsm))
-          (dotimes (iface (1+ d))
-            (declare (fixnum iface))
-            (with-absm (dgop gmsm) (face smst iface d gmsm)
-                       (declare (fixnum dgop) (type gmsm gmsm))
-              (pushnew gmsm (svref prslt (- d 1 (logcount dgop)))
-                       :test cmpr=)))))
-      (let ((rslt-basis #'(lambda (k)
-                            (declare (fixnum dmns))
-                            (the list
-                              (if (<= 0 k dmns) 
-                                  (aref prslt k)
-                                +empty-list+)))))
-        (declare (type (function (fixnum) list) rslt-basis))
-        (let ((subsmst (build-smst
-                        :cmpr (cmpr smst)
-                        :basis rslt-basis
-                        :bspn (let ((bspn (bspn smst)))
-                                (declare (type gmsm bspn))
-                                (pushnew bspn (svref prslt 0) :test cmpr=)
-                                bspn)
-                        :face (face smst)
-                        :orgn `(gmsms-subsmst ,gmsms))))
-          (declare (type simplicial-set subsmst))
-          (values subsmst
-                  (build-mrph :sorc subsmst
-                              :trgt smst
-                              :degr 0
-                              :intr #'(lambda (cmbn)
-                                        (declare (type cmbn cmbn))
-                                        (the cmbn cmbn))
-                              :strt :cmbn
-                              :orgn `(gmsms-subsmst-incl ,gmsms))))))))
-                            
-                            
-                            
-#|
-()
-(cat-init)
-(setf k (k-z 2))
-(setf efhm (efhm k))
-(setf *homology-verbose* nil)
-(chcm-homology-gen (rbcc efhm) 4)
-(setf g (first *))
-(setf cmbn (lf efhm (rg efhm g)))
-(multiple-value-setq (kf incl) (gmsms-subsmst k cmbn))
-(setf cone (cone incl))
-(efhm cone)
-(homology kf 0 5)
-(homology (cone incl) 0 6)
-
-(chcm-homology-gen (rbcc efhm) 8)
-(setf g (first *))
-(setf cmbn (lf efhm (rg efhm g)))
-(multiple-value-setq (kf incl) (gmsms-subsmst k cmbn))
-(setf cone (cone incl))
-(efhm cone)
-(homology kf 0 9)
-(homology (cone incl) 0 10)
-(dotimes (i 9) (print (length (basis kf i))))
-
-()
-(setf s2 (sphere 2))
-(setf cl2 (chml-clss s2 2))
-(setf f2 (z-whitehead s2 cl2))
-(setf s3 (fibration-total f2))
-(setf efhm (efhm s3))
-(basis (rbcc efhm) 3)
-(setf cmbn (lf efhm (rg efhm 3 (first (basis (rbcc efhm) 3)))))
-(setf kf (gmsms-subsmst s3 cmbn))
-(homology kf 0 4)
-|#
\ No newline at end of file
diff --git a/archive/Kenzo-1/suspensions.cl b/archive/Kenzo-1/suspensions.cl
deleted file mode 100644
index 9e07aeb..0000000
--- a/archive/Kenzo-1/suspensions.cl
+++ /dev/null
@@ -1,321 +0,0 @@
-;;;  SUSPENSIONS  SUSPENSIONS  SUSPENSIONS  SUSPENSIONS
-;;;  SUSPENSIONS  SUSPENSIONS  SUSPENSIONS  SUSPENSIONS
-;;;  SUSPENSIONS  SUSPENSIONS  SUSPENSIONS  SUSPENSIONS
-
-(IN-PACKAGE "COMMON-LISP-USER")
-
-(PROVIDE "suspensions")
-
-(DEFUN SUSPENSION-CMPR (cmpr)
-  (declare (type cmprf cmpr))
-  (flet ((rslt (gnrt1 gnrt2)
-	   (declare (type gnrt gnrt1 gnrt2))
-	   (if (eq gnrt1 :s-bsgn)
-	       :equal
-	     (funcall cmpr gnrt1 gnrt2))))
-    (the cmprf #'rslt)))
-
-#|
-  (setf cc (deltab))
-  (setf cmpr (suspension-cmpr (cmpr cc)))
-  (funcall cmpr :s-bsgn :s-bsgn)
-  (funcall cmpr 6 5)
-|#
-
-(DEFUN SUSPENSION-BASIS (basis)
-  (declare (type basis basis))
-  (when (eq basis :locally-effective)
-    (return-from suspension-basis :locally-effective))
-  (flet ((rslt (degr)
-	   (declare (fixnum degr))
-	   (case degr
-	     (0 (list :s-bsgn))
-	     (1 +empty-list+)
-	     (otherwise (funcall basis (1- degr))))))
-    (the basis #'rslt)))
-
-#|
-  (setf cc (sphere 2))
-  (setf basis (suspension-basis (basis cc)))
-  (dotimes (i 6)
-    (print (funcall basis i)))
-  (suspension-basis :locally-effective)
-|#
-
-(DEFUN SUSPENSION-INTR-DFFR (dffr)
-  (declare (type morphism dffr))
-  (flet ((rslt (cmbn)
-	   (declare (type cmbn cmbn))
-	   (with-cmbn (degr list) cmbn
-	     (decf degr)
-	     (if (<= degr 0)
-		 (zero-cmbn degr)
-	       (make-cmbn :degr degr
-			  :list (cmbn-list
-				 (cmbn-? dffr
-				   (make-cmbn :degr degr
-					      :list list))))))))
-    (the intr-mrph #'rslt)))
-
-#|
-  (setf cc (deltab))
-  (setf intr (suspension-intr-dffr (dffr cc)))
-  (funcall intr (cmbn 0 3 :s-bsgn))
-  (funcall intr (cmbn 3 66 7))
-|#
-
-(DEFUN SUSPENSION (obj &optional (n 1))
-  (declare (type (or chain-complex morphism reduction
-		     homotopy-equivalence) obj)
-	   (fixnum n))
-  (if (= n 0)
-      obj
-    (suspension-1 (suspension obj (1- n)))))    
-
-(DEFMETHOD SUSPENSION-1 ((chcm chain-complex))
-  (the chain-complex
-    (with-slots (cmpr basis dffr) chcm
-      (build-chcm
-        :cmpr (suspension-cmpr cmpr)
-	:basis (suspension-basis basis)
-	:bsgn :s-bsgn
-	:intr-dffr (suspension-intr-dffr dffr)
-	:strt :cmbn
-	:orgn `(suspension ,chcm)))))
-
-#|
-  (cat-init)
-  (setf cc (deltab))
-  (setf scc (suspension cc))
-  (cmpr scc 7 11)
-  (basis scc 3)  ;; error
-  (bsgn scc)
-  (? scc 3 11)
-  (setf scc (suspension cc 2))
-  (? scc 4 11)
-|#
-
-(DEFUN SUSPENSION-INTR-CPRD (cmbn)
-  (declare (type cmbn cmbn))
-  (the cmbn
-    (with-cmbn (degr list) cmbn
-      (if (zerop degr)
-	  (make-cmbn :degr 0
-		     :list (if list
-			       (list (term (-cffc list)
-					   (tnpr 0 :s-bsgn
-						 0 :s-bsgn)))
-			     +empty-list+))
-	(make-cmbn :degr degr
-		   :list (let ((list1 +empty-list+)
-			       (list2 +empty-list+))
-			   (declare (list list1 list2))
-			   (mapc
-			    #'(lambda (term)
-				(declare (type term term))
-				(with-term (cffc gnrt) term
-				  (push (term cffc
-					      (tnpr 0 :s-bsgn
-						    degr gnrt))
-					list1)
-				  (push (term cffc
-					      (tnpr degr gnrt
-						    0 :s-bsgn))
-					list2)))
-			    list)
-			   (nreconc list1 (nreverse list2))))))))
-
-#|
- (suspension-intr-cprd (cmbn 0))
- (suspension-intr-cprd (cmbn 0 5 :s-bsgn))
- (suspension-intr-cprd (cmbn 3 4 7 5 11))
-|#
-
-(DEFMETHOD SUSPENSION-1 ((clgb coalgebra))
-  (the coalgebra
-    (let ((irslt (call-next-method)))
-      (declare (type (or chain-complex coalgebra) irslt))
-      (when (typep irslt 'coalgebra)
-	(return-from suspension-1 irslt))
-      (change-chcm-to-clgb irslt :intr-cprd #'suspension-intr-cprd
-			         :cprd-strt :cmbn)
-      (setf (slot-value irslt 'orgn) `(suspension ,clgb))
-      (setf (slot-value (slot-value irslt 'cprd) 'orgn)
-	    `(coproduct ,irslt))
-      irslt)))
-
-#|
-  (cat-init)
-  (setf coal (deltab))
-  (setf scoal (suspension coal))
-  (setf scoal (suspension coal))
-  (? scoal 3 7)
-  (cprd scoal 3 7)
-|#
-
-(DEFUN SUSPENSION-FACE (face)
-  (declare (type face face))
-  (flet ((rslt (indx dmns gmsm)
-	   (declare
-	     (fixnum indx dmns)
-	     (type gmsm gmsm))
-	   (assert (> dmns 1))
-	   (if (= indx dmns)
-	       (absm (mask (1- dmns)) :s-bsgn)
-	     (let ((irslt (funcall face indx (1- dmns) gmsm)))
-	       (declare (type absm irslt))
-	       (if (= (dgop irslt) (mask (- dmns 2)))
-		   (absm (mask (1- dmns)) :s-bsgn)
-		 irslt)))))
-     (the face #'rslt)))
-
-#|
-  (setf ss (deltab))
-  (setf face (suspension-face (face ss)))
-  (funcall face 4 4 15)
-  (funcall face 0 4 15)
-  (check-faces #'f-cmpr face 4 15)
-  (check-faces #'f-cmpr face 3 7)
-  (check-faces #'f-cmpr face 2 3)
-  (setf m (moore 2 3))
-  (setf face (suspension-face (face m)))
-  (dotimes (i 5) (print (funcall face i 4 'm3)))
-  (dotimes (i 6) (print (funcall face i 5 'mm4)))
-  (check-faces #'s-cmpr face 4 'm3)
-  (check-faces #'s-cmpr face 5 'mm4)
-|#
-
-(DEFMETHOD SUSPENSION-1 ((smst simplicial-set))
-  (the simplicial-set
-    (let ((irslt (call-next-method)))
-      (declare (type coalgebra irslt))
-      (when (typep irslt 'simplicial-set)
-	(return-from suspension-1 irslt))
-      (change-class irslt 'simplicial-set)
-      (setf (slot-value irslt 'face)
-	    (suspension-face (face smst)))
-      (setf (slot-value (slot-value irslt 'cprd) 'orgn)
-	    `(diagonal ,irslt))
-      irslt)))
-
-#|
-  (cat-init)
-  (setf d (deltab))
-  (setf sd (suspension d))
-  (setf sd (suspension d))
-  (inspect sd)
-  (? sd 3 7)
-  (cprd sd 3 7)
-  (face sd 3 3 7)
-  (face sd 2 3 7)
-  (setf m (moore 2 1))
-  (setf sm (suspension m))
-  (homology sm 0 5)
-  (setf ssm (suspension sm))
-  (homology ssm 0 6)
-|#
-
-(DEFUN SUSPENSION-INTR (mrph)
-  (declare (type morphism mrph))
-  (let ((mdegr (degr mrph)))
-    (declare (fixnum mdegr))
-    (flet ((rslt (cmbn)
-	     (declare (type cmbn cmbn))
-	     (with-cmbn (cdegr list) cmbn
-	       (when (zerop cdegr)
-		 (return-from rslt
-		   (if (zerop mdegr)
-		       cmbn
-		     (zero-cmbn (+ mdegr cdegr)))))
-	       (make-cmbn :degr (+ mdegr cdegr)
-			  :list (cmbn-list
-				 (cmbn-? mrph (make-cmbn :degr (1- cdegr)
-							 :list list)))))))
-    (the intr-mrph #'rslt))))
-
-#|
-  (setf f (idnt-mrph (deltab)))
-  (setf sf (suspension-intr f))
-  (funcall sf (cmbn 0 3 :s-bsgn))
-  (funcall sf (cmbn 2 4 3))
-  (setf d (dffr (deltab)))
-  (setf sd (suspension-intr d))
-  (funcall sd (cmbn 0 3 :s-bsgn))
-  (funcall sd (cmbn 2 4 3))
-  (funcall sd (cmbn 3 4 7))
-|#
-	 
-(DEFMETHOD SUSPENSION-1 ((mrph morphism))
-  (the morphism
-    (let ((orgn (orgn mrph)))
-      (declare (list orgn))
-      (when (eq (first orgn) 'zero-mrph)
-	(return-from suspension-1
-	  (zero-mrph (suspension (sorc mrph))
-		     (suspension (trgt mrph))
-		     (degr mrph))))
-      (when (eq (first orgn) 'idnt-mrph)
-	(return-from suspension-1
-	  (idnt-mrph (suspension (sorc mrph)))))
-      (build-mrph
-       :sorc (suspension (sorc mrph))
-       :trgt (suspension (trgt mrph))
-       :degr (degr mrph)
-       :intr (suspension-intr mrph)
-       :strt :cmbn
-       :orgn `(suspension ,mrph)))))
-
-#|
-  (setf f (idnt-mrph (deltab)))
-  (setf sf (suspension f))
-  (? sf (cmbn 0 3 :s-bsgn))
-  (? sf (cmbn 2 4 3))
-  (setf d (dffr (deltab)))
-  (setf sd (suspension d))
-  (? sd (cmbn 0 3 :s-bsgn))
-  (? sd (cmbn 2 4 3))
-  (? sd (cmbn 3 4 7))
-|#
-
-(DEFMETHOD SUSPENSION-1 ((rdct reduction))
-  (the reduction (progn
-    (when (eq (first (orgn rdct)) 'trivial-rdct)
-      (return-from suspension-1
-	(trivial-rdct (suspension (second (orgn rdct))))))
-    (build-rdct
-      :f (suspension (f rdct))
-      :g (suspension (g rdct))
-      :h (suspension (h rdct))
-      :orgn `(suspension ,rdct)))))
-
-#|
-  (setf rdct (ez (deltab) (deltab)))
-  (setf srdct (suspension rdct))
-  (pre-check-rdct srdct)
-  (setf *tc* (cmbn 4 1 (crpr 0 15 0 15)))
-  (setf *bc* (cmbn 4 1 (tnpr 0 1 3 15)
-                     5 (tnpr 1 3 2 7)
-                     10 (tnpr 2 7 1 3)
-                     100 (tnpr 3 15 0 1)))
-  (check-rdct)
-|#
-
-(DEFMETHOD SUSPENSION-1 ((hmeq homotopy-equivalence))
-  (the homotopy-equivalence (progn
-    (when (eq (first (orgn hmeq)) 'trivial-hmeq)
-      (return-from suspension-1
-	(trivial-hmeq (suspension (second (orgn hmeq))))))
-    (build-hmeq
-      :lrdct (suspension (lrdct hmeq))
-      :rrdct (suspension (rrdct hmeq))
-      :orgn `(suspension ,hmeq)))))
-
-(DEFMETHOD SEARCH-EFHM (suspension (orgn (eql 'suspension)))
-  (declare (type chain-complex suspension))
-  (suspension (efhm (second (orgn suspension)))))
-
-#|
-  (setf sk (suspension (k-z 2)))
-  (homology sk 0 10)
-|#
-  
\ No newline at end of file
diff --git a/archive/Kenzo-1/tensor-products.cl b/archive/Kenzo-1/tensor-products.cl
deleted file mode 100644
index 45f1d1c..0000000
--- a/archive/Kenzo-1/tensor-products.cl
+++ /dev/null
@@ -1,369 +0,0 @@
-;;;  TENSOR-PRODUCTS  TENSOR-PRODUCTS  TENSOR-PRODUCTS  TENSOR-PRODUCTS  TENSOR-PRODUCTS
-;;;  TENSOR-PRODUCTS  TENSOR-PRODUCTS  TENSOR-PRODUCTS  TENSOR-PRODUCTS  TENSOR-PRODUCTS
-;;;  TENSOR-PRODUCTS  TENSOR-PRODUCTS  TENSOR-PRODUCTS  TENSOR-PRODUCTS  TENSOR-PRODUCTS
-
-(IN-PACKAGE "COMMON-LISP-USER")
-
-(PROVIDE "tensor-products")
-
-(DEFVAR *TNPR-WITH-DEGREES* nil)
-
-(DEFUN TNPR-PRINT (tnpr stream depth)
-  (declare
-   (type tnpr tnpr) (stream stream)
-   (ignore depth))
-  (the tnpr
-    (progn
-      (with-tnpr (degr1 gnrt1 degr2 gnrt2) tnpr
-                 (format stream
-                     "<TnPr~:[~*~; ~D~] ~A~:[~*~; ~D~] ~A>"
-                   *tnpr-with-degrees* degr1 gnrt1
-                   *tnpr-with-degrees* degr2 gnrt2))
-      tnpr)))
-
-
-
-#|
-  (tnpr 2 'a 3 'b)
-  (setf *tnpr-with-degrees* t)    
-  (tnpr 2 'a 3 'b)
-  (setf *tnpr-with-degrees* nil)
-|#
-
-(DEFUN 2CMBN-TNPR (cmbn1 cmbn2)
-   (declare (type cmbn cmbn1 cmbn2))
-   (the cmbn
-      (with-cmbn (degr1 list1) cmbn1
-      (with-cmbn (degr2 list2) cmbn2
-         (make-cmbn
-            :degr (+ degr1 degr2)
-            :list (mapcan
-                     #'(lambda (term1)
-                          (declare (type term term1))
-                          (the list
-                             (with-term (cffc1 gnrt1) term1
-                                (mapcar
-                                   #'(lambda (term2)
-                                        (declare (type term term2))
-                                        (the term
-                                           (term
-                                              (* cffc1 (cffc term2))
-                                              (tnpr degr1 gnrt1 degr2 (gnrt term2)))))
-                                   list2))))
-                     list1))))))
-#|
-  (setf *tnpr-with-degrees* t)
-  (2cmbn-tnpr (cmbn 2 3 'a 4 'b -5 'c) (cmbn 3 4 'x -3 'y 2 'z)))
-|#
-
-
-#|
-(DEFUN TNSR-PRDC-CMPR (cmpr1 cmpr2)
-   (declare (type cmprf cmpr1 cmpr2))
-   (flet ((rslt (tnpr1 tnpr2)
-             (declare (type tnpr tnpr1 tnpr2))
-             (let ((left-cons-1 (cadr tnpr1))
-                   (left-cons-2 (cadr tnpr2)))
-                (declare (cons left-cons-1 left-cons-2))
-                (lexico
-                   (f-cmpr (car left-cons-1) (car left-cons-2))
-                   (funcall cmpr1 (cdr left-cons-1) (cdr left-cons-2))
-                   (funcall cmpr2 (gnrt2 tnpr1) (gnrt2 tnpr2))))))
-      (the cmprf #'rslt)))
-|#
-(DEFUN TNSR-PRDC-CMPR (cmpr1 cmpr2)
-  (declare (type cmprf cmpr1 cmpr2))
-  (flet ((rslt (tnpr1 tnpr2)
-           (declare (type tnpr tnpr1 tnpr2))
-           (the cmpr
-             (lexico
-              (f-cmpr (degr1 tnpr1) (degr1 tnpr2))
-              (funcall cmpr1 (gnrt1 tnpr1) (gnrt1 tnpr2))
-              (funcall cmpr2 (gnrt2 tnpr1) (gnrt2 tnpr2))))))
-    (the cmprf #'rslt)))
-
-
-#|
-  (setf cmpr (tnsr-prdc-cmpr #'s-cmpr #'s-cmpr))
-  (funcall cmpr (tnpr 2 'a 3 'b) (tnpr 3 'a 2 'b))
-  (funcall cmpr (tnpr 3 'a 2 'b) (tnpr 2 'a 3 'b))
-  (funcall cmpr (tnpr 2 'a 3 'b) (tnpr 2 'b 3 'b))
-  (funcall cmpr (tnpr 2 'b 3 'b) (tnpr 2 'a 3 'b))
-  (funcall cmpr (tnpr 2 'a 3 'a) (tnpr 2 'a 3 'b))
-  (funcall cmpr (tnpr 2 'a 3 'c) (tnpr 2 'a 3 'b))
-  (funcall cmpr (tnpr 2 'a 3 'b) (tnpr 2 'a 3 'b)))
-|#
-
-(DEFUN TNSR-PRDC-BASIS (basis1 basis2)
-   (declare (type basis basis1 basis2))
-   (when (or (eq basis1 :locally-effective)
-             (eq basis2 :locally-effective))
-      (return-from tnsr-prdc-basis :locally-effective))
-   (flet ((rslt (degr)
-             (declare (fixnum degr))
-             (the list
-                (progn
-                   (when (minusp degr)
-                      (return-from rslt +empty-list+))
-                   (mapcan
-                      #'(lambda (degr1)
-                           (declare (fixnum degr1))
-                           (let* ((basis1 (funcall basis1 degr1))
-                                  (degr2 (- degr degr1))
-                                  (basis2 (funcall basis2 degr2)))
-                              (declare
-                                 (fixnum degr2)
-                                 (list basis1 basis2))
-                              (the list
-                                 (mapcan
-                                    #'(lambda (gnrt1)
-                                         (declare (type gnrt gnrt1))
-                                         (the list
-                                            (mapcar
-                                               #'(lambda (gnrt2)
-                                                    (declare (type gnrt gnrt2))
-                                                    (the tnpr
-                                                       (tnpr degr1 gnrt1 degr2 gnrt2)))
-                                               basis2)))
-                                    basis1))))
-                      (<a-b> 0 degr))))))
-      (the basis #'rslt)))
-
-#|
-  (defun bas (degr)
-     (case degr
-        (0 '(a b c))
-        (1 '(d))
-        (2 nil)
-        (3 '(x y))))
-  (setf bas (tnsr-prdc-basis #'bas #'bas))
-  (dotimes (i 8)
-     (print (funcall bas i))))
-|#
-
-(DEFUN TNSR-PRDC-INTR-DFFR (dffr1 dffr2)
-   (declare (type morphism dffr1 dffr2))
-   (flet ((rslt (degr tnpr)
-             (declare
-                (fixnum degr)
-                (type tnpr tnpr))
-             (the cmbn
-                (with-tnpr (degr1 gnrt1 degr2 gnrt2) tnpr
-                   (let ((degr1-1 (1- degr1))
-                         (degr2-1 (1- degr2))
-                         (sign (oddp degr1))
-                         (list1 (cmbn-list (gnrt-? dffr1 degr1 gnrt1)))
-                         (list2 (cmbn-list (gnrt-? dffr2 degr2 gnrt2))))
-                      (declare
-                         (fixnum degr1-1 degr2-1 sign)
-                         (list list1 list2))
-                      (make-cmbn
-                         :degr (1- degr)
-                         :list (nconc
-                                  (mapcar
-                                     #'(lambda (term1)
-                                          (declare (type term term1))
-                                          (with-term (cffc1 gnrt1) term1
-                                             (term cffc1
-                                                (tnpr degr1-1 gnrt1 degr2 gnrt2))))
-                                     list1)
-                                  (mapcar
-                                     #'(lambda (term2)
-                                          (declare (type term term2))
-                                          (with-term (cffc2 gnrt2) term2
-                                             (term (if sign (- cffc2) cffc2)
-                                                (tnpr degr1 gnrt1 degr2-1 gnrt2))))
-                                     list2))))))))
-      (the intr-mrph #'rslt)))
-
-#|
-  (cat-init)
-  (setf chcm (build-chcm :cmpr #'s-cmpr :strt :gnrt :orgn '(test-1)))
-  (setf dffr (build-mrph :sorc chcm :trgt chcm :degr -1
-                         :intr #'(lambda (degr gnrt)
-                                    (ecase gnrt
-                                       (a (cmbn (1- degr) 2 'd1a -3 'd2a))
-                                       (b (cmbn (1- degr) 3 'd1b -4 'd2b))))
-                         :strt :gnrt :orgn '(test-2)))
-  (setf rslt (tnsr-prdc-intr-dffr dffr dffr))
-  (funcall rslt 4 (tnpr 2 'a 2 'b))
-  (funcall rslt 5 (tnpr 3 'a 2 'b))
-  (funcall rslt 5 (tnpr 2 'a 3 'b))
-  (funcall rslt 6 (tnpr 3 'a 3 'b)))
-|#
-
-(DEFMETHOD TNSR-PRDC ((chcm1 chain-complex) (chcm2 chain-complex))
-   (the chain-complex
-      (with-slots ((cmpr1 cmpr) (basis1 basis) (dffr1 dffr)) chcm1
-         (declare
-            (type cmprf cmpr1)
-            (type basis basis1)
-	    (type morphism dffr1))
-      (with-slots ((cmpr2 cmpr) (basis2 basis) (dffr2 dffr)) chcm2
-         (declare
-            (type cmprf cmpr2)
-            (type basis basis2)
-	    (type morphism dffr2))
-	 (let ((rslt
-		(build-chcm
-		 :cmpr (tnsr-prdc-cmpr cmpr1 cmpr2)
-		 :basis (tnsr-prdc-basis basis1 basis2)
-		 :intr-dffr (tnsr-prdc-intr-dffr dffr1 dffr2)
-		 :strt :gnrt
-		 :orgn `(tnsr-prdc ,chcm1 ,chcm2))))
-	   (declare (type chain-complex rslt))
-	   (if (and (slot-boundp chcm1 'bsgn)
-		    (slot-boundp chcm2 'bsgn))
-	      (setf (slot-value rslt 'bsgn)
-		    (tnpr 0 (bsgn chcm1) 0 (bsgn chcm2)))
-	      (slot-makunbound rslt 'bsgn))
-	   rslt)))))
-
-#|
-  (setf dd (tnsr-prdc (delta 2) (delta 3)))
-  (cmpr dd (tnpr 2 7 2 11) (tnpr 2 7 2 14))
-  (basis dd 3)
-  (? dd 4 (tnpr 2 7 2 14))
-  (? dd 3 (tnpr 1 6 2 14))
-  (? dd (? dd 4 (tnpr 2 7 2 14)))
-  (? dd (? dd 3 (tnpr 1 6 2 14))))
-|#
-
-(DEFUN TNSR-PRDC-INTR (mrph1 mrph2)
-   (declare
-      (type morphism mrph1 mrph2))
-   (let ((mrph2-sign (oddp (degr mrph2))))
-      (declare (type boolean mrph2-sign))         
-      (flet ((rslt (degr tnpr)
-              (declare
-                 (ignore degr)
-                 (type tnpr tnpr))
-              (with-tnpr (degr1 gnrt1 degr2 gnrt2) tnpr
-                 (let ((rslt (2cmbn-tnpr
-                                (gnrt-? mrph1 degr1 gnrt1)
-                                (gnrt-? mrph2 degr2 gnrt2))))
-                    (declare (type cmbn rslt))
-                    (when (and mrph2-sign
-                               (oddp degr1))
-                       (mapc #'(lambda (term)
-                                  (declare (type term term))
-                                  (setf (the fixnum (cffc term))
-                                        (the fixnum (- (cffc term)))))
-                          (cmbn-list rslt)))
-                    rslt))))
-         (the intr-mrph #'rslt))))
-
-#|
-  (cat-init)
-  (setf chcm (build-chcm :cmpr #'s-cmpr :strt :gnrt :orgn '(test-1)))
-  (setf mrph (build-mrph :sorc chcm :trgt chcm :degr 0
-                         :intr #'(lambda (degr gnrt)
-                                    (ecase gnrt
-                                       (a (cmbn degr 2 'd1a -3 'd2a))
-                                       (b (cmbn degr 3 'd1b -4 'd2b))))
-                         :strt :gnrt :orgn '(test-2)))
-  (setf rslt (tnsr-prdc-intr mrph mrph))
-  (funcall rslt 6 (tnpr 2 'a 4 'b))
-  (funcall rslt 5 (tnpr 3 'a 2 'b))
-  (setf mrph (build-mrph :sorc chcm :trgt chcm :degr 1
-                         :intr #'(lambda (degr gnrt)
-                                    (ecase gnrt
-                                       (a (cmbn (1+ degr) 2 'd1a -3 'd2a))
-                                       (b (cmbn (1+ degr) 3 'd1b -4 'd2b))))
-                         :strt :gnrt :orgn '(test-3)))
-  (setf rslt (tnsr-prdc-intr mrph mrph))
-  (funcall rslt 6 (tnpr 2 'a 4 'b))
-  (funcall rslt 5 (tnpr 3 'a 2 'b)))
-|#
-
-(DEFMETHOD TNSR-PRDC ((mrph1 morphism) (mrph2 morphism))
-  (the morphism
-   (with-slots ((sorc1 sorc) (trgt1 trgt) (degr1 degr)) mrph1
-   (with-slots ((sorc2 sorc) (trgt2 trgt) (degr2 degr)) mrph2
-      (the morphism
-	 (progn
-	   (when (and (eq 'idnt-mrph (first (orgn mrph1)))
-		      (eq 'idnt-mrph (first (orgn mrph2))))
-	      (return-from tnsr-prdc
-		 (idnt-mrph (tnsr-prdc sorc1 sorc2))))
-	   (when (or (eq 'zero-mrph (first (orgn mrph1)))
-		     (eq 'zero-mrph (first (orgn mrph2))))
-	      (return-from tnsr-prdc
-		 (zero-mrph (tnsr-prdc sorc1 sorc2)
-			    (tnsr-prdc trgt1 trgt2)
-			    (+ degr1 degr2))))
-	   (build-mrph
-              :sorc (tnsr-prdc sorc1 sorc2)
-	      :trgt (tnsr-prdc trgt1 trgt2)
-	      :degr (+ degr1 degr2)
-	      :intr (tnsr-prdc-intr mrph1 mrph2)
-	      :strt :gnrt
-	      :orgn `(tnsr-prdc ,mrph1 ,mrph2))))))))
-
-#|
-  (cat-init)
-  (setf d (dffr (delta-infinity)))
-  (setf dd (tnsr-prdc d d))
-  (eq (sorc dd) (tnsr-prdc (delta-infinity) (delta-infinity)))
-  (? dd 5 (tnpr 2 7 3 15))
-  (? dd 5 (tnpr 3 15 2 7))
-  (? dd (? dd 5 (tnpr 2 7 3 15)))
-  (? dd (? dd 5 (tnpr 3 15 2 7)))
-  (setf ddd (cmps dd dd))
-  (? ddd 5 (tnpr 2 7 3 15))
-  (? ddd 5 (tnpr 3 15 2 7))
-|#
-
-(DEFMETHOD TNSR-PRDC ((rdct1 reduction) (rdct2 reduction))
-  (the reduction
-     (progn
-       (when (and (eq 'trivial-rdct (first (orgn rdct1)))
-		  (eq 'trivial-rdct (first (orgn rdct2))))
-          (return-from tnsr-prdc
-	     (trivial-rdct (tnsr-prdc (bcc rdct1) (bcc rdct2)))))
-       (with-slots ((tcc1 tcc) (bcc1 bcc) (f1 f) (g1 g) (h1 h)) rdct1
-          (declare
-             (type chain-complex tcc1 bcc1)
-	     (type morphism f1 g1 h1))
-       (with-slots ((tcc2 tcc) (bcc2 bcc) (f2 f) (g2 g) (h2 h)) rdct2
-          (declare
-             (type chain-complex tcc2 bcc2)
-	     (type morphism f2 g2 h2))
-	  (build-rdct
-	     :f (tnsr-prdc f1 f2)
-	     :g (tnsr-prdc g1 g2)
-	     :h (add
-	         (tnsr-prdc h1 (cmps g2 f2))
-		 (tnsr-prdc (idnt-mrph tcc1) h2))
-	     :orgn `(tnsr-prdc ,rdct1 ,rdct2)))))))
-
-#|
-  (cat-init)
-  (setf r (ez (delta-infinity) (delta-infinity)))
-  (setf r2 (tnsr-prdc r r))
-  (setf *bc* (cmbn 4 1 (tnpr 2 (tnpr 1 3 1 3) 2 (tnpr 1 3 1 3)))
-        *tc* (cmbn 2 1 (tnpr 1 (crpr 0 3 0 3) 1 (crpr 0 3 0 3))))
-  (pre-check-rdct r2)
-  (check-rdct)
-|#
-
-(DEFMETHOD TNSR-PRDC ((hmeq1 homotopy-equivalence)
-		      (hmeq2 homotopy-equivalence))
-  (the homotopy-equivalence
-     (build-hmeq
-        :lrdct (tnsr-prdc (lrdct hmeq1) (lrdct hmeq2))
-	:rrdct (tnsr-prdc (rrdct hmeq1) (rrdct hmeq2))
-	:orgn `(tnsr-prdc ,hmeq1 ,hmeq2))))
-
-(DEFMETHOD SEARCH-EFHM (chcm (orgn (eql 'tnsr-prdc)))
-  (declare (type chain-complex chcm))
-  (the homotopy-equivalence
-       (tnsr-prdc (efhm (second (orgn chcm)))
-		  (efhm (third (orgn chcm))))))
-
-#|
-(cat-init)
-(setf k (k-z 2))
-(setf k2 (tnsr-prdc k k))
-(homology k2 0 10)
-|#
\ No newline at end of file
diff --git a/archive/Kenzo-1/various.cl b/archive/Kenzo-1/various.cl
deleted file mode 100644
index 566a86d..0000000
--- a/archive/Kenzo-1/various.cl
+++ /dev/null
@@ -1,144 +0,0 @@
-;;;  VARIOUS  VARIOUS  VARIOUS  VARIOUS  VARIOUS  VARIOUS
-;;;  VARIOUS  VARIOUS  VARIOUS  VARIOUS  VARIOUS  VARIOUS
-;;;  VARIOUS  VARIOUS  VARIOUS  VARIOUS  VARIOUS  VARIOUS
-
-(IN-PACKAGE "COMMON-LISP-USER")
-
-(PROVIDE "various")
-
-(DEFCONSTANT +EMPTY-LIST+ '())
-
-(DEFCONSTANT +F-EMPTY-VECTOR+
-   (make-array 0 :element-type 'fixnum))
-
-(DEFCONSTANT +S-EMPTY-VECTOR+
-   #())
-
-(DEFCONSTANT +TRUE+ t)
-
-(DEFCONSTANT +FALSE+ nil)
-
-(DEFCONSTANT +2-EXP+
-  (let ((rslt (make-array (integer-length most-positive-fixnum)
-                        :element-type 'fixnum)))
-    (declare (type (array fixnum 1) rslt))
-    (dotimes (i (integer-length most-positive-fixnum) rslt)
-      (setf (aref rslt i) (the fixnum (expt 2 i))))))
-
-(DEFCONSTANT +MASK+
-  (let ((rslt (make-array (integer-length most-positive-fixnum)
-                        :element-type 'fixnum)))
-    (declare (type (array fixnum 1) rslt))
-    (dotimes (i (integer-length most-positive-fixnum) rslt)
-      (setf (aref rslt i) (the fixnum (1- (expt 2 i)))))))
-
-(DEFUN BINOMIAL-N-P (n p)
-  (declare (fixnum n p))
-  (when (> (2-exp p) n)
-     (setf p (- n p)))
-  (the fixnum
-     (do ((nn n (1- nn))
-	  (pp 1 (1+ pp))
-	  (rslt 1 (/ (* rslt nn) pp)))
-	 ((> pp p) rslt)
-	(declare (fixnum nn pp rslt)))))
-
-#|
-  (dotimes (i 6)
-     (print (binomial-n-p 5 i)))
-  (dotimes (i 6)
-     (print (binomial-p-q (- 5 i) i))))
-|#
-
-(SETF *PRINT-LEVEL* 5
-  *PRINT-LENGTH* 10)
-
-(DEFUN <A-B< (a b)
-   (declare (fixnum a b))
-   (the list
-      (do ((i (1- b) (1- i))
-           (rslt +empty-list+ (cons i rslt)))
-          ((< i a) rslt)
-         (declare (fixnum i) (list rslt)))))
- 
-(DEFUN <A-B> (a b)
-  (declare (fixnum a b))
- (the list
-   (do ((i b (1- i))
-       (rslt +empty-list+ (cons i rslt)))
-      ((< i a) rslt)
-    (declare (fixnum i) (list rslt)))))
-
-(DEFUN >A-B< (a b)
-  (declare (fixnum a b))
- (the list
-  (do ((i (1- b) (1- i))
-       (rslt +empty-list+ (cons i rslt)))
-      ((= i a) rslt)
-    (declare (fixnum i) (list rslt)))))
-
-(DEFUN >A-B> (a b)
-  (declare (fixnum a b))
- (the list
-  (do ((i b (1- i))
-       (rslt +empty-list+ (cons i rslt)))
-      ((= i a) rslt)
-    (declare (fixnum i) (list rslt)))))
-
-#|
-  (<a-b< 0 5)
-  (<a-b> 0 5)
-  (>a-b< 0 5)
-  (>a-b> 0 5))
-|#
-
-(DEFUN V<A-B> (a b)
-   (declare (fixnum a b))
- (the (vector fixnum)
-    (let ((rslt (make-array (1+ (- b a)) :element-type 'fixnum)))
-       (declare (type (vector fixnum) rslt))
-       (do ((i a (1+ i))
-            (mark 0 (1+ mark)))
-           ((> i b))
-          (declare (fixnum i mark))
-          (setf (aref rslt mark) i))
-       rslt)))
-
-#|
-  (v<a-b> -5 5))
-|#
-
-(DEFUN SRANDOM (max)
-   (declare (fixnum max))
-   (the fixnum
-      (let ((rslt (- (random (+ max max)) max)))
-         (declare (fixnum rslt))
-         (if (zerop rslt)
-            max
-            rslt))))
-
-#|
-  (dotimes (i 20) (print (srandom 3))))
-|#
-
-(DEFUN CLOCK ()
-  (multiple-value-bind (sec min hour day month year)
-		       (get-decoded-time)
-    (format t "~%;; Clock -> ~4D-~2,'0D-~2,'0D, ~Dh ~Dm ~Ds.~%"
-	      year month day hour min sec))
-  (values))
-
-#|
-  (clock))
-|#
-
-(DEFUN DONE ()
-   (format t "~%---done---")
-   (values))
-   
-#|
-  (done))
-|#
-
-
-
diff --git a/archive/Kenzo-1/whitehead.cl b/archive/Kenzo-1/whitehead.cl
deleted file mode 100644
index df05d28..0000000
--- a/archive/Kenzo-1/whitehead.cl
+++ /dev/null
@@ -1,338 +0,0 @@
-;;;  WHITEHEAD  WHITEHEAD  WHITEHEAD  WHITEHEAD  WHITEHEAD  WHITEHEAD  WHITEHEAD
-;;;  WHITEHEAD  WHITEHEAD  WHITEHEAD  WHITEHEAD  WHITEHEAD  WHITEHEAD  WHITEHEAD
-;;;  WHITEHEAD  WHITEHEAD  WHITEHEAD  WHITEHEAD  WHITEHEAD  WHITEHEAD  WHITEHEAD
-
-(IN-PACKAGE "COMMON-LISP-USER")
-
-(provide "whitehead")
-
-;;;
-;;; Z
-;;;
-
-(DEFUN Z-WWHITEHEAD-SINTR (smst n chml-clss
-				&aux (face (face smst))
-				     (k-z-n (k-z n))
-				     (idnt (bspn k-z-n))
-				     (efhm (efhm smst)))
-   (declare
-      (type simplicial-set smst)
-      (fixnum n)
-      (type morphism chml-clss)
-      (type face face)
-      (type ab-simplicial-group k-z-n)
-      (type gmsm idnt)
-      (type homotopy-equivalence efhm))
-   (setf chml-clss
-	 (i-cmps chml-clss (rf efhm) (lg efhm)))
-   (flet ((rslt (dmns gmsm)
-	    (declare
-	      (fixnum dmns)
-	      (type gmsm gmsm))
-	    (if (< dmns n)
-	        (absm (mask dmns) idnt)
-	      (z-cocycle-gbar n dmns
-		(gmsm-cocycle face n dmns gmsm chml-clss)))))
-     (the sintr #'rslt)))
-
-#|
-(cat-init)
-(setf k (k-z 2))
-(setf ecc (echcm k))
-(setf chml-clss
-      (build-mrph
-        :sorc ecc :trgt (z-chcm) :degr 2
-	:intr #'(lambda (degr gnrt)
-		  (if (= degr 2)
-		      (term-cmbn 0 1 :z-gnrt)
-		    (zero-cmbn (- degr 2))))
-	:strt :gnrt :orgn '(fundamental-class k-z-2)))
-(setf tw (z-wwhitehead-sintr k 2 chml-clss))
-(a-sintr3 tw 1 (absm 1 +null-gbar+))  ;;; cf old-macro cancelled
-(a-sintr3 tw 2 (absm 3 +null-gbar+))  ;;; in macros.cl
-(funcall tw 2 (gbar 2 0 '(55) 0 '()))
-(funcall tw 3 (gbar 3 0 '(12 23)
-                      0 '(34)
-                      0 '()))
-(funcall tw 4 (gbar 4 0 '(12 23 34)
-                      2 '(45)
-                      0 '(56)
-                      0 '()))
-(setf k (k-z 3))
-(setf ecc (echcm k))
-(setf chml-clss
-      (build-mrph
-        :sorc ecc :trgt (z-chcm) :degr 3
-	:intr #'(lambda (degr gnrt)
-		  (if (= degr 3)
-		      (term-cmbn 0 -1 :z-gnrt)
-		    (zero-cmbn (- degr 3))))
-	:strt :gnrt :orgn '(fundamental-class k-z-3)))
-(setf tw (z-wwhitehead-sintr k 3 chml-clss))
-(a-sintr3 tw 1 (absm 1 +null-gbar+))
-(a-sintr3 tw 2 (absm 3 +null-gbar+))
-(a-sintr3 tw 3 (absm 7 +null-gbar+))
-(funcall tw 3 (z-fundamental-gmsm 3 55))
-(equal (funcall tw 3 (z-fundamental-gmsm 3 55))
-       (absm 0 (z-fundamental-gmsm 3 55)))
-(funcall tw 4 (gbar 4 0 (gbar 3 0 '(12 23) 0 '(34) 0 '())
-                      0 (gbar 2 0 '(45) 0 '())
-                      1 (gbar 0)
-                      0 (gbar 0)))
-|#
-
-(DEFUN Z-WHITEHEAD-SINTR (smst n chml-clss
-				&aux (face (face smst))
-				     (k-z-n-1 (k-z (1- n)))
-				     (idnt (bspn k-z-n-1))
-				     (efhm (efhm smst)))
-   (declare
-      (type simplicial-set smst)
-      (fixnum n)
-      (type morphism chml-clss)
-      (type face face)
-      (type ab-simplicial-group k-z-n-1)
-      (type gmsm idnt)
-      (type homotopy-equivalence efhm))
-   (setf chml-clss
-	 (i-cmps chml-clss (rf efhm) (lg efhm)))
-   (flet ((rslt (dmns gmsm)
-	    (declare
-	      (fixnum dmns)
-	      (type gmsm gmsm))
-	    (if (< dmns n)
-	        (absm (mask (1- dmns)) idnt)
-	      (z-cocycle-gbar-head n dmns
-		(gmsm-cocycle face n dmns gmsm chml-clss)))))
-     (the sintr #'rslt)))
-
-#|
-(cat-init)
-(setf k (k-z 2))
-(setf ecc (echcm k))
-(setf chml-clss
-      (build-mrph
-        :sorc ecc :trgt (z-chcm) :degr 2
-	:intr #'(lambda (degr gnrt)
-		  (if (= degr 2)
-		      (term-cmbn 0 1 :z-gnrt)
-		    (zero-cmbn (- degr 2))))
-	:strt :gnrt :orgn '(fundamental-class k-z-2)))
-(setf tw (z-whitehead-sintr k 2 chml-clss))
-(tw-a-sintr3 tw 1 (absm 1 +null-gbar+) '())
-(tw-a-sintr3 tw 2 (absm 3 +null-gbar+) '())
-(funcall tw 2 (gbar 2 0 '(55) 0 '()))
-(funcall tw 3 (gbar 3 0 '(12 23)
-                      0 '(34)
-                      0 '()))
-(funcall tw 4 (gbar 4 0 '(12 23 34)
-                      2 '(45)
-                      0 '(56)
-                      0 '()))
-(setf k (k-z 3))
-(setf ecc (echcm k))
-(setf chml-clss
-      (build-mrph
-        :sorc ecc :trgt (z-chcm) :degr 3
-	:intr #'(lambda (degr gnrt)
-		  (if (= degr 3)
-		      (term-cmbn 0 -1 :z-gnrt)
-		    (zero-cmbn (- degr 3))))
-	:strt :gnrt :orgn '(fundamental-class k-z-3)))
-(setf tw (z-whitehead-sintr k 3 chml-clss))
-(tw-a-sintr3 tw 1 (absm 1 +null-gbar+) +null-gbar+)
-(tw-a-sintr3 tw 2 (absm 3 +null-gbar+) +null-gbar+)
-(tw-a-sintr3 tw 3 (absm 7 +null-gbar+) +null-gbar+)
-(funcall tw 3 (z-fundamental-gmsm 3 55))
-(equal (funcall tw 3 (z-fundamental-gmsm 3 55))
-       (absm 0 (z-fundamental-gmsm 2 55)))
-(funcall tw 4 (gbar 4 0 (gbar 3 0 '(12 23) 0 '(34) 0 '())
-                      0 (gbar 2 0 '(45) 0 '())
-                      1 (gbar 0)
-                      0 (gbar 0)))
-|#
-
-(DEFUN Z-WHITEHEAD (smst chml-clss &aux (n (- (degr chml-clss))))
-   (declare
-      (type simplicial-set smst)
-      (fixnum n)
-      (type morphism chml-clss))
-   (the fibration
-      (build-smmr
-         :sorc smst :trgt (k-z (1- n)) :degr -1
-         :sintr (z-whitehead-sintr smst n chml-clss)
-         :orgn `(z-whitehead ,smst))))
-
-;;;
-;;; Z/2Z
-;;;
-
-(DEFUN Z2-WWHITEHEAD-SINTR (smst n chml-clss
-				&aux (face (face smst))
-				     (k-z2-n (k-z2 n))
-				     (idnt (bspn k-z2-n))
-				     (efhm (efhm smst)))
-   (declare
-      (type simplicial-set smst)
-      (fixnum n)
-      (type morphism chml-clss)
-      (type face face)
-      (type ab-simplicial-group k-z2-n)
-      (type gmsm idnt)
-      (type homotopy-equivalence efhm))
-   (setf chml-clss
-	 (i-cmps chml-clss (rf efhm) (lg efhm)))
-   (flet ((rslt (dmns gmsm)
-	    (declare
-	      (fixnum dmns)
-	      (type gmsm gmsm))
-	    (if (< dmns n)
-	        (absm (mask dmns) idnt)
-	      (z2-cocycle-gbar n dmns
-		(gmsm-cocycle face n dmns gmsm chml-clss)))))
-     (the sintr #'rslt)))
-
-#|
-(cat-init)
-(setf k (k-z2 2))
-(setf ecc (echcm k))
-(setf chml-clss
-      (build-mrph
-        :sorc ecc :trgt (z-chcm) :degr 2
-	:intr #'(lambda (degr gnrt)
-		  (if (= degr 2)
-		      (term-cmbn 0 1 :z-gnrt)
-		    (zero-cmbn (- degr 2))))
-	:strt :gnrt :orgn '(fundamental-class k-z-2)))
-(setf tw (Z2-wwhitehead-sintr k 2 chml-clss))
-(a-sintr3 tw 1 (absm 1 +null-gbar+))
-(a-sintr3 tw 2 (absm 3 +null-gbar+))
-(funcall tw 2 (gbar 2 0 1 0 0))
-(funcall tw 3 (gbar 3 0 2
-                      0 1
-                      0 0))
-(funcall tw 4 (gbar 4 0 3
-                      2 1
-                      0 1
-                      0 0))
-(setf k (k-z2 3))
-(setf ecc (echcm k))
-(setf chml-clss
-      (build-mrph
-        :sorc ecc :trgt (z-chcm) :degr 3
-	:intr #'(lambda (degr gnrt)
-		  (if (= degr 3)
-		      (term-cmbn 0 -1 :z-gnrt)
-		    (zero-cmbn (- degr 3))))
-	:strt :gnrt :orgn '(fundamental-class k-z-3)))
-(setf tw (Z2-wwhitehead-sintr k 3 chml-clss))
-(a-sintr3 tw 1 (absm 1 +null-gbar+))
-(a-sintr3 tw 2 (absm 3 +null-gbar+))
-(a-sintr3 tw 3 (absm 7 +null-gbar+))
-(funcall tw 3 (Z2-fundamental-gmsm 3 1))
-(equal (funcall tw 3 (Z2-fundamental-gmsm 3 1))
-       (absm 0 (Z2-fundamental-gmsm 3 1)))
-(funcall tw 4 (gbar 4 0 (gbar 3 0 2 0 1 0 0)
-                      0 (gbar 2 0 1 0 0)
-                      1 (gbar 0)
-                      0 (gbar 0)))
-|#
-
-(DEFUN Z2-WHITEHEAD-SINTR (smst n chml-clss
-				&aux (face (face smst))
-				     (k-z2-n-1 (k-z2 (1- n)))
-				     (idnt (bspn k-z2-n-1))
-				     (efhm (efhm smst)))
-   (declare
-      (type simplicial-set smst)
-      (fixnum n)
-      (type morphism chml-clss)
-      (type face face)
-      (type ab-simplicial-group k-z2-n-1)
-      (type gmsm idnt)
-      (type homotopy-equivalence efhm))
-   (setf chml-clss
-	 (i-cmps chml-clss (rf efhm) (lg efhm)))
-   (flet ((rslt (dmns gmsm)
-	    (declare
-	      (fixnum dmns)
-	      (type gmsm gmsm))
-	    (if (< dmns n)
-	        (absm (mask (1- dmns)) idnt)
-	      (z2-cocycle-gbar-head n dmns
-		(gmsm-cocycle face n dmns gmsm chml-clss)))))     
-     (the sintr #'rslt)))
-
-#|
-(cat-init)
-(setf k (k-z2 2))
-(setf ecc (echcm k))
-(setf chml-clss
-      (build-mrph
-        :sorc ecc :trgt (z-chcm) :degr 2
-	:intr #'(lambda (degr gnrt)
-		  (if (= degr 2)
-		      (term-cmbn 0 1 :z-gnrt)
-		    (zero-cmbn (- degr 2))))
-	:strt :gnrt :orgn '(fundamental-class k-z-2)))
-(setf tw (Z2-whitehead-sintr k 2 chml-clss))
-(tw-a-sintr3 tw 1 (absm 1 +null-gbar+) 0)
-(tw-a-sintr3 tw 2 (absm 3 +null-gbar+) 0)
-(funcall tw 2 (gbar 2 0 1 0 '()))
-(funcall tw 3 (gbar 3 0 2
-                      0 1
-                      0 0))
-(funcall tw 4 (gbar 4 0 3
-                      2 1
-                      0 1
-                      0 0))
-(setf k (k-z2 3))
-(setf ecc (echcm k))
-(setf chml-clss
-      (build-mrph
-        :sorc ecc :trgt (z-chcm) :degr 3
-	:intr #'(lambda (degr gnrt)
-		  (if (= degr 3)
-		      (term-cmbn 0 -1 :z-gnrt)
-		    (zero-cmbn (- degr 3))))
-	:strt :gnrt :orgn '(fundamental-class k-z-3)))
-(setf tw (Z2-whitehead-sintr k 3 chml-clss))
-(tw-a-sintr3 tw 1 (absm 1 +null-gbar+) 0)
-(tw-a-sintr3 tw 2 (absm 3 +null-gbar+) 0)
-(tw-a-sintr3 tw 3 (absm 7 +null-gbar+) 0)
-(funcall tw 3 (Z2-fundamental-gmsm 3 1))
-(equal (funcall tw 3 (Z2-fundamental-gmsm 3 1))
-       (absm 0 (Z2-fundamental-gmsm 2 1)))
-(funcall tw 4 (gbar 4 0 (gbar 3 0 2 0 1 0 0)
-                      0 (gbar 2 0 1 0 0)
-                      1 (gbar 0)
-                      0 (gbar 0)))
-|#
-
-(DEFUN Z2-WHITEHEAD (smst chml-clss &aux (n (- (degr chml-clss))))
-   (declare
-      (type simplicial-set smst)
-      (fixnum n)
-      (type morphism chml-clss))
-   (the fibration
-      (build-smmr
-         :sorc smst :trgt (k-z2 (1- n)) :degr -1
-         :sintr (Z2-whitehead-sintr smst n chml-clss)
-         :orgn `(Z2-whitehead ,smst))))
-
-#|
-(setf m (moore 2 4))
-(setf chml-clss
-      (build-mrph
-         :sorc m :trgt (z-chcm) :degr -4
-         :intr #'(lambda (dmns gmsm)
-                    (if (= 4 dmns)
-                       (cmbn 0 1 :z-gnrt)
-                       (zero-cmbn (- dmns 4))))
-         :strt :gnrt
-         :orgn '(chml-clss moore 2 4)))
-(setf mf (z2-whitehead m 4 chml-clss))
-(setf mt (fibration-total mf))
-(homology mt 0 10)
-|#
-         
\ No newline at end of file
diff --git a/archive/Kenzo-2/Kenzo-2-Acl5/Alexis.cl b/archive/Kenzo-2/Kenzo-2-Acl5/Alexis.cl
deleted file mode 100644
index d563a16..0000000
--- a/archive/Kenzo-2/Kenzo-2-Acl5/Alexis.cl
+++ /dev/null
@@ -1,56 +0,0 @@
-
-(setf p (k-z2 1))
-
-(setf sp (suspension p))
-
-(setf s2p (suspension sp))
-
-(setf s3p (suspension s2p))
-
-(setf s4p (suspension s3p))
-
-(homology s4p 5)
-
-(setf ch5 (chml-clss s4p 5))
-
-(setf f5 (z2-whitehead s4p ch5))
-
-(setf x6 (fibration-total f5))
-
-(homology x6 6)
-
-(setf ch6 (chml-clss x6 6))
-
-(setf f6 (z2-whitehead x6 ch6))
-
-(setf x7 (fibration-total f6))
-
-(homology x7 7)
-
-(setf ch71 (chml-clss x7 7))
-
-(setf f71 (z2-whitehead x7 ch71))
-
-(setf x71 (fibration-total f71))
-
-(homology x71 7)
-
-(setf ch72 (chml-clss x71 7))
-
-(setf f72 (z2-whitehead x71 ch72))
-
-(setf x72 (fibration-total f72))
-
-(homology x72 7)
-
-(setf ch73 (chml-clss x72 7))
-
-(setf f73 (z2-whitehead x72 ch73))
-
-(setf x8 (fibration-total f73))
-
-(homology x71 7)
-
-(homology x71 8)
-
-
diff --git a/archive/Kenzo-2/Kenzo-2-Acl5/Compile.txt b/archive/Kenzo-2/Kenzo-2-Acl5/Compile.txt
deleted file mode 100644
index c48baa3..0000000
--- a/archive/Kenzo-2/Kenzo-2-Acl5/Compile.txt
+++ /dev/null
@@ -1,331 +0,0 @@
-Allegro CL Personal Edition 5.0.1 [Windows/x86] (6/29/99 16:56)
-Copyright (C) 1985-1999, Franz Inc., Berkeley, CA, USA.  All Rights Reserved.
-CG/IDE Version: 1.323.2.169
-
-[changing package from "COMMON-LISP-USER" to "COMMON-GRAPHICS-USER"]
-
-> (load "file-list")
-; Loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\file-list.cl
-
- FILE  1: classes
- FILE  2: macros
- FILE  3: various
- FILE  4: combinations
- FILE  5: chain-complexes
- FILE  6: chcm-elementary-op
- FILE  7: effective-homology
- FILE  8: homology-groups
- FILE  9: searching-homology
- FILE 10: cones
- FILE 11: tensor-products
- FILE 12: coalgebras
- FILE 13: cobar
- FILE 14: algebras
- FILE 15: bar
- FILE 16: simplicial-sets
- FILE 17: simplicial-mrphs
- FILE 18: delta
- FILE 19: special-smsts
- FILE 20: suspensions
- FILE 21: disk-pasting
- FILE 22: cartesian-products
- FILE 23: eilenberg-zilber
- FILE 24: kan
- FILE 25: simplicial-groups
- FILE 26: fibrations
- FILE 27: loop-spaces
- FILE 28: ls-twisted-products
- FILE 29: lp-space-efhm
- FILE 30: classifying-spaces
- FILE 31: k-pi-n
- FILE 32: serre
- FILE 33: cs-twisted-products
- FILE 34: cl-space-efhm
- FILE 35: whitehead
- FILE 36: smith
-T
-> (in-package :cat)
-#<The CAT package>
-> (compile-files)
-
-SPEED-PARAMETER = 3
-
- *CMBN-CONTROL* = T
-
-;;; Compiling file classes.cl
-;;; Writing fasl file classes.fasl
-;;; Fasl write complete
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\classes.fasl
-;;; Compiling file macros.cl
-;;; Writing fasl file macros.fasl
-;;; Fasl write complete
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\macros.fasl
-;;; Compiling file various.cl
-;;; Writing fasl file various.fasl
-;;; Fasl write complete
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\various.fasl
-;;; Compiling file combinations.cl
-;;; Writing fasl file combinations.fasl
-;;; Fasl write complete
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\combinations.fasl
-;;; Compiling file chain-complexes.cl
-;;; Writing fasl file chain-complexes.fasl
-;;; Fasl write complete
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\chain-complexes.fasl
-;;; Compiling file chcm-elementary-op.cl
-;;; Writing fasl file chcm-elementary-op.fasl
-;;; Fasl write complete
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\chcm-elementary-op.fasl
-;;; Compiling file effective-homology.cl
-;;; Writing fasl file effective-homology.fasl
-;;; Fasl write complete
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\effective-homology.fasl
-;;; Compiling file homology-groups.cl
-;;; Writing fasl file homology-groups.fasl
-;;; Fasl write complete
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\homology-groups.fasl
-;;; Compiling file searching-homology.cl
-;;; Writing fasl file searching-homology.fasl
-;;; Fasl write complete
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\searching-homology.fasl
-;;; Compiling file cones.cl
-;;; Writing fasl file cones.fasl
-;;; Fasl write complete
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\cones.fasl
-;;; Compiling file tensor-products.cl
-;;; Writing fasl file tensor-products.fasl
-;;; Fasl write complete
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\tensor-products.fasl
-;;; Compiling file coalgebras.cl
-;;; Writing fasl file coalgebras.fasl
-;;; Fasl write complete
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\coalgebras.fasl
-;;; Compiling file cobar.cl
-;;; Writing fasl file cobar.fasl
-;;; Fasl write complete
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\cobar.fasl
-;;; Compiling file algebras.cl
-;;; Writing fasl file algebras.fasl
-;;; Fasl write complete
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\algebras.fasl
-;;; Compiling file bar.cl
-;;; Writing fasl file bar.fasl
-;;; Fasl write complete
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\bar.fasl
-;;; Compiling file simplicial-sets.cl
-;;; Writing fasl file simplicial-sets.fasl
-;;; Fasl write complete
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\simplicial-sets.fasl
-;;; Compiling file simplicial-mrphs.cl
-;;; Writing fasl file simplicial-mrphs.fasl
-;;; Fasl write complete
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\simplicial-mrphs.fasl
-;;; Compiling file delta.cl
-;;; Writing fasl file delta.fasl
-;;; Fasl write complete
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\delta.fasl
-;;; Compiling file special-smsts.cl
-;;; Writing fasl file special-smsts.fasl
-;;; Fasl write complete
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\special-smsts.fasl
-;;; Compiling file suspensions.cl
-;;; Writing fasl file suspensions.fasl
-;;; Fasl write complete
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\suspensions.fasl
-;;; Compiling file disk-pasting.cl
-;;; Writing fasl file disk-pasting.fasl
-;;; Fasl write complete
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\disk-pasting.fasl
-;;; Compiling file cartesian-products.cl
-;;; Writing fasl file cartesian-products.fasl
-;;; Fasl write complete
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\cartesian-products.fasl
-;;; Compiling file eilenberg-zilber.cl
-;;; Writing fasl file eilenberg-zilber.fasl
-;;; Fasl write complete
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\eilenberg-zilber.fasl
-;;; Compiling file kan.cl
-;;; Writing fasl file kan.fasl
-;;; Fasl write complete
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\kan.fasl
-;;; Compiling file simplicial-groups.cl
-;;; Writing fasl file simplicial-groups.fasl
-;;; Fasl write complete
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\simplicial-groups.fasl
-;;; Compiling file fibrations.cl
-;;; Writing fasl file fibrations.fasl
-;;; Fasl write complete
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\fibrations.fasl
-;;; Compiling file loop-spaces.cl
-;;; Writing fasl file loop-spaces.fasl
-;;; Fasl write complete
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\loop-spaces.fasl
-;;; Compiling file ls-twisted-products.cl
-;;; Writing fasl file ls-twisted-products.fasl
-;;; Fasl write complete
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\ls-twisted-products.fasl
-;;; Compiling file lp-space-efhm.cl
-;;; Writing fasl file lp-space-efhm.fasl
-;;; Fasl write complete
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\lp-space-efhm.fasl
-;;; Compiling file classifying-spaces.cl
-;;; Writing fasl file classifying-spaces.fasl
-;;; Fasl write complete
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\classifying-spaces.fasl
-;;; Compiling file k-pi-n.cl
-;;; Writing fasl file k-pi-n.fasl
-;;; Fasl write complete
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\k-pi-n.fasl
-;;; Compiling file serre.cl
-;;; Writing fasl file serre.fasl
-;;; Fasl write complete
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\serre.fasl
-;;; Compiling file cs-twisted-products.cl
-;;; Writing fasl file cs-twisted-products.fasl
-;;; Fasl write complete
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\cs-twisted-products.fasl
-;;; Compiling file cl-space-efhm.cl
-;;; Writing fasl file cl-space-efhm.fasl
-;;; Fasl write complete
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\cl-space-efhm.fasl
-;;; Compiling file whitehead.cl
-;;; Writing fasl file whitehead.fasl
-;;; Fasl write complete
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\whitehead.fasl
-;;; Compiling file smith.cl
-;;; Writing fasl file smith.fasl
-;;; Fasl write complete
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\smith.fasl
---- done ---
-> (time (homology (loop-space (moore 2 4) 2) 7))
-
-Computing boundary-matrix in dimension 7.
-Rank of the source-module : 6.
-
-
-;; Clock -> 2005-10-03, 15h 6m 53s.
-Computing the boundary of the generator 1 (dimension 7) :
-<<AlLp[7 <<AlLp[4 N5][4 N5]>>]>> 
-End of computing.
-
-
-;; Clock -> 2005-10-03, 15h 6m 53s.
-Computing the boundary of the generator 2 (dimension 7) :
-<<AlLp[2 <<AlLp[3 M4]>>][5 <<AlLp[3 M4][3 M4]>>]>> 
-End of computing.
-
-
-;; Clock -> 2005-10-03, 15h 6m 53s.
-Computing the boundary of the generator 3 (dimension 7) :
-<<AlLp[5 <<AlLp[3 M4][3 M4]>>][2 <<AlLp[3 M4]>>]>> 
-End of computing.
-
-
-;; Clock -> 2005-10-03, 15h 6m 53s.
-Computing the boundary of the generator 4 (dimension 7) :
-<<AlLp[2 <<AlLp[3 M4]>>][2 <<AlLp[3 M4]>>][3 <<AlLp[4 N5]>>]>> 
-End of computing.
-
-
-;; Clock -> 2005-10-03, 15h 6m 53s.
-Computing the boundary of the generator 5 (dimension 7) :
-<<AlLp[2 <<AlLp[3 M4]>>][3 <<AlLp[4 N5]>>][2 <<AlLp[3 M4]>>]>> 
-End of computing.
-
-
-;; Clock -> 2005-10-03, 15h 6m 53s.
-Computing the boundary of the generator 6 (dimension 7) :
-<<AlLp[3 <<AlLp[4 N5]>>][2 <<AlLp[3 M4]>>][2 <<AlLp[3 M4]>>]>> 
-End of computing.
-
-
-Computing boundary-matrix in dimension 8.
-Rank of the source-module : 11.
-
-
-;; Clock -> 2005-10-03, 15h 6m 53s.
-Computing the boundary of the generator 1 (dimension 8) :
-<<AlLp[8 <<AlLp[3 M4][3 M4][3 M4]>>]>> 
-End of computing.
-
-
-;; Clock -> 2005-10-03, 15h 6m 58s.
-Computing the boundary of the generator 2 (dimension 8) :
-<<AlLp[2 <<AlLp[3 M4]>>][6 <<AlLp[3 M4][4 N5]>>]>> 
-End of computing.
-
-
-;; Clock -> 2005-10-03, 15h 6m 58s.
-Computing the boundary of the generator 3 (dimension 8) :
-<<AlLp[2 <<AlLp[3 M4]>>][6 <<AlLp[4 N5][3 M4]>>]>> 
-End of computing.
-
-
-;; Clock -> 2005-10-03, 15h 6m 58s.
-Computing the boundary of the generator 4 (dimension 8) :
-<<AlLp[3 <<AlLp[4 N5]>>][5 <<AlLp[3 M4][3 M4]>>]>> 
-End of computing.
-
-
-;; Clock -> 2005-10-03, 15h 6m 58s.
-Computing the boundary of the generator 5 (dimension 8) :
-<<AlLp[5 <<AlLp[3 M4][3 M4]>>][3 <<AlLp[4 N5]>>]>> 
-End of computing.
-
-
-;; Clock -> 2005-10-03, 15h 6m 58s.
-Computing the boundary of the generator 6 (dimension 8) :
-<<AlLp[6 <<AlLp[3 M4][4 N5]>>][2 <<AlLp[3 M4]>>]>> 
-End of computing.
-
-
-;; Clock -> 2005-10-03, 15h 6m 58s.
-Computing the boundary of the generator 7 (dimension 8) :
-<<AlLp[6 <<AlLp[4 N5][3 M4]>>][2 <<AlLp[3 M4]>>]>> 
-End of computing.
-
-
-;; Clock -> 2005-10-03, 15h 6m 58s.
-Computing the boundary of the generator 8 (dimension 8) :
-<<AlLp[2 <<AlLp[3 M4]>>][3 <<AlLp[4 N5]>>][3 <<AlLp[4 N5]>>]>> 
-End of computing.
-
-
-;; Clock -> 2005-10-03, 15h 6m 58s.
-Computing the boundary of the generator 9 (dimension 8) :
-<<AlLp[3 <<AlLp[4 N5]>>][2 <<AlLp[3 M4]>>][3 <<AlLp[4 N5]>>]>> 
-End of computing.
-
-
-;; Clock -> 2005-10-03, 15h 6m 58s.
-Computing the boundary of the generator 10 (dimension 8) :
-<<AlLp[3 <<AlLp[4 N5]>>][3 <<AlLp[4 N5]>>][2 <<AlLp[3 M4]>>]>> 
-End of computing.
-
-
-;; Clock -> 2005-10-03, 15h 6m 58s.
-Computing the boundary of the generator 11 (dimension 8) :
-<<AlLp[2 <<AlLp[3 M4]>>][2 <<AlLp[3 M4]>>][2 <<AlLp[3 M4]>>][2 <<AlLp[3 M4]>>]>> 
-End of computing.
-
-
-
-
-Homology in dimension 7 :
-
-
-Component Z/2Z
-
-
----done---
-
-;; Clock -> 2005-10-03, 15h 6m 58s.
-
-; cpu time (non-gc) 4,735 msec user, 0 msec system
-; cpu time (gc)     640 msec user, 0 msec system
-; cpu time (total)  5,375 msec user, 0 msec system
-; real time  5,375 msec
-; space allocation:
-;  2,916,685 cons cells, 2 symbols, 7,077,280 other bytes, 3484 static bytes
-NIL
-> 
\ No newline at end of file
diff --git a/archive/Kenzo-2/Kenzo-2-Acl5/Demo.cl b/archive/Kenzo-2/Kenzo-2-Acl5/Demo.cl
deleted file mode 100644
index a989251..0000000
--- a/archive/Kenzo-2/Kenzo-2-Acl5/Demo.cl
+++ /dev/null
@@ -1,113 +0,0 @@
-;;; DEMO DEMO DEMO DEMO DEMO DEMO DEMO DEMO DEMO DEMO DEMO
-;;; DEMO DEMO DEMO DEMO DEMO DEMO DEMO DEMO DEMO DEMO DEMO
-;;; DEMO DEMO DEMO DEMO DEMO DEMO DEMO DEMO DEMO DEMO DEMO
-
-(IN-PACKAGE :USER)
-
-(DEFVAR *STATEMENT*)
-
-;; C = comment
-(DEFUN C (string)
-  (terpri)
-  (dotimes (i 50) (princ "-"))
-  (princ "<Comment>")
-;  (dotimes (i 31) (princ "-"))
-;  (terpri)
-  (princ string)
-;  (terpri)
-  (dotimes (i 50) (princ "-"))
-  (values))
-
-;; R = read
-(DEFMACRO R (statement)
-  (declare (special *statement*))
-  (setf *statement* statement)
-  `(progn
-     (terpri)
-     (dotimes (i 50) (princ "-"))
-     (princ "<Lisp Statement>")
-;     (dotimes (i 29) (princ "-"))
-;     (terpri)
-     (pprint ',statement)
-     (terpri) ; (terpri)
-     (dotimes (i 50) (princ "-"))
-     (values)))
-
-(DEFUN STRIP-INITIAL-SPACES (st)
-  (let ((st2 (make-string (- (length st) (count #\Newline st)))))
-    (declare (type string st2))
-    (do ((i 0 (1+ i))
-         (j 0 (1+ j)))
-        ((= i (length st)))
-      (let ((char (aref st i)))
-        (when (char= char #\newline)
-          (incf i))
-        (setf (aref st2 j) char)))
-    st2))
-
-(DEFMACRO R2 (dstatement)
-  (declare (special *statement* *dstatement*))
-  (setf *dstatement* dstatement)
-  (setf *statement* (read-from-string dstatement))
-  `(progn
-     (terpri)
-      (dotimes (i 50) (princ "-"))
-      (princ "<Lisp Statement>")
-      ;  (dotimes (i 31) (princ "-"))
-      ;  (terpri)
-      (princ (strip-initial-spaces *dstatement*))
-      ;  (terpri)
-      (dotimes (i 50) (princ "-"))
-      (values)))
-
-;; E = EXECUTE
-(DEFUN E ()
-  (declare (special *statement*))
-  (terpri)
-  (dotimes (i 50) (princ "-"))
-  (princ "<Result>")
-;  (dotimes (i 32) (princ "-"))
-  (terpri) ; (terpri)
-  (prin1 (eval *statement*))
-  (terpri) ; (terpri)
-  (dotimes (i 50) (princ "-"))
-  (values))
-
-;; EP = EXECUTE by PRINT
-(DEFUN EP ()
-  (declare (special *statement*))
-  (terpri)
-  (dotimes (i 50) (princ "-"))
-  (princ "<Result>")
-;  (dotimes (i 32) (princ "-"))
-  (terpri) ; (terpri)
-  (eval *statement*)
-  (terpri) ; (terpri)
-  (dotimes (i 50) (princ "-"))
-  (values))
-
-(DEFUN EE ()
-  (declare (special *statement*))
-  (terpri)
-  (dotimes (i 10) (princ "-"))
-  (princ " Error ")
-  (dotimes (i 33) (princ "-"))
-  (terpri) (terpri)
-  (restart-case
-      (handler-bind ((error
-                         #'(lambda (condition)
-                             (format t "Type-error: ~S~&"
-                               (class-name (class-of condition)))
-                             (apply #'format t
-                                    (simple-condition-format-control condition)
-                                    (simple-condition-format-arguments condition))
-                             (invoke-restart 'my-restart))))
-                  (eval *statement*))
-    (my-restart () (values)))
-  (terpri) (terpri)
-  (dotimes (i 50) (princ "-"))
-  (values))
-
-(DEFMACRO M (statement)
-  (eval statement)
-  '(values ))
\ No newline at end of file
diff --git a/archive/Kenzo-2/Kenzo-2-Acl5/Release.txt b/archive/Kenzo-2/Kenzo-2-Acl5/Release.txt
deleted file mode 100644
index 1789408..0000000
--- a/archive/Kenzo-2/Kenzo-2-Acl5/Release.txt
+++ /dev/null
@@ -1,10 +0,0 @@
-Kenzo-2-2 => Kenzo-2-3
-
-  The speial-smsts.cl is modified ; the bsgn slot had been forgotten
-  in the sphere-wedge constructor.
-
-Kenzo-2-1 => Kenzo-2-2
-
-  The delta.cl file is modified, but the modification is not
-  satisfactory : the slot face *should_be* able to generate the slot
-  dffr.
diff --git a/archive/Kenzo-2/Kenzo-2-Acl5/Start.txt b/archive/Kenzo-2/Kenzo-2-Acl5/Start.txt
deleted file mode 100644
index 50e0707..0000000
--- a/archive/Kenzo-2/Kenzo-2-Acl5/Start.txt
+++ /dev/null
@@ -1,218 +0,0 @@
-Allegro CL Personal Edition 5.0.1 [Windows/x86] (6/29/99 16:56)
-Copyright (C) 1985-1999, Franz Inc., Berkeley, CA, USA.  All Rights Reserved.
-CG/IDE Version: 1.323.2.169
-
-[changing package from "COMMON-LISP-USER" to "COMMON-GRAPHICS-USER"]
-
-> (load "file-list")
-; Loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\file-list.cl
-
- FILE  1: classes
- FILE  2: macros
- FILE  3: various
- FILE  4: combinations
- FILE  5: chain-complexes
- FILE  6: chcm-elementary-op
- FILE  7: effective-homology
- FILE  8: homology-groups
- FILE  9: searching-homology
- FILE 10: cones
- FILE 11: tensor-products
- FILE 12: coalgebras
- FILE 13: cobar
- FILE 14: algebras
- FILE 15: bar
- FILE 16: simplicial-sets
- FILE 17: simplicial-mrphs
- FILE 18: delta
- FILE 19: special-smsts
- FILE 20: suspensions
- FILE 21: disk-pasting
- FILE 22: cartesian-products
- FILE 23: eilenberg-zilber
- FILE 24: kan
- FILE 25: simplicial-groups
- FILE 26: fibrations
- FILE 27: loop-spaces
- FILE 28: ls-twisted-products
- FILE 29: lp-space-efhm
- FILE 30: classifying-spaces
- FILE 31: k-pi-n
- FILE 32: serre
- FILE 33: cs-twisted-products
- FILE 34: cl-space-efhm
- FILE 35: whitehead
- FILE 36: smith
-T
-> (in-package :cat)
-#<The CAT package>
-> (load-cfiles)
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\classes.fasl
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\macros.fasl
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\various.fasl
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\combinations.fasl
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\chain-complexes.fasl
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\chcm-elementary-op.fasl
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\effective-homology.fasl
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\homology-groups.fasl
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\searching-homology.fasl
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\cones.fasl
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\tensor-products.fasl
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\coalgebras.fasl
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\cobar.fasl
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\algebras.fasl
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\bar.fasl
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\simplicial-sets.fasl
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\simplicial-mrphs.fasl
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\delta.fasl
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\special-smsts.fasl
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\suspensions.fasl
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\disk-pasting.fasl
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\cartesian-products.fasl
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\eilenberg-zilber.fasl
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\kan.fasl
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\simplicial-groups.fasl
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\fibrations.fasl
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\loop-spaces.fasl
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\ls-twisted-products.fasl
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\lp-space-efhm.fasl
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\classifying-spaces.fasl
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\k-pi-n.fasl
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\serre.fasl
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\cs-twisted-products.fasl
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\cl-space-efhm.fasl
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\whitehead.fasl
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\smith.fasl
---- done ---
-> (time (homology (loop-space (moore 2 4) 2) 7))
-
-Computing boundary-matrix in dimension 7.
-Rank of the source-module : 6.
-
-
-;; Clock -> 2005-10-03, 15h 9m 19s.
-Computing the boundary of the generator 1 (dimension 7) :
-<<AlLp[7 <<AlLp[4 N5][4 N5]>>]>> 
-End of computing.
-
-
-;; Clock -> 2005-10-03, 15h 9m 19s.
-Computing the boundary of the generator 2 (dimension 7) :
-<<AlLp[2 <<AlLp[3 M4]>>][5 <<AlLp[3 M4][3 M4]>>]>> 
-End of computing.
-
-
-;; Clock -> 2005-10-03, 15h 9m 19s.
-Computing the boundary of the generator 3 (dimension 7) :
-<<AlLp[5 <<AlLp[3 M4][3 M4]>>][2 <<AlLp[3 M4]>>]>> 
-End of computing.
-
-
-;; Clock -> 2005-10-03, 15h 9m 19s.
-Computing the boundary of the generator 4 (dimension 7) :
-<<AlLp[2 <<AlLp[3 M4]>>][2 <<AlLp[3 M4]>>][3 <<AlLp[4 N5]>>]>> 
-End of computing.
-
-
-;; Clock -> 2005-10-03, 15h 9m 19s.
-Computing the boundary of the generator 5 (dimension 7) :
-<<AlLp[2 <<AlLp[3 M4]>>][3 <<AlLp[4 N5]>>][2 <<AlLp[3 M4]>>]>> 
-End of computing.
-
-
-;; Clock -> 2005-10-03, 15h 9m 19s.
-Computing the boundary of the generator 6 (dimension 7) :
-<<AlLp[3 <<AlLp[4 N5]>>][2 <<AlLp[3 M4]>>][2 <<AlLp[3 M4]>>]>> 
-End of computing.
-
-
-Computing boundary-matrix in dimension 8.
-Rank of the source-module : 11.
-
-
-;; Clock -> 2005-10-03, 15h 9m 19s.
-Computing the boundary of the generator 1 (dimension 8) :
-<<AlLp[8 <<AlLp[3 M4][3 M4][3 M4]>>]>> 
-End of computing.
-
-
-;; Clock -> 2005-10-03, 15h 9m 24s.
-Computing the boundary of the generator 2 (dimension 8) :
-<<AlLp[2 <<AlLp[3 M4]>>][6 <<AlLp[3 M4][4 N5]>>]>> 
-End of computing.
-
-
-;; Clock -> 2005-10-03, 15h 9m 24s.
-Computing the boundary of the generator 3 (dimension 8) :
-<<AlLp[2 <<AlLp[3 M4]>>][6 <<AlLp[4 N5][3 M4]>>]>> 
-End of computing.
-
-
-;; Clock -> 2005-10-03, 15h 9m 24s.
-Computing the boundary of the generator 4 (dimension 8) :
-<<AlLp[3 <<AlLp[4 N5]>>][5 <<AlLp[3 M4][3 M4]>>]>> 
-End of computing.
-
-
-;; Clock -> 2005-10-03, 15h 9m 24s.
-Computing the boundary of the generator 5 (dimension 8) :
-<<AlLp[5 <<AlLp[3 M4][3 M4]>>][3 <<AlLp[4 N5]>>]>> 
-End of computing.
-
-
-;; Clock -> 2005-10-03, 15h 9m 24s.
-Computing the boundary of the generator 6 (dimension 8) :
-<<AlLp[6 <<AlLp[3 M4][4 N5]>>][2 <<AlLp[3 M4]>>]>> 
-End of computing.
-
-
-;; Clock -> 2005-10-03, 15h 9m 24s.
-Computing the boundary of the generator 7 (dimension 8) :
-<<AlLp[6 <<AlLp[4 N5][3 M4]>>][2 <<AlLp[3 M4]>>]>> 
-End of computing.
-
-
-;; Clock -> 2005-10-03, 15h 9m 24s.
-Computing the boundary of the generator 8 (dimension 8) :
-<<AlLp[2 <<AlLp[3 M4]>>][3 <<AlLp[4 N5]>>][3 <<AlLp[4 N5]>>]>> 
-End of computing.
-
-
-;; Clock -> 2005-10-03, 15h 9m 24s.
-Computing the boundary of the generator 9 (dimension 8) :
-<<AlLp[3 <<AlLp[4 N5]>>][2 <<AlLp[3 M4]>>][3 <<AlLp[4 N5]>>]>> 
-End of computing.
-
-
-;; Clock -> 2005-10-03, 15h 9m 24s.
-Computing the boundary of the generator 10 (dimension 8) :
-<<AlLp[3 <<AlLp[4 N5]>>][3 <<AlLp[4 N5]>>][2 <<AlLp[3 M4]>>]>> 
-End of computing.
-
-
-;; Clock -> 2005-10-03, 15h 9m 24s.
-Computing the boundary of the generator 11 (dimension 8) :
-<<AlLp[2 <<AlLp[3 M4]>>][2 <<AlLp[3 M4]>>][2 <<AlLp[3 M4]>>][2 <<AlLp[3 M4]>>]>> 
-End of computing.
-
-
-
-
-Homology in dimension 7 :
-
-
-Component Z/2Z
-
-
----done---
-
-;; Clock -> 2005-10-03, 15h 9m 24s.
-
-; cpu time (non-gc) 4,735 msec user, 0 msec system
-; cpu time (gc)     656 msec user, 0 msec system
-; cpu time (total)  5,391 msec user, 0 msec system
-; real time  5,390 msec
-; space allocation:
-;  2,917,299 cons cells, 2 symbols, 7,081,936 other bytes, 3484 static bytes
-NIL
-> 
\ No newline at end of file
diff --git a/archive/Kenzo-2/Kenzo-2-Acl5/algebras.cl b/archive/Kenzo-2/Kenzo-2-Acl5/algebras.cl
deleted file mode 100644
index 6c40079..0000000
--- a/archive/Kenzo-2/Kenzo-2-Acl5/algebras.cl
+++ /dev/null
@@ -1,53 +0,0 @@
-;;;  ALGEBRAS  ALGEBRAS  ALGEBRAS  ALGEBRAS  ALGEBRAS  ALGEBRAS
-;;;  ALGEBRAS  ALGEBRAS  ALGEBRAS  ALGEBRAS  ALGEBRAS  ALGEBRAS
-;;;  ALGEBRAS  ALGEBRAS  ALGEBRAS  ALGEBRAS  ALGEBRAS  ALGEBRAS
-
-(IN-PACKAGE "CAT")
-
-(PROVIDE "algebras")
-
-(DEFMETHOD PRINT-OBJECT ((algb algebra) stream)
- (the algebra
-   (progn
-      (format stream "[K~D Algebra]" (idnm algb))
-      algb)))
-
-(DEFUN ALGEBRA (&rest rest &key dfnt &allow-other-keys)
-  (declare (type list dfnt))
-  (already algebra dfnt)
-  (the algebra
-    (apply #'make-instance 'algebra rest)))
-
-(DEFMETHOD SHARED-INITIALIZE
-    ((algb algebra) slot-names &key aprd-intr aprd-strt)
-  (declare
-   (type (or (eql t) list) slot-names)
-   (type intr aprd-intr)
-   (type strt aprd-strt))
-  (call-next-method)
-  (when-slot aprd
-             (with-slots (aprd) algb
-               (declare (type morphism aprd))
-               (when aprd-intr
-                 (unless aprd-strt
-                   (error "In ALGEBRA, an APRD-INTR is given, but not its APRD-STRT."))
-                 (setf aprd (morphism :sorc (tnsr-prdc algb algb) :trgt algb :degr 0
-                                      :intr aprd-intr :strt aprd-strt
-                                      :dfnt `(algebra-product ,algb))))))
-  algb)
-
-(DEFMETHOD PRINT-OBJECT ((hopf hopf-algebra) stream)
- (the hopf-algebra
-   (progn
-      (format stream "[K~D Hopf-Algebra]" (idnm hopf))
-      hopf)))
-
-(DEFUN HOPF-ALGEBRA (&rest rest &key dfnt &allow-other-keys)
-  (declare (type list dfnt))
-  (already hopf-algebra dfnt)
-  (the hopf-algebra
-    (apply #'make-instance 'hopf-algebra rest)))
-
-(DEFMETHOD SHARED-INITIALIZE ((hplg hopf-algebra) slot-names &rest rest)
-  (declare (ignore slot-names rest))
-  (call-next-method))
\ No newline at end of file
diff --git a/archive/Kenzo-2/Kenzo-2-Acl5/bar.cl b/archive/Kenzo-2/Kenzo-2-Acl5/bar.cl
deleted file mode 100644
index d8799d1..0000000
--- a/archive/Kenzo-2/Kenzo-2-Acl5/bar.cl
+++ /dev/null
@@ -1,701 +0,0 @@
-;;;  BAR  BAR  BAR  BAR  BAR  BAR  BAR  BAR  BAR
-;;;  BAR  BAR  BAR  BAR  BAR  BAR  BAR  BAR  BAR
-;;;  BAR  BAR  BAR  BAR  BAR  BAR  BAR  BAR  BAR
-
-;;;
-;;;  MAC-LANE signs (p. 306)
-;;;
-
-(IN-PACKAGE "CAT")
-
-(PROVIDE "bar")
-
-(DEFUN ABAR (&rest list)
-   (when (= 1 (length list))
-      (setf list (first list)))
-   (unless (evenp (length list))
-      (error "In ABAR, the length list should be even."))
-   (the abar
-      (let ((rslt (list :abar)))
-         (declare (list rslt))
-         (do ((mark list (cddr mark)))
-             ((endp mark))
-            (declare (list mark))
-            (push (brgn (car mark) (cadr mark)) rslt))
-         (nreverse rslt))))
-
-#|
-  (abar )
-  (abar '(2 a 3 b))
-  (abar 2 'a 3 'b)
-  (abar 2 'a 3))  ;; error
-|#
-
-(DEFCONSTANT +NULL-ABAR+ (make-abar :list +empty-list+))
-
-(DEFMETHOD PRINT-KEYCONS ((car (eql :abar)) cdr stream)
-   (declare
-      (list cdr)
-      (stream stream))
-   (the abar
-      (progn
-         (format stream "<<Abar")
-         (dolist (brgn cdr)
-            (declare (type brgn brgn))
-            (with-brgn (degr gnrt) brgn
-               (format stream "[~D ~A]" degr gnrt)))
-         (format stream ">>")
-         (cons car cdr))))
-
-(DEFUN BAR-CMPR (cmpr)
-   (declare (type cmprf cmpr))
-   (flet ((rslt (abar1 abar2)
-             (declare (type abar abar1 abar2))
-             (the cmpr
-                (lexico
-                   (f-cmpr (length abar1) (length abar2))
-                   (maplexico
-                      #'(lambda (brgn1 brgn2)
-                           (lexico
-                              (f-cmpr (bdegr brgn1) (bdegr brgn2))
-                              (funcall cmpr (bgnrt brgn1) (bgnrt brgn2))))
-                      (abar-list abar1)
-                      (abar-list abar2))))))
-      (the cmprf #'rslt)))
-
-#|
-  (setf r (bar-cmpr #'s-cmpr))
-  (funcall r (abar) (abar))
-  (funcall r (abar 3 'a) (abar))
-  (funcall r (abar 3 'a) (abar 2 'a 1 'b))
-  (funcall r (abar 3 'a) (abar 3 'b))
-  (funcall r (abar 3 'a) (abar 3 'a)))
-|#
-
-(DEFUN BAR-BASIS-LENGTH (basis degr length)
-   (declare
-      (type basis basis)
-      (fixnum degr length))
-   (the list
-      (progn
-	(when (= 1 length)
-	      (return-from bar-basis-length
-			   (mapcar
-			    #'(lambda (item)
-				(declare (type gnrt item))
-				(list (brgn degr item)))
-			    (funcall basis (1- degr)))))
-	(when (< degr 4)
-	      (return-from bar-basis-length +empty-list+))
-	(mapcan
-	 #'(lambda (degr1)
-	     (declare (fixnum degr1))
-	     (let ((list1 (funcall basis (1- degr1)))
-		   (list2 (bar-basis-length
-			    basis (- degr degr1) (1- length))))
-	       (declare (list list1 list2))
-	       (mapcan
-		#'(lambda (item1)
-		    (declare (type gnrt item1))
-		    (mapcar
-		     #'(lambda (item2)
-			 (declare (type iabar item2))
-			 (cons (brgn degr1 item1) item2))
-		     list2))
-		list1)))
-	 (>a-b< 1 (1- degr))))))
-
-#|
-  (setf basis #'(lambda (degr)
-                   (list degr)))
-  (bar-basis-length basis 2 1)
-  (bar-basis-length basis 2 2)
-  (bar-basis-length basis 3 1)
-  (bar-basis-length basis 3 2)
-  (bar-basis-length basis 4 1)
-  (bar-basis-length basis 4 2)
-  (bar-basis-length basis 4 3)
-  (bar-basis-length basis 4 4)
-  (bar-basis-length basis 8 1)
-  (bar-basis-length basis 8 2)
-  (bar-basis-length basis 8 3)
-  (bar-basis-length basis 8 4)
-  (bar-basis-length basis 8 5)
-  (bar-basis-length basis 8 6)
-  (bar-basis-length basis 8 11))
-|#
-
-(DEFUN BAR-BASIS (basis)
-   (declare (type basis basis))
-   (the basis
-      (progn
-         (when (eq :locally-effective basis)
-            (return-from bar-basis :locally-effective))
-	 (flet ((rslt (degr)
-		      (declare (fixnum degr))
-		      (cond ((zerop degr) (list +null-abar+))
-			    ((< degr 2) +empty-list+)
-			    (t
-			     (mapcan
-			      #'(lambda (length)
-				  (declare (fixnum length))
-				  (mapcar
-                                 #'(lambda (iabar)
-				     (declare (type iabar iabar))
-				     (make-abar :list iabar))
-                                 (bar-basis-length basis degr length)))
-			      (>a-b> 0 (floor degr 2)))))))
-	       #'rslt))))
-
-#|
-  (setf basis #'(lambda (degr)
-                   (list degr)))
-  (setf r (bar-basis basis))
-  (funcall r 0)
-  (funcall r 1)
-  (funcall r 2)
-  (dotimes (i 7)
-     (print (funcall r i)))
-  (bar-basis :locally-effective))
-|#
-
-(DEFUN BAR-INTR-VRTC-DFFR (dffr)
-   (declare (type morphism dffr))
-   (labels ((rslt (degr iabar)
-               ;; the argument iabar is an internal algebraic bar,
-               ;;     without the keyword :abar
-               ;; rslt returns an internal combination
-               ;;     without the keyword :cmbn, without degree
-               (declare
-                  (fixnum degr)
-                  (type iabar iabar))
-	       (progn
-		 (unless iabar
-		   (return-from rslt +empty-list+))
-		 (let ((brgn1 (first iabar))
-		       (rest2 (rest iabar)))
-		   (declare
-		     (type brgn brgn1)
-		     (type iabar rest2))
-		   (with-brgn (degr1 gnrt1) brgn1
-		   (let ((d-gnrt1 (cmbn-list (gnrt-? dffr (1- degr1) gnrt1)))
-			 (d-rest2 (rslt (- degr degr1) rest2))
-			 (degr1-1 (1- degr1))
-			 (rest-sign (-1-expt-n degr1)))
-		     (declare
-		       (type icmbn d-gnrt1 d-rest2)
-		       (fixnum degr1-1 rest-sign))
-		     (nconc
-		       (mapcar
-			 #'(lambda (term)
-			     (declare (type term term))
-			     (with-term (cffc gnrt) term
-			       (term (- cffc)
-				     (cons (brgn degr1-1 gnrt) rest2))))
-			 d-gnrt1)
-		       (mapcar
-			 #'(lambda (term)
-			     (with-term (cffc gnrt) term
-			       (term (* rest-sign cffc)
-				     (cons brgn1 gnrt))))
-			 d-rest2))))))))
-	(the intr
-	  #'(lambda (degr abar)
-	      (declare
-	        (fixnum degr)
-		(type abar abar))
-              (make-cmbn
-	        :degr (1- degr)
-		:list (mapcar
-		        #'(lambda (term)
-			    (with-term (cffc iabar) term
-			      (term cffc (make-abar :list iabar))))
-			(rslt degr (abar-list abar))))))))
-
-#|
-  (setf d (soft-delta-infinity))
-  (setf r (bar-intr-vrtc-dffr (dffr d)))
-  (funcall r 0 (abar))
-  (funcall r 3 (abar 3 (d 7)))
-  (funcall r 5 (abar 3 (d 7) 2 (d 3)))
-  (funcall r 5 (abar 2 (d 3) 3 (d 7))))
-|#
-
-(DEFMETHOD VRTC-BAR ((chcm chain-complex))
-   (the chain-complex
-     (let ((dfnt `(vrtc-bar ,chcm)))
-       (declare (type list dfnt))
-       (already vrtc-bar dfnt)
-       (with-slots (cmpr basis dffr) chcm
-         (declare
-          (type cmprf cmpr)
-          (type basis basis)
-          (type morphism dffr))
-         (chain-complex
-          :cmpr (bar-cmpr cmpr)
-          :basis (bar-basis basis)
-          :bsgn +null-abar+
-          :dffr-intr (bar-intr-vrtc-dffr dffr)
-          :dffr-strt :gnrt
-          :dfnt dfnt)))))
-
-#|
-  (cat-init)
-  (setf v (vrtc-bar (soft-delta-infinity)))
-  (defun random-abar (length)
-     (let ((rslt nil))
-        (dotimes (i length)
-           (let* ((gmsm (random (mask 7)))
-                  (dmns (1- (logcount gmsm))))
-              (when (plusp dmns)
-                 (push (brgn (1+ dmns) (d gmsm)) rslt))))
-        (make-abar :list rslt)))
-  (dotimes (i 10) (print (random-abar 5)))
-  (dotimes (i 10)
-     (let ((abar (random-abar 3)))
-        (print abar)
-        (print (? v (apply #'+ (mapcar #'car (abar-list abar))) abar))
-        (print (? v (? v (apply #'+ (mapcar #'car (abar-list abar))) abar)))))
-|#
-
-(DEFUN BAR-INTR-HRZN-DFFR (aprd)
-   (declare (type morphism aprd))
-   (labels ((rslt (degr iabar)
-               (declare
-                  (fixnum degr)
-                  (type iabar iabar))
-               (the icmbn
-                  (progn
-                     (unless (cdr iabar)
-                        (return-from rslt +empty-list+))
-                     (let ((brgn1 (first iabar))
-			   (brgn2 (second iabar))
-			   (rest1 (rest iabar))
-			   (rest2 (cddr iabar)))
-                        (declare
-                           (type brgn brgn1 brgn2)
-                           (type iabar rest1 rest2))
-                        (with-brgn (degr1 gnrt1) brgn1
-			(with-brgn (degr2 gnrt2) brgn2
-                           (let ((sign (-1-expt-n degr1))
-				 (aprd-brgn1-brgn2 (gnrt-? aprd (+ degr1 degr2 -2)
-							   (tnpr (1- degr1) gnrt1
-								 (1- degr2) gnrt2)))
-				 (aprd-rest1 (rslt (- degr degr1) rest1)))				  
-			     (declare
-			      (type icmbn aprd-brgn1-brgn2 aprd-rest1))
-			     (with-cmbn (degr12 icmbn12) aprd-brgn1-brgn2
-			       (incf degr12)
-			       (nconc
-			        (mapcar
-				 #'(lambda (term2)
-				     (declare (type term term2))
-				     (with-term (cffc2 iabar2) term2
-				       (term (* sign cffc2) (cons brgn1 iabar2))))
-				  aprd-rest1)
-				(mapcar
-				  #'(lambda (term1)
-				      (declare (type term term1))
-				      (with-term (cffc1 gnrt12) term1
-					(term (* sign cffc1) (cons (brgn degr12 gnrt12) rest2))))
-				  icmbn12)))))))))))
-      (the intr
-         #'(lambda (degr abar)
-              (declare
-                 (fixnum degr)
-                 (type abar abar))
-              (the cmbn
-                 (make-cmbn :degr (1- degr)
-                    :list (mapcar #'(lambda (term)
-                                       (declare (type term term))
-                                       (with-term (cffc iabar) term
-                                          (term cffc (make-abar :list iabar))))
-                             (rslt degr (abar-list abar)))))))))
-
-#|
-  (setf k (k-z-1))
-  (setf r (bar-intr-hrzn-dffr (aprd k)))
-  (funcall r 0 (abar ))
-  (funcall r 3 (abar 3 '(2 3)))
-  (funcall r 6 (abar 3 '(2 3) 3 '(-2 -3)))
-  (funcall r 9 (abar 3 '(2 3) 3 '(-2 -3) 3 '(2 3)))
-  (funcall r 11 (abar 3 '(2 3) 3 '(-2 -3) 2 '(-2) 3 '(-2 -3))))
-|#
-
-(DEFUN BAR-HRZN-DFFR (algb)
-   (declare (type algebra algb))
-   (the morphism
-      (with-slots (aprd) algb
-         (declare (type morphism aprd))
-         (morphism
-            :sorc (vrtc-bar algb) :trgt (vrtc-bar algb) :degr -1
-            :intr (bar-intr-hrzn-dffr aprd) :strt :gnrt
-            :dfnt `(bar-hrzn-dffr ,algb)))))
-
-#|
-  (cat-init)
-  (setf h (bar-hrzn-dffr (k-z-1)))
-  (defun random-abar (tot-degr~ max-degr)
-    (do ((rslt nil)
-         (cum-degr 0 (+ cum-degr degr 1))
-         (degr))
-        ((>= cum-degr tot-degr~) (make-abar :list rslt))
-       (setf degr (1+ (random max-degr)))
-       (push (brgn (1+ degr)
-                   (let ((list (make-list degr)))
-                     (mapl
-                       #'(lambda (sublist)
-                           (setf (car sublist) (- (random 21) 10)))
-                       list)
-                     list))
-             rslt)))
-  (dotimes (i 10) (print (random-abar 10 5)))
-  (setf abar (random-abar 10 5))
-  (? h (apply #'+ (mapcar #'car (abar-list abar))) abar)
-  (? h (? h (apply #'+ (mapcar #'car (abar-list abar))) abar))
-  (dotimes (i 10)
-     (let ((abar (random-abar 10 3)))
-        (print abar)
-        (print (? h (apply #'+ (mapcar #'car (abar-list abar))) abar))
-        (print (? h (? h (apply #'+ (mapcar #'car (abar-list abar))) abar)))))
-|#
-
-(DEFUN BAR-INTR-DFFR (vrtc-dffr hrzn-dffr)
-   (declare (type morphism vrtc-dffr hrzn-dffr))
-   (flet ((rslt (degr abar)
-             (declare
-                (fixnum degr)
-                (type abar abar))
-             (make-cmbn :degr (1- degr)
-                :list (append       ;;; and not nconc, otherwise a terrible bug, when the
-                                    ;;;   first result is stored in memory...
-                         (cmbn-list (gnrt-? hrzn-dffr degr abar))
-                         (cmbn-list (gnrt-? vrtc-dffr degr abar))))))
-      (the intr #'rslt)))
-
-(DEFMETHOD BAR ((algebra algebra))
-  (the chain-complex
-    (let ((vrtc-bar (vrtc-bar algebra))
-          (bar-hrzn-dffr (bar-hrzn-dffr algebra)))
-      (declare (type chain-complex vrtc-bar hrzn-bar))
-      (let ((rslt (chain-complex
-                   :cmpr (cmpr vrtc-bar)
-                   :basis (basis vrtc-bar)
-                   :bsgn +null-abar+
-                   :dffr-intr (bar-intr-dffr (dffr vrtc-bar) bar-hrzn-dffr)
-                   :dffr-strt :gnrt
-                   :dfnt `(add ,vrtc-bar ,bar-hrzn-dffr))))
-          (declare (type chain-complex rslt))
-          (setf (slot-value rslt 'grmd) (grmd vrtc-bar))
-          rslt))))
-
-#|
-(cat-init)
-(setf b (bar (k-z-1)))   
-(defun random-abar (tot-degr~ max-degr)
-  (do ((rslt nil)
-       (cum-degr 0 (+ cum-degr degr 1))
-       (degr))
-      ((>= cum-degr tot-degr~) (make-abar :list rslt))
-    (setf degr (1+ (random max-degr)))
-    (push (brgn (1+ degr)
-                (let ((list (make-list degr)))
-                  (mapl
-                      #'(lambda (sublist)
-                          (setf (car sublist) (- (random 21) 10)))
-                    list)
-                  list))
-          rslt)))
-(setf abar (random-abar 10 3))
-(? b (apply #'+ (mapcar #'car (abar-list abar))) abar)
-(? b (? b (apply #'+ (mapcar #'car (abar-list abar))) abar))
-(dotimes (i 10)
-  (let ((abar (random-abar 10 3)))
-    (print abar)
-    (print (? b (apply #'+ (mapcar #'car (abar-list abar))) abar))
-    (print (? b (? b (apply #'+ (mapcar #'car (abar-list abar))) abar)))))
-|#
-
-(DEFUN CMBN-ABAR-CMBN-TNPR (cmbn abar-cmbn)
-   (declare (type cmbn cmbn abar-cmbn))
-   (the cmbn
-      (with-cmbn (degr1 list1) cmbn
-         (incf degr1)     ;; because abar organization
-      (with-cmbn (degrr listr) abar-cmbn
-         (make-cmbn
-            :degr (+ degr1 degrr)
-            :list
-            (mapcan
-               #'(lambda (term1)
-                    (declare (type term term1))
-                    (with-term (cffc1 gnrt1) term1
-                       (let ((brgn1 (brgn degr1 gnrt1)))
-                          (declare (type brgn brgn1))
-                          (mapcar
-                             #'(lambda (termr)
-                                  (declare (type term termr))
-                                  (with-term (cffcr abarr) termr
-                                     (term (* cffc1 cffcr)
-                                        (make-abar
-                                           :list (cons brgn1 (abar-list abarr))))))
-                             listr))))
-               list1))))))
-
-(DEFUN NCMBN-BAR (cmbn-list)
-   (declare (list cmbn-list))
-   (the cmbn
-      (progn
-         (unless cmbn-list
-            (return-from ncmbn-bar (cmbn 0 1 +null-abar+)))
-         (cmbn-abar-cmbn-tnpr
-            (first cmbn-list)
-            (ncmbn-bar (rest cmbn-list))))))
-#|
-  (ncmbn-bar nil)
-  (ncmbn-bar (list (cmbn 3 2 'a 3 'b)))
-  (ncmbn-bar (list (cmbn 1 2 'a 3 'b) (cmbn 2 4 'c 5 'd)))
-  (ncmbn-bar (list (cmbn 1 2 'a 3 'b) (cmbn 1 4 'c 5 'd) (cmbn 1 6 'e 7 'f))))
-|#
-
-(DEFUN MRPH-VRTC-BAR-INTR (mrph)
-   (declare (type morphism mrph))
-   (flet ((rslt (degr abar)
-             (declare
-                (ignore degr)
-                (type abar abar))
-             (the cmbn
-                (ncmbn-bar
-                   (mapcar #'(lambda (brgn)
-                                (declare (type brgn brgn))
-                                (with-brgn (degr gnrt) brgn
-                                   (gnrt-? mrph (1- degr) gnrt)))
-                      (abar-list abar))))))
-      (the intr #'rslt)))
-
-#|
-  (setf cc (chain-complex :cmpr #'f-cmpr :dffr-strt :cmbn))
-  (setf m (morphism :sorc cc :trgt cc :degr 0 :intr
-            #'(lambda (degr gnrt) (cmbn degr 2 gnrt 3 (1+ gnrt)))
-            :strt :gnrt :dfnt '(test)))
-  (setf r (mrph-vrtc-bar-intr m))
-  (funcall r 4 (abar 2 3 2 4))
-|#
-
-(DEFMETHOD VRTC-BAR ((mrph morphism))
-  (the morphism
-    (let ((dfnt `(vrtc-bar ,mrph)))
-      (declare (type list dfnt))
-      (if (eq (first (dfnt mrph)) 'idnt-mrph)
-          (idnt-mrph (vrtc-bar (sorc mrph)))
-        (morphism
-         :sorc (vrtc-bar (sorc mrph))
-         :trgt (vrtc-bar (trgt mrph))
-         :degr 0
-         :intr (mrph-vrtc-bar-intr mrph)
-         :strt :gnrt
-         :dfnt dfnt)))))
-
-#|
-  (cat-init)
-  (setf f (aw (soft-delta-infinity) (soft-delta-infinity)))
-  (setf cf (vrtc-bar f))
-  (? cf 6 (abar 3 (crpr 0 (d 7) 0 (d 7)) 3 (crpr 0 (d 56) 0 (d 56))))
-|#
-
-(DEFUN HMTP-VRTC-BAR-INTR (h gf)
-   (declare (type morphism h gf))
-   (labels ((rslt (degr iabar)
-	      (declare
-	       (fixnum degr)
-	       (type iabar iabar))
-	      (unless iabar
-		(return-from rslt +empty-list+))
-	      (let ((brgn1 (first iabar))
-		    (rest2 (rest iabar)))
-		(declare
-		 (type brgn brgn1)
-		 (list rest2))
-		(with-brgn (degr1 gnrt1) brgn1
-		  (let ((h-gnrt1 (cmbn-list (gnrt-? h (1- degr1) gnrt1)))
-			(h-rest2 (rslt (- degr degr1) rest2))
-			(degr1+1 (1+ degr1))
-			(rest-sign (-1-expt-n degr1))
-			(gf-gnrt1 (cmbn-list (gnrt-? gf (1- degr1) gnrt1))))
-		    (declare
-		      (fixnum degr1+1 rest-sign)
-		      (type icmbn h-gnrt1 h-rest2 gf-gnrt1))
-		    (nconc
-		     (mapcan
-		      #'(lambda (term1)
-			  (declare (type term term1))
-			  (with-term (cffc1 gnrt11) term1
-			    (mapcar
-			     #'(lambda (term2)
-				 (declare (type term term2))
-				 (with-term (cffc2 iabar2) term2
-				   (term (* rest-sign cffc1 cffc2)
-					 (cons (brgn degr1 gnrt11) iabar2))))
-			     h-rest2)))
-		      gf-gnrt1)
-		     (mapcar
-		      #'(lambda (term1)
-			  (declare (type term term1))
-			  (with-term (cffc1 gnrt11) term1
-			    (term (- cffc1)
-				  (cons (brgn degr1+1 gnrt11) rest2))))
-		      h-gnrt1)))))))
-	   (the intr
-	      #'(lambda (degr abar)
-		  (declare
-		    (fixnum degr)
-		    (type abar abar))
-		  (make-cmbn
-		   :degr (1+ degr)
-		   :list (mapcar
-			  #'(lambda (term)
-			      (declare (type term term))
-			      (with-term (cffc iabar) term
-				(declare
-				   (fixnum cffc)
-				   (type iabar iabar))
-				(term cffc (make-abar :list iabar))))
-			  (rslt degr (abar-list abar))))))))
-
-#|
-  (cat-init)
-  (setf ez (ez (delta-infinity) (delta-infinity)))
-  (setf h (h ez) gf (cmps (g ez) (f ez)))
-  (setf r (hmtp-vrtc-bar-intr h gf))
-  (funcall r 3 (abar 3 (crpr 0 7 0 7)))
-  (funcall r 9 (abar 3 (crpr 0 7 0 7) 3 (crpr 0 14 0 14) 3 (crpr 0 14 0 14)))
-|#
-
-(DEFUN HMTP-VRTC-BAR (h gf)
-   (declare (type morphism h gf))
-   (unless (and (= +1 (degr h))
-                (= +0 (degr gf)))
-      (error "In HMTP-VRTC-BAR, the morphism degrees are not the right ones."))
-   (unless (and (eq (sorc h) (trgt h))
-                (eq (trgt h) (sorc gf))
-                (eq (sorc gf) (trgt gf)))
-      (error "In HMTP-VRTC-BAR, fg-h sources and targets are not the same."))
-   (the morphism
-      (if (eq (first (dfnt h)) 'zero-mrph)
-         (zero-mrph (vrtc-bar (sorc h)))
-         (morphism
-            :sorc (vrtc-bar (sorc h)) :trgt (vrtc-bar (sorc h)) :degr +1
-            :intr (hmtp-vrtc-bar-intr h gf)
-            :strt :gnrt
-            :dfnt `(hmtp-vrtc-bar ,h ,gf)))))
-
-(DEFMETHOD VRTC-BAR ((rdct reduction))
-  (the reduction
-    (let ((dfnt `(vrtc-bar ,rdct)))
-      (declare (type list dfnt))
-      (if (eq (first (dfnt rdct)) 'trivial-rdct)
-          (trivial-rdct (vrtc-bar (bcc rdct)))
-        (with-slots (f g h) rdct
-          (reduction
-           :f (vrtc-bar f)
-           :g (vrtc-bar g)
-           :h (hmtp-vrtc-bar h (cmps g f))
-           :dfnt dfnt))))))
-  
-#|
-  (cat-init)
-  (setf tcc (chain-complex
-               :cmpr #'s-cmpr
-               :basis #'(lambda (degr) '(a b c d))
-               :bsgn 'd
-               :dffr-intr #'(lambda (degr gnrt)
-                               (ecase gnrt
-                                  (a (cmbn (1- degr) 1 'b 1 'd))
-                                  ((b d) (cmbn (1- degr)))
-                                  (c (cmbn (1- degr) 1 'd))))
-               :dffr-strt :gnrt
-               :dfnt '(tcc)))
-  (setf bcc (chain-complex
-               :cmpr #'s-cmpr
-               :basis #'(lambda (degr) '(c d))
-               :bsgn 'd
-               :dffr-intr #'(lambda (degr gnrt)
-                               (ecase gnrt
-                                  (d (cmbn (1- degr)))
-                                  (c (cmbn (1- degr) 1 'd))))
-               :dffr-strt :gnrt
-               :dfnt '(bcc)))
-  (setf f (morphism :sorc tcc :trgt bcc :degr 0
-             :intr #'(lambda (degr gnrt)
-                        (ecase gnrt
-                           (a (cmbn degr 1 'c 1 'd))
-                           (b (cmbn degr))
-                           ((c d) (cmbn degr 1 gnrt))))
-             :strt :gnrt :dfnt '(f)))
-  (setf g (morphism :sorc bcc :trgt tcc :degr 0
-             :intr #'identity :strt :cmbn :dfnt '(g)))
-  (setf h (morphism :sorc tcc :trgt tcc :degr +1
-             :intr #'(lambda (degr gnrt)
-                        (ecase gnrt
-                           ((a b) (cmbn (1+ degr) 1 'a -1 'b -1 'c -1 'd))
-                           ((c d) (cmbn (1+ degr)))))
-             :strt :gnrt :dfnt '(h)))
-  (setf rdct (reduction :f f :g g :h h :dfnt '(rdct)))
-  (tcc rdct 3 'a)
-  (g rdct (f rdct 3 'a))
-  (h rdct 3 'a)
-  (setf bar (vrtc-bar rdct))
-  (pre-check-rdct bar)
-  (defun aleat-tc ()
-     (do ((tdegr 0 (+ tdegr degr))
-          (degr (+ 2 (random 3)) (+ 2 (random 3)))
-          (gnrt (intern (coerce (vector (code-char (+ 65 (random 4)))) 'string))
-                (intern (coerce (vector (code-char (+ 65 (random 4)))) 'string)))
-          (rslt nil (cons (brgn degr gnrt) rslt)))
-         ((> tdegr 10) (setf *tc* (cmbn tdegr 1 (make-abar :list rslt))))))
-  (aleat-tc)
-  (defun aleat-bc ()
-     (do ((tdegr 0 (+ tdegr degr))
-          (degr (+ 2 (random 3)) (+ 2 (random 3)))
-          (gnrt (intern (coerce (vector (code-char (+ 67 (random 2)))) 'string))
-                (intern (coerce (vector (code-char (+ 67 (random 2)))) 'string)))
-          (rslt nil (cons (brgn degr gnrt) rslt)))
-         ((> tdegr 10) (setf *bc* (cmbn tdegr 1 (make-abar :list rslt))))))
-  (aleat-bc)
-  (defun c ()
-     (aleat-tc)
-     (aleat-bc)
-     (check-rdct))
-  (loop (c))  ;; degrees >= 15 is possible => error.
-|#
-
-(DEFMETHOD VRTC-BAR ((eqvl equivalence))
-  (the equivalence
-    (let ((dfnt `(vrtc-bar ,eqvl)))
-      (declare (type list dfnt))
-      (already vrtc-bar dfnt)
-      (if (eq (first (dfnt eqvl)) 'trivial-eqvl)
-          (trivial-eqvl (vrtc-bar (lbcc eqvl)))
-        (with-slots (lrdct rrdct) eqvl
-          (equivalence 
-           :lrdct (vrtc-bar lrdct)
-           :rrdct (vrtc-bar rrdct)
-           :dfnt dfnt))))))
-
-(DEFMETHOD BAR ((eqvl equivalence))
-  (unless (typep (lbcc eqvl) 'algebra)
-    (error "In (BAR eqvl), the LBCC should be a algebra."))
-  (the equivalence
-    (if (eq (first (dfnt eqvl)) 'trivial-eqvl)
-        (trivial-eqvl (bar (lbcc eqvl)))
-      (add (vrtc-bar eqvl) (bar-hrzn-dffr (lbcc eqvl))))))
-
-#|
-  (cat-init)
-  (setf h (efhm (k-z-1)))
-  (setf b (bar h))
-  (inspect b)
-  (homology (rbcc b) 0 11)
-|#
-
-  
-
diff --git a/archive/Kenzo-2/Kenzo-2-Acl5/cartesian-products.cl b/archive/Kenzo-2/Kenzo-2-Acl5/cartesian-products.cl
deleted file mode 100644
index edc1cda..0000000
--- a/archive/Kenzo-2/Kenzo-2-Acl5/cartesian-products.cl
+++ /dev/null
@@ -1,311 +0,0 @@
-;;;  CARTESIAN-PRODUCTS  CARTESIAN-PRODUCTS  CARTESIAN-PRODUCTS  CARTESIAN-PRODUCTS
-;;;  CARTESIAN-PRODUCTS  CARTESIAN-PRODUCTS  CARTESIAN-PRODUCTS  CARTESIAN-PRODUCTS
-;;;  CARTESIAN-PRODUCTS  CARTESIAN-PRODUCTS  CARTESIAN-PRODUCTS  CARTESIAN-PRODUCTS
-
-(IN-PACKAGE "CAT")
-
-(PROVIDE "cartesian-products")
-
-(DEFMETHOD PRINT-KEYCONS ((car (eql :crpr)) cdr stream)
-   (declare
-      (cons cdr)
-      (stream stream))
-   (the (eql t)
-      (progn
-         (setf cdr (cons car cdr))
-         (with-crpr (dgop1 gmsm1 dgop2 gmsm2) cdr
-            (format stream
-               "<CrPr ~A ~A ~A ~A>"
-               (hyphenize-list (dgop-int-ext dgop1)) gmsm1
-               (hyphenize-list (dgop-int-ext dgop2)) gmsm2)
-            cdr)
-         t)))
-
-(DEFUN EXTRACT-COMMON-DGOP (dgop1 dgop2)
-   (declare (fixnum dgop1 dgop2))
-   (let ((dgop (logand dgop1 dgop2)))
-      (declare (fixnum dgop))
-      (do ((indx (1- (integer-length dgop)) (1- indx)))
-          ((minusp indx))
-         (declare (fixnum indx))
-         (when (logbitp indx dgop)
-            (setf dgop1 (remove-bit dgop1 indx)
-                  dgop2 (remove-bit dgop2 indx))))
-      (values dgop dgop1 dgop2)))
-
-#|
-  (dotimes (i 100)
-     (dotimes (j 100)
-        (multiple-value-bind (dgop dgop1 dgop2) (extract-common-dgop i j)
-           (unless (and (= i (dgop*dgop dgop dgop1))
-                        (= j (dgop*dgop dgop dgop2)))
-              (error "i = ~D, j = ~D, dgop = ~D, dgop1 = ~D, dgop2 = ~D"
-                 i j dgop dgop1 dgop2)))))
-|#
-
-(DEFUN 2ABSM-ACRPR (absm1 absm2)
-   (declare (type absm absm1 absm2))
-   (the absm
-      (with-absm (dgop1 gmsm1) absm1
-      (with-absm (dgop2 gmsm2) absm2
-         (multiple-value-bind (dgop dgop11 dgop22) (extract-common-dgop dgop1 dgop2)
-            (declare (fixnum dgop dgop11 dgop22))
-            (absm dgop
-               (crpr dgop11 gmsm1 dgop22 gmsm2)))))))
-
-#|
-  (2absm-acrpr (absm 5 'a) (absm 3 'b))
-|#
-
-(DEFUN CRTS-PRDC-CMPR (cmpr1 cmpr2)
-   (declare (type cmprf cmpr1 cmpr2))
-   (flet ((rslt (crpr1 crpr2)
-             (declare (type crpr crpr1 crpr2))
-             (the cmpr
-                (let ((left-cons-1 (cadr crpr1))
-                      (left-cons-2 (cadr crpr2)))
-                   (declare (cons left-cons-1 left-cons-2))
-                   (lexico
-                      (f-cmpr (car left-cons-1) (car left-cons-2))
-                      (let ((right-cons-1 (cddr crpr1))
-                            (right-cons-2 (cddr crpr2)))
-                         (declare (cons right-cons-1 right-cons-2))
-                         (lexico
-                            (f-cmpr (car right-cons-1) (car right-cons-2))
-                            (funcall cmpr1 (cdr left-cons-1) (cdr left-cons-2))
-                            (funcall cmpr2 (cdr right-cons-1) (cdr right-cons-2)))))))))
-      (the cmprf #'rslt)))
-
-#|
-  (setf c (cmpr (delta-infinity)))
-  (setf rslt (crts-prdc-cmpr c c))
-  (funcall rslt (crpr 0 3 0 3) (crpr 1 1 0 3))
-  (funcall rslt (crpr 4 3 0 7) (crpr 3 1 0 7))
-  (funcall rslt (crpr 0 3 0 3) (crpr 0 3 1 1))
-  (funcall rslt (crpr 0 3 0 3) (crpr 0 5 0 3))
-  (funcall rslt (crpr 0 3 0 3) (crpr 0 3 0 5))
-  (funcall rslt (crpr 0 3 0 3) (crpr 0 3 0 3)))
-|#
-           
-(DEFUN CRTS-PRDC-BASIS (basis1 basis2)
-   (declare (type basis basis1 basis2))
-   (when (or (eq basis1 :locally-effective)
-             (eq basis2 :locally-effective))
-      (return-from crts-prdc-basis :locally-effective))
-   (flet ((rslt (dmns)
-             (declare (fixnum dmns))
-             (the list
-                (progn
-                   (when (minusp dmns)
-                      (return-from rslt +empty-list+))
-                   (let ((array1 (make-array (1+ dmns)))
-                         (array2 (make-array (1+ dmns)))
-                         (rslt +empty-list+)
-                         (mask (mask dmns)))
-                      (declare
-                         (simple-vector array1 array2)
-                         (list rslt)
-                         (fixnum mask))
-                      (dotimes (i (1+ dmns))
-                         (setf (svref array1 i) (funcall basis1 i)
-                               (svref array2 i) (funcall basis2 i)))
-                      (do ((dgop1 mask (1- dgop1)))
-                          ((minusp dgop1))
-                         (declare (fixnum dgop1))
-                         (let ((dmns1 (- dmns (logcount dgop1))))
-                            (declare (fixnum dmns1))
-                            (do ((dgop2 mask (1- dgop2)))
-                                ((minusp dgop2))
-                               (declare (fixnum dgop2))
-                               (unless (plusp (logand dgop1 dgop2))
-                                  (setf rslt
-                                        (nconc
-                                           (mapcan
-                                              #'(lambda (item1)
-                                                   (declare (type gmsm item1))
-                                                   (mapcar
-                                                      #'(lambda (item2)
-                                                           (declare (type gmsm item2))
-                                                           (crpr dgop1 item1 dgop2 item2))
-                                                      (svref array2 (- dmns (logcount dgop2)))))
-                                              (svref array1 dmns1))
-                                           rslt))))))
-                      rslt)))))
-          (the basis #'rslt)))
-
-#|
-  (setf b (basis (delta 1)))
-  (setf r (crts-prdc-basis b b))
-  (funcall r 0)
-  (funcall r 1)
-  (funcall r 2)
-  (funcall r 3)
-  (setf d3 (basis (delta 3)))
-  (setf r (crts-prdc-basis d3 d3))
-  (time (dotimes (i 7)
-           (print (length (funcall r i)))))
-  (setf s3 (basis (sphere 3)))
-  (setf p (crts-prdc-basis s3 s3))
-  (dotimes (i 8)
-     (print (funcall p i)))
-|#
-
-(DEFUN CRTS-PRDC-FACE (face1 face2)
-   (declare (type face face1 face2))
-   (flet ((rslt (indx dmns crpr)
-             (declare
-                (fixnum indx dmns)
-                (type crpr crpr))
-             (with-crpr (dgop1 gmsm1 dgop2 gmsm2) crpr
-                (multiple-value-bind (dgop1 del1) (1dlop-dgop indx dgop1)
-                   (declare
-                      (fixnum dgop1)
-                      (type (or null fixnum) del1))
-                (multiple-value-bind (dgop2 del2) (1dlop-dgop indx dgop2)
-                   (declare
-                      (fixnum dgop2)
-                      (type (or null fixnum) del2))
-                   (when del1
-                      (let ((absm1 (funcall face1 del1 (- dmns (logcount dgop1)) gmsm1)))
-                         (declare (type absm absm1))
-                         (setf dgop1 (dgop*dgop dgop1 (dgop absm1))
-                               gmsm1 (gmsm absm1))))
-                   (when del2
-                      (let ((absm2 (funcall face2 del2 (- dmns (logcount dgop2)) gmsm2)))
-                         (declare (type absm absm2))
-                         (setf dgop2 (dgop*dgop dgop2 (dgop absm2))
-                               gmsm2 (gmsm absm2))))
-                   (multiple-value-bind (dgop dgop1 dgop2) (extract-common-dgop dgop1 dgop2)
-                            (declare (fixnum dgop dgop1 dgop2))
-                            (absm dgop (crpr dgop1 gmsm1 dgop2 gmsm2))))))))
-         (the face #'rslt)))
-
-#|
-  (setf d2 (delta 2))
-  (setf b2 (basis d2))
-  (setf f2 (face d2))
-  (setf b (crts-prdc-basis b2 b2))
-  (setf r (crts-prdc-face f2 f2))
-  (dotimes (i 5)
-     (unless (zerop i)
-        (dolist (item (funcall b i))
-           (dotimes (j (1+ i))
-              (format t "~%del-~D ~A = ~A"
-                 j item (funcall r j i item))))))
-|#
-
-(DEFUN CRTS-PRDC-FACE* (face1 face2)
-   (declare (type face face1 face2))
-   (flet ((rslt (indx dmns crpr)
-             (declare
-                (fixnum indx dmns)
-                (type crpr crpr))
-             (with-crpr (dgop1 gmsm1 dgop2 gmsm2) crpr
-                (multiple-value-bind (dgop1 del1) (1dlop-dgop indx dgop1)
-                   (declare
-                      (fixnum dgop1)
-                      (type (or null fixnum) del1))
-                (multiple-value-bind (dgop2 del2) (1dlop-dgop indx dgop2)
-                   (declare
-                      (fixnum dgop2)
-                      (type (or null fixnum) del2))
-                   (when del1
-                      (let ((absm1 (funcall face1 del1 (- dmns (logcount dgop1)) gmsm1)))
-                         (declare (type absm absm1))
-                         (setf dgop1 (dgop*dgop dgop1 (dgop absm1))
-                               gmsm1 (gmsm absm1))))
-                   (when del2
-                      (let ((absm2 (funcall face2 del2 (- dmns (logcount dgop2)) gmsm2)))
-                         (declare (type absm absm2))
-                         (setf dgop2 (dgop*dgop dgop2 (dgop absm2))
-                               gmsm2 (gmsm absm2))))
-                   (if (plusp (logand dgop1 dgop2))
-                      :degenerate
-                      (crpr dgop1 gmsm1 dgop2 gmsm2)))))))
-         (the intr #'rslt)))
-
-#|
-  (setf d2 (delta 2))
-  (setf b2 (basis d2))
-  (setf f2 (face d2))
-  (setf b (crts-prdc-basis b2 b2))
-  (setf r (crts-prdc-face* f2 f2))
-  (dotimes (i 5)
-     (unless (zerop i)
-        (dolist (item (coerce (funcall b i) 'list))
-           (dotimes (j (1+ i))
-              (format t "~%del-~D ~A = ~A"
-                 j item (funcall r j i item))))))
-  (setf s3 (sphere 3))
-  (setf b3 (basis s3))
-  (setf f3 (face s3))
-  (setf b (crts-prdc-basis b3 b3))
-  (setf r (crts-prdc-face* f3 f3))
-  (dotimes (i 7)
-     (unless (zerop i)
-        (dolist (item (coerce (funcall b i) 'list))
-           (dotimes (j (1+ i))
-              (format t "~%del-~D ~A = ~A"
-                 j item (funcall r j i item))))))
-|#
-
-(DEFUN CRTS-PRDC (smst1 smst2)
-  (declare (type simplicial-set smst1 smst2))
-  (the simplicial-set
-    (with-slots ((cmpr1 cmpr) (basis1 basis) (face1 face) (bsgn1 bsgn)) smst1
-      (declare
-       (type cmprf cmpr1)
-       (type basis basis1)
-       (type face face1))
-      (with-slots ((cmpr2 cmpr) (basis2 basis) (face2 face) (bsgn2 bsgn)) smst2
-        (declare
-         (type cmprf cmpr2)
-         (type basis basis2)
-         (type face face2))
-        (simplicial-set
-         :cmpr (crts-prdc-cmpr cmpr1 cmpr2)
-         :basis (crts-prdc-basis basis1 basis2)
-         :bsgn (crpr 0 bsgn1 0 bsgn2)
-         :face (crts-prdc-face face1 face2)
-         :face* (crts-prdc-face* face1 face2)
-         :dfnt `(crts-prdc ,smst1 ,smst2))))))
-
-#|
-  (setf p (crts-prdc (delta 3) (delta 3)))
-  (? p 0 (crpr 0 1 0 2))
-  (? p 1 (crpr 0 3 0 3))
-  (? p 2 (crpr 0 7 0 7))
-  (? p 3 (crpr 0 15 0 15))
-  (? p 4 (crpr 1 15 2 15))
-|#
-
-#|
-  ;; For comparison with EAT.
-  ;; In CAT.
-  (setf s5 (sphere 5))
-  (setf p (crts-prdc s5 s5))
-  (setf b (basis p))
-  (setf d (dffr p))
-  (setf basis (funcall b 10))
-  (length basis)
-  (setf c (make-cmbn :degr 10 :list (mapcar #'(lambda (item)
-                                                (term (1+ (random 5)) item))
-                                      basis)))
-  (setf +too-much-time+ -1)
-  (cmbn-? d (cmbn-? d c))
-  (time (dotimes (i 5) (cmbn-? d (cmbn-? d c))))
-|#
-
-#|
-  ;; In EAT.
-  (setf s5 (sphere 5))
-  (setf p (cpr-2ss s5 s5))
-  (setf d (cc-d (ss-cc p)))
-  (setf basis (sbs p 10))
-  (length basis)
-  (setf c (make-cmb :dgr 10 :lst (mapcar #'(lambda (item)
-                                                (mnm (1+ (random 5)) item))
-                                     basis)))
-  (??? d (??? d c))
-  (time (dotimes (i 5) (??? d (??? d c))))
-|#
diff --git a/archive/Kenzo-2/Kenzo-2-Acl5/chain-complexes.cl b/archive/Kenzo-2/Kenzo-2-Acl5/chain-complexes.cl
deleted file mode 100644
index 8e5b5a5..0000000
--- a/archive/Kenzo-2/Kenzo-2-Acl5/chain-complexes.cl
+++ /dev/null
@@ -1,526 +0,0 @@
-;;;  CHAIN-COMPLEXES  CHAIN-COMPLEXES  CHAIN-COMPLEXES  CHAIN-COMPLEXES
-;;;  CHAIN-COMPLEXES  CHAIN-COMPLEXES  CHAIN-COMPLEXES  CHAIN-COMPLEXES
-;;;  CHAIN-COMPLEXES  CHAIN-COMPLEXES  CHAIN-COMPLEXES  CHAIN-COMPLEXES
-
-(IN-PACKAGE "CAT")
-
-(PROVIDE "chain-complexes")
-
-(DEFVAR *K-LIST* +empty-list+)
-
-(DEFUN CAT-INIT (&optional (idnm 0))
-  (declare (type fixnum idnm))
-  (setf *idnm-counter* idnm
-    *k-list* (member idnm *k-list* :key #'idnm))
-  (done))
-
-(DEFUN ALL-OBJECTS ()
-  (dolist (item *k-list*)
-    (declare (type kenzo-object item))
-    (format t "~%~A = ~A" item (dfnt item)))
-  (done))
-
-(DEFUN KD (idnm)
-  (declare (fixnum idnm))
-  (let ((found (find idnm *k-list* :key #'idnm)))
-    (when found
-      (format t "~%Object: ~A~@
-                   ~3TOrigin: ~A~2%" found (dfnt found))))
-  (values))
-
-(DEFUN K (idnm)
-  (declare (fixnum idnm))
-  (let ((found (find idnm *k-list* :key #'idnm)))
-    (when found
-      (return-from k found))))
-
-(DEFUN KD2 (idnm)
-  (declare (fixnum idnm))
-  (let ((k-list (k idnm)))
-    (declare (type (or kenzo-object list) k-list))
-    (unless k-list
-      (return-from kd2 nil))
-    (setf k-list (list k-list))
-    (do ((idnm (1- idnm) (1- idnm)))
-        ((zerop idnm))
-      (declare (fixnum idnm))
-      (let ((found (find-if
-                    #'(lambda (item)
-                        (declare (type (or chain-complex morphism) item))
-                        (member (k idnm) (dfnt item)))
-                    k-list)))
-        (declare (type (or null chain-complex morphism) found))
-        (when found
-          (push (k idnm) k-list))))
-    (mapc #'kd (nreverse (mapcar #'idnm k-list)))))
-    
-(DEFMETHOD PRINT-OBJECT ((chcm chain-complex) stream)
- (the chain-complex
-   (progn
-      (format stream "[K~D Chain-Complex]" (idnm chcm))
-      chcm)))
-
-;;; Result = (:rslt gnrt value clnm rntm . prpr)
-
-(DEFMETHOD PRINT-KEYCONS ((key (eql :rslt)) cdr stream)
-   (the list
-      (progn
-         (setf cdr (cons key cdr))
-         (format stream "~%<Rslt>~@
-	                 ~4TGNRT-> ~A~@
-                         ~3TVALUE-> ~A~@
-                         ~4TCLNM-> ~6D~@
-                         ~4TRNTM-> ~11,3F"
-            (rslt-gnrt cdr) (rslt-value cdr)
-            (rslt-clnm cdr) (rslt-rntm cdr))
-         cdr)))
-
-#|
-  (make-rslt :gnrt 'a :value '(a a) :clnm 23 :rntm 2.345)
-|#
-
-(DEFPARAMETER +MAXIMAL-DIMENSION+ 15)
-
-(DEFMETHOD ?2 ((mrph morphism) cmbn)
-   (declare (type cmbn cmbn))
-   (the cmbn
-      (cmbn-? mrph cmbn)))
-
-(DEFMETHOD ?2 ((chcm chain-complex) cmbn)
-   (declare
-      (type cmbn cmbn))
-   (the cmbn
-      (cmbn-? (dffr1 chcm) cmbn)))
-
-(DEFMETHOD ?3 ((mrph morphism) degr gnrt)
-   (declare
-      (fixnum degr)
-      (type gnrt gnrt))
-   (the cmbn
-      (gnrt-? mrph degr gnrt)))
-
-(DEFMETHOD ?3 ((chcm chain-complex) degr gnrt)
-   (declare
-      (fixnum degr)
-      (type gnrt gnrt))
-   (gnrt-? (dffr1 chcm) degr gnrt))
-
-(DEFMETHOD PRINT-OBJECT ((mrph morphism) stream)
-   (the morphism
-      (progn
-	(if (eq (first (dfnt (trgt mrph))) 'z-chcm)
-	    (format stream "[K~D Cohomology-Class on K~D of degree ~D]"
-		    (idnm mrph) (idnm (sorc mrph)) (- (degr mrph)))
-	  (format stream "[K~D Morphism (degree ~D): K~D -> K~D]"
-		  (idnm mrph) (degr mrph)
-		  (idnm (sorc mrph)) (idnm (trgt mrph))))
-        mrph)))
-
-(DEFMETHOD SHARED-INITIALIZE ((k kenzo-object) slot-names &key dfnt prpr cmmn)
-  (declare
-   (type (or (eql t) list) slot-names)
-   (type list dfnt))
-  (when-slot dfnt
-             (with-slots (idnm (dfnts dfnt) (prprs prpr) (cmmns cmmn)) k
-               (declare
-                (type fixnum idnm)
-                (type list dfnts))
-               (setf idnm (incf *idnm-counter*))
-               (when dfnt
-                 (setf dfnts dfnt))
-               (when prpr
-                 (setf prprs prpr))
-               (when cmmn
-                 (setf cmmns cmmn))))
-  k)
-             
-(DEFMETHOD INITIALIZE-INSTANCE :after ((k kenzo-object) &rest rest)
-  (push k *k-list*))
-             
-(DEFUN CHAIN-COMPLEX (&rest rest &key dfnt &allow-other-keys)
-  (declare (type list dfnt))
-  (already chain-complex dfnt)
-  (the chain-complex
-    (apply #'make-instance 'chain-complex rest)))
-
-(DEFMETHOD SHARED-INITIALIZE
-    ((chcm chain-complex) slot-names
-     &key cmpr basis (bsgn :undefined) dffr-intr dffr-strt grmd)
-  (declare
-   (type (or (eql t) list) slot-names)
-   (type cmprf cmpr)
-   (type basis basis)
-   (type gnrt bsgn)
-   (type intr dffr-intr)
-   (type strt dffr-strt)
-   (type chain-complex grmd))
-  (call-next-method)
-  (when-slot cmpr
-             (with-slots ((cmprs cmpr) (basiss basis) (bsgns bsgn)
-                          dffr (grmds grmd)) chcm
-               (declare
-                (type cmprf cmprs)
-                (type basis basiss)
-                (type gnrt bsgns)
-                (type morphism dffr)
-                (type chain-complex grmds))
-               (when cmpr (setf cmprs cmpr))
-               (when basis (setf basiss basis))
-               (unless (eq bsgn :undefined)
-                 (setf bsgns bsgn))
-               (when dffr-intr
-                 (unless dffr-strt
-                   (error "In CHAIN-COMPLEX, a DFFR-INTR is given but not its DFFR-STRT."))
-                 (setf dffr
-                   (morphism :sorc chcm :trgt chcm :degr -1
-                             :intr dffr-intr :strt dffr-strt
-                             :dfnt `(dffr ,chcm))))
-               (when grmd (setf grmds grmd))))
-  chcm)
-
-(DEFMETHOD SLOT-UNBOUND (class (chcm chain-complex) (slot-name (eql 'grmd)))
-  (declare (ignore class))
-  (the chain-complex
-    (setf (slot-value chcm 'grmd) chcm)))
-
-    
-(DEFUN MORPHISM (&rest rest &key dfnt &allow-other-keys)
-  (declare (type list dfnt))
-  (already morphism dfnt)
-  (the morphism
-    (apply #'make-instance 'morphism rest)))
-
-(DEFMETHOD SHARED-INITIALIZE
-    ((mrph morphism) slot-names &key sorc trgt degr intr strt)
-  (declare
-   (type (or (eql t) list) slot-names)
-   (type chain-complex sorc trgt)
-   (type fixnum degr)
-   (type intr intr)
-   (type strt strt))
-  (call-next-method)
-  (when-slot sorc
-             (with-slots ((sorcs sorc) (trgts trgt) (degrs degr)
-                          (intrs intr) (strts strt)) mrph
-               (declare
-                (type chain-complex sorc trgt)
-                (type fixnum degrs)
-                (type intr intrs)
-                (type strt strts))
-               (when sorc (setf sorcs sorc))
-               (when trgt (setf trgts trgt))
-               (when degr (setf degrs degr))
-               (when intr
-                 (unless strt
-                   (error "IN MORPHISM, an INTR is given, but not its STRT."))
-                 (setf intrs intr)
-                 (setf strts strt))))
-  mrph)
-
-(DEFMETHOD SLOT-UNBOUND (class (mrph morphism) slot-name)
-  (declare
-   (ignore class)
-   (type (or symbol string) slot-name))
-  (setf slot-name (symbol-name slot-name))
-  (unless (member slot-name '("RSLTS" "?-CLNM" "???-CLNM") :test #'string=)
-    (call-next-method))
-  (with-slots (strt rslts ?-clnm ???-clnm) mrph
-    (declare
-     (type strt strt)
-     (type (or null vector) rslts)
-     (type fixnum ?-clnm ???-clnm))
-    (setf rslts
-      (ecase (slot-value mrph 'strt)
-        (:gnrt (map 'simple-vector
-                 ;; (vector (vector result))
-                 #'(lambda (dummy)
-                     (declare (ignore dummy))
-                     (make-array 0
-                                 :adjustable t
-                                 :fill-pointer 0))
-                 (make-list +maximal-dimension+)))
-        (:cmbn nil)))
-    (setf ?-clnm (setf ???-clnm 0))
-    (cond ((string= slot-name "RSLTS") rslts)
-          ((string= slot-name "?-CLNM") ?-clnm)
-          ((string= slot-name "???-CLNM") ???-clnm)
-          (t (error "Something wrong in (SLOT-UNBOUND t morphism t).")))))
-
-               
-               
-               
-;;; FUNCTIONS
-
-(DEFVAR *START-STACK* +empty-list+)
-
-(DEFPARAMETER +TOO-MUCH-TIME+ -1)
-
-(DEFUN MRPH-GNRT (cmpr2 intr degr gnrt memory &optional (left -1) (right (fill-pointer memory)))
-  (declare
-     (type intr intr)
-     ;; (function (fixnum gnrt) cmbn)
-     (type cmprf cmpr2)
-     (fixnum degr left right)
-     (type gnrt gnrt)
-     (vector memory))
-   ;; (vector result)
-   (the (values cmbn fixnum)
-      ;;; cmbn = image of the generator
-      ;;; fixnum = index "exact" or just "lower" of the maybe stored result
-      (loop
-         (when (= right (1+ left))            ;; the result for gnrt is not available
-            (push (get-internal-run-time) *start-stack*)
-            (let ((value (funcall intr degr gnrt))
-                  (runtime (- (get-internal-run-time) (pop *start-stack*))))
-               (declare
-                  (type cmbn value)
-                  (integer runtime))
-               (if (> runtime +too-much-time+)
-                  ;;; the condition deciding whether
-                  ;;;   storing must happen
-                  (let ((old-length (vector-push-extend nil memory)))
-                     (declare (fixnum old-length))
-                     (replace memory memory
-                        :start1 (1+ right) :end1 (1+ old-length)
-                        :start2 right :end2 old-length)
-                     (setf (aref memory right)
-                           (make-rslt
-                              :gnrt gnrt :value value
-                              :clnm 1
-                              :rntm (float (/ runtime internal-time-units-per-second))))
-                     (mapl #'(lambda (mark)
-                                (declare (cons mark))
-                                (incf (car mark) runtime))
-                        *start-stack*)
-                     (return (values value right)))
-                  (return (values value left)))))
-         (let ((middle (truncate (+ right left) 2)))
-            (declare (fixnum middle))
-            (ecase (funcall cmpr2 gnrt (rslt-gnrt (aref memory middle)))
-               (:equal (let ((rslt (aref memory middle)))
-			  (declare (type cons rslt))
-			  (incf (rslt-clnm rslt))
-			  (return (values (rslt-value rslt) middle))))
-               (:less (setf right middle))
-               (:greater (setf left middle)))))))
-	   
-(DEFUN MRPH-CMBN (scmpr2 tcmpr2 intr cmbn memory)
-   (declare
-      (type intr intr)
-      ;; (function (fixnum gnrt) cmbn)
-      (type cmprf scmpr2 tcmpr2)
-      (type cmbn cmbn)                    ;;; cmbn is a non-zero one
-      (vector memory))
-      ;; (vector result)
-   (the cmbn
-      (with-cmbn (degr list) cmbn
-         (let ((n-cmbn-list +empty-list+))
-            (declare (list n-cmbn-list))
-            (do ((mark list (cdr mark))
-                 (left -1))
-                ((endp mark))
-               (declare (list mark))
-               (multiple-value-bind (rslt new-left)
-                                    (mrph-gnrt scmpr2 intr degr (-gnrt mark) memory left)
-                  (setf left new-left)
-                  (push (cons (-cffc mark) rslt) n-cmbn-list)))
-	    (cmbn-cmbn tcmpr2 n-cmbn-list)))))
-
-(DEFUN DO-CONTROL (cmpr cmbn)
-   (declare
-      (type cmprf cmpr)
-      (type cmbn cmbn))
-   (let ((list (cmbn-list cmbn)))
-      (declare (list list))
-      (do ((mark1 (rest list) (cdr mark1))
-	   (mark2 list mark1))
-	  ((endp mark1))
-	 (declare (list mark1 mark2))
-	 (unless (eq :less (funcall cmpr (-gnrt mark2) (-gnrt mark1)))
-	    (setf *wrong-cmbn* cmbn)
-	    (error "In the combination located by *WRONG-CMBN*, the generators:~@
-                    ~A and ~A are in a wrong order." (cdar mark2) (cdar mark1)))))
-   cmbn)
-
-#|
-  (do-control #'s-cmpr (cmbn 0 1 'a 1 'b -1 'c))
-  (do-control #'s-cmpr (cmbn 0 1 'b 1 'b -1 'c))
-  (do-control #'s-cmpr (cmbn 0 1 'a 1 'b -1 'b))
-  (setf *cmbn-control* nil)
-  (control #'s-cmpr (cmbn 0 1 'a 1 'b -1 'b))
-  (setf *cmbn-control* t)
-  (control #'s-cmpr (cmbn 0 1 'a 1 'b -1 'b))
-|#
-
-#|
-(DEFVAR *PROFILER-STACK*)
-(SETF *PROFILER-STACK* +empty-list+)
-
-(DEFUN PROFILER-INIT ()
-   (mapc #'(lambda (mrph)
-              (declare (type morphism mrph))
-              (setf (wrtm mrph) 0))
-      *k-list*))
-
-(DEFUN PROFILER-ON ()
-   (push (get-internal-run-time) *profiler-stack*))
-
-(DEFUN PROFILER-OFF (mrph)
-   (declare (type morphism mrph))
-   (let ((time-spent 
-          (- (get-internal-run-time) (pop *profiler-stack*))))
-      (declare (integer time-spent))
-      (mapl #'(lambda (mark)
-                 (declare (cons mark))
-                 (incf (car mark) time-spent))
-         *profiler-stack*)
-      (incf (wrtm mrph) time-spent)))
-|#
-
-(DEFVAR *FUTURE-DISPLAY* nil)
-
-(DEFVAR *TIME-INTERVAL* 60000)
-
-(DEFUN GNRT-? (mrph degr gnrt)
-   (declare
-      (type morphism mrph)
-      (fixnum degr)
-    (type gnrt gnrt))
-   (the cmbn
-      (progn
-;;         (profiler-on)
-         (when (and *future-display*
-                    (> (get-internal-run-time) *future-display*))
-            (format t "~%GNRT-?~@
-                       ~3T~A  DFNT = ~A~@
-                       ~3TDEGR = ~D~@
-                       ~3TGNRT = ~A"
-               mrph (dfnt mrph) degr gnrt)
-            (setf *future-display* (+ (get-internal-run-time) *time-interval*)))
-         (with-slots (sorc (mdegr degr) intr strt ?-clnm) mrph
-            (declare
-               (type chain-complex sorc)
-               (fixnum mdegr ?-clnm)
-               (type intr intr)
-               (type strt strt))
-         (with-slots ((scmpr cmpr)) sorc
-            (declare (type cmprf scmpr))
-            (control (slot-value (slot-value mrph 'trgt) 'cmpr)
-               (progn
-                  (incf ?-clnm)
-                  (prog1
-                     (ecase strt
-                        (:gnrt
-                         (mrph-gnrt scmpr intr
-                            degr gnrt (svref (rslts mrph) degr)))
-                        (:cmbn
-                         (funcall intr (term-cmbn degr 1 gnrt))))
-;;                     (profiler-off mrph)
-                     ))))))))
-
-#|
-(cat-init)
-(setf cc (chain-complex :cmpr #'f-cmpr
-                        :basis :locally-effective
-                        :bsgn 0
-                        :dffr-intr #'(lambda (cmbn)
-                                       (cmbn (1- (cmbn-degr cmbn))))
-                        :dffr-strt :cmbn
-                        :dfnt '(Z of Z)))
-(setf cc (chain-complex :cmpr #'f-cmpr
-                        :basis :locally-effective
-                        :bsgn 0
-                        :dffr-intr #'(lambda (cmbn)
-                                       (cmbn (1- (cmbn-degr cmbn))))
-                        :dffr-strt :cmbn
-                        :dfnt '(Z of Z)))
-(setf ff (morphism :sorc cc :trgt cc :degr 0
-                   :intr #'(lambda (degr n) (cmbn degr 1 n))
-                     :strt :gnrt :dfnt '(test)))
-(setf ff (morphism :sorc cc :trgt cc :degr 0
-                     :intr #'(lambda (degr n) (cmbn degr 1 n))
-                     :strt :gnrt :dfnt '(test)))
-(dotimes (i 20)
-  (let ((n (- (random 50) 50)))
-    (format t "~%~D   ~D" n (gnrt-? ff 0 n))))
-(setf +too-much-time+ -1)
-(dotimes (i 20)
-  (let ((n (- (random 50) 50)))
-    (format t "~%~D   ~D" n (gnrt-? ff 0 n))))
-(setf +too-much-time+ 50)
-|#
-
-(DEFUN CMBN-? (mrph cmbn)
-   (declare
-      (type morphism mrph)
-      (type cmbn cmbn))
-   (the cmbn
-      (progn
-;;         (profiler-on)
-         (when (and *future-display*
-                    (> (get-internal-run-time) *future-display*))
-            (format t "~%CMBN-?~@
-                       ~3T~A  DFNT = ~A~@
-                       ~3TCMBN = ~A"
-               mrph (dfnt mrph) cmbn)
-            (setf *future-display* (+ (get-internal-run-time) *time-interval*)))
-         (with-slots (sorc trgt degr intr strt ???-clnm) mrph
-            (declare
-               (type chain-complex sorc trgt)
-               (fixnum degr ???-clnm)
-               (type intr intr)
-               (type strt strt))
-         (with-slots ((scmpr cmpr)) sorc
-            (declare (type cmprf scmpr))
-         (with-slots ((tcmpr cmpr)) trgt
-            (declare (type cmprf scmpr))
-            (control tcmpr
-               (progn
-                  (controln scmpr cmbn)
-                  (incf ???-clnm)
-                  (when (eq strt :cmbn)
-                     (return-from cmbn-? (funcall intr cmbn)))
-                  (prog1
-                     (if (cmbn-zero-p cmbn)
-                        (zero-cmbn (+ (cmbn-degr cmbn) degr))
-                        (mrph-cmbn scmpr tcmpr intr
-                           cmbn (svref (rslts mrph) (cmbn-degr cmbn))))
-;;                     (profiler-off mrph)
-                     )))))))))
-
-#|
-(cat-init)
-(setf cc (chain-complex :cmpr #'f-cmpr
-                        :basis :locally-effective
-                        :bsgn 0
-                        :dffr-intr #'(lambda (cmbn)
-                                       (cmbn (1- (cmbn-degr cmbn))))
-                        :dffr-strt :cmbn
-                        :dfnt '(Z of Z)))
-(setf *n* 10)
-(defun ff (degr i)
-  (do ((*2n* (ash *n* 1))
-       (rslt +empty-list+
-             (cons (cons (let ((cffc (- (random *2n*) *n*)))
-                           (if (minusp cffc) cffc (1+ cffc)))
-                         (decf gnrt (1+ (random *n*))))
-                   rslt))
-       (gnrt i)
-       (k 0 (1+ k)))
-      ((= k *n*)
-       (make-cmbn
-        :degr 0
-        :list rslt))))
-(ff 0 20)
-(compile 'ff)
-(setf mrph (morphism :sorc cc :trgt cc :degr 0
-                     :intr #'ff :strt :gnrt :dfnt '(test)))
-(cmbn-? mrph (cmbn 0 1 100))
-(cmbn-? mrph *)
-(cmbn-? mrph *)
-(cmbn-? mrph *)
-(cmbn-? mrph *)
-(cmbn-? mrph *)
-(time (cmbn-? mrph *))
-(inspect mrph))
-|#
diff --git a/archive/Kenzo-2/Kenzo-2-Acl5/chcm-elementary-op.cl b/archive/Kenzo-2/Kenzo-2-Acl5/chcm-elementary-op.cl
deleted file mode 100644
index 7a296c5..0000000
--- a/archive/Kenzo-2/Kenzo-2-Acl5/chcm-elementary-op.cl
+++ /dev/null
@@ -1,461 +0,0 @@
-;;;  CHCM-ELEMENTARY-OP  CHCM-ELEMENTARY-OP  CHCM-ELEMENTARY-OP  CHCM-ELEMENTARY-OP
-;;;  CHCM-ELEMENTARY-OP  CHCM-ELEMENTARY-OP  CHCM-ELEMENTARY-OP  CHCM-ELEMENTARY-OP
-;;;  CHCM-ELEMENTARY-OP  CHCM-ELEMENTARY-OP  CHCM-ELEMENTARY-OP  CHCM-ELEMENTARY-OP
-
-(IN-PACKAGE "CAT")
-
-(PROVIDE "chcm-elementary-op")
-
-(DEFUN Z-CHCM ()
-   (the chain-complex
-      (chain-complex
-         :cmpr #'(lambda (gnrt1 gnrt2)
-                    (declare (ignore gnrt1 gnrt2))
-                    (the cmpr :equal))
-         :basis #'(lambda (n)
-                     (declare (type fixnum n))
-                     (the list
-                        (if (zerop n)
-                           (list :Z-gnrt)
-                           +empty-list+)))
-         :bsgn :Z-gnrt
-         :dffr-intr #'zero-dffr-intr
-         :dffr-strt :cmbn
-         :dfnt '(Z-chcm))))
-
-(DEFUN ZERO-MRPH (chcm1 &optional (chcm2 chcm1) (degr 0))
-   (declare (type chain-complex chcm1 chcm2)
-            (type fixnum degr))
-   (the morphism
-      (morphism
-         :sorc chcm1 :trgt chcm2 :degr degr
-         :intr #'(lambda (cmbn)
-                    (declare (type cmbn cmbn))
-                    (zero-cmbn (+ (cmbn-degr cmbn) degr)))
-         :strt :cmbn
-         :dfnt `(zero-mrph ,chcm1 ,chcm2 ,degr))))
-
-#|
-  (cat-init)
-  (setf z (zero-mrph (Z-chcm) (Z-chcm) 2))
-  (gnrt-? z 0 :z-gnrt)
-  (cmbn-? z (cmbn 3))
-  (setf z2 (zero-mrph (Z-chcm) (Z-chcm) 2))
-  (eq z z2)
-  (setf z3 (zero-mrph (Z-chcm) (Z-chcm) 3))
-  (gnrt-? z3 0 :z-gnrt)
-  (eq z z3))
-|#    
-
-(DEFUN IDNT-MRPH (chcm)
-   (declare (type chain-complex chcm))
-   (the morphism
-      (morphism
-         :sorc chcm :trgt chcm :degr 0
-         :intr #'identity
-         :strt :cmbn
-         :dfnt `(idnt-mrph ,chcm))))
-
-#|
-  (setf zi (idnt-mrph (Z-chcm)))
-  (gnrt-? zi 0 :z-gnrt)
-  (setf zi2 (idnt-mrph (Z-chcm)))
-  (eq zi zi2))
-|#
-
-(DEFUN OPPS (mrph)
-   (declare (type morphism mrph))
-   (the morphism
-      (with-slots (sorc trgt degr) mrph
-         (morphism
-            :sorc sorc :trgt trgt :degr degr
-            :intr #'(lambda (cmbn)
-                       (declare (type cmbn cmbn))
-                       (cmbn-opps (cmbn-? mrph cmbn)))
-            :strt :cmbn
-            :dfnt `(opps ,mrph)))))
-
-#|
-  (cat-init)
-  (setf -zi (opps (idnt-mrph (Z-chcm))))
-  (gnrt-? -zi 0 :z-gnrt)
-  (setf -zi2 (opps (idnt-mrph (Z-chcm))))
-  (eq -zi -zi2))
-|#
-
-(DEFMETHOD CMPS ((chcm1 chain-complex) (chcm2 chain-complex) &optional strt)
-   (declare (type (or strt null) strt))
-   (the morphism
-      (cmps (dffr chcm1) (dffr chcm2) strt)))
-
-(DEFMETHOD CMPS ((chcm1 chain-complex) (mrph2 morphism) &optional strt)
-   (declare (type (or strt null) strt))
-   (the morphism
-      (cmps (dffr chcm1) mrph2 strt)))
-
-(DEFMETHOD CMPS ((mrph1 morphism) (chcm2 chain-complex) &optional strt)
-   (declare (type (or strt null) strt))
-   (the morphism
-      (cmps mrph1 (dffr chcm2) strt)))
-
-(DEFMETHOD CMPS ((mrph1 morphism) (mrph2 morphism) &optional strt)
-   (declare (type (or strt null) strt))
-   (the morphism
-      (with-slots ((sorc1 sorc) (trgt1 trgt) (degr1 degr) (strt1 strt)) mrph1
-         (declare
-            (type chain-complex sorc1 trgt1)
-            (fixnum degr1)
-            (type strt strt1))
-      (with-slots ((sorc2 sorc) (trgt2 trgt) (degr2 degr) (strt2 strt)) mrph2
-         (declare
-            (type chain-complex sorc2 trgt2)
-            (fixnum degr2)
-            (type strt strt2))
-         (unless (eq (grmd sorc1) (grmd trgt2))
-            (error "In 2MRPH-CMPS, the morphisms ~A and ~A may not be composed (cf source and target)."
-               mrph1 mrph2))
-         (unless strt
-           (setf strt (if (and (eq strt1 :gnrt)
-                               (eq strt2 :gnrt))
-                          :gnrt
-                        :cmbn)))
-         (when (or (eq (first (dfnt mrph1)) 'zero-mrph)
-                   (eq (first (dfnt mrph2)) 'zero-mrph))
-            (return-from cmps
-               (zero-mrph sorc2 trgt1 (+ degr1 degr2))))
-         (when (eq (first (dfnt mrph1)) 'idnt-mrph)
-            (return-from cmps mrph2))
-         (when (eq (first (dfnt mrph2)) 'idnt-mrph)
-            (return-from cmps mrph1))
-         (ecase strt
-            (:cmbn (morphism
-                      :sorc sorc2 :trgt trgt1 :degr (+ degr1 degr2)
-                      :intr #'(lambda (cmbn)
-                                 (declare (type cmbn cmbn))
-                                 (the cmbn
-                                    (cmbn-? mrph1 (cmbn-? mrph2 cmbn))))
-                      :strt :cmbn :dfnt `(2mrph-cmps ,mrph1 ,mrph2 ,strt)))
-            (:gnrt (morphism
-                      :sorc sorc2 :trgt trgt1 :degr (+ degr1 degr2)
-                      :intr #'(lambda (degr gnrt)
-                                 (declare
-                                    (type fixnum degr)
-                                    (type gnrt gnrt))
-                                 (the cmbn
-                                    (cmbn-? mrph1 (gnrt-? mrph2 degr gnrt))))
-                      :strt :gnrt :dfnt `(2mrph-cmps ,mrph1 ,mrph2 ,strt))))))))
-  
-#|
-  (cat-init)
-  (setf cc (chain-complex :cmpr #'f-cmpr
-                       :basis :locally-effective
-                       :bsgn 0
-                       :dffr-intr #'(lambda (cmbn)
-                                       (cmbn (1- (cmbn-degr cmbn))))
-                       :dffr-strt :cmbn
-                       :dfnt '(Z of Z)))
-  (setf *n* 5)
-  (defun ff (degr i)
-     (do ((*2n* (ash *n* 1))
-          (rslt +empty-list+
-                (cons (cons (let ((cffc (- (random *2n*) *n*)))
-                               (if (minusp cffc) cffc (1+ cffc)))
-                            (decf gnrt (1+ (random *n*))))
-                      rslt))
-          (gnrt i)
-          (k 0 (1+ k)))
-         ((= k *n*)
-          (make-cmbn
-             :degr 0
-             :list rslt))))
-  (setf mrph (morphism :sorc cc :trgt cc :degr 0
-			 :intr #'ff :strt :gnrt :dfnt '(test)))
-  (setf mrph2 (2mrph-cmps mrph mrph :gnrt))
-  (gnrt-? mrph2 0 0) 
-  (dotimes (i 5)
-     (print (gnrt-? mrph2 0 i)))
-  (setf mrph (morphism :sorc cc :trgt cc :degr 0
-			 :intr #'ff :strt :gnrt :dfnt '(test)))
-  (setf mrph3 (cmps mrph mrph :cmbn))
-  (gnrt-? mrph3 0 0) 
-  (dotimes (i 5)
-     (print (gnrt-? mrph3 0 i)))
-  (setf mrph33 (cmps mrph mrph :cmbn))
-  (eq mrph3 mrph33))
-|# 
-
-(DEFUN N-MRPH-INTR (n mrph)
-  (declare
-    (fixnum n)
-    (type morphism mrph))
-  (flet ((rslt (cmbn)
-	   (declare (type cmbn cmbn))
-	   (n-cmbn n (cmbn-? mrph cmbn))))
-     (the intr #'rslt)))
-
-(DEFUN N-MRPH (n mrph)
-  (declare
-    (fixnum n)
-    (type morphism mrph))
-  (the morphism
-    (with-slots (sorc trgt degr) mrph
-      (declare
-        (type chain-complex sorc trgt)
-	(fixnum degr))
-      (morphism
-        :sorc sorc :trgt trgt :degr degr
-	:intr (n-mrph-intr n mrph) :strt :cmbn
-	:dfnt `(n-mrph ,n ,mrph)))))
-
-#|
-  (setf s3 (sphere 3))
-  (setf ch3 (chml-clss s3 3))
-  (setf 2ch3 (n-mrph 2 ch3))
-  (setf f3 (z-whitehead s3 2ch3))
-  (setf x (fibration-total f3))
-  (homology x 0 10)
-  (setf k (k-z 3))
-  (setf ch3 (chml-clss k 3))
-  (setf 2ch3 (n-mrph 2 ch3))
-  (setf f3 (z-whitehead k 2ch3))
-  (setf x (fibration-total f3))
-  (homology x 0 10)
-|#  
-
-(DEFMETHOD ADD ((mrph1 morphism) (mrph2 morphism) &optional strt)
-   (declare (type (or null strt) strt))
-   (the morphism
-      (with-slots ((sorc1 sorc) (trgt1 trgt) (degr1 degr) (strt1 strt)) mrph1
-         (declare
-            (type chain-complex sorc1 trgt1)
-            (fixnum degr1)
-            (type strt strt1))
-      (with-slots ((sorc2 sorc) (trgt2 trgt) (degr2 degr) (strt2 strt)) mrph2
-         (declare
-            (type chain-complex sorc2 trgt2)
-            (fixnum degr2)
-            (type strt strt2))
-         (unless (and (eq (grmd sorc1) (grmd sorc2))
-                      (eq (grmd trgt1) (grmd trgt2))
-                      (= degr1 degr2))
-            (error "In 2MRPH-ADD, ~A and ~A may not be added." mrph1 mrph2))
-         (when (eq (first (dfnt mrph1)) 'zero-mrph)
-            (return-from add mrph2))
-         (when (eq (first (dfnt mrph2)) 'zero-mrph)
-            (return-from add mrph1))
-         (unless strt
-            (setf strt
-                  (if (and (eq strt1 :gnrt)
-                           (eq strt2 :gnrt))
-                     :gnrt
-                     :cmbn)))
-         (when (or (eq (first (dfnt mrph1)) 'idnt-mrph)
-                   (eq (first (dfnt mrph2)) 'idnt-mrph))
-            (setf strt :cmbn))
-         (let ((cmpr (cmpr trgt1)))
-            (declare (type cmprf cmpr))
-            (ecase strt
-               (:gnrt (morphism
-                         :sorc sorc1 :trgt trgt1 :degr degr1
-                         :intr #'(lambda (degr gnrt)
-                                    (declare (type fixnum degr) (type gnrt gnrt))
-                                    (2cmbn-add cmpr
-                                       (gnrt-? mrph1 degr gnrt)
-                                       (gnrt-? mrph2 degr gnrt)))
-                         :strt :gnrt
-                         :dfnt `(2mrph-add ,mrph1 ,mrph2 ,strt)))
-               (:cmbn (morphism
-                         :sorc sorc1 :trgt trgt1 :degr degr1
-                         :intr #'(lambda (cmbn)
-                                    (declare (type cmbn cmbn))
-                                    (2cmbn-add cmpr
-                                       (cmbn-? mrph1 cmbn)
-                                       (cmbn-? mrph2 cmbn)))
-                         :strt :cmbn
-                         :dfnt `(2mrph-add ,mrph1 ,mrph2 ,strt)))))))))
-
-#|
-  (cat-init)
-  (setf cc (chain-complex :cmpr #'f-cmpr
-                       :basis :locally-effective
-                       :bsgn 0
-                       :dffr-intr #'(lambda (cmbn)
-                                       (cmbn (1- (cmbn-degr cmbn))))
-                       :dffr-strt :cmbn
-                       :dfnt '(Z of Z)))
-  (setf *n* 10)
-  (defun ff (degr i)
-     (do ((*2n* (ash *n* 1))
-          (rslt +empty-list+
-                (cons (cons (let ((cffc (- (random *2n*) *n*)))
-                               (if (minusp cffc) cffc (1+ cffc)))
-                            (decf gnrt (1+ (random *n*))))
-                      rslt))
-          (gnrt i)
-          (k 0 (1+ k)))
-         ((= k *n*)
-          (make-cmbn
-             :degr 0
-             :list rslt))))
-  (setf mrph1 (morphism :sorc cc :trgt cc :degr 0
-                          :intr #'ff :strt :gnrt :dfnt '(test)))
-  (setf mrph2 (morphism :sorc cc :trgt cc :degr 0
-                          :intr #'ff :strt :gnrt :dfnt '(test2)))
-  (setf mrph3 (add mrph1 mrph2 :gnrt))
-  (setf +too-much-time+ -1)
-  (gnrt-? mrph1 0 0)
-  (gnrt-? mrph2 0 0)
-  (gnrt-? mrph3 0 0)
-  (setf mrph4 (add mrph1 mrph2 :cmbn))
-  (gnrt-? mrph4 0 0)
-  (setf mrph44 (add mrph1 mrph2 :cmbn))
-  (eq mrph4 mrph44))
-|#
-
-(DEFMETHOD SBTR ((mrph1 morphism) (mrph2 morphism) &optional strt)
-   (declare (type (or null strt) strt))
-   (the morphism
-      (with-slots ((sorc1 sorc) (trgt1 trgt) (degr1 degr) (strt1 strt)) mrph1
-         (declare
-            (type chain-complex sorc1 trgt1)
-            (fixnum degr1)
-            (type strt strt1))
-      (with-slots ((sorc2 sorc) (trgt2 trgt) (degr2 degr) (strt2 strt)) mrph2
-         (declare
-            (type chain-complex sorc2 trgt2)
-            (fixnum degr2)
-            (type strt strt2))
-         (unless (and (eq (grmd sorc1) (grmd sorc2))
-                      (eq (grmd trgt1) (grmd trgt2))
-                      (= degr1 degr2))
-            (error "In 2MRPH-SBTR, ~A and ~A may not be subtracteded." mrph1 mrph2))
-         (when (eq (first (dfnt mrph1)) 'zero-mrph)
-            (return-from sbtr mrph2))
-         (when (eq (first (dfnt mrph2)) 'zero-mrph)
-            (return-from sbtr mrph1))
-         (unless strt
-            (setf strt
-                  (if (and (eq strt1 :gnrt)
-                           (eq strt2 :gnrt))
-                     :gnrt
-                     :cmbn)))
-         (when (or (eq (first (dfnt mrph1)) 'idnt-mrph)
-                   (eq (first (dfnt mrph2)) 'idnt-mrph))
-            (setf strt :cmbn))
-         (let ((cmpr (cmpr trgt1)))
-            (declare (type cmprf cmpr))
-            (ecase strt
-               (:gnrt (morphism
-                         :sorc sorc1 :trgt trgt1 :degr degr1
-                         :intr #'(lambda (degr gnrt)
-                                    (declare (type fixnum degr) (type gnrt gnrt))
-                                    (2cmbn-sbtr cmpr
-                                       (gnrt-? mrph1 degr gnrt)
-                                       (gnrt-? mrph2 degr gnrt)))
-                         :strt :gnrt
-                         :dfnt `(2mrph-sbtr ,mrph1 ,mrph2 ,strt)))
-               (:cmbn (morphism
-                         :sorc sorc1 :trgt trgt1 :degr degr1
-                         :intr #'(lambda (cmbn)
-                                    (declare (type cmbn cmbn))
-                                    (2cmbn-sbtr cmpr
-                                       (cmbn-? mrph1 cmbn)
-                                       (cmbn-? mrph2 cmbn)))
-                         :strt :cmbn
-                         :dfnt `(2mrph-sbtr ,mrph1 ,mrph2 ,strt)))))))))
-
-#|
-  (cat-init)
-  (setf cc (chain-complex :cmpr #'f-cmpr
-                       :basis :locally-effective
-                       :bsgn 0
-                       :dffr-intr #'(lambda (cmbn)
-                                       (cmbn (1- (cmbn-degr cmbn))))
-                       :dffr-strt :cmbn
-                       :dfnt '(Z of Z)))
-  (setf *n* 10)
-  (defun ff (degr i)
-     (do ((*2n* (ash *n* 1))
-          (rslt +empty-list+
-                (cons (cons (let ((cffc (- (random *2n*) *n*)))
-                               (if (minusp cffc) cffc (1+ cffc)))
-                            (decf gnrt (1+ (random *n*))))
-                      rslt))
-          (gnrt i)
-          (k 0 (1+ k)))
-         ((= k *n*)
-          (make-cmbn
-             :degr 0
-             :list rslt))))
-  (setf mrph1 (morphism :sorc cc :trgt cc :degr 0
-                          :intr #'ff :strt :gnrt :dfnt '(test)))
-  (setf mrph2 (morphism :sorc cc :trgt cc :degr 0
-                          :intr #'ff :strt :gnrt :dfnt '(test2)))
-  (setf mrph3 (sbtr mrph1 mrph2 :gnrt))
-  (setf +too-much-time+ -1)
-  (gnrt-? mrph1 0 0)
-  (gnrt-? mrph2 0 0)
-  (gnrt-? mrph3 0 0)
-  (setf mrph4 (sbtr mrph1 mrph2 :cmbn))
-  (gnrt-? mrph4 0 0)
-  (setf mrph44 (sbtr mrph1 mrph2 :cmbn))
-  (eq mrph4 mrph44))
-|#
-
-(DEFUN CHANGE-SORC-TRGT (mrph &key new-sorc new-trgt)
-   (declare
-      (type morphism mrph)
-      (type (or null chain-complex) new-sorc new-trgt))
-   (the morphism
-      (with-slots (sorc trgt degr intr strt) mrph
-         (morphism
-            :sorc (or new-sorc sorc)
-            :trgt (or new-trgt trgt)
-            :degr degr
-            :intr intr
-            :strt strt
-            :dfnt `(change-sorc-trgt ,mrph ,new-sorc ,new-trgt)))))
-
-(DEFUN DSTR-CHANGE-SORC-TRGT (mrph &key new-sorc new-trgt)
-   (declare
-      (type morphism mrph)
-      (type (or null chain-complex) new-sorc new-trgt)
-      (list new-dfnt))
-   (the morphism
-      (with-slots (sorc trgt) mrph
-         (when new-sorc 
-            (setf sorc new-sorc))
-         (when new-trgt
-            (setf trgt new-trgt))
-         mrph)))
-
-(DEFMETHOD ADD ((chcm chain-complex) (perturbation morphism) &optional strt)
-  (declare (type (or strt null) strt))
-  (the chain-complex
-    (with-slots (cmpr basis bsgn dffr) chcm
-      (declare
-       (type cmprf cmpr)
-       (type basis basis)
-       (type morphism dffr))
-      (with-slots (sorc trgt degr) perturbation
-        (declare
-         (type chain-complex sorc trgt)
-         (fixnum degr))
-        (unless (and (eq (grmd sorc) (grmd chcm))
-                     (eq (grmd trgt) (grmd chcm))
-                     (= degr -1))
-          (error "In (METHOD ADD CHAIN-COMPLEX MORPHISM), the data are not coherent."))
-        (let ((new-dffr (add dffr perturbation strt)))
-          (declare (type morphism new-dffr))
-          (let ((new-chcm (chain-complex
-                           :cmpr cmpr
-                           :basis basis
-                           :dffr-intr (intr new-dffr)
-                           :dffr-strt (strt new-dffr)
-                           :dfnt  `(add ,chcm ,perturbation))))
-            (declare (type chain-complex new-chcm))
-            (if (slot-boundp chcm 'bsgn)
-                (setf (slot-value new-chcm 'bsgn) bsgn)
-              (slot-makunbound new-chcm 'bsgn))
-            (setf (slot-value new-chcm 'grmd) (grmd chcm))
-            new-chcm))))))
\ No newline at end of file
diff --git a/archive/Kenzo-2/Kenzo-2-Acl5/cl-space-efhm.cl b/archive/Kenzo-2/Kenzo-2-Acl5/cl-space-efhm.cl
deleted file mode 100644
index f21ebfe..0000000
--- a/archive/Kenzo-2/Kenzo-2-Acl5/cl-space-efhm.cl
+++ /dev/null
@@ -1,875 +0,0 @@
-;;;  CL-SPACE-EFHM  CL-SPACE-EFHM  CL-SPACE-EFHM  CL-SPACE-EFHM
-;;;  CL-SPACE-EFHM  CL-SPACE-EFHM  CL-SPACE-EFHM  CL-SPACE-EFHM
-;;;  CL-SPACE-EFHM  CL-SPACE-EFHM  CL-SPACE-EFHM  CL-SPACE-EFHM
-
-(IN-PACKAGE "CAT")
-
-(provide "cl-space-efhm")
-
-(DEFUN CS-HAT-U-U (smgr
-		     &aux (bar (bar smgr))
-		          (cl-space (classifying-space smgr))
-			  (clsp-tnsr-smgr (tnsr-prdc cl-space smgr)))
-  (declare
-    (type simplicial-group smgr)
-    (type chain-complex bar clsp-tnsr-smgr)
-    (type simplicial-set cl-space))
-  (the chain-complex
-     (tnsr-prdc clsp-tnsr-smgr bar)))
-
-(DEFUN CS-HAT-RIGHT-PERTURBATION-INTR (smgr)
-  (declare (type simplicial-group smgr))
-  (let ((aprd (aprd smgr)))
-    (flet ((rslt (degr tnpr)
-	     (declare
-	       (fixnum degr)
-	       (type tnpr tnpr))
-	     (with-tnpr (degr1 tnpr1 degr2 abar2) tnpr
-	       (when (zerop degr2)
-		 (return-from rslt (zero-cmbn (1- degr))))
-	       (with-tnpr (degr11 gbar11 degr12 gmsm12) tnpr1
-		 (let ((sign (-1-expt-n degr1))
-		       (brgn21 (first (abar-list abar2)))
-		       (bar22 (make-abar :list (rest (abar-list abar2)))))
-		   (declare
-		     (fixnum sign)
-		     (type brgn brgn21)
-		     (type abar r-bar))
-		   (with-brgn (degr21 gmsm21) brgn21
-		   (let ((degr22 (- degr2 degr21)))
-		     (declare (fixnum degr22))
-		     (decf degr21) ;; = dmns(gmsm21)
-		     (let ((aprd (gnrt-? aprd (+ degr12 degr21)
-					 (tnpr degr12 gmsm12 degr21 gmsm21))))
-		       (declare (type cmbn aprd))
-		       (with-cmbn (degr12+21 list) aprd
-			 (make-cmbn :degr (1- degr)
-			   :list
-			   (mapcar
-			     #'(lambda (term)
-				 (declare (type term term))
-				 (with-term (cffc gmsm) term
-				   (term (* sign cffc)
-					 (tnpr (+ degr1 degr21)
-					       (tnpr degr11 gbar11 degr12+21 gmsm)
-					       degr22 bar22))))
-			     list)))))))))))
-	  (the intr #'rslt))))
-
-(DEFUN CS-HAT-RIGHT-PERTURBATION (smgr
-				    &aux (hat-u-u (cs-hat-u-u smgr)))
-  (declare
-    (type simplicial-group smgr)
-    (type chain-complex hat-u-u))
-  (the morphism
-     (morphism
-        :sorc hat-u-u
-	:trgt hat-u-u
-	:degr -1
-	:intr (cs-hat-right-perturbation-intr smgr)
-	:strt :gnrt
-	:dfnt `(cs-hat-right-perturbation ,smgr))))
-
-(DEFUN CS-HAT-U-T (smgr
-		     &aux (hat-u-u (cs-hat-u-u smgr))
-		          (hat-right-perturbation
-			    (cs-hat-right-perturbation smgr)))
-  (declare
-    (type simplicial-group smgr)
-    (type chain-complex hat-u-u)
-    (type morphism hat-right-perturbation))
-  (the chain-complex
-    (progn
-      (setf (slot-value hat-right-perturbation 'sorc) hat-u-u
-	    (slot-value hat-right-perturbation 'trgt) hat-u-u)
-      ;; cf lp-space-efhm.lisp
-      (add hat-u-u hat-right-perturbation))))
-
-#|
-  (cat-init)
-  (setf c (cs-hat-u-t (k-z-1)))
-  (defun random-abar (tot-degr~ max-degr)
-    (do ((rslt nil)
-         (cum-degr 0 (+ cum-degr degr 1))
-         (degr))
-        ((>= cum-degr tot-degr~) (make-abar :list rslt))
-       (setf degr (1+ (random max-degr)))
-       (push (brgn (1+ degr)
-                   (let ((list (make-list degr)))
-                     (mapl
-                       #'(lambda (sublist)
-                           (setf (car sublist) (- (random 21) 10)))
-                       list)
-                     list))
-             rslt)))
-  (dotimes (i 5) (print (random-abar 8 4)))
-  (setf abar (random-abar 8 4))
-  (setf abar-degr (apply #'+ (mapcar #'car (abar-list abar))))
-  (setf gnrt (tnpr 5 (tnpr 3 (gbar 3 0 '(1 2) 0 '(3) 0 '()) 2 '(4 5))
-                   abar-degr abar))
-  (? c (+ 5 abar-degr) gnrt)
-  (? c *)
-  (dotimes (i 10)
-    (let ((abar (random-abar 8 4)))
-      (setf abar-degr (apply #'+ (mapcar #'car (abar-list abar))))
-      (setf gnrt (tnpr 5 (tnpr 3 (gbar 3 0 '(1 2) 0 '(3) 0 '()) 2 '(4 5))
-                       abar-degr abar))
-      (unless (>= abar-degr 10)
-         (print (? c (+ 5 abar-degr) gnrt))
-         (print (? c (? c (+ 5 abar-degr) gnrt))))))
-  (dotimes (i 10)
-    (let ((abar (random-abar 8 4)))
-      (setf abar-degr (apply #'+ (mapcar #'car (abar-list abar))))
-      (setf gnrt (tnpr 6 (tnpr 3 (gbar 3 0 '(1 2) 0 '(3) 0 '()) 3 '(4 5 6))
-                       abar-degr abar))
-      (unless (>= abar-degr 9)
-         (print (? c (+ 6 abar-degr) gnrt))
-         (print (? c (? c (+ 6 abar-degr) gnrt))))))
-  (dotimes (i 10)
-    (let ((abar (random-abar 8 4)))
-      (setf abar-degr (apply #'+ (mapcar #'car (abar-list abar))))
-      (setf gnrt (tnpr 5 (tnpr 2 (gbar 2 0 '(3) 0 '()) 3 '(4 5 6))
-	   	     abar-degr abar))
-      (unless (>= abar-degr 10)
-        (print (? c (+ 5 abar-degr) gnrt))
-        (print (? c (? c (+ 5 abar-degr) gnrt))))))
-  (dotimes (i 10)
-    (let ((abar (random-abar 8 4)))
-      (setf abar-degr (apply #'+ (mapcar #'car (abar-list abar))))
-      (setf gnrt (tnpr 4 (tnpr 2 (gbar 2 0 '(3) 0 '()) 2 '(4 5))
-                       abar-degr abar))
-      (unless (>= abar-degr 11)
-         (print (? c (+ 4 abar-degr) gnrt))
-         (print (? c (? c (+ 4 abar-degr) gnrt))))))
-|#
-
-(DEFUN CS-HAT-LEFT-PERTURBATION (smgr
-			       &aux (fibration (smgr-fibration smgr))
-			            (bar (bar smgr))
-			            (hat-u-t (cs-hat-u-t smgr)))
-  (declare
-    (type simplicial-group smgr)
-    (type fibration fibration)
-    (type chain-complex bar hat-u-t))
-  (the morphism
-    (multiple-value-bind (brown bottom-perturbation)
-			 (brown-reduction fibration)
-      (declare
-        (ignore brown)
-	(type morphism bottom-perturbation))
-      (let ((rslt (tnsr-prdc bottom-perturbation (idnt-mrph bar))))
-	(declare (type morphism rslt))
-	(setf (slot-value rslt 'sorc) hat-u-t
-	      (slot-value rslt 'trgt) hat-u-t)
-	rslt))))
-
-(DEFUN CS-HAT-T-U (smgr
-		    &aux (bar (bar smgr))
-		         (fibration (smgr-fibration smgr))
-		         (brown (brown-reduction fibration))
-		         (twisted-tnsr-prdc (bcc brown))
-		         (hat-u-u (cs-hat-u-u smgr)))
-  (declare
-    (type simplicial-group smgr)
-    (type chain-complex bar twisted-tnsr-prdc hat-u-u)
-    (type fibration fibration)
-    (type reduction brown))
-  (the chain-complex
-    (let ((rslt (tnsr-prdc twisted-tnsr-prdc bar)))
-      (declare (type chain-complex rslt))
-      (setf (slot-value rslt 'grmd) hat-u-u)
-      rslt)))
-
-#|
-  (cat-init)
-  (setf c (cs-hat-t-u (k-z-1)))
-  (defun random-abar (tot-degr~ max-degr)
-    (do ((rslt nil)
-         (cum-degr 0 (+ cum-degr degr 1))
-         (degr))
-        ((>= cum-degr tot-degr~) (make-abar :list rslt))
-       (setf degr (1+ (random max-degr)))
-       (push (brgn (1+ degr)
-                   (let ((list (make-list degr)))
-                     (mapl
-                       #'(lambda (sublist)
-                           (setf (car sublist) (- (random 21) 10)))
-                       list)
-                     list))
-             rslt)))
-  (dotimes (i 5) (print (random-abar 8 4)))
-  (setf abar (random-abar 8 4))
-  (setf abar-degr (apply #'+ (mapcar #'car (abar-list abar))))
-  (setf gnrt (tnpr 5 (tnpr 3 (gbar 3 0 '(1 2) 0 '(3) 0 '()) 2 '(4 5))
-                   abar-degr abar))
-  (? c (+ 5 abar-degr) gnrt)
-  (? c *)
-  (dotimes (i 10)
-    (let ((abar (random-abar 8 4)))
-      (setf abar-degr (apply #'+ (mapcar #'car (abar-list abar))))
-      (setf gnrt (tnpr 5 (tnpr 3 (gbar 3 0 '(1 2) 0 '(3) 0 '()) 2 '(4 5))
-                       abar-degr abar))
-      (unless (>= abar-degr 10)
-         (print (? c (+ 5 abar-degr) gnrt))
-         (print (? c (? c (+ 5 abar-degr) gnrt))))))
-  (dotimes (i 10)
-    (let ((abar (random-abar 8 4)))
-      (setf abar-degr (apply #'+ (mapcar #'car (abar-list abar))))
-      (setf gnrt (tnpr 6 (tnpr 3 (gbar 3 0 '(1 2) 0 '(3) 0 '()) 3 '(4 5 6))
-                       abar-degr abar))
-      (unless (>= abar-degr 9)
-         (print (? c (+ 6 abar-degr) gnrt))
-         (print (? c (? c (+ 6 abar-degr) gnrt))))))
-  (dotimes (i 10)
-    (let ((abar (random-abar 8 4)))
-      (setf abar-degr (apply #'+ (mapcar #'car (abar-list abar))))
-      (setf gnrt (tnpr 5 (tnpr 2 (gbar 2 0 '(3) 0 '()) 3 '(4 5 6))
-	   	     abar-degr abar))
-      (unless (>= abar-degr 10)
-        (print (? c (+ 5 abar-degr) gnrt))
-        (print (? c (? c (+ 5 abar-degr) gnrt))))))
-  (dotimes (i 10)
-    (let ((abar (random-abar 8 4)))
-      (setf abar-degr (apply #'+ (mapcar #'car (abar-list abar))))
-      (setf gnrt (tnpr 4 (tnpr 2 (gbar 2 0 '(3) 0 '()) 2 '(4 5))
-                       abar-degr abar))
-      (unless (>= abar-degr 11)
-         (print (? c (+ 4 abar-degr) gnrt))
-         (print (? c (? c (+ 4 abar-degr) gnrt))))))
-|#
-
-(DEFUN CS-LEFT-EQVL-HAT (smgr
-			   &aux (hat-t-u (cs-hat-t-u smgr))
-			        (hat-right-perturbation
-				  (cs-hat-right-perturbation smgr)))
-  (declare
-    (type simplicial-group smgr)
-    (type chain-complex hat-t-u)
-    (type morphism hat-right-perturbation))
-  (the chain-complex
-    (add hat-t-u hat-right-perturbation)))
-
-#|
-  (cat-init)
-  (setf c (cs-left-eqvl-hat (k-z-1)))
-  (defun random-abar (tot-degr~ max-degr)
-    (do ((rslt nil)
-         (cum-degr 0 (+ cum-degr degr 1))
-         (degr))
-        ((>= cum-degr tot-degr~) (make-abar :list rslt))
-       (setf degr (1+ (random max-degr)))
-       (push (brgn (1+ degr)
-                   (let ((list (make-list degr)))
-                     (mapl
-                       #'(lambda (sublist)
-                           (setf (car sublist) (- (random 21) 10)))
-                       list)
-                     list))
-             rslt)))
-   (dotimes (i 10)
-    (let ((abar (random-abar 8 4)))
-      (setf abar-degr (apply #'+ (mapcar #'car (abar-list abar))))
-      (setf gnrt (tnpr 5 (tnpr 3 (gbar 3 0 '(1 2) 0 '(3) 0 '()) 2 '(4 5))
-                       abar-degr abar))
-      (unless (>= abar-degr 10)
-         (print (? c (+ 5 abar-degr) gnrt))
-         (print (? c (? c (+ 5 abar-degr) gnrt))))))
-  (dotimes (i 10)
-    (let ((abar (random-abar 8 4)))
-      (setf abar-degr (apply #'+ (mapcar #'car (abar-list abar))))
-      (setf gnrt (tnpr 6 (tnpr 3 (gbar 3 0 '(1 2) 0 '(3) 0 '()) 3 '(4 5 6))
-                       abar-degr abar))
-      (unless (>= abar-degr 9)
-         (print (? c (+ 6 abar-degr) gnrt))
-         (print (? c (? c (+ 6 abar-degr) gnrt))))))
-  (dotimes (i 10)
-    (let ((abar (random-abar 8 4)))
-      (setf abar-degr (apply #'+ (mapcar #'car (abar-list abar))))
-      (setf gnrt (tnpr 5 (tnpr 2 (gbar 2 0 '(3) 0 '()) 3 '(4 5 6))
-	   	     abar-degr abar))
-      (unless (>= abar-degr 10)
-        (print (? c (+ 5 abar-degr) gnrt))
-        (print (? c (? c (+ 5 abar-degr) gnrt))))))
-  (dotimes (i 10)
-    (let ((abar (random-abar 8 4)))
-      (setf abar-degr (apply #'+ (mapcar #'car (abar-list abar))))
-      (setf gnrt (tnpr 4 (tnpr 2 (gbar 2 0 '(3) 0 '()) 2 '(4 5))
-                       abar-degr abar))
-      (unless (>= abar-degr 11)
-         (print (? c (+ 4 abar-degr) gnrt))
-         (print (? c (? c (+ 4 abar-degr) gnrt))))))
-|#
-
-(DEFUN CS-PRE-LEFT-EQVL-LEFT-REDUCTION-INTR-F (cmbn)
-  (declare (type cmbn cmbn))
-  (the cmbn
-    (with-cmbn (degr list) cmbn
-      (make-cmbn
-        :degr degr
-	:list (mapcar
-	        #'(lambda (term)
-		    (declare (type term term))
-		    (with-term (cffc tnpr) term
-		      (term cffc (gnrt1 (gnrt1 tnpr)))))		    
-	        (member-if	       
-		  #'(lambda (term)
-		      (declare (type term term))
-		      (with-term (cffc tnpr) term
-			(declare (ignore cffc))
-		      (with-tnpr (degr1 tnpr1 degr2 abar2) tnpr
-			(declare (ignore degr1 abar2))
-			(and (zerop degr2) (zerop (degr2 tnpr1))))))
-		  list))))))
-
-#|
-  (cs-pre-left-eqvl-left-reduction-intr-f
-    (cmbn 6 100 (tnpr 4 (tnpr 2 'a 2 'b) 2 'c)
-            10  (tnpr 6 (tnpr 2 'a 4 'b) 0 'c)
-            50  (tnpr 6 (tnpr 6 'a 0 'b) 0 'c)
-            1   (tnpr 6 (tnpr 6 'aa 0 'b) 0 'c)))
-|#
-
-(DEFUN CS-PRE-LEFT-EQVL-LEFT-REDUCTION-F (smgr
-					   &aux (hat-u-t (cs-hat-u-t smgr))
-					        (classifying-space (classifying-space smgr)))
-  (declare
-    (type simplicial-group smgr)
-    (type chain-complex hat-u-t)
-    (type simplicial-set classifying-space))
-  (the morphism
-    (morphism
-      :sorc hat-u-t
-      :trgt classifying-space
-      :degr 0
-      :intr #'cs-pre-left-eqvl-left-reduction-intr-f
-      :strt :cmbn
-      :dfnt `(cs-pre-left-eqvl-left-reduction-f ,smgr))))
-
-(DEFUN CS-PRE-LEFT-EQVL-LEFT-REDUCTION-INTR-G (idnt)
-  (declare (type gmsm idnt))
-  (flet ((rslt (cmbn)
-	   (declare (type cmbn cmbn))
-	   (the cmbn
-	     (with-cmbn (degr list) cmbn
-	       (make-cmbn
-		 :degr degr
-		 :list (mapcar
-			 #'(lambda (term)
-			     (declare (type term term))
-			     (with-term (cffc gbar) term
-			       (term cffc
-				     (tnpr degr
-					   (tnpr degr gbar 0 idnt)
-					   0 +null-abar+))))
-			 list))))))
-     (the intr #'rslt)))
-
-#|
-  (setf g (cs-pre-left-eqvl-left-reduction-intr-g '()))
-  (funcall g (cmbn 3 14 (gbar 3 0 'a 1 'b 0 '())))
-|#
-
-(DEFUN CS-PRE-LEFT-EQVL-LEFT-REDUCTION-G (smgr
-					   &aux (hat-u-t (cs-hat-u-t smgr))
-					        (classifying-space (classifying-space smgr)))
-  (declare
-    (type simplicial-group smgr)
-    (type chain-complex hat-u-t)
-    (type simplicial-set classifying-space))
-  (the morphism
-    (morphism
-      :sorc classifying-space
-      :trgt hat-u-t
-      :degr 0
-      :intr (cs-pre-left-eqvl-left-reduction-intr-g (bsgn smgr))
-      :strt :cmbn
-      :dfnt `(cs-pre-left-eqvl-left-reduction-g ,smgr))))
-
-(DEFUN CS-PRE-LEFT-EQVL-LEFT-REDUCTION-INTR-H (cmpr idnt)
-  (declare (type gmsm idnt))
-  (flet ((rslt (cmbn)
-	   (declare (type cmbn cmbn))
-	   (the cmbn
-	     (with-cmbn (degr list) cmbn
-	       (do ((rslt (zero-cmbn (1+ degr)))
-		    (mark list (cdr mark)))
-		   ((endp mark) rslt)
-		   (declare
-		     (type cmbn rslt)
-		     (list mark))
-		  (let ((term (car mark)))
-		    (declare (type term term))
-		    (with-term (cffc tnpr) term
-		    (with-tnpr (degr1 tnpr1 degr2 abar2) tnpr
-		      (declare (ignore degr1))
-		    (with-tnpr (degr11 gbar11 degr12 gmsm12) tnpr1
-		      (unless (zerop degr12)
-			(dstr-add-term-to-cmbn
-			  cmpr
-			  (if (evenp degr11) cffc (- cffc))
-			  (tnpr degr11
-				(tnpr degr11 gbar11 0 idnt)
-				(+ 1 degr12 degr2)
-				(make-abar
-				 :list
-				 (cons (brgn (1+ degr12)
-					     gmsm12)
-				       (abar-list abar2))))
-			  rslt)))))))))))
-     (the intr #'rslt)))
-
-(DEFUN CS-PRE-LEFT-EQVL-LEFT-REDUCTION-H (smgr
-					   &aux (hat-u-t (cs-hat-u-t smgr)))
-  (declare
-    (type simplicial-group smgr)
-    (type chain-complex hat-u-t))
-  (the morphism
-    (morphism
-      :sorc hat-u-t
-      :trgt hat-u-t
-      :degr +1
-      :intr (cs-pre-left-eqvl-left-reduction-intr-h (cmpr hat-u-t) (bsgn smgr))
-      :strt :cmbn
-      :dfnt `(cs-pre-left-eqvl-left-reduction-h ,smgr))))
-
-
-
-(DEFUN CS-PRE-LEFT-EQVL-LEFT-REDUCTION (smgr)
-  (declare (type simplicial-group smgr))
-  (the reduction
-    (reduction
-      :f (cs-pre-left-eqvl-left-reduction-f smgr)
-      :g (cs-pre-left-eqvl-left-reduction-g smgr)
-      :h (cs-pre-left-eqvl-left-reduction-h smgr)
-      :dfnt `(cs-pre-left-eqvl-left-reduction ,smgr))))
-
-#|
-  (cat-init)
-  (defun random-abar (tot-degr~ max-degr)
-    (do ((rslt nil)
-         (cum-degr 0 (+ cum-degr degr 1))
-         (degr))
-        ((>= cum-degr tot-degr~) (make-abar :list rslt))
-       (setf degr (1+ (random max-degr)))
-       (push (brgn (1+ degr)
-                   (let ((list (make-list degr)))
-                     (mapl
-                       #'(lambda (sublist)
-                           (setf (car sublist) (- (random 21) 10)))
-                       list)
-                     list))
-             rslt)))
-  (setf rdct (cs-pre-left-eqvl-left-reduction (k-z-1)))
-  (pre-check-rdct rdct)
-  (setf *tc* (cmbn 0 1 (tnpr 0 (tnpr 0 +null-gbar+ 0 '()) 0 +null-abar+))
-        *bc* (cmbn 0 1 +null-gbar+))
-  (check-rdct)
-  (setf *tc* (cmbn 1 1 (tnpr 1 (tnpr 0 +null-gbar+ 1 '(13)) 0 +null-abar+)))
-  (check-rdct)
-  (dotimes (i 10)
-    (let ((abar (random-abar 8 4)))
-      (setf abar-degr (apply #'+ (mapcar #'car (abar-list abar))))
-      (setf gnrt (tnpr 5 (tnpr 3 (gbar 3 0 '(1 2) 0 '(3) 0 '()) 2 '(4 5))
-                       abar-degr abar))
-      (setf gbar (gbar 2 0 '(1) 0 '()))
-      (unless (>= abar-degr 9)
-        (setf *tc* (cmbn (+ 5 abar-degr) 1 gnrt)
-              *bc* (cmbn 2 1 gbar))
-        (check-rdct))))
-  (dotimes (i 10)
-    (let ((abar (random-abar 6 4)))
-      (setf abar-degr (apply #'+ (mapcar #'car (abar-list abar))))
-      (setf gnrt (tnpr 6 (tnpr 3 (gbar 3 0 '(1 2) 0 '(3) 0 '()) 3 '(4 5 6))
-                       abar-degr abar))
-      (setf gbar (gbar 3 0 '(1 2) 1 '() 0 '()))
-      (unless (>= abar-degr 8)
-        (setf *tc* (cmbn (+ 6 abar-degr) 1 gnrt)
-              *bc* (cmbn 3 1 gbar))
-        (check-rdct))))
-  (dotimes (i 10)
-    (let ((abar (random-abar 6 4)))
-      (setf abar-degr (apply #'+ (mapcar #'car (abar-list abar))))
-      (setf gnrt (tnpr 5 (tnpr 2 (gbar 2 0 '(3) 0 '()) 3 '(4 5 6))
-	   	     abar-degr abar))
-      (setf gbar (gbar 4 0 '(1 2 3) 0 '(4 5) 0 '(6) 0 '()))
-      (unless (>= abar-degr 9)
-        (setf *tc* (cmbn (+ 5 abar-degr) 1 gnrt))
-        (setf *bc* (cmbn 4 1 gbar))
-        (check-rdct))))
-  (dotimes (i 10)
-    (let ((abar (random-abar 6 4)))
-      (setf abar-degr (apply #'+ (mapcar #'car (abar-list abar))))
-      (setf gnrt (tnpr 4 (tnpr 2 (gbar 2 0 '(3) 0 '()) 2 '(4 5))
-                       abar-degr abar))
-      (setf gbar (gbar 5 8 '(1 2 3) 0 '(4 5 6) 0 '(7 8) 0 '(9) 0 '()))
-      (unless (>= abar-degr 10)
-         (setf *tc* (cmbn (+ 4 abar-degr) 1 gnrt))
-         (setf *bc* (cmbn 5 1 gbar))
-         (check-rdct))))
-|#
-
-(DEFUN CS-LEFT-EQVL-LEFT-REDUCTION (smgr
-				     &aux (pre-left-eqvl-left-reduction
-					     (cs-pre-left-eqvl-left-reduction smgr))
-				          (hat-left-perturbation
-					     (cs-hat-left-perturbation smgr)))
-  (declare
-    (type simplicial-group smgr)
-    (type reduction pre-left-eqvl-left-reduction)
-    (type morphism hat-left-perturbation))
-  (the reduction
-    (progn
-      (dstr-change-sorc-trgt hat-left-perturbation
-	:new-sorc (tcc pre-left-eqvl-left-reduction)
-	:new-trgt (tcc pre-left-eqvl-left-reduction))
-      (let ((rslt (special-bpl-2 pre-left-eqvl-left-reduction
-				 hat-left-perturbation)))
-	(declare (type reduction rslt))
-	(with-slots (tcc f g h) rslt
-	  (setf tcc (cs-left-eqvl-hat smgr)
-		(slot-value f 'sorc) tcc
-		(slot-value g 'trgt) tcc
-		(slot-value h 'sorc) tcc
-		(slot-value h 'trgt) tcc))
-	rslt))))
-	
-
-#|
-  (cat-init)
-  (defun random-abar (tot-degr~ max-degr)
-    (do ((rslt nil)
-         (cum-degr 0 (+ cum-degr degr 1))
-         (degr))
-        ((>= cum-degr tot-degr~) (make-abar :list rslt))
-       (setf degr (1+ (random max-degr)))
-       (push (brgn (1+ degr)
-                   (let ((list (make-list degr)))
-                     (mapl
-                       #'(lambda (sublist)
-                           (setf (car sublist) (- (random 21) 10)))
-                       list)
-                     list))
-             rslt)))
-  (setf rdct (cs-left-eqvl-left-reduction (k-z-1)))
-  (pre-check-rdct rdct)
-  (setf *tc* (cmbn 0 1 (tnpr 0 (tnpr 0 +null-gbar+ 0 '()) 0 +null-abar+))
-        *bc* (cmbn 0 1 +null-gbar+))
-  (check-rdct)
-  (setf *tc* (cmbn 1 1 (tnpr 1 (tnpr 0 +null-gbar+ 1 '(13)) 0 +null-abar+)))
-  (check-rdct)
-  (dotimes (i 10)
-    (let ((abar (random-abar 8 4)))
-      (setf abar-degr (apply #'+ (mapcar #'car (abar-list abar))))
-      (setf gnrt (tnpr 5 (tnpr 3 (gbar 3 0 '(1 2) 0 '(3) 0 '()) 2 '(4 5))
-                       abar-degr abar))
-      (setf gbar (gbar 2 0 '(1) 0 '()))
-      (unless (>= abar-degr 9)
-        (setf *tc* (cmbn (+ 5 abar-degr) 1 gnrt)
-              *bc* (cmbn 2 1 gbar))
-        (check-rdct))))
-  (dotimes (i 10)
-    (let ((abar (random-abar 6 4)))
-      (setf abar-degr (apply #'+ (mapcar #'car (abar-list abar))))
-      (setf gnrt (tnpr 6 (tnpr 3 (gbar 3 0 '(1 2) 0 '(3) 0 '()) 3 '(4 5 6))
-                       abar-degr abar))
-      (setf gbar (gbar 3 0 '(1 2) 1 '() 0 '()))
-      (unless (>= abar-degr 8)
-        (setf *tc* (cmbn (+ 6 abar-degr) 1 gnrt)
-              *bc* (cmbn 3 1 gbar))
-        (check-rdct))))
-  (dotimes (i 10)
-    (let ((abar (random-abar 6 4)))
-      (setf abar-degr (apply #'+ (mapcar #'car (abar-list abar))))
-      (setf gnrt (tnpr 5 (tnpr 2 (gbar 2 0 '(3) 0 '()) 3 '(4 5 6))
-	   	     abar-degr abar))
-      (setf gbar (gbar 4 0 '(1 2 3) 0 '(4 5) 0 '(6) 0 '()))
-      (unless (>= abar-degr 9)
-        (setf *tc* (cmbn (+ 5 abar-degr) 1 gnrt))
-        (setf *bc* (cmbn 4 1 gbar))
-        (check-rdct))))
-  (dotimes (i 10)
-    (let ((abar (random-abar 6 4)))
-      (setf abar-degr (apply #'+ (mapcar #'car (abar-list abar))))
-      (setf gnrt (tnpr 4 (tnpr 2 (gbar 2 0 '(3) 0 '()) 2 '(4 5))
-                       abar-degr abar))
-      (setf gbar (gbar 5 8 '(1 2 3) 0 '(4 5 6) 0 '(7 8) 0 '(9) 0 '()))
-      (unless (>= abar-degr 10)
-         (setf *tc* (cmbn (+ 4 abar-degr) 1 gnrt))
-         (setf *bc* (cmbn 5 1 gbar))
-         (check-rdct))))
-|#
-
-(DEFUN CS-PRE-LEFT-EQVL-RIGHT-REDUCTION-INTR-F (cmbn)
-  (declare (type cmbn cmbn))
-  (the cmbn
-     (with-cmbn (degr list) cmbn
-     (let ((rslt +empty-list+))
-       (declare (list rslt))
-       (do ((mark list (cdr mark)))
-	   ((endp mark))
-	   (declare (list mark))
-	  (with--term (cffc tnpr) mark
-	  (with-tnpr (degr1 nil nil abar2) tnpr
-	    (if (zerop degr1)
-	       (push (term cffc abar2) rslt)
-	       (return)))))
-       (make-cmbn :degr degr
-		  :list (nreverse rslt))))))
-
-#|
-  (cs-pre-left-eqvl-right-reduction-intr-f
-    (cmbn 4 2 (tnpr 0 (tnpr 0 +null-gbar+ 0 'i)
-                    4 (abar 2 'a 2 'b))
-            3 (tnpr 0 (tnpr 0 +null-gbar+ 0 'i)
-                    4 (abar 2 'a 2 'c))
-            5 (tnpr 1 (tnpr 0 +null-gbar+ 1 'a)
-                    3 (abar 1 'a 2 'b))))
-|#
-
-(DEFUN CS-PRE-LEFT-EQVL-RIGHT-REDUCTION-F (smgr
-					     &aux (hat-t-u (cs-hat-t-u smgr))
-					          (bar (bar smgr)))
-  (declare
-    (type simplicial-group smgr)
-    (type chain-complex hat-t-u bar))
-  (the morphism
-    (morphism
-      :sorc hat-t-u :trgt bar :degr 0
-      :intr #'cs-pre-left-eqvl-right-reduction-intr-f
-      :strt :cmbn
-      :dfnt `(cs-pre-left-eqvl-right-reduction-f ,smgr))))
-
-(DEFUN CS-PRE-LEFT-EQVL-RIGHT-REDUCTION-INTR-G (idnt)
-  (declare (type gmsm idnt))
-  (flet ((rslt (cmbn)
-	   (declare (type cmbn cmbn))
-	   (the cmbn
-	     (with-cmbn (degr list) cmbn
-	     (let ((bsgn (tnpr 0 +null-gbar+ 0 idnt)))
-	       (declare (type tnpr bsgn))
-	       (make-cmbn :degr degr
-		 :list (mapcar
-			 #'(lambda (term)
-			     (declare (type term term))
-			     (with-term (cffc abar) term
-			       (term cffc
-				     (tnpr 0 bsgn
-					   degr abar))))
-			 list)))))))
-    (the intr #'rslt)))
-
-#|
-  (setf g (cs-pre-left-eqvl-right-reduction-intr-g 'i))
-  (funcall g (cmbn 3 2 (abar 1 'a 2 'b)))
-|#
-
-(DEFUN CS-PRE-LEFT-EQVL-RIGHT-REDUCTION-G (smgr
-					    &aux (hat-t-u (cs-hat-t-u smgr))
-					         (bar (bar smgr))
-						 (idnt (bsgn smgr)))
-  (declare
-    (type simplicial-group smgr)
-    (type chain-complex hat-t-u bar)
-    (type gmsm idnt))
-  (the morphism
-    (morphism
-      :sorc bar :trgt hat-t-u :degr 0
-      :intr (cs-pre-left-eqvl-right-reduction-intr-g idnt)
-      :strt :cmbn
-      :dfnt `(cs-pre-left-eqvl-right-reduction-g ,smgr))))
-
-(DEFUN CS-PRE-LEFT-EQVL-RIGHT-REDUCTION-H (smgr
-					    &aux (bar (bar smgr))
-					         (tnpr-contraction
-						   (smgr-tnpr-contraction smgr)))
-  (declare
-    (type simplicial-group smgr)
-    (type chain-complex bar)
-    (type morphism tnpr-contraction))
-  (the morphism
-    (tnsr-prdc tnpr-contraction (idnt-mrph bar))))
-
-(DEFUN CS-PRE-LEFT-EQVL-RIGHT-REDUCTION (smgr)
-  (declare (type simplicial-group smgr))
-  (the reduction
-    (reduction
-      :f (cs-pre-left-eqvl-right-reduction-f smgr)
-      :g (cs-pre-left-eqvl-right-reduction-g smgr)
-      :h (cs-pre-left-eqvl-right-reduction-h smgr)
-      :dfnt `(cs-pre-left-eqvl-right-reduction ,smgr))))
-
-#|
-  (cat-init)
-  (defun random-abar (tot-degr~ max-degr)
-    (do ((rslt nil)
-         (cum-degr 0 (+ cum-degr degr 1))
-         (degr))
-        ((>= cum-degr tot-degr~) (make-abar :list rslt))
-       (setf degr (1+ (random max-degr)))
-       (push (brgn (1+ degr)
-                   (let ((list (make-list degr)))
-                     (mapl
-                       #'(lambda (sublist)
-                           (setf (car sublist) (- (random 21) 10)))
-                       list)
-                     list))
-             rslt)))
-  (setf rdct (cs-pre-left-eqvl-right-reduction (k-z-1)))
-  (pre-check-rdct rdct)
-  (setf *tc* (cmbn 0 1 (tnpr 0 (tnpr 0 +null-gbar+ 0 '()) 0 +null-abar+))
-        *bc* (cmbn 0 1 +null-abar+))
-  (check-rdct)
-  (setf *tc* (cmbn 1 1 (tnpr 1 (tnpr 0 +null-gbar+ 1 '(13)) 0 +null-abar+)))
-  (check-rdct)
-  (dotimes (i 10)
-    (let ((abar (random-abar 8 4)))
-      (setf abar-degr (apply #'+ (mapcar #'car (abar-list abar))))
-      (setf gnrt (tnpr 5 (tnpr 3 (gbar 3 0 '(1 2) 0 '(3) 0 '()) 2 '(4 5))
-                       abar-degr abar))
-      (unless (>= abar-degr 9)
-        (setf *tc* (cmbn (+ 5 abar-degr) 1 gnrt)
-              *bc* (cmbn abar-degr 1 abar))
-        (check-rdct))))
-  (dotimes (i 10)
-    (let ((abar (random-abar 6 4)))
-      (setf abar-degr (apply #'+ (mapcar #'car (abar-list abar))))
-      (setf gnrt (tnpr 6 (tnpr 3 (gbar 3 0 '(1 2) 0 '(3) 0 '()) 3 '(4 5 6))
-                       abar-degr abar))
-      (unless (>= abar-degr 8)
-        (setf *tc* (cmbn (+ 6 abar-degr) 1 gnrt)
-              *bc* (cmbn abar-degr 1 abar))
-        (check-rdct))))
-  (dotimes (i 10)
-    (let ((abar (random-abar 6 4)))
-      (setf abar-degr (apply #'+ (mapcar #'car (abar-list abar))))
-      (setf gnrt (tnpr 5 (tnpr 2 (gbar 2 0 '(3) 0 '()) 3 '(4 5 6))
-	   	     abar-degr abar))
-      (unless (>= abar-degr 9)
-        (setf *tc* (cmbn (+ 5 abar-degr) 1 gnrt))
-        (setf *bc* (cmbn abar-degr 1 abar))
-        (check-rdct))))
-  (dotimes (i 10)
-    (let ((abar (random-abar 6 4)))
-      (setf abar-degr (apply #'+ (mapcar #'car (abar-list abar))))
-      (setf gnrt (tnpr 4 (tnpr 2 (gbar 2 0 '(3) 0 '()) 2 '(4 5))
-                       abar-degr abar))
-      (unless (>= abar-degr 10)
-         (setf *tc* (cmbn (+ 4 abar-degr) 1 gnrt))
-         (setf *bc* (cmbn abar-degr 1 abar))
-         (check-rdct))))
-|#
-
-(DEFUN CS-LEFT-EQVL-RIGHT-REDUCTION (smgr
-				      &aux (pre-reduction
-					     (cs-pre-left-eqvl-right-reduction smgr))
-				           (perturbation
-					     (cs-hat-right-perturbation smgr)))
-  (declare
-    (type simplicial-group smgr)
-    (type reduction pre-reduction)
-    (type morphism perturbation))
-  (the reduction
-    (progn
-      (setf (slot-value perturbation 'sorc) (tcc pre-reduction)
-	    (slot-value perturbation 'trgt) (tcc pre-reduction))
-      (special-bpl-2 pre-reduction perturbation))))
-
-#|
-  (cat-init)
-  (defun random-abar (tot-degr~ max-degr)
-    (do ((rslt nil)
-         (cum-degr 0 (+ cum-degr degr 1))
-         (degr))
-        ((>= cum-degr tot-degr~) (make-abar :list rslt))
-       (setf degr (1+ (random max-degr)))
-       (push (brgn (1+ degr)
-                   (let ((list (make-list degr)))
-                     (mapl
-                       #'(lambda (sublist)
-                           (setf (car sublist) (- (random 21) 10)))
-                       list)
-                     list))
-             rslt)))
-  (setf rdct (cs-left-eqvl-right-reduction (k-z-1)))
-  (pre-check-rdct rdct)
-  (setf *tc* (cmbn 0 1 (tnpr 0 (tnpr 0 +null-gbar+ 0 '()) 0 +null-abar+))
-        *bc* (cmbn 0 1 +null-abar+))
-  (check-rdct)
-  (setf *tc* (cmbn 1 1 (tnpr 1 (tnpr 0 +null-gbar+ 1 '(13)) 0 +null-abar+)))
-  (check-rdct)
-  (dotimes (i 10)
-    (let ((abar (random-abar 4 2)))
-      (setf abar-degr (apply #'+ (mapcar #'car (abar-list abar))))
-      (setf gnrt (tnpr 3 (tnpr 2 (gbar 2 0 '(3) 0 '()) 1 '(4))
-                       abar-degr abar))
-      (unless (>= abar-degr 9)
-        (setf *tc* (cmbn (+ 3 abar-degr) 1 gnrt)
-              *bc* (cmbn abar-degr 1 abar))
-        (check-rdct))))
-  (dotimes (i 10)
-    (let ((abar (random-abar 3 1)))
-      (setf abar-degr (apply #'+ (mapcar #'car (abar-list abar))))
-      (setf gnrt (tnpr 4 (tnpr 2 (gbar 2 0 '(3) 0 '()) 2 '(5 6))
-                       abar-degr abar))
-      (unless (>= abar-degr 8)
-        (setf *tc* (cmbn (+ 4 abar-degr) 1 gnrt)
-              *bc* (cmbn abar-degr 1 abar))
-        (check-rdct))))
-  (dotimes (i 10)
-    (let ((abar (random-abar 3 1)))
-      (setf abar-degr (apply #'+ (mapcar #'car (abar-list abar))))
-      (setf gnrt (tnpr 5 (tnpr 3 (gbar 3 0 '(1 2) 1 '() 0 '()) 2 '(5 6))
-	   	     abar-degr abar))
-      (unless (>= abar-degr 9)
-        (setf *tc* (cmbn (+ 5 abar-degr) 1 gnrt))
-        (setf *bc* (cmbn abar-degr 1 abar))
-        (check-rdct))))
-  (dotimes (i 10)
-    (let ((abar (random-abar 6 4)))
-      (setf abar-degr (apply #'+ (mapcar #'car (abar-list abar))))
-      (setf gnrt (tnpr 4 (tnpr 2 (gbar 2 0 '(3) 0 '()) 2 '(4 5))
-                       abar-degr abar))
-      (unless (>= abar-degr 10)
-         (setf *tc* (cmbn (+ 4 abar-degr) 1 gnrt))
-         (setf *bc* (cmbn abar-degr 1 abar))
-         (check-rdct))))
-|#
-
-(DEFUN CS-LEFT-EQVL (smgr)
-  (declare (type simplicial-group smgr))
-  (the equivalence
-    (equivalence
-     :lrdct (cs-left-eqvl-left-reduction smgr)
-     :rrdct (cs-left-eqvl-right-reduction smgr)
-     :dfnt `(cs-left-eqvl ,smgr))))
-
-#|
-  (cat-init)
-  (setf h (cs-left-eqvl (k-z-1)))
-  (setf abar (abar 2 '(2) 3 '(3 4)))
-  (rg h 5 abar)
-  (lf h *)
-  (lg h *)
-  (rf h *)
-|#
-
-(DEFUN CLASSIFYING-SPACE-EFHM (smgr)
-  (declare (type simplicial-group smgr))
-  (let ((left-eqvl (cs-left-eqvl smgr))
-	(right-eqvl (bar (efhm smgr))))
-    (declare (type equivalence left-eqvl right-eqvl))
-    (cmps left-eqvl right-eqvl)))
-
-(DEFMETHOD SEARCH-EFHM (classifying-space (dfnt (eql 'classifying-space)))
-  (declare (type simplicial-set classifying-space))
-  (classifying-space-efhm (second (dfnt classifying-space))))
-
-#|
-  (cat-init)
-  (setf k (k-z-1))
-  (homology k 0 10)
-  (setf bk (classifying-space k))
-  (homology bk 0 10)
-  (setf obk (loop-space bk))
-  (homology obk 0 6)
-|#
\ No newline at end of file
diff --git a/archive/Kenzo-2/Kenzo-2-Acl5/classes.cl b/archive/Kenzo-2/Kenzo-2-Acl5/classes.cl
deleted file mode 100644
index 84b6e56..0000000
--- a/archive/Kenzo-2/Kenzo-2-Acl5/classes.cl
+++ /dev/null
@@ -1,522 +0,0 @@
-;;;  CLASSES  CLASSES  CLASSES  CLASSES  CLASSES  CLASSES  CLASSES
-;;;  CLASSES  CLASSES  CLASSES  CLASSES  CLASSES  CLASSES  CLASSES
-;;;  CLASSES  CLASSES  CLASSES  CLASSES  CLASSES  CLASSES  CLASSES
-
-(IN-PACKAGE "CAT")
-
-(PROVIDE "classes")
-
-;;;
-;;; VARIOUS
-;;;
-
-(DEFTYPE ANY () t)
-
-;;; 
-;;;  COMBINATIONS
-;;;
-
-;; CFFC = CoeFFiCient
-(DEFUN CFFC-P (object)
-   (declare (type any object))
-   (the boolean
-      (and (typep object 'fixnum)
-           (/= 0 object))))
-
-(DEFTYPE CFFC () '(satisfies cffc-p))
-
-;; GNRT = GeNeRaTor
-(DEFTYPE GNRT () 'any)
-
-;; CMPR = CoMPaRison
-(DEFTYPE CMPR () '(member :less :equal :greater))
-
-;; CMPRF = CoMPaRison Function
-(DEFTYPE CMPRF () 'function)
-               ;; (function (gnrt gnrt) cmpr)
-
-(DEFUN TERM-P (object)
-   (declare (type any object))
-   (the boolean
-      (and (consp object)
-           (typep (car object) 'cffc)
-           (typep (cdr object) 'gnrt))))
-
-(DEFTYPE TERM () '(satisfies term-p))
-
-;; ICMBN = Internal-CoMBiNation
-(DEFUN ICMBN-P (object)
-   ;; ICMBN = Internal CoMBiNation,
-   ;;   without the keyword and the degree
-   (declare (type any object))
-   (the boolean
-      (and (listp object)
-           (every #'term-p object))))
-
-(DEFTYPE ICMBN () '(satisfies icmbn-p))
-
-;; CMBN = CoMBiNation
-(DEFUN CMBN-P (object)
-   (declare (type any object))
-   (the boolean
-      (and (consp object)
-           (eql (car object) :cmbn)
-           (consp (cdr object))
-           (typep (second object) 'fixnum)
-           (typep (cddr object) 'icmbn))))
-
-(DEFTYPE CMBN () '(satisfies cmbn-p))
-
-(DEFTYPE BASIS () '(or function (eql :locally-effective)))
-                   ;; (function (degr) (list gnrt))
-
-;; INTR = INTeRNal-morphism
-(DEFTYPE INTR () 'function)
-               ;; (or (function (degr gnrt) cmbn)  ;; if :gnrt strategy
-               ;;     (function (cmbn) (cmbn))     ;; if :cmbn strategy
-
-(DEFVAR REDEFINITION-WARNINGS-SAVED)
-
-(eval-when (:compile-toplevel :load-toplevel :execute)
- (WHEN
-  (AND (FIND-PACKAGE "EXCL")
-       (FIND-SYMBOL "*REDEFINITION-WARNINGS*" "EXCL"))
-  (setf redefinition-warnings-saved
-	excl:*redefinition-warnings*
-	excl:*redefinition-warnings* nil)))
-
-(DEFCLASS CHAIN-COMPLEX () ())  ;; will be redefined later.
-
-(DEFCLASS MORPHISM () ())  ;; will be redefined later.
-
-(DEFCLASS EQUIVALENCE () ())  ;;  will be redefined later
-
-;;  IDNM = IDentification NuMber
-(DEFVAR *IDNM-COUNTER*)
-(SETF *IDNM-COUNTER* 0)
-
-(DEFCLASS KENZO-OBJECT ()
-  ;; IDentification NuMber
-  ((idnm :type fixnum :reader idnm)
-   ;; ORiGiN
-   (dfnt :type list :reader dfnt)
-   (prpr :type list :reader prpr)
-   (cmmn :type list :reader cmmn)))
-
-(DEFCLASS CHAIN-COMPLEX (kenzo-object)
-  ((cmpr :type cmprf :reader cmpr1)
-   (basis :type basis :reader basis1)
-   ;; BaSe GeNerator
-   (bsgn :type gnrt :reader bsgn)
-   ;; DiFFeRential
-   (dffr :type morphism :reader dffr1)
-   ;; GRound MoDule
-   (grmd :type chain-complex :reader grmd)
-   ;; EFfective HoMology
-   (efhm :type equivalence :accessor efhm)))
-
-;; STRT = STRaTegy
-(DEFTYPE STRT () '(member :gnrt :cmbn))
-
-(DEFCLASS MORPHISM (kenzo-object)
-     ;; SOuRCe
-  ((sorc :type chain-complex :reader sorc)
-   ;; TaRGeT
-   (trgt :type chain-complex :reader trgt)
-   ;; DEGRee
-   (degr :type fixnum :reader degr)
-   ;; INTeRnal
-   (intr :type intr :reader intr)
-   ;; STRaTegy
-   (strt :type strt :reader strt)
-;;     ;; WoRk-TiMe
-;;     (wrtm :type integer :initform 0 :accessor wrtm)
-   ;; CaLl NuMber
-   (???-clnm :type fixnum :accessor ???-clnm)
-   (?-clnm :type fixnum :accessor ?-clnm)
-   ;; ReSuLTS
-   (rslts :type simple-vector :reader rslts)))
-            ;; (vector (vector result))
-
-;;;
-;;;  EFFECTIVE HOMOLOGY
-;;;
-
-(DEFCLASS REDUCTION (kenzo-object)
-  ;; Top Chain Complex
-  ((tcc :type chain-complex :reader tcc1)
-   ;; Bottom Chain Complex
-   (bcc :type chain-complex :reader bcc1)
-   (f :type morphism :reader f1)
-   (g :type morphism :reader g1)
-   (h :type morphism :reader h1)))
-
-(DEFCLASS EQUIVALENCE (kenzo-object)
-     ;; Left Bottom Chain Complex
-    ((lbcc :type chain-complex :reader lbcc1)
-     ;; Top Chain Complex
-     (tcc  :type chain-complex  :reader tcc1)
-     ;; Bottom Right Chain Complex
-     (rbcc :type chain-complex :reader rbcc1)
-     ;; Left f
-     (lf :type morphism        :reader lf1)
-     ;; Left g
-     (lg :type morphism        :reader lg1)
-     ;; Left h
-     (lh :type morphism        :reader lh1)
-     ;; Right f
-     (rf :type morphism        :reader rf1)
-     ;; Right g
-     (rg :type morphism        :reader rg1)
-     ;; Right h
-     (rh :type morphism        :reader rh1)
-     ;; Left ReDuCTion
-     (lrdct :type reduction    :reader lrdct)
-     ;; Right ReDuCTion
-     (rrdct :type reduction    :reader rrdct)))
-
-(eval-when (:compile-toplevel :load-toplevel :execute)
- (WHEN
-  (AND (FIND-PACKAGE "EXCL")
-       (FIND-SYMBOL "*REDEFINITION-WARNINGS*" "EXCL"))
-  (setf excl:*redefinition-warnings*
-	redefinition-warnings-saved)))
-
-;;;
-;;;  CONES
-;;;
-
-;; BICN = bicone
-(DEFUN BICN-P (object)
-   (declare (type any object))
-   (the boolean
-      (and (consp object)
-           (typep (car object) '(member :bcnb :bcnc :bcnd))
-           (typep (cdr object) 'gnrt))))
-
-(DEFTYPE BICN () '(satisfies bicn-p))
-
-;;;
-;;;  TENSOR PRODUCTS
-;;;
-
-(DEFUN TNPR-P (object)
-   (declare (type any object))
-   (the boolean
-      (and (consp object)
-           (eql :tnpr (car object))
-           (consp (cdr object))
-           (consp (cadr object))
-           (consp (cddr object))
-           (typep (caadr object) 'fixnum)
-           (typep (caddr object) 'fixnum))))
-
-(DEFTYPE TNPR () '(satisfies tnpr-p))
-
-;;;
-;;;  COALGEBRAS
-;;;
-
-(DEFCLASS COALGEBRA (chain-complex)
-    ((cprd :type morphism :reader cprd1)))   ;; coproduct
-
-;;;
-;;;  COBAR
-;;;
-
-;; CBGN CoBar-GeNerator
-(DEFUN CBGN-P (object)
-   ;; CBGN = CoBar GeNerator
-   (declare (type any object))
-   (the boolean
-      (and (consp object)
-           (typep (car object) 'fixnum)      ;; degree *in* the cobar
-           (typep (cdr object) 'gnrt))))
-
-(DEFTYPE CBGN () '(satisfies cbgn-p))
-
-;; IALLP = Internal-ALgebraic LooP
-(DEFUN IALLP-P (object)
-   (declare (type any object))
-   (the boolean
-      (and (listp object)
-           (every #'cbgn-p object))))
-
-(DEFTYPE IALLP () '(satisfies iallp-p))
-
-;; ALLP = ALgebraic LooP
-(DEFUN ALLP-P (object)
-   ;; ALLP = ALgebraic LooP
-   (declare (type any object))
-   (the boolean
-      (and (consp object)
-           (eq :allp (car object))
-           (typep (cdr object) 'iallp))))
-
-(DEFTYPE ALLP () '(satisfies allp-p))
-
-;;;
-;;;  ALGEBRAS
-;;;
-
-(DEFCLASS ALGEBRA (chain-complex)
-    ((aprd :type morphism :reader aprd1)))   ;; product
-
-
-;;;
-;;;  HOPH-ALGEBRAS
-;;;
-
-(DEFCLASS HOPF-ALGEBRA (coalgebra algebra)
-  ())
-
-;;;
-;;;  BAR
-;;;
-
-;; BRGN BaR-GeNerator
-(DEFUN BRGN-P (object)
-   ;; BRGN = BaR GeNerator
-   (declare (type any object))
-   (the boolean
-      (and (consp object)
-           (typep (car object) 'fixnum)      ;; degree *in* the cobar
-           (typep (cdr object) 'gnrt))))
-
-(DEFTYPE BRGN () '(satisfies brgn-p))
-
-;; IABAR = Internal-ALgebraic LooP
-(DEFUN IABAR-P (object)
-   (declare (type any object))
-   (the boolean
-      (and (listp object)
-           (every #'brgn-p object))))
-
-(DEFTYPE IABAR () '(satisfies iabar-p))
-
-;; ABAR = ALgebraic BAR
-(DEFUN ABAR-P (object)
-   (declare (type any object))
-   (the boolean
-      (and (consp object)
-           (eq :abar (car object))
-           (typep (cdr object) 'iabar))))
-
-(DEFTYPE ABAR () '(satisfies abar-p))
-
-;;;
-;;;  SIMPLICIAL SETS
-;;;
-
-;;  DGOP = DeGeneray OPerator
-(DEFTYPE DGOP () `(integer 0 ,most-positive-fixnum))
-
-;; GMSM = GeoMetric SiMplex
-(DEFTYPE GMSM () 'gnrt)
-
-;;  DLOP = DeL OPerator
-(DEFTYPE DLOP () 'dgop) 
-
-;; IABSM = Internal ABstract SiMplex
-(DEFUN IABSM-P (object)
-  (declare (type any object))
-  (the boolean
-     (and (consp object)
-	  (typep (car object) 'dgop)
-	  (typep (cdr object) 'gmsm))))	   
-
-(DEFTYPE IABSM () '(satisfies iabsm-p))
-
-;; ABSM = ABstract SiMplex
-(DEFUN ABSM-P (object)
-   (declare (type any object))
-   (the boolean
-      (and (consp object)
-           (eq :absm (car object))
-           (typep (cdr object) 'iabsm))))
-
-
-(DEFTYPE ABSM () '(satisfies absm-p))
-
-(DEFTYPE FACE () 'function)
-            ;;   (function (indx dmns gmsm) absm)
-
-(DEFTYPE FACE* () 'function)
-            ;;    (function (indx dmns gmsm) (or gmsm (eql :degenerate)))
-
-(DEFCLASS SIMPLICIAL-SET (coalgebra)
-    ((face :type face :reader face1)))
-
-;;;
-;;;  SPECIAL SMSTS
-;;;
-
-;;  DLOP = DeL OPerator
-(DEFUN SOFT-DLOP-P (object)
-   (declare (type any object))
-   (the boolean
-      (and (consp object)
-           (eq :delt (car object))
-           (typep (cdr object) 'dgop))))
-
-(DEFTYPE SOFT-DLOP () '(satisfies soft-dlop-p))
-
-;;;
-;;;  CARTESIAN PRODUCTS
-;;;
-
-;;  CRPR = CaRtesian PRoduct
-(DEFUN CRPR-P (object)
-   (declare (type any object))
-   (the boolean
-      (and (consp object)
-           (eq (car object) :crpr)
-           (consp (cdr object))
-           (consp (cadr object))
-           (consp (cddr object))
-           (typep (caadr object) 'dgop)
-           (typep (cdadr object) 'gmsm)
-           (typep (caddr object) 'dgop)
-           (typep (cdddr object) 'gmsm))))
-
-(DEFTYPE CRPR () '(satisfies crpr-p))
-
-;;;
-;;;  LOOP SPACES
-;;;
-
-;;  EXPN = EXPoNent
-(DEFUN EXPN-P (object)
-   (declare (type any object))
-   (the boolean
-      (typep object '(and fixnum
-                          (not (eql 0))))))
-
-(DEFTYPE EXPN () '(satisfies expn-p))
-
-;;  POWR = POWeR
-(DEFUN POWR-P (object)
-   (declare (type any object))
-   (the boolean
-      (and (consp object)
-           (typep (car object) 'gmsm)
-           (typep (cdr object) 'expn))))
-
-(DEFTYPE POWR () '(satisfies powr-p))
-
-;;  APOWR = Abstract POWeR
-(DEFUN APOWR-P (object)
-   (declare (type any object))
-   (the boolean
-      (and (consp object)
-           (typep (car object) 'dgop)
-           (typep (cdr object) 'powr))))
-
-(DEFTYPE APOWR () '(satisfies apowr-p))
-
-;;  ILOOP = Internal LOOP
-(DEFUN ILOOP-P (object)
-   (declare (type any object))
-   (the boolean
-      (and (listp object)
-           (every #'apowr-p object))))
-
-(DEFTYPE ILOOP () '(satisfies iloop-p))
-
-(DEFUN LOOP-P (object)
-   (declare (type any object))
-   (the boolean
-      (and (consp object)
-           (eq :loop (car object))
-           (iloop-p (cdr object)))))
-
-;;;----------------------------
-;;; Correction 2000 January 19
-;;;------------------------------------
-;;;#+(or (and :mswindows :allegro-v5.0)
-;;;------------------------------------
-#+(or (and :mswindows :allegro-v5.0)
-      (and :mswindows :allegro-v5.0.1)
-;;;-----------------------------------
-      (and :unix :allegro-v4.3)
-      (and :unix :allegro-v5.0))
-  (eval-when (:compile-toplevel :load-toplevel :execute)
-     (setf excl:*enable-package-locked-errors* nil))
-
-(DEFTYPE LOOP () '(satisfies loop-p))
-
-#+(or (and :mswindows :allegro-v5.0)
-      (and :unix :allegro-v4.3)
-      (and :unix :allegro-v5.0))
-  (eval-when (:compile-toplevel :load-toplevel :execute)
-     (setf excl:*enable-package-locked-errors* t))
-
-;;;;
-;;;;
-;;;;
-
-(DEFTYPE KFLL () 'function)
-              ;; (function (indx dmns (list absm)) absm)
-
-(DEFCLASS KAN (simplicial-set)
-  ((kfll :type kfll :reader kfll1)))
-
-(DEFTYPE SINTR () 'function)
-               ;; (function (dmns gmsm) absm)
-
-(DEFCLASS SIMPLICIAL-MRPH (morphism)
-  ((sintr :type sintr :reader sintr)))
-
-(DEFUN FIBRATION-P (object)
-  (declare (type any object))
-  (the boolean
-     (and (typep object 'simplicial-mrph)
-	  (= -1 (degr object)))))
-
-(DEFTYPE FIBRATION ()
-  '(satisfies fibration-p))
-
-(DEFCLASS SIMPLICIAL-GROUP (kan hopf-algebra)
-   ((grml :type simplicial-mrph :reader grml1)
-    (grin :type simplicial-mrph :reader grin1)))
-
-(DEFCLASS AB-SIMPLICIAL-GROUP (simplicial-group) ())
-
-(DEFMACRO GRML (smgr &rest rest)
-   (ecase (length rest)
-      (0 `(grml1 ,smgr))
-      ((1 2) `(? (grml1 ,smgr) ,@rest))))
-
-(DEFMACRO GRIN (smgr &rest rest)
-   (case (length rest)
-      (0 `(grin1 ,smgr))
-      (otherwise `(? (grin1 ,smgr) ,@rest))))
-
-;;;
-;;;  GBAR
-;;;
-
-;;  IGBAR Internal Geometrical BAR
-;;  (dmns absm_(m-1) ... absm_1 absm_0)
-(DEFUN IGBAR-P (object)
-   (declare (type any object))
-   (the boolean
-      (and (listp object)
-	   (typep (first object) '(integer 0 *))
-	   (= (length object) (1+ (first object)))
-	   (every #'absm-p (rest object)))))
-
-(DEFTYPE IGBAR () '(satisfies igbar-p))
-
-;;  GBAR Geometrical BAR
-;;  (:gbar dmns absm_(m-1) ... absm_1)
-(DEFUN GBAR-P (object)
-   (declare (type any object))
-   (the boolean
-      (and (consp object)
-           (eq :gbar (car object))
-           (igbar-p (cdr object)))))
-
-(DEFTYPE GBAR () '(satisfies gbar-p))
-
-
diff --git a/archive/Kenzo-2/Kenzo-2-Acl5/classifying-spaces.cl b/archive/Kenzo-2/Kenzo-2-Acl5/classifying-spaces.cl
deleted file mode 100644
index a94fb16..0000000
--- a/archive/Kenzo-2/Kenzo-2-Acl5/classifying-spaces.cl
+++ /dev/null
@@ -1,383 +0,0 @@
-;;;  CLASSIFYING-SPACES  CLASSIFYING-SPACES  CLASSIFYING-SPACES
-;;;  CLASSIFYING-SPACES  CLASSIFYING-SPACES  CLASSIFYING-SPACES
-;;;  CLASSIFYING-SPACES  CLASSIFYING-SPACES  CLASSIFYING-SPACES
-
-(IN-PACKAGE "CAT")
-
-(provide "classifying-spaces")
-
-(DEFCONSTANT +NULL-GBAR+ (make-gbar :dmns 0 :list +empty-list+))
-
-;;; NIGBAR = non-normalized igbar (with dimension)
-
-(DEFUN NORMALIZE-GBAR (nigbar)
-  (declare (list nigbar))
-  (the absm
-    (let ((dmns (first nigbar))
-	  (igbar (rest nigbar)))
-      (declare
-        (fixnum dmns)
-	(list igbar))
-      (when (zerop dmns)
-	(return-from normalize-gbar (absm 0 +null-gbar+)))
-      (do ((mark igbar (cdr mark))
-	   (indx (1- dmns) (1- indx))
-	   (2-indx (2-exp (1- dmns)) (ash 2-indx -1))
-	   (mask (mask (1- dmns)) (ash mask -1))
-	   (and-dgops -1 (logand and-dgops (dgop (car mark))))
-	   ;; r = result
-	   (r-dgop 0)
-	   (r-absm-list +empty-list+))
-	  ((endp mark)
-	   (absm r-dgop
-		 (make-gbar
-		  :dmns (- dmns (logcount r-dgop))
-		  :list (nreverse r-absm-list))))	   
-	  (declare
-	   (list mark r-absm-list)
-	   (fixnum indx 2-indx mask and-dgops rdgop))
-	  (when (zerop and-dgops)
-	    (return-from normalize-gbar
-	      (absm r-dgop
-		    (make-gbar
-		     :dmns (- dmns (logcount r-dgop))
-		     :list (nreconc r-absm-list mark)))))
-	  (let ((absm (car mark)))
-	    (with-absm (dgop gmsm) absm
-	      (declare (ignore gmsm))
-	      (if (and (= dgop mask)
-		       (logbitp indx and-dgops))
-		 (progn
-		   (incf r-dgop 2-indx)
-		   (mapl
-		    #'(lambda (sublist)
-			(declare (list sublist))
-			(setf (car sublist)
-			      (let ((absm (car sublist)))
-				(declare (type absm absm))
-				(with-absm (dgop gmsm) absm
-				  (absm (multiple-value-bind (q r)
-							     (floor dgop 2-indx)
-					  (declare (fixnum q r))
-					  (+ (ash (1- q) (1- indx)) r))
-					gmsm)))))
-		    r-absm-list))
-		 (push absm r-absm-list))))))))
-
-#|
-  (normalize-gbar (list 0))
-  (normalize-gbar (list 1 (absm 0 'i)))
-  (normalize-gbar (list 2 (absm 1 'i) (absm 0 'i)))
-  (normalize-gbar (list 2 (absm 0 'a) (absm 0 'i)))
-  (normalize-gbar (list 4 (absm 0 'a) (absm 0 'b) (absm 0 'c) (absm 0 'i)))
-  (normalize-gbar (list 4 (absm 7 'i) (absm 3 'i) (absm 1 'i) (absm 0 'i)))
-  (normalize-gbar (list 4 (absm 0 'a) (absm 3 'i) (absm 0 'c) (absm 0 'i)))
-  (normalize-gbar (list 4 (absm 1 'a) (absm 3 'i) (absm 0 'c) (absm 0 'i)))
-  (normalize-gbar (list 4 (absm 2 'a) (absm 3 'i) (absm 0 'c) (absm 0 'i)))
-  (normalize-gbar (list 4 (absm 4 'a) (absm 3 'i) (absm 0 'c) (absm 0 'i)))
-  (normalize-gbar (list 4 (absm 3 'a) (absm 3 'i) (absm 0 'c) (absm 0 'i)))
-  (normalize-gbar (list 4 (absm 5 'a) (absm 3 'i) (absm 0 'c) (absm 0 'i)))
-  (normalize-gbar (list 4 (absm 6 'a) (absm 3 'i) (absm 0 'c) (absm 0 'i)))
-  (normalize-gbar (list 4 (absm 1 'a) (absm 3 'i) (absm 1 'i) (absm 0 'i)))
-|#
-
-(DEFMETHOD PRINT-KEYCONS ((car (eql :gbar)) cdr stream)
-  (declare
-    (list cdr)
-    (stream stream))
-  (the (eql t)
-     (progn
-       (princ "<<GBar" stream)
-      (dolist (absm (rest cdr))
-	 (declare (type absm absm))
-	 (with-absm (dgop gmsm) absm
-	   (format stream "<~A ~A>"
-		   (hyphenize-list (dgop-int-ext dgop))
-		   gmsm)))
-       (princ ">>" stream)
-       t)))
-
-(DEFUN UNNORMALIZE-GBAR (absm idnt)
-  (declare
-     (type absm absm)
-     (type gmsm idnt))
-  (the igbar
-    (with-absm (dgop gbar) absm
-    (with-gbar (dmns list) gbar
-      (setf list (reverse list))
-      (do ((dgop2 dgop (ash dgop2 -1))
-	   (indx 0 (1+ indx))
-	   (2-indx 1 (ash 2-indx 1))
-	   (dgop3 0)
-	   (rslt +empty-list+))
-	  ((zerop dgop2)
-	   (cons (+ dmns (logcount dgop))
-		 (nreconc
-		  (mapcar
-		   #'(lambda (absm)
-		       (declare (type absm absm))
-		       (ndgnr dgop3 absm))
-		   list)
-		  rslt)))
-	  (declare
-	    (list rslt)
-	    (fixnum dgop2 2-indx dgop3))
-	 (if (oddp dgop2)
-	    (progn
-	      (push (absm (mask indx) idnt) rslt)
-	      (incf dgop3 2-indx))
-	    (push (ndgnr dgop3 (pop list)) rslt)))))))
-
-#|
-  (unnormalize-gbar (absm 1 +null-gbar+) 'i)
-  (unnormalize-gbar (absm 15 +null-gbar+) 'i)
-  (normalize-gbar (unnormalize-gbar (absm 15 +null-gbar+) 'i))
-  (unnormalize-gbar
-     (absm 0 (make-gbar :dmns 4
-                        :list (list (absm 0 'a) (absm 0 'b)
-                                    (absm 0 'c) (absm 0 'i)))) 'i)
-  (normalize-gbar
-   (unnormalize-gbar
-     (absm 0 (make-gbar :dmns 4
-                        :list (list (absm 0 'a) (absm 0 'b)
-                                    (absm 0 'c) (absm 0 'i)))) 'i))
-  (unnormalize-gbar
-     (absm 5 (make-gbar :dmns 4
-                        :list (list (absm 0 'a) (absm 0 'b)
-                                    (absm 0 'c) (absm 0 'i)))) 'i)
-  (normalize-gbar
-   (unnormalize-gbar
-     (absm 5 (make-gbar :dmns 4
-                        :list (list (absm 0 'a) (absm 0 'b)
-                                    (absm 0 'c) (absm 0 'i)))) 'i))
-  (unnormalize-gbar
-     (absm 9 (make-gbar :dmns 4
-                        :list (list (absm 0 'a) (absm 0 'b)
-                                    (absm 0 'c) (absm 0 'i)))) 'i)
-  (normalize-gbar
-   (unnormalize-gbar
-     (absm 9 (make-gbar :dmns 4
-                        :list (list (absm 0 'a) (absm 0 'b)
-                                    (absm 0 'c) (absm 0 'i)))) 'i))
-|#
-
-(DEFUN GBAR (dmns &rest rest)
-  (the gbar
-    (progn
-      (unless (= (+ dmns dmns) (length rest))
-	(error "In GBAR, the argument list has a wrong length."))
-      (make-gbar :dmns dmns
-		 :list (do ((mark rest (cddr mark))
-			    (rslt +empty-list+
-				  (cons (absm (car mark) (cadr mark))
-					rslt)))
-			   ((endp mark) (nreverse rslt))
-			   (declare (list mark rslt)))))))
-
-#|
-  (gbar 0)
-  (gbar 1)
-  (gbar 2 1 'a 2 'b)
-|#
-
-(DEFUN CLASSIFYING-SPACE-CMPR (cmpr)
-  (declare (type cmprf cmpr))
-  (flet ((rslt (gbar1 gbar2)
-	   (declare (type gbar gbar1 gbar2))
-	   (maplexico
-	    #'(lambda (absm1 absm2)
-		(declare (type absm absm1 absm2))
-		(a-cmpr3 cmpr absm1 absm2))
-	    (gbar-list gbar1) (gbar-list gbar2))))
-     (the cmprf #'rslt)))
-
-#|
-  (setf cmpr (classifying-space-cmpr 's-cmpr))
-  (funcall cmpr (gbar 2 0 'a 0 'a) (gbar 2 1 'a 0 'a))
-  (funcall cmpr (gbar 2 0 'a 0 'a) (gbar 2 0 'b 0 'a))
-  (funcall cmpr (gbar 2 0 'a 0 'a) (gbar 2 0 'a 0 'a))
-|#
-
-(DEFUN CLASSIFYING-SPACE-BASIS (basis)
-  (declare (type basis basis))
-  (when (eq basis :locally-effective)
-    (return-from classifying-space-basis :locally-effective))
-  (let ((crts-basis :locally-effective)  ;; to be redefined
-	(idnt (first (funcall basis 0))))
-    (declare
-      (type basis crts-basis)
-      (type gmsm idnt))
-    (labels ((rslt (dmns)
-	       (declare (fixnum dmns))
-	       (when (minusp dmns)
-		 (return-from rslt +empty-list+))
-	       (when (zerop dmns)
-		 (return-from rslt (list +null-gbar+)))
-	       (let ((basis-1 (funcall crts-basis (1- dmns))))
-		 (declare (list basis-1))
-		 (nreverse
-		  (mapcar
-		   #'(lambda (crpr)
-		       (declare (type crpr crpr))
-		       (with-crpr (absm1 absm2) crpr
-			 (make-gbar
-			  :dmns dmns
-			  :list (cons absm1
-				      (rest (unnormalize-gbar absm2 idnt))))))
-		   (member-if
-		    #'(lambda (dgop)
-			(declare (fixnum dgop))
-			(< dgop (mask (1- dmns))))
-		    (reverse basis-1)
-		    :key #'caadr))))))
-	    (setf crts-basis (crts-prdc-basis basis #'rslt))
-	    (the basis #'rslt))))
-
-#|
-  (cat-init)
-  (setf k (k-z2-1))
-  (setf b (classifying-space-basis (basis k)))
-  (dotimes (i 5) (print (funcall b i)))
-|#
-
-(DEFUN CLASSIFYING-SPACE-FACE (face grml-sintr)
-  (declare
-     (type face face)
-     (type sintr grml-sintr))
-  (flet ((rslt (indx dmns gbar)
-	   (declare
-	     (fixnum indx dmns)
-	     (type gbar gbar))
-	   (when (= indx dmns)
-	     (return-from rslt
-	       (normalize-gbar (cons (1- dmns) (rest (gbar-list gbar))))))
-	   (do ((mark (gbar-list gbar) (cdr mark))
-		(dmns2 (1- dmns) (1- dmns2))
-		(rslt +empty-list+
-		      (cons (a-face4 face indx dmns2 (car mark))
-			    rslt)))
-	       ((= dmns2 indx)
-		(if (zerop indx)
-		   (normalize-gbar (cons (1- dmns) (nreverse rslt)))
-		   (normalize-gbar
-		    (cons (1- dmns)
-			  (nreconc
-			    rslt
-			    (cons (a-grml4 grml-sintr (1- indx)
-					   (second mark)
-					   (a-face4 face indx indx (first mark)))
-				  (nthcdr 2 mark))))))))))
-     (the face #'rslt)))
-
-#|
-  (setf om (loop-space (moore 2 2)))
-  (setf face (classifying-space-face (face om) (sintr (grml om))))
-  (setf gbar (gbar 4 0 (loop3 3 'm2 1 4 'n3 1)
-                     0 (loop3 0 'n3 1)
-                     0 (loop3 0 'm2 1)
-                     0 +null-loop+))
-  (dotimes (i 5)
-    (print (funcall face i 4 gbar)))
-|#
-
-(DEFMETHOD CLASSIFYING-SPACE ((smgr simplicial-group))
-  (the simplicial-set
-    (simplicial-set :cmpr (classifying-space-cmpr (cmpr smgr))
-                    :basis (classifying-space-basis (basis smgr))
-                    :bsgn +null-gbar+
-                    :face (classifying-space-face (face smgr) (sintr (grml smgr)))
-                    :dfnt `(classifying-space ,smgr))))
-
-#|
-  (cat-init)
-  (setf c (classifying-space (k-z2-1)))
-  (dfnt c)
-  (first (basis c 4))
-  (? c 4 (first (basis c 4)))
-  (? c *)
-  (cprd c 4 ***)
-  (dotimes (i 5)
-    (print (face c i 4 (first (basis c 4)))))
-|#
-
-(DEFUN CLASSIFYING-SPACE-GRML-SINTR (idnt grml-sintr)
-  (declare
-    (type gmsm idnt)
-    (type sintr grml-sintr))
-  (flet ((rslt (dmns crpr)
-	   (declare
-	     (fixnum dmns)
-	     (type crpr crpr))
-	   (with-crpr (absm1 absm2) crpr
-	   (let ((absm-list-1 (rest (unnormalize-gbar absm1 idnt)))
-		 (absm-list-2 (rest (unnormalize-gbar absm2 idnt))))
-	     (declare (list absm-list-1 absm-list-2))
-	     (normalize-gbar
-	       (cons dmns
-		 (mapcar
-		   #'(lambda (absm1 absm2)
-		       (declare (type absm absm1 absm2))
-		       (decf dmns) ;; !!
-		       (a-grml4 grml-sintr dmns absm1 absm2))
-		   absm-list-1 absm-list-2)))))))
-    (the sintr #'rslt)))
-
-#|
-  (setf grml (classifying-space-grml-sintr '() (sintr (grml (k-z-1)))))
-  (funcall grml 3 (crpr 0 (gbar 3 0 '(1 2) 0 '(3) 0 '())
-                        0 (gbar 3 0 '(-1 -2) 0 '(-3) 0 '())))
-  (funcall grml 3 (crpr 0 (gbar 3 0 '(1 2) 0 '(3) 0 '())
-                        4 (gbar 2 0 '(-3) 0 '())))
-  (funcall grml 3 (crpr 0 (gbar 3 0 '(1 2) 0 '(3) 0 '())
-                        1 (gbar 2 0 '(-3) 0 '())))
-|#
-
-
-(DEFUN CLASSIFYING-SPACE-GRIN-SINTR (grin-sintr)
-  (declare (type sintr grin-sintr))
-  (flet ((rslt (dmns gbar)
-	   (declare
-	     (fixnum dmns)
-	     (type gbar gbar))
-	   (absm 0
-	     (make-gbar
-	       :dmns dmns
-	       :list (mapcar
-		       #'(lambda (absm)
-			   (declare (type absm absm))
-			   (a-grin4 grin-sintr dmns absm))
-		       (gbar-list gbar))))))
-    (the sintr #'rslt)))
-
-#|
-  (setf grin (classifying-space-grin-sintr (sintr (grin (k-z-1)))))
-  (funcall grin 3 (gbar 3 0 '(1 2) 1 '() 0 '()))
-|#
-
-(DEFMETHOD CLASSIFYING-SPACE ((smgr ab-simplicial-group))
-  (the ab-simplicial-group
-     (change-class 
-       (simplicial-group :cmpr (classifying-space-cmpr (cmpr smgr))
-		   :basis (classifying-space-basis (basis smgr))
-		   :bsgn +null-gbar+
-		   :face (classifying-space-face (face smgr) (sintr (grml smgr)))
-		   :grml-sintr (classifying-space-grml-sintr
-				 (bsgn smgr)
-				 (sintr (grml smgr)))
-		   :grin-sintr (classifying-space-grin-sintr
-				 (sintr (grin smgr)))
-		   :dfnt `(classifying-space ,smgr))
-       'ab-simplicial-group)))
-
-#|
-  (setf k-z-1 (k-z-1))
-  (setf k-z-2 (classifying-space k-z-1))
-  (setf k-z-3 (classifying-space k-z-2))
-  (homology k-z-3 0 10)
-  (setf k-z2-1 (k-z2-1))
-  (setf k-z2-2 (classifying-space k-z2-1))
-  (setf k-z2-3 (classifying-space k-z2-2))
-  (setf k-z2-4 (classifying-space k-z2-3))
-  (setf k-z2-5 (classifying-space k-z2-4))
-  (homology k-z2-5 0 7)
-|#
diff --git a/archive/Kenzo-2/Kenzo-2-Acl5/coalgebras.cl b/archive/Kenzo-2/Kenzo-2-Acl5/coalgebras.cl
deleted file mode 100644
index 13c8098..0000000
--- a/archive/Kenzo-2/Kenzo-2-Acl5/coalgebras.cl
+++ /dev/null
@@ -1,58 +0,0 @@
-;;;  COALGEBRAS  COALGEBRAS  COALGEBRAS  COALGEBRAS  COALGEBRAS  COALGEBRAS
-;;;  COALGEBRAS  COALGEBRAS  COALGEBRAS  COALGEBRAS  COALGEBRAS  COALGEBRAS
-;;;  COALGEBRAS  COALGEBRAS  COALGEBRAS  COALGEBRAS  COALGEBRAS  COALGEBRAS
-
-(IN-PACKAGE "CAT")
-
-(PROVIDE "coalgebras")
-
-(DEFMETHOD PRINT-OBJECT ((clgb coalgebra) stream)
- (the coalgebra
-   (progn
-      (format stream "[K~D Coalgebra]" (idnm clgb))
-      clgb)))
-
-(DEFUN COALGEBRA (&rest rest &key dfnt &allow-other-keys)
-  (declare (type list dfnt))
-  (already coalgebra dfnt)
-  (the coalgebra
-    (apply #'make-instance 'coalgebra rest)))
-
-(DEFMETHOD SHARED-INITIALIZE ((clgb coalgebra) slot-names &key cprd-intr cprd-strt)
-  (declare
-   (type (or (eql t) list) slot-names)
-   (type intr cprd-intr)
-   (type strt cprd-strt))
-  (call-next-method)
-  (when-slot cprd
-             (with-slots (cprd) clgb
-               (declare (type morphism cprd))
-               (when cprd-intr
-                 (unless cprd-strt
-                   (error "IN COALGEBRA, a CPRD-INTR is given, but not its CPRD-STRT."))
-                 (setf cprd (morphism :sorc clgb :trgt (tnsr-prdc clgb clgb) :degr 0
-                                      :intr cprd-intr :strt cprd-strt
-                                      :dfnt `(coalgebra-coproduct ,clgb))))))
-  clgb)
-
-(DEFUN CHANGE-CHCM-TO-CLGB (chcm &key cprd-intr cprd-strt dfnt)
-  (declare
-   (type chain-complex chcm)
-   (type intr cprd-intr)
-   (type strt cprd-strt)
-   (list dfnt))
-  (the coalgebra
-    (progn
-      (change-class chcm 'coalgebra)
-      (setf dfnt (list (dfnt chcm) 'then dfnt))
-      (let ((already (find dfnt *k-list* :key #'dfnt :test #'equal)))
-        (declare (type (or null coalgebra) already))
-        (when already
-          (return-from change-chcm-to-clgb already)))
-      (setf (slot-value chcm 'cprd) (morphism
-                                     :sorc chcm :trgt (tnsr-prdc chcm chcm)
-                                     :degr 0
-                                     :intr cprd-intr :strt cprd-strt
-                                     :dfnt dfnt))
-      chcm)))
-
diff --git a/archive/Kenzo-2/Kenzo-2-Acl5/cobar.cl b/archive/Kenzo-2/Kenzo-2-Acl5/cobar.cl
deleted file mode 100644
index 06e62f6..0000000
--- a/archive/Kenzo-2/Kenzo-2-Acl5/cobar.cl
+++ /dev/null
@@ -1,734 +0,0 @@
-;;;  COBAR  COBAR  COBAR  COBAR  COBAR  COBAR  COBAR  COBAR  COBAR
-;;;  COBAR  COBAR  COBAR  COBAR  COBAR  COBAR  COBAR  COBAR  COBAR
-;;;  COBAR  COBAR  COBAR  COBAR  COBAR  COBAR  COBAR  COBAR  COBAR
-
-(IN-PACKAGE "CAT")
-
-(PROVIDE "cobar")
-
-(DEFUN ALLP (&rest list)
-   (when (= 1 (length list))
-      (setf list (first list)))
-   (unless (evenp (length list))
-      (error "In ALLP, the length list should be even."))
-   (the allp
-      (let ((rslt (list :allp)))
-         (declare (list rslt))
-         (do ((mark list (cddr mark)))
-             ((endp mark))
-            (declare (list mark))
-            (push (cbgn (car mark) (cadr mark)) rslt))
-         (nreverse rslt))))
-
-#|
-  (allp )
-  (allp '(2 a 3 b))
-  (allp 2 'a 3 'b)
-  (allp 2 'a 3))  ;; error
-|#
-
-(DEFCONSTANT +NULL-ALLP+ (make-allp :list +empty-list+))
-
-(DEFMETHOD PRINT-KEYCONS ((car (eql :allp)) cdr stream)
-   (declare
-      (list cdr)
-      (stream stream))
-   (the allp
-      (progn
-         (format stream "<<AlLp")
-         (dolist (cbgn cdr)
-            (declare (type cbgn cbgn))
-            (with-cbgn (degr gnrt) cbgn
-               (format stream "[~D ~A]" degr gnrt)))
-         (format stream ">>")
-         (cons car cdr))))
-            
-(DEFUN COBAR-CMPR (cmpr)
-   (declare (type cmprf cmpr))
-   (flet ((rslt (allp1 allp2)
-             (declare (type allp allp1 allp2))
-             (the cmpr
-                (lexico
-                   (f-cmpr (length allp1) (length allp2))
-                   (maplexico
-                      #'(lambda (cbgn1 cbgn2)
-                           (lexico
-                              (f-cmpr (cdegr cbgn1) (cdegr cbgn2))
-                              (funcall cmpr (cgnrt cbgn1) (cgnrt cbgn2))))
-                      (allp-list allp1)
-                      (allp-list allp2))))))
-      (the cmprf #'rslt)))
-
-#|
-  (setf r (cobar-cmpr #'s-cmpr))
-  (funcall r (allp) (allp))
-  (funcall r (allp 3 'a) (allp))
-  (funcall r (allp 3 'a) (allp 2 'a 1 'b))
-  (funcall r (allp 3 'a) (allp 3 'b))
-  (funcall r (allp 3 'a) (allp 3 'a)))
-|#
-
-(DEFUN COBAR-BASIS-LENGTH (basis degr length)
-   (declare
-      (type basis basis)
-      (fixnum degr length))
-   (the list
-      (progn
-	(when (= 1 length)
-	      (return-from cobar-basis-length
-			   (mapcar
-			    #'(lambda (item)
-				(declare (type gnrt item))
-				(list (cbgn degr item)))
-			    (funcall basis (1+ degr)))))                                         
-	(mapcan
-	 #'(lambda (degr1)
-	     (declare (fixnum degr1))
-	     (let ((list1 (funcall basis (1+ degr1)))
-		   (list2 (cobar-basis-length
-			    basis (- degr degr1) (1- length))))
-	       (declare (list list1 lis2))
-	       (mapcan
-		#'(lambda (item1)
-		    (declare (type gnrt item1))
-		    (mapcar
-		     #'(lambda (item2)
-			 (declare (type iallp item2))
-			 (cons (cbgn degr1 item1) item2))
-		     list2))
-		list1)))
-	 (>a-b< 0 degr)))))
-
-#|
-  (setf basis #'(lambda (degr)
-                   (list degr)))
-  (cobar-basis-length basis 1 1)
-  (cobar-basis-length basis 2 1)
-  (cobar-basis-length basis 2 2)
-  (cobar-basis-length basis 3 1)
-  (cobar-basis-length basis 3 2)
-  (cobar-basis-length basis 3 3)
-|#
-
-(DEFUN COBAR-BASIS (basis)
-   (declare (type basis basis))
-   (the basis
-      (progn
-	(when (eq :locally-effective basis)
-	  (return-from cobar-basis :locally-effective))
-	(flet ((rslt (degr)
-		     (declare (fixnum degr))
-		     (cond ((minusp degr) +empty-list+)
-			   ((zerop degr) (list +null-allp+))
-			   (t
-			    (mapcan
-			     #'(lambda (length)
-				 (declare (fixnum length))
-				 (mapcar
-				  #'(lambda (iallp)
-                                      (declare (type iallp iallp))
-                                      (make-allp :list iallp))
-				  (cobar-basis-length basis degr length)))
-			     (>a-b> 0 degr))))))
-	      #'rslt))))
-   
-#| The following version of the COBAR-BASIS function is
-   not correctly compiled with ACL-Unix, probably
-   because the too complicated (but natural and correct)
-   structure of closures. This version works on ACL-PC.
-(DEFUN COBAR-BASIS (basis)
-   (declare
-      (type basis basis))
-   ;; if the coalgebra is effective, it is assumed simply-connected :
-   ;;   (length (funcall basis 0))  ==>  1
-   ;;   (length (funcall basis 1))  ==>  0
-   (the basis
-      (progn
-         (when (eq :locally-effective basis)
-            (return-from cobar-basis :locally-effecive))
-         (labels ((rslt (degr length)
-                     (declare (fixnum degr length))
-                     (when (= 1 length)
-                        (return-from rslt
-                           (mapcar
-                              #'(lambda (item)
-                                   (declare (type gnrt item))
-                                   (list (cbgn degr item)))
-                              (funcall basis (1+ degr)))))                                         
-                     (mapcan
-                        #'(lambda (degr1)
-                             (declare (fixnum degr1))
-                             (let ((list1 (funcall basis (1+ degr1)))
-                                   (list2 (rslt (- degr degr1) (1- length))))
-                                (declare (list list1 lis2))
-                                (mapcan
-                                   #'(lambda (item1)
-                                        (declare (type gnrt item1))
-                                        (mapcar
-                                           #'(lambda (item2)
-                                                (declare (type iallp item2))
-                                                (cons (cbgn degr1 item1) item2))
-                                           list2))
-                                   list1)))
-                        (>a-b< 0 degr))))
-            #'(lambda (degr)
-                 (declare (fixnum degr))
-                 (if (zerop degr)
-                    (list (make-allp :list +empty-list+))
-                    (mapcan
-                       #'(lambda (length)
-                            (declare (fixnum length))
-                            (mapcar
-                               #'(lambda (iallp)
-                                    (declare (type iallp iallp))
-                                    (make-allp :list iallp))
-                               (rslt degr length)))
-                       (>a-b> 0 degr))))))))
-|#
-
-#|
-  (setf basis #'(lambda (degr)
-                   (list degr)))
-  (setf r (cobar-basis basis))
-  (funcall r 0)
-  (funcall r 1)
-  (funcall r 2)
-  (dotimes (i 7)
-     (print (funcall r i)))
-  (cobar-basis :locally-effective)
-|#
-
-(DEFUN COBAR-INTR-VRTC-DFFR (dffr)
-   (declare (type morphism dffr))
-   (labels ((rslt (degr iallp)
-               ;; the argument iallp is an internal algebraic loop,
-               ;;     without the keyword :allp
-               ;; rslt returns an internal combination
-               ;;     without the keyword :cmbn, without degree
-               (declare
-                  (fixnum degr)
-                  (type iallp iallp))
-               (the icmbn
-                  (progn
-                     (unless iallp
-                        (return-from rslt +empty-list+))
-                     (let ((cbgn1 (first iallp))
-                           (rest (rest iallp)))
-                        (declare
-                           (type cbgn cbgn1)
-                           (type iallp rest))
-                        (with-cbgn (degr1 gnrt1) cbgn1
-                           (let ((d-gnrt1 (cmbn-list (gnrt-? dffr (1+ degr1) gnrt1)))
-                                 (d-rest (rslt (- degr degr1) rest))
-                                 (degr1-1 (1- degr1))
-                                 (first-sign (-1-expt-n-1 (length rest)))
-                                 (rest-sign (-1-expt-n degr1)))
-                              (declare
-                                 (type icmbn d-gnrt1 d-rest)
-                                 (fixnum degr1-1 rest-sign))
-                              (nconc
-                                 (mapcar
-                                    #'(lambda (term)
-                                         (with-term (cffc gnrt) term
-                                            (term (* first-sign cffc)
-                                               (cons (cbgn degr1-1 gnrt) rest))))
-                                    d-gnrt1)
-                                 (mapcar
-                                    #'(lambda (term)
-                                         (with-term (cffc gnrt) term
-                                            (term (* rest-sign cffc)
-                                               (cons cbgn1 gnrt))))
-                                    d-rest)))))))))
-      (the intr
-         #'(lambda (degr allp)
-              (make-cmbn
-                 :degr (1- degr)
-                 :list (mapcar
-                          #'(lambda (term)
-                               (with-term (cffc iallp) term
-                                  (term cffc (make-allp :list iallp))))
-                          (rslt degr (allp-list allp))))))))
-         
-
-#|
-  (require "special-smsts"
-            #-ACLPC "special-smsts"
-            #+ACLPC "special-smsts.fsl")
-  (setf d (soft-delta-infinity))
-  (setf r (cobar-intr-vrtc-dffr (dffr d)))
-  (funcall r 0 (allp))
-  (funcall r 3 (allp 3 (d 15)))
-  (funcall r 5 (allp 3 (d (mask 5)) 2 (d (mask 4))))
-  (funcall r 5 (allp 2 (d (mask 4)) 3 (d (mask 5)))))
-|#
-
-(DEFMETHOD VRTC-COBAR ((chcm chain-complex))
-   (the chain-complex
-      (with-slots (cmpr basis dffr) chcm
-         (declare
-            (type cmprf cmpr)
-            (type basis basis)
-            (type morphism dffr))
-         (chain-complex
-            :cmpr (cobar-cmpr cmpr)
-            :basis (cobar-basis basis)
-            :bsgn +null-allp+
-            :dffr-intr (cobar-intr-vrtc-dffr dffr)
-            :dffr-strt :gnrt
-            :dfnt `(vrtc-cobar ,chcm)))))
-
-#|
-  (cat-init)
-  (setf v (vrtc-cobar (soft-delta-infinity)))
-  (defun random-allp (length)
-     (let ((rslt nil))
-        (dotimes (i length)
-           (let* ((gmsm (random (mask 9)))
-                  (dmns (1- (logcount gmsm))))
-              (when (plusp dmns)
-                 (push (cbgn (1- dmns) (d gmsm)) rslt))))
-        (make-allp :list rslt)))
-  (dotimes (i 10) (print (random-allp 5)))
-  (dotimes (i 10)
-     (let ((allp (random-allp 3)))
-        (print allp)
-        (print (? v (apply #'+ (mapcar #'car (allp-list allp))) allp))
-        (print (? v (? v (apply #'+ (mapcar #'car (allp-list allp))) allp)))))
-|#
-
-(DEFUN COBAR-INTR-HRZN-DFFR (cprd)
-   (declare (type morphism cprd))
-   (labels ((rslt (degr iallp)
-               (declare
-                  (fixnum degr)
-                  (type iallp iallp))
-               (the icmbn
-                  (progn
-                     (unless iallp
-                        (return-from rslt +empty-list+))
-                     (let ((cbgn1 (first iallp))
-                           (rest (rest iallp)))
-                        (declare
-                           (type cbgn cbgn1)
-                           (type iallp rest))
-                        (with-cbgn (degr1 gnrt1) cbgn1
-                           (let ((cprd-gnrt1 (cmbn-list (gnrt-? cprd (1+ degr1) gnrt1)))
-                                 (cprd-rest (rslt (- degr degr1) rest))
-                                 (sign (-1-expt-n-1 (length rest))))
-                              (declare
-                                 (type icmbn cprd-gnrt1 cprd-rest)
-                                 (fixnum sign))
-                              (setf cprd-gnrt1 (rest (butlast cprd-gnrt1)))  ;;; because \bar{A}
-                              (nconc
-                                 (mapcar
-                                    #'(lambda (term1)
-                                         (declare (type term temr1))
-                                         (with-term (nil tnpr) term1  ;;; cffc is in fact 1
-                                            (with-tnpr (degr1 gnrt1 degr2 gnrt2) tnpr
-                                               (term sign              ;;; (* cffc sign)
-                                                  (cons (cbgn (1- degr1) gnrt1)
-                                                     (cons (cbgn (1- degr2) gnrt2)
-                                                        rest))))))
-                                    cprd-gnrt1)
-                                 (mapcar
-                                    #'(lambda (term2)
-                                         (declare (type term term2))
-                                         (with-term (cffc allp2) term2
-                                            (term cffc
-                                               (cons cbgn1 allp2))))
-                                    cprd-rest)))))))))
-      (the intr
-         #'(lambda (degr allp)
-              (declare
-                 (fixnum degr)
-                 (type allp allp))
-              (the cmbn
-                 (make-cmbn :degr (1- degr)
-                    :list (mapcar #'(lambda (term)
-                                       (declare (type term term))
-                                       (with-term (cffc iallp) term
-                                          (term cffc (make-allp :list iallp))))
-                             (rslt degr (allp-list allp)))))))))
-
-#|
-  (setf d (soft-delta-infinity))
-  (setf r (cobar-intr-hrzn-dffr (cprd d)))
-  (funcall r 0 (allp))
-  (funcall r 3 (allp 3 (d (mask 5))))
-  (funcall r 5 (allp 3 (d (mask 5)) 2 (d (mask 4))))
-  (funcall r 5 (allp 2 (d (mask 4)) 3 (d (mask 5))))
-|#
-
-(DEFUN COBAR-HRZN-DFFR (clgb)
-   (declare (type coalgebra clgb))
-   (the morphism
-      (with-slots (cprd) clgb
-         (declare (type morphism cprd))
-         (morphism
-            :sorc (vrtc-cobar clgb) :trgt (vrtc-cobar clgb) :degr -1
-            :intr (cobar-intr-hrzn-dffr cprd) :strt :gnrt
-            :dfnt `(cobar-hrzn-dffr ,clgb)))))
-
-#|
-  (cat-init)
-  (setf h (cobar-hrzn-dffr (soft-delta-infinity)))
-  (defun random-allp (length)
-     (let ((rslt nil))
-        (dotimes (i length)
-           (let* ((gmsm (random (mask 9)))
-                  (dmns (1- (logcount gmsm))))
-              (when (plusp dmns)
-                 (push (cbgn (1- dmns) (d gmsm)) rslt))))
-        (make-allp :list rslt)))
-  (dotimes (i 10) (print (random-allp 5)))
-  (setf allp (random-allp 4))
-  (? h (apply #'+ (mapcar #'car (allp-list allp))) allp)
-  (? h (? h (apply #'+ (mapcar #'car (allp-list allp))) allp))
-  (dotimes (i 10)
-     (let ((allp (random-allp 3)))
-        (print allp)
-        (print (? h (apply #'+ (mapcar #'car (allp-list allp))) allp))
-        (print (? h (? h (apply #'+ (mapcar #'car (allp-list allp))) allp)))))
-|#
-
-(DEFUN COBAR-INTR-DFFR (vrtc-dffr hrzn-dffr)
-   (declare (type morphism vrtc-dffr hrzn-dffr))
-   (flet ((rslt (degr allp)
-             (declare
-                (fixnum degr)
-                (type allp allp))
-             (make-cmbn :degr (1- degr)
-                :list (append       ;;; and not nconc, otherwise a terrible bug, when the
-                                    ;;;   first result is stored in memory...
-                         (cmbn-list (gnrt-? vrtc-dffr degr allp))
-                         (cmbn-list (gnrt-? hrzn-dffr degr allp))))))
-      (the intr #'rslt)))
-
-(DEFMETHOD COBAR ((coalgebra coalgebra))
-   (let ((vrtc-cobar (vrtc-cobar coalgebra))
-         (cobar-hrzn-dffr (cobar-hrzn-dffr coalgebra)))
-      (declare (type chain-complex vrtc-cobar hrzn-cobar))
-      (the chain-complex
-	 (let ((rslt (chain-complex
-		      :cmpr (cmpr vrtc-cobar)
-		      :basis (basis vrtc-cobar)
-		      :bsgn +null-allp+
-		      :dffr-intr (cobar-intr-dffr (dffr vrtc-cobar) cobar-hrzn-dffr)
-		      :dffr-strt :gnrt
-		      :dfnt `(add ,vrtc-cobar ,cobar-hrzn-dffr))))
-	   (declare (type chain-complex rslt))
-	   (setf (slot-value rslt 'grmd) (grmd vrtc-cobar))
-	   rslt))))
-
-#|
-  (cat-init)
-  (setf c (cobar (deltab)))   
-  (defun random-allp (length)
-     (let ((rslt nil))
-        (dotimes (i length)
-           (let* ((gmsm (random (mask 9)))
-                  (dmns (1- (logcount gmsm))))
-              (when (plusp dmns)
-                 (push (cbgn (1- dmns) gmsm) rslt))))
-        (make-allp :list rslt)))
-  (dotimes (i 10) (print (random-allp 5)))
-  (setf allp (random-allp 4))
-  (? c (apply #'+ (mapcar #'car (allp-list allp))) allp)
-  (? c (? c (apply #'+ (mapcar #'car (allp-list allp))) allp))
-  (dotimes (i 10)
-     (let ((allp (random-allp 3)))
-        (print allp)
-        (print (? c (apply #'+ (mapcar #'car (allp-list allp))) allp))
-        (print (? c (? c (apply #'+ (mapcar #'car (allp-list allp))) allp)))))
-|#
-
-(DEFUN CMBN-ALLP-CMBN-TNPR (cmbn allp-cmbn)
-   (declare (type cmbn cmbn allp-cmbn))
-   (the cmbn
-      (with-cmbn (degr1 list1) cmbn
-         (decf degr1)     ;; because allp organization
-      (with-cmbn (degrr listr) allp-cmbn
-         (make-cmbn
-            :degr (+ degr1 degrr)
-            :list
-            (mapcan
-               #'(lambda (term1)
-                    (declare (type term term1))
-                    (with-term (cffc1 gnrt1) term1
-                       (let ((cbgn1 (cbgn degr1 gnrt1)))
-                          (declare (type cbgn cbgn1))
-                          (mapcar
-                             #'(lambda (termr)
-                                  (declare (type term termr))
-                                  (with-term (cffcr allpr) termr
-                                     (term (* cffc1 cffcr)
-                                        (make-allp
-                                           :list (cons cbgn1 (allp-list allpr))))))
-                             listr))))
-               list1))))))
-
-(DEFUN NCMBN-COBAR (cmbn-list)
-   (declare (list cmbn-list))
-   (the cmbn
-      (progn
-         (unless cmbn-list
-            (return-from ncmbn-cobar (cmbn 0 1 +null-allp+)))
-         (cmbn-allp-cmbn-tnpr
-            (first cmbn-list)
-            (ncmbn-cobar (rest cmbn-list))))))
-#|
-  (ncmbn-cobar nil)
-  (ncmbn-cobar (list (cmbn 3 2 'a 3 'b)))
-  (ncmbn-cobar (list (cmbn 1 2 'a 3 'b) (cmbn 2 4 'c 5 'd)))
-  (ncmbn-cobar (list (cmbn 1 2 'a 3 'b) (cmbn 1 4 'c 5 'd) (cmbn 1 6 'e 7 'f)))
-|#
-
-(DEFUN MRPH-VRTC-COBAR-INTR (mrph)
-   (declare (type morphism mrph))
-   (flet ((rslt (degr allp)
-             (declare
-                (ignore degr)
-                (type allp allp))
-             (the cmbn
-                (ncmbn-cobar
-                   (mapcar #'(lambda (cbgn)
-                                (declare (type cbgn cbgn))
-                                (with-cbgn (degr gnrt) cbgn
-                                   (gnrt-? mrph (1+ degr) gnrt)))
-                      (allp-list allp))))))
-      (the intr #'rslt)))
-
-#|
-  (setf cc (chain-complex :cmpr #'f-cmpr :dffr-strt :cmbn))
-  (setf m (morphism :sorc cc :trgt cc :degr 0 :intr
-            #'(lambda (degr gnrt) (cmbn degr 2 gnrt 3 (1+ gnrt)))
-            :strt :gnrt :dfnt '(test)))
-  (setf r (mrph-vrtc-cobar-intr m))
-  (funcall r 4 (allp 2 3 2 4))
-|#
-
-(DEFMETHOD VRTC-COBAR ((mrph morphism))
-   (the morphism
-      (if (eq (first (dfnt mrph)) 'idnt-mrph)
-         (idnt-mrph (vrtc-cobar (sorc mrph)))
-         (morphism
-            :sorc (vrtc-cobar (sorc mrph))
-            :trgt (vrtc-cobar (trgt mrph))
-            :degr 0
-            :intr (mrph-vrtc-cobar-intr mrph)
-            :strt :gnrt
-            :dfnt `(vrtc-cobar ,mrph)))))
-
-#|
-  (cat-init)
-  (setf f (aw (soft-delta-infinity) (soft-delta-infinity)))
-  (setf cf (vrtc-cobar f))
-  (? cf 2 (allp 1 (crpr 0 (d 7) 0 (d 7)) 1 (crpr 0 (d 56) 0 (d 56))))
-|#
-
-(DEFUN HMTP-VRTC-COBAR-INTR (h gf)
-   (declare (type morphism h gf))
-   (flet ((rslt (degr allp)
-             (declare
-                (fixnum degr)
-                (type allp allp))
-             (let* ((cbgn-list (reverse (allp-list allp)))
-                    (rslt (list nil))
-                    (sign (oddp (apply #'+ (mapcar #'car cbgn-list))))  ;; nil = -1 ;; t = +1
-                    (gfgf-tail (term-cmbn 0 1 +null-allp+)))
-                (declare
-                   (list cbgn-list rslt)
-                   (fixnum sign)
-                   (type cmbn gfgf-tail))
-                (unless cbgn-list
-                   (return-from rslt (zero-cmbn 1)))
-                (loop
-                   (let ((cbgn (car cbgn-list)))
-                      (declare (type cbgn cbgn))
-                      (with-cbgn (degr gnrt) cbgn
-                         (when (evenp degr)
-                            (setf sign (not sign)))
-                         (incf degr)
-                         (let ((h-gnrt (gnrt-? h degr gnrt)))
-                            (declare (type cmbn h-gnrt))
-                            (let ((hgfgf (cmbn-list (cmbn-allp-cmbn-tnpr h-gnrt gfgf-tail))))
-                               (declare (type cmbn hgfgf))
-                               (when sign
-                                  (mapc #'(lambda (term)
-                                             (declare (type term term))
-                                             (setf (cffc term) (- (cffc term))))
-                                     hgfgf))
-                               (setf cbgn-list (rest cbgn-list))
-                               (let ((head (reverse cbgn-list)))
-                                  (declare (list head))
-                                  (mapc #'(lambda (term)
-                                             (setf (allp-list (gnrt term))
-                                                   (append head (allp-list (gnrt term)))))
-                                     hgfgf))
-                               (nconc rslt hgfgf)))
-                         (unless cbgn-list (return))
-                         (setf gfgf-tail
-                               (cmbn-allp-cmbn-tnpr
-                                  (gnrt-? gf degr gnrt) gfgf-tail)))))
-                (make-cmbn
-                   :degr (1+ degr)
-                   :list (rest rslt)))))
-      (the intr #'rslt)))
-
-#|
-  (require "special-smsts")
-  (require "eilenberg-zilber")
-  (cat-init)
-  (setf ez (ez (delta-infinity) (delta-infinity)))
-  (setf h (h ez) gf (cmps (g ez) (f ez)))
-  (setf r (hmtp-vrtc-cobar-intr h gf))
-  (funcall r 3 (allp 1 (crpr 0 7 0 7) 1 (crpr 0 14 0 14) 1 (crpr 0 14 0 14)))
-|#
-
-(DEFUN HMTP-VRTC-COBAR (h gf)
-   (declare (type morphism h gf))
-   (unless (and (= +1 (degr h))
-                (= +0 (degr gf)))
-      (error "In HMTP-VRTC-COBAR, the morphism degrees are not the right ones."))
-   (unless (and (eq (sorc h) (trgt h))
-                (eq (trgt h) (sorc gf))
-                (eq (sorc gf) (trgt gf)))
-      (error "In HMTP-VRTC-COBAR, fg-h sources and targets are not the same."))
-   (the morphism
-      (if (eq (first (dfnt h)) 'zero-mrph)
-         (zero-mrph (vrtc-cobar (sorc h)))
-         (morphism
-            :sorc (vrtc-cobar (sorc h)) :trgt (vrtc-cobar (sorc h)) :degr +1
-            :intr (hmtp-vrtc-cobar-intr h gf)
-            :strt :gnrt
-            :dfnt `(hmtp-vrtc-cobar ,h ,gf)))))
-
-(DEFMETHOD VRTC-COBAR ((rdct reduction))
-   (the reduction
-      (if (eq (first (dfnt rdct)) 'trivial-rdct)
-         (trivial-rdct (vrtc-cobar (bcc rdct)))
-         (with-slots (f g h) rdct
-            (reduction
-               :f (vrtc-cobar f)
-               :g (vrtc-cobar g)
-               :h (hmtp-vrtc-cobar h (cmps g f))
-               :dfnt `(vrtc-cobar ,rdct))))))
-
-#|
-  (cat-init)
-  (setf tcc (chain-complex
-               :cmpr #'s-cmpr
-               :basis #'(lambda (degr) '(a b c d))
-               :bsgn 'd
-               :dffr-intr #'(lambda (degr gnrt)
-                               (ecase gnrt
-                                  (a (cmbn (1- degr) 1 'b 1 'd))
-                                  ((b d) (cmbn (1- degr)))
-                                  (c (cmbn (1- degr) 1 'd))))
-               :dffr-strt :gnrt
-               :dfnt '(tcc)))
-  (setf bcc (chain-complex
-               :cmpr #'s-cmpr
-               :basis #'(lambda (degr) '(c d))
-               :bsgn 'd
-               :dffr-intr #'(lambda (degr gnrt)
-                               (ecase gnrt
-                                  (d (cmbn (1- degr)))
-                                  (c (cmbn (1- degr) 1 'd))))
-               :dffr-strt :gnrt
-               :dfnt '(bcc)))
-  (setf f (morphism :sorc tcc :trgt bcc :degr 0
-             :intr #'(lambda (degr gnrt)
-                        (ecase gnrt
-                           (a (cmbn degr 1 'c 1 'd))
-                           (b (cmbn degr))
-                           ((c d) (cmbn degr 1 gnrt))))
-             :strt :gnrt :dfnt '(f)))
-  (setf g (morphism :sorc bcc :trgt tcc :degr 0
-             :intr #'identity :strt :cmbn :dfnt '(g)))
-  (setf h (morphism :sorc tcc :trgt tcc :degr +1
-             :intr #'(lambda (degr gnrt)
-                        (ecase gnrt
-                           ((a b) (cmbn (1+ degr) 1 'a -1 'b -1 'c -1 'd))
-                           ((c d) (cmbn (1+ degr)))))
-             :strt :gnrt :dfnt '(h)))
-  (setf rdct (reduction :f f :g g :h h :dfnt '(rdct)))
-  (tcc rdct 3 'a)
-  (g rdct (f rdct 3 'a))
-  (h rdct 3 'a)
-  (setf cobar (vrtc-cobar rdct))
-  (pre-check-rdct cobar)
-  (defun aleat-tc ()
-     (do ((tdegr 0 (+ tdegr degr))
-          (degr (1+ (random 4)) (1+ (random 4)))
-          (gnrt (intern (coerce (vector (+ 65 (random 4))) 'string))
-                (intern (coerce (vector (+ 65 (random 4))) 'string)))
-          (rslt nil (cons (cbgn degr gnrt) rslt)))
-         ((> tdegr 10) (setf *tc* (cmbn tdegr 1 (make-allp :list rslt))))))
-  (aleat-tc)
-  (defun aleat-bc ()
-     (do ((tdegr 0 (+ tdegr degr))
-          (degr (1+ (random 4)) (1+ (random 4)))
-          (gnrt (intern (coerce (vector (+ 67 (random 2))) 'string))
-                (intern (coerce (vector (+ 67 (random 2))) 'string)))
-          (rslt nil (cons (cbgn degr gnrt) rslt)))
-         ((> tdegr 10) (setf *bc* (cmbn tdegr 1 (make-allp :list rslt))))))
-  (aleat-bc)
-  (defun c ()
-     (aleat-tc)
-     (aleat-bc)
-     (check-rdct))
-  (loop (c))  ;; degrees >= 15 is possible => error.
-|#
-
-(DEFMETHOD VRTC-COBAR ((eqvl equivalence))
-  (the equivalence
-    (if (eq (first (dfnt eqvl)) 'trivial-eqvl)
-        (trivial-eqvl (vrtc-cobar (lbcc eqvl)))
-      (with-slots (lrdct rrdct) eqvl
-        (equivalence 
-         :lrdct (vrtc-cobar lrdct)
-         :rrdct (vrtc-cobar rrdct)
-         :dfnt `(vrtc-cobar ,eqvl))))))
-
-(DEFMETHOD COBAR ((rdct reduction))
-   (unless (typep (tcc rdct) 'coalgebra)
-      (error "In (COBAR rdct), the TCC should be a coalgebra."))
-   (the reduction
-      (if (eq (first (dfnt rdct)) 'trivial-rdct)
-         (trivial-rdct (cobar (tcc rdct)))
-        (add (vrtc-cobar rdct) (cobar-hrzn-dffr (tcc rdct))))))
-
-#|
-()
-(cat-init)
-(setf k (k-z 2))
-(setf efhm (efhm k))
-(slot-boundp k 'efhm)
-(setf f (cmps (rf efhm) (lg efhm)))
-(setf g (cmps (lf efhm) (rg efhm)))
-(setf h (cmps (lf efhm) (cmps (rh efhm) (lg efhm))))
-(setf rho (reduction :f f :g g :h h :dfnt '(w-b (k-z 2))))
-(setf bg (first (basis (bcc rho) 4)))
-(g rho 4 bg)
-(setf *tc* (make-cmbn :degr 4 :list (rest (cmbn-list *))))
-(setf *bc* (cmbn 4 bg))
-(pre-check-rdct rho)
-
-|#
-
-
-(DEFMETHOD COBAR ((eqvl equivalence))
-   (unless (typep (lbcc eqvl) 'coalgebra)
-      (error "In (COBAR eqvl), the LBCC should be a coalgebra."))
-   (the equivalence
-      (if (eq (first (dfnt eqvl)) 'trivial-eqvl)
-         (trivial-eqvl (cobar (lbcc eqvl)))
-         (add (vrtc-cobar eqvl) (cobar-hrzn-dffr (lbcc eqvl))))))
-
-#|
-  (cat-init)
-  (setf h (left-eqvl (sphere 3)))
-  (setf c (cobar h))
-  (inspect c)
-|#
\ No newline at end of file
diff --git a/archive/Kenzo-2/Kenzo-2-Acl5/combinations.cl b/archive/Kenzo-2/Kenzo-2-Acl5/combinations.cl
deleted file mode 100644
index 2f721e1..0000000
--- a/archive/Kenzo-2/Kenzo-2-Acl5/combinations.cl
+++ /dev/null
@@ -1,687 +0,0 @@
-;;;  COMBINATIONS  COMBINATIONS  COMBINATIONS  COMBINATIONS  COMBINATIONS
-;;;  COMBINATIONS  COMBINATIONS  COMBINATIONS  COMBINATIONS  COMBINATIONS
-;;;  COMBINATIONS  COMBINATIONS  COMBINATIONS  COMBINATIONS  COMBINATIONS
-
-(IN-PACKAGE "CAT")
-
-(provide "combinations")
-
-;;;;
-;;;;  COMPARISONS.
-;;;;
-
-
-(DEFUN MAPLEXICO (cmpr list1 list2)
-   (declare
-      (type cmprf cmpr)
-      (list list1 list2))
-   (the boolean
-      (do ((mark1 list1 (cdr mark1))
-           (mark2 list2 (cdr mark2)))
-          (nil)
-         (declare (list mark1 mark2))
-         (unless mark1
-            (return-from maplexico
-               (if mark2 :less :equal)))
-         (unless mark2
-            (return-from maplexico :greater))
-         (case (funcall cmpr (car mark1) (car mark2))
-            (:less (return-from maplexico :less))
-            (:greater (return-from maplexico :greater))))))
-
-#|
-  (maplexico #'f-cmpr '(1 2 3) '(1 3))
-  (maplexico #'f-cmpr '(1 2 3) '(1 1))
-  (maplexico #'f-cmpr '(1 1) '(1 1 0))
-  (maplexico #'f-cmpr '(1 1 0) '(1 1))
-  (maplexico #'f-cmpr '(1 1) '(1 1))
-  (maplexico #'f-cmpr nil nil)
-|#
-
-(DEFUN S-CMPR (symbol1 symbol2)
-   (declare (symbol symbol1 symbol2))
-   (the cmpr
-      (if (#+aclpc acl:whole-string<
-           #-aclpc string< symbol1 symbol2)
-         :less
-         (if (#+aclpc acl:whole-string=
-              #-aclpc string= symbol1 symbol2)
-            :equal
-            :greater))))
-
-(DEFUN F-CMPR (n1 n2)
-   (declare (fixnum n1 n2))
-   (the cmpr
-      (if (< n1 n2)
-         :less
-         (if (= n1 n2)
-            :equal
-            :greater))))
-
-(DEFUN L-CMPR (list1 list2)
-   (declare (list list1 list2))
-   (unless list1
-      (return-from l-cmpr (if list2 :less :equal)))
-   (unless list2
-      (return-from l-cmpr :greater))
-   (if (symbolp (first list1))
-      (if (symbolp (first list2))
-         (lexico
-            (s-cmpr (first list1) (first list2))
-            (l-cmpr (rest list1) (rest list2)))
-         :greater)
-      (if (symbolp (first list2))
-         :less
-         (lexico
-            (f-cmpr (first list1) (first list2))
-            (l-cmpr (rest list1) (rest list2))))))
-
-#|
-  (s-cmpr 'a 'b)
-  (s-cmpr 'b 'b)
-  (s-cmpr 'c 'b)
-  (f-cmpr 1 2)
-  (f-cmpr 2 2)
-  (f-cmpr 3 2)
-  (l-cmpr nil nil)
-  (l-cmpr nil '(1))
-  (l-cmpr '(1) nil)
-  (l-cmpr '(a) '(a))
-  (l-cmpr '(a) '(1))
-  (l-cmpr '(1) '(a))
-  (l-cmpr '(1) '(1))
-  (l-cmpr '(1 a) '(1 1))
-  (l-cmpr '(1 a) '(1 a b)))
-|# 
-
-
-;;;;
-;;;;  COMBINATIONS
-;;;;
-
-(DEFUN CMBN (degr &rest rest)
-   (declare (fixnum degr))
-   (the cmbn
-      (let ((rslt (list degr :cmbn)))
-	(do ((mark rest (cddr mark)))
-	    ((endp mark) (nreverse rslt))
-	   (declare (list mark))
-	   (push (term (car mark) (cadr mark)) rslt)))))
-
-#|
-  (cmbn 2)
-  (cmbn 2 2 'a)
-  (cmbn 2 'a)
-  (cmbn 2 2 'a -3 'b))
-  (term-cmbn 3 -5 'a)
-|#
-
-#+(or (and allegro unix)
-      (and :mswindows :allegro-v5.0))
-      (and :mswindows :allegro-v5.0.1)
-  (setf *print-pretty* nil)
-
-#+(and allegro unix)
-  (eval-when (:compile-toplevel :load-toplevel :execute)
-     (setf excl:*enable-package-locked-errors* nil))
-
-(DEFMETHOD PRINT-OBJECT :around ((cons cons) stream)
-   (declare (stream stream))
-   (when (keywordp (car cons))
-      (when (print-keycons (car cons) (cdr cons) stream)
-         (return-from print-object cons)))
-   (call-next-method))
-
-#+(and allegro unix)
-  (eval-when (:compile-toplevel :load-toplevel :execute)
-     (setf excl:*enable-package-locked-errors* t))
-
-(DEFMETHOD PRINT-KEYCONS (key cdr stream)
-   (declare (ignore key cdr stream))
-   nil)
-
-(DEFMETHOD PRINT-KEYCONS ((key (eql :cmbn)) cdr stream)
-   (declare
-      (list cdr)
-      (stream stream))
-   (the (eql t)
-      (let ((degr (first cdr))
-            (list (rest cdr)))
-         (declare
-            (fixnum degr)
-            (list list))
-         (format stream "~%~70@{-~}{CMBN ~D}" degr)
-         (do ((mark list (cdr mark))
-              (nth 0 (1+ nth)))
-             ((endp mark))
-            (declare
-               (list mark)
-               (fixnum nth))
-            (when (and *print-length* (= nth *print-length*))
-               (format stream "~%... ...")
-               (return))
-            (format stream "~%<~D * ~A>" (-cffc mark) (-gnrt mark)))
-         (format stream "~%~78@{-~}~%" t)
-         t)))
-
-#|
-  (list 1 2)
-  (list :cmbn 2 (cons 1 'a))
-|#
-
-(DEFUN CHECK-CMBN (chcm cmbn)
-  (declare
-    (type chain-complex chcm)
-    (type cmbn cmbn))
-  (the boolean
-    (do ((cmpr (cmpr chcm))
-	 (mark2 (cmbn-list cmbn) mark1)
-	 (mark1 (rest (cmbn-list cmbn)) (cdr mark1)))
-	((endp mark1) t)
-	(declare
-	  (type cmprf cmpr)
-	  (list mark1 mark2))
-      (unless (eq :less (funcall cmpr (-gnrt mark2) (-gnrt mark1)))
-	(error "In CHECK-CMBN, bad order; the generator:~@
-                ~A~@
-                is not less than the generator:~@
-                ~A."
-	       (-gnrt mark2) (-gnrt mark1))))))
-
-(DEFUN ZERO-CMBN (degr)
-   (declare (fixnum degr))
-   (the cmbn
-      (make-cmbn
-       :degr degr
-       :list +empty-list+)))
-
-#|
-  (zero-cmbn 3))
-|#  
-
-(DEFUN ZERO-DFFR-INTR (cmbn)
-   (declare (type cmbn cmbn))
-   (the cmbn (zero-cmbn (1- (cmbn-degr cmbn)))))
-
-#|
-  (zero-dffr-intr (cmbn 2))
-|#
-
-(DEFCONSTANT +ZERO-NEGATIVE-CMBN+
-   (list :cmbn -1))
-
-#|
-  (cmbn-non-zero-p (cmbn 0))
-  (cmbn-non-zero-p (cmbn 0 1 'a)))
-  (cmbn-zero-p (cmbn 0))
-  (cmbn-zero-p (cmbn 0 1 'a)))
-|#
-
-(DEFUN CMBN-OPPS (cmbn)
-   (declare (type cmbn cmbn))
-   (the cmbn
-      (with-cmbn (degr list) cmbn
-         (make-cmbn
-            :degr degr
-            :list (mapcar #'(lambda (term)
-                               (declare (type term term))
-                               (with-term (cffc gnrt) term
-                                  (term (- cffc) gnrt)))
-                     list)))))
-
-#|
-  (setf c (cmbn 0 1 'a -2 'b))
-  (cmbn-opps c)
-  (symbol-value 'c))
-|#
-
-(DEFUN N-CMBN (n cmbn)
-   ;; n is assumed non-zero
-   (declare
-      (fixnum n)
-      (type cmbn cmbn))
-   (the cmbn
-      (if (= n 1)
-         cmbn
-         (with-cmbn (degr list) cmbn
-            (make-cmbn
-               :degr degr
-               :list (mapcar #'(lambda (term)
-                                  (declare (type term term))
-                                  (with-term (cffc gnrt) term
-                                     (term (* n cffc) gnrt)))
-                        list))))))
-
-#|
-  (setf c (cmbn 2 3 'a))
-  (setf c2 (n-cmbn 1 c))
-  (eq c c2)
-  (n-cmbn -1 c)
-  (n-cmbn -3 c))
-|#
-
-(DEFUN 2CMBN-ADD (cmpr cmbn1 cmbn2)
-   (declare
-      (type cmprf cmpr)
-      (type cmbn cmbn1 cmbn2))
-   (the cmbn
-      (with-cmbn (degr1 list1) cmbn1
-      (with-cmbn (degr2 list2) cmbn2
-         (unless (= degr1 degr2)
-            (error "In ADD, the combination arguments have different degrees ~D and ~D."
-               degr1 degr2))
-         (unless list1
-            (return-from 2cmbn-add cmbn2))
-         (unless list2
-            (return-from 2cmbn-add cmbn1))
-         (let ((pre-rslt +empty-list+)
-               (mark1 list1)
-               (mark2 list2))
-            (declare (list pre-rslt mark1 mark2))
-            (with--term (cffc1 gnrt1) mark1
-            (with--term (cffc2 gnrt2) mark2
-               (tagbody
-                  :begin
-                  (ecase (funcall cmpr gnrt1 gnrt2)
-                     (:equal
-                      (let ((cffc (+ cffc1 cffc2)))
-                         (declare (fixnum cffc))
-                         (unless (zerop cffc)
-                            (push (term cffc gnrt1) pre-rslt))
-                         (setf mark1 (cdr mark1)
-                               mark2 (cdr mark2))
-                         (unless mark1 (go :cmbn1-is-finished))
-                         (unless mark2 (go :cmbn2-is-finished))
-                         (setf cffc1 (-cffc mark1)
-                               gnrt1 (-gnrt mark1)
-                               cffc2 (-cffc mark2)
-                               gnrt2 (-gnrt mark2))
-                         (go :begin)))
-                     (:less
-                      (push (-term mark1) pre-rslt)
-                      (setf mark1 (cdr mark1))
-                      (unless mark1 (go :cmbn1-is-finished))
-                      (setf cffc1 (-cffc mark1)
-                            gnrt1 (-gnrt mark1))
-                      (go :begin))
-                     (:greater
-                      (push (-term mark2) pre-rslt)
-                      (setf mark2 (cdr mark2))
-                      (unless mark2 (go :cmbn2-is-finished))
-                      (setf cffc2 (-cffc mark2)
-                            gnrt2 (-gnrt mark2))
-                      (go :begin)))
-                  :cmbn1-is-finished
-                  (setf pre-rslt (nreconc pre-rslt mark2))
-                  (go :exit)
-                  :cmbn2-is-finished
-                  (setf pre-rslt (nreconc pre-rslt mark1))
-                  :exit))
-            (make-cmbn :degr degr1 :list pre-rslt)))))))
-
-#|
-  (2cmbn-add #'s-cmpr (cmbn 0) (cmbn 1))
-  (2cmbn-add #'s-cmpr (cmbn 0) (cmbn 0))
-  (2cmbn-add #'s-cmpr (cmbn 0 1 'a) (cmbn 0))
-  (2cmbn-add #'s-cmpr (cmbn 0 1 'a) (cmbn 0 2 'a))
-  (2cmbn-add #'s-cmpr (cmbn 0 1 'a) (cmbn 0 -1 'a))
-  (2cmbn-add #'s-cmpr (cmbn 0 1 'a) (cmbn 0 2 'b))
-  (2cmbn-add #'s-cmpr (cmbn 0 2 'b) (cmbn 0 1 'a))
-  (2cmbn-add #'s-cmpr (cmbn 0 1 'a -2 'b) (cmbn 0 2 'b))
-  (2cmbn-add #'s-cmpr (cmbn 0 2 'b) (cmbn 0 1 'a 3 'c)))
-|#
-
-(DEFUN 2CMBN-SBTR (cmpr cmbn1 cmbn2)
-   (declare
-      (type cmprf cmpr)
-      (type cmbn cmbn1 cmbn2))
-   (the cmbn
-      (with-cmbn (degr1 list1) cmbn1
-      (with-cmbn (degr2 list2) cmbn2
-         (unless (= degr1 degr2)
-            (error "In SBTR, the combination arguments have different degrees ~D and ~D."
-               degr1 degr2))
-         (unless list1
-            (return-from 2cmbn-sbtr (cmbn-opps cmbn2)))
-         (unless list2
-            (return-from 2cmbn-sbtr cmbn1))
-         (let ((pre-rslt +empty-list+)
-               (mark1 list1)
-               (mark2 list2))
-            (declare (list pre-rslt mark1 mark2))
-            (with--term (cffc1 gnrt1) mark1
-            (with--term (cffc2 gnrt2) mark2
-               (tagbody
-                  :begin
-                  (ecase (funcall cmpr gnrt1 gnrt2)
-                     (:equal
-                      (let ((cffc (- cffc1 cffc2)))
-                         (declare (fixnum cffc))
-                         (unless (zerop cffc)
-                            (push (term cffc gnrt1) pre-rslt))
-                                                  (unless mark1 (go :cmbn1-is-finished))
-                         (setf mark1 (cdr mark1)
-                               mark2 (cdr mark2))
-                         (unless mark1 (go :cmbn1-is-finished))
-                         (unless mark2 (go :cmbn2-is-finished))
-                         (setf cffc1 (-cffc mark1)
-                               gnrt1 (-gnrt mark1)
-                               cffc2 (-cffc mark2)
-                               gnrt2 (-gnrt mark2))
-                         (go :begin)))
-                     (:less
-                      (push (-term mark1) pre-rslt)
-                      (setf mark1 (cdr mark1))
-                      (unless mark1 (go :cmbn1-is-finished))
-                      (setf cffc1 (-cffc mark1)
-                            gnrt1 (-gnrt mark1))
-                      (go :begin))
-                     (:greater
-                      (push (term (- cffc2) gnrt2) pre-rslt)
-                      (setf mark2 (cdr mark2))
-                      (unless mark2 (go :cmbn2-is-finished))
-                      (setf cffc2 (-cffc mark2)
-                            gnrt2 (-gnrt mark2))
-                      (go :begin)))
-                  :cmbn1-is-finished
-                  (setf pre-rslt
-                        (nreconc pre-rslt
-                           (mapcar #'(lambda (term)
-                                        (declare (cons term))
-                                        (with-term (cffc gnrt) term
-                                           (term (- cffc) gnrt)))
-                              mark2)))
-                  (go :exit)
-                  :cmbn2-is-finished
-                  (setf pre-rslt (nreconc pre-rslt mark1))
-                  :exit))
-            (make-cmbn
-               :degr degr1
-               :list pre-rslt)))))))
-
-#|
-  (2cmbn-sbtr #'s-cmpr (cmbn 0) (cmbn 1))
-  (2cmbn-sbtr #'s-cmpr (cmbn 0) (cmbn 0))
-  (2cmbn-sbtr #'s-cmpr (cmbn 0) (cmbn 0 1 'a))
-  (2cmbn-sbtr #'s-cmpr (cmbn 0 2 'b) (cmbn 0))
-  (2cmbn-sbtr #'s-cmpr (cmbn 0 3 'b) (cmbn 0 3 'b))
-  (2cmbn-sbtr #'s-cmpr (cmbn 0 3 'b) (cmbn 0 4 'b))
-  (2cmbn-sbtr #'s-cmpr
-    (cmbn 0 1 'a 2 'c  2 'd       3 'g)
-    (cmbn 0      1 'c -2 'd 4 'f -3 'g 4 'h))
-  (2cmbn-sbtr #'s-cmpr
-    (cmbn 0      1 'c -2 'd 4 'f -3 'g 4 'h)
-    (cmbn 0 1 'a 2 'c  2 'd       3 'g))
-  (2cmbn-sbtr #'s-cmpr
-    (cmbn 0      1 'c -2 'd 4 'f -3 'g)
-    (cmbn 0 1 'a 2 'c  2 'd       3 'g))
-  (2cmbn-sbtr #'s-cmpr
-    (cmbn 0 1 'b 2 'a)
-    (cmbn 0 1 'a 1 'b)))  ;;; !!!
-  (2cmbn-sbtr #'s-cmpr
-    (cmbn 0 1 'b 2 'c)
-    (cmbn 0 1 'a 1 'b)))
-|#
-
-(DEFUN 2N-2CMBN (cmpr n1 cmbn1 n2 cmbn2)
-   ;; n1 * cmbn1 + n2 * cmbn2
-   ;; combinations may be null but not n1 and n2
-   (declare
-      (type cmprf cmpr)
-      (fixnum n1 n2)
-      (type cmbn cmbn1 cmbn2))
-   (the cmbn
-      (with-cmbn (degr1 list1) cmbn1
-      (with-cmbn (degr2 list2) cmbn2
-         (unless (= degr1 degr2)
-            (error "In 2N-2CMBN, the combination arguments have different degrees ~D and ~D."
-               degr1 degr2))
-         (unless list1
-            (return-from 2n-2cmbn (n-cmbn n2 cmbn2)))
-         (unless list2
-            (return-from 2n-2cmbn (n-cmbn n1 cmbn1)))
-         (let ((pre-rslt +empty-list+)
-               (mark1 list1)
-               (mark2 list2))
-            (declare (list pre-rslt mark1 mark2))
-            (with--term (cffc1 gnrt1) mark1
-            (with--term (cffc2 gnrt2) mark2
-               (setf cffc1 (* n1 cffc1)
-                     cffc2 (* n2 cffc2))
-               (tagbody
-                  :begin
-                  (ecase (funcall cmpr gnrt1 gnrt2)
-                     (:equal
-                      (let ((cffc (+ cffc1 cffc2)))
-                         (declare (fixnum cffc))
-                         (unless (zerop cffc)
-                            (push (term cffc gnrt1) pre-rslt))
-                         (setf mark1 (cdr mark1)
-                               mark2 (cdr mark2))
-                         (unless mark1 (go :cmbn1-is-finished))
-                         (unless mark2 (go :cmbn2-is-finished))
-                         (setf cffc1 (* n1 (-cffc mark1))
-                               gnrt1 (-gnrt mark1)
-                               cffc2 (* n2 (-cffc mark2))
-                               gnrt2 (-gnrt mark2))
-                         (go :begin)))
-                     (:less
-                      (push (term cffc1 gnrt1) pre-rslt)
-                      (setf mark1 (cdr mark1))
-                      (unless mark1 (go :cmbn1-is-finished))
-                      (setf cffc1 (* n1 (-cffc mark1))
-                            gnrt1 (-gnrt mark1))
-                      (go :begin))
-                     (:greater
-                      (push (term cffc2 gnrt2) pre-rslt)
-                      (setf mark2 (cdr mark2))
-                      (unless mark2 (go :cmbn2-is-finished))
-                      (setf cffc2 (* n2 (-cffc mark2))
-                            gnrt2 (-gnrt mark2))
-                      (go :begin)))
-                  :cmbn1-is-finished
-                  (setf pre-rslt
-                        (nreconc pre-rslt
-                           (if (= 1 n2)
-                              mark2
-                              (mapcar #'(lambda (term)
-                                           (declare (cons term))
-                                           (with-term (cffc gnrt) term
-                                              (term (* n2 cffc) gnrt)))
-                                 mark2))))
-                  (go :exit)
-                  :cmbn2-is-finished
-                  (setf pre-rslt
-                        (nreconc pre-rslt
-                           (if (= 1 n1)
-                              mark1
-                              (mapcar #'(lambda (term)
-                                           (declare (cons term))
-                                           (with-term (cffc gnrt) term
-                                              (term (* n1 cffc) gnrt)))
-                                 mark1))))
-                  :exit))
-            (make-cmbn
-               :degr degr1
-               :list pre-rslt)))))))
-
-#|
-  (2n-2cmbn #'s-cmpr 3 (cmbn 0) 4 (cmbn 1))
-  (2n-2cmbn #'s-cmpr 3 (cmbn 0) 4 (cmbn 0))
-  (2n-2cmbn #'s-cmpr 3 (cmbn 0 1 'a) 4 (cmbn 0))
-  (2n-2cmbn #'s-cmpr 3 (cmbn 0  1 'a 2 'b 3 'c     )
-                     1 (cmbn 0 -3 'a 2 'b      4 'd))
-  (2n-2cmbn #'s-cmpr 3 (cmbn 0 -3 'a 2 'b     4 'd)
-                     1 (cmbn 0  1 'a 2 'b 3 'c    ))
-  (2n-2cmbn #'s-cmpr 1 (cmbn 0  1 'a 2 'b 3 'c     )
-                     1 (cmbn 0 -3 'a 2 'b      4 'd))
-  (2n-2cmbn #'s-cmpr 1 (cmbn 0 -3 'a 2 'b     4 'd)
-                     1 (cmbn 0  1 'a 2 'b 3 'c    ))
-  (2n-2cmbn #'s-cmpr 1 (cmbn 0 -3 'a 2 'b     4 'd)
-                     3 (cmbn 0  1 'a 2 'b 3 'c    )))
-|#
-
-(DEFUN CMBN-CMBN (cmpr n-cmbn-list)
-  ;; n-cmbn-list = list of (cons n cmbn)
-  ;;               non-empty-list
-  ;;            every n is non-null
-  (declare
-     (type cmprf cmpr)
-     (list n-cmbn-list))
-  (unless (rest n-cmbn-list)
-     (return-from cmbn-cmbn
-	(n-cmbn (caar n-cmbn-list) (cdar n-cmbn-list))))
-  (unless (cddr n-cmbn-list)
-     (return-from cmbn-cmbn
-	(2n-2cmbn cmpr
-		  (caar n-cmbn-list) (cdar n-cmbn-list)
-		  (caadr n-cmbn-list) (cdadr n-cmbn-list))))
-  (the cmbn
-     (let ((new-rslt +empty-list+))
-        (declare (list new-rslt))
-	(do ((mark1 (rest n-cmbn-list) (cddr mark1))
-	     (mark2 n-cmbn-list (cdr mark1)))
-	    ((endp mark2))
-	   (declare (list mark1 mark2))
-	   (when (endp mark1)
-	      (push (n-cmbn (caar mark2) (cdar mark2)) new-rslt)
-	      (return))
-	   (push (2n-2cmbn cmpr
-			   (caar mark2) (cdar mark2)
-			   (caar mark1) (cdar mark1))
-		 new-rslt))
-	(let ((old-rslt +empty-list+))
-	  (declare (list old-rslt))
-	  (loop
-	   (unless (rest new-rslt)
-	      (return-from cmbn-cmbn (first new-rslt)))
-	   (setf old-rslt new-rslt
-		 new-rslt +empty-list+)
-	   (do ((mark1 (rest old-rslt) (cddr mark1))
-		(mark2 old-rslt (cdr mark1)))
-	       ((endp mark2))
-	      (declare (list mark1 mark2))
-	      (when (endp mark1)
-		 (push (car mark2) new-rslt)
-		 (return))
-	      (push (2cmbn-add cmpr (car mark2) (car mark1))
-		    new-rslt)))))))
-
-#|
-  (setf cons (cons 3 (cmbn 0 4 'a)))
-  (cmbn-cmbn #'s-cmpr (make-list 5 :initial-element cons))
-  (dotimes (i 10)
-     (print
-       (cffc (first (cmbn-list
-          (cmbn-cmbn #'s-cmpr (make-list (1+ i) :initial-element cons))))))))
-|#
-
-(DEFUN NTERM-ADD (cmpr degr &rest rest)
-   (declare
-      (type cmprf cmpr)
-      (fixnum degr)
-      (list rest))
-      ;; (list term)
-   (unless rest
-      (return-from nterm-add (zero-cmbn degr)))
-   (the cmbn
-      (let ((rslt (list (first rest))))
-         (declare (list rslt))
-         (dolist (term (rest rest))
-            (declare (type term term))
-            (with-term  (cffc gnrt) term
-               (do ((mark1 rslt (cdr mark1))
-                    (mark2 nil mark1))
-                   ((endp mark1) (setf (cdr mark2) (list term)))
-                  (ecase (funcall cmpr gnrt (-gnrt mark1))
-                     (:less
-                      (if mark2
-                         (push term (cdr mark2))
-                         (push term rslt))
-                      (return))                     
-                     (:equal
-                      (incf (-cffc mark1) cffc)
-                      (return))                     
-                     (:greater )))))
-         (make-cmbn
-            :degr degr
-            :list (delete 0 rslt :key #'car)))))
-
-#|
-  (nterm-add #'s-cmpr 11)
-  (nterm-add #'s-cmpr 11 (term 1 'a))
-  (nterm-add #'s-cmpr 11 (term 1 'a) (term 2 'b))
-  (nterm-add #'s-cmpr 11 (term 1 'b) (term 2 'a) (term 3 'aa)
-                         (term -2 'aa) (term -2 'a) (term 4 'aab)
-                         (term 5 'c))
-|#
-
-(DEFUN NCMBN-ADD (cmpr cmbn &rest rest)
-   (declare
-      (type cmprf cmpr)
-      (type cmbn cmbn))
-   (the cmbn
-      (cmbn-cmbn cmpr (mapcar #'(lambda (cmbn)
-                                   (declare (type cmbn cmbn))
-                                   (cons 1 cmbn))
-                         (cons cmbn rest)))))
-
-#|
-  (setf c (cmbn 3 4 'a))
-  (ncmbn-add #'s-cmpr c c c c c)
-|#
-
-(DEFUN DSTR-ADD-TERM-TO-CMBN (cmpr cffc gnrt cmbn)
-   (declare
-      (type cmprf cmpr)
-      (fixnum cffc)  ;; non-zero
-      (type gnrt gnrt)
-      (type cmbn cmbn))
-   (the cmbn
-      (let ((list (cmbn-list cmbn)))
-         (declare (list list))
-         (unless list
-            (push (term cffc gnrt) (cmbn-list cmbn))
-            (return-from dstr-add-term-to-cmbn cmbn))
-         (do ((mark2 nil mark1)
-              (mark1 list (cdr mark1)))
-             ((endp mark1) (setf (cdr mark2) (list (term cffc gnrt))))
-            (declare (list mark1 mark2))
-            (ecase (funcall cmpr gnrt (-gnrt mark1))
-               (:less
-                (if mark2
-                   (push (term cffc gnrt) (cdr mark2))
-                   (push (term cffc gnrt) (cmbn-list cmbn)))
-                (return))
-               (:equal
-                (let ((new-cffc (+ cffc (-cffc mark1))))
-                   (declare (fixnum new-cffc))
-                   (if (zerop new-cffc)
-                      (if mark2
-                         (pop (cdr mark2))
-                         (pop (cmbn-list cmbn)))
-                      (setf (-cffc mark1) new-cffc))
-                   (return)))
-               (:greater)))
-         cmbn)))
-
-#|
-  (setf c (zero-cmbn 10))
-  (dstr-add-term-to-cmbn #'s-cmpr 3 'f c)
-  (eq * c)
-  (dstr-add-term-to-cmbn #'s-cmpr 3 'g c)
-  (eq * c)
-  (dstr-add-term-to-cmbn #'s-cmpr 3 'a c)
-  (eq * c)
-  (dstr-add-term-to-cmbn #'s-cmpr 3 'd c)
-  (eq * c)
-  (dstr-add-term-to-cmbn #'s-cmpr -3 'd c)
-  (eq * c)
-  (dstr-add-term-to-cmbn #'s-cmpr -2 'a c)
-  (dstr-add-term-to-cmbn #'s-cmpr -1 'a c)
-  (eq * c)
-  (dstr-add-term-to-cmbn #'s-cmpr -3 'g c)
-  (eq * c)
-  (dstr-add-term-to-cmbn #'s-cmpr -3 'f c)
-  (eq * c))
-|#
diff --git a/archive/Kenzo-2/Kenzo-2-Acl5/cones.cl b/archive/Kenzo-2/Kenzo-2-Acl5/cones.cl
deleted file mode 100644
index 8ffd4e8..0000000
--- a/archive/Kenzo-2/Kenzo-2-Acl5/cones.cl
+++ /dev/null
@@ -1,443 +0,0 @@
-;;;  CONES  CONES  CONES  CONES  CONES  CONES  CONES  CONES  CONES  CONES
-;;;  CONES  CONES  CONES  CONES  CONES  CONES  CONES  CONES  CONES  CONES
-;;;  CONES  CONES  CONES  CONES  CONES  CONES  CONES  CONES  CONES  CONES
-
-(IN-PACKAGE "CAT")
-
-(PROVIDE "cones")
-
-(DEFUN DISPATCH-BICN-CMBN (cmbn)
-   (declare (type cmbn cmbn))
-   (the (values cmbn cmbn cmbn)
-      (with-cmbn (degr list) cmbn
-         (let ((listb +empty-list+)
-               (listc +empty-list+)
-               (listd +empty-list+))
-            (declare (list listb listc listd))
-            (dolist (term list)
-               (declare (type term term))
-               (with-term (cffc bicn) term
-                  (with-bicn (bcnx ibicn) bicn
-                     (ecase bcnx
-                        (:bcnb (push (term cffc ibicn) listb))
-                        (:bcnc (push (term cffc ibicn) listc))
-                        (:bcnd (push (term cffc ibicn) listd))))))
-            (values
-               (make-cmbn :degr degr :list (nreverse listb))
-               (make-cmbn :degr (1+ degr) :list (nreverse listc))
-               (make-cmbn :degr degr :list (nreverse listd)))))))
-
-#|
-  (dispatch-bicn-cmbn (cmbn 3 3 (bcnb 'b1) 4 (bcnb 'b2) 33 (bcnc 'c) 333 (bcnd 'd)))
-|#
-
-(DEFUN BICN-CMBN-CMBNB (cmbn)
-   (declare (type cmbn cmbn))
-   (the cmbn
-      (with-cmbn (degr list) cmbn
-         (make-cmbn :degr degr
-            :list (do ((rslt +empty-list+)
-                       (mark list (cdr mark)))
-                      ((endp mark) (nreverse rslt))
-                     (declare (list rslt mark))
-                     (with--term (cffc bicn) mark
-                     (with-bicn (bcnx gnrtB) bicn
-                        (if (eq bcnx :bcnB)
-                           (push (term cffc gnrtB) rslt)
-                           (return (nreverse rslt))))))))))
-
-(DEFUN BICN-CMBN-CMBNC (cmbn)
-   (declare (type cmbn cmbn))
-   (the cmbn
-      (with-cmbn (degr list) cmbn
-         (make-cmbn :degr (1+ degr)
-            :list (do ((rslt +empty-list+)
-                       (mark (member :bcnc list :key #'cadr) (cdr mark)))
-                      ((endp mark) (nreverse rslt))
-                     (declare (list rslt mark))
-                     (with--term (cffc bicn) mark
-                     (with-bicn (bcnx gnrtC) bicn
-                        (if (eq bcnx :bcnC)
-                           (push (term cffc gnrtC) rslt)
-                           (return (nreverse rslt))))))))))
-
-(DEFUN BICN-CMBN-CMBND (cmbn)
-   (declare (type cmbn cmbn))
-   (the cmbn
-      (with-cmbn (degr list) cmbn
-         (make-cmbn :degr degr
-            :list (mapcar
-                     #'(lambda (term)
-                          (declare (type term term))
-                          (with-term (cffc bicn) term
-                             (term cffc (ibicn bicn))))
-                     (member :bcnd list :key #'cadr))))))
-
-#|
-  (bicn-cmbn-cmbnb (cmbn 3 1 (bcnb 'a) 2 (bcnc 'b)))
-  (bicn-cmbn-cmbnb (cmbn 3 2 (bcnc 'b)))
-  (bicn-cmbn-cmbnc (cmbn 3 1 (bcnb 'a) 2 (bcnc 'b) 3 (bcnd 'c)))
-  (bicn-cmbn-cmbnc (cmbn 3 1 (bcnb 'a) 3 (bcnd 'c)))
-  (bicn-cmbn-cmbnd (cmbn 3 1 (bcnb 'a) 2 (bcnc 'b) 3 (bcnd 'c)))
-  (bicn-cmbn-cmbnd (cmbn 3 2 (bcnb 'b)))
-|#
-
-(DEFUN MAKE-BICN-CMBN (cmbnb cmbnc cmbnd)
-   (declare (type cmbn cmbnb cmbnc cmbnd))
-   (the cmbn
-      (with-cmbn (degrb listb) cmbnb
-      (with-cmbn (degrc listc) cmbnc
-      (with-cmbn (degrd listd) cmbnd
-         (unless (= degrb (1- degrc) degrd)
-            (error "In MAKE-BICN-CMBN, the degrees are not coherent."))
-         (make-cmbn :degr degrb
-            :list (nconc
-                     (mapcar #'(lambda (termb)
-                                  (declare (type term termb))
-                                  (with-term (cffc gnrtb) termb
-                                     (term cffc (bcnb gnrtb))))
-                        listb)
-                     (mapcar #'(lambda (termc)
-                                  (declare (type term termc))
-                                  (with-term (cffc gnrtc) termc
-                                     (term cffc (bcnc gnrtc))))
-                        listc)
-                     (mapcar #'(lambda (termd)
-                                  (declare (type term termd))
-                                  (with-term (cffc gnrtd) termd
-                                     (term cffc (bcnd gnrtd))))
-                        listd))))))))
-
-#|
-  (multiple-value-call #'make-bicn-cmbn 
-     (dispatch-bicn-cmbn (cmbn 3 3 (bcnb 'b1) 4 (bcnb 'b2) 33 (bcnc 'c) 333 (bcnd 'd))))
-|#
-
-(DEFMETHOD PRINT-KEYCONS ((car (eql :bcnb)) cdr stream)
-   (declare
-      (type gnrt cdr)
-      (stream stream))
-   (the (eql t)
-      (progn
-         (format stream "<BcnB ~A>" cdr)
-         t)))
-
-(DEFMETHOD PRINT-KEYCONS ((car (eql :bcnc)) cdr stream)
-   (declare
-      (type gnrt cdr)
-      (stream stream))
-   (the (eql t)
-      (progn
-         (format stream "<BcnC ~A>" cdr)
-         t)))
-
-(DEFMETHOD PRINT-KEYCONS ((car (eql :bcnd)) cdr stream)
-   (declare
-      (type gnrt cdr)
-      (stream stream))
-   (the (eql t)
-      (progn
-         (format stream "<BcnD ~A>" cdr)
-         t)))
-
-#|
-  (bcnb 'a)
-  (bcnc 'b)
-  (bcnd 'c)
-|#
-
-(DEFUN BICONE-CMPR (cmprb cmprc cmprd)
-   (declare (type cmprf cmpra cmprb cmprd))
-   (flet ((rslt (bicn1 bicn2)
-             (declare (type bicn bicn1 bicn2))
-             (let ((bcnx1 (bcnx bicn1)))
-                (declare (type (member :bcnb :bcnc :bcnd) bcnx))
-                (lexico
-                   (s-cmpr bcnx1 (bcnx bicn2))
-                   (case bcnx1
-                      (:bcnb (funcall cmprb (ibicn bicn1) (ibicn bicn2)))
-                      (:bcnc (funcall cmprc (ibicn bicn1) (ibicn bicn2)))
-                      (:bcnd (funcall cmprd (ibicn bicn1) (ibicn bicn2))))))))
-      (the cmprf #'rslt)))
-
-#|
-  (setf r (bicone-cmpr #'f-cmpr #'f-cmpr #'f-cmpr))
-  (funcall r (bcnb 1) (bcnc 0))
-  (funcall r (bcnb 1) (bcnb 2))
-|#
-
-(DEFUN BICONE-BASIS (basisb basisc basisd)
-   (declare (type basis basisb basisc basisd))
-   (the basis
-      (if (or (eq :locally-effective basisb)
-              (eq :locally-effective basisc)
-              (eq :locally-effective basisd))
-         :locally-effective
-         (flet ((rslt (degr)
-                   (declare (fixnum degr))
-                   (append
-                      (mapcar #'(lambda (item)
-                                   (declare (type gnrt item))
-                                   (bcnb item))
-                         (funcall basisb degr))
-                      (mapcar #'(lambda (item)
-                                   (declare (type gnrt item))
-                                   (bcnc item))
-                         (funcall basisc (1+ degr)))
-                      (mapcar #'(lambda (item)
-                                   (declare (type gnrt item))
-                                   (bcnd item))
-                         (funcall basisd degr)))))
-            (the basis #'rslt)))))
-
-#|
-  (bicone-basis :locally-effective :locally-effective :locally-effective)
-  (setf b #'(lambda (degr) (mapcar #'(lambda (item) (cons degr item)) (<a-b> 0 degr))))
-  (setf r (bicone-basis b b b))
-  (funcall r 3)
-|#
-
-(DEFUN BICONE-DFFR-INTR (cmprc dffrb dffrc dffrd f1 f2)
-   (declare
-      (type cmprf cmprc)
-      (type morphism dffrb dffrc dffrd f1 f2))
-   (flet ((rslt (cmbn)
-             (declare (type cmbn cmbn))
-             (the cmbn
-                (multiple-value-bind (cmbnb cmbnc cmbnd) (dispatch-bicn-cmbn cmbn)
-                   (declare (type cmbn cmbnb cmbnc cmbnd))
-                   (let ((dffrb (cmbn-? dffrb cmbnb))
-                         (dffrc (cmbn-? dffrc cmbnc))
-                         (dffrd (cmbn-? dffrd cmbnd))
-                         (f1 (cmbn-? f1 cmbnb))
-                         (f2 (cmbn-? f2 cmbnd)))
-                      (declare (type cmbn dffrb dffrc dffrd f1 f2))
-                      (let ((cmbnc (2cmbn-sbtr cmprc (2cmbn-add cmprc f1 f2) dffrc)))
-                         (declare (type cmbn cmbnc))
-                         (make-bicn-cmbn dffrb cmbnc dffrd)))))))
-      (the intr #'rslt)))
-                      
-(DEFUN BICONE (rdct1 rdct2)
-   (declare (type reduction rdct1 rdct2))
-   (the chain-complex
-      (with-slots ((tcc1 tcc) (bcc1 bcc) (f1 f)) rdct1
-         (declare
-            (type chain-complex tcc1 bcc1)
-            (type morphism f1 g1 h1))
-      (with-slots ((tcc2 tcc) (bcc2 bcc) (f2 f)) rdct2
-         (declare
-            (type chain-complex tcc2 bcc2)
-            (type morphism f2 g2 h2))
-         (unless (eq bcc1 bcc2)
-            (error "In BICONE, both reductions have different BCC's."))
-         (let ((rslt (chain-complex
-                        :cmpr (bicone-cmpr (cmpr tcc1) (cmpr bcc1) (cmpr tcc2))
-                        :basis (bicone-basis (basis tcc1) (basis bcc1) (basis tcc2))
-                        :bsgn :undefined
-                        :dffr-intr (bicone-dffr-intr (cmpr bcc1)
-                                      (dffr tcc1) (dffr bcc1) (dffr tcc2)
-                                      f1 f2)
-                        :dffr-strt :cmbn
-                        :dfnt `(bicone ,rdct1 ,rdct2))))
-            (declare (type chain-complex rslt))
-            (slot-makunbound rslt 'bsgn)
-            rslt)))))
-
-#|
-  (cat-init)
-  (progn
-   (defun cdelta (dmns)
-     (chain-complex
-        :cmpr #'l-cmpr
-        :basis #'(lambda (n)
-                    (mapcar #'dlop-int-ext (funcall (delta-n-basis dmns) n)))
-        :bsgn '(0)
-        :dffr-intr #'(lambda (degr gmsm)
-                        (make-cmbn
-                           :degr (1- degr)
-                           :list (do ((rslt +empty-list+
-                                           (cons (cons sign (append
-                                                               (subseq gmsm 0 nark)
-                                                               (subseq gmsm (1+ nark))))
-                                                 rslt))
-                                     (sign 1 (- sign))
-                                     (nark 0 (1+ nark)))
-                                    ((> nark degr) rslt))))                                           
-        :dffr-strt :gnrt
-        :dfnt `(locally effective version of C_* delta ,dmns)))
-   (defun make-f (tdmns bdmns)
-     (morphism
-        :sorc (cdelta tdmns) :trgt (cdelta bdmns) :degr 0
-        :intr #'(lambda (degr gmsm)
-                   (let ((pos (position-if #'(lambda (vertex) (>= vertex bdmns)) gmsm)))
-                      (if pos
-                         (if (< pos degr)
-                            (zero-cmbn degr)
-                            (cmbn degr 1 (nconc (butlast gmsm) (list bdmns))))
-                         (cmbn degr 1 gmsm))))
-        :strt :gnrt
-        :dfnt `(projection delta ,tdmns => delta ,bdmns)))
-   (defun make-g (tdmns bdmns)
-     (morphism
-        :sorc (cdelta bdmns) :trgt (cdelta tdmns) :degr 0
-        :intr #'identity
-        :strt :cmbn
-        :dfnt `(injection delta ,bdmns => delta ,tdmns)))
-   (defun make-h (tdmns bdmns)
-     (morphism
-        :sorc (cdelta tdmns) :trgt (cdelta tdmns) :degr +1
-        :intr #'(lambda (degr gmsm)
-                   (let ((pos (position-if #'(lambda (vertex) (>= vertex bdmns)) gmsm)))
-                      (if pos
-                         (if (member bdmns gmsm)
-                            (zero-cmbn (1+ degr))
-                            (cmbn (1+ degr) (-1-expt-n pos)
-                               (append (subseq gmsm 0 pos) (list bdmns) (subseq gmsm pos))))
-                         (zero-cmbn (1+ degr)))))
-        :strt :gnrt
-        :dfnt `(homotopy for delta ,tdmns => ,bdmns)))
-   (defun make-rdct (tdmns bdmns)
-       (setf rdct (reduction
-                    :f (make-f tdmns bdmns)
-                    :g (make-g tdmns bdmns)
-                    :h (make-h tdmns bdmns)
-                    :dfnt `(reduction delta ,tdmns ,bdmns)))))
-  (setf b (bicone (make-rdct 3 2) (make-rdct 4 2)))
-  (basis b 1)
-  (? b (cmbn 1 3 (bcnb '(0 3)) 4 (bcnc '(0 1 2)) 5 (bcnd '(0 4))))
-|#
-
-(DEFMETHOD CMPS ((eqvl1 equivalence) (eqvl2 equivalence) &optional dummy)
-   (declare (ignore dummy))
-   (the equivalence
-      (progn
-         (when (eq 'trivial-eqvl (dfnt eqvl2))
-            (return-from cmps eqvl1))
-         (with-slots ((cc-A lbcc) (cc-B tcc) (cc-C rbcc)
-                      (f1 lf) (g1 lg) (h1 lh) (f2 rf) (g2 rg) (h2 rh)) eqvl1
-            (declare
-               (type chain-complex cc-A cc-B cc-C)
-               (type morphism f1 g1 h1 f2 g2 h2))
-         (with-slots ((cc-C2 lbcc) (cc-D tcc) (cc-E rbcc)
-                      (f3 lf) (g3 lg) (h3 lh) (f4 rf) (g4 rg) (h4 rh)) eqvl2
-            (declare
-               (type chain-complex cc-C2 cc-D cc-E)
-               (type morphism f3 g3 h3 f4 g4 h4))
-            (unless (eq (grmd cc-C) (grmd cc-C2))
-               (error "In (CMPS eqvl eqvl), both eqvl's may not be composed."))
-            (let ((bicone (bicone (rrdct eqvl1) (lrdct eqvl2)))
-                  (cmpr-B (cmpr cc-B))
-                  (cmpr-D (cmpr cc-D)))
-               (declare (type chain-complex bicone))
-               (let ((lf (morphism
-                            :sorc bicone :trgt cc-A :degr 0
-                            :intr #'(lambda (cmbn)
-                                       (declare (type cmbn cmbn))
-                                       (cmbn-? f1 (bicn-cmbn-cmbnB cmbn)))
-                            :strt :cmbn
-                            :dfnt `(cmps ,eqvl1 ,eqvl2 lf)))
-                     (lg (morphism
-                            :sorc cc-A :trgt bicone :degr 0
-                            :intr #'(lambda (cmbn)
-                                       (declare (type cmbn cmbn))
-                                       (let* ((cmbnB (cmbn-? g1 cmbn))
-                                              (cmbnC (zero-cmbn (1+ (cmbn-degr cmbn))))
-                                              (cmbnD (cmbn-? g3 (cmbn-? f2 (cmbn-opps cmbnB)))))
-                                          (declare (type cmbn cmbnB cmbnC cmbnD))
-                                          (make-bicn-cmbn cmbnB cmbnC cmbnD)))
-                            :strt :cmbn
-                            :dfnt `(cmps ,eqvl1 ,eqvl2 lg)))
-                     (lh (morphism
-                            :sorc bicone :trgt bicone :degr +1
-                            :intr #'(lambda (cmbn)
-                                       (declare (type cmbn cmbn))
-                                       (multiple-value-bind (cmbnB cmbnC cmbnD) 
-                                           (dispatch-bicn-cmbn cmbn)
-                                          (declare (type cmbn cmbnB cmbnC cmbnD))
-                                          (setf cmbnB (cmbn-? h1 cmbnB))
-                                          (let ((cmbnC (zero-cmbn (1+ (cmbn-degr cmbnC))))
-                                                (cmbnD1 (cmbn-? g3 (cmbn-? f2 cmbnB)))
-                                                (cmbnD2 (cmbn-? g3 cmbnC))  ;; let, not let*
-                                                (cmbnD3 (cmbn-? h3 cmbnD)))
-                                             (declare (type cmbn cmbnC cmbnD1 cmbnD2 cmbnD3))
-                                             (make-bicn-cmbn
-                                                cmbnB
-                                                cmbnC
-                                                (2cmbn-sbtr cmpr-D
-                                                   (2cmbn-add cmpr-D cmbnD2 cmbnD3)
-                                                   cmbnD1)))))
-                            :strt :cmbn
-                            :dfnt `(cmps ,eqvl1 ,eqvl2 lh)))
-                     (rf (morphism
-                            :sorc bicone :trgt cc-E :degr 0
-                            :intr #'(lambda (cmbn)
-                                       (declare (type cmbn cmbn))
-                                       (cmbn-? f4 (bicn-cmbn-cmbnD cmbn)))
-                            :strt :cmbn
-                            :dfnt `(cmps ,eqvl1 ,eqvl2 rf)))
-                     (rg (morphism
-                            :sorc cc-E :trgt bicone :degr 0
-                            :intr #'(lambda (cmbn)
-                                       (declare (type cmbn cmbn))
-                                       (let* ((cmbnD (cmbn-? g4 cmbn))
-                                              (cmbnC (zero-cmbn (1+ (cmbn-degr cmbn))))
-                                              (cmbnB (cmbn-? g2 (cmbn-? f3 (cmbn-opps cmbnD)))))
-                                          (declare (type cmbn cmbnD cmbnC cmbnB))
-                                          (make-bicn-cmbn cmbnB cmbnC cmbnD)))
-                            :strt :cmbn
-                            :dfnt `(cmps ,eqvl1 ,eqvl2 rg)))
-                     (rh (morphism
-                            :sorc bicone :trgt bicone :degr +1
-                            :intr #'(lambda (cmbn)
-                                       (declare (type cmbn cmbn))
-                                       (multiple-value-bind (cmbnB cmbnC cmbnD) 
-                                           (dispatch-bicn-cmbn cmbn)
-                                          (declare (type cmbn cmbnB cmbnC cmbnD))
-                                          (setf cmbnD (cmbn-? h4 cmbnD))
-                                          (let ((cmbnC (zero-cmbn (1+ (cmbn-degr cmbnC))))
-                                                (cmbnB1 (cmbn-? g2 (cmbn-? f3 cmbnD)))
-                                                (cmbnB2 (cmbn-? g2 cmbnC))  ;; let, not let*
-                                                (cmbnB3 (cmbn-? h2 cmbnB)))
-                                             (declare (type cmbn cmbnC cmbnB1 cmbnB2 cmbnB3))
-                                             (make-bicn-cmbn
-                                                (2cmbn-sbtr cmpr-B
-                                                   (2cmbn-add cmpr-B cmbnB2 cmbnB3)
-                                                   cmbnB1)
-                                                cmbnC
-                                                cmbnD))))
-                            :strt :cmbn
-                            :dfnt `(cmps ,eqvl1 ,eqvl2 rh))))
-                  (declare
-                     (type chain-complex lbcc tcc rbcc)
-                     (type morphism lf lg lh rf rg rh))
-                  (equivalence
-                   :lrdct (reduction :f lf :g lg :h lh :dfnt `(cmps ,eqvl1 ,eqvl2 :lrdct))
-                   :rrdct (reduction :f rf :g rg :h rh :dfnt `(cmps ,eqvl1 ,eqvl2 :rrdct))
-                   :dfnt `(cmps ,eqvl1 ,eqvl2)))))))))
-
-#|
-  (cat-init)
-  (setf c (chain-complex
-             :cmpr #'s-cmpr
-             :basis #'(lambda (dmns) '(a))
-             :bsgn 'a
-             :dffr-intr #'zero-dffr-intr
-             :dffr-strt :cmbn
-             :dfnt '(c)))
-  (setf h1 (trivial-eqvl c))
-  (setf h2 (cmps h1 h1))
-  (pre-check-rdct (lrdct h2))
-  (setf *tc* (cmbn 3 1 (bcnB 'a) 10 (bcnC 'a) 100 (bcnD 'a)))
-  (setf *bc* (cmbn 3 1 'a))
-  (check-rdct)
-  (pre-check-rdct (rrdct h2))
-  (check-rdct)
-  (setf h3 (cmps h2 h2))
-  (setf *tc* (cmbn 3 1 (bcnB (bcnB 'a)) 10 (bcnB (bcnC 'a)) 100 (bcnB (bcnD 'a))
-                     1000 (bcnC 'a)
-                    10000 (bcnD (bcnB 'a)) 5234 (bcnD (bcnC 'a)) 223 (bcnD (bcnD 'a))))
-  (pre-check-rdct (lrdct h3))
-  (check-rdct)
-  (pre-check-rdct (rrdct h3))
-  (check-rdct)
-|#
diff --git a/archive/Kenzo-2/Kenzo-2-Acl5/cs-twisted-products.cl b/archive/Kenzo-2/Kenzo-2-Acl5/cs-twisted-products.cl
deleted file mode 100644
index 3d3d0e4..0000000
--- a/archive/Kenzo-2/Kenzo-2-Acl5/cs-twisted-products.cl
+++ /dev/null
@@ -1,146 +0,0 @@
-;;;  CS-TWISTED-PRODUCTS  CS-TWISTED-PRODUCTS  CS-TWISTED-PRODUCTS
-;;;  CS-TWISTED-PRODUCTS  CS-TWISTED-PRODUCTS  CS-TWISTED-PRODUCTS
-;;;  CS-TWISTED-PRODUCTS  CS-TWISTED-PRODUCTS  CS-TWISTED-PRODUCTS
-
-(IN-PACKAGE "CAT")
-
-(PROVIDE "cs-twisted-products")
-
-(DEFUN SMGR-FIBRATION-SINTR (dmns gbar)
-  (declare
-    (ignore dmns)
-    (type gbar gbar))
-  (the absm
-    (first (gbar-list gbar))))
-
-(DEFUN SMGR-FIBRATION (smgr)
-  (declare (type simplicial-group smgr))
-  (the fibration
-    (simplicial-mrph
-      :sorc (classifying-space smgr)
-      :trgt smgr
-      :degr -1
-      :sintr #'smgr-fibration-sintr
-      :dfnt `(simplicial-group-fibration ,smgr))))
-
-#|
-  (setf k1 (k-z-1))
-  (setf tw (smgr-fibration k1))
-  (setf k2 (sorc tw))
-  (setf tt (fibration-total tw))
-  (setf gmsm (crpr 0 (gbar 4 0 '(10 11 12) 0 '(20 21) 0 '(30) 0 '())
-                   0 '(2 4 6 8)))
-  (dotimes (i 5)
-    (print (face tt i 4 gmsm)))
-  (setf br (brown-reduction tw))
-  (setf tw-pr (bcc br))
-  (? tw-pr 4 (tnpr 4 (gbar 4 0 '(1 10 100) 0 '(1000 10000)
-                             0 '(100000) 0 '())
-                   0 '()))
-|#
-
-(DEFUN SMGR-CRTS-CONTRACTION-INTR (idnt)
-  (declare
-    (type gmsm idnt))
-  (flet ((rslt (degr crpr
-		     &aux (degr+1 (1+ degr)))
-	   (declare
-	    (fixnum degr degr+1)
-	    (type crpr crpr))
-	   (the cmbn
-	     (with-crpr (absm1 absm2) crpr
-	       (if (= (dgop absm2) (mask degr))
-		 (zero-cmbn degr+1)
-		 (term-cmbn degr+1
-		   (-1-expt-n+1 degr)
-		   (crpr 0 (make-gbar
-			    :dmns degr+1
-			    :list (cons absm2
-					(rest (unnormalize-gbar absm1 idnt))))
-			 (mask degr+1) idnt)))))))
-     (the intr #'rslt)))
-
-(DEFUN SMGR-CRTS-CONTRACTION (smgr)
-  (declare (type simplicial-group smgr))
-  (the morphism
-    (morphism
-      :sorc (fibration-total (smgr-fibration smgr))
-      :trgt (fibration-total (smgr-fibration smgr))
-      :degr +1
-      :intr (smgr-crts-contraction-intr (bsgn smgr))
-      :strt :gnrt
-      :dfnt `(smgr-crts-contraction ,smgr))))
-
-#|
-  (cat-init)
-  (setf chi (smgr-crts-contraction (k-z-1)))
-  (setf rdct (reduction :f (zero-mrph (sorc chi) (z-chcm))
-                         :g (zero-mrph (z-chcm) (sorc chi))
-                         :h chi))
-  (pre-check-rdct rdct)
-  (setf *tc* (cmbn 0 1 (crpr 0 +null-gbar+ 0 '())))
-  (setf *bc* (cmbn 0 1 :z-gnrt))
-  (check-rdct)
-  (setf *tc* (cmbn 1 1 (crpr 1 +null-gbar+ 0 '(1))))
-  (check-rdct)
-  (setf *tc* (cmbn 4 1 (crpr 0 (gbar 4 0 '(10 11 12) 0 '(20 21) 0 '(30) 0 '())
-                             0 '(2 4 6 8))))
-  (check-rdct)
-  (setf *tc* (cmbn 3 1 (crpr 0 (gbar 3 0 '(10 11) 0 '(20) 0 '())
-                             0 '(2 4 6))))
-  (check-rdct)
-|#
-
-(DEFUN SMGR-TNPR-CONTRACTION (smgr
-			        &aux (fibration (smgr-fibration smgr))
-				     (brown (brown-reduction fibration))
-				     (f (f brown))
-				     (g (g brown))
-				     (chi (smgr-crts-contraction smgr)))
-  (declare
-    (type simplicial-group smgr)
-    (type fibration fibration)
-    (type reduction brown)
-    (type morphism f g chi))
-  (the morphism
-    (i-cmps f chi g)))
-
-#|
-  (cat-init)
-  (setf chi (smgr-tnpr-contraction (k-z-1)))
-  (setf rdct (reduction :f (zero-mrph (sorc chi) (z-chcm))
-                         :g (zero-mrph (z-chcm) (sorc chi))
-                         :h chi))
-  (pre-check-rdct rdct)
-  (setf *tc* (cmbn 0 1 (tnpr 0 +null-gbar+ 0 '())))
-  (setf *bc* (cmbn 0 1 :z-gnrt))
-  (check-rdct)
-  (setf *tc* (cmbn 1 1 (tnpr 0 +null-gbar+ 1 '(1))))
-  (check-rdct)
-  (setf *tc* (cmbn 3 1 (tnpr 0 +null-gbar+ 3 '(1 10 100))))
-  (? chi *tc*)
-  (check-rdct)
-  (setf *tc* (cmbn 3 1 (tnpr 2 (gbar 2 0 '(1) 0 '()) 1 '(10))))
-  (? chi *tc*)
-  (check-rdct)
-  (setf *tc* (cmbn 3 1 (tnpr 3 (gbar 3 0 '(1 10) 0 '(100) 0 '()) 0 '())))
-  (? chi *tc*)
-  (check-rdct)
-  (setf *tc* (cmbn 4 1 (tnpr 0 +null-gbar+ 4 '(1 10 100 1000))))
-  (? chi *tc*)
-  (check-rdct)
-  (setf *tc* (cmbn 4 1 (tnpr 2 (gbar 2 0 '(1) 0 '()) 2 '(10 100))))
-  (? chi *tc*)
-  (check-rdct)
-  (setf *tc* (cmbn 4 1 (tnpr 3 (gbar 3 0 '(1 10) 0 '(100) 0 '())
-                             1 '(1000))))
-  (? chi *tc*)
-  (check-rdct)
-  (setf *tc* (cmbn 4 1 (tnpr 4 (gbar 4 0 '(1 10 100)
-                                       0 '(1000 10000)
-                                       0 '(100000)
-                                       0 '())
-                              0 '())))
-  (? chi *tc*)
-  (check-rdct)
-|#
\ No newline at end of file
diff --git a/archive/Kenzo-2/Kenzo-2-Acl5/delta.cl b/archive/Kenzo-2/Kenzo-2-Acl5/delta.cl
deleted file mode 100644
index c8cdd99..0000000
--- a/archive/Kenzo-2/Kenzo-2-Acl5/delta.cl
+++ /dev/null
@@ -1,408 +0,0 @@
-;;;  DELTA  DELTA  DELTA  DELTA  DELTA  DELTA  DELTA  DELTA  DELTA
-;;;  DELTA  DELTA  DELTA  DELTA  DELTA  DELTA  DELTA  DELTA  DELTA
-;;;  DELTA  DELTA  DELTA  DELTA  DELTA  DELTA  DELTA  DELTA  DELTA
-
-(IN-PACKAGE "CAT")
-
-(PROVIDE "delta")
-
-(DEFMETHOD PRINT-KEYCONS ((car (eql :delt)) cdr stream)
-   (format stream "~A" (hyphenize-list (dlop-int-ext cdr)))
-   (cons car cdr))
-
-(DEFUN SOFT-DELTA-CMPR (gmsm1 gmsm2)
-   (f-cmpr (cdr gmsm1) (cdr gmsm2)))
-
-#|
-  (soft-delta-cmpr (d 12) (d 23))
-|#
-   
-(DEFUN DELTA-FACE (indx dmns gmsm)
-   (declare
-      (fixnum indx gmsm)
-      (ignore dmns))
-   (the absm
-      (do ((pmark 1 (ash pmark 1))
-           (bmark indx)
-           (gmsm2 gmsm (ash gmsm2 -1)))
-          (nil)
-         (declare (fixnum pmark bmark gmsm2))
-         (when (oddp gmsm2)
-            (when (minusp (decf bmark))
-               (return-from delta-face (absm 0 (logxor gmsm pmark))))))))
-
-(DEFUN SOFT-DELTA-FACE (indx dmns gmsm)
-   (declare
-      (fixnum indx dmns)
-      (type soft-dlop gmsm))
-   (absm 0 (d (gmsm (delta-face indx dmns (cdr gmsm))))))
-
-#|
-  (dotimes (i 4)
-     (print (dlop-int-ext (gmsm (delta-face i 3 (dlop-ext-int '(0 1 2 3)))))))
-  (dotimes (i 4)
-     (print (dlop-int-ext (gmsm (delta-face i 3 (dlop-ext-int '(0 2 4 6))))))))
-  (dotimes (i 4)
-     (print (soft-delta-face i 3 (d (mask 4)))))
-  (dotimes (i 4)
-     (print (soft-delta-face i 3 (d (dlop-ext-int '(0 2 4 6))))))
-|#
-
-(DEFUN DELTA-dffr (dmns gmsm)
-   (declare (fixnum dmns gmsm))
-   (the cmbn
-      (if (zerop dmns)
-         +zero-negative-cmbn+
-         (make-cmbn
-            :degr (1- dmns)
-            :list (do ((rslt +empty-list+)
-                      (gmsm2 gmsm (ash gmsm2 -1))
-                      (pmark 1 (ash pmark +1))
-                      (sign 1))
-                     ((zerop gmsm2) rslt)
-                    (declare
-                       (list rslt)
-                       (fixnum gmsm2 pmark sign))
-                    (when (oddp gmsm2)
-                       (push (term sign (logxor gmsm pmark)) rslt)
-                       (setf sign (- sign))))))))
-
-(DEFUN SOFT-DELTA-dffr (dmns gmsm)
-   (declare
-      (fixnum dmns)
-      (type soft-dlop gmsm))
-   (make-cmbn
-      :degr (1- dmns)
-      :list (mapcar #'(lambda (term)
-                         (with-term (cffc gmsm) term
-                            (term cffc (d gmsm))))
-               (cmbn-list (delta-dffr dmns (cdr gmsm))))))
-
-#|
-  (delta-dffr 0 4)
-  (delta-dffr 1 3)
-  (delta-dffr 1 5)
-  (delta-dffr 1 10)
-  (delta-dffr 5 63)
-  (soft-delta-dffr 5 (d (mask 6)))
-|#
-
-
-(DEFUN DELTA-CPRD (dmns gmsm)
-   (declare (fixnum dmns gmsm))
-   (the cmbn
-      (make-cmbn
-         :degr dmns
-         :list (do ((rslt +empty-list+)
-                    (ldegr dmns)
-                    (indx (1- (integer-length gmsm)) (1- indx)))
-                   ((minusp indx))
-                  (declare
-                     (list rslt)
-                     (fixnum indx))
-                  (when (logbitp indx gmsm)
-                     (push (term 1 (tnpr
-                                    ldegr (logand gmsm (mask (1+ indx)))
-                                    (- dmns ldegr) (logandc2 gmsm (mask indx))))
-                        rslt)
-                     (when (minusp (decf ldegr))
-                        (return rslt)))))))
-
-(DEFUN SOFT-DELTA-CPRD (dmns gmsm)
-   (declare
-      (fixnum dmns)
-      (type soft-dlop gmsm))
-   (make-cmbn :degr dmns
-      :list (mapcar
-               #'(lambda (term)
-                    (with-term (cffc tnpr) term
-                       (with-tnpr (degr1 gmsm1 degr2 gmsm2) tnpr
-                          (term cffc
-                             (tnpr degr1 (d gmsm1) degr2 (d gmsm2))))))
-               (cmbn-list (delta-cprd dmns (cdr gmsm))))))
-
-#|
-  (delta-cprd 3 15)
-  (delta-cprd 3 170)
-  (soft-delta-cprd 3 (d (dlop-ext-int '(1 3 5 7))))
-  (delta-cprd 0 64)
-|#
-                                        
-(DEFUN DELTA-INFINITY ()
-  (the simplicial-set
-    (simplicial-set
-     :cmpr #'f-cmpr
-     :basis :locally-effective
-     :bsgn 1
-     :face #'delta-face
-     :cprd-intr #'delta-cprd
-     :cprd-strt :gnrt
-     :dffr-intr #'delta-dffr
-     :dffr-strt :gnrt
-     :dfnt '(delta-infinity))))
-
-#|
-  (cmpr (delta-infinity) 2 4)
-  (cmpr (delta-infinity) 4 4)
-  (cmpr (delta-infinity) 8 4)
-  (basis (delta-infinity) 1)   ;;; => error
-  (face (delta-infinity) 1 2 21)
-  (cprd (delta-infinity) 3 15)
-  (cprd (delta-infinity) 3 15)
-  (? (delta-infinity) 2 21))
-|#
-
-(DEFUN SOFT-DELTA-INFINITY ()
-  (the simplicial-set
-    (simplicial-set
-     :cmpr #'soft-delta-cmpr
-     :basis :locally-effective
-     :bsgn (d 1)
-     :face #'soft-delta-face
-     :cprd-intr #'soft-delta-cprd :cprd-strt :gnrt
-     :dffr-intr #'soft-delta-dffr :dffr-strt :gnrt
-     :dfnt '(soft-delta-infinity))))
-
-#|
-  (cat-init)
-  (cmpr (soft-delta-infinity) (d 2) (d 4))
-  (face (soft-delta-infinity) 1 2 (d (dlop-ext-int '(1 3 5))))
-  (cprd (soft-delta-infinity) 3 (d 15))
-  (cprd (soft-delta-infinity) 3 (d 15))
-  (? (soft-delta-infinity) 2 (d (dlop-ext-int '(0 2 4))))
-|#
-
-(DEFUN DELTA-N-BASIS (n)
-   (declare (fixnum n dmns))
-   (flet ((rslt (dmns)
-             (when (> dmns n)
-                (return-from rslt +empty-list+))
-             (setf dmns (1+ dmns))
-             (do ((rslt +empty-list+)
-                  (count (binomial-n-p (1+ n) dmns))
-                  (gmsm (mask (1+ n)) (1- gmsm)))
-                 ((zerop count) rslt)
-                (when (= (logcount gmsm) dmns)
-                   (push gmsm rslt)
-                   (decf count)))))
-      (the basis #'rslt)))
-
-(DEFUN SOFT-DELTA-N-BASIS (n)
-   (declare (fixnum n))
-   (flet ((rslt (dmns)
-             (when (> dmns n)
-                (return-from rslt +empty-list+))
-             (setf dmns (1+ dmns))
-             (do ((rslt +empty-list+)
-                  (count (binomial-n-p (1+ n) dmns))
-                  (gmsm (mask (1+ n)) (1- gmsm)))
-                 ((zerop count) rslt)
-                (when (= (logcount gmsm) dmns)
-                   (push (d gmsm) rslt)
-                   (decf count)))))
-      (the basis #'rslt)))
-      
-
-#|
-  (setf basis (delta-n-basis 3))
-  (setf soft-basis (soft-delta-n-basis 3))
-  (dotimes (i 5)
-     (print (funcall basis i)))
-  (dotimes (i 5)
-     (print (funcall soft-basis i)))))
-|#   
-
-(DEFUN DELTA (dmns)
-  (declare (fixnum dmns))
-  (the simplicial-set
-    (simplicial-set
-     :cmpr #'f-cmpr
-     :basis (delta-n-basis dmns)
-     :bsgn 1
-     :face #'delta-face
-     :cprd-intr #'delta-cprd
-     :cprd-strt :gnrt
-     :dffr-intr #'delta-dffr
-     :dffr-strt :gnrt
-     :dfnt `(delta ,dmns))))
-
-#|
-  (cat-init)
-  (setf d3 (delta 3))
-  (cmpr d3 2 4)
-  (cmpr d3 4 4)
-  (cmpr d3 8 4)
-  (basis d3 1)
-  (cprd d3 3 15)
-  (face d3 1 2 21)
-  (? d3 2 13)
-  (setf d (delta-infinity))
-  (basis d)
-  (setf d (delta-infinity)))
-|#
-
-(DEFUN SOFT-DELTA (dmns)
-  (declare (fixnum dmns))
-  (the simplicial-set
-    (simplicial-set
-     :cmpr #'soft-delta-cmpr
-     :basis (soft-delta-n-basis dmns)
-     :bsgn (d 1)
-     :face #'soft-delta-face
-     :cprd-intr #'soft-delta-cprd :cprd-strt :gnrt
-     :dffr-intr #'soft-delta-dffr :dffr-strt :gnrt
-     :dfnt `(soft-delta ,dmns))))
-      
-#|
-  (cat-init)
-  (setf d3 (soft-delta 3))
-  (cmpr d3 (d 2) (d 4))
-  (basis d3 1)
-  (cprd d3 3 (d 15))
-  (face d3 1 2 (d 21))
-  (? d3 2 (d 13))
-|#
-
-#| For comparison with EAT.
-   In 
-  (setf delta (delta-infinity))
-  (setf d (dffr delta))
-  (setf s14 (mask 15))
-  (cmbn-? d (gnrt-? d 14 s14))
-  (defun t1 (n)
-     (time (dotimes (i n) (cmbn-? d (gnrt-? d 14 s14)))))
-  (compile 't1)
-  (t1 500)
-  (setf +too-much-time+ -1)
-  (t1 500)
-|#
-#|
-  In EAT:
-  (setf delta *delta*)
-  (setf d (cc-d (ss-cc delta)))
-  (setf s14 (<a-b> 0 14))
-  (??? d (? d 14 s14))
-  (defun t1 (n)
-     (time (dotimes (i n) (??? d (? d 14 s14)))))
-  (compile 't1)
-  (t1 500)
-|#
-
-(DEFUN DELTAB-CMPR (gmsm1 gmsm2)
-   (declare (fixnum gmsm1 gmsm2))
-   (if (= 1 (logcount gmsm1))
-      :equal
-      (f-cmpr gmsm1 gmsm2)))
-
-(DEFUN DELTAB-dffr (dmns gmsm)
-   (declare (fixnum dmns gmsm))
-   (the cmbn
-      (if (< dmns 2)
-         (zero-cmbn (1- dmns))
-         (make-cmbn
-            :degr (1- dmns)
-            :list (do ((rslt +empty-list+)
-                      (gmsm2 gmsm (ash gmsm2 -1))
-                      (pmark 1 (ash pmark +1))
-                      (sign 1))
-                     ((zerop gmsm2) rslt)
-                    (declare
-                       (list rslt)
-                       (fixnum gmsm2 pmark sign))
-                    (when (oddp gmsm2)
-                       (push (term sign (logxor gmsm pmark)) rslt)
-                       (setf sign (- sign))))))))
-
-(DEFUN DELTAB2-FACE (indx dmns gmsm)
-   (declare
-      (fixnum indx dmns gmsm))
-   (the absm
-      (progn
-	(when (= 2 dmns)
-	   (return-from deltab2-face (absm 1 1)))
-	(do ((pmark 1 (ash pmark 1))
-	     (bmark indx)
-	     (gmsm2 gmsm (ash gmsm2 -1)))
-	    (nil)
-	    (declare (fixnum pmark bmark gmsm2))
-	    (when (oddp gmsm2)
-		  (when (minusp (decf bmark))
-			(return-from deltab2-face (absm 0 (logxor gmsm pmark)))))))))
-
-(DEFUN DELTAB2-cprd (dmns gmsm)
-   (declare (fixnum dmns gmsm))
-   (the cmbn
-      (make-cmbn
-         :degr dmns
-         :list (if (zerop dmns)
-		   (list (term 1 (tnpr 0 gmsm 0 gmsm)))
-		 (do ((rslt +empty-list+)
-		      (ldegr dmns)
-		      (indx (1- (integer-length gmsm)) (1- indx)))
-		     ((minusp indx))
-		     (declare
-		      (list rslt)
-		      (fixnum indx))
-		     (when (logbitp indx gmsm)
-			   (push (term 1 (tnpr
-					  ldegr (logand gmsm (mask (1+ indx)))
-					  (- dmns ldegr) (logandc2 gmsm (mask indx))))
-				 rslt)
-			   (when (minusp (decf ldegr))
-			      (setf rslt (delete 1 rslt :key #'caaddr))
-			      (setf (gnrt1 (gnrt (first rslt)))
-				    (setf (gnrt2 (gnrt (car (last rslt))))
-					  1))				    
-			      (return (delete 1 rslt :key #'cadddr)))))))))
-
-#|
-  (dotimes (i 7)
-    (print (deltab2-cprd i (mask (1+ i)))))
-|#
-  
-
-(DEFUN DELTAB2-dffr (dmns gmsm)
-   (declare (fixnum dmns gmsm))
-   (the cmbn
-      (if (< dmns 3)
-         (zero-cmbn (1- dmns))
-         (make-cmbn
-            :degr (1- dmns)
-            :list (do ((rslt +empty-list+)
-                      (gmsm2 gmsm (ash gmsm2 -1))
-                      (pmark 1 (ash pmark +1))
-                      (sign 1))
-                     ((zerop gmsm2) rslt)
-                    (declare
-                       (list rslt)
-                       (fixnum gmsm2 pmark sign))
-                    (when (oddp gmsm2)
-                       (push (term sign (logxor gmsm pmark)) rslt)
-                       (setf sign (- sign))))))))
-
-#|
-  (deltab-dffr 1 5)
-  (deltab-dffr 3 15)
-|#
-
-(DEFUN DELTAB ()
-  (the simplicial-set
-    (simplicial-set
-     :cmpr #'deltab-cmpr
-     :basis :locally-effective
-     :bsgn 1
-     :face #'delta-face
-     :cprd-intr #'delta-cprd
-     :cprd-strt :gnrt
-     :dfnt '(deltab))))
-
-(DEFUN DELTAB2 ()
-  (the simplicial-set
-    (simplicial-set
-     :cmpr #'f-cmpr
-     :basis :locally-effective
-     :bsgn 1
-     :face #'deltab2-face
-     :cprd-intr #'deltab2-cprd
-     :cprd-strt :gnrt
-     :dfnt '(deltab2))))
diff --git a/archive/Kenzo-2/Kenzo-2-Acl5/disk-pasting.cl b/archive/Kenzo-2/Kenzo-2-Acl5/disk-pasting.cl
deleted file mode 100644
index d6fd1aa..0000000
--- a/archive/Kenzo-2/Kenzo-2-Acl5/disk-pasting.cl
+++ /dev/null
@@ -1,399 +0,0 @@
-;;;  DISK-PASTING  DISK-PASTING  DISK-PASTING  DISK-PASTING
-;;;  DISK-PASTING  DISK-PASTING  DISK-PASTING  DISK-PASTING
-;;;  DISK-PASTING  DISK-PASTING  DISK-PASTING  DISK-PASTING
-
-(IN-PACKAGE "CAT")
-
-(provide "disk-pasting")
-
-(DEFUN DISK-PASTING-CMPR (cmpr new)
-  (declare
-    (type cmprf cmpr)
-    (symbol new))
-  (flet ((rslt (gnrt1 gnrt2)
-	   (declare (type gnrt gnrt1 gnrt2))
-	   (if (eq gnrt1 new)
-	       (if (eq gnrt2 new)
-		   :equal
-		 :less)
-	     (if (eq gnrt2 new)
-		 :greater
-	       (funcall cmpr gnrt1 gnrt2)))))
-    (the cmprf #'rslt)))
-
-#|
-  (setf c (delta 3))
-  (setf cmpr (disk-pasting-cmpr (cmpr c) 'new))
-  (funcall cmpr 'new 'new)
-  (funcall cmpr 'new 5)
-  (funcall cmpr 5 'new)
-  (funcall cmpr 5 5)
-  (funcall cmpr 5 6)
-  (funcall cmpr 6 5)
-|#
-
-(DEFUN DISK-PASTING-BASIS (basis dmns new)
-  (declare
-    (type basis basis)
-    (fixnum dmns)
-    (symbol new))
-  (flet ((rslt (degr)
-	   (declare (fixnum degr))
-	   (if (= degr dmns)
-	       (cons new (funcall basis dmns))
-	     (funcall basis degr))))
-    (the basis #'rslt)))
-
-#|
-  (setf c (delta 3))
-  (setf basis (disk-pasting-basis (basis c) 3 'new))
-  (funcall basis 3)
-  (funcall basis 2)
-|#
-
-(DEFUN DISK-PASTING-DFFR-INTR (old-dffr degr new dffr)
-  (declare
-    (type morphism old-dffr)
-    (fixnum degr)
-    (symbol new)
-    (type cmbn dffr))
-  (when (cddr (cmbn-? old-dffr dffr))
-    (error "In CHCM-DISK-PASTING, the given boundary has a non-null boundary."))
-  (let ((cmpr (cmpr (trgt old-dffr))))
-    (declare (type cmprf cmpr))
-    (flet ((rslt (cmbn)
-	     (declare (type cmbn cmbn))
-	     (with-cmbn (degr2 list) cmbn
-	       (unless (= degr degr2)
-		 (return-from rslt
-		   (cmbn-? old-dffr cmbn)))
-	       (unless list
-		 (return-from rslt
-		   (zero-cmbn (1- degr))))
-	       (unless (eq (-gnrt list) new)
-		 (return-from rslt
-		   (cmbn-? old-dffr cmbn)))
-	       (2cmbn-add cmpr
-		 (n-cmbn (-cffc list) dffr)
-		 (cmbn-? old-dffr
-			 (make-cmbn :degr degr
-				    :list (rest list)))))))
-      (the intr #'rslt))))
-
-#|
-  (cat-init)
-  (setf c (delta 3))
-  (setf intr (disk-pasting-dffr-intr (dffr c) 3 'new (cmbn 2 1 7)))
-  (setf intr (disk-pasting-dffr-intr (dffr c) 3 'new (? c 3 15)))
-  (funcall intr (cmbn 2 1 7))
-  (funcall intr (cmbn 3))
-  (funcall intr (cmbn 3 1 15))
-  (funcall intr (cmbn 3 1 'new 1 15))
-  (funcall intr (cmbn 3 1 'new -1 15))
-  (funcall intr (cmbn 3 -1 'new 1 15))
-  (funcall intr (cmbn 3 -1 'new -1 15))
-|#
- 
-(DEFUN CHCM-DISK-PASTING (chcm dmns new new-dffr)
-  (declare
-    (type chain-complex chcm)
-    (fixnum dmns)
-    (symbol new)
-    (type cmbn new-dffr))
-  (the chain-complex
-    (with-slots (cmpr basis dffr) chcm
-      (declare
-        (type cmprf cmpr)
-	(type basis basis)
-	(type gnrt bsgn)
-	(type morphism dffr))
-      (let ((rslt (chain-complex
-		   :cmpr (disk-pasting-cmpr cmpr new)
-		   :basis (disk-pasting-basis basis dmns new)
-		   :dffr-intr (disk-pasting-dffr-intr dffr dmns new new-dffr)
-		   :dffr-strt :cmbn
-		   :dfnt `(chcm-disk-pasting ,chcm ,dmns ,new ,new-dffr))))
-	(declare (type chain-complex rslt))
-	(when (slot-boundp chcm 'bsgn)
-	  (setf (slot-value rslt 'bsgn) (slot-value chcm 'bsgn)))
-	rslt))))
-
-#|
-  (setf c (delta 3))
-  (setf s3 (chcm-disk-pasting c 3 'new (? c 3 15)))
-  (homology s3 0 5))
-|#
-
-(DEFUN DISK-PASTING-FACE (cmpr face dmns new faces)
-  (declare
-    (type cmprf cmpr)
-    (type face face)
-    (fixnum dmns)
-    (symbol new)
-    (list faces))
-  (unless (= (1+ dmns) (length faces))
-    (error "In DISK-PASTING, non-coherent arguments."))
-  (mapl #'(lambda (mark)
-	    (declare (list mark))
-	    (unless (typep (car mark) 'absm)
-	      (setf (car mark) (absm 0 (car mark)))))
-	faces)
-  (flet ((rslt (indx dmns2 gmsm)
-	   (declare
-	     (fixnum indx dmns2)
-	     (type gmsm gmsm))
-	   (unless (= dmns dmns2)
-	     (return-from rslt
-	       (funcall face indx dmns2 gmsm)))
-	   (if (eq gmsm new)
-	       (nth indx faces)
-	     (funcall face indx dmns gmsm))))
-    (unless (check-faces cmpr #'rslt dmns new)
-      (error "The new simplicial-set is not constructed."))
-    (the face #'rslt)))
-
-#|
-  (cat-init)
-  (setf c (delta 3))
-  (setf face (disk-pasting-face (cmpr c) (face c)
-                3 'new (list 14 (absm 0 13) 11 7)))
-  (funcall face 0 2 7)
-  (funcall face 0 3 15)
-  (dotimes (i 4) (print (funcall face i 3 'new)))
-|#
-
-(DEFUN DISK-PASTING (smst dmns new faces)
-  (declare
-   (type simplicial-set smst)
-   (fixnum dmns)
-   (symbol new)
-   (list faces))
-  (the simplicial-set
-    (with-slots (cmpr basis bsgn face dffr) smst
-      (declare
-       (type cmprf cmpr)
-       (type basis basis)
-       (type gmsm bsgn)
-       (type face face)
-       (type morphism dffr))
-      (let ((new-face (disk-pasting-face (cmpr smst) face
-                                         dmns new faces))
-            (new-dffr (zero-cmbn (1- dmns))))
-        (declare
-         (type face new-face)
-         (type cmbn new-dffr))
-        (do ((mark faces (cdr mark))
-             (sign 1 (- sign)))
-            ((endp mark))
-          (declare
-           (list mark)
-           (fixnum sign))
-          (let ((absm (car mark)))
-            (declare (type absm absm))
-            (with-absm (dgop gmsm) absm
-                       (unless (plusp dgop)
-                         (dstr-add-term-to-cmbn cmpr sign gmsm new-dffr)))))
-        (simplicial-set
-         :cmpr (disk-pasting-cmpr cmpr new)
-         :basis (disk-pasting-basis basis dmns new)
-         :bsgn bsgn
-         :face new-face
-         :dffr-intr (disk-pasting-dffr-intr dffr dmns new new-dffr)
-         :dffr-strt :cmbn
-         :dfnt `(disk-pasting ,smst ,dmns ,new ,faces))))))
-
-#|
-  (setf d2 (delta 2))
-  (setf s2 (disk-pasting d2 2 'new '(6 5 3)))
-  (homology s2 0 4)
-  (setf s2xs2 (crts-prdc s2 s2))
-  (homology s2xs2 0 6)
-|#
-
-(DEFUN MRPH-DISK-PASTING-INTR (mrph trgt-cmpr dmns new new-im)
-  (declare
-    (type morphism mrph)
-    (type cmprf trgt-cmpr)
-    (fixnum dmns)
-    (symbol new)
-    (type cmbn new-im))
-  (let ((mrph-degr (degr mrph)))
-    (declare (fixnum mrph-degr))
-    (flet ((rslt (cmbn)
-	     (declare (type cmbn cmbn))
-	     (with-cmbn (degr list) cmbn
-	       (unless (= degr dmns)
-		 (return-from rslt
-		   (cmbn-? mrph cmbn)))
-	       (unless list
-		 (return-from rslt
-		   (zero-cmbn (+ degr mrph-degr))))
-	       (unless (eq new (-gnrt list))
-		 (return-from rslt
-		   (cmbn-? mrph cmbn)))
-	       (2cmbn-add trgt-cmpr
-		 (n-cmbn (-cffc list) new-im)
-		 (cmbn-? mrph
-			 (make-cmbn :degr degr
-				    :list (rest list)))))))
-      (the intr #'rslt))))
-
-#|
-  (setf m (idnt-mrph (delta 3)))
-  (setf intr
-        (mrph-disk-pasting-intr m (cmpr (delta 3))
-                                3 'new (cmbn 3 -1 15)))
-  (funcall intr (cmbn 2 3 7))
-  (funcall intr (cmbn 3))
-  (funcall intr (cmbn 3 4 15))
-  (funcall intr (cmbn 3 1 'new 1 15))
-  (funcall intr (cmbn 3 -1 'new 1 15))
-|#
-
-(DEFUN MRPH-DISK-PASTING (mrph new-sorc new-trgt dmns new new-im)
-  (declare
-    (type morphism mrph)
-    (type chain-complex new-sorc new-trgt)
-    (fixnum dmns)
-    (symbol new)
-    (type cmbn new-im))
-  (the morphism
-    (morphism
-      :sorc new-sorc :trgt new-trgt :degr (degr mrph)
-      :intr (mrph-disk-pasting-intr mrph (cmpr new-trgt)
-				    dmns new new-im)
-      :strt :cmbn
-      :dfnt `(mrph-disk-pasting ,mrph ,new-sorc ,new-trgt
-				,dmns ,new ,new-im))))
-
-#|
-  (setf d (delta 3))
-  (setf m (idnt-mrph d))
-  (setf sorc (chcm-disk-pasting d 3 'new (? d 3 15)))
-  (setf nm (mrph-disk-pasting m sorc sorc 3 'new (cmbn 3 1 'new)))
-  (? nm (cmbn 3 2 'new 3 15))
-|#
-
-(DEFUN EQVL-DISK-PASTING (eqvl dmns new dffr &key new-lbcc)
-  (declare
-   (type equivalence eqvl)
-   (fixnum dmns)
-   (symbol new)
-   (type cmbn dffr)
-   (type (or null chain-complex) new-lbcc))
-  (let* ((lg (lg eqvl))
-         (rf (rf eqvl))
-         (rh (rh eqvl))
-         (t-dffr (cmbn-? lg dffr))
-         (rb-dffr (cmbn-? rf t-dffr))
-         (new-lbcc (or new-lbcc
-                       (chcm-disk-pasting (lbcc eqvl)
-                                          dmns new dffr)))
-         (new-tcc (chcm-disk-pasting (tcc eqvl)
-                                     dmns new t-dffr))
-         (new-rbcc (chcm-disk-pasting (rbcc eqvl)
-                                      dmns new rb-dffr))
-         (1+dmns (1+ dmns)))
-    (declare
-     (type morphism lg rf rh)
-     (type cmbn t-dffr rb-dffr)
-     (type chain-complex new-lbcc new-tcc new-rbcc)
-     (fixnum 1+dmns))
-    (equivalence
-     :lrdct (reduction
-             :f (mrph-disk-pasting (lf eqvl) new-tcc new-lbcc
-                                   dmns new (cmbn dmns 1 new))
-             :g (mrph-disk-pasting lg new-lbcc new-tcc
-                                   dmns new (cmbn dmns 1 new))
-             :h (mrph-disk-pasting (lh eqvl) new-tcc new-tcc
-                                   dmns new (zero-cmbn 1+dmns))
-             :dfnt `(eqvl-disk-pasting ,eqvl ,dmns ,new ,dffr :lrdct))              
-     :rrdct (reduction
-             :f (mrph-disk-pasting rf new-tcc new-rbcc
-                                   dmns new (cmbn dmns 1 new))
-             :g (mrph-disk-pasting (rg eqvl) new-rbcc new-tcc
-                                   dmns new
-                                   (make-cmbn
-                                    :degr dmns
-                                    :list (cons (term 1 new)
-                                                (cmbn-list
-                                                 (cmbn-opps
-                                                  (cmbn-? rh t-dffr))))))
-             :h (mrph-disk-pasting rh new-tcc new-tcc
-                                   dmns new (zero-cmbn 1+dmns))
-             :dfnt `(eqvl-disk-pasting ,eqvl ,dmns ,new ,dffr :rrdct))
-     :dfnt `(eqvl-disk-pasting ,eqvl ,dmns ,new ,dffr))))
-				     
-#|
-(cat-init)
-(setf tcc
-      (chain-complex
-       :cmpr #'s-cmpr
-       :basis #'(lambda (degr)
-		  (case degr
-			(0 (list 'a))
-			(1 (list 'b))
-			(otherwise nil)))
-       :dffr-intr #'(lambda (degr gnrt)
-		      (if (= 1 degr)
-			  (cmbn 0 1 'a)
-			(zero-cmbn (1- degr))))
-       :dffr-strt :gnrt
-       :dfnt '(z-z)))
-(setf bcc
-      (chain-complex
-       :cmpr #'s-cmpr
-       :basis #'(lambda (degr) nil)
-       :dffr-intr #'(lambda (degr gnrt) (error "Impossible."))
-       :dffr-strt :gnrt
-       :dfnt '(zero)))
-(setf rh (morphism
-	  :sorc tcc :trgt tcc :degr +1
-	  :intr #'(lambda (degr gnrt)
-		    (if (zerop degr)
-			(cmbn 1 1 'b)
-		      (zero-cmbn 2)))
-	  :strt :gnrt
-	  :dfnt '(rh)))
-(setf eqvl (equivalence
-            :lrdct (trivial-rdct tcc)
-            :rrdct (reduction
-                    :f (zero-mrph tcc bcc 0)
-                    :g (zero-mrph bcc tcc 0)
-                    :h rh
-                    :dfnt '(rrdct))))
-(setf neqvl (eqvl-disk-pasting eqvl 1 'new (cmbn 0 1 'a)))
-(pre-check-rdct (lrdct neqvl))
-(setf *tc* (cmbn 0 1 'a))
-(setf *bc* *tc*)
-(check-rdct)
-(setf *tc* (cmbn 1 1 'new 10 'b))
-(setf *bc* *tc*)
-(check-rdct)
-(pre-check-rdct (rrdct neqvl))
-(setf *bc* (zero-cmbn 0))
-(check-rdct)
-(setf *tc* (cmbn 0 1 'a))
-(check-rdct)
-|#
-
-(DEFMETHOD SEARCH-EFHM (smst (dfnt (eql 'disk-pasting)))
-  (declare (type simplicial-set smst))
-  (the equivalence
-    (destructuring-bind (old-smst dmns new faces) (rest (dfnt smst))
-			(declare
-			  (type simplicial-set old-smst)
-			  (fixnum dmns)
-			  (symbol new)
-			  (ignore faces))
-      (eqvl-disk-pasting (efhm old-smst)
-			 dmns new (? smst dmns new)
-			 :new-lbcc smst))))
-
-#|
-(cat-init)
-(setf d (delta 2))
-(setf s2 (disk-pasting d 2 'new '(6 5
-  3)))
-(homology s2 0 4)
-|#
diff --git a/archive/Kenzo-2/Kenzo-2-Acl5/effective-homology.cl b/archive/Kenzo-2/Kenzo-2-Acl5/effective-homology.cl
deleted file mode 100644
index f491264..0000000
--- a/archive/Kenzo-2/Kenzo-2-Acl5/effective-homology.cl
+++ /dev/null
@@ -1,539 +0,0 @@
-;;;  EFFECTIVE-HOMOLOGY  EFFECTIVE-HOMOLOGY  EFFECTIVE-HOMOLOGY
-;;;  EFFECTIVE-HOMOLOGY  EFFECTIVE-HOMOLOGY  EFFECTIVE-HOMOLOGY
-;;;  EFFECTIVE-HOMOLOGY  EFFECTIVE-HOMOLOGY  EFFECTIVE-HOMOLOGY
-
-(IN-PACKAGE "CAT")
-
-(PROVIDE "effective-homology")
-
-;;;
-;;;  REDUCTIONS
-;;;
-
-(DEFMETHOD PRINT-OBJECT ((rdct reduction) (stream stream))
- (the reduction
-   (progn
-      (format stream "[K~D Reduction K~D => K~D]"
-	      (idnm rdct) (idnm (tcc rdct)) (idnm (bcc rdct)))
-      rdct)))
-
-(DEFUN REDUCTION (&rest rest &key dfnt &allow-other-keys)
-  (declare (type list dfnt))
-  (already reduction dfnt)
-  (the reduction
-    (apply #'make-instance 'reduction rest)))
-
-(DEFMETHOD SHARED-INITIALIZE
-    ((rdct reduction) slot-names &key f g h)
-  (declare
-   (type (or (eql t) list) slot-names)
-   (type morphism f g h))
-  (call-next-method)
-  (when-slot f
-             (with-slots (tcc bcc (fs f) (gs g) (hs h) dfnt) rdct
-               (declare
-                (type morphism fs gs hs)
-                (type list dfnt))
-               (when f
-                 (setf fs f tcc (sorc f) bcc (trgt f)))
-               (when g
-                 (setf gs g tcc (trgt g) bcc (sorc g)))
-               (when h
-                 (setf hs h tcc (sorc h)))
-               (when (and f g)
-                 (unless (eq (grmd (sorc f)) (grmd (trgt g)))
-                   (error "In REDUCTION ~S, (sorc f) <> (trgt g)." rdct))
-                 (unless (eq (grmd (trgt f)) (grmd (sorc g)))
-                   (error "In REDUCTION ~S, (trgt f) <> (sorc g)." rdct)))
-               (when h
-                 (unless (eq (sorc h) (trgt h))
-                   (error "In REDUCTION ~S, (sorc h) <> (trgt h)." rdct)))
-               (when (and f h)
-                 (unless (eq (grmd (sorc f)) (grmd (sorc h)))
-                   (error "In REDUCTION ~S, (sorc f) <> (sorc h)." rdct)))
-               (when (and g h)
-                 (unless (eq (grmd (trgt g)) (grmd (sorc h)))
-                   (error "In REDUCTION ~S, (trgt g) <> (sorc h)." rdct)))
-               (unless dfnt
-                 (setf dfnt `(reduction ,f ,g ,h)))))
-  rdct)
-
-(DEFUN TRIVIAL-RDCT (chcm)
-  (declare (type chain-complex chcm))
-   (reduction
-    :f (idnt-mrph chcm)
-    :g (idnt-mrph chcm)
-    :h (zero-mrph chcm chcm +1) 
-    :dfnt `(trivial-rdct ,chcm)))
-
-;;;
-;;;  EQUIVALENCES
-;;;
-
-(DEFUN EQUIVALENCE (&rest rest &key dfnt &allow-other-keys)
-  (declare (type list dfnt))
-  (already equivalence dfnt)
-  (the equivalence
-    (apply #'make-instance 'equivalence rest)))
-
-(DEFMETHOD SHARED-INITIALIZE ((eqvl equivalence) slot-names &key lrdct rrdct)
-  (declare
-   (type (or (eql t) list) slot-names)
-   (type reduction lrdct rrdct))
-  (call-next-method)
-  (when-slot lrdct
-             (with-slots ((lrdcts lrdct) (rrdcts rrdct)
-                          lbcc tcc rbcc
-                          lf lg lh rf rg rh
-                          dfnt)
-                 eqvl
-               (declare
-                (type reduction lrdcts rrdcts)
-                (type chain-complex lbcc tcc rbcc)
-                (type morphism lf lg lh rf rg rh)
-                (type list dfnt))
-               (when lrdct
-                 (setf lrdcts lrdct
-                   lf (f lrdct) lg (g lrdct) lh (h lrdct)
-                   lbcc (bcc lrdct) tcc (tcc lrdct)))
-               (when rrdct
-                 (setf rrdcts rrdct
-                   rf (f rrdct) rg (g rrdct) rh (h rrdct)
-                   tcc (tcc rrdct) rbcc (bcc rrdct)))
-               (when (and lrdct rrdct)
-                 (unless (eq (grmd (tcc lrdct)) (grmd (tcc rrdct)))
-                   (error "In EQUIVALENCE ~S, (tcc lrdct) <> (tcc rrdct)." eqvl)))
-               (unless dfnt
-                 (setf dfnt `(equivalence ,lrdct ,rrdct)))))
-  eqvl)
-
-#|
-  (cat-init)
-  (progn ;;;; reused in another test
-   (defun cdelta (dmns)
-     (chain-complex
-        :cmpr #'l-cmpr
-        :basis :locally-effective
-        :bsgn '(0)
-        :dffr-intr #'(lambda (degr gmsm)
-                        (make-cmbn
-                           :degr (1- degr)
-                           :list (do ((rslt +empty-list+
-                                           (cons (cons sign (append
-                                                               (subseq gmsm 0 nark)
-                                                               (subseq gmsm (1+ nark))))
-                                                 rslt))
-                                     (sign 1 (- sign))
-                                     (nark 0 (1+ nark)))
-                                    ((> nark degr) rslt))))                                           
-        :dffr-strt :gnrt
-        :dfnt `(locally effective version of C_* delta ,dmns)))
-   (defun make-f (tdmns bdmns)
-     (morphism
-        :sorc (cdelta tdmns) :trgt (cdelta bdmns) :degr 0
-        :intr #'(lambda (degr gmsm)
-                   (let ((pos (position-if #'(lambda (vertex) (>= vertex bdmns)) gmsm)))
-                      (if pos
-                         (if (< pos degr)
-                            (zero-cmbn degr)
-                            (cmbn degr 1 (nconc (butlast gmsm) (list bdmns))))
-                         (cmbn degr 1 gmsm))))
-        :strt :gnrt
-        :dfnt `(projection delta ,tdmns => delta ,bdmns)))
-   (defun make-g (tdmns bdmns)
-     (morphism
-        :sorc (cdelta bdmns) :trgt (cdelta tdmns) :degr 0
-        :intr #'identity
-        :strt :cmbn
-        :dfnt `(injection delta ,bdmns => delta ,tdmns)))
-   (defun make-h (tdmns bdmns)
-     (morphism
-        :sorc (cdelta tdmns) :trgt (cdelta tdmns) :degr +1
-        :intr #'(lambda (degr gmsm)
-                   (let ((pos (position-if #'(lambda (vertex) (>= vertex bdmns)) gmsm)))
-                      (if pos
-                         (if (member bdmns gmsm)
-                            (zero-cmbn (1+ degr))
-                            (cmbn (1+ degr) (-1-expt-n pos)
-                               (append (subseq gmsm 0 pos) (list bdmns) (subseq gmsm pos))))
-                         (zero-cmbn (1+ degr)))))
-        :strt :gnrt
-        :dfnt `(homotopy for delta ,tdmns => ,bdmns)))
-   (defun make-rdct (tdmns bdmns)
-       (setf rdct (reduction
-                    :f (make-f tdmns bdmns)
-                    :g (make-g tdmns bdmns)
-                    :h (make-h tdmns bdmns)
-                    :dfnt `(reduction delta ,tdmns ,bdmns)))))
-  (setf rdct (make-rdct 6 3))
-  (setf f (f rdct) g (g rdct) h (h rdct)
-        tcc (tcc rdct) bcc (bcc rdct))
-  (setf dh (cmps (dffr tcc) h))
-  (setf hd (cmps h (dffr tcc)))
-  (setf gf (cmps g f))
-  (setf id-gf-dh-hd (i-sbtr (idnt-mrph tcc) gf dh hd))
-  (setf c (cmbn 2 1 '(0 1 2) 10 '(1 2 3) 100 '(1 2 4) 1000 '(2 3 4)))
-  (cmbn-? id-gf-dh-hd c)
-|#                                   
-
-(DEFMETHOD PRINT-OBJECT ((eqvl equivalence) (stream stream))
- (the equivalence
-   (progn
-      (format stream "[K~D Equivalence K~D <= K~D => K~D]"
-	      (idnm eqvl)
-	      (idnm (lbcc eqvl)) (idnm (tcc eqvl)) (idnm (rbcc eqvl)))
-      eqvl)))
-
-(DEFUN TRIVIAL-EQVL (chcm)
-   (declare (type chain-complex chcm))
-   (equivalence
-    :lrdct (trivial-rdct chcm)
-    :rrdct (trivial-rdct chcm)
-    :dfnt `(trivial-eqvl ,chcm)))
-
-#|
-  (cat-init)
-  (setf cc (cdelta 5))
-  (setf eqvl (trivial-eqvl cc))
-|# 
-
-;; Functions.
-
-(DEFVAR *TDD*)
-(DEFVAR *BDD*)
-(DEFVAR *ID-FG*)
-(DEFVAR *ID-GF-DH-HD*)
-(DEFVAR *HH*)
-(DEFVAR *FH*)
-(DEFVAR *HG*)
-(DEFVAR *DF-FD*)
-(DEFVAR *DG-GD*)
-
-(DEFUN PRE-CHECK-RDCT (rdct)
-   (declare (type reduction rdct))
-   (with-slots (bcc tcc f g h) rdct
-      (declare
-         (type chain-complex bcc tcc)
-         (type morphism f g h))
-      (setf *tdd* (cmps tcc tcc)
-            *bdd* (cmps bcc bcc)
-            *df-fd* (sbtr
-                       (cmps bcc f)
-                       (cmps f tcc))
-            *dg-gd* (sbtr
-                       (cmps tcc g)
-                       (cmps g bcc))
-            *id-fg* (sbtr (idnt-mrph bcc) (cmps f g))
-            *id-gf-dh-hd* (i-sbtr (idnt-mrph tcc)
-                             (cmps g f)
-                             (cmps tcc h)
-                             (cmps h tcc))
-            *hh* (cmps h h)
-            *fh* (cmps f h)
-            *hg* (cmps h g)))
-   (done))
-
-(DEFVAR *TC*)
-(DEFVAR *BC*)
-
-(DEFUN CHECK-RDCT ()
-  (dolist (cmbn '(*tc* *bc*))
-    (declare (type symbol cmbn))
-    (format t "~%~A => ~A" cmbn (eval cmbn)))
-  (dolist (phi '(*tdd* *bdd* *df-fd* *dg-gd* *id-fg* *id-gf-dh-hd*
-		       *hh* *fh* *hg*))
-    (declare (type symbol phi))
-    (format t "~%Checking ~A = 0" phi)
-    (format t "~%Result: ")
-    (princ (cmbn-? (eval phi)
-              (if (member phi '(*bdd* *dg-gd* *id-fg* *dg-gd* *hg*))
-                 *bc* *tc*)))
-    (read-line))
-  (done))
-
-#|
-  (setf rdct (make-rdct 6 3))        ;;; defined in a previous test
-  (pre-check-rdct rdct)
-  (setf *tc* (cmbn 2 1 '(0 1 2) 10 '(1 2 3) 100 '(1 2 4) 1000 '(2 3 4)))
-  (setf *bc* (cmbn 3 4 '(0 1 2 3)))  
-  (check-rdct))
-|#                                   
-
-(DEFMETHOD CMPS ((brdct reduction) (trdct reduction) &optional dummy)
-  (declare (ignore dummy))
-  (when (eq (first (dfnt brdct)) 'trivial-rdct)
-     (return-from cmps trdct))
-  (when (eq (first (dfnt trdct)) 'trivial-rdct)
-     (return-from cmps brdct))
-  (with-slots ((tf f) (tg g) (th h)) trdct
-    (declare (type morphism tf tg th))
-  (with-slots ((bf f) (bg g) (bh h)) brdct
-    (declare (type morphism bf bg bh))
-    (reduction
-       :f (cmps bf tf)
-       :g (cmps tg bg)
-       :h (add th (i-cmps tg bh tf))
-       :dfnt `(cmps ,brdct ,trdct)))))
-
-#|
-  (setf trdct (make-rdct 6 4))
-  (setf brdct (make-rdct 4 3))
-  (setf rdct (cmps brdct trdct))
-  (pre-check-rdct rdct)
-  (setf *tcc* (cmbn 2 1 '(0 1 2) 10 '(1 2 3) 100 '(1 2 4)
-                      100 '(1 3 5) 10 '(1 4 5) 1 '(3 4 5))
-        *bcc* (cmbn 2 1 '(0 1 3)))
-  (check-rdct))
-|#
-
-;
-; BASIC PERTURBATION LEMMA.
-;
-
-(DEFMETHOD ADD ((rdct reduction) (perturbation morphism) &optional dummy)
-   (declare (type null dummy))
-   (when dummy
-      (error "Why a third argument in (ADD REDUCTION MORPHISM)?"))
-   (when (eq (grmd (tcc rdct)) (grmd (sorc perturbation)))
-      (return-from add
-         (basic-perturbation-lemma rdct perturbation)))
-   (when (eq (grmd (bcc rdct)) (grmd (sorc perturbation)))
-      (return-from add
-         (easy-perturbation-lemma rdct perturbation)))
-   (error "In (METHOD ADD REDUCTION MORPHISM),~@
-           the data do not sound like coherent."))
-
-(DEFUN BASIC-PERTURBATION-LEMMA (reduction top-perturbation)
-   (declare
-      (type reduction reduction)
-      (type morphism top-perturbation))
-   (the (values reduction morphism)
-      (with-slots ((old-tcc tcc) (old-bcc bcc)
-                   (old-f f) (old-g g) (old-h h)) reduction
-         (declare
-            (type chain-complex old-tcc old-bcc)
-            (type morphism old-f old-g old-h))
-         (when (eq (first (dfnt top-perturbation)) 'zero-mrph)
-            (return-from basic-perturbation-lemma
-               (values reduction (zero-mrph old-bcc))))
-         (when (eq (first (dfnt (h reduction))) 'zero-mrph)
-            (return-from basic-perturbation-lemma
-               (values
-                  (trivial-rdct (add old-tcc top-perturbation))
-                  (i-cmps old-f top-perturbation old-g))))      
-         (let* ((sigma (bpl-*-sigma old-h top-perturbation))
-                (new-f (cmps old-f 
-                          (sbtr (idnt-mrph old-tcc)
-                             (i-cmps
-                                top-perturbation
-                                sigma
-                                old-h))))
-                (new-g (cmps sigma old-g))
-                (new-h (cmps sigma old-h))
-                (bottom-perturbation (i-cmps
-                                        old-f
-                                        top-perturbation
-                                        new-g))
-                (new-tcc (add old-tcc top-perturbation))
-                (new-bcc (add old-bcc bottom-perturbation)))
-            (declare
-               (type chain-complex new-tcc new-bcc)
-               (type morphism sigma new-f new-g new-h bottom-perturbation))
-            (setf new-f (dstr-change-sorc-trgt new-f :new-sorc new-tcc :new-trgt new-bcc)
-                  new-g (dstr-change-sorc-trgt new-g :new-sorc new-bcc :new-trgt new-tcc)
-                  new-h (dstr-change-sorc-trgt new-h :new-sorc new-tcc :new-trgt new-tcc))
-            (values
-               (reduction :f new-f :g new-g :h new-h
-                  :dfnt `(basic-perturbation-lemma ,reduction ,top-perturbation))
-               bottom-perturbation)))))
-
-(DEFUN EASY-PERTURBATION-LEMMA (reduction bottom-perturbation)
-   (declare
-      (type reduction reduction)
-      (type morphism bottom-perturbation))
-   (the (values reduction morphism)
-      (with-slots ((old-tcc tcc) (old-bcc bcc)
-                   (old-f f) (old-g g) (old-h h)) reduction
-         (declare
-            (type chain-complex old-tcc old-bcc)
-            (type morphism old-f old-g old-h))
-         (when (eq 'zero-mrph (first (dfnt bottom-perturbation)))
-            (return-from easy-perturbation-lemma
-               (values reduction (zero-mrph old-tcc))))
-	 (when (eq 'trivial-rdct (first (dfnt reduction)))
-	    (return-from easy-perturbation-lemma
-	       (trivial-rdct (add (bcc reduction) bottom-perturbation))))
-         (let ((top-perturbation (i-cmps old-g bottom-perturbation old-f)))
-            (declare (type morphism top-perturbation))
-            (let ((new-bcc (add old-bcc bottom-perturbation))
-                  (new-tcc (add old-tcc top-perturbation)))
-               (declare (type chain-complex new-bcc new-tcc))
-               (values
-                  (reduction
-                     :f (dstr-change-sorc-trgt old-f :new-sorc new-tcc :new-trgt new-bcc)
-                     :g (dstr-change-sorc-trgt old-g :new-sorc new-bcc :new-trgt new-tcc)
-                     :h (dstr-change-sorc-trgt old-h :new-sorc new-tcc :new-trgt new-tcc)
-                     :dfnt `(easy-perturbation-lemma ,reduction ,bottom-perturbation))
-                  top-perturbation))))))
-
-(DEFUN SPECIAL-BPL (reduction top-perturbation)
-   (declare
-      (type reduction reduction)
-      (type morphism top-perturbation))
-   (when (eq (first (dfnt top-perturbation)) 'zero-mrph)
-      (return-from special-bpl reduction))
-   (the reduction
-      (with-slots ((old-tcc tcc) (old-bcc bcc)
-                   (old-f f) (old-g g) (old-h h)) reduction
-         (declare
-            (type chain-complex old-tcc old-bcc)
-            (type morphism old-f old-g old-h))
-         (let* ((sigma (bpl-*-sigma old-h top-perturbation))
-                (new-f (cmps old-f 
-                          (sbtr (idnt-mrph old-tcc)
-                             (i-cmps
-                                top-perturbation
-                                sigma
-                                old-h))))
-                (new-h (cmps sigma old-h))
-                (new-tcc (add old-tcc top-perturbation)))
-            (declare
-               (type chain-complex new-tcc)
-               (type morphism sigma new-f new-h))
-            (setf new-f (dstr-change-sorc-trgt new-f :new-sorc new-tcc)
-                  old-g (dstr-change-sorc-trgt old-g :new-trgt new-tcc)
-                  new-h (dstr-change-sorc-trgt new-h :new-sorc new-tcc :new-trgt new-tcc))
-            (reduction :f new-f :g old-g :h new-h
-               :dfnt `(special-bpl ,reduction ,top-perturbation))))))
-
-(DEFUN SPECIAL-BPL-2 (reduction top-perturbation)
-   (declare
-      (type reduction reduction)
-      (type morphism top-perturbation))
-   (the reduction
-      (with-slots ((old-tcc tcc) (old-bcc bcc)
-                   (old-f f) (old-g g) (old-h h)) reduction
-         (declare
-            (type chain-complex old-tcc old-bcc)
-            (type morphism old-f old-g old-h))
-         (when (eq (first (dfnt top-perturbation)) 'zero-mrph)
-            (return-from special-bpl-2
-               (values reduction (zero-mrph old-bcc))))
-         (when (eq (first (dfnt (h reduction))) 'zero-mrph)
-            (return-from special-bpl-2
-               (values
-                  (trivial-rdct (add old-tcc top-perturbation))
-                  (i-cmps old-f top-perturbation old-g))))      
-         (let* ((sigma (bpl-*-sigma old-h top-perturbation))
-                (new-g (cmps sigma old-g))
-                (new-h (cmps sigma old-h))
-                (new-tcc (add old-tcc top-perturbation)))
-            (declare
-               (type chain-complex new-tcc)
-               (type morphism sigma new-g new-h))
-            (setf old-f (dstr-change-sorc-trgt old-f :new-sorc new-tcc)
-		  new-g (dstr-change-sorc-trgt new-g :new-trgt new-tcc)
-                  new-h (dstr-change-sorc-trgt new-h :new-sorc new-tcc :new-trgt new-tcc))
-            (values
-               (reduction :f old-f :g new-g :h new-h
-                  :dfnt `(special-bpl-2 ,reduction ,top-perturbation)))))))
-
-(DEFUN BPL-*-sigma (homotopy perturbation)
-   (declare (type morphism homotopy perturbation))
-   (the morphism
-      (let ((cmpr (cmpr (sorc perturbation)))
-            (h-delta (cmps homotopy perturbation)))
-         (declare
-            (type cmprf cmpr)
-            (type morphism h-delta))
-         (flet
-            ((sigma-* (degr gnrt)
-                (declare
-                   (fixnum degr)
-                   (type gnrt gnrt))
-                (do ((rslt (zero-cmbn degr) (2cmbn-add cmpr rslt iterated))
-                     (iterated (term-cmbn degr 1 gnrt) (cmbn-opps (cmbn-? h-delta iterated))))
-                    ((cmbn-zero-p iterated) rslt)
-                   (declare (type cmbn rslt iterated)))))
-            (morphism
-               :sorc (sorc homotopy) :trgt (sorc homotopy) :degr 0
-               :intr #'sigma-*
-               :strt :gnrt
-               :dfnt `(bpl-*-sigma ,homotopy ,perturbation))))))
-     
-#|
-  (cat-init)
-  (setf rdct (make-rdct 6 3))
-  (setf perturb (zero-mrph (cdelta 6) (cdelta 6) -1))
-  (setf new-rdct (add rdct perturb))
-  (pre-check-rdct new-rdct)
-  (setf *tc* (cmbn 2 3 '(0 1 2))
-        *bc* (cmbn 3 4 '(0 1 2 3)))
-  (check-rdct))
-|#
-
-#|
-  (cat-init)
-  (setf rdct (make-rdct 6 3))
-  (setf perturb (opps (dffr (tcc rdct))))
-  (setf new-rdct (add rdct perturb))
-  (pre-check-rdct new-rdct)
-  (setf *tc* (cmbn 2 3 '(0 1 2))
-        *bc* (cmbn 3 4 '(0 1 2 3)))
-  (check-rdct))
-|#
-
-#|  ;; an absurd reduction ; just to test bpl-*-sigma
-  (cat-init)
-  (setf tcc (chain-complex
-               :cmpr #'l-cmpr
-               :basis :locally-effective
-               :bsgn '(0)
-               :dffr-intr #'(lambda (degr gnrt)
-                               (cmbn (1- degr) 1 gnrt))
-               :dffr-strt :gnrt
-               :dfnt '(test1)))
-  (setf rdct (trivial-rdct tcc))
-  (setf (slot-value rdct 'h)
-        (morphism
-           :sorc tcc :trgt tcc :degr +1
-           :intr #'(lambda (degr gnrt)
-                      (cmbn (1+ degr) 1 gnrt))
-           :strt :gnrt
-           :dfnt '(test2)))
-  (setf perturb
-        (morphism
-           :sorc tcc :trgt tcc :degr -1
-           :intr #'(lambda (degr gnrt)
-                      (if (zerop (first gnrt))
-                         (zero-cmbn (1- degr))   
-                         (cmbn (1- degr) 1 (list (1- (first gnrt)) (1+ (second gnrt))))))
-           :strt :gnrt
-           :dfnt '(test3)))
-  (setf new-rdct (add rdct perturb))
-  (gnrt-? (dffr (tcc new-rdct)) 3 '(3 5))
-  (gnrt-? (dffr (bcc new-rdct)) 3 '(3 5))
-|#
-
-(DEFMETHOD ADD ((eqvl equivalence) (lb-perturbation morphism) &optional dummy)
-  (declare (ignore dummy))
-  (the equivalence
-    (with-slots (lrdct rrdct) eqvl
-      (declare (type reduction lrdct rrdct))
-      (multiple-value-bind (new-lrdct top-perturbation)
-          (add lrdct lb-perturbation)
-        (declare
-         (type reduction new-lrdct)
-         (type morphism lb-perturbation))
-        (equivalence
-         :lrdct new-lrdct
-         :rrdct (add rrdct top-perturbation)
-         :dfnt `(add ,eqvl ,lb-perturbation))))))
-
-#|
-(cat-init)
-(setf eqvl (trivial-eqvl (cdelta 4)))
-(add (lrdct eqvl) (opps (dffr (cdelta 4))))
-(setf eqvl (add eqvl (opps (dffr (cdelta 4)))))
-(gnrt-? (dffr (rbcc eqvl)) 3 '(0 1 2 3)))
-|#
diff --git a/archive/Kenzo-2/Kenzo-2-Acl5/eilenberg-zilber.cl b/archive/Kenzo-2/Kenzo-2-Acl5/eilenberg-zilber.cl
deleted file mode 100644
index 39195fa..0000000
--- a/archive/Kenzo-2/Kenzo-2-Acl5/eilenberg-zilber.cl
+++ /dev/null
@@ -1,479 +0,0 @@
-;;;  EILENBERG-ZILBER  EILENBERG-ZILBER  EILENBERG-ZILBER
-;;;  EILENBERG-ZILBER  EILENBERG-ZILBER  EILENBERG-ZILBER
-;;;  EILENBERG-ZILBER  EILENBERG-ZILBER  EILENBERG-ZILBER
-
-(IN-PACKAGE "CAT")
-
-(PROVIDE "eilenberg-zilber")
-
-(DEFUN SHUFFLE-SIGN (dgop)
-   (declare (fixnum dgop))
-   (the fixnum
-      (do ((rslt +1)
-           (bit-position (- (integer-length dgop) 2) (1- bit-position))
-           (factor -1))
-          ((minusp bit-position) rslt)
-         (declare (fixnum rslt bit-position factor))
-         (if (logbitp bit-position dgop)
-            (setf factor (- factor))
-            (setf rslt (* rslt factor))))))
-
-#|
-  (dotimes (i 30)
-     (format t "~%~A => ~@D" (hyphenize-list (dlop-int-ext i)) (shuffle-sign i)))
-|#       
-
-(DEFUN INTR-EML (cmbn)
-   (declare (type cmbn cmbn))
-   (when (cmbn-zero-p cmbn)
-      (return-from intr-eml cmbn))
-   (the cmbn
-      (with-cmbn (degr list) cmbn
-         (let* ((limits (make-array (+ degr 2)))
-                (rslt (list nil))
-                (rslt-mark rslt)
-                (mask (mask degr)))
-            (declare
-               (simple-vector limits)
-               (list rslt rslt-mark)
-               (fixnum mask))
-            (do ((mark list (member i mark
-                               :test #'<
-                               :key #'(lambda (term)
-                                         (declare (type term term))
-                                         (degr1 (gnrt term)))))
-                 (i 0 (1+ i)))
-                ((> i degr) (setf (svref limits i) nil))
-               (declare
-                  (list mark)
-                  (fixnum i))
-               (setf (svref limits i) mark))
-            (dotimes (dgop1 (1+ mask))
-               (declare (fixnum dgop1))
-               (let* ((i (- degr (logcount dgop1)))
-                      (dgop2 (- mask dgop1))
-                      (sign (shuffle-sign dgop2)))
-                  (declare (fixnum i dgop2 sign))
-                  (do ((mark (svref limits i) (cdr mark))
-                       (stop (svref limits (1+ i))))
-                      ((eq mark stop))
-                     (declare (list mark stop))
-                     (with--term (cffc tnpr) mark
-                        (setf rslt-mark
-                              (setf (cdr rslt-mark)
-                                    (list (term
-                                             (* sign cffc)
-                                             (crpr
-                                                dgop1 (gnrt1 tnpr)
-                                                dgop2 (gnrt2 tnpr))))))))))
-            (make-cmbn
-               :degr degr
-               :list (rest rslt))))))
-
-#|
-  (intr-eml (cmbn 3 1 (tnpr 0 'a 3 'b) 2 (tnpr 2 'a 1 'b) 3 (tnpr 2 'aa 1 'bb) 4 (tnpr 3 'a 0 'b)))
-  (intr-eml (cmbn 3 1 (tnpr 1 'c 2 'd) 10 (tnpr 2 'a 1 'b)))
-  (intr-eml (cmbn 3 10 (tnpr 1 'c 2 'd) 1 (tnpr 2 'a 1 'b) 100 (tnpr 2 'aa 1 'bb)))
-  (intr-eml (cmbn 3 10 (tnpr 1 'c 2 'd) 100 (tnpr 1 'cc 2 'dd) 1 (tnpr 2 'a 1 'b)))
-|#
-                                                    
-(DEFUN EML (smst1 smst2)
-   (morphism
-      :sorc (tnsr-prdc smst1 smst2)
-      :trgt (crts-prdc smst1 smst2)
-      :degr 0
-      :intr #'intr-eml
-      :strt :cmbn
-      :dfnt `(eml ,smst1 ,smst2)))
-
-#|
-  (cat-init)
-  (setf d (delta-infinity))
-  (setf eml (eml d d))
-  (? eml (cmbn 3 1 (tnpr 0 1 3 30) 10 (tnpr 1 3 2 28) 100 (tnpr 2 7 1 24) 1000 (tnpr 3 15 0 16)))
-|#
-
-(DEFUN INTR-PHI (smst1 smst2
-                   &aux (crts-prdc (crts-prdc smst1 smst2))
-                        (cmpr (cmpr crts-prdc))
-                        (face1 (face smst1))
-                        (face2 (face smst2)))
-  (declare
-     (type simplicial-set smst1 smst2 crts-prdc)
-     (type cmprf cmpr)
-     (type face face1 face2))
-   (flet ((rslt (cmbn)
-             (declare (type cmbn cmbn))
-             (when (cmbn-zero-p cmbn)
-                (return-from rslt (zero-cmbn (1+ (cmbn-degr cmbn)))))
-             (the cmbn
-                (let* ((n (cmbn-degr cmbn))
-                       (n+1 (1+ n))
-                       (array-pq (make-array (list (1+ n+1) (1+ n+1)))))
-                   (declare
-                      (fixnum n n+1)
-                      (simple-array array-pq))
-                   (do ((i 1 (1+ i)))
-                       ((> i n+1))
-                      (declare (fixnum i))
-                      (do ((p i (1+ p))
-                           (q n+1 (1- q)))
-                          ((> p n+1))
-                         (declare (fixnum p q))
-                         (setf (aref array-pq p q) (zero-cmbn i))))
-                   (dolist (term (cmbn-list cmbn))
-                      (declare (type term term))
-                      (with-term (cffc crpr) term
-                         (let ((absm1 (absm1 crpr))
-                               (absm2 (absm2 crpr)))
-                            (declare (type absm absm1 absm2))
-                            (do ((n-alpha n (1- n-alpha))
-                                 (left-d absm1 (a-face4 face1 n-alpha n-alpha left-d)))
-                                ((zerop n-alpha))
-                               (declare
-                                  (fixnum n-alpha)
-                                  (type absm left-d))
-                               (do ((beta 0 (1+ beta))
-                                    (i n-alpha (1- i))  ;; pseudo-degree
-                                    (sign (-1-expt-n n-alpha) (- sign))
-                                    (right-d absm2
-                                       (a-face4 face2 (1- i) dim-right-d right-d))
-                                    (dim-right-d n (1- dim-right-d)))
-                                   ((= beta n-alpha))
-                                  (declare
-                                     (fixnum beta i sign dim-right-d)
-                                     (type absm right-d))
-                                  (let ((absm1 (1dgnr (1- i) left-d)))
-                                     (declare (type absm absm1))
-                                     (with-absm (dgop1 gmsm1) absm1
-                                     (with-absm (dgop2 gmsm2) right-d
-                                        (or (> (integer-length dgop1) i)
-                                            (> (integer-length dgop2) i)
-                                            (plusp (logand dgop1 dgop2))
-                                            (dstr-add-term-to-cmbn
-                                               cmpr
-                                               (* sign cffc)
-                                               (crpr dgop1 gmsm1 dgop2 gmsm2)
-                                               (aref array-pq (1+ n-alpha) (- n beta))))))))))))
-;;                 array-pq)))  ;; in case of debu gging
-                (intr-phi-2 array-pq cmpr)))))
-      (the intr #'rslt)))
-
-#|
-  (setf d (delta-infinity))
-  (setf rslt (intr-phi d d))
-  (funcall rslt (cmbn 3 1 (crpr 0 15 0 15)))
-|#
-
-#|
-
-(DEFUN INTR-PHI-22 (array-pq cmpr)
-   (declare
-      (type (simple-array cmbn (* *)) array-pq)
-      (type cmprf cmpr))
-;   (format t "  -22-  ")
-   (the cmbn
-      (let* ((n+1 (1- (array-dimension array-pq 0)))
-             (n (1- n+1)))
-         (declare (fixnum n n+1))
-         (flet ((step-i (i)
-                   (declare (fixnum i))
-                 (do ((p (1+ i) (1+ p))
-                      (p-1 i p)
-                      (q n+1 q-1)
-                      (q-1 n (1- q-1))
-                      (sign t (not sign))
-                      (ibit (2-exp i)))
-                     ((> p n+1))
-                    (declare
-                       (fixnum p p-1 q q-1 ibit)
-                       (type boolean sign))
-                    (setf (aref array-pq p q)
-                          (2cmbn-add cmpr
-                             (aref array-pq p q)
-                             (make-cmbn
-                                :degr (1+ i)
-                                :list (nconc
-                                         (mapcar
-                                            #'(lambda (term)
-                                                 (declare (type term term))
-                                                 (with-term (cffc crpr) term
-                                                    (with-crpr (dgop1 gmsm1 dgop2 gmsm2) crpr
-                                                       (term cffc (crpr
-                                                                     dgop1 gmsm1
-                                                                     (+ ibit dgop2) gmsm2)))))
-                                            (cmbn-list (aref array-pq p q-1)))
-                                         (let ((list (cmbn-list (aref array-pq p-1 q))))
-                                            (declare (list lst))
-                                            (unless sign
-                                               (dolist (term list)
-                                                  (declare (type term term))
-                                                  (setf (cffc term) (- (cffc term)))))
-                                            (dolist (term list)
-                                               (declare (type term term))
-                                               (incf (dgop1 (gnrt term)) ibit))
-                                           list))))))))
-            (do ((i 1 (1+ i)))
-                ((= i n+1))
-               (declare (type fixnum i))
-               (step-i i))
-            (aref array-pq n+1 n+1)))))
-|#
-
-(DEFUN INTR-PHI-2 (array-pq cmpr)
-   (declare
-      (type (simple-array cmbn (* *)) array-pq)
-      (type cmprf cmpr))
-;   (format t "  -2-  ")
-   (the cmbn
-      (let* ((n+1 (1- (array-dimension array-pq 0)))
-             (n (1- n+1))
-             (cmbn-list +empty-list+))
-         (declare
-            (fixnum n n+1)
-            (list cmbn-list))
-         (do ((i 1 (1+ i))
-              (cmbn-i (list nil) (list nil))
-              (mask (mask n) (ash mask -1)))
-             ((= i n+1))
-            (declare
-               (fixnum i mask)
-               (list cmbn-i))
-            (let ((cmbn-i-tail cmbn-i))
-               (declare (list cmbn-i-tail))
-               (do ((dgop1 0 (1+ dgop1)))
-                   ((> dgop1 mask)
-                    (push (make-cmbn
-                             :degr n+1
-                             :list (rest cmbn-i)) 
-                       cmbn-list))
-                  (declare (fixnum dgop1))
-                  (let ((p (- n+1 (logcount dgop1)))
-                        (dgop2 (- mask dgop1)))
-                     (declare (fixnum p dgop2))
-                     (unless (= p i)
-                        (let ((q (- (+ n+1 i) p))
-                              (sign (shuffle-sign dgop2))
-                              (dgop1-ashed (ash dgop1 i))
-                              (dgop2-ashed (ash dgop2 i)))
-                           (declare (fixnum q sign dgop1-ashed dgop2-ashed))
-                           (dolist (term (cmbn-list (aref array-pq p q)))
-                              (declare (type term term))
-                              (with-term (cffc crpr) term
-                                 (with-crpr (dgop1 gmsm1 dgop2 gmsm2) crpr
-                                    (setf cmbn-i-tail
-                                          (setf (cdr cmbn-i-tail)
-                                                (list (term (* sign cffc)
-                                                         (crpr
-                                                            (+ dgop1 dgop1-ashed) gmsm1
-                                                            (+ dgop2 dgop2-ashed) 
-                                                            gmsm2))))))))))))))
-         (if cmbn-list
-            (apply #'ncmbn-add cmpr cmbn-list)
-            (zero-cmbn n+1)))))
-
-#|
-  (setf d (delta-infinity))
-  (setf rslt (intr-phi d d))
-  (funcall rslt (cmbn 3 1 (crpr 0 15 0 15)))
-  (funcall rslt (cmbn 2 1 (crpr 0 7 0 7)))
-  (funcall rslt (cmbn 1 1 (crpr 0 3 0 3)))
-  (funcall rslt (cmbn 0 1 (crpr 0 1 0 1)))
-|#
-
-(DEFUN PHI (smst1 smst2)
-   (declare (type simplicial-set smst1 smst2))
-   (the morphism
-      (morphism
-         :sorc (crts-prdc smst1 smst2)
-         :trgt (crts-prdc smst1 smst2)
-         :degr +1
-         :intr (intr-phi smst1 smst2)
-         :strt :cmbn
-         :dfnt `(phi ,smst1 ,smst2))))
-
-#|
-  (setf phi (phi (delta-infinity) (delta-infinity)))
-  (? phi 3 (crpr 0 15 0 15))
-|#
-
-#|  ;; Comparison with EAT.
-    ;; In Kenzo.
-  (cat-init)
-  (setf s (sphere 5))
-  (setf p (crts-prdc s s))
-  (setf b (basis p 8))
-  (setf c (make-cmbn :degr 8
-             :list (mapcar #'(lambda (item)
-                                (term (1+ (random 5)) item))
-                      b)))
-  (setf phi (phi s s))
-  (time (? phi c)))
-|#
-
-#|  ;; in EAT
-  (setf s (sphere 5))
-  (setf p (cpr-2ss s s))
-  (setf b (sbs p 8))
-  (setf c (make-cmb :dgr 8
-             :lst (mapcar #'(lambda (item)
-                               (mnm (1+ (random 5)) item))
-                     b)))
-  (setf phi (phi s s))
-  (time (??? phi c))
-|#
-
-(DEFUN INTR-AW (face1 face2)
-   (declare (type face face1 face2))
-   (flet ((rslt (dmns crpr)
-           (declare
-              (fixnum dmns)
-              (type crpr crpr))
-           (the cmbn
-              (let ((absm1 (absm1 crpr))
-                    (absm2 (absm2 crpr))
-                    (rslt +empty-list+)
-                    (del-0-s +empty-list+))
-                 (declare
-                    (type absm absm1 absm2)
-                    (list rslt del-0-s))
-                 (do ((face absm2 (a-face4 face2 0 dmns2 face))
-                      (dmns2 dmns (1- dmns2)))
-                     ((zerop dmns2) (push face del-0-s))
-                    (declare
-                       (type absm face)
-                       (fixnum dmns))
-                    (push face del-0-s))
-                 (do ((face absm1 (a-face4 face1 dmns1 dmns1 face))
-                      (dmns1 dmns (1- dmns1))
-                      (dmns2 0 (1+ dmns2))
-                      (mark del-0-s (cdr mark)))
-                     ((zerop dmns1)
-                      (unless (degenerate-p absm2)
-                         (push
-                            (term 1
-                               (tnpr 0 (gmsm face) dmns (gmsm absm2)))
-                            rslt)))
-                    (declare
-                       (type absm face)
-                       (fixnum dmns1 dmns2)
-                       (list mark))
-                    (unless (or (degenerate-p face)
-                                (degenerate-p (car mark)))
-                       (push
-                          (term 1
-                             (tnpr dmns1 (gmsm face) dmns2 (gmsm (car mark))))
-                          rslt)))
-                 (make-cmbn
-                    :degr dmns
-                    :list rslt)))))
-      (the intr #'rslt)))
-
-#|
-  (setf r (intr-aw #'delta-face #'delta-face))
-  (funcall r 3 (crpr 0 15 0 15))
-  (setf s (sphere 3))
-  (setf f (face s))
-  (setf r (intr-aw f f))
-  (funcall r 3 (crpr 0 's3 0 's3))
-|#
-
-(DEFUN AW (smst1 smst2
-             &aux (crts-prdc (crts-prdc smst1 smst2))
-                  (tnsr-prdc (tnsr-prdc smst1 smst2))
-                  (face1 (face smst1))
-                  (face2 (face smst2)))
-   (declare
-      (type simplicial-set smst1 smst2)
-      (type face face1 face2))
-   (the morphism
-      (morphism
-         :sorc crts-prdc
-         :trgt tnsr-prdc
-         :degr 0
-         :intr (intr-aw face1 face2)
-         :strt :gnrt
-         :dfnt `(aw ,smst1 ,smst2))))
-
-#|
-  (setf aw (aw (delta-infinity) (delta-infinity)))
-  (? aw (cmbn 3 1 (crpr 0 15 0 30) -1 (crpr 0 23 0 29)))
-|#
-
-(DEFUN EZ (smst1 smst2)
-   (declare (type simplicial-set smst1 smst2))
-   (the reduction
-      (reduction
-         :f (aw smst1 smst2)
-         :g (eml smst1 smst2)
-         :h (phi smst1 smst2)
-         :dfnt `(eilenberg-zilber ,smst1 ,smst2))))
-
-#|
-(setf ez (ez (delta-infinity) (delta-infinity)))
-(setf *bc* (cmbn 3 1 (tnpr 0 1 3 30)
-             10 (tnpr 1 96 2 896)
-             100 (tnpr 2 7168 1 3)
-             1000 (tnpr 3 15 0 4096)))
-(setf *tc* (cmbn 3 1 (crpr 0 15 0 480)
-             100 (crpr 0 15 5 96)
-             10 (crpr 6 3 0 480)
-             1000 (crpr 6 3 1 224)))
-(pre-check-rdct ez)
-(check-rdct)
-|#
-
-
-#|
-  ;; Comparison EAT.
-  ;; In Kenzo.
-  (cat-init)
-  (setf s (sphere 5))
-  (setf ez (ez s s))
-  (setf b (basis (tcc ez) 8))
-  (setf c (make-cmbn :degr 8
-             :list (mapcar #'(lambda (item)
-                                (term (1+ (random 5)) item))
-                      b)))
-  (pre-check-rdct ez)
-  (setf +too-much-time+ -1)
-  (time (? *id-gf-dh-hd* c))
-  (time (? *id-gf-dh-hd* c))
-|#
-
-#|
-  ;; in EAT
-  (setf s (sphere 5))
-  (setf ez (ez s s))
-  (setf b (cbs (rdc-tcc ez) 8))
-  (setf c (make-cmb :dgr 8
-           :lst (mapcar #'(lambda (item)
-                             (mnm (1+ (random 5)) item))
-                   b)))
-  (verif-rdc ez)
-  (time (??? *id-gf-dh-hd* c))
-  (time (??? *id-gf-dh-hd* c))
-|#
-
-(DEFUN LEFT-CRTS-PRDC-EFHM (smst1 smst2)
-  (declare (type simplicial-set smst1 smst2))
-  (the equivalence
-    (equivalence
-     :lrdct (trivial-rdct (crts-prdc smst1 smst2))
-     :rrdct (ez smst1 smst2)
-     :dfnt `(left-crts-prdc-efhm ,smst1 ,smst2))))
-
-(DEFMETHOD SEARCH-EFHM (smst (dfnt (eql 'crts-prdc)))
-  (declare (type simplicial-set smst))
-  (the equivalence
-    (cmps
-      (left-crts-prdc-efhm (second (dfnt smst)) (third (dfnt smst)))
-      (tnsr-prdc (efhm (second (dfnt smst)))
-		 (efhm (third (dfnt smst)))))))
-
-#|
-  (cat-init)
-  (setf k (k-z 2))
-  (setf k2 (crts-prdc k k))
-  (homology k2 0 10)
-|#
\ No newline at end of file
diff --git a/archive/Kenzo-2/Kenzo-2-Acl5/fibrations.cl b/archive/Kenzo-2/Kenzo-2-Acl5/fibrations.cl
deleted file mode 100644
index 0f69835..0000000
--- a/archive/Kenzo-2/Kenzo-2-Acl5/fibrations.cl
+++ /dev/null
@@ -1,186 +0,0 @@
-;;;  FIBRATIONS  FIBRATIONS  FIBRATIONS  FIBRATIONS  FIBRATIONS
-;;;  FIBRATIONS  FIBRATIONS  FIBRATIONS  FIBRATIONS  FIBRATIONS
-;;;  FIBRATIONS  FIBRATIONS  FIBRATIONS  FIBRATIONS  FIBRATIONS
-
-(IN-PACKAGE "CAT")
-
-(PROVIDE "fibrations")
-
-(DEFUN FIBRATION-TOTAL-FACE (fibration
-		     &aux (base (sorc fibration))
-		          (bface (face base))
-		          (fibr (trgt fibration))
-			  (fbsgn (bsgn fibr))
-			  (fface (face fibr))
-			  (grml (grml fibr))
-			  (grml-sintr (sintr grml))
-			  (totl (crts-prdc base fibr))
-			  (uface (face totl))
-			  (sintr-twist (sintr fibration)))			  
-  (declare
-     (type fibration fibration)
-     (type simplicial-mrph grml)
-     (type simplicial-set base totl)
-     (type simplicial-group fibr)
-     (type gmsm fbsgn)
-     (type face bface fface uface)
-     (type sintr grml-sintr sintr-twist))
-  (flet ((rslt (indx dmns crpr)
-	    (declare
-	       (fixnum indx dmns)
-	       (type crpr crpr))
-	    (the absm
-	       (progn
-		 (when (< indx dmns)
-		    (return-from rslt
-		       (funcall uface indx dmns crpr)))
-		 (with-crpr (b-absm f-absm) crpr
-		    (let ((deln-b
-			   (a-face4 bface dmns dmns
-				     b-absm))
-			  (deln-f
-			   (a-face4 fface dmns dmns
-				     f-absm))
-			  (tau-b
-			   (tw-a-sintr3 sintr-twist dmns
-					b-absm fbsgn)))
-		      (declare
-		         ( type absm deln-b deln-f tau-b))
-		      (2absm-acrpr
-		        deln-b
-		        (a-grml4 grml-sintr (1- dmns)
-				 tau-b deln-f))))))))
-	(the face #'rslt)))
-
-#|
-  (cat-init)
-  (setf h (hopf 1))
-  (setf sf (serre-face h))
-  (funcall sf 0 2 (crpr 0 's2 0 '(2 4)))
-  (funcall sf 1 2 (crpr 0 's2 0 '(2 4)))
-  (funcall sf 2 2 (crpr 0 's2 0 '(2 4)))
-  (funcall sf 3 3 (crpr 1 's2 2 '(2 4)))
-|#
-
-(DEFUN FIBRATION-TOTAL (fibration
-                        &aux
-                        (base (sorc fibration))
-                        (fibre (trgt fibration))
-                        (untwisted-prdc
-                         (crts-prdc base fibre)))
-  (declare (type fibration fibration))
-  (the simplicial-set
-    (let ((rslt (simplicial-set
-                 :cmpr (cmpr untwisted-prdc)
-                 :basis (basis untwisted-prdc)
-                 :bsgn (bsgn untwisted-prdc)
-                 :face (fibration-total-face fibration)
-                 :dfnt `(fibration-total ,fibration))))
-      (declare (type simplicial-set rslt))
-      (setf (slot-value rslt 'grmd) untwisted-prdc) 
-      (when (and (typep base 'kan)
-                 (typep fibre 'kan))
-        (change-class rslt 'kan)
-        (setf (slot-value rslt 'kfll)
-          (fibration-kfll fibration)))
-      rslt)))
-
-#|
-  (cat-init)
-  (setf s2 (sphere 2))
-  (setf k (k-z-1))
-  (setf tw (simplicial-mrph
-             :sorc s2
-	     :trgt k
-	     :degr -1
-	     :sintr #'(lambda (dmns gmsm)
-			(absm 0 (list 1)))
-	     :dfnt '(s2-tw-kz1)))
-  (setf e (fibration-total tw))
-  (homology e 2)
-  (homology e 0 8)
-  (cat-init)
-  (setf s2 (sphere 2))
-  (setf k (k-z2-1))
-  (setf tw (simplicial-mrph
-             :sorc s2
-	     :trgt k
-	     :degr -1
-	     :sintr #'(lambda (dmns gmsm)
-			(absm 0 1))
-	     :dfnt '(s2-tw-kz2)))
-  (setf e (fibration-total tw))
-  (homology e 2)
-  (homology e 0 8)
-|#
-		 
-(DEFUN FIBRATION-KFLL (twist
-		        &aux (sintr-twist (sintr twist))
-			     (base (sorc twist))
-			     (fibre (trgt twist))
-			     (fbsgn (bsgn fibre))
-			     (bkfll (kfll base))
-			     (fkfll (kfll fibre))
-			     (grml-sintr (sintr (grml fibre)))
-			     (grin-sintr (sintr (grin fibre))))
-  (declare
-     (type fibration twist)
-     (type kan base fibre)
-     (type gmsm fbsgn)
-     (type kfll bkfll fkfll)
-     (type sintr grml-sintr grin-sintr))
-  (flet ((rslt (indx dmns hat)
-	   (declare
-	      (fixnum indx dmns)
-	      (list hat))
-	   (let (bhat fhat)
-	     (declare (type list bhat fhat))
-	     (do ((mark hat (cdr mark)))
-		 ((endp mark))
-		(declare (list mark))
-		(let ((absm (car mark)))
-		  (declare (type absm absm))
-		  (with-absm (dgop crpr) absm
-		  (with-crpr (dgop1 gmsm1 dgop2 gmsm2) crpr
-		     (push (absm (dgop*dgop dgop dgop1) gmsm1) bhat)
-		     (push (absm (dgop*dgop dgop dgop2) gmsm2) fhat)))))
-	     (setf bhat (nreverse bhat))
-	     (let ((bkfll (funcall bkfll indx dmns bhat)))
-	       (declare (type absm bkfll))
-	       (when (< indx dmns)
-		 (setf (first fhat)
-		       (a-grml4 grml-sintr (1- dmns)
-				(a-grin4 grin-sintr (1- dmns)
-					 (tw-a-sintr3 sintr-twist dmns bkfll fbsgn))
-				(first fhat))))
-	       (setf fhat (nreverse fhat))
-	       (let ((fkfll (funcall fkfll indx dmns fhat)))
-		 (declare (type absm fkfll))
-		 (2absm-acrpr bkfll fkfll))))))
-	(the kfll #'rslt)))
-
-#|
-  (cat-init)
-  (load "r-proj-space")
-  (setf tw (kdivide-z2-twist opr opr-chml-clss))
-  (setf pr-4 (fibration-total tw))
-  (setf absm (absm 0 (crpr 0 (loop3 0 5 2) 0 4)))
-  (setf hat (mapcar #'(lambda (i) (face pr-4 i 4 absm))
-                    (<a-b> 0 4)))
-  (dotimes (i 5)
-    (print (kfll pr-4 i 4 (remove (nth i hat) hat)))
-    (check-kan pr-4 i 4 (remove (nth i hat) hat)))
-|#
-
-#|
-  (cat-init)
-  (setf os3-fibration os3-fibration)
-  (setf total (fibration-total os3-fibration))
-  (setf absm (absm 1 (crpr 0 (loop3 1 's3 1 2 's3 -2)
-				   0 '(-2 1 1))))
-  (setf hat (mapcar #'(lambda (i) (face total i 4 absm))
-                    '(0 1 2 3 4)))
-  (dotimes (i 5)
-    (print (kfll total i 4 (remove (nth i hat) hat)))
-    (check-kan total i 4 (remove (nth i hat) hat)))
-|#
\ No newline at end of file
diff --git a/archive/Kenzo-2/Kenzo-2-Acl5/file-list.cl b/archive/Kenzo-2/Kenzo-2-Acl5/file-list.cl
deleted file mode 100644
index 00c28f3..0000000
--- a/archive/Kenzo-2/Kenzo-2-Acl5/file-list.cl
+++ /dev/null
@@ -1,110 +0,0 @@
-;;;  FILES  FILES  FILES  FILES  FILES  FILES  FILES  FILES  FILES  FILES
-;;;  FILES  FILES  FILES  FILES  FILES  FILES  FILES  FILES  FILES  FILES
-;;;  FILES  FILES  FILES  FILES  FILES  FILES  FILES  FILES  FILES  FILES
-
-(IN-PACKAGE "COMMON-LISP-USER")
-
-(DEFPACKAGE "CAT"
-  (:use "COMMON-LISP"))
-
-(IN-PACKAGE "CAT")
-
-(USE-PACKAGE "CAT" "COMMON-LISP-USER")
-
-(PROCLAIM '(OPTIMIZE (speed 3) (safety 1) (space 0) (debug 0)))
-
-(EXPORT '(+file-list+ load-sfiles compile-files load-cfiles cat-files))
-
-(DEFCONSTANT +FILE-LIST+
-   '("classes"
-     "macros"
-     "various"
-     "combinations"
-     "chain-complexes"
-     "chcm-elementary-op"
-     "effective-homology"
-     "homology-groups"
-     "searching-homology"
-     "cones"
-     "tensor-products"
-     "coalgebras"
-     "cobar"
-     "algebras"
-     "bar"
-     "simplicial-sets"
-     "simplicial-mrphs"
-     "delta"
-     "special-smsts"
-     "suspensions"
-     "disk-pasting"
-     "cartesian-products"
-     "eilenberg-zilber"
-     "kan"
-     "simplicial-groups"
-     "fibrations"
-     "loop-spaces"
-     "ls-twisted-products"
-     "lp-space-efhm"
-     "classifying-spaces"
-     "k-pi-n"
-     "serre"
-     "cs-twisted-products"
-     "cl-space-efhm"
-     "whitehead"
-     "smith"
-     ))
-
-(DO ((mark +file-list+ (cdr mark))
-     (i 1 (1+ i)))
-    ((endp mark) (terpri))
-   (format t "~% FILE ~2D: ~A" i (car mark)))
-
-(DEFCONSTANT +SOURCE-EXTENSION+ ".cl")
-
-(DEFCONSTANT +COMPILED-EXTENSION+ ".fasl")
-
-(DEFUN LOAD-SFILES ()
-  (mapc #'(lambda (file-name)
-            (load (concatenate 'string file-name +source-extension+)))
-    +file-list+)
-  (princ "--- done ---")
-  (values ))
-
-(DEFVAR *CMBN-CONTROL*)
-(SETF *CMBN-CONTROL* T)
-
-(DEFUN COMPILE-FILES ()
-  (format t
-      "~%SPEED-PARAMETER = ~D~@
-       ~% *CMBN-CONTROL* = ~A~2%"
-    excl::.speed. *cmbn-control*)
-  (mapc #'(lambda (file-name)
-            (compile-file (concatenate 'string file-name +source-extension+))
-            (load (concatenate 'string file-name +compiled-extension+)))
-    +file-list+)
-  (princ "--- done ---")
-  (values))
-
-(DEFUN LOAD-CFILES ()
-  (mapc #'(lambda (file-name)
-            (load (concatenate 'string file-name +compiled-extension+)))
-    +file-list+)
-  (princ "--- done ---")
-  (values ))
-
-(DEFUN CAT-FILES (file1)
-  (declare (type string file1))
-  (setf file1 (concatenate 'string file1 +source-extension+))
-  (when (probe-file file1)
-    (delete-file file1))
-  (with-open-file (output file1 :direction :output)
-    (dolist (file2 +file-list+)
-      (declare (type string file2))
-      (setf file2 (concatenate 'string file2 +source-extension+))
-      (with-open-file (input file2 :direction :input)
-        (do ((line (read-line input)
-                   (read-line input nil :eof)))
-            ((eq line :eof))
-          (declare (type (or string (eql :eof)) line))
-          (princ line output)
-          (terpri output))))))
\ No newline at end of file
diff --git a/archive/Kenzo-2/Kenzo-2-Acl5/homology-groups.cl b/archive/Kenzo-2/Kenzo-2-Acl5/homology-groups.cl
deleted file mode 100644
index e1f8439..0000000
--- a/archive/Kenzo-2/Kenzo-2-Acl5/homology-groups.cl
+++ /dev/null
@@ -1,676 +0,0 @@
-;;  HOMOLOGY-GROUPS  HOMOLOGY-GROUPS  HOMOLOGY-GROUPS  HOMOLOGY-GROUPS
-;;  HOMOLOGY-GROUPS  HOMOLOGY-GROUPS  HOMOLOGY-GROUPS  HOMOLOGY-GROUPS
-;;  HOMOLOGY-GROUPS  HOMOLOGY-GROUPS  HOMOLOGY-GROUPS  HOMOLOGY-GROUPS
-
-(IN-PACKAGE "CAT")
-
-(provide "homology-groups")
-
-;;
-;;  Computing ordinary homology-groups. 
-;;  
-
-;; Structures.
-
-(DEFSTRUCT (matrice (:conc-name nil))
-  leftcol uplig)
-
-(DEFSTRUCT (t-mat (:conc-name nil))
-  val ilig icol left up)
-
-(defmacro baselig (mat n)
-  `(aref (leftcol ,mat) ,n))
-
-(defmacro basecol (mat n)
-  `(aref (uplig ,mat) ,n))
-
-;; Functions.
-
-(defun creer-matrice (n1 n2)
-   (let ((mat (make-matrice
-                 :leftcol (make-array (1+ n1))
-                 :uplig (make-array (1+ n2)))))
-      (setf (baselig mat 0) (make-t-mat :ilig 0 :icol 0))
-      (setf (basecol mat 0) (baselig mat 0))
-      (do ((i 1 (1+ i)))
-         ((> i n1))
-         (setf (baselig mat i)
-            (make-t-mat :ilig i :icol 0 :up (baselig mat (1- i))))
-         (setf (left (baselig mat i)) (baselig mat i)))
-      (do ((j 1 (1+ j)))
-         ((> j n2))
-         (setf (basecol mat j)
-            (make-t-mat :ilig 0 :icol j :left (basecol mat (1- j))))
-         (setf (up (basecol mat j)) (basecol mat j)))
-      (setf (up (baselig mat 0)) (baselig mat n1))
-      (setf (left (basecol mat 0)) (basecol mat n2))
-      mat))
-
-(defun chercher-hor (p ic)
-   (do ((p2 p p1)
-        (p1 (left p) (left p1)))
-        ((<= (icol p1) ic) p2)))
-
-(defun chercher-ver (p il)
-   (do ((p2 p p1)
-        (p1 (up p) (up p1)))
-       ((<= (ilig p1) il) p2)))
-
-(defun inserer-terme (pl pc val)
-   (setf (left pl) (make-t-mat :val val
-                               :ilig (ilig pl)
-                               :icol (icol pc)
-                               :left (left pl)
-                               :up (up pc))
-         (up pc) (left pl)))
-
-(defun supprimer-terme (pl pc)
-   (setf (left pl) (left (left pl))
-         (up pc) (up (up pc))))
-
-(defun maj-terme (pl pc val)
-  (if (= val 0)
-      (if (eq (left pl) (up pc)) (supprimer-terme pl pc))
-      (if (eq (left pl) (up pc))
-          (setf (val (left pl)) val)
-          (inserer-terme pl pc val))))
-
-(defun maj-ligne (mat il liste)
-   (let ((ptl (baselig mat il)))
-        (mapcar
-           #'(lambda (elem)
-                (maj-terme (chercher-hor ptl (first elem))
-                           (chercher-ver (basecol mat (first elem)) il)
-                           (second elem)))
-           liste)
-        ptl))
-
-(defun maj-colonne (mat ic liste)
-   (let ((ptc (basecol mat ic)))
-        (mapcar
-           #'(lambda (elem)
-                (maj-terme (chercher-hor (baselig mat (first elem)) ic)
-			   (chercher-ver ptc (first elem))
-                           (second elem)))
-           liste)
-        ptc))
-
-(defun maj-matrice (mat liste)
-  (mapcar
-     #'(lambda (elem) (apply #'maj-ligne mat elem))
-     liste)
-  mat)
-
-(defun disp-p (p)
-   `((,(ilig p) ,(icol p) ,(val p))
-     (,(ilig (left p)) ,(icol (left p)) ,(val (left p)))
-     (,(ilig (up p)) ,(icol (up p)) ,(val (up p)))))
-
-(defun disp-ligne (mat il)
-   (terpri)
-   (princ "L")
-   (princ il)
-   (princ "=")
-   (mapcar
-      #'(lambda (elem)
-           (princ "(")
-           (princ (first elem))
-           (princ ":")
-           (princ (second elem))
-           (princ ")"))
-      (let ((ptl (baselig mat il))
-            (res '()))
-         (do ((pl (left ptl) (left pl)))
-             ((eq pl ptl))
-            (push (list (icol pl) (val pl)) res))
-         res))
-  (values ))
-
-(defun disp-colonne (mat ic)
-   (terpri)
-   (princ "C")
-   (princ ic)
-   (princ "=")
-   (mapcar
-      #'(lambda (elem)
-           (princ "(")
-           (princ (first elem))
-           (princ ":")
-           (princ (second elem))
-           (princ ")"))
-      (let ((ptc (basecol mat ic))
-            (res '()))
-         (do ((pc (up ptc) (up pc)))
-             ((eq pc ptc))
-            (push (list (ilig pc) (val pc)) res))
-         res))
-   (values ))
-
-(defun nlig (mat) (1- (array-dimension (leftcol mat) 0)))
-(defun ncol (mat) (1- (array-dimension (uplig mat) 0)))
-
-(defun disp-matrice (mat)
-   (let ((nlig (nlig mat)))
-      (do ((i 1 (1+ i)))
-          ((> i nlig))
-          (disp-ligne mat i)))
-   (done))
-
-(DEFMETHOD PRINT-OBJECT ((mtrx matrice) stream)
-  (declare (stream stream))
-  (the matrice (progn
-    (let ((nlig (nlig mtrx))
-	  (ncol (ncol mtrx)))
-      (declare (fixnum nlig ncol))
-      (format stream "~%========== MATRIX ~D lines + ~D columns ====="
-	      nlig ncol)
-      (do ((ilig 1 (1+ ilig)))
-	  ((> ilig nlig))
-	  (declare (fixnum ilig))
-	(format stream "~%L~D=" ilig)
-	(dolist (item (let ((baselig (baselig mtrx ilig)))
-			(declare (type t-mat baselig))
-			(do ((rslt +empty-list+ (cons t-mat rslt))
-			     (t-mat (left baselig) (left t-mat)))
-			    ((eq t-mat baselig) rslt)
-			    (declare
-			      (list rslt)
-			      (type t-mat t-mat)))))
-	   (declare (type t-mat item))
-	   (format stream "[C~D=~D]" (icol item) (val item))))
-      (format stream "~%========== END-MATRIX"))
-    mtrx)))    
-
-(defun disp-matrice-colonnes (mat)
-   (let ((ncol (ncol mat)))
-      (do ((i 1 (1+ i)))
-          ((> i ncol))
-          (disp-colonne mat i)))
-   (done))
-
-(defun terme (mat i j)
-   (let ((p (left (chercher-hor (baselig mat i) j))))
-        (if (= j (icol p))
-            (val (left p))
-            nil)))
-
-(defun mat-aleat (n1 n2 dens x)
-   (let ((mat (creer-matrice n1 n2))
-         (n (truncate (* dens n1 n2)))
-         (2x (* 2 x))
-         (res nil))
-      (dotimes (i n)
-         (let* ((il (1+ (random n1)))
-                (ic (1+ (random n2)))
-                (val (let ((pval (- (random 2x) x)))
-                        (if (minusp pval)
-                            pval
-                            (1+ pval))))
-                (elem (member il res
-                         :test #'(lambda (x y) (eql x (first y))))))
-            (if elem
-                (push (list ic val) (cadar elem))
-                (push (list il (list (list ic val))) res))))
-      (maj-matrice mat res)))
-
-(defun op-elem (pl pc alpha)
-   (if (eq (left pl) (up pc))
-       (if (= alpha (val (left pl)))
-           (supprimer-terme pl pc)
-           (decf (val (left pl)) alpha))
-       (inserer-terme pl pc (- alpha))))
-
-(defun peigne-ver (mat ptl il)
-       (if (< il (ilig ptl))
-           (do ((res nil (cons (chercher-ver pl il)
-                               res))
-                (pl (left ptl) (left pl)))
-               ((eq pl ptl) (nreverse res)))
-           (do ((res nil (cons (chercher-ver (basecol mat (icol pl)) il)
-                               res))
-                (pl (left ptl) (left pl)))
-               ((eq pl ptl) (nreverse res)))))
-
-(defun peigne-hor (mat ptc ic)
-       (if (< ic (icol ptc))
-           (do ((res nil (cons (chercher-hor pc ic)
-                               res))
-                (pc (up ptc) (up pc)))
-               ((eq pc ptc) (nreverse res)))
-           (do ((res nil (cons (chercher-hor (baselig mat (ilig pc)) ic)
-                               res))
-                (pc (up ptc) (up pc)))
-               ((eq pc ptc) (nreverse res)))))
-
-(defun op-lig (ptl1 ptl2 peigne lambda)
-  (do ((pl1 (left ptl1) (left pl1))
-       (pp peigne (rest pp))
-       (pl2 ptl2))
-      ((endp pp) ptl2)
-    (setf pl2 (chercher-hor pl2 (icol pl1)))
-    (op-elem pl2 (first pp) (* lambda (val pl1)))))
-
-(defun op-col (ptc1 ptc2 peigne lambda)
-  (do ((pc1 (up ptc1) (up pc1))
-       (pp peigne (rest pp))
-       (pc2 ptc2))
-      ((endp pp) ptc2)
-    (setf pc2 (chercher-ver pc2 (ilig pc1)))
-    (op-elem (first pp) pc2 (* lambda (val pc1)))))
-
-(defun op-lig-n (mat l1 l2 lambda)
-  (op-lig (baselig mat l1)
-          (baselig mat l2)
-          (peigne-ver mat (baselig mat l1) l2)
-          lambda))
-
-(defun op-col-n (mat c1 c2 lambda)
-  (op-col (basecol mat c1)
-          (basecol mat c2)
-          (peigne-hor mat (basecol mat c1) c2)
-          lambda))
-
-(defun n-lig (mat)
-  (1- (array-dimension (leftcol mat) 0)))
-
-(defun n-col (mat)
-  (1- (array-dimension (uplig mat) 0)))
-
-(defun copier-matrice (mat)
-  (let ((mat2 (creer-matrice (n-lig mat) (n-col mat))))
-    (do ((i 1 (1+ i)))
-        ((> i (n-lig mat)) mat2)
-      (do ((ptl1 (baselig mat i))
-           (pl1 (left (baselig mat i)) (left pl1))
-           (pl2 (baselig mat2 i) (left pl2)))
-          ((eq pl1 ptl1))
-        (inserer-terme pl2 (basecol mat2 (icol pl1)) (val pl1))))))
-
-(defun reste (a b)
-  (second (multiple-value-list (round a b))))
-
-(defun diviseur (a b)
-  (round a b))
-
-(defun maj-peigne-ver (peigne il)
-  (do ((pp peigne (rest pp)))
-      ((endp pp) peigne)
-    (setf (first pp) (chercher-ver (first pp) il))))
-
-(defun maj-peigne-hor (peigne ic)
-  (do ((pp peigne (rest pp)))
-      ((endp pp) peigne)
-    (setf (first pp) (chercher-hor (first pp) ic))))
-
-(defun identite (n)
-  (let ((mat (creer-matrice n n)))
-    (do ((ptl (baselig mat n) (up ptl))
-         (ptc (basecol mat n) (left ptc)))
-        ((eq ptl ptc))
-      (inserer-terme ptl ptc 1))
-    mat))
-
-(defun init-peigne-ver (mat ptl)
-  (do ((res nil (cons (basecol mat (icol pl))
-                      res))
-       (pl (left ptl) (left pl)))
-      ((eq pl ptl) (nreverse res))))
-
-(defun init-peigne-hor (mat ptc)
-  (do ((res nil (cons (baselig mat (ilig pc))
-                      res))
-       (pc (up ptc) (up pc)))
-      ((eq pc ptc) (nreverse res))))
-
-(defun disp-peigne (peigne)
-  (mapcar #'(lambda (elem) (first (disp-p elem)))
-          peigne))
-
-(defun terme-minimal-matrice (mat)
-  (catch '?
-    (do* ((fin (baselig mat 0))
-          (ptl (up fin) (up ptl)))
-         ((eq ptl fin) (throw '? nil))
-      (if (not (eq ptl (left ptl)))
-          (let* ((pmin (left ptl))
-                 (min (abs (val pmin))))
-            (if (= min 1) (throw '? pmin))
-            (do ((ptl ptl (up ptl)))
-                ((eq ptl fin) (throw '? pmin))
-              (do ((pl (left ptl) (left pl)))
-                  ((eq pl ptl))
-                (let ((val (abs (val pl))))
-                  (when (< val min)
-                    (if (= val 1) (throw '? pl))
-                    (setq pmin pl min val))))))))))
-
-(defun tuer-ligne (mat il)
-  (let* ((ptl (baselig mat il))
-         (peigne (peigne-ver mat ptl il)))
-    (do ((pp peigne (rest pp)))
-        ((endp pp))
-      (supprimer-terme ptl (first pp)))
-    (setf (up (chercher-ver (baselig mat 0) il)) (up ptl)))
-  mat)
-
-(defun tuer-colonne (mat ic)
-  (let* ((ptc (basecol mat ic))
-         (peigne (peigne-hor mat ptc ic)))
-    (do ((pp peigne (rest pp)))
-        ((endp pp))
-      (supprimer-terme (first pp) ptc))
-    (setf (left (chercher-hor (basecol mat 0) ic)) (left ptc)))
-  mat)
-
-(defun pivot (mat p)
-  (let* ((div (val p))
-         (ptl (baselig mat (ilig p)))
-         (ptc (basecol mat (icol p)))
-         (peigne (init-peigne-ver mat ptl))
-         (peigne2 '*non-defini*))
-    (do ((pc (up ptc) (up pc)))
-        ((eq pc ptc))
-      (maj-peigne-ver peigne (ilig pc))
-      (if (eq pc p)
-          (setf peigne2 (copy-list peigne))
-          (op-lig ptl
-                  (baselig mat (ilig pc))
-                  peigne
-                  (truncate (val pc) div))))
-    (do ((pp peigne2 (rest pp)))
-        ((endp pp))
-      (supprimer-terme ptl (first pp)))
-    (setf (left (chercher-hor (basecol mat 0) (icol p))) (left ptc))
-    (setf (up   (chercher-ver (baselig mat 0) (ilig p))) (up   ptl))
-    (list (ilig p) (icol p) (val p))))
-
-(defun pivot-parallele (M N p)
-  (let* ((div (val p))
-         (ic (icol p))
-         (ptl (baselig M (ilig p)))
-         (ptc (basecol N ic))
-         (peigne (init-peigne-hor N ptc))
-         (peigne2 '*non-defini*))
-    (do ((pl (left ptl) (left pl)))
-        ((eq pl ptl))
-      (maj-peigne-hor peigne (icol pl))
-      (if (eq pl p)
-          (setf peigne2 (copy-list peigne))
-          (op-col ptc
-                  (basecol N (icol pl))
-                  peigne
-                  (truncate (val pl) div))))
-    (do ((pp peigne2 (rest pp)))
-        ((endp pp))
-      (supprimer-terme (first pp) ptc))
-    (setf (left (chercher-hor (basecol N 0) ic)) (left ptc))))
-
-(defun generateur-torsion-H* (B N p)
-  (let ((tab (make-array (1+ (n-lig B)) :initial-element 0))
-        (ptcN (basecol N (icol p))))
-    (do ((pcN (up ptcN) (up pcN)))
-        ((eq pcN ptcN))
-      (let ((facteur (truncate (val pcN) (val p)))
-            (ptcB (basecol B (ilig pcN))))
-        (do ((pcB (up ptcB) (up pcB)))
-            ((eq pcB ptcB))
-          (incf (aref tab (ilig pcB)) (* (val pcB) facteur)))))
-    (cons (abs (val p))
-          (let ((res '()))
-            (do ((ind (n-lig B) (1- ind)))
-                ((zerop ind) res)
-              (if (/= 0 (aref tab ind))
-                  (push (cons (aref tab ind) ind) res)))))))
-
-(defun terminer-H* (B)
-  (let ((res '())
-        (fin (basecol B 0)))
-    (do ((ptc (left fin) (left ptc)))
-        ((eq ptc fin) res)
-      (push (cons 0
-                  (do ((pc (up ptc) (up pc))
-                       (res '() (cons (cons (val pc) (ilig pc)) res)))
-                      ((eq pc ptc) res)))
-            res))))
-
-(defun reste-minimal-ligne (mat p)
-  (block ?
-    (let ((div (val p))
-          (ptl (baselig mat (ilig p))))
-      (do ((pl (left ptl) (left pl)))
-          ((eq pl ptl) (return-from ? nil))
-        (let ((val (reste (val pl) div)))
-          (if (/= 0 val)
-              (if (= 1 val)
-                  (return-from ? pl)
-                  (let ((pmin pl)
-                        (min val))
-                    (do ((pl (left pl) (left pl)))
-                        ((eq pl ptl) (return-from ? pmin))
-                      (let ((val (reste (val pl) div)))
-                        (if (and (/= 0 val) (< val min))
-                            (if (= 1 val)
-                                (return-from ? pl)
-                                (setf pmin pl min val)))))))))))))
-
-(defun reste-minimal-colonne (mat p)
-  (block ?
-    (let ((div (val p))
-          (ptc (basecol mat (icol p))))
-      (do ((pc (up ptc) (up pc)))
-          ((eq pc ptc) (return-from ? nil))
-        (let ((val (reste (val pc) div)))
-          (if (/= 0 val)
-              (if (= 1 val)
-                  (return-from ? pc)
-                  (let ((pmin pc)
-                        (min val))
-                    (do ((pc (up pc) (up pc)))
-                        ((eq pc ptc) (return-from ? pmin))
-                      (let ((val (reste (val pc) div)))
-                        (if (and (/= 0 val) (< val min))
-                            (if (= 1 val)
-                                (return-from ? pc)
-                                (setf pmin pc min val)))))))))))))
-
-
-
-(defun homologie (M N)
-  (prog ((B (identite (n-col M)))
-         (res nil)
-         (p1) (p2) (div))
-    depart1
-      (setf p1 (terme-minimal-matrice M))
-    loop1
-      (if (null p1)
-          (go depart2)
-          (if (= 1 (abs (val p1)))
-              (go pivot1)
-              (progn (setf p2 (reste-minimal-colonne M p1))
-                     (if (null p2)
-                         (progn (setf p2 (reste-minimal-ligne M p1))
-                                (if (null p2)
-                                    (go pivot1)
-                                    (go op-col1)))
-                         (go op-lig1)))))
-    op-lig1
-      (op-lig-n M (ilig p1) (ilig p2) (diviseur (val p2) (val p1)))
-      (setf p1 p2)
-      (go loop1)
-    op-col1
-      (setf div (diviseur (val p2) (val p1)))
-      (op-col-n M (icol p1) (icol p2) div)
-      (op-col-n B (icol p1) (icol p2) div)
-      (op-lig-n N (icol p2) (icol p1) (- div))
-      (setf p1 p2)
-      (go loop1)
-    pivot1
-      (tuer-ligne N (icol p1))
-      (pivot-parallele M B p1)
-      (pivot M p1)
-      (go depart1)
-
-    depart2
-      (setf p1 (terme-minimal-matrice N))
-    loop2
-      (if (null p1)
-          (go depart3)
-          (if (= 1 (abs (val p1)))
-              (go pivot2)
-              (progn (setf p2 (reste-minimal-ligne N p1))
-                     (if (null p2)
-                         (progn (setf p2 (reste-minimal-colonne N p1))
-                                (if (null p2)
-                                    (go pivot2-torsion)
-                                    (go op-lig2)))
-                         (go op-col2)))))
-    op-lig2
-      (setf div (diviseur (val p2) (val p1)))
-      (op-col-n B (ilig p2) (ilig p1) (- div))
-      (op-lig-n N (ilig p1) (ilig p2) div)
-      (setf p1 p2)
-      (go loop2)
-    op-col2
-      (op-col-n N (icol p1) (icol p2) (diviseur (val p2) (val p1)))
-      (setf p1 p2)
-      (go loop2)
-    pivot2-torsion
-      (setf res (cons (generateur-torsion-H* B N p1) res))
-    pivot2
-      (tuer-colonne B (ilig p1))
-      (pivot N p1)
-      (go depart2)
-
-    depart3
-      (return (append res (terminer-H* B)))))
-
-(defun chcm-mat (chcm n)
-  (declare
-     (type chain-complex chcm)
-     (fixnum n))
-   (when (eq (basis chcm) :locally-effective)
-    (error "CHCMC-MAT cannot work with a LOCALLY-EFFECTIVE chain complex."))
-  (let ((sorc (basis chcm n))
-	(trgt (basis chcm (1- n)))
-	(cmpr (cmpr chcm)))
-    (declare
-       (list sorc trgt)
-       (type cmprf cmpr))
-     (format t "~%Computing boundary-matrix in dimension ~D.~@
-                Rank of the source-module : ~D.~2%"
-        n (length sorc))
-    (let ((mat (creer-matrice (length trgt) (length sorc)))
-          (test #'(lambda (gnrt1 gnrt2)
-                     (eq (funcall cmpr gnrt1 gnrt2) :equal))))
-       (declare
-          (type matrice mat)
-          (function test))
-       (do ((i 1 (1+ i))
-            (mark sorc (cdr mark)))
-           ((endp mark))
-          (declare
-             (fixnum i)
-             (list mark))
-          (clock)
-          (format t "Computing the boundary of the generator ~D (dimension ~D) :"
-             i n)
-          (print (car mark))
-          (maj-colonne mat i
-             (mapcar #'(lambda (term)
-                          (declare (type term term))
-                          (list
-                             (1+ (position (gnrt term) trgt :test test))
-                             (cffc term)))
-                (cmbn-list (? chcm n (car mark)))))
-          (format t "~%End of computing.~2%"))
-       mat)))
-
-#|
-  (require "special-smsts")
-  (setf d (delta 3))
-  (disp-matrice (chcm-mat d 2))
-  (disp-matrice (chcm-mat d 3))
-  (disp-matrice (chcm-mat d 4))
-|#
-
-(defun chcm-homology (cc n)
-  (declare (type chain-complex cc) (type fixnum n))
-  (let ((rsl (homologie (chcm-mat cc n) (chcm-mat cc (1+ n)))))
-    (declare (type list rsl))    
-    (format t "~3%Homology in dimension ~D :~%" n)
-    (dolist (item rsl)
-      (declare (type list item))
-      (format t "~2%Component Z")
-      (unless (zerop (first item)) 
-	(format t "/~DZ" (first item)))))
-  (terpri) (terpri)
-  (done))
-
-(defun homology-gen (cc n)
-  (declare (type chain-complex cc) (type fixnum n))
-  (let ((src (cons :unused (basis cc n)))
-        (rsl (homologie (chcm-mat cc n) (chcm-mat cc (1+ n)))))
-    (declare (type list src rsl))
-    (format t "~3%Homology in dimension ~D :~%" n)
-    (dolist (item rsl)
-      (declare (type list item))
-      (format t "~%Component Z")
-      (unless (zerop (first item)) 
-        (format t "/~DZ" (first item))))
-    (terpri) (terpri)
-    (setf rsl (mapcar #'cdr rsl))
-    (setf rsl (mapcar #'(lambda (item)
-                          (declare (type list item))
-                          (mapcar #'(lambda (term)
-                                      (declare (type term term))
-                                      (term (car term) (nth (cdr term) src)))
-                            item))
-                rsl))
-    (setf rsl (mapcar #'(lambda (item)
-                          (declare (type list item))
-                          (make-cmbn :degr n :list item))
-                rsl))
-    rsl))    
-
-(defun chcm-homology-gen (cc n)
-  (declare (type chain-complex cc) (type fixnum n))
-  (let ((src (cons :unused (basis cc n)))
-	(rsl (homologie (chcm-mat cc n) (chcm-mat cc (1+ n)))))
-    (declare (type list src rsl))
-    (format t "~3%Homology in dimension ~D :~%" n)
-    (dolist (item rsl)
-      (declare (type list item))
-      (format t "~2%Component Z")
-      (unless (zerop (first item)) 
-	(format t "/~DZ" (first item)))
-      (format t "~2%Generator :")
-      (dolist (item2 (rest item))
-	(declare (type cons item2))
-	(format t "~%~D~6T*  ~S" (car item2) (nth (cdr item2) src)))))
-  (done))
-
-#|
-(defun heq-homology (heq n)
-  (declare (type heq heq) (type fixnum n))
-  (let ((ecc (heq-rbcc heq))
-	(rep (cmp-mrp (heq-lf heq) (heq-rg heq))))
-    (declare (type chain-complex ecc) (type mrp rep))
-    (let ((src (cons :unused (cbs ecc n)))	
-	  (rsl (homologie (chcm-mat ecc n) (chcm-mat ecc (1+ n)))))
-      (declare (type list src rsl))
-      (format t "~3%Homology in dimension ~D :~%" n)
-      (dolist (item rsl)
-	(declare (type list item))
-	(format t "~2%Component Z")
-	(unless (zerop (first item))
-	  (format t "/~DZ" (first item)))
-	(format t "~2%Generator :~%")
-	(princ (??? rep (make-cmb :dgr n
-				  :lst (mapcar #'(lambda (item2)
-						   (declare (type cons item2))
-						   (mnm (car item2)
-							(nth (cdr item2) src)))
-					       (rest item))))))))
-  (done))
-|#
-
diff --git a/archive/Kenzo-2/Kenzo-2-Acl5/k-pi-n.cl b/archive/Kenzo-2/Kenzo-2-Acl5/k-pi-n.cl
deleted file mode 100644
index f47616a..0000000
--- a/archive/Kenzo-2/Kenzo-2-Acl5/k-pi-n.cl
+++ /dev/null
@@ -1,1070 +0,0 @@
-;;;  K-PI-1  K-PI-1  K-PI-1  K-PI-1  K-PI-1  K-PI-1  K-PI-1
-;;;  K-PI-1  K-PI-1  K-PI-1  K-PI-1  K-PI-1  K-PI-1  K-PI-1
-;;;  K-PI-1  K-PI-1  K-PI-1  K-PI-1  K-PI-1  K-PI-1  K-PI-1
-
-(IN-PACKAGE "CAT")
-
-(PROVIDE "k-pi-1")
-
-(DEFUN K-Z-1-CMPR (gnrt1 gnrt2)
-   (declare (list gnrt1 gnrt2))
-   (the cmpr
-   (do ((mark1 gnrt1 (cdr mark1))
-	(mark2 gnrt2 (cdr mark2)))
-       ((endp mark1) :equal)
-       (case (f-cmpr (car mark1) (car mark2))
-	  (:equal)
-	  (:less (return-from k-z-1-cmpr :less))
-	  (:greater (return-from k-z-1-cmpr :greater))))))
-
-#|
-  (k-z-1-cmpr '(1 1 2) '(1 2 2))
-  (k-z-1-cmpr '(1 1 2) '(1 1 2))
-  (k-z-1-cmpr '(1 1 2) '(1 1 -1))
-|#
-
-(DEFUN K-Z-1-FACE (indx dmns gmsm)
-   (declare
-      (fixnum indx dmns)
-      (list gmsm))
-   (the absm
-   (cond ((zerop indx) (absm 0 (rest gmsm)))
-	 ((= indx dmns) (absm 0 (butlast gmsm)))
-	 (t
-	  (do ((rslt +empty-list+ (cons (car mark) rslt))
-	       (mark gmsm (cdr mark))
-	       (i 1 (1+ i)))
-	      ((= i indx) (let ((new-k (+ (car mark) (cadr mark))))
-			    (declare (fixnum new-k))
-			    (if (zerop new-k)
-			       (absm (2-exp (1- indx)) (nreconc rslt (cddr mark)))
-			       (absm 0 (nreconc rslt (cons new-k (cddr mark)))))))
-	     (declare
-	        (list rslt mark)
-		(fixnum i)))))))
-
-#|
-  (k-z-1-face 0 1 '(3))
-  (k-z-1-face 1 1 '(3))
-  (k-z-1-face 0 3 '(1 2 3))
-  (k-z-1-face 1 3 '(1 2 3))
-  (k-z-1-face 2 3 '(1 2 3))
-  (k-z-1-face 2 3 '(1 2 -2))
-  (k-z-1-face 3 3 '(1 2 3))
-|#
-
-(DEFUN Z-ABSM-BAR (absm)
-  (declare (type absm absm))
-  (the list
-    (with-absm (dgop bar1) absm
-      (do ((dgop dgop (ash dgop -1))
-	   (rslt +empty-list+))
-	  ((and (zerop dgop) (endp bar1)) (nreverse rslt))
-	  (declare
-	     (fixnum dgop)
-	     (list rslt))
-	  (push (if (oddp dgop)
-		    0
-		  (pop bar1))
-		rslt)))))
-
-#|
-  (z-absm-bar (absm 0 '()))
-  (z-absm-bar (absm 1 '()))
-  (z-absm-bar (absm 0 '(2)))
-  (dotimes (i 8)
-    (print (z-absm-bar (absm i '(3 6)))))
-|#
-
-(DEFUN Z-BAR-ABSM (bar)
-  (declare (list bar))
-  (the absm
-     (do ((rslt-dgop 0)
-	  (rslt-bar +empty-list+)
-	  (mark bar (cdr mark))
-	  (bark 1 (+ bark bark)))
-	 ((endp mark) (absm rslt-dgop (nreverse rslt-bar)))
-	(declare
-	   (fixnum rslt-dgop bark)
-	   (list rslt-bar mark))
-	(let ((k-i (car mark)))
-	  (declare (fixnum k-i))
-	  (if (zerop k-i)
-	     (incf rslt-dgop bark)
-	     (push k-i rslt-bar))))))
-
-#|
-  (z-bar-absm (z-absm-bar (absm 0 '())))
-  (z-bar-absm (z-absm-bar (absm 1 '())))
-  (z-bar-absm (z-absm-bar (absm 0 '(2))))
-  (dotimes (i 8)
-    (print (z-bar-absm (z-absm-bar (absm i '(3 6))))))
-|#
-
-(DEFUN K-Z-1-GRML (dmns crpr)
-   (declare
-      (fixnum dmns)
-      (type crpr crpr))
-   (the absm
-      (with-crpr (dgop1 bar1 dgop2 bar2) crpr
-	 (do ((indx 1 (1+ indx))
-	      (dgop1 dgop1 (ash dgop1 -1))
-	      (dgop2 dgop2 (ash dgop2 -1))
-	      (bark 1 (ash bark +1))
-	      (rslt-dgop 0)
-	      (rslt-bar +empty-list+))
-	     ((> indx dmns) (absm rslt-dgop (nreverse rslt-bar)))
-	     (declare
-	        (fixnum indx dgop1 dgop2 bark rslt-dgop)
-		(list rslt-bar))
-	     (let ((item (if (evenp dgop1)
-			     (if (evenp dgop2)
-				 (+ (pop bar1) (pop bar2))
-			       (pop bar1))
-			   (if (evenp dgop2)
-			       (pop bar2)
-			     0))))
-	       (declare (fixnum item))
-	       (if (zerop item)
-		   (incf rslt-dgop bark)
-		 (push item rslt-bar)))))))
-
-#|
-  (k-z-1-grml 0 (crpr 0 nil 0 nil))
-  (k-z-1-grml 1 (crpr 0 '(3) 0 '(4)))
-  (k-z-1-grml 1 (crpr 0 '(3) 0 '(-3)))
-  (k-z-1-grml 1 (crpr 0 '(3) 1 '()))
-  (k-z-1-grml 1 (crpr 1 '() 0 '(3)))
-  (k-z-1-grml 1 (crpr 1 '() 1 '()))
-  (k-z-1-grml 5 (crpr 24 '(2 2 3) 20 '(-2 2 4)))
-|#
-
-(DEFUN K-Z-1-GRIN (dmns bar)
-  (declare
-     (ignore dmns)
-     (list bar))
-  (the absm
-     (absm 0 (mapcar #'- bar))))
-
-#|
-  (k-z-1-grin 3 '(2 3 -4))
-  (setf gmsm '(2 3 -4))
-  (k-z-1-grml 3 (crpr 0 gmsm 0 (gmsm (k-z-1-grin 3 gmsm))))
-|#
-
-#|
-(DEFUN K-Z-1-KFLL (indx dmns hat)
-  (declare
-     (fixnum indx dmns)
-     (list hat))
-  (the absm
-     (cond ((= 1 dmns)
-	    (absm 1 +empty-list+))
-	   ((zerop indx)
-	    (let ((del-1 (first hat))
-		  (del-2 (second hat)))
-	      (declare (type absm del-1 del-2))
-	      (with-absm (dgop1 bar1) del-1
-	      (with-absm (dgop2 bar2) del-2
-		 (let ((bar01 (if (oddp dgop2)
-				 0
-				 (first bar2)))
-		       (bar02 (if (oddp dgop1)
-				 0
-				 (first bar1))))
-		   (declare (fixnum bar01 bar02))
-		   (let ((bar12 (- bar02 bar01)))
-		     (declare (fixnum bar02))
-		     (if (zerop bar01)
-			(1dgnr 0 del-1)
-		        (if (zerop bar12)
-			   (1gnr 1 del-1)
-			   (let (del-01 (k-z-1-face 0 (1- dmns)
-						    del-1))
-			     (declare (type absm del-01))
-			     (with-absm (dgop01 gmsm01) del-01
-				(absm (* 4 dgop01)
-				      (cons bar01
-					    (cons bar02 gmsm01)))))))))))))
-	   ((= 1 indx)
-	    (let ((del-0 (first hat))
-		  (del-2 (second hat)))
-	      (declare (type absm del-0 del-2))
-	      (with-absm (dgop0 gmsm0) del-0
-	      (with-absm (dgop2 gmsm2) del-2
-		 (if (oddp dgop2 )))))))))
-
-|#
-
-(DEFUN K-Z-1 ()
-  (the ab-simplicial-group
-     (ab-simplicial-group
-      :cmpr #'k-z-1-cmpr
-      :basis :locally-effective
-      :bsgn +empty-list+
-      :face #'k-z-1-face
-      :grml-sintr #'k-z-1-grml
-	:grin-sintr #'k-z-1-grin
-	:dfnt '(k-z-1))))
-
-#|
-  (setf k (k-z-1))
-  (defun aleat-list (max length)
-     (let ((rslt nil)
-           (2max (+ max max)))
-        (dotimes (i length)
-           (push (let ((k (- (random 2max) max)))
-                    (if (zerop k)
-                       max
-                       k))
-              rslt))
-        rslt))
-  (? k (? k 14 (aleat-list 200 14)))
-  (setf zero? (add (idnt-mrph k) (grin k)))
-  (? zero? 14 (aleat-list 200 14))
-|#
-
-(DEFUN K-Z (n)
-   (declare (fixnum n))
-   (the ab-simplicial-group
-      (if (= n 1)
-         (k-z-1)
-         (classifying-space (k-z (1- n))))))
-
-(DEFUN CIRCLE-CMPR (gnrt1 gnrt2)
-   (declare (ignore gnrt1 gnrt2))
-   (the cmpr :equal))
-
-(DEFUN CIRCLE-BASIS (dmns)
-   (declare (fixnum dmns))
-   (the list
-      (case dmns
-	 (0 '(*))
-	 (1 '(s1))
-	 (otherwise +empty-list+))))
-
-(DEFUN CIRCLE ()
-   (the chain-complex
-      (chain-complex
-         :cmpr #'circle-cmpr
-	 :basis #'circle-basis
-	 :bsgn '*
-	 :dffr-intr #'zero-dffr-intr
-	 :dffr-strt :cmbn
-	 :dfnt '(circle))))
-
-#|
-  (setf c (circle))
-  (cmpr c '* '*)
-  (basis c 1)
-  (? c 1 's1)
-|#
-
-(DEFUN KZ1-RDCT-F-INTR (cmbn)
-  (declare (type cmbn cmbn))
-  (the cmbn
-     (with-cmbn (degr list) cmbn
-	(case degr
-	   (0 (if list
-		 (term-cmbn 0 (-cffc list) '*)
-		 (zero-cmbn 0)))
-	   (1 (let ((rslt
-		     (apply #'+
-			(mapcar
-			 #'(lambda (term)
-			     (declare (type term term))
-			     (with-term (cffc gnrt) term
-					(the fixnum (* cffc
-						       (first gnrt)))))
-			 list))))
-		(if (zerop rslt)
-		    (zero-cmbn 1)
-		  (term-cmbn 1 rslt 's1))))
-	   (otherwise (zero-cmbn degr))))))
-
-#|
-  (kz1-rdct-f-intr (cmbn 0))
-  (kz1-rdct-f-intr (cmbn 0 4 '()))
-  (kz1-rdct-f-intr (cmbn 1))
-  (kz1-rdct-f-intr (cmbn 1 4 '(3)))
-  (kz1-rdct-f-intr (cmbn 1 4 '(3) 5 '(2)))
-  (kz1-rdct-f-intr (cmbn 1 4 '(3) -3 '(4)))
-  (kz1-rdct-f-intr (cmbn -3))
-|#
-
-(DEFUN KZ1-RDCT-F ()
-  (the morphism
-     (morphism
-        :sorc (k-z-1)
-	:trgt (circle)
-	:degr 0
-	:intr #'kz1-rdct-f-intr
-	:strt :cmbn
-	:dfnt '(kz1-rdct-f))))
-
-(DEFUN KZ1-RDCT-G-INTR (cmbn)
-  (declare (type cmbn cmbn))
-  (the cmbn
-     (with-cmbn (degr list) cmbn
-	(if list
-	    (ecase degr
-	       (0 (term-cmbn 0 (-cffc list) +empty-list+))
-	       (1 (term-cmbn 1 (-cffc list) (list 1))))
-	  (zero-cmbn degr)))))
-
-(DEFUN KZ1-RDCT-G ()
-  (the morphism
-     (morphism
-        :sorc (circle)
-	:trgt (k-z-1)
-	:degr 0
-	:intr #'kz1-rdct-g-intr
-	:strt :cmbn
-	:dfnt '(kz1-rdct-g))))
-
-(DEFUN KZ1-RDCT-H-INTR (dmns bar)
-  (declare
-     (fixnum dmns)
-     (list bar))
-  (the cmbn
-     (progn
-       (when (zerop dmns)
-	  (return-from kz1-rdct-h-intr (zero-cmbn +1)))
-       (let ((k1 (first bar))
-	     (tail (rest bar)))
-	 (declare
-	    (fixnum k1)
-	    (list tail))
-	 (if (plusp k1)
-	    (do ((rslt +empty-list+
-		       (cons (term -1
-				   (cons 1 (cons i tail)))
-			     rslt))
-		 (i (1- k1) (1- i)))
-		((zerop i) (make-cmbn :degr (1+ dmns)
-				      :list rslt))
-	       (declare
-		  (list rslt)
-		  (fixnum i)))
-	    (do ((rslt +empty-list+
-		       (cons (term +1
-				   (cons 1 (cons i tail)))
-			     rslt))
-		 (i -1 (1- i)))
-		((< i k1) (make-cmbn :degr (1+ dmns)
-				     :list rslt))))))))
-
-#|
-  (kz1-rdct-h-intr 0 nil)
-  (kz1-rdct-h-intr 1 '(-4))
-  (kz1-rdct-h-intr 1 '(-1))
-  (kz1-rdct-h-intr 1 '(1))
-  (kz1-rdct-h-intr 1 '(4))
-  (kz1-rdct-h-intr 3 '(-4 3 5))
-  (kz1-rdct-h-intr 3 '(-1 3 -1))
-  (kz1-rdct-h-intr 3 '(1 2 2))
-  (kz1-rdct-h-intr 3 '(4 3 5))
-|#
-
-(DEFUN KZ1-RDCT-H ()
-  (the morphism
-     (morphism
-        :sorc (k-z-1)
-	:trgt (k-z-1)
-	:degr +1
-	:intr #'kz1-rdct-h-intr
-	:strt :gnrt
-	:dfnt '(kz1-rdct-h))))
-
-(DEFUN KZ1-RDCT ()
-  (the reduction
-     (reduction
-        :f (kz1-rdct-f)
-	:g (kz1-rdct-g)
-	:h (kz1-rdct-h)
-	:dfnt '(kz1-rdct))))
-
-#|
-  (pre-check-rdct (kz1-rdct))
-  (setf *tc* (cmbn 0 1 '()))
-  (setf *bc* (cmbn 0 1 '*))
-  (check-rdct)
-  (setf *tc* (cmbn 1 1 '(-4) 10 '(-1) 100 '(1) 1000 '(5)))
-  (setf *bc* (cmbn 1 1 's1))
-  (check-rdct)
-  (setf *tc* (cmbn 2 1 '(-4 2) 10 '(-1 3) 100 '(1 -4) 1000 '(5 5)))
-  (check-rdct)
-  (setf *tc* (cmbn 3 1 '(-4 -4 5) 10 '(-1 2 1)
-                     100 '(1 4 2) 1000 '(5 1 -1)))
-  (check-rdct)
-|#
-
-(DEFUN KZ1-EFHM ()
-  (the equivalence
-     (equivalence
-      :lrdct (trivial-rdct (k-z-1))
-      :rrdct (kz1-rdct)
-      :dfnt '(kz1-efhm))))
-
-(DEFMETHOD SEARCH-EFHM (k-z-1 (dfnt (eql 'k-z-1)))
-  (declare (ignore k-z-1))
-  (kz1-efhm))
-
-#|
-(cat-init)
-(homology (k-z-1) 1)
-|#
-
-(DEFUN K-Z2-1-GRML-INTR (dmns crpr)
-  (declare
-     (fixnum dmns)
-     (type crpr crpr))
-  (the absm
-     (with-crpr (dgop1 gmsm1 dgop2 gmsm2) crpr
-	(declare (ignore gmsm1 gmsm2))
-	(let ((dgop (- (mask dmns) (logxor dgop1 dgop2))))
-	  (declare (fixnum dgop))
-	  (absm dgop (- dmns (logcount dgop)))))))
-
-(DEFUN K-Z2-1-GRML ()
-  (the simplicial-mrph
-     (simplicial-mrph
-        :sorc (crts-prdc (r-proj-space) (r-proj-space))
-	:trgt (r-proj-space)
-	:degr 0
-	:sintr #'k-z2-1-grml-intr
-	:dfnt '(k-z2-1-grml))))
-
-(DEFUN K-Z2-1-GRIN-INTR (dmns gmsm)
-  (declare
-     (ignore dmns)
-     (fixnum gmsm))
-  (the absm
-     (absm 0 gmsm)))
-
-(DEFUN K-Z2-1-GRIN ()
-  (the simplicial-mrph
-     (simplicial-mrph
-        :sorc (r-proj-space)
-	:trgt (r-proj-space)
-	:degr 0
-	:sintr #'k-z2-1-grin-intr
-	:intr #'identity
-	:strt :cmbn
-	:dfnt '(k-z2-1-grin))))
-
-(DEFUN K-Z2-1 ()
-  (the ab-simplicial-group
-     (let ((rslt (r-proj-space)))
-       (declare (type simplicial-set rslt))
-       (change-class rslt 'ab-simplicial-group)
-       (setf (slot-value rslt 'grml)
-	     (k-z2-1-grml)
-	     (slot-value rslt 'grin)
-	     (k-z2-1-grin))
-       rslt)))
-
-#|
-  (setf k (k-z2-1))
-  (homology k 0 4)
-|#
-
-(DEFUN K-Z2 (n)
-   (declare (fixnum n))
-   (the ab-simplicial-group
-      (if (= n 1)
-         (k-z2-1)
-         (classifying-space (k-z2 (1- n))))))
-
-#|
-  (setf k3 (k-z2 3))
-  (homology k3 7)
-|#
-
-(DEFUN Z2-ABSM-BAR (absm)
-  (declare (type absm absm))
-  (the list
-     (with-absm (dgop gmsm) absm
-       (do ((bmark (1- (+ (logcount dgop) gmsm)) (1- bmark))
-	    (rslt +empty-list+
-		  (cons (if (logbitp bmark dgop)
-			    0 1)
-			rslt)))
-	   ((minusp bmark) rslt)
-	  (declare
-	     (fixnum bmark)
-	     (list rslt))))))
-
-(DEFUN Z2-BAR-ABSM (bar)
-  (declare (list bar))
-  (the absm
-     (do ((dgop 0)
-	  (2-pwr 1 (+ 2-pwr 2-pwr))
-	  (gmsm 0)
-	  (mark bar (cdr mark)))
-	 ((endp mark) (absm dgop gmsm))
-	(declare
-	   (fixnum dgop 2-pwr gmsm)
-	   (list mark))
-	(if (zerop (car mark))
-	   (incf dgop 2-pwr)
-	   (incf gmsm)))))
-
-#|
-  (dotimes (i 8)    ;;; not really legal
-  (dotimes (j 8)
-    (print (z2-bar-absm (z2-absm-bar (absm i j))))))
-|#
-
-
-(DEFUN HOPF-FIBRATION-SINTR (n)
-  (declare (fixnum n))
-  (flet ((rslt (dmns gmsm)
-	   (declare (ignore dmns gmsm))
-	   (if (zerop n)
-	      (absm 1 +empty-list+)
-	      (absm 0 (list n)))))
-     (the sintr #'rslt)))
-
-(DEFUN HOPF-FIBRATION (n)
-  (declare (fixnum n))
-  (the simplicial-mrph
-     (simplicial-mrph
-        :sorc (sphere 2)
-	:trgt (k-z-1)
-	:degr -1
-	:sintr (hopf-fibration-sintr n)
-	:dfnt `(hopf-fibration ,n))))
-
-(DEFUN Z-FUNDAMENTAL-GMSM (dmns pi-elm)   ;;; pi-elm not equal to 0
-   (declare (fixnum dmns pi-elm))
-   (the gmsm
-      (if (= 1 dmns)
-         (list pi-elm)
-         (let ((bsgn (if (= 2 dmns) +empty-list+ +null-gbar+)))
-            (declare (type gmsm bsgn))
-            (make-gbar :dmns dmns
-               :list (cons (absm 0 (z-fundamental-gmsm (1- dmns) pi-elm))
-                        (mapcar
-                           #'(lambda (k)
-                                (declare (fixnum k))
-                                (absm (mask k) bsgn))
-                           (nreverse (<a-b> 0 (- dmns 2))))))))))
-
-#|
-  (z-fundamental-gmsm 1 33)
-  (z-fundamental-gmsm 2 33)
-  (z-fundamental-gmsm 3 33)
-  (z-fundamental-gmsm 4 33)
-|#
-
-(DEFUN INTERESTING-FACES (face small-dmns high-dmns gmsm)
-  (declare
-    (type face face)
-    (fixnum small-dmns high-dmns)
-    (type gmsm gmsm))
-  (the list
-    (let ((max (mask high-dmns)))
-      (declare (fixnum max))
-      (if (= small-dmns high-dmns)
-	 (list (cons max (absm 0 gmsm)))
-	 (do ((prev-list (interesting-faces face (1+ small-dmns) high-dmns gmsm))
-	      (k (1- max) (1- k))
-	      (rslt +empty-list+)
-	      (count (binomial-n-p high-dmns small-dmns)))
-	     ((zerop count) rslt)
-	     (declare
-	       (list prev-list rslt)
-	       (fixnum k count))
-	    (when (= small-dmns (logcount k))
-	      (decf count)
-	      (do ((i 0 (1+ i)))
-	          ((not (logbitp i k))
-		   (push (cons k
-			       (a-face4 face
-					(- small-dmns -1
-					   (if (= i (integer-length k)) (1+ i) i))
-					(1+ small-dmns)
-					(cdr (assoc (+ k (2-exp i)) prev-list))))
-			 rslt)))))))))
-
-#|
-  (setf d (delta 14))
-  (setf f (face d))
-  (do ((i 5 (1- i)))
-      ((minusp i))
-    (print (interesting-faces f i 5 (mask 6))))
-|#     
-
-(DEFUN GMSM-COCYCLE (face small-dmns high-dmns gmsm chml-clss)
-  (declare
-    (type face face)
-    (fixnum small-dmns high-dmns)
-    (type gmsm gmsm)
-    (type morphism chml-clss))
-  (the list
-    (let ((int-faces (interesting-faces face small-dmns high-dmns gmsm)))
-      (declare (list int-faces))
-      (mapc
-        #'(lambda (cons)
-	    (declare (cons cons))
-	    (setf (cdr cons)
-		  (let ((absm (cdr cons)))
-		    (declare (type absm absm))
-		    (with-absm (dgop gmsm2) absm
-		      (if (plusp dgop)
-			 0
-			(let ((cmbn-list (cmbn-list (gnrt-? chml-clss
-						 small-dmns gmsm2))))
-			  (declare (list cmbn-list))
-			  (if cmbn-list
-			      (-cffc cmbn-list)
-			    0)))))))
-        int-faces)
-      int-faces)))
-
-#|
-  (cat-init)
-  (setf d (delta 10))
-  (setf chml-clss
-    (morphism :sorc d :trgt (z-chcm) :degr -2
-                :intr #'(lambda (dmns gmsm)
-                          (term-cmbn 0 gmsm :gnrt-z))
-                :strt :gnrt
-                :dfnt '(essai-1)))
-  (gmsm-cocycle (face d) 2 4 31 chml-clss)
-  (setf chml-clss
-    (morphism :sorc d :trgt (z-chcm) :degr -1
-                :intr #'(lambda (dmns gmsm)
-                          (term-cmbn 0 gmsm :gnrt-z))
-                :strt :gnrt
-                :dfnt '(essai-2)))
-  (gmsm-cocycle (face d) 1 4 31 chml-clss)
-|#
-
-(DEFUN Z-COCYCLE-GBAR (n dmns cocycle)
-  ;; cocycle \in Z^n(\Delta^{dmns}, \pi) with \pi = Z
-  (declare
-    (fixnum n dmns)
-    (list cocycle))
-  (the absm
-    (cond ((= n 1)
-	   (z-bar-absm (nreverse (mapcar #'cdr cocycle))))
-	  ((= n dmns)
-	   (let ((value (cdr (first cocycle))))
-	     (declare (fixnum value))
-	     (if (zerop value)
-		(absm (mask dmns) +null-gbar+)
-	        (absm 0 (z-fundamental-gmsm dmns value)))))
-	  (t
-	   (let ((cocycle1 +empty-list+)
-		 (cocycle2 +empty-list+))
-	     (declare (list cocycle1 cocycle2))
-	     (dolist (cons cocycle)
-	       (declare (cons cons))
-	       (if (evenp (car cons))
-		  (push (cons (ash (car cons) -1) (cdr cons))
-			cocycle1)
-		  (push (cons (ash (car cons) -1) (cdr cons))
-			cocycle2)))
-	     (setf cocycle1 (nreverse cocycle1)
-		   cocycle2 (nreverse cocycle2))
-	     (mapc
-	       #'(lambda (cons)
-		   (declare (cons cons))
-		   (when (evenp (car cons))
-		     (decf (cdr cons)
-			   (cdr (assoc (1+ (car cons)) cocycle1)))))
-	       cocycle2)
-	     (let ((head-absm (z-cocycle-gbar (1- n) (1- dmns) cocycle2))
-		   (tail-absm (z-cocycle-gbar n (1- dmns) cocycle1)))
-	       (declare (type absm head-absm tail-absm))
-	       (normalize-gbar
-		 (cons dmns
-		       (cons head-absm
-			     (rest (unnormalize-gbar tail-absm
-				     (if (= n 2) () +null-gbar+))))))))))))
-
-#|
-  (cat-init)
-  (setf d (delta 10))
-  (setf chml-clss
-    (morphism :sorc d :trgt (z-chcm) :degr -1
-                :intr #'(lambda (dmns gmsm)
-                          (term-cmbn 0 gmsm :gnrt-z))
-                :strt :gnrt
-                :dfnt '(essai-1)))
-  (gmsm-cocycle (face d) 1 4 31 chml-clss)
-  (z-cocycle-gbar 1 4 *)
-  (setf chml-clss
-    (morphism :sorc d :trgt (z-chcm) :degr -2
-                :intr #'(lambda (dmns gmsm)
-                          (term-cmbn 0 gmsm :gnrt-z))
-                :strt :gnrt
-                :dfnt '(essai-2)))
-  (gmsm-cocycle (face d) 2 2 7 chml-clss)
-  (z-cocycle-gbar 2 2 *)
-  (gmsm-cocycle (face d) 2 2 0 chml-clss) ;; normally illegal
-  (z-cocycle-gbar 2 2 *)
-  (gmsm-cocycle (face d) 2 3 15 chml-clss)
-  (z-cocycle-gbar 2 3 *)
-  (gmsm-cocycle (face d) 2 4 31 chml-clss)
-  (z-cocycle-gbar 2 4 *)
-  (setf chml-clss
-    (morphism :sorc d :trgt (z-chcm) :degr -3
-                :intr #'(lambda (dmns gmsm)
-                          (term-cmbn 0 gmsm :gnrt-z))
-                :strt :gnrt
-                :dfnt '(essai-3)))
-  (gmsm-cocycle (face d) 3 4 31 chml-clss)
-  (z-cocycle-gbar 3 4 *)
-  (setf chml-clss
-    (morphism :sorc d :trgt (z-chcm) :degr -3
-                :intr #'(lambda (dmns gmsm)
-                          (zero-cmbn 0))
-                :strt :gnrt
-                :dfnt '(essai-33)))
-  (gmsm-cocycle (face d) 3 4 31 chml-clss)
-  (z-cocycle-gbar 3 4 *)
-|#
-
-(DEFUN Z-COCYCLE-GBAR-HEAD (n dmns cocycle)
-  ;; cocycle \in Z^n(\Delta^{dmns}, \pi) with \pi = Z
-  (declare
-    (fixnum n dmns)
-    (list cocycle))
-  (the absm
-    (cond ((= n 1)
-	   (error "In Z-COCYCLE-GBAR-HEAD, this point should not have been reached."))
-	   ; (z-bar-absm (nreverse (mapcar #'cdr cocycle))))
-	  ((= n dmns)
-	   (let ((value (cdr (first cocycle))))
-	     (declare (fixnum value))
-	     (if (zerop value)
-		(if (= n 2)
-		   (absm 1 +empty-list+)
-		   (absm (mask (1- dmns)) +null-gbar+))
-	       (absm 0 (z-fundamental-gmsm (1- dmns) value)))))
-	  (t
-	   (let ((cocycle1 +empty-list+)
-		 (cocycle2 +empty-list+))
-	     (declare (list cocycle1 cocycle2))
-	     (dolist (cons cocycle)
-	       (declare (cons cons))
-	       (if (evenp (car cons))
-		  (push (cons (ash (car cons) -1) (cdr cons))
-			cocycle1)
-		  (push (cons (ash (car cons) -1) (cdr cons))
-			cocycle2)))
-	     (setf cocycle1 (nreverse cocycle1)
-		   cocycle2 (nreverse cocycle2))
-	     (mapc
-	       #'(lambda (cons)
-		   (declare (cons cons))
-		   (when (evenp (car cons))
-		     (decf (cdr cons)
-			   (cdr (assoc (1+ (car cons)) cocycle1)))))
-	       cocycle2)
-	     (z-cocycle-gbar (1- n) (1- dmns) cocycle2))))))
-
-#|
-  (cat-init)
-  (setf d (delta 10))
-  (setf chml-clss
-    (morphism :sorc d :trgt (z-chcm) :degr -1
-                :intr #'(lambda (dmns gmsm)
-                          (term-cmbn 0 gmsm :gnrt-z))
-                :strt :gnrt
-                :dfnt '(essai-1)))
-  (gmsm-cocycle (face d) 1 4 31 chml-clss)
-  (z-cocycle-gbar 1 4 *)
-  (z-cocycle-gbar-head 1 4 **)
-  (setf chml-clss
-    (morphism :sorc d :trgt (z-chcm) :degr -2
-                :intr #'(lambda (dmns gmsm)
-                          (term-cmbn 0 gmsm :gnrt-z))
-                :strt :gnrt
-                :dfnt '(essai-2)))
-  (gmsm-cocycle (face d) 2 2 7 chml-clss)
-  (z-cocycle-gbar 2 2 *)
-  (z-cocycle-gbar-head 2 2 **)
-  (gmsm-cocycle (face d) 2 2 0 chml-clss) ;; normally illegal
-  (z-cocycle-gbar 2 2 *)
-  (z-cocycle-gbar-head 2 2 **)
-  (gmsm-cocycle (face d) 2 3 15 chml-clss)
-  (z-cocycle-gbar 2 3 *)
-  (z-cocycle-gbar-head 2 3 **)
-  (gmsm-cocycle (face d) 2 4 31 chml-clss)
-  (z-cocycle-gbar 2 4 *)
-  (z-cocycle-gbar-head 2 4 **)
-  (setf chml-clss
-    (morphism :sorc d :trgt (z-chcm) :degr -3
-                :intr #'(lambda (dmns gmsm)
-                          (term-cmbn 0 gmsm :gnrt-z))
-                :strt :gnrt
-                :dfnt '(essai-3)))
-  (gmsm-cocycle (face d) 3 4 31 chml-clss)
-  (z-cocycle-gbar 3 4 *)
-  (z-cocycle-gbar-head 3 4 **)
-  (setf chml-clss
-    (morphism :sorc d :trgt (z-chcm) :degr -3
-                :intr #'(lambda (dmns gmsm)
-                          (zero-cmbn 0))
-                :strt :gnrt
-                :dfnt '(essai-33)))
-  (gmsm-cocycle (face d) 3 4 31 chml-clss)
-  (z-cocycle-gbar 3 4 *)
-  (z-cocycle-gbar-head 3 4 **)
-|#
-
-(DEFUN Z2-FUNDAMENTAL-GMSM (dmns pi-elm)  ;; pi-elm not "equal" to 0, therefore 1.
-   (declare (fixnum dmns pi-elm))
-   (the gmsm
-      (if (= 1 dmns)
-         1
-         (let ((bsgn (if (= 2 dmns) 0 +null-gbar+)))
-            (declare (type gmsm bsgn))
-            (make-gbar :dmns dmns
-               :list (cons (absm 0 (Z2-fundamental-gmsm (1- dmns) pi-elm))
-                        (mapcar
-                           #'(lambda (k)
-                                (declare (fixnum k))
-                                (absm (mask k) bsgn))
-                           (nreverse (<a-b> 0 (- dmns 2))))))))))
-
-#|
-  (Z2-fundamental-gmsm 1 1)
-  (Z2-fundamental-gmsm 2 1)
-  (Z2-fundamental-gmsm 3 1)
-  (Z2-fundamental-gmsm 4 1)
-|#    
-
-(DEFUN Z2-COCYCLE-GBAR (n dmns cocycle)
-  ;; cocycle \in Z^n(\Delta^{dmns}, \pi) with \pi = Z/2Z
-  (declare
-    (fixnum n dmns)
-    (list cocycle))
-  (the absm
-    (progn
-      (mapc
-        #'(lambda (cons)
-	    (declare (cons cons))
-	    (setf (cdr cons)
-		  (if (evenp (cdr cons)) 0 1)))
-        cocycle)
-      (cond ((= n 1)
-	     (z2-bar-absm (nreverse (mapcar #'cdr cocycle))))
-	    ((= n dmns)
-	     (let ((value (cdr (first cocycle))))
-	       (declare (fixnum value))
-	       (if (zerop value)
-		   (absm (mask dmns) +null-gbar+)
-		 (absm 0 (z2-fundamental-gmsm dmns value)))))
-	    (t
-	     (let ((cocycle1 +empty-list+)
-		   (cocycle2 +empty-list+))
-	       (declare (list cocycle1 cocycle2))
-	       (dolist (cons cocycle)
-		 (declare (cons cons))
-		 (if (evenp (car cons))
-		     (push (cons (ash (car cons) -1) (cdr cons))
-			   cocycle1)
-		   (push (cons (ash (car cons) -1) (cdr cons))
-			 cocycle2)))
-	       (setf cocycle1 (nreverse cocycle1)
-		     cocycle2 (nreverse cocycle2))
-	       (mapc
-		#'(lambda (cons)
-		    (declare (cons cons))
-		    (when (evenp (car cons))
-			  (setf (cdr cons)
-				(mod (- (cdr cons)
-					(cdr (assoc (1+ (car cons)) cocycle1)))
-				     2))))
-		cocycle2)
-	       (let ((head-absm (z2-cocycle-gbar (1- n) (1- dmns) cocycle2))
-		     (tail-absm (z2-cocycle-gbar n (1- dmns) cocycle1)))
-		 (declare (type absm head-absm tail-absm))
-		 (normalize-gbar
-		  (cons dmns
-			(cons head-absm
-			      (rest (unnormalize-gbar tail-absm
-						      (if (= n 2) 0 +null-gbar+)))))))))))))
-
-#|
-  (cat-init)
-  (setf d (delta 10))
-  (setf chml-clss
-    (morphism :sorc d :trgt (z-chcm) :degr -1
-                :intr #'(lambda (dmns gmsm)
-                          (term-cmbn 0 (mod gmsm 2) :gnrt-z))
-                :strt :gnrt
-                :dfnt '(essai-1)))
-  (gmsm-cocycle (face d) 1 4 31 chml-clss)
-  (z2-cocycle-gbar 1 4 *)
-  (setf chml-clss
-    (morphism :sorc d :trgt (z-chcm) :degr -2
-                :intr #'(lambda (dmns gmsm)
-                          (term-cmbn 0 (mod gmsm 2) :gnrt-z))
-                :strt :gnrt
-                :dfnt '(essai-2)))
-  (gmsm-cocycle (face d) 2 2 7 chml-clss)
-  (z2-cocycle-gbar 2 2 *)
-  (gmsm-cocycle (face d) 2 2 0 chml-clss) ;; normally illegal
-  (z2-cocycle-gbar 2 2 *)
-  (gmsm-cocycle (face d) 2 3 15 chml-clss)
-  (z2-cocycle-gbar 2 3 *)
-  (gmsm-cocycle (face d) 2 4 31 chml-clss)
-  (z2-cocycle-gbar 2 4 *)
-  (setf chml-clss
-    (morphism :sorc d :trgt (z-chcm) :degr -3
-                :intr #'(lambda (dmns gmsm)
-                          (term-cmbn 0 (mod gmsm 2) :gnrt-z))
-                :strt :gnrt
-                :dfnt '(essai-3)))
-  (gmsm-cocycle (face d) 3 4 31 chml-clss)
-  (z2-cocycle-gbar 3 4 *)
-|#
-
-(DEFUN Z2-COCYCLE-GBAR-HEAD (n dmns cocycle)
-  ;; cocycle \in Z^n(\Delta^{dmns}, \pi) with \pi = Z/2Z
-  (declare
-    (fixnum n dmns)
-    (list cocycle))
-  (the absm
-    (progn
-      (mapc
-        #'(lambda (cons)
-	    (setf (cdr cons)
-		  (if (evenp (cdr cons)) 0 1)))
-        cocycle)
-      (cond ((= n 1)
-	     (error "In Z2-COCYCLE-GBAR-HEAD, this point should not have been reached."))
-		 ; (z2-bar-absm (nreverse (mapcar #'cdr cocycle))))
-	    ((= n dmns)
-	     (let ((value (cdr (first cocycle))))
-	       (declare (fixnum value))
-	       (if (zerop value)
-		   (if (= n 2)
-		       (absm 1 0)
-		     (absm (mask (1- dmns)) +null-gbar+))
-		 (absm 0 (z2-fundamental-gmsm (1- dmns) value)))))
-	    (t
-	     (let ((cocycle1 +empty-list+)
-		   (cocycle2 +empty-list+))
-	       (declare (list cocycle1 cocycle2))
-	       (dolist (cons cocycle)
-		 (declare (cons cons))
-		 (if (evenp (car cons))
-		     (push (cons (ash (car cons) -1) (cdr cons))
-			   cocycle1)
-		   (push (cons (ash (car cons) -1) (cdr cons))
-			 cocycle2)))
-	       (setf cocycle1 (nreverse cocycle1)
-		     cocycle2 (nreverse cocycle2))
-	       (mapc
-		#'(lambda (cons)
-		    (declare (cons cons))
-		    (when (evenp (car cons))
-			  (setf (cdr cons)
-				(mod (- (cdr cons)
-					(cdr (assoc (1+ (car cons)) cocycle1)))
-				     2))))
-		cocycle2)
-	       (z2-cocycle-gbar (1- n) (1- dmns) cocycle2)))))))
-
-#|
-  (cat-init)
-  (setf d (delta 10))
-  (setf chml-clss
-    (morphism :sorc d :trgt (z-chcm) :degr -1
-                :intr #'(lambda (dmns gmsm)
-                          (term-cmbn 0 (mod gmsm 2) :gnrt-z))
-                :strt :gnrt
-                :dfnt '(essai-1)))
-  (gmsm-cocycle (face d) 1 4 31 chml-clss)
-  (z2-cocycle-gbar 1 4 *)
-  (z2-cocycle-gbar-head 1 4 **)
-  (setf chml-clss
-    (morphism :sorc d :trgt (z-chcm) :degr -2
-                :intr #'(lambda (dmns gmsm)
-                          (term-cmbn 0 (mod gmsm 2) :gnrt-z))
-                :strt :gnrt
-                :dfnt '(essai-2)))
-  (gmsm-cocycle (face d) 2 2 7 chml-clss)
-  (z2-cocycle-gbar 2 2 *)
-  (z2-cocycle-gbar-head 2 2 **)
-  (gmsm-cocycle (face d) 2 2 0 chml-clss) ;; normally illegal
-  (z2-cocycle-gbar 2 2 *)
-  (z2-cocycle-gbar-head 2 2 **)
-  (gmsm-cocycle (face d) 2 3 15 chml-clss)
-  (z2-cocycle-gbar 2 3 *)
-  (z2-cocycle-gbar-head 2 3 **)
-  (gmsm-cocycle (face d) 2 4 31 chml-clss)
-  (z2-cocycle-gbar 2 4 *)
-  (z2-cocycle-gbar-head 2 4 **)
-  (setf chml-clss
-    (morphism :sorc d :trgt (z-chcm) :degr -3
-                :intr #'(lambda (dmns gmsm)
-                          (term-cmbn 0 (mod gmsm 2) :gnrt-z))
-                :strt :gnrt
-                :dfnt '(essai-3)))
-  (gmsm-cocycle (face d) 3 4 31 chml-clss)
-  (z2-cocycle-gbar 3 4 *)
-  (z2-cocycle-gbar-head 3 4 **)
-|#
-
-(DEFUN K-Z-FUNDAMENTAL-CLASS (n)
-  (declare (fixnum n))
-  (the morphism
-    (morphism
-      :sorc (k-z n) :trgt (z-chcm) :degr (- n)
-      :intr #'(lambda (dmns gmsm)
-		(declare
-		  (fixnum dmns)
-		  (type gmsm gmsm))
-		(if (= dmns n)
-		   (do ((gmsm gmsm (gmsm (first (gbar-list gmsm))))
-			(dmns dmns (1- dmns)))
-		       ((= 1 dmns)
-			(term-cmbn 0 (first gmsm) :z-gnrt))
-		       (declare
-			 (type gmsm gmsm)
-			 (fixnum dmns)))
-		  (zero-cmbn (- dmns n))))
-      :strt :gnrt
-      :dfnt `(k-z-fundamental-class ,n))))
-
-#|
-  (cat-init)
-  (setf c1 (k-z-fundamental-class 1))
-  (? c1 1 '(34))
-  (? c1 2 '(34 45))
-  (setf c3 (k-z-fundamental-class 3))
-  (? c3 3 (z-fundamental-gmsm 3 45))
-|#
-
-(DEFUN K-Z2-FUNDAMENTAL-CLASS (n)
-  (declare (fixnum n))
-  (the morphism
-    (morphism
-      :sorc (k-z2 n) :trgt (z-chcm) :degr (- n)
-      :intr #'(lambda (dmns gmsm)
-		(declare
-		  (fixnum dmns)
-		  (ignore gmsm))
-		(if (= dmns n)
-		   (term-cmbn 0 1 :z-gnrt)
-		  (zero-cmbn (- dmns n))))
-      :strt :gnrt
-      :dfnt `(k-z2-fundamental-class ,n))))
-
-#|
-  (cat-init)
-  (setf c1 (k-z2-fundamental-class 1))
-  (? c1 1 1)
-  (? c1 2 2)
-  (setf c3 (k-z2-fundamental-class 3))
-  (? c3 3 (z2-fundamental-gmsm 3 1))
-|#
-
diff --git a/archive/Kenzo-2/Kenzo-2-Acl5/kan.cl b/archive/Kenzo-2/Kenzo-2-Acl5/kan.cl
deleted file mode 100644
index 7b8f305..0000000
--- a/archive/Kenzo-2/Kenzo-2-Acl5/kan.cl
+++ /dev/null
@@ -1,182 +0,0 @@
-;;;  KAN  KAN  KAN  KAN  KAN  KAN  KAN  KAN  KAN  KAN  KAN  KAN
-;;;  KAN  KAN  KAN  KAN  KAN  KAN  KAN  KAN  KAN  KAN  KAN  KAN
-;;;  KAN  KAN  KAN  KAN  KAN  KAN  KAN  KAN  KAN  KAN  KAN  KAN
-
-(IN-PACKAGE "CAT")
-
-(provide "kan")
-
-(DEFMETHOD PRINT-OBJECT ((kan kan) stream)
-  (the kan
-     (progn
-       (format stream "[K~D Kan-Simplicial-Set]" (idnm kan))
-       kan)))
-
-(DEFMACRO KFLL (&rest rest)
-  (ecase (length rest)
-     (1 `(kfll1 ,@rest))
-     (4 `(kfll4 ,@rest))))
-
-(DEFMACRO KFLL4 (kan indx dmns hat)
-  `(funcall (kfll1 ,kan) ,indx ,dmns ,hat))
-
-#|
-  (setf d (delta-infinity))
-  (defun vertex-i (absm i)
-     (with-absm (dgop gmsm) absm
-       (let ((dgop (nreverse (dgop-int-ext dgop)))
-             (gmsm (dlop-int-ext gmsm)))
-         (do ((dgop-mark dgop)
-              (gmsm-mark gmsm)
-              (ii 0 (1+ ii)))
-             ((= i ii) (car gmsm-mark))
-            (if (and dgop-mark
-                     (= ii (car dgop-mark)))
-               (pop dgop-mark)
-               (pop gmsm-mark))))))
-  (vertex-i (absm 0 1) 0)
-  (vertex-i (absm 1 1) 0)
-  (vertex-i (absm 1 1) 1)
-  (vertex-i (absm 0 3) 0)
-  (vertex-i (absm 0 3) 1)
-  (vertex-i (absm 3 1) 0)
-  (vertex-i (absm 3 1) 1)
-  (vertex-i (absm 3 1) 2)
-  (vertex-i (absm 1 3) 0)
-  (vertex-i (absm 1 3) 1)
-  (vertex-i (absm 1 3) 2)
-  (vertex-i (absm 2 3) 0)
-  (vertex-i (absm 2 3) 1)
-  (vertex-i (absm 2 3) 2)
-  (vertex-i (absm 0 7) 0)
-  (vertex-i (absm 0 7) 1)
-  (vertex-i (absm 0 7) 2)
-  (defun absm-int-ext (absm)
-     (with-absm (dgop gmsm) absm
-        (do ((dgop (nreverse (dgop-int-ext dgop)))
-             (gmsm (rest (dlop-int-ext gmsm)))
-             (i 0 (1+ i))
-             (rslt (list (first (dlop-int-ext gmsm)))))
-            ((and (endp dgop) (endp gmsm)) (nreverse rslt))
-           (if dgop
-              (if (= i (car dgop))
-                 (progn
-                   (pop dgop)
-                   (push (first rslt) rslt))
-                 (push (pop gmsm) rslt))
-              (return (nreconc rslt gmsm))))))
-  (defun absm-ext-int (vlist)
-     (do ((dgop nil)
-          (gmsm (list (first vlist)))
-          (mark (rest vlist) (cdr mark))
-          (idgop 0 (1+ idgop)))
-         ((endp mark) (absm (dgop-ext-int dgop)
-                            (dgop-ext-int gmsm)))
-        (if (= (first gmsm) (car mark))
-           (push idgop dgop)
-           (push (car mark) gmsm))))
-  (absm-ext-int '(0 0 0 1 2 3 3 3))
-  (absm-ext-int '(0 1 1 1 2))
-  (absm-int-ext (absm-ext-int '(0 0 0 1 2 3 3 3)))
-  (absm-int-ext (absm-ext-int '(0 1 1 1 2)))
-  (defun dkfll (indx dmns hat)
-     (cond ((= 1 dmns)
-            (absm 1 (gmsm (first hat))))
-           ((= 0 indx)
-            (let ((del-1 (absm-int-ext (first hat)))
-                  (del-2 (absm-int-ext (second hat))))
-              (absm-ext-int
-                 (cons (first del-1)
-                       (cons (second del-2) (rest del-1))))))
-           ((= 1 indx)
-            (let ((del-0 (absm-int-ext (first hat)))
-                  (del-2 (absm-int-ext (second hat))))
-              (absm-ext-int
-                 (cons (first del-2) del-0))))
-           (t
-            (let ((del-0 (absm-int-ext (first hat)))
-                  (del-1 (absm-int-ext (second hat))))
-              (absm-ext-int
-                 (cons (first del-1) del-0))))))
-  (smst-kan d #'dkfll)
-  (kfll d 0 1 (list (absm 0 1)))
-  (kfll d 0 2 (list (absm 0 5) (absm 0 3)))
-  (kfll d 1 2 (list (absm 0 6) (absm 0 3)))
-  (kfll d 2 2 (list (absm 0 6) (absm 0 5)))
-  (kfll d 0 2 (list (absm 0 3) (absm 0 3)))
-  (kfll d 1 2 (list (absm 1 2) (absm 0 3)))
-|#
-
-(DEFUN CHECK-HAT (kan indx dmns hat)
-  (declare
-     (type kan kan)
-     (fixnum indx dmns)  ;;; dmns like in (funcall kfll ...)
-     (list hat))
-  (assert (= dmns (length hat)))
-  (setf hat
-	(append (subseq hat 0 indx)
-		(list :hole)
-		(nthcdr indx hat)))
-  (do ((cmpr (cmpr kan))
-       (j 0 (1+ j)))
-      ((> j dmns) t)
-      (declare
-         (type cmprf cmpr)
-	 (fixnum j))
-     (unless (= j indx)
-       (let ((del-j (nth j hat)))
-	 (declare (type absm del-j))
-	 (do ((i j (1+ i)))
-	     ((= i dmns))
-	     (declare (fixnum i))
-	    (unless (= i (1- indx))
-	      (let ((del-i-del-j (face kan i (1- dmns) del-j))
-		    (del-j-del-i+1 (face kan j (1- dmns)
-					 (nth (1+ i) hat))))
-		(declare (type absm del-i-del-j del-j-del-i+1))
-		(assert (eq :equal
-			    (a-cmpr3 cmpr del-i-del-j del-j-del-i+1))))))))))
-
-#|
-  (setf od (gdeltab))
-  (setf s (loop3 0 31 2))
-  (setf faces (mapcar #'(lambda (indx) (face od indx 3 s))
-                      '(0 1 2 3)))
-  (delete (nth 1 faces) faces)
-  (check-hat od 1 3 faces)
-  (setf (nth 2 faces) (nth 1 faces))
-  (check-hat od 1 3 faces)
-|#
-
-
-(DEFUN CHECK-KAN (kan indx dmns hat)
-  (declare
-     (type kan kan)
-     (fixnum indx dmns)
-     (list hat))
-  (the (values)
-     (let ((rslt (kfll kan indx dmns hat))
-	   (cmpr (cmpr kan))
-	   (face (face kan)))
-       (declare
-	  (type absm rslt)
-	  (type cmprf cmpr)
-	  (type face face))
-       (check-hat kan indx dmns hat)
-       (do ((i 0 (1+ i)))
-	   ((> i dmns))
-	  (declare (fixnum i))
-	  (unless (= i indx)
-	    (let ((x-i (pop hat))
-		  (del-i-rslt (a-face4 face i dmns rslt)))
-	      (declare (type absm x-i del-i-rslt))
-	      (with-absm (dgop1 gmsm1) x-i
-	      (with-absm (dgop2 gmsm2) del-i-rslt
-		 (unless (and (= dgop1 dgop2)
-			      (eq (funcall cmpr gmsm1 gmsm2) :equal))
-		    (error "Wrong result:~@
-                            Fill = ~A~@
-                            Del-~D(Fill) = ~A~@
-                            Hat-~D = ~A"
-		       rslt i del-i-rslt i x-i)))))))
-       (done))))
\ No newline at end of file
diff --git a/archive/Kenzo-2/Kenzo-2-Acl5/loop-spaces.cl b/archive/Kenzo-2/Kenzo-2-Acl5/loop-spaces.cl
deleted file mode 100644
index 1beb970..0000000
--- a/archive/Kenzo-2/Kenzo-2-Acl5/loop-spaces.cl
+++ /dev/null
@@ -1,610 +0,0 @@
-;;;  LOOP-SPACES  LOOP-SPACES  LOOP-SPACES  LOOP-SPACES  LOOP-SPACES  LOOP-SPACES
-;;;  LOOP-SPACES  LOOP-SPACES  LOOP-SPACES  LOOP-SPACES  LOOP-SPACES  LOOP-SPACES
-;;;  LOOP-SPACES  LOOP-SPACES  LOOP-SPACES  LOOP-SPACES  LOOP-SPACES  LOOP-SPACES
-
-(IN-PACKAGE "CAT")
-
-(PROVIDE "loop-spaces")
-
-(DEFCONSTANT +NULL-LOOP+ (make-loop :list +empty-list+))
-
-;;; NILOOP = non-normalized iloop; a common dgop is possible.
-
-(DEFUN NORMALIZE-LOOP (dmns niloop)
-   (declare (list niloop))      
-   (the absm
-      (progn
-         (unless niloop
-            (return-from normalize-loop
-               (absm (mask dmns) +null-loop+)))
-         (let ((dgop (apply #'logand (mapcar #'car niloop))))
-            (declare (fixnum dgop))
-            (if (zerop dgop)
-               (absm 0 (make-loop :list niloop))
-               (absm dgop
-                  (make-loop
-                     :list (mapcar #'(lambda (apowr)
-                                        (cons
-                                           (dgop/dgop (apdgop apowr) dgop)
-                                           (cdr apowr)))
-                              niloop))))))))
-
-#|
-  (normalize-loop 4 +empty-list+)
-  (normalize-loop 4 '((1 a . 1)))
-  (normalize-loop 4 '((1 a . 1) (3 b . 1) (5 b . 1)))
-|#
-
-(DEFUN UNNORMALIZE-LOOP (absm)
-  (declare (type absm absm))
-  (the iloop
-     (with-absm (dgop loop) absm
-        (mapcar #'(lambda (apowr)
-		    (declare (type apowr apowr))
-		    (cons (dgop*dgop dgop (car apowr))
-			  (cdr apowr)))
-		(loop-list loop)))))
-
-#|
-  (unnormalize-loop (absm 1 (loop3 2 'a 3)))
-|#
-
-(DEFUN LOOP3 (&rest list)
-   (when (and (= 1 (length list))
-              (listp (first list)))
-      (setf list (first list)))
-   (unless (zerop (mod (length list) 3))
-      (error "In LOOP3, 3 should divide the list length."))
-   (flet ((fixnumpp (object)
-             (unless (typep object 'fixnum)
-                (error "In LOOP3, ~A should be a fixnum." object))
-             object))
-      (do ((rslt +empty-list+ (cons (apowr
-                                       (fixnumpp (car mark))
-                                       (cadr mark)
-                                       (fixnumpp (caddr mark)))
-                                 rslt))
-           (mark list (cdddr mark)))
-          ((endp mark) (make-loop :list (nreverse rslt)))
-         (declare (list rslt mark)))))
-
-#|
-  (loop3 nil)
-  (loop3 '(1 a 2 3 b -2))
-  (loop3 '(1 a 2 3 b b))
-  (loop3 '(1 a 2 3 b))
-  (loop3 1 'a 2 3 'b 4)
-  (loop3 1 'a 2 3 'b)
-|#
-
-(DEFMETHOD PRINT-KEYCONS ((car (eql :loop)) cdr stream)
-   (declare
-      (list cdr)
-      (stream stream))
-   (the loop
-      (progn
-         (format stream "<<Loop")
-         (dolist (apowr cdr)
-            (declare (type apowr apowr))
-            (with-apowr (dgop gmsm expn) apowr
-               (format stream "[")
-               (unless (zerop dgop)
-                  (format stream "~A " (hyphenize-list (dgop-int-ext dgop))))
-               (format stream "~A" gmsm)
-               (unless (= 1 expn)
-                  (format stream "\\~D" expn))
-               (format stream "]")))
-         (format stream ">>")
-         (cons car cdr))))
-
-#|
-  (loop3 nil)
-  (loop3 '(0 a 2))
-  (loop3 '(1 a 2))
-  (loop3 '(3 a 2 5 b -1 6 c 4))
-  (loop3 '(7 a 1 11 b 1 13 c 1 14 d 1))
-  (loop3 '(7 a 1 11 b 1 13 c 1 7 d 1))
-  (loop3 '(0 a 1 0 b 2 0 c -1 1 d 1))
-|#
-
-(DEFUN APOWR-NILOOP (cmpr apowr niloop)
-   (declare
-      (type cmprf cmpr)
-      (type apowr apowr)
-      (type iloop niloop))
-   (the iloop
-      (progn
-         (unless niloop
-            (return-from apowr-niloop
-               (list apowr)))
-         (let ((apowr2 (first niloop)))
-            (declare (type apowr apowr2))
-            (with-apowr (dgop2 gmsm2 expn2) apowr2
-               (unless (and (= (apdgop apowr) dgop2)
-                            (eq :equal (funcall cmpr (apgmsm apowr) gmsm2)))
-                  (return-from apowr-niloop
-                     (cons apowr niloop)))
-               (incf expn2 (apexpn apowr))
-               (if (zerop expn2)
-                  (rest niloop)
-                  (cons (apowr dgop2 gmsm2 expn2) (rest niloop))))))))
-
-#|
-  (apowr-niloop #'s-cmpr '(0 a . 1) +empty-list+)
-  (apowr-niloop #'s-cmpr '(0 a . 1) '((1 a . 1)))
-  (apowr-niloop #'s-cmpr '(0 a . 1) '((0 b . 1)))
-  (apowr-niloop #'s-cmpr '(0 a . 1) '((0 a . 1) (0 b . 1)))
-  (apowr-niloop #'s-cmpr '(0 a . 1) '((0 a . -1) (0 b . 1)))
-|#
-
-(DEFUN LOOP-SPACE-CMPR (cmpr)
-   (declare (type cmprf cmpr))
-   (flet ((2apowr-cmpr (apowr1 apowr2)
-           (declare (type apowr apowr1 apowr2))
-           (lexico
-              (f-cmpr (apdgop apowr1) (apdgop apowr2))
-              (funcall cmpr (apgmsm apowr1) (apgmsm apowr2))
-              (f-cmpr (apexpn apowr1) (apexpn apowr2)))))
-      (flet ((rslt (loop1 loop2)
-              (declare (type loop loop1 loop2))
-              (maplexico #'2apowr-cmpr (loop-list loop1) (loop-list loop2))))
-         (the cmprf #'rslt))))
-
-#|
-  (setf cmpr (loop-space-cmpr #'s-cmpr))
-  (funcall cmpr (loop3 '(1 a 2)) (loop3 '(1 a -1)))
-  (funcall cmpr (loop3 '(3 b 4 1 a 2)) (loop3 '(3 b 4 1 a -1)))
-|#
-
-(DEFUN APOWR-FACE4 (face indx dmns apowr)
-   ;; dmns = dimension in the loop-space
-   (declare
-      (type face face)
-      (type apowr apowr))
-   (with-apowr (dgop gmsm expn) apowr
-      (let ((face (a-face4 face indx (1+ dmns) (absm dgop gmsm))))
-         (declare (type absm face))
-         (with-absm (dgop gmsm) face
-            (if (logbitp (1- dmns) dgop)
-               nil
-               (apowr dgop gmsm expn))))))
-
-#|
-  (setf face (face (delta-infinity)))
-  (apowr-face4 face 3 4 (apowr 1 31 5))
-  (setf face (face (sphere 5)))
-  (apowr-face4 face 2 5 (apowr 1 's5 4))
-  (apowr-face4 face 2 5 (apowr 2 's5 4))
-|#
-
-(DEFUN APOWR-LASTFACE4 (cmpr face dmns apowr)
-   ;; indx =dmns
-   (declare
-      (type cmprf cmpr)
-      (type face face)
-      (fixnum dmns)
-      (type apowr apowr))
-   (the list
-      (with-apowr (dgop gmsm expn) apowr
-         (let ((absm (absm dgop gmsm)))
-            (declare (type absm absm))
-            (let ((face-n (a-face4 face dmns (1+ dmns) absm))
-                  (face-n+1 (a-face4 face (1+ dmns) (1+ dmns) absm)))
-               (declare (type absm face-n face-n+1))
-               (with-absm (dgop1 gmsm1) face-n
-               (with-absm (dgop2 gmsm2) face-n+1
-                  (if (logbitp (1- dmns) dgop1)
-                     (if (logbitp (1- dmns) dgop2)
-                        (return-from apowr-lastface4 +empty-list+)
-                        (return-from apowr-lastface4
-                           (list (apowr dgop2 gmsm2 (- expn)))))
-                     (when (logbitp (1- dmns) dgop2)
-                        (return-from apowr-lastface4
-                           (list (apowr dgop1 gmsm1 expn)))))
-                  (when (and (= dgop1 dgop2)
-                             (eq :equal (funcall cmpr gmsm1 gmsm2)))
-                     (return-from apowr-lastface4 +empty-list+))
-                  (case expn
-                     (+1 (list (apowr dgop2 gmsm2 -1) (apowr dgop1 gmsm1 +1)))
-                     (-1 (list (apowr dgop1 gmsm1 -1) (apowr dgop2 gmsm2 +1)))
-                     (otherwise
-                        (if (plusp expn)
-                           (do ((rslt +empty-list+ (cons apowr2 (cons apowr1 rslt)))
-                                (apowr1 (apowr dgop1 gmsm1 +1))
-                                (apowr2 (apowr dgop2 gmsm2 -1))
-                                (nark expn (1- nark)))
-                               ((zerop nark) rslt)
-                              (declare
-                                 (list rslt)
-                                 (type apowr apowr1 apowr2)))
-                              (do ((rslt +empty-list+ (cons apowr1 (cons apowr2 rslt)))
-                                   (apowr1 (apowr dgop1 gmsm1 -1))
-                                   (apowr2 (apowr dgop2 gmsm2 +1))
-                                   (nark expn (1+ nark)))
-                                  ((zerop nark) rslt)
-                                 (declare
-                                    (list rslt)
-                                    (type apowr apowr1 apowr2)))))))))))))
-
-#|
-  (setf cmpr #'f-cmpr face (face (delta-infinity)))
-  (apowr-lastface4 cmpr face 4 (apowr 0 63 1))
-  (apowr-lastface4 cmpr face 4 (apowr 0 63 -1))
-  (apowr-lastface4 cmpr face 4 (apowr 0 63 3))
-  (apowr-lastface4 cmpr face 4 (apowr 0 63 -3))
-  (apowr-lastface4 cmpr face 4 (apowr 8 31 1))
-  (setf face #'(lambda (indx dmns gmsm)  ;  dmns = 5
-                  (case indx
-                     (5 (absm 8 'a))
-                     (4 (absm 8 'a)))))
-  (setf cmpr #'s-cmpr)
-  (apowr-lastface4 cmpr face 4 (apowr 0 'a 2))
-  (setf face #'(lambda (indx dmns gmsm)  ;  dmns = 5
-                  (case indx
-                     (5 (absm 1 'a))
-                     (4 (absm 8 'a)))))
-  (apowr-lastface4 cmpr face 4 (apowr 0 'a 2))
-  (setf face #'(lambda (indx dmns gmsm)  ;  dmns = 5
-                  (case indx
-                     (5 (absm 1 'a))
-                     (4 (absm 1 'a)))))
-  (apowr-lastface4 cmpr face 4 (apowr 0 'a 2))
-|#
-                                   
-(DEFUN LOOP-SPACE-FACE (cmpr face)
-   (declare
-      (type cmprf cmpr)
-      (type face face))
-   (flet ((rslt (indx dmns loop)
-             (declare
-                (fixnum indx dmns)
-                (type loop loop))
-             (the absm
-                (let ((rslt +empty-list+))
-                   (declare (type iloop rslt))
-                   (if (< indx dmns)
-                      (dolist (apowr (loop-list loop))
-                         (declare (type apowr apowr))
-                         (let ((lface (apowr-face4 face indx dmns apowr)))
-                            (declare (type (or null apowr) lface))
-                            (when lface (setf rslt (apowr-niloop cmpr lface rslt)))))
-                      (dolist (apowr (loop-list loop))
-                         (declare (type apowr apowr))
-                         (let ((lface (apowr-lastface4 cmpr face dmns apowr)))
-                            (declare (list lface))
-                            (dolist (apowr lface)
-                               (declare (type apowr apowr))
-                               (setf rslt (apowr-niloop cmpr apowr rslt))))))
-                   (normalize-loop (1- dmns) (nreverse rslt))))))
-      (the face #'rslt)))
-
-#|
-  (setf cmpr #'f-cmpr
-        face (face (delta-infinity)))
-  (setf rslt (loop-space-face cmpr face))
-  (funcall rslt 2 4 (loop3 '(0 63 3 1 31 -3)))
-  (funcall rslt 2 4 (loop3 '(0 63 3 0 63 -3)))
-  (funcall rslt 4 4 (loop3 '(0 63 3 0 63 -3)))
-  (funcall rslt 4 4 (loop3 '(0 63 3)))
-|#
-
-(DEFUN LOOP-SPACE-FACE* (cmpr face)
-   (declare
-      (type cmprf cmpr)
-      (type face face))
-   (flet ((rslt (indx dmns loop)
-             (declare
-                (fixnum indx dmns)
-                (type loop loop))
-             (the (or loop (eql :degenerate))
-                (let ((rslt +empty-list+))
-                   (declare (type iloop rslt))
-                   (if (< indx dmns)
-                      (dolist (apowr (loop-list loop))
-                         (declare (type apowr apowr))
-                         (let ((lface (apowr-face4 face indx dmns apowr)))
-                            (declare (type (or null apowr) lface))
-                            (when lface (setf rslt (apowr-niloop cmpr lface rslt)))))
-                      (dolist (apowr (loop-list loop))
-                         (declare (type apowr apowr))
-                         (let ((lface (apowr-lastface4 cmpr face dmns apowr)))
-                            (declare (list lface))
-                            (dolist (apowr lface)
-                               (declare (type apowr apowr))
-                               (setf rslt (apowr-niloop cmpr apowr rslt))))))
-                   (if (zerop (apply #'logand (mapcar #'car rslt)))
-                      (make-loop :list (nreverse rslt))
-                      :degenerate)))))
-      (the face* #'rslt)))
-
-(DEFUN LOOP-SPACE-GRIN-SINTR (dmns loop)
-  (declare
-     (ignore dmns)
-     (type loop loop))
-  (the absm
-     (absm 0 (make-loop
-	      :list (mapcar #'(lambda (apowr)
-				(declare (type apowr apowr))
-				(with-apowr (dgop gmsm expn) apowr
-					    (apowr dgop gmsm (- expn))))
-			    (reverse (loop-list loop)))))))
-
-#|
-  (loop-space-grin-sintr 5 (loop3 0 'a 2 3 'b -3))
-|#
-
-(DEFUN LOOP-SPACE-GRML-SINTR (cmpr)
-  (declare (type cmprf cmpr))
-  (flet ((rslt (dmns crpr)
-	    (declare
-	       (fixnum dmns)
-	       (type crpr crpr))
-	    (the absm
-	       (with-crpr (absm1 absm2) crpr
-	         (let ((niloop1 (nreverse (unnormalize-loop absm1)))
-		       (niloop2 (unnormalize-loop absm2)))
-		   (declare (type iloop niloop1 niloop2))
-		   (loop
-		    (unless niloop1 (return))
-		    (unless niloop2 (return))
-		    (let ((apowr1 (first niloop1))
-			  (apowr2 (first niloop2)))
-		      (declare (type apowr apowr1 apowr2))
-		      (with-apowr (dgop1 gmsm1 expn1) apowr1
-		      (with-apowr (dgop2 gmsm2 expn2) apowr2
-		         (unless (and (= dgop1 dgop2)
-				      (eq :equal (funcall cmpr gmsm1 gmsm2)))
-			    (return))
-			 (incf expn1 expn2)
-			 (cond ((zerop expn1)
-				(pop niloop1)
-				(pop niloop2))
-			       (t
-				(pop niloop1)
-				(setf niloop2
-				      (cons (apowr dgop2 gmsm2 expn1)
-					    (rest niloop2)))
-				(return)))))))
-		   (normalize-loop dmns
-				   (nreconc niloop1 niloop2)))))))
-     (the sintr #'rslt)))
-
-#|
-  (setf cmpr #'s-cmpr)
-  (setf ml (loop-space-grml-sintr cmpr))
-  (funcall ml 2 (crpr 3 (loop3) 0 (loop3 0 'a 2)))
-  (funcall ml 2 (crpr 0 (loop3 0 'a 2) 3 (loop3)))
-  (funcall ml 2 (crpr 0 (loop3 0 'a 2) 0 (loop3 0 'a -2)))
-  (funcall ml 2 (crpr 0 (loop3 0 'a 2) 0 (loop3 0 'a -3)))
-  (funcall ml 2 (crpr 0 (loop3 0 'a 2) 0 (loop3 0 'b -3)))
-  (funcall ml 2 (crpr 0 (loop3 0 'a 2 0 'b -3)
-                      0 (loop3 0 'b +3 0 'a -2)))
-|#
-
-(DEFUN LOOP-SPACE (smst &optional (n 1))
-   (declare
-      (type simplicial-set smst)
-      (fixnum n))   
-   (the simplicial-group
-      (if (= n 1)
-         (with-slots (cmpr face) smst
-            (declare
-               (type cmprf cmpr)
-	       (type face face))
-	    (simplicial-group
-	       :cmpr (loop-space-cmpr cmpr)
-	       :basis :locally-effective
-	       :bsgn +null-loop+
-	       :face (loop-space-face cmpr face)
-	       :face* (loop-space-face* cmpr face)
-	       :grml-sintr (loop-space-grml-sintr cmpr)
-	       :grin-sintr #'loop-space-grin-sintr
-	       :dfnt `(loop-space ,smst)))
-	(loop-space (loop-space smst) (1- n)))))
-
-(DEFUN GDELTAB ()
-   (loop-space (deltab)))
-
-#|
-  (cat-init)
-  (setf g (gdeltab))
-  (cmpr g (loop3 0 3 2) (loop3 0 3 2))
-  (cmpr g (loop3 0 3 2) (loop3 0 3 3))
-  (cmpr g (loop3 0 3 2) (loop3 0 5 2))
-  (cmpr g (loop3 0 5 2) (loop3 0 3 2))
-  (face g 3 3 (loop3 12 7 3))
-  (face g 3 3 (loop3 5 7 3))
-  (face g 3 3 (loop3 6 7 3 5 7 3 3 7 3))
-  (face g 4 4 (absm 4 (loop3 6 7 3 5 7 3 3 7 3)))
-  (check-faces (cmpr g) (face g) 3 (loop3 6 7 -3 5 7 -3 3 7 -3))
-  (setf dd (cmps g g))
-  (? dd 3 (loop3 6 7 3 5 7 3 3 7 3))
-  (grml g 2 (crpr 0 (loop3 0 15 3) 0 (loop3 0 15 4)))
-  (grin g 2 (loop3 0 15 -2))
-  (setf rslt (loop3 0 31 1))
-  (setf hat (mapcar #'(lambda (i) (face g i 3 rslt))
-                    (<a-b> 0 3)))
-  (dotimes (i 4)
-    (print (kfll g i 3 (remove (nth i hat) hat :test #'equal)))
-    (check-kan g i 3 (remove (nth i hat) hat :test #'equal)))
-
-  (setf g (loop-space (sphere 2)))
-  (setf rslt (loop3 3 's2 2 5 's2 -2 6 's2 2))
-  (setf hat (mapcar #'(lambda (i) (face g i 3 rslt))
-                    (<a-b> 0 3)))
-  (dotimes (i 4)
-    (print (kfll g i 3 (remove (nth i hat) hat :test #'equal)))
-    (check-kan g i 3 (remove (nth i hat) hat :test #'equal)))
-
-  (setf g (loop-space (sphere 3) 2))
-  (setf x (first (basis (echcm g) 4)))
-  (setf efhm (efhm g))
-  (setf x (lf efhm (rg efhm 4 x)))
-  (setf rslt (gnrt (first (cmbn-list x))))
-  (setf hat (mapcar #'(lambda (i) (face g i 4 rslt))
-                    (<a-b> 0 4)))
-  (dotimes (i 5)
-    (print (kfll g i 4 (remove (nth i hat) hat :test #'equal)))
-    (check-kan g i 4 (remove (nth i hat) hat :test #'equal)))
-
-  (setf rslt (gnrt (third (cmbn-list x))))
-  (setf hat (mapcar #'(lambda (i) (face g i 4 rslt))
-                    (<a-b> 0 4)))
-  (dotimes (i 5)
-    (print (kfll g i 4 (remove (nth i hat) hat :test #'equal)))
-    (check-kan g i 4 (remove (nth i hat) hat :test #'equal)))
-
-  (setf g (loop-space (sphere 3) 2))
-  (setf efhm (efhm g))
-  (setf echcm (rbcc efhm))
-  (setf basis (basis echcm 4))
-  (setf cmbn (cmbn 4 1 (first basis) 10 (second basis)
-                     100 (third basis)))
-  (setf cmbn2 (lf efhm (rg efhm cmbn)))
-  (setf loop-list (mapcar #'cdr (cmbn-list cmbn2)))
-  (dolist (loop loop-list)
-    (setf hat (mapcar #'(lambda (i) (face g i 4 loop))
-                      (<a-b> 0 4)))
-    (dotimes (i 5)
-      (print (kfll g i 4 (remove (nth i hat) hat)))
-      (check-kan g i 4 (remove (nth i hat) hat))))
-|#
-
-#|
-  (cat-init)
-  (setf p (r-proj-space 3))
-  (setf op (loop-space p))
-  (defun random-apowr (dmns max-expn)
-     (loop
-        (let* ((dgop (random (2-exp (1- dmns))))
-               (gmsm (- dmns (logcount dgop))))
-           (unless (< 0 gmsm 3)
-              (return-from random-apowr
-                 (apowr dgop gmsm (srandom max-expn)))))))
-  (dotimes (i 15) (print (random-apowr 8 3)))
-  (defun random-niloop (dmns max-expn length)
-     (mapcar #'(lambda (dummy)
-                  (random-apowr (1+ dmns) max-expn))
-        (make-list length)))
-  (dotimes (i 20)
-     (print (normalize-loop 7 (random-niloop 7 3 3))))
-  (defun random-loop-cmbn (cmpr degr max-cffc max-expn loop-length cmbn-length)
-     (do ((rslt +empty-list+ (cons term rslt))
-          (i cmbn-length (1- i))
-          (term))
-         ((zerop i)
-          (apply #'nterm-add cmpr degr rslt))
-        (setf term
-              (term (srandom max-cffc)
-                 (make-loop :list (random-niloop degr max-expn loop-length))))))
-  (setf cmpr (cmpr op))
-  (setf +too-much-time+ -1)
-  (setf c (random-loop-cmbn cmpr 8 10 4 4 100))
-  (time (? op (? op c)))
-  (time (? op (? op c)))
-|#
-  
-#|  ;; in EAT.
-  (DEFUN PR-INFINITY-EQS (gsm1 gsm2)
-     (declare (fixnum gsm1 gsm2))
-     t)
-
-  (DEFUN PR-INFINITY-BASIS (k)
-     (declare (fixnum k))
-     (flet ((rslt (dmns)
-               (declare (fixnum dmns))
-               (if (< 0 dmns k)
-                  empty-list
-                  (list dmns))))
-        (the basis #'rslt)))
-
-  (DEFUN PR-INFINITY-GDL (k)
-     (declare (fixnum k))
-     (flet ((rslt (indx dmns gsm)
-             (declare (fixnum indx dmns gsm))
-             (if (<= dmns k)
-                (asm (nreverse (<a-b< 0 (1- dmns))) 0)
-                (if (or (zerop indx)
-                        (= indx dmns))
-                   (asm nil (1- dmns))
-                   (if (= dmns (1+ k))
-                      (asm (nreverse (<a-b< 0 (1- dmns))) 0)
-                      (asm (list (1- indx)) (- dmns 2)))))))
-        (the function #'rslt)))
-
-  (DEFUN PR-INFINITY (&optional (k 1))
-     (declare (fixnum k))
-     (build-ss
-         :eqs #'pr-infinity-eqs
-         :sbs (pr-infinity-basis k)
-         :bsp 0
-         :gdl (pr-infinity-gdl k)
-         :org `(pr-infinity ,k)))
-
-  (setf p (pr-infinity))
-  (sbs p 4)
-  (dotimes (i 5)
-     (print (gdl p i 4 4)))
-  (setf cc (ss-cc p))
-  (dotimes (i 5)
-     (print (d-? cc i i)))
-  (setf dd (cmp-mrp (cc-d cc) (cc-d cc)))
-  (dotimes (i 6)
-     (print (? dd i i)))
-  (setf p (pr-infinity 3))
-  (dotimes (i 7)
-     (print (sbs p i)))
-  (dotimes (i 5)
-     (print (gdl p i 4 4)))
-  (setf d (cc-d (ss-cc p)))
-  (dotimes (i 7)
-     (print (? d i i)))
-  (setf dd (cmp-mrp d d))
-  (dotimes (i 7)
-     (print (? dd i i)))
-
-  (setf p (pr-infinity 3))
-  (setf op (loop-space p))
-  (defun srandom (max)
-     (let ((rslt (- (random (+ max max)) max)))
-        (if (zerop rslt)
-           max
-           rslt)))
-  (dotimes (i 20) (print (srandom 3)))
-  (DEFUN DGOP-INT-EXT (dop)
-     (declare (fixnum dop))
-     (the list
-        (do ((dop dop (ash dop -1))
-             (rslt empty-list)
-             (bmark 0 (1+ bmark)))
-            ((zerop dop) rslt)
-           (declare
-              (fixnum dop bmark)
-              (list rslt))
-           (when (oddp dop)
-              (push bmark rslt)))))
-  (defun random-apowr (dmns max-expn)
-     (let ((dgop (dgop-int-ext (* 2 (random (2-exp (1- dmns)))))))
-        (pwr (asm dgop (- 8 (length dgop))) (srandom max-expn))))
-  (dotimes (i 5) (print (random-apowr 8 3)))
-  (defun random-niloop (dmns max-expn length)
-     (mapcar #'(lambda (dummy)
-                  (random-apowr (1+ dmns) max-expn))
-        (make-list length)))
-  (dotimes (i 20)
-     (print (normalize-loop 7 (make-strloop :lst (random-niloop 7 3 3)))))
-  (defun random-loop-cmbn (degr max-cffc max-expn loop-length cmbn-length)
-     (do ((rslt empty-list (cons mnm rslt))
-          (i cmbn-length (1- i))
-          (term))
-         ((zerop i)
-          (make-cmb :dgr degr :lst rslt))
-        (setf mnm
-              (mnm (srandom max-cffc)
-                 (make-strloop :lst (random-niloop degr max-expn loop-length))))))
-  (setf d (cc-d (ss-cc op)))
-  (setf c (random-loop-cmbn 8 10 4 4 100))
-  (time (??? d (??? d c)))
-  (time (??? d (??? d c)))
-|#
-
diff --git a/archive/Kenzo-2/Kenzo-2-Acl5/lp-space-efhm.cl b/archive/Kenzo-2/Kenzo-2-Acl5/lp-space-efhm.cl
deleted file mode 100644
index e8ba2b5..0000000
--- a/archive/Kenzo-2/Kenzo-2-Acl5/lp-space-efhm.cl
+++ /dev/null
@@ -1,644 +0,0 @@
-;;;  LP-SPACE-EFHM  LP-SPACE-EFHM  LP-SPACE-EFHM  LP-SPACE-EFHM
-;;;  LP-SPACE-EFHM  LP-SPACE-EFHM  LP-SPACE-EFHM  LP-SPACE-EFHM
-;;;  LP-SPACE-EFHM  LP-SPACE-EFHM  LP-SPACE-EFHM  LP-SPACE-EFHM
-
-(IN-PACKAGE "CAT")
-
-(PROVIDE "lp-space-efhm")
-
-(DEFUN LS-HAT-U-U (space
-                  &aux (cobar (cobar space))
-                       (loop-space (loop-space space))
-                       (spac-tnsr-lpsp (tnsr-prdc space loop-space)))
-   (declare
-      (type simplicial-set space)
-      (type chain-complex cobar spac-tnsr-lpsp)
-      (type simplicial-group loop-space))
-   (the chain-complex
-      (tnsr-prdc cobar spac-tnsr-lpsp)))
-
-(DEFUN LS-HAT-LEFT-PERTURBATION-INTR (space)
-   (declare (type simplicial-set space))
-   (let ((cprd (cprd space)))
-      (flet ((rslt (degr tnpr)
-                (declare
-                   (fixnum degr)
-                   (type tnpr tnpr))
-                (with-tnpr (degr1 allp1 nil tnpr2) tnpr
-                (with-tnpr (degr21 gmsm21 degr22 loop22) tnpr2
-                   (let ((cprd (cmbn-list (gnrt-? cprd degr21 gmsm21))))
-                      (declare (list cprd))
-                      (setf cprd (rest cprd))    ;;; because \bar{A}
-                      (make-cmbn :degr (1- degr)
-                         :list
-                         (mapcar
-                            #'(lambda (term)
-                                 (declare (type term term))
-                                 (with-term (cffc tnpr21) term
-                                 (with-tnpr (degr211 gmsm211 degr212 gmsm212) tnpr21
-                                    (decf degr211)
-                                    (term cffc
-                                       (tnpr
-                                          (+ degr1 degr211)
-                                          (make-allp
-                                             :list (append
-                                                      (allp-list allp1)
-                                                      (list (cbgn degr211 gmsm211))))
-                                          (+ degr212 degr22)
-                                          (tnpr degr212 gmsm212 degr22 loop22))))))
-                            cprd)))))))
-         (the intr #'rslt))))
-
-(DEFUN LS-HAT-LEFT-PERTURBATION (space)
-   (declare (type simplicial-set space))
-   (the morphism
-      (let ((ls-hat-u-u (ls-hat-u-u space)))
-         (morphism
-            :sorc ls-hat-u-u
-            :trgt ls-hat-u-u
-            :degr -1
-            :intr (ls-hat-left-perturbation-intr space)
-            :strt :gnrt
-            :dfnt `(ls-hat-left-perturbation ,space)))))
-
-(DEFUN LS-HAT-T-U (space
-                  &aux (ls-hat-u-u (ls-hat-u-u space))
-                       (ls-hat-left-perturbation
-                          (ls-hat-left-perturbation space)))
-   (declare
-      (type simplicial-set space)
-      (type chain-complex ls-hat-u-u)
-      (type morphism ls-hat-left-perturbation))
-   (the chain-complex
-      (progn
-         (setf (slot-value ls-hat-left-perturbation 'sorc) ls-hat-u-u
-               (slot-value ls-hat-left-perturbation 'trgt) ls-hat-u-u)
-         ;; because maybe these slots have been modified when constructing
-         ;;   the ls-left-eqvl-right-reduction
-         (add ls-hat-u-u ls-hat-left-perturbation))))
-
-#|
-  (cat-init)
-  (setf c (ls-hat-t-u (deltab)))
-  (defun random-allp (length)
-     (let ((rslt nil))
-        (dotimes (i length)
-           (let* ((gmsm (random (mask 9)))
-                  (dmns (1- (logcount gmsm))))
-              (when (plusp dmns)
-                 (push (cbgn (1- dmns) gmsm) rslt))))
-        (make-allp :list rslt)))
-  (dotimes (i 10) (print (random-allp 5)))
-  (setf allp (random-allp 4))  ;; the degree could be too big
-                               ;; then redo
-  (setf allp-degr (apply #'+ (mapcar #'car (allp-list allp))))
-  (setf gnrt (tnpr allp-degr allp 4 (tnpr 2 7 2 (loop3 0 15 2))))
-  (? c (+ 4 allp-degr) gnrt)
-  (? c *)
-  (dotimes (i 10)
-     (let ((allp (random-allp 3)))
-        (setf allp-degr (apply #'+ (mapcar #'car (allp-list allp))))
-        (setf gnrt (tnpr allp-degr allp 4 (tnpr 2 7 2 (loop3 0 15 2))))
-        (unless (>= allp-degr 11)
-           (print (? c (+ 4 allp-degr) gnrt))
-           (print (? c (? c (+ 4 allp-degr) gnrt))))))
-  (dotimes (i 20)
-     (let ((allp (random-allp 3)))
-        (setf allp-degr (apply #'+ (mapcar #'car (allp-list allp))))
-        (setf gnrt (tnpr allp-degr allp 5 (tnpr 3 15 2 (loop3 0 15 2))))
-        (unless (>= allp-degr 10)
-           (print (? c (+ 5 allp-degr) gnrt))
-           (print (? c (? c (+ 5 allp-degr) gnrt))))))
-  (dotimes (i 20)
-     (let ((allp (random-allp 3)))
-        (setf allp-degr (apply #'+ (mapcar #'car (allp-list allp))))
-        (setf gnrt (tnpr allp-degr allp 5 (tnpr 2 7 3 (loop3 0 31 2))))
-        (unless (>= allp-degr 10)
-           (print (? c (+ 5 allp-degr) gnrt))
-           (print (? c (? c (+ 5 allp-degr) gnrt))))))
-|#
-
-(DEFUN LS-HAT-RIGHT-PERTURBATION (space
-                                 &aux (cobar (cobar space))
-                                      (ls-hat-t-u (ls-hat-t-u space)))
-   (declare
-      (type simplicial-set space)
-      (type chain-complex cobar ls-hat-t-u))
-   (the morphism
-      (multiple-value-bind (szczarba bottom-perturbation)
-                           (szczarba space)
-         (declare
-            (ignore szczarba)
-            (type morphism bottom-perturbation))
-         (let ((rslt (tnsr-prdc (idnt-mrph cobar) bottom-perturbation)))
-	    (declare (type morphism rslt))
-            (setf (slot-value rslt 'sorc) ls-hat-t-u
-                  (slot-value rslt 'trgt) ls-hat-t-u)
-            rslt))))
-
-(DEFUN LS-HAT-U-T (space
-                  &aux (cobar (cobar space))
-                       (twisted-tnsr-prdc (twisted-tnsr-prdc space))
-                       (ls-hat-u-u (ls-hat-u-u space)))
-   (declare
-      (type simplicial-set space)
-      (type chain-complex cobar twisted-tnsr-prdc ls-hat-u-u))
-   (the chain-complex
-      (let ((rslt (tnsr-prdc cobar twisted-tnsr-prdc)))
-         (declare (type chain-complex rslt))
-         (setf (slot-value rslt 'grmd) ls-hat-u-u)
-         rslt)))
-
-#|
-  (cat-init)
-  (setf c (ls-hat-u-t (deltab)))
-  (defun random-allp (length)
-     (let ((rslt nil))
-        (dotimes (i length)
-           (let* ((gmsm (random (mask 9)))
-                  (dmns (1- (logcount gmsm))))
-              (when (plusp dmns)
-                 (push (cbgn (1- dmns) gmsm) rslt))))
-        (make-allp :list rslt)))
-  (dotimes (i 10) (print (random-allp 5)))
-  (setf allp (random-allp 3))
-  (setf allp-degr (apply #'+ (mapcar #'car (allp-list allp))))
-  (setf gnrt (tnpr allp-degr allp 4 (tnpr 2 7 2 (loop3 0 15 2))))
-  (? c (+ 4 allp-degr) gnrt)
-  (? c *)
-  (dotimes (i 10)
-     (let ((allp (random-allp 3)))
-        (setf allp-degr (apply #'+ (mapcar #'car (allp-list allp))))
-        (setf gnrt (tnpr allp-degr allp 4 (tnpr 2 7 2 (loop3 0 15 2))))
-        (unless (>= allp-degr 11)
-           (print (? c (+ 4 allp-degr) gnrt))
-           (print (? c (? c (+ 4 allp-degr) gnrt))))))
-  (dotimes (i 20)
-     (let ((allp (random-allp 3)))
-        (setf allp-degr (apply #'+ (mapcar #'car (allp-list allp))))
-        (setf gnrt (tnpr allp-degr allp 5 (tnpr 3 15 2 (loop3 0 15 2))))
-        (unless (>= allp-degr 10)
-           (print (? c (+ 5 allp-degr) gnrt))
-           (print (? c (? c (+ 5 allp-degr) gnrt))))))
-  (dotimes (i 20)
-     (let ((allp (random-allp 3)))
-        (setf allp-degr (apply #'+ (mapcar #'car (allp-list allp))))
-        (setf gnrt (tnpr allp-degr allp 5 (tnpr 2 7 3 (loop3 0 31 2))))
-        (unless (>= allp-degr 10)
-           (print (? c (+ 5 allp-degr) gnrt))
-           (print (? c (? c (+ 5 allp-degr) gnrt))))))
-|#
-
-(DEFUN LS-LEFT-EQVL-HAT (space
-                    &aux
-                    (ls-hat-u-t (ls-hat-u-t space))
-                    (ls-hat-left-perturbation
-                       (ls-hat-left-perturbation space)))
-   (declare
-      (type simplicial-set space)
-      (type chain-complex ls-hat-u-t)
-      (type morphism ls-hat-left-perturbation))
-   (the chain-complex
-      (add ls-hat-u-t ls-hat-left-perturbation)))
-
-#|
-  (cat-init)
-  (setf c (ls-left-eqvl-hat (deltab)))
-  (defun random-allp (length)
-     (let ((rslt nil))
-        (dotimes (i length)
-           (let* ((gmsm (random (mask 9)))
-                  (dmns (1- (logcount gmsm))))
-              (when (plusp dmns)
-                 (push (cbgn (1- dmns) gmsm) rslt))))
-        (make-allp :list rslt)))
-  (dotimes (i 10) (print (random-allp 5)))
-  (setf allp (random-allp 3))
-  (setf allp-degr (apply #'+ (mapcar #'car (allp-list allp))))
-  (setf gnrt (tnpr allp-degr allp 4 (tnpr 2 7 2 (loop3 0 15 2))))
-  (? c (+ 4 allp-degr) gnrt)
-  (? c *)
-  (dotimes (i 10)
-     (let ((allp (random-allp 3)))
-        (setf allp-degr (apply #'+ (mapcar #'car (allp-list allp))))
-        (setf gnrt (tnpr allp-degr allp 4 (tnpr 2 7 2 (loop3 0 15 2))))
-        (unless (>= allp-degr 11)
-           (print (? c (+ 4 allp-degr) gnrt))
-           (print (? c (? c (+ 4 allp-degr) gnrt))))))
-  (dotimes (i 20)
-     (let ((allp (random-allp 3)))
-        (setf allp-degr (apply #'+ (mapcar #'car (allp-list allp))))
-        (setf gnrt (tnpr allp-degr allp 5 (tnpr 3 15 2 (loop3 0 15 2))))
-        (unless (>= allp-degr 10)
-           (print (? c (+ 5 allp-degr) gnrt))
-           (print (? c (? c (+ 5 allp-degr) gnrt))))))
-  (dotimes (i 20)
-     (let ((allp (random-allp 3)))
-        (setf allp-degr (apply #'+ (mapcar #'car (allp-list allp))))
-        (setf gnrt (tnpr allp-degr allp 5 (tnpr 2 7 3 (loop3 0 31 2))))
-        (unless (>= allp-degr 10)
-           (print (? c (+ 5 allp-degr) gnrt))
-           (print (? c (? c (+ 5 allp-degr) gnrt))))))
-|#
-
-(DEFUN LS-PRE-LEFT-EQVL-LEFT-REDUCTION-INTR-F (cmbn)
-   (declare (type cmbn cmbn))
-   (the cmbn
-      (let ((rslt +empty-list+))
-         (declare (list rslt))
-         (dolist (term (cmbn-list cmbn))
-            (declare (type term term))
-            (with-term (cffc tnpr) term
-            (with-tnpr (degr1 nil nil tnpr2) tnpr
-               (if (zerop degr1)
-                  (with-tnpr (degr21 nil nil loop22) tnpr2
-                     (if (zerop degr21)
-                        (push (term cffc loop22) rslt)
-                        (return)))
-                  (return)))))
-         (make-cmbn :degr (cmbn-degr cmbn)
-            :list (nreverse rslt)))))
-
-#|
-  (ls-pre-left-eqvl-left-reduction-intr-f
-    (cmbn 6 100 (tnpr 0 'a 6 (tnpr 0 'b 6 'c))
-            50 (tnpr 0 'a 6 (tnpr 0 'b 6 'cc))
-            10 (tnpr 0 'a 6 (tnpr 2 'b 4 'c))
-            1 (tnpr 2 'a 4 (tnpr 2 'b 2 'cc))))            
-|#
-
-(DEFUN LS-PRE-LEFT-EQVL-LEFT-REDUCTION-F (space
-                                         &aux (ls-hat-t-u (ls-hat-t-u space))
-                                              (loop-space (loop-space space)))
-   (declare
-      (type simplicial-set space loop-space)
-      (type chain-complex ls-hat-t-u))      
-   (the morphism
-      (morphism  
-         :sorc ls-hat-t-u
-         :trgt loop-space
-         :degr 0
-         :intr #'ls-pre-left-eqvl-left-reduction-intr-f
-         :strt :cmbn
-         :dfnt `(ls-pre-left-eqvl-left-reduction-f ,space))))
-
-(DEFUN LS-LEFT-EQVL-LEFT-REDUCTION-G-INTR (bsgn)
-   (declare (type gmsm bsgn))
-   (flet ((rslt (cmbn)
-             (declare (type cmbn cmbn))
-             (the cmbn
-                (with-cmbn (degr list) cmbn
-                   (make-cmbn :degr degr
-                      :list (mapcar
-                               #'(lambda (term)
-                                    (declare (type term term))
-                                    (with-term (cffc loop) term
-                                       (term cffc
-                                          (tnpr
-                                             0 +null-allp+
-                                             degr (tnpr 0 bsgn degr loop)))))
-                               list))))))
-      (the intr #'rslt)))
-
-#|
-  (setf r (ls-left-eqvl-left-reduction-g-intr '*))
-  (funcall r (cmbn 3 4 'loop))
-|#
-
-(DEFUN LS-LEFT-EQVL-LEFT-REDUCTION-G (space
-                                     &aux (bsgn (bsgn space))
-                                          (ls-hat-t-u (ls-hat-t-u space))
-                                          (loop-space (loop-space space)))
-   (declare
-      (type simplicial-set space loop-space)
-      (type gmsm bsgn)
-      (type chain-complex ls-hat-t-u))      
-   (the morphism
-      (morphism  
-         :sorc loop-space
-         :trgt ls-hat-t-u
-         :degr 0
-         :intr (ls-left-eqvl-left-reduction-g-intr bsgn)
-         :strt :cmbn
-         :dfnt `(ls-left-eqvl-left-reduction-g ,space))))
-
-(DEFUN LS-PRE-LEFT-EQVL-LEFT-REDUCTION-H-INTR (space
-                                          &aux (ls-hat-t-u (ls-hat-t-u space))
-                                               (cmpr (cmpr ls-hat-t-u)))
-   (declare
-      (type simplicial-set space)
-      (type chain-complex ls-hat-t-u)
-      (type cmprf cmpr))
-   (flet ((rslt (cmbn)
-             (declare (type cmbn cmbn))
-             (the cmbn
-                (with-cmbn (degr list) cmbn
-                   (let ((rslt (zero-cmbn (1+ degr))))
-                      (declare (type cmbn rslt))
-                      (dolist (term list)
-                         (declare (type term term))
-                         (with-term (cffc tnpr) term
-                            (with-tnpr (degr1 allp1 degr2 tnpr2) tnpr
-                               (unless (zerop degr1)
-                                  (with-tnpr (degr21 nil degr22 loop22) tnpr2
-                                     (when (zerop degr21)
-                                        (let ((last-cbgn (car (last allp1))))
-                                           (declare (type cbgn last-cbgn))
-                                           (with-cbgn (degrl gmsml) last-cbgn
-                                              (dstr-add-term-to-cmbn cmpr
-                                                 cffc
-                                                 (tnpr
-                                                    (- degr1 degrl)
-                                                    (butlast allp1)
-                                                    (+ degr2 degrl 1)
-                                                    (tnpr
-                                                       (1+ degrl)
-                                                       gmsml
-                                                       degr22
-                                                       loop22))
-                                                 rslt)))))))))
-                      rslt)))))
-      (the intr #'rslt)))
-
-#|
-  (setf r (ls-pre-left-eqvl-left-reduction-h-intr (deltab)))
-  (setf *tnpr-with-degrees* t)
-  (funcall r (cmbn 10 1 (tnpr 3 (allp 2 'a 1 'b) 7 (tnpr 5 'c 2 'd)) 
-                      1 (tnpr 7 (allp 2 'a 5 'b) 3 (tnpr 0 '* 3 'c))
-                      10 (tnpr 8 (allp 4 'aa 4 'bb) 2 (tnpr 0 '* 2 'cc))))
-  (funcall r (cmbn 10 1 (tnpr 3 (allp 2 'a 1 'b) 7 (tnpr 5 'c 2 'd)) 
-                      1 (tnpr 7 (allp 4 'a 3 'b) 3 (tnpr 0 '* 3 'c))
-                      10 (tnpr 8 (allp 3 'aa 5 'bb) 2 (tnpr 0 '* 2 'cc))))
-  (setf *tnpr-with-degrees* nil)
-|#
-
-(DEFUN LS-PRE-LEFT-EQVL-LEFT-REDUCTION-H (space
-                                     &aux (ls-hat-t-u (ls-hat-t-u space)))
-   (declare
-      (type simplicial-set space)
-      (type chain-complex ls-hat-t-u))      
-   (the morphism
-      (morphism
-         :sorc ls-hat-t-u
-         :trgt ls-hat-t-u
-         :degr +1
-         :intr (ls-pre-left-eqvl-left-reduction-h-intr space)
-         :strt :cmbn
-         :dfnt `(ls-pre-left-eqvl-left-reduction-h ,space))))
-
-(DEFUN LS-PRE-LEFT-EQVL-LEFT-REDUCTION (space)
-   (declare (type simplicial-set space))
-   (the reduction
-      (reduction
-         :f (ls-pre-left-eqvl-left-reduction-f space)
-         :g (ls-left-eqvl-left-reduction-g space)
-         :h (ls-pre-left-eqvl-left-reduction-h space)
-         :dfnt `(ls-pre-left-eqvl-left-reduction ,space))))
-
-#|
-  (cat-init)
-  (setf rdct (ls-pre-left-eqvl-left-reduction (deltab)))
-  (pre-check-rdct rdct)
-  (defun random-allp (length)
-     (let ((rslt nil))
-        (dotimes (i length)
-           (let* ((gmsm (random (mask 9)))
-                  (dmns (1- (logcount gmsm))))
-              (when (plusp dmns)
-                 (push (cbgn (1- dmns) gmsm) rslt))))
-        (make-allp :list rslt)))
-  (setf allp (random-allp 3))
-  (setf allp-degr (apply #'+ (mapcar #'car (allp-list allp))))
-  (setf gnrt (tnpr allp-degr allp 4 (tnpr 2 7 2 (loop3 0 15 2))))
-  (setf *tc* (cmbn (+ 4 allp-degr) 1 gnrt))
-  (setf *bc* (cmbn 2 1 (loop3 0 15 2)))
-  (check-rdct)
-  (setf gnrt (tnpr allp-degr allp 4 (tnpr 0 1 4 (loop3 0 (mask 6) 2))))
-  (setf *tc* (cmbn (+ 4 allp-degr) 1 gnrt))
-  (check-rdct)
-  (setf *bc* (cmbn 0 1 (bsgn (bcc rdct)))
-  (setf *tc* (cmbn 0 1 (bsgn (tcc rdct)))
-  (check-rdct)
-|#
-
-(DEFUN LS-LEFT-EQVL-LEFT-REDUCTION (space
-                                   &aux (ls-pre-left-eqvl-left-reduction
-                                           (ls-pre-left-eqvl-left-reduction space))
-                                        (ls-hat-right-perturbation
-                                           (ls-hat-right-perturbation space)))			            
-   (declare
-      (type simplicial-set space)
-      (type reduction ls-pre-left-eqvl-left-reduction)
-      (type morphism ls-hat-right-perturbation))
-   (the reduction
-      (progn
-	 (dstr-change-sorc-trgt ls-hat-right-perturbation
-	    :new-sorc (tcc ls-pre-left-eqvl-left-reduction)
-	    :new-trgt (tcc ls-pre-left-eqvl-left-reduction))
-         (let ((rslt (special-bpl ls-pre-left-eqvl-left-reduction
-                        ls-hat-right-perturbation)))
-            (declare (type reduction rslt))
-            (with-slots (tcc f g h) rslt
-               (setf tcc (ls-left-eqvl-hat space)
-                     (slot-value f 'sorc) tcc
-                     (slot-value g 'trgt) tcc
-                     (slot-value h 'sorc) tcc
-                     (slot-value h 'trgt) tcc)
-               rslt)))))
-
-#|
-  (cat-init)
-  (setf rdct (ls-left-eqvl-left-reduction (deltab2)))
-  (pre-check-rdct rdct)
-  (defun a (d1 d2 d3)
-     (setf *tc* (cmbn (+ d1 d2 d3)
-                 1 (tnpr d1 (allp d1 (mask (+ d1 2)))
-                         (+ d2 d3)
-                      (tnpr d2 (mask (1+ d2))
-                            d3 (loop3 0 (mask (+ d3 2)) 1))))
-           *bc* (cmbn d3 1
-                  (loop3 0 (mask (+ d3 2)) -1)))
-      (check-rdct))
-  (a 1 0 1)
-  (a 1 1 1)  ;; error because 3 does not exist in deltab2
-  (a 1 2 1)
-  (a 2 2 1)
-|#
- 
-(DEFUN LS-PRE-LEFT-EQVL-RIGHT-REDUCTION-INTR-F (cmbn)
-   (declare (type cmbn cmbn))
-   (the cmbn
-      (with-cmbn (degr list) cmbn
-         (let ((tail (member 0 list :test #'= :key #'cadddr)))
-            (make-cmbn :degr degr
-               :list (mapcar
-                        #'(lambda (term)
-                             (declare (type term term))
-                             (with-term (cffc tnpr) term
-                                (term cffc (gnrt1 tnpr))))
-                        tail))))))
-
-#|
-  (ls-pre-left-eqvl-right-reduction-intr-f
-     (cmbn 3 12 (tnpr 2 'a 1 'b) 14 (tnpr 3 'aa 0 '*))))
-|#
-
-(DEFUN LS-PRE-LEFT-EQVL-RIGHT-REDUCTION-F (space
-                                          &aux (ls-hat-u-t (ls-hat-u-t space))
-                                               (cobar (cobar space)))
-   (declare
-      (type simplicial-set space)
-      (type chain-complex ls-hat-u-t cobar))
-   (the morphism
-      (morphism
-         :sorc ls-hat-u-t :trgt cobar :degr 0
-         :intr #'ls-pre-left-eqvl-right-reduction-intr-f
-         :strt :cmbn
-         :dfnt `(ls-pre-left-eqvl-right-reduction-f ,space))))
-
-(DEFUN LS-PRE-LEFT-EQVL-RIGHT-REDUCTION-INTR-G (bsgn)
-   (declare (type gmsm bsgn))
-   (flet ((rslt (cmbn)
-             (declare (type cmbn cmbn))
-             (the cmbn
-                (with-cmbn (degr list) cmbn
-                   (let ((bsgn (tnpr 0 bsgn 0 +null-loop+)))
-                      (declare (type tnpr bsgn))
-                      (make-cmbn :degr degr
-                         :list (mapcar
-                                  #'(lambda (term)
-                                       (declare (type term term))
-                                       (with-term (cffc gnrt) term
-                                          (term cffc (tnpr degr gnrt 0 bsgn))))
-                                  list)))))))
-      (the intr #'rslt)))
-
-#|
-  (setf r (ls-pre-left-eqvl-right-reduction-intr-g '*))
-  (funcall r (cmbn 3 4 'a))
-|#
-
-(DEFUN LS-PRE-LEFT-EQVL-RIGHT-REDUCTION-G (space
-                                          &aux (ls-hat-u-t (ls-hat-u-t space))
-                                               (cobar (cobar space))
-                                               (bsgn (bsgn space)))
-   (declare
-      (type simplicial-set space)
-      (type chain-complex ls-hat-u-t cobar)
-      (type gmsm bsgn))
-   (the morphism
-      (morphism
-         :sorc cobar :trgt ls-hat-u-t :degr 0
-         :intr (ls-pre-left-eqvl-right-reduction-intr-g bsgn)
-         :strt :cmbn
-         :dfnt `(ls-pre-left-eqvl-right-reduction-g ,space))))
-
-(DEFUN LS-PRE-LEFT-EQVL-RIGHT-REDUCTION-H (space
-                                          &aux (cobar (cobar space))
-                                               (tnpr-contraction (tnpr-contraction space)))
-   (declare
-      (type simplicial-set space)
-      (type chain-complex cobar)
-      (type morphism tnpr-contraction))
-   (the morphism
-      (tnsr-prdc (idnt-mrph cobar) tnpr-contraction)))
-
-(DEFUN LS-PRE-LEFT-EQVL-RIGHT-REDUCTION (space)
-   (declare (type simplicial-set space))
-   (the reduction
-      (reduction
-         :f (ls-pre-left-eqvl-right-reduction-f space)
-         :g (ls-pre-left-eqvl-right-reduction-g space)
-         :h (ls-pre-left-eqvl-right-reduction-h space)
-         :dfnt `(ls-pre-left-eqvl-right-reduction ,space))))
-
-#|
-  (cat-init)
-  (setf r (ls-pre-left-eqvl-right-reduction (deltab2)))
-  (pre-check-rdct r)
-  (setf *tc* (cmbn 0 1 (bsgn (tcc r))))
-  (setf *bc* (cmbn 0 1 (bsgn (bcc r))))
-  (check-rdct)
-  (setf *tc* (cmbn 3 1 (tnpr 3 (allp 3 (mask 5)) 0 (tnpr 0 1 0 +null-loop+))))
-  (setf *bc* (cmbn 3 1 (allp 1 7 2 15)))
-  (check-rdct)
-  (setf *tc* (cmbn 6 1 (tnpr 3 (allp 1 7 2 15) 3 (tnpr 2 7 1 (loop3 0 7 2)))))
-  (check-rdct)
-  (setf *tc* (cmbn 6 1 (tnpr 3 (allp 1 7 2 15) 3 (tnpr 0 1 3 (loop3 0 (mask 5) 2)))))
-  (check-rdct)
-|#
-
-(DEFUN LS-LEFT-EQVL-RIGHT-REDUCTION (space
-                                    &aux (pre-reduction
-                                            (ls-pre-left-eqvl-right-reduction space))
-                                         (perturbation
-                                            (ls-hat-left-perturbation space)))                                    
-   (declare
-     (type simplicial-set space)
-     (type reduction pre-reduction)
-     (type morphism perturbation))
-   (the reduction
-      (progn
-         (setf (slot-value perturbation 'sorc) (tcc pre-reduction)
-               (slot-value perturbation 'trgt) (tcc pre-reduction))
-         (special-bpl pre-reduction perturbation))))
-
-#|
-  (cat-init)
-  (setf r (ls-left-eqvl-right-reduction (deltab2)))
-  (pre-check-rdct r)
-  (setf *tc* (cmbn 0 1 (bsgn (tcc r))))
-  (setf *bc* (cmbn 0 1 (bsgn (bcc r))))
-  (check-rdct)
-  (setf *tc* (cmbn 3 1 (tnpr 3 (allp 3 (mask 5)) 0 (tnpr 0 1 0 +null-loop+))))
-  (setf *bc* (cmbn 3 1 (allp 1 7 2 15)))
-  (check-rdct)
-  (setf *tc* (cmbn 6 1 (tnpr 3 (allp 1 7 2 15) 3 (tnpr 2 7 1 (loop3 0 7 2)))))
-  (check-rdct)
-  (setf *tc* (cmbn 6 1 (tnpr 3 (allp 1 7 2 15) 3 (tnpr 0 1 3 (loop3 0 (mask 5) 2)))))
-  (check-rdct)
-|#
-
-(DEFUN LS-LEFT-EQVL (space)
-   (declare (type simplicial-set space))
-   (the equivalence
-      (equivalence 
-       :lrdct (ls-left-eqvl-left-reduction space)
-       :rrdct (ls-left-eqvl-right-reduction space)
-       :dfnt `(ls-left-eqvl ,space))))
-
-#|
-  (cat-init)
-  (setf h (ls-left-eqvl (deltab2)))
-  (setf loop (loop3 0 (mask 5) 2))
-  (lg h 3 loop)
-  (rf h *)
-  (rg h *)
-  (lf h *)
-  (setf allp (allp 2 (mask 4) 3 (mask 5)))
-  (rg h 5 allp)
-  (lf h *)
-  (lg h *)
-  (rf h *)  ;; = allp, but why ?
-|#
-
-(DEFUN LOOP-SPACE-EFHM (space)
-  (declare (type simplicial-set space))
-  (let ((ls-left-eqvl (ls-left-eqvl space))
-	(right-eqvl (cobar (efhm space))))
-    (declare (type equivalence ls-left-eqvl right-eqvl))
-    (cmps ls-left-eqvl right-eqvl)))
-
-(DEFMETHOD SEARCH-EFHM (loop-space (dfnt (eql 'loop-space)))
-  (declare (type simplicial-set loop-space))
-  (loop-space-efhm (second (dfnt loop-space))))
-
-#|
-  (cat-init)
-  (setf l (loop-space (sphere 2)))
-  (homology l 6)
-  (setf oos3 (loop-space (loop-space (sphere 3))))
-  (homology oos3 3)
-  (setf ooos4 (loop-space (loop-space (loop-space (sphere 4)))))
-  (homology ooos4 2)
-|#
diff --git a/archive/Kenzo-2/Kenzo-2-Acl5/ls-twisted-products.cl b/archive/Kenzo-2/Kenzo-2-Acl5/ls-twisted-products.cl
deleted file mode 100644
index d21cec0..0000000
--- a/archive/Kenzo-2/Kenzo-2-Acl5/ls-twisted-products.cl
+++ /dev/null
@@ -1,521 +0,0 @@
-;;;  LS-TWISTED-PRODUCTS  LS-TWISTED-PRODUCTS  LS-TWISTED-PRODUCTS
-;;;  LS-TWISTED-PRODUCTS  LS-TWISTED-PRODUCTS  LS-TWISTED-PRODUCTS
-;;;  LS-TWISTED-PRODUCTS  LS-TWISTED-PRODUCTS  LS-TWISTED-PRODUCTS
-
-(IN-PACKAGE "CAT")
-
-(PROVIDE "ls-twisted-products")
-
-;; ABSM-LOOPABSM is the "twisted" product of ABSM, a simplex of the base
-;;   space of dimension DMNS by LOOP-ABSM, a simplex of the corresponding
-;;   loop-space, of dimension (1- DMNS). The returned object is
-;;   a loop-absm of dimension (1- DMNS).
-
-(DEFUN ABSM-LOOPABSM (cmpr dmns absm loop-absm)
-   (declare
-      (type cmprf cmpr)
-      (fixnum dmns)  ;; dimension of ABSM
-      (type absm absm loop-absm))
-   (the absm
-      (with-absm (dgop1 gmsm1) absm
-         (when (logbitp (1- dmns) dgop1)
-            (return-from absm-loopabsm loop-absm))                  
-         (with-absm (dgop2 loop2) loop-absm
-            (let ((iloop2 (loop-list loop2)))
-               (declare (list iloop2))
-               (unless iloop2
-                  (return-from absm-loopabsm
-                     (absm dgop1 (make-loop :list (list (apowr 0 gmsm1 +1))))))
-               (let ((apowr (first iloop2)))
-                  (declare (type apowr apowr))
-                  (with-apowr (dgop22 gmsm2 expn2) apowr
-                     (if (and (= dgop1 (dgop*dgop dgop2 dgop22))
-                              (eq :equal (funcall cmpr gmsm1 gmsm2)))
-                        ;; the absm is eaten by the first component of the loop
-                        (if (= -1 expn2)
-                           ;; the first item of the loop disappears.
-                           (let ((iloop2-rest (rest iloop2)))
-                              (if iloop2-rest
-                                 (let ((loop-rest (normalize-loop (1- dmns) iloop2-rest)))
-                                    (declare (type absm loop-rest))
-                                    (absm (dgop*dgop dgop2 (dgop loop-rest)) (gmsm loop-rest)))
-                                 (absm (mask (1- dmns)) +null-loop+)))
-                           ;; the exponent of the first item is increased by 1
-                           (absm dgop2 (make-loop :list (cons (apowr dgop22 gmsm2 (1+ expn2))
-                                                           (rest iloop2)))))
-                        ;; a concatenation must be done
-                        (multiple-value-bind (dgop dgop1 dgop2) (extract-common-dgop dgop1 dgop2)
-                           (declare (fixnum dgop dgop1 dgop2))
-                           (absm dgop
-                              (make-loop
-                                 :list (cons (apowr dgop1 gmsm1 +1)
-                                          (if (zerop dgop2)
-                                             iloop2
-                                             (mapcar #'(lambda (apowr)
-                                                          (declare (type apowr apowr))
-                                                          (cons (dgop*dgop dgop2 (apdgop apowr))
-                                                             (cdr apowr)))
-                                                iloop2))))))))))))))
-
-#|
-  (setf cmpr (cmpr (deltab)))
-  (absm-loopabsm cmpr 3 (absm 4 7) (absm 7 +null-loop+))
-  (absm-loopabsm cmpr 3 (absm 0 15) (absm 7 +null-loop+))
-  (absm-loopabsm cmpr 3 (absm 2 7) (absm 2 (loop3 0 7 4)))
-  (absm-loopabsm cmpr 3 (absm 2 7) (absm 2 (loop3 0 7 4 1 12 -1)))
-  (absm-loopabsm cmpr 3 (absm 2 7) (absm 2 (loop3 0 7 -1)))
-  (absm-loopabsm cmpr 3 (absm 2 7) (absm 2 (loop3 0 7 -1 1 12 -1)))
-  (absm-loopabsm cmpr 3 (absm 2 7) (absm 2 (loop3 0 7 4)))
-  (absm-loopabsm cmpr 3 (absm 2 7) (absm 0 (loop3 2 7 4 1 14 -1)))
-  (absm-loopabsm cmpr 3 (absm 2 7) (absm 0 (loop3 2 7 -1)))  ;; in principle illegal but works
-  (absm-loopabsm cmpr 3 (absm 2 7) (absm 0 (loop3 2 7 -1 1 14 -1)))
-  (absm-loopabsm cmpr 3 (absm 2 7) (absm 0 (loop3 0 15 -1 1 14 -1)))
-  (absm-loopabsm cmpr 3 (absm 0 15) (absm 2 (loop3 0 7 -1 0 14 -1)))
-  (absm-loopabsm cmpr 3 (absm 2 7) (absm 2 (loop3 0 28 -1 0 14 -1))))
-|#
-
-(DEFUN TWISTED-CRTS-PRDC-FACE (cmpr space-face loop-space-face non-twisted-face)
-   (declare
-      (type cmprf cmpr)
-      (type face space-face loop-space-face non-twisted-face))
-   (flet ((rslt (indx dmns crpr)
-             (declare
-                (fixnum indx dmns)
-                (type crpr crpr))
-             (the absm
-                (progn
-                   (unless (= indx dmns)
-                      (return-from rslt
-                         (funcall non-twisted-face indx dmns crpr)))
-                   (with-crpr (absm1 absm2) crpr
-                      (let ((face1 (a-face4 space-face dmns dmns absm1))
-                            (face2 (a-face4 loop-space-face dmns dmns absm2)))
-                         (declare (type absm face1 face2))
-                         (setf face2 (absm-loopabsm cmpr dmns absm1 face2))
-                         (2absm-acrpr face1 face2)))))))
-      (the face #'rslt)))
-
-(DEFUN TWISTED-CRTS-PRDC (space
-                          &aux
-                          (loop-space (loop-space space))
-                          (crts-prdc (crts-prdc space loop-space)))
-  (declare (type simplicial-set space loop-space crts-prdc))
-  (the simplicial-set
-    (with-slots ((space-cmpr cmpr) (space-face face)) space
-      (declare
-       (type cmprf space-cmpr)
-       (type face space-face))
-      (with-slots ((loop-space-face face)) loop-space
-        (declare (type face loop-space-face))
-        (with-slots ((crts-prdc-cmpr cmpr) basis bsgn (crts-prdc-face face)) crts-prdc
-          (declare
-           (type cmprf crts-prdc-cmpr)
-           (type basis basis)
-           (type face non-twisted-face)
-           (type gmsm bsgn))
-          (let ((rslt (simplicial-set
-                       :cmpr crts-prdc-cmpr
-                       :basis basis
-                       :bsgn bsgn
-                       :face (twisted-crts-prdc-face
-                              space-cmpr space-face loop-space-face crts-prdc-face)
-                       :dfnt `(twisted-crts-prdc ,space))))
-            (setf (slot-value rslt 'grmd) crts-prdc)
-            rslt))))))
-
-#|
-  (setf p (r-proj-space 3))
-  (setf tw (twisted-crts-prdc p))
-  (defun random-apowr (dmns max-expn)
-     (loop
-        (let* ((dgop (random (2-exp (1- dmns))))
-               (gmsm (- dmns (logcount dgop))))
-           (unless (< 0 gmsm 3)
-              (return-from random-apowr
-                 (apowr dgop gmsm (srandom max-expn)))))))
-  (defun random-niloop (dmns max-expn length)
-     (mapcar #'(lambda (dummy)
-                  (random-apowr (1+ dmns) max-expn))
-        (make-list length)))
-  (defun random-crpr (dmns max-expn length)
-     (loop
-        (let ((loop (normalize-loop dmns (random-niloop dmns max-expn length)))
-              (dgop (random (2-exp dmns))))
-           (let ((absm (2absm-acrpr (absm dgop (- dmns (logcount dgop))) loop)))
-              (when (and (zerop (dgop absm))
-                         (not (< (gmsm1 (gmsm absm)) 3)))
-                 (return (gmsm absm)))))))
-  (setf cmpr (cmpr tw))
-  (defun random-cmbn (degr max-cffc max-expn loop-length cmbn-length)
-     (apply #'nterm-add cmpr degr
-        (mapcar #'(lambda (dummy)
-                     (term (srandom max-cffc) (random-crpr degr max-expn loop-length)))
-           (make-list cmbn-length))))
-  (setf c (random-cmbn 8 10 4 4 100))
-  (time (? tw (? tw c)))
-  (time (? tw (? tw c)))
-|#
-
-(DEFUN DTAU-D-INTR (crts-prdc-cmpr crts-prdc-face twisted-crts-prdc-face)
-   (declare
-      (type cmprf crts-prdc-cmpr)
-      (type face crts-prdc-face twisted-crts-prdc-face))
-   (flet ((rslt (dmns crpr)
-             (declare
-                (fixnum indx dmns)
-                (type crpr crpr))
-             (when (zerop dmns)
-                (return-from rslt +zero-negative-cmbn+))
-             (the cmbn
-                (let ((dmns-1 (1- dmns)))
-                   (declare (fixnum dmns-1))
-                   (when (logbitp dmns-1 (dgop1 crpr))
-                      (return-from rslt (zero-cmbn dmns-1)))
-                   (let ((face-tau (funcall twisted-crts-prdc-face dmns dmns crpr))
-                         (face (funcall crts-prdc-face dmns dmns crpr))
-                         (sign (-1-expt-n dmns)))
-                      (declare
-                         (type absm face-tau face)
-                         (fixnum sign))
-                      (with-absm (dgop-tau gmsm-tau) face-tau
-                      (with-absm (dgop gmsm) face
-                         (if (plusp dgop-tau)
-                            (if (plusp dgop)
-                               (zero-cmbn dmns-1)
-                               (term-cmbn dmns-1 (- sign) gmsm))
-                            (if (plusp dgop)
-                               (term-cmbn dmns-1 sign gmsm-tau)
-                               (ecase (funcall crts-prdc-cmpr gmsm-tau gmsm)
-                                  (:less
-                                   (cmbn dmns-1 sign gmsm-tau (- sign) gmsm))
-                                  (:greater
-                                   (cmbn dmns-1 (- sign) gmsm sign gmsm-tau))
-                                  (:equal
-                                   (error "Surprise in DTAU-D-INTR.~@
-                                           Crpr = ~A~@
-                                           D-tau = ~A~@
-                                           D = ~A"
-                                      crpr gmsm-tau gmsm))))))))))))
-      (the intr #'rslt)))
-
-#|
-  (setf d (deltab))
-  (setf p (crts-prdc d (loop-space d)))
-  (setf tw (twisted-crts-prdc d))
-  (setf crts-prdc-cmpr (cmpr p)
-        crts-prdc-face (face p)
-        twisted-crts-prdc-face (face tw))
-  (setf delta (dtau-d-intr crts-prdc-cmpr crts-prdc-face twisted-crts-prdc-face))
-  (funcall delta 3 (crpr 0 15 0 (loop3 0 (- 2048 64) 1)))
-  (funcall delta 5 (crpr 10 15 5 (loop3 0 (- 2048 64) 1)))
-  (funcall delta 5 (crpr 5 15 10 (loop3 0 (- 2048 64) 1)))
-|#
-
-(DEFUN DTAU-D (space
-                 &aux (loop-space (loop-space space))
-                      (crts-prdc (crts-prdc space loop-space))
-                      (crts-prdc-cmpr (cmpr crts-prdc))
-                      (crts-prdc-face (face crts-prdc))
-                      (twisted-crts-prdc (twisted-crts-prdc space))
-                      (twisted-crts-prdc-face (face twisted-crts-prdc)))
-   (declare
-      (type simplicial-set space loop-space crts-prdc twisted-crts-prdc)
-      (type cmprf crts-prdc-cmpr)
-      (type face crts-prdc-face twisted-crts-prdc-face))
-   (the morphism
-      (morphism
-         :sorc crts-prdc :trgt crts-prdc :degr -1
-         :intr (dtau-d-intr crts-prdc-cmpr crts-prdc-face twisted-crts-prdc-face)
-         :strt :gnrt
-         :dfnt `(dtau-d ,space))))
-
-(DEFUN SZCZARBA (space
-                   &aux (loop-space (loop-space space))
-                        (twisted-crts-prdc (twisted-crts-prdc space))
-                        (ez (ez space loop-space))
-                        (dtau-d (dtau-d space)))
-   (declare
-      (type simplicial-set space loop-space)
-      (type reduction ez szczarba)
-      (type morphism dtau-d))
-   (the (values reduction morphism)
-      (multiple-value-bind (szczarba bottom-perturbation)
-                           (add ez dtau-d)
-         (with-slots (tcc f g h) szczarba
-            (setf tcc twisted-crts-prdc
-                  (slot-value f 'sorc) twisted-crts-prdc
-                  (slot-value g 'trgt) twisted-crts-prdc
-                  (slot-value h 'sorc) twisted-crts-prdc
-                  (slot-value h 'trgt) twisted-crts-prdc))
-         (values szczarba bottom-perturbation))))
- 
-#|
-  (cat-init)
-  (setf rdct (szczarba (deltab)))
-  (pre-check-rdct rdct)
-  (setf *tc* (cmbn 2 1 (crpr 0 7 0 (loop3 0 (- 512 32) 1)))
-        *bc* (cmbn 2 1 (tnpr 0 1 2 (loop3 0 (- 512 32) 1))
-                     10 (tnpr 1 (- 4096 1024) 1 (loop3 0 7 1))
-                     100 (tnpr 2 7 0 (loop3 0 (- 4096 1024) 1))))
-  (check-rdct) 
-  (setf bcc (bcc rdct))
-  (time (? bcc 5 (tnpr 5 (mask 6) 0 +null-loop+)))
-  (time (? bcc 6 (tnpr 6 (mask 7) 0 +null-loop+)))
-|#
-
-(DEFUN TWISTED-TNSR-PRDC (space
-                            &aux (szczarba (szczarba space)))
-   (declare
-      (type simplicial-set space)
-      (type reduction szczarba))
-   (the chain-complex
-      (bcc szczarba)))
-
-;;;
-;;;  The important contraction.
-;;;
-
-(DEFUN POP-FIRST-ABSM (dmns iloop)
-   (declare (type iloop iloop))
-   (the (values (member -1 0 1) (or nil absm) absm)
-      (progn
-         (unless iloop
-            (return-from pop-first-absm
-               (values 0 nil iloop)))
-         (let ((apowr (first iloop))
-               (niloop-rest (rest iloop)))
-            (declare
-               (type apowr apowr)
-               (type iloop niloop-rest))
-            (with-apowr (dgop gmsm expn) apowr
-               (let ((popped-absm (absm dgop gmsm)))
-                  (declare (type absm popped-absm))
-                  (cond ((< expn -1)
-                         (values -1 popped-absm
-                            (absm 0
-                               (make-loop
-                                  :list (cons (apowr dgop gmsm (1+ expn)) niloop-rest)))))
-                        ((> expn +1)
-                         (values +1 popped-absm
-                            (absm 0
-                               (make-loop
-                                  :list (cons (apowr dgop gmsm (1- expn)) niloop-rest)))))
-                        (t
-                           (values expn popped-absm
-                              (normalize-loop dmns niloop-rest))))))))))
-
-#|
-  (pop-first-absm 4 (cdr +null-loop+))
-  (pop-first-absm 4 (cdr (loop3 0 'a -2)))
-  (pop-first-absm 4 (cdr (loop3 0 'a +2)))
-  (pop-first-absm 4 (cdr (loop3 0 'a -1)))
-  (pop-first-absm 4 (cdr (loop3 0 'a +1)))
-  (pop-first-absm 4 (cdr (loop3 1 'a -2 2 'b 3)))
-  (pop-first-absm 4 (cdr (loop3 0 'a +2 2 'b -3)))
-  (pop-first-absm 4 (cdr (loop3 1 'a -1 2 'b 3)))
-  (pop-first-absm 4 (cdr (loop3 0 'a +1 2 'b 5)))
-  (pop-first-absm 4 (cdr (loop3 2 'a -1 1 'b 3)))
-  (pop-first-absm 4 (cdr (loop3 2 'a +1 1 'b 3))))
-|#
-
-(DEFUN CRTS-CONTRACTION-INTR (base-cmpr base-bsgn base-face crts-cmpr)
-   (declare
-      (type cmprf base-cmpr crts-cmpr)
-      (type gmsm base-bsgn)
-      (type face base-face))
-   
-   (flet ((rslt (n crpr)
-             (declare
-                (fixnum n)
-                (type crpr crpr))
-             (the cmbn
-                (let ((n+1 (1+ n)))
-                   (declare (fixnum n+1))
- (labels (
-  (hh (x-n g-n)
-     (declare (type absm x-n g-n))
-     (if (bsgn-p base-cmpr base-bsgn n x-n)
-        (if (degenerate-p g-n)
-           (zero-cmbn n+1)
-           (h-hat (loop-list (gmsm g-n))))
-        (if (degenerate-p g-n)
-           (h-tilde (1dgnr n x-n) g-n)
-           (2cmbn-add crts-cmpr (h-hat (loop-list (gmsm g-n)))
-              (h-tilde (1dgnr n x-n) g-n)))))
-  (h-tilde (x-n+1 g-n)
-     (declare (type absm x-n+1 g-n))
-     (when (bsgn-p base-cmpr base-bsgn n+1 x-n+1)
-        (return-from h-tilde
-           (zero-cmbn n+1)))
-     (do ((i n (1- i))
-          (dgop 0 (+ dgop (2-exp i)))
-          (sign (-1-expt-n+1 n) (- sign))
-          (del-i x-n+1  (a-face4 base-face i (1+ i) del-i))
-          (rslt (zero-cmbn n+1)))
-         ((minusp i) rslt)
-        (declare
-           (fixnum i dgop sign)
-           (type absm del-i)
-           (type cmbn rslt))
-        (let ((absm1 (ndgnr dgop del-i))
-              (loop-absm2 (1dgnr i g-n)))
-           (declare (type absm absm1 loop-absm2))
-           (unless (plusp (logand (dgop absm1) (dgop loop-absm2)))
-              (dstr-add-term-to-cmbn
-                 crts-cmpr
-                 sign (crpr absm1 loop-absm2)
-                 rslt)))))
-  (h-hat (g-n)
-     (declare (type iloop g-n))  ;;; ***
-     (multiple-value-bind (expn y-n+1 gp-n) (pop-first-absm n g-n)
-        (declare
-           (fixnum expn)
-           (type absm y-n+1)
-           (type loop gp-n))  ;;; ***
-        (ecase expn
-           (0 (zero-cmbn (1+ n)))
-           (+1
-            (let ((h-tildes (2cmbn-sbtr crts-cmpr
-                               (h-tilde y-n+1 gp-n)
-                               (h-tilde
-                                  (1dgnr n (a-face4 base-face (1+ n) (1+ n) y-n+1))
-                                  (absm 0 (make-loop :list g-n))))))
-               (declare (type cmbn h-tildes))
-               (if (degenerate-p gp-n)
-                  h-tildes 
-                  (2cmbn-add crts-cmpr (h-hat (loop-list (gmsm gp-n))) h-tildes))))
-           (-1
-            (let ((next-x-n (a-face4 base-face (1+ n) (1+ n) y-n+1))
-                  (h-tilde (h-tilde y-n+1 (absm 0 (make-loop :list g-n)))))
-               (declare
-                  (type absm next-x-n)
-                  (type cmbn h-tilde))
-               (if (zerop (logand (dgop next-x-n) (dgop gp-n)))
-                  (2cmbn-sbtr crts-cmpr
-                     (hh next-x-n gp-n) h-tilde)
-                  (cmbn-opps h-tilde))))))))
-    
-    (with-crpr (absm1 loop-absm2) crpr
-       (hh absm1 loop-absm2)))))))
-    
-    (the intr #'rslt)))
-
-#|
-  (cat-init)
-  (setf delta (deltab))
-  (setf tw (twisted-crts-prdc delta))
-  (setf d (dffr tw))
-  (setf base-cmpr (cmpr delta)
-        base-bsgn (bsgn delta)
-        base-face (face delta)
-        crts-cmpr (cmpr tw))
-  (setf r (crts-contraction-intr base-cmpr base-bsgn base-face crts-cmpr))
-  (setf h (morphism :sorc tw :trgt tw :degr +1
-             :intr r :strt :gnrt :dfnt `(crts-contraction ,delta)))
-  (setf z (i-sbtr (idnt-mrph tw) (cmps d h) (cmps h d)))
-  (? z 0 (crpr 0 1 0 +null-loop+))
-  (? z 0 (crpr 0 1 0 (loop3 0 96 1)))
-  (? z 0 (crpr 0 1 0 (loop3 0 96 1 0 (+ 256 128) 1)))
-  (? z 0 (crpr 0 1 0 (loop3 0 96 1 0 (+ 256 128) 1 0 (+ 512 1024) 1)))
-  (? z 0 (crpr 0 1 0 (loop3 0 96 2)))
-  (? z 1 (crpr 0 3 0 (loop3 0 (+ 32 64 128) 1)))
-  (? z 2 (crpr 0 7 0 (loop3 0 (+ 32 64 128 256) 1)))
-  (? z 3 (crpr 2 7 1 (loop3 2 (+ 32 64 128) 2 4 (+ 32 64 128) -2)))
-  (? z 3 (crpr 2 7 4 (loop3 2 (+ 32 64 128) 2 1 (+ 32 64 128) -2)))
-  (? z 3 (crpr 2 7 1 (loop3 2 (+ 32 64 128) -2 4 (+ 32 64 128) 2)))
-  (? z 3 (crpr 2 7 4 (loop3 2 (+ 32 64 128) -2 1 (+ 32 64 128) 2)))
-  (? z 3 (crpr 1 7 2 (loop3 2 (+ 32 64 128) 2 4 (+ 32 64 128) -2)))
-  (? z 3 (crpr 4 7 2 (loop3 2 (+ 32 64 128) 2 1 (+ 32 64 128) -2)))
-  (? z 3 (crpr 1 7 2 (loop3 2 (+ 32 64 128) -2 4 (+ 32 64 128) 2)))
-  (? z 3 (crpr 4 7 2 (loop3 2 (+ 32 64 128) -2 1 (+ 32 64 128) 2)))
-|#
- 
-
-#|
-  (cat-init)
-  (setf p (r-proj-space 3))
-  (setf tw (twisted-crts-prdc p))
-  (setf r (crts-contraction-intr (cmpr p) (bsgn p) (face p) (cmpr tw)))
-  (defun random-apowr (dmns max-expn)
-     (loop
-        (let* ((dgop (random (2-exp (1- dmns))))
-               (gmsm (- dmns (logcount dgop))))
-           (unless (< 0 gmsm 3)
-              (return-from random-apowr
-                 (apowr dgop gmsm (srandom max-expn)))))))
-  (defun random-niloop (dmns max-expn length)
-     (mapcar #'(lambda (dummy)
-                  (random-apowr (1+ dmns) max-expn))
-        (make-list length)))
-  (defun random-crpr (dmns max-expn length)
-     (loop
-        (let ((loop (normalize-loop dmns (random-niloop dmns max-expn length)))
-              (dgop (random (2-exp dmns))))
-           (let ((absm (2absm-acrpr (absm dgop (- dmns (logcount dgop))) loop)))
-              (when (and (zerop (dgop absm))
-                         (not (< (gmsm1 (gmsm absm)) 3)))
-                 (return (gmsm absm)))))))
-  (setf cmpr (cmpr tw))
-  (defun random-cmbn (degr max-cffc max-expn loop-length cmbn-length)
-     (apply #'nterm-add cmpr degr
-        (mapcar #'(lambda (dummy)
-                     (term (srandom max-cffc) (random-crpr degr max-expn loop-length)))
-           (make-list cmbn-length))))
-  (setf h (morphism :sorc tw :trgt tw :degr +1
-             :intr r :strt :gnrt :dfnt `(crts-contraction ,p)))
-  (setf d (dffr tw))
-  (setf z (i-sbtr (idnt-mrph tw) (cmps h d) (cmps d h)))
-  (setf c (random-cmbn 5 10 2 2 1))
-  (? z c)
-  (setf c (random-cmbn 6 10 3 3 3))
-  (? z c)
-  (setf c (random-cmbn 7 10 4 4 6))
-  (? z c)
-  (setf c (random-cmbn 8 10 4 4 20))
-  (? z c)
-  (? h c)
-  (? d *)
-  (length *)
-|#
-
-(DEFUN CRTS-CONTRACTION (space
-                           &aux (twisted-crts-prdc (twisted-crts-prdc space)))
-   (declare (type simplicial-set space twisted-crts-prdc))
-   (the morphism
-      (morphism
-         :sorc twisted-crts-prdc :trgt twisted-crts-prdc :degr +1
-         :intr (crts-contraction-intr (cmpr space) (bsgn space) (face space)
-                  (cmpr twisted-crts-prdc))
-         :strt :gnrt
-         :dfnt `(crts-contraction ,space))))
-
-#|
-  (setf h (crts-contraction (deltab)))
-  (setf d (dffr (twisted-crts-prdc (deltab))))
-  (setf z (i-sbtr (idnt-mrph (sorc d)) (cmps d h) (cmps h d)))
-  (? z 3 (crpr 4 7 2 (loop3 2 (+ 32 64 128) -2 1 (+ 32 64 128) 2)))
-|#
-
-(DEFUN TNPR-CONTRACTION (space
-                           &aux
-                           (szczarba (szczarba space))
-                           (f (f szczarba))
-                           (g (g szczarba))
-                           (crts-contraction (crts-contraction space)))
-   (declare
-      (type simplicial-set space)
-      (type reduction szczarba)
-      (type morphism f g crts-contraction))
-   (the morphism
-      (i-cmps f crts-contraction g)))
-
-#|
-  (cat-init)
-  (setf delta (deltab))
-  (setf sz (szczarba (deltab)))
-  (setf tw (bcc sz))
-  (setf h (tnpr-contraction delta))
-  (setf z (i-sbtr (idnt-mrph tw) (cmps tw h) (cmps h tw)))
-  (time (? z 3 (tnpr 0 1 3 (loop3 0 (mask 5) 2 0 (* 32 (mask 5)) -1))))
-  (? h 4 (tnpr 0 1 0 (loop3 0 (mask 6) 1)))
-|#
diff --git a/archive/Kenzo-2/Kenzo-2-Acl5/macros.cl b/archive/Kenzo-2/Kenzo-2-Acl5/macros.cl
deleted file mode 100644
index 4a534f8..0000000
--- a/archive/Kenzo-2/Kenzo-2-Acl5/macros.cl
+++ /dev/null
@@ -1,816 +0,0 @@
-;;;  MACROS  MACROS  MACROS  MACROS  MACROS  MACROS  MACROS
-;;;  MACROS  MACROS  MACROS  MACROS  MACROS  MACROS  MACROS
-;;;  MACROS  MACROS  MACROS  MACROS  MACROS  MACROS  MACROS
-
-(IN-PACKAGE "CAT")
-
-(PROVIDE "macros")
-
-;;;
-;;;  VARIOUS
-;;;
-
-(DEFMACRO -1-EXPT-N (n)
-  `(the fixnum (if (evenp (the fixnum ,n)) 1 -1)))
-
-(DEFMACRO -1-EXPT-N+1 (n)
-  `(the fixnum (if (evenp (the fixnum ,n)) -1 1)))
-
-(DEFMACRO -1-EXPT-N-1 (n)
-  `(-1-expt-n+1 ,n))
-
-#|
-  (-1-expt-n 5)
-  (-1-expt-n 6)
-  (-1-expt-n+1 5)
-  (-1-expt-n+1 6)
-  (-1-expt-n-1 5)
-  (-1-expt-n-1 6))
-|#
-
-;;; (DEFCONSTANT +2-EXP+ (make-array (integer-length most-positive-fixnum)
-;;;                         :element-type 'fixnum))
-;;; 
-;;; (dotimes (i (integer-length most-positive-fixnum))
-;;;    (setf (aref +2-exp+ i) (the fixnum (expt 2 i))))
-
-
-(DEFCONSTANT +2-EXP+
-  (let ((rslt (make-array (integer-length most-positive-fixnum)
-                        :element-type 'fixnum)))
-    (declare (type (array fixnum 1) rslt))
-    (dotimes (i (integer-length most-positive-fixnum) rslt)
-      (setf (aref rslt i) (the fixnum (expt 2 i))))))
-
-(DEFMACRO 2-EXP (n)
-   `(aref +2-exp+ ,n))
-
-;;; (DEFCONSTANT +MASK+ (make-array (1+ (integer-length most-positive-fixnum))
-;;;                         :element-type 'fixnum))
-;;; 
-;;; (dotimes (i (1+ (integer-length most-positive-fixnum)))
-;;;    (setf (aref +mask+ i) (the fixnum (1- (expt 2 i)))))
-
-(DEFCONSTANT +MASK+
-  (let ((rslt (make-array (integer-length most-positive-fixnum)
-                        :element-type 'fixnum)))
-    (declare (type (array fixnum 1) rslt))
-    (dotimes (i (integer-length most-positive-fixnum) rslt)
-      (setf (aref rslt i) (the fixnum (1- (expt 2 i)))))))
-
-
-(DEFMACRO MASK (n)
-   `(aref +mask+ ,n))
-
-(DEFMACRO BINOMIAL-P-Q (p q)
-  `(binomial-n-p (+ ,p ,q) ,p))
-
-;;;
-;;;  COMBINATIONS
-;;;
-
-(DEFMACRO LEXICO (&rest rest)
-   (unless (cdr rest)
-      (return-from lexico (first rest)))
-   (let ((vrslt (gensym)))
-      `(let ((,vrslt ,(first rest)))
-          (declare (type cmpr ,vrslt))
-          (if (eq ,vrslt :equal)
-             (lexico ,@(rest rest))
-             ,vrslt))))
-
-#|
-  (let ((#+ACLPC allegro:*top-print-level*
-         #-ACLPC     *print-level* nil))
-    (declare (special
-                #+aclpc allegro:*top-print-level*
-                #-aclpc *print-level*))
-     (pprint (macroexpand-1
-               '(lexico
-                   comparison1
-                   comparison2
-                   comparison3
-                   comparison4)))))
-|#
-
-(DEFMACRO TERM (cffc gnrt)
-  `(cons ,cffc ,gnrt))
-
-(DEFMACRO -TERM (mark)
-   `(car ,mark))
-
-(DEFMACRO CFFC (term)
-   `(car ,term))
-
-(DEFMACRO -CFFC (mark)
-   `(caar ,mark))
-
-(DEFMACRO GNRT (term)
-  `(cdr ,term))
-
-(DEFMACRO -GNRT (mark)
-   `(cdar ,mark))
-
-(DEFMACRO WITH-TERM ((cffc gnrt) term . body)
-   `(let (,@(if cffc `((,cffc (cffc ,term))) nil)
-          ,@(if gnrt `((,gnrt (gnrt ,term))) nil))
-       (declare
-          (fixnum ,@(if cffc `(,cffc) nil))
-          (type gnrt ,@(if gnrt `(,gnrt) nil)))
-       ,@body))
-
-#|
-  (macroexpand-1 '(with-term (cffc gnrt) term
-                     (statement-1)
-                     (statement-2)))
-  (macroexpand-1 '(with-term (nil gnrt) term
-                     (statement-1)
-                     (statement-2)))
-|#
-
-(DEFMACRO WITH--TERM ((cffc gnrt) mark . body)
-   `(let ((,cffc (-cffc ,mark))
-          (,gnrt (-gnrt ,mark)))
-       (declare
-          (fixnum ,cffc)
-          (type gnrt ,gnrt))
-       ,@body))
-
-#|
-  (macroexpand-1 '(with--term (cffc gnrt) mark
-                     (statement-1)
-                     (statement-2)))
-|#
-
-(DEFMACRO MAKE-CMBN (&key degr list)
-   `(cons :cmbn
-       (cons ,degr ,list)))
-
-#|
-  (make-cmbn :degr 3 :list '((1 . a) (2 . b)))
-|#          
-
-(DEFMACRO CMBN-DEGR (cmbn)
-   `(cadr ,cmbn))
-
-(DEFMACRO CMBN-LIST (cmbn)
-   `(cddr ,cmbn))
-
-#|
-  (cmbn-degr (cons :cmbn (cons 5 nil)))
-  (cmbn-list (cons :cmbn (cons 5 nil)))
-|#
-
-(DEFMACRO WITH-CMBN ((degr list) cmbn . body)
-   `(let ((,degr (cmbn-degr ,cmbn))
-          (,list (cmbn-list ,cmbn)))
-       (declare
-          (fixnum ,degr)
-          (list ,list))
-       ,@body))
-
-#|
-  (macroexpand-1 '(with-cmbn (degr list) cmbn
-                     (statement-1)
-                     (statement-2)))
-|#
-
-(DEFMACRO TERM-CMBN (degr cffc gnrt)
-   `(cons :cmbn (cons ,degr (cons (cons ,cffc ,gnrt) nil))))
-
-(DEFMACRO CMBN-NON-ZERO-P (cmbn)
-   `(cmbn-list ,cmbn)) 
-
-(DEFMACRO CMBN-ZERO-P (cmbn)
-  `(null (cmbn-list ,cmbn)))
-
-
-;;;
-;;;  CHAIN COMPLEXES
-;;;
-
-(DEFMACRO CMPR (&rest rest)
-   (ecase (length rest)
-      (1 `(cmpr1 ,@rest))
-      (3 `(cmpr3 ,@rest))))
-
-(DEFMACRO CMPR3 (object item1 item2)
-   `(funcall (cmpr1 ,object) ,item1 ,item2))
-
-#|
-  (macroexpand '(cmpr chcm))
-  (macroexpand '(cmpr chcm item1 item2))
-|#
-
-(DEFMACRO BASIS (&rest rest)
-   (ecase (length rest)
-      (1 `(basis1 ,@rest))
-      (2 `(basis2 ,@rest))
-      (3 `(basis3 ,@rest))))
-
-(DEFUN BASIS2 (object n)         ;;;
-   (declare
-      (type t object)
-      (fixnum n))
-   (the list
-      (with-slots (basis) object
-         (declare (type basis basis))
-         (when (eq :locally-effective basis)
-            (error "The object ~A is locally-effective." object))
-         (funcall basis n))))
-
-(DEFMACRO BASIS3 (smst dmns keyword)
-  (declare (ignore keyword))  
-  `(a-basis2 (basis ,smst) ,dmns))
-
-(DEFMACRO DFFR (&rest rest)
-   (ecase (length rest)
-      (1 `(dffr1 ,@rest))
-      ((2 3) `(? (dffr1 ,(first rest)) ,@(rest rest)))))
-
-#|
-  (macroexpand '(dffr chcm))
-  (macroexpand '(dffr chcm cmbn))
-  (macroexpand '(dffr chcm degr gnrt))
-|#
-
-;;; Result = (:rslt gnrt value clnm rntm . prpr)
-
-(DEFMACRO MAKE-RSLT (&key gnrt value clnm rntm)
-   `(list :rslt ,gnrt ,value ,clnm ,rntm))
-
-(DEFMACRO RSLT-GNRT (rslt)
-   `(second ,rslt))
-
-(DEFMACRO RSLT-VALUE (rslt)
-   `(third ,rslt))
-
-(DEFMACRO RSLT-CLNM (rslt)
-   `(fourth ,rslt))
-
-(DEFMACRO RSLT-RNTM (rslt)
-   `(fifth ,rslt))
-
-(DEFMACRO ? (&rest rest)
-   (ecase (length rest)
-      (2 `(?2 ,@rest))
-      (3 `(?3 ,@rest))))
-
-(DEFMACRO CONTROL (cmpr cmbn)
-   (if *cmbn-control*
-      `(do-control ,cmpr ,cmbn)
-      cmbn))
-
-(DEFMACRO CONTROLN (cmpr cmbn)
-   (if *cmbn-control*
-      `(do-control ,cmpr ,cmbn)
-      nil))
-
-(DEFVAR *WRONG-CMBN*)
-
-
-;;;
-;;;  CHCM-ELEMENTARY-OP
-;;;
-
-(DEFMACRO I-CMPS (mrph1 &rest rest)
-   (if rest
-      `(cmps ,mrph1 (i-cmps ,@rest))
-      mrph1))
-
-#|
-  (macroexpand '(i-cmps m1))
-  (macroexpand '(i-cmps m1 m2))
-  (macroexpand '(i-cmps m1 m2 m3))
-|#
-
-(DEFMACRO I-ADD (mrph1 &rest rest)
-   (if rest
-      `(add ,mrph1 (i-add ,@rest))
-      mrph1))
-
-#|
-  (macroexpand '(i-add m1))
-  (macroexpand '(i-add m1 m2))
-  (macroexpand '(i-add m1 m2 m3))
-|#
-
-(DEFMACRO I-SBTR (mrph1 mrph2 &rest rest)
-   `(sbtr ,mrph1 (i-add ,mrph2 ,@rest)))
-   
-#|
-  (macroexpand '(i-sbtr m1 m2))
-  (macroexpand '(i-sbtr m1 m2 m3))
-|#
-
-;;;
-;;;  EFFECTIVE HOMOLOGY
-;;;
-
-(DEFMACRO BCC (&rest rest)
-   (case (length rest)
-      (1 `(bcc1 ,@rest))
-      (otherwise
-         `(? (bcc1 ,(first rest)) ,@(rest rest)))))
-
-(DEFMACRO TCC (&rest rest)
-   (case (length rest)
-      (1 `(tcc1 ,@rest))
-      (otherwise
-         `(? (tcc1 ,(first rest)) ,@(rest rest)))))
-
-(DEFMACRO F (&rest rest)
-   (case (length rest)
-      (1 `(f1 ,@rest))
-      (otherwise
-         `(? (f1 ,(first rest)) ,@(rest rest)))))
-
-#|
-  (macroexpand '(f rdct))
-  (macroexpand '(f rdct cmbn))
-  (macroexpand '(f rdct degr gnrt))
-|#
-
-(DEFMACRO G (&rest rest)
-   (case (length rest)
-      (1 `(g1 ,@rest))
-      (otherwise
-         `(? (g1 ,(first rest)) ,@(rest rest)))))
-
-(DEFMACRO H (&rest rest)
-   (case (length rest)
-      (1 `(h1 ,@rest))
-      (otherwise
-         `(? (h1 ,(first rest)) ,@(rest rest)))))
-
-(DEFMACRO LBCC (&rest rest)
-   (case (length rest)
-      (1 `(lbcc1 ,@rest))
-      (otherwise
-         `(? (lbcc1 ,(first rest)) ,@(rest rest)))))
-
-(DEFMACRO RBCC (&rest rest)
-   (case (length rest)
-      (1 `(rbcc1 ,@rest))
-      (otherwise
-         `(? (rbcc1 ,(first rest)) ,@(rest rest)))))
-
-(DEFMACRO LF (&rest rest)
-   (case (length rest)
-      (1 `(lf1 ,@rest))
-      (otherwise
-         `(? (lf1 ,(first rest)) ,@(rest rest)))))
-
-(DEFMACRO LG (&rest rest)
-   (case (length rest)
-      (1 `(lg1 ,@rest))
-      (otherwise
-         `(? (lg1 ,(first rest)) ,@(rest rest)))))
-
-(DEFMACRO LH (&rest rest)
-   (case (length rest)
-      (1 `(lh1 ,@rest))
-      (otherwise
-         `(? (lh1 ,(first rest)) ,@(rest rest)))))
-
-(DEFMACRO RF (&rest rest)
-   (case (length rest)
-      (1 `(rf1 ,@rest))
-      (otherwise
-         `(? (rf1 ,(first rest)) ,@(rest rest)))))
-
-(DEFMACRO RG (&rest rest)
-   (case (length rest)
-      (1 `(rg1 ,@rest))
-      (otherwise
-         `(? (rg1 ,(first rest)) ,@(rest rest)))))
-
-(DEFMACRO RH (&rest rest)
-   (case (length rest)
-      (1 `(rh1 ,@rest))
-      (otherwise
-         `(? (rh1 ,(first rest)) ,@(rest rest)))))
-
-;;;
-;;;  CONES
-;;;
-
-(DEFMACRO BCNX (bicn)
-   `(car ,bicn))
-
-(DEFMACRO IBICN (bicn)
-   `(cdr ,bicn))
-
-(DEFMACRO BCNB (gnrt)
-   `(cons :bcnb ,gnrt))
-
-(DEFMACRO BCNC (gnrt)
-   `(cons :bcnc ,gnrt))
-
-(DEFMACRO BCND (gnrt)
-   `(cons :bcnd ,gnrt))
-
-(DEFMACRO WITH-BICN ((bcnx ibicn) bicn . body)
-   `(let ((,bcnx (bcnx ,bicn))
-          (,ibicn (ibicn ,bicn)))
-       (declare
-          (type (member :bcnb :bcnc :bcnd) ,bcnx)
-          (type gnrt ,ibicn))
-       ,@body))
-
-
-;;;
-;;;  TENSOR PRODUCTS
-;;;
-
-(DEFMACRO TNPR (degr1 gnrt1 degr2 gnrt2)
-   `(cons :tnpr (cons (cons ,degr1 ,gnrt1) (cons ,degr2 ,gnrt2))))
-
-(DEFMACRO DEGR1 (tnpr)
-   `(caadr ,tnpr))
-
-(DEFMACRO GNRT1 (tnpr)
-   `(cdadr ,tnpr))
-
-(DEFMACRO DEGR2 (tnpr)
-   `(caddr ,tnpr))
-
-(DEFMACRO GNRT2 (tnpr)
-   `(cdddr ,tnpr))
-
-(DEFMACRO WITH-TNPR ((degr1 gnrt1 degr2 gnrt2) tnpr . body)
-   `(let (,@(if degr1 `((,degr1 (degr1 ,tnpr))) nil)
-          ,@(if gnrt1 `((,gnrt1 (gnrt1 ,tnpr))) nil)
-          ,@(if degr2 `((,degr2 (degr2 ,tnpr))) nil)
-          ,@(if gnrt2 `((,gnrt2 (gnrt2 ,tnpr))) nil))
-       (declare
-          (fixnum ,@(if degr1 `(,degr1) nil) ,@(if degr2 `(,degr2) nil))
-          (type gnrt ,@(if gnrt1 `(,gnrt1) nil) ,@(if gnrt2 `(,gnrt2) nil)))
-       ,@body))
-
-#|
-  (macroexpand '(tnpr 1 a 2 b))
-            1 (tnpr 2 'a 4 (tnpr 2 'b 2 'c))
-  (macroexpand-1 '(with-tnpr (degr1 gnrt1 degr2 gnrt2) tnpr
-                    (statement-1)
-                    (statement-2)))
-  (macroexpand-1 '(with-tnpr (nil gnrt1 degr2 gnrt2) tnpr
-                    (statement-1)
-                    (statement-2)))
-|#
-
-;;;
-;;;  COALGEBRAS
-;;;
-
-(DEFMACRO CPRD (&rest rest)
-   (case (length rest)
-      (1 `(cprd1 ,@rest))
-      ((2 3) `(? (cprd1 ,(first rest)) ,@(rest rest)))))
-
-;;;
-;;;  COBAR
-;;;
-
-(DEFMACRO CBGN (degr gnrt)
-   `(cons ,degr ,gnrt))
-
-(DEFMACRO CDEGR (cbgn)
-   `(car ,cbgn))
-
-(DEFMACRO CGNRT (cbgn)
-   `(cdr ,cbgn))
-
-(DEFMACRO -CDEGR (cbgn)
-   `(caar ,cbgn))
-
-(DEFMACRO -CGNRT (cbgn)
-   `(cdar ,cbgn))
-
-(DEFMACRO WITH-CBGN ((cdegr cgnrt) cbgn . body)
-   `(let ((,cdegr (cdegr ,cbgn))
-          (,cgnrt (cgnrt ,cbgn)))
-       (declare
-          (fixnum ,cdegr)
-          (type gnrt ,cgnrt))
-       ,@body))
-
-(DEFMACRO WITH--CBGN ((cdegr cgnrt) cbgn . body)
-   `(let ((,cdegr (-cdegr ,cbgn))
-          (,cgnrt (-cgnrt ,cbgn)))
-       (declare
-          (fixnum ,cdegr)
-          (type gnrt ,cgnrt))
-       ,@body))
-
-(DEFMACRO MAKE-ALLP (&key list)
-   `(cons :allp ,list))
-
-(DEFMACRO ALLP-LIST (allp)
-   `(cdr ,allp))
-
-(DEFMACRO WITH-ALLP ((list) allp . body)
-   `(let ((,list (allp-list ,allp)))
-       (declare (list ,list))
-       ,@body))
-
-(DEFMACRO GNRT-ALLP-TNPR (degr gnrt allp)
-   `(make-allp :list (cons (cbgn (1- ,degr) ,gnrt) ,allp)))
-
-
-;;;
-;;;  ALGEBRAS
-;;;
-
-(DEFMACRO APRD (&rest rest)
-   (case (length rest)
-      (1 `(aprd1 ,@rest))
-      ((2 3) `(? (aprd1 ,(first rest)) ,@(rest rest)))))
-
-;;;
-;;;  BAR
-;;;
-
-(DEFMACRO BRGN (degr gnrt)
-   `(cons ,degr ,gnrt))
-
-(DEFMACRO BDEGR (brgn)
-   `(car ,brgn))
-
-(DEFMACRO BGNRT (brgn)
-   `(cdr ,brgn))
-
-(DEFMACRO -BDEGR (brgn)
-   `(caar ,brgn))
-
-(DEFMACRO -BGNRT (brgn)
-   `(cdar ,brgn))
-
-(DEFMACRO WITH-BRGN ((bdegr bgnrt) brgn . body)
-   `(let ((,bdegr (bdegr ,brgn))
-          (,bgnrt (bgnrt ,brgn)))
-       (declare
-          (fixnum ,bdegr)
-          (type gnrt ,bgnrt))
-       ,@body))
-
-(DEFMACRO WITH--BRGN ((bdegr bgnrt) brgn . body)
-   `(let ((,bdegr (-bdegr ,brgn))
-          (,bgnrt (-bgnrt ,brgn)))
-       (declare
-          (fixnum ,bdegr)
-          (type gnrt ,bgnrt))
-       ,@body))
-
-(DEFMACRO MAKE-ABAR (&key list)
-   `(cons :abar ,list))
-
-(DEFMACRO ABAR-LIST (abar)
-   `(cdr ,abar))
-
-(DEFMACRO WITH-ABAR ((list) abar . body)
-   `(let ((,list (abar-list ,abar)))
-       (declare (list ,list))
-       ,@body))
-
-(DEFMACRO MAKE-GBAR (&key dmns list)
-   `(cons :gbar (cons ,dmns ,list)))
-
-(DEFMACRO GBAR-DMNS (gbar)
-   `(cadr ,gbar))
-
-(DEFMACRO GBAR-LIST (gbar)
-   `(cddr ,gbar))
-
-(DEFMACRO WITH-GBAR ((dmns list) gbar . body)
-   `(let ((,dmns (gbar-dmns ,gbar))
-	  (,list (gbar-list ,gbar)))
-       (declare
-	 (fixnum ,dmns)
-	 (list ,list))
-       ,@body))
-
-(DEFMACRO GNRT-GBAR-TNPR (degr gnrt gbar)
-   `(make-gbar :list (cons (brgn (1- ,degr) ,gnrt) ,gbar)))
-
-;;;
-;;;  SIMPLICIAL SETS
-;;;
-
-(DEFMACRO ABSM (dgop gmsm)
-   `(cons :absm (cons ,dgop ,gmsm)))
-
-(DEFMACRO DGOP (absm)
-   `(cadr ,absm))
-
-(DEFMACRO GMSM (absm)
-   `(cddr ,absm))
-
-(DEFMACRO WITH-ABSM ((dgop-var gmsm-var) absm . body)
-   `(let ((,dgop-var (dgop ,absm))
-          (,gmsm-var (gmsm ,absm)))
-       (declare
-          (fixnum ,dgop-var)
-          (type gmsm ,gmsm-var))
-       ,@body))
-
-(DEFMACRO DEGENERATE-P (absm)
-   `(plusp (dgop ,absm)))
-
-(DEFMACRO NON-DEGENERATE-P (absm)
-   `(zerop (dgop ,absm)))
-
-(DEFMACRO FACE (&rest rest)
-   (ecase (length rest)
-      (1 `(face1 ,@rest))
-      (4 `(face4 ,@rest))))
-
-(DEFMACRO A-FACE4 (face indx dmns absm)
-   `(ia-face4 ,face ,indx ,dmns (cdr ,absm)))
-
-;;;
-;;;  DELTA
-;;;
-
-(DEFMACRO D (igmsm)
-   `(cons :delt ,igmsm))
-
-;;;
-;;;  SPECIAL-SMSTS
-;;;
-
-;;; GMSM-FACES-INFO = (gmsm (simple-vector absm) . dffr)
-;;;                         faces
-       
-(DEFMACRO MAKE-GMSM-FACES-INFO (&key gmsm faces dffr)
-   `(cons ,gmsm (cons ,faces ,dffr)))
-
-(DEFMACRO INFO-GMSM (gmsm-faces-info)
-   `(car ,gmsm-faces-info))
-
-(DEFMACRO INFO-FACES (gmsm-faces-info)
-   `(cadr ,gmsm-faces-info))
-
-(DEFMACRO INFO-FACE-I (gmsm-faces-info i)
-   `(svref (cadr ,gmsm-faces-info) ,i))
-
-(DEFMACRO INFO-DFFR (gmsm-faces-info)
-   `(cddr ,gmsm-faces-info))
-
-;;;
-;;;  CARTESIAN PRODUCTS
-;;;
-
-(DEFMACRO CRPR (&rest rest)
-   (ecase (length rest)
-      (2 `(cons :crpr (cons (cdr ,(first rest)) (cdr ,(second rest)))))
-      (4 `(cons :crpr (cons
-                         (cons ,(first rest) ,(second rest))
-                         (cons ,(third rest) ,(fourth rest)))))))
-
-#|
-  (macroexpand '(crpr absm1 absm2))
-  (macroexpand '(crpr dgop1 gmsm1 dgop2 gmsm2))
-|#
-
-(DEFMACRO DGOP1 (crpr)
-   `(caadr ,crpr))
-
-(DEFMACRO GMSM1 (crpr)
-   `(cdadr ,crpr))
-
-(DEFMACRO DGOP2 (crpr)
-   `(caddr ,crpr))
-
-(DEFMACRO GMSM2 (crpr)
-   `(cdddr ,crpr))
-
-(DEFMACRO ABSM1 (crpr)
-   `(cons :absm (cadr ,crpr)))
-
-(DEFMACRO ABSM2 (crpr)
-   `(cons :absm (cddr ,crpr)))
-
-#|
-  (setf c (crpr 1 'a 2 'b))
-  (dgop1 c)
-  (gmsm1 c)
-  (dgop2 c)
-  (gmsm2 c)
-  (absm1 c)
-  (absm2 c)
-|#
-
-(DEFMACRO WITH-CRPR (&rest rest)
-   (ecase (length (first rest))
-      (2 `(with-crpr-2 ,@rest))
-      (4 `(with-crpr-4 ,@rest))))
-
-(DEFMACRO WITH-CRPR-2 ((absm1 absm2) crpr . body)
-   `(let ((,absm1 (cons :absm (cadr ,crpr)))
-          (,absm2 (cons :absm (cddr ,crpr))))
-       (declare (type absm ,absm1 ,absm2))
-       ,@body))
-
-(DEFMACRO WITH-CRPR-4 ((dgop1 gmsm1 dgop2 gmsm2) crpr . body)
-   `(let ((,dgop1 (dgop1 ,crpr))
-          (,gmsm1 (gmsm1 ,crpr))
-          (,dgop2 (dgop2 ,crpr))
-          (,gmsm2 (gmsm2 ,crpr)))
-       (declare
-          (fixnum ,dgop1 ,dgop2)
-          (type gmsm ,gmsm1 ,gmsm2))
-       ,@body))
-
-#|
-  (macroexpand-1
-  (macroexpand-1 '(with-crpr (dgop1 gmsm1 dgop2 gmsm2) crpr
-                     (statement-1)
-                     (statement-2))))
-  (macroexpand-1
-  (macroexpand-1 '(with-crpr (absm1 absm2) crpr
-                     (statement-1)
-                     (statement-2))))
-|#
-
-;;;
-;;;  EILENBERG-ZILBER
-;;;
-
-(DEFMACRO EILENBERG-ZILBER (&rest rest)
-   `(ez ,@rest))
-
-;;;
-;;;  LOOP SPACES
-;;;
-
-(DEFMACRO POWR (gmsm expn)
-   `(cons ,gmsm ,expn))
-
-(DEFMACRO PGMSM (powr)
-   `(car ,powr))
-
-(DEFMACRO EXPN (powr)
-   `(cdr ,powr))
-
-(DEFMACRO WITH-POWR ((gmsm expn) powr . body)
-   `(let ((,gmsm (car ,powr))
-          (,expn (cdr ,powr)))
-       (declare
-          (type gmsm ,gmsm)
-          (fixnum expn))
-       ,@body))
-
-(DEFMACRO WITH-APOWR ((dgop gmsm expn) apowr . body)
-   `(let ((,dgop (apdgop ,apowr))
-          (,gmsm (cadr ,apowr))
-          (,expn (cddr ,apowr)))
-       (declare
-          (fixnum ,dgop ,expn)
-          (type gmsm ,gmsm))
-       ,@body))
-
-(DEFMACRO APOWR (dgop gmsm expn)
-   `(cons ,dgop (cons ,gmsm ,expn)))
-   
-(DEFMACRO APDGOP (apowr)
-   `(car ,apowr))
-
-(DEFMACRO APGMSM (apowr)
-   `(cadr ,apowr))
-
-(DEFMACRO APEXPN (apowr)
-   `(cddr ,apowr))
-
-(DEFMACRO MAKE-LOOP (&key list)
-   `(cons :loop ,list))
-
-(DEFMACRO LOOP-LIST (loop)
-   `(cdr ,loop))
-
-;; CONSTRUCTOR
-
-(DEFMACRO WHEN-SLOT (slot-name . body)
-  `(when (or (eq slot-names t)
-             (member ',slot-name slot-names))
-     ,@body))
-
-#|
-(pprint
- (macroexpand-1
-  '(when-slot dfnt (statement-1) (statement-2))))
-|#
-
-(DEFMACRO ALREADY (object dfnt)
-  (let ((sfound (gensym)))
-  `(let ((,sfound (find ,dfnt *k-list* :key #'dfnt :test #'equal)))
-     (declare (type (or kenzo-object null) ,sfound))
-     (when ,sfound
-       (return-from ,object ,sfound)))))
-
-#|
-(pprint
- (macroexpand-1
-  '(already chain-complex '(z-chcm))))
-|#
-
diff --git a/archive/Kenzo-2/Kenzo-2-Acl5/searching-homology.cl b/archive/Kenzo-2/Kenzo-2-Acl5/searching-homology.cl
deleted file mode 100644
index fa3e863..0000000
--- a/archive/Kenzo-2/Kenzo-2-Acl5/searching-homology.cl
+++ /dev/null
@@ -1,43 +0,0 @@
-;;;  SEARCHING-HOMOLOGY  SEARCHING-HOMOLOGY  SEARCHING-HOMOLOGY
-;;;  SEARCHING-HOMOLOGY  SEARCHING-HOMOLOGY  SEARCHING-HOMOLOGY
-;;;  SEARCHING-HOMOLOGY  SEARCHING-HOMOLOGY  SEARCHING-HOMOLOGY
-
-(IN-PACKAGE "CAT")
-
-(PROVIDE "searching-homology")
-
-(DEFUN ECHCM (chcm)
-   (rbcc (efhm chcm)))
-
-(DEFMETHOD HOMOLOGY ((chcm chain-complex) degr1 &optional (degr2 (1+ degr1)))
-   (declare (fixnum degr1 degr2))
-   (do ((degr degr1 (1+ degr)))
-       ((>= degr degr2))
-      (declare (fixnum degr))
-      (chcm-homology (echcm chcm) degr)
-      (terpri) (clock) (terpri)))
-
-(DEFGENERIC SEARCH-EFHM (chcm dfnt))
-
-(DEFMETHOD SEARCH-EFHM (chcm dfnt)
-  (declare (ignore chcm dfnt))
-  nil)
-
-(DEFMETHOD SLOT-UNBOUND (class (chcm chain-complex) (slot-name (eql 'efhm)))
-  (declare (ignore class))
-  (the equivalence
-    (let ((efhm (search-efhm chcm (first (dfnt chcm)))))
-      (declare (type (or null equivalence) efhm))
-      (setf (efhm chcm)
-        (or efhm
-            (when (functionp (basis chcm))
-              (trivial-eqvl chcm))
-            (error "I don't know how to determine ~
-                    the effective homology of:~@
-                    ~A (Origin: ~A)." chcm (dfnt chcm)))))))
-
-#|
-  (cat-init)
-  (setf d (delta 3))
-  (homology d 0)
-|#
diff --git a/archive/Kenzo-2/Kenzo-2-Acl5/serre.cl b/archive/Kenzo-2/Kenzo-2-Acl5/serre.cl
deleted file mode 100644
index ba175ad..0000000
--- a/archive/Kenzo-2/Kenzo-2-Acl5/serre.cl
+++ /dev/null
@@ -1,288 +0,0 @@
-;;;  SERRE  SERRE  SERRE  SERRE  SERRE  SERRE  SERRE  SERRE  SERRE
-;;;  SERRE  SERRE  SERRE  SERRE  SERRE  SERRE  SERRE  SERRE  SERRE
-;;;  SERRE  SERRE  SERRE  SERRE  SERRE  SERRE  SERRE  SERRE  SERRE
-
-(IN-PACKAGE "CAT")
-
-(PROVIDE "serre")
-
-(DEFUN FIBRATION-DTAU-D-INTR
-  (fibration &aux (base (sorc fibration))
-	          (bface (face base))
-	          (fibre (trgt fibration))
-		  (fface (face fibre))
-		  (grml-sintr (sintr (grml fibre)))
-		  (fbsgn (bsgn fibre))
-		  (sintr-twist (sintr fibration))
-		  (total (fibration-total fibration))
-		  (total-cmpr (cmpr total)))
-  (declare
-     (type fibration fibration)
-     (type simplicial-set base total)
-     (type face bface fface)
-     (type simplicial-group fibre)
-     (type gmsm fbsgn)
-     (type sintr grml-sintr sintr-twist)
-     (type cmprf total-cmpr))
-  (flet ((rslt (dmns crpr
-		     &aux (dmns-1 (1- dmns)))
-	    (declare
-	       (fixnum dmns dmns-1)
-	       (type crpr crpr))
-	    (unless (plusp dmns)
-	       (return-from rslt
-		  (zero-cmbn dmns-1)))
-	    (with-crpr (b-absm f-absm) crpr
-	       (let ((tau-b
-		      (tw-a-sintr3 sintr-twist dmns
-				   b-absm fbsgn)))
-		 (declare (type absm tau-b))
-		 (when (= (dgop tau-b) (mask dmns-1))
-		    (return-from rslt
-				 (zero-cmbn dmns-1)))
-		 (let ((deln-b
-			(a-face4 bface dmns dmns
-				 b-absm))
-		       (deln-f
-			(a-face4 fface dmns dmns
-				 f-absm)))
-		   (declare
-                      (type absm deln-b deln-f tau-b))
-		   (let ((acrpr1 (2absm-acrpr deln-b deln-f))
-			 (acrpr2 
-			  (2absm-acrpr
-			     deln-b
-			     (a-grml4 grml-sintr (1- dmns)
-				      tau-b deln-f))))
-		      (declare (type absm crpr1 crpr2))
-		      (with-absm (dgop1 crpr1) acrpr1
-		      (with-absm (dgop2 crpr2) acrpr2
-			 (if (zerop dgop1)
-			    (if (zerop dgop2)
-			       (dstr-add-term-to-cmbn
-				  total-cmpr
-				  (-1-expt-n+1 dmns) crpr1
-				  (term-cmbn dmns-1
-					     (-1-expt-n dmns)
-					     crpr2))
-			       (term-cmbn dmns-1
-					  (-1-expt-n+1 dmns)
-					  crpr1))
-			    (if (zerop dgop2)
-			       (term-cmbn dmns-1
-					  (-1-expt-n dmns)
-					  crpr2)
-			       (zero-cmbn dmns-1)))))))))))
-	(the intr #'rslt)))
-
-#|
-  (cat-init)
-  (setf s2 (sphere 2))
-  (setf k (k-z2-1))
-  (setf tw (simplicial-mrph
-             :sorc s2
-	     :trgt k
-	     :degr -1
-	     :sintr #'(lambda (dmns gmsm)
-			(absm 0 1))
-	     :dfnt '(s2-tw-kz2)))
-  (setf dt-d (fibration-dtau-d-intr tw))
-  (funcall dt-d 0 (crpr 0 '* 0 0))
-  (funcall dt-d 3 (crpr 4 's2 0 3))
-  (funcall dt-d 3 (crpr 2 's2 0 3))
-  (funcall dt-d 3 (crpr 2 's2 5 1))
-  (funcall dt-d 2 (crpr 0 's2 0 2))
-  (cat-init)
-  (setf s2 (sphere 2))
-  (setf k (k-z-1))
-  (setf tw (simplicial-mrph
-             :sorc s2
-	     :trgt k
-	     :degr -1
-	     :sintr #'(lambda (dmns gmsm)
-			(absm 0 (list 1)))
-	     :dfnt '(s2-tw-kz)))
-  (setf dt-d (fibration-dtau-d-intr tw))
-  (funcall dt-d 0 (crpr 0 '* 0 nil))
-  (funcall dt-d 3 (crpr 4 's2 0 '(2 3 4)))
-  (funcall dt-d 3 (crpr 2 's2 0 '(2 3 4)))
-  (funcall dt-d 3 (crpr 2 's2 5 '(5)))
-  (funcall dt-d 2 (crpr 0 's2 0 '(3 -2)))
-|#
-
-(DEFUN FIBRATION-DTAU-D (fibration
-			   &aux (base (sorc fibration))
-			        (fibre (trgt fibration))
-				(utotal (crts-prdc base fibre)))
-  (declare (type fibration fibration))
-  (the morphism
-     (morphism
-        :sorc utotal
-	:trgt utotal
-	:degr -1
-	:intr (fibration-dtau-d-intr fibration)
-	:strt :gnrt
-	:dfnt `(fibration-dtau-d ,fibration))))
-
-#|
-  (cat-init)
-  (setf s2 (sphere 2))
-  (setf k (k-z-1))
-  (setf tw (simplicial-mrph
-             :sorc s2
-	     :trgt k
-	     :degr -1
-	     :sintr #'(lambda (dmns gmsm)
-			(absm 0 (list 1)))
-	     :dfnt '(s2-tw-kz)))
-  (setf dt-d (fibration-dtau-d tw))
-  (? dt-d 0 (crpr 0 '* 0 nil))
-  (? dt-d 3 (crpr 4 's2 0 '(2 3 4)))
-  (? dt-d 3 (crpr 2 's2 0 '(2 3 4)))
-  (? dt-d 3 (crpr 2 's2 5 '(5)))
-  (? dt-d 2 (crpr 0 's2 0 '(3 -2)))
-|#
-
-(DEFUN BROWN-REDUCTION (fibration
-		        &aux (base (sorc fibration))
-			      (fibre (trgt fibration))
-			      (total (fibration-total fibration))
-			      (ez (eilenberg-zilber base fibre))
-			      (t-perturbation (fibration-dtau-d fibration)))
-  (declare
-     (type fibration fibration)
-     (type simplicial-set base fibre total)
-     (type reduction ez)
-     (type morphism t-perturbation))
-  (the (values reduction morphism)
-     (multiple-value-bind (rslt b-perturbation) (add ez t-perturbation)
-	(declare
-	   (type reduction rslt)
-	   (type morphism b-perturbation))
-        (with-slots (f g h tcc) rslt
-	   (setf tcc total)
-	   (dstr-change-sorc-trgt f :new-sorc total)
-	   (dstr-change-sorc-trgt g :new-trgt total)
-	   (dstr-change-sorc-trgt h :new-sorc total :new-trgt total)
-	   (values rslt b-perturbation)))))
-
-#|
-  (cat-init)
-  (setf s2 (sphere 2))
-  (setf k (k-z2-1))
-  (setf tw (simplicial-mrph
-             :sorc s2
-	     :trgt k
-	     :degr -1
-	     :sintr #'(lambda (dmns gmsm)
-			(absm 0 1))
-	     :dfnt '(s2-tw-kz2)))
-  (setf brown (brown-reduction tw))
-  (setf tcc (tcc brown) bcc (bcc brown))
-  (homology bcc 3)
-  (homology tcc 1 8)
-  (homology bcc 1 8)
-  (cat-init)
-  (setf s2 (sphere 2))
-  (setf k (k-z-1))
-  (setf tw (simplicial-mrph
-             :sorc s2
-	     :trgt k
-	     :degr -1
-	     :sintr #'(lambda (dmns gmsm)
-			(absm 0 (list 1)))
-	     :dfnt '(s2-tw-kz1)))
-  (setf brown (brown-reduction tw))
-  (homology (tcc brown) 1 5)
-  (homology (bcc brown) 1 5)
-|#
-
-(DEFUN LEFT-SERRE-EFHM (fibration)
-  (declare (type fibration fibration))
-  (the equivalence
-     (equivalence
-      :lrdct (trivial-rdct (fibration-total fibration))
-      :rrdct (brown-reduction fibration)
-      :dfnt `(left-serre-efhm ,fibration))))
-
-(DEFUN RIGHT-SERRE-EFHM (fibration &aux
-                                   (base (sorc fibration))
-                                   (fibre (trgt fibration))
-                                   (base-efhm (efhm base))
-                                   (fibre-efhm (efhm fibre))
-                                   (uprdc-efhm (tnsr-prdc base-efhm fibre-efhm)))
-  (declare
-   (type fibration fibration)
-   (type simplicial-set base fibre)
-   (type equivalence base-efhm fibre-efhm uprdc-efhm))
-  (the equivalence
-     (multiple-value-bind (brown b-perturbation) (brown-reduction fibration)
-       (declare
-        (type reduction brown)
-        (type morphism b-perturbation))
-       (let ((rslt (add uprdc-efhm b-perturbation)))
-         (declare (type equivalence rslt))
-         (with-slots (lbcc lf lg lrdct) rslt
-           (declare
-            (type chain-complex lbcc)
-            (type morphism lf lg)
-            (type reduction lrdct))
-           (setf lbcc (bcc brown))
-           (dstr-change-sorc-trgt lf :new-trgt lbcc)
-           (dstr-change-sorc-trgt lg :new-sorc lbcc)
-           (with-slots (bcc f g) lrdct
-             (declare
-              (type chain-complex bcc)
-              (type morphism f g))
-             (setf bcc lbcc)
-             (dstr-change-sorc-trgt f :new-trgt lbcc)
-             (dstr-change-sorc-trgt g :new-sorc lbcc)))
-         rslt))))
-
-#|
-(cat-init)
-(setf s2 (sphere 2))
-(setf k (k-z-1))
-(setf tw (simplicial-mrph
-          :sorc s2
-          :trgt k
-          :degr -1
-          :sintr #'(lambda (dmns gmsm)
-                     (absm 0 (list 1)))
-          :dfnt '(s2-tw-kz1)))
-(setf rh (right-serre-efhm tw))
-(setf rbcc (rbcc rh))
-(homology rbcc 0 5)  
-|#
-
-(DEFUN FIBRATION-TOTAL-EFHM (fibration)
-  (declare (type fibration fibration))
-  (the equivalence
-    (cmps
-     (left-serre-efhm fibration)
-     (right-serre-efhm fibration))))
-
-(DEFMETHOD SEARCH-EFHM (smst (dfnt (eql 'fibration-total)))
-  (declare
-     (type simplicial-set smst))
-  (the equivalence
-     (fibration-total-efhm (second (dfnt smst)))))
-
-#|
-  (cat-init)
-  (setf s2 (sphere 2))
-  (setf k (k-z-1))
-  (setf tw (simplicial-mrph
-             :sorc s2
-	     :trgt k
-	     :degr -1
-	     :sintr #'(lambda (dmns gmsm)
-			(absm 0 (list 2)))
-	     :dfnt '(s2-tw-kz1)))
-  (setf p3r (fibration-total tw))
-  (homology p3r 1 )
-|#
-
-
-     
-  
\ No newline at end of file
diff --git a/archive/Kenzo-2/Kenzo-2-Acl5/simplicial-groups.cl b/archive/Kenzo-2/Kenzo-2-Acl5/simplicial-groups.cl
deleted file mode 100644
index 5addaf2..0000000
--- a/archive/Kenzo-2/Kenzo-2-Acl5/simplicial-groups.cl
+++ /dev/null
@@ -1,175 +0,0 @@
-;;;  SIMPLICIAL-GROUPS  SIMPLICIAL-GROUPS  SIMPLICIAL-GROUPS
-;;;  SIMPLICIAL-GROUPS  SIMPLICIAL-GROUPS  SIMPLICIAL-GROUPS
-;;;  SIMPLICIAL-GROUPS  SIMPLICIAL-GROUPS  SIMPLICIAL-GROUPS
-
-(IN-PACKAGE "CAT")
-
-(PROVIDE "simplicial-groups")
-
-(DEFMETHOD PRINT-OBJECT ((smgr simplicial-group) stream)
-  (the simplicial-group
-     (progn
-       (format stream "[K~D Simplicial-Group]" (idnm smgr))
-       smgr)))
-
-(DEFMETHOD PRINT-OBJECT ((smgr ab-simplicial-group) stream)
-  (the simplicial-group
-     (progn
-       (format stream "[K~D Abelian-Simplicial-Group]" (idnm smgr))
-       smgr)))
-
-(DEFUN SIMPLICIAL-GROUP (&rest rest &key dfnt &allow-other-keys)
-  (declare (type list dfnt))
-  (already simplicial-group dfnt)
-  (the simplicial-group
-    (apply #'make-instance 'simplicial-group rest)))
-
-(DEFMETHOD SHARED-INITIALIZE ((smgr simplicial-group) slot-names
-                              &key grml-sintr grin-sintr)
-  (declare
-   (type (or (eql t) list) slot-names)
-   (type sintr grml grin))
-  (call-next-method)
-  (when-slot grml
-             (when grml-sintr
-               (setf (slot-value smgr 'grml)
-                 (simplicial-mrph
-                  :sorc (crts-prdc smgr smgr) :trgt smgr :degr 0
-                  :sintr grml-sintr :dfnt `(group-multiplication ,smgr))))
-             (when grin-sintr
-               (setf (slot-value smgr 'grin)
-                 (simplicial-mrph
-                  :sorc smgr :trgt smgr :degr 0
-                  :sintr grin-sintr :dfnt `(group-inversion ,smgr)))))
-  smgr)
-
-(DEFUN AB-SIMPLICIAL-GROUP (&rest rest &key dfnt &allow-other-keys)
-  (declare (type list dfnt))
-  (already ab-simplicial-group dfnt)
-  (the ab-simplicial-group
-    (apply #'make-instance 'ab-simplicial-group rest)))
-  
-(DEFMETHOD SHARED-INITIALIZE ((asmgr ab-simplicial-group) slot-names &rest rest)
-  (declare (ignore slot-names rest))
-  (call-next-method))
-
-(DEFMETHOD SLOT-UNBOUND (class (smgr simplicial-group)
-			       (name (eql 'kfll)))
-  (declare (ignore class))
-  (the kfll
-     (progn
-       (setf (slot-value smgr 'kfll) (smgr-kfll smgr)))))
-
-(DEFMETHOD SLOT-UNBOUND (class (smgr simplicial-group)
-			       (name (eql 'aprd)))
-  (declare (ignore class))
-  (the morphism
-     (progn
-       (setf (slot-value smgr 'aprd) (smgr-aprd smgr)))))
-
-(DEFUN A-GRML4 (grml-sintr dmns absm1 absm2)
-  (declare
-     (fixnum dmns)
-     (type absm absm1 absm2))
-  (the absm
-     (let ((acrpr (2absm-acrpr absm1 absm2)))
-       (declare (type absm acrpr))
-       (with-absm (dgop crpr) acrpr
-          (ndgnr dgop
-		 (funcall grml-sintr
-			  (- dmns (logcount dgop))
-			  crpr))))))
-
-(DEFUN A-GRIN4 (grin-sintr dmns absm)
-  (declare
-     (type sintr grin-sintr)
-     (fixnum dmns)
-     (type absm absm))
-  (the absm
-     (with-absm (dgop gmsm) absm
-	(absm dgop
-	      (gmsm
-	       (funcall grin-sintr (- dmns (logcount dgop)) gmsm))))))
-
-(DEFUN SMGR-KFLL-INTR (face grml-sintr grin-sintr)
-  (flet ((rslt (indx dmns hat
-		     &aux (dmns-1 (1- dmns)))
-	    (declare
-	       (fixnum indx dmns dmns-1)
-	       (list hat))
-	    (the absm
-	      (let ((rslt (absm 0 nil)))
-		(declare (type absm rslt))
-		(when (plusp indx)
-		   (setf rslt (1dgnr 0 (pop hat)))
-		   (do ((i 1 (1+ i)))
-		       ((= i indx))
-		      (declare (fixnum i))
-		      (setf rslt
-			    (a-grml4
-			     grml-sintr dmns
-			     rslt
-			     (1dgnr i
-				    (a-grml4
-				     grml-sintr dmns-1
-				     (a-grin4
-				      grin-sintr dmns-1
-				      (a-face4 face
-					i dmns rslt))
-				     (pop hat)))))))
-		(when (< indx dmns)
-		  (setf hat (reverse hat))
-                  (when (zerop indx) 
-		  (setf rslt (1dgnr dmns-1 (pop hat))))
-		  (do ((i (if (zerop indx)
-			      dmns-1
-			      dmns)
-			  (1- i)))
-		      ((endp hat) rslt)
-		     (declare
-		        (type absm rslt)
-			(fixnum i))
-		     (setf rslt
-			   (a-grml4
-			    grml-sintr dmns
-			    rslt
-			    (1dgnr (1- i)
-				   (a-grml4
-				    grml-sintr dmns-1
-				    (a-grin4
-				     grin-sintr dmns-1
-				     (a-face4
-				      face
-				      i dmns rslt))
-				    (pop hat)))))))
-		rslt))))
-     (the kfll #'rslt)))
-
-(DEFUN SMGR-KFLL (smgr)
-  (declare (type simplicial-group smgr))
-  (with-slots (face grml grin) smgr
-     (declare
-        (type face face)
-	(type simplicial-mrph grml grin))
-     (smgr-kfll-intr face (sintr grml) (sintr grin))))
-
-#|
-  (cat-init)
-  (setf k (k-z-1))
-  (setf rslt '(1 10 100))
-  (setf hat (mapcar #'(lambda (i) (face k i 3 rslt)) (<a-b> 0 3)))
-  (dotimes (i 4)
-    (check-kan k i 3 (remove (nth i hat) hat :test #'equal)))
-|#
-
-(DEFUN SMGR-APRD (smgr)
-  (declare (type simplicial-group smgr))
-  (the morphism
-    (let ((eml (eml smgr smgr))
-	  (grml (grml smgr)))
-      (declare
-        (type morphism eml)
-	(type simplicial-mrph grml))
-      (cmps grml eml))))
-
-       
\ No newline at end of file
diff --git a/archive/Kenzo-2/Kenzo-2-Acl5/simplicial-mrphs.cl b/archive/Kenzo-2/Kenzo-2-Acl5/simplicial-mrphs.cl
deleted file mode 100644
index 04f2eb7..0000000
--- a/archive/Kenzo-2/Kenzo-2-Acl5/simplicial-mrphs.cl
+++ /dev/null
@@ -1,143 +0,0 @@
-;;;  SIMPLICIAL-MRPHS  SIMPLICIAL-MRPHS  SIMPLICIAL-MRPHS
-;;;  SIMPLICIAL-MRPHS  SIMPLICIAL-MRPHS  SIMPLICIAL-MRPHS
-;;;  SIMPLICIAL-MRPHS  SIMPLICIAL-MRPHS  SIMPLICIAL-MRPHS
-
-(IN-PACKAGE "CAT")
-
-(PROVIDE "simplicial-mrphs")
-
-(DEFMETHOD ?3 ((smmr simplicial-mrph) dmns absm-or-gmsm)
-  (declare
-     (fixnum dmns)
-     (type (or absm gmsm) absm-or-gmsm))
-  (typecase absm-or-gmsm
-     (absm
-      (with-absm (dgop gmsm) absm-or-gmsm
-         (let ((gmsm-smmr (funcall (sintr smmr)
-			     (- dmns (logcount dgop)) gmsm)))
-	   (declare (type absm gmsm-smmr))
-	   (ndgnr dgop gmsm-smmr))))
-     (otherwise
-      (funcall (sintr smmr) dmns absm-or-gmsm))))  
-
-(DEFMETHOD PRINT-OBJECT ((smmr simplicial-mrph) stream)
-  (the simplicial-mrph
-     (progn
-       (if (= -1 (degr smmr))
-	   (format stream "[K~D Fibration K~D -> K~D]"
-		   (idnm smmr) (idnm (sorc smmr)) (idnm (trgt smmr)))
-	 (format stream "[K~D Simplicial-Morphism K~D -> K~D]"
-		 (idnm smmr) (idnm (sorc smmr)) (idnm (trgt smmr))))
-       smmr)))
-
-(DEFUN SINTR-INTR (sintr)
-   (declare (type sintr sintr))
-   (flet ((rslt (dmns gmsm)
-	     (declare
-	        (fixnum dmns)
-		(type gmsm gmsm))
-	     (when (minusp dmns)
-		(return-from rslt (zero-cmbn dmns)))
-	     (let ((rslt (funcall sintr dmns gmsm)))
-	        (declare (type absm rslt))
-		(if (degenerate-p rslt)
-		   (zero-cmbn dmns)
-		   (term-cmbn dmns 1 (gmsm rslt))))))
-       (the intr #'rslt)))
-
-(DEFUN SIMPLICIAL-MRPH (&rest rest &key dfnt &allow-other-keys)
-  (declare (type list dfnt))
-  (already simplicial-mrph dfnt)
-  (the simplicial-mrph
-    (apply #'make-instance 'simplicial-mrph rest)))
-
-(DEFMETHOD SHARED-INITIALIZE ((smmr simplicial-mrph) slot-names &key sintr)
-  (declare
-   (type (or (eql t) list) slot-names)
-   (type sintr sintr))
-  (call-next-method)
-  (when-slot sintr
-             (when sintr (setf (slot-value smmr 'sintr) sintr)))
-  smmr)
-
-(DEFMETHOD SLOT-UNBOUND (class (smmr simplicial-mrph) slot-name)
-  (declare
-   (ignore class)
-   (type symbol slot-name))
-  (let ((name (symbol-name slot-name)))
-    (declare (type string name))
-    (unless (member name '("INTR" "STRT") :test #'string=)
-      (call-next-method))
-    (the (or intr strt)
-      (with-slots ((ssintr intr) strt sintr) smmr
-        (declare
-         (type intr ssintr)
-         (type strt strt)
-         (type sintr sintr))
-        (setf
-         ssintr (sintr-intr sintr)
-         strt :gnrt)
-        (if (string= name "INTR") ssintr strt)))))
-        
-#|
-  (setf d (delta 3))
-  (setf m (simplicial-mrph
-            :sorc d :trgt d :degr 0
-            :sintr #'(lambda (dmns gmsm)
-                        (absm 0 gmsm))
-            :dfnt '(identity delta-3)))
-  (setf m2 (simplicial-mrph
-            :sorc d :trgt d :degr 0
-            :sintr #'(lambda (dmns gmsm)
-                       (absm (mask dmns) 1))
-            :dfnt '(null delta-3)))
-  (? m2 2 7)
-;;  (s? m2 2 7)
-|#
-
-(DEFMACRO WITH-IABSM ((dgop gmsm) iabsm . body)
-  `(let ((,dgop (car ,iabsm))
-	 (,gmsm (cdr ,iabsm)))
-     (declare
-        (fixnum ,dgop)
-	(type gmsm ,gmsm))
-     ,@body))
-
-#|
-  (macroexpand-1 '(with-iabsm (dgop gmsm) iabsm
-                    (statement-1)
-                    (statement-2)))
-|#
-                 
-(DEFMACRO A-SINTR3 (sintr dmns absm)
-  ;; BE CAREFUL: works only if  degr (sintr) = 0.
-  ;; if degr = -1 (fibration), use tw-a-sintr3
-  `(ia-sintr3 ,sintr ,dmns (cdr ,absm)))
-
-(DEFUN IA-SINTR3 (sintr dmns iabsm)
-  (declare
-     (type sintr sintr)
-     (fixnum dmns)
-     (type iabsm iabsm))
-  (the absm
-     (with-iabsm (dgop gmsm) iabsm
-	(ndgnr dgop (funcall sintr (- dmns (logcount dgop)) gmsm)))))
-
-(DEFMACRO TW-A-SINTR3 (sintr dmns absm bsgn)
-  `(tw-ia-sintr3 ,sintr ,dmns (cdr ,absm) ,bsgn))
-
-(DEFUN TW-IA-SINTR3 (sintr dmns iabsm bsgn)
-  (declare
-     (type sintr sintr)
-     (fixnum dmns)
-     (type iabsm iabsm)
-     (type gmsm bsgn))
-  (the absm
-     (with-iabsm (dgop gmsm) iabsm
-	(let ((dmns-1 (1- dmns)))
-	  (declare (fixnum dmns-1))
-	  (if (logbitp dmns-1 dgop)
-	     (absm (mask dmns-1) bsgn)
-	     (ndgnr dgop (funcall sintr
-			    (- dmns (logcount dgop))
-			    gmsm)))))))
\ No newline at end of file
diff --git a/archive/Kenzo-2/Kenzo-2-Acl5/simplicial-sets.cl b/archive/Kenzo-2/Kenzo-2-Acl5/simplicial-sets.cl
deleted file mode 100644
index fe96a65..0000000
--- a/archive/Kenzo-2/Kenzo-2-Acl5/simplicial-sets.cl
+++ /dev/null
@@ -1,679 +0,0 @@
-;;;  SIMPLICIAL-SETS  SIMPLICIAL-SETS  SIMPLICIAL-SETS
-;;;  SIMPLICIAL-SETS  SIMPLICIAL-SETS  SIMPLICIAL-SETS
-;;;  SIMPLICIAL-SETS  SIMPLICIAL-SETS  SIMPLICIAL-SETS
-
-(IN-PACKAGE "CAT")
-
-(PROVIDE "simplicial-sets")
-
-(DEFUN DGOP-EXT-INT (ext-dgop)
-   (declare (list ext-dgop))
-          ;; (list fixnum)
-   (when ext-dgop   
-      (unless (apply #'> ext-dgop)
-         (error "In DGOP-EXT-INT, the external dgop ~A is not decreasing." ext-dgop)))
-   (the fixnum
-      (apply #'logxor (mapcar
-                         #'(lambda (item)
-                              (declare (fixnum item))
-                              (the fixnum (2-exp item)))
-                         ext-dgop))))
-#|
-  (dgop-ext-int '())
-  (dgop-ext-int '(2 2))
-  (dgop-ext-int '(4 0))
-|#
-
-(DEFUN DGOP-INT-EXT (dgop)
-   (declare (fixnum dgop))
-   (unless (typep dgop 'dgop)
-      (error "In DXOP-INT-EXT, ~A is not a dxop." dgop))
-   (the list
-      (do ((dgop dgop (ash dgop -1))
-           (rslt +empty-list+)
-           (bmark 0 (1+ bmark)))
-          ((zerop dgop) rslt)
-         (declare
-            (fixnum dgop bmark)
-            (list rslt))
-         (when (oddp dgop)
-            (push bmark rslt)))))
-
-#|
-  (dgop-int-ext 0)
-  (dgop-int-ext 4)
-  (dgop-int-ext 63)
-  (dotimes (i 33)
-     (print (dgop-ext-int (dgop-int-ext i)))))
-|#
-
-(DEFUN HYPHENIZE-LIST (list)
-   (declare (list list))
-   (if list
-      (format nil "~D~{-~D~}" (first list) (rest list))
-      (format nil "-")))
-
-#|
-  (hyphenize-list '())
-  (hyphenize-list '(3))
-  (hyphenize-list '(5 3 1)))
-|#
-
-
-#|
-  (absm-p 1)
-  (absm-p '(1))
-  (absm-p '(:absm nil))  ;; printer-error
-  (absm-p '(:absm 5 . a))
-  (absm-p '(:absm -5 . a)) ;; printer-error
-|#
-      
-(DEFMETHOD PRINT-KEYCONS ((key (eql :absm)) cdr stream)
-   (setf cdr (cons :absm cdr))
-   (format stream
-      "<AbSm ~A ~A>"
-      (hyphenize-list (dgop-int-ext (dgop cdr)))
-      (gmsm cdr))
-   cdr)
-
-#|
-  (absm 5 'a)
-|#
-
-#|
-  (degenerate-p (absm 0 'a))
-  (degenerate-p (absm 4 'a))
-  (non-degenerate-p (absm 0 'a))
-  (non-degenerate-p (absm 4 'a)))
-|#
-
-(DEFUN FACE4 (smst indx dmns gmsm-or-absm)
-   (if (typep gmsm-or-absm 'absm)
-      (a-face4 (face1 smst) indx dmns gmsm-or-absm)
-      (funcall (face1 smst) indx dmns gmsm-or-absm)))
-
-(DEFMETHOD PRINT-OBJECT ((smst simplicial-set) stream)
-   (the simplicial-set
-      (progn
-         (format stream "[K~D Simplicial-Set]" (idnm smst))
-         smst)))
-
-(DEFUN SIMPLICIAL-SET (&rest rest &key dfnt &allow-other-keys)
-  (declare (type list dfnt))
-  (already simplicial-set dfnt)
-  (the simplicial-set
-    (apply #'make-instance 'simplicial-set rest)))
-
-(DEFMETHOD SHARED-INITIALIZE
-    ((smst simplicial-set) slot-names &key face face*)
-  (declare
-   (type (or (eql t) list) slot-names)
-   (type face face)
-   (type (or face* null) face*))
-  (call-next-method)
-  (when-slot face
-             (when face (setf (slot-value smst 'face) face))
-             (when face*
-               (if (slot-boundp smst 'dffr)
-                   (error "IN SIMPLICIAL-SET, an FACE* initial-argument is given, ~
-                         but the DFFR slot is elsewhere defined.")
-                 (setf (slot-value smst 'dffr)
-                   (morphism :dfnt `(dffr ,smst)
-                             :sorc smst :trgt smst :degr -1
-                             :intr (face*-dffr (cmpr smst) face*) :strt :gnrt))))))
-
-(DEFMETHOD SLOT-UNBOUND (class (smst simplicial-set) (slot (eql 'dffr)))
-  (declare (ignore class))
-  (the morphism
-    (setf (slot-value smst 'dffr)
-      (morphism :dfnt `(dffr ,smst)
-                :sorc smst :trgt smst :degr -1
-                :intr (face-dffr-intr (cmpr smst) (face smst))
-                :strt :gnrt))))
-
-(DEFMETHOD SLOT-UNBOUND (class (smst simplicial-set) (slot (eql 'cprd)))
-  (declare (ignore class))
-  (the morphism
-    (setf (slot-value smst 'cprd)
-      (morphism :dfnt `(cprd ,smst)
-                :sorc smst :trgt (tnsr-prdc smst smst) :degr 0
-                :intr (face-cprd-intr (face smst)) :strt :gnrt))))
-
-(DEFUN A-BASIS2 (basis dmns)
-  (declare
-     (type basis basis)
-     (fixnum dmns))
-  (the list
-    (let ((basis-array (make-array (1+ dmns) :element-type 'list)))
-      (declare (type (vector list) basis-array))
-      (dotimes (i (1+ dmns))
-	(declare (fixnum i))
-	(setf (aref basis-array i) (funcall basis i)))
-      (do ((dgop (mask dmns) (1- dgop))
-	   (rslt +empty-list+
-		 (nconc (mapcar
-			 #'(lambda (gmsm)
-			     (declare (type gmsm gmsm))
-			     (absm dgop gmsm))
-			 (aref basis-array (- dmns (logcount dgop))))
-			rslt)))
-	  ((minusp dgop) rslt)))))
-
-#|
-  (setf m (moore 2 2))
-  (dotimes (i 4)
-    (print (basis m i :dgnr)))
-|#
-
-(DEFUN FACE-CPRD-INTR (face)
-   (declare (type face face))
-   (flet ((rslt (dmns gmsm)
-             (declare
-                (fixnum dmns)
-                (type gmsm gmsm))
-             (the cmbn
-                (let ((del-0-s +empty-list+)
-                      (rslt +empty-list+))
-                   (declare (list del-0-s rslt))
-                   (do ((dmns dmns (1- dmns))
-                        (iabsm (cons 0 gmsm) (cdr (ia-face4 face 0 dmns iabsm))))
-                       ((zerop dmns) (push iabsm del-0-s))
-                      (declare
-                         (fixnum dmns)
-                         (cons iabsm))
-                      (push iabsm del-0-s))
-                   (do ((ldmns dmns (1- ldmns))
-                        (rdmns 0 (1+ rdmns))
-                        (iabsm (cons 0 gmsm) (cdr (ia-face4 face ldmns ldmns iabsm)))
-                        (mark-del-0 del-0-s (cdr mark-del-0)))
-                       ((zerop ldmns) (push (term 1 (tnpr 0 (cdr iabsm) dmns gmsm))
-                                        rslt))
-                      (declare
-                         (fixnum ldmns rdmns)
-                         (type gmsm gmsm)
-                         (list mark-del-0))
-                      (unless (or (plusp (car iabsm))
-                                  (plusp (caar mark-del-0)))
-                         (push (term 1 (tnpr ldmns (cdr iabsm) rdmns (cdar mark-del-0)))
-                            rslt)))
-                   (make-cmbn :degr dmns :list rslt)))))
-      (the intr #'rslt)))
-
-#|
-  (setf cmpr #'f-cmpr
-        face #'delta-face)
-  (setf diag (face-cprd-intr face))
-  (funcall diag 4 (mask 5))
-  (funcall diag 0 4)
-  (setf cmpr #'s-cmpr
-        face (sphere-face 4))
-  (setf diag (face-cprd-intr face))
-  (funcall diag 4 's4)
-  (funcall diag 0 '*)
-  (setf s4 (sphere 4))
-  (cprd s4 4 's4)
-|#                 
-
-(DEFUN FACE-DFFR-INTR (cmpr face)
-   (declare
-      (type cmprf cmpr)
-      (type face face))
-   (flet ((rslt (dmns gmsm)
-             (declare
-                (fixnum dmns)
-                (type gmsm gmsm))
-             (the cmbn
-                (progn
-                   (when (zerop dmns)
-                      (return-from rslt +zero-negative-cmbn+))
-                   (let ((pre-rslt +empty-list+))
-                      (declare (list pre-rslt))
-                             ;; (list (cons cffc face))
-                      (dotimes (indx (1+ dmns))
-                         (declare (fixnum indx))
-                         (let ((face (funcall face indx dmns gmsm)))
-                            (declare (type absm face))
-                            (unless (degenerate-p face)
-                               (push (term (-1-expt-n indx) (gmsm face))
-                                  pre-rslt))))
-                      (apply #'nterm-add cmpr (1- dmns) pre-rslt))))))
-      (the intr #'rslt)))
-
-#|
-  (setf face #'(lambda (indx dmns gmsm)
-                  (absm 0 (append
-                             (subseq gmsm 0 indx)
-                             (subseq gmsm (1+ indx))))))
-  (setf dffr (face-dffr-intr #'l-cmpr face))
-  (funcall dffr 0 '(a))
-  (funcall dffr 1 '(a b))
-  (funcall dffr 2 '(a b c))
-  (funcall dffr 3 '(a b c d))
-  (funcall dffr 3 '(d c b a))
-  (funcall dffr 1 '(a a))
-  (funcall dffr 2 '(a a a))
-  (funcall dffr 3 '(a a a a))
-  (setf face #'(lambda (index dmns gmsm)
-                  (absm (dgop-ext-int (nreverse (<a-b< 0 (1- dmns)))) 'a)))
-  (setf dffr (face-dffr-intr #'s-cmpr face))
-  (funcall dffr 1 '(a b))
-  (funcall dffr 2 '(a b c)))
-|#
-
-(DEFUN FACE*-DFFR (cmpr face*)
-  (declare
-   (type cmprf cmpr)
-   (type face* face*))
-  (flet ((rslt (dmns gmsm)
-               (declare
-                (fixnum dmns)
-                (type gmsm gmsm))
-               (the cmbn
-                 (progn
-                   (when (zerop dmns)
-                     (return-from rslt +zero-negative-cmbn+))
-                   (let ((pre-rslt +empty-list+))
-                     (declare (list pre-rslt))
-                     ;; (list (list gmsm fixnum))
-                     (dotimes (indx (1+ dmns))
-                       (declare (fixnum indx))
-                       (let ((face (funcall face* indx dmns gmsm)))
-                         (declare (type (or gmsm (eql :degenerate)) face))
-                         (unless (eq face :degenerate)
-                           (push (term (-1-expt-n indx) face) pre-rslt))))
-                     (apply #'nterm-add cmpr (1- dmns) pre-rslt))))))
-    (the intr #'rslt)))
-
-#|
-  (setf face* 
-        #'(lambda (indx dmns gmsm)
-             (if (and (= dmns 3) (evenp indx))
-                'm2
-                :degenerate)))
-  (setf dffr (face*-dffr #'s-cmpr face*))
-  (funcall dffr 3 'm3)
-  (funcall dffr 2 'm2)
-  (funcall dffr 0 '*)
-  (setf face* 
-        #'(lambda (indx dmns gmsm)
-             (if (and (= dmns 3) (< indx 2))
-                'm2
-                :degenerate)))
-  (setf dffr (face*-dffr #'s-cmpr face*))
-  (funcall dffr 3 'm3)
-  (funcall dffr 2 'm2)
-  (funcall dffr 0 '*))
-|#
-
-(DEFUN A-CMPR3 (cmpr absm1 absm2)
-   (declare
-      (type cmprf cmpr)
-      (type absm absm1 absm2))
-   (the cmpr
-      (with-absm (dgop1 gmsm1) absm1
-      (with-absm (dgop2 gmsm2) absm2
-         (lexico
-            (f-cmpr dgop1 dgop2)
-            (funcall cmpr gmsm1 gmsm2))))))
-
-#|
-  (a-cmpr3 #'s-cmpr (absm 0 'a) (absm 1 'b))
-  (a-cmpr3 #'s-cmpr (absm 2 'a) (absm 1 'b))
-  (a-cmpr3 #'s-cmpr (absm 1 'a) (absm 1 'b))
-  (a-cmpr3 #'s-cmpr (absm 1 'c) (absm 1 'b))
-  (a-cmpr3 #'s-cmpr (absm 1 'a) (absm 1 'a))
-|#
-
-(DEFUN BSGN-P (cmpr bsgn dmns absm)
-   ;; this function makes sense only in the simplicial context
-   ;; so that the basg (= base-generator) is called bsgn (= base-point)
-   (declare
-      (type gmsm bsgn)
-      (fixnum dmns)
-      (type absm absm))
-   (the boolean
-      (with-absm (dgop gmsm) absm
-         (and (= dgop (mask dmns))
-              (eq :equal (funcall cmpr bsgn gmsm))))))
-
-#|
-  (setf d (delta-infinity))
-  (setf cmpr (cmpr d))
-  (bsgn-p cmpr 1 5 (absm (mask 5) 1))
-  (bsgn-p cmpr 1 5 (absm (mask 5) 2))
-  (bsgn-p cmpr 1 5 (absm (mask 4) 3))
-|#
-
-(DEFUN DLOP-EXT-INT (ext-dlop)
-   (declare (list ext-dlop))
-          ;; (list fixnum)
-   (when ext-dlop   
-      (unless (apply #'< ext-dlop)
-         (error "In DLOP-EXT-INT, the external dlop ~A is not increasing." ext-dlop)))
-   (the fixnum
-      (apply #'logxor
-         (mapcar #'(lambda (item)
-                      (declare (fixnum item))
-                      (the fixnum (2-exp item)))
-            ext-dlop))))
-#|
-  (dlop-ext-int '())
-  (dlop-ext-int '(2 2))
-  (dlop-ext-int '(0 4)))
-|#
-
-(DEFUN DLOP-INT-EXT (dlop)
-   (declare (fixnum dlop))
-   (the list
-      (nreverse (dgop-int-ext dlop))))
-
-#|
-  (dlop-int-ext 0)
-  (dlop-int-ext 4)
-  (dlop-int-ext 63)
-  (dotimes (i 33)
-     (print (dlop-ext-int (dlop-int-ext i)))))
-|#
-
-(DEFUN 1DGOP*DGOP (1dgop dgop)
-   (declare (fixnum 1dgop dgop))
-   ;; 1dgop is an ordinary integer
-   ;; dgop is a bit string
-   (the fixnum
-      (let ((share (ash -1 1dgop)))
-         (declare (fixnum share))
-         (logxor
-            (ash (logand share dgop) 1)
-            (2-exp 1dgop)
-            (logandc1 share dgop)))))
-      
-#|
-  (dotimes (i 20)
-     (dotimes (j 5)
-       (format t "~% (~D) o ~A = ~A"
-                 j (dgop-int-ext i) (dgop-int-ext (1dgop*dgop j i))))))
-|#
-
-(DEFUN DGOP*DGOP (dgop1 dgop2)
-   (declare (type fixnum dgop1 dgop2))
-   (let ((dgop 0)
-         (bmark 0))
-      (declare (fixnum dgop bmark))
-      (loop
-         (when (zerop dgop1)
-            (return-from dgop*dgop
-               (logxor dgop (ash dgop2 bmark))))
-         (when (zerop dgop2)
-            (return-from dgop*dgop
-               (logxor dgop (ash dgop1 bmark))))
-         (cond ((evenp dgop1)
-                (when (oddp dgop2)
-                   (incf dgop (2-exp bmark)))
-                (setf dgop2 (ash dgop2 -1)))
-               (t
-                  (incf dgop (2-exp bmark))))
-         (setf dgop1 (ash dgop1 -1))
-         (incf bmark))))
-
-#|
-  (dotimes (i 10)
-     (dotimes (j 10)
-        (format t "~%~A o ~A = ~A"
-                  (dgop-int-ext i) (dgop-int-ext j)
-                  (dgop-int-ext (dgop*dgop i j))))))
-|#
-
-(DEFUN REMOVE-BIT (n indx)
-   (declare (fixnum n indx))
-   (the fixnum
-      (let ((cut (2-exp indx)))
-         (multiple-value-bind (quotient remainder) (truncate n cut)
-            (declare (fixnum quotient remainder))
-            (+ (ash (ash quotient -1) indx) remainder)))))
-
-#|
-  (remove-bit 107 3)  ;; 51
-|#
-
-(DEFUN DGOP/DGOP (dgop1 dgop2)
-   (declare (fixnum dgop1 dgop2))
-   (the fixnum
-      (do ((indx (1- (integer-length dgop2)) (1- indx)))
-          ((minusp indx) dgop1)
-         (declare (fixnum indx))
-         (when (logbitp indx dgop2)
-            (setf dgop1 (remove-bit dgop1 indx))))))
-
-#|
-  (dgop/dgop 67 0)
-  (dgop/dgop 68 4)
-  (dgop/dgop 31 5)
-|#      
-
-(DEFUN 1DLOP-DGOP (1dlop dgop)
-   (declare (fixnum 1dlop dgop))
-   ;; 1dlop is an ordinary fixnum
-   ;; dgop is a bit string
-   (the (values fixnum (or fixnum null))
-      (progn
-         (when (logbitp 1dlop dgop)
-            (let ((share (ash -1 1dlop)))
-               (declare (fixnum share))
-               (return-from 1dlop-dgop
-                  (values
-                     (logxor
-                        (logand share (ash dgop -1))
-                        (logandc1 share dgop))
-                     nil))))
-         (when (and (plusp 1dlop)
-                    (logbitp (1- 1dlop) dgop))
-            (let ((share (ash -1 1dlop)))   ;;;
-               (declare (fixnum share))
-	       (setf share (ash share -1))  ;;; because of the compiler bug
-               (return-from 1dlop-dgop
-                  (values
-                     (logxor
-                        (logand share (ash dgop -1))
-                        (logandc1 share dgop))
-                     nil))))
-         (let ((share (ash -1 1dlop)))
-            (declare (fixnum share))
-            (let ((right (logandc1 share dgop)))
-               (declare (fixnum right))
-               (values
-                  (logxor right (logand share (ash dgop -1)))
-                  (- 1dlop (logcount right))))))))
-
-#|
-  (dotimes (i 5)
-     (dotimes (j 17)
-        (multiple-value-bind (dgop 1dlop) (1dlop-dgop i j)
-           (format t "~% del-~D o ~A = ~A o del-~A"
-                     i (dgop-int-ext j) (dgop-int-ext dgop) 1dlop)))))
-|#
-
-(DEFUN IA-FACE4 (face indx dmns iabsm) 
-   ;; iabsm = "internal" absm, that is an absm without the keyword :absm.
-   ;; absm = (cons :absm (cons dgop gmsm))
-   ;; iabsm =            (cons dgop gmsm)
-   (declare
-      (type face face)
-      (fixnum indx dmns)
-      (type absm absm))
-   (the absm
-      (let ((dgop (car iabsm))
-            (gmsm (cdr iabsm)))
-         (declare
-            (fixnum dgop)
-            (type gmsm gmsm))
-         (multiple-value-bind (dgop2 1dlop) (1dlop-dgop indx dgop)
-            (declare
-               (fixnum dgop2)
-               (type (or fixnum nil) 1dlop))
-            (unless 1dlop
-               (return-from ia-face4 (absm dgop2 gmsm)))
-            (locally (declare (fixnum 1dlop))
-               (let ((gmsm-face (funcall face 1dlop (- dmns (logcount dgop)) gmsm)))
-                  (declare (type absm gmsm-face))
-                  (with-absm (dgop3 gmsm3) gmsm-face
-                     (absm (dgop*dgop dgop2 dgop3) gmsm3))))))))
-
-#|
-  (require "special-smsts"
-            #-ACLPC "special-smsts"
-            #+ACLPC "special-smsts.fsl")
-  (let ((simp (dlop-ext-int '(0 1 2 3 4 5 6))))
-     (dotimes (i 5)
-        (dotimes (j 17)
-           (let ((face (a-face4 (face (delta-infinity))
-                          i (+ 6 (logcount j)) (absm j simp))))
-              (format t "~%del-~D o ~A (0 1 2 3 4 5 6) = ~A ~A"
-                        i (dgop-int-ext j)
-                        (dgop-int-ext (dgop face))
-                        (dlop-int-ext (gmsm face)))))))
-|#
-
-(DEFUN 1DGNR (indx absm)
-   (declare
-      (fixnum indx)
-      (type absm absm))
-   (the absm
-      (with-absm (dgop gmsm) absm
-         (absm (1dgop*dgop indx dgop) gmsm))))
-
-#|
-  (1dgnr 2 (absm 17 'a))
-|#
-
-(DEFUN NDGNR (dgop absm)
-   (declare
-      (fixnum dgop)
-      (type absm absm))
-   (the absm
-      (with-absm (dgop2 gmsm) absm
-         (absm (dgop*dgop dgop dgop2) gmsm))))
-
-#|
-  (ndgnr 2 (absm 17 'a))
-|#
-
-(DEFMACRO NVERTICES (face dlop-bar dmns gmsm)
-  `(nface ,face (- (mask (1+ ,dmns)) ,dlop-bar) ,dmns ,gmsm))
-
-#|
-  (setf f (face (delta-infinity)))
-  (dotimes (dlop 31)
-    (print (dlop-int-ext (gmsm (nvertices f (1+ dlop) 4 31)))))
-  (setf p (r-proj-space))
-  (setf f (face p))
-  (dotimes (dlop 31)
-    (format t "~%~A ~A"
-       (hyphenize-list (dlop-int-ext (1+ dlop)))
-       (nvertices f (1+ dlop) 4 4)))
-|#
-
-(DEFUN NFACE (face dlop dmns gmsm)
-  (declare
-     (type face face)
-     (type dlop dlop)
-     (fixnum dmns)
-     (type gmsm gmsm))
-  (do* ((gmsm gmsm)
-	(dmns dmns)
-	(dgop 0)
-	(dlop dlop (- dlop (2-exp bark)))
-	(bark (1- (integer-length dlop))
-	      (1- (integer-length dlop))))
-       ((zerop dlop) (absm dgop gmsm))
-      (declare
-         (type gmsm gmsm)
-	 (fixnum dgop dlop bark))
-      (multiple-value-bind (dgop2 indx) (1dlop-dgop bark dgop)
-	 (declare
-	    (fixnum dgop2)
-	    (type (or null fixnum) indx))
-	 (if indx
-	    (locally (declare (fixnum indx))
-	       (let ((new-absm (funcall face indx dmns gmsm)))
-		  (declare (type absm new-absm))
-		  (with-absm (dgop3 gmsm2) new-absm
-		     (setf gmsm gmsm2
-			   dmns (- dmns 1
-				   (logcount dgop3))
-			   dgop (dgop*dgop dgop2 dgop3)))))
-  	     (setf dgop dgop2)))))
-
-#|
-  (setf f (face (delta-infinity)))
-  (dotimes (dlop 31)
-    (print (dlop-int-ext (gmsm (nface f dlop 4 31)))))
-  (setf p (r-proj-space))
-  (setf f (face p))
-  (dotimes (dlop 31)
-    (format t "~%~A ~A"
-       (hyphenize-list (dlop-int-ext dlop))
-       (nface f dlop 4 4)))
-|#
-
-(DEFUN CHECK-FACES (cmpr face dmns gmsm)
-   (declare
-      (type cmprf cmpr)
-      (type face face)
-      (fixnum dmns)
-      (type gmsm gmsm))
-   (the boolean
-      (progn      
-         (when (> dmns 1)
-            (let ((dmns-1 (1- dmns)))
-               (declare (fixnum dmns-1))
-               (dotimes (i dmns)
-                  (declare (fixnum i))
-                  (dotimes (j (1+ i))
-                     (declare (fixnum j))
-                     (let ((rslt1 (a-face4 face i dmns-1 (funcall face j dmns gmsm)))
-                           (rslt2 (a-face4 face j dmns-1 (funcall face (1+ i) dmns gmsm))))
-                        (declare (type absm rslt1 rslt2))
-                        (unless (eq (a-cmpr3 cmpr rslt1 rslt2) :equal)
-                           (cerror "CHECK-FACES will return NIL."
-                              "Noncoherent boundary operators detected by CHECK-FACES :~@
-                               Simplex => ~A~@
-                               del_~D o del_~D => ~A~@
-                               del_~D o del_~D => ~A"
-                              gmsm i j rslt1 j (1+ i) rslt2)
-                              (return-from check-faces nil)))))))
-         t)))
-
-#|
-  (setf d (delta-infinity))
-  (check-faces #'f-cmpr (face d) 4 31)
-|#
-
-(DEFUN CHECK-SMST (smst dmns1 &optional (dmns2 (1+ dmns1)))
-   (declare
-      (type simplicial-set smst)
-      (fixnum dmns1 dmns2))
-   (with-slots (cmpr basis face) smst
-      (declare
-         (type cmprf cmpr)
-         (type face face))
-   (when (eq basis :locally-effective)
-      (error "In CHECK-SMST, the locally-effective simplicial-set ~A~@
-              cannot be checked." smst))
-      (do ((rslt t)
-           (dmns dmns1 (1+ dmns)))
-          ((>= dmns dmns2) rslt)
-         (declare
-            (type boolean rslt)
-            (fixnum dmns))
-         (format t "~%Checking the ~D-simplices..." dmns)
-         (dolist (gmsm (funcall basis dmns))
-            (declare (type gmsm gmsm))
-            (unless (check-faces cmpr face dmns gmsm)
-               (setf rslt nil))))))
-
-#|
-  (check-smst (delta-infinity) 5)
-  (check-smst (delta 3) 2)
-  (check-smst (delta 3) 2 4)
-|#
-
diff --git a/archive/Kenzo-2/Kenzo-2-Acl5/smith.cl b/archive/Kenzo-2/Kenzo-2-Acl5/smith.cl
deleted file mode 100644
index 4b5c6b0..0000000
--- a/archive/Kenzo-2/Kenzo-2-Acl5/smith.cl
+++ /dev/null
@@ -1,1239 +0,0 @@
-;;;  SMITH  SMITH  SMITH  SMITH  SMITH  SMITH  SMITH  SMITH
-;;;  SMITH  SMITH  SMITH  SMITH  SMITH  SMITH  SMITH  SMITH
-;;;  SMITH  SMITH  SMITH  SMITH  SMITH  SMITH  SMITH  SMITH
-
-(IN-PACKAGE "CAT")
-
-(PROVIDE "smith")
-
-(DEFTYPE MATRIX () '(array fixnum (* *)))
-
-(DEFMACRO LINE-NUMBER (mtrx)
-  `(first (array-dimensions ,mtrx)))
-
-(DEFMACRO COLUMN-NUMBER (mtrx)
-  `(second (array-dimensions ,mtrx)))
-
-(DEFUN RANDOM-MATRIX (line-n column-n max)
-  (declare (fixnum line-n column-n max))
-  (the matrix
-    (let ((rslt (make-array (list line-n column-n)
-			    :element-type 'fixnum))
-	  (2max+1 (+ max max 1)))
-      (declare
-        (type matrix rslt)
-	(fixnum 2max+1))
-      (dotimes (i line-n)
-	(declare (fixnum i))
-	(dotimes (j column-n)
-	  (declare (fixnum j))
-	  (setf (aref rslt i j)
-		(- (random 2max+1) max))))
-      rslt)))
-
-#|
-  (random-matrix 2 3 10)
-|#
-
-(DEFUN IDNT-MTRX (n)
-  (declare (fixnum n))
-  (the matrix
-    (let ((rslt
-            #-ACLPC (make-array (list n n)
-		        :element-type 'fixnum
-		        :initial-element 0)
-            #+ACLPC (if (zerop n)
-                       (make-array '(0 0)
-                          :element-type 'fixnum)
-                       (make-array (list n n)
-		          :element-type 'fixnum
-		          :initial-element 0))))
-      (declare (type matrix rslt))
-      (dotimes (i n)
-	(declare (fixnum i))
-	(setf (aref rslt i i) 1))
-      rslt)))
-
-#|
-(idnt-mtrx 3)
-|#
-
-(DEFUN COPY-MTRX (mtrx)
-  (declare (type matrix mtrx))
-  (the matrix
-    (let ((line-n (line-number mtrx))
-	  (column-n (column-number mtrx)))
-      (declare (fixnum line-n column-n))
-      (let ((rslt (make-array (list line-n column-n)
-			      :element-type 'fixnum)))
-	(declare (type matrix rslt))
-	(dotimes (il line-n)
-	  (declare (fixnum il))
-	(dotimes (ic column-n)
-	  (declare (fixnum ic))
-	  (setf (aref rslt il ic) (aref mtrx il ic))))
-	rslt))))
-
-#|
-(setf m (random-matrix 3 4 10))
-(equalp m (copy-mtrx m))
-|#
-
-(DEFUN LEFT-SUBMATRIX (mtrx k)
-  (declare (type matrix mtrx))
-  (the matrix
-    (let ((line-n (line-number mtrx))
-	  (column-n (column-number mtrx)))
-      (declare (fixnum line-n column-n))
-      (assert (<= k column-n))
-      (let ((rslt (make-array (list line-n k)
-			      :element-type 'fixnum)))
-	(declare (type matrix rslt))
-	(dotimes (il line-n)
-	  (declare (fixnum il))
-	(dotimes (ic k)
-	  (declare (fixnum ic))
-	  (setf (aref rslt il ic) (aref mtrx il ic))))
-	rslt))))
-
-#|
-(setf m (random-matrix 3 4 10))
-(left-submatrix m 2)
-|#
-
-(DEFUN MTRX-PRDC (mtrx1 mtrx2)
-  (declare (type matrix mtrx1 mtrx2))
-  (the matrix
-    (let ((rslt-line-n (line-number mtrx1))
-	  (mtrx1-column-n (column-number mtrx1))
-	  (mtrx2-line-n (line-number mtrx2))
-	  (rslt-column-n (column-number mtrx2)))
-      (declare (fixnum rslt-line-n mtrx1-column-n
-		       mtrx2-line-n rslt-column-n))
-      (unless (= mtrx1-column-n mtrx2-line-n)
-	(error "In MTRX-PRDC, bad line or column number."))
-      (let ((rslt (make-array (list rslt-line-n rslt-column-n)
-			      :element-type 'fixnum)))
-	(declare (type matrix rslt))
-	(dotimes (il rslt-line-n)
-	  (declare (fixnum il))
-	(dotimes (ic rslt-column-n)
-	  (declare (fixnum ic))
-	  (do ((k 0 (1+ k))
-	       (sum 0 (+ sum
-			 (* (aref mtrx1 il k) (aref mtrx2 k ic)))))
-	      ((= k mtrx1-column-n) (setf (aref rslt il ic) sum)))))
-	rslt))))
-
-#|
-(setf m1 (random-matrix 2 3 10))
-(setf m2 (random-matrix 3 2 10))
-(mtrx-prdc m1 m2)
-(mtrx-prdc m2 m1)
-|#
-
-(DEFUN CHCM-MTRX (chcm degr)
-  (declare
-    (type chain-complex chcm)
-    (fixnum degr))
-  (the matrix
-    (let ((cmpr (cmpr1 chcm))
-	  (dffr (dffr chcm))
-	  (sbasis (basis chcm degr))
-	  (tbasis (basis chcm (1- degr))))
-      (declare
-        (type cmprf cmpr)
-	(type morphism dffr)
-	(list sbasis tbasis))
-      (let ((srank (length sbasis))
-	    (trank (length tbasis)))
-	(declare (fixnum srank trank))
-	(let ((rslt 
-               #-ACLPC
-                    (make-array (list trank srank)
-				:element-type 'fixnum
-				:initial-element 0)
-               #+ACLPC
-                    (if (or (zerop srank) (zerop trank))
-                       (make-array (list trank srank)
-                          :element-type 'fixnum)
-                       (make-array (list trank srank)
-                          :element-type 'fixnum
-                          :initial-element 0))
-               ))               
-	  (declare (type matrix rslt))
-	  (do ((j 0 (1+ j))
-	       (mark sbasis (cdr mark)))
-	      ((endp mark))
-	      (declare
-	        (fixnum j)
-		(list mark))
-	      (let ((cmbn (gnrt-? dffr degr (car mark))))
-		(declare (type cmbn cmbn))
-		(do ((mark1 (cmbn-list cmbn) (cdr mark1))
-		     (mark2 tbasis)
-		     (i 0))
-		    ((endp mark1))
-		    (declare
-		      (list mark1 mark2)
-		      (fixnum i))
-		  (with--term (cffc gnrt) mark1
-		    (loop
-		     (cond ((eq :equal (funcall cmpr gnrt (car mark2)))
-			    (setf (aref rslt i j) cffc)
-			    (incf i)
-			    (pop mark2)
-			    (return))
-			   (t (incf i)
-			      (pop mark2))))))))
-	  rslt)))))
-
-#|
-  (setf d (delta 5))
-  (chcm-mtrx d 3))
-  (setf m (moore 2 2))
-  (dotimes (i 5)
-    (print (chcm-mtrx m i)))
-  (dotimes (i 6)
-    (print (array-dimensions (chcm-mtrx m i))))
-|#
-
-(DEFUN LINE-OP (mtrx begin lambda line1 line2)
-  ;; line2 := line2 + lambda * line1
-  (declare
-    (type matrix mtrx)
-    (fixnum begin lambda line1 line2))
-  (the matrix
-  (progn
-  (do ((column-number (column-number mtrx))
-       (j begin (1+ j)))
-      ((= j column-number))
-      (declare (fixnum column-number j))
-    (incf (aref mtrx line2 j)
-	  (* lambda (aref mtrx line1 j))))
-  mtrx)))
-	
-#|
-(setf m (random-matrix 3 4 10))
-(line-op m 1 3 2 0)
-|#
-
-;; mtrx-list = (P P^-1 M Q Q^-1)
-
-(DEFMACRO LINE-OP-5 (mtrx-list begin lambda line1 line2)
-  (let ((slambda (gensym)))
-    `(let ((,slambda ,lambda))
-       (column-op (first ,mtrx-list) 0 (- ,slambda) ,line2 ,line1)
-       (line-op (second ,mtrx-list) 0 ,slambda ,line1 ,line2)
-       (line-op (third ,mtrx-list) ,begin ,slambda ,line1 ,line2))))
-     
-#|
-(setf p (idnt-mtrx 4) p-1 (idnt-mtrx 4)
-      m (random-matrix 4 5 10)
-      q (idnt-mtrx 5) q-1 (idnt-mtrx 5))
-(setf list (list p p-1 m q q-1))
-(setf t1 (mtrx-prdc p (mtrx-prdc m q-1)))
-(line-op-5 list 0 3 1 3)
-(equalp t1 (mtrx-prdc p (mtrx-prdc m q-1)))
-(mtrx-prdc p p-1)
-|#
-
-(DEFUN COLUMN-OP (mtrx begin lambda column1 column2)
-  (declare
-    (type matrix mtrx)
-    (fixnum begin lambda column1 column2))
-  (the matrix
-  (progn
-  (do ((line-number (line-number mtrx))
-       (i begin (1+ i)))
-      ((= i line-number))
-      (declare (fixnum line-number i))
-    (incf (aref mtrx i column2)
-	  (* lambda (aref mtrx i column1))))
-  mtrx)))
-	
-#|
-(setf m (random-matrix 3 4 10))
-(column-op m 1 3 2 0)
-|#
-
-(DEFMACRO COLUMN-OP-5 (mtrx-list begin lambda column1 column2)
-  (let ((slambda (gensym)))
-    `(let ((,slambda ,lambda))
-       (column-op (third ,mtrx-list) ,begin ,slambda ,column1 ,column2)
-       (column-op (fourth ,mtrx-list) 0 ,slambda ,column1 ,column2)
-       (line-op (fifth ,mtrx-list) 0 (- ,slambda) ,column2 ,column1))))
-
-#|
-(setf p (idnt-mtrx 4) p-1 (idnt-mtrx 4)
-      m (random-matrix 4 5 10)
-      q (idnt-mtrx 5) q-1 (idnt-mtrx 5))
-(setf list (list p p-1 m q q-1))
-(setf t1 (mtrx-prdc p (mtrx-prdc m q-1)))
-(column-op-5 list 0 3 1 3)
-(equalp t1 (mtrx-prdc p (mtrx-prdc m q-1)))
-(mtrx-prdc p p-1)
-(mtrx-prdc q q-1)
-|#
-
-
-(DEFUN LINE-SWAP (mtrx begin line1 line2)
-  (declare
-    (type matrix mtrx)
-    (fixnum begin line1 line2))
-  (the matrix
-  (progn
-  (do ((column-number (column-number mtrx))
-       (j begin (1+ j)))       
-      ((= j column-number))
-      (declare (fixnum column-number j))
-    (rotatef (aref mtrx line1 j) (aref mtrx line2 j)))
-  mtrx)))
-
-#|
-(setf m (random-matrix 3 4 10))
-(line-swap m 1 0 2)
-|#
-
-(DEFMACRO LINE-SWAP-5 (mtrx-list begin line1 line2)
-  `(progn
-     (column-swap (first ,mtrx-list) 0 ,line1 ,line2)
-     (line-swap (second ,mtrx-list) 0 ,line1 ,line2)
-     (line-swap (third ,mtrx-list) ,begin ,line1 ,line2)))
-
-
-#|
-(setf p (idnt-mtrx 4) p-1 (idnt-mtrx 4)
-      m (random-matrix 4 5 10)
-      q (idnt-mtrx 5) q-1 (idnt-mtrx 5))
-(setf list (list p p-1 m q q-1))
-(setf t1 (mtrx-prdc p (mtrx-prdc m q-1)))
-(line-swap-5 list 0 1 3)
-(equalp t1 (mtrx-prdc p (mtrx-prdc m q-1)))
-(mtrx-prdc p p-1)
-(mtrx-prdc q q-1)
-|#
-
-(DEFUN COLUMN-SWAP (mtrx begin column1 column2)
-  (declare
-    (type matrix mtrx)
-    (fixnum begin column1 column2))
-  (the matrix (progn
-  (do ((line-number (line-number mtrx))
-       (i begin (1+ i)))       
-      ((= i line-number))
-      (declare (fixnum line-number i))
-    (rotatef (aref mtrx i column1) (aref mtrx i column2)))
-  mtrx)))
-
-#|
-(setf m (random-matrix 3 4 10))
-(column-swap m 1 0 2)
-|#
-
-(DEFMACRO COLUMN-SWAP-5 (mtrx-list begin column1 column2)
-  `(progn
-     (column-swap (third ,mtrx-list) ,begin ,column1 ,column2)
-     (column-swap (fourth ,mtrx-list) 0 ,column1 ,column2)
-     (line-swap (fifth ,mtrx-list) 0 ,column1 ,column2)))
-
-#|
-(setf p (idnt-mtrx 4) p-1 (idnt-mtrx 4)
-      m (random-matrix 4 5 10)
-      q (idnt-mtrx 5) q-1 (idnt-mtrx 5))
-(setf list (list p p-1 m q q-1))
-(setf t1 (mtrx-prdc p (mtrx-prdc m q-1)))
-(column-swap-5 list 0 1 3)
-(equalp t1 (mtrx-prdc p (mtrx-prdc m q-1)))
-(mtrx-prdc p p-1)
-(mtrx-prdc q q-1)
-|#
-
-(DEFUN LINE-MINUS (mtrx begin line)
-  (declare
-    (type matrix mtrx)
-    (fixnum begin line))
-  (the matrix (progn
-  (do ((column-number (column-number mtrx))
-       (j begin (1+ j)))
-      ((= j column-number))
-      (declare (fixnum column-number j))
-    (setf (aref mtrx line j) (- (aref mtrx line j))))
-  mtrx)))
-
-(DEFMACRO LINE-MINUS-5 (mtrx-list begin line)
-  `(progn
-     (column-minus (first ,mtrx-list) 0 ,line)
-     (line-minus (second ,mtrx-list) 0 ,line)
-     (line-minus (third ,mtrx-list) ,begin ,line)))
-
-(DEFUN COLUMN-MINUS (mtrx begin column)
-  (declare
-    (type matrix mtrx)
-    (fixnum begin column))
-  (the matrix (progn
-  (do ((line-number (line-number mtrx))
-       (i begin (1+ i)))
-      ((= i line-number))
-      (declare (fixnum line-number i))
-    (setf (aref mtrx i column) (- (aref mtrx i column))))
-  mtrx)))
-
-(DEFMACRO COLUMN-MINUS-5 (mtrx-list begin column)
-  `(progn
-     (column-minus (third ,mtrx-list) ,begin ,column)
-     (column-minus (fourth ,mtrx-list) 0 ,column)
-     (line-minus (fifth ,mtrx-list) 0 ,column)))
-
-#|
-(setf m (random-matrix 3 4 10))
-(line-minus m 1 2)
-(column-minus m 1 2)
-|#
-
-#|
-(setf p (idnt-mtrx 4) p-1 (idnt-mtrx 4)
-      m (random-matrix 4 5 10)
-      q (idnt-mtrx 5) q-1 (idnt-mtrx 5))
-(setf list (list p p-1 m q q-1))
-(setf t1 (mtrx-prdc p (mtrx-prdc m q-1)))
-(line-minus-5 list 0 3)
-(equalp t1 (mtrx-prdc p (mtrx-prdc m q-1)))
-(mtrx-prdc p p-1)
-(mtrx-prdc q q-1)
-(column-minus-5 list 0 2)
-(equalp t1 (mtrx-prdc p (mtrx-prdc m q-1)))
-(mtrx-prdc p p-1)
-(mtrx-prdc q q-1)
-|#
-
-(DEFUN MINIMAL-TERM (matrix begin)
-  (declare
-    (type matrix matrix)
-    (fixnum begin))
-  (the (values fixnum fixnum fixnum)
-  (do ((line-number (line-number matrix))
-       (column-number (column-number matrix))
-       (min 0)
-       (min-il -1)
-       (min-ic -1)
-       (il begin (1+ il)))
-      ((= il line-number) (values min min-il min-ic))
-      (declare (fixnum line-number column-number
-		       min min-il min-ic il))
-      (do ((ic begin (1+ ic)))
-          ((= ic column-number))
-         (declare (fixnum ic))
-         (let ((term (abs (aref matrix il ic))))
-	   (declare (fixnum term))
-            (when (= term 1)
-               (return-from minimal-term (values 1 il ic)))
-            (when (plusp term)
-               (when (or (< term min)
-                         (zerop min))               
-                  (setf min term
-                        min-il il
-                        min-ic ic))))))))
-
-#|
-(setf m (random-matrix 4 5 10))
-(minimal-term m 1)
-|#
-
-(DEFUN MINIMAL-REST-1 (matrix begin)
-  (declare
-    (type matrix matrix)
-    (fixnum begin))
-  (the (values fixnum fixnum fixnum)
-   (let ((line-number (line-number matrix))
-	 (column-number (column-number matrix))
-	 (corner (aref matrix begin begin))
-         (min 0)
-         (min-il -1)
-         (min-ic -1))
-      (declare (fixnum corner min min-il min-ic))
-      (do ((ic (1+ begin) (1+ ic)))
-          ((= ic column-number))
-         (declare (fixnum ic))
-         (let ((term (abs (second (multiple-value-list (round (aref matrix begin ic) 
-                                                          corner))))))
-            (declare (fixnum term))
-            (when (= term 1)
-               (return-from minimal-rest-1 (values 1 begin ic)))
-            (when (plusp term)
-               (when (or (< term min)
-                         (zerop min))               
-                  (setf min term
-                        min-il begin
-                        min-ic ic)))))
-      (do ((il (1+ begin) (1+ il)))
-          ((= il line-number))
-         (declare (fixnum il))
-         (let ((term (abs (second (multiple-value-list (round (aref matrix il begin)
-                                                          corner))))))
-            (declare (fixnum term))
-            (when (= term 1)
-               (return-from minimal-rest-1 (values 1 il begin)))
-            (when (plusp term)
-               (when (or (< term min)
-                         (zerop min))               
-                  (setf min term
-                        min-il il
-                        min-ic begin)))))
-      (values min min-il min-ic))))
-
-#|
-(setf m (random-matrix 4 5 10))
-(minimal-rest-1 m 1)
-|#
-
-(DEFUN MINIMAL-REST-2 (matrix begin)
-  (declare
-    (type matrix matrix)
-    (fixnum begin))
-  (the (values fixnum fixnum fixnum)
-   (let ((line-number (line-number matrix))
-	 (column-number (column-number matrix))		      
-	 (corner (aref matrix begin begin))
-         (min 0)
-         (min-il  -1)
-         (min-ic -1))
-      (declare (fixnum corner min min-il min-ic))
-      (do ((il (1+ begin) (1+ il)))
-          ((= il line-number))
-         (declare (fixnum il))
-         (do ((ic (1+ begin) (1+ ic)))
-             ((= ic column-number))
-            (declare (fixnum il))
-            (let ((term (abs (second (multiple-value-list (round (aref matrix il ic)
-                                                             corner))))))
-               (declare (fixnum term))
-               (when (= 1 term)
-                  (return-from minimal-rest-2 (values 1 il ic)))
-               (when (plusp term)
-                  (when (or (< term min)
-                            (zerop min))
-                     (setf min term
-                           min-il il
-                           min-ic ic))))))
-      (values min min-il min-ic))))
-
-#|
-(setf m (random-matrix 4 5 10))
-(minimal-rest-2 m 1)
-|#
-
-(DEFUN MINIMAL-TERM-TOP-LEFT (mtrx-list begin il ic)
-  (declare
-   (list mtrx-list)
-   (fixnum begin il ic))
-  (the list
-    (progn
-      (when (< begin il)
-        (line-swap-5 mtrx-list begin begin il))
-      (when (< begin ic)
-        (column-swap-5 mtrx-list begin begin ic))
-      (when (minusp (aref (third mtrx-list) begin begin))
-        (line-minus-5 mtrx-list begin begin))
-      mtrx-list)))
-
-#|
-(setf p (idnt-mtrx 4) p-1 (idnt-mtrx 4)
-      m (random-matrix 4 5 10)
-      q (idnt-mtrx 5) q-1 (idnt-mtrx 5))
-(setf list (list p p-1 m q q-1))
-(setf t1 (mtrx-prdc p (mtrx-prdc m q-1)))
-(minimal-term-top-left list 0 1 3)
-(equalp t1 (mtrx-prdc p (mtrx-prdc m q-1)))
-(mtrx-prdc p p-1)
-(mtrx-prdc q q-1))
-|#
-
-(DEFUN PIVOTT (mtrx-list begin)
-  (declare
-    (list mtrx-list)
-    (fixnum begin))
-  (the list (progn
-  (let ((line-number (line-number (third mtrx-list)))
-	(column-number (column-number (third mtrx-list)))
-	(corner (aref (third mtrx-list) begin begin)))
-    (declare (fixnum line-number column-number corner))
-    (do ((il (1+ begin) (1+ il)))
-	((= il line-number))
-	(declare (fixnum il))
-      (line-op-5 mtrx-list begin
-		 (- (round (aref (third mtrx-list) il begin) corner))
-		 begin il))
-    (do ((ic (1+ begin) (1+ ic)))
-	((= ic column-number))
-	(declare (fixnum ic))
-      (column-op-5 mtrx-list begin
-		   (- (round (aref (third mtrx-list) begin ic) corner))
-		   begin ic)))
-  mtrx-list)))
-
-#|
-(setf p (idnt-mtrx 4) p-1 (idnt-mtrx 4)
-      m (random-matrix 4 5 10)
-      q (idnt-mtrx 5) q-1 (idnt-mtrx 5))
-(setf (aref m 0 0) -1)
-(setf list (list p p-1 m q q-1))
-(setf t1 (mtrx-prdc p (mtrx-prdc m q-1)))
-(pivott list 0)
-(equalp t1 (mtrx-prdc p (mtrx-prdc m q-1)))
-(mtrx-prdc p p-1)
-(mtrx-prdc q q-1)
-|#
-
-(DEFUN MATRIX-MODULO (mtrx modulo)
-  (declare (type matrix mtrx) (type fixnum modulo))
-  (the matrix
-    (let ((line-number (line-number mtrx))
-          (column-number (column-number mtrx)))
-      (declare (type fixnum line-number column-number))
-      (do ((il 0 (1+ il)))
-          ((= il line-number))
-        (declare (type fixnum il))
-        (do ((ic 0 (1+ ic)))
-            ((= ic column-number))
-          (declare (type fixnum ic))
-          (setf (aref mtrx il ic)
-            (mod (aref mtrx il ic) modulo))))
-      mtrx)))
-
-#|
-()
-(setf m (random-matrix 3 4 100))
-(matrix-modulo m 10)
-|#
-
-(DEFUN MATRIX-MODULO-5 (list modulo)
-  (declare (type list list))
-  (the list
-    (mapcar #'(lambda (item)
-                (matrix-modulo item modulo))
-      list)))
-
-(DEFUN LIST-SMITH (mtrx-list modulo) 
-  (declare (list mtrx-list) (type fixnum modulo))
-  (the list (progn
-  (let ((matrix (third mtrx-list))
-	(begin 0))
-    (declare
-      (type matrix matrix)
-      (fixnum begin))
-    (loop
-      (when (plusp modulo)
-        (matrix-modulo-5 mtrx-list modulo))
-      (multiple-value-bind (term il ic) (minimal-term matrix begin)
-	(declare (fixnum term il ic))
-        ;; (format t "~%*BEGIN* = ~D ; MIN = ~D." begin term)
-	(when (zerop term)
-	  (return-from list-smith mtrx-list))
-	(minimal-term-top-left mtrx-list begin il ic))
-      (loop
-        (when (plusp modulo)
-          (matrix-modulo-5 mtrx-list modulo))
-        (multiple-value-bind (term il ic) (minimal-rest-1 matrix begin)
-          (declare (fixnum term il ic))
-          (cond ((zerop term)
-                 (pivott mtrx-list begin)
-                 (multiple-value-bind (term il ic) (minimal-rest-2 matrix begin)
-                   (declare
-                    (fixnum term il)
-                    (ignore ic))
-                   (if (zerop term)
-                       (return)
-                     (line-op-5 mtrx-list begin 1 il begin))))
-                ((= il begin)
-                 (column-op-5 mtrx-list begin
-                              (- (round (aref matrix begin ic)
-                                        (aref matrix begin begin)))
-                              begin ic)
-                 (column-swap-5 mtrx-list begin begin ic)
-                 (when (minusp (aref matrix begin begin))
-                   (column-minus-5 mtrx-list begin begin)))
-                (t
-                 (line-op-5 mtrx-list begin
-                            (- (round (aref matrix il begin)
-                                      (aref matrix begin begin)))
-                            begin il)
-                 (line-swap-5 mtrx-list begin begin il)
-                 (when (minusp (aref matrix begin begin))
-                   (column-minus-5 mtrx-list begin begin))))))
-      ;; (Format t "~%  Finally the diagonal term is ~D." (aref matrix begin begin))
-      (incf begin)))
-              mtrx-list)))
-
-#|
-()
-(setf p (idnt-mtrx 4) p-1 (idnt-mtrx 4)
-      m (random-matrix 4 5 10)
-      q (idnt-mtrx 5) q-1 (idnt-mtrx 5))
-(setf list (list p p-1 m q q-1))
-(setf t1 (mtrx-prdc p (mtrx-prdc m q-1)))
-(third (list-smith list 0))
-(equalp t1 (mtrx-prdc p (mtrx-prdc m q-1)))
-(mtrx-prdc p p-1)
-(mtrx-prdc q q-1)
-(setf p (idnt-mtrx 4) p-1 (idnt-mtrx 4)
-      m (random-matrix 4 5 10)
-      q (idnt-mtrx 5) q-1 (idnt-mtrx 5))
-(setf list (list p p-1 m q q-1))
-(setf t1 (matrix-modulo (mtrx-prdc p (mtrx-prdc m q-1)) 10))
-(third (list-smith list 10))
-(equalp t1 (matrix-modulo (mtrx-prdc p (mtrx-prdc m q-1)) 10))
-(matrix-modulo (mtrx-prdc p p-1) 10)
-(matrix-modulo (mtrx-prdc q q-1) 10)
-
-(setf p (idnt-mtrx 10) p-1 (idnt-mtrx 10)
-      m (random-matrix 10 15 40)
-      q (idnt-mtrx 15) q-1 (idnt-mtrx 15))
-(setf list (list p p-1 m q q-1))
-(setf t1 (matrix-modulo (mtrx-prdc p (mtrx-prdc m q-1)) 10000))
-(third (list-smith list 10000))
-(equalp t1 (matrix-modulo (mtrx-prdc p (mtrx-prdc m q-1)) 10000))
-(matrix-modulo (mtrx-prdc p p-1) 10000)
-(matrix-modulo (mtrx-prdc q q-1) 10000)
-
-(setf m (random-matrix 5 5 10))
-(setf mm (copy-mtrx m))
-(third (smith m))
-(third (smith mm 1000))
-|#
-
-(DEFUN SMITH (matrix &optional (modulo 0))
-  (declare (type matrix matrix))
-  (the list
-  (let ((line-n (line-number matrix))
-	(column-n (column-number matrix)))
-    (declare (fixnum line-n column-n))
-    (list-smith
-     (list (idnt-mtrx line-n) (idnt-mtrx line-n)
-	   matrix
-           (idnt-mtrx column-n) (idnt-mtrx column-n))
-     modulo))))
-
-;;; ECHCM -> The same without the first epimorphism
-;;;
-;;; epi: C_f <- C_{f+1}
-;;  rank(C_f) = n
-;;  rank(C_{f+1}) = m
-;;  f = first
-
-(eval-when (:compile-toplevel :load-toplevel :execute)
-  (UNLESS (FIND-PACKAGE "GNRTS")
-    (make-package "GNRTS"))
-  (DEFCONSTANT +GNRTS-PCKG+
-    (find-package "GNRTS")))
-
-(DEFMACRO GNRT-NAME (i)
-  `(intern (format nil "GN-~D" ,i) +gnrts-pckg+))
-
-(DEFUN GNRT-NAME-BASIS (n)
-  (declare (fixnum n))
-  (the list
-  (do ((i (1- n) (1- i))
-       (rslt +empty-list+ (cons (gnrt-name i) rslt)))
-      ((minusp i) rslt)
-      (declare
-        (fixnum i)
-	(list rslt)))))
-
-#|
-(gnrt-name 4)
-(gnrt-name-basis 4)
-|#
-
-(DEFUN ECHCM-KILL-EPI-F-INTR (cmpr first n m f+1-basis mtrx-list)
-  (declare
-    (type cmprf cmpr)
-    (fixnum first n m)
-    (list f+1-basis mtrx-list))
-  (let ((f+1 (1+ first))
-	(m-n (- m n))
-	(q-1 (fifth mtrx-list)))
-    (declare
-      (fixnum f+1 m-n)
-      (type matrix q-1))
-    (flet ((rslt (cmbn)
-	     (declare (type cmbn cmbn))
-	     (with-cmbn (degr list) cmbn
-	       (when (= degr first)
-		 (return-from rslt (zero-cmbn degr)))
-	       (unless (= degr f+1)
-		 (return-from rslt cmbn))
-	       (let ((rslt-cffcs
-                      #-ACLPC (make-array m-n :element-type 'fixnum
-			         :initial-element 0)
-                      #+ACLPC (if (zerop m-n)
-                                 (make-array 0 :element-type 'fixnum)
-                                 (make-array m-n :element-type 'fixnum
-                                   :initial-element 0))
-                      ))
-		 (declare (type (array fixnum *) rslt-cffcs))
-		 (do ((cmbn-mark list (cdr cmbn-mark))
-		      (basis-mark f+1-basis)
-		      (ic 0))
-		     ((endp cmbn-mark))
-		     (declare
-		       (list cmbn-mark basis-mark)
-		       (fixnum ic))
-		   (with--term (cffc gnrt) cmbn-mark
-		     (loop (when (eq :equal (funcall cmpr gnrt (car basis-mark)))
-			     (return))
-			   (pop basis-mark)
-			   (incf ic))
-		     (dotimes (il m-n)
-		       (incf (aref rslt-cffcs il)
-			     (* cffc (aref q-1 (+ n il) ic))))
-		     (pop basis-mark)
-		     (incf ic)))
-		 (do ((term-list +empty-list+)
-		      (il (1- m-n) (1- il)))
-		     ((minusp il) (make-cmbn :degr degr
-					     :list term-list))
-		     (declare
-		       (list term-list)
-		       (fixnum il))
-		   (let ((cffc (aref rslt-cffcs il)))
-		     (declare (fixnum cffc))
-		     (unless (zerop cffc)
-		       (push (term cffc (gnrt-name il)) term-list))))))))
-      (the intr #'rslt))))
-	      
-#|
-(setf q-1 (random-matrix 5 5 10))
-(setf f (echcm-kill-epi-f-intr #'s-cmpr 2 2 5 '(a b c d e)
-		      (list 0 0 0 0 q-1)))
-(funcall f (cmbn 2 1 'a))
-(funcall f (cmbn 4 1 'a))
-(funcall f (cmbn 3 1 'a 10 'b 100 'c 1000 'd 10000 'e))
-|#
-
-(DEFUN ECHCM-KILL-EPI-G-INTR (first n m f+1-basis mtrx-list)
-  (declare
-    (fixnum first n m)
-    (list f+1-basis mtrx-list))
-  (let ((f+1 (1+ first))
-	(m-n (- m n))
-	(q (fourth mtrx-list)))
-    (declare
-      (fixnum f+1 m-n)
-      (type matrix q))
-    (flet ((rslt (cmbn)
-	     (declare (type cmbn cmbn))
-	     (with-cmbn (degr list) cmbn
-	       (unless (= degr f+1)
-		 (return-from rslt cmbn))
-	       (let ((rslt-cffcs
-                      #-ACLPC (make-array m :element-type 'fixnum
-			         :initial-element 0)
-                      #+ACLPC (if (zerop m)
-                                 (make-array 0 :element-type 'fixnum)
-                                 (make-array m :element-type 'fixnum
-                                   :initial-element 0))
-                      ))
-		 (declare (type (array fixnum *) rslt-cffcs))
-		 (do ((cmbn-mark list (cdr cmbn-mark))
-		      (basis-mark (gnrt-name-basis m-n))
-		      (ic 0))
-		     ((endp cmbn-mark))
-		     (declare
-		       (list cmbn-mark basis-mark)
-		       (fixnum ic))
-		   (with--term (cffc gnrt) cmbn-mark
-		     (loop (when (eq :equal (s-cmpr gnrt (car basis-mark)))
-			     (return))
-			   (pop basis-mark)
-			   (incf ic))
-		     (dotimes (il m)
-		       (incf (aref rslt-cffcs il)
-			     (* cffc (aref q il (+ n ic)))))
-		     (pop basis-mark)
-		     (incf ic)))
-		 (do ((term-list +empty-list+)
-		      (il (1- m) (1- il)))
-		     ((minusp il) (make-cmbn :degr degr
-					     :list term-list))
-		     (declare
-		       (list term-list)
-		       (fixnum il))
-		   (let ((cffc (aref rslt-cffcs il)))
-		     (declare (fixnum cffc))
-		     (unless (zerop cffc)
-		       (push (term cffc (nth il f+1-basis)) term-list))))))))
-      (the intr #'rslt))))
-    
-#|
-(setf q (random-matrix 5 5 10))
-(setf g (echcm-kill-epi-g-intr 2 2 5 '(a b c d e)
-		      (list 0 0 0 q 0)))
-(funcall g (cmbn 2))
-(funcall g (cmbn 4 1 'a))
-(funcall g (cmbn 3 1 :gn-0 10 :gn-1 100 :gn-2))
-|#
-
-(DEFUN ECHCM-KILL-EPI-H-INTR (cmpr first n m f-basis f+1-basis mtrx-list)
-  (declare
-    (type cmprf cmpr)
-    (fixnum first n m)
-    (list f-basis f+1-basis mtrx-list))
-  (let ((lqxp-1 (mtrx-prdc (left-submatrix (fourth mtrx-list) n)
-			   (second mtrx-list))))
-    (declare (type matrix lqxp-1))
-    (flet ((rslt (cmbn)
-	     (declare (type cmbn cmbn))
-	     (with-cmbn (degr list) cmbn
-	       (unless (= degr first)
-		 (return-from rslt (zero-cmbn (1+ degr))))
-	       (let ((rslt-cffcs
-                      #-ACLPC (make-array m :element-type 'fixnum
-			        :initial-element 0)
-                      #+ACLPC (if (zerop m)
-                                 (make-array 0 :element-type 'fixnum)
-                                 (make-array m :element-type 'fixnum
-                                   :initial-element 0))
-                      ))
-		 (declare (type (array fixnum *) rslt-cffcs))
-		 (do ((cmbn-mark list (cdr cmbn-mark))
-		      (basis-mark f-basis)
-		      (ic 0))
-		     ((endp cmbn-mark))
-		     (declare
-		       (list cmbn-mark basis-mark)
-		       (fixnum ic))
-		   (with--term (cffc gnrt) cmbn-mark
-		     (loop (when (eq :equal (funcall cmpr gnrt (car basis-mark)))
-			     (return))
-			   (pop basis-mark)
-			   (incf ic))
-		     (dotimes (il m)
-		       (incf (aref rslt-cffcs il)
-			     (* cffc (aref lqxp-1 il ic))))
-		     (pop basis-mark)
-		     (incf ic)))
-		 (do ((term-list +empty-list+)
-		      (il (1- m) (1- il)))
-		     ((minusp il) (make-cmbn :degr (1+ degr)
-					     :list term-list))
-		     (declare
-		       (list term-list)
-		       (fixnum il))
-		   (let ((cffc (aref rslt-cffcs il)))
-		     (declare (fixnum cffc))
-		     (unless (zerop cffc)
-		       (push (term cffc (nth il f+1-basis)) term-list))))))))
-      (the intr #'rslt))))
-	      
-#|
-(setf p-1 (random-matrix 2 2 10))
-(setf q (random-matrix 5 5 10))
-(setf h (echcm-kill-epi-h-intr #'s-cmpr 2 2 5 '(a b) '(a b c d e)
-		      (list 0 p-1 0 q 0)))
-(funcall h (cmbn 2 1 'a 1000 'b))
-(funcall h (cmbn 4 1 'a))
-|#
-
-(DEFUN ECHCM-WITHOUT-EPI (echcm first n m intr-f)
-  (declare
-    (type chain-complex echcm)
-    (fixnum first n m)
-    (type intr intr-f))
-  (the chain-complex
-  (with-slots (cmpr basis dffr dfnt) echcm
-    (declare
-      (type cmprf cmpr)
-      (type basis basis)
-      (type morphism dffr)
-      (list dfnt))
-    (chain-complex
-     :cmpr #'(lambda (gnrt1 gnrt2)
-	       (if (and (symbolp gnrt1)
-			(eq (symbol-package gnrt1)
-			    +gnrts-pckg+))
-		   (s-cmpr gnrt1 gnrt2)
-		 (funcall cmpr gnrt1 gnrt2)))
-     :basis #'(lambda (degr)
-		(declare (fixnum degr))
-		(cond ((= degr first)
-		       +empty-list+)
-		      ((= degr (1+ first))
-		       (gnrt-name-basis (- m n)))
-		      (t
-		       (funcall basis degr))))
-     :dffr-intr #'(lambda (cmbn)
-		    (declare (type cmbn cmbn))
-		    (case (- (cmbn-degr cmbn) first)
-		      (1 (zero-cmbn first))
-		      (2 (funcall intr-f
-			   (cmbn-? dffr cmbn)))
-		      (otherwise
-		         (cmbn-? dffr cmbn))))
-     :dffr-strt :cmbn
-     :dfnt `(echcm-without-epi ,echcm)))))
-
-(DEFUN ECHCM-KILL-EPI (echcm first)
-  (declare
-    (type chain-complex echcm)
-    (fixnum first))
-  (the reduction
-  (with-slots (cmpr basis) echcm
-    (declare
-      (type cmprf cmpr)
-      (type basis basis))
-    (assert (not (eq basis :locally-effective)))
-    (let* ((f-basis (funcall basis first))
-	   (f+1-basis (funcall basis (1+ first)))
-	   (mtrx-list (smith (chcm-mtrx echcm (1+ first))))
-	   (smith (third mtrx-list))
-	   (m (column-number smith))
-	   (n (line-number smith))
-	   (intr-f (echcm-kill-epi-f-intr cmpr first n m
-				    f+1-basis
-				    mtrx-list))
-	   (intr-g (echcm-kill-epi-g-intr first n m f+1-basis mtrx-list))
-	   (intr-h (echcm-kill-epi-h-intr cmpr first n m
-				    f-basis f+1-basis
-				    mtrx-list))
-	   (echcm2 (echcm-without-epi echcm first n m intr-f)))				      
-      (declare
-        (list mtrx-list)
-	(type matrix smith)
-	(fixnum m n)
-	(type intr intr-f intr-g intr-h)
-	(type chain-complex echcm2))
-      (assert (dotimes (i n +true+)
-		(unless (= 1 (aref smith i i))
-		  (return +false+))))
-      (reduction
-       :f (morphism
-	    :sorc echcm :trgt echcm2 :degr 0
-	    :intr intr-f :strt :cmbn
-	    :dfnt `(echcm-kill-epi-f ,echcm))
-       :g (morphism
-	    :sorc echcm2 :trgt echcm :degr 0
-	    :intr intr-g :strt :cmbn
-	    :dfnt `(echcm-kill-epi-g ,echcm))
-       :h (morphism
-	    :sorc echcm :trgt echcm :degr +1
-	    :intr intr-h :strt :cmbn
-	    :dfnt `(echcm-kill-epi-h ,echcm))
-       :dfnt `(echcm-kill-epi ,echcm))))))
-
-#|
-(cat-init)
-(setf s3 (sphere 3))
-(setf s3-chml-clss (chml-clss 's3))
-(setf s3-fibration (z-whitehead s3 3 s3-chml-clss))
-(setf s3-4 (fibration-total s3-fibration))
-(setf ecc (echcm s3-4))
-(setf rdct (echcm-kill-epi ecc 2))
-(pre-check-rdct rdct)
-(setf *tc* (cmbn 0 1 (bsgn ecc))
-      *bc* *tc*)
-(check-rdct)
-(setf *tc* (cmbn 2 1 (first (basis ecc 2))))
-(check-rdct)
-(setf *tc* (cmbn 3 1 (first (basis ecc 3))))
-(check-rdct)
-(setf *tc* (cmbn 4 1 (first (basis ecc 4)))
-      *bc* *tc*)
-(check-rdct)
-(setf s3-4-chml-clss (chml-clss 's3-4))
-(setf s3-4-fibration (z2-whitehead s3-4 4 s3-4-chml-clss))
-(setf s3-5 (fibration-total s3-4-fibration))
-(setf ecc (echcm s3-5))
-(dotimes (i 7)
-  (format t "~%DIM = ~D ; LENGTH = ~D" i (length (basis ecc i))))
-(setf rdct1 (echcm-kill-epi ecc 2))
-(setf rdct2 (echcm-kill-epi (bcc rdct1) 3))
-(setf rdct3 (echcm-kill-epi (bcc rdct2) 4))
-(setf rdct12 (cmps rdct2 rdct1))
-(setf rdct123 (cmps rdct3 rdct12))
-(pre-check-rdct rdct123)
-(setf *tc* (cmbn 0 1 (bsgn ecc)) *bc* *tc*)
-(check-rdct)
-(setf *tc* (cmbn 2 1 (first (basis ecc 2))))
-(check-rdct)
-(let ((b3 (basis ecc 3)))
-  (setf *tc* (cmbn 3 1 (first b3) 10 (second b3))))
-(check-rdct)
-(let ((b4 (basis ecc 4)))
-  (setf *tc* (cmbn 4 1 (first b4) 10 (second b4))))
-(check-rdct)
-(let ((b5 (basis ecc 5)))
-  (setf *tc* (cmbn 5 1 (first b5)
-		     10 (second b5)
-		     100 (third b5)
-		     1000 (fourth b5))))
-(check-rdct)
-(let ((b6 (basis ecc 6)))
-  (setf *tc* (cmbn 6 1 (first b6)
-		     10 (second b6)
-		     100 (third b6)
-		     1000 (fourth b6)
-		     10000 (fifth b6)
-		     100000 (sixth b6)
-		     1000000 (seventh b6))))
-(check-rdct)
-|#
- 
-(DEFUN KILL-EPI (chcm first)
-  (declare
-   (type chain-complex chcm)
-   (fixnum first))
-  (the equivalence
-    (let ((efhm (efhm chcm))
-          (echcm (echcm chcm)))
-      (declare
-       (type equivalence efhm)
-       (type chain-complex echcm))
-      (let ((last-rdct (echcm-kill-epi echcm first)))
-        (declare (type reduction last-rdct))
-        (setf (slot-value chcm 'efhm)
-          (equivalence
-           :lrdct (lrdct efhm)
-           :rrdct (cmps last-rdct (rrdct efhm))
-           :dfnt `(kill-epi ,chcm ,first)))))))
-
-(DEFUN KILL-EPIS (chcm first end)
-  (declare
-    (type chain-complex chcm)
-    (fixnum first end))
-  (the equivalence (progn
-    (do ((indx first (1+ indx)))
-	((= indx end))
-        (declare (fixnum indx))
-      (kill-epi chcm indx))
-    (efhm chcm))))
-
-#|
-(cat-init)
-(setf s3 (sphere 3))
-(setf s3-chml-clss (chml-clss 's3))
-(setf s3-fibration (z-whitehead s3 3 s3-chml-clss))
-(setf s3-4 (fibration-total s3-fibration))
-(setf s3-4-chml-clss (chml-clss 's3-4))
-(setf s3-4-fibration (z2-whitehead s3-4 4 s3-4-chml-clss))
-(setf s3-5 (fibration-total s3-4-fibration))
-(time (homology s3-5 6))
-(kill-epis s3-5 2 5)
-(homology s3-5 0 7)
-
-(cat-init)
-(setf s3 (sphere 3))
-(setf s3-chml-clss (chml-clss 's3))
-(setf s3-fibration (z-whitehead s3 3 s3-chml-clss))
-(setf s3-4 (fibration-total s3-fibration))
-(kill-epi s3-4 2)
-(setf s3-4-chml-clss (chml-clss 's3-4))
-(setf s3-4-fibration (z2-whitehead s3-4 4 s3-4-chml-clss))
-(setf s3-5 (fibration-total s3-4-fibration))
-(time (homology s3-5 6))
-|#
-
-(DEFUN CHML-CLSS-INTR (chcm first)
-  (declare
-    (type chain-complex chcm)
-    (fixnum first))
-  (let* ((echcm (echcm chcm))
-	 (cmpr (cmpr echcm))
-	 (basis (basis echcm))
-	 (f-basis (funcall basis first))
-	 (mtrx-list (smith (chcm-mtrx echcm (1+ first))))
-	 (p-1 (second mtrx-list))
-	 (smith (third mtrx-list))
-	 (n (line-number smith))
-	 (m (column-number smith))
-         (diag-indx (dotimes (indx (min n m)
-			       (if (> n m)
-				   m
-				 (error "In CHML-CLSS, the cohomology-ring ~@
-                                      is null.")))
-		      (declare (fixnum indx))
-		      (unless (= 1 (aref smith indx indx))
-			(return indx)))))
-    (declare
-      (type chain-complex echcm)
-      (type cmprf cmpr)
-      (type basis basis)
-      (fixnum n m diag-indx)
-      (list f-basis mtrx-list)
-      (type matrix p-1 smith))
-    (flet ((rslt (cmbn)
-	     (declare (type cmbn cmbn))
-	     (with-cmbn (degr list) cmbn
-	       (unless (= degr first)
-		 (return-from rslt (zero-cmbn (- degr first))))
-	       (do ((rslt 0)
-		    (bmark f-basis)
-		    (ic 0)
-		    (cmark list (cdr cmark)))
-		   ((endp cmark)
-		    (if (zerop rslt)
-			(zero-cmbn 0)
-		      (term-cmbn 0 rslt :z-gnrt)))
-		   (declare
-		     (fixnum rslt)
-		     (list bmark cmark))
-		 (with--term (cffc gnrt) cmark
-		   (loop
-		    (when (eq :equal (funcall cmpr gnrt (car bmark)))
-		      (return))
-		    (pop bmark)
-		    (incf ic))
-		   (incf rslt (* cffc (aref p-1 diag-indx ic)))
-		   (pop bmark)
-		   (incf ic))))))
-      (the intr #'rslt))))
-
-#|
-(cat-init)
-(setf s3 (sphere 3))
-(setf c (chml-clss-intr s3 3))
-(funcall c (cmbn 3 5 's3))
-(setf s3-chml-clss (chml-clss 's3))
-(setf s3-fibration (z-whitehead s3 3 s3-chml-clss))
-(setf s3-4 (fibration-total s3-fibration))
-(kill-epi s3-4 2)
-(setf c (chml-clss-intr s3-4 4))
-(funcall c (cmbn 4 5 (first (basis (echcm s3-4) 4))))
-(setf s3-4-chml-clss (chml-clss 's3-4))
-(setf s3-4-fibration (z2-whitehead s3-4 4 s3-4-chml-clss))
-(setf s3-5 (fibration-total s3-4-fibration))
-(kill-epis s3-5 3 5)
-(setf c (chml-clss-intr s3-5 5))
-(let ((b5 (basis (echcm s3-5) 5)))
-  (funcall c (cmbn 5 1 (first b5) 10 (second b5))))
-|#
-
-(DEFUN CHML-CLSS (chcm first)
-  (declare
-    (type chain-complex chcm)
-    (fixnum first))
-  (the morphism
-    (morphism
-      :sorc (echcm chcm) :trgt (z-chcm) :degr (- first)
-      :intr (chml-clss-intr chcm first)
-      :strt :cmbn
-      :dfnt `(chml-clss ,chcm ,first))))
-
-#|
-(cat-init)
-(setf s3 (sphere 3))
-(setf s3-chml-clss (chml-clss s3 3))
-(setf s3-fibration (z-whitehead s3 3 s3-chml-clss))
-(setf s3-4 (fibration-total s3-fibration))
-(homology s3-4 0 6)
-(kill-epi s3-4 2)
-(setf s3-4-chml-clss (chml-clss s3-4 4))
-(setf s3-4-fibration (z2-whitehead s3-4 4 s3-4-chml-clss))
-(setf s3-5 (fibration-total s3-4-fibration))
-(homology s3-5 0 6)
-(kill-epis s3-5 3 5)
-(setf s3-5-chml-clss (chml-clss s3-5 5))
-(setf s3-5-fibration (z2-whitehead s3-5 5 s3-5-chml-clss))
-(setf s3-6 (fibration-total s3-5-fibration))
-(homology s3-6 0 7)
-|#
diff --git a/archive/Kenzo-2/Kenzo-2-Acl5/special-smsts.cl b/archive/Kenzo-2/Kenzo-2-Acl5/special-smsts.cl
deleted file mode 100644
index 3600e66..0000000
--- a/archive/Kenzo-2/Kenzo-2-Acl5/special-smsts.cl
+++ /dev/null
@@ -1,552 +0,0 @@
-;;;  SPECIAL-SMSTS  SPECIAL-SMSTS  SPECIAL-SMSTS  SPECIAL-SMSTS  SPECIAL-SMSTS
-;;;  SPECIAL-SMSTS  SPECIAL-SMSTS  SPECIAL-SMSTS  SPECIAL-SMSTS  SPECIAL-SMSTS
-;;;  SPECIAL-SMSTS  SPECIAL-SMSTS  SPECIAL-SMSTS  SPECIAL-SMSTS  SPECIAL-SMSTS
-
-(IN-PACKAGE "CAT")
-
-(PROVIDE "special-smsts")
-
-;;; GMSM-FACES-INFO = (gmsm (simple-vector absm) . dffr)
-;;;                         faces
-
-(DEFUN FINITE-SS-PRE-TABLE (list)
-   (declare (list list))
-   (the list
-      (let ((pre-rslt +empty-list+)
-            (dmns-mark nil)
-            (gmsm-mark nil))
-         (declare (list pre-rslt dmns-mark gmsm-mark))
-         (dolist (item list)
-            (declare (type (or fixnum symbol list) item))
-            (cond ((typep item 'fixnum)
-                   (let ((found (assoc item pre-rslt)))
-                      (declare (list found))
-                      (setf dmns-mark 
-                            (or found
-                                (car (push (list item) pre-rslt)))
-                            gmsm-mark nil)))
-                  ((symbolp item)
-                   (when (assoc item (cdr dmns-mark))
-                      (error "In BUILD-FINITE-SS, the symbol ~A is present two times."
-                         item))
-                   (setf gmsm-mark (car (push (list item) (cdr dmns-mark)))))
-                  ((listp item)
-                   (unless gmsm-mark
-                      (error "In BUILD-FINITE-SS, the face list ~A~@
-                              is not after a symbol." item))
-                   (nconc gmsm-mark item)
-                   (setf gmsm-mark nil))
-                  (t
-                     (error "In BUILD-FINITE-SS, the argument ~A does not make sense." item))))         
-         (do ((mark1 pre-rslt (cdr mark1)))
-             ((endp mark1))
-             (declare (list mark1))
-            (do ((mark2 (rest mark1) (cdr mark2)))
-                ((endp mark2))
-               (declare (list mark2))
-               (let ((inter (intersection (cdar mark1) (cdar mark2) :key #'first)))
-                  (declare (list inter))
-                  (when inter
-                     (error "In BUILD-FINITE-SS, the symbol ~A is present two times."
-                        (caar inter))))))
-         pre-rslt)))
-
-#|
-  (setf p (finite-ss-pre-table '(0 v0 v1 v2)))
-  (finite-ss-pre-table '(0 v0 v0 v2))
-  (setf p (finite-ss-pre-table '(0 v0 v1 1 e0 e1 e2)))
-  (finite-ss-pre-table '(0 v0 v1 1 e0 e1 v1))
-  (setf p (finite-ss-pre-table '(0 v0 (v0 v0))))
-  (setf p (finite-ss-pre-table '(0 v0 v1 v2 0 v3)))
-  (finite-ss-pre-table '(0 v0 (v0 v0) (v1 v1)))
-  (finite-ss-pre-table '(0 (v0 v0) (v1 v1)))
-  (finite-ss-pre-table '(0 v0 (v0 v0) #(1 2))))
-|#
-
-(DEFUN FINITE-SS-PRE-TABLE-TABLE (pre-table)
-   (declare (list pre-table))
-   (let* ((maxdim (1+ (apply #'max (mapcar #'first pre-table))))
-          (table (make-array maxdim :initial-element +empty-list+)))
-      (declare
-         (fixnum maxdim)
-         (simple-vector table))
-      (dolist (item pre-table)
-         (declare (list item))
-         (setf (svref table (first item))
-               (sort (rest item) #'string< :key #'first)))
-      table))
-
-#|
-  (setf p (finite-ss-pre-table-table
-             (finite-ss-pre-table '(2 v0 (e1 e2) v1 1 e0 e1 e2)))))
-|#
-
-(DEFUN FINITE-SS-FIND-GMSM (table gmsm dmns &optional (max-dmns (1+ dmns)))
-   (declare
-      (type gmsm gmsm)
-      (fixnum dmns max-dmns))
-   (do ((dmns dmns (1+ dmns)))
-       ((>= dmns max-dmns) nil)
-      (declare (fixnum dmns))
-      (let ((found (find gmsm (svref table dmns) :test #'eq :key #'car)))
-         (declare (type (or cons null) found))
-         (when found
-            (return-from finite-ss-find-gmsm dmns)))))
- 
-(DEFUN FINITE-SS-FINISH-TABLE (table bsgn)
-   (declare (simple-vector table))
-   (dotimes (dmns (length table))
-      (declare (fixnum dmns))
-      (finite-ss-finish-line table dmns bsgn))
-   table)
-
-(DEFUN FINITE-SS-FINISH-LINE (table dmns bsgn)
-   (declare
-      (simple-vector table)
-      (fixnum dmns))
-   (setf (svref table dmns)
-         (mapcar
-            #'(lambda (entry)
-                 (finite-ss-finish-entry table entry dmns bsgn))
-            (svref table dmns))))
-
-(DEFUN FINITE-SS-FINISH-ENTRY (table entry dmns bsgn)
-   (declare
-      (simple-vector table)
-      (list entry)
-      (fixnum dmns)
-      (symbol bsgn))
-   (let ((simplex (first entry))
-         (faces (rest entry)))
-      (declare
-         (symbol simplex)
-         (list faces))
-      (when (zerop dmns)
-         (return-from finite-ss-finish-entry
-            (make-gmsm-faces-info
-               :gmsm simplex :faces +s-empty-vector+
-               :dffr +zero-negative-cmbn+)))
-      (setf faces (nconc faces (make-list (1+ (- dmns (length faces)))
-                                  :initial-element bsgn)))
-      (let ((rslt (make-gmsm-faces-info :gmsm simplex)))
-         (declare (cons rslt))
-         (flet ((process-face (face)
-                 (declare (type (or symbol list) face))
-                 (when (symbolp face)
-                    (setf face (list face)))
-                 (let* ((gmsm2 (car (last face)))
-                        (dgop-ext (nbutlast face))
-                        (dmns2 (finite-ss-find-gmsm table gmsm2 0 dmns)))
-                    (declare
-                       (symbol gmsm2)
-                       (list dgop-ext)
-                       (type (or fixnum null) dmns2))
-                    (unless dmns2
-                       (error "In BUILD-FINITE-SS, the face ~A is absent." gmsm2))
-                    (when (zerop (length dgop-ext))
-                       (setf dgop-ext (nreverse (<a-b< dmns2 (1- dmns)))))
-                    (unless (= (+ (length dgop-ext) dmns2 1) dmns)
-                       (error "In BUILD-FINITE-SS, the face ~A has a wrong dimension."
-                          (append dgop-ext (list gmsm2))))
-                    (absm (dgop-ext-int dgop-ext) gmsm2))))
-            (setf (info-faces rslt)
-                  (map 'simple-vector #'process-face faces))
-            (setf (info-dffr rslt)
-                  (apply #'nterm-add #'s-cmpr (1- dmns)
-                     (do ((rslt +empty-list+)
-                          (faces (info-faces rslt))
-                          (indx dmns (1- indx)))
-                         ((minusp indx) rslt)
-                        (declare
-                           (list rslt)
-                           (simple-vector faces)
-                           (fixnum indx))
-                        (let ((face (svref faces indx)))
-                           (declare (type absm face))
-                           (unless (degenerate-p face)
-                              (push (term (-1-expt-n indx) (gmsm face))
-                                 rslt))))))
-            rslt))))
-
-(DEFUN FINITE-SS-TABLE (list)
-   (declare (list list))
-   (setf list (cons 0 list))
-   (let* ((bsgn (second list))
-          (pre-table (finite-ss-pre-table list))
-          (table (finite-ss-pre-table-table pre-table)))
-      (declare
-         (symbol bsgn)
-         (list pre-table)
-         (simple-vector table))
-      ;; (vector (vector gmsm-faces-info))
-      (finite-ss-finish-table table bsgn)))
-
-#|
-  (finite-ss-table '(*))
-  (finite-ss-table '(a b))
-  (finite-ss-table '(a b 1 c (b a)))
-  (finite-ss-table '(* 2 s2 3 s3))
-  (finite-ss-table '(s0 s1 s2 1 s01 (s1 s0) s02 (s2 s0) s12 (s2 s1) 2 s012 (s12 s02 s01)))
-  (finite-ss-table '(* 4 s4 ((2 1 0 *))))
-  (finite-ss-table '(* 4 s4 ((1 1 0 *))))
-  (finite-ss-table '(* 1 s (t)))
-  (finite-ss-table '(* 4 s4 ((1 0 *)))))
-|#
-
-(DEFUN FINITE-SS-BASIS (table)
-   (declare (simple-vector table))
-   (flet ((rslt (dmns)
-             (declare (fixnum dmns))
-             (the list
-                (if (< -1 dmns (length table))
-                   (mapcar #'car (svref table dmns))
-                   +empty-list+))))
-      #'rslt))
-
-(DEFUN FINITE-SS-FACE (ind-smst table)
-   (declare
-      (symbol ind-smst)
-      (simple-vector table))
-   (flet ((rslt (indx dmns gmsm)
-           (declare
-              (fixnum indx dmns)
-              (symbol gmsm))
-           (let ((found (find gmsm (svref table dmns) :key #'car)))
-              (unless found
-                 (error "In the finite simplicial set ~A,~@
-                         the simplex ~A is absent in dimension ~D." (eval ind-smst) gmsm dmns))
-              (svref (info-faces found) indx))))
-      #'rslt))
-
-(DEFUN FINITE-SS-DFFR-INTR (ind-smst table)
-   (declare
-      (symbol ind-smst)
-      (simple-vector table))
-   (flet ((rslt (dmns gmsm)
-           (declare
-              (fixnum dmns)
-              (symbol gmsm))
-           (let ((found (find gmsm (svref table dmns) :key #'car)))
-              (unless found
-                 (error "In the finite simplicial set ~A,~@
-                         the simplex ~A is absent in dimension ~D." (eval ind-smst) gmsm dmns))
-              (info-dffr found))))
-      #'rslt))
-
-(DEFUN BUILD-FINITE-SS (list)
-  (declare (list list))
-  (let ((bsgn (first list))
-        (table (finite-ss-table list))
-        (ind-smst (gensym)))
-    (declare
-     (symbol bsgn ind-smst)
-     (simple-vector table))
-    ;;  (vector (vector gmsm-faces-info))
-    (let ((rslt (simplicial-set
-                 :cmpr #'s-cmpr
-                 :basis (finite-ss-basis table)
-                 :bsgn bsgn
-                 :face (finite-ss-face ind-smst table)
-                 :dffr-intr (finite-ss-dffr-intr ind-smst table)
-                 :dffr-strt :gnrt
-                 :dfnt `(build-finite-ss ,list))))
-      (set ind-smst rslt)
-      (unless (check-smst rslt 0 (length table))
-        ;; ???            (pop *k-list*)
-        ;; ???            (pop *k-list*)
-        (return-from build-finite-ss nil))
-      rslt)))
-
-#|
-  (cat-init)
-  (setf tr (build-finite-ss '(s0 s1 s2
-                            1 s01 (s1 s0) s02 (s2 s0) s12 (s2 s1)
-                            2 s012 (s12 s02 s01))))
-  (cmpr tr 's01 's02)
-  (basis tr 2)
-  (bsgn tr)
-  (face tr 1 2 's012)
-  (? tr 2 's012)
-  (? tr *)
-  (inspect tr)
-  (mapcar #'(lambda (s) (length (eval s))) *k-list*)
-  (setf tr (build-finite-ss '(s0 s1 s2
-                            1 s01 (s1 s1) s02 (s2 s0) s12 (s2 s1)
-                            2 s012 (s12 s02 s01))))
-  (mapcar #'(lambda (s) (length (eval s))) *k-list*))
-|#
-
-(DEFUN SPHERE-CMPR (gmsm1 gmsm2)
-   (declare (ignore gmsm1 gmsm2))
-   (the cmpr :equal))
-
-(DEFUN SPHERE-BASIS (dmns)
-   (declare (fixnum dmns))
-   (let ((fund-gmsm (intern (format nil "S~D" dmns))))
-      (declare (symbol fund-gmsm))
-      (flet ((rslt (dmns2)
-                (declare (fixnum dmns2))
-                (cond ((zerop dmns2)
-                       (list '*))
-                      ((= dmns2 dmns)
-                       (list fund-gmsm))
-                      (t
-                         +empty-list+))))
-         (the basis #'rslt))))
-
-(DEFUN SPHERE-FACE (dmns)
-   (declare (fixnum dmns))
-   (let ((face (absm (mask (1- dmns)) '*)))
-      (declare (type absm absm))
-      (flet ((rslt (indx dmns2 gmsm)
-                (declare (ignore indx dmns2 gmsm))
-                (the absm face)))
-         #'rslt)))
-
-(DEFUN SPHERE (dmns)
-  (declare (fixnum dmns))
-  (unless (plusp dmns)
-    (error "In SPHERE, the dimension ~D should be positive." dmns))
-  (unless (< dmns +maximal-dimension+)
-    (error "In SPHERE, the dimension ~D should be < ~D."
-      dmns +maximal-dimension+))
-  (the simplicial-set
-    (let ((rslt (simplicial-set
-                 :cmpr #'sphere-cmpr
-                 :basis (sphere-basis dmns)
-                 :bsgn '*
-                 :face (sphere-face dmns)
-                 :dffr-intr #'zero-dffr-intr
-                 :dffr-strt :cmbn
-                 :dfnt `(sphere ,dmns))))
-      (declare (type simplicial-set rslt))
-      (setf (slot-value (dffr rslt) 'dfnt)
-        `(zero-mrph ,rslt ,rslt -1))
-      rslt)))
-
-#|
-  (cat-init)
-  (setf s3 (sphere 3))
-  (funcall (cmpr s3) 's3 's3)
-  (dotimes (i 5)
-     (print (funcall (basis s3) i)))
-  (mapcar #'(lambda (i) (funcall (face s3) i 3 's3)) (<a-b> 0 3))
-  (? s3 3 's3)
-  (smst (idnm s3))
-  (chcm (idnm s3))
-  (setf d (dffr s3))
-  (add d d))
-|#
-
-(DEFUN SPHERE-WEDGE-BASIS (dmns-list)
-   (declare (list dmns-list))
-   (flet ((rslt (dmns)
-             (declare (fixnum dmns))
-             (when (zerop dmns)
-                (return-from rslt '(*)))
-             (do ((i (count dmns dmns-list) (1- i))
-                  (basis +empty-list+
-                         (cons (intern (format nil "S~D-~D" dmns i))
-                               basis)))
-                 ((zerop i) basis)
-                (declare
-                   (fixnum i)
-                   (list basis)))))
-      (the basis #'rslt)))
-
-(DEFUN SPHERE-WEDGE-FACE (indx dmns gmsm)
-   (declare
-      (ignore indx gmsm)
-      (fixnum dmns))
-   (the absm
-      (absm (mask (1- dmns)) '*)))
-
-(DEFUN SPHERE-WEDGE (&rest dmns-list)
-  (declare (list dmns-list))
-  (the simplicial-set
-    (let ((rslt (simplicial-set
-                 :cmpr #'s-cmpr
-                 :bsgn '*
-                 :basis (sphere-wedge-basis dmns-list)
-                 :face #'sphere-wedge-face
-                 :dffr-intr #'zero-dffr-intr
-                 :dffr-strt :cmbn
-                 :dfnt `(sphere-wedge ,@dmns-list))))
-      (declare (type simplicial-set rslt))
-      (setf (slot-value (dffr rslt) 'dfnt)
-        `(zero-mrph ,rslt ,rslt -1))
-      rslt)))
-
-#|
-  (cat-init)
-  (setf w (sphere-wedge 3 2 3))
-  (funcall (cmpr w) 's3-1 's3-2)
-  (dotimes (i 5) (print (funcall (basis w) i)))
-  (funcall (face w) 2 3 's3-1)
-  (gnrt-? (dffr w) 3 's3-2))
-|#
-
-(DEFUN MOORE-CMPR (gmsm1 gmsm2)
-   (declare (ignore gmsm1 gmsm2))
-   (the cmpr :equal))
-
-(DEFUN MOORE-BASIS (dmns)
-   (declare (fixnum dmns))
-   (let ((lgmsm1 (list (intern (format nil "M~D" dmns))))
-         (lgmsm2 (list (intern (format nil "N~D" (1+ dmns))))))
-      (declare (symbol gmsm1 gmsm2))
-      (flet ((rslt (dmns2)
-                (declare (fixnum dmns2))
-                (cond ((zerop dmns2) '(*))
-                      ((= dmns dmns2) lgmsm1)
-                      ((= (1+ dmns) dmns2) lgmsm2)
-                      (t +empty-list+))))
-         (the basis #'rslt))))
-
-(DEFUN MOORE-FACE (pii dmns)
-   (declare (fixnum pii dmns))
-   (let ((face (absm 0 (intern (format nil "M~D" dmns))))
-         (bsgn1 (absm (mask (1- dmns)) '*))
-         (bsgn2 (absm (mask dmns) '*))
-         (2pii (ash pii 1)))
-      (declare
-         (type absm face)
-         (type absm bsgn1 bsgn2)
-         (fixnum 2pii))
-      (flet ((rslt (indx dmns2 gmsm)
-                (declare
-                   (fixnum indx dmns2)
-                   (ignore gmsm))
-                (the absm
-                   (if (= dmns dmns2)
-                      bsgn1
-                      (if (oddp indx)
-                         bsgn2
-                         (if (< indx 2pii)
-                            face
-                            bsgn2))))))
-         (the face #'rslt))))
-
-(DEFUN MOORE-DFFR-INTR (pii dmns)
-   (declare (fixnum pii dmns))
-   (let ((1+dmns (1+ dmns))
-         (gmsm1 (intern (format nil "M~D" dmns))))
-      (declare
-         (fixnum 1+dmns)
-         (type symbol gmsm1))
-      (flet ((rslt (cmbn)
-                (declare
-                   (type cmbn cmbn))
-                (with-cmbn (degr list) cmbn
-                   (unless list
-                      (return-from rslt (zero-cmbn (1- (cmbn-degr cmbn)))))
-                   (if (= degr 1+dmns)
-                      (term-cmbn dmns (* (cffc (first list)) pii) gmsm1)
-                      (zero-cmbn (1- (cmbn-degr cmbn)))))))
-         (the intr #'rslt))))
-
-(DEFUN MOORE (pii dmns)
-  (declare (fixnum pii dmns))
-  (the simplicial-set
-    (simplicial-set
-     :bsgn '*
-     :cmpr #'moore-cmpr
-     :basis (moore-basis dmns)
-     :face (moore-face pii dmns)
-     :dffr-intr (moore-dffr-intr pii dmns)
-     :dffr-strt :cmbn
-     :dfnt `(moore ,pii ,dmns))))
-
-#|
-  (cat-init)
-  (setf m4 (moore 2 4))
-  (cmpr m4 'n5 'n5)
-  (dotimes (i 7)
-     (print (basis m4 i)))
-  (mapcar #'(lambda (i) (face m4 i 5 'n5)) (<a-b> 0 5))
-  (? m4 4 'm4)
-  (? m4 5 'n5))
-|#
-
-(DEFUN R-PROJ-SPACE-CMPR (gmsm1 gmsm2)
-   (declare (ignore gmsm1 gmsm2))
-   (the cmpr :equal))
-
-(DEFUN R-PROJ-SPACE-BASIS (k &optional (l 15))
-   (declare (fixnum k))
-   (flet ((rslt (dmns)
-             (declare (fixnum dmns))
-             (the list
-                (if (or (minusp dmns)
-                        (< 0 dmns k)
-		        (>= dmns l))
-                   +empty-list+
-                   (list dmns)))))
-      (the basis #'rslt)))
-
-(DEFUN R-PROJ-SPACE-FACE (k)
-   (declare (fixnum k))
-   (flet ((rslt (indx dmns gmsm)
-           (declare
-	      (fixnum indx dmns)
-	      (ignore gmsm))
-           (if (<= dmns k)
-              (absm (mask (1- dmns)) 0)
-              (if (or (zerop indx)
-                      (= indx dmns))
-                 (absm 0 (1- dmns))
-                 (if (= dmns (1+ k))
-                    (absm (mask (1- dmns)) 0)
-                    (absm (2-exp (1- indx)) (- dmns 2)))))))
-      (the face #'rslt)))
-
-(DEFUN R-PROJ-SPACE-DFFR-INTR (k)
-   (declare (fixnum k))
-   (flet ((rslt (cmbn)
-           (declare (type cmbn cmbn))
-           (with-cmbn (degr list) cmbn
-              (unless list
-                 (return-from rslt (zero-cmbn (1- degr))))
-              (if (<= degr k)
-                 (zero-cmbn (1- degr))
-                 (if (evenp degr)
-                    (make-cmbn
-                       :degr (1- degr)
-                       :list (list (term (* 2 (-cffc list)) (1- degr))))
-                    (zero-cmbn (1- degr)))))))
-      (the intr #'rslt)))
-
-(DEFUN R-PROJ-SPACE (&optional (k 1) (l 15))
-  (declare (fixnum k))
-  (the simplicial-set
-    (simplicial-set
-     :cmpr #'R-proj-space-cmpr
-     :basis (R-proj-space-basis k l)
-     :bsgn 0
-     :face (R-proj-space-face k)
-     :dffr-intr (R-proj-space-dffr-intr k)
-     :dffr-strt :cmbn
-     :dfnt `(R-proj-space ,k))))
-
-#|
-  (cat-init)
-  (setf p (R-proj-space))
-  (basis p 4)
-  (dotimes (i 5)
-     (print (face p i 4 4)))
-  (dotimes (i 5)
-     (print (? p i i)))
-  (setf dd (cmps p p))
-  (dotimes (i 6)
-     (print (? dd i i)))
-  (setf p (R-proj-space 3))
-  (dotimes (i 7)
-     (print (basis p i)))
-  (dotimes (i 5)
-     (print (face p i 4 4)))
-  (dotimes (i 7)
-     (print (? p i i)))
-  (setf dd (cmps p p))
-  (dotimes (i 7)
-     (print (? dd i i)))
-|#
diff --git a/archive/Kenzo-2/Kenzo-2-Acl5/suspensions.cl b/archive/Kenzo-2/Kenzo-2-Acl5/suspensions.cl
deleted file mode 100644
index 8997ff1..0000000
--- a/archive/Kenzo-2/Kenzo-2-Acl5/suspensions.cl
+++ /dev/null
@@ -1,321 +0,0 @@
-;;;  SUSPENSIONS  SUSPENSIONS  SUSPENSIONS  SUSPENSIONS
-;;;  SUSPENSIONS  SUSPENSIONS  SUSPENSIONS  SUSPENSIONS
-;;;  SUSPENSIONS  SUSPENSIONS  SUSPENSIONS  SUSPENSIONS
-
-(IN-PACKAGE "CAT")
-
-(PROVIDE "suspensions")
-
-(DEFUN SUSPENSION-CMPR (cmpr)
-  (declare (type cmprf cmpr))
-  (flet ((rslt (gnrt1 gnrt2)
-	   (declare (type gnrt gnrt1 gnrt2))
-	   (if (eq gnrt1 :s-bsgn)
-	       :equal
-	     (funcall cmpr gnrt1 gnrt2))))
-    (the cmprf #'rslt)))
-
-#|
-  (setf cc (deltab))
-  (setf cmpr (suspension-cmpr (cmpr cc)))
-  (funcall cmpr :s-bsgn :s-bsgn)
-  (funcall cmpr 6 5)
-|#
-
-(DEFUN SUSPENSION-BASIS (basis)
-  (declare (type basis basis))
-  (when (eq basis :locally-effective)
-    (return-from suspension-basis :locally-effective))
-  (flet ((rslt (degr)
-	   (declare (fixnum degr))
-	   (case degr
-	     (0 (list :s-bsgn))
-	     (1 +empty-list+)
-	     (otherwise (funcall basis (1- degr))))))
-    (the basis #'rslt)))
-
-#|
-  (setf cc (sphere 2))
-  (setf basis (suspension-basis (basis cc)))
-  (dotimes (i 6)
-    (print (funcall basis i)))
-  (suspension-basis :locally-effective)
-|#
-
-(DEFUN SUSPENSION-DFFR-INTR (dffr)
-  (declare (type morphism dffr))
-  (flet ((rslt (cmbn)
-	   (declare (type cmbn cmbn))
-	   (with-cmbn (degr list) cmbn
-	     (decf degr)
-	     (if (<= degr 0)
-		 (zero-cmbn degr)
-	       (make-cmbn :degr degr
-			  :list (cmbn-list
-				 (cmbn-? dffr
-				   (make-cmbn :degr degr
-					      :list list))))))))
-    (the intr #'rslt)))
-
-#|
-  (setf cc (deltab))
-  (setf intr (suspension-dffr-intr (dffr cc)))
-  (funcall intr (cmbn 0 3 :s-bsgn))
-  (funcall intr (cmbn 3 66 7))
-|#
-
-(DEFUN SUSPENSION (obj &optional (n 1))
-  (declare (type (or chain-complex morphism reduction
-		     equivalence) obj)
-	   (fixnum n))
-  (if (= n 0)
-      obj
-    (suspension-1 (suspension obj (1- n)))))    
-
-(DEFMETHOD SUSPENSION-1 ((chcm chain-complex))
-  (the chain-complex
-    (with-slots (cmpr basis dffr) chcm
-      (chain-complex
-        :cmpr (suspension-cmpr cmpr)
-	:basis (suspension-basis basis)
-	:bsgn :s-bsgn
-	:dffr-intr (suspension-dffr-intr dffr)
-	:dffr-strt :cmbn
-	:dfnt `(suspension ,chcm)))))
-
-#|
-  (cat-init)
-  (setf cc (deltab))
-  (setf scc (suspension cc))
-  (cmpr scc 7 11)
-  (basis scc 3)  ;; error
-  (bsgn scc)
-  (? scc 3 11)
-  (setf scc (suspension cc 2))
-  (? scc 4 11)
-|#
-
-(DEFUN SUSPENSION-CPRD-INTR (cmbn)
-  (declare (type cmbn cmbn))
-  (the cmbn
-    (with-cmbn (degr list) cmbn
-      (if (zerop degr)
-	  (make-cmbn :degr 0
-		     :list (if list
-			       (list (term (-cffc list)
-					   (tnpr 0 :s-bsgn
-						 0 :s-bsgn)))
-			     +empty-list+))
-	(make-cmbn :degr degr
-		   :list (let ((list1 +empty-list+)
-			       (list2 +empty-list+))
-			   (declare (list list1 list2))
-			   (mapc
-			    #'(lambda (term)
-				(declare (type term term))
-				(with-term (cffc gnrt) term
-				  (push (term cffc
-					      (tnpr 0 :s-bsgn
-						    degr gnrt))
-					list1)
-				  (push (term cffc
-					      (tnpr degr gnrt
-						    0 :s-bsgn))
-					list2)))
-			    list)
-			   (nreconc list1 (nreverse list2))))))))
-
-#|
-(suspension-cprd-intr (cmbn 0))
-(suspension-cprd-intr (cmbn 0 5 :s-bsgn))
-(suspension-cprd-intr (cmbn 3 4 7 5 11))
-|#
-
-(DEFMETHOD SUSPENSION-1 ((clgb coalgebra))
-  (the coalgebra
-    (let ((irslt (call-next-method)))
-      (declare (type (or chain-complex coalgebra) irslt))
-      (when (typep irslt 'coalgebra)
-        (return-from suspension-1 irslt))
-      (change-chcm-to-clgb irslt :cprd-intr #'suspension-cprd-intr
-                           :cprd-strt :cmbn)
-      (setf (slot-value irslt 'dfnt) `(suspension ,clgb))
-      (setf (slot-value (slot-value irslt 'cprd) 'dfnt)
-        `(coproduct ,irslt))
-      irslt)))
-
-#|
-  (cat-init)
-  (setf coal (deltab))
-  (setf scoal (suspension coal))
-  (setf scoal (suspension coal))
-  (? scoal 3 7)
-  (cprd scoal 3 7)
-|#
-
-(DEFUN SUSPENSION-FACE (face)
-  (declare (type face face))
-  (flet ((rslt (indx dmns gmsm)
-	   (declare
-	     (fixnum indx dmns)
-	     (type gmsm gmsm))
-	   (assert (> dmns 1))
-	   (if (= indx dmns)
-	       (absm (mask (1- dmns)) :s-bsgn)
-	     (let ((irslt (funcall face indx (1- dmns) gmsm)))
-	       (declare (type absm irslt))
-	       (if (= (dgop irslt) (mask (- dmns 2)))
-		   (absm (mask (1- dmns)) :s-bsgn)
-		 irslt)))))
-     (the face #'rslt)))
-
-#|
-  (setf ss (deltab))
-  (setf face (suspension-face (face ss)))
-  (funcall face 4 4 15)
-  (funcall face 0 4 15)
-  (check-faces #'f-cmpr face 4 15)
-  (check-faces #'f-cmpr face 3 7)
-  (check-faces #'f-cmpr face 2 3)
-  (setf m (moore 2 3))
-  (setf face (suspension-face (face m)))
-  (dotimes (i 5) (print (funcall face i 4 'm3)))
-  (dotimes (i 6) (print (funcall face i 5 'mm4)))
-  (check-faces #'s-cmpr face 4 'm3)
-  (check-faces #'s-cmpr face 5 'mm4)
-|#
-
-(DEFMETHOD SUSPENSION-1 ((smst simplicial-set))
-  (the simplicial-set
-    (let ((irslt (call-next-method)))
-      (declare (type coalgebra irslt))
-      (when (typep irslt 'simplicial-set)
-	(return-from suspension-1 irslt))
-      (change-class irslt 'simplicial-set)
-      (setf (slot-value irslt 'face)
-	    (suspension-face (face smst)))
-      (setf (slot-value (slot-value irslt 'cprd) 'dfnt)
-	    `(diagonal ,irslt))
-      irslt)))
-
-#|
-  (cat-init)
-  (setf d (deltab))
-  (setf sd (suspension d))
-  (setf sd (suspension d))
-  (inspect sd)
-  (? sd 3 7)
-  (cprd sd 3 7)
-  (face sd 3 3 7)
-  (face sd 2 3 7)
-  (setf m (moore 2 1))
-  (setf sm (suspension m))
-  (homology sm 0 5)
-  (setf ssm (suspension sm))
-  (homology ssm 0 6)
-|#
-
-(DEFUN SUSPENSION-INTR (mrph)
-  (declare (type morphism mrph))
-  (let ((mdegr (degr mrph)))
-    (declare (fixnum mdegr))
-    (flet ((rslt (cmbn)
-	     (declare (type cmbn cmbn))
-	     (with-cmbn (cdegr list) cmbn
-	       (when (zerop cdegr)
-		 (return-from rslt
-		   (if (zerop mdegr)
-		       cmbn
-		     (zero-cmbn (+ mdegr cdegr)))))
-	       (make-cmbn :degr (+ mdegr cdegr)
-			  :list (cmbn-list
-				 (cmbn-? mrph (make-cmbn :degr (1- cdegr)
-							 :list list)))))))
-    (the intr #'rslt))))
-
-#|
-  (setf f (idnt-mrph (deltab)))
-  (setf sf (suspension-intr f))
-  (funcall sf (cmbn 0 3 :s-bsgn))
-  (funcall sf (cmbn 2 4 3))
-  (setf d (dffr (deltab)))
-  (setf sd (suspension-intr d))
-  (funcall sd (cmbn 0 3 :s-bsgn))
-  (funcall sd (cmbn 2 4 3))
-  (funcall sd (cmbn 3 4 7))
-|#
-	 
-(DEFMETHOD SUSPENSION-1 ((mrph morphism))
-  (the morphism
-    (let ((dfnt (dfnt mrph)))
-      (declare (list dfnt))
-      (when (eq (first dfnt) 'zero-mrph)
-	(return-from suspension-1
-	  (zero-mrph (suspension (sorc mrph))
-		     (suspension (trgt mrph))
-		     (degr mrph))))
-      (when (eq (first dfnt) 'idnt-mrph)
-	(return-from suspension-1
-	  (idnt-mrph (suspension (sorc mrph)))))
-      (morphism
-       :sorc (suspension (sorc mrph))
-       :trgt (suspension (trgt mrph))
-       :degr (degr mrph)
-       :intr (suspension-intr mrph)
-       :strt :cmbn
-       :dfnt `(suspension ,mrph)))))
-
-#|
-  (setf f (idnt-mrph (deltab)))
-  (setf sf (suspension f))
-  (? sf (cmbn 0 3 :s-bsgn))
-  (? sf (cmbn 2 4 3))
-  (setf d (dffr (deltab)))
-  (setf sd (suspension d))
-  (? sd (cmbn 0 3 :s-bsgn))
-  (? sd (cmbn 2 4 3))
-  (? sd (cmbn 3 4 7))
-|#
-
-(DEFMETHOD SUSPENSION-1 ((rdct reduction))
-  (the reduction (progn
-    (when (eq (first (dfnt rdct)) 'trivial-rdct)
-      (return-from suspension-1
-	(trivial-rdct (suspension (second (dfnt rdct))))))
-    (reduction
-      :f (suspension (f rdct))
-      :g (suspension (g rdct))
-      :h (suspension (h rdct))
-      :dfnt `(suspension ,rdct)))))
-
-#|
-  (setf rdct (ez (deltab) (deltab)))
-  (setf srdct (suspension rdct))
-  (pre-check-rdct srdct)
-  (setf *tc* (cmbn 4 1 (crpr 0 15 0 15)))
-  (setf *bc* (cmbn 4 1 (tnpr 0 1 3 15)
-                     5 (tnpr 1 3 2 7)
-                     10 (tnpr 2 7 1 3)
-                     100 (tnpr 3 15 0 1)))
-  (check-rdct)
-|#
-
-(DEFMETHOD SUSPENSION-1 ((eqvl equivalence))
-  (the equivalence (progn
-    (when (eq (first (dfnt eqvl)) 'trivial-eqvl)
-      (return-from suspension-1
-	(trivial-eqvl (suspension (second (dfnt eqvl))))))
-    (equivalence
-     :lrdct (suspension (lrdct eqvl))
-     :rrdct (suspension (rrdct eqvl))
-     :dfnt `(suspension ,eqvl)))))
-
-(DEFMETHOD SEARCH-EFHM (suspension (dfnt (eql 'suspension)))
-  (declare (type chain-complex suspension))
-  (suspension (efhm (second (dfnt suspension)))))
-
-#|
-  (setf sk (suspension (k-z 2)))
-  (homology sk 0 10)
-|#
-  
\ No newline at end of file
diff --git a/archive/Kenzo-2/Kenzo-2-Acl5/tensor-products.cl b/archive/Kenzo-2/Kenzo-2-Acl5/tensor-products.cl
deleted file mode 100644
index eec5b67..0000000
--- a/archive/Kenzo-2/Kenzo-2-Acl5/tensor-products.cl
+++ /dev/null
@@ -1,354 +0,0 @@
-;;;  TENSOR-PRODUCTS  TENSOR-PRODUCTS  TENSOR-PRODUCTS  TENSOR-PRODUCTS  TENSOR-PRODUCTS
-;;;  TENSOR-PRODUCTS  TENSOR-PRODUCTS  TENSOR-PRODUCTS  TENSOR-PRODUCTS  TENSOR-PRODUCTS
-;;;  TENSOR-PRODUCTS  TENSOR-PRODUCTS  TENSOR-PRODUCTS  TENSOR-PRODUCTS  TENSOR-PRODUCTS
-
-(IN-PACKAGE "CAT")
-
-(PROVIDE "tensor-products")
-
-(DEFVAR *TNPR-WITH-DEGREES* nil)
-
-(DEFMETHOD PRINT-KEYCONS ((car (eql :tnpr)) cdr stream)
-   (declare
-      (cons cdr)
-      (stream stream))
-   (the (eql t)
-      (progn
-         (setf cdr (cons car cdr))
-         (with-tnpr (degr1 gnrt1 degr2 gnrt2) cdr
-            (format stream
-               "<TnPr~:[~*~; ~D~] ~A~:[~*~; ~D~] ~A>"
-               *tnpr-with-degrees* degr1 gnrt1
-               *tnpr-with-degrees* degr2 gnrt2))
-         t)))
-
-#|
-  (tnpr 2 'a 3 'b)
-  (setf *tnpr-with-degrees* t)    
-  (tnpr 2 'a 3 'b)
-  (setf *tnpr-with-degrees* nil)
-|#
-
-(DEFUN 2CMBN-TNPR (cmbn1 cmbn2)
-   (declare (type cmbn cmbn1 cmbn2))
-   (the cmbn
-      (with-cmbn (degr1 list1) cmbn1
-      (with-cmbn (degr2 list2) cmbn2
-         (make-cmbn
-            :degr (+ degr1 degr2)
-            :list (mapcan
-                     #'(lambda (term1)
-                          (declare (type term term1))
-                          (the list
-                             (with-term (cffc1 gnrt1) term1
-                                (mapcar
-                                   #'(lambda (term2)
-                                        (declare (type term term2))
-                                        (the term
-                                           (term
-                                              (* cffc1 (cffc term2))
-                                              (tnpr degr1 gnrt1 degr2 (gnrt term2)))))
-                                   list2))))
-                     list1))))))
-#|
-  (setf *tnpr-with-degrees* t)
-  (2cmbn-tnpr (cmbn 2 3 'a 4 'b -5 'c) (cmbn 3 4 'x -3 'y 2 'z)))
-|#
-
-(DEFUN TNSR-PRDC-CMPR (cmpr1 cmpr2)
-   (declare (type cmprf cmpr1 cmpr2))
-   (flet ((rslt (tnpr1 tnpr2)
-             (declare (type tnpr tnpr1 tnpr2))
-             (let ((left-cons-1 (cadr tnpr1))
-                   (left-cons-2 (cadr tnpr2)))
-                (declare (cons left-cons-1 left-cons-2))
-                (lexico
-                   (f-cmpr (car left-cons-1) (car left-cons-2))
-                   (funcall cmpr1 (cdr left-cons-1) (cdr left-cons-2))
-                   (funcall cmpr2 (gnrt2 tnpr1) (gnrt2 tnpr2))))))
-      (the cmprf #'rslt)))
-
-#|
-  (setf cmpr (tnsr-prdc-cmpr #'s-cmpr #'s-cmpr))
-  (funcall cmpr (tnpr 2 'a 3 'b) (tnpr 3 'a 2 'b))
-  (funcall cmpr (tnpr 3 'a 2 'b) (tnpr 2 'a 3 'b))
-  (funcall cmpr (tnpr 2 'a 3 'b) (tnpr 2 'b 3 'b))
-  (funcall cmpr (tnpr 2 'b 3 'b) (tnpr 2 'a 3 'b))
-  (funcall cmpr (tnpr 2 'a 3 'a) (tnpr 2 'a 3 'b))
-  (funcall cmpr (tnpr 2 'a 3 'c) (tnpr 2 'a 3 'b))
-  (funcall cmpr (tnpr 2 'a 3 'b) (tnpr 2 'a 3 'b)))
-|#
-
-(DEFUN TNSR-PRDC-BASIS (basis1 basis2)
-   (declare (type basis basis1 basis2))
-   (when (or (eq basis1 :locally-effective)
-             (eq basis2 :locally-effective))
-      (return-from tnsr-prdc-basis :locally-effective))
-   (flet ((rslt (degr)
-             (declare (fixnum degr))
-             (the list
-                (progn
-                   (when (minusp degr)
-                      (return-from rslt +empty-list+))
-                   (mapcan
-                      #'(lambda (degr1)
-                           (declare (fixnum degr1))
-                           (let* ((basis1 (funcall basis1 degr1))
-                                  (degr2 (- degr degr1))
-                                  (basis2 (funcall basis2 degr2)))
-                              (declare
-                                 (fixnum degr2)
-                                 (list basis1 basis2))
-                              (the list
-                                 (mapcan
-                                    #'(lambda (gnrt1)
-                                         (declare (type gnrt gnrt1))
-                                         (the list
-                                            (mapcar
-                                               #'(lambda (gnrt2)
-                                                    (declare (type gnrt gnrt2))
-                                                    (the tnpr
-                                                       (tnpr degr1 gnrt1 degr2 gnrt2)))
-                                               basis2)))
-                                    basis1))))
-                      (<a-b> 0 degr))))))
-      (the basis #'rslt)))
-
-#|
-  (defun bas (degr)
-     (case degr
-        (0 '(a b c))
-        (1 '(d))
-        (2 nil)
-        (3 '(x y))))
-  (setf bas (tnsr-prdc-basis #'bas #'bas))
-  (dotimes (i 8)
-     (print (funcall bas i))))
-|#
-
-(DEFUN TNSR-PRDC-DFFR-INTR (dffr1 dffr2)
-   (declare (type morphism dffr1 dffr2))
-   (flet ((rslt (degr tnpr)
-             (declare
-                (fixnum degr)
-                (type tnpr tnpr))
-             (the cmbn
-                (with-tnpr (degr1 gnrt1 degr2 gnrt2) tnpr
-                   (let ((degr1-1 (1- degr1))
-                         (degr2-1 (1- degr2))
-                         (sign (oddp degr1))
-                         (list1 (cmbn-list (gnrt-? dffr1 degr1 gnrt1)))
-                         (list2 (cmbn-list (gnrt-? dffr2 degr2 gnrt2))))
-                      (declare
-                         (fixnum degr1-1 degr2-1 sign)
-                         (list list1 list2))
-                      (make-cmbn
-                         :degr (1- degr)
-                         :list (nconc
-                                  (mapcar
-                                     #'(lambda (term1)
-                                          (declare (type term term1))
-                                          (with-term (cffc1 gnrt1) term1
-                                             (term cffc1
-                                                (tnpr degr1-1 gnrt1 degr2 gnrt2))))
-                                     list1)
-                                  (mapcar
-                                     #'(lambda (term2)
-                                          (declare (type term term2))
-                                          (with-term (cffc2 gnrt2) term2
-                                             (term (if sign (- cffc2) cffc2)
-                                                (tnpr degr1 gnrt1 degr2-1 gnrt2))))
-                                     list2))))))))
-      (the intr #'rslt)))
-
-#|
-  (cat-init)
-  (setf chcm (chain-complex :cmpr #'s-cmpr :dffr-strt :gnrt :dfnt '(test-1)))
-  (setf dffr (morphism :sorc chcm :trgt chcm :degr -1
-                         :intr #'(lambda (degr gnrt)
-                                    (ecase gnrt
-                                       (a (cmbn (1- degr) 2 'd1a -3 'd2a))
-                                       (b (cmbn (1- degr) 3 'd1b -4 'd2b))))
-                         :strt :gnrt :dfnt '(test-2)))
-  (setf rslt (tnsr-prdc-dffr-intr dffr dffr))
-  (funcall rslt 4 (tnpr 2 'a 2 'b))
-  (funcall rslt 5 (tnpr 3 'a 2 'b))
-  (funcall rslt 5 (tnpr 2 'a 3 'b))
-  (funcall rslt 6 (tnpr 3 'a 3 'b)))
-|#
-
-(DEFMETHOD TNSR-PRDC ((chcm1 chain-complex) (chcm2 chain-complex))
-  (the chain-complex
-    (with-slots ((cmpr1 cmpr) (basis1 basis) (dffr1 dffr)) chcm1
-      (declare
-       (type cmprf cmpr1)
-       (type basis basis1)
-       (type morphism dffr1))
-      (with-slots ((cmpr2 cmpr) (basis2 basis) (dffr2 dffr)) chcm2
-        (declare
-         (type cmprf cmpr2)
-         (type basis basis2)
-         (type morphism dffr2))
-        (let ((rslt
-               (chain-complex
-                :cmpr (tnsr-prdc-cmpr cmpr1 cmpr2)
-                :basis (tnsr-prdc-basis basis1 basis2)
-                :dffr-intr (tnsr-prdc-dffr-intr dffr1 dffr2)
-                :dffr-strt :gnrt
-                :dfnt `(tnsr-prdc ,chcm1 ,chcm2))))
-          (declare (type chain-complex rslt))
-          (if (and (slot-boundp chcm1 'bsgn)
-                   (slot-boundp chcm2 'bsgn))
-              (setf (slot-value rslt 'bsgn)
-                (tnpr 0 (bsgn chcm1) 0 (bsgn chcm2)))
-            (slot-makunbound rslt 'bsgn))
-          rslt)))))
-
-#|
-  (setf dd (tnsr-prdc (delta 2) (delta 3)))
-  (cmpr dd (tnpr 2 7 2 11) (tnpr 2 7 2 14))
-  (basis dd 3)
-  (? dd 4 (tnpr 2 7 2 14))
-  (? dd 3 (tnpr 1 6 2 14))
-  (? dd (? dd 4 (tnpr 2 7 2 14)))
-  (? dd (? dd 3 (tnpr 1 6 2 14))))
-|#
-
-(DEFUN TNSR-PRDC-INTR (mrph1 mrph2)
-   (declare
-      (type morphism mrph1 mrph2))
-   (let ((mrph2-sign (oddp (degr mrph2))))
-      (declare (type boolean mrph2-sign))         
-      (flet ((rslt (degr tnpr)
-              (declare
-                 (ignore degr)
-                 (type tnpr tnpr))
-              (with-tnpr (degr1 gnrt1 degr2 gnrt2) tnpr
-                 (let ((rslt (2cmbn-tnpr
-                                (gnrt-? mrph1 degr1 gnrt1)
-                                (gnrt-? mrph2 degr2 gnrt2))))
-                    (declare (type cmbn rslt))
-                    (when (and mrph2-sign
-                               (oddp degr1))
-                       (mapc #'(lambda (term)
-                                  (declare (type term term))
-                                  (setf (the fixnum (cffc term))
-                                        (the fixnum (- (cffc term)))))
-                          (cmbn-list rslt)))
-                    rslt))))
-         (the intr #'rslt))))
-
-#|
-  (cat-init)
-  (setf chcm (chain-complex :cmpr #'s-cmpr :dffr-strt :gnrt :dfnt '(test-1)))
-  (setf mrph (morphism :sorc chcm :trgt chcm :degr 0
-                         :intr #'(lambda (degr gnrt)
-                                    (ecase gnrt
-                                       (a (cmbn degr 2 'd1a -3 'd2a))
-                                       (b (cmbn degr 3 'd1b -4 'd2b))))
-                         :strt :gnrt :dfnt '(test-2)))
-  (setf rslt (tnsr-prdc-intr mrph mrph))
-  (funcall rslt 6 (tnpr 2 'a 4 'b))
-  (funcall rslt 5 (tnpr 3 'a 2 'b))
-  (setf mrph (morphism :sorc chcm :trgt chcm :degr 1
-                         :intr #'(lambda (degr gnrt)
-                                    (ecase gnrt
-                                       (a (cmbn (1+ degr) 2 'd1a -3 'd2a))
-                                       (b (cmbn (1+ degr) 3 'd1b -4 'd2b))))
-                         :strt :gnrt :dfnt '(test-3)))
-  (setf rslt (tnsr-prdc-intr mrph mrph))
-  (funcall rslt 6 (tnpr 2 'a 4 'b))
-  (funcall rslt 5 (tnpr 3 'a 2 'b)))
-|#
-
-(DEFMETHOD TNSR-PRDC ((mrph1 morphism) (mrph2 morphism))
-  (the morphism
-   (with-slots ((sorc1 sorc) (trgt1 trgt) (degr1 degr)) mrph1
-   (with-slots ((sorc2 sorc) (trgt2 trgt) (degr2 degr)) mrph2
-      (the morphism
-	 (progn
-	   (when (and (eq 'idnt-mrph (first (dfnt mrph1)))
-		      (eq 'idnt-mrph (first (dfnt mrph2))))
-	      (return-from tnsr-prdc
-		 (idnt-mrph (tnsr-prdc sorc1 sorc2))))
-	   (when (or (eq 'zero-mrph (first (dfnt mrph1)))
-		     (eq 'zero-mrph (first (dfnt mrph2))))
-	      (return-from tnsr-prdc
-		 (zero-mrph (tnsr-prdc sorc1 sorc2)
-			    (tnsr-prdc trgt1 trgt2)
-			    (+ degr1 degr2))))
-	   (morphism
-              :sorc (tnsr-prdc sorc1 sorc2)
-	      :trgt (tnsr-prdc trgt1 trgt2)
-	      :degr (+ degr1 degr2)
-	      :intr (tnsr-prdc-intr mrph1 mrph2)
-	      :strt :gnrt
-	      :dfnt `(tnsr-prdc ,mrph1 ,mrph2))))))))
-
-#|
-  (cat-init)
-  (setf d (dffr (delta-infinity)))
-  (setf dd (tnsr-prdc d d))
-  (eq (sorc dd) (tnsr-prdc (delta-infinity) (delta-infinity)))
-  (? dd 5 (tnpr 2 7 3 15))
-  (? dd 5 (tnpr 3 15 2 7))
-  (? dd (? dd 5 (tnpr 2 7 3 15)))
-  (? dd (? dd 5 (tnpr 3 15 2 7)))
-  (setf ddd (cmps dd dd))
-  (? ddd 5 (tnpr 2 7 3 15))
-  (? ddd 5 (tnpr 3 15 2 7))
-|#
-
-(DEFMETHOD TNSR-PRDC ((rdct1 reduction) (rdct2 reduction))
-  (the reduction
-     (progn
-       (when (and (eq 'trivial-rdct (first (dfnt rdct1)))
-		  (eq 'trivial-rdct (first (dfnt rdct2))))
-          (return-from tnsr-prdc
-	     (trivial-rdct (tnsr-prdc (bcc rdct1) (bcc rdct2)))))
-       (with-slots ((tcc1 tcc) (bcc1 bcc) (f1 f) (g1 g) (h1 h)) rdct1
-          (declare
-             (type chain-complex tcc1 bcc1)
-	     (type morphism f1 g1 h1))
-       (with-slots ((tcc2 tcc) (bcc2 bcc) (f2 f) (g2 g) (h2 h)) rdct2
-          (declare
-             (type chain-complex tcc2 bcc2)
-	     (type morphism f2 g2 h2))
-	  (reduction
-	     :f (tnsr-prdc f1 f2)
-	     :g (tnsr-prdc g1 g2)
-	     :h (add
-	         (tnsr-prdc h1 (cmps g2 f2))
-		 (tnsr-prdc (idnt-mrph tcc1) h2))
-	     :dfnt `(tnsr-prdc ,rdct1 ,rdct2)))))))
-
-#|
-  (cat-init)
-  (setf r (ez (delta-infinity) (delta-infinity)))
-  (setf r2 (tnsr-prdc r r))
-  (setf *bc* (cmbn 4 1 (tnpr 2 (tnpr 1 3 1 3) 2 (tnpr 1 3 1 3)))
-        *tc* (cmbn 2 1 (tnpr 1 (crpr 0 3 0 3) 1 (crpr 0 3 0 3))))
-  (pre-check-rdct r2)
-  (check-rdct)
-|#
-
-(DEFMETHOD TNSR-PRDC ((eqvl1 equivalence)
-		      (eqvl2 equivalence))
-  (the equivalence
-     (equivalence
-      :lrdct (tnsr-prdc (lrdct eqvl1) (lrdct eqvl2))
-      :rrdct (tnsr-prdc (rrdct eqvl1) (rrdct eqvl2))
-      :dfnt `(tnsr-prdc ,eqvl1 ,eqvl2))))
-
-(DEFMETHOD SEARCH-EFHM (chcm (dfnt (eql 'tnsr-prdc)))
-  (declare (type chain-complex chcm))
-  (the equivalence
-       (tnsr-prdc (efhm (second (dfnt chcm)))
-		  (efhm (third (dfnt chcm))))))
-
-#|
-(cat-init)
-(setf k (k-z 2))
-(setf k2 (tnsr-prdc k k))
-(homology k2 0 10)
-|#
\ No newline at end of file
diff --git a/archive/Kenzo-2/Kenzo-2-Acl5/test.cl b/archive/Kenzo-2/Kenzo-2-Acl5/test.cl
deleted file mode 100644
index bb81a58..0000000
--- a/archive/Kenzo-2/Kenzo-2-Acl5/test.cl
+++ /dev/null
@@ -1,42 +0,0 @@
-(in-package "CAT")
-(load "file-list")
-(load-cfiles)
-
-(cat-init)
-
-(setf s3 (sphere 3))
-(setf oos3 (loop-space s3 2))
-(homology oos3 5)
-
-(cat-init)
-
-(setf p (r-proj-space 4))
-(setf oop (loop-space p 2))
-(setf faces
-  (list (loop3 0 (loop3 0 'p 1) 2)
-        +null-loop+ +null-loop+ +null-loop+ ))
-(setf doop (disk-pasting oop 3 'D3 faces))
-(setf odoop (loop-space doop))
-(homology odoop 4)
-
-(cat-init)
-
-(setf s3 (sphere 3))
-(setf ch3 (chml-clss s3 3))
-(setf f3 (z-whitehead s3 ch3))
-(setf x4 (fibration-total f3))
-(homology x4 4)
-
-(setf ch4 (chml-clss x4 4))
-(setf f4 (z2-whitehead x4 ch4))
-(setf x5 (fibration-total f4))
-(homology x5 5)
-
-(setf ch5 (chml-clss x5 5))
-(setf f5 (z2-whitehead x5 ch5))
-
-(right-serre-efhm f5)
-
-(setf x6 (fibration-total f5))
-(homology x6 6)
-
diff --git a/archive/Kenzo-2/Kenzo-2-Acl5/various.cl b/archive/Kenzo-2/Kenzo-2-Acl5/various.cl
deleted file mode 100644
index 4cde7e7..0000000
--- a/archive/Kenzo-2/Kenzo-2-Acl5/various.cl
+++ /dev/null
@@ -1,130 +0,0 @@
-;;;  VARIOUS  VARIOUS  VARIOUS  VARIOUS  VARIOUS  VARIOUS
-;;;  VARIOUS  VARIOUS  VARIOUS  VARIOUS  VARIOUS  VARIOUS
-;;;  VARIOUS  VARIOUS  VARIOUS  VARIOUS  VARIOUS  VARIOUS
-
-(IN-PACKAGE "CAT")
-
-(PROVIDE "various")
-
-(DEFCONSTANT +EMPTY-LIST+ '())
-
-(DEFCONSTANT +F-EMPTY-VECTOR+
-   (make-array 0 :element-type 'fixnum))
-
-(DEFCONSTANT +S-EMPTY-VECTOR+
-   #())
-
-(DEFCONSTANT +TRUE+ t)
-
-(DEFCONSTANT +FALSE+ nil)
-
-(DEFUN BINOMIAL-N-P (n p)
-  (declare (fixnum n p))
-  (when (> (2-exp p) n)
-     (setf p (- n p)))
-  (the fixnum
-     (do ((nn n (1- nn))
-	  (pp 1 (1+ pp))
-	  (rslt 1 (/ (* rslt nn) pp)))
-	 ((> pp p) rslt)
-	(declare (fixnum nn pp rslt)))))
-
-#|
-  (dotimes (i 6)
-     (print (binomial-n-p 5 i)))
-  (dotimes (i 6)
-     (print (binomial-p-q (- 5 i) i))))
-|#
-
-(SETF #-ACLPC *PRINT-LEVEL* #+ACLPC ALLEGRO:*TOP-PRINT-LEVEL* 5
-      #-ACLPC *PRINT-LENGTH* #+ACLPC ALLEGRO:*TOP-PRINT-LENGTH* 10)
-
-(DEFUN <A-B< (a b)
-   (declare (fixnum a b))
-   (the list
-      (do ((i (1- b) (1- i))
-           (rslt +empty-list+ (cons i rslt)))
-          ((< i a) rslt)
-         (declare (fixnum i) (list rslt)))))
- 
-(DEFUN <A-B> (a b)
-  (declare (fixnum a b))
- (the list
-   (do ((i b (1- i))
-       (rslt +empty-list+ (cons i rslt)))
-      ((< i a) rslt)
-    (declare (fixnum i) (list rslt)))))
-
-(DEFUN >A-B< (a b)
-  (declare (fixnum a b))
- (the list
-  (do ((i (1- b) (1- i))
-       (rslt +empty-list+ (cons i rslt)))
-      ((= i a) rslt)
-    (declare (fixnum i) (list rslt)))))
-
-(DEFUN >A-B> (a b)
-  (declare (fixnum a b))
- (the list
-  (do ((i b (1- i))
-       (rslt +empty-list+ (cons i rslt)))
-      ((= i a) rslt)
-    (declare (fixnum i) (list rslt)))))
-
-#|
-  (<a-b< 0 5)
-  (<a-b> 0 5)
-  (>a-b< 0 5)
-  (>a-b> 0 5))
-|#
-
-(DEFUN V<A-B> (a b)
-   (declare (fixnum a b))
- (the (vector fixnum)
-    (let ((rslt (make-array (1+ (- b a)) :element-type 'fixnum)))
-       (declare (type (vector fixnum) rslt))
-       (do ((i a (1+ i))
-            (mark 0 (1+ mark)))
-           ((> i b))
-          (declare (fixnum i mark))
-          (setf (aref rslt mark) i))
-       rslt)))
-
-#|
-  (v<a-b> -5 5))
-|#
-
-(DEFUN SRANDOM (max)
-   (declare (fixnum max))
-   (the fixnum
-      (let ((rslt (- (random (+ max max)) max)))
-         (declare (fixnum rslt))
-         (if (zerop rslt)
-            max
-            rslt))))
-
-#|
-  (dotimes (i 20) (print (srandom 3))))
-|#
-
-(DEFUN CLOCK ()
-  (multiple-value-bind (sec min hour day month year)
-		       (get-decoded-time)
-    (format t "~%;; Clock -> ~4D-~2,'0D-~2,'0D, ~Dh ~Dm ~Ds.~%"
-	      year month day hour min sec))
-  (values))
-
-#|
-  (clock))
-|#
-
-(DEFUN DONE ()
-   (format t "~%---done---")
-   (values))
-   
-#|
-  (done))
-|#
-
-
-
diff --git a/archive/Kenzo-2/Kenzo-2-Acl5/whitehead.cl b/archive/Kenzo-2/Kenzo-2-Acl5/whitehead.cl
deleted file mode 100644
index b22fef9..0000000
--- a/archive/Kenzo-2/Kenzo-2-Acl5/whitehead.cl
+++ /dev/null
@@ -1,338 +0,0 @@
-;;;  WHITEHEAD  WHITEHEAD  WHITEHEAD  WHITEHEAD  WHITEHEAD  WHITEHEAD  WHITEHEAD
-;;;  WHITEHEAD  WHITEHEAD  WHITEHEAD  WHITEHEAD  WHITEHEAD  WHITEHEAD  WHITEHEAD
-;;;  WHITEHEAD  WHITEHEAD  WHITEHEAD  WHITEHEAD  WHITEHEAD  WHITEHEAD  WHITEHEAD
-
-(IN-PACKAGE "CAT")
-
-(provide "whitehead")
-
-;;;
-;;; Z
-;;;
-
-(DEFUN Z-WWHITEHEAD-SINTR (smst n chml-clss
-				&aux (face (face smst))
-				     (k-z-n (k-z n))
-				     (idnt (bsgn k-z-n))
-				     (efhm (efhm smst)))
-   (declare
-      (type simplicial-set smst)
-      (fixnum n)
-      (type morphism chml-clss)
-      (type face face)
-      (type ab-simplicial-group k-z-n)
-      (type gmsm idnt)
-      (type equivalence efhm))
-   (setf chml-clss
-	 (i-cmps chml-clss (rf efhm) (lg efhm)))
-   (flet ((rslt (dmns gmsm)
-	    (declare
-	      (fixnum dmns)
-	      (type gmsm gmsm))
-	    (if (< dmns n)
-	        (absm (mask dmns) idnt)
-	      (z-cocycle-gbar n dmns
-		(gmsm-cocycle face n dmns gmsm chml-clss)))))
-     (the sintr #'rslt)))
-
-#|
-(cat-init)
-(setf k (k-z 2))
-(setf ecc (echcm k))
-(setf chml-clss
-      (morphism
-        :sorc ecc :trgt (z-chcm) :degr 2
-	:intr #'(lambda (degr gnrt)
-		  (if (= degr 2)
-		      (term-cmbn 0 1 :z-gnrt)
-		    (zero-cmbn (- degr 2))))
-	:strt :gnrt :dfnt '(fundamental-class k-z-2)))
-(setf tw (z-wwhitehead-sintr k 2 chml-clss))
-(a-sintr3 tw 1 (absm 1 +null-gbar+))
-(a-sintr3 tw 2 (absm 3 +null-gbar+))
-(funcall tw 2 (gbar 2 0 '(55) 0 '()))
-(funcall tw 3 (gbar 3 0 '(12 23)
-                      0 '(34)
-                      0 '()))
-(funcall tw 4 (gbar 4 0 '(12 23 34)
-                      2 '(45)
-                      0 '(56)
-                      0 '()))
-(setf k (k-z 3))
-(setf ecc (echcm k))
-(setf chml-clss
-      (morphism
-        :sorc ecc :trgt (z-chcm) :degr 3
-	:intr #'(lambda (degr gnrt)
-		  (if (= degr 3)
-		      (term-cmbn 0 -1 :z-gnrt)
-		    (zero-cmbn (- degr 3))))
-	:strt :gnrt :dfnt '(fundamental-class k-z-3)))
-(setf tw (z-wwhitehead-sintr k 3 chml-clss))
-(a-sintr3 tw 1 (absm 1 +null-gbar+))
-(a-sintr3 tw 2 (absm 3 +null-gbar+))
-(a-sintr3 tw 3 (absm 7 +null-gbar+))
-(funcall tw 3 (z-fundamental-gmsm 3 55))
-(equal (funcall tw 3 (z-fundamental-gmsm 3 55))
-       (absm 0 (z-fundamental-gmsm 3 55)))
-(funcall tw 4 (gbar 4 0 (gbar 3 0 '(12 23) 0 '(34) 0 '())
-                      0 (gbar 2 0 '(45) 0 '())
-                      1 (gbar 0)
-                      0 (gbar 0)))
-|#
-
-(DEFUN Z-WHITEHEAD-SINTR (smst n chml-clss
-				&aux (face (face smst))
-				     (k-z-n-1 (k-z (1- n)))
-				     (idnt (bsgn k-z-n-1))
-				     (efhm (efhm smst)))
-   (declare
-      (type simplicial-set smst)
-      (fixnum n)
-      (type morphism chml-clss)
-      (type face face)
-      (type ab-simplicial-group k-z-n-1)
-      (type gmsm idnt)
-      (type equivalence efhm))
-   (setf chml-clss
-	 (i-cmps chml-clss (rf efhm) (lg efhm)))
-   (flet ((rslt (dmns gmsm)
-	    (declare
-	      (fixnum dmns)
-	      (type gmsm gmsm))
-	    (if (< dmns n)
-	        (absm (mask (1- dmns)) idnt)
-	      (z-cocycle-gbar-head n dmns
-		(gmsm-cocycle face n dmns gmsm chml-clss)))))
-     (the sintr #'rslt)))
-
-#|
-(cat-init)
-(setf k (k-z 2))
-(setf ecc (echcm k))
-(setf chml-clss
-      (morphism
-        :sorc ecc :trgt (z-chcm) :degr 2
-	:intr #'(lambda (degr gnrt)
-		  (if (= degr 2)
-		      (term-cmbn 0 1 :z-gnrt)
-		    (zero-cmbn (- degr 2))))
-	:strt :gnrt :dfnt '(fundamental-class k-z-2)))
-(setf tw (z-whitehead-sintr k 2 chml-clss))
-(tw-a-sintr3 tw 1 (absm 1 +null-gbar+) '())
-(tw-a-sintr3 tw 2 (absm 3 +null-gbar+) '())
-(funcall tw 2 (gbar 2 0 '(55) 0 '()))
-(funcall tw 3 (gbar 3 0 '(12 23)
-                      0 '(34)
-                      0 '()))
-(funcall tw 4 (gbar 4 0 '(12 23 34)
-                      2 '(45)
-                      0 '(56)
-                      0 '()))
-(setf k (k-z 3))
-(setf ecc (echcm k))
-(setf chml-clss
-      (morphism
-        :sorc ecc :trgt (z-chcm) :degr 3
-	:intr #'(lambda (degr gnrt)
-		  (if (= degr 3)
-		      (term-cmbn 0 -1 :z-gnrt)
-		    (zero-cmbn (- degr 3))))
-	:strt :gnrt :dfnt '(fundamental-class k-z-3)))
-(setf tw (z-whitehead-sintr k 3 chml-clss))
-(tw-a-sintr3 tw 1 (absm 1 +null-gbar+) +null-gbar+)
-(tw-a-sintr3 tw 2 (absm 3 +null-gbar+) +null-gbar+)
-(tw-a-sintr3 tw 3 (absm 7 +null-gbar+) +null-gbar+)
-(funcall tw 3 (z-fundamental-gmsm 3 55))
-(equal (funcall tw 3 (z-fundamental-gmsm 3 55))
-       (absm 0 (z-fundamental-gmsm 2 55)))
-(funcall tw 4 (gbar 4 0 (gbar 3 0 '(12 23) 0 '(34) 0 '())
-                      0 (gbar 2 0 '(45) 0 '())
-                      1 (gbar 0)
-                      0 (gbar 0)))
-|#
-
-(DEFUN Z-WHITEHEAD (smst chml-clss &aux (n (- (degr chml-clss))))
-   (declare
-      (type simplicial-set smst)
-      (fixnum n)
-      (type morphism chml-clss))
-   (the fibration
-      (simplicial-mrph
-         :sorc smst :trgt (k-z (1- n)) :degr -1
-         :sintr (z-whitehead-sintr smst n chml-clss)
-         :dfnt `(z-whitehead ,smst))))
-
-;;;
-;;; Z/2Z
-;;;
-
-(DEFUN Z2-WWHITEHEAD-SINTR (smst n chml-clss
-				&aux (face (face smst))
-				     (k-z2-n (k-z2 n))
-				     (idnt (bsgn k-z2-n))
-				     (efhm (efhm smst)))
-   (declare
-      (type simplicial-set smst)
-      (fixnum n)
-      (type morphism chml-clss)
-      (type face face)
-      (type ab-simplicial-group k-z2-n)
-      (type gmsm idnt)
-      (type equivalence efhm))
-   (setf chml-clss
-	 (i-cmps chml-clss (rf efhm) (lg efhm)))
-   (flet ((rslt (dmns gmsm)
-	    (declare
-	      (fixnum dmns)
-	      (type gmsm gmsm))
-	    (if (< dmns n)
-	        (absm (mask dmns) idnt)
-	      (z2-cocycle-gbar n dmns
-		(gmsm-cocycle face n dmns gmsm chml-clss)))))
-     (the sintr #'rslt)))
-
-#|
-(cat-init)
-(setf k (k-z2 2))
-(setf ecc (echcm k))
-(setf chml-clss
-      (morphism
-        :sorc ecc :trgt (z-chcm) :degr 2
-	:intr #'(lambda (degr gnrt)
-		  (if (= degr 2)
-		      (term-cmbn 0 1 :z-gnrt)
-		    (zero-cmbn (- degr 2))))
-	:strt :gnrt :dfnt '(fundamental-class k-z-2)))
-(setf tw (Z2-wwhitehead-sintr k 2 chml-clss))
-(a-sintr3 tw 1 (absm 1 +null-gbar+))
-(a-sintr3 tw 2 (absm 3 +null-gbar+))
-(funcall tw 2 (gbar 2 0 1 0 0))
-(funcall tw 3 (gbar 3 0 2
-                      0 1
-                      0 0))
-(funcall tw 4 (gbar 4 0 3
-                      2 1
-                      0 1
-                      0 0))
-(setf k (k-z2 3))
-(setf ecc (echcm k))
-(setf chml-clss
-      (morphism
-        :sorc ecc :trgt (z-chcm) :degr 3
-	:intr #'(lambda (degr gnrt)
-		  (if (= degr 3)
-		      (term-cmbn 0 -1 :z-gnrt)
-		    (zero-cmbn (- degr 3))))
-	:strt :gnrt :dfnt '(fundamental-class k-z-3)))
-(setf tw (Z2-wwhitehead-sintr k 3 chml-clss))
-(a-sintr3 tw 1 (absm 1 +null-gbar+))
-(a-sintr3 tw 2 (absm 3 +null-gbar+))
-(a-sintr3 tw 3 (absm 7 +null-gbar+))
-(funcall tw 3 (Z2-fundamental-gmsm 3 1))
-(equal (funcall tw 3 (Z2-fundamental-gmsm 3 1))
-       (absm 0 (Z2-fundamental-gmsm 3 1)))
-(funcall tw 4 (gbar 4 0 (gbar 3 0 2 0 1 0 0)
-                      0 (gbar 2 0 1 0 0)
-                      1 (gbar 0)
-                      0 (gbar 0)))
-|#
-
-(DEFUN Z2-WHITEHEAD-SINTR (smst n chml-clss
-				&aux (face (face smst))
-				     (k-z2-n-1 (k-z2 (1- n)))
-				     (idnt (bsgn k-z2-n-1))
-				     (efhm (efhm smst)))
-   (declare
-      (type simplicial-set smst)
-      (fixnum n)
-      (type morphism chml-clss)
-      (type face face)
-      (type ab-simplicial-group k-z2-n-1)
-      (type gmsm idnt)
-      (type equivalence efhm))
-   (setf chml-clss
-	 (i-cmps chml-clss (rf efhm) (lg efhm)))
-   (flet ((rslt (dmns gmsm)
-	    (declare
-	      (fixnum dmns)
-	      (type gmsm gmsm))
-	    (if (< dmns n)
-	        (absm (mask (1- dmns)) idnt)
-	      (z2-cocycle-gbar-head n dmns
-		(gmsm-cocycle face n dmns gmsm chml-clss)))))     
-     (the sintr #'rslt)))
-
-#|
-(cat-init)
-(setf k (k-z2 2))
-(setf ecc (echcm k))
-(setf chml-clss
-      (morphism
-        :sorc ecc :trgt (z-chcm) :degr 2
-	:intr #'(lambda (degr gnrt)
-		  (if (= degr 2)
-		      (term-cmbn 0 1 :z-gnrt)
-		    (zero-cmbn (- degr 2))))
-	:strt :gnrt :dfnt '(fundamental-class k-z-2)))
-(setf tw (Z2-whitehead-sintr k 2 chml-clss))
-(tw-a-sintr3 tw 1 (absm 1 +null-gbar+) 0)
-(tw-a-sintr3 tw 2 (absm 3 +null-gbar+) 0)
-(funcall tw 2 (gbar 2 0 1 0 '()))
-(funcall tw 3 (gbar 3 0 2
-                      0 1
-                      0 0))
-(funcall tw 4 (gbar 4 0 3
-                      2 1
-                      0 1
-                      0 0))
-(setf k (k-z2 3))
-(setf ecc (echcm k))
-(setf chml-clss
-      (morphism
-        :sorc ecc :trgt (z-chcm) :degr 3
-	:intr #'(lambda (degr gnrt)
-		  (if (= degr 3)
-		      (term-cmbn 0 -1 :z-gnrt)
-		    (zero-cmbn (- degr 3))))
-	:strt :gnrt :dfnt '(fundamental-class k-z-3)))
-(setf tw (Z2-whitehead-sintr k 3 chml-clss))
-(tw-a-sintr3 tw 1 (absm 1 +null-gbar+) 0)
-(tw-a-sintr3 tw 2 (absm 3 +null-gbar+) 0)
-(tw-a-sintr3 tw 3 (absm 7 +null-gbar+) 0)
-(funcall tw 3 (Z2-fundamental-gmsm 3 1))
-(equal (funcall tw 3 (Z2-fundamental-gmsm 3 1))
-       (absm 0 (Z2-fundamental-gmsm 2 1)))
-(funcall tw 4 (gbar 4 0 (gbar 3 0 2 0 1 0 0)
-                      0 (gbar 2 0 1 0 0)
-                      1 (gbar 0)
-                      0 (gbar 0)))
-|#
-
-(DEFUN Z2-WHITEHEAD (smst chml-clss &aux (n (- (degr chml-clss))))
-   (declare
-      (type simplicial-set smst)
-      (fixnum n)
-      (type morphism chml-clss))
-   (the fibration
-      (simplicial-mrph
-         :sorc smst :trgt (k-z2 (1- n)) :degr -1
-         :sintr (Z2-whitehead-sintr smst n chml-clss)
-         :dfnt `(Z2-whitehead ,smst))))
-
-#|
-(setf m (moore 2 4))
-(setf chml-clss
-      (morphism
-         :sorc m :trgt (z-chcm) :degr -4
-         :intr #'(lambda (dmns gmsm)
-                    (if (= 4 dmns)
-                       (cmbn 0 1 :z-gnrt)
-                       (zero-cmbn (- dmns 4))))
-         :strt :gnrt
-         :dfnt '(chml-clss moore 2 4)))
-(setf mf (z2-whitehead m 4 chml-clss))
-(setf mt (fibration-total mf))
-(homology mt 0 10)
-|#
-         
\ No newline at end of file
diff --git a/archive/Kenzo-2/Kenzo-2-Acl8/Alexis.cl b/archive/Kenzo-2/Kenzo-2-Acl8/Alexis.cl
deleted file mode 100644
index d563a16..0000000
--- a/archive/Kenzo-2/Kenzo-2-Acl8/Alexis.cl
+++ /dev/null
@@ -1,56 +0,0 @@
-
-(setf p (k-z2 1))
-
-(setf sp (suspension p))
-
-(setf s2p (suspension sp))
-
-(setf s3p (suspension s2p))
-
-(setf s4p (suspension s3p))
-
-(homology s4p 5)
-
-(setf ch5 (chml-clss s4p 5))
-
-(setf f5 (z2-whitehead s4p ch5))
-
-(setf x6 (fibration-total f5))
-
-(homology x6 6)
-
-(setf ch6 (chml-clss x6 6))
-
-(setf f6 (z2-whitehead x6 ch6))
-
-(setf x7 (fibration-total f6))
-
-(homology x7 7)
-
-(setf ch71 (chml-clss x7 7))
-
-(setf f71 (z2-whitehead x7 ch71))
-
-(setf x71 (fibration-total f71))
-
-(homology x71 7)
-
-(setf ch72 (chml-clss x71 7))
-
-(setf f72 (z2-whitehead x71 ch72))
-
-(setf x72 (fibration-total f72))
-
-(homology x72 7)
-
-(setf ch73 (chml-clss x72 7))
-
-(setf f73 (z2-whitehead x72 ch73))
-
-(setf x8 (fibration-total f73))
-
-(homology x71 7)
-
-(homology x71 8)
-
-
diff --git a/archive/Kenzo-2/Kenzo-2-Acl8/Compile.txt b/archive/Kenzo-2/Kenzo-2-Acl8/Compile.txt
deleted file mode 100644
index c48baa3..0000000
--- a/archive/Kenzo-2/Kenzo-2-Acl8/Compile.txt
+++ /dev/null
@@ -1,331 +0,0 @@
-Allegro CL Personal Edition 5.0.1 [Windows/x86] (6/29/99 16:56)
-Copyright (C) 1985-1999, Franz Inc., Berkeley, CA, USA.  All Rights Reserved.
-CG/IDE Version: 1.323.2.169
-
-[changing package from "COMMON-LISP-USER" to "COMMON-GRAPHICS-USER"]
-
-> (load "file-list")
-; Loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\file-list.cl
-
- FILE  1: classes
- FILE  2: macros
- FILE  3: various
- FILE  4: combinations
- FILE  5: chain-complexes
- FILE  6: chcm-elementary-op
- FILE  7: effective-homology
- FILE  8: homology-groups
- FILE  9: searching-homology
- FILE 10: cones
- FILE 11: tensor-products
- FILE 12: coalgebras
- FILE 13: cobar
- FILE 14: algebras
- FILE 15: bar
- FILE 16: simplicial-sets
- FILE 17: simplicial-mrphs
- FILE 18: delta
- FILE 19: special-smsts
- FILE 20: suspensions
- FILE 21: disk-pasting
- FILE 22: cartesian-products
- FILE 23: eilenberg-zilber
- FILE 24: kan
- FILE 25: simplicial-groups
- FILE 26: fibrations
- FILE 27: loop-spaces
- FILE 28: ls-twisted-products
- FILE 29: lp-space-efhm
- FILE 30: classifying-spaces
- FILE 31: k-pi-n
- FILE 32: serre
- FILE 33: cs-twisted-products
- FILE 34: cl-space-efhm
- FILE 35: whitehead
- FILE 36: smith
-T
-> (in-package :cat)
-#<The CAT package>
-> (compile-files)
-
-SPEED-PARAMETER = 3
-
- *CMBN-CONTROL* = T
-
-;;; Compiling file classes.cl
-;;; Writing fasl file classes.fasl
-;;; Fasl write complete
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\classes.fasl
-;;; Compiling file macros.cl
-;;; Writing fasl file macros.fasl
-;;; Fasl write complete
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\macros.fasl
-;;; Compiling file various.cl
-;;; Writing fasl file various.fasl
-;;; Fasl write complete
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\various.fasl
-;;; Compiling file combinations.cl
-;;; Writing fasl file combinations.fasl
-;;; Fasl write complete
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\combinations.fasl
-;;; Compiling file chain-complexes.cl
-;;; Writing fasl file chain-complexes.fasl
-;;; Fasl write complete
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\chain-complexes.fasl
-;;; Compiling file chcm-elementary-op.cl
-;;; Writing fasl file chcm-elementary-op.fasl
-;;; Fasl write complete
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\chcm-elementary-op.fasl
-;;; Compiling file effective-homology.cl
-;;; Writing fasl file effective-homology.fasl
-;;; Fasl write complete
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\effective-homology.fasl
-;;; Compiling file homology-groups.cl
-;;; Writing fasl file homology-groups.fasl
-;;; Fasl write complete
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\homology-groups.fasl
-;;; Compiling file searching-homology.cl
-;;; Writing fasl file searching-homology.fasl
-;;; Fasl write complete
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\searching-homology.fasl
-;;; Compiling file cones.cl
-;;; Writing fasl file cones.fasl
-;;; Fasl write complete
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\cones.fasl
-;;; Compiling file tensor-products.cl
-;;; Writing fasl file tensor-products.fasl
-;;; Fasl write complete
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\tensor-products.fasl
-;;; Compiling file coalgebras.cl
-;;; Writing fasl file coalgebras.fasl
-;;; Fasl write complete
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\coalgebras.fasl
-;;; Compiling file cobar.cl
-;;; Writing fasl file cobar.fasl
-;;; Fasl write complete
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\cobar.fasl
-;;; Compiling file algebras.cl
-;;; Writing fasl file algebras.fasl
-;;; Fasl write complete
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\algebras.fasl
-;;; Compiling file bar.cl
-;;; Writing fasl file bar.fasl
-;;; Fasl write complete
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\bar.fasl
-;;; Compiling file simplicial-sets.cl
-;;; Writing fasl file simplicial-sets.fasl
-;;; Fasl write complete
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\simplicial-sets.fasl
-;;; Compiling file simplicial-mrphs.cl
-;;; Writing fasl file simplicial-mrphs.fasl
-;;; Fasl write complete
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\simplicial-mrphs.fasl
-;;; Compiling file delta.cl
-;;; Writing fasl file delta.fasl
-;;; Fasl write complete
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\delta.fasl
-;;; Compiling file special-smsts.cl
-;;; Writing fasl file special-smsts.fasl
-;;; Fasl write complete
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\special-smsts.fasl
-;;; Compiling file suspensions.cl
-;;; Writing fasl file suspensions.fasl
-;;; Fasl write complete
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\suspensions.fasl
-;;; Compiling file disk-pasting.cl
-;;; Writing fasl file disk-pasting.fasl
-;;; Fasl write complete
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\disk-pasting.fasl
-;;; Compiling file cartesian-products.cl
-;;; Writing fasl file cartesian-products.fasl
-;;; Fasl write complete
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\cartesian-products.fasl
-;;; Compiling file eilenberg-zilber.cl
-;;; Writing fasl file eilenberg-zilber.fasl
-;;; Fasl write complete
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\eilenberg-zilber.fasl
-;;; Compiling file kan.cl
-;;; Writing fasl file kan.fasl
-;;; Fasl write complete
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\kan.fasl
-;;; Compiling file simplicial-groups.cl
-;;; Writing fasl file simplicial-groups.fasl
-;;; Fasl write complete
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\simplicial-groups.fasl
-;;; Compiling file fibrations.cl
-;;; Writing fasl file fibrations.fasl
-;;; Fasl write complete
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\fibrations.fasl
-;;; Compiling file loop-spaces.cl
-;;; Writing fasl file loop-spaces.fasl
-;;; Fasl write complete
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\loop-spaces.fasl
-;;; Compiling file ls-twisted-products.cl
-;;; Writing fasl file ls-twisted-products.fasl
-;;; Fasl write complete
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\ls-twisted-products.fasl
-;;; Compiling file lp-space-efhm.cl
-;;; Writing fasl file lp-space-efhm.fasl
-;;; Fasl write complete
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\lp-space-efhm.fasl
-;;; Compiling file classifying-spaces.cl
-;;; Writing fasl file classifying-spaces.fasl
-;;; Fasl write complete
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\classifying-spaces.fasl
-;;; Compiling file k-pi-n.cl
-;;; Writing fasl file k-pi-n.fasl
-;;; Fasl write complete
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\k-pi-n.fasl
-;;; Compiling file serre.cl
-;;; Writing fasl file serre.fasl
-;;; Fasl write complete
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\serre.fasl
-;;; Compiling file cs-twisted-products.cl
-;;; Writing fasl file cs-twisted-products.fasl
-;;; Fasl write complete
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\cs-twisted-products.fasl
-;;; Compiling file cl-space-efhm.cl
-;;; Writing fasl file cl-space-efhm.fasl
-;;; Fasl write complete
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\cl-space-efhm.fasl
-;;; Compiling file whitehead.cl
-;;; Writing fasl file whitehead.fasl
-;;; Fasl write complete
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\whitehead.fasl
-;;; Compiling file smith.cl
-;;; Writing fasl file smith.fasl
-;;; Fasl write complete
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\smith.fasl
---- done ---
-> (time (homology (loop-space (moore 2 4) 2) 7))
-
-Computing boundary-matrix in dimension 7.
-Rank of the source-module : 6.
-
-
-;; Clock -> 2005-10-03, 15h 6m 53s.
-Computing the boundary of the generator 1 (dimension 7) :
-<<AlLp[7 <<AlLp[4 N5][4 N5]>>]>> 
-End of computing.
-
-
-;; Clock -> 2005-10-03, 15h 6m 53s.
-Computing the boundary of the generator 2 (dimension 7) :
-<<AlLp[2 <<AlLp[3 M4]>>][5 <<AlLp[3 M4][3 M4]>>]>> 
-End of computing.
-
-
-;; Clock -> 2005-10-03, 15h 6m 53s.
-Computing the boundary of the generator 3 (dimension 7) :
-<<AlLp[5 <<AlLp[3 M4][3 M4]>>][2 <<AlLp[3 M4]>>]>> 
-End of computing.
-
-
-;; Clock -> 2005-10-03, 15h 6m 53s.
-Computing the boundary of the generator 4 (dimension 7) :
-<<AlLp[2 <<AlLp[3 M4]>>][2 <<AlLp[3 M4]>>][3 <<AlLp[4 N5]>>]>> 
-End of computing.
-
-
-;; Clock -> 2005-10-03, 15h 6m 53s.
-Computing the boundary of the generator 5 (dimension 7) :
-<<AlLp[2 <<AlLp[3 M4]>>][3 <<AlLp[4 N5]>>][2 <<AlLp[3 M4]>>]>> 
-End of computing.
-
-
-;; Clock -> 2005-10-03, 15h 6m 53s.
-Computing the boundary of the generator 6 (dimension 7) :
-<<AlLp[3 <<AlLp[4 N5]>>][2 <<AlLp[3 M4]>>][2 <<AlLp[3 M4]>>]>> 
-End of computing.
-
-
-Computing boundary-matrix in dimension 8.
-Rank of the source-module : 11.
-
-
-;; Clock -> 2005-10-03, 15h 6m 53s.
-Computing the boundary of the generator 1 (dimension 8) :
-<<AlLp[8 <<AlLp[3 M4][3 M4][3 M4]>>]>> 
-End of computing.
-
-
-;; Clock -> 2005-10-03, 15h 6m 58s.
-Computing the boundary of the generator 2 (dimension 8) :
-<<AlLp[2 <<AlLp[3 M4]>>][6 <<AlLp[3 M4][4 N5]>>]>> 
-End of computing.
-
-
-;; Clock -> 2005-10-03, 15h 6m 58s.
-Computing the boundary of the generator 3 (dimension 8) :
-<<AlLp[2 <<AlLp[3 M4]>>][6 <<AlLp[4 N5][3 M4]>>]>> 
-End of computing.
-
-
-;; Clock -> 2005-10-03, 15h 6m 58s.
-Computing the boundary of the generator 4 (dimension 8) :
-<<AlLp[3 <<AlLp[4 N5]>>][5 <<AlLp[3 M4][3 M4]>>]>> 
-End of computing.
-
-
-;; Clock -> 2005-10-03, 15h 6m 58s.
-Computing the boundary of the generator 5 (dimension 8) :
-<<AlLp[5 <<AlLp[3 M4][3 M4]>>][3 <<AlLp[4 N5]>>]>> 
-End of computing.
-
-
-;; Clock -> 2005-10-03, 15h 6m 58s.
-Computing the boundary of the generator 6 (dimension 8) :
-<<AlLp[6 <<AlLp[3 M4][4 N5]>>][2 <<AlLp[3 M4]>>]>> 
-End of computing.
-
-
-;; Clock -> 2005-10-03, 15h 6m 58s.
-Computing the boundary of the generator 7 (dimension 8) :
-<<AlLp[6 <<AlLp[4 N5][3 M4]>>][2 <<AlLp[3 M4]>>]>> 
-End of computing.
-
-
-;; Clock -> 2005-10-03, 15h 6m 58s.
-Computing the boundary of the generator 8 (dimension 8) :
-<<AlLp[2 <<AlLp[3 M4]>>][3 <<AlLp[4 N5]>>][3 <<AlLp[4 N5]>>]>> 
-End of computing.
-
-
-;; Clock -> 2005-10-03, 15h 6m 58s.
-Computing the boundary of the generator 9 (dimension 8) :
-<<AlLp[3 <<AlLp[4 N5]>>][2 <<AlLp[3 M4]>>][3 <<AlLp[4 N5]>>]>> 
-End of computing.
-
-
-;; Clock -> 2005-10-03, 15h 6m 58s.
-Computing the boundary of the generator 10 (dimension 8) :
-<<AlLp[3 <<AlLp[4 N5]>>][3 <<AlLp[4 N5]>>][2 <<AlLp[3 M4]>>]>> 
-End of computing.
-
-
-;; Clock -> 2005-10-03, 15h 6m 58s.
-Computing the boundary of the generator 11 (dimension 8) :
-<<AlLp[2 <<AlLp[3 M4]>>][2 <<AlLp[3 M4]>>][2 <<AlLp[3 M4]>>][2 <<AlLp[3 M4]>>]>> 
-End of computing.
-
-
-
-
-Homology in dimension 7 :
-
-
-Component Z/2Z
-
-
----done---
-
-;; Clock -> 2005-10-03, 15h 6m 58s.
-
-; cpu time (non-gc) 4,735 msec user, 0 msec system
-; cpu time (gc)     640 msec user, 0 msec system
-; cpu time (total)  5,375 msec user, 0 msec system
-; real time  5,375 msec
-; space allocation:
-;  2,916,685 cons cells, 2 symbols, 7,077,280 other bytes, 3484 static bytes
-NIL
-> 
\ No newline at end of file
diff --git a/archive/Kenzo-2/Kenzo-2-Acl8/Demo.cl b/archive/Kenzo-2/Kenzo-2-Acl8/Demo.cl
deleted file mode 100644
index 9cada96..0000000
--- a/archive/Kenzo-2/Kenzo-2-Acl8/Demo.cl
+++ /dev/null
@@ -1,100 +0,0 @@
-;;; DEMO DEMO DEMO DEMO DEMO DEMO DEMO DEMO DEMO DEMO DEMO
-;;; DEMO DEMO DEMO DEMO DEMO DEMO DEMO DEMO DEMO DEMO DEMO
-;;; DEMO DEMO DEMO DEMO DEMO DEMO DEMO DEMO DEMO DEMO DEMO
-
-(IN-PACKAGE :USER)
-
-(DEFVAR *STATEMENT*)
-
-;; C = comment
-(DEFUN C (string)
-  (terpri)
-  (dotimes (i 50) (princ "-"))
-  (princ "<Comment>")
-;  (dotimes (i 31) (princ "-"))
-;  (terpri)
-  (princ string)
-;  (terpri)
-  (dotimes (i 50) (princ "-"))
-  (values))
-
-;; R = read
-(DEFMACRO R (statement)
-  (declare (special *statement*))
-  (setf *statement* statement)
-  `(progn
-     (terpri)
-     (dotimes (i 50) (princ "-"))
-     (princ "<Lisp Statement>")
-;     (dotimes (i 29) (princ "-"))
-;     (terpri)
-     (pprint ',statement)
-     (terpri) ; (terpri)
-     (dotimes (i 50) (princ "-"))
-     (values)))
-
-(DEFUN STRIP-INITIAL-SPACES (st)
-  (let ((st2 (make-string (- (length st) (count #\Newline st)))))
-    (declare (type string st2))
-    (do ((i 0 (1+ i))
-         (j 0 (1+ j)))
-        ((= i (length st)))
-      (let ((char (aref st i)))
-        (when (char= char #\newline)
-          (incf i))
-        (setf (aref st2 j) char)))
-    st2))
-
-(DEFMACRO R2 (dstatement)
-  (declare (special *statement* *dstatement*))
-  (setf *dstatement* dstatement)
-  (setf *statement* (read-from-string dstatement))
-  `(progn
-     (terpri)
-      (dotimes (i 50) (princ "-"))
-      (princ "<Lisp Statement>")
-      ;  (dotimes (i 31) (princ "-"))
-      ;  (terpri)
-      (princ (strip-initial-spaces *dstatement*))
-      ;  (terpri)
-      (dotimes (i 50) (princ "-"))
-      (values)))
-
-;; E = EXECUTE
-(DEFUN E ()
-  (declare (special *statement*))
-  (terpri)
-  (dotimes (i 50) (princ "-"))
-  (princ "<Result>")
-;  (dotimes (i 32) (princ "-"))
-  (terpri) ; (terpri)
-  (prin1 (eval *statement*))
-  (terpri) ; (terpri)
-  (dotimes (i 50) (princ "-"))
-  (values))
-
-(DEFUN EE ()
-  (declare (special *statement*))
-  (terpri)
-  (dotimes (i 10) (princ "-"))
-  (princ " Error ")
-  (dotimes (i 33) (princ "-"))
-  (terpri) (terpri)
-  (restart-case
-      (handler-bind ((error
-                         #'(lambda (condition)
-                             (format t "Type-error: ~S~&"
-                               (class-name (class-of condition)))
-                             (apply #'format t
-                                    (simple-condition-format-control condition)
-                                    (simple-condition-format-arguments condition))
-                             (invoke-restart 'my-restart))))
-                  (eval *statement*))
-    (my-restart () (values)))
-  (terpri) (terpri)
-  (dotimes (i 50) (princ "-"))
-  (values))
-
-(DEFMACRO M (statement)
-  (eval statement)
-  '(values ))
\ No newline at end of file
diff --git a/archive/Kenzo-2/Kenzo-2-Acl8/Release.txt b/archive/Kenzo-2/Kenzo-2-Acl8/Release.txt
deleted file mode 100644
index 1789408..0000000
--- a/archive/Kenzo-2/Kenzo-2-Acl8/Release.txt
+++ /dev/null
@@ -1,10 +0,0 @@
-Kenzo-2-2 => Kenzo-2-3
-
-  The speial-smsts.cl is modified ; the bsgn slot had been forgotten
-  in the sphere-wedge constructor.
-
-Kenzo-2-1 => Kenzo-2-2
-
-  The delta.cl file is modified, but the modification is not
-  satisfactory : the slot face *should_be* able to generate the slot
-  dffr.
diff --git a/archive/Kenzo-2/Kenzo-2-Acl8/Start.txt b/archive/Kenzo-2/Kenzo-2-Acl8/Start.txt
deleted file mode 100644
index 50e0707..0000000
--- a/archive/Kenzo-2/Kenzo-2-Acl8/Start.txt
+++ /dev/null
@@ -1,218 +0,0 @@
-Allegro CL Personal Edition 5.0.1 [Windows/x86] (6/29/99 16:56)
-Copyright (C) 1985-1999, Franz Inc., Berkeley, CA, USA.  All Rights Reserved.
-CG/IDE Version: 1.323.2.169
-
-[changing package from "COMMON-LISP-USER" to "COMMON-GRAPHICS-USER"]
-
-> (load "file-list")
-; Loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\file-list.cl
-
- FILE  1: classes
- FILE  2: macros
- FILE  3: various
- FILE  4: combinations
- FILE  5: chain-complexes
- FILE  6: chcm-elementary-op
- FILE  7: effective-homology
- FILE  8: homology-groups
- FILE  9: searching-homology
- FILE 10: cones
- FILE 11: tensor-products
- FILE 12: coalgebras
- FILE 13: cobar
- FILE 14: algebras
- FILE 15: bar
- FILE 16: simplicial-sets
- FILE 17: simplicial-mrphs
- FILE 18: delta
- FILE 19: special-smsts
- FILE 20: suspensions
- FILE 21: disk-pasting
- FILE 22: cartesian-products
- FILE 23: eilenberg-zilber
- FILE 24: kan
- FILE 25: simplicial-groups
- FILE 26: fibrations
- FILE 27: loop-spaces
- FILE 28: ls-twisted-products
- FILE 29: lp-space-efhm
- FILE 30: classifying-spaces
- FILE 31: k-pi-n
- FILE 32: serre
- FILE 33: cs-twisted-products
- FILE 34: cl-space-efhm
- FILE 35: whitehead
- FILE 36: smith
-T
-> (in-package :cat)
-#<The CAT package>
-> (load-cfiles)
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\classes.fasl
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\macros.fasl
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\various.fasl
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\combinations.fasl
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\chain-complexes.fasl
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\chcm-elementary-op.fasl
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\effective-homology.fasl
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\homology-groups.fasl
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\searching-homology.fasl
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\cones.fasl
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\tensor-products.fasl
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\coalgebras.fasl
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\cobar.fasl
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\algebras.fasl
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\bar.fasl
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\simplicial-sets.fasl
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\simplicial-mrphs.fasl
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\delta.fasl
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\special-smsts.fasl
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\suspensions.fasl
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\disk-pasting.fasl
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\cartesian-products.fasl
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\eilenberg-zilber.fasl
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\kan.fasl
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\simplicial-groups.fasl
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\fibrations.fasl
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\loop-spaces.fasl
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\ls-twisted-products.fasl
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\lp-space-efhm.fasl
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\classifying-spaces.fasl
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\k-pi-n.fasl
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\serre.fasl
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\cs-twisted-products.fasl
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\cl-space-efhm.fasl
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\whitehead.fasl
-; Fast loading C:\Docume~1\Francis\AA\Kenzo\Kenzo-2\smith.fasl
---- done ---
-> (time (homology (loop-space (moore 2 4) 2) 7))
-
-Computing boundary-matrix in dimension 7.
-Rank of the source-module : 6.
-
-
-;; Clock -> 2005-10-03, 15h 9m 19s.
-Computing the boundary of the generator 1 (dimension 7) :
-<<AlLp[7 <<AlLp[4 N5][4 N5]>>]>> 
-End of computing.
-
-
-;; Clock -> 2005-10-03, 15h 9m 19s.
-Computing the boundary of the generator 2 (dimension 7) :
-<<AlLp[2 <<AlLp[3 M4]>>][5 <<AlLp[3 M4][3 M4]>>]>> 
-End of computing.
-
-
-;; Clock -> 2005-10-03, 15h 9m 19s.
-Computing the boundary of the generator 3 (dimension 7) :
-<<AlLp[5 <<AlLp[3 M4][3 M4]>>][2 <<AlLp[3 M4]>>]>> 
-End of computing.
-
-
-;; Clock -> 2005-10-03, 15h 9m 19s.
-Computing the boundary of the generator 4 (dimension 7) :
-<<AlLp[2 <<AlLp[3 M4]>>][2 <<AlLp[3 M4]>>][3 <<AlLp[4 N5]>>]>> 
-End of computing.
-
-
-;; Clock -> 2005-10-03, 15h 9m 19s.
-Computing the boundary of the generator 5 (dimension 7) :
-<<AlLp[2 <<AlLp[3 M4]>>][3 <<AlLp[4 N5]>>][2 <<AlLp[3 M4]>>]>> 
-End of computing.
-
-
-;; Clock -> 2005-10-03, 15h 9m 19s.
-Computing the boundary of the generator 6 (dimension 7) :
-<<AlLp[3 <<AlLp[4 N5]>>][2 <<AlLp[3 M4]>>][2 <<AlLp[3 M4]>>]>> 
-End of computing.
-
-
-Computing boundary-matrix in dimension 8.
-Rank of the source-module : 11.
-
-
-;; Clock -> 2005-10-03, 15h 9m 19s.
-Computing the boundary of the generator 1 (dimension 8) :
-<<AlLp[8 <<AlLp[3 M4][3 M4][3 M4]>>]>> 
-End of computing.
-
-
-;; Clock -> 2005-10-03, 15h 9m 24s.
-Computing the boundary of the generator 2 (dimension 8) :
-<<AlLp[2 <<AlLp[3 M4]>>][6 <<AlLp[3 M4][4 N5]>>]>> 
-End of computing.
-
-
-;; Clock -> 2005-10-03, 15h 9m 24s.
-Computing the boundary of the generator 3 (dimension 8) :
-<<AlLp[2 <<AlLp[3 M4]>>][6 <<AlLp[4 N5][3 M4]>>]>> 
-End of computing.
-
-
-;; Clock -> 2005-10-03, 15h 9m 24s.
-Computing the boundary of the generator 4 (dimension 8) :
-<<AlLp[3 <<AlLp[4 N5]>>][5 <<AlLp[3 M4][3 M4]>>]>> 
-End of computing.
-
-
-;; Clock -> 2005-10-03, 15h 9m 24s.
-Computing the boundary of the generator 5 (dimension 8) :
-<<AlLp[5 <<AlLp[3 M4][3 M4]>>][3 <<AlLp[4 N5]>>]>> 
-End of computing.
-
-
-;; Clock -> 2005-10-03, 15h 9m 24s.
-Computing the boundary of the generator 6 (dimension 8) :
-<<AlLp[6 <<AlLp[3 M4][4 N5]>>][2 <<AlLp[3 M4]>>]>> 
-End of computing.
-
-
-;; Clock -> 2005-10-03, 15h 9m 24s.
-Computing the boundary of the generator 7 (dimension 8) :
-<<AlLp[6 <<AlLp[4 N5][3 M4]>>][2 <<AlLp[3 M4]>>]>> 
-End of computing.
-
-
-;; Clock -> 2005-10-03, 15h 9m 24s.
-Computing the boundary of the generator 8 (dimension 8) :
-<<AlLp[2 <<AlLp[3 M4]>>][3 <<AlLp[4 N5]>>][3 <<AlLp[4 N5]>>]>> 
-End of computing.
-
-
-;; Clock -> 2005-10-03, 15h 9m 24s.
-Computing the boundary of the generator 9 (dimension 8) :
-<<AlLp[3 <<AlLp[4 N5]>>][2 <<AlLp[3 M4]>>][3 <<AlLp[4 N5]>>]>> 
-End of computing.
-
-
-;; Clock -> 2005-10-03, 15h 9m 24s.
-Computing the boundary of the generator 10 (dimension 8) :
-<<AlLp[3 <<AlLp[4 N5]>>][3 <<AlLp[4 N5]>>][2 <<AlLp[3 M4]>>]>> 
-End of computing.
-
-
-;; Clock -> 2005-10-03, 15h 9m 24s.
-Computing the boundary of the generator 11 (dimension 8) :
-<<AlLp[2 <<AlLp[3 M4]>>][2 <<AlLp[3 M4]>>][2 <<AlLp[3 M4]>>][2 <<AlLp[3 M4]>>]>> 
-End of computing.
-
-
-
-
-Homology in dimension 7 :
-
-
-Component Z/2Z
-
-
----done---
-
-;; Clock -> 2005-10-03, 15h 9m 24s.
-
-; cpu time (non-gc) 4,735 msec user, 0 msec system
-; cpu time (gc)     656 msec user, 0 msec system
-; cpu time (total)  5,391 msec user, 0 msec system
-; real time  5,390 msec
-; space allocation:
-;  2,917,299 cons cells, 2 symbols, 7,081,936 other bytes, 3484 static bytes
-NIL
-> 
\ No newline at end of file
diff --git a/archive/Kenzo-2/Kenzo-2-Acl8/algebras.cl b/archive/Kenzo-2/Kenzo-2-Acl8/algebras.cl
deleted file mode 100644
index 6c40079..0000000
--- a/archive/Kenzo-2/Kenzo-2-Acl8/algebras.cl
+++ /dev/null
@@ -1,53 +0,0 @@
-;;;  ALGEBRAS  ALGEBRAS  ALGEBRAS  ALGEBRAS  ALGEBRAS  ALGEBRAS
-;;;  ALGEBRAS  ALGEBRAS  ALGEBRAS  ALGEBRAS  ALGEBRAS  ALGEBRAS
-;;;  ALGEBRAS  ALGEBRAS  ALGEBRAS  ALGEBRAS  ALGEBRAS  ALGEBRAS
-
-(IN-PACKAGE "CAT")
-
-(PROVIDE "algebras")
-
-(DEFMETHOD PRINT-OBJECT ((algb algebra) stream)
- (the algebra
-   (progn
-      (format stream "[K~D Algebra]" (idnm algb))
-      algb)))
-
-(DEFUN ALGEBRA (&rest rest &key dfnt &allow-other-keys)
-  (declare (type list dfnt))
-  (already algebra dfnt)
-  (the algebra
-    (apply #'make-instance 'algebra rest)))
-
-(DEFMETHOD SHARED-INITIALIZE
-    ((algb algebra) slot-names &key aprd-intr aprd-strt)
-  (declare
-   (type (or (eql t) list) slot-names)
-   (type intr aprd-intr)
-   (type strt aprd-strt))
-  (call-next-method)
-  (when-slot aprd
-             (with-slots (aprd) algb
-               (declare (type morphism aprd))
-               (when aprd-intr
-                 (unless aprd-strt
-                   (error "In ALGEBRA, an APRD-INTR is given, but not its APRD-STRT."))
-                 (setf aprd (morphism :sorc (tnsr-prdc algb algb) :trgt algb :degr 0
-                                      :intr aprd-intr :strt aprd-strt
-                                      :dfnt `(algebra-product ,algb))))))
-  algb)
-
-(DEFMETHOD PRINT-OBJECT ((hopf hopf-algebra) stream)
- (the hopf-algebra
-   (progn
-      (format stream "[K~D Hopf-Algebra]" (idnm hopf))
-      hopf)))
-
-(DEFUN HOPF-ALGEBRA (&rest rest &key dfnt &allow-other-keys)
-  (declare (type list dfnt))
-  (already hopf-algebra dfnt)
-  (the hopf-algebra
-    (apply #'make-instance 'hopf-algebra rest)))
-
-(DEFMETHOD SHARED-INITIALIZE ((hplg hopf-algebra) slot-names &rest rest)
-  (declare (ignore slot-names rest))
-  (call-next-method))
\ No newline at end of file
diff --git a/archive/Kenzo-2/Kenzo-2-Acl8/bar.cl b/archive/Kenzo-2/Kenzo-2-Acl8/bar.cl
deleted file mode 100644
index d8799d1..0000000
--- a/archive/Kenzo-2/Kenzo-2-Acl8/bar.cl
+++ /dev/null
@@ -1,701 +0,0 @@
-;;;  BAR  BAR  BAR  BAR  BAR  BAR  BAR  BAR  BAR
-;;;  BAR  BAR  BAR  BAR  BAR  BAR  BAR  BAR  BAR
-;;;  BAR  BAR  BAR  BAR  BAR  BAR  BAR  BAR  BAR
-
-;;;
-;;;  MAC-LANE signs (p. 306)
-;;;
-
-(IN-PACKAGE "CAT")
-
-(PROVIDE "bar")
-
-(DEFUN ABAR (&rest list)
-   (when (= 1 (length list))
-      (setf list (first list)))
-   (unless (evenp (length list))
-      (error "In ABAR, the length list should be even."))
-   (the abar
-      (let ((rslt (list :abar)))
-         (declare (list rslt))
-         (do ((mark list (cddr mark)))
-             ((endp mark))
-            (declare (list mark))
-            (push (brgn (car mark) (cadr mark)) rslt))
-         (nreverse rslt))))
-
-#|
-  (abar )
-  (abar '(2 a 3 b))
-  (abar 2 'a 3 'b)
-  (abar 2 'a 3))  ;; error
-|#
-
-(DEFCONSTANT +NULL-ABAR+ (make-abar :list +empty-list+))
-
-(DEFMETHOD PRINT-KEYCONS ((car (eql :abar)) cdr stream)
-   (declare
-      (list cdr)
-      (stream stream))
-   (the abar
-      (progn
-         (format stream "<<Abar")
-         (dolist (brgn cdr)
-            (declare (type brgn brgn))
-            (with-brgn (degr gnrt) brgn
-               (format stream "[~D ~A]" degr gnrt)))
-         (format stream ">>")
-         (cons car cdr))))
-
-(DEFUN BAR-CMPR (cmpr)
-   (declare (type cmprf cmpr))
-   (flet ((rslt (abar1 abar2)
-             (declare (type abar abar1 abar2))
-             (the cmpr
-                (lexico
-                   (f-cmpr (length abar1) (length abar2))
-                   (maplexico
-                      #'(lambda (brgn1 brgn2)
-                           (lexico
-                              (f-cmpr (bdegr brgn1) (bdegr brgn2))
-                              (funcall cmpr (bgnrt brgn1) (bgnrt brgn2))))
-                      (abar-list abar1)
-                      (abar-list abar2))))))
-      (the cmprf #'rslt)))
-
-#|
-  (setf r (bar-cmpr #'s-cmpr))
-  (funcall r (abar) (abar))
-  (funcall r (abar 3 'a) (abar))
-  (funcall r (abar 3 'a) (abar 2 'a 1 'b))
-  (funcall r (abar 3 'a) (abar 3 'b))
-  (funcall r (abar 3 'a) (abar 3 'a)))
-|#
-
-(DEFUN BAR-BASIS-LENGTH (basis degr length)
-   (declare
-      (type basis basis)
-      (fixnum degr length))
-   (the list
-      (progn
-	(when (= 1 length)
-	      (return-from bar-basis-length
-			   (mapcar
-			    #'(lambda (item)
-				(declare (type gnrt item))
-				(list (brgn degr item)))
-			    (funcall basis (1- degr)))))
-	(when (< degr 4)
-	      (return-from bar-basis-length +empty-list+))
-	(mapcan
-	 #'(lambda (degr1)
-	     (declare (fixnum degr1))
-	     (let ((list1 (funcall basis (1- degr1)))
-		   (list2 (bar-basis-length
-			    basis (- degr degr1) (1- length))))
-	       (declare (list list1 list2))
-	       (mapcan
-		#'(lambda (item1)
-		    (declare (type gnrt item1))
-		    (mapcar
-		     #'(lambda (item2)
-			 (declare (type iabar item2))
-			 (cons (brgn degr1 item1) item2))
-		     list2))
-		list1)))
-	 (>a-b< 1 (1- degr))))))
-
-#|
-  (setf basis #'(lambda (degr)
-                   (list degr)))
-  (bar-basis-length basis 2 1)
-  (bar-basis-length basis 2 2)
-  (bar-basis-length basis 3 1)
-  (bar-basis-length basis 3 2)
-  (bar-basis-length basis 4 1)
-  (bar-basis-length basis 4 2)
-  (bar-basis-length basis 4 3)
-  (bar-basis-length basis 4 4)
-  (bar-basis-length basis 8 1)
-  (bar-basis-length basis 8 2)
-  (bar-basis-length basis 8 3)
-  (bar-basis-length basis 8 4)
-  (bar-basis-length basis 8 5)
-  (bar-basis-length basis 8 6)
-  (bar-basis-length basis 8 11))
-|#
-
-(DEFUN BAR-BASIS (basis)
-   (declare (type basis basis))
-   (the basis
-      (progn
-         (when (eq :locally-effective basis)
-            (return-from bar-basis :locally-effective))
-	 (flet ((rslt (degr)
-		      (declare (fixnum degr))
-		      (cond ((zerop degr) (list +null-abar+))
-			    ((< degr 2) +empty-list+)
-			    (t
-			     (mapcan
-			      #'(lambda (length)
-				  (declare (fixnum length))
-				  (mapcar
-                                 #'(lambda (iabar)
-				     (declare (type iabar iabar))
-				     (make-abar :list iabar))
-                                 (bar-basis-length basis degr length)))
-			      (>a-b> 0 (floor degr 2)))))))
-	       #'rslt))))
-
-#|
-  (setf basis #'(lambda (degr)
-                   (list degr)))
-  (setf r (bar-basis basis))
-  (funcall r 0)
-  (funcall r 1)
-  (funcall r 2)
-  (dotimes (i 7)
-     (print (funcall r i)))
-  (bar-basis :locally-effective))
-|#
-
-(DEFUN BAR-INTR-VRTC-DFFR (dffr)
-   (declare (type morphism dffr))
-   (labels ((rslt (degr iabar)
-               ;; the argument iabar is an internal algebraic bar,
-               ;;     without the keyword :abar
-               ;; rslt returns an internal combination
-               ;;     without the keyword :cmbn, without degree
-               (declare
-                  (fixnum degr)
-                  (type iabar iabar))
-	       (progn
-		 (unless iabar
-		   (return-from rslt +empty-list+))
-		 (let ((brgn1 (first iabar))
-		       (rest2 (rest iabar)))
-		   (declare
-		     (type brgn brgn1)
-		     (type iabar rest2))
-		   (with-brgn (degr1 gnrt1) brgn1
-		   (let ((d-gnrt1 (cmbn-list (gnrt-? dffr (1- degr1) gnrt1)))
-			 (d-rest2 (rslt (- degr degr1) rest2))
-			 (degr1-1 (1- degr1))
-			 (rest-sign (-1-expt-n degr1)))
-		     (declare
-		       (type icmbn d-gnrt1 d-rest2)
-		       (fixnum degr1-1 rest-sign))
-		     (nconc
-		       (mapcar
-			 #'(lambda (term)
-			     (declare (type term term))
-			     (with-term (cffc gnrt) term
-			       (term (- cffc)
-				     (cons (brgn degr1-1 gnrt) rest2))))
-			 d-gnrt1)
-		       (mapcar
-			 #'(lambda (term)
-			     (with-term (cffc gnrt) term
-			       (term (* rest-sign cffc)
-				     (cons brgn1 gnrt))))
-			 d-rest2))))))))
-	(the intr
-	  #'(lambda (degr abar)
-	      (declare
-	        (fixnum degr)
-		(type abar abar))
-              (make-cmbn
-	        :degr (1- degr)
-		:list (mapcar
-		        #'(lambda (term)
-			    (with-term (cffc iabar) term
-			      (term cffc (make-abar :list iabar))))
-			(rslt degr (abar-list abar))))))))
-
-#|
-  (setf d (soft-delta-infinity))
-  (setf r (bar-intr-vrtc-dffr (dffr d)))
-  (funcall r 0 (abar))
-  (funcall r 3 (abar 3 (d 7)))
-  (funcall r 5 (abar 3 (d 7) 2 (d 3)))
-  (funcall r 5 (abar 2 (d 3) 3 (d 7))))
-|#
-
-(DEFMETHOD VRTC-BAR ((chcm chain-complex))
-   (the chain-complex
-     (let ((dfnt `(vrtc-bar ,chcm)))
-       (declare (type list dfnt))
-       (already vrtc-bar dfnt)
-       (with-slots (cmpr basis dffr) chcm
-         (declare
-          (type cmprf cmpr)
-          (type basis basis)
-          (type morphism dffr))
-         (chain-complex
-          :cmpr (bar-cmpr cmpr)
-          :basis (bar-basis basis)
-          :bsgn +null-abar+
-          :dffr-intr (bar-intr-vrtc-dffr dffr)
-          :dffr-strt :gnrt
-          :dfnt dfnt)))))
-
-#|
-  (cat-init)
-  (setf v (vrtc-bar (soft-delta-infinity)))
-  (defun random-abar (length)
-     (let ((rslt nil))
-        (dotimes (i length)
-           (let* ((gmsm (random (mask 7)))
-                  (dmns (1- (logcount gmsm))))
-              (when (plusp dmns)
-                 (push (brgn (1+ dmns) (d gmsm)) rslt))))
-        (make-abar :list rslt)))
-  (dotimes (i 10) (print (random-abar 5)))
-  (dotimes (i 10)
-     (let ((abar (random-abar 3)))
-        (print abar)
-        (print (? v (apply #'+ (mapcar #'car (abar-list abar))) abar))
-        (print (? v (? v (apply #'+ (mapcar #'car (abar-list abar))) abar)))))
-|#
-
-(DEFUN BAR-INTR-HRZN-DFFR (aprd)
-   (declare (type morphism aprd))
-   (labels ((rslt (degr iabar)
-               (declare
-                  (fixnum degr)
-                  (type iabar iabar))
-               (the icmbn
-                  (progn
-                     (unless (cdr iabar)
-                        (return-from rslt +empty-list+))
-                     (let ((brgn1 (first iabar))
-			   (brgn2 (second iabar))
-			   (rest1 (rest iabar))
-			   (rest2 (cddr iabar)))
-                        (declare
-                           (type brgn brgn1 brgn2)
-                           (type iabar rest1 rest2))
-                        (with-brgn (degr1 gnrt1) brgn1
-			(with-brgn (degr2 gnrt2) brgn2
-                           (let ((sign (-1-expt-n degr1))
-				 (aprd-brgn1-brgn2 (gnrt-? aprd (+ degr1 degr2 -2)
-							   (tnpr (1- degr1) gnrt1
-								 (1- degr2) gnrt2)))
-				 (aprd-rest1 (rslt (- degr degr1) rest1)))				  
-			     (declare
-			      (type icmbn aprd-brgn1-brgn2 aprd-rest1))
-			     (with-cmbn (degr12 icmbn12) aprd-brgn1-brgn2
-			       (incf degr12)
-			       (nconc
-			        (mapcar
-				 #'(lambda (term2)
-				     (declare (type term term2))
-				     (with-term (cffc2 iabar2) term2
-				       (term (* sign cffc2) (cons brgn1 iabar2))))
-				  aprd-rest1)
-				(mapcar
-				  #'(lambda (term1)
-				      (declare (type term term1))
-				      (with-term (cffc1 gnrt12) term1
-					(term (* sign cffc1) (cons (brgn degr12 gnrt12) rest2))))
-				  icmbn12)))))))))))
-      (the intr
-         #'(lambda (degr abar)
-              (declare
-                 (fixnum degr)
-                 (type abar abar))
-              (the cmbn
-                 (make-cmbn :degr (1- degr)
-                    :list (mapcar #'(lambda (term)
-                                       (declare (type term term))
-                                       (with-term (cffc iabar) term
-                                          (term cffc (make-abar :list iabar))))
-                             (rslt degr (abar-list abar)))))))))
-
-#|
-  (setf k (k-z-1))
-  (setf r (bar-intr-hrzn-dffr (aprd k)))
-  (funcall r 0 (abar ))
-  (funcall r 3 (abar 3 '(2 3)))
-  (funcall r 6 (abar 3 '(2 3) 3 '(-2 -3)))
-  (funcall r 9 (abar 3 '(2 3) 3 '(-2 -3) 3 '(2 3)))
-  (funcall r 11 (abar 3 '(2 3) 3 '(-2 -3) 2 '(-2) 3 '(-2 -3))))
-|#
-
-(DEFUN BAR-HRZN-DFFR (algb)
-   (declare (type algebra algb))
-   (the morphism
-      (with-slots (aprd) algb
-         (declare (type morphism aprd))
-         (morphism
-            :sorc (vrtc-bar algb) :trgt (vrtc-bar algb) :degr -1
-            :intr (bar-intr-hrzn-dffr aprd) :strt :gnrt
-            :dfnt `(bar-hrzn-dffr ,algb)))))
-
-#|
-  (cat-init)
-  (setf h (bar-hrzn-dffr (k-z-1)))
-  (defun random-abar (tot-degr~ max-degr)
-    (do ((rslt nil)
-         (cum-degr 0 (+ cum-degr degr 1))
-         (degr))
-        ((>= cum-degr tot-degr~) (make-abar :list rslt))
-       (setf degr (1+ (random max-degr)))
-       (push (brgn (1+ degr)
-                   (let ((list (make-list degr)))
-                     (mapl
-                       #'(lambda (sublist)
-                           (setf (car sublist) (- (random 21) 10)))
-                       list)
-                     list))
-             rslt)))
-  (dotimes (i 10) (print (random-abar 10 5)))
-  (setf abar (random-abar 10 5))
-  (? h (apply #'+ (mapcar #'car (abar-list abar))) abar)
-  (? h (? h (apply #'+ (mapcar #'car (abar-list abar))) abar))
-  (dotimes (i 10)
-     (let ((abar (random-abar 10 3)))
-        (print abar)
-        (print (? h (apply #'+ (mapcar #'car (abar-list abar))) abar))
-        (print (? h (? h (apply #'+ (mapcar #'car (abar-list abar))) abar)))))
-|#
-
-(DEFUN BAR-INTR-DFFR (vrtc-dffr hrzn-dffr)
-   (declare (type morphism vrtc-dffr hrzn-dffr))
-   (flet ((rslt (degr abar)
-             (declare
-                (fixnum degr)
-                (type abar abar))
-             (make-cmbn :degr (1- degr)
-                :list (append       ;;; and not nconc, otherwise a terrible bug, when the
-                                    ;;;   first result is stored in memory...
-                         (cmbn-list (gnrt-? hrzn-dffr degr abar))
-                         (cmbn-list (gnrt-? vrtc-dffr degr abar))))))
-      (the intr #'rslt)))
-
-(DEFMETHOD BAR ((algebra algebra))
-  (the chain-complex
-    (let ((vrtc-bar (vrtc-bar algebra))
-          (bar-hrzn-dffr (bar-hrzn-dffr algebra)))
-      (declare (type chain-complex vrtc-bar hrzn-bar))
-      (let ((rslt (chain-complex
-                   :cmpr (cmpr vrtc-bar)
-                   :basis (basis vrtc-bar)
-                   :bsgn +null-abar+
-                   :dffr-intr (bar-intr-dffr (dffr vrtc-bar) bar-hrzn-dffr)
-                   :dffr-strt :gnrt
-                   :dfnt `(add ,vrtc-bar ,bar-hrzn-dffr))))
-          (declare (type chain-complex rslt))
-          (setf (slot-value rslt 'grmd) (grmd vrtc-bar))
-          rslt))))
-
-#|
-(cat-init)
-(setf b (bar (k-z-1)))   
-(defun random-abar (tot-degr~ max-degr)
-  (do ((rslt nil)
-       (cum-degr 0 (+ cum-degr degr 1))
-       (degr))
-      ((>= cum-degr tot-degr~) (make-abar :list rslt))
-    (setf degr (1+ (random max-degr)))
-    (push (brgn (1+ degr)
-                (let ((list (make-list degr)))
-                  (mapl
-                      #'(lambda (sublist)
-                          (setf (car sublist) (- (random 21) 10)))
-                    list)
-                  list))
-          rslt)))
-(setf abar (random-abar 10 3))
-(? b (apply #'+ (mapcar #'car (abar-list abar))) abar)
-(? b (? b (apply #'+ (mapcar #'car (abar-list abar))) abar))
-(dotimes (i 10)
-  (let ((abar (random-abar 10 3)))
-    (print abar)
-    (print (? b (apply #'+ (mapcar #'car (abar-list abar))) abar))
-    (print (? b (? b (apply #'+ (mapcar #'car (abar-list abar))) abar)))))
-|#
-
-(DEFUN CMBN-ABAR-CMBN-TNPR (cmbn abar-cmbn)
-   (declare (type cmbn cmbn abar-cmbn))
-   (the cmbn
-      (with-cmbn (degr1 list1) cmbn
-         (incf degr1)     ;; because abar organization
-      (with-cmbn (degrr listr) abar-cmbn
-         (make-cmbn
-            :degr (+ degr1 degrr)
-            :list
-            (mapcan
-               #'(lambda (term1)
-                    (declare (type term term1))
-                    (with-term (cffc1 gnrt1) term1
-                       (let ((brgn1 (brgn degr1 gnrt1)))
-                          (declare (type brgn brgn1))
-                          (mapcar
-                             #'(lambda (termr)
-                                  (declare (type term termr))
-                                  (with-term (cffcr abarr) termr
-                                     (term (* cffc1 cffcr)
-                                        (make-abar
-                                           :list (cons brgn1 (abar-list abarr))))))
-                             listr))))
-               list1))))))
-
-(DEFUN NCMBN-BAR (cmbn-list)
-   (declare (list cmbn-list))
-   (the cmbn
-      (progn
-         (unless cmbn-list
-            (return-from ncmbn-bar (cmbn 0 1 +null-abar+)))
-         (cmbn-abar-cmbn-tnpr
-            (first cmbn-list)
-            (ncmbn-bar (rest cmbn-list))))))
-#|
-  (ncmbn-bar nil)
-  (ncmbn-bar (list (cmbn 3 2 'a 3 'b)))
-  (ncmbn-bar (list (cmbn 1 2 'a 3 'b) (cmbn 2 4 'c 5 'd)))
-  (ncmbn-bar (list (cmbn 1 2 'a 3 'b) (cmbn 1 4 'c 5 'd) (cmbn 1 6 'e 7 'f))))
-|#
-
-(DEFUN MRPH-VRTC-BAR-INTR (mrph)
-   (declare (type morphism mrph))
-   (flet ((rslt (degr abar)
-             (declare
-                (ignore degr)
-                (type abar abar))
-             (the cmbn
-                (ncmbn-bar
-                   (mapcar #'(lambda (brgn)
-                                (declare (type brgn brgn))
-                                (with-brgn (degr gnrt) brgn
-                                   (gnrt-? mrph (1- degr) gnrt)))
-                      (abar-list abar))))))
-      (the intr #'rslt)))
-
-#|
-  (setf cc (chain-complex :cmpr #'f-cmpr :dffr-strt :cmbn))
-  (setf m (morphism :sorc cc :trgt cc :degr 0 :intr
-            #'(lambda (degr gnrt) (cmbn degr 2 gnrt 3 (1+ gnrt)))
-            :strt :gnrt :dfnt '(test)))
-  (setf r (mrph-vrtc-bar-intr m))
-  (funcall r 4 (abar 2 3 2 4))
-|#
-
-(DEFMETHOD VRTC-BAR ((mrph morphism))
-  (the morphism
-    (let ((dfnt `(vrtc-bar ,mrph)))
-      (declare (type list dfnt))
-      (if (eq (first (dfnt mrph)) 'idnt-mrph)
-          (idnt-mrph (vrtc-bar (sorc mrph)))
-        (morphism
-         :sorc (vrtc-bar (sorc mrph))
-         :trgt (vrtc-bar (trgt mrph))
-         :degr 0
-         :intr (mrph-vrtc-bar-intr mrph)
-         :strt :gnrt
-         :dfnt dfnt)))))
-
-#|
-  (cat-init)
-  (setf f (aw (soft-delta-infinity) (soft-delta-infinity)))
-  (setf cf (vrtc-bar f))
-  (? cf 6 (abar 3 (crpr 0 (d 7) 0 (d 7)) 3 (crpr 0 (d 56) 0 (d 56))))
-|#
-
-(DEFUN HMTP-VRTC-BAR-INTR (h gf)
-   (declare (type morphism h gf))
-   (labels ((rslt (degr iabar)
-	      (declare
-	       (fixnum degr)
-	       (type iabar iabar))
-	      (unless iabar
-		(return-from rslt +empty-list+))
-	      (let ((brgn1 (first iabar))
-		    (rest2 (rest iabar)))
-		(declare
-		 (type brgn brgn1)
-		 (list rest2))
-		(with-brgn (degr1 gnrt1) brgn1
-		  (let ((h-gnrt1 (cmbn-list (gnrt-? h (1- degr1) gnrt1)))
-			(h-rest2 (rslt (- degr degr1) rest2))
-			(degr1+1 (1+ degr1))
-			(rest-sign (-1-expt-n degr1))
-			(gf-gnrt1 (cmbn-list (gnrt-? gf (1- degr1) gnrt1))))
-		    (declare
-		      (fixnum degr1+1 rest-sign)
-		      (type icmbn h-gnrt1 h-rest2 gf-gnrt1))
-		    (nconc
-		     (mapcan
-		      #'(lambda (term1)
-			  (declare (type term term1))
-			  (with-term (cffc1 gnrt11) term1
-			    (mapcar
-			     #'(lambda (term2)
-				 (declare (type term term2))
-				 (with-term (cffc2 iabar2) term2
-				   (term (* rest-sign cffc1 cffc2)
-					 (cons (brgn degr1 gnrt11) iabar2))))
-			     h-rest2)))
-		      gf-gnrt1)
-		     (mapcar
-		      #'(lambda (term1)
-			  (declare (type term term1))
-			  (with-term (cffc1 gnrt11) term1
-			    (term (- cffc1)
-				  (cons (brgn degr1+1 gnrt11) rest2))))
-		      h-gnrt1)))))))
-	   (the intr
-	      #'(lambda (degr abar)
-		  (declare
-		    (fixnum degr)
-		    (type abar abar))
-		  (make-cmbn
-		   :degr (1+ degr)
-		   :list (mapcar
-			  #'(lambda (term)
-			      (declare (type term term))
-			      (with-term (cffc iabar) term
-				(declare
-				   (fixnum cffc)
-				   (type iabar iabar))
-				(term cffc (make-abar :list iabar))))
-			  (rslt degr (abar-list abar))))))))
-
-#|
-  (cat-init)
-  (setf ez (ez (delta-infinity) (delta-infinity)))
-  (setf h (h ez) gf (cmps (g ez) (f ez)))
-  (setf r (hmtp-vrtc-bar-intr h gf))
-  (funcall r 3 (abar 3 (crpr 0 7 0 7)))
-  (funcall r 9 (abar 3 (crpr 0 7 0 7) 3 (crpr 0 14 0 14) 3 (crpr 0 14 0 14)))
-|#
-
-(DEFUN HMTP-VRTC-BAR (h gf)
-   (declare (type morphism h gf))
-   (unless (and (= +1 (degr h))
-                (= +0 (degr gf)))
-      (error "In HMTP-VRTC-BAR, the morphism degrees are not the right ones."))
-   (unless (and (eq (sorc h) (trgt h))
-                (eq (trgt h) (sorc gf))
-                (eq (sorc gf) (trgt gf)))
-      (error "In HMTP-VRTC-BAR, fg-h sources and targets are not the same."))
-   (the morphism
-      (if (eq (first (dfnt h)) 'zero-mrph)
-         (zero-mrph (vrtc-bar (sorc h)))
-         (morphism
-            :sorc (vrtc-bar (sorc h)) :trgt (vrtc-bar (sorc h)) :degr +1
-            :intr (hmtp-vrtc-bar-intr h gf)
-            :strt :gnrt
-            :dfnt `(hmtp-vrtc-bar ,h ,gf)))))
-
-(DEFMETHOD VRTC-BAR ((rdct reduction))
-  (the reduction
-    (let ((dfnt `(vrtc-bar ,rdct)))
-      (declare (type list dfnt))
-      (if (eq (first (dfnt rdct)) 'trivial-rdct)
-          (trivial-rdct (vrtc-bar (bcc rdct)))
-        (with-slots (f g h) rdct
-          (reduction
-           :f (vrtc-bar f)
-           :g (vrtc-bar g)
-           :h (hmtp-vrtc-bar h (cmps g f))
-           :dfnt dfnt))))))
-  
-#|
-  (cat-init)
-  (setf tcc (chain-complex
-               :cmpr #'s-cmpr
-               :basis #'(lambda (degr) '(a b c d))
-               :bsgn 'd
-               :dffr-intr #'(lambda (degr gnrt)
-                               (ecase gnrt
-                                  (a (cmbn (1- degr) 1 'b 1 'd))
-                                  ((b d) (cmbn (1- degr)))
-                                  (c (cmbn (1- degr) 1 'd))))
-               :dffr-strt :gnrt
-               :dfnt '(tcc)))
-  (setf bcc (chain-complex
-               :cmpr #'s-cmpr
-               :basis #'(lambda (degr) '(c d))
-               :bsgn 'd
-               :dffr-intr #'(lambda (degr gnrt)
-                               (ecase gnrt
-                                  (d (cmbn (1- degr)))
-                                  (c (cmbn (1- degr) 1 'd))))
-               :dffr-strt :gnrt
-               :dfnt '(bcc)))
-  (setf f (morphism :sorc tcc :trgt bcc :degr 0
-             :intr #'(lambda (degr gnrt)
-                        (ecase gnrt
-                           (a (cmbn degr 1 'c 1 'd))
-                           (b (cmbn degr))
-                           ((c d) (cmbn degr 1 gnrt))))
-             :strt :gnrt :dfnt '(f)))
-  (setf g (morphism :sorc bcc :trgt tcc :degr 0
-             :intr #'identity :strt :cmbn :dfnt '(g)))
-  (setf h (morphism :sorc tcc :trgt tcc :degr +1
-             :intr #'(lambda (degr gnrt)
-                        (ecase gnrt
-                           ((a b) (cmbn (1+ degr) 1 'a -1 'b -1 'c -1 'd))
-                           ((c d) (cmbn (1+ degr)))))
-             :strt :gnrt :dfnt '(h)))
-  (setf rdct (reduction :f f :g g :h h :dfnt '(rdct)))
-  (tcc rdct 3 'a)
-  (g rdct (f rdct 3 'a))
-  (h rdct 3 'a)
-  (setf bar (vrtc-bar rdct))
-  (pre-check-rdct bar)
-  (defun aleat-tc ()
-     (do ((tdegr 0 (+ tdegr degr))
-          (degr (+ 2 (random 3)) (+ 2 (random 3)))
-          (gnrt (intern (coerce (vector (code-char (+ 65 (random 4)))) 'string))
-                (intern (coerce (vector (code-char (+ 65 (random 4)))) 'string)))
-          (rslt nil (cons (brgn degr gnrt) rslt)))
-         ((> tdegr 10) (setf *tc* (cmbn tdegr 1 (make-abar :list rslt))))))
-  (aleat-tc)
-  (defun aleat-bc ()
-     (do ((tdegr 0 (+ tdegr degr))
-          (degr (+ 2 (random 3)) (+ 2 (random 3)))
-          (gnrt (intern (coerce (vector (code-char (+ 67 (random 2)))) 'string))
-                (intern (coerce (vector (code-char (+ 67 (random 2)))) 'string)))
-          (rslt nil (cons (brgn degr gnrt) rslt)))
-         ((> tdegr 10) (setf *bc* (cmbn tdegr 1 (make-abar :list rslt))))))
-  (aleat-bc)
-  (defun c ()
-     (aleat-tc)
-     (aleat-bc)
-     (check-rdct))
-  (loop (c))  ;; degrees >= 15 is possible => error.
-|#
-
-(DEFMETHOD VRTC-BAR ((eqvl equivalence))
-  (the equivalence
-    (let ((dfnt `(vrtc-bar ,eqvl)))
-      (declare (type list dfnt))
-      (already vrtc-bar dfnt)
-      (if (eq (first (dfnt eqvl)) 'trivial-eqvl)
-          (trivial-eqvl (vrtc-bar (lbcc eqvl)))
-        (with-slots (lrdct rrdct) eqvl
-          (equivalence 
-           :lrdct (vrtc-bar lrdct)
-           :rrdct (vrtc-bar rrdct)
-           :dfnt dfnt))))))
-
-(DEFMETHOD BAR ((eqvl equivalence))
-  (unless (typep (lbcc eqvl) 'algebra)
-    (error "In (BAR eqvl), the LBCC should be a algebra."))
-  (the equivalence
-    (if (eq (first (dfnt eqvl)) 'trivial-eqvl)
-        (trivial-eqvl (bar (lbcc eqvl)))
-      (add (vrtc-bar eqvl) (bar-hrzn-dffr (lbcc eqvl))))))
-
-#|
-  (cat-init)
-  (setf h (efhm (k-z-1)))
-  (setf b (bar h))
-  (inspect b)
-  (homology (rbcc b) 0 11)
-|#
-
-  
-
diff --git a/archive/Kenzo-2/Kenzo-2-Acl8/cartesian-products.cl b/archive/Kenzo-2/Kenzo-2-Acl8/cartesian-products.cl
deleted file mode 100644
index edc1cda..0000000
--- a/archive/Kenzo-2/Kenzo-2-Acl8/cartesian-products.cl
+++ /dev/null
@@ -1,311 +0,0 @@
-;;;  CARTESIAN-PRODUCTS  CARTESIAN-PRODUCTS  CARTESIAN-PRODUCTS  CARTESIAN-PRODUCTS
-;;;  CARTESIAN-PRODUCTS  CARTESIAN-PRODUCTS  CARTESIAN-PRODUCTS  CARTESIAN-PRODUCTS
-;;;  CARTESIAN-PRODUCTS  CARTESIAN-PRODUCTS  CARTESIAN-PRODUCTS  CARTESIAN-PRODUCTS
-
-(IN-PACKAGE "CAT")
-
-(PROVIDE "cartesian-products")
-
-(DEFMETHOD PRINT-KEYCONS ((car (eql :crpr)) cdr stream)
-   (declare
-      (cons cdr)
-      (stream stream))
-   (the (eql t)
-      (progn
-         (setf cdr (cons car cdr))
-         (with-crpr (dgop1 gmsm1 dgop2 gmsm2) cdr
-            (format stream
-               "<CrPr ~A ~A ~A ~A>"
-               (hyphenize-list (dgop-int-ext dgop1)) gmsm1
-               (hyphenize-list (dgop-int-ext dgop2)) gmsm2)
-            cdr)
-         t)))
-
-(DEFUN EXTRACT-COMMON-DGOP (dgop1 dgop2)
-   (declare (fixnum dgop1 dgop2))
-   (let ((dgop (logand dgop1 dgop2)))
-      (declare (fixnum dgop))
-      (do ((indx (1- (integer-length dgop)) (1- indx)))
-          ((minusp indx))
-         (declare (fixnum indx))
-         (when (logbitp indx dgop)
-            (setf dgop1 (remove-bit dgop1 indx)
-                  dgop2 (remove-bit dgop2 indx))))
-      (values dgop dgop1 dgop2)))
-
-#|
-  (dotimes (i 100)
-     (dotimes (j 100)
-        (multiple-value-bind (dgop dgop1 dgop2) (extract-common-dgop i j)
-           (unless (and (= i (dgop*dgop dgop dgop1))
-                        (= j (dgop*dgop dgop dgop2)))
-              (error "i = ~D, j = ~D, dgop = ~D, dgop1 = ~D, dgop2 = ~D"
-                 i j dgop dgop1 dgop2)))))
-|#
-
-(DEFUN 2ABSM-ACRPR (absm1 absm2)
-   (declare (type absm absm1 absm2))
-   (the absm
-      (with-absm (dgop1 gmsm1) absm1
-      (with-absm (dgop2 gmsm2) absm2
-         (multiple-value-bind (dgop dgop11 dgop22) (extract-common-dgop dgop1 dgop2)
-            (declare (fixnum dgop dgop11 dgop22))
-            (absm dgop
-               (crpr dgop11 gmsm1 dgop22 gmsm2)))))))
-
-#|
-  (2absm-acrpr (absm 5 'a) (absm 3 'b))
-|#
-
-(DEFUN CRTS-PRDC-CMPR (cmpr1 cmpr2)
-   (declare (type cmprf cmpr1 cmpr2))
-   (flet ((rslt (crpr1 crpr2)
-             (declare (type crpr crpr1 crpr2))
-             (the cmpr
-                (let ((left-cons-1 (cadr crpr1))
-                      (left-cons-2 (cadr crpr2)))
-                   (declare (cons left-cons-1 left-cons-2))
-                   (lexico
-                      (f-cmpr (car left-cons-1) (car left-cons-2))
-                      (let ((right-cons-1 (cddr crpr1))
-                            (right-cons-2 (cddr crpr2)))
-                         (declare (cons right-cons-1 right-cons-2))
-                         (lexico
-                            (f-cmpr (car right-cons-1) (car right-cons-2))
-                            (funcall cmpr1 (cdr left-cons-1) (cdr left-cons-2))
-                            (funcall cmpr2 (cdr right-cons-1) (cdr right-cons-2)))))))))
-      (the cmprf #'rslt)))
-
-#|
-  (setf c (cmpr (delta-infinity)))
-  (setf rslt (crts-prdc-cmpr c c))
-  (funcall rslt (crpr 0 3 0 3) (crpr 1 1 0 3))
-  (funcall rslt (crpr 4 3 0 7) (crpr 3 1 0 7))
-  (funcall rslt (crpr 0 3 0 3) (crpr 0 3 1 1))
-  (funcall rslt (crpr 0 3 0 3) (crpr 0 5 0 3))
-  (funcall rslt (crpr 0 3 0 3) (crpr 0 3 0 5))
-  (funcall rslt (crpr 0 3 0 3) (crpr 0 3 0 3)))
-|#
-           
-(DEFUN CRTS-PRDC-BASIS (basis1 basis2)
-   (declare (type basis basis1 basis2))
-   (when (or (eq basis1 :locally-effective)
-             (eq basis2 :locally-effective))
-      (return-from crts-prdc-basis :locally-effective))
-   (flet ((rslt (dmns)
-             (declare (fixnum dmns))
-             (the list
-                (progn
-                   (when (minusp dmns)
-                      (return-from rslt +empty-list+))
-                   (let ((array1 (make-array (1+ dmns)))
-                         (array2 (make-array (1+ dmns)))
-                         (rslt +empty-list+)
-                         (mask (mask dmns)))
-                      (declare
-                         (simple-vector array1 array2)
-                         (list rslt)
-                         (fixnum mask))
-                      (dotimes (i (1+ dmns))
-                         (setf (svref array1 i) (funcall basis1 i)
-                               (svref array2 i) (funcall basis2 i)))
-                      (do ((dgop1 mask (1- dgop1)))
-                          ((minusp dgop1))
-                         (declare (fixnum dgop1))
-                         (let ((dmns1 (- dmns (logcount dgop1))))
-                            (declare (fixnum dmns1))
-                            (do ((dgop2 mask (1- dgop2)))
-                                ((minusp dgop2))
-                               (declare (fixnum dgop2))
-                               (unless (plusp (logand dgop1 dgop2))
-                                  (setf rslt
-                                        (nconc
-                                           (mapcan
-                                              #'(lambda (item1)
-                                                   (declare (type gmsm item1))
-                                                   (mapcar
-                                                      #'(lambda (item2)
-                                                           (declare (type gmsm item2))
-                                                           (crpr dgop1 item1 dgop2 item2))
-                                                      (svref array2 (- dmns (logcount dgop2)))))
-                                              (svref array1 dmns1))
-                                           rslt))))))
-                      rslt)))))
-          (the basis #'rslt)))
-
-#|
-  (setf b (basis (delta 1)))
-  (setf r (crts-prdc-basis b b))
-  (funcall r 0)
-  (funcall r 1)
-  (funcall r 2)
-  (funcall r 3)
-  (setf d3 (basis (delta 3)))
-  (setf r (crts-prdc-basis d3 d3))
-  (time (dotimes (i 7)
-           (print (length (funcall r i)))))
-  (setf s3 (basis (sphere 3)))
-  (setf p (crts-prdc-basis s3 s3))
-  (dotimes (i 8)
-     (print (funcall p i)))
-|#
-
-(DEFUN CRTS-PRDC-FACE (face1 face2)
-   (declare (type face face1 face2))
-   (flet ((rslt (indx dmns crpr)
-             (declare
-                (fixnum indx dmns)
-                (type crpr crpr))
-             (with-crpr (dgop1 gmsm1 dgop2 gmsm2) crpr
-                (multiple-value-bind (dgop1 del1) (1dlop-dgop indx dgop1)
-                   (declare
-                      (fixnum dgop1)
-                      (type (or null fixnum) del1))
-                (multiple-value-bind (dgop2 del2) (1dlop-dgop indx dgop2)
-                   (declare
-                      (fixnum dgop2)
-                      (type (or null fixnum) del2))
-                   (when del1
-                      (let ((absm1 (funcall face1 del1 (- dmns (logcount dgop1)) gmsm1)))
-                         (declare (type absm absm1))
-                         (setf dgop1 (dgop*dgop dgop1 (dgop absm1))
-                               gmsm1 (gmsm absm1))))
-                   (when del2
-                      (let ((absm2 (funcall face2 del2 (- dmns (logcount dgop2)) gmsm2)))
-                         (declare (type absm absm2))
-                         (setf dgop2 (dgop*dgop dgop2 (dgop absm2))
-                               gmsm2 (gmsm absm2))))
-                   (multiple-value-bind (dgop dgop1 dgop2) (extract-common-dgop dgop1 dgop2)
-                            (declare (fixnum dgop dgop1 dgop2))
-                            (absm dgop (crpr dgop1 gmsm1 dgop2 gmsm2))))))))
-         (the face #'rslt)))
-
-#|
-  (setf d2 (delta 2))
-  (setf b2 (basis d2))
-  (setf f2 (face d2))
-  (setf b (crts-prdc-basis b2 b2))
-  (setf r (crts-prdc-face f2 f2))
-  (dotimes (i 5)
-     (unless (zerop i)
-        (dolist (item (funcall b i))
-           (dotimes (j (1+ i))
-              (format t "~%del-~D ~A = ~A"
-                 j item (funcall r j i item))))))
-|#
-
-(DEFUN CRTS-PRDC-FACE* (face1 face2)
-   (declare (type face face1 face2))
-   (flet ((rslt (indx dmns crpr)
-             (declare
-                (fixnum indx dmns)
-                (type crpr crpr))
-             (with-crpr (dgop1 gmsm1 dgop2 gmsm2) crpr
-                (multiple-value-bind (dgop1 del1) (1dlop-dgop indx dgop1)
-                   (declare
-                      (fixnum dgop1)
-                      (type (or null fixnum) del1))
-                (multiple-value-bind (dgop2 del2) (1dlop-dgop indx dgop2)
-                   (declare
-                      (fixnum dgop2)
-                      (type (or null fixnum) del2))
-                   (when del1
-                      (let ((absm1 (funcall face1 del1 (- dmns (logcount dgop1)) gmsm1)))
-                         (declare (type absm absm1))
-                         (setf dgop1 (dgop*dgop dgop1 (dgop absm1))
-                               gmsm1 (gmsm absm1))))
-                   (when del2
-                      (let ((absm2 (funcall face2 del2 (- dmns (logcount dgop2)) gmsm2)))
-                         (declare (type absm absm2))
-                         (setf dgop2 (dgop*dgop dgop2 (dgop absm2))
-                               gmsm2 (gmsm absm2))))
-                   (if (plusp (logand dgop1 dgop2))
-                      :degenerate
-                      (crpr dgop1 gmsm1 dgop2 gmsm2)))))))
-         (the intr #'rslt)))
-
-#|
-  (setf d2 (delta 2))
-  (setf b2 (basis d2))
-  (setf f2 (face d2))
-  (setf b (crts-prdc-basis b2 b2))
-  (setf r (crts-prdc-face* f2 f2))
-  (dotimes (i 5)
-     (unless (zerop i)
-        (dolist (item (coerce (funcall b i) 'list))
-           (dotimes (j (1+ i))
-              (format t "~%del-~D ~A = ~A"
-                 j item (funcall r j i item))))))
-  (setf s3 (sphere 3))
-  (setf b3 (basis s3))
-  (setf f3 (face s3))
-  (setf b (crts-prdc-basis b3 b3))
-  (setf r (crts-prdc-face* f3 f3))
-  (dotimes (i 7)
-     (unless (zerop i)
-        (dolist (item (coerce (funcall b i) 'list))
-           (dotimes (j (1+ i))
-              (format t "~%del-~D ~A = ~A"
-                 j item (funcall r j i item))))))
-|#
-
-(DEFUN CRTS-PRDC (smst1 smst2)
-  (declare (type simplicial-set smst1 smst2))
-  (the simplicial-set
-    (with-slots ((cmpr1 cmpr) (basis1 basis) (face1 face) (bsgn1 bsgn)) smst1
-      (declare
-       (type cmprf cmpr1)
-       (type basis basis1)
-       (type face face1))
-      (with-slots ((cmpr2 cmpr) (basis2 basis) (face2 face) (bsgn2 bsgn)) smst2
-        (declare
-         (type cmprf cmpr2)
-         (type basis basis2)
-         (type face face2))
-        (simplicial-set
-         :cmpr (crts-prdc-cmpr cmpr1 cmpr2)
-         :basis (crts-prdc-basis basis1 basis2)
-         :bsgn (crpr 0 bsgn1 0 bsgn2)
-         :face (crts-prdc-face face1 face2)
-         :face* (crts-prdc-face* face1 face2)
-         :dfnt `(crts-prdc ,smst1 ,smst2))))))
-
-#|
-  (setf p (crts-prdc (delta 3) (delta 3)))
-  (? p 0 (crpr 0 1 0 2))
-  (? p 1 (crpr 0 3 0 3))
-  (? p 2 (crpr 0 7 0 7))
-  (? p 3 (crpr 0 15 0 15))
-  (? p 4 (crpr 1 15 2 15))
-|#
-
-#|
-  ;; For comparison with EAT.
-  ;; In CAT.
-  (setf s5 (sphere 5))
-  (setf p (crts-prdc s5 s5))
-  (setf b (basis p))
-  (setf d (dffr p))
-  (setf basis (funcall b 10))
-  (length basis)
-  (setf c (make-cmbn :degr 10 :list (mapcar #'(lambda (item)
-                                                (term (1+ (random 5)) item))
-                                      basis)))
-  (setf +too-much-time+ -1)
-  (cmbn-? d (cmbn-? d c))
-  (time (dotimes (i 5) (cmbn-? d (cmbn-? d c))))
-|#
-
-#|
-  ;; In EAT.
-  (setf s5 (sphere 5))
-  (setf p (cpr-2ss s5 s5))
-  (setf d (cc-d (ss-cc p)))
-  (setf basis (sbs p 10))
-  (length basis)
-  (setf c (make-cmb :dgr 10 :lst (mapcar #'(lambda (item)
-                                                (mnm (1+ (random 5)) item))
-                                     basis)))
-  (??? d (??? d c))
-  (time (dotimes (i 5) (??? d (??? d c))))
-|#
diff --git a/archive/Kenzo-2/Kenzo-2-Acl8/chain-complexes.cl b/archive/Kenzo-2/Kenzo-2-Acl8/chain-complexes.cl
deleted file mode 100644
index 8e5b5a5..0000000
--- a/archive/Kenzo-2/Kenzo-2-Acl8/chain-complexes.cl
+++ /dev/null
@@ -1,526 +0,0 @@
-;;;  CHAIN-COMPLEXES  CHAIN-COMPLEXES  CHAIN-COMPLEXES  CHAIN-COMPLEXES
-;;;  CHAIN-COMPLEXES  CHAIN-COMPLEXES  CHAIN-COMPLEXES  CHAIN-COMPLEXES
-;;;  CHAIN-COMPLEXES  CHAIN-COMPLEXES  CHAIN-COMPLEXES  CHAIN-COMPLEXES
-
-(IN-PACKAGE "CAT")
-
-(PROVIDE "chain-complexes")
-
-(DEFVAR *K-LIST* +empty-list+)
-
-(DEFUN CAT-INIT (&optional (idnm 0))
-  (declare (type fixnum idnm))
-  (setf *idnm-counter* idnm
-    *k-list* (member idnm *k-list* :key #'idnm))
-  (done))
-
-(DEFUN ALL-OBJECTS ()
-  (dolist (item *k-list*)
-    (declare (type kenzo-object item))
-    (format t "~%~A = ~A" item (dfnt item)))
-  (done))
-
-(DEFUN KD (idnm)
-  (declare (fixnum idnm))
-  (let ((found (find idnm *k-list* :key #'idnm)))
-    (when found
-      (format t "~%Object: ~A~@
-                   ~3TOrigin: ~A~2%" found (dfnt found))))
-  (values))
-
-(DEFUN K (idnm)
-  (declare (fixnum idnm))
-  (let ((found (find idnm *k-list* :key #'idnm)))
-    (when found
-      (return-from k found))))
-
-(DEFUN KD2 (idnm)
-  (declare (fixnum idnm))
-  (let ((k-list (k idnm)))
-    (declare (type (or kenzo-object list) k-list))
-    (unless k-list
-      (return-from kd2 nil))
-    (setf k-list (list k-list))
-    (do ((idnm (1- idnm) (1- idnm)))
-        ((zerop idnm))
-      (declare (fixnum idnm))
-      (let ((found (find-if
-                    #'(lambda (item)
-                        (declare (type (or chain-complex morphism) item))
-                        (member (k idnm) (dfnt item)))
-                    k-list)))
-        (declare (type (or null chain-complex morphism) found))
-        (when found
-          (push (k idnm) k-list))))
-    (mapc #'kd (nreverse (mapcar #'idnm k-list)))))
-    
-(DEFMETHOD PRINT-OBJECT ((chcm chain-complex) stream)
- (the chain-complex
-   (progn
-      (format stream "[K~D Chain-Complex]" (idnm chcm))
-      chcm)))
-
-;;; Result = (:rslt gnrt value clnm rntm . prpr)
-
-(DEFMETHOD PRINT-KEYCONS ((key (eql :rslt)) cdr stream)
-   (the list
-      (progn
-         (setf cdr (cons key cdr))
-         (format stream "~%<Rslt>~@
-	                 ~4TGNRT-> ~A~@
-                         ~3TVALUE-> ~A~@
-                         ~4TCLNM-> ~6D~@
-                         ~4TRNTM-> ~11,3F"
-            (rslt-gnrt cdr) (rslt-value cdr)
-            (rslt-clnm cdr) (rslt-rntm cdr))
-         cdr)))
-
-#|
-  (make-rslt :gnrt 'a :value '(a a) :clnm 23 :rntm 2.345)
-|#
-
-(DEFPARAMETER +MAXIMAL-DIMENSION+ 15)
-
-(DEFMETHOD ?2 ((mrph morphism) cmbn)
-   (declare (type cmbn cmbn))
-   (the cmbn
-      (cmbn-? mrph cmbn)))
-
-(DEFMETHOD ?2 ((chcm chain-complex) cmbn)
-   (declare
-      (type cmbn cmbn))
-   (the cmbn
-      (cmbn-? (dffr1 chcm) cmbn)))
-
-(DEFMETHOD ?3 ((mrph morphism) degr gnrt)
-   (declare
-      (fixnum degr)
-      (type gnrt gnrt))
-   (the cmbn
-      (gnrt-? mrph degr gnrt)))
-
-(DEFMETHOD ?3 ((chcm chain-complex) degr gnrt)
-   (declare
-      (fixnum degr)
-      (type gnrt gnrt))
-   (gnrt-? (dffr1 chcm) degr gnrt))
-
-(DEFMETHOD PRINT-OBJECT ((mrph morphism) stream)
-   (the morphism
-      (progn
-	(if (eq (first (dfnt (trgt mrph))) 'z-chcm)
-	    (format stream "[K~D Cohomology-Class on K~D of degree ~D]"
-		    (idnm mrph) (idnm (sorc mrph)) (- (degr mrph)))
-	  (format stream "[K~D Morphism (degree ~D): K~D -> K~D]"
-		  (idnm mrph) (degr mrph)
-		  (idnm (sorc mrph)) (idnm (trgt mrph))))
-        mrph)))
-
-(DEFMETHOD SHARED-INITIALIZE ((k kenzo-object) slot-names &key dfnt prpr cmmn)
-  (declare
-   (type (or (eql t) list) slot-names)
-   (type list dfnt))
-  (when-slot dfnt
-             (with-slots (idnm (dfnts dfnt) (prprs prpr) (cmmns cmmn)) k
-               (declare
-                (type fixnum idnm)
-                (type list dfnts))
-               (setf idnm (incf *idnm-counter*))
-               (when dfnt
-                 (setf dfnts dfnt))
-               (when prpr
-                 (setf prprs prpr))
-               (when cmmn
-                 (setf cmmns cmmn))))
-  k)
-             
-(DEFMETHOD INITIALIZE-INSTANCE :after ((k kenzo-object) &rest rest)
-  (push k *k-list*))
-             
-(DEFUN CHAIN-COMPLEX (&rest rest &key dfnt &allow-other-keys)
-  (declare (type list dfnt))
-  (already chain-complex dfnt)
-  (the chain-complex
-    (apply #'make-instance 'chain-complex rest)))
-
-(DEFMETHOD SHARED-INITIALIZE
-    ((chcm chain-complex) slot-names
-     &key cmpr basis (bsgn :undefined) dffr-intr dffr-strt grmd)
-  (declare
-   (type (or (eql t) list) slot-names)
-   (type cmprf cmpr)
-   (type basis basis)
-   (type gnrt bsgn)
-   (type intr dffr-intr)
-   (type strt dffr-strt)
-   (type chain-complex grmd))
-  (call-next-method)
-  (when-slot cmpr
-             (with-slots ((cmprs cmpr) (basiss basis) (bsgns bsgn)
-                          dffr (grmds grmd)) chcm
-               (declare
-                (type cmprf cmprs)
-                (type basis basiss)
-                (type gnrt bsgns)
-                (type morphism dffr)
-                (type chain-complex grmds))
-               (when cmpr (setf cmprs cmpr))
-               (when basis (setf basiss basis))
-               (unless (eq bsgn :undefined)
-                 (setf bsgns bsgn))
-               (when dffr-intr
-                 (unless dffr-strt
-                   (error "In CHAIN-COMPLEX, a DFFR-INTR is given but not its DFFR-STRT."))
-                 (setf dffr
-                   (morphism :sorc chcm :trgt chcm :degr -1
-                             :intr dffr-intr :strt dffr-strt
-                             :dfnt `(dffr ,chcm))))
-               (when grmd (setf grmds grmd))))
-  chcm)
-
-(DEFMETHOD SLOT-UNBOUND (class (chcm chain-complex) (slot-name (eql 'grmd)))
-  (declare (ignore class))
-  (the chain-complex
-    (setf (slot-value chcm 'grmd) chcm)))
-
-    
-(DEFUN MORPHISM (&rest rest &key dfnt &allow-other-keys)
-  (declare (type list dfnt))
-  (already morphism dfnt)
-  (the morphism
-    (apply #'make-instance 'morphism rest)))
-
-(DEFMETHOD SHARED-INITIALIZE
-    ((mrph morphism) slot-names &key sorc trgt degr intr strt)
-  (declare
-   (type (or (eql t) list) slot-names)
-   (type chain-complex sorc trgt)
-   (type fixnum degr)
-   (type intr intr)
-   (type strt strt))
-  (call-next-method)
-  (when-slot sorc
-             (with-slots ((sorcs sorc) (trgts trgt) (degrs degr)
-                          (intrs intr) (strts strt)) mrph
-               (declare
-                (type chain-complex sorc trgt)
-                (type fixnum degrs)
-                (type intr intrs)
-                (type strt strts))
-               (when sorc (setf sorcs sorc))
-               (when trgt (setf trgts trgt))
-               (when degr (setf degrs degr))
-               (when intr
-                 (unless strt
-                   (error "IN MORPHISM, an INTR is given, but not its STRT."))
-                 (setf intrs intr)
-                 (setf strts strt))))
-  mrph)
-
-(DEFMETHOD SLOT-UNBOUND (class (mrph morphism) slot-name)
-  (declare
-   (ignore class)
-   (type (or symbol string) slot-name))
-  (setf slot-name (symbol-name slot-name))
-  (unless (member slot-name '("RSLTS" "?-CLNM" "???-CLNM") :test #'string=)
-    (call-next-method))
-  (with-slots (strt rslts ?-clnm ???-clnm) mrph
-    (declare
-     (type strt strt)
-     (type (or null vector) rslts)
-     (type fixnum ?-clnm ???-clnm))
-    (setf rslts
-      (ecase (slot-value mrph 'strt)
-        (:gnrt (map 'simple-vector
-                 ;; (vector (vector result))
-                 #'(lambda (dummy)
-                     (declare (ignore dummy))
-                     (make-array 0
-                                 :adjustable t
-                                 :fill-pointer 0))
-                 (make-list +maximal-dimension+)))
-        (:cmbn nil)))
-    (setf ?-clnm (setf ???-clnm 0))
-    (cond ((string= slot-name "RSLTS") rslts)
-          ((string= slot-name "?-CLNM") ?-clnm)
-          ((string= slot-name "???-CLNM") ???-clnm)
-          (t (error "Something wrong in (SLOT-UNBOUND t morphism t).")))))
-
-               
-               
-               
-;;; FUNCTIONS
-
-(DEFVAR *START-STACK* +empty-list+)
-
-(DEFPARAMETER +TOO-MUCH-TIME+ -1)
-
-(DEFUN MRPH-GNRT (cmpr2 intr degr gnrt memory &optional (left -1) (right (fill-pointer memory)))
-  (declare
-     (type intr intr)
-     ;; (function (fixnum gnrt) cmbn)
-     (type cmprf cmpr2)
-     (fixnum degr left right)
-     (type gnrt gnrt)
-     (vector memory))
-   ;; (vector result)
-   (the (values cmbn fixnum)
-      ;;; cmbn = image of the generator
-      ;;; fixnum = index "exact" or just "lower" of the maybe stored result
-      (loop
-         (when (= right (1+ left))            ;; the result for gnrt is not available
-            (push (get-internal-run-time) *start-stack*)
-            (let ((value (funcall intr degr gnrt))
-                  (runtime (- (get-internal-run-time) (pop *start-stack*))))
-               (declare
-                  (type cmbn value)
-                  (integer runtime))
-               (if (> runtime +too-much-time+)
-                  ;;; the condition deciding whether
-                  ;;;   storing must happen
-                  (let ((old-length (vector-push-extend nil memory)))
-                     (declare (fixnum old-length))
-                     (replace memory memory
-                        :start1 (1+ right) :end1 (1+ old-length)
-                        :start2 right :end2 old-length)
-                     (setf (aref memory right)
-                           (make-rslt
-                              :gnrt gnrt :value value
-                              :clnm 1
-                              :rntm (float (/ runtime internal-time-units-per-second))))
-                     (mapl #'(lambda (mark)
-                                (declare (cons mark))
-                                (incf (car mark) runtime))
-                        *start-stack*)
-                     (return (values value right)))
-                  (return (values value left)))))
-         (let ((middle (truncate (+ right left) 2)))
-            (declare (fixnum middle))
-            (ecase (funcall cmpr2 gnrt (rslt-gnrt (aref memory middle)))
-               (:equal (let ((rslt (aref memory middle)))
-			  (declare (type cons rslt))
-			  (incf (rslt-clnm rslt))
-			  (return (values (rslt-value rslt) middle))))
-               (:less (setf right middle))
-               (:greater (setf left middle)))))))
-	   
-(DEFUN MRPH-CMBN (scmpr2 tcmpr2 intr cmbn memory)
-   (declare
-      (type intr intr)
-      ;; (function (fixnum gnrt) cmbn)
-      (type cmprf scmpr2 tcmpr2)
-      (type cmbn cmbn)                    ;;; cmbn is a non-zero one
-      (vector memory))
-      ;; (vector result)
-   (the cmbn
-      (with-cmbn (degr list) cmbn
-         (let ((n-cmbn-list +empty-list+))
-            (declare (list n-cmbn-list))
-            (do ((mark list (cdr mark))
-                 (left -1))
-                ((endp mark))
-               (declare (list mark))
-               (multiple-value-bind (rslt new-left)
-                                    (mrph-gnrt scmpr2 intr degr (-gnrt mark) memory left)
-                  (setf left new-left)
-                  (push (cons (-cffc mark) rslt) n-cmbn-list)))
-	    (cmbn-cmbn tcmpr2 n-cmbn-list)))))
-
-(DEFUN DO-CONTROL (cmpr cmbn)
-   (declare
-      (type cmprf cmpr)
-      (type cmbn cmbn))
-   (let ((list (cmbn-list cmbn)))
-      (declare (list list))
-      (do ((mark1 (rest list) (cdr mark1))
-	   (mark2 list mark1))
-	  ((endp mark1))
-	 (declare (list mark1 mark2))
-	 (unless (eq :less (funcall cmpr (-gnrt mark2) (-gnrt mark1)))
-	    (setf *wrong-cmbn* cmbn)
-	    (error "In the combination located by *WRONG-CMBN*, the generators:~@
-                    ~A and ~A are in a wrong order." (cdar mark2) (cdar mark1)))))
-   cmbn)
-
-#|
-  (do-control #'s-cmpr (cmbn 0 1 'a 1 'b -1 'c))
-  (do-control #'s-cmpr (cmbn 0 1 'b 1 'b -1 'c))
-  (do-control #'s-cmpr (cmbn 0 1 'a 1 'b -1 'b))
-  (setf *cmbn-control* nil)
-  (control #'s-cmpr (cmbn 0 1 'a 1 'b -1 'b))
-  (setf *cmbn-control* t)
-  (control #'s-cmpr (cmbn 0 1 'a 1 'b -1 'b))
-|#
-
-#|
-(DEFVAR *PROFILER-STACK*)
-(SETF *PROFILER-STACK* +empty-list+)
-
-(DEFUN PROFILER-INIT ()
-   (mapc #'(lambda (mrph)
-              (declare (type morphism mrph))
-              (setf (wrtm mrph) 0))
-      *k-list*))
-
-(DEFUN PROFILER-ON ()
-   (push (get-internal-run-time) *profiler-stack*))
-
-(DEFUN PROFILER-OFF (mrph)
-   (declare (type morphism mrph))
-   (let ((time-spent 
-          (- (get-internal-run-time) (pop *profiler-stack*))))
-      (declare (integer time-spent))
-      (mapl #'(lambda (mark)
-                 (declare (cons mark))
-                 (incf (car mark) time-spent))
-         *profiler-stack*)
-      (incf (wrtm mrph) time-spent)))
-|#
-
-(DEFVAR *FUTURE-DISPLAY* nil)
-
-(DEFVAR *TIME-INTERVAL* 60000)
-
-(DEFUN GNRT-? (mrph degr gnrt)
-   (declare
-      (type morphism mrph)
-      (fixnum degr)
-    (type gnrt gnrt))
-   (the cmbn
-      (progn
-;;         (profiler-on)
-         (when (and *future-display*
-                    (> (get-internal-run-time) *future-display*))
-            (format t "~%GNRT-?~@
-                       ~3T~A  DFNT = ~A~@
-                       ~3TDEGR = ~D~@
-                       ~3TGNRT = ~A"
-               mrph (dfnt mrph) degr gnrt)
-            (setf *future-display* (+ (get-internal-run-time) *time-interval*)))
-         (with-slots (sorc (mdegr degr) intr strt ?-clnm) mrph
-            (declare
-               (type chain-complex sorc)
-               (fixnum mdegr ?-clnm)
-               (type intr intr)
-               (type strt strt))
-         (with-slots ((scmpr cmpr)) sorc
-            (declare (type cmprf scmpr))
-            (control (slot-value (slot-value mrph 'trgt) 'cmpr)
-               (progn
-                  (incf ?-clnm)
-                  (prog1
-                     (ecase strt
-                        (:gnrt
-                         (mrph-gnrt scmpr intr
-                            degr gnrt (svref (rslts mrph) degr)))
-                        (:cmbn
-                         (funcall intr (term-cmbn degr 1 gnrt))))
-;;                     (profiler-off mrph)
-                     ))))))))
-
-#|
-(cat-init)
-(setf cc (chain-complex :cmpr #'f-cmpr
-                        :basis :locally-effective
-                        :bsgn 0
-                        :dffr-intr #'(lambda (cmbn)
-                                       (cmbn (1- (cmbn-degr cmbn))))
-                        :dffr-strt :cmbn
-                        :dfnt '(Z of Z)))
-(setf cc (chain-complex :cmpr #'f-cmpr
-                        :basis :locally-effective
-                        :bsgn 0
-                        :dffr-intr #'(lambda (cmbn)
-                                       (cmbn (1- (cmbn-degr cmbn))))
-                        :dffr-strt :cmbn
-                        :dfnt '(Z of Z)))
-(setf ff (morphism :sorc cc :trgt cc :degr 0
-                   :intr #'(lambda (degr n) (cmbn degr 1 n))
-                     :strt :gnrt :dfnt '(test)))
-(setf ff (morphism :sorc cc :trgt cc :degr 0
-                     :intr #'(lambda (degr n) (cmbn degr 1 n))
-                     :strt :gnrt :dfnt '(test)))
-(dotimes (i 20)
-  (let ((n (- (random 50) 50)))
-    (format t "~%~D   ~D" n (gnrt-? ff 0 n))))
-(setf +too-much-time+ -1)
-(dotimes (i 20)
-  (let ((n (- (random 50) 50)))
-    (format t "~%~D   ~D" n (gnrt-? ff 0 n))))
-(setf +too-much-time+ 50)
-|#
-
-(DEFUN CMBN-? (mrph cmbn)
-   (declare
-      (type morphism mrph)
-      (type cmbn cmbn))
-   (the cmbn
-      (progn
-;;         (profiler-on)
-         (when (and *future-display*
-                    (> (get-internal-run-time) *future-display*))
-            (format t "~%CMBN-?~@
-                       ~3T~A  DFNT = ~A~@
-                       ~3TCMBN = ~A"
-               mrph (dfnt mrph) cmbn)
-            (setf *future-display* (+ (get-internal-run-time) *time-interval*)))
-         (with-slots (sorc trgt degr intr strt ???-clnm) mrph
-            (declare
-               (type chain-complex sorc trgt)
-               (fixnum degr ???-clnm)
-               (type intr intr)
-               (type strt strt))
-         (with-slots ((scmpr cmpr)) sorc
-            (declare (type cmprf scmpr))
-         (with-slots ((tcmpr cmpr)) trgt
-            (declare (type cmprf scmpr))
-            (control tcmpr
-               (progn
-                  (controln scmpr cmbn)
-                  (incf ???-clnm)
-                  (when (eq strt :cmbn)
-                     (return-from cmbn-? (funcall intr cmbn)))
-                  (prog1
-                     (if (cmbn-zero-p cmbn)
-                        (zero-cmbn (+ (cmbn-degr cmbn) degr))
-                        (mrph-cmbn scmpr tcmpr intr
-                           cmbn (svref (rslts mrph) (cmbn-degr cmbn))))
-;;                     (profiler-off mrph)
-                     )))))))))
-
-#|
-(cat-init)
-(setf cc (chain-complex :cmpr #'f-cmpr
-                        :basis :locally-effective
-                        :bsgn 0
-                        :dffr-intr #'(lambda (cmbn)
-                                       (cmbn (1- (cmbn-degr cmbn))))
-                        :dffr-strt :cmbn
-                        :dfnt '(Z of Z)))
-(setf *n* 10)
-(defun ff (degr i)
-  (do ((*2n* (ash *n* 1))
-       (rslt +empty-list+
-             (cons (cons (let ((cffc (- (random *2n*) *n*)))
-                           (if (minusp cffc) cffc (1+ cffc)))
-                         (decf gnrt (1+ (random *n*))))
-                   rslt))
-       (gnrt i)
-       (k 0 (1+ k)))
-      ((= k *n*)
-       (make-cmbn
-        :degr 0
-        :list rslt))))
-(ff 0 20)
-(compile 'ff)
-(setf mrph (morphism :sorc cc :trgt cc :degr 0
-                     :intr #'ff :strt :gnrt :dfnt '(test)))
-(cmbn-? mrph (cmbn 0 1 100))
-(cmbn-? mrph *)
-(cmbn-? mrph *)
-(cmbn-? mrph *)
-(cmbn-? mrph *)
-(cmbn-? mrph *)
-(time (cmbn-? mrph *))
-(inspect mrph))
-|#
diff --git a/archive/Kenzo-2/Kenzo-2-Acl8/chcm-elementary-op.cl b/archive/Kenzo-2/Kenzo-2-Acl8/chcm-elementary-op.cl
deleted file mode 100644
index 7a296c5..0000000
--- a/archive/Kenzo-2/Kenzo-2-Acl8/chcm-elementary-op.cl
+++ /dev/null
@@ -1,461 +0,0 @@
-;;;  CHCM-ELEMENTARY-OP  CHCM-ELEMENTARY-OP  CHCM-ELEMENTARY-OP  CHCM-ELEMENTARY-OP
-;;;  CHCM-ELEMENTARY-OP  CHCM-ELEMENTARY-OP  CHCM-ELEMENTARY-OP  CHCM-ELEMENTARY-OP
-;;;  CHCM-ELEMENTARY-OP  CHCM-ELEMENTARY-OP  CHCM-ELEMENTARY-OP  CHCM-ELEMENTARY-OP
-
-(IN-PACKAGE "CAT")
-
-(PROVIDE "chcm-elementary-op")
-
-(DEFUN Z-CHCM ()
-   (the chain-complex
-      (chain-complex
-         :cmpr #'(lambda (gnrt1 gnrt2)
-                    (declare (ignore gnrt1 gnrt2))
-                    (the cmpr :equal))
-         :basis #'(lambda (n)
-                     (declare (type fixnum n))
-                     (the list
-                        (if (zerop n)
-                           (list :Z-gnrt)
-                           +empty-list+)))
-         :bsgn :Z-gnrt
-         :dffr-intr #'zero-dffr-intr
-         :dffr-strt :cmbn
-         :dfnt '(Z-chcm))))
-
-(DEFUN ZERO-MRPH (chcm1 &optional (chcm2 chcm1) (degr 0))
-   (declare (type chain-complex chcm1 chcm2)
-            (type fixnum degr))
-   (the morphism
-      (morphism
-         :sorc chcm1 :trgt chcm2 :degr degr
-         :intr #'(lambda (cmbn)
-                    (declare (type cmbn cmbn))
-                    (zero-cmbn (+ (cmbn-degr cmbn) degr)))
-         :strt :cmbn
-         :dfnt `(zero-mrph ,chcm1 ,chcm2 ,degr))))
-
-#|
-  (cat-init)
-  (setf z (zero-mrph (Z-chcm) (Z-chcm) 2))
-  (gnrt-? z 0 :z-gnrt)
-  (cmbn-? z (cmbn 3))
-  (setf z2 (zero-mrph (Z-chcm) (Z-chcm) 2))
-  (eq z z2)
-  (setf z3 (zero-mrph (Z-chcm) (Z-chcm) 3))
-  (gnrt-? z3 0 :z-gnrt)
-  (eq z z3))
-|#    
-
-(DEFUN IDNT-MRPH (chcm)
-   (declare (type chain-complex chcm))
-   (the morphism
-      (morphism
-         :sorc chcm :trgt chcm :degr 0
-         :intr #'identity
-         :strt :cmbn
-         :dfnt `(idnt-mrph ,chcm))))
-
-#|
-  (setf zi (idnt-mrph (Z-chcm)))
-  (gnrt-? zi 0 :z-gnrt)
-  (setf zi2 (idnt-mrph (Z-chcm)))
-  (eq zi zi2))
-|#
-
-(DEFUN OPPS (mrph)
-   (declare (type morphism mrph))
-   (the morphism
-      (with-slots (sorc trgt degr) mrph
-         (morphism
-            :sorc sorc :trgt trgt :degr degr
-            :intr #'(lambda (cmbn)
-                       (declare (type cmbn cmbn))
-                       (cmbn-opps (cmbn-? mrph cmbn)))
-            :strt :cmbn
-            :dfnt `(opps ,mrph)))))
-
-#|
-  (cat-init)
-  (setf -zi (opps (idnt-mrph (Z-chcm))))
-  (gnrt-? -zi 0 :z-gnrt)
-  (setf -zi2 (opps (idnt-mrph (Z-chcm))))
-  (eq -zi -zi2))
-|#
-
-(DEFMETHOD CMPS ((chcm1 chain-complex) (chcm2 chain-complex) &optional strt)
-   (declare (type (or strt null) strt))
-   (the morphism
-      (cmps (dffr chcm1) (dffr chcm2) strt)))
-
-(DEFMETHOD CMPS ((chcm1 chain-complex) (mrph2 morphism) &optional strt)
-   (declare (type (or strt null) strt))
-   (the morphism
-      (cmps (dffr chcm1) mrph2 strt)))
-
-(DEFMETHOD CMPS ((mrph1 morphism) (chcm2 chain-complex) &optional strt)
-   (declare (type (or strt null) strt))
-   (the morphism
-      (cmps mrph1 (dffr chcm2) strt)))
-
-(DEFMETHOD CMPS ((mrph1 morphism) (mrph2 morphism) &optional strt)
-   (declare (type (or strt null) strt))
-   (the morphism
-      (with-slots ((sorc1 sorc) (trgt1 trgt) (degr1 degr) (strt1 strt)) mrph1
-         (declare
-            (type chain-complex sorc1 trgt1)
-            (fixnum degr1)
-            (type strt strt1))
-      (with-slots ((sorc2 sorc) (trgt2 trgt) (degr2 degr) (strt2 strt)) mrph2
-         (declare
-            (type chain-complex sorc2 trgt2)
-            (fixnum degr2)
-            (type strt strt2))
-         (unless (eq (grmd sorc1) (grmd trgt2))
-            (error "In 2MRPH-CMPS, the morphisms ~A and ~A may not be composed (cf source and target)."
-               mrph1 mrph2))
-         (unless strt
-           (setf strt (if (and (eq strt1 :gnrt)
-                               (eq strt2 :gnrt))
-                          :gnrt
-                        :cmbn)))
-         (when (or (eq (first (dfnt mrph1)) 'zero-mrph)
-                   (eq (first (dfnt mrph2)) 'zero-mrph))
-            (return-from cmps
-               (zero-mrph sorc2 trgt1 (+ degr1 degr2))))
-         (when (eq (first (dfnt mrph1)) 'idnt-mrph)
-            (return-from cmps mrph2))
-         (when (eq (first (dfnt mrph2)) 'idnt-mrph)
-            (return-from cmps mrph1))
-         (ecase strt
-            (:cmbn (morphism
-                      :sorc sorc2 :trgt trgt1 :degr (+ degr1 degr2)
-                      :intr #'(lambda (cmbn)
-                                 (declare (type cmbn cmbn))
-                                 (the cmbn
-                                    (cmbn-? mrph1 (cmbn-? mrph2 cmbn))))
-                      :strt :cmbn :dfnt `(2mrph-cmps ,mrph1 ,mrph2 ,strt)))
-            (:gnrt (morphism
-                      :sorc sorc2 :trgt trgt1 :degr (+ degr1 degr2)
-                      :intr #'(lambda (degr gnrt)
-                                 (declare
-                                    (type fixnum degr)
-                                    (type gnrt gnrt))
-                                 (the cmbn
-                                    (cmbn-? mrph1 (gnrt-? mrph2 degr gnrt))))
-                      :strt :gnrt :dfnt `(2mrph-cmps ,mrph1 ,mrph2 ,strt))))))))
-  
-#|
-  (cat-init)
-  (setf cc (chain-complex :cmpr #'f-cmpr
-                       :basis :locally-effective
-                       :bsgn 0
-                       :dffr-intr #'(lambda (cmbn)
-                                       (cmbn (1- (cmbn-degr cmbn))))
-                       :dffr-strt :cmbn
-                       :dfnt '(Z of Z)))
-  (setf *n* 5)
-  (defun ff (degr i)
-     (do ((*2n* (ash *n* 1))
-          (rslt +empty-list+
-                (cons (cons (let ((cffc (- (random *2n*) *n*)))
-                               (if (minusp cffc) cffc (1+ cffc)))
-                            (decf gnrt (1+ (random *n*))))
-                      rslt))
-          (gnrt i)
-          (k 0 (1+ k)))
-         ((= k *n*)
-          (make-cmbn
-             :degr 0
-             :list rslt))))
-  (setf mrph (morphism :sorc cc :trgt cc :degr 0
-			 :intr #'ff :strt :gnrt :dfnt '(test)))
-  (setf mrph2 (2mrph-cmps mrph mrph :gnrt))
-  (gnrt-? mrph2 0 0) 
-  (dotimes (i 5)
-     (print (gnrt-? mrph2 0 i)))
-  (setf mrph (morphism :sorc cc :trgt cc :degr 0
-			 :intr #'ff :strt :gnrt :dfnt '(test)))
-  (setf mrph3 (cmps mrph mrph :cmbn))
-  (gnrt-? mrph3 0 0) 
-  (dotimes (i 5)
-     (print (gnrt-? mrph3 0 i)))
-  (setf mrph33 (cmps mrph mrph :cmbn))
-  (eq mrph3 mrph33))
-|# 
-
-(DEFUN N-MRPH-INTR (n mrph)
-  (declare
-    (fixnum n)
-    (type morphism mrph))
-  (flet ((rslt (cmbn)
-	   (declare (type cmbn cmbn))
-	   (n-cmbn n (cmbn-? mrph cmbn))))
-     (the intr #'rslt)))
-
-(DEFUN N-MRPH (n mrph)
-  (declare
-    (fixnum n)
-    (type morphism mrph))
-  (the morphism
-    (with-slots (sorc trgt degr) mrph
-      (declare
-        (type chain-complex sorc trgt)
-	(fixnum degr))
-      (morphism
-        :sorc sorc :trgt trgt :degr degr
-	:intr (n-mrph-intr n mrph) :strt :cmbn
-	:dfnt `(n-mrph ,n ,mrph)))))
-
-#|
-  (setf s3 (sphere 3))
-  (setf ch3 (chml-clss s3 3))
-  (setf 2ch3 (n-mrph 2 ch3))
-  (setf f3 (z-whitehead s3 2ch3))
-  (setf x (fibration-total f3))
-  (homology x 0 10)
-  (setf k (k-z 3))
-  (setf ch3 (chml-clss k 3))
-  (setf 2ch3 (n-mrph 2 ch3))
-  (setf f3 (z-whitehead k 2ch3))
-  (setf x (fibration-total f3))
-  (homology x 0 10)
-|#  
-
-(DEFMETHOD ADD ((mrph1 morphism) (mrph2 morphism) &optional strt)
-   (declare (type (or null strt) strt))
-   (the morphism
-      (with-slots ((sorc1 sorc) (trgt1 trgt) (degr1 degr) (strt1 strt)) mrph1
-         (declare
-            (type chain-complex sorc1 trgt1)
-            (fixnum degr1)
-            (type strt strt1))
-      (with-slots ((sorc2 sorc) (trgt2 trgt) (degr2 degr) (strt2 strt)) mrph2
-         (declare
-            (type chain-complex sorc2 trgt2)
-            (fixnum degr2)
-            (type strt strt2))
-         (unless (and (eq (grmd sorc1) (grmd sorc2))
-                      (eq (grmd trgt1) (grmd trgt2))
-                      (= degr1 degr2))
-            (error "In 2MRPH-ADD, ~A and ~A may not be added." mrph1 mrph2))
-         (when (eq (first (dfnt mrph1)) 'zero-mrph)
-            (return-from add mrph2))
-         (when (eq (first (dfnt mrph2)) 'zero-mrph)
-            (return-from add mrph1))
-         (unless strt
-            (setf strt
-                  (if (and (eq strt1 :gnrt)
-                           (eq strt2 :gnrt))
-                     :gnrt
-                     :cmbn)))
-         (when (or (eq (first (dfnt mrph1)) 'idnt-mrph)
-                   (eq (first (dfnt mrph2)) 'idnt-mrph))
-            (setf strt :cmbn))
-         (let ((cmpr (cmpr trgt1)))
-            (declare (type cmprf cmpr))
-            (ecase strt
-               (:gnrt (morphism
-                         :sorc sorc1 :trgt trgt1 :degr degr1
-                         :intr #'(lambda (degr gnrt)
-                                    (declare (type fixnum degr) (type gnrt gnrt))
-                                    (2cmbn-add cmpr
-                                       (gnrt-? mrph1 degr gnrt)
-                                       (gnrt-? mrph2 degr gnrt)))
-                         :strt :gnrt
-                         :dfnt `(2mrph-add ,mrph1 ,mrph2 ,strt)))
-               (:cmbn (morphism
-                         :sorc sorc1 :trgt trgt1 :degr degr1
-                         :intr #'(lambda (cmbn)
-                                    (declare (type cmbn cmbn))
-                                    (2cmbn-add cmpr
-                                       (cmbn-? mrph1 cmbn)
-                                       (cmbn-? mrph2 cmbn)))
-                         :strt :cmbn
-                         :dfnt `(2mrph-add ,mrph1 ,mrph2 ,strt)))))))))
-
-#|
-  (cat-init)
-  (setf cc (chain-complex :cmpr #'f-cmpr
-                       :basis :locally-effective
-                       :bsgn 0
-                       :dffr-intr #'(lambda (cmbn)
-                                       (cmbn (1- (cmbn-degr cmbn))))
-                       :dffr-strt :cmbn
-                       :dfnt '(Z of Z)))
-  (setf *n* 10)
-  (defun ff (degr i)
-     (do ((*2n* (ash *n* 1))
-          (rslt +empty-list+
-                (cons (cons (let ((cffc (- (random *2n*) *n*)))
-                               (if (minusp cffc) cffc (1+ cffc)))
-                            (decf gnrt (1+ (random *n*))))
-                      rslt))
-          (gnrt i)
-          (k 0 (1+ k)))
-         ((= k *n*)
-          (make-cmbn
-             :degr 0
-             :list rslt))))
-  (setf mrph1 (morphism :sorc cc :trgt cc :degr 0
-                          :intr #'ff :strt :gnrt :dfnt '(test)))
-  (setf mrph2 (morphism :sorc cc :trgt cc :degr 0
-                          :intr #'ff :strt :gnrt :dfnt '(test2)))
-  (setf mrph3 (add mrph1 mrph2 :gnrt))
-  (setf +too-much-time+ -1)
-  (gnrt-? mrph1 0 0)
-  (gnrt-? mrph2 0 0)
-  (gnrt-? mrph3 0 0)
-  (setf mrph4 (add mrph1 mrph2 :cmbn))
-  (gnrt-? mrph4 0 0)
-  (setf mrph44 (add mrph1 mrph2 :cmbn))
-  (eq mrph4 mrph44))
-|#
-
-(DEFMETHOD SBTR ((mrph1 morphism) (mrph2 morphism) &optional strt)
-   (declare (type (or null strt) strt))
-   (the morphism
-      (with-slots ((sorc1 sorc) (trgt1 trgt) (degr1 degr) (strt1 strt)) mrph1
-         (declare
-            (type chain-complex sorc1 trgt1)
-            (fixnum degr1)
-            (type strt strt1))
-      (with-slots ((sorc2 sorc) (trgt2 trgt) (degr2 degr) (strt2 strt)) mrph2
-         (declare
-            (type chain-complex sorc2 trgt2)
-            (fixnum degr2)
-            (type strt strt2))
-         (unless (and (eq (grmd sorc1) (grmd sorc2))
-                      (eq (grmd trgt1) (grmd trgt2))
-                      (= degr1 degr2))
-            (error "In 2MRPH-SBTR, ~A and ~A may not be subtracteded." mrph1 mrph2))
-         (when (eq (first (dfnt mrph1)) 'zero-mrph)
-            (return-from sbtr mrph2))
-         (when (eq (first (dfnt mrph2)) 'zero-mrph)
-            (return-from sbtr mrph1))
-         (unless strt
-            (setf strt
-                  (if (and (eq strt1 :gnrt)
-                           (eq strt2 :gnrt))
-                     :gnrt
-                     :cmbn)))
-         (when (or (eq (first (dfnt mrph1)) 'idnt-mrph)
-                   (eq (first (dfnt mrph2)) 'idnt-mrph))
-            (setf strt :cmbn))
-         (let ((cmpr (cmpr trgt1)))
-            (declare (type cmprf cmpr))
-            (ecase strt
-               (:gnrt (morphism
-                         :sorc sorc1 :trgt trgt1 :degr degr1
-                         :intr #'(lambda (degr gnrt)
-                                    (declare (type fixnum degr) (type gnrt gnrt))
-                                    (2cmbn-sbtr cmpr
-                                       (gnrt-? mrph1 degr gnrt)
-                                       (gnrt-? mrph2 degr gnrt)))
-                         :strt :gnrt
-                         :dfnt `(2mrph-sbtr ,mrph1 ,mrph2 ,strt)))
-               (:cmbn (morphism
-                         :sorc sorc1 :trgt trgt1 :degr degr1
-                         :intr #'(lambda (cmbn)
-                                    (declare (type cmbn cmbn))
-                                    (2cmbn-sbtr cmpr
-                                       (cmbn-? mrph1 cmbn)
-                                       (cmbn-? mrph2 cmbn)))
-                         :strt :cmbn
-                         :dfnt `(2mrph-sbtr ,mrph1 ,mrph2 ,strt)))))))))
-
-#|
-  (cat-init)
-  (setf cc (chain-complex :cmpr #'f-cmpr
-                       :basis :locally-effective
-                       :bsgn 0
-                       :dffr-intr #'(lambda (cmbn)
-                                       (cmbn (1- (cmbn-degr cmbn))))
-                       :dffr-strt :cmbn
-                       :dfnt '(Z of Z)))
-  (setf *n* 10)
-  (defun ff (degr i)
-     (do ((*2n* (ash *n* 1))
-          (rslt +empty-list+
-                (cons (cons (let ((cffc (- (random *2n*) *n*)))
-                               (if (minusp cffc) cffc (1+ cffc)))
-                            (decf gnrt (1+ (random *n*))))
-                      rslt))
-          (gnrt i)
-          (k 0 (1+ k)))
-         ((= k *n*)
-          (make-cmbn
-             :degr 0
-             :list rslt))))
-  (setf mrph1 (morphism :sorc cc :trgt cc :degr 0
-                          :intr #'ff :strt :gnrt :dfnt '(test)))
-  (setf mrph2 (morphism :sorc cc :trgt cc :degr 0
-                          :intr #'ff :strt :gnrt :dfnt '(test2)))
-  (setf mrph3 (sbtr mrph1 mrph2 :gnrt))
-  (setf +too-much-time+ -1)
-  (gnrt-? mrph1 0 0)
-  (gnrt-? mrph2 0 0)
-  (gnrt-? mrph3 0 0)
-  (setf mrph4 (sbtr mrph1 mrph2 :cmbn))
-  (gnrt-? mrph4 0 0)
-  (setf mrph44 (sbtr mrph1 mrph2 :cmbn))
-  (eq mrph4 mrph44))
-|#
-
-(DEFUN CHANGE-SORC-TRGT (mrph &key new-sorc new-trgt)
-   (declare
-      (type morphism mrph)
-      (type (or null chain-complex) new-sorc new-trgt))
-   (the morphism
-      (with-slots (sorc trgt degr intr strt) mrph
-         (morphism
-            :sorc (or new-sorc sorc)
-            :trgt (or new-trgt trgt)
-            :degr degr
-            :intr intr
-            :strt strt
-            :dfnt `(change-sorc-trgt ,mrph ,new-sorc ,new-trgt)))))
-
-(DEFUN DSTR-CHANGE-SORC-TRGT (mrph &key new-sorc new-trgt)
-   (declare
-      (type morphism mrph)
-      (type (or null chain-complex) new-sorc new-trgt)
-      (list new-dfnt))
-   (the morphism
-      (with-slots (sorc trgt) mrph
-         (when new-sorc 
-            (setf sorc new-sorc))
-         (when new-trgt
-            (setf trgt new-trgt))
-         mrph)))
-
-(DEFMETHOD ADD ((chcm chain-complex) (perturbation morphism) &optional strt)
-  (declare (type (or strt null) strt))
-  (the chain-complex
-    (with-slots (cmpr basis bsgn dffr) chcm
-      (declare
-       (type cmprf cmpr)
-       (type basis basis)
-       (type morphism dffr))
-      (with-slots (sorc trgt degr) perturbation
-        (declare
-         (type chain-complex sorc trgt)
-         (fixnum degr))
-        (unless (and (eq (grmd sorc) (grmd chcm))
-                     (eq (grmd trgt) (grmd chcm))
-                     (= degr -1))
-          (error "In (METHOD ADD CHAIN-COMPLEX MORPHISM), the data are not coherent."))
-        (let ((new-dffr (add dffr perturbation strt)))
-          (declare (type morphism new-dffr))
-          (let ((new-chcm (chain-complex
-                           :cmpr cmpr
-                           :basis basis
-                           :dffr-intr (intr new-dffr)
-                           :dffr-strt (strt new-dffr)
-                           :dfnt  `(add ,chcm ,perturbation))))
-            (declare (type chain-complex new-chcm))
-            (if (slot-boundp chcm 'bsgn)
-                (setf (slot-value new-chcm 'bsgn) bsgn)
-              (slot-makunbound new-chcm 'bsgn))
-            (setf (slot-value new-chcm 'grmd) (grmd chcm))
-            new-chcm))))))
\ No newline at end of file
diff --git a/archive/Kenzo-2/Kenzo-2-Acl8/cl-space-efhm.cl b/archive/Kenzo-2/Kenzo-2-Acl8/cl-space-efhm.cl
deleted file mode 100644
index f21ebfe..0000000
--- a/archive/Kenzo-2/Kenzo-2-Acl8/cl-space-efhm.cl
+++ /dev/null
@@ -1,875 +0,0 @@
-;;;  CL-SPACE-EFHM  CL-SPACE-EFHM  CL-SPACE-EFHM  CL-SPACE-EFHM
-;;;  CL-SPACE-EFHM  CL-SPACE-EFHM  CL-SPACE-EFHM  CL-SPACE-EFHM
-;;;  CL-SPACE-EFHM  CL-SPACE-EFHM  CL-SPACE-EFHM  CL-SPACE-EFHM
-
-(IN-PACKAGE "CAT")
-
-(provide "cl-space-efhm")
-
-(DEFUN CS-HAT-U-U (smgr
-		     &aux (bar (bar smgr))
-		          (cl-space (classifying-space smgr))
-			  (clsp-tnsr-smgr (tnsr-prdc cl-space smgr)))
-  (declare
-    (type simplicial-group smgr)
-    (type chain-complex bar clsp-tnsr-smgr)
-    (type simplicial-set cl-space))
-  (the chain-complex
-     (tnsr-prdc clsp-tnsr-smgr bar)))
-
-(DEFUN CS-HAT-RIGHT-PERTURBATION-INTR (smgr)
-  (declare (type simplicial-group smgr))
-  (let ((aprd (aprd smgr)))
-    (flet ((rslt (degr tnpr)
-	     (declare
-	       (fixnum degr)
-	       (type tnpr tnpr))
-	     (with-tnpr (degr1 tnpr1 degr2 abar2) tnpr
-	       (when (zerop degr2)
-		 (return-from rslt (zero-cmbn (1- degr))))
-	       (with-tnpr (degr11 gbar11 degr12 gmsm12) tnpr1
-		 (let ((sign (-1-expt-n degr1))
-		       (brgn21 (first (abar-list abar2)))
-		       (bar22 (make-abar :list (rest (abar-list abar2)))))
-		   (declare
-		     (fixnum sign)
-		     (type brgn brgn21)
-		     (type abar r-bar))
-		   (with-brgn (degr21 gmsm21) brgn21
-		   (let ((degr22 (- degr2 degr21)))
-		     (declare (fixnum degr22))
-		     (decf degr21) ;; = dmns(gmsm21)
-		     (let ((aprd (gnrt-? aprd (+ degr12 degr21)
-					 (tnpr degr12 gmsm12 degr21 gmsm21))))
-		       (declare (type cmbn aprd))
-		       (with-cmbn (degr12+21 list) aprd
-			 (make-cmbn :degr (1- degr)
-			   :list
-			   (mapcar
-			     #'(lambda (term)
-				 (declare (type term term))
-				 (with-term (cffc gmsm) term
-				   (term (* sign cffc)
-					 (tnpr (+ degr1 degr21)
-					       (tnpr degr11 gbar11 degr12+21 gmsm)
-					       degr22 bar22))))
-			     list)))))))))))
-	  (the intr #'rslt))))
-
-(DEFUN CS-HAT-RIGHT-PERTURBATION (smgr
-				    &aux (hat-u-u (cs-hat-u-u smgr)))
-  (declare
-    (type simplicial-group smgr)
-    (type chain-complex hat-u-u))
-  (the morphism
-     (morphism
-        :sorc hat-u-u
-	:trgt hat-u-u
-	:degr -1
-	:intr (cs-hat-right-perturbation-intr smgr)
-	:strt :gnrt
-	:dfnt `(cs-hat-right-perturbation ,smgr))))
-
-(DEFUN CS-HAT-U-T (smgr
-		     &aux (hat-u-u (cs-hat-u-u smgr))
-		          (hat-right-perturbation
-			    (cs-hat-right-perturbation smgr)))
-  (declare
-    (type simplicial-group smgr)
-    (type chain-complex hat-u-u)
-    (type morphism hat-right-perturbation))
-  (the chain-complex
-    (progn
-      (setf (slot-value hat-right-perturbation 'sorc) hat-u-u
-	    (slot-value hat-right-perturbation 'trgt) hat-u-u)
-      ;; cf lp-space-efhm.lisp
-      (add hat-u-u hat-right-perturbation))))
-
-#|
-  (cat-init)
-  (setf c (cs-hat-u-t (k-z-1)))
-  (defun random-abar (tot-degr~ max-degr)
-    (do ((rslt nil)
-         (cum-degr 0 (+ cum-degr degr 1))
-         (degr))
-        ((>= cum-degr tot-degr~) (make-abar :list rslt))
-       (setf degr (1+ (random max-degr)))
-       (push (brgn (1+ degr)
-                   (let ((list (make-list degr)))
-                     (mapl
-                       #'(lambda (sublist)
-                           (setf (car sublist) (- (random 21) 10)))
-                       list)
-                     list))
-             rslt)))
-  (dotimes (i 5) (print (random-abar 8 4)))
-  (setf abar (random-abar 8 4))
-  (setf abar-degr (apply #'+ (mapcar #'car (abar-list abar))))
-  (setf gnrt (tnpr 5 (tnpr 3 (gbar 3 0 '(1 2) 0 '(3) 0 '()) 2 '(4 5))
-                   abar-degr abar))
-  (? c (+ 5 abar-degr) gnrt)
-  (? c *)
-  (dotimes (i 10)
-    (let ((abar (random-abar 8 4)))
-      (setf abar-degr (apply #'+ (mapcar #'car (abar-list abar))))
-      (setf gnrt (tnpr 5 (tnpr 3 (gbar 3 0 '(1 2) 0 '(3) 0 '()) 2 '(4 5))
-                       abar-degr abar))
-      (unless (>= abar-degr 10)
-         (print (? c (+ 5 abar-degr) gnrt))
-         (print (? c (? c (+ 5 abar-degr) gnrt))))))
-  (dotimes (i 10)
-    (let ((abar (random-abar 8 4)))
-      (setf abar-degr (apply #'+ (mapcar #'car (abar-list abar))))
-      (setf gnrt (tnpr 6 (tnpr 3 (gbar 3 0 '(1 2) 0 '(3) 0 '()) 3 '(4 5 6))
-                       abar-degr abar))
-      (unless (>= abar-degr 9)
-         (print (? c (+ 6 abar-degr) gnrt))
-         (print (? c (? c (+ 6 abar-degr) gnrt))))))
-  (dotimes (i 10)
-    (let ((abar (random-abar 8 4)))
-      (setf abar-degr (apply #'+ (mapcar #'car (abar-list abar))))
-      (setf gnrt (tnpr 5 (tnpr 2 (gbar 2 0 '(3) 0 '()) 3 '(4 5 6))
-	   	     abar-degr abar))
-      (unless (>= abar-degr 10)
-        (print (? c (+ 5 abar-degr) gnrt))
-        (print (? c (? c (+ 5 abar-degr) gnrt))))))
-  (dotimes (i 10)
-    (let ((abar (random-abar 8 4)))
-      (setf abar-degr (apply #'+ (mapcar #'car (abar-list abar))))
-      (setf gnrt (tnpr 4 (tnpr 2 (gbar 2 0 '(3) 0 '()) 2 '(4 5))
-                       abar-degr abar))
-      (unless (>= abar-degr 11)
-         (print (? c (+ 4 abar-degr) gnrt))
-         (print (? c (? c (+ 4 abar-degr) gnrt))))))
-|#
-
-(DEFUN CS-HAT-LEFT-PERTURBATION (smgr
-			       &aux (fibration (smgr-fibration smgr))
-			            (bar (bar smgr))
-			            (hat-u-t (cs-hat-u-t smgr)))
-  (declare
-    (type simplicial-group smgr)
-    (type fibration fibration)
-    (type chain-complex bar hat-u-t))
-  (the morphism
-    (multiple-value-bind (brown bottom-perturbation)
-			 (brown-reduction fibration)
-      (declare
-        (ignore brown)
-	(type morphism bottom-perturbation))
-      (let ((rslt (tnsr-prdc bottom-perturbation (idnt-mrph bar))))
-	(declare (type morphism rslt))
-	(setf (slot-value rslt 'sorc) hat-u-t
-	      (slot-value rslt 'trgt) hat-u-t)
-	rslt))))
-
-(DEFUN CS-HAT-T-U (smgr
-		    &aux (bar (bar smgr))
-		         (fibration (smgr-fibration smgr))
-		         (brown (brown-reduction fibration))
-		         (twisted-tnsr-prdc (bcc brown))
-		         (hat-u-u (cs-hat-u-u smgr)))
-  (declare
-    (type simplicial-group smgr)
-    (type chain-complex bar twisted-tnsr-prdc hat-u-u)
-    (type fibration fibration)
-    (type reduction brown))
-  (the chain-complex
-    (let ((rslt (tnsr-prdc twisted-tnsr-prdc bar)))
-      (declare (type chain-complex rslt))
-      (setf (slot-value rslt 'grmd) hat-u-u)
-      rslt)))
-
-#|
-  (cat-init)
-  (setf c (cs-hat-t-u (k-z-1)))
-  (defun random-abar (tot-degr~ max-degr)
-    (do ((rslt nil)
-         (cum-degr 0 (+ cum-degr degr 1))
-         (degr))
-        ((>= cum-degr tot-degr~) (make-abar :list rslt))
-       (setf degr (1+ (random max-degr)))
-       (push (brgn (1+ degr)
-                   (let ((list (make-list degr)))
-                     (mapl
-                       #'(lambda (sublist)
-                           (setf (car sublist) (- (random 21) 10)))
-                       list)
-                     list))
-             rslt)))
-  (dotimes (i 5) (print (random-abar 8 4)))
-  (setf abar (random-abar 8 4))
-  (setf abar-degr (apply #'+ (mapcar #'car (abar-list abar))))
-  (setf gnrt (tnpr 5 (tnpr 3 (gbar 3 0 '(1 2) 0 '(3) 0 '()) 2 '(4 5))
-                   abar-degr abar))
-  (? c (+ 5 abar-degr) gnrt)
-  (? c *)
-  (dotimes (i 10)
-    (let ((abar (random-abar 8 4)))
-      (setf abar-degr (apply #'+ (mapcar #'car (abar-list abar))))
-      (setf gnrt (tnpr 5 (tnpr 3 (gbar 3 0 '(1 2) 0 '(3) 0 '()) 2 '(4 5))
-                       abar-degr abar))
-      (unless (>= abar-degr 10)
-         (print (? c (+ 5 abar-degr) gnrt))
-         (print (? c (? c (+ 5 abar-degr) gnrt))))))
-  (dotimes (i 10)
-    (let ((abar (random-abar 8 4)))
-      (setf abar-degr (apply #'+ (mapcar #'car (abar-list abar))))
-      (setf gnrt (tnpr 6 (tnpr 3 (gbar 3 0 '(1 2) 0 '(3) 0 '()) 3 '(4 5 6))
-                       abar-degr abar))
-      (unless (>= abar-degr 9)
-         (print (? c (+ 6 abar-degr) gnrt))
-         (print (? c (? c (+ 6 abar-degr) gnrt))))))
-  (dotimes (i 10)
-    (let ((abar (random-abar 8 4)))
-      (setf abar-degr (apply #'+ (mapcar #'car (abar-list abar))))
-      (setf gnrt (tnpr 5 (tnpr 2 (gbar 2 0 '(3) 0 '()) 3 '(4 5 6))
-	   	     abar-degr abar))
-      (unless (>= abar-degr 10)
-        (print (? c (+ 5 abar-degr) gnrt))
-        (print (? c (? c (+ 5 abar-degr) gnrt))))))
-  (dotimes (i 10)
-    (let ((abar (random-abar 8 4)))
-      (setf abar-degr (apply #'+ (mapcar #'car (abar-list abar))))
-      (setf gnrt (tnpr 4 (tnpr 2 (gbar 2 0 '(3) 0 '()) 2 '(4 5))
-                       abar-degr abar))
-      (unless (>= abar-degr 11)
-         (print (? c (+ 4 abar-degr) gnrt))
-         (print (? c (? c (+ 4 abar-degr) gnrt))))))
-|#
-
-(DEFUN CS-LEFT-EQVL-HAT (smgr
-			   &aux (hat-t-u (cs-hat-t-u smgr))
-			        (hat-right-perturbation
-				  (cs-hat-right-perturbation smgr)))
-  (declare
-    (type simplicial-group smgr)
-    (type chain-complex hat-t-u)
-    (type morphism hat-right-perturbation))
-  (the chain-complex
-    (add hat-t-u hat-right-perturbation)))
-
-#|
-  (cat-init)
-  (setf c (cs-left-eqvl-hat (k-z-1)))
-  (defun random-abar (tot-degr~ max-degr)
-    (do ((rslt nil)
-         (cum-degr 0 (+ cum-degr degr 1))
-         (degr))
-        ((>= cum-degr tot-degr~) (make-abar :list rslt))
-       (setf degr (1+ (random max-degr)))
-       (push (brgn (1+ degr)
-                   (let ((list (make-list degr)))
-                     (mapl
-                       #'(lambda (sublist)
-                           (setf (car sublist) (- (random 21) 10)))
-                       list)
-                     list))
-             rslt)))
-   (dotimes (i 10)
-    (let ((abar (random-abar 8 4)))
-      (setf abar-degr (apply #'+ (mapcar #'car (abar-list abar))))
-      (setf gnrt (tnpr 5 (tnpr 3 (gbar 3 0 '(1 2) 0 '(3) 0 '()) 2 '(4 5))
-                       abar-degr abar))
-      (unless (>= abar-degr 10)
-         (print (? c (+ 5 abar-degr) gnrt))
-         (print (? c (? c (+ 5 abar-degr) gnrt))))))
-  (dotimes (i 10)
-    (let ((abar (random-abar 8 4)))
-      (setf abar-degr (apply #'+ (mapcar #'car (abar-list abar))))
-      (setf gnrt (tnpr 6 (tnpr 3 (gbar 3 0 '(1 2) 0 '(3) 0 '()) 3 '(4 5 6))
-                       abar-degr abar))
-      (unless (>= abar-degr 9)
-         (print (? c (+ 6 abar-degr) gnrt))
-         (print (? c (? c (+ 6 abar-degr) gnrt))))))
-  (dotimes (i 10)
-    (let ((abar (random-abar 8 4)))
-      (setf abar-degr (apply #'+ (mapcar #'car (abar-list abar))))
-      (setf gnrt (tnpr 5 (tnpr 2 (gbar 2 0 '(3) 0 '()) 3 '(4 5 6))
-	   	     abar-degr abar))
-      (unless (>= abar-degr 10)
-        (print (? c (+ 5 abar-degr) gnrt))
-        (print (? c (? c (+ 5 abar-degr) gnrt))))))
-  (dotimes (i 10)
-    (let ((abar (random-abar 8 4)))
-      (setf abar-degr (apply #'+ (mapcar #'car (abar-list abar))))
-      (setf gnrt (tnpr 4 (tnpr 2 (gbar 2 0 '(3) 0 '()) 2 '(4 5))
-                       abar-degr abar))
-      (unless (>= abar-degr 11)
-         (print (? c (+ 4 abar-degr) gnrt))
-         (print (? c (? c (+ 4 abar-degr) gnrt))))))
-|#
-
-(DEFUN CS-PRE-LEFT-EQVL-LEFT-REDUCTION-INTR-F (cmbn)
-  (declare (type cmbn cmbn))
-  (the cmbn
-    (with-cmbn (degr list) cmbn
-      (make-cmbn
-        :degr degr
-	:list (mapcar
-	        #'(lambda (term)
-		    (declare (type term term))
-		    (with-term (cffc tnpr) term
-		      (term cffc (gnrt1 (gnrt1 tnpr)))))		    
-	        (member-if	       
-		  #'(lambda (term)
-		      (declare (type term term))
-		      (with-term (cffc tnpr) term
-			(declare (ignore cffc))
-		      (with-tnpr (degr1 tnpr1 degr2 abar2) tnpr
-			(declare (ignore degr1 abar2))
-			(and (zerop degr2) (zerop (degr2 tnpr1))))))
-		  list))))))
-
-#|
-  (cs-pre-left-eqvl-left-reduction-intr-f
-    (cmbn 6 100 (tnpr 4 (tnpr 2 'a 2 'b) 2 'c)
-            10  (tnpr 6 (tnpr 2 'a 4 'b) 0 'c)
-            50  (tnpr 6 (tnpr 6 'a 0 'b) 0 'c)
-            1   (tnpr 6 (tnpr 6 'aa 0 'b) 0 'c)))
-|#
-
-(DEFUN CS-PRE-LEFT-EQVL-LEFT-REDUCTION-F (smgr
-					   &aux (hat-u-t (cs-hat-u-t smgr))
-					        (classifying-space (classifying-space smgr)))
-  (declare
-    (type simplicial-group smgr)
-    (type chain-complex hat-u-t)
-    (type simplicial-set classifying-space))
-  (the morphism
-    (morphism
-      :sorc hat-u-t
-      :trgt classifying-space
-      :degr 0
-      :intr #'cs-pre-left-eqvl-left-reduction-intr-f
-      :strt :cmbn
-      :dfnt `(cs-pre-left-eqvl-left-reduction-f ,smgr))))
-
-(DEFUN CS-PRE-LEFT-EQVL-LEFT-REDUCTION-INTR-G (idnt)
-  (declare (type gmsm idnt))
-  (flet ((rslt (cmbn)
-	   (declare (type cmbn cmbn))
-	   (the cmbn
-	     (with-cmbn (degr list) cmbn
-	       (make-cmbn
-		 :degr degr
-		 :list (mapcar
-			 #'(lambda (term)
-			     (declare (type term term))
-			     (with-term (cffc gbar) term
-			       (term cffc
-				     (tnpr degr
-					   (tnpr degr gbar 0 idnt)
-					   0 +null-abar+))))
-			 list))))))
-     (the intr #'rslt)))
-
-#|
-  (setf g (cs-pre-left-eqvl-left-reduction-intr-g '()))
-  (funcall g (cmbn 3 14 (gbar 3 0 'a 1 'b 0 '())))
-|#
-
-(DEFUN CS-PRE-LEFT-EQVL-LEFT-REDUCTION-G (smgr
-					   &aux (hat-u-t (cs-hat-u-t smgr))
-					        (classifying-space (classifying-space smgr)))
-  (declare
-    (type simplicial-group smgr)
-    (type chain-complex hat-u-t)
-    (type simplicial-set classifying-space))
-  (the morphism
-    (morphism
-      :sorc classifying-space
-      :trgt hat-u-t
-      :degr 0
-      :intr (cs-pre-left-eqvl-left-reduction-intr-g (bsgn smgr))
-      :strt :cmbn
-      :dfnt `(cs-pre-left-eqvl-left-reduction-g ,smgr))))
-
-(DEFUN CS-PRE-LEFT-EQVL-LEFT-REDUCTION-INTR-H (cmpr idnt)
-  (declare (type gmsm idnt))
-  (flet ((rslt (cmbn)
-	   (declare (type cmbn cmbn))
-	   (the cmbn
-	     (with-cmbn (degr list) cmbn
-	       (do ((rslt (zero-cmbn (1+ degr)))
-		    (mark list (cdr mark)))
-		   ((endp mark) rslt)
-		   (declare
-		     (type cmbn rslt)
-		     (list mark))
-		  (let ((term (car mark)))
-		    (declare (type term term))
-		    (with-term (cffc tnpr) term
-		    (with-tnpr (degr1 tnpr1 degr2 abar2) tnpr
-		      (declare (ignore degr1))
-		    (with-tnpr (degr11 gbar11 degr12 gmsm12) tnpr1
-		      (unless (zerop degr12)
-			(dstr-add-term-to-cmbn
-			  cmpr
-			  (if (evenp degr11) cffc (- cffc))
-			  (tnpr degr11
-				(tnpr degr11 gbar11 0 idnt)
-				(+ 1 degr12 degr2)
-				(make-abar
-				 :list
-				 (cons (brgn (1+ degr12)
-					     gmsm12)
-				       (abar-list abar2))))
-			  rslt)))))))))))
-     (the intr #'rslt)))
-
-(DEFUN CS-PRE-LEFT-EQVL-LEFT-REDUCTION-H (smgr
-					   &aux (hat-u-t (cs-hat-u-t smgr)))
-  (declare
-    (type simplicial-group smgr)
-    (type chain-complex hat-u-t))
-  (the morphism
-    (morphism
-      :sorc hat-u-t
-      :trgt hat-u-t
-      :degr +1
-      :intr (cs-pre-left-eqvl-left-reduction-intr-h (cmpr hat-u-t) (bsgn smgr))
-      :strt :cmbn
-      :dfnt `(cs-pre-left-eqvl-left-reduction-h ,smgr))))
-
-
-
-(DEFUN CS-PRE-LEFT-EQVL-LEFT-REDUCTION (smgr)
-  (declare (type simplicial-group smgr))
-  (the reduction
-    (reduction
-      :f (cs-pre-left-eqvl-left-reduction-f smgr)
-      :g (cs-pre-left-eqvl-left-reduction-g smgr)
-      :h (cs-pre-left-eqvl-left-reduction-h smgr)
-      :dfnt `(cs-pre-left-eqvl-left-reduction ,smgr))))
-
-#|
-  (cat-init)
-  (defun random-abar (tot-degr~ max-degr)
-    (do ((rslt nil)
-         (cum-degr 0 (+ cum-degr degr 1))
-         (degr))
-        ((>= cum-degr tot-degr~) (make-abar :list rslt))
-       (setf degr (1+ (random max-degr)))
-       (push (brgn (1+ degr)
-                   (let ((list (make-list degr)))
-                     (mapl
-                       #'(lambda (sublist)
-                           (setf (car sublist) (- (random 21) 10)))
-                       list)
-                     list))
-             rslt)))
-  (setf rdct (cs-pre-left-eqvl-left-reduction (k-z-1)))
-  (pre-check-rdct rdct)
-  (setf *tc* (cmbn 0 1 (tnpr 0 (tnpr 0 +null-gbar+ 0 '()) 0 +null-abar+))
-        *bc* (cmbn 0 1 +null-gbar+))
-  (check-rdct)
-  (setf *tc* (cmbn 1 1 (tnpr 1 (tnpr 0 +null-gbar+ 1 '(13)) 0 +null-abar+)))
-  (check-rdct)
-  (dotimes (i 10)
-    (let ((abar (random-abar 8 4)))
-      (setf abar-degr (apply #'+ (mapcar #'car (abar-list abar))))
-      (setf gnrt (tnpr 5 (tnpr 3 (gbar 3 0 '(1 2) 0 '(3) 0 '()) 2 '(4 5))
-                       abar-degr abar))
-      (setf gbar (gbar 2 0 '(1) 0 '()))
-      (unless (>= abar-degr 9)
-        (setf *tc* (cmbn (+ 5 abar-degr) 1 gnrt)
-              *bc* (cmbn 2 1 gbar))
-        (check-rdct))))
-  (dotimes (i 10)
-    (let ((abar (random-abar 6 4)))
-      (setf abar-degr (apply #'+ (mapcar #'car (abar-list abar))))
-      (setf gnrt (tnpr 6 (tnpr 3 (gbar 3 0 '(1 2) 0 '(3) 0 '()) 3 '(4 5 6))
-                       abar-degr abar))
-      (setf gbar (gbar 3 0 '(1 2) 1 '() 0 '()))
-      (unless (>= abar-degr 8)
-        (setf *tc* (cmbn (+ 6 abar-degr) 1 gnrt)
-              *bc* (cmbn 3 1 gbar))
-        (check-rdct))))
-  (dotimes (i 10)
-    (let ((abar (random-abar 6 4)))
-      (setf abar-degr (apply #'+ (mapcar #'car (abar-list abar))))
-      (setf gnrt (tnpr 5 (tnpr 2 (gbar 2 0 '(3) 0 '()) 3 '(4 5 6))
-	   	     abar-degr abar))
-      (setf gbar (gbar 4 0 '(1 2 3) 0 '(4 5) 0 '(6) 0 '()))
-      (unless (>= abar-degr 9)
-        (setf *tc* (cmbn (+ 5 abar-degr) 1 gnrt))
-        (setf *bc* (cmbn 4 1 gbar))
-        (check-rdct))))
-  (dotimes (i 10)
-    (let ((abar (random-abar 6 4)))
-      (setf abar-degr (apply #'+ (mapcar #'car (abar-list abar))))
-      (setf gnrt (tnpr 4 (tnpr 2 (gbar 2 0 '(3) 0 '()) 2 '(4 5))
-                       abar-degr abar))
-      (setf gbar (gbar 5 8 '(1 2 3) 0 '(4 5 6) 0 '(7 8) 0 '(9) 0 '()))
-      (unless (>= abar-degr 10)
-         (setf *tc* (cmbn (+ 4 abar-degr) 1 gnrt))
-         (setf *bc* (cmbn 5 1 gbar))
-         (check-rdct))))
-|#
-
-(DEFUN CS-LEFT-EQVL-LEFT-REDUCTION (smgr
-				     &aux (pre-left-eqvl-left-reduction
-					     (cs-pre-left-eqvl-left-reduction smgr))
-				          (hat-left-perturbation
-					     (cs-hat-left-perturbation smgr)))
-  (declare
-    (type simplicial-group smgr)
-    (type reduction pre-left-eqvl-left-reduction)
-    (type morphism hat-left-perturbation))
-  (the reduction
-    (progn
-      (dstr-change-sorc-trgt hat-left-perturbation
-	:new-sorc (tcc pre-left-eqvl-left-reduction)
-	:new-trgt (tcc pre-left-eqvl-left-reduction))
-      (let ((rslt (special-bpl-2 pre-left-eqvl-left-reduction
-				 hat-left-perturbation)))
-	(declare (type reduction rslt))
-	(with-slots (tcc f g h) rslt
-	  (setf tcc (cs-left-eqvl-hat smgr)
-		(slot-value f 'sorc) tcc
-		(slot-value g 'trgt) tcc
-		(slot-value h 'sorc) tcc
-		(slot-value h 'trgt) tcc))
-	rslt))))
-	
-
-#|
-  (cat-init)
-  (defun random-abar (tot-degr~ max-degr)
-    (do ((rslt nil)
-         (cum-degr 0 (+ cum-degr degr 1))
-         (degr))
-        ((>= cum-degr tot-degr~) (make-abar :list rslt))
-       (setf degr (1+ (random max-degr)))
-       (push (brgn (1+ degr)
-                   (let ((list (make-list degr)))
-                     (mapl
-                       #'(lambda (sublist)
-                           (setf (car sublist) (- (random 21) 10)))
-                       list)
-                     list))
-             rslt)))
-  (setf rdct (cs-left-eqvl-left-reduction (k-z-1)))
-  (pre-check-rdct rdct)
-  (setf *tc* (cmbn 0 1 (tnpr 0 (tnpr 0 +null-gbar+ 0 '()) 0 +null-abar+))
-        *bc* (cmbn 0 1 +null-gbar+))
-  (check-rdct)
-  (setf *tc* (cmbn 1 1 (tnpr 1 (tnpr 0 +null-gbar+ 1 '(13)) 0 +null-abar+)))
-  (check-rdct)
-  (dotimes (i 10)
-    (let ((abar (random-abar 8 4)))
-      (setf abar-degr (apply #'+ (mapcar #'car (abar-list abar))))
-      (setf gnrt (tnpr 5 (tnpr 3 (gbar 3 0 '(1 2) 0 '(3) 0 '()) 2 '(4 5))
-                       abar-degr abar))
-      (setf gbar (gbar 2 0 '(1) 0 '()))
-      (unless (>= abar-degr 9)
-        (setf *tc* (cmbn (+ 5 abar-degr) 1 gnrt)
-              *bc* (cmbn 2 1 gbar))
-        (check-rdct))))
-  (dotimes (i 10)
-    (let ((abar (random-abar 6 4)))
-      (setf abar-degr (apply #'+ (mapcar #'car (abar-list abar))))
-      (setf gnrt (tnpr 6 (tnpr 3 (gbar 3 0 '(1 2) 0 '(3) 0 '()) 3 '(4 5 6))
-                       abar-degr abar))
-      (setf gbar (gbar 3 0 '(1 2) 1 '() 0 '()))
-      (unless (>= abar-degr 8)
-        (setf *tc* (cmbn (+ 6 abar-degr) 1 gnrt)
-              *bc* (cmbn 3 1 gbar))
-        (check-rdct))))
-  (dotimes (i 10)
-    (let ((abar (random-abar 6 4)))
-      (setf abar-degr (apply #'+ (mapcar #'car (abar-list abar))))
-      (setf gnrt (tnpr 5 (tnpr 2 (gbar 2 0 '(3) 0 '()) 3 '(4 5 6))
-	   	     abar-degr abar))
-      (setf gbar (gbar 4 0 '(1 2 3) 0 '(4 5) 0 '(6) 0 '()))
-      (unless (>= abar-degr 9)
-        (setf *tc* (cmbn (+ 5 abar-degr) 1 gnrt))
-        (setf *bc* (cmbn 4 1 gbar))
-        (check-rdct))))
-  (dotimes (i 10)
-    (let ((abar (random-abar 6 4)))
-      (setf abar-degr (apply #'+ (mapcar #'car (abar-list abar))))
-      (setf gnrt (tnpr 4 (tnpr 2 (gbar 2 0 '(3) 0 '()) 2 '(4 5))
-                       abar-degr abar))
-      (setf gbar (gbar 5 8 '(1 2 3) 0 '(4 5 6) 0 '(7 8) 0 '(9) 0 '()))
-      (unless (>= abar-degr 10)
-         (setf *tc* (cmbn (+ 4 abar-degr) 1 gnrt))
-         (setf *bc* (cmbn 5 1 gbar))
-         (check-rdct))))
-|#
-
-(DEFUN CS-PRE-LEFT-EQVL-RIGHT-REDUCTION-INTR-F (cmbn)
-  (declare (type cmbn cmbn))
-  (the cmbn
-     (with-cmbn (degr list) cmbn
-     (let ((rslt +empty-list+))
-       (declare (list rslt))
-       (do ((mark list (cdr mark)))
-	   ((endp mark))
-	   (declare (list mark))
-	  (with--term (cffc tnpr) mark
-	  (with-tnpr (degr1 nil nil abar2) tnpr
-	    (if (zerop degr1)
-	       (push (term cffc abar2) rslt)
-	       (return)))))
-       (make-cmbn :degr degr
-		  :list (nreverse rslt))))))
-
-#|
-  (cs-pre-left-eqvl-right-reduction-intr-f
-    (cmbn 4 2 (tnpr 0 (tnpr 0 +null-gbar+ 0 'i)
-                    4 (abar 2 'a 2 'b))
-            3 (tnpr 0 (tnpr 0 +null-gbar+ 0 'i)
-                    4 (abar 2 'a 2 'c))
-            5 (tnpr 1 (tnpr 0 +null-gbar+ 1 'a)
-                    3 (abar 1 'a 2 'b))))
-|#
-
-(DEFUN CS-PRE-LEFT-EQVL-RIGHT-REDUCTION-F (smgr
-					     &aux (hat-t-u (cs-hat-t-u smgr))
-					          (bar (bar smgr)))
-  (declare
-    (type simplicial-group smgr)
-    (type chain-complex hat-t-u bar))
-  (the morphism
-    (morphism
-      :sorc hat-t-u :trgt bar :degr 0
-      :intr #'cs-pre-left-eqvl-right-reduction-intr-f
-      :strt :cmbn
-      :dfnt `(cs-pre-left-eqvl-right-reduction-f ,smgr))))
-
-(DEFUN CS-PRE-LEFT-EQVL-RIGHT-REDUCTION-INTR-G (idnt)
-  (declare (type gmsm idnt))
-  (flet ((rslt (cmbn)
-	   (declare (type cmbn cmbn))
-	   (the cmbn
-	     (with-cmbn (degr list) cmbn
-	     (let ((bsgn (tnpr 0 +null-gbar+ 0 idnt)))
-	       (declare (type tnpr bsgn))
-	       (make-cmbn :degr degr
-		 :list (mapcar
-			 #'(lambda (term)
-			     (declare (type term term))
-			     (with-term (cffc abar) term
-			       (term cffc
-				     (tnpr 0 bsgn
-					   degr abar))))
-			 list)))))))
-    (the intr #'rslt)))
-
-#|
-  (setf g (cs-pre-left-eqvl-right-reduction-intr-g 'i))
-  (funcall g (cmbn 3 2 (abar 1 'a 2 'b)))
-|#
-
-(DEFUN CS-PRE-LEFT-EQVL-RIGHT-REDUCTION-G (smgr
-					    &aux (hat-t-u (cs-hat-t-u smgr))
-					         (bar (bar smgr))
-						 (idnt (bsgn smgr)))
-  (declare
-    (type simplicial-group smgr)
-    (type chain-complex hat-t-u bar)
-    (type gmsm idnt))
-  (the morphism
-    (morphism
-      :sorc bar :trgt hat-t-u :degr 0
-      :intr (cs-pre-left-eqvl-right-reduction-intr-g idnt)
-      :strt :cmbn
-      :dfnt `(cs-pre-left-eqvl-right-reduction-g ,smgr))))
-
-(DEFUN CS-PRE-LEFT-EQVL-RIGHT-REDUCTION-H (smgr
-					    &aux (bar (bar smgr))
-					         (tnpr-contraction
-						   (smgr-tnpr-contraction smgr)))
-  (declare
-    (type simplicial-group smgr)
-    (type chain-complex bar)
-    (type morphism tnpr-contraction))
-  (the morphism
-    (tnsr-prdc tnpr-contraction (idnt-mrph bar))))
-
-(DEFUN CS-PRE-LEFT-EQVL-RIGHT-REDUCTION (smgr)
-  (declare (type simplicial-group smgr))
-  (the reduction
-    (reduction
-      :f (cs-pre-left-eqvl-right-reduction-f smgr)
-      :g (cs-pre-left-eqvl-right-reduction-g smgr)
-      :h (cs-pre-left-eqvl-right-reduction-h smgr)
-      :dfnt `(cs-pre-left-eqvl-right-reduction ,smgr))))
-
-#|
-  (cat-init)
-  (defun random-abar (tot-degr~ max-degr)
-    (do ((rslt nil)
-         (cum-degr 0 (+ cum-degr degr 1))
-         (degr))
-        ((>= cum-degr tot-degr~) (make-abar :list rslt))
-       (setf degr (1+ (random max-degr)))
-       (push (brgn (1+ degr)
-                   (let ((list (make-list degr)))
-                     (mapl
-                       #'(lambda (sublist)
-                           (setf (car sublist) (- (random 21) 10)))
-                       list)
-                     list))
-             rslt)))
-  (setf rdct (cs-pre-left-eqvl-right-reduction (k-z-1)))
-  (pre-check-rdct rdct)
-  (setf *tc* (cmbn 0 1 (tnpr 0 (tnpr 0 +null-gbar+ 0 '()) 0 +null-abar+))
-        *bc* (cmbn 0 1 +null-abar+))
-  (check-rdct)
-  (setf *tc* (cmbn 1 1 (tnpr 1 (tnpr 0 +null-gbar+ 1 '(13)) 0 +null-abar+)))
-  (check-rdct)
-  (dotimes (i 10)
-    (let ((abar (random-abar 8 4)))
-      (setf abar-degr (apply #'+ (mapcar #'car (abar-list abar))))
-      (setf gnrt (tnpr 5 (tnpr 3 (gbar 3 0 '(1 2) 0 '(3) 0 '()) 2 '(4 5))
-                       abar-degr abar))
-      (unless (>= abar-degr 9)
-        (setf *tc* (cmbn (+ 5 abar-degr) 1 gnrt)
-              *bc* (cmbn abar-degr 1 abar))
-        (check-rdct))))
-  (dotimes (i 10)
-    (let ((abar (random-abar 6 4)))
-      (setf abar-degr (apply #'+ (mapcar #'car (abar-list abar))))
-      (setf gnrt (tnpr 6 (tnpr 3 (gbar 3 0 '(1 2) 0 '(3) 0 '()) 3 '(4 5 6))
-                       abar-degr abar))
-      (unless (>= abar-degr 8)
-        (setf *tc* (cmbn (+ 6 abar-degr) 1 gnrt)
-              *bc* (cmbn abar-degr 1 abar))
-        (check-rdct))))
-  (dotimes (i 10)
-    (let ((abar (random-abar 6 4)))
-      (setf abar-degr (apply #'+ (mapcar #'car (abar-list abar))))
-      (setf gnrt (tnpr 5 (tnpr 2 (gbar 2 0 '(3) 0 '()) 3 '(4 5 6))
-	   	     abar-degr abar))
-      (unless (>= abar-degr 9)
-        (setf *tc* (cmbn (+ 5 abar-degr) 1 gnrt))
-        (setf *bc* (cmbn abar-degr 1 abar))
-        (check-rdct))))
-  (dotimes (i 10)
-    (let ((abar (random-abar 6 4)))
-      (setf abar-degr (apply #'+ (mapcar #'car (abar-list abar))))
-      (setf gnrt (tnpr 4 (tnpr 2 (gbar 2 0 '(3) 0 '()) 2 '(4 5))
-                       abar-degr abar))
-      (unless (>= abar-degr 10)
-         (setf *tc* (cmbn (+ 4 abar-degr) 1 gnrt))
-         (setf *bc* (cmbn abar-degr 1 abar))
-         (check-rdct))))
-|#
-
-(DEFUN CS-LEFT-EQVL-RIGHT-REDUCTION (smgr
-				      &aux (pre-reduction
-					     (cs-pre-left-eqvl-right-reduction smgr))
-				           (perturbation
-					     (cs-hat-right-perturbation smgr)))
-  (declare
-    (type simplicial-group smgr)
-    (type reduction pre-reduction)
-    (type morphism perturbation))
-  (the reduction
-    (progn
-      (setf (slot-value perturbation 'sorc) (tcc pre-reduction)
-	    (slot-value perturbation 'trgt) (tcc pre-reduction))
-      (special-bpl-2 pre-reduction perturbation))))
-
-#|
-  (cat-init)
-  (defun random-abar (tot-degr~ max-degr)
-    (do ((rslt nil)
-         (cum-degr 0 (+ cum-degr degr 1))
-         (degr))
-        ((>= cum-degr tot-degr~) (make-abar :list rslt))
-       (setf degr (1+ (random max-degr)))
-       (push (brgn (1+ degr)
-                   (let ((list (make-list degr)))
-                     (mapl
-                       #'(lambda (sublist)
-                           (setf (car sublist) (- (random 21) 10)))
-                       list)
-                     list))
-             rslt)))
-  (setf rdct (cs-left-eqvl-right-reduction (k-z-1)))
-  (pre-check-rdct rdct)
-  (setf *tc* (cmbn 0 1 (tnpr 0 (tnpr 0 +null-gbar+ 0 '()) 0 +null-abar+))
-        *bc* (cmbn 0 1 +null-abar+))
-  (check-rdct)
-  (setf *tc* (cmbn 1 1 (tnpr 1 (tnpr 0 +null-gbar+ 1 '(13)) 0 +null-abar+)))
-  (check-rdct)
-  (dotimes (i 10)
-    (let ((abar (random-abar 4 2)))
-      (setf abar-degr (apply #'+ (mapcar #'car (abar-list abar))))
-      (setf gnrt (tnpr 3 (tnpr 2 (gbar 2 0 '(3) 0 '()) 1 '(4))
-                       abar-degr abar))
-      (unless (>= abar-degr 9)
-        (setf *tc* (cmbn (+ 3 abar-degr) 1 gnrt)
-              *bc* (cmbn abar-degr 1 abar))
-        (check-rdct))))
-  (dotimes (i 10)
-    (let ((abar (random-abar 3 1)))
-      (setf abar-degr (apply #'+ (mapcar #'car (abar-list abar))))
-      (setf gnrt (tnpr 4 (tnpr 2 (gbar 2 0 '(3) 0 '()) 2 '(5 6))
-                       abar-degr abar))
-      (unless (>= abar-degr 8)
-        (setf *tc* (cmbn (+ 4 abar-degr) 1 gnrt)
-              *bc* (cmbn abar-degr 1 abar))
-        (check-rdct))))
-  (dotimes (i 10)
-    (let ((abar (random-abar 3 1)))
-      (setf abar-degr (apply #'+ (mapcar #'car (abar-list abar))))
-      (setf gnrt (tnpr 5 (tnpr 3 (gbar 3 0 '(1 2) 1 '() 0 '()) 2 '(5 6))
-	   	     abar-degr abar))
-      (unless (>= abar-degr 9)
-        (setf *tc* (cmbn (+ 5 abar-degr) 1 gnrt))
-        (setf *bc* (cmbn abar-degr 1 abar))
-        (check-rdct))))
-  (dotimes (i 10)
-    (let ((abar (random-abar 6 4)))
-      (setf abar-degr (apply #'+ (mapcar #'car (abar-list abar))))
-      (setf gnrt (tnpr 4 (tnpr 2 (gbar 2 0 '(3) 0 '()) 2 '(4 5))
-                       abar-degr abar))
-      (unless (>= abar-degr 10)
-         (setf *tc* (cmbn (+ 4 abar-degr) 1 gnrt))
-         (setf *bc* (cmbn abar-degr 1 abar))
-         (check-rdct))))
-|#
-
-(DEFUN CS-LEFT-EQVL (smgr)
-  (declare (type simplicial-group smgr))
-  (the equivalence
-    (equivalence
-     :lrdct (cs-left-eqvl-left-reduction smgr)
-     :rrdct (cs-left-eqvl-right-reduction smgr)
-     :dfnt `(cs-left-eqvl ,smgr))))
-
-#|
-  (cat-init)
-  (setf h (cs-left-eqvl (k-z-1)))
-  (setf abar (abar 2 '(2) 3 '(3 4)))
-  (rg h 5 abar)
-  (lf h *)
-  (lg h *)
-  (rf h *)
-|#
-
-(DEFUN CLASSIFYING-SPACE-EFHM (smgr)
-  (declare (type simplicial-group smgr))
-  (let ((left-eqvl (cs-left-eqvl smgr))
-	(right-eqvl (bar (efhm smgr))))
-    (declare (type equivalence left-eqvl right-eqvl))
-    (cmps left-eqvl right-eqvl)))
-
-(DEFMETHOD SEARCH-EFHM (classifying-space (dfnt (eql 'classifying-space)))
-  (declare (type simplicial-set classifying-space))
-  (classifying-space-efhm (second (dfnt classifying-space))))
-
-#|
-  (cat-init)
-  (setf k (k-z-1))
-  (homology k 0 10)
-  (setf bk (classifying-space k))
-  (homology bk 0 10)
-  (setf obk (loop-space bk))
-  (homology obk 0 6)
-|#
\ No newline at end of file
diff --git a/archive/Kenzo-2/Kenzo-2-Acl8/classes.cl b/archive/Kenzo-2/Kenzo-2-Acl8/classes.cl
deleted file mode 100644
index ba4bca3..0000000
--- a/archive/Kenzo-2/Kenzo-2-Acl8/classes.cl
+++ /dev/null
@@ -1,526 +0,0 @@
-;;;  CLASSES  CLASSES  CLASSES  CLASSES  CLASSES  CLASSES  CLASSES
-;;;  CLASSES  CLASSES  CLASSES  CLASSES  CLASSES  CLASSES  CLASSES
-;;;  CLASSES  CLASSES  CLASSES  CLASSES  CLASSES  CLASSES  CLASSES
-
-(IN-PACKAGE "CAT")
-
-(PROVIDE "classes")
-
-;;;
-;;; VARIOUS
-;;;
-
-(DEFTYPE ANY () t)
-
-;;; 
-;;;  COMBINATIONS
-;;;
-
-;; CFFC = CoeFFiCient
-(DEFUN CFFC-P (object)
-   (declare (type any object))
-   (the boolean
-      (and (typep object 'fixnum)
-           (/= 0 object))))
-
-(DEFTYPE CFFC () '(satisfies cffc-p))
-
-;; GNRT = GeNeRaTor
-(DEFTYPE GNRT () 'any)
-
-;; CMPR = CoMPaRison
-(DEFTYPE CMPR () '(member :less :equal :greater))
-
-;; CMPRF = CoMPaRison Function
-(DEFTYPE CMPRF () 'function)
-               ;; (function (gnrt gnrt) cmpr)
-
-(DEFUN TERM-P (object)
-   (declare (type any object))
-   (the boolean
-      (and (consp object)
-           (typep (car object) 'cffc)
-           (typep (cdr object) 'gnrt))))
-
-(DEFTYPE TERM () '(satisfies term-p))
-
-;; ICMBN = Internal-CoMBiNation
-(DEFUN ICMBN-P (object)
-   ;; ICMBN = Internal CoMBiNation,
-   ;;   without the keyword and the degree
-   (declare (type any object))
-   (the boolean
-      (and (listp object)
-           (every #'term-p object))))
-
-(DEFTYPE ICMBN () '(satisfies icmbn-p))
-
-;; CMBN = CoMBiNation
-(DEFUN CMBN-P (object)
-   (declare (type any object))
-   (the boolean
-      (and (consp object)
-           (eql (car object) :cmbn)
-           (consp (cdr object))
-           (typep (second object) 'fixnum)
-           (typep (cddr object) 'icmbn))))
-
-(DEFTYPE CMBN () '(satisfies cmbn-p))
-
-(DEFTYPE BASIS () '(or function (eql :locally-effective)))
-                   ;; (function (degr) (list gnrt))
-
-;; INTR = INTeRNal-morphism
-(DEFTYPE INTR () 'function)
-               ;; (or (function (degr gnrt) cmbn)  ;; if :gnrt strategy
-               ;;     (function (cmbn) (cmbn))     ;; if :cmbn strategy
-
-(DEFVAR REDEFINITION-WARNINGS-SAVED)
-
-(eval-when (:compile-toplevel :load-toplevel :execute)
- (WHEN
-  (AND (FIND-PACKAGE "EXCL")
-       (FIND-SYMBOL "*REDEFINITION-WARNINGS*" "EXCL"))
-  (setf redefinition-warnings-saved
-	excl:*redefinition-warnings*
-	excl:*redefinition-warnings* nil)))
-
-(DEFCLASS CHAIN-COMPLEX () ())  ;; will be redefined later.
-
-(DEFCLASS MORPHISM () ())  ;; will be redefined later.
-
-(DEFCLASS EQUIVALENCE () ())  ;;  will be redefined later
-
-;;  IDNM = IDentification NuMber
-(DEFVAR *IDNM-COUNTER*)
-(SETF *IDNM-COUNTER* 0)
-
-(DEFCLASS KENZO-OBJECT ()
-  ;; IDentification NuMber
-  ((idnm :type fixnum :reader idnm)
-   ;; ORiGiN
-   (dfnt :type list :reader dfnt)
-   (prpr :type list :reader prpr)
-   (cmmn :type list :reader cmmn)))
-
-(DEFCLASS CHAIN-COMPLEX (kenzo-object)
-  ((cmpr :type cmprf :reader cmpr1)
-   (basis :type basis :reader basis1)
-   ;; BaSe GeNerator
-   (bsgn :type gnrt :reader bsgn)
-   ;; DiFFeRential
-   (dffr :type morphism :reader dffr1)
-   ;; GRound MoDule
-   (grmd :type chain-complex :reader grmd)
-   ;; EFfective HoMology
-   (efhm :type equivalence :accessor efhm)))
-
-;; STRT = STRaTegy
-(DEFTYPE STRT () '(member :gnrt :cmbn))
-
-(DEFCLASS MORPHISM (kenzo-object)
-     ;; SOuRCe
-  ((sorc :type chain-complex :reader sorc)
-   ;; TaRGeT
-   (trgt :type chain-complex :reader trgt)
-   ;; DEGRee
-   (degr :type fixnum :reader degr)
-   ;; INTeRnal
-   (intr :type intr :reader intr)
-   ;; STRaTegy
-   (strt :type strt :reader strt)
-;;     ;; WoRk-TiMe
-;;     (wrtm :type integer :initform 0 :accessor wrtm)
-   ;; CaLl NuMber
-   (???-clnm :type fixnum :accessor ???-clnm)
-   (?-clnm :type fixnum :accessor ?-clnm)
-   ;; ReSuLTS
-   (rslts :type simple-vector :reader rslts)))
-            ;; (vector (vector result))
-
-;;;
-;;;  EFFECTIVE HOMOLOGY
-;;;
-
-(DEFCLASS REDUCTION (kenzo-object)
-  ;; Top Chain Complex
-  ((tcc :type chain-complex :reader tcc1)
-   ;; Bottom Chain Complex
-   (bcc :type chain-complex :reader bcc1)
-   (f :type morphism :reader f1)
-   (g :type morphism :reader g1)
-   (h :type morphism :reader h1)))
-
-(DEFCLASS EQUIVALENCE (kenzo-object)
-     ;; Left Bottom Chain Complex
-    ((lbcc :type chain-complex :reader lbcc1)
-     ;; Top Chain Complex
-     (tcc  :type chain-complex  :reader tcc1)
-     ;; Bottom Right Chain Complex
-     (rbcc :type chain-complex :reader rbcc1)
-     ;; Left f
-     (lf :type morphism        :reader lf1)
-     ;; Left g
-     (lg :type morphism        :reader lg1)
-     ;; Left h
-     (lh :type morphism        :reader lh1)
-     ;; Right f
-     (rf :type morphism        :reader rf1)
-     ;; Right g
-     (rg :type morphism        :reader rg1)
-     ;; Right h
-     (rh :type morphism        :reader rh1)
-     ;; Left ReDuCTion
-     (lrdct :type reduction    :reader lrdct)
-     ;; Right ReDuCTion
-     (rrdct :type reduction    :reader rrdct)))
-
-(eval-when (:compile-toplevel :load-toplevel :execute)
- (WHEN
-  (AND (FIND-PACKAGE "EXCL")
-       (FIND-SYMBOL "*REDEFINITION-WARNINGS*" "EXCL"))
-  (setf excl:*redefinition-warnings*
-	redefinition-warnings-saved)))
-
-;;;
-;;;  CONES
-;;;
-
-;; BICN = bicone
-(DEFUN BICN-P (object)
-   (declare (type any object))
-   (the boolean
-      (and (consp object)
-           (typep (car object) '(member :bcnb :bcnc :bcnd))
-           (typep (cdr object) 'gnrt))))
-
-(DEFTYPE BICN () '(satisfies bicn-p))
-
-;;;
-;;;  TENSOR PRODUCTS
-;;;
-
-(DEFUN TNPR-P (object)
-   (declare (type any object))
-   (the boolean
-      (and (consp object)
-           (eql :tnpr (car object))
-           (consp (cdr object))
-           (consp (cadr object))
-           (consp (cddr object))
-           (typep (caadr object) 'fixnum)
-           (typep (caddr object) 'fixnum))))
-
-(DEFTYPE TNPR () '(satisfies tnpr-p))
-
-;;;
-;;;  COALGEBRAS
-;;;
-
-(DEFCLASS COALGEBRA (chain-complex)
-    ((cprd :type morphism :reader cprd1)))   ;; coproduct
-
-;;;
-;;;  COBAR
-;;;
-
-;; CBGN CoBar-GeNerator
-(DEFUN CBGN-P (object)
-   ;; CBGN = CoBar GeNerator
-   (declare (type any object))
-   (the boolean
-      (and (consp object)
-           (typep (car object) 'fixnum)      ;; degree *in* the cobar
-           (typep (cdr object) 'gnrt))))
-
-(DEFTYPE CBGN () '(satisfies cbgn-p))
-
-;; IALLP = Internal-ALgebraic LooP
-(DEFUN IALLP-P (object)
-   (declare (type any object))
-   (the boolean
-      (and (listp object)
-           (every #'cbgn-p object))))
-
-(DEFTYPE IALLP () '(satisfies iallp-p))
-
-;; ALLP = ALgebraic LooP
-(DEFUN ALLP-P (object)
-   ;; ALLP = ALgebraic LooP
-   (declare (type any object))
-   (the boolean
-      (and (consp object)
-           (eq :allp (car object))
-           (typep (cdr object) 'iallp))))
-
-(DEFTYPE ALLP () '(satisfies allp-p))
-
-;;;
-;;;  ALGEBRAS
-;;;
-
-(DEFCLASS ALGEBRA (chain-complex)
-    ((aprd :type morphism :reader aprd1)))   ;; product
-
-
-;;;
-;;;  HOPH-ALGEBRAS
-;;;
-
-(DEFCLASS HOPF-ALGEBRA (coalgebra algebra)
-  ())
-
-;;;
-;;;  BAR
-;;;
-
-;; BRGN BaR-GeNerator
-(DEFUN BRGN-P (object)
-   ;; BRGN = BaR GeNerator
-   (declare (type any object))
-   (the boolean
-      (and (consp object)
-           (typep (car object) 'fixnum)      ;; degree *in* the cobar
-           (typep (cdr object) 'gnrt))))
-
-(DEFTYPE BRGN () '(satisfies brgn-p))
-
-;; IABAR = Internal-ALgebraic LooP
-(DEFUN IABAR-P (object)
-   (declare (type any object))
-   (the boolean
-      (and (listp object)
-           (every #'brgn-p object))))
-
-(DEFTYPE IABAR () '(satisfies iabar-p))
-
-;; ABAR = ALgebraic BAR
-(DEFUN ABAR-P (object)
-   (declare (type any object))
-   (the boolean
-      (and (consp object)
-           (eq :abar (car object))
-           (typep (cdr object) 'iabar))))
-
-(DEFTYPE ABAR () '(satisfies abar-p))
-
-;;;
-;;;  SIMPLICIAL SETS
-;;;
-
-;;  DGOP = DeGeneray OPerator
-(DEFTYPE DGOP () `(integer 0 ,most-positive-fixnum))
-
-;; GMSM = GeoMetric SiMplex
-(DEFTYPE GMSM () 'gnrt)
-
-;;  DLOP = DeL OPerator
-(DEFTYPE DLOP () 'dgop) 
-
-;; IABSM = Internal ABstract SiMplex
-(DEFUN IABSM-P (object)
-  (declare (type any object))
-  (the boolean
-     (and (consp object)
-	  (typep (car object) 'dgop)
-	  (typep (cdr object) 'gmsm))))	   
-
-(DEFTYPE IABSM () '(satisfies iabsm-p))
-
-;; ABSM = ABstract SiMplex
-(DEFUN ABSM-P (object)
-   (declare (type any object))
-   (the boolean
-      (and (consp object)
-           (eq :absm (car object))
-           (typep (cdr object) 'iabsm))))
-
-
-(DEFTYPE ABSM () '(satisfies absm-p))
-
-(DEFTYPE FACE () 'function)
-            ;;   (function (indx dmns gmsm) absm)
-
-(DEFTYPE FACE* () 'function)
-            ;;    (function (indx dmns gmsm) (or gmsm (eql :degenerate)))
-
-(DEFCLASS SIMPLICIAL-SET (coalgebra)
-    ((face :type face :reader face1)))
-
-;;;
-;;;  SPECIAL SMSTS
-;;;
-
-;;  DLOP = DeL OPerator
-(DEFUN SOFT-DLOP-P (object)
-   (declare (type any object))
-   (the boolean
-      (and (consp object)
-           (eq :delt (car object))
-           (typep (cdr object) 'dgop))))
-
-(DEFTYPE SOFT-DLOP () '(satisfies soft-dlop-p))
-
-;;;
-;;;  CARTESIAN PRODUCTS
-;;;
-
-;;  CRPR = CaRtesian PRoduct
-(DEFUN CRPR-P (object)
-   (declare (type any object))
-   (the boolean
-      (and (consp object)
-           (eq (car object) :crpr)
-           (consp (cdr object))
-           (consp (cadr object))
-           (consp (cddr object))
-           (typep (caadr object) 'dgop)
-           (typep (cdadr object) 'gmsm)
-           (typep (caddr object) 'dgop)
-           (typep (cdddr object) 'gmsm))))
-
-(DEFTYPE CRPR () '(satisfies crpr-p))
-
-;;;
-;;;  LOOP SPACES
-;;;
-
-;;  EXPN = EXPoNent
-(DEFUN EXPN-P (object)
-   (declare (type any object))
-   (the boolean
-      (typep object '(and fixnum
-                          (not (eql 0))))))
-
-(DEFTYPE EXPN () '(satisfies expn-p))
-
-;;  POWR = POWeR
-(DEFUN POWR-P (object)
-   (declare (type any object))
-   (the boolean
-      (and (consp object)
-           (typep (car object) 'gmsm)
-           (typep (cdr object) 'expn))))
-
-(DEFTYPE POWR () '(satisfies powr-p))
-
-;;  APOWR = Abstract POWeR
-(DEFUN APOWR-P (object)
-   (declare (type any object))
-   (the boolean
-      (and (consp object)
-           (typep (car object) 'dgop)
-           (typep (cdr object) 'powr))))
-
-(DEFTYPE APOWR () '(satisfies apowr-p))
-
-;;  ILOOP = Internal LOOP
-(DEFUN ILOOP-P (object)
-   (declare (type any object))
-   (the boolean
-      (and (listp object)
-           (every #'apowr-p object))))
-
-(DEFTYPE ILOOP () '(satisfies iloop-p))
-
-(DEFUN LOOP-P (object)
-   (declare (type any object))
-   (the boolean
-      (and (consp object)
-           (eq :loop (car object))
-           (iloop-p (cdr object)))))
-
-;;;----------------------------
-;;; Correction 2000 January 19
-;;;------------------------------------
-;;;#+(or (and :mswindows :allegro-v5.0)
-;;;------------------------------------
-#+(or (and :mswindows :allegro-v5.0)
-      (and :mswindows :allegro-v5.0.1)
-      (and :mswindows :allegro-v7.0)
-      (and :mswindows :allegro-v8.0)
-;;;-----------------------------------
-      (and :unix :allegro-v4.3)
-      (and :unix :allegro-v5.0))
-  (eval-when (:compile-toplevel :load-toplevel :execute)
-     (setf excl:*enable-package-locked-errors* nil))
-
-(DEFTYPE LOOP () '(satisfies loop-p))
-
-#+(or (and :mswindows :allegro-v5.0)
-      (and :unix :allegro-v4.3)
-      (and :unix :allegro-v5.0)
-      (and :mswindows :allegro-v7.0)
-      (and :mswindows :allegro-v8.0))
-  (eval-when (:compile-toplevel :load-toplevel :execute)
-     (setf excl:*enable-package-locked-errors* t))
-
-;;;;
-;;;;
-;;;;
-
-(DEFTYPE KFLL () 'function)
-              ;; (function (indx dmns (list absm)) absm)
-
-(DEFCLASS KAN (simplicial-set)
-  ((kfll :type kfll :reader kfll1)))
-
-(DEFTYPE SINTR () 'function)
-               ;; (function (dmns gmsm) absm)
-
-(DEFCLASS SIMPLICIAL-MRPH (morphism)
-  ((sintr :type sintr :reader sintr)))
-
-(DEFUN FIBRATION-P (object)
-  (declare (type any object))
-  (the boolean
-     (and (typep object 'simplicial-mrph)
-	  (= -1 (degr object)))))
-
-(DEFTYPE FIBRATION ()
-  '(satisfies fibration-p))
-
-(DEFCLASS SIMPLICIAL-GROUP (kan hopf-algebra)
-   ((grml :type simplicial-mrph :reader grml1)
-    (grin :type simplicial-mrph :reader grin1)))
-
-(DEFCLASS AB-SIMPLICIAL-GROUP (simplicial-group) ())
-
-(DEFMACRO GRML (smgr &rest rest)
-   (ecase (length rest)
-      (0 `(grml1 ,smgr))
-      ((1 2) `(? (grml1 ,smgr) ,@rest))))
-
-(DEFMACRO GRIN (smgr &rest rest)
-   (case (length rest)
-      (0 `(grin1 ,smgr))
-      (otherwise `(? (grin1 ,smgr) ,@rest))))
-
-;;;
-;;;  GBAR
-;;;
-
-;;  IGBAR Internal Geometrical BAR
-;;  (dmns absm_(m-1) ... absm_1 absm_0)
-(DEFUN IGBAR-P (object)
-   (declare (type any object))
-   (the boolean
-      (and (listp object)
-	   (typep (first object) '(integer 0 *))
-	   (= (length object) (1+ (first object)))
-	   (every #'absm-p (rest object)))))
-
-(DEFTYPE IGBAR () '(satisfies igbar-p))
-
-;;  GBAR Geometrical BAR
-;;  (:gbar dmns absm_(m-1) ... absm_1)
-(DEFUN GBAR-P (object)
-   (declare (type any object))
-   (the boolean
-      (and (consp object)
-           (eq :gbar (car object))
-           (igbar-p (cdr object)))))
-
-(DEFTYPE GBAR () '(satisfies gbar-p))
-
-
diff --git a/archive/Kenzo-2/Kenzo-2-Acl8/classifying-spaces.cl b/archive/Kenzo-2/Kenzo-2-Acl8/classifying-spaces.cl
deleted file mode 100644
index a94fb16..0000000
--- a/archive/Kenzo-2/Kenzo-2-Acl8/classifying-spaces.cl
+++ /dev/null
@@ -1,383 +0,0 @@
-;;;  CLASSIFYING-SPACES  CLASSIFYING-SPACES  CLASSIFYING-SPACES
-;;;  CLASSIFYING-SPACES  CLASSIFYING-SPACES  CLASSIFYING-SPACES
-;;;  CLASSIFYING-SPACES  CLASSIFYING-SPACES  CLASSIFYING-SPACES
-
-(IN-PACKAGE "CAT")
-
-(provide "classifying-spaces")
-
-(DEFCONSTANT +NULL-GBAR+ (make-gbar :dmns 0 :list +empty-list+))
-
-;;; NIGBAR = non-normalized igbar (with dimension)
-
-(DEFUN NORMALIZE-GBAR (nigbar)
-  (declare (list nigbar))
-  (the absm
-    (let ((dmns (first nigbar))
-	  (igbar (rest nigbar)))
-      (declare
-        (fixnum dmns)
-	(list igbar))
-      (when (zerop dmns)
-	(return-from normalize-gbar (absm 0 +null-gbar+)))
-      (do ((mark igbar (cdr mark))
-	   (indx (1- dmns) (1- indx))
-	   (2-indx (2-exp (1- dmns)) (ash 2-indx -1))
-	   (mask (mask (1- dmns)) (ash mask -1))
-	   (and-dgops -1 (logand and-dgops (dgop (car mark))))
-	   ;; r = result
-	   (r-dgop 0)
-	   (r-absm-list +empty-list+))
-	  ((endp mark)
-	   (absm r-dgop
-		 (make-gbar
-		  :dmns (- dmns (logcount r-dgop))
-		  :list (nreverse r-absm-list))))	   
-	  (declare
-	   (list mark r-absm-list)
-	   (fixnum indx 2-indx mask and-dgops rdgop))
-	  (when (zerop and-dgops)
-	    (return-from normalize-gbar
-	      (absm r-dgop
-		    (make-gbar
-		     :dmns (- dmns (logcount r-dgop))
-		     :list (nreconc r-absm-list mark)))))
-	  (let ((absm (car mark)))
-	    (with-absm (dgop gmsm) absm
-	      (declare (ignore gmsm))
-	      (if (and (= dgop mask)
-		       (logbitp indx and-dgops))
-		 (progn
-		   (incf r-dgop 2-indx)
-		   (mapl
-		    #'(lambda (sublist)
-			(declare (list sublist))
-			(setf (car sublist)
-			      (let ((absm (car sublist)))
-				(declare (type absm absm))
-				(with-absm (dgop gmsm) absm
-				  (absm (multiple-value-bind (q r)
-							     (floor dgop 2-indx)
-					  (declare (fixnum q r))
-					  (+ (ash (1- q) (1- indx)) r))
-					gmsm)))))
-		    r-absm-list))
-		 (push absm r-absm-list))))))))
-
-#|
-  (normalize-gbar (list 0))
-  (normalize-gbar (list 1 (absm 0 'i)))
-  (normalize-gbar (list 2 (absm 1 'i) (absm 0 'i)))
-  (normalize-gbar (list 2 (absm 0 'a) (absm 0 'i)))
-  (normalize-gbar (list 4 (absm 0 'a) (absm 0 'b) (absm 0 'c) (absm 0 'i)))
-  (normalize-gbar (list 4 (absm 7 'i) (absm 3 'i) (absm 1 'i) (absm 0 'i)))
-  (normalize-gbar (list 4 (absm 0 'a) (absm 3 'i) (absm 0 'c) (absm 0 'i)))
-  (normalize-gbar (list 4 (absm 1 'a) (absm 3 'i) (absm 0 'c) (absm 0 'i)))
-  (normalize-gbar (list 4 (absm 2 'a) (absm 3 'i) (absm 0 'c) (absm 0 'i)))
-  (normalize-gbar (list 4 (absm 4 'a) (absm 3 'i) (absm 0 'c) (absm 0 'i)))
-  (normalize-gbar (list 4 (absm 3 'a) (absm 3 'i) (absm 0 'c) (absm 0 'i)))
-  (normalize-gbar (list 4 (absm 5 'a) (absm 3 'i) (absm 0 'c) (absm 0 'i)))
-  (normalize-gbar (list 4 (absm 6 'a) (absm 3 'i) (absm 0 'c) (absm 0 'i)))
-  (normalize-gbar (list 4 (absm 1 'a) (absm 3 'i) (absm 1 'i) (absm 0 'i)))
-|#
-
-(DEFMETHOD PRINT-KEYCONS ((car (eql :gbar)) cdr stream)
-  (declare
-    (list cdr)
-    (stream stream))
-  (the (eql t)
-     (progn
-       (princ "<<GBar" stream)
-      (dolist (absm (rest cdr))
-	 (declare (type absm absm))
-	 (with-absm (dgop gmsm) absm
-	   (format stream "<~A ~A>"
-		   (hyphenize-list (dgop-int-ext dgop))
-		   gmsm)))
-       (princ ">>" stream)
-       t)))
-
-(DEFUN UNNORMALIZE-GBAR (absm idnt)
-  (declare
-     (type absm absm)
-     (type gmsm idnt))
-  (the igbar
-    (with-absm (dgop gbar) absm
-    (with-gbar (dmns list) gbar
-      (setf list (reverse list))
-      (do ((dgop2 dgop (ash dgop2 -1))
-	   (indx 0 (1+ indx))
-	   (2-indx 1 (ash 2-indx 1))
-	   (dgop3 0)
-	   (rslt +empty-list+))
-	  ((zerop dgop2)
-	   (cons (+ dmns (logcount dgop))
-		 (nreconc
-		  (mapcar
-		   #'(lambda (absm)
-		       (declare (type absm absm))
-		       (ndgnr dgop3 absm))
-		   list)
-		  rslt)))
-	  (declare
-	    (list rslt)
-	    (fixnum dgop2 2-indx dgop3))
-	 (if (oddp dgop2)
-	    (progn
-	      (push (absm (mask indx) idnt) rslt)
-	      (incf dgop3 2-indx))
-	    (push (ndgnr dgop3 (pop list)) rslt)))))))
-
-#|
-  (unnormalize-gbar (absm 1 +null-gbar+) 'i)
-  (unnormalize-gbar (absm 15 +null-gbar+) 'i)
-  (normalize-gbar (unnormalize-gbar (absm 15 +null-gbar+) 'i))
-  (unnormalize-gbar
-     (absm 0 (make-gbar :dmns 4
-                        :list (list (absm 0 'a) (absm 0 'b)
-                                    (absm 0 'c) (absm 0 'i)))) 'i)
-  (normalize-gbar
-   (unnormalize-gbar
-     (absm 0 (make-gbar :dmns 4
-                        :list (list (absm 0 'a) (absm 0 'b)
-                                    (absm 0 'c) (absm 0 'i)))) 'i))
-  (unnormalize-gbar
-     (absm 5 (make-gbar :dmns 4
-                        :list (list (absm 0 'a) (absm 0 'b)
-                                    (absm 0 'c) (absm 0 'i)))) 'i)
-  (normalize-gbar
-   (unnormalize-gbar
-     (absm 5 (make-gbar :dmns 4
-                        :list (list (absm 0 'a) (absm 0 'b)
-                                    (absm 0 'c) (absm 0 'i)))) 'i))
-  (unnormalize-gbar
-     (absm 9 (make-gbar :dmns 4
-                        :list (list (absm 0 'a) (absm 0 'b)
-                                    (absm 0 'c) (absm 0 'i)))) 'i)
-  (normalize-gbar
-   (unnormalize-gbar
-     (absm 9 (make-gbar :dmns 4
-                        :list (list (absm 0 'a) (absm 0 'b)
-                                    (absm 0 'c) (absm 0 'i)))) 'i))
-|#
-
-(DEFUN GBAR (dmns &rest rest)
-  (the gbar
-    (progn
-      (unless (= (+ dmns dmns) (length rest))
-	(error "In GBAR, the argument list has a wrong length."))
-      (make-gbar :dmns dmns
-		 :list (do ((mark rest (cddr mark))
-			    (rslt +empty-list+
-				  (cons (absm (car mark) (cadr mark))
-					rslt)))
-			   ((endp mark) (nreverse rslt))
-			   (declare (list mark rslt)))))))
-
-#|
-  (gbar 0)
-  (gbar 1)
-  (gbar 2 1 'a 2 'b)
-|#
-
-(DEFUN CLASSIFYING-SPACE-CMPR (cmpr)
-  (declare (type cmprf cmpr))
-  (flet ((rslt (gbar1 gbar2)
-	   (declare (type gbar gbar1 gbar2))
-	   (maplexico
-	    #'(lambda (absm1 absm2)
-		(declare (type absm absm1 absm2))
-		(a-cmpr3 cmpr absm1 absm2))
-	    (gbar-list gbar1) (gbar-list gbar2))))
-     (the cmprf #'rslt)))
-
-#|
-  (setf cmpr (classifying-space-cmpr 's-cmpr))
-  (funcall cmpr (gbar 2 0 'a 0 'a) (gbar 2 1 'a 0 'a))
-  (funcall cmpr (gbar 2 0 'a 0 'a) (gbar 2 0 'b 0 'a))
-  (funcall cmpr (gbar 2 0 'a 0 'a) (gbar 2 0 'a 0 'a))
-|#
-
-(DEFUN CLASSIFYING-SPACE-BASIS (basis)
-  (declare (type basis basis))
-  (when (eq basis :locally-effective)
-    (return-from classifying-space-basis :locally-effective))
-  (let ((crts-basis :locally-effective)  ;; to be redefined
-	(idnt (first (funcall basis 0))))
-    (declare
-      (type basis crts-basis)
-      (type gmsm idnt))
-    (labels ((rslt (dmns)
-	       (declare (fixnum dmns))
-	       (when (minusp dmns)
-		 (return-from rslt +empty-list+))
-	       (when (zerop dmns)
-		 (return-from rslt (list +null-gbar+)))
-	       (let ((basis-1 (funcall crts-basis (1- dmns))))
-		 (declare (list basis-1))
-		 (nreverse
-		  (mapcar
-		   #'(lambda (crpr)
-		       (declare (type crpr crpr))
-		       (with-crpr (absm1 absm2) crpr
-			 (make-gbar
-			  :dmns dmns
-			  :list (cons absm1
-				      (rest (unnormalize-gbar absm2 idnt))))))
-		   (member-if
-		    #'(lambda (dgop)
-			(declare (fixnum dgop))
-			(< dgop (mask (1- dmns))))
-		    (reverse basis-1)
-		    :key #'caadr))))))
-	    (setf crts-basis (crts-prdc-basis basis #'rslt))
-	    (the basis #'rslt))))
-
-#|
-  (cat-init)
-  (setf k (k-z2-1))
-  (setf b (classifying-space-basis (basis k)))
-  (dotimes (i 5) (print (funcall b i)))
-|#
-
-(DEFUN CLASSIFYING-SPACE-FACE (face grml-sintr)
-  (declare
-     (type face face)
-     (type sintr grml-sintr))
-  (flet ((rslt (indx dmns gbar)
-	   (declare
-	     (fixnum indx dmns)
-	     (type gbar gbar))
-	   (when (= indx dmns)
-	     (return-from rslt
-	       (normalize-gbar (cons (1- dmns) (rest (gbar-list gbar))))))
-	   (do ((mark (gbar-list gbar) (cdr mark))
-		(dmns2 (1- dmns) (1- dmns2))
-		(rslt +empty-list+
-		      (cons (a-face4 face indx dmns2 (car mark))
-			    rslt)))
-	       ((= dmns2 indx)
-		(if (zerop indx)
-		   (normalize-gbar (cons (1- dmns) (nreverse rslt)))
-		   (normalize-gbar
-		    (cons (1- dmns)
-			  (nreconc
-			    rslt
-			    (cons (a-grml4 grml-sintr (1- indx)
-					   (second mark)
-					   (a-face4 face indx indx (first mark)))
-				  (nthcdr 2 mark))))))))))
-     (the face #'rslt)))
-
-#|
-  (setf om (loop-space (moore 2 2)))
-  (setf face (classifying-space-face (face om) (sintr (grml om))))
-  (setf gbar (gbar 4 0 (loop3 3 'm2 1 4 'n3 1)
-                     0 (loop3 0 'n3 1)
-                     0 (loop3 0 'm2 1)
-                     0 +null-loop+))
-  (dotimes (i 5)
-    (print (funcall face i 4 gbar)))
-|#
-
-(DEFMETHOD CLASSIFYING-SPACE ((smgr simplicial-group))
-  (the simplicial-set
-    (simplicial-set :cmpr (classifying-space-cmpr (cmpr smgr))
-                    :basis (classifying-space-basis (basis smgr))
-                    :bsgn +null-gbar+
-                    :face (classifying-space-face (face smgr) (sintr (grml smgr)))
-                    :dfnt `(classifying-space ,smgr))))
-
-#|
-  (cat-init)
-  (setf c (classifying-space (k-z2-1)))
-  (dfnt c)
-  (first (basis c 4))
-  (? c 4 (first (basis c 4)))
-  (? c *)
-  (cprd c 4 ***)
-  (dotimes (i 5)
-    (print (face c i 4 (first (basis c 4)))))
-|#
-
-(DEFUN CLASSIFYING-SPACE-GRML-SINTR (idnt grml-sintr)
-  (declare
-    (type gmsm idnt)
-    (type sintr grml-sintr))
-  (flet ((rslt (dmns crpr)
-	   (declare
-	     (fixnum dmns)
-	     (type crpr crpr))
-	   (with-crpr (absm1 absm2) crpr
-	   (let ((absm-list-1 (rest (unnormalize-gbar absm1 idnt)))
-		 (absm-list-2 (rest (unnormalize-gbar absm2 idnt))))
-	     (declare (list absm-list-1 absm-list-2))
-	     (normalize-gbar
-	       (cons dmns
-		 (mapcar
-		   #'(lambda (absm1 absm2)
-		       (declare (type absm absm1 absm2))
-		       (decf dmns) ;; !!
-		       (a-grml4 grml-sintr dmns absm1 absm2))
-		   absm-list-1 absm-list-2)))))))
-    (the sintr #'rslt)))
-
-#|
-  (setf grml (classifying-space-grml-sintr '() (sintr (grml (k-z-1)))))
-  (funcall grml 3 (crpr 0 (gbar 3 0 '(1 2) 0 '(3) 0 '())
-                        0 (gbar 3 0 '(-1 -2) 0 '(-3) 0 '())))
-  (funcall grml 3 (crpr 0 (gbar 3 0 '(1 2) 0 '(3) 0 '())
-                        4 (gbar 2 0 '(-3) 0 '())))
-  (funcall grml 3 (crpr 0 (gbar 3 0 '(1 2) 0 '(3) 0 '())
-                        1 (gbar 2 0 '(-3) 0 '())))
-|#
-
-
-(DEFUN CLASSIFYING-SPACE-GRIN-SINTR (grin-sintr)
-  (declare (type sintr grin-sintr))
-  (flet ((rslt (dmns gbar)
-	   (declare
-	     (fixnum dmns)
-	     (type gbar gbar))
-	   (absm 0
-	     (make-gbar
-	       :dmns dmns
-	       :list (mapcar
-		       #'(lambda (absm)
-			   (declare (type absm absm))
-			   (a-grin4 grin-sintr dmns absm))
-		       (gbar-list gbar))))))
-    (the sintr #'rslt)))
-
-#|
-  (setf grin (classifying-space-grin-sintr (sintr (grin (k-z-1)))))
-  (funcall grin 3 (gbar 3 0 '(1 2) 1 '() 0 '()))
-|#
-
-(DEFMETHOD CLASSIFYING-SPACE ((smgr ab-simplicial-group))
-  (the ab-simplicial-group
-     (change-class 
-       (simplicial-group :cmpr (classifying-space-cmpr (cmpr smgr))
-		   :basis (classifying-space-basis (basis smgr))
-		   :bsgn +null-gbar+
-		   :face (classifying-space-face (face smgr) (sintr (grml smgr)))
-		   :grml-sintr (classifying-space-grml-sintr
-				 (bsgn smgr)
-				 (sintr (grml smgr)))
-		   :grin-sintr (classifying-space-grin-sintr
-				 (sintr (grin smgr)))
-		   :dfnt `(classifying-space ,smgr))
-       'ab-simplicial-group)))
-
-#|
-  (setf k-z-1 (k-z-1))
-  (setf k-z-2 (classifying-space k-z-1))
-  (setf k-z-3 (classifying-space k-z-2))
-  (homology k-z-3 0 10)
-  (setf k-z2-1 (k-z2-1))
-  (setf k-z2-2 (classifying-space k-z2-1))
-  (setf k-z2-3 (classifying-space k-z2-2))
-  (setf k-z2-4 (classifying-space k-z2-3))
-  (setf k-z2-5 (classifying-space k-z2-4))
-  (homology k-z2-5 0 7)
-|#
diff --git a/archive/Kenzo-2/Kenzo-2-Acl8/coalgebras.cl b/archive/Kenzo-2/Kenzo-2-Acl8/coalgebras.cl
deleted file mode 100644
index 13c8098..0000000
--- a/archive/Kenzo-2/Kenzo-2-Acl8/coalgebras.cl
+++ /dev/null
@@ -1,58 +0,0 @@
-;;;  COALGEBRAS  COALGEBRAS  COALGEBRAS  COALGEBRAS  COALGEBRAS  COALGEBRAS
-;;;  COALGEBRAS  COALGEBRAS  COALGEBRAS  COALGEBRAS  COALGEBRAS  COALGEBRAS
-;;;  COALGEBRAS  COALGEBRAS  COALGEBRAS  COALGEBRAS  COALGEBRAS  COALGEBRAS
-
-(IN-PACKAGE "CAT")
-
-(PROVIDE "coalgebras")
-
-(DEFMETHOD PRINT-OBJECT ((clgb coalgebra) stream)
- (the coalgebra
-   (progn
-      (format stream "[K~D Coalgebra]" (idnm clgb))
-      clgb)))
-
-(DEFUN COALGEBRA (&rest rest &key dfnt &allow-other-keys)
-  (declare (type list dfnt))
-  (already coalgebra dfnt)
-  (the coalgebra
-    (apply #'make-instance 'coalgebra rest)))
-
-(DEFMETHOD SHARED-INITIALIZE ((clgb coalgebra) slot-names &key cprd-intr cprd-strt)
-  (declare
-   (type (or (eql t) list) slot-names)
-   (type intr cprd-intr)
-   (type strt cprd-strt))
-  (call-next-method)
-  (when-slot cprd
-             (with-slots (cprd) clgb
-               (declare (type morphism cprd))
-               (when cprd-intr
-                 (unless cprd-strt
-                   (error "IN COALGEBRA, a CPRD-INTR is given, but not its CPRD-STRT."))
-                 (setf cprd (morphism :sorc clgb :trgt (tnsr-prdc clgb clgb) :degr 0
-                                      :intr cprd-intr :strt cprd-strt
-                                      :dfnt `(coalgebra-coproduct ,clgb))))))
-  clgb)
-
-(DEFUN CHANGE-CHCM-TO-CLGB (chcm &key cprd-intr cprd-strt dfnt)
-  (declare
-   (type chain-complex chcm)
-   (type intr cprd-intr)
-   (type strt cprd-strt)
-   (list dfnt))
-  (the coalgebra
-    (progn
-      (change-class chcm 'coalgebra)
-      (setf dfnt (list (dfnt chcm) 'then dfnt))
-      (let ((already (find dfnt *k-list* :key #'dfnt :test #'equal)))
-        (declare (type (or null coalgebra) already))
-        (when already
-          (return-from change-chcm-to-clgb already)))
-      (setf (slot-value chcm 'cprd) (morphism
-                                     :sorc chcm :trgt (tnsr-prdc chcm chcm)
-                                     :degr 0
-                                     :intr cprd-intr :strt cprd-strt
-                                     :dfnt dfnt))
-      chcm)))
-
diff --git a/archive/Kenzo-2/Kenzo-2-Acl8/cobar.cl b/archive/Kenzo-2/Kenzo-2-Acl8/cobar.cl
deleted file mode 100644
index 06e62f6..0000000
--- a/archive/Kenzo-2/Kenzo-2-Acl8/cobar.cl
+++ /dev/null
@@ -1,734 +0,0 @@
-;;;  COBAR  COBAR  COBAR  COBAR  COBAR  COBAR  COBAR  COBAR  COBAR
-;;;  COBAR  COBAR  COBAR  COBAR  COBAR  COBAR  COBAR  COBAR  COBAR
-;;;  COBAR  COBAR  COBAR  COBAR  COBAR  COBAR  COBAR  COBAR  COBAR
-
-(IN-PACKAGE "CAT")
-
-(PROVIDE "cobar")
-
-(DEFUN ALLP (&rest list)
-   (when (= 1 (length list))
-      (setf list (first list)))
-   (unless (evenp (length list))
-      (error "In ALLP, the length list should be even."))
-   (the allp
-      (let ((rslt (list :allp)))
-         (declare (list rslt))
-         (do ((mark list (cddr mark)))
-             ((endp mark))
-            (declare (list mark))
-            (push (cbgn (car mark) (cadr mark)) rslt))
-         (nreverse rslt))))
-
-#|
-  (allp )
-  (allp '(2 a 3 b))
-  (allp 2 'a 3 'b)
-  (allp 2 'a 3))  ;; error
-|#
-
-(DEFCONSTANT +NULL-ALLP+ (make-allp :list +empty-list+))
-
-(DEFMETHOD PRINT-KEYCONS ((car (eql :allp)) cdr stream)
-   (declare
-      (list cdr)
-      (stream stream))
-   (the allp
-      (progn
-         (format stream "<<AlLp")
-         (dolist (cbgn cdr)
-            (declare (type cbgn cbgn))
-            (with-cbgn (degr gnrt) cbgn
-               (format stream "[~D ~A]" degr gnrt)))
-         (format stream ">>")
-         (cons car cdr))))
-            
-(DEFUN COBAR-CMPR (cmpr)
-   (declare (type cmprf cmpr))
-   (flet ((rslt (allp1 allp2)
-             (declare (type allp allp1 allp2))
-             (the cmpr
-                (lexico
-                   (f-cmpr (length allp1) (length allp2))
-                   (maplexico
-                      #'(lambda (cbgn1 cbgn2)
-                           (lexico
-                              (f-cmpr (cdegr cbgn1) (cdegr cbgn2))
-                              (funcall cmpr (cgnrt cbgn1) (cgnrt cbgn2))))
-                      (allp-list allp1)
-                      (allp-list allp2))))))
-      (the cmprf #'rslt)))
-
-#|
-  (setf r (cobar-cmpr #'s-cmpr))
-  (funcall r (allp) (allp))
-  (funcall r (allp 3 'a) (allp))
-  (funcall r (allp 3 'a) (allp 2 'a 1 'b))
-  (funcall r (allp 3 'a) (allp 3 'b))
-  (funcall r (allp 3 'a) (allp 3 'a)))
-|#
-
-(DEFUN COBAR-BASIS-LENGTH (basis degr length)
-   (declare
-      (type basis basis)
-      (fixnum degr length))
-   (the list
-      (progn
-	(when (= 1 length)
-	      (return-from cobar-basis-length
-			   (mapcar
-			    #'(lambda (item)
-				(declare (type gnrt item))
-				(list (cbgn degr item)))
-			    (funcall basis (1+ degr)))))                                         
-	(mapcan
-	 #'(lambda (degr1)
-	     (declare (fixnum degr1))
-	     (let ((list1 (funcall basis (1+ degr1)))
-		   (list2 (cobar-basis-length
-			    basis (- degr degr1) (1- length))))
-	       (declare (list list1 lis2))
-	       (mapcan
-		#'(lambda (item1)
-		    (declare (type gnrt item1))
-		    (mapcar
-		     #'(lambda (item2)
-			 (declare (type iallp item2))
-			 (cons (cbgn degr1 item1) item2))
-		     list2))
-		list1)))
-	 (>a-b< 0 degr)))))
-
-#|
-  (setf basis #'(lambda (degr)
-                   (list degr)))
-  (cobar-basis-length basis 1 1)
-  (cobar-basis-length basis 2 1)
-  (cobar-basis-length basis 2 2)
-  (cobar-basis-length basis 3 1)
-  (cobar-basis-length basis 3 2)
-  (cobar-basis-length basis 3 3)
-|#
-
-(DEFUN COBAR-BASIS (basis)
-   (declare (type basis basis))
-   (the basis
-      (progn
-	(when (eq :locally-effective basis)
-	  (return-from cobar-basis :locally-effective))
-	(flet ((rslt (degr)
-		     (declare (fixnum degr))
-		     (cond ((minusp degr) +empty-list+)
-			   ((zerop degr) (list +null-allp+))
-			   (t
-			    (mapcan
-			     #'(lambda (length)
-				 (declare (fixnum length))
-				 (mapcar
-				  #'(lambda (iallp)
-                                      (declare (type iallp iallp))
-                                      (make-allp :list iallp))
-				  (cobar-basis-length basis degr length)))
-			     (>a-b> 0 degr))))))
-	      #'rslt))))
-   
-#| The following version of the COBAR-BASIS function is
-   not correctly compiled with ACL-Unix, probably
-   because the too complicated (but natural and correct)
-   structure of closures. This version works on ACL-PC.
-(DEFUN COBAR-BASIS (basis)
-   (declare
-      (type basis basis))
-   ;; if the coalgebra is effective, it is assumed simply-connected :
-   ;;   (length (funcall basis 0))  ==>  1
-   ;;   (length (funcall basis 1))  ==>  0
-   (the basis
-      (progn
-         (when (eq :locally-effective basis)
-            (return-from cobar-basis :locally-effecive))
-         (labels ((rslt (degr length)
-                     (declare (fixnum degr length))
-                     (when (= 1 length)
-                        (return-from rslt
-                           (mapcar
-                              #'(lambda (item)
-                                   (declare (type gnrt item))
-                                   (list (cbgn degr item)))
-                              (funcall basis (1+ degr)))))                                         
-                     (mapcan
-                        #'(lambda (degr1)
-                             (declare (fixnum degr1))
-                             (let ((list1 (funcall basis (1+ degr1)))
-                                   (list2 (rslt (- degr degr1) (1- length))))
-                                (declare (list list1 lis2))
-                                (mapcan
-                                   #'(lambda (item1)
-                                        (declare (type gnrt item1))
-                                        (mapcar
-                                           #'(lambda (item2)
-                                                (declare (type iallp item2))
-                                                (cons (cbgn degr1 item1) item2))
-                                           list2))
-                                   list1)))
-                        (>a-b< 0 degr))))
-            #'(lambda (degr)
-                 (declare (fixnum degr))
-                 (if (zerop degr)
-                    (list (make-allp :list +empty-list+))
-                    (mapcan
-                       #'(lambda (length)
-                            (declare (fixnum length))
-                            (mapcar
-                               #'(lambda (iallp)
-                                    (declare (type iallp iallp))
-                                    (make-allp :list iallp))
-                               (rslt degr length)))
-                       (>a-b> 0 degr))))))))
-|#
-
-#|
-  (setf basis #'(lambda (degr)
-                   (list degr)))
-  (setf r (cobar-basis basis))
-  (funcall r 0)
-  (funcall r 1)
-  (funcall r 2)
-  (dotimes (i 7)
-     (print (funcall r i)))
-  (cobar-basis :locally-effective)
-|#
-
-(DEFUN COBAR-INTR-VRTC-DFFR (dffr)
-   (declare (type morphism dffr))
-   (labels ((rslt (degr iallp)
-               ;; the argument iallp is an internal algebraic loop,
-               ;;     without the keyword :allp
-               ;; rslt returns an internal combination
-               ;;     without the keyword :cmbn, without degree
-               (declare
-                  (fixnum degr)
-                  (type iallp iallp))
-               (the icmbn
-                  (progn
-                     (unless iallp
-                        (return-from rslt +empty-list+))
-                     (let ((cbgn1 (first iallp))
-                           (rest (rest iallp)))
-                        (declare
-                           (type cbgn cbgn1)
-                           (type iallp rest))
-                        (with-cbgn (degr1 gnrt1) cbgn1
-                           (let ((d-gnrt1 (cmbn-list (gnrt-? dffr (1+ degr1) gnrt1)))
-                                 (d-rest (rslt (- degr degr1) rest))
-                                 (degr1-1 (1- degr1))
-                                 (first-sign (-1-expt-n-1 (length rest)))
-                                 (rest-sign (-1-expt-n degr1)))
-                              (declare
-                                 (type icmbn d-gnrt1 d-rest)
-                                 (fixnum degr1-1 rest-sign))
-                              (nconc
-                                 (mapcar
-                                    #'(lambda (term)
-                                         (with-term (cffc gnrt) term
-                                            (term (* first-sign cffc)
-                                               (cons (cbgn degr1-1 gnrt) rest))))
-                                    d-gnrt1)
-                                 (mapcar
-                                    #'(lambda (term)
-                                         (with-term (cffc gnrt) term
-                                            (term (* rest-sign cffc)
-                                               (cons cbgn1 gnrt))))
-                                    d-rest)))))))))
-      (the intr
-         #'(lambda (degr allp)
-              (make-cmbn
-                 :degr (1- degr)
-                 :list (mapcar
-                          #'(lambda (term)
-                               (with-term (cffc iallp) term
-                                  (term cffc (make-allp :list iallp))))
-                          (rslt degr (allp-list allp))))))))
-         
-
-#|
-  (require "special-smsts"
-            #-ACLPC "special-smsts"
-            #+ACLPC "special-smsts.fsl")
-  (setf d (soft-delta-infinity))
-  (setf r (cobar-intr-vrtc-dffr (dffr d)))
-  (funcall r 0 (allp))
-  (funcall r 3 (allp 3 (d 15)))
-  (funcall r 5 (allp 3 (d (mask 5)) 2 (d (mask 4))))
-  (funcall r 5 (allp 2 (d (mask 4)) 3 (d (mask 5)))))
-|#
-
-(DEFMETHOD VRTC-COBAR ((chcm chain-complex))
-   (the chain-complex
-      (with-slots (cmpr basis dffr) chcm
-         (declare
-            (type cmprf cmpr)
-            (type basis basis)
-            (type morphism dffr))
-         (chain-complex
-            :cmpr (cobar-cmpr cmpr)
-            :basis (cobar-basis basis)
-            :bsgn +null-allp+
-            :dffr-intr (cobar-intr-vrtc-dffr dffr)
-            :dffr-strt :gnrt
-            :dfnt `(vrtc-cobar ,chcm)))))
-
-#|
-  (cat-init)
-  (setf v (vrtc-cobar (soft-delta-infinity)))
-  (defun random-allp (length)
-     (let ((rslt nil))
-        (dotimes (i length)
-           (let* ((gmsm (random (mask 9)))
-                  (dmns (1- (logcount gmsm))))
-              (when (plusp dmns)
-                 (push (cbgn (1- dmns) (d gmsm)) rslt))))
-        (make-allp :list rslt)))
-  (dotimes (i 10) (print (random-allp 5)))
-  (dotimes (i 10)
-     (let ((allp (random-allp 3)))
-        (print allp)
-        (print (? v (apply #'+ (mapcar #'car (allp-list allp))) allp))
-        (print (? v (? v (apply #'+ (mapcar #'car (allp-list allp))) allp)))))
-|#
-
-(DEFUN COBAR-INTR-HRZN-DFFR (cprd)
-   (declare (type morphism cprd))
-   (labels ((rslt (degr iallp)
-               (declare
-                  (fixnum degr)
-                  (type iallp iallp))
-               (the icmbn
-                  (progn
-                     (unless iallp
-                        (return-from rslt +empty-list+))
-                     (let ((cbgn1 (first iallp))
-                           (rest (rest iallp)))
-                        (declare
-                           (type cbgn cbgn1)
-                           (type iallp rest))
-                        (with-cbgn (degr1 gnrt1) cbgn1
-                           (let ((cprd-gnrt1 (cmbn-list (gnrt-? cprd (1+ degr1) gnrt1)))
-                                 (cprd-rest (rslt (- degr degr1) rest))
-                                 (sign (-1-expt-n-1 (length rest))))
-                              (declare
-                                 (type icmbn cprd-gnrt1 cprd-rest)
-                                 (fixnum sign))
-                              (setf cprd-gnrt1 (rest (butlast cprd-gnrt1)))  ;;; because \bar{A}
-                              (nconc
-                                 (mapcar
-                                    #'(lambda (term1)
-                                         (declare (type term temr1))
-                                         (with-term (nil tnpr) term1  ;;; cffc is in fact 1
-                                            (with-tnpr (degr1 gnrt1 degr2 gnrt2) tnpr
-                                               (term sign              ;;; (* cffc sign)
-                                                  (cons (cbgn (1- degr1) gnrt1)
-                                                     (cons (cbgn (1- degr2) gnrt2)
-                                                        rest))))))
-                                    cprd-gnrt1)
-                                 (mapcar
-                                    #'(lambda (term2)
-                                         (declare (type term term2))
-                                         (with-term (cffc allp2) term2
-                                            (term cffc
-                                               (cons cbgn1 allp2))))
-                                    cprd-rest)))))))))
-      (the intr
-         #'(lambda (degr allp)
-              (declare
-                 (fixnum degr)
-                 (type allp allp))
-              (the cmbn
-                 (make-cmbn :degr (1- degr)
-                    :list (mapcar #'(lambda (term)
-                                       (declare (type term term))
-                                       (with-term (cffc iallp) term
-                                          (term cffc (make-allp :list iallp))))
-                             (rslt degr (allp-list allp)))))))))
-
-#|
-  (setf d (soft-delta-infinity))
-  (setf r (cobar-intr-hrzn-dffr (cprd d)))
-  (funcall r 0 (allp))
-  (funcall r 3 (allp 3 (d (mask 5))))
-  (funcall r 5 (allp 3 (d (mask 5)) 2 (d (mask 4))))
-  (funcall r 5 (allp 2 (d (mask 4)) 3 (d (mask 5))))
-|#
-
-(DEFUN COBAR-HRZN-DFFR (clgb)
-   (declare (type coalgebra clgb))
-   (the morphism
-      (with-slots (cprd) clgb
-         (declare (type morphism cprd))
-         (morphism
-            :sorc (vrtc-cobar clgb) :trgt (vrtc-cobar clgb) :degr -1
-            :intr (cobar-intr-hrzn-dffr cprd) :strt :gnrt
-            :dfnt `(cobar-hrzn-dffr ,clgb)))))
-
-#|
-  (cat-init)
-  (setf h (cobar-hrzn-dffr (soft-delta-infinity)))
-  (defun random-allp (length)
-     (let ((rslt nil))
-        (dotimes (i length)
-           (let* ((gmsm (random (mask 9)))
-                  (dmns (1- (logcount gmsm))))
-              (when (plusp dmns)
-                 (push (cbgn (1- dmns) (d gmsm)) rslt))))
-        (make-allp :list rslt)))
-  (dotimes (i 10) (print (random-allp 5)))
-  (setf allp (random-allp 4))
-  (? h (apply #'+ (mapcar #'car (allp-list allp))) allp)
-  (? h (? h (apply #'+ (mapcar #'car (allp-list allp))) allp))
-  (dotimes (i 10)
-     (let ((allp (random-allp 3)))
-        (print allp)
-        (print (? h (apply #'+ (mapcar #'car (allp-list allp))) allp))
-        (print (? h (? h (apply #'+ (mapcar #'car (allp-list allp))) allp)))))
-|#
-
-(DEFUN COBAR-INTR-DFFR (vrtc-dffr hrzn-dffr)
-   (declare (type morphism vrtc-dffr hrzn-dffr))
-   (flet ((rslt (degr allp)
-             (declare
-                (fixnum degr)
-                (type allp allp))
-             (make-cmbn :degr (1- degr)
-                :list (append       ;;; and not nconc, otherwise a terrible bug, when the
-                                    ;;;   first result is stored in memory...
-                         (cmbn-list (gnrt-? vrtc-dffr degr allp))
-                         (cmbn-list (gnrt-? hrzn-dffr degr allp))))))
-      (the intr #'rslt)))
-
-(DEFMETHOD COBAR ((coalgebra coalgebra))
-   (let ((vrtc-cobar (vrtc-cobar coalgebra))
-         (cobar-hrzn-dffr (cobar-hrzn-dffr coalgebra)))
-      (declare (type chain-complex vrtc-cobar hrzn-cobar))
-      (the chain-complex
-	 (let ((rslt (chain-complex
-		      :cmpr (cmpr vrtc-cobar)
-		      :basis (basis vrtc-cobar)
-		      :bsgn +null-allp+
-		      :dffr-intr (cobar-intr-dffr (dffr vrtc-cobar) cobar-hrzn-dffr)
-		      :dffr-strt :gnrt
-		      :dfnt `(add ,vrtc-cobar ,cobar-hrzn-dffr))))
-	   (declare (type chain-complex rslt))
-	   (setf (slot-value rslt 'grmd) (grmd vrtc-cobar))
-	   rslt))))
-
-#|
-  (cat-init)
-  (setf c (cobar (deltab)))   
-  (defun random-allp (length)
-     (let ((rslt nil))
-        (dotimes (i length)
-           (let* ((gmsm (random (mask 9)))
-                  (dmns (1- (logcount gmsm))))
-              (when (plusp dmns)
-                 (push (cbgn (1- dmns) gmsm) rslt))))
-        (make-allp :list rslt)))
-  (dotimes (i 10) (print (random-allp 5)))
-  (setf allp (random-allp 4))
-  (? c (apply #'+ (mapcar #'car (allp-list allp))) allp)
-  (? c (? c (apply #'+ (mapcar #'car (allp-list allp))) allp))
-  (dotimes (i 10)
-     (let ((allp (random-allp 3)))
-        (print allp)
-        (print (? c (apply #'+ (mapcar #'car (allp-list allp))) allp))
-        (print (? c (? c (apply #'+ (mapcar #'car (allp-list allp))) allp)))))
-|#
-
-(DEFUN CMBN-ALLP-CMBN-TNPR (cmbn allp-cmbn)
-   (declare (type cmbn cmbn allp-cmbn))
-   (the cmbn
-      (with-cmbn (degr1 list1) cmbn
-         (decf degr1)     ;; because allp organization
-      (with-cmbn (degrr listr) allp-cmbn
-         (make-cmbn
-            :degr (+ degr1 degrr)
-            :list
-            (mapcan
-               #'(lambda (term1)
-                    (declare (type term term1))
-                    (with-term (cffc1 gnrt1) term1
-                       (let ((cbgn1 (cbgn degr1 gnrt1)))
-                          (declare (type cbgn cbgn1))
-                          (mapcar
-                             #'(lambda (termr)
-                                  (declare (type term termr))
-                                  (with-term (cffcr allpr) termr
-                                     (term (* cffc1 cffcr)
-                                        (make-allp
-                                           :list (cons cbgn1 (allp-list allpr))))))
-                             listr))))
-               list1))))))
-
-(DEFUN NCMBN-COBAR (cmbn-list)
-   (declare (list cmbn-list))
-   (the cmbn
-      (progn
-         (unless cmbn-list
-            (return-from ncmbn-cobar (cmbn 0 1 +null-allp+)))
-         (cmbn-allp-cmbn-tnpr
-            (first cmbn-list)
-            (ncmbn-cobar (rest cmbn-list))))))
-#|
-  (ncmbn-cobar nil)
-  (ncmbn-cobar (list (cmbn 3 2 'a 3 'b)))
-  (ncmbn-cobar (list (cmbn 1 2 'a 3 'b) (cmbn 2 4 'c 5 'd)))
-  (ncmbn-cobar (list (cmbn 1 2 'a 3 'b) (cmbn 1 4 'c 5 'd) (cmbn 1 6 'e 7 'f)))
-|#
-
-(DEFUN MRPH-VRTC-COBAR-INTR (mrph)
-   (declare (type morphism mrph))
-   (flet ((rslt (degr allp)
-             (declare
-                (ignore degr)
-                (type allp allp))
-             (the cmbn
-                (ncmbn-cobar
-                   (mapcar #'(lambda (cbgn)
-                                (declare (type cbgn cbgn))
-                                (with-cbgn (degr gnrt) cbgn
-                                   (gnrt-? mrph (1+ degr) gnrt)))
-                      (allp-list allp))))))
-      (the intr #'rslt)))
-
-#|
-  (setf cc (chain-complex :cmpr #'f-cmpr :dffr-strt :cmbn))
-  (setf m (morphism :sorc cc :trgt cc :degr 0 :intr
-            #'(lambda (degr gnrt) (cmbn degr 2 gnrt 3 (1+ gnrt)))
-            :strt :gnrt :dfnt '(test)))
-  (setf r (mrph-vrtc-cobar-intr m))
-  (funcall r 4 (allp 2 3 2 4))
-|#
-
-(DEFMETHOD VRTC-COBAR ((mrph morphism))
-   (the morphism
-      (if (eq (first (dfnt mrph)) 'idnt-mrph)
-         (idnt-mrph (vrtc-cobar (sorc mrph)))
-         (morphism
-            :sorc (vrtc-cobar (sorc mrph))
-            :trgt (vrtc-cobar (trgt mrph))
-            :degr 0
-            :intr (mrph-vrtc-cobar-intr mrph)
-            :strt :gnrt
-            :dfnt `(vrtc-cobar ,mrph)))))
-
-#|
-  (cat-init)
-  (setf f (aw (soft-delta-infinity) (soft-delta-infinity)))
-  (setf cf (vrtc-cobar f))
-  (? cf 2 (allp 1 (crpr 0 (d 7) 0 (d 7)) 1 (crpr 0 (d 56) 0 (d 56))))
-|#
-
-(DEFUN HMTP-VRTC-COBAR-INTR (h gf)
-   (declare (type morphism h gf))
-   (flet ((rslt (degr allp)
-             (declare
-                (fixnum degr)
-                (type allp allp))
-             (let* ((cbgn-list (reverse (allp-list allp)))
-                    (rslt (list nil))
-                    (sign (oddp (apply #'+ (mapcar #'car cbgn-list))))  ;; nil = -1 ;; t = +1
-                    (gfgf-tail (term-cmbn 0 1 +null-allp+)))
-                (declare
-                   (list cbgn-list rslt)
-                   (fixnum sign)
-                   (type cmbn gfgf-tail))
-                (unless cbgn-list
-                   (return-from rslt (zero-cmbn 1)))
-                (loop
-                   (let ((cbgn (car cbgn-list)))
-                      (declare (type cbgn cbgn))
-                      (with-cbgn (degr gnrt) cbgn
-                         (when (evenp degr)
-                            (setf sign (not sign)))
-                         (incf degr)
-                         (let ((h-gnrt (gnrt-? h degr gnrt)))
-                            (declare (type cmbn h-gnrt))
-                            (let ((hgfgf (cmbn-list (cmbn-allp-cmbn-tnpr h-gnrt gfgf-tail))))
-                               (declare (type cmbn hgfgf))
-                               (when sign
-                                  (mapc #'(lambda (term)
-                                             (declare (type term term))
-                                             (setf (cffc term) (- (cffc term))))
-                                     hgfgf))
-                               (setf cbgn-list (rest cbgn-list))
-                               (let ((head (reverse cbgn-list)))
-                                  (declare (list head))
-                                  (mapc #'(lambda (term)
-                                             (setf (allp-list (gnrt term))
-                                                   (append head (allp-list (gnrt term)))))
-                                     hgfgf))
-                               (nconc rslt hgfgf)))
-                         (unless cbgn-list (return))
-                         (setf gfgf-tail
-                               (cmbn-allp-cmbn-tnpr
-                                  (gnrt-? gf degr gnrt) gfgf-tail)))))
-                (make-cmbn
-                   :degr (1+ degr)
-                   :list (rest rslt)))))
-      (the intr #'rslt)))
-
-#|
-  (require "special-smsts")
-  (require "eilenberg-zilber")
-  (cat-init)
-  (setf ez (ez (delta-infinity) (delta-infinity)))
-  (setf h (h ez) gf (cmps (g ez) (f ez)))
-  (setf r (hmtp-vrtc-cobar-intr h gf))
-  (funcall r 3 (allp 1 (crpr 0 7 0 7) 1 (crpr 0 14 0 14) 1 (crpr 0 14 0 14)))
-|#
-
-(DEFUN HMTP-VRTC-COBAR (h gf)
-   (declare (type morphism h gf))
-   (unless (and (= +1 (degr h))
-                (= +0 (degr gf)))
-      (error "In HMTP-VRTC-COBAR, the morphism degrees are not the right ones."))
-   (unless (and (eq (sorc h) (trgt h))
-                (eq (trgt h) (sorc gf))
-                (eq (sorc gf) (trgt gf)))
-      (error "In HMTP-VRTC-COBAR, fg-h sources and targets are not the same."))
-   (the morphism
-      (if (eq (first (dfnt h)) 'zero-mrph)
-         (zero-mrph (vrtc-cobar (sorc h)))
-         (morphism
-            :sorc (vrtc-cobar (sorc h)) :trgt (vrtc-cobar (sorc h)) :degr +1
-            :intr (hmtp-vrtc-cobar-intr h gf)
-            :strt :gnrt
-            :dfnt `(hmtp-vrtc-cobar ,h ,gf)))))
-
-(DEFMETHOD VRTC-COBAR ((rdct reduction))
-   (the reduction
-      (if (eq (first (dfnt rdct)) 'trivial-rdct)
-         (trivial-rdct (vrtc-cobar (bcc rdct)))
-         (with-slots (f g h) rdct
-            (reduction
-               :f (vrtc-cobar f)
-               :g (vrtc-cobar g)
-               :h (hmtp-vrtc-cobar h (cmps g f))
-               :dfnt `(vrtc-cobar ,rdct))))))
-
-#|
-  (cat-init)
-  (setf tcc (chain-complex
-               :cmpr #'s-cmpr
-               :basis #'(lambda (degr) '(a b c d))
-               :bsgn 'd
-               :dffr-intr #'(lambda (degr gnrt)
-                               (ecase gnrt
-                                  (a (cmbn (1- degr) 1 'b 1 'd))
-                                  ((b d) (cmbn (1- degr)))
-                                  (c (cmbn (1- degr) 1 'd))))
-               :dffr-strt :gnrt
-               :dfnt '(tcc)))
-  (setf bcc (chain-complex
-               :cmpr #'s-cmpr
-               :basis #'(lambda (degr) '(c d))
-               :bsgn 'd
-               :dffr-intr #'(lambda (degr gnrt)
-                               (ecase gnrt
-                                  (d (cmbn (1- degr)))
-                                  (c (cmbn (1- degr) 1 'd))))
-               :dffr-strt :gnrt
-               :dfnt '(bcc)))
-  (setf f (morphism :sorc tcc :trgt bcc :degr 0
-             :intr #'(lambda (degr gnrt)
-                        (ecase gnrt
-                           (a (cmbn degr 1 'c 1 'd))
-                           (b (cmbn degr))
-                           ((c d) (cmbn degr 1 gnrt))))
-             :strt :gnrt :dfnt '(f)))
-  (setf g (morphism :sorc bcc :trgt tcc :degr 0
-             :intr #'identity :strt :cmbn :dfnt '(g)))
-  (setf h (morphism :sorc tcc :trgt tcc :degr +1
-             :intr #'(lambda (degr gnrt)
-                        (ecase gnrt
-                           ((a b) (cmbn (1+ degr) 1 'a -1 'b -1 'c -1 'd))
-                           ((c d) (cmbn (1+ degr)))))
-             :strt :gnrt :dfnt '(h)))
-  (setf rdct (reduction :f f :g g :h h :dfnt '(rdct)))
-  (tcc rdct 3 'a)
-  (g rdct (f rdct 3 'a))
-  (h rdct 3 'a)
-  (setf cobar (vrtc-cobar rdct))
-  (pre-check-rdct cobar)
-  (defun aleat-tc ()
-     (do ((tdegr 0 (+ tdegr degr))
-          (degr (1+ (random 4)) (1+ (random 4)))
-          (gnrt (intern (coerce (vector (+ 65 (random 4))) 'string))
-                (intern (coerce (vector (+ 65 (random 4))) 'string)))
-          (rslt nil (cons (cbgn degr gnrt) rslt)))
-         ((> tdegr 10) (setf *tc* (cmbn tdegr 1 (make-allp :list rslt))))))
-  (aleat-tc)
-  (defun aleat-bc ()
-     (do ((tdegr 0 (+ tdegr degr))
-          (degr (1+ (random 4)) (1+ (random 4)))
-          (gnrt (intern (coerce (vector (+ 67 (random 2))) 'string))
-                (intern (coerce (vector (+ 67 (random 2))) 'string)))
-          (rslt nil (cons (cbgn degr gnrt) rslt)))
-         ((> tdegr 10) (setf *bc* (cmbn tdegr 1 (make-allp :list rslt))))))
-  (aleat-bc)
-  (defun c ()
-     (aleat-tc)
-     (aleat-bc)
-     (check-rdct))
-  (loop (c))  ;; degrees >= 15 is possible => error.
-|#
-
-(DEFMETHOD VRTC-COBAR ((eqvl equivalence))
-  (the equivalence
-    (if (eq (first (dfnt eqvl)) 'trivial-eqvl)
-        (trivial-eqvl (vrtc-cobar (lbcc eqvl)))
-      (with-slots (lrdct rrdct) eqvl
-        (equivalence 
-         :lrdct (vrtc-cobar lrdct)
-         :rrdct (vrtc-cobar rrdct)
-         :dfnt `(vrtc-cobar ,eqvl))))))
-
-(DEFMETHOD COBAR ((rdct reduction))
-   (unless (typep (tcc rdct) 'coalgebra)
-      (error "In (COBAR rdct), the TCC should be a coalgebra."))
-   (the reduction
-      (if (eq (first (dfnt rdct)) 'trivial-rdct)
-         (trivial-rdct (cobar (tcc rdct)))
-        (add (vrtc-cobar rdct) (cobar-hrzn-dffr (tcc rdct))))))
-
-#|
-()
-(cat-init)
-(setf k (k-z 2))
-(setf efhm (efhm k))
-(slot-boundp k 'efhm)
-(setf f (cmps (rf efhm) (lg efhm)))
-(setf g (cmps (lf efhm) (rg efhm)))
-(setf h (cmps (lf efhm) (cmps (rh efhm) (lg efhm))))
-(setf rho (reduction :f f :g g :h h :dfnt '(w-b (k-z 2))))
-(setf bg (first (basis (bcc rho) 4)))
-(g rho 4 bg)
-(setf *tc* (make-cmbn :degr 4 :list (rest (cmbn-list *))))
-(setf *bc* (cmbn 4 bg))
-(pre-check-rdct rho)
-
-|#
-
-
-(DEFMETHOD COBAR ((eqvl equivalence))
-   (unless (typep (lbcc eqvl) 'coalgebra)
-      (error "In (COBAR eqvl), the LBCC should be a coalgebra."))
-   (the equivalence
-      (if (eq (first (dfnt eqvl)) 'trivial-eqvl)
-         (trivial-eqvl (cobar (lbcc eqvl)))
-         (add (vrtc-cobar eqvl) (cobar-hrzn-dffr (lbcc eqvl))))))
-
-#|
-  (cat-init)
-  (setf h (left-eqvl (sphere 3)))
-  (setf c (cobar h))
-  (inspect c)
-|#
\ No newline at end of file
diff --git a/archive/Kenzo-2/Kenzo-2-Acl8/combinations.cl b/archive/Kenzo-2/Kenzo-2-Acl8/combinations.cl
deleted file mode 100644
index 2f721e1..0000000
--- a/archive/Kenzo-2/Kenzo-2-Acl8/combinations.cl
+++ /dev/null
@@ -1,687 +0,0 @@
-;;;  COMBINATIONS  COMBINATIONS  COMBINATIONS  COMBINATIONS  COMBINATIONS
-;;;  COMBINATIONS  COMBINATIONS  COMBINATIONS  COMBINATIONS  COMBINATIONS
-;;;  COMBINATIONS  COMBINATIONS  COMBINATIONS  COMBINATIONS  COMBINATIONS
-
-(IN-PACKAGE "CAT")
-
-(provide "combinations")
-
-;;;;
-;;;;  COMPARISONS.
-;;;;
-
-
-(DEFUN MAPLEXICO (cmpr list1 list2)
-   (declare
-      (type cmprf cmpr)
-      (list list1 list2))
-   (the boolean
-      (do ((mark1 list1 (cdr mark1))
-           (mark2 list2 (cdr mark2)))
-          (nil)
-         (declare (list mark1 mark2))
-         (unless mark1
-            (return-from maplexico
-               (if mark2 :less :equal)))
-         (unless mark2
-            (return-from maplexico :greater))
-         (case (funcall cmpr (car mark1) (car mark2))
-            (:less (return-from maplexico :less))
-            (:greater (return-from maplexico :greater))))))
-
-#|
-  (maplexico #'f-cmpr '(1 2 3) '(1 3))
-  (maplexico #'f-cmpr '(1 2 3) '(1 1))
-  (maplexico #'f-cmpr '(1 1) '(1 1 0))
-  (maplexico #'f-cmpr '(1 1 0) '(1 1))
-  (maplexico #'f-cmpr '(1 1) '(1 1))
-  (maplexico #'f-cmpr nil nil)
-|#
-
-(DEFUN S-CMPR (symbol1 symbol2)
-   (declare (symbol symbol1 symbol2))
-   (the cmpr
-      (if (#+aclpc acl:whole-string<
-           #-aclpc string< symbol1 symbol2)
-         :less
-         (if (#+aclpc acl:whole-string=
-              #-aclpc string= symbol1 symbol2)
-            :equal
-            :greater))))
-
-(DEFUN F-CMPR (n1 n2)
-   (declare (fixnum n1 n2))
-   (the cmpr
-      (if (< n1 n2)
-         :less
-         (if (= n1 n2)
-            :equal
-            :greater))))
-
-(DEFUN L-CMPR (list1 list2)
-   (declare (list list1 list2))
-   (unless list1
-      (return-from l-cmpr (if list2 :less :equal)))
-   (unless list2
-      (return-from l-cmpr :greater))
-   (if (symbolp (first list1))
-      (if (symbolp (first list2))
-         (lexico
-            (s-cmpr (first list1) (first list2))
-            (l-cmpr (rest list1) (rest list2)))
-         :greater)
-      (if (symbolp (first list2))
-         :less
-         (lexico
-            (f-cmpr (first list1) (first list2))
-            (l-cmpr (rest list1) (rest list2))))))
-
-#|
-  (s-cmpr 'a 'b)
-  (s-cmpr 'b 'b)
-  (s-cmpr 'c 'b)
-  (f-cmpr 1 2)
-  (f-cmpr 2 2)
-  (f-cmpr 3 2)
-  (l-cmpr nil nil)
-  (l-cmpr nil '(1))
-  (l-cmpr '(1) nil)
-  (l-cmpr '(a) '(a))
-  (l-cmpr '(a) '(1))
-  (l-cmpr '(1) '(a))
-  (l-cmpr '(1) '(1))
-  (l-cmpr '(1 a) '(1 1))
-  (l-cmpr '(1 a) '(1 a b)))
-|# 
-
-
-;;;;
-;;;;  COMBINATIONS
-;;;;
-
-(DEFUN CMBN (degr &rest rest)
-   (declare (fixnum degr))
-   (the cmbn
-      (let ((rslt (list degr :cmbn)))
-	(do ((mark rest (cddr mark)))
-	    ((endp mark) (nreverse rslt))
-	   (declare (list mark))
-	   (push (term (car mark) (cadr mark)) rslt)))))
-
-#|
-  (cmbn 2)
-  (cmbn 2 2 'a)
-  (cmbn 2 'a)
-  (cmbn 2 2 'a -3 'b))
-  (term-cmbn 3 -5 'a)
-|#
-
-#+(or (and allegro unix)
-      (and :mswindows :allegro-v5.0))
-      (and :mswindows :allegro-v5.0.1)
-  (setf *print-pretty* nil)
-
-#+(and allegro unix)
-  (eval-when (:compile-toplevel :load-toplevel :execute)
-     (setf excl:*enable-package-locked-errors* nil))
-
-(DEFMETHOD PRINT-OBJECT :around ((cons cons) stream)
-   (declare (stream stream))
-   (when (keywordp (car cons))
-      (when (print-keycons (car cons) (cdr cons) stream)
-         (return-from print-object cons)))
-   (call-next-method))
-
-#+(and allegro unix)
-  (eval-when (:compile-toplevel :load-toplevel :execute)
-     (setf excl:*enable-package-locked-errors* t))
-
-(DEFMETHOD PRINT-KEYCONS (key cdr stream)
-   (declare (ignore key cdr stream))
-   nil)
-
-(DEFMETHOD PRINT-KEYCONS ((key (eql :cmbn)) cdr stream)
-   (declare
-      (list cdr)
-      (stream stream))
-   (the (eql t)
-      (let ((degr (first cdr))
-            (list (rest cdr)))
-         (declare
-            (fixnum degr)
-            (list list))
-         (format stream "~%~70@{-~}{CMBN ~D}" degr)
-         (do ((mark list (cdr mark))
-              (nth 0 (1+ nth)))
-             ((endp mark))
-            (declare
-               (list mark)
-               (fixnum nth))
-            (when (and *print-length* (= nth *print-length*))
-               (format stream "~%... ...")
-               (return))
-            (format stream "~%<~D * ~A>" (-cffc mark) (-gnrt mark)))
-         (format stream "~%~78@{-~}~%" t)
-         t)))
-
-#|
-  (list 1 2)
-  (list :cmbn 2 (cons 1 'a))
-|#
-
-(DEFUN CHECK-CMBN (chcm cmbn)
-  (declare
-    (type chain-complex chcm)
-    (type cmbn cmbn))
-  (the boolean
-    (do ((cmpr (cmpr chcm))
-	 (mark2 (cmbn-list cmbn) mark1)
-	 (mark1 (rest (cmbn-list cmbn)) (cdr mark1)))
-	((endp mark1) t)
-	(declare
-	  (type cmprf cmpr)
-	  (list mark1 mark2))
-      (unless (eq :less (funcall cmpr (-gnrt mark2) (-gnrt mark1)))
-	(error "In CHECK-CMBN, bad order; the generator:~@
-                ~A~@
-                is not less than the generator:~@
-                ~A."
-	       (-gnrt mark2) (-gnrt mark1))))))
-
-(DEFUN ZERO-CMBN (degr)
-   (declare (fixnum degr))
-   (the cmbn
-      (make-cmbn
-       :degr degr
-       :list +empty-list+)))
-
-#|
-  (zero-cmbn 3))
-|#  
-
-(DEFUN ZERO-DFFR-INTR (cmbn)
-   (declare (type cmbn cmbn))
-   (the cmbn (zero-cmbn (1- (cmbn-degr cmbn)))))
-
-#|
-  (zero-dffr-intr (cmbn 2))
-|#
-
-(DEFCONSTANT +ZERO-NEGATIVE-CMBN+
-   (list :cmbn -1))
-
-#|
-  (cmbn-non-zero-p (cmbn 0))
-  (cmbn-non-zero-p (cmbn 0 1 'a)))
-  (cmbn-zero-p (cmbn 0))
-  (cmbn-zero-p (cmbn 0 1 'a)))
-|#
-
-(DEFUN CMBN-OPPS (cmbn)
-   (declare (type cmbn cmbn))
-   (the cmbn
-      (with-cmbn (degr list) cmbn
-         (make-cmbn
-            :degr degr
-            :list (mapcar #'(lambda (term)
-                               (declare (type term term))
-                               (with-term (cffc gnrt) term
-                                  (term (- cffc) gnrt)))
-                     list)))))
-
-#|
-  (setf c (cmbn 0 1 'a -2 'b))
-  (cmbn-opps c)
-  (symbol-value 'c))
-|#
-
-(DEFUN N-CMBN (n cmbn)
-   ;; n is assumed non-zero
-   (declare
-      (fixnum n)
-      (type cmbn cmbn))
-   (the cmbn
-      (if (= n 1)
-         cmbn
-         (with-cmbn (degr list) cmbn
-            (make-cmbn
-               :degr degr
-               :list (mapcar #'(lambda (term)
-                                  (declare (type term term))
-                                  (with-term (cffc gnrt) term
-                                     (term (* n cffc) gnrt)))
-                        list))))))
-
-#|
-  (setf c (cmbn 2 3 'a))
-  (setf c2 (n-cmbn 1 c))
-  (eq c c2)
-  (n-cmbn -1 c)
-  (n-cmbn -3 c))
-|#
-
-(DEFUN 2CMBN-ADD (cmpr cmbn1 cmbn2)
-   (declare
-      (type cmprf cmpr)
-      (type cmbn cmbn1 cmbn2))
-   (the cmbn
-      (with-cmbn (degr1 list1) cmbn1
-      (with-cmbn (degr2 list2) cmbn2
-         (unless (= degr1 degr2)
-            (error "In ADD, the combination arguments have different degrees ~D and ~D."
-               degr1 degr2))
-         (unless list1
-            (return-from 2cmbn-add cmbn2))
-         (unless list2
-            (return-from 2cmbn-add cmbn1))
-         (let ((pre-rslt +empty-list+)
-               (mark1 list1)
-               (mark2 list2))
-            (declare (list pre-rslt mark1 mark2))
-            (with--term (cffc1 gnrt1) mark1
-            (with--term (cffc2 gnrt2) mark2
-               (tagbody
-                  :begin
-                  (ecase (funcall cmpr gnrt1 gnrt2)
-                     (:equal
-                      (let ((cffc (+ cffc1 cffc2)))
-                         (declare (fixnum cffc))
-                         (unless (zerop cffc)
-                            (push (term cffc gnrt1) pre-rslt))
-                         (setf mark1 (cdr mark1)
-                               mark2 (cdr mark2))
-                         (unless mark1 (go :cmbn1-is-finished))
-                         (unless mark2 (go :cmbn2-is-finished))
-                         (setf cffc1 (-cffc mark1)
-                               gnrt1 (-gnrt mark1)
-                               cffc2 (-cffc mark2)
-                               gnrt2 (-gnrt mark2))
-                         (go :begin)))
-                     (:less
-                      (push (-term mark1) pre-rslt)
-                      (setf mark1 (cdr mark1))
-                      (unless mark1 (go :cmbn1-is-finished))
-                      (setf cffc1 (-cffc mark1)
-                            gnrt1 (-gnrt mark1))
-                      (go :begin))
-                     (:greater
-                      (push (-term mark2) pre-rslt)
-                      (setf mark2 (cdr mark2))
-                      (unless mark2 (go :cmbn2-is-finished))
-                      (setf cffc2 (-cffc mark2)
-                            gnrt2 (-gnrt mark2))
-                      (go :begin)))
-                  :cmbn1-is-finished
-                  (setf pre-rslt (nreconc pre-rslt mark2))
-                  (go :exit)
-                  :cmbn2-is-finished
-                  (setf pre-rslt (nreconc pre-rslt mark1))
-                  :exit))
-            (make-cmbn :degr degr1 :list pre-rslt)))))))
-
-#|
-  (2cmbn-add #'s-cmpr (cmbn 0) (cmbn 1))
-  (2cmbn-add #'s-cmpr (cmbn 0) (cmbn 0))
-  (2cmbn-add #'s-cmpr (cmbn 0 1 'a) (cmbn 0))
-  (2cmbn-add #'s-cmpr (cmbn 0 1 'a) (cmbn 0 2 'a))
-  (2cmbn-add #'s-cmpr (cmbn 0 1 'a) (cmbn 0 -1 'a))
-  (2cmbn-add #'s-cmpr (cmbn 0 1 'a) (cmbn 0 2 'b))
-  (2cmbn-add #'s-cmpr (cmbn 0 2 'b) (cmbn 0 1 'a))
-  (2cmbn-add #'s-cmpr (cmbn 0 1 'a -2 'b) (cmbn 0 2 'b))
-  (2cmbn-add #'s-cmpr (cmbn 0 2 'b) (cmbn 0 1 'a 3 'c)))
-|#
-
-(DEFUN 2CMBN-SBTR (cmpr cmbn1 cmbn2)
-   (declare
-      (type cmprf cmpr)
-      (type cmbn cmbn1 cmbn2))
-   (the cmbn
-      (with-cmbn (degr1 list1) cmbn1
-      (with-cmbn (degr2 list2) cmbn2
-         (unless (= degr1 degr2)
-            (error "In SBTR, the combination arguments have different degrees ~D and ~D."
-               degr1 degr2))
-         (unless list1
-            (return-from 2cmbn-sbtr (cmbn-opps cmbn2)))
-         (unless list2
-            (return-from 2cmbn-sbtr cmbn1))
-         (let ((pre-rslt +empty-list+)
-               (mark1 list1)
-               (mark2 list2))
-            (declare (list pre-rslt mark1 mark2))
-            (with--term (cffc1 gnrt1) mark1
-            (with--term (cffc2 gnrt2) mark2
-               (tagbody
-                  :begin
-                  (ecase (funcall cmpr gnrt1 gnrt2)
-                     (:equal
-                      (let ((cffc (- cffc1 cffc2)))
-                         (declare (fixnum cffc))
-                         (unless (zerop cffc)
-                            (push (term cffc gnrt1) pre-rslt))
-                                                  (unless mark1 (go :cmbn1-is-finished))
-                         (setf mark1 (cdr mark1)
-                               mark2 (cdr mark2))
-                         (unless mark1 (go :cmbn1-is-finished))
-                         (unless mark2 (go :cmbn2-is-finished))
-                         (setf cffc1 (-cffc mark1)
-                               gnrt1 (-gnrt mark1)
-                               cffc2 (-cffc mark2)
-                               gnrt2 (-gnrt mark2))
-                         (go :begin)))
-                     (:less
-                      (push (-term mark1) pre-rslt)
-                      (setf mark1 (cdr mark1))
-                      (unless mark1 (go :cmbn1-is-finished))
-                      (setf cffc1 (-cffc mark1)
-                            gnrt1 (-gnrt mark1))
-                      (go :begin))
-                     (:greater
-                      (push (term (- cffc2) gnrt2) pre-rslt)
-                      (setf mark2 (cdr mark2))
-                      (unless mark2 (go :cmbn2-is-finished))
-                      (setf cffc2 (-cffc mark2)
-                            gnrt2 (-gnrt mark2))
-                      (go :begin)))
-                  :cmbn1-is-finished
-                  (setf pre-rslt
-                        (nreconc pre-rslt
-                           (mapcar #'(lambda (term)
-                                        (declare (cons term))
-                                        (with-term (cffc gnrt) term
-                                           (term (- cffc) gnrt)))
-                              mark2)))
-                  (go :exit)
-                  :cmbn2-is-finished
-                  (setf pre-rslt (nreconc pre-rslt mark1))
-                  :exit))
-            (make-cmbn
-               :degr degr1
-               :list pre-rslt)))))))
-
-#|
-  (2cmbn-sbtr #'s-cmpr (cmbn 0) (cmbn 1))
-  (2cmbn-sbtr #'s-cmpr (cmbn 0) (cmbn 0))
-  (2cmbn-sbtr #'s-cmpr (cmbn 0) (cmbn 0 1 'a))
-  (2cmbn-sbtr #'s-cmpr (cmbn 0 2 'b) (cmbn 0))
-  (2cmbn-sbtr #'s-cmpr (cmbn 0 3 'b) (cmbn 0 3 'b))
-  (2cmbn-sbtr #'s-cmpr (cmbn 0 3 'b) (cmbn 0 4 'b))
-  (2cmbn-sbtr #'s-cmpr
-    (cmbn 0 1 'a 2 'c  2 'd       3 'g)
-    (cmbn 0      1 'c -2 'd 4 'f -3 'g 4 'h))
-  (2cmbn-sbtr #'s-cmpr
-    (cmbn 0      1 'c -2 'd 4 'f -3 'g 4 'h)
-    (cmbn 0 1 'a 2 'c  2 'd       3 'g))
-  (2cmbn-sbtr #'s-cmpr
-    (cmbn 0      1 'c -2 'd 4 'f -3 'g)
-    (cmbn 0 1 'a 2 'c  2 'd       3 'g))
-  (2cmbn-sbtr #'s-cmpr
-    (cmbn 0 1 'b 2 'a)
-    (cmbn 0 1 'a 1 'b)))  ;;; !!!
-  (2cmbn-sbtr #'s-cmpr
-    (cmbn 0 1 'b 2 'c)
-    (cmbn 0 1 'a 1 'b)))
-|#
-
-(DEFUN 2N-2CMBN (cmpr n1 cmbn1 n2 cmbn2)
-   ;; n1 * cmbn1 + n2 * cmbn2
-   ;; combinations may be null but not n1 and n2
-   (declare
-      (type cmprf cmpr)
-      (fixnum n1 n2)
-      (type cmbn cmbn1 cmbn2))
-   (the cmbn
-      (with-cmbn (degr1 list1) cmbn1
-      (with-cmbn (degr2 list2) cmbn2
-         (unless (= degr1 degr2)
-            (error "In 2N-2CMBN, the combination arguments have different degrees ~D and ~D."
-               degr1 degr2))
-         (unless list1
-            (return-from 2n-2cmbn (n-cmbn n2 cmbn2)))
-         (unless list2
-            (return-from 2n-2cmbn (n-cmbn n1 cmbn1)))
-         (let ((pre-rslt +empty-list+)
-               (mark1 list1)
-               (mark2 list2))
-            (declare (list pre-rslt mark1 mark2))
-            (with--term (cffc1 gnrt1) mark1
-            (with--term (cffc2 gnrt2) mark2
-               (setf cffc1 (* n1 cffc1)
-                     cffc2 (* n2 cffc2))
-               (tagbody
-                  :begin
-                  (ecase (funcall cmpr gnrt1 gnrt2)
-                     (:equal
-                      (let ((cffc (+ cffc1 cffc2)))
-                         (declare (fixnum cffc))
-                         (unless (zerop cffc)
-                            (push (term cffc gnrt1) pre-rslt))
-                         (setf mark1 (cdr mark1)
-                               mark2 (cdr mark2))
-                         (unless mark1 (go :cmbn1-is-finished))
-                         (unless mark2 (go :cmbn2-is-finished))
-                         (setf cffc1 (* n1 (-cffc mark1))
-                               gnrt1 (-gnrt mark1)
-                               cffc2 (* n2 (-cffc mark2))
-                               gnrt2 (-gnrt mark2))
-                         (go :begin)))
-                     (:less
-                      (push (term cffc1 gnrt1) pre-rslt)
-                      (setf mark1 (cdr mark1))
-                      (unless mark1 (go :cmbn1-is-finished))
-                      (setf cffc1 (* n1 (-cffc mark1))
-                            gnrt1 (-gnrt mark1))
-                      (go :begin))
-                     (:greater
-                      (push (term cffc2 gnrt2) pre-rslt)
-                      (setf mark2 (cdr mark2))
-                      (unless mark2 (go :cmbn2-is-finished))
-                      (setf cffc2 (* n2 (-cffc mark2))
-                            gnrt2 (-gnrt mark2))
-                      (go :begin)))
-                  :cmbn1-is-finished
-                  (setf pre-rslt
-                        (nreconc pre-rslt
-                           (if (= 1 n2)
-                              mark2
-                              (mapcar #'(lambda (term)
-                                           (declare (cons term))
-                                           (with-term (cffc gnrt) term
-                                              (term (* n2 cffc) gnrt)))
-                                 mark2))))
-                  (go :exit)
-                  :cmbn2-is-finished
-                  (setf pre-rslt
-                        (nreconc pre-rslt
-                           (if (= 1 n1)
-                              mark1
-                              (mapcar #'(lambda (term)
-                                           (declare (cons term))
-                                           (with-term (cffc gnrt) term
-                                              (term (* n1 cffc) gnrt)))
-                                 mark1))))
-                  :exit))
-            (make-cmbn
-               :degr degr1
-               :list pre-rslt)))))))
-
-#|
-  (2n-2cmbn #'s-cmpr 3 (cmbn 0) 4 (cmbn 1))
-  (2n-2cmbn #'s-cmpr 3 (cmbn 0) 4 (cmbn 0))
-  (2n-2cmbn #'s-cmpr 3 (cmbn 0 1 'a) 4 (cmbn 0))
-  (2n-2cmbn #'s-cmpr 3 (cmbn 0  1 'a 2 'b 3 'c     )
-                     1 (cmbn 0 -3 'a 2 'b      4 'd))
-  (2n-2cmbn #'s-cmpr 3 (cmbn 0 -3 'a 2 'b     4 'd)
-                     1 (cmbn 0  1 'a 2 'b 3 'c    ))
-  (2n-2cmbn #'s-cmpr 1 (cmbn 0  1 'a 2 'b 3 'c     )
-                     1 (cmbn 0 -3 'a 2 'b      4 'd))
-  (2n-2cmbn #'s-cmpr 1 (cmbn 0 -3 'a 2 'b     4 'd)
-                     1 (cmbn 0  1 'a 2 'b 3 'c    ))
-  (2n-2cmbn #'s-cmpr 1 (cmbn 0 -3 'a 2 'b     4 'd)
-                     3 (cmbn 0  1 'a 2 'b 3 'c    )))
-|#
-
-(DEFUN CMBN-CMBN (cmpr n-cmbn-list)
-  ;; n-cmbn-list = list of (cons n cmbn)
-  ;;               non-empty-list
-  ;;            every n is non-null
-  (declare
-     (type cmprf cmpr)
-     (list n-cmbn-list))
-  (unless (rest n-cmbn-list)
-     (return-from cmbn-cmbn
-	(n-cmbn (caar n-cmbn-list) (cdar n-cmbn-list))))
-  (unless (cddr n-cmbn-list)
-     (return-from cmbn-cmbn
-	(2n-2cmbn cmpr
-		  (caar n-cmbn-list) (cdar n-cmbn-list)
-		  (caadr n-cmbn-list) (cdadr n-cmbn-list))))
-  (the cmbn
-     (let ((new-rslt +empty-list+))
-        (declare (list new-rslt))
-	(do ((mark1 (rest n-cmbn-list) (cddr mark1))
-	     (mark2 n-cmbn-list (cdr mark1)))
-	    ((endp mark2))
-	   (declare (list mark1 mark2))
-	   (when (endp mark1)
-	      (push (n-cmbn (caar mark2) (cdar mark2)) new-rslt)
-	      (return))
-	   (push (2n-2cmbn cmpr
-			   (caar mark2) (cdar mark2)
-			   (caar mark1) (cdar mark1))
-		 new-rslt))
-	(let ((old-rslt +empty-list+))
-	  (declare (list old-rslt))
-	  (loop
-	   (unless (rest new-rslt)
-	      (return-from cmbn-cmbn (first new-rslt)))
-	   (setf old-rslt new-rslt
-		 new-rslt +empty-list+)
-	   (do ((mark1 (rest old-rslt) (cddr mark1))
-		(mark2 old-rslt (cdr mark1)))
-	       ((endp mark2))
-	      (declare (list mark1 mark2))
-	      (when (endp mark1)
-		 (push (car mark2) new-rslt)
-		 (return))
-	      (push (2cmbn-add cmpr (car mark2) (car mark1))
-		    new-rslt)))))))
-
-#|
-  (setf cons (cons 3 (cmbn 0 4 'a)))
-  (cmbn-cmbn #'s-cmpr (make-list 5 :initial-element cons))
-  (dotimes (i 10)
-     (print
-       (cffc (first (cmbn-list
-          (cmbn-cmbn #'s-cmpr (make-list (1+ i) :initial-element cons))))))))
-|#
-
-(DEFUN NTERM-ADD (cmpr degr &rest rest)
-   (declare
-      (type cmprf cmpr)
-      (fixnum degr)
-      (list rest))
-      ;; (list term)
-   (unless rest
-      (return-from nterm-add (zero-cmbn degr)))
-   (the cmbn
-      (let ((rslt (list (first rest))))
-         (declare (list rslt))
-         (dolist (term (rest rest))
-            (declare (type term term))
-            (with-term  (cffc gnrt) term
-               (do ((mark1 rslt (cdr mark1))
-                    (mark2 nil mark1))
-                   ((endp mark1) (setf (cdr mark2) (list term)))
-                  (ecase (funcall cmpr gnrt (-gnrt mark1))
-                     (:less
-                      (if mark2
-                         (push term (cdr mark2))
-                         (push term rslt))
-                      (return))                     
-                     (:equal
-                      (incf (-cffc mark1) cffc)
-                      (return))                     
-                     (:greater )))))
-         (make-cmbn
-            :degr degr
-            :list (delete 0 rslt :key #'car)))))
-
-#|
-  (nterm-add #'s-cmpr 11)
-  (nterm-add #'s-cmpr 11 (term 1 'a))
-  (nterm-add #'s-cmpr 11 (term 1 'a) (term 2 'b))
-  (nterm-add #'s-cmpr 11 (term 1 'b) (term 2 'a) (term 3 'aa)
-                         (term -2 'aa) (term -2 'a) (term 4 'aab)
-                         (term 5 'c))
-|#
-
-(DEFUN NCMBN-ADD (cmpr cmbn &rest rest)
-   (declare
-      (type cmprf cmpr)
-      (type cmbn cmbn))
-   (the cmbn
-      (cmbn-cmbn cmpr (mapcar #'(lambda (cmbn)
-                                   (declare (type cmbn cmbn))
-                                   (cons 1 cmbn))
-                         (cons cmbn rest)))))
-
-#|
-  (setf c (cmbn 3 4 'a))
-  (ncmbn-add #'s-cmpr c c c c c)
-|#
-
-(DEFUN DSTR-ADD-TERM-TO-CMBN (cmpr cffc gnrt cmbn)
-   (declare
-      (type cmprf cmpr)
-      (fixnum cffc)  ;; non-zero
-      (type gnrt gnrt)
-      (type cmbn cmbn))
-   (the cmbn
-      (let ((list (cmbn-list cmbn)))
-         (declare (list list))
-         (unless list
-            (push (term cffc gnrt) (cmbn-list cmbn))
-            (return-from dstr-add-term-to-cmbn cmbn))
-         (do ((mark2 nil mark1)
-              (mark1 list (cdr mark1)))
-             ((endp mark1) (setf (cdr mark2) (list (term cffc gnrt))))
-            (declare (list mark1 mark2))
-            (ecase (funcall cmpr gnrt (-gnrt mark1))
-               (:less
-                (if mark2
-                   (push (term cffc gnrt) (cdr mark2))
-                   (push (term cffc gnrt) (cmbn-list cmbn)))
-                (return))
-               (:equal
-                (let ((new-cffc (+ cffc (-cffc mark1))))
-                   (declare (fixnum new-cffc))
-                   (if (zerop new-cffc)
-                      (if mark2
-                         (pop (cdr mark2))
-                         (pop (cmbn-list cmbn)))
-                      (setf (-cffc mark1) new-cffc))
-                   (return)))
-               (:greater)))
-         cmbn)))
-
-#|
-  (setf c (zero-cmbn 10))
-  (dstr-add-term-to-cmbn #'s-cmpr 3 'f c)
-  (eq * c)
-  (dstr-add-term-to-cmbn #'s-cmpr 3 'g c)
-  (eq * c)
-  (dstr-add-term-to-cmbn #'s-cmpr 3 'a c)
-  (eq * c)
-  (dstr-add-term-to-cmbn #'s-cmpr 3 'd c)
-  (eq * c)
-  (dstr-add-term-to-cmbn #'s-cmpr -3 'd c)
-  (eq * c)
-  (dstr-add-term-to-cmbn #'s-cmpr -2 'a c)
-  (dstr-add-term-to-cmbn #'s-cmpr -1 'a c)
-  (eq * c)
-  (dstr-add-term-to-cmbn #'s-cmpr -3 'g c)
-  (eq * c)
-  (dstr-add-term-to-cmbn #'s-cmpr -3 'f c)
-  (eq * c))
-|#
diff --git a/archive/Kenzo-2/Kenzo-2-Acl8/cones.cl b/archive/Kenzo-2/Kenzo-2-Acl8/cones.cl
deleted file mode 100644
index 8ffd4e8..0000000
--- a/archive/Kenzo-2/Kenzo-2-Acl8/cones.cl
+++ /dev/null
@@ -1,443 +0,0 @@
-;;;  CONES  CONES  CONES  CONES  CONES  CONES  CONES  CONES  CONES  CONES
-;;;  CONES  CONES  CONES  CONES  CONES  CONES  CONES  CONES  CONES  CONES
-;;;  CONES  CONES  CONES  CONES  CONES  CONES  CONES  CONES  CONES  CONES
-
-(IN-PACKAGE "CAT")
-
-(PROVIDE "cones")
-
-(DEFUN DISPATCH-BICN-CMBN (cmbn)
-   (declare (type cmbn cmbn))
-   (the (values cmbn cmbn cmbn)
-      (with-cmbn (degr list) cmbn
-         (let ((listb +empty-list+)
-               (listc +empty-list+)
-               (listd +empty-list+))
-            (declare (list listb listc listd))
-            (dolist (term list)
-               (declare (type term term))
-               (with-term (cffc bicn) term
-                  (with-bicn (bcnx ibicn) bicn
-                     (ecase bcnx
-                        (:bcnb (push (term cffc ibicn) listb))
-                        (:bcnc (push (term cffc ibicn) listc))
-                        (:bcnd (push (term cffc ibicn) listd))))))
-            (values
-               (make-cmbn :degr degr :list (nreverse listb))
-               (make-cmbn :degr (1+ degr) :list (nreverse listc))
-               (make-cmbn :degr degr :list (nreverse listd)))))))
-
-#|
-  (dispatch-bicn-cmbn (cmbn 3 3 (bcnb 'b1) 4 (bcnb 'b2) 33 (bcnc 'c) 333 (bcnd 'd)))
-|#
-
-(DEFUN BICN-CMBN-CMBNB (cmbn)
-   (declare (type cmbn cmbn))
-   (the cmbn
-      (with-cmbn (degr list) cmbn
-         (make-cmbn :degr degr
-            :list (do ((rslt +empty-list+)
-                       (mark list (cdr mark)))
-                      ((endp mark) (nreverse rslt))
-                     (declare (list rslt mark))
-                     (with--term (cffc bicn) mark
-                     (with-bicn (bcnx gnrtB) bicn
-                        (if (eq bcnx :bcnB)
-                           (push (term cffc gnrtB) rslt)
-                           (return (nreverse rslt))))))))))
-
-(DEFUN BICN-CMBN-CMBNC (cmbn)
-   (declare (type cmbn cmbn))
-   (the cmbn
-      (with-cmbn (degr list) cmbn
-         (make-cmbn :degr (1+ degr)
-            :list (do ((rslt +empty-list+)
-                       (mark (member :bcnc list :key #'cadr) (cdr mark)))
-                      ((endp mark) (nreverse rslt))
-                     (declare (list rslt mark))
-                     (with--term (cffc bicn) mark
-                     (with-bicn (bcnx gnrtC) bicn
-                        (if (eq bcnx :bcnC)
-                           (push (term cffc gnrtC) rslt)
-                           (return (nreverse rslt))))))))))
-
-(DEFUN BICN-CMBN-CMBND (cmbn)
-   (declare (type cmbn cmbn))
-   (the cmbn
-      (with-cmbn (degr list) cmbn
-         (make-cmbn :degr degr
-            :list (mapcar
-                     #'(lambda (term)
-                          (declare (type term term))
-                          (with-term (cffc bicn) term
-                             (term cffc (ibicn bicn))))
-                     (member :bcnd list :key #'cadr))))))
-
-#|
-  (bicn-cmbn-cmbnb (cmbn 3 1 (bcnb 'a) 2 (bcnc 'b)))
-  (bicn-cmbn-cmbnb (cmbn 3 2 (bcnc 'b)))
-  (bicn-cmbn-cmbnc (cmbn 3 1 (bcnb 'a) 2 (bcnc 'b) 3 (bcnd 'c)))
-  (bicn-cmbn-cmbnc (cmbn 3 1 (bcnb 'a) 3 (bcnd 'c)))
-  (bicn-cmbn-cmbnd (cmbn 3 1 (bcnb 'a) 2 (bcnc 'b) 3 (bcnd 'c)))
-  (bicn-cmbn-cmbnd (cmbn 3 2 (bcnb 'b)))
-|#
-
-(DEFUN MAKE-BICN-CMBN (cmbnb cmbnc cmbnd)
-   (declare (type cmbn cmbnb cmbnc cmbnd))
-   (the cmbn
-      (with-cmbn (degrb listb) cmbnb
-      (with-cmbn (degrc listc) cmbnc
-      (with-cmbn (degrd listd) cmbnd
-         (unless (= degrb (1- degrc) degrd)
-            (error "In MAKE-BICN-CMBN, the degrees are not coherent."))
-         (make-cmbn :degr degrb
-            :list (nconc
-                     (mapcar #'(lambda (termb)
-                                  (declare (type term termb))
-                                  (with-term (cffc gnrtb) termb
-                                     (term cffc (bcnb gnrtb))))
-                        listb)
-                     (mapcar #'(lambda (termc)
-                                  (declare (type term termc))
-                                  (with-term (cffc gnrtc) termc
-                                     (term cffc (bcnc gnrtc))))
-                        listc)
-                     (mapcar #'(lambda (termd)
-                                  (declare (type term termd))
-                                  (with-term (cffc gnrtd) termd
-                                     (term cffc (bcnd gnrtd))))
-                        listd))))))))
-
-#|
-  (multiple-value-call #'make-bicn-cmbn 
-     (dispatch-bicn-cmbn (cmbn 3 3 (bcnb 'b1) 4 (bcnb 'b2) 33 (bcnc 'c) 333 (bcnd 'd))))
-|#
-
-(DEFMETHOD PRINT-KEYCONS ((car (eql :bcnb)) cdr stream)
-   (declare
-      (type gnrt cdr)
-      (stream stream))
-   (the (eql t)
-      (progn
-         (format stream "<BcnB ~A>" cdr)
-         t)))
-
-(DEFMETHOD PRINT-KEYCONS ((car (eql :bcnc)) cdr stream)
-   (declare
-      (type gnrt cdr)
-      (stream stream))
-   (the (eql t)
-      (progn
-         (format stream "<BcnC ~A>" cdr)
-         t)))
-
-(DEFMETHOD PRINT-KEYCONS ((car (eql :bcnd)) cdr stream)
-   (declare
-      (type gnrt cdr)
-      (stream stream))
-   (the (eql t)
-      (progn
-         (format stream "<BcnD ~A>" cdr)
-         t)))
-
-#|
-  (bcnb 'a)
-  (bcnc 'b)
-  (bcnd 'c)
-|#
-
-(DEFUN BICONE-CMPR (cmprb cmprc cmprd)
-   (declare (type cmprf cmpra cmprb cmprd))
-   (flet ((rslt (bicn1 bicn2)
-             (declare (type bicn bicn1 bicn2))
-             (let ((bcnx1 (bcnx bicn1)))
-                (declare (type (member :bcnb :bcnc :bcnd) bcnx))
-                (lexico
-                   (s-cmpr bcnx1 (bcnx bicn2))
-                   (case bcnx1
-                      (:bcnb (funcall cmprb (ibicn bicn1) (ibicn bicn2)))
-                      (:bcnc (funcall cmprc (ibicn bicn1) (ibicn bicn2)))
-                      (:bcnd (funcall cmprd (ibicn bicn1) (ibicn bicn2))))))))
-      (the cmprf #'rslt)))
-
-#|
-  (setf r (bicone-cmpr #'f-cmpr #'f-cmpr #'f-cmpr))
-  (funcall r (bcnb 1) (bcnc 0))
-  (funcall r (bcnb 1) (bcnb 2))
-|#
-
-(DEFUN BICONE-BASIS (basisb basisc basisd)
-   (declare (type basis basisb basisc basisd))
-   (the basis
-      (if (or (eq :locally-effective basisb)
-              (eq :locally-effective basisc)
-              (eq :locally-effective basisd))
-         :locally-effective
-         (flet ((rslt (degr)
-                   (declare (fixnum degr))
-                   (append
-                      (mapcar #'(lambda (item)
-                                   (declare (type gnrt item))
-                                   (bcnb item))
-                         (funcall basisb degr))
-                      (mapcar #'(lambda (item)
-                                   (declare (type gnrt item))
-                                   (bcnc item))
-                         (funcall basisc (1+ degr)))
-                      (mapcar #'(lambda (item)
-                                   (declare (type gnrt item))
-                                   (bcnd item))
-                         (funcall basisd degr)))))
-            (the basis #'rslt)))))
-
-#|
-  (bicone-basis :locally-effective :locally-effective :locally-effective)
-  (setf b #'(lambda (degr) (mapcar #'(lambda (item) (cons degr item)) (<a-b> 0 degr))))
-  (setf r (bicone-basis b b b))
-  (funcall r 3)
-|#
-
-(DEFUN BICONE-DFFR-INTR (cmprc dffrb dffrc dffrd f1 f2)
-   (declare
-      (type cmprf cmprc)
-      (type morphism dffrb dffrc dffrd f1 f2))
-   (flet ((rslt (cmbn)
-             (declare (type cmbn cmbn))
-             (the cmbn
-                (multiple-value-bind (cmbnb cmbnc cmbnd) (dispatch-bicn-cmbn cmbn)
-                   (declare (type cmbn cmbnb cmbnc cmbnd))
-                   (let ((dffrb (cmbn-? dffrb cmbnb))
-                         (dffrc (cmbn-? dffrc cmbnc))
-                         (dffrd (cmbn-? dffrd cmbnd))
-                         (f1 (cmbn-? f1 cmbnb))
-                         (f2 (cmbn-? f2 cmbnd)))
-                      (declare (type cmbn dffrb dffrc dffrd f1 f2))
-                      (let ((cmbnc (2cmbn-sbtr cmprc (2cmbn-add cmprc f1 f2) dffrc)))
-                         (declare (type cmbn cmbnc))
-                         (make-bicn-cmbn dffrb cmbnc dffrd)))))))
-      (the intr #'rslt)))
-                      
-(DEFUN BICONE (rdct1 rdct2)
-   (declare (type reduction rdct1 rdct2))
-   (the chain-complex
-      (with-slots ((tcc1 tcc) (bcc1 bcc) (f1 f)) rdct1
-         (declare
-            (type chain-complex tcc1 bcc1)
-            (type morphism f1 g1 h1))
-      (with-slots ((tcc2 tcc) (bcc2 bcc) (f2 f)) rdct2
-         (declare
-            (type chain-complex tcc2 bcc2)
-            (type morphism f2 g2 h2))
-         (unless (eq bcc1 bcc2)
-            (error "In BICONE, both reductions have different BCC's."))
-         (let ((rslt (chain-complex
-                        :cmpr (bicone-cmpr (cmpr tcc1) (cmpr bcc1) (cmpr tcc2))
-                        :basis (bicone-basis (basis tcc1) (basis bcc1) (basis tcc2))
-                        :bsgn :undefined
-                        :dffr-intr (bicone-dffr-intr (cmpr bcc1)
-                                      (dffr tcc1) (dffr bcc1) (dffr tcc2)
-                                      f1 f2)
-                        :dffr-strt :cmbn
-                        :dfnt `(bicone ,rdct1 ,rdct2))))
-            (declare (type chain-complex rslt))
-            (slot-makunbound rslt 'bsgn)
-            rslt)))))
-
-#|
-  (cat-init)
-  (progn
-   (defun cdelta (dmns)
-     (chain-complex
-        :cmpr #'l-cmpr
-        :basis #'(lambda (n)
-                    (mapcar #'dlop-int-ext (funcall (delta-n-basis dmns) n)))
-        :bsgn '(0)
-        :dffr-intr #'(lambda (degr gmsm)
-                        (make-cmbn
-                           :degr (1- degr)
-                           :list (do ((rslt +empty-list+
-                                           (cons (cons sign (append
-                                                               (subseq gmsm 0 nark)
-                                                               (subseq gmsm (1+ nark))))
-                                                 rslt))
-                                     (sign 1 (- sign))
-                                     (nark 0 (1+ nark)))
-                                    ((> nark degr) rslt))))                                           
-        :dffr-strt :gnrt
-        :dfnt `(locally effective version of C_* delta ,dmns)))
-   (defun make-f (tdmns bdmns)
-     (morphism
-        :sorc (cdelta tdmns) :trgt (cdelta bdmns) :degr 0
-        :intr #'(lambda (degr gmsm)
-                   (let ((pos (position-if #'(lambda (vertex) (>= vertex bdmns)) gmsm)))
-                      (if pos
-                         (if (< pos degr)
-                            (zero-cmbn degr)
-                            (cmbn degr 1 (nconc (butlast gmsm) (list bdmns))))
-                         (cmbn degr 1 gmsm))))
-        :strt :gnrt
-        :dfnt `(projection delta ,tdmns => delta ,bdmns)))
-   (defun make-g (tdmns bdmns)
-     (morphism
-        :sorc (cdelta bdmns) :trgt (cdelta tdmns) :degr 0
-        :intr #'identity
-        :strt :cmbn
-        :dfnt `(injection delta ,bdmns => delta ,tdmns)))
-   (defun make-h (tdmns bdmns)
-     (morphism
-        :sorc (cdelta tdmns) :trgt (cdelta tdmns) :degr +1
-        :intr #'(lambda (degr gmsm)
-                   (let ((pos (position-if #'(lambda (vertex) (>= vertex bdmns)) gmsm)))
-                      (if pos
-                         (if (member bdmns gmsm)
-                            (zero-cmbn (1+ degr))
-                            (cmbn (1+ degr) (-1-expt-n pos)
-                               (append (subseq gmsm 0 pos) (list bdmns) (subseq gmsm pos))))
-                         (zero-cmbn (1+ degr)))))
-        :strt :gnrt
-        :dfnt `(homotopy for delta ,tdmns => ,bdmns)))
-   (defun make-rdct (tdmns bdmns)
-       (setf rdct (reduction
-                    :f (make-f tdmns bdmns)
-                    :g (make-g tdmns bdmns)
-                    :h (make-h tdmns bdmns)
-                    :dfnt `(reduction delta ,tdmns ,bdmns)))))
-  (setf b (bicone (make-rdct 3 2) (make-rdct 4 2)))
-  (basis b 1)
-  (? b (cmbn 1 3 (bcnb '(0 3)) 4 (bcnc '(0 1 2)) 5 (bcnd '(0 4))))
-|#
-
-(DEFMETHOD CMPS ((eqvl1 equivalence) (eqvl2 equivalence) &optional dummy)
-   (declare (ignore dummy))
-   (the equivalence
-      (progn
-         (when (eq 'trivial-eqvl (dfnt eqvl2))
-            (return-from cmps eqvl1))
-         (with-slots ((cc-A lbcc) (cc-B tcc) (cc-C rbcc)
-                      (f1 lf) (g1 lg) (h1 lh) (f2 rf) (g2 rg) (h2 rh)) eqvl1
-            (declare
-               (type chain-complex cc-A cc-B cc-C)
-               (type morphism f1 g1 h1 f2 g2 h2))
-         (with-slots ((cc-C2 lbcc) (cc-D tcc) (cc-E rbcc)
-                      (f3 lf) (g3 lg) (h3 lh) (f4 rf) (g4 rg) (h4 rh)) eqvl2
-            (declare
-               (type chain-complex cc-C2 cc-D cc-E)
-               (type morphism f3 g3 h3 f4 g4 h4))
-            (unless (eq (grmd cc-C) (grmd cc-C2))
-               (error "In (CMPS eqvl eqvl), both eqvl's may not be composed."))
-            (let ((bicone (bicone (rrdct eqvl1) (lrdct eqvl2)))
-                  (cmpr-B (cmpr cc-B))
-                  (cmpr-D (cmpr cc-D)))
-               (declare (type chain-complex bicone))
-               (let ((lf (morphism
-                            :sorc bicone :trgt cc-A :degr 0
-                            :intr #'(lambda (cmbn)
-                                       (declare (type cmbn cmbn))
-                                       (cmbn-? f1 (bicn-cmbn-cmbnB cmbn)))
-                            :strt :cmbn
-                            :dfnt `(cmps ,eqvl1 ,eqvl2 lf)))
-                     (lg (morphism
-                            :sorc cc-A :trgt bicone :degr 0
-                            :intr #'(lambda (cmbn)
-                                       (declare (type cmbn cmbn))
-                                       (let* ((cmbnB (cmbn-? g1 cmbn))
-                                              (cmbnC (zero-cmbn (1+ (cmbn-degr cmbn))))
-                                              (cmbnD (cmbn-? g3 (cmbn-? f2 (cmbn-opps cmbnB)))))
-                                          (declare (type cmbn cmbnB cmbnC cmbnD))
-                                          (make-bicn-cmbn cmbnB cmbnC cmbnD)))
-                            :strt :cmbn
-                            :dfnt `(cmps ,eqvl1 ,eqvl2 lg)))
-                     (lh (morphism
-                            :sorc bicone :trgt bicone :degr +1
-                            :intr #'(lambda (cmbn)
-                                       (declare (type cmbn cmbn))
-                                       (multiple-value-bind (cmbnB cmbnC cmbnD) 
-                                           (dispatch-bicn-cmbn cmbn)
-                                          (declare (type cmbn cmbnB cmbnC cmbnD))
-                                          (setf cmbnB (cmbn-? h1 cmbnB))
-                                          (let ((cmbnC (zero-cmbn (1+ (cmbn-degr cmbnC))))
-                                                (cmbnD1 (cmbn-? g3 (cmbn-? f2 cmbnB)))
-                                                (cmbnD2 (cmbn-? g3 cmbnC))  ;; let, not let*
-                                                (cmbnD3 (cmbn-? h3 cmbnD)))
-                                             (declare (type cmbn cmbnC cmbnD1 cmbnD2 cmbnD3))
-                                             (make-bicn-cmbn
-                                                cmbnB
-                                                cmbnC
-                                                (2cmbn-sbtr cmpr-D
-                                                   (2cmbn-add cmpr-D cmbnD2 cmbnD3)
-                                                   cmbnD1)))))
-                            :strt :cmbn
-                            :dfnt `(cmps ,eqvl1 ,eqvl2 lh)))
-                     (rf (morphism
-                            :sorc bicone :trgt cc-E :degr 0
-                            :intr #'(lambda (cmbn)
-                                       (declare (type cmbn cmbn))
-                                       (cmbn-? f4 (bicn-cmbn-cmbnD cmbn)))
-                            :strt :cmbn
-                            :dfnt `(cmps ,eqvl1 ,eqvl2 rf)))
-                     (rg (morphism
-                            :sorc cc-E :trgt bicone :degr 0
-                            :intr #'(lambda (cmbn)
-                                       (declare (type cmbn cmbn))
-                                       (let* ((cmbnD (cmbn-? g4 cmbn))
-                                              (cmbnC (zero-cmbn (1+ (cmbn-degr cmbn))))
-                                              (cmbnB (cmbn-? g2 (cmbn-? f3 (cmbn-opps cmbnD)))))
-                                          (declare (type cmbn cmbnD cmbnC cmbnB))
-                                          (make-bicn-cmbn cmbnB cmbnC cmbnD)))
-                            :strt :cmbn
-                            :dfnt `(cmps ,eqvl1 ,eqvl2 rg)))
-                     (rh (morphism
-                            :sorc bicone :trgt bicone :degr +1
-                            :intr #'(lambda (cmbn)
-                                       (declare (type cmbn cmbn))
-                                       (multiple-value-bind (cmbnB cmbnC cmbnD) 
-                                           (dispatch-bicn-cmbn cmbn)
-                                          (declare (type cmbn cmbnB cmbnC cmbnD))
-                                          (setf cmbnD (cmbn-? h4 cmbnD))
-                                          (let ((cmbnC (zero-cmbn (1+ (cmbn-degr cmbnC))))
-                                                (cmbnB1 (cmbn-? g2 (cmbn-? f3 cmbnD)))
-                                                (cmbnB2 (cmbn-? g2 cmbnC))  ;; let, not let*
-                                                (cmbnB3 (cmbn-? h2 cmbnB)))
-                                             (declare (type cmbn cmbnC cmbnB1 cmbnB2 cmbnB3))
-                                             (make-bicn-cmbn
-                                                (2cmbn-sbtr cmpr-B
-                                                   (2cmbn-add cmpr-B cmbnB2 cmbnB3)
-                                                   cmbnB1)
-                                                cmbnC
-                                                cmbnD))))
-                            :strt :cmbn
-                            :dfnt `(cmps ,eqvl1 ,eqvl2 rh))))
-                  (declare
-                     (type chain-complex lbcc tcc rbcc)
-                     (type morphism lf lg lh rf rg rh))
-                  (equivalence
-                   :lrdct (reduction :f lf :g lg :h lh :dfnt `(cmps ,eqvl1 ,eqvl2 :lrdct))
-                   :rrdct (reduction :f rf :g rg :h rh :dfnt `(cmps ,eqvl1 ,eqvl2 :rrdct))
-                   :dfnt `(cmps ,eqvl1 ,eqvl2)))))))))
-
-#|
-  (cat-init)
-  (setf c (chain-complex
-             :cmpr #'s-cmpr
-             :basis #'(lambda (dmns) '(a))
-             :bsgn 'a
-             :dffr-intr #'zero-dffr-intr
-             :dffr-strt :cmbn
-             :dfnt '(c)))
-  (setf h1 (trivial-eqvl c))
-  (setf h2 (cmps h1 h1))
-  (pre-check-rdct (lrdct h2))
-  (setf *tc* (cmbn 3 1 (bcnB 'a) 10 (bcnC 'a) 100 (bcnD 'a)))
-  (setf *bc* (cmbn 3 1 'a))
-  (check-rdct)
-  (pre-check-rdct (rrdct h2))
-  (check-rdct)
-  (setf h3 (cmps h2 h2))
-  (setf *tc* (cmbn 3 1 (bcnB (bcnB 'a)) 10 (bcnB (bcnC 'a)) 100 (bcnB (bcnD 'a))
-                     1000 (bcnC 'a)
-                    10000 (bcnD (bcnB 'a)) 5234 (bcnD (bcnC 'a)) 223 (bcnD (bcnD 'a))))
-  (pre-check-rdct (lrdct h3))
-  (check-rdct)
-  (pre-check-rdct (rrdct h3))
-  (check-rdct)
-|#
diff --git a/archive/Kenzo-2/Kenzo-2-Acl8/cs-twisted-products.cl b/archive/Kenzo-2/Kenzo-2-Acl8/cs-twisted-products.cl
deleted file mode 100644
index 3d3d0e4..0000000
--- a/archive/Kenzo-2/Kenzo-2-Acl8/cs-twisted-products.cl
+++ /dev/null
@@ -1,146 +0,0 @@
-;;;  CS-TWISTED-PRODUCTS  CS-TWISTED-PRODUCTS  CS-TWISTED-PRODUCTS
-;;;  CS-TWISTED-PRODUCTS  CS-TWISTED-PRODUCTS  CS-TWISTED-PRODUCTS
-;;;  CS-TWISTED-PRODUCTS  CS-TWISTED-PRODUCTS  CS-TWISTED-PRODUCTS
-
-(IN-PACKAGE "CAT")
-
-(PROVIDE "cs-twisted-products")
-
-(DEFUN SMGR-FIBRATION-SINTR (dmns gbar)
-  (declare
-    (ignore dmns)
-    (type gbar gbar))
-  (the absm
-    (first (gbar-list gbar))))
-
-(DEFUN SMGR-FIBRATION (smgr)
-  (declare (type simplicial-group smgr))
-  (the fibration
-    (simplicial-mrph
-      :sorc (classifying-space smgr)
-      :trgt smgr
-      :degr -1
-      :sintr #'smgr-fibration-sintr
-      :dfnt `(simplicial-group-fibration ,smgr))))
-
-#|
-  (setf k1 (k-z-1))
-  (setf tw (smgr-fibration k1))
-  (setf k2 (sorc tw))
-  (setf tt (fibration-total tw))
-  (setf gmsm (crpr 0 (gbar 4 0 '(10 11 12) 0 '(20 21) 0 '(30) 0 '())
-                   0 '(2 4 6 8)))
-  (dotimes (i 5)
-    (print (face tt i 4 gmsm)))
-  (setf br (brown-reduction tw))
-  (setf tw-pr (bcc br))
-  (? tw-pr 4 (tnpr 4 (gbar 4 0 '(1 10 100) 0 '(1000 10000)
-                             0 '(100000) 0 '())
-                   0 '()))
-|#
-
-(DEFUN SMGR-CRTS-CONTRACTION-INTR (idnt)
-  (declare
-    (type gmsm idnt))
-  (flet ((rslt (degr crpr
-		     &aux (degr+1 (1+ degr)))
-	   (declare
-	    (fixnum degr degr+1)
-	    (type crpr crpr))
-	   (the cmbn
-	     (with-crpr (absm1 absm2) crpr
-	       (if (= (dgop absm2) (mask degr))
-		 (zero-cmbn degr+1)
-		 (term-cmbn degr+1
-		   (-1-expt-n+1 degr)
-		   (crpr 0 (make-gbar
-			    :dmns degr+1
-			    :list (cons absm2
-					(rest (unnormalize-gbar absm1 idnt))))
-			 (mask degr+1) idnt)))))))
-     (the intr #'rslt)))
-
-(DEFUN SMGR-CRTS-CONTRACTION (smgr)
-  (declare (type simplicial-group smgr))
-  (the morphism
-    (morphism
-      :sorc (fibration-total (smgr-fibration smgr))
-      :trgt (fibration-total (smgr-fibration smgr))
-      :degr +1
-      :intr (smgr-crts-contraction-intr (bsgn smgr))
-      :strt :gnrt
-      :dfnt `(smgr-crts-contraction ,smgr))))
-
-#|
-  (cat-init)
-  (setf chi (smgr-crts-contraction (k-z-1)))
-  (setf rdct (reduction :f (zero-mrph (sorc chi) (z-chcm))
-                         :g (zero-mrph (z-chcm) (sorc chi))
-                         :h chi))
-  (pre-check-rdct rdct)
-  (setf *tc* (cmbn 0 1 (crpr 0 +null-gbar+ 0 '())))
-  (setf *bc* (cmbn 0 1 :z-gnrt))
-  (check-rdct)
-  (setf *tc* (cmbn 1 1 (crpr 1 +null-gbar+ 0 '(1))))
-  (check-rdct)
-  (setf *tc* (cmbn 4 1 (crpr 0 (gbar 4 0 '(10 11 12) 0 '(20 21) 0 '(30) 0 '())
-                             0 '(2 4 6 8))))
-  (check-rdct)
-  (setf *tc* (cmbn 3 1 (crpr 0 (gbar 3 0 '(10 11) 0 '(20) 0 '())
-                             0 '(2 4 6))))
-  (check-rdct)
-|#
-
-(DEFUN SMGR-TNPR-CONTRACTION (smgr
-			        &aux (fibration (smgr-fibration smgr))
-				     (brown (brown-reduction fibration))
-				     (f (f brown))
-				     (g (g brown))
-				     (chi (smgr-crts-contraction smgr)))
-  (declare
-    (type simplicial-group smgr)
-    (type fibration fibration)
-    (type reduction brown)
-    (type morphism f g chi))
-  (the morphism
-    (i-cmps f chi g)))
-
-#|
-  (cat-init)
-  (setf chi (smgr-tnpr-contraction (k-z-1)))
-  (setf rdct (reduction :f (zero-mrph (sorc chi) (z-chcm))
-                         :g (zero-mrph (z-chcm) (sorc chi))
-                         :h chi))
-  (pre-check-rdct rdct)
-  (setf *tc* (cmbn 0 1 (tnpr 0 +null-gbar+ 0 '())))
-  (setf *bc* (cmbn 0 1 :z-gnrt))
-  (check-rdct)
-  (setf *tc* (cmbn 1 1 (tnpr 0 +null-gbar+ 1 '(1))))
-  (check-rdct)
-  (setf *tc* (cmbn 3 1 (tnpr 0 +null-gbar+ 3 '(1 10 100))))
-  (? chi *tc*)
-  (check-rdct)
-  (setf *tc* (cmbn 3 1 (tnpr 2 (gbar 2 0 '(1) 0 '()) 1 '(10))))
-  (? chi *tc*)
-  (check-rdct)
-  (setf *tc* (cmbn 3 1 (tnpr 3 (gbar 3 0 '(1 10) 0 '(100) 0 '()) 0 '())))
-  (? chi *tc*)
-  (check-rdct)
-  (setf *tc* (cmbn 4 1 (tnpr 0 +null-gbar+ 4 '(1 10 100 1000))))
-  (? chi *tc*)
-  (check-rdct)
-  (setf *tc* (cmbn 4 1 (tnpr 2 (gbar 2 0 '(1) 0 '()) 2 '(10 100))))
-  (? chi *tc*)
-  (check-rdct)
-  (setf *tc* (cmbn 4 1 (tnpr 3 (gbar 3 0 '(1 10) 0 '(100) 0 '())
-                             1 '(1000))))
-  (? chi *tc*)
-  (check-rdct)
-  (setf *tc* (cmbn 4 1 (tnpr 4 (gbar 4 0 '(1 10 100)
-                                       0 '(1000 10000)
-                                       0 '(100000)
-                                       0 '())
-                              0 '())))
-  (? chi *tc*)
-  (check-rdct)
-|#
\ No newline at end of file
diff --git a/archive/Kenzo-2/Kenzo-2-Acl8/delta.cl b/archive/Kenzo-2/Kenzo-2-Acl8/delta.cl
deleted file mode 100644
index c8cdd99..0000000
--- a/archive/Kenzo-2/Kenzo-2-Acl8/delta.cl
+++ /dev/null
@@ -1,408 +0,0 @@
-;;;  DELTA  DELTA  DELTA  DELTA  DELTA  DELTA  DELTA  DELTA  DELTA
-;;;  DELTA  DELTA  DELTA  DELTA  DELTA  DELTA  DELTA  DELTA  DELTA
-;;;  DELTA  DELTA  DELTA  DELTA  DELTA  DELTA  DELTA  DELTA  DELTA
-
-(IN-PACKAGE "CAT")
-
-(PROVIDE "delta")
-
-(DEFMETHOD PRINT-KEYCONS ((car (eql :delt)) cdr stream)
-   (format stream "~A" (hyphenize-list (dlop-int-ext cdr)))
-   (cons car cdr))
-
-(DEFUN SOFT-DELTA-CMPR (gmsm1 gmsm2)
-   (f-cmpr (cdr gmsm1) (cdr gmsm2)))
-
-#|
-  (soft-delta-cmpr (d 12) (d 23))
-|#
-   
-(DEFUN DELTA-FACE (indx dmns gmsm)
-   (declare
-      (fixnum indx gmsm)
-      (ignore dmns))
-   (the absm
-      (do ((pmark 1 (ash pmark 1))
-           (bmark indx)
-           (gmsm2 gmsm (ash gmsm2 -1)))
-          (nil)
-         (declare (fixnum pmark bmark gmsm2))
-         (when (oddp gmsm2)
-            (when (minusp (decf bmark))
-               (return-from delta-face (absm 0 (logxor gmsm pmark))))))))
-
-(DEFUN SOFT-DELTA-FACE (indx dmns gmsm)
-   (declare
-      (fixnum indx dmns)
-      (type soft-dlop gmsm))
-   (absm 0 (d (gmsm (delta-face indx dmns (cdr gmsm))))))
-
-#|
-  (dotimes (i 4)
-     (print (dlop-int-ext (gmsm (delta-face i 3 (dlop-ext-int '(0 1 2 3)))))))
-  (dotimes (i 4)
-     (print (dlop-int-ext (gmsm (delta-face i 3 (dlop-ext-int '(0 2 4 6))))))))
-  (dotimes (i 4)
-     (print (soft-delta-face i 3 (d (mask 4)))))
-  (dotimes (i 4)
-     (print (soft-delta-face i 3 (d (dlop-ext-int '(0 2 4 6))))))
-|#
-
-(DEFUN DELTA-dffr (dmns gmsm)
-   (declare (fixnum dmns gmsm))
-   (the cmbn
-      (if (zerop dmns)
-         +zero-negative-cmbn+
-         (make-cmbn
-            :degr (1- dmns)
-            :list (do ((rslt +empty-list+)
-                      (gmsm2 gmsm (ash gmsm2 -1))
-                      (pmark 1 (ash pmark +1))
-                      (sign 1))
-                     ((zerop gmsm2) rslt)
-                    (declare
-                       (list rslt)
-                       (fixnum gmsm2 pmark sign))
-                    (when (oddp gmsm2)
-                       (push (term sign (logxor gmsm pmark)) rslt)
-                       (setf sign (- sign))))))))
-
-(DEFUN SOFT-DELTA-dffr (dmns gmsm)
-   (declare
-      (fixnum dmns)
-      (type soft-dlop gmsm))
-   (make-cmbn
-      :degr (1- dmns)
-      :list (mapcar #'(lambda (term)
-                         (with-term (cffc gmsm) term
-                            (term cffc (d gmsm))))
-               (cmbn-list (delta-dffr dmns (cdr gmsm))))))
-
-#|
-  (delta-dffr 0 4)
-  (delta-dffr 1 3)
-  (delta-dffr 1 5)
-  (delta-dffr 1 10)
-  (delta-dffr 5 63)
-  (soft-delta-dffr 5 (d (mask 6)))
-|#
-
-
-(DEFUN DELTA-CPRD (dmns gmsm)
-   (declare (fixnum dmns gmsm))
-   (the cmbn
-      (make-cmbn
-         :degr dmns
-         :list (do ((rslt +empty-list+)
-                    (ldegr dmns)
-                    (indx (1- (integer-length gmsm)) (1- indx)))
-                   ((minusp indx))
-                  (declare
-                     (list rslt)
-                     (fixnum indx))
-                  (when (logbitp indx gmsm)
-                     (push (term 1 (tnpr
-                                    ldegr (logand gmsm (mask (1+ indx)))
-                                    (- dmns ldegr) (logandc2 gmsm (mask indx))))
-                        rslt)
-                     (when (minusp (decf ldegr))
-                        (return rslt)))))))
-
-(DEFUN SOFT-DELTA-CPRD (dmns gmsm)
-   (declare
-      (fixnum dmns)
-      (type soft-dlop gmsm))
-   (make-cmbn :degr dmns
-      :list (mapcar
-               #'(lambda (term)
-                    (with-term (cffc tnpr) term
-                       (with-tnpr (degr1 gmsm1 degr2 gmsm2) tnpr
-                          (term cffc
-                             (tnpr degr1 (d gmsm1) degr2 (d gmsm2))))))
-               (cmbn-list (delta-cprd dmns (cdr gmsm))))))
-
-#|
-  (delta-cprd 3 15)
-  (delta-cprd 3 170)
-  (soft-delta-cprd 3 (d (dlop-ext-int '(1 3 5 7))))
-  (delta-cprd 0 64)
-|#
-                                        
-(DEFUN DELTA-INFINITY ()
-  (the simplicial-set
-    (simplicial-set
-     :cmpr #'f-cmpr
-     :basis :locally-effective
-     :bsgn 1
-     :face #'delta-face
-     :cprd-intr #'delta-cprd
-     :cprd-strt :gnrt
-     :dffr-intr #'delta-dffr
-     :dffr-strt :gnrt
-     :dfnt '(delta-infinity))))
-
-#|
-  (cmpr (delta-infinity) 2 4)
-  (cmpr (delta-infinity) 4 4)
-  (cmpr (delta-infinity) 8 4)
-  (basis (delta-infinity) 1)   ;;; => error
-  (face (delta-infinity) 1 2 21)
-  (cprd (delta-infinity) 3 15)
-  (cprd (delta-infinity) 3 15)
-  (? (delta-infinity) 2 21))
-|#
-
-(DEFUN SOFT-DELTA-INFINITY ()
-  (the simplicial-set
-    (simplicial-set
-     :cmpr #'soft-delta-cmpr
-     :basis :locally-effective
-     :bsgn (d 1)
-     :face #'soft-delta-face
-     :cprd-intr #'soft-delta-cprd :cprd-strt :gnrt
-     :dffr-intr #'soft-delta-dffr :dffr-strt :gnrt
-     :dfnt '(soft-delta-infinity))))
-
-#|
-  (cat-init)
-  (cmpr (soft-delta-infinity) (d 2) (d 4))
-  (face (soft-delta-infinity) 1 2 (d (dlop-ext-int '(1 3 5))))
-  (cprd (soft-delta-infinity) 3 (d 15))
-  (cprd (soft-delta-infinity) 3 (d 15))
-  (? (soft-delta-infinity) 2 (d (dlop-ext-int '(0 2 4))))
-|#
-
-(DEFUN DELTA-N-BASIS (n)
-   (declare (fixnum n dmns))
-   (flet ((rslt (dmns)
-             (when (> dmns n)
-                (return-from rslt +empty-list+))
-             (setf dmns (1+ dmns))
-             (do ((rslt +empty-list+)
-                  (count (binomial-n-p (1+ n) dmns))
-                  (gmsm (mask (1+ n)) (1- gmsm)))
-                 ((zerop count) rslt)
-                (when (= (logcount gmsm) dmns)
-                   (push gmsm rslt)
-                   (decf count)))))
-      (the basis #'rslt)))
-
-(DEFUN SOFT-DELTA-N-BASIS (n)
-   (declare (fixnum n))
-   (flet ((rslt (dmns)
-             (when (> dmns n)
-                (return-from rslt +empty-list+))
-             (setf dmns (1+ dmns))
-             (do ((rslt +empty-list+)
-                  (count (binomial-n-p (1+ n) dmns))
-                  (gmsm (mask (1+ n)) (1- gmsm)))
-                 ((zerop count) rslt)
-                (when (= (logcount gmsm) dmns)
-                   (push (d gmsm) rslt)
-                   (decf count)))))
-      (the basis #'rslt)))
-      
-
-#|
-  (setf basis (delta-n-basis 3))
-  (setf soft-basis (soft-delta-n-basis 3))
-  (dotimes (i 5)
-     (print (funcall basis i)))
-  (dotimes (i 5)
-     (print (funcall soft-basis i)))))
-|#   
-
-(DEFUN DELTA (dmns)
-  (declare (fixnum dmns))
-  (the simplicial-set
-    (simplicial-set
-     :cmpr #'f-cmpr
-     :basis (delta-n-basis dmns)
-     :bsgn 1
-     :face #'delta-face
-     :cprd-intr #'delta-cprd
-     :cprd-strt :gnrt
-     :dffr-intr #'delta-dffr
-     :dffr-strt :gnrt
-     :dfnt `(delta ,dmns))))
-
-#|
-  (cat-init)
-  (setf d3 (delta 3))
-  (cmpr d3 2 4)
-  (cmpr d3 4 4)
-  (cmpr d3 8 4)
-  (basis d3 1)
-  (cprd d3 3 15)
-  (face d3 1 2 21)
-  (? d3 2 13)
-  (setf d (delta-infinity))
-  (basis d)
-  (setf d (delta-infinity)))
-|#
-
-(DEFUN SOFT-DELTA (dmns)
-  (declare (fixnum dmns))
-  (the simplicial-set
-    (simplicial-set
-     :cmpr #'soft-delta-cmpr
-     :basis (soft-delta-n-basis dmns)
-     :bsgn (d 1)
-     :face #'soft-delta-face
-     :cprd-intr #'soft-delta-cprd :cprd-strt :gnrt
-     :dffr-intr #'soft-delta-dffr :dffr-strt :gnrt
-     :dfnt `(soft-delta ,dmns))))
-      
-#|
-  (cat-init)
-  (setf d3 (soft-delta 3))
-  (cmpr d3 (d 2) (d 4))
-  (basis d3 1)
-  (cprd d3 3 (d 15))
-  (face d3 1 2 (d 21))
-  (? d3 2 (d 13))
-|#
-
-#| For comparison with EAT.
-   In 
-  (setf delta (delta-infinity))
-  (setf d (dffr delta))
-  (setf s14 (mask 15))
-  (cmbn-? d (gnrt-? d 14 s14))
-  (defun t1 (n)
-     (time (dotimes (i n) (cmbn-? d (gnrt-? d 14 s14)))))
-  (compile 't1)
-  (t1 500)
-  (setf +too-much-time+ -1)
-  (t1 500)
-|#
-#|
-  In EAT:
-  (setf delta *delta*)
-  (setf d (cc-d (ss-cc delta)))
-  (setf s14 (<a-b> 0 14))
-  (??? d (? d 14 s14))
-  (defun t1 (n)
-     (time (dotimes (i n) (??? d (? d 14 s14)))))
-  (compile 't1)
-  (t1 500)
-|#
-
-(DEFUN DELTAB-CMPR (gmsm1 gmsm2)
-   (declare (fixnum gmsm1 gmsm2))
-   (if (= 1 (logcount gmsm1))
-      :equal
-      (f-cmpr gmsm1 gmsm2)))
-
-(DEFUN DELTAB-dffr (dmns gmsm)
-   (declare (fixnum dmns gmsm))
-   (the cmbn
-      (if (< dmns 2)
-         (zero-cmbn (1- dmns))
-         (make-cmbn
-            :degr (1- dmns)
-            :list (do ((rslt +empty-list+)
-                      (gmsm2 gmsm (ash gmsm2 -1))
-                      (pmark 1 (ash pmark +1))
-                      (sign 1))
-                     ((zerop gmsm2) rslt)
-                    (declare
-                       (list rslt)
-                       (fixnum gmsm2 pmark sign))
-                    (when (oddp gmsm2)
-                       (push (term sign (logxor gmsm pmark)) rslt)
-                       (setf sign (- sign))))))))
-
-(DEFUN DELTAB2-FACE (indx dmns gmsm)
-   (declare
-      (fixnum indx dmns gmsm))
-   (the absm
-      (progn
-	(when (= 2 dmns)
-	   (return-from deltab2-face (absm 1 1)))
-	(do ((pmark 1 (ash pmark 1))
-	     (bmark indx)
-	     (gmsm2 gmsm (ash gmsm2 -1)))
-	    (nil)
-	    (declare (fixnum pmark bmark gmsm2))
-	    (when (oddp gmsm2)
-		  (when (minusp (decf bmark))
-			(return-from deltab2-face (absm 0 (logxor gmsm pmark)))))))))
-
-(DEFUN DELTAB2-cprd (dmns gmsm)
-   (declare (fixnum dmns gmsm))
-   (the cmbn
-      (make-cmbn
-         :degr dmns
-         :list (if (zerop dmns)
-		   (list (term 1 (tnpr 0 gmsm 0 gmsm)))
-		 (do ((rslt +empty-list+)
-		      (ldegr dmns)
-		      (indx (1- (integer-length gmsm)) (1- indx)))
-		     ((minusp indx))
-		     (declare
-		      (list rslt)
-		      (fixnum indx))
-		     (when (logbitp indx gmsm)
-			   (push (term 1 (tnpr
-					  ldegr (logand gmsm (mask (1+ indx)))
-					  (- dmns ldegr) (logandc2 gmsm (mask indx))))
-				 rslt)
-			   (when (minusp (decf ldegr))
-			      (setf rslt (delete 1 rslt :key #'caaddr))
-			      (setf (gnrt1 (gnrt (first rslt)))
-				    (setf (gnrt2 (gnrt (car (last rslt))))
-					  1))				    
-			      (return (delete 1 rslt :key #'cadddr)))))))))
-
-#|
-  (dotimes (i 7)
-    (print (deltab2-cprd i (mask (1+ i)))))
-|#
-  
-
-(DEFUN DELTAB2-dffr (dmns gmsm)
-   (declare (fixnum dmns gmsm))
-   (the cmbn
-      (if (< dmns 3)
-         (zero-cmbn (1- dmns))
-         (make-cmbn
-            :degr (1- dmns)
-            :list (do ((rslt +empty-list+)
-                      (gmsm2 gmsm (ash gmsm2 -1))
-                      (pmark 1 (ash pmark +1))
-                      (sign 1))
-                     ((zerop gmsm2) rslt)
-                    (declare
-                       (list rslt)
-                       (fixnum gmsm2 pmark sign))
-                    (when (oddp gmsm2)
-                       (push (term sign (logxor gmsm pmark)) rslt)
-                       (setf sign (- sign))))))))
-
-#|
-  (deltab-dffr 1 5)
-  (deltab-dffr 3 15)
-|#
-
-(DEFUN DELTAB ()
-  (the simplicial-set
-    (simplicial-set
-     :cmpr #'deltab-cmpr
-     :basis :locally-effective
-     :bsgn 1
-     :face #'delta-face
-     :cprd-intr #'delta-cprd
-     :cprd-strt :gnrt
-     :dfnt '(deltab))))
-
-(DEFUN DELTAB2 ()
-  (the simplicial-set
-    (simplicial-set
-     :cmpr #'f-cmpr
-     :basis :locally-effective
-     :bsgn 1
-     :face #'deltab2-face
-     :cprd-intr #'deltab2-cprd
-     :cprd-strt :gnrt
-     :dfnt '(deltab2))))
diff --git a/archive/Kenzo-2/Kenzo-2-Acl8/disk-pasting.cl b/archive/Kenzo-2/Kenzo-2-Acl8/disk-pasting.cl
deleted file mode 100644
index d6fd1aa..0000000
--- a/archive/Kenzo-2/Kenzo-2-Acl8/disk-pasting.cl
+++ /dev/null
@@ -1,399 +0,0 @@
-;;;  DISK-PASTING  DISK-PASTING  DISK-PASTING  DISK-PASTING
-;;;  DISK-PASTING  DISK-PASTING  DISK-PASTING  DISK-PASTING
-;;;  DISK-PASTING  DISK-PASTING  DISK-PASTING  DISK-PASTING
-
-(IN-PACKAGE "CAT")
-
-(provide "disk-pasting")
-
-(DEFUN DISK-PASTING-CMPR (cmpr new)
-  (declare
-    (type cmprf cmpr)
-    (symbol new))
-  (flet ((rslt (gnrt1 gnrt2)
-	   (declare (type gnrt gnrt1 gnrt2))
-	   (if (eq gnrt1 new)
-	       (if (eq gnrt2 new)
-		   :equal
-		 :less)
-	     (if (eq gnrt2 new)
-		 :greater
-	       (funcall cmpr gnrt1 gnrt2)))))
-    (the cmprf #'rslt)))
-
-#|
-  (setf c (delta 3))
-  (setf cmpr (disk-pasting-cmpr (cmpr c) 'new))
-  (funcall cmpr 'new 'new)
-  (funcall cmpr 'new 5)
-  (funcall cmpr 5 'new)
-  (funcall cmpr 5 5)
-  (funcall cmpr 5 6)
-  (funcall cmpr 6 5)
-|#
-
-(DEFUN DISK-PASTING-BASIS (basis dmns new)
-  (declare
-    (type basis basis)
-    (fixnum dmns)
-    (symbol new))
-  (flet ((rslt (degr)
-	   (declare (fixnum degr))
-	   (if (= degr dmns)
-	       (cons new (funcall basis dmns))
-	     (funcall basis degr))))
-    (the basis #'rslt)))
-
-#|
-  (setf c (delta 3))
-  (setf basis (disk-pasting-basis (basis c) 3 'new))
-  (funcall basis 3)
-  (funcall basis 2)
-|#
-
-(DEFUN DISK-PASTING-DFFR-INTR (old-dffr degr new dffr)
-  (declare
-    (type morphism old-dffr)
-    (fixnum degr)
-    (symbol new)
-    (type cmbn dffr))
-  (when (cddr (cmbn-? old-dffr dffr))
-    (error "In CHCM-DISK-PASTING, the given boundary has a non-null boundary."))
-  (let ((cmpr (cmpr (trgt old-dffr))))
-    (declare (type cmprf cmpr))
-    (flet ((rslt (cmbn)
-	     (declare (type cmbn cmbn))
-	     (with-cmbn (degr2 list) cmbn
-	       (unless (= degr degr2)
-		 (return-from rslt
-		   (cmbn-? old-dffr cmbn)))
-	       (unless list
-		 (return-from rslt
-		   (zero-cmbn (1- degr))))
-	       (unless (eq (-gnrt list) new)
-		 (return-from rslt
-		   (cmbn-? old-dffr cmbn)))
-	       (2cmbn-add cmpr
-		 (n-cmbn (-cffc list) dffr)
-		 (cmbn-? old-dffr
-			 (make-cmbn :degr degr
-				    :list (rest list)))))))
-      (the intr #'rslt))))
-
-#|
-  (cat-init)
-  (setf c (delta 3))
-  (setf intr (disk-pasting-dffr-intr (dffr c) 3 'new (cmbn 2 1 7)))
-  (setf intr (disk-pasting-dffr-intr (dffr c) 3 'new (? c 3 15)))
-  (funcall intr (cmbn 2 1 7))
-  (funcall intr (cmbn 3))
-  (funcall intr (cmbn 3 1 15))
-  (funcall intr (cmbn 3 1 'new 1 15))
-  (funcall intr (cmbn 3 1 'new -1 15))
-  (funcall intr (cmbn 3 -1 'new 1 15))
-  (funcall intr (cmbn 3 -1 'new -1 15))
-|#
- 
-(DEFUN CHCM-DISK-PASTING (chcm dmns new new-dffr)
-  (declare
-    (type chain-complex chcm)
-    (fixnum dmns)
-    (symbol new)
-    (type cmbn new-dffr))
-  (the chain-complex
-    (with-slots (cmpr basis dffr) chcm
-      (declare
-        (type cmprf cmpr)
-	(type basis basis)
-	(type gnrt bsgn)
-	(type morphism dffr))
-      (let ((rslt (chain-complex
-		   :cmpr (disk-pasting-cmpr cmpr new)
-		   :basis (disk-pasting-basis basis dmns new)
-		   :dffr-intr (disk-pasting-dffr-intr dffr dmns new new-dffr)
-		   :dffr-strt :cmbn
-		   :dfnt `(chcm-disk-pasting ,chcm ,dmns ,new ,new-dffr))))
-	(declare (type chain-complex rslt))
-	(when (slot-boundp chcm 'bsgn)
-	  (setf (slot-value rslt 'bsgn) (slot-value chcm 'bsgn)))
-	rslt))))
-
-#|
-  (setf c (delta 3))
-  (setf s3 (chcm-disk-pasting c 3 'new (? c 3 15)))
-  (homology s3 0 5))
-|#
-
-(DEFUN DISK-PASTING-FACE (cmpr face dmns new faces)
-  (declare
-    (type cmprf cmpr)
-    (type face face)
-    (fixnum dmns)
-    (symbol new)
-    (list faces))
-  (unless (= (1+ dmns) (length faces))
-    (error "In DISK-PASTING, non-coherent arguments."))
-  (mapl #'(lambda (mark)
-	    (declare (list mark))
-	    (unless (typep (car mark) 'absm)
-	      (setf (car mark) (absm 0 (car mark)))))
-	faces)
-  (flet ((rslt (indx dmns2 gmsm)
-	   (declare
-	     (fixnum indx dmns2)
-	     (type gmsm gmsm))
-	   (unless (= dmns dmns2)
-	     (return-from rslt
-	       (funcall face indx dmns2 gmsm)))
-	   (if (eq gmsm new)
-	       (nth indx faces)
-	     (funcall face indx dmns gmsm))))
-    (unless (check-faces cmpr #'rslt dmns new)
-      (error "The new simplicial-set is not constructed."))
-    (the face #'rslt)))
-
-#|
-  (cat-init)
-  (setf c (delta 3))
-  (setf face (disk-pasting-face (cmpr c) (face c)
-                3 'new (list 14 (absm 0 13) 11 7)))
-  (funcall face 0 2 7)
-  (funcall face 0 3 15)
-  (dotimes (i 4) (print (funcall face i 3 'new)))
-|#
-
-(DEFUN DISK-PASTING (smst dmns new faces)
-  (declare
-   (type simplicial-set smst)
-   (fixnum dmns)
-   (symbol new)
-   (list faces))
-  (the simplicial-set
-    (with-slots (cmpr basis bsgn face dffr) smst
-      (declare
-       (type cmprf cmpr)
-       (type basis basis)
-       (type gmsm bsgn)
-       (type face face)
-       (type morphism dffr))
-      (let ((new-face (disk-pasting-face (cmpr smst) face
-                                         dmns new faces))
-            (new-dffr (zero-cmbn (1- dmns))))
-        (declare
-         (type face new-face)
-         (type cmbn new-dffr))
-        (do ((mark faces (cdr mark))
-             (sign 1 (- sign)))
-            ((endp mark))
-          (declare
-           (list mark)
-           (fixnum sign))
-          (let ((absm (car mark)))
-            (declare (type absm absm))
-            (with-absm (dgop gmsm) absm
-                       (unless (plusp dgop)
-                         (dstr-add-term-to-cmbn cmpr sign gmsm new-dffr)))))
-        (simplicial-set
-         :cmpr (disk-pasting-cmpr cmpr new)
-         :basis (disk-pasting-basis basis dmns new)
-         :bsgn bsgn
-         :face new-face
-         :dffr-intr (disk-pasting-dffr-intr dffr dmns new new-dffr)
-         :dffr-strt :cmbn
-         :dfnt `(disk-pasting ,smst ,dmns ,new ,faces))))))
-
-#|
-  (setf d2 (delta 2))
-  (setf s2 (disk-pasting d2 2 'new '(6 5 3)))
-  (homology s2 0 4)
-  (setf s2xs2 (crts-prdc s2 s2))
-  (homology s2xs2 0 6)
-|#
-
-(DEFUN MRPH-DISK-PASTING-INTR (mrph trgt-cmpr dmns new new-im)
-  (declare
-    (type morphism mrph)
-    (type cmprf trgt-cmpr)
-    (fixnum dmns)
-    (symbol new)
-    (type cmbn new-im))
-  (let ((mrph-degr (degr mrph)))
-    (declare (fixnum mrph-degr))
-    (flet ((rslt (cmbn)
-	     (declare (type cmbn cmbn))
-	     (with-cmbn (degr list) cmbn
-	       (unless (= degr dmns)
-		 (return-from rslt
-		   (cmbn-? mrph cmbn)))
-	       (unless list
-		 (return-from rslt
-		   (zero-cmbn (+ degr mrph-degr))))
-	       (unless (eq new (-gnrt list))
-		 (return-from rslt
-		   (cmbn-? mrph cmbn)))
-	       (2cmbn-add trgt-cmpr
-		 (n-cmbn (-cffc list) new-im)
-		 (cmbn-? mrph
-			 (make-cmbn :degr degr
-				    :list (rest list)))))))
-      (the intr #'rslt))))
-
-#|
-  (setf m (idnt-mrph (delta 3)))
-  (setf intr
-        (mrph-disk-pasting-intr m (cmpr (delta 3))
-                                3 'new (cmbn 3 -1 15)))
-  (funcall intr (cmbn 2 3 7))
-  (funcall intr (cmbn 3))
-  (funcall intr (cmbn 3 4 15))
-  (funcall intr (cmbn 3 1 'new 1 15))
-  (funcall intr (cmbn 3 -1 'new 1 15))
-|#
-
-(DEFUN MRPH-DISK-PASTING (mrph new-sorc new-trgt dmns new new-im)
-  (declare
-    (type morphism mrph)
-    (type chain-complex new-sorc new-trgt)
-    (fixnum dmns)
-    (symbol new)
-    (type cmbn new-im))
-  (the morphism
-    (morphism
-      :sorc new-sorc :trgt new-trgt :degr (degr mrph)
-      :intr (mrph-disk-pasting-intr mrph (cmpr new-trgt)
-				    dmns new new-im)
-      :strt :cmbn
-      :dfnt `(mrph-disk-pasting ,mrph ,new-sorc ,new-trgt
-				,dmns ,new ,new-im))))
-
-#|
-  (setf d (delta 3))
-  (setf m (idnt-mrph d))
-  (setf sorc (chcm-disk-pasting d 3 'new (? d 3 15)))
-  (setf nm (mrph-disk-pasting m sorc sorc 3 'new (cmbn 3 1 'new)))
-  (? nm (cmbn 3 2 'new 3 15))
-|#
-
-(DEFUN EQVL-DISK-PASTING (eqvl dmns new dffr &key new-lbcc)
-  (declare
-   (type equivalence eqvl)
-   (fixnum dmns)
-   (symbol new)
-   (type cmbn dffr)
-   (type (or null chain-complex) new-lbcc))
-  (let* ((lg (lg eqvl))
-         (rf (rf eqvl))
-         (rh (rh eqvl))
-         (t-dffr (cmbn-? lg dffr))
-         (rb-dffr (cmbn-? rf t-dffr))
-         (new-lbcc (or new-lbcc
-                       (chcm-disk-pasting (lbcc eqvl)
-                                          dmns new dffr)))
-         (new-tcc (chcm-disk-pasting (tcc eqvl)
-                                     dmns new t-dffr))
-         (new-rbcc (chcm-disk-pasting (rbcc eqvl)
-                                      dmns new rb-dffr))
-         (1+dmns (1+ dmns)))
-    (declare
-     (type morphism lg rf rh)
-     (type cmbn t-dffr rb-dffr)
-     (type chain-complex new-lbcc new-tcc new-rbcc)
-     (fixnum 1+dmns))
-    (equivalence
-     :lrdct (reduction
-             :f (mrph-disk-pasting (lf eqvl) new-tcc new-lbcc
-                                   dmns new (cmbn dmns 1 new))
-             :g (mrph-disk-pasting lg new-lbcc new-tcc
-                                   dmns new (cmbn dmns 1 new))
-             :h (mrph-disk-pasting (lh eqvl) new-tcc new-tcc
-                                   dmns new (zero-cmbn 1+dmns))
-             :dfnt `(eqvl-disk-pasting ,eqvl ,dmns ,new ,dffr :lrdct))              
-     :rrdct (reduction
-             :f (mrph-disk-pasting rf new-tcc new-rbcc
-                                   dmns new (cmbn dmns 1 new))
-             :g (mrph-disk-pasting (rg eqvl) new-rbcc new-tcc
-                                   dmns new
-                                   (make-cmbn
-                                    :degr dmns
-                                    :list (cons (term 1 new)
-                                                (cmbn-list
-                                                 (cmbn-opps
-                                                  (cmbn-? rh t-dffr))))))
-             :h (mrph-disk-pasting rh new-tcc new-tcc
-                                   dmns new (zero-cmbn 1+dmns))
-             :dfnt `(eqvl-disk-pasting ,eqvl ,dmns ,new ,dffr :rrdct))
-     :dfnt `(eqvl-disk-pasting ,eqvl ,dmns ,new ,dffr))))
-				     
-#|
-(cat-init)
-(setf tcc
-      (chain-complex
-       :cmpr #'s-cmpr
-       :basis #'(lambda (degr)
-		  (case degr
-			(0 (list 'a))
-			(1 (list 'b))
-			(otherwise nil)))
-       :dffr-intr #'(lambda (degr gnrt)
-		      (if (= 1 degr)
-			  (cmbn 0 1 'a)
-			(zero-cmbn (1- degr))))
-       :dffr-strt :gnrt
-       :dfnt '(z-z)))
-(setf bcc
-      (chain-complex
-       :cmpr #'s-cmpr
-       :basis #'(lambda (degr) nil)
-       :dffr-intr #'(lambda (degr gnrt) (error "Impossible."))
-       :dffr-strt :gnrt
-       :dfnt '(zero)))
-(setf rh (morphism
-	  :sorc tcc :trgt tcc :degr +1
-	  :intr #'(lambda (degr gnrt)
-		    (if (zerop degr)
-			(cmbn 1 1 'b)
-		      (zero-cmbn 2)))
-	  :strt :gnrt
-	  :dfnt '(rh)))
-(setf eqvl (equivalence
-            :lrdct (trivial-rdct tcc)
-            :rrdct (reduction
-                    :f (zero-mrph tcc bcc 0)
-                    :g (zero-mrph bcc tcc 0)
-                    :h rh
-                    :dfnt '(rrdct))))
-(setf neqvl (eqvl-disk-pasting eqvl 1 'new (cmbn 0 1 'a)))
-(pre-check-rdct (lrdct neqvl))
-(setf *tc* (cmbn 0 1 'a))
-(setf *bc* *tc*)
-(check-rdct)
-(setf *tc* (cmbn 1 1 'new 10 'b))
-(setf *bc* *tc*)
-(check-rdct)
-(pre-check-rdct (rrdct neqvl))
-(setf *bc* (zero-cmbn 0))
-(check-rdct)
-(setf *tc* (cmbn 0 1 'a))
-(check-rdct)
-|#
-
-(DEFMETHOD SEARCH-EFHM (smst (dfnt (eql 'disk-pasting)))
-  (declare (type simplicial-set smst))
-  (the equivalence
-    (destructuring-bind (old-smst dmns new faces) (rest (dfnt smst))
-			(declare
-			  (type simplicial-set old-smst)
-			  (fixnum dmns)
-			  (symbol new)
-			  (ignore faces))
-      (eqvl-disk-pasting (efhm old-smst)
-			 dmns new (? smst dmns new)
-			 :new-lbcc smst))))
-
-#|
-(cat-init)
-(setf d (delta 2))
-(setf s2 (disk-pasting d 2 'new '(6 5
-  3)))
-(homology s2 0 4)
-|#
diff --git a/archive/Kenzo-2/Kenzo-2-Acl8/effective-homology.cl b/archive/Kenzo-2/Kenzo-2-Acl8/effective-homology.cl
deleted file mode 100644
index f491264..0000000
--- a/archive/Kenzo-2/Kenzo-2-Acl8/effective-homology.cl
+++ /dev/null
@@ -1,539 +0,0 @@
-;;;  EFFECTIVE-HOMOLOGY  EFFECTIVE-HOMOLOGY  EFFECTIVE-HOMOLOGY
-;;;  EFFECTIVE-HOMOLOGY  EFFECTIVE-HOMOLOGY  EFFECTIVE-HOMOLOGY
-;;;  EFFECTIVE-HOMOLOGY  EFFECTIVE-HOMOLOGY  EFFECTIVE-HOMOLOGY
-
-(IN-PACKAGE "CAT")
-
-(PROVIDE "effective-homology")
-
-;;;
-;;;  REDUCTIONS
-;;;
-
-(DEFMETHOD PRINT-OBJECT ((rdct reduction) (stream stream))
- (the reduction
-   (progn
-      (format stream "[K~D Reduction K~D => K~D]"
-	      (idnm rdct) (idnm (tcc rdct)) (idnm (bcc rdct)))
-      rdct)))
-
-(DEFUN REDUCTION (&rest rest &key dfnt &allow-other-keys)
-  (declare (type list dfnt))
-  (already reduction dfnt)
-  (the reduction
-    (apply #'make-instance 'reduction rest)))
-
-(DEFMETHOD SHARED-INITIALIZE
-    ((rdct reduction) slot-names &key f g h)
-  (declare
-   (type (or (eql t) list) slot-names)
-   (type morphism f g h))
-  (call-next-method)
-  (when-slot f
-             (with-slots (tcc bcc (fs f) (gs g) (hs h) dfnt) rdct
-               (declare
-                (type morphism fs gs hs)
-                (type list dfnt))
-               (when f
-                 (setf fs f tcc (sorc f) bcc (trgt f)))
-               (when g
-                 (setf gs g tcc (trgt g) bcc (sorc g)))
-               (when h
-                 (setf hs h tcc (sorc h)))
-               (when (and f g)
-                 (unless (eq (grmd (sorc f)) (grmd (trgt g)))
-                   (error "In REDUCTION ~S, (sorc f) <> (trgt g)." rdct))
-                 (unless (eq (grmd (trgt f)) (grmd (sorc g)))
-                   (error "In REDUCTION ~S, (trgt f) <> (sorc g)." rdct)))
-               (when h
-                 (unless (eq (sorc h) (trgt h))
-                   (error "In REDUCTION ~S, (sorc h) <> (trgt h)." rdct)))
-               (when (and f h)
-                 (unless (eq (grmd (sorc f)) (grmd (sorc h)))
-                   (error "In REDUCTION ~S, (sorc f) <> (sorc h)." rdct)))
-               (when (and g h)
-                 (unless (eq (grmd (trgt g)) (grmd (sorc h)))
-                   (error "In REDUCTION ~S, (trgt g) <> (sorc h)." rdct)))
-               (unless dfnt
-                 (setf dfnt `(reduction ,f ,g ,h)))))
-  rdct)
-
-(DEFUN TRIVIAL-RDCT (chcm)
-  (declare (type chain-complex chcm))
-   (reduction
-    :f (idnt-mrph chcm)
-    :g (idnt-mrph chcm)
-    :h (zero-mrph chcm chcm +1) 
-    :dfnt `(trivial-rdct ,chcm)))
-
-;;;
-;;;  EQUIVALENCES
-;;;
-
-(DEFUN EQUIVALENCE (&rest rest &key dfnt &allow-other-keys)
-  (declare (type list dfnt))
-  (already equivalence dfnt)
-  (the equivalence
-    (apply #'make-instance 'equivalence rest)))
-
-(DEFMETHOD SHARED-INITIALIZE ((eqvl equivalence) slot-names &key lrdct rrdct)
-  (declare
-   (type (or (eql t) list) slot-names)
-   (type reduction lrdct rrdct))
-  (call-next-method)
-  (when-slot lrdct
-             (with-slots ((lrdcts lrdct) (rrdcts rrdct)
-                          lbcc tcc rbcc
-                          lf lg lh rf rg rh
-                          dfnt)
-                 eqvl
-               (declare
-                (type reduction lrdcts rrdcts)
-                (type chain-complex lbcc tcc rbcc)
-                (type morphism lf lg lh rf rg rh)
-                (type list dfnt))
-               (when lrdct
-                 (setf lrdcts lrdct
-                   lf (f lrdct) lg (g lrdct) lh (h lrdct)
-                   lbcc (bcc lrdct) tcc (tcc lrdct)))
-               (when rrdct
-                 (setf rrdcts rrdct
-                   rf (f rrdct) rg (g rrdct) rh (h rrdct)
-                   tcc (tcc rrdct) rbcc (bcc rrdct)))
-               (when (and lrdct rrdct)
-                 (unless (eq (grmd (tcc lrdct)) (grmd (tcc rrdct)))
-                   (error "In EQUIVALENCE ~S, (tcc lrdct) <> (tcc rrdct)." eqvl)))
-               (unless dfnt
-                 (setf dfnt `(equivalence ,lrdct ,rrdct)))))
-  eqvl)
-
-#|
-  (cat-init)
-  (progn ;;;; reused in another test
-   (defun cdelta (dmns)
-     (chain-complex
-        :cmpr #'l-cmpr
-        :basis :locally-effective
-        :bsgn '(0)
-        :dffr-intr #'(lambda (degr gmsm)
-                        (make-cmbn
-                           :degr (1- degr)
-                           :list (do ((rslt +empty-list+
-                                           (cons (cons sign (append
-                                                               (subseq gmsm 0 nark)
-                                                               (subseq gmsm (1+ nark))))
-                                                 rslt))
-                                     (sign 1 (- sign))
-                                     (nark 0 (1+ nark)))
-                                    ((> nark degr) rslt))))                                           
-        :dffr-strt :gnrt
-        :dfnt `(locally effective version of C_* delta ,dmns)))
-   (defun make-f (tdmns bdmns)
-     (morphism
-        :sorc (cdelta tdmns) :trgt (cdelta bdmns) :degr 0
-        :intr #'(lambda (degr gmsm)
-                   (let ((pos (position-if #'(lambda (vertex) (>= vertex bdmns)) gmsm)))
-                      (if pos
-                         (if (< pos degr)
-                            (zero-cmbn degr)
-                            (cmbn degr 1 (nconc (butlast gmsm) (list bdmns))))
-                         (cmbn degr 1 gmsm))))
-        :strt :gnrt
-        :dfnt `(projection delta ,tdmns => delta ,bdmns)))
-   (defun make-g (tdmns bdmns)
-     (morphism
-        :sorc (cdelta bdmns) :trgt (cdelta tdmns) :degr 0
-        :intr #'identity
-        :strt :cmbn
-        :dfnt `(injection delta ,bdmns => delta ,tdmns)))
-   (defun make-h (tdmns bdmns)
-     (morphism
-        :sorc (cdelta tdmns) :trgt (cdelta tdmns) :degr +1
-        :intr #'(lambda (degr gmsm)
-                   (let ((pos (position-if #'(lambda (vertex) (>= vertex bdmns)) gmsm)))
-                      (if pos
-                         (if (member bdmns gmsm)
-                            (zero-cmbn (1+ degr))
-                            (cmbn (1+ degr) (-1-expt-n pos)
-                               (append (subseq gmsm 0 pos) (list bdmns) (subseq gmsm pos))))
-                         (zero-cmbn (1+ degr)))))
-        :strt :gnrt
-        :dfnt `(homotopy for delta ,tdmns => ,bdmns)))
-   (defun make-rdct (tdmns bdmns)
-       (setf rdct (reduction
-                    :f (make-f tdmns bdmns)
-                    :g (make-g tdmns bdmns)
-                    :h (make-h tdmns bdmns)
-                    :dfnt `(reduction delta ,tdmns ,bdmns)))))
-  (setf rdct (make-rdct 6 3))
-  (setf f (f rdct) g (g rdct) h (h rdct)
-        tcc (tcc rdct) bcc (bcc rdct))
-  (setf dh (cmps (dffr tcc) h))
-  (setf hd (cmps h (dffr tcc)))
-  (setf gf (cmps g f))
-  (setf id-gf-dh-hd (i-sbtr (idnt-mrph tcc) gf dh hd))
-  (setf c (cmbn 2 1 '(0 1 2) 10 '(1 2 3) 100 '(1 2 4) 1000 '(2 3 4)))
-  (cmbn-? id-gf-dh-hd c)
-|#                                   
-
-(DEFMETHOD PRINT-OBJECT ((eqvl equivalence) (stream stream))
- (the equivalence
-   (progn
-      (format stream "[K~D Equivalence K~D <= K~D => K~D]"
-	      (idnm eqvl)
-	      (idnm (lbcc eqvl)) (idnm (tcc eqvl)) (idnm (rbcc eqvl)))
-      eqvl)))
-
-(DEFUN TRIVIAL-EQVL (chcm)
-   (declare (type chain-complex chcm))
-   (equivalence
-    :lrdct (trivial-rdct chcm)
-    :rrdct (trivial-rdct chcm)
-    :dfnt `(trivial-eqvl ,chcm)))
-
-#|
-  (cat-init)
-  (setf cc (cdelta 5))
-  (setf eqvl (trivial-eqvl cc))
-|# 
-
-;; Functions.
-
-(DEFVAR *TDD*)
-(DEFVAR *BDD*)
-(DEFVAR *ID-FG*)
-(DEFVAR *ID-GF-DH-HD*)
-(DEFVAR *HH*)
-(DEFVAR *FH*)
-(DEFVAR *HG*)
-(DEFVAR *DF-FD*)
-(DEFVAR *DG-GD*)
-
-(DEFUN PRE-CHECK-RDCT (rdct)
-   (declare (type reduction rdct))
-   (with-slots (bcc tcc f g h) rdct
-      (declare
-         (type chain-complex bcc tcc)
-         (type morphism f g h))
-      (setf *tdd* (cmps tcc tcc)
-            *bdd* (cmps bcc bcc)
-            *df-fd* (sbtr
-                       (cmps bcc f)
-                       (cmps f tcc))
-            *dg-gd* (sbtr
-                       (cmps tcc g)
-                       (cmps g bcc))
-            *id-fg* (sbtr (idnt-mrph bcc) (cmps f g))
-            *id-gf-dh-hd* (i-sbtr (idnt-mrph tcc)
-                             (cmps g f)
-                             (cmps tcc h)
-                             (cmps h tcc))
-            *hh* (cmps h h)
-            *fh* (cmps f h)
-            *hg* (cmps h g)))
-   (done))
-
-(DEFVAR *TC*)
-(DEFVAR *BC*)
-
-(DEFUN CHECK-RDCT ()
-  (dolist (cmbn '(*tc* *bc*))
-    (declare (type symbol cmbn))
-    (format t "~%~A => ~A" cmbn (eval cmbn)))
-  (dolist (phi '(*tdd* *bdd* *df-fd* *dg-gd* *id-fg* *id-gf-dh-hd*
-		       *hh* *fh* *hg*))
-    (declare (type symbol phi))
-    (format t "~%Checking ~A = 0" phi)
-    (format t "~%Result: ")
-    (princ (cmbn-? (eval phi)
-              (if (member phi '(*bdd* *dg-gd* *id-fg* *dg-gd* *hg*))
-                 *bc* *tc*)))
-    (read-line))
-  (done))
-
-#|
-  (setf rdct (make-rdct 6 3))        ;;; defined in a previous test
-  (pre-check-rdct rdct)
-  (setf *tc* (cmbn 2 1 '(0 1 2) 10 '(1 2 3) 100 '(1 2 4) 1000 '(2 3 4)))
-  (setf *bc* (cmbn 3 4 '(0 1 2 3)))  
-  (check-rdct))
-|#                                   
-
-(DEFMETHOD CMPS ((brdct reduction) (trdct reduction) &optional dummy)
-  (declare (ignore dummy))
-  (when (eq (first (dfnt brdct)) 'trivial-rdct)
-     (return-from cmps trdct))
-  (when (eq (first (dfnt trdct)) 'trivial-rdct)
-     (return-from cmps brdct))
-  (with-slots ((tf f) (tg g) (th h)) trdct
-    (declare (type morphism tf tg th))
-  (with-slots ((bf f) (bg g) (bh h)) brdct
-    (declare (type morphism bf bg bh))
-    (reduction
-       :f (cmps bf tf)
-       :g (cmps tg bg)
-       :h (add th (i-cmps tg bh tf))
-       :dfnt `(cmps ,brdct ,trdct)))))
-
-#|
-  (setf trdct (make-rdct 6 4))
-  (setf brdct (make-rdct 4 3))
-  (setf rdct (cmps brdct trdct))
-  (pre-check-rdct rdct)
-  (setf *tcc* (cmbn 2 1 '(0 1 2) 10 '(1 2 3) 100 '(1 2 4)
-                      100 '(1 3 5) 10 '(1 4 5) 1 '(3 4 5))
-        *bcc* (cmbn 2 1 '(0 1 3)))
-  (check-rdct))
-|#
-
-;
-; BASIC PERTURBATION LEMMA.
-;
-
-(DEFMETHOD ADD ((rdct reduction) (perturbation morphism) &optional dummy)
-   (declare (type null dummy))
-   (when dummy
-      (error "Why a third argument in (ADD REDUCTION MORPHISM)?"))
-   (when (eq (grmd (tcc rdct)) (grmd (sorc perturbation)))
-      (return-from add
-         (basic-perturbation-lemma rdct perturbation)))
-   (when (eq (grmd (bcc rdct)) (grmd (sorc perturbation)))
-      (return-from add
-         (easy-perturbation-lemma rdct perturbation)))
-   (error "In (METHOD ADD REDUCTION MORPHISM),~@
-           the data do not sound like coherent."))
-
-(DEFUN BASIC-PERTURBATION-LEMMA (reduction top-perturbation)
-   (declare
-      (type reduction reduction)
-      (type morphism top-perturbation))
-   (the (values reduction morphism)
-      (with-slots ((old-tcc tcc) (old-bcc bcc)
-                   (old-f f) (old-g g) (old-h h)) reduction
-         (declare
-            (type chain-complex old-tcc old-bcc)
-            (type morphism old-f old-g old-h))
-         (when (eq (first (dfnt top-perturbation)) 'zero-mrph)
-            (return-from basic-perturbation-lemma
-               (values reduction (zero-mrph old-bcc))))
-         (when (eq (first (dfnt (h reduction))) 'zero-mrph)
-            (return-from basic-perturbation-lemma
-               (values
-                  (trivial-rdct (add old-tcc top-perturbation))
-                  (i-cmps old-f top-perturbation old-g))))      
-         (let* ((sigma (bpl-*-sigma old-h top-perturbation))
-                (new-f (cmps old-f 
-                          (sbtr (idnt-mrph old-tcc)
-                             (i-cmps
-                                top-perturbation
-                                sigma
-                                old-h))))
-                (new-g (cmps sigma old-g))
-                (new-h (cmps sigma old-h))
-                (bottom-perturbation (i-cmps
-                                        old-f
-                                        top-perturbation
-                                        new-g))
-                (new-tcc (add old-tcc top-perturbation))
-                (new-bcc (add old-bcc bottom-perturbation)))
-            (declare
-               (type chain-complex new-tcc new-bcc)
-               (type morphism sigma new-f new-g new-h bottom-perturbation))
-            (setf new-f (dstr-change-sorc-trgt new-f :new-sorc new-tcc :new-trgt new-bcc)
-                  new-g (dstr-change-sorc-trgt new-g :new-sorc new-bcc :new-trgt new-tcc)
-                  new-h (dstr-change-sorc-trgt new-h :new-sorc new-tcc :new-trgt new-tcc))
-            (values
-               (reduction :f new-f :g new-g :h new-h
-                  :dfnt `(basic-perturbation-lemma ,reduction ,top-perturbation))
-               bottom-perturbation)))))
-
-(DEFUN EASY-PERTURBATION-LEMMA (reduction bottom-perturbation)
-   (declare
-      (type reduction reduction)
-      (type morphism bottom-perturbation))
-   (the (values reduction morphism)
-      (with-slots ((old-tcc tcc) (old-bcc bcc)
-                   (old-f f) (old-g g) (old-h h)) reduction
-         (declare
-            (type chain-complex old-tcc old-bcc)
-            (type morphism old-f old-g old-h))
-         (when (eq 'zero-mrph (first (dfnt bottom-perturbation)))
-            (return-from easy-perturbation-lemma
-               (values reduction (zero-mrph old-tcc))))
-	 (when (eq 'trivial-rdct (first (dfnt reduction)))
-	    (return-from easy-perturbation-lemma
-	       (trivial-rdct (add (bcc reduction) bottom-perturbation))))
-         (let ((top-perturbation (i-cmps old-g bottom-perturbation old-f)))
-            (declare (type morphism top-perturbation))
-            (let ((new-bcc (add old-bcc bottom-perturbation))
-                  (new-tcc (add old-tcc top-perturbation)))
-               (declare (type chain-complex new-bcc new-tcc))
-               (values
-                  (reduction
-                     :f (dstr-change-sorc-trgt old-f :new-sorc new-tcc :new-trgt new-bcc)
-                     :g (dstr-change-sorc-trgt old-g :new-sorc new-bcc :new-trgt new-tcc)
-                     :h (dstr-change-sorc-trgt old-h :new-sorc new-tcc :new-trgt new-tcc)
-                     :dfnt `(easy-perturbation-lemma ,reduction ,bottom-perturbation))
-                  top-perturbation))))))
-
-(DEFUN SPECIAL-BPL (reduction top-perturbation)
-   (declare
-      (type reduction reduction)
-      (type morphism top-perturbation))
-   (when (eq (first (dfnt top-perturbation)) 'zero-mrph)
-      (return-from special-bpl reduction))
-   (the reduction
-      (with-slots ((old-tcc tcc) (old-bcc bcc)
-                   (old-f f) (old-g g) (old-h h)) reduction
-         (declare
-            (type chain-complex old-tcc old-bcc)
-            (type morphism old-f old-g old-h))
-         (let* ((sigma (bpl-*-sigma old-h top-perturbation))
-                (new-f (cmps old-f 
-                          (sbtr (idnt-mrph old-tcc)
-                             (i-cmps
-                                top-perturbation
-                                sigma
-                                old-h))))
-                (new-h (cmps sigma old-h))
-                (new-tcc (add old-tcc top-perturbation)))
-            (declare
-               (type chain-complex new-tcc)
-               (type morphism sigma new-f new-h))
-            (setf new-f (dstr-change-sorc-trgt new-f :new-sorc new-tcc)
-                  old-g (dstr-change-sorc-trgt old-g :new-trgt new-tcc)
-                  new-h (dstr-change-sorc-trgt new-h :new-sorc new-tcc :new-trgt new-tcc))
-            (reduction :f new-f :g old-g :h new-h
-               :dfnt `(special-bpl ,reduction ,top-perturbation))))))
-
-(DEFUN SPECIAL-BPL-2 (reduction top-perturbation)
-   (declare
-      (type reduction reduction)
-      (type morphism top-perturbation))
-   (the reduction
-      (with-slots ((old-tcc tcc) (old-bcc bcc)
-                   (old-f f) (old-g g) (old-h h)) reduction
-         (declare
-            (type chain-complex old-tcc old-bcc)
-            (type morphism old-f old-g old-h))
-         (when (eq (first (dfnt top-perturbation)) 'zero-mrph)
-            (return-from special-bpl-2
-               (values reduction (zero-mrph old-bcc))))
-         (when (eq (first (dfnt (h reduction))) 'zero-mrph)
-            (return-from special-bpl-2
-               (values
-                  (trivial-rdct (add old-tcc top-perturbation))
-                  (i-cmps old-f top-perturbation old-g))))      
-         (let* ((sigma (bpl-*-sigma old-h top-perturbation))
-                (new-g (cmps sigma old-g))
-                (new-h (cmps sigma old-h))
-                (new-tcc (add old-tcc top-perturbation)))
-            (declare
-               (type chain-complex new-tcc)
-               (type morphism sigma new-g new-h))
-            (setf old-f (dstr-change-sorc-trgt old-f :new-sorc new-tcc)
-		  new-g (dstr-change-sorc-trgt new-g :new-trgt new-tcc)
-                  new-h (dstr-change-sorc-trgt new-h :new-sorc new-tcc :new-trgt new-tcc))
-            (values
-               (reduction :f old-f :g new-g :h new-h
-                  :dfnt `(special-bpl-2 ,reduction ,top-perturbation)))))))
-
-(DEFUN BPL-*-sigma (homotopy perturbation)
-   (declare (type morphism homotopy perturbation))
-   (the morphism
-      (let ((cmpr (cmpr (sorc perturbation)))
-            (h-delta (cmps homotopy perturbation)))
-         (declare
-            (type cmprf cmpr)
-            (type morphism h-delta))
-         (flet
-            ((sigma-* (degr gnrt)
-                (declare
-                   (fixnum degr)
-                   (type gnrt gnrt))
-                (do ((rslt (zero-cmbn degr) (2cmbn-add cmpr rslt iterated))
-                     (iterated (term-cmbn degr 1 gnrt) (cmbn-opps (cmbn-? h-delta iterated))))
-                    ((cmbn-zero-p iterated) rslt)
-                   (declare (type cmbn rslt iterated)))))
-            (morphism
-               :sorc (sorc homotopy) :trgt (sorc homotopy) :degr 0
-               :intr #'sigma-*
-               :strt :gnrt
-               :dfnt `(bpl-*-sigma ,homotopy ,perturbation))))))
-     
-#|
-  (cat-init)
-  (setf rdct (make-rdct 6 3))
-  (setf perturb (zero-mrph (cdelta 6) (cdelta 6) -1))
-  (setf new-rdct (add rdct perturb))
-  (pre-check-rdct new-rdct)
-  (setf *tc* (cmbn 2 3 '(0 1 2))
-        *bc* (cmbn 3 4 '(0 1 2 3)))
-  (check-rdct))
-|#
-
-#|
-  (cat-init)
-  (setf rdct (make-rdct 6 3))
-  (setf perturb (opps (dffr (tcc rdct))))
-  (setf new-rdct (add rdct perturb))
-  (pre-check-rdct new-rdct)
-  (setf *tc* (cmbn 2 3 '(0 1 2))
-        *bc* (cmbn 3 4 '(0 1 2 3)))
-  (check-rdct))
-|#
-
-#|  ;; an absurd reduction ; just to test bpl-*-sigma
-  (cat-init)
-  (setf tcc (chain-complex
-               :cmpr #'l-cmpr
-               :basis :locally-effective
-               :bsgn '(0)
-               :dffr-intr #'(lambda (degr gnrt)
-                               (cmbn (1- degr) 1 gnrt))
-               :dffr-strt :gnrt
-               :dfnt '(test1)))
-  (setf rdct (trivial-rdct tcc))
-  (setf (slot-value rdct 'h)
-        (morphism
-           :sorc tcc :trgt tcc :degr +1
-           :intr #'(lambda (degr gnrt)
-                      (cmbn (1+ degr) 1 gnrt))
-           :strt :gnrt
-           :dfnt '(test2)))
-  (setf perturb
-        (morphism
-           :sorc tcc :trgt tcc :degr -1
-           :intr #'(lambda (degr gnrt)
-                      (if (zerop (first gnrt))
-                         (zero-cmbn (1- degr))   
-                         (cmbn (1- degr) 1 (list (1- (first gnrt)) (1+ (second gnrt))))))
-           :strt :gnrt
-           :dfnt '(test3)))
-  (setf new-rdct (add rdct perturb))
-  (gnrt-? (dffr (tcc new-rdct)) 3 '(3 5))
-  (gnrt-? (dffr (bcc new-rdct)) 3 '(3 5))
-|#
-
-(DEFMETHOD ADD ((eqvl equivalence) (lb-perturbation morphism) &optional dummy)
-  (declare (ignore dummy))
-  (the equivalence
-    (with-slots (lrdct rrdct) eqvl
-      (declare (type reduction lrdct rrdct))
-      (multiple-value-bind (new-lrdct top-perturbation)
-          (add lrdct lb-perturbation)
-        (declare
-         (type reduction new-lrdct)
-         (type morphism lb-perturbation))
-        (equivalence
-         :lrdct new-lrdct
-         :rrdct (add rrdct top-perturbation)
-         :dfnt `(add ,eqvl ,lb-perturbation))))))
-
-#|
-(cat-init)
-(setf eqvl (trivial-eqvl (cdelta 4)))
-(add (lrdct eqvl) (opps (dffr (cdelta 4))))
-(setf eqvl (add eqvl (opps (dffr (cdelta 4)))))
-(gnrt-? (dffr (rbcc eqvl)) 3 '(0 1 2 3)))
-|#
diff --git a/archive/Kenzo-2/Kenzo-2-Acl8/eilenberg-zilber.cl b/archive/Kenzo-2/Kenzo-2-Acl8/eilenberg-zilber.cl
deleted file mode 100644
index 39195fa..0000000
--- a/archive/Kenzo-2/Kenzo-2-Acl8/eilenberg-zilber.cl
+++ /dev/null
@@ -1,479 +0,0 @@
-;;;  EILENBERG-ZILBER  EILENBERG-ZILBER  EILENBERG-ZILBER
-;;;  EILENBERG-ZILBER  EILENBERG-ZILBER  EILENBERG-ZILBER
-;;;  EILENBERG-ZILBER  EILENBERG-ZILBER  EILENBERG-ZILBER
-
-(IN-PACKAGE "CAT")
-
-(PROVIDE "eilenberg-zilber")
-
-(DEFUN SHUFFLE-SIGN (dgop)
-   (declare (fixnum dgop))
-   (the fixnum
-      (do ((rslt +1)
-           (bit-position (- (integer-length dgop) 2) (1- bit-position))
-           (factor -1))
-          ((minusp bit-position) rslt)
-         (declare (fixnum rslt bit-position factor))
-         (if (logbitp bit-position dgop)
-            (setf factor (- factor))
-            (setf rslt (* rslt factor))))))
-
-#|
-  (dotimes (i 30)
-     (format t "~%~A => ~@D" (hyphenize-list (dlop-int-ext i)) (shuffle-sign i)))
-|#       
-
-(DEFUN INTR-EML (cmbn)
-   (declare (type cmbn cmbn))
-   (when (cmbn-zero-p cmbn)
-      (return-from intr-eml cmbn))
-   (the cmbn
-      (with-cmbn (degr list) cmbn
-         (let* ((limits (make-array (+ degr 2)))
-                (rslt (list nil))
-                (rslt-mark rslt)
-                (mask (mask degr)))
-            (declare
-               (simple-vector limits)
-               (list rslt rslt-mark)
-               (fixnum mask))
-            (do ((mark list (member i mark
-                               :test #'<
-                               :key #'(lambda (term)
-                                         (declare (type term term))
-                                         (degr1 (gnrt term)))))
-                 (i 0 (1+ i)))
-                ((> i degr) (setf (svref limits i) nil))
-               (declare
-                  (list mark)
-                  (fixnum i))
-               (setf (svref limits i) mark))
-            (dotimes (dgop1 (1+ mask))
-               (declare (fixnum dgop1))
-               (let* ((i (- degr (logcount dgop1)))
-                      (dgop2 (- mask dgop1))
-                      (sign (shuffle-sign dgop2)))
-                  (declare (fixnum i dgop2 sign))
-                  (do ((mark (svref limits i) (cdr mark))
-                       (stop (svref limits (1+ i))))
-                      ((eq mark stop))
-                     (declare (list mark stop))
-                     (with--term (cffc tnpr) mark
-                        (setf rslt-mark
-                              (setf (cdr rslt-mark)
-                                    (list (term
-                                             (* sign cffc)
-                                             (crpr
-                                                dgop1 (gnrt1 tnpr)
-                                                dgop2 (gnrt2 tnpr))))))))))
-            (make-cmbn
-               :degr degr
-               :list (rest rslt))))))
-
-#|
-  (intr-eml (cmbn 3 1 (tnpr 0 'a 3 'b) 2 (tnpr 2 'a 1 'b) 3 (tnpr 2 'aa 1 'bb) 4 (tnpr 3 'a 0 'b)))
-  (intr-eml (cmbn 3 1 (tnpr 1 'c 2 'd) 10 (tnpr 2 'a 1 'b)))
-  (intr-eml (cmbn 3 10 (tnpr 1 'c 2 'd) 1 (tnpr 2 'a 1 'b) 100 (tnpr 2 'aa 1 'bb)))
-  (intr-eml (cmbn 3 10 (tnpr 1 'c 2 'd) 100 (tnpr 1 'cc 2 'dd) 1 (tnpr 2 'a 1 'b)))
-|#
-                                                    
-(DEFUN EML (smst1 smst2)
-   (morphism
-      :sorc (tnsr-prdc smst1 smst2)
-      :trgt (crts-prdc smst1 smst2)
-      :degr 0
-      :intr #'intr-eml
-      :strt :cmbn
-      :dfnt `(eml ,smst1 ,smst2)))
-
-#|
-  (cat-init)
-  (setf d (delta-infinity))
-  (setf eml (eml d d))
-  (? eml (cmbn 3 1 (tnpr 0 1 3 30) 10 (tnpr 1 3 2 28) 100 (tnpr 2 7 1 24) 1000 (tnpr 3 15 0 16)))
-|#
-
-(DEFUN INTR-PHI (smst1 smst2
-                   &aux (crts-prdc (crts-prdc smst1 smst2))
-                        (cmpr (cmpr crts-prdc))
-                        (face1 (face smst1))
-                        (face2 (face smst2)))
-  (declare
-     (type simplicial-set smst1 smst2 crts-prdc)
-     (type cmprf cmpr)
-     (type face face1 face2))
-   (flet ((rslt (cmbn)
-             (declare (type cmbn cmbn))
-             (when (cmbn-zero-p cmbn)
-                (return-from rslt (zero-cmbn (1+ (cmbn-degr cmbn)))))
-             (the cmbn
-                (let* ((n (cmbn-degr cmbn))
-                       (n+1 (1+ n))
-                       (array-pq (make-array (list (1+ n+1) (1+ n+1)))))
-                   (declare
-                      (fixnum n n+1)
-                      (simple-array array-pq))
-                   (do ((i 1 (1+ i)))
-                       ((> i n+1))
-                      (declare (fixnum i))
-                      (do ((p i (1+ p))
-                           (q n+1 (1- q)))
-                          ((> p n+1))
-                         (declare (fixnum p q))
-                         (setf (aref array-pq p q) (zero-cmbn i))))
-                   (dolist (term (cmbn-list cmbn))
-                      (declare (type term term))
-                      (with-term (cffc crpr) term
-                         (let ((absm1 (absm1 crpr))
-                               (absm2 (absm2 crpr)))
-                            (declare (type absm absm1 absm2))
-                            (do ((n-alpha n (1- n-alpha))
-                                 (left-d absm1 (a-face4 face1 n-alpha n-alpha left-d)))
-                                ((zerop n-alpha))
-                               (declare
-                                  (fixnum n-alpha)
-                                  (type absm left-d))
-                               (do ((beta 0 (1+ beta))
-                                    (i n-alpha (1- i))  ;; pseudo-degree
-                                    (sign (-1-expt-n n-alpha) (- sign))
-                                    (right-d absm2
-                                       (a-face4 face2 (1- i) dim-right-d right-d))
-                                    (dim-right-d n (1- dim-right-d)))
-                                   ((= beta n-alpha))
-                                  (declare
-                                     (fixnum beta i sign dim-right-d)
-                                     (type absm right-d))
-                                  (let ((absm1 (1dgnr (1- i) left-d)))
-                                     (declare (type absm absm1))
-                                     (with-absm (dgop1 gmsm1) absm1
-                                     (with-absm (dgop2 gmsm2) right-d
-                                        (or (> (integer-length dgop1) i)
-                                            (> (integer-length dgop2) i)
-                                            (plusp (logand dgop1 dgop2))
-                                            (dstr-add-term-to-cmbn
-                                               cmpr
-                                               (* sign cffc)
-                                               (crpr dgop1 gmsm1 dgop2 gmsm2)
-                                               (aref array-pq (1+ n-alpha) (- n beta))))))))))))
-;;                 array-pq)))  ;; in case of debu gging
-                (intr-phi-2 array-pq cmpr)))))
-      (the intr #'rslt)))
-
-#|
-  (setf d (delta-infinity))
-  (setf rslt (intr-phi d d))
-  (funcall rslt (cmbn 3 1 (crpr 0 15 0 15)))
-|#
-
-#|
-
-(DEFUN INTR-PHI-22 (array-pq cmpr)
-   (declare
-      (type (simple-array cmbn (* *)) array-pq)
-      (type cmprf cmpr))
-;   (format t "  -22-  ")
-   (the cmbn
-      (let* ((n+1 (1- (array-dimension array-pq 0)))
-             (n (1- n+1)))
-         (declare (fixnum n n+1))
-         (flet ((step-i (i)
-                   (declare (fixnum i))
-                 (do ((p (1+ i) (1+ p))
-                      (p-1 i p)
-                      (q n+1 q-1)
-                      (q-1 n (1- q-1))
-                      (sign t (not sign))
-                      (ibit (2-exp i)))
-                     ((> p n+1))
-                    (declare
-                       (fixnum p p-1 q q-1 ibit)
-                       (type boolean sign))
-                    (setf (aref array-pq p q)
-                          (2cmbn-add cmpr
-                             (aref array-pq p q)
-                             (make-cmbn
-                                :degr (1+ i)
-                                :list (nconc
-                                         (mapcar
-                                            #'(lambda (term)
-                                                 (declare (type term term))
-                                                 (with-term (cffc crpr) term
-                                                    (with-crpr (dgop1 gmsm1 dgop2 gmsm2) crpr
-                                                       (term cffc (crpr
-                                                                     dgop1 gmsm1
-                                                                     (+ ibit dgop2) gmsm2)))))
-                                            (cmbn-list (aref array-pq p q-1)))
-                                         (let ((list (cmbn-list (aref array-pq p-1 q))))
-                                            (declare (list lst))
-                                            (unless sign
-                                               (dolist (term list)
-                                                  (declare (type term term))
-                                                  (setf (cffc term) (- (cffc term)))))
-                                            (dolist (term list)
-                                               (declare (type term term))
-                                               (incf (dgop1 (gnrt term)) ibit))
-                                           list))))))))
-            (do ((i 1 (1+ i)))
-                ((= i n+1))
-               (declare (type fixnum i))
-               (step-i i))
-            (aref array-pq n+1 n+1)))))
-|#
-
-(DEFUN INTR-PHI-2 (array-pq cmpr)
-   (declare
-      (type (simple-array cmbn (* *)) array-pq)
-      (type cmprf cmpr))
-;   (format t "  -2-  ")
-   (the cmbn
-      (let* ((n+1 (1- (array-dimension array-pq 0)))
-             (n (1- n+1))
-             (cmbn-list +empty-list+))
-         (declare
-            (fixnum n n+1)
-            (list cmbn-list))
-         (do ((i 1 (1+ i))
-              (cmbn-i (list nil) (list nil))
-              (mask (mask n) (ash mask -1)))
-             ((= i n+1))
-            (declare
-               (fixnum i mask)
-               (list cmbn-i))
-            (let ((cmbn-i-tail cmbn-i))
-               (declare (list cmbn-i-tail))
-               (do ((dgop1 0 (1+ dgop1)))
-                   ((> dgop1 mask)
-                    (push (make-cmbn
-                             :degr n+1
-                             :list (rest cmbn-i)) 
-                       cmbn-list))
-                  (declare (fixnum dgop1))
-                  (let ((p (- n+1 (logcount dgop1)))
-                        (dgop2 (- mask dgop1)))
-                     (declare (fixnum p dgop2))
-                     (unless (= p i)
-                        (let ((q (- (+ n+1 i) p))
-                              (sign (shuffle-sign dgop2))
-                              (dgop1-ashed (ash dgop1 i))
-                              (dgop2-ashed (ash dgop2 i)))
-                           (declare (fixnum q sign dgop1-ashed dgop2-ashed))
-                           (dolist (term (cmbn-list (aref array-pq p q)))
-                              (declare (type term term))
-                              (with-term (cffc crpr) term
-                                 (with-crpr (dgop1 gmsm1 dgop2 gmsm2) crpr
-                                    (setf cmbn-i-tail
-                                          (setf (cdr cmbn-i-tail)
-                                                (list (term (* sign cffc)
-                                                         (crpr
-                                                            (+ dgop1 dgop1-ashed) gmsm1
-                                                            (+ dgop2 dgop2-ashed) 
-                                                            gmsm2))))))))))))))
-         (if cmbn-list
-            (apply #'ncmbn-add cmpr cmbn-list)
-            (zero-cmbn n+1)))))
-
-#|
-  (setf d (delta-infinity))
-  (setf rslt (intr-phi d d))
-  (funcall rslt (cmbn 3 1 (crpr 0 15 0 15)))
-  (funcall rslt (cmbn 2 1 (crpr 0 7 0 7)))
-  (funcall rslt (cmbn 1 1 (crpr 0 3 0 3)))
-  (funcall rslt (cmbn 0 1 (crpr 0 1 0 1)))
-|#
-
-(DEFUN PHI (smst1 smst2)
-   (declare (type simplicial-set smst1 smst2))
-   (the morphism
-      (morphism
-         :sorc (crts-prdc smst1 smst2)
-         :trgt (crts-prdc smst1 smst2)
-         :degr +1
-         :intr (intr-phi smst1 smst2)
-         :strt :cmbn
-         :dfnt `(phi ,smst1 ,smst2))))
-
-#|
-  (setf phi (phi (delta-infinity) (delta-infinity)))
-  (? phi 3 (crpr 0 15 0 15))
-|#
-
-#|  ;; Comparison with EAT.
-    ;; In Kenzo.
-  (cat-init)
-  (setf s (sphere 5))
-  (setf p (crts-prdc s s))
-  (setf b (basis p 8))
-  (setf c (make-cmbn :degr 8
-             :list (mapcar #'(lambda (item)
-                                (term (1+ (random 5)) item))
-                      b)))
-  (setf phi (phi s s))
-  (time (? phi c)))
-|#
-
-#|  ;; in EAT
-  (setf s (sphere 5))
-  (setf p (cpr-2ss s s))
-  (setf b (sbs p 8))
-  (setf c (make-cmb :dgr 8
-             :lst (mapcar #'(lambda (item)
-                               (mnm (1+ (random 5)) item))
-                     b)))
-  (setf phi (phi s s))
-  (time (??? phi c))
-|#
-
-(DEFUN INTR-AW (face1 face2)
-   (declare (type face face1 face2))
-   (flet ((rslt (dmns crpr)
-           (declare
-              (fixnum dmns)
-              (type crpr crpr))
-           (the cmbn
-              (let ((absm1 (absm1 crpr))
-                    (absm2 (absm2 crpr))
-                    (rslt +empty-list+)
-                    (del-0-s +empty-list+))
-                 (declare
-                    (type absm absm1 absm2)
-                    (list rslt del-0-s))
-                 (do ((face absm2 (a-face4 face2 0 dmns2 face))
-                      (dmns2 dmns (1- dmns2)))
-                     ((zerop dmns2) (push face del-0-s))
-                    (declare
-                       (type absm face)
-                       (fixnum dmns))
-                    (push face del-0-s))
-                 (do ((face absm1 (a-face4 face1 dmns1 dmns1 face))
-                      (dmns1 dmns (1- dmns1))
-                      (dmns2 0 (1+ dmns2))
-                      (mark del-0-s (cdr mark)))
-                     ((zerop dmns1)
-                      (unless (degenerate-p absm2)
-                         (push
-                            (term 1
-                               (tnpr 0 (gmsm face) dmns (gmsm absm2)))
-                            rslt)))
-                    (declare
-                       (type absm face)
-                       (fixnum dmns1 dmns2)
-                       (list mark))
-                    (unless (or (degenerate-p face)
-                                (degenerate-p (car mark)))
-                       (push
-                          (term 1
-                             (tnpr dmns1 (gmsm face) dmns2 (gmsm (car mark))))
-                          rslt)))
-                 (make-cmbn
-                    :degr dmns
-                    :list rslt)))))
-      (the intr #'rslt)))
-
-#|
-  (setf r (intr-aw #'delta-face #'delta-face))
-  (funcall r 3 (crpr 0 15 0 15))
-  (setf s (sphere 3))
-  (setf f (face s))
-  (setf r (intr-aw f f))
-  (funcall r 3 (crpr 0 's3 0 's3))
-|#
-
-(DEFUN AW (smst1 smst2
-             &aux (crts-prdc (crts-prdc smst1 smst2))
-                  (tnsr-prdc (tnsr-prdc smst1 smst2))
-                  (face1 (face smst1))
-                  (face2 (face smst2)))
-   (declare
-      (type simplicial-set smst1 smst2)
-      (type face face1 face2))
-   (the morphism
-      (morphism
-         :sorc crts-prdc
-         :trgt tnsr-prdc
-         :degr 0
-         :intr (intr-aw face1 face2)
-         :strt :gnrt
-         :dfnt `(aw ,smst1 ,smst2))))
-
-#|
-  (setf aw (aw (delta-infinity) (delta-infinity)))
-  (? aw (cmbn 3 1 (crpr 0 15 0 30) -1 (crpr 0 23 0 29)))
-|#
-
-(DEFUN EZ (smst1 smst2)
-   (declare (type simplicial-set smst1 smst2))
-   (the reduction
-      (reduction
-         :f (aw smst1 smst2)
-         :g (eml smst1 smst2)
-         :h (phi smst1 smst2)
-         :dfnt `(eilenberg-zilber ,smst1 ,smst2))))
-
-#|
-(setf ez (ez (delta-infinity) (delta-infinity)))
-(setf *bc* (cmbn 3 1 (tnpr 0 1 3 30)
-             10 (tnpr 1 96 2 896)
-             100 (tnpr 2 7168 1 3)
-             1000 (tnpr 3 15 0 4096)))
-(setf *tc* (cmbn 3 1 (crpr 0 15 0 480)
-             100 (crpr 0 15 5 96)
-             10 (crpr 6 3 0 480)
-             1000 (crpr 6 3 1 224)))
-(pre-check-rdct ez)
-(check-rdct)
-|#
-
-
-#|
-  ;; Comparison EAT.
-  ;; In Kenzo.
-  (cat-init)
-  (setf s (sphere 5))
-  (setf ez (ez s s))
-  (setf b (basis (tcc ez) 8))
-  (setf c (make-cmbn :degr 8
-             :list (mapcar #'(lambda (item)
-                                (term (1+ (random 5)) item))
-                      b)))
-  (pre-check-rdct ez)
-  (setf +too-much-time+ -1)
-  (time (? *id-gf-dh-hd* c))
-  (time (? *id-gf-dh-hd* c))
-|#
-
-#|
-  ;; in EAT
-  (setf s (sphere 5))
-  (setf ez (ez s s))
-  (setf b (cbs (rdc-tcc ez) 8))
-  (setf c (make-cmb :dgr 8
-           :lst (mapcar #'(lambda (item)
-                             (mnm (1+ (random 5)) item))
-                   b)))
-  (verif-rdc ez)
-  (time (??? *id-gf-dh-hd* c))
-  (time (??? *id-gf-dh-hd* c))
-|#
-
-(DEFUN LEFT-CRTS-PRDC-EFHM (smst1 smst2)
-  (declare (type simplicial-set smst1 smst2))
-  (the equivalence
-    (equivalence
-     :lrdct (trivial-rdct (crts-prdc smst1 smst2))
-     :rrdct (ez smst1 smst2)
-     :dfnt `(left-crts-prdc-efhm ,smst1 ,smst2))))
-
-(DEFMETHOD SEARCH-EFHM (smst (dfnt (eql 'crts-prdc)))
-  (declare (type simplicial-set smst))
-  (the equivalence
-    (cmps
-      (left-crts-prdc-efhm (second (dfnt smst)) (third (dfnt smst)))
-      (tnsr-prdc (efhm (second (dfnt smst)))
-		 (efhm (third (dfnt smst)))))))
-
-#|
-  (cat-init)
-  (setf k (k-z 2))
-  (setf k2 (crts-prdc k k))
-  (homology k2 0 10)
-|#
\ No newline at end of file
diff --git a/archive/Kenzo-2/Kenzo-2-Acl8/fibrations.cl b/archive/Kenzo-2/Kenzo-2-Acl8/fibrations.cl
deleted file mode 100644
index 0f69835..0000000
--- a/archive/Kenzo-2/Kenzo-2-Acl8/fibrations.cl
+++ /dev/null
@@ -1,186 +0,0 @@
-;;;  FIBRATIONS  FIBRATIONS  FIBRATIONS  FIBRATIONS  FIBRATIONS
-;;;  FIBRATIONS  FIBRATIONS  FIBRATIONS  FIBRATIONS  FIBRATIONS
-;;;  FIBRATIONS  FIBRATIONS  FIBRATIONS  FIBRATIONS  FIBRATIONS
-
-(IN-PACKAGE "CAT")
-
-(PROVIDE "fibrations")
-
-(DEFUN FIBRATION-TOTAL-FACE (fibration
-		     &aux (base (sorc fibration))
-		          (bface (face base))
-		          (fibr (trgt fibration))
-			  (fbsgn (bsgn fibr))
-			  (fface (face fibr))
-			  (grml (grml fibr))
-			  (grml-sintr (sintr grml))
-			  (totl (crts-prdc base fibr))
-			  (uface (face totl))
-			  (sintr-twist (sintr fibration)))			  
-  (declare
-     (type fibration fibration)
-     (type simplicial-mrph grml)
-     (type simplicial-set base totl)
-     (type simplicial-group fibr)
-     (type gmsm fbsgn)
-     (type face bface fface uface)
-     (type sintr grml-sintr sintr-twist))
-  (flet ((rslt (indx dmns crpr)
-	    (declare
-	       (fixnum indx dmns)
-	       (type crpr crpr))
-	    (the absm
-	       (progn
-		 (when (< indx dmns)
-		    (return-from rslt
-		       (funcall uface indx dmns crpr)))
-		 (with-crpr (b-absm f-absm) crpr
-		    (let ((deln-b
-			   (a-face4 bface dmns dmns
-				     b-absm))
-			  (deln-f
-			   (a-face4 fface dmns dmns
-				     f-absm))
-			  (tau-b
-			   (tw-a-sintr3 sintr-twist dmns
-					b-absm fbsgn)))
-		      (declare
-		         ( type absm deln-b deln-f tau-b))
-		      (2absm-acrpr
-		        deln-b
-		        (a-grml4 grml-sintr (1- dmns)
-				 tau-b deln-f))))))))
-	(the face #'rslt)))
-
-#|
-  (cat-init)
-  (setf h (hopf 1))
-  (setf sf (serre-face h))
-  (funcall sf 0 2 (crpr 0 's2 0 '(2 4)))
-  (funcall sf 1 2 (crpr 0 's2 0 '(2 4)))
-  (funcall sf 2 2 (crpr 0 's2 0 '(2 4)))
-  (funcall sf 3 3 (crpr 1 's2 2 '(2 4)))
-|#
-
-(DEFUN FIBRATION-TOTAL (fibration
-                        &aux
-                        (base (sorc fibration))
-                        (fibre (trgt fibration))
-                        (untwisted-prdc
-                         (crts-prdc base fibre)))
-  (declare (type fibration fibration))
-  (the simplicial-set
-    (let ((rslt (simplicial-set
-                 :cmpr (cmpr untwisted-prdc)
-                 :basis (basis untwisted-prdc)
-                 :bsgn (bsgn untwisted-prdc)
-                 :face (fibration-total-face fibration)
-                 :dfnt `(fibration-total ,fibration))))
-      (declare (type simplicial-set rslt))
-      (setf (slot-value rslt 'grmd) untwisted-prdc) 
-      (when (and (typep base 'kan)
-                 (typep fibre 'kan))
-        (change-class rslt 'kan)
-        (setf (slot-value rslt 'kfll)
-          (fibration-kfll fibration)))
-      rslt)))
-
-#|
-  (cat-init)
-  (setf s2 (sphere 2))
-  (setf k (k-z-1))
-  (setf tw (simplicial-mrph
-             :sorc s2
-	     :trgt k
-	     :degr -1
-	     :sintr #'(lambda (dmns gmsm)
-			(absm 0 (list 1)))
-	     :dfnt '(s2-tw-kz1)))
-  (setf e (fibration-total tw))
-  (homology e 2)
-  (homology e 0 8)
-  (cat-init)
-  (setf s2 (sphere 2))
-  (setf k (k-z2-1))
-  (setf tw (simplicial-mrph
-             :sorc s2
-	     :trgt k
-	     :degr -1
-	     :sintr #'(lambda (dmns gmsm)
-			(absm 0 1))
-	     :dfnt '(s2-tw-kz2)))
-  (setf e (fibration-total tw))
-  (homology e 2)
-  (homology e 0 8)
-|#
-		 
-(DEFUN FIBRATION-KFLL (twist
-		        &aux (sintr-twist (sintr twist))
-			     (base (sorc twist))
-			     (fibre (trgt twist))
-			     (fbsgn (bsgn fibre))
-			     (bkfll (kfll base))
-			     (fkfll (kfll fibre))
-			     (grml-sintr (sintr (grml fibre)))
-			     (grin-sintr (sintr (grin fibre))))
-  (declare
-     (type fibration twist)
-     (type kan base fibre)
-     (type gmsm fbsgn)
-     (type kfll bkfll fkfll)
-     (type sintr grml-sintr grin-sintr))
-  (flet ((rslt (indx dmns hat)
-	   (declare
-	      (fixnum indx dmns)
-	      (list hat))
-	   (let (bhat fhat)
-	     (declare (type list bhat fhat))
-	     (do ((mark hat (cdr mark)))
-		 ((endp mark))
-		(declare (list mark))
-		(let ((absm (car mark)))
-		  (declare (type absm absm))
-		  (with-absm (dgop crpr) absm
-		  (with-crpr (dgop1 gmsm1 dgop2 gmsm2) crpr
-		     (push (absm (dgop*dgop dgop dgop1) gmsm1) bhat)
-		     (push (absm (dgop*dgop dgop dgop2) gmsm2) fhat)))))
-	     (setf bhat (nreverse bhat))
-	     (let ((bkfll (funcall bkfll indx dmns bhat)))
-	       (declare (type absm bkfll))
-	       (when (< indx dmns)
-		 (setf (first fhat)
-		       (a-grml4 grml-sintr (1- dmns)
-				(a-grin4 grin-sintr (1- dmns)
-					 (tw-a-sintr3 sintr-twist dmns bkfll fbsgn))
-				(first fhat))))
-	       (setf fhat (nreverse fhat))
-	       (let ((fkfll (funcall fkfll indx dmns fhat)))
-		 (declare (type absm fkfll))
-		 (2absm-acrpr bkfll fkfll))))))
-	(the kfll #'rslt)))
-
-#|
-  (cat-init)
-  (load "r-proj-space")
-  (setf tw (kdivide-z2-twist opr opr-chml-clss))
-  (setf pr-4 (fibration-total tw))
-  (setf absm (absm 0 (crpr 0 (loop3 0 5 2) 0 4)))
-  (setf hat (mapcar #'(lambda (i) (face pr-4 i 4 absm))
-                    (<a-b> 0 4)))
-  (dotimes (i 5)
-    (print (kfll pr-4 i 4 (remove (nth i hat) hat)))
-    (check-kan pr-4 i 4 (remove (nth i hat) hat)))
-|#
-
-#|
-  (cat-init)
-  (setf os3-fibration os3-fibration)
-  (setf total (fibration-total os3-fibration))
-  (setf absm (absm 1 (crpr 0 (loop3 1 's3 1 2 's3 -2)
-				   0 '(-2 1 1))))
-  (setf hat (mapcar #'(lambda (i) (face total i 4 absm))
-                    '(0 1 2 3 4)))
-  (dotimes (i 5)
-    (print (kfll total i 4 (remove (nth i hat) hat)))
-    (check-kan total i 4 (remove (nth i hat) hat)))
-|#
\ No newline at end of file
diff --git a/archive/Kenzo-2/Kenzo-2-Acl8/file-list.cl b/archive/Kenzo-2/Kenzo-2-Acl8/file-list.cl
deleted file mode 100644
index e0c0e00..0000000
--- a/archive/Kenzo-2/Kenzo-2-Acl8/file-list.cl
+++ /dev/null
@@ -1,114 +0,0 @@
-;;;  FILES  FILES  FILES  FILES  FILES  FILES  FILES  FILES  FILES  FILES
-;;;  FILES  FILES  FILES  FILES  FILES  FILES  FILES  FILES  FILES  FILES
-;;;  FILES  FILES  FILES  FILES  FILES  FILES  FILES  FILES  FILES  FILES
-
-(IN-PACKAGE "COMMON-LISP-USER")
-
-(DEFPACKAGE "CAT"
-  (:use "COMMON-LISP"))
-
-(IN-PACKAGE "CAT")
-
-(USE-PACKAGE "CAT" "COMMON-LISP-USER")
-
-(PROCLAIM '(OPTIMIZE (speed 3) (safety 1) (space 0) (debug 0)))
-
-(EXPORT '(+file-list+ load-sfiles compile-files load-cfiles cat-files))
-
-(DEFCONSTANT +FILE-LIST+
-   '("classes"
-     "macros"
-     "various"
-     "combinations"
-     "chain-complexes"
-     "chcm-elementary-op"
-     "effective-homology"
-     "homology-groups"
-     "searching-homology"
-     "cones"
-     "tensor-products"
-     "coalgebras"
-     "cobar"
-     "algebras"
-     "bar"
-     "simplicial-sets"
-     "simplicial-mrphs"
-     "delta"
-     "special-smsts"
-     "suspensions"
-     "disk-pasting"
-     "cartesian-products"
-     "eilenberg-zilber"
-     "kan"
-     "simplicial-groups"
-     "fibrations"
-     "loop-spaces"
-     "ls-twisted-products"
-     "lp-space-efhm"
-     "classifying-spaces"
-     "k-pi-n"
-     "serre"
-     "cs-twisted-products"
-     "cl-space-efhm"
-     "whitehead"
-     "smith"
-     ))
-
-(DO ((mark +file-list+ (cdr mark))
-     (i 1 (1+ i)))
-    ((endp mark) (terpri))
-   (format t "~% FILE ~2D: ~A" i (car mark)))
-
-(DEFCONSTANT +SOURCE-EXTENSION+ ".cl")
-
-(DEFCONSTANT +COMPILED-EXTENSION+ ".fasl")
-
-(DEFUN LOAD-SFILES ()
-  (mapc #'(lambda (file-name)
-            (load (concatenate 'string file-name +source-extension+)))
-    +file-list+)
-  (princ "--- done ---")
-  (values ))
-
-(DEFVAR *CMBN-CONTROL*)
-(SETF *CMBN-CONTROL* T)
-
-(DEFUN COMPILE-FILES ()
-  (format t
-#-ALLEGRO-V8.0
-    "~%SPEED-PARAMETER = ~D~@
-     ~% *CMBN-CONTROL* = ~A~2%"
-#+ALLEGRO-V8.0
-    "~% *CMBN-CONTROL* = ~A~2%"
-#-ALLEGRO-V8.0  excl::.speed. 
-    *cmbn-control*)
-  (mapc #'(lambda (file-name)
-            (compile-file (concatenate 'string file-name +source-extension+))
-            (load (concatenate 'string file-name +compiled-extension+)))
-    +file-list+)
-  (princ "--- done ---")
-  (values))
-
-(DEFUN LOAD-CFILES ()
-  (mapc #'(lambda (file-name)
-            (load (concatenate 'string file-name +compiled-extension+)))
-    +file-list+)
-  (princ "--- done ---")
-  (values ))
-
-(DEFUN CAT-FILES (file1)
-  (declare (type string file1))
-  (setf file1 (concatenate 'string file1 +source-extension+))
-  (when (probe-file file1)
-    (delete-file file1))
-  (with-open-file (output file1 :direction :output)
-    (dolist (file2 +file-list+)
-      (declare (type string file2))
-      (setf file2 (concatenate 'string file2 +source-extension+))
-      (with-open-file (input file2 :direction :input)
-        (do ((line (read-line input)
-                   (read-line input nil :eof)))
-            ((eq line :eof))
-          (declare (type (or string (eql :eof)) line))
-          (princ line output)
-          (terpri output))))))
\ No newline at end of file
diff --git a/archive/Kenzo-2/Kenzo-2-Acl8/homology-groups.cl b/archive/Kenzo-2/Kenzo-2-Acl8/homology-groups.cl
deleted file mode 100644
index acd8db9..0000000
--- a/archive/Kenzo-2/Kenzo-2-Acl8/homology-groups.cl
+++ /dev/null
@@ -1,650 +0,0 @@
-;;  HOMOLOGY-GROUPS  HOMOLOGY-GROUPS  HOMOLOGY-GROUPS  HOMOLOGY-GROUPS
-;;  HOMOLOGY-GROUPS  HOMOLOGY-GROUPS  HOMOLOGY-GROUPS  HOMOLOGY-GROUPS
-;;  HOMOLOGY-GROUPS  HOMOLOGY-GROUPS  HOMOLOGY-GROUPS  HOMOLOGY-GROUPS
-
-(IN-PACKAGE "CAT")
-
-(provide "homology-groups")
-
-;;
-;;  Computing ordinary homology-groups. 
-;;  
-
-;; Structures.
-
-(DEFSTRUCT (matrice (:conc-name nil))
-  leftcol uplig)
-
-(DEFSTRUCT (t-mat (:conc-name nil))
-  val ilig icol left up)
-
-(defmacro baselig (mat n)
-  `(aref (leftcol ,mat) ,n))
-
-(defmacro basecol (mat n)
-  `(aref (uplig ,mat) ,n))
-
-;; Functions.
-
-(defun creer-matrice (n1 n2)
-   (let ((mat (make-matrice
-                 :leftcol (make-array (1+ n1))
-                 :uplig (make-array (1+ n2)))))
-      (setf (baselig mat 0) (make-t-mat :ilig 0 :icol 0))
-      (setf (basecol mat 0) (baselig mat 0))
-      (do ((i 1 (1+ i)))
-         ((> i n1))
-         (setf (baselig mat i)
-            (make-t-mat :ilig i :icol 0 :up (baselig mat (1- i))))
-         (setf (left (baselig mat i)) (baselig mat i)))
-      (do ((j 1 (1+ j)))
-         ((> j n2))
-         (setf (basecol mat j)
-            (make-t-mat :ilig 0 :icol j :left (basecol mat (1- j))))
-         (setf (up (basecol mat j)) (basecol mat j)))
-      (setf (up (baselig mat 0)) (baselig mat n1))
-      (setf (left (basecol mat 0)) (basecol mat n2))
-      mat))
-
-(defun chercher-hor (p ic)
-   (do ((p2 p p1)
-        (p1 (left p) (left p1)))
-        ((<= (icol p1) ic) p2)))
-
-(defun chercher-ver (p il)
-   (do ((p2 p p1)
-        (p1 (up p) (up p1)))
-       ((<= (ilig p1) il) p2)))
-
-(defun inserer-terme (pl pc val)
-   (setf (left pl) (make-t-mat :val val
-                               :ilig (ilig pl)
-                               :icol (icol pc)
-                               :left (left pl)
-                               :up (up pc))
-         (up pc) (left pl)))
-
-(defun supprimer-terme (pl pc)
-   (setf (left pl) (left (left pl))
-         (up pc) (up (up pc))))
-
-(defun maj-terme (pl pc val)
-  (if (= val 0)
-      (if (eq (left pl) (up pc)) (supprimer-terme pl pc))
-      (if (eq (left pl) (up pc))
-          (setf (val (left pl)) val)
-          (inserer-terme pl pc val))))
-
-(defun maj-ligne (mat il liste)
-   (let ((ptl (baselig mat il)))
-        (mapcar
-           #'(lambda (elem)
-                (maj-terme (chercher-hor ptl (first elem))
-                           (chercher-ver (basecol mat (first elem)) il)
-                           (second elem)))
-           liste)
-        ptl))
-
-(defun maj-colonne (mat ic liste)
-   (let ((ptc (basecol mat ic)))
-        (mapcar
-           #'(lambda (elem)
-                (maj-terme (chercher-hor (baselig mat (first elem)) ic)
-			   (chercher-ver ptc (first elem))
-                           (second elem)))
-           liste)
-        ptc))
-
-(defun maj-matrice (mat liste)
-  (mapcar
-     #'(lambda (elem) (apply #'maj-ligne mat elem))
-     liste)
-  mat)
-
-(defun disp-p (p)
-   `((,(ilig p) ,(icol p) ,(val p))
-     (,(ilig (left p)) ,(icol (left p)) ,(val (left p)))
-     (,(ilig (up p)) ,(icol (up p)) ,(val (up p)))))
-
-(defun disp-ligne (mat il)
-   (terpri)
-   (princ "L")
-   (princ il)
-   (princ "=")
-   (mapcar
-      #'(lambda (elem)
-           (princ "(")
-           (princ (first elem))
-           (princ ":")
-           (princ (second elem))
-           (princ ")"))
-      (let ((ptl (baselig mat il))
-            (res '()))
-         (do ((pl (left ptl) (left pl)))
-             ((eq pl ptl))
-            (push (list (icol pl) (val pl)) res))
-         res))
-  (values ))
-
-(defun disp-colonne (mat ic)
-   (terpri)
-   (princ "C")
-   (princ ic)
-   (princ "=")
-   (mapcar
-      #'(lambda (elem)
-           (princ "(")
-           (princ (first elem))
-           (princ ":")
-           (princ (second elem))
-           (princ ")"))
-      (let ((ptc (basecol mat ic))
-            (res '()))
-         (do ((pc (up ptc) (up pc)))
-             ((eq pc ptc))
-            (push (list (ilig pc) (val pc)) res))
-         res))
-   (values ))
-
-(defun nlig (mat) (1- (array-dimension (leftcol mat) 0)))
-(defun ncol (mat) (1- (array-dimension (uplig mat) 0)))
-
-(defun disp-matrice (mat)
-   (let ((nlig (nlig mat)))
-      (do ((i 1 (1+ i)))
-          ((> i nlig))
-          (disp-ligne mat i)))
-   (done))
-
-(DEFMETHOD PRINT-OBJECT ((mtrx matrice) stream)
-  (declare (stream stream))
-  (the matrice (progn
-    (let ((nlig (nlig mtrx))
-	  (ncol (ncol mtrx)))
-      (declare (fixnum nlig ncol))
-      (format stream "~%========== MATRIX ~D lines + ~D columns ====="
-	      nlig ncol)
-      (do ((ilig 1 (1+ ilig)))
-	  ((> ilig nlig))
-	  (declare (fixnum ilig))
-	(format stream "~%L~D=" ilig)
-	(dolist (item (let ((baselig (baselig mtrx ilig)))
-			(declare (type t-mat baselig))
-			(do ((rslt +empty-list+ (cons t-mat rslt))
-			     (t-mat (left baselig) (left t-mat)))
-			    ((eq t-mat baselig) rslt)
-			    (declare
-			      (list rslt)
-			      (type t-mat t-mat)))))
-	   (declare (type t-mat item))
-	   (format stream "[C~D=~D]" (icol item) (val item))))
-      (format stream "~%========== END-MATRIX"))
-    mtrx)))    
-
-(defun disp-matrice-colonnes (mat)
-   (let ((ncol (ncol mat)))
-      (do ((i 1 (1+ i)))
-          ((> i ncol))
-          (disp-colonne mat i)))
-   (done))
-
-(defun terme (mat i j)
-   (let ((p (left (chercher-hor (baselig mat i) j))))
-        (if (= j (icol p))
-            (val (left p))
-            nil)))
-
-(defun mat-aleat (n1 n2 dens x)
-   (let ((mat (creer-matrice n1 n2))
-         (n (truncate (* dens n1 n2)))
-         (2x (* 2 x))
-         (res nil))
-      (dotimes (i n)
-         (let* ((il (1+ (random n1)))
-                (ic (1+ (random n2)))
-                (val (let ((pval (- (random 2x) x)))
-                        (if (minusp pval)
-                            pval
-                            (1+ pval))))
-                (elem (member il res
-                         :test #'(lambda (x y) (eql x (first y))))))
-            (if elem
-                (push (list ic val) (cadar elem))
-                (push (list il (list (list ic val))) res))))
-      (maj-matrice mat res)))
-
-(defun op-elem (pl pc alpha)
-   (if (eq (left pl) (up pc))
-       (if (= alpha (val (left pl)))
-           (supprimer-terme pl pc)
-           (decf (val (left pl)) alpha))
-       (inserer-terme pl pc (- alpha))))
-
-(defun peigne-ver (mat ptl il)
-       (if (< il (ilig ptl))
-           (do ((res nil (cons (chercher-ver pl il)
-                               res))
-                (pl (left ptl) (left pl)))
-               ((eq pl ptl) (nreverse res)))
-           (do ((res nil (cons (chercher-ver (basecol mat (icol pl)) il)
-                               res))
-                (pl (left ptl) (left pl)))
-               ((eq pl ptl) (nreverse res)))))
-
-(defun peigne-hor (mat ptc ic)
-       (if (< ic (icol ptc))
-           (do ((res nil (cons (chercher-hor pc ic)
-                               res))
-                (pc (up ptc) (up pc)))
-               ((eq pc ptc) (nreverse res)))
-           (do ((res nil (cons (chercher-hor (baselig mat (ilig pc)) ic)
-                               res))
-                (pc (up ptc) (up pc)))
-               ((eq pc ptc) (nreverse res)))))
-
-(defun op-lig (ptl1 ptl2 peigne lambda)
-  (do ((pl1 (left ptl1) (left pl1))
-       (pp peigne (rest pp))
-       (pl2 ptl2))
-      ((endp pp) ptl2)
-    (setf pl2 (chercher-hor pl2 (icol pl1)))
-    (op-elem pl2 (first pp) (* lambda (val pl1)))))
-
-(defun op-col (ptc1 ptc2 peigne lambda)
-  (do ((pc1 (up ptc1) (up pc1))
-       (pp peigne (rest pp))
-       (pc2 ptc2))
-      ((endp pp) ptc2)
-    (setf pc2 (chercher-ver pc2 (ilig pc1)))
-    (op-elem (first pp) pc2 (* lambda (val pc1)))))
-
-(defun op-lig-n (mat l1 l2 lambda)
-  (op-lig (baselig mat l1)
-          (baselig mat l2)
-          (peigne-ver mat (baselig mat l1) l2)
-          lambda))
-
-(defun op-col-n (mat c1 c2 lambda)
-  (op-col (basecol mat c1)
-          (basecol mat c2)
-          (peigne-hor mat (basecol mat c1) c2)
-          lambda))
-
-(defun n-lig (mat)
-  (1- (array-dimension (leftcol mat) 0)))
-
-(defun n-col (mat)
-  (1- (array-dimension (uplig mat) 0)))
-
-(defun copier-matrice (mat)
-  (let ((mat2 (creer-matrice (n-lig mat) (n-col mat))))
-    (do ((i 1 (1+ i)))
-        ((> i (n-lig mat)) mat2)
-      (do ((ptl1 (baselig mat i))
-           (pl1 (left (baselig mat i)) (left pl1))
-           (pl2 (baselig mat2 i) (left pl2)))
-          ((eq pl1 ptl1))
-        (inserer-terme pl2 (basecol mat2 (icol pl1)) (val pl1))))))
-
-(defun reste (a b)
-  (second (multiple-value-list (round a b))))
-
-(defun diviseur (a b)
-  (round a b))
-
-(defun maj-peigne-ver (peigne il)
-  (do ((pp peigne (rest pp)))
-      ((endp pp) peigne)
-    (setf (first pp) (chercher-ver (first pp) il))))
-
-(defun maj-peigne-hor (peigne ic)
-  (do ((pp peigne (rest pp)))
-      ((endp pp) peigne)
-    (setf (first pp) (chercher-hor (first pp) ic))))
-
-(defun identite (n)
-  (let ((mat (creer-matrice n n)))
-    (do ((ptl (baselig mat n) (up ptl))
-         (ptc (basecol mat n) (left ptc)))
-        ((eq ptl ptc))
-      (inserer-terme ptl ptc 1))
-    mat))
-
-(defun init-peigne-ver (mat ptl)
-  (do ((res nil (cons (basecol mat (icol pl))
-                      res))
-       (pl (left ptl) (left pl)))
-      ((eq pl ptl) (nreverse res))))
-
-(defun init-peigne-hor (mat ptc)
-  (do ((res nil (cons (baselig mat (ilig pc))
-                      res))
-       (pc (up ptc) (up pc)))
-      ((eq pc ptc) (nreverse res))))
-
-(defun disp-peigne (peigne)
-  (mapcar #'(lambda (elem) (first (disp-p elem)))
-          peigne))
-
-(defun terme-minimal-matrice (mat)
-  (catch '?
-    (do* ((fin (baselig mat 0))
-          (ptl (up fin) (up ptl)))
-         ((eq ptl fin) (throw '? nil))
-      (if (not (eq ptl (left ptl)))
-          (let* ((pmin (left ptl))
-                 (min (abs (val pmin))))
-            (if (= min 1) (throw '? pmin))
-            (do ((ptl ptl (up ptl)))
-                ((eq ptl fin) (throw '? pmin))
-              (do ((pl (left ptl) (left pl)))
-                  ((eq pl ptl))
-                (let ((val (abs (val pl))))
-                  (when (< val min)
-                    (if (= val 1) (throw '? pl))
-                    (setq pmin pl min val))))))))))
-
-(defun tuer-ligne (mat il)
-  (let* ((ptl (baselig mat il))
-         (peigne (peigne-ver mat ptl il)))
-    (do ((pp peigne (rest pp)))
-        ((endp pp))
-      (supprimer-terme ptl (first pp)))
-    (setf (up (chercher-ver (baselig mat 0) il)) (up ptl)))
-  mat)
-
-(defun tuer-colonne (mat ic)
-  (let* ((ptc (basecol mat ic))
-         (peigne (peigne-hor mat ptc ic)))
-    (do ((pp peigne (rest pp)))
-        ((endp pp))
-      (supprimer-terme (first pp) ptc))
-    (setf (left (chercher-hor (basecol mat 0) ic)) (left ptc)))
-  mat)
-
-(defun pivot (mat p)
-  (let* ((div (val p))
-         (ptl (baselig mat (ilig p)))
-         (ptc (basecol mat (icol p)))
-         (peigne (init-peigne-ver mat ptl))
-         (peigne2 '*non-defini*))
-    (do ((pc (up ptc) (up pc)))
-        ((eq pc ptc))
-      (maj-peigne-ver peigne (ilig pc))
-      (if (eq pc p)
-          (setf peigne2 (copy-list peigne))
-          (op-lig ptl
-                  (baselig mat (ilig pc))
-                  peigne
-                  (truncate (val pc) div))))
-    (do ((pp peigne2 (rest pp)))
-        ((endp pp))
-      (supprimer-terme ptl (first pp)))
-    (setf (left (chercher-hor (basecol mat 0) (icol p))) (left ptc))
-    (setf (up   (chercher-ver (baselig mat 0) (ilig p))) (up   ptl))
-    (list (ilig p) (icol p) (val p))))
-
-(defun pivot-parallele (M N p)
-  (let* ((div (val p))
-         (ic (icol p))
-         (ptl (baselig M (ilig p)))
-         (ptc (basecol N ic))
-         (peigne (init-peigne-hor N ptc))
-         (peigne2 '*non-defini*))
-    (do ((pl (left ptl) (left pl)))
-        ((eq pl ptl))
-      (maj-peigne-hor peigne (icol pl))
-      (if (eq pl p)
-          (setf peigne2 (copy-list peigne))
-          (op-col ptc
-                  (basecol N (icol pl))
-                  peigne
-                  (truncate (val pl) div))))
-    (do ((pp peigne2 (rest pp)))
-        ((endp pp))
-      (supprimer-terme (first pp) ptc))
-    (setf (left (chercher-hor (basecol N 0) ic)) (left ptc))))
-
-(defun generateur-torsion-H* (B N p)
-  (let ((tab (make-array (1+ (n-lig B)) :initial-element 0))
-        (ptcN (basecol N (icol p))))
-    (do ((pcN (up ptcN) (up pcN)))
-        ((eq pcN ptcN))
-      (let ((facteur (truncate (val pcN) (val p)))
-            (ptcB (basecol B (ilig pcN))))
-        (do ((pcB (up ptcB) (up pcB)))
-            ((eq pcB ptcB))
-          (incf (aref tab (ilig pcB)) (* (val pcB) facteur)))))
-    (cons (abs (val p))
-          (let ((res '()))
-            (do ((ind (n-lig B) (1- ind)))
-                ((zerop ind) res)
-              (if (/= 0 (aref tab ind))
-                  (push (cons (aref tab ind) ind) res)))))))
-
-(defun terminer-H* (B)
-  (let ((res '())
-        (fin (basecol B 0)))
-    (do ((ptc (left fin) (left ptc)))
-        ((eq ptc fin) res)
-      (push (cons 0
-                  (do ((pc (up ptc) (up pc))
-                       (res '() (cons (cons (val pc) (ilig pc)) res)))
-                      ((eq pc ptc) res)))
-            res))))
-
-(defun reste-minimal-ligne (mat p)
-  (block ?
-    (let ((div (val p))
-          (ptl (baselig mat (ilig p))))
-      (do ((pl (left ptl) (left pl)))
-          ((eq pl ptl) (return-from ? nil))
-        (let ((val (reste (val pl) div)))
-          (if (/= 0 val)
-              (if (= 1 val)
-                  (return-from ? pl)
-                  (let ((pmin pl)
-                        (min val))
-                    (do ((pl (left pl) (left pl)))
-                        ((eq pl ptl) (return-from ? pmin))
-                      (let ((val (reste (val pl) div)))
-                        (if (and (/= 0 val) (< val min))
-                            (if (= 1 val)
-                                (return-from ? pl)
-                                (setf pmin pl min val)))))))))))))
-
-(defun reste-minimal-colonne (mat p)
-  (block ?
-    (let ((div (val p))
-          (ptc (basecol mat (icol p))))
-      (do ((pc (up ptc) (up pc)))
-          ((eq pc ptc) (return-from ? nil))
-        (let ((val (reste (val pc) div)))
-          (if (/= 0 val)
-              (if (= 1 val)
-                  (return-from ? pc)
-                  (let ((pmin pc)
-                        (min val))
-                    (do ((pc (up pc) (up pc)))
-                        ((eq pc ptc) (return-from ? pmin))
-                      (let ((val (reste (val pc) div)))
-                        (if (and (/= 0 val) (< val min))
-                            (if (= 1 val)
-                                (return-from ? pc)
-                                (setf pmin pc min val)))))))))))))
-
-
-
-(defun homologie (M N)
-  (prog ((B (identite (n-col M)))
-         (res nil)
-         (p1) (p2) (div))
-    depart1
-      (setf p1 (terme-minimal-matrice M))
-    loop1
-      (if (null p1)
-          (go depart2)
-          (if (= 1 (abs (val p1)))
-              (go pivot1)
-              (progn (setf p2 (reste-minimal-colonne M p1))
-                     (if (null p2)
-                         (progn (setf p2 (reste-minimal-ligne M p1))
-                                (if (null p2)
-                                    (go pivot1)
-                                    (go op-col1)))
-                         (go op-lig1)))))
-    op-lig1
-      (op-lig-n M (ilig p1) (ilig p2) (diviseur (val p2) (val p1)))
-      (setf p1 p2)
-      (go loop1)
-    op-col1
-      (setf div (diviseur (val p2) (val p1)))
-      (op-col-n M (icol p1) (icol p2) div)
-      (op-col-n B (icol p1) (icol p2) div)
-      (op-lig-n N (icol p2) (icol p1) (- div))
-      (setf p1 p2)
-      (go loop1)
-    pivot1
-      (tuer-ligne N (icol p1))
-      (pivot-parallele M B p1)
-      (pivot M p1)
-      (go depart1)
-
-    depart2
-      (setf p1 (terme-minimal-matrice N))
-    loop2
-      (if (null p1)
-          (go depart3)
-          (if (= 1 (abs (val p1)))
-              (go pivot2)
-              (progn (setf p2 (reste-minimal-ligne N p1))
-                     (if (null p2)
-                         (progn (setf p2 (reste-minimal-colonne N p1))
-                                (if (null p2)
-                                    (go pivot2-torsion)
-                                    (go op-lig2)))
-                         (go op-col2)))))
-    op-lig2
-      (setf div (diviseur (val p2) (val p1)))
-      (op-col-n B (ilig p2) (ilig p1) (- div))
-      (op-lig-n N (ilig p1) (ilig p2) div)
-      (setf p1 p2)
-      (go loop2)
-    op-col2
-      (op-col-n N (icol p1) (icol p2) (diviseur (val p2) (val p1)))
-      (setf p1 p2)
-      (go loop2)
-    pivot2-torsion
-      (setf res (cons (generateur-torsion-H* B N p1) res))
-    pivot2
-      (tuer-colonne B (ilig p1))
-      (pivot N p1)
-      (go depart2)
-
-    depart3
-      (return (append res (terminer-H* B)))))
-
-(defun chcm-mat (chcm n)
-  (declare
-     (type chain-complex chcm)
-     (fixnum n))
-   (when (eq (basis chcm) :locally-effective)
-    (error "CHCMC-MAT cannot work with a LOCALLY-EFFECTIVE chain complex."))
-  (let ((sorc (basis chcm n))
-	(trgt (basis chcm (1- n)))
-	(cmpr (cmpr chcm)))
-    (declare
-       (list sorc trgt)
-       (type cmprf cmpr))
-     (format t "~%Computing boundary-matrix in dimension ~D.~@
-                Rank of the source-module : ~D.~2%"
-        n (length sorc))
-    (let ((mat (creer-matrice (length trgt) (length sorc)))
-          (test #'(lambda (gnrt1 gnrt2)
-                     (eq (funcall cmpr gnrt1 gnrt2) :equal))))
-       (declare
-          (type matrice mat)
-          (function test))
-       (do ((i 1 (1+ i))
-            (mark sorc (cdr mark)))
-           ((endp mark))
-          (declare
-             (fixnum i)
-             (list mark))
-          (clock)
-          (format t "Computing the boundary of the generator ~D (dimension ~D) :"
-             i n)
-          (print (car mark))
-          (maj-colonne mat i
-             (mapcar #'(lambda (term)
-                          (declare (type term term))
-                          (list
-                             (1+ (position (gnrt term) trgt :test test))
-                             (cffc term)))
-                (cmbn-list (? chcm n (car mark)))))
-          (format t "~%End of computing.~2%"))
-       mat)))
-
-#|
-  (require "special-smsts")
-  (setf d (delta 3))
-  (disp-matrice (chcm-mat d 2))
-  (disp-matrice (chcm-mat d 3))
-  (disp-matrice (chcm-mat d 4))
-|#
-
-(defun chcm-homology (cc n)
-  (declare (type chain-complex cc) (type fixnum n))
-  (let ((rsl (homologie (chcm-mat cc n) (chcm-mat cc (1+ n)))))
-    (declare (type list rsl))    
-    (format t "~3%Homology in dimension ~D :~%" n)
-    (dolist (item rsl)
-      (declare (type list item))
-      (format t "~2%Component Z")
-      (unless (zerop (first item)) 
-	(format t "/~DZ" (first item)))))
-  (terpri) (terpri)
-  (done))
-
-(defun chcm-homology-gen (cc n)
-  (declare (type chain-complex cc) (type fixnum n))
-  (let ((src (cons :unused (basis cc n)))
-	(rsl (homologie (chcm-mat cc n) (chcm-mat cc (1+ n)))))
-    (declare (type list src rsl))
-    (format t "~3%Homology in dimension ~D :~%" n)
-    (dolist (item rsl)
-      (declare (type list item))
-      (format t "~2%Component Z")
-      (unless (zerop (first item)) 
-	(format t "/~DZ" (first item)))
-      (format t "~2%Generator :")
-      (dolist (item2 (rest item))
-	(declare (type cons item2))
-	(format t "~%~D~6T*  ~S" (car item2) (nth (cdr item2) src)))))
-  (done))
-
-#|
-(defun heq-homology (heq n)
-  (declare (type heq heq) (type fixnum n))
-  (let ((ecc (heq-rbcc heq))
-	(rep (cmp-mrp (heq-lf heq) (heq-rg heq))))
-    (declare (type chain-complex ecc) (type mrp rep))
-    (let ((src (cons :unused (cbs ecc n)))	
-	  (rsl (homologie (chcm-mat ecc n) (chcm-mat ecc (1+ n)))))
-      (declare (type list src rsl))
-      (format t "~3%Homology in dimension ~D :~%" n)
-      (dolist (item rsl)
-	(declare (type list item))
-	(format t "~2%Component Z")
-	(unless (zerop (first item))
-	  (format t "/~DZ" (first item)))
-	(format t "~2%Generator :~%")
-	(princ (??? rep (make-cmb :dgr n
-				  :lst (mapcar #'(lambda (item2)
-						   (declare (type cons item2))
-						   (mnm (car item2)
-							(nth (cdr item2) src)))
-					       (rest item))))))))
-  (done))
-|#
-
diff --git a/archive/Kenzo-2/Kenzo-2-Acl8/k-pi-n.cl b/archive/Kenzo-2/Kenzo-2-Acl8/k-pi-n.cl
deleted file mode 100644
index f47616a..0000000
--- a/archive/Kenzo-2/Kenzo-2-Acl8/k-pi-n.cl
+++ /dev/null
@@ -1,1070 +0,0 @@
-;;;  K-PI-1  K-PI-1  K-PI-1  K-PI-1  K-PI-1  K-PI-1  K-PI-1
-;;;  K-PI-1  K-PI-1  K-PI-1  K-PI-1  K-PI-1  K-PI-1  K-PI-1
-;;;  K-PI-1  K-PI-1  K-PI-1  K-PI-1  K-PI-1  K-PI-1  K-PI-1
-
-(IN-PACKAGE "CAT")
-
-(PROVIDE "k-pi-1")
-
-(DEFUN K-Z-1-CMPR (gnrt1 gnrt2)
-   (declare (list gnrt1 gnrt2))
-   (the cmpr
-   (do ((mark1 gnrt1 (cdr mark1))
-	(mark2 gnrt2 (cdr mark2)))
-       ((endp mark1) :equal)
-       (case (f-cmpr (car mark1) (car mark2))
-	  (:equal)
-	  (:less (return-from k-z-1-cmpr :less))
-	  (:greater (return-from k-z-1-cmpr :greater))))))
-
-#|
-  (k-z-1-cmpr '(1 1 2) '(1 2 2))
-  (k-z-1-cmpr '(1 1 2) '(1 1 2))
-  (k-z-1-cmpr '(1 1 2) '(1 1 -1))
-|#
-
-(DEFUN K-Z-1-FACE (indx dmns gmsm)
-   (declare
-      (fixnum indx dmns)
-      (list gmsm))
-   (the absm
-   (cond ((zerop indx) (absm 0 (rest gmsm)))
-	 ((= indx dmns) (absm 0 (butlast gmsm)))
-	 (t
-	  (do ((rslt +empty-list+ (cons (car mark) rslt))
-	       (mark gmsm (cdr mark))
-	       (i 1 (1+ i)))
-	      ((= i indx) (let ((new-k (+ (car mark) (cadr mark))))
-			    (declare (fixnum new-k))
-			    (if (zerop new-k)
-			       (absm (2-exp (1- indx)) (nreconc rslt (cddr mark)))
-			       (absm 0 (nreconc rslt (cons new-k (cddr mark)))))))
-	     (declare
-	        (list rslt mark)
-		(fixnum i)))))))
-
-#|
-  (k-z-1-face 0 1 '(3))
-  (k-z-1-face 1 1 '(3))
-  (k-z-1-face 0 3 '(1 2 3))
-  (k-z-1-face 1 3 '(1 2 3))
-  (k-z-1-face 2 3 '(1 2 3))
-  (k-z-1-face 2 3 '(1 2 -2))
-  (k-z-1-face 3 3 '(1 2 3))
-|#
-
-(DEFUN Z-ABSM-BAR (absm)
-  (declare (type absm absm))
-  (the list
-    (with-absm (dgop bar1) absm
-      (do ((dgop dgop (ash dgop -1))
-	   (rslt +empty-list+))
-	  ((and (zerop dgop) (endp bar1)) (nreverse rslt))
-	  (declare
-	     (fixnum dgop)
-	     (list rslt))
-	  (push (if (oddp dgop)
-		    0
-		  (pop bar1))
-		rslt)))))
-
-#|
-  (z-absm-bar (absm 0 '()))
-  (z-absm-bar (absm 1 '()))
-  (z-absm-bar (absm 0 '(2)))
-  (dotimes (i 8)
-    (print (z-absm-bar (absm i '(3 6)))))
-|#
-
-(DEFUN Z-BAR-ABSM (bar)
-  (declare (list bar))
-  (the absm
-     (do ((rslt-dgop 0)
-	  (rslt-bar +empty-list+)
-	  (mark bar (cdr mark))
-	  (bark 1 (+ bark bark)))
-	 ((endp mark) (absm rslt-dgop (nreverse rslt-bar)))
-	(declare
-	   (fixnum rslt-dgop bark)
-	   (list rslt-bar mark))
-	(let ((k-i (car mark)))
-	  (declare (fixnum k-i))
-	  (if (zerop k-i)
-	     (incf rslt-dgop bark)
-	     (push k-i rslt-bar))))))
-
-#|
-  (z-bar-absm (z-absm-bar (absm 0 '())))
-  (z-bar-absm (z-absm-bar (absm 1 '())))
-  (z-bar-absm (z-absm-bar (absm 0 '(2))))
-  (dotimes (i 8)
-    (print (z-bar-absm (z-absm-bar (absm i '(3 6))))))
-|#
-
-(DEFUN K-Z-1-GRML (dmns crpr)
-   (declare
-      (fixnum dmns)
-      (type crpr crpr))
-   (the absm
-      (with-crpr (dgop1 bar1 dgop2 bar2) crpr
-	 (do ((indx 1 (1+ indx))
-	      (dgop1 dgop1 (ash dgop1 -1))
-	      (dgop2 dgop2 (ash dgop2 -1))
-	      (bark 1 (ash bark +1))
-	      (rslt-dgop 0)
-	      (rslt-bar +empty-list+))
-	     ((> indx dmns) (absm rslt-dgop (nreverse rslt-bar)))
-	     (declare
-	        (fixnum indx dgop1 dgop2 bark rslt-dgop)
-		(list rslt-bar))
-	     (let ((item (if (evenp dgop1)
-			     (if (evenp dgop2)
-				 (+ (pop bar1) (pop bar2))
-			       (pop bar1))
-			   (if (evenp dgop2)
-			       (pop bar2)
-			     0))))
-	       (declare (fixnum item))
-	       (if (zerop item)
-		   (incf rslt-dgop bark)
-		 (push item rslt-bar)))))))
-
-#|
-  (k-z-1-grml 0 (crpr 0 nil 0 nil))
-  (k-z-1-grml 1 (crpr 0 '(3) 0 '(4)))
-  (k-z-1-grml 1 (crpr 0 '(3) 0 '(-3)))
-  (k-z-1-grml 1 (crpr 0 '(3) 1 '()))
-  (k-z-1-grml 1 (crpr 1 '() 0 '(3)))
-  (k-z-1-grml 1 (crpr 1 '() 1 '()))
-  (k-z-1-grml 5 (crpr 24 '(2 2 3) 20 '(-2 2 4)))
-|#
-
-(DEFUN K-Z-1-GRIN (dmns bar)
-  (declare
-     (ignore dmns)
-     (list bar))
-  (the absm
-     (absm 0 (mapcar #'- bar))))
-
-#|
-  (k-z-1-grin 3 '(2 3 -4))
-  (setf gmsm '(2 3 -4))
-  (k-z-1-grml 3 (crpr 0 gmsm 0 (gmsm (k-z-1-grin 3 gmsm))))
-|#
-
-#|
-(DEFUN K-Z-1-KFLL (indx dmns hat)
-  (declare
-     (fixnum indx dmns)
-     (list hat))
-  (the absm
-     (cond ((= 1 dmns)
-	    (absm 1 +empty-list+))
-	   ((zerop indx)
-	    (let ((del-1 (first hat))
-		  (del-2 (second hat)))
-	      (declare (type absm del-1 del-2))
-	      (with-absm (dgop1 bar1) del-1
-	      (with-absm (dgop2 bar2) del-2
-		 (let ((bar01 (if (oddp dgop2)
-				 0
-				 (first bar2)))
-		       (bar02 (if (oddp dgop1)
-				 0
-				 (first bar1))))
-		   (declare (fixnum bar01 bar02))
-		   (let ((bar12 (- bar02 bar01)))
-		     (declare (fixnum bar02))
-		     (if (zerop bar01)
-			(1dgnr 0 del-1)
-		        (if (zerop bar12)
-			   (1gnr 1 del-1)
-			   (let (del-01 (k-z-1-face 0 (1- dmns)
-						    del-1))
-			     (declare (type absm del-01))
-			     (with-absm (dgop01 gmsm01) del-01
-				(absm (* 4 dgop01)
-				      (cons bar01
-					    (cons bar02 gmsm01)))))))))))))
-	   ((= 1 indx)
-	    (let ((del-0 (first hat))
-		  (del-2 (second hat)))
-	      (declare (type absm del-0 del-2))
-	      (with-absm (dgop0 gmsm0) del-0
-	      (with-absm (dgop2 gmsm2) del-2
-		 (if (oddp dgop2 )))))))))
-
-|#
-
-(DEFUN K-Z-1 ()
-  (the ab-simplicial-group
-     (ab-simplicial-group
-      :cmpr #'k-z-1-cmpr
-      :basis :locally-effective
-      :bsgn +empty-list+
-      :face #'k-z-1-face
-      :grml-sintr #'k-z-1-grml
-	:grin-sintr #'k-z-1-grin
-	:dfnt '(k-z-1))))
-
-#|
-  (setf k (k-z-1))
-  (defun aleat-list (max length)
-     (let ((rslt nil)
-           (2max (+ max max)))
-        (dotimes (i length)
-           (push (let ((k (- (random 2max) max)))
-                    (if (zerop k)
-                       max
-                       k))
-              rslt))
-        rslt))
-  (? k (? k 14 (aleat-list 200 14)))
-  (setf zero? (add (idnt-mrph k) (grin k)))
-  (? zero? 14 (aleat-list 200 14))
-|#
-
-(DEFUN K-Z (n)
-   (declare (fixnum n))
-   (the ab-simplicial-group
-      (if (= n 1)
-         (k-z-1)
-         (classifying-space (k-z (1- n))))))
-
-(DEFUN CIRCLE-CMPR (gnrt1 gnrt2)
-   (declare (ignore gnrt1 gnrt2))
-   (the cmpr :equal))
-
-(DEFUN CIRCLE-BASIS (dmns)
-   (declare (fixnum dmns))
-   (the list
-      (case dmns
-	 (0 '(*))
-	 (1 '(s1))
-	 (otherwise +empty-list+))))
-
-(DEFUN CIRCLE ()
-   (the chain-complex
-      (chain-complex
-         :cmpr #'circle-cmpr
-	 :basis #'circle-basis
-	 :bsgn '*
-	 :dffr-intr #'zero-dffr-intr
-	 :dffr-strt :cmbn
-	 :dfnt '(circle))))
-
-#|
-  (setf c (circle))
-  (cmpr c '* '*)
-  (basis c 1)
-  (? c 1 's1)
-|#
-
-(DEFUN KZ1-RDCT-F-INTR (cmbn)
-  (declare (type cmbn cmbn))
-  (the cmbn
-     (with-cmbn (degr list) cmbn
-	(case degr
-	   (0 (if list
-		 (term-cmbn 0 (-cffc list) '*)
-		 (zero-cmbn 0)))
-	   (1 (let ((rslt
-		     (apply #'+
-			(mapcar
-			 #'(lambda (term)
-			     (declare (type term term))
-			     (with-term (cffc gnrt) term
-					(the fixnum (* cffc
-						       (first gnrt)))))
-			 list))))
-		(if (zerop rslt)
-		    (zero-cmbn 1)
-		  (term-cmbn 1 rslt 's1))))
-	   (otherwise (zero-cmbn degr))))))
-
-#|
-  (kz1-rdct-f-intr (cmbn 0))
-  (kz1-rdct-f-intr (cmbn 0 4 '()))
-  (kz1-rdct-f-intr (cmbn 1))
-  (kz1-rdct-f-intr (cmbn 1 4 '(3)))
-  (kz1-rdct-f-intr (cmbn 1 4 '(3) 5 '(2)))
-  (kz1-rdct-f-intr (cmbn 1 4 '(3) -3 '(4)))
-  (kz1-rdct-f-intr (cmbn -3))
-|#
-
-(DEFUN KZ1-RDCT-F ()
-  (the morphism
-     (morphism
-        :sorc (k-z-1)
-	:trgt (circle)
-	:degr 0
-	:intr #'kz1-rdct-f-intr
-	:strt :cmbn
-	:dfnt '(kz1-rdct-f))))
-
-(DEFUN KZ1-RDCT-G-INTR (cmbn)
-  (declare (type cmbn cmbn))
-  (the cmbn
-     (with-cmbn (degr list) cmbn
-	(if list
-	    (ecase degr
-	       (0 (term-cmbn 0 (-cffc list) +empty-list+))
-	       (1 (term-cmbn 1 (-cffc list) (list 1))))
-	  (zero-cmbn degr)))))
-
-(DEFUN KZ1-RDCT-G ()
-  (the morphism
-     (morphism
-        :sorc (circle)
-	:trgt (k-z-1)
-	:degr 0
-	:intr #'kz1-rdct-g-intr
-	:strt :cmbn
-	:dfnt '(kz1-rdct-g))))
-
-(DEFUN KZ1-RDCT-H-INTR (dmns bar)
-  (declare
-     (fixnum dmns)
-     (list bar))
-  (the cmbn
-     (progn
-       (when (zerop dmns)
-	  (return-from kz1-rdct-h-intr (zero-cmbn +1)))
-       (let ((k1 (first bar))
-	     (tail (rest bar)))
-	 (declare
-	    (fixnum k1)
-	    (list tail))
-	 (if (plusp k1)
-	    (do ((rslt +empty-list+
-		       (cons (term -1
-				   (cons 1 (cons i tail)))
-			     rslt))
-		 (i (1- k1) (1- i)))
-		((zerop i) (make-cmbn :degr (1+ dmns)
-				      :list rslt))
-	       (declare
-		  (list rslt)
-		  (fixnum i)))
-	    (do ((rslt +empty-list+
-		       (cons (term +1
-				   (cons 1 (cons i tail)))
-			     rslt))
-		 (i -1 (1- i)))
-		((< i k1) (make-cmbn :degr (1+ dmns)
-				     :list rslt))))))))
-
-#|
-  (kz1-rdct-h-intr 0 nil)
-  (kz1-rdct-h-intr 1 '(-4))
-  (kz1-rdct-h-intr 1 '(-1))
-  (kz1-rdct-h-intr 1 '(1))
-  (kz1-rdct-h-intr 1 '(4))
-  (kz1-rdct-h-intr 3 '(-4 3 5))
-  (kz1-rdct-h-intr 3 '(-1 3 -1))
-  (kz1-rdct-h-intr 3 '(1 2 2))
-  (kz1-rdct-h-intr 3 '(4 3 5))
-|#
-
-(DEFUN KZ1-RDCT-H ()
-  (the morphism
-     (morphism
-        :sorc (k-z-1)
-	:trgt (k-z-1)
-	:degr +1
-	:intr #'kz1-rdct-h-intr
-	:strt :gnrt
-	:dfnt '(kz1-rdct-h))))
-
-(DEFUN KZ1-RDCT ()
-  (the reduction
-     (reduction
-        :f (kz1-rdct-f)
-	:g (kz1-rdct-g)
-	:h (kz1-rdct-h)
-	:dfnt '(kz1-rdct))))
-
-#|
-  (pre-check-rdct (kz1-rdct))
-  (setf *tc* (cmbn 0 1 '()))
-  (setf *bc* (cmbn 0 1 '*))
-  (check-rdct)
-  (setf *tc* (cmbn 1 1 '(-4) 10 '(-1) 100 '(1) 1000 '(5)))
-  (setf *bc* (cmbn 1 1 's1))
-  (check-rdct)
-  (setf *tc* (cmbn 2 1 '(-4 2) 10 '(-1 3) 100 '(1 -4) 1000 '(5 5)))
-  (check-rdct)
-  (setf *tc* (cmbn 3 1 '(-4 -4 5) 10 '(-1 2 1)
-                     100 '(1 4 2) 1000 '(5 1 -1)))
-  (check-rdct)
-|#
-
-(DEFUN KZ1-EFHM ()
-  (the equivalence
-     (equivalence
-      :lrdct (trivial-rdct (k-z-1))
-      :rrdct (kz1-rdct)
-      :dfnt '(kz1-efhm))))
-
-(DEFMETHOD SEARCH-EFHM (k-z-1 (dfnt (eql 'k-z-1)))
-  (declare (ignore k-z-1))
-  (kz1-efhm))
-
-#|
-(cat-init)
-(homology (k-z-1) 1)
-|#
-
-(DEFUN K-Z2-1-GRML-INTR (dmns crpr)
-  (declare
-     (fixnum dmns)
-     (type crpr crpr))
-  (the absm
-     (with-crpr (dgop1 gmsm1 dgop2 gmsm2) crpr
-	(declare (ignore gmsm1 gmsm2))
-	(let ((dgop (- (mask dmns) (logxor dgop1 dgop2))))
-	  (declare (fixnum dgop))
-	  (absm dgop (- dmns (logcount dgop)))))))
-
-(DEFUN K-Z2-1-GRML ()
-  (the simplicial-mrph
-     (simplicial-mrph
-        :sorc (crts-prdc (r-proj-space) (r-proj-space))
-	:trgt (r-proj-space)
-	:degr 0
-	:sintr #'k-z2-1-grml-intr
-	:dfnt '(k-z2-1-grml))))
-
-(DEFUN K-Z2-1-GRIN-INTR (dmns gmsm)
-  (declare
-     (ignore dmns)
-     (fixnum gmsm))
-  (the absm
-     (absm 0 gmsm)))
-
-(DEFUN K-Z2-1-GRIN ()
-  (the simplicial-mrph
-     (simplicial-mrph
-        :sorc (r-proj-space)
-	:trgt (r-proj-space)
-	:degr 0
-	:sintr #'k-z2-1-grin-intr
-	:intr #'identity
-	:strt :cmbn
-	:dfnt '(k-z2-1-grin))))
-
-(DEFUN K-Z2-1 ()
-  (the ab-simplicial-group
-     (let ((rslt (r-proj-space)))
-       (declare (type simplicial-set rslt))
-       (change-class rslt 'ab-simplicial-group)
-       (setf (slot-value rslt 'grml)
-	     (k-z2-1-grml)
-	     (slot-value rslt 'grin)
-	     (k-z2-1-grin))
-       rslt)))
-
-#|
-  (setf k (k-z2-1))
-  (homology k 0 4)
-|#
-
-(DEFUN K-Z2 (n)
-   (declare (fixnum n))
-   (the ab-simplicial-group
-      (if (= n 1)
-         (k-z2-1)
-         (classifying-space (k-z2 (1- n))))))
-
-#|
-  (setf k3 (k-z2 3))
-  (homology k3 7)
-|#
-
-(DEFUN Z2-ABSM-BAR (absm)
-  (declare (type absm absm))
-  (the list
-     (with-absm (dgop gmsm) absm
-       (do ((bmark (1- (+ (logcount dgop) gmsm)) (1- bmark))
-	    (rslt +empty-list+
-		  (cons (if (logbitp bmark dgop)
-			    0 1)
-			rslt)))
-	   ((minusp bmark) rslt)
-	  (declare
-	     (fixnum bmark)
-	     (list rslt))))))
-
-(DEFUN Z2-BAR-ABSM (bar)
-  (declare (list bar))
-  (the absm
-     (do ((dgop 0)
-	  (2-pwr 1 (+ 2-pwr 2-pwr))
-	  (gmsm 0)
-	  (mark bar (cdr mark)))
-	 ((endp mark) (absm dgop gmsm))
-	(declare
-	   (fixnum dgop 2-pwr gmsm)
-	   (list mark))
-	(if (zerop (car mark))
-	   (incf dgop 2-pwr)
-	   (incf gmsm)))))
-
-#|
-  (dotimes (i 8)    ;;; not really legal
-  (dotimes (j 8)
-    (print (z2-bar-absm (z2-absm-bar (absm i j))))))
-|#
-
-
-(DEFUN HOPF-FIBRATION-SINTR (n)
-  (declare (fixnum n))
-  (flet ((rslt (dmns gmsm)
-	   (declare (ignore dmns gmsm))
-	   (if (zerop n)
-	      (absm 1 +empty-list+)
-	      (absm 0 (list n)))))
-     (the sintr #'rslt)))
-
-(DEFUN HOPF-FIBRATION (n)
-  (declare (fixnum n))
-  (the simplicial-mrph
-     (simplicial-mrph
-        :sorc (sphere 2)
-	:trgt (k-z-1)
-	:degr -1
-	:sintr (hopf-fibration-sintr n)
-	:dfnt `(hopf-fibration ,n))))
-
-(DEFUN Z-FUNDAMENTAL-GMSM (dmns pi-elm)   ;;; pi-elm not equal to 0
-   (declare (fixnum dmns pi-elm))
-   (the gmsm
-      (if (= 1 dmns)
-         (list pi-elm)
-         (let ((bsgn (if (= 2 dmns) +empty-list+ +null-gbar+)))
-            (declare (type gmsm bsgn))
-            (make-gbar :dmns dmns
-               :list (cons (absm 0 (z-fundamental-gmsm (1- dmns) pi-elm))
-                        (mapcar
-                           #'(lambda (k)
-                                (declare (fixnum k))
-                                (absm (mask k) bsgn))
-                           (nreverse (<a-b> 0 (- dmns 2))))))))))
-
-#|
-  (z-fundamental-gmsm 1 33)
-  (z-fundamental-gmsm 2 33)
-  (z-fundamental-gmsm 3 33)
-  (z-fundamental-gmsm 4 33)
-|#
-
-(DEFUN INTERESTING-FACES (face small-dmns high-dmns gmsm)
-  (declare
-    (type face face)
-    (fixnum small-dmns high-dmns)
-    (type gmsm gmsm))
-  (the list
-    (let ((max (mask high-dmns)))
-      (declare (fixnum max))
-      (if (= small-dmns high-dmns)
-	 (list (cons max (absm 0 gmsm)))
-	 (do ((prev-list (interesting-faces face (1+ small-dmns) high-dmns gmsm))
-	      (k (1- max) (1- k))
-	      (rslt +empty-list+)
-	      (count (binomial-n-p high-dmns small-dmns)))
-	     ((zerop count) rslt)
-	     (declare
-	       (list prev-list rslt)
-	       (fixnum k count))
-	    (when (= small-dmns (logcount k))
-	      (decf count)
-	      (do ((i 0 (1+ i)))
-	          ((not (logbitp i k))
-		   (push (cons k
-			       (a-face4 face
-					(- small-dmns -1
-					   (if (= i (integer-length k)) (1+ i) i))
-					(1+ small-dmns)
-					(cdr (assoc (+ k (2-exp i)) prev-list))))
-			 rslt)))))))))
-
-#|
-  (setf d (delta 14))
-  (setf f (face d))
-  (do ((i 5 (1- i)))
-      ((minusp i))
-    (print (interesting-faces f i 5 (mask 6))))
-|#     
-
-(DEFUN GMSM-COCYCLE (face small-dmns high-dmns gmsm chml-clss)
-  (declare
-    (type face face)
-    (fixnum small-dmns high-dmns)
-    (type gmsm gmsm)
-    (type morphism chml-clss))
-  (the list
-    (let ((int-faces (interesting-faces face small-dmns high-dmns gmsm)))
-      (declare (list int-faces))
-      (mapc
-        #'(lambda (cons)
-	    (declare (cons cons))
-	    (setf (cdr cons)
-		  (let ((absm (cdr cons)))
-		    (declare (type absm absm))
-		    (with-absm (dgop gmsm2) absm
-		      (if (plusp dgop)
-			 0
-			(let ((cmbn-list (cmbn-list (gnrt-? chml-clss
-						 small-dmns gmsm2))))
-			  (declare (list cmbn-list))
-			  (if cmbn-list
-			      (-cffc cmbn-list)
-			    0)))))))
-        int-faces)
-      int-faces)))
-
-#|
-  (cat-init)
-  (setf d (delta 10))
-  (setf chml-clss
-    (morphism :sorc d :trgt (z-chcm) :degr -2
-                :intr #'(lambda (dmns gmsm)
-                          (term-cmbn 0 gmsm :gnrt-z))
-                :strt :gnrt
-                :dfnt '(essai-1)))
-  (gmsm-cocycle (face d) 2 4 31 chml-clss)
-  (setf chml-clss
-    (morphism :sorc d :trgt (z-chcm) :degr -1
-                :intr #'(lambda (dmns gmsm)
-                          (term-cmbn 0 gmsm :gnrt-z))
-                :strt :gnrt
-                :dfnt '(essai-2)))
-  (gmsm-cocycle (face d) 1 4 31 chml-clss)
-|#
-
-(DEFUN Z-COCYCLE-GBAR (n dmns cocycle)
-  ;; cocycle \in Z^n(\Delta^{dmns}, \pi) with \pi = Z
-  (declare
-    (fixnum n dmns)
-    (list cocycle))
-  (the absm
-    (cond ((= n 1)
-	   (z-bar-absm (nreverse (mapcar #'cdr cocycle))))
-	  ((= n dmns)
-	   (let ((value (cdr (first cocycle))))
-	     (declare (fixnum value))
-	     (if (zerop value)
-		(absm (mask dmns) +null-gbar+)
-	        (absm 0 (z-fundamental-gmsm dmns value)))))
-	  (t
-	   (let ((cocycle1 +empty-list+)
-		 (cocycle2 +empty-list+))
-	     (declare (list cocycle1 cocycle2))
-	     (dolist (cons cocycle)
-	       (declare (cons cons))
-	       (if (evenp (car cons))
-		  (push (cons (ash (car cons) -1) (cdr cons))
-			cocycle1)
-		  (push (cons (ash (car cons) -1) (cdr cons))
-			cocycle2)))
-	     (setf cocycle1 (nreverse cocycle1)
-		   cocycle2 (nreverse cocycle2))
-	     (mapc
-	       #'(lambda (cons)
-		   (declare (cons cons))
-		   (when (evenp (car cons))
-		     (decf (cdr cons)
-			   (cdr (assoc (1+ (car cons)) cocycle1)))))
-	       cocycle2)
-	     (let ((head-absm (z-cocycle-gbar (1- n) (1- dmns) cocycle2))
-		   (tail-absm (z-cocycle-gbar n (1- dmns) cocycle1)))
-	       (declare (type absm head-absm tail-absm))
-	       (normalize-gbar
-		 (cons dmns
-		       (cons head-absm
-			     (rest (unnormalize-gbar tail-absm
-				     (if (= n 2) () +null-gbar+))))))))))))
-
-#|
-  (cat-init)
-  (setf d (delta 10))
-  (setf chml-clss
-    (morphism :sorc d :trgt (z-chcm) :degr -1
-                :intr #'(lambda (dmns gmsm)
-                          (term-cmbn 0 gmsm :gnrt-z))
-                :strt :gnrt
-                :dfnt '(essai-1)))
-  (gmsm-cocycle (face d) 1 4 31 chml-clss)
-  (z-cocycle-gbar 1 4 *)
-  (setf chml-clss
-    (morphism :sorc d :trgt (z-chcm) :degr -2
-                :intr #'(lambda (dmns gmsm)
-                          (term-cmbn 0 gmsm :gnrt-z))
-                :strt :gnrt
-                :dfnt '(essai-2)))
-  (gmsm-cocycle (face d) 2 2 7 chml-clss)
-  (z-cocycle-gbar 2 2 *)
-  (gmsm-cocycle (face d) 2 2 0 chml-clss) ;; normally illegal
-  (z-cocycle-gbar 2 2 *)
-  (gmsm-cocycle (face d) 2 3 15 chml-clss)
-  (z-cocycle-gbar 2 3 *)
-  (gmsm-cocycle (face d) 2 4 31 chml-clss)
-  (z-cocycle-gbar 2 4 *)
-  (setf chml-clss
-    (morphism :sorc d :trgt (z-chcm) :degr -3
-                :intr #'(lambda (dmns gmsm)
-                          (term-cmbn 0 gmsm :gnrt-z))
-                :strt :gnrt
-                :dfnt '(essai-3)))
-  (gmsm-cocycle (face d) 3 4 31 chml-clss)
-  (z-cocycle-gbar 3 4 *)
-  (setf chml-clss
-    (morphism :sorc d :trgt (z-chcm) :degr -3
-                :intr #'(lambda (dmns gmsm)
-                          (zero-cmbn 0))
-                :strt :gnrt
-                :dfnt '(essai-33)))
-  (gmsm-cocycle (face d) 3 4 31 chml-clss)
-  (z-cocycle-gbar 3 4 *)
-|#
-
-(DEFUN Z-COCYCLE-GBAR-HEAD (n dmns cocycle)
-  ;; cocycle \in Z^n(\Delta^{dmns}, \pi) with \pi = Z
-  (declare
-    (fixnum n dmns)
-    (list cocycle))
-  (the absm
-    (cond ((= n 1)
-	   (error "In Z-COCYCLE-GBAR-HEAD, this point should not have been reached."))
-	   ; (z-bar-absm (nreverse (mapcar #'cdr cocycle))))
-	  ((= n dmns)
-	   (let ((value (cdr (first cocycle))))
-	     (declare (fixnum value))
-	     (if (zerop value)
-		(if (= n 2)
-		   (absm 1 +empty-list+)
-		   (absm (mask (1- dmns)) +null-gbar+))
-	       (absm 0 (z-fundamental-gmsm (1- dmns) value)))))
-	  (t
-	   (let ((cocycle1 +empty-list+)
-		 (cocycle2 +empty-list+))
-	     (declare (list cocycle1 cocycle2))
-	     (dolist (cons cocycle)
-	       (declare (cons cons))
-	       (if (evenp (car cons))
-		  (push (cons (ash (car cons) -1) (cdr cons))
-			cocycle1)
-		  (push (cons (ash (car cons) -1) (cdr cons))
-			cocycle2)))
-	     (setf cocycle1 (nreverse cocycle1)
-		   cocycle2 (nreverse cocycle2))
-	     (mapc
-	       #'(lambda (cons)
-		   (declare (cons cons))
-		   (when (evenp (car cons))
-		     (decf (cdr cons)
-			   (cdr (assoc (1+ (car cons)) cocycle1)))))
-	       cocycle2)
-	     (z-cocycle-gbar (1- n) (1- dmns) cocycle2))))))
-
-#|
-  (cat-init)
-  (setf d (delta 10))
-  (setf chml-clss
-    (morphism :sorc d :trgt (z-chcm) :degr -1
-                :intr #'(lambda (dmns gmsm)
-                          (term-cmbn 0 gmsm :gnrt-z))
-                :strt :gnrt
-                :dfnt '(essai-1)))
-  (gmsm-cocycle (face d) 1 4 31 chml-clss)
-  (z-cocycle-gbar 1 4 *)
-  (z-cocycle-gbar-head 1 4 **)
-  (setf chml-clss
-    (morphism :sorc d :trgt (z-chcm) :degr -2
-                :intr #'(lambda (dmns gmsm)
-                          (term-cmbn 0 gmsm :gnrt-z))
-                :strt :gnrt
-                :dfnt '(essai-2)))
-  (gmsm-cocycle (face d) 2 2 7 chml-clss)
-  (z-cocycle-gbar 2 2 *)
-  (z-cocycle-gbar-head 2 2 **)
-  (gmsm-cocycle (face d) 2 2 0 chml-clss) ;; normally illegal
-  (z-cocycle-gbar 2 2 *)
-  (z-cocycle-gbar-head 2 2 **)
-  (gmsm-cocycle (face d) 2 3 15 chml-clss)
-  (z-cocycle-gbar 2 3 *)
-  (z-cocycle-gbar-head 2 3 **)
-  (gmsm-cocycle (face d) 2 4 31 chml-clss)
-  (z-cocycle-gbar 2 4 *)
-  (z-cocycle-gbar-head 2 4 **)
-  (setf chml-clss
-    (morphism :sorc d :trgt (z-chcm) :degr -3
-                :intr #'(lambda (dmns gmsm)
-                          (term-cmbn 0 gmsm :gnrt-z))
-                :strt :gnrt
-                :dfnt '(essai-3)))
-  (gmsm-cocycle (face d) 3 4 31 chml-clss)
-  (z-cocycle-gbar 3 4 *)
-  (z-cocycle-gbar-head 3 4 **)
-  (setf chml-clss
-    (morphism :sorc d :trgt (z-chcm) :degr -3
-                :intr #'(lambda (dmns gmsm)
-                          (zero-cmbn 0))
-                :strt :gnrt
-                :dfnt '(essai-33)))
-  (gmsm-cocycle (face d) 3 4 31 chml-clss)
-  (z-cocycle-gbar 3 4 *)
-  (z-cocycle-gbar-head 3 4 **)
-|#
-
-(DEFUN Z2-FUNDAMENTAL-GMSM (dmns pi-elm)  ;; pi-elm not "equal" to 0, therefore 1.
-   (declare (fixnum dmns pi-elm))
-   (the gmsm
-      (if (= 1 dmns)
-         1
-         (let ((bsgn (if (= 2 dmns) 0 +null-gbar+)))
-            (declare (type gmsm bsgn))
-            (make-gbar :dmns dmns
-               :list (cons (absm 0 (Z2-fundamental-gmsm (1- dmns) pi-elm))
-                        (mapcar
-                           #'(lambda (k)
-                                (declare (fixnum k))
-                                (absm (mask k) bsgn))
-                           (nreverse (<a-b> 0 (- dmns 2))))))))))
-
-#|
-  (Z2-fundamental-gmsm 1 1)
-  (Z2-fundamental-gmsm 2 1)
-  (Z2-fundamental-gmsm 3 1)
-  (Z2-fundamental-gmsm 4 1)
-|#    
-
-(DEFUN Z2-COCYCLE-GBAR (n dmns cocycle)
-  ;; cocycle \in Z^n(\Delta^{dmns}, \pi) with \pi = Z/2Z
-  (declare
-    (fixnum n dmns)
-    (list cocycle))
-  (the absm
-    (progn
-      (mapc
-        #'(lambda (cons)
-	    (declare (cons cons))
-	    (setf (cdr cons)
-		  (if (evenp (cdr cons)) 0 1)))
-        cocycle)
-      (cond ((= n 1)
-	     (z2-bar-absm (nreverse (mapcar #'cdr cocycle))))
-	    ((= n dmns)
-	     (let ((value (cdr (first cocycle))))
-	       (declare (fixnum value))
-	       (if (zerop value)
-		   (absm (mask dmns) +null-gbar+)
-		 (absm 0 (z2-fundamental-gmsm dmns value)))))
-	    (t
-	     (let ((cocycle1 +empty-list+)
-		   (cocycle2 +empty-list+))
-	       (declare (list cocycle1 cocycle2))
-	       (dolist (cons cocycle)
-		 (declare (cons cons))
-		 (if (evenp (car cons))
-		     (push (cons (ash (car cons) -1) (cdr cons))
-			   cocycle1)
-		   (push (cons (ash (car cons) -1) (cdr cons))
-			 cocycle2)))
-	       (setf cocycle1 (nreverse cocycle1)
-		     cocycle2 (nreverse cocycle2))
-	       (mapc
-		#'(lambda (cons)
-		    (declare (cons cons))
-		    (when (evenp (car cons))
-			  (setf (cdr cons)
-				(mod (- (cdr cons)
-					(cdr (assoc (1+ (car cons)) cocycle1)))
-				     2))))
-		cocycle2)
-	       (let ((head-absm (z2-cocycle-gbar (1- n) (1- dmns) cocycle2))
-		     (tail-absm (z2-cocycle-gbar n (1- dmns) cocycle1)))
-		 (declare (type absm head-absm tail-absm))
-		 (normalize-gbar
-		  (cons dmns
-			(cons head-absm
-			      (rest (unnormalize-gbar tail-absm
-						      (if (= n 2) 0 +null-gbar+)))))))))))))
-
-#|
-  (cat-init)
-  (setf d (delta 10))
-  (setf chml-clss
-    (morphism :sorc d :trgt (z-chcm) :degr -1
-                :intr #'(lambda (dmns gmsm)
-                          (term-cmbn 0 (mod gmsm 2) :gnrt-z))
-                :strt :gnrt
-                :dfnt '(essai-1)))
-  (gmsm-cocycle (face d) 1 4 31 chml-clss)
-  (z2-cocycle-gbar 1 4 *)
-  (setf chml-clss
-    (morphism :sorc d :trgt (z-chcm) :degr -2
-                :intr #'(lambda (dmns gmsm)
-                          (term-cmbn 0 (mod gmsm 2) :gnrt-z))
-                :strt :gnrt
-                :dfnt '(essai-2)))
-  (gmsm-cocycle (face d) 2 2 7 chml-clss)
-  (z2-cocycle-gbar 2 2 *)
-  (gmsm-cocycle (face d) 2 2 0 chml-clss) ;; normally illegal
-  (z2-cocycle-gbar 2 2 *)
-  (gmsm-cocycle (face d) 2 3 15 chml-clss)
-  (z2-cocycle-gbar 2 3 *)
-  (gmsm-cocycle (face d) 2 4 31 chml-clss)
-  (z2-cocycle-gbar 2 4 *)
-  (setf chml-clss
-    (morphism :sorc d :trgt (z-chcm) :degr -3
-                :intr #'(lambda (dmns gmsm)
-                          (term-cmbn 0 (mod gmsm 2) :gnrt-z))
-                :strt :gnrt
-                :dfnt '(essai-3)))
-  (gmsm-cocycle (face d) 3 4 31 chml-clss)
-  (z2-cocycle-gbar 3 4 *)
-|#
-
-(DEFUN Z2-COCYCLE-GBAR-HEAD (n dmns cocycle)
-  ;; cocycle \in Z^n(\Delta^{dmns}, \pi) with \pi = Z/2Z
-  (declare
-    (fixnum n dmns)
-    (list cocycle))
-  (the absm
-    (progn
-      (mapc
-        #'(lambda (cons)
-	    (setf (cdr cons)
-		  (if (evenp (cdr cons)) 0 1)))
-        cocycle)
-      (cond ((= n 1)
-	     (error "In Z2-COCYCLE-GBAR-HEAD, this point should not have been reached."))
-		 ; (z2-bar-absm (nreverse (mapcar #'cdr cocycle))))
-	    ((= n dmns)
-	     (let ((value (cdr (first cocycle))))
-	       (declare (fixnum value))
-	       (if (zerop value)
-		   (if (= n 2)
-		       (absm 1 0)
-		     (absm (mask (1- dmns)) +null-gbar+))
-		 (absm 0 (z2-fundamental-gmsm (1- dmns) value)))))
-	    (t
-	     (let ((cocycle1 +empty-list+)
-		   (cocycle2 +empty-list+))
-	       (declare (list cocycle1 cocycle2))
-	       (dolist (cons cocycle)
-		 (declare (cons cons))
-		 (if (evenp (car cons))
-		     (push (cons (ash (car cons) -1) (cdr cons))
-			   cocycle1)
-		   (push (cons (ash (car cons) -1) (cdr cons))
-			 cocycle2)))
-	       (setf cocycle1 (nreverse cocycle1)
-		     cocycle2 (nreverse cocycle2))
-	       (mapc
-		#'(lambda (cons)
-		    (declare (cons cons))
-		    (when (evenp (car cons))
-			  (setf (cdr cons)
-				(mod (- (cdr cons)
-					(cdr (assoc (1+ (car cons)) cocycle1)))
-				     2))))
-		cocycle2)
-	       (z2-cocycle-gbar (1- n) (1- dmns) cocycle2)))))))
-
-#|
-  (cat-init)
-  (setf d (delta 10))
-  (setf chml-clss
-    (morphism :sorc d :trgt (z-chcm) :degr -1
-                :intr #'(lambda (dmns gmsm)
-                          (term-cmbn 0 (mod gmsm 2) :gnrt-z))
-                :strt :gnrt
-                :dfnt '(essai-1)))
-  (gmsm-cocycle (face d) 1 4 31 chml-clss)
-  (z2-cocycle-gbar 1 4 *)
-  (z2-cocycle-gbar-head 1 4 **)
-  (setf chml-clss
-    (morphism :sorc d :trgt (z-chcm) :degr -2
-                :intr #'(lambda (dmns gmsm)
-                          (term-cmbn 0 (mod gmsm 2) :gnrt-z))
-                :strt :gnrt
-                :dfnt '(essai-2)))
-  (gmsm-cocycle (face d) 2 2 7 chml-clss)
-  (z2-cocycle-gbar 2 2 *)
-  (z2-cocycle-gbar-head 2 2 **)
-  (gmsm-cocycle (face d) 2 2 0 chml-clss) ;; normally illegal
-  (z2-cocycle-gbar 2 2 *)
-  (z2-cocycle-gbar-head 2 2 **)
-  (gmsm-cocycle (face d) 2 3 15 chml-clss)
-  (z2-cocycle-gbar 2 3 *)
-  (z2-cocycle-gbar-head 2 3 **)
-  (gmsm-cocycle (face d) 2 4 31 chml-clss)
-  (z2-cocycle-gbar 2 4 *)
-  (z2-cocycle-gbar-head 2 4 **)
-  (setf chml-clss
-    (morphism :sorc d :trgt (z-chcm) :degr -3
-                :intr #'(lambda (dmns gmsm)
-                          (term-cmbn 0 (mod gmsm 2) :gnrt-z))
-                :strt :gnrt
-                :dfnt '(essai-3)))
-  (gmsm-cocycle (face d) 3 4 31 chml-clss)
-  (z2-cocycle-gbar 3 4 *)
-  (z2-cocycle-gbar-head 3 4 **)
-|#
-
-(DEFUN K-Z-FUNDAMENTAL-CLASS (n)
-  (declare (fixnum n))
-  (the morphism
-    (morphism
-      :sorc (k-z n) :trgt (z-chcm) :degr (- n)
-      :intr #'(lambda (dmns gmsm)
-		(declare
-		  (fixnum dmns)
-		  (type gmsm gmsm))
-		(if (= dmns n)
-		   (do ((gmsm gmsm (gmsm (first (gbar-list gmsm))))
-			(dmns dmns (1- dmns)))
-		       ((= 1 dmns)
-			(term-cmbn 0 (first gmsm) :z-gnrt))
-		       (declare
-			 (type gmsm gmsm)
-			 (fixnum dmns)))
-		  (zero-cmbn (- dmns n))))
-      :strt :gnrt
-      :dfnt `(k-z-fundamental-class ,n))))
-
-#|
-  (cat-init)
-  (setf c1 (k-z-fundamental-class 1))
-  (? c1 1 '(34))
-  (? c1 2 '(34 45))
-  (setf c3 (k-z-fundamental-class 3))
-  (? c3 3 (z-fundamental-gmsm 3 45))
-|#
-
-(DEFUN K-Z2-FUNDAMENTAL-CLASS (n)
-  (declare (fixnum n))
-  (the morphism
-    (morphism
-      :sorc (k-z2 n) :trgt (z-chcm) :degr (- n)
-      :intr #'(lambda (dmns gmsm)
-		(declare
-		  (fixnum dmns)
-		  (ignore gmsm))
-		(if (= dmns n)
-		   (term-cmbn 0 1 :z-gnrt)
-		  (zero-cmbn (- dmns n))))
-      :strt :gnrt
-      :dfnt `(k-z2-fundamental-class ,n))))
-
-#|
-  (cat-init)
-  (setf c1 (k-z2-fundamental-class 1))
-  (? c1 1 1)
-  (? c1 2 2)
-  (setf c3 (k-z2-fundamental-class 3))
-  (? c3 3 (z2-fundamental-gmsm 3 1))
-|#
-
diff --git a/archive/Kenzo-2/Kenzo-2-Acl8/kan.cl b/archive/Kenzo-2/Kenzo-2-Acl8/kan.cl
deleted file mode 100644
index 7b8f305..0000000
--- a/archive/Kenzo-2/Kenzo-2-Acl8/kan.cl
+++ /dev/null
@@ -1,182 +0,0 @@
-;;;  KAN  KAN  KAN  KAN  KAN  KAN  KAN  KAN  KAN  KAN  KAN  KAN
-;;;  KAN  KAN  KAN  KAN  KAN  KAN  KAN  KAN  KAN  KAN  KAN  KAN
-;;;  KAN  KAN  KAN  KAN  KAN  KAN  KAN  KAN  KAN  KAN  KAN  KAN
-
-(IN-PACKAGE "CAT")
-
-(provide "kan")
-
-(DEFMETHOD PRINT-OBJECT ((kan kan) stream)
-  (the kan
-     (progn
-       (format stream "[K~D Kan-Simplicial-Set]" (idnm kan))
-       kan)))
-
-(DEFMACRO KFLL (&rest rest)
-  (ecase (length rest)
-     (1 `(kfll1 ,@rest))
-     (4 `(kfll4 ,@rest))))
-
-(DEFMACRO KFLL4 (kan indx dmns hat)
-  `(funcall (kfll1 ,kan) ,indx ,dmns ,hat))
-
-#|
-  (setf d (delta-infinity))
-  (defun vertex-i (absm i)
-     (with-absm (dgop gmsm) absm
-       (let ((dgop (nreverse (dgop-int-ext dgop)))
-             (gmsm (dlop-int-ext gmsm)))
-         (do ((dgop-mark dgop)
-              (gmsm-mark gmsm)
-              (ii 0 (1+ ii)))
-             ((= i ii) (car gmsm-mark))
-            (if (and dgop-mark
-                     (= ii (car dgop-mark)))
-               (pop dgop-mark)
-               (pop gmsm-mark))))))
-  (vertex-i (absm 0 1) 0)
-  (vertex-i (absm 1 1) 0)
-  (vertex-i (absm 1 1) 1)
-  (vertex-i (absm 0 3) 0)
-  (vertex-i (absm 0 3) 1)
-  (vertex-i (absm 3 1) 0)
-  (vertex-i (absm 3 1) 1)
-  (vertex-i (absm 3 1) 2)
-  (vertex-i (absm 1 3) 0)
-  (vertex-i (absm 1 3) 1)
-  (vertex-i (absm 1 3) 2)
-  (vertex-i (absm 2 3) 0)
-  (vertex-i (absm 2 3) 1)
-  (vertex-i (absm 2 3) 2)
-  (vertex-i (absm 0 7) 0)
-  (vertex-i (absm 0 7) 1)
-  (vertex-i (absm 0 7) 2)
-  (defun absm-int-ext (absm)
-     (with-absm (dgop gmsm) absm
-        (do ((dgop (nreverse (dgop-int-ext dgop)))
-             (gmsm (rest (dlop-int-ext gmsm)))
-             (i 0 (1+ i))
-             (rslt (list (first (dlop-int-ext gmsm)))))
-            ((and (endp dgop) (endp gmsm)) (nreverse rslt))
-           (if dgop
-              (if (= i (car dgop))
-                 (progn
-                   (pop dgop)
-                   (push (first rslt) rslt))
-                 (push (pop gmsm) rslt))
-              (return (nreconc rslt gmsm))))))
-  (defun absm-ext-int (vlist)
-     (do ((dgop nil)
-          (gmsm (list (first vlist)))
-          (mark (rest vlist) (cdr mark))
-          (idgop 0 (1+ idgop)))
-         ((endp mark) (absm (dgop-ext-int dgop)
-                            (dgop-ext-int gmsm)))
-        (if (= (first gmsm) (car mark))
-           (push idgop dgop)
-           (push (car mark) gmsm))))
-  (absm-ext-int '(0 0 0 1 2 3 3 3))
-  (absm-ext-int '(0 1 1 1 2))
-  (absm-int-ext (absm-ext-int '(0 0 0 1 2 3 3 3)))
-  (absm-int-ext (absm-ext-int '(0 1 1 1 2)))
-  (defun dkfll (indx dmns hat)
-     (cond ((= 1 dmns)
-            (absm 1 (gmsm (first hat))))
-           ((= 0 indx)
-            (let ((del-1 (absm-int-ext (first hat)))
-                  (del-2 (absm-int-ext (second hat))))
-              (absm-ext-int
-                 (cons (first del-1)
-                       (cons (second del-2) (rest del-1))))))
-           ((= 1 indx)
-            (let ((del-0 (absm-int-ext (first hat)))
-                  (del-2 (absm-int-ext (second hat))))
-              (absm-ext-int
-                 (cons (first del-2) del-0))))
-           (t
-            (let ((del-0 (absm-int-ext (first hat)))
-                  (del-1 (absm-int-ext (second hat))))
-              (absm-ext-int
-                 (cons (first del-1) del-0))))))
-  (smst-kan d #'dkfll)
-  (kfll d 0 1 (list (absm 0 1)))
-  (kfll d 0 2 (list (absm 0 5) (absm 0 3)))
-  (kfll d 1 2 (list (absm 0 6) (absm 0 3)))
-  (kfll d 2 2 (list (absm 0 6) (absm 0 5)))
-  (kfll d 0 2 (list (absm 0 3) (absm 0 3)))
-  (kfll d 1 2 (list (absm 1 2) (absm 0 3)))
-|#
-
-(DEFUN CHECK-HAT (kan indx dmns hat)
-  (declare
-     (type kan kan)
-     (fixnum indx dmns)  ;;; dmns like in (funcall kfll ...)
-     (list hat))
-  (assert (= dmns (length hat)))
-  (setf hat
-	(append (subseq hat 0 indx)
-		(list :hole)
-		(nthcdr indx hat)))
-  (do ((cmpr (cmpr kan))
-       (j 0 (1+ j)))
-      ((> j dmns) t)
-      (declare
-         (type cmprf cmpr)
-	 (fixnum j))
-     (unless (= j indx)
-       (let ((del-j (nth j hat)))
-	 (declare (type absm del-j))
-	 (do ((i j (1+ i)))
-	     ((= i dmns))
-	     (declare (fixnum i))
-	    (unless (= i (1- indx))
-	      (let ((del-i-del-j (face kan i (1- dmns) del-j))
-		    (del-j-del-i+1 (face kan j (1- dmns)
-					 (nth (1+ i) hat))))
-		(declare (type absm del-i-del-j del-j-del-i+1))
-		(assert (eq :equal
-			    (a-cmpr3 cmpr del-i-del-j del-j-del-i+1))))))))))
-
-#|
-  (setf od (gdeltab))
-  (setf s (loop3 0 31 2))
-  (setf faces (mapcar #'(lambda (indx) (face od indx 3 s))
-                      '(0 1 2 3)))
-  (delete (nth 1 faces) faces)
-  (check-hat od 1 3 faces)
-  (setf (nth 2 faces) (nth 1 faces))
-  (check-hat od 1 3 faces)
-|#
-
-
-(DEFUN CHECK-KAN (kan indx dmns hat)
-  (declare
-     (type kan kan)
-     (fixnum indx dmns)
-     (list hat))
-  (the (values)
-     (let ((rslt (kfll kan indx dmns hat))
-	   (cmpr (cmpr kan))
-	   (face (face kan)))
-       (declare
-	  (type absm rslt)
-	  (type cmprf cmpr)
-	  (type face face))
-       (check-hat kan indx dmns hat)
-       (do ((i 0 (1+ i)))
-	   ((> i dmns))
-	  (declare (fixnum i))
-	  (unless (= i indx)
-	    (let ((x-i (pop hat))
-		  (del-i-rslt (a-face4 face i dmns rslt)))
-	      (declare (type absm x-i del-i-rslt))
-	      (with-absm (dgop1 gmsm1) x-i
-	      (with-absm (dgop2 gmsm2) del-i-rslt
-		 (unless (and (= dgop1 dgop2)
-			      (eq (funcall cmpr gmsm1 gmsm2) :equal))
-		    (error "Wrong result:~@
-                            Fill = ~A~@
-                            Del-~D(Fill) = ~A~@
-                            Hat-~D = ~A"
-		       rslt i del-i-rslt i x-i)))))))
-       (done))))
\ No newline at end of file
diff --git a/archive/Kenzo-2/Kenzo-2-Acl8/loop-spaces.cl b/archive/Kenzo-2/Kenzo-2-Acl8/loop-spaces.cl
deleted file mode 100644
index 1beb970..0000000
--- a/archive/Kenzo-2/Kenzo-2-Acl8/loop-spaces.cl
+++ /dev/null
@@ -1,610 +0,0 @@
-;;;  LOOP-SPACES  LOOP-SPACES  LOOP-SPACES  LOOP-SPACES  LOOP-SPACES  LOOP-SPACES
-;;;  LOOP-SPACES  LOOP-SPACES  LOOP-SPACES  LOOP-SPACES  LOOP-SPACES  LOOP-SPACES
-;;;  LOOP-SPACES  LOOP-SPACES  LOOP-SPACES  LOOP-SPACES  LOOP-SPACES  LOOP-SPACES
-
-(IN-PACKAGE "CAT")
-
-(PROVIDE "loop-spaces")
-
-(DEFCONSTANT +NULL-LOOP+ (make-loop :list +empty-list+))
-
-;;; NILOOP = non-normalized iloop; a common dgop is possible.
-
-(DEFUN NORMALIZE-LOOP (dmns niloop)
-   (declare (list niloop))      
-   (the absm
-      (progn
-         (unless niloop
-            (return-from normalize-loop
-               (absm (mask dmns) +null-loop+)))
-         (let ((dgop (apply #'logand (mapcar #'car niloop))))
-            (declare (fixnum dgop))
-            (if (zerop dgop)
-               (absm 0 (make-loop :list niloop))
-               (absm dgop
-                  (make-loop
-                     :list (mapcar #'(lambda (apowr)
-                                        (cons
-                                           (dgop/dgop (apdgop apowr) dgop)
-                                           (cdr apowr)))
-                              niloop))))))))
-
-#|
-  (normalize-loop 4 +empty-list+)
-  (normalize-loop 4 '((1 a . 1)))
-  (normalize-loop 4 '((1 a . 1) (3 b . 1) (5 b . 1)))
-|#
-
-(DEFUN UNNORMALIZE-LOOP (absm)
-  (declare (type absm absm))
-  (the iloop
-     (with-absm (dgop loop) absm
-        (mapcar #'(lambda (apowr)
-		    (declare (type apowr apowr))
-		    (cons (dgop*dgop dgop (car apowr))
-			  (cdr apowr)))
-		(loop-list loop)))))
-
-#|
-  (unnormalize-loop (absm 1 (loop3 2 'a 3)))
-|#
-
-(DEFUN LOOP3 (&rest list)
-   (when (and (= 1 (length list))
-              (listp (first list)))
-      (setf list (first list)))
-   (unless (zerop (mod (length list) 3))
-      (error "In LOOP3, 3 should divide the list length."))
-   (flet ((fixnumpp (object)
-             (unless (typep object 'fixnum)
-                (error "In LOOP3, ~A should be a fixnum." object))
-             object))
-      (do ((rslt +empty-list+ (cons (apowr
-                                       (fixnumpp (car mark))
-                                       (cadr mark)
-                                       (fixnumpp (caddr mark)))
-                                 rslt))
-           (mark list (cdddr mark)))
-          ((endp mark) (make-loop :list (nreverse rslt)))
-         (declare (list rslt mark)))))
-
-#|
-  (loop3 nil)
-  (loop3 '(1 a 2 3 b -2))
-  (loop3 '(1 a 2 3 b b))
-  (loop3 '(1 a 2 3 b))
-  (loop3 1 'a 2 3 'b 4)
-  (loop3 1 'a 2 3 'b)
-|#
-
-(DEFMETHOD PRINT-KEYCONS ((car (eql :loop)) cdr stream)
-   (declare
-      (list cdr)
-      (stream stream))
-   (the loop
-      (progn
-         (format stream "<<Loop")
-         (dolist (apowr cdr)
-            (declare (type apowr apowr))
-            (with-apowr (dgop gmsm expn) apowr
-               (format stream "[")
-               (unless (zerop dgop)
-                  (format stream "~A " (hyphenize-list (dgop-int-ext dgop))))
-               (format stream "~A" gmsm)
-               (unless (= 1 expn)
-                  (format stream "\\~D" expn))
-               (format stream "]")))
-         (format stream ">>")
-         (cons car cdr))))
-
-#|
-  (loop3 nil)
-  (loop3 '(0 a 2))
-  (loop3 '(1 a 2))
-  (loop3 '(3 a 2 5 b -1 6 c 4))
-  (loop3 '(7 a 1 11 b 1 13 c 1 14 d 1))
-  (loop3 '(7 a 1 11 b 1 13 c 1 7 d 1))
-  (loop3 '(0 a 1 0 b 2 0 c -1 1 d 1))
-|#
-
-(DEFUN APOWR-NILOOP (cmpr apowr niloop)
-   (declare
-      (type cmprf cmpr)
-      (type apowr apowr)
-      (type iloop niloop))
-   (the iloop
-      (progn
-         (unless niloop
-            (return-from apowr-niloop
-               (list apowr)))
-         (let ((apowr2 (first niloop)))
-            (declare (type apowr apowr2))
-            (with-apowr (dgop2 gmsm2 expn2) apowr2
-               (unless (and (= (apdgop apowr) dgop2)
-                            (eq :equal (funcall cmpr (apgmsm apowr) gmsm2)))
-                  (return-from apowr-niloop
-                     (cons apowr niloop)))
-               (incf expn2 (apexpn apowr))
-               (if (zerop expn2)
-                  (rest niloop)
-                  (cons (apowr dgop2 gmsm2 expn2) (rest niloop))))))))
-
-#|
-  (apowr-niloop #'s-cmpr '(0 a . 1) +empty-list+)
-  (apowr-niloop #'s-cmpr '(0 a . 1) '((1 a . 1)))
-  (apowr-niloop #'s-cmpr '(0 a . 1) '((0 b . 1)))
-  (apowr-niloop #'s-cmpr '(0 a . 1) '((0 a . 1) (0 b . 1)))
-  (apowr-niloop #'s-cmpr '(0 a . 1) '((0 a . -1) (0 b . 1)))
-|#
-
-(DEFUN LOOP-SPACE-CMPR (cmpr)
-   (declare (type cmprf cmpr))
-   (flet ((2apowr-cmpr (apowr1 apowr2)
-           (declare (type apowr apowr1 apowr2))
-           (lexico
-              (f-cmpr (apdgop apowr1) (apdgop apowr2))
-              (funcall cmpr (apgmsm apowr1) (apgmsm apowr2))
-              (f-cmpr (apexpn apowr1) (apexpn apowr2)))))
-      (flet ((rslt (loop1 loop2)
-              (declare (type loop loop1 loop2))
-              (maplexico #'2apowr-cmpr (loop-list loop1) (loop-list loop2))))
-         (the cmprf #'rslt))))
-
-#|
-  (setf cmpr (loop-space-cmpr #'s-cmpr))
-  (funcall cmpr (loop3 '(1 a 2)) (loop3 '(1 a -1)))
-  (funcall cmpr (loop3 '(3 b 4 1 a 2)) (loop3 '(3 b 4 1 a -1)))
-|#
-
-(DEFUN APOWR-FACE4 (face indx dmns apowr)
-   ;; dmns = dimension in the loop-space
-   (declare
-      (type face face)
-      (type apowr apowr))
-   (with-apowr (dgop gmsm expn) apowr
-      (let ((face (a-face4 face indx (1+ dmns) (absm dgop gmsm))))
-         (declare (type absm face))
-         (with-absm (dgop gmsm) face
-            (if (logbitp (1- dmns) dgop)
-               nil
-               (apowr dgop gmsm expn))))))
-
-#|
-  (setf face (face (delta-infinity)))
-  (apowr-face4 face 3 4 (apowr 1 31 5))
-  (setf face (face (sphere 5)))
-  (apowr-face4 face 2 5 (apowr 1 's5 4))
-  (apowr-face4 face 2 5 (apowr 2 's5 4))
-|#
-
-(DEFUN APOWR-LASTFACE4 (cmpr face dmns apowr)
-   ;; indx =dmns
-   (declare
-      (type cmprf cmpr)
-      (type face face)
-      (fixnum dmns)
-      (type apowr apowr))
-   (the list
-      (with-apowr (dgop gmsm expn) apowr
-         (let ((absm (absm dgop gmsm)))
-            (declare (type absm absm))
-            (let ((face-n (a-face4 face dmns (1+ dmns) absm))
-                  (face-n+1 (a-face4 face (1+ dmns) (1+ dmns) absm)))
-               (declare (type absm face-n face-n+1))
-               (with-absm (dgop1 gmsm1) face-n
-               (with-absm (dgop2 gmsm2) face-n+1
-                  (if (logbitp (1- dmns) dgop1)
-                     (if (logbitp (1- dmns) dgop2)
-                        (return-from apowr-lastface4 +empty-list+)
-                        (return-from apowr-lastface4
-                           (list (apowr dgop2 gmsm2 (- expn)))))
-                     (when (logbitp (1- dmns) dgop2)
-                        (return-from apowr-lastface4
-                           (list (apowr dgop1 gmsm1 expn)))))
-                  (when (and (= dgop1 dgop2)
-                             (eq :equal (funcall cmpr gmsm1 gmsm2)))
-                     (return-from apowr-lastface4 +empty-list+))
-                  (case expn
-                     (+1 (list (apowr dgop2 gmsm2 -1) (apowr dgop1 gmsm1 +1)))
-                     (-1 (list (apowr dgop1 gmsm1 -1) (apowr dgop2 gmsm2 +1)))
-                     (otherwise
-                        (if (plusp expn)
-                           (do ((rslt +empty-list+ (cons apowr2 (cons apowr1 rslt)))
-                                (apowr1 (apowr dgop1 gmsm1 +1))
-                                (apowr2 (apowr dgop2 gmsm2 -1))
-                                (nark expn (1- nark)))
-                               ((zerop nark) rslt)
-                              (declare
-                                 (list rslt)
-                                 (type apowr apowr1 apowr2)))
-                              (do ((rslt +empty-list+ (cons apowr1 (cons apowr2 rslt)))
-                                   (apowr1 (apowr dgop1 gmsm1 -1))
-                                   (apowr2 (apowr dgop2 gmsm2 +1))
-                                   (nark expn (1+ nark)))
-                                  ((zerop nark) rslt)
-                                 (declare
-                                    (list rslt)
-                                    (type apowr apowr1 apowr2)))))))))))))
-
-#|
-  (setf cmpr #'f-cmpr face (face (delta-infinity)))
-  (apowr-lastface4 cmpr face 4 (apowr 0 63 1))
-  (apowr-lastface4 cmpr face 4 (apowr 0 63 -1))
-  (apowr-lastface4 cmpr face 4 (apowr 0 63 3))
-  (apowr-lastface4 cmpr face 4 (apowr 0 63 -3))
-  (apowr-lastface4 cmpr face 4 (apowr 8 31 1))
-  (setf face #'(lambda (indx dmns gmsm)  ;  dmns = 5
-                  (case indx
-                     (5 (absm 8 'a))
-                     (4 (absm 8 'a)))))
-  (setf cmpr #'s-cmpr)
-  (apowr-lastface4 cmpr face 4 (apowr 0 'a 2))
-  (setf face #'(lambda (indx dmns gmsm)  ;  dmns = 5
-                  (case indx
-                     (5 (absm 1 'a))
-                     (4 (absm 8 'a)))))
-  (apowr-lastface4 cmpr face 4 (apowr 0 'a 2))
-  (setf face #'(lambda (indx dmns gmsm)  ;  dmns = 5
-                  (case indx
-                     (5 (absm 1 'a))
-                     (4 (absm 1 'a)))))
-  (apowr-lastface4 cmpr face 4 (apowr 0 'a 2))
-|#
-                                   
-(DEFUN LOOP-SPACE-FACE (cmpr face)
-   (declare
-      (type cmprf cmpr)
-      (type face face))
-   (flet ((rslt (indx dmns loop)
-             (declare
-                (fixnum indx dmns)
-                (type loop loop))
-             (the absm
-                (let ((rslt +empty-list+))
-                   (declare (type iloop rslt))
-                   (if (< indx dmns)
-                      (dolist (apowr (loop-list loop))
-                         (declare (type apowr apowr))
-                         (let ((lface (apowr-face4 face indx dmns apowr)))
-                            (declare (type (or null apowr) lface))
-                            (when lface (setf rslt (apowr-niloop cmpr lface rslt)))))
-                      (dolist (apowr (loop-list loop))
-                         (declare (type apowr apowr))
-                         (let ((lface (apowr-lastface4 cmpr face dmns apowr)))
-                            (declare (list lface))
-                            (dolist (apowr lface)
-                               (declare (type apowr apowr))
-                               (setf rslt (apowr-niloop cmpr apowr rslt))))))
-                   (normalize-loop (1- dmns) (nreverse rslt))))))
-      (the face #'rslt)))
-
-#|
-  (setf cmpr #'f-cmpr
-        face (face (delta-infinity)))
-  (setf rslt (loop-space-face cmpr face))
-  (funcall rslt 2 4 (loop3 '(0 63 3 1 31 -3)))
-  (funcall rslt 2 4 (loop3 '(0 63 3 0 63 -3)))
-  (funcall rslt 4 4 (loop3 '(0 63 3 0 63 -3)))
-  (funcall rslt 4 4 (loop3 '(0 63 3)))
-|#
-
-(DEFUN LOOP-SPACE-FACE* (cmpr face)
-   (declare
-      (type cmprf cmpr)
-      (type face face))
-   (flet ((rslt (indx dmns loop)
-             (declare
-                (fixnum indx dmns)
-                (type loop loop))
-             (the (or loop (eql :degenerate))
-                (let ((rslt +empty-list+))
-                   (declare (type iloop rslt))
-                   (if (< indx dmns)
-                      (dolist (apowr (loop-list loop))
-                         (declare (type apowr apowr))
-                         (let ((lface (apowr-face4 face indx dmns apowr)))
-                            (declare (type (or null apowr) lface))
-                            (when lface (setf rslt (apowr-niloop cmpr lface rslt)))))
-                      (dolist (apowr (loop-list loop))
-                         (declare (type apowr apowr))
-                         (let ((lface (apowr-lastface4 cmpr face dmns apowr)))
-                            (declare (list lface))
-                            (dolist (apowr lface)
-                               (declare (type apowr apowr))
-                               (setf rslt (apowr-niloop cmpr apowr rslt))))))
-                   (if (zerop (apply #'logand (mapcar #'car rslt)))
-                      (make-loop :list (nreverse rslt))
-                      :degenerate)))))
-      (the face* #'rslt)))
-
-(DEFUN LOOP-SPACE-GRIN-SINTR (dmns loop)
-  (declare
-     (ignore dmns)
-     (type loop loop))
-  (the absm
-     (absm 0 (make-loop
-	      :list (mapcar #'(lambda (apowr)
-				(declare (type apowr apowr))
-				(with-apowr (dgop gmsm expn) apowr
-					    (apowr dgop gmsm (- expn))))
-			    (reverse (loop-list loop)))))))
-
-#|
-  (loop-space-grin-sintr 5 (loop3 0 'a 2 3 'b -3))
-|#
-
-(DEFUN LOOP-SPACE-GRML-SINTR (cmpr)
-  (declare (type cmprf cmpr))
-  (flet ((rslt (dmns crpr)
-	    (declare
-	       (fixnum dmns)
-	       (type crpr crpr))
-	    (the absm
-	       (with-crpr (absm1 absm2) crpr
-	         (let ((niloop1 (nreverse (unnormalize-loop absm1)))
-		       (niloop2 (unnormalize-loop absm2)))
-		   (declare (type iloop niloop1 niloop2))
-		   (loop
-		    (unless niloop1 (return))
-		    (unless niloop2 (return))
-		    (let ((apowr1 (first niloop1))
-			  (apowr2 (first niloop2)))
-		      (declare (type apowr apowr1 apowr2))
-		      (with-apowr (dgop1 gmsm1 expn1) apowr1
-		      (with-apowr (dgop2 gmsm2 expn2) apowr2
-		         (unless (and (= dgop1 dgop2)
-				      (eq :equal (funcall cmpr gmsm1 gmsm2)))
-			    (return))
-			 (incf expn1 expn2)
-			 (cond ((zerop expn1)
-				(pop niloop1)
-				(pop niloop2))
-			       (t
-				(pop niloop1)
-				(setf niloop2
-				      (cons (apowr dgop2 gmsm2 expn1)
-					    (rest niloop2)))
-				(return)))))))
-		   (normalize-loop dmns
-				   (nreconc niloop1 niloop2)))))))
-     (the sintr #'rslt)))
-
-#|
-  (setf cmpr #'s-cmpr)
-  (setf ml (loop-space-grml-sintr cmpr))
-  (funcall ml 2 (crpr 3 (loop3) 0 (loop3 0 'a 2)))
-  (funcall ml 2 (crpr 0 (loop3 0 'a 2) 3 (loop3)))
-  (funcall ml 2 (crpr 0 (loop3 0 'a 2) 0 (loop3 0 'a -2)))
-  (funcall ml 2 (crpr 0 (loop3 0 'a 2) 0 (loop3 0 'a -3)))
-  (funcall ml 2 (crpr 0 (loop3 0 'a 2) 0 (loop3 0 'b -3)))
-  (funcall ml 2 (crpr 0 (loop3 0 'a 2 0 'b -3)
-                      0 (loop3 0 'b +3 0 'a -2)))
-|#
-
-(DEFUN LOOP-SPACE (smst &optional (n 1))
-   (declare
-      (type simplicial-set smst)
-      (fixnum n))   
-   (the simplicial-group
-      (if (= n 1)
-         (with-slots (cmpr face) smst
-            (declare
-               (type cmprf cmpr)
-	       (type face face))
-	    (simplicial-group
-	       :cmpr (loop-space-cmpr cmpr)
-	       :basis :locally-effective
-	       :bsgn +null-loop+
-	       :face (loop-space-face cmpr face)
-	       :face* (loop-space-face* cmpr face)
-	       :grml-sintr (loop-space-grml-sintr cmpr)
-	       :grin-sintr #'loop-space-grin-sintr
-	       :dfnt `(loop-space ,smst)))
-	(loop-space (loop-space smst) (1- n)))))
-
-(DEFUN GDELTAB ()
-   (loop-space (deltab)))
-
-#|
-  (cat-init)
-  (setf g (gdeltab))
-  (cmpr g (loop3 0 3 2) (loop3 0 3 2))
-  (cmpr g (loop3 0 3 2) (loop3 0 3 3))
-  (cmpr g (loop3 0 3 2) (loop3 0 5 2))
-  (cmpr g (loop3 0 5 2) (loop3 0 3 2))
-  (face g 3 3 (loop3 12 7 3))
-  (face g 3 3 (loop3 5 7 3))
-  (face g 3 3 (loop3 6 7 3 5 7 3 3 7 3))
-  (face g 4 4 (absm 4 (loop3 6 7 3 5 7 3 3 7 3)))
-  (check-faces (cmpr g) (face g) 3 (loop3 6 7 -3 5 7 -3 3 7 -3))
-  (setf dd (cmps g g))
-  (? dd 3 (loop3 6 7 3 5 7 3 3 7 3))
-  (grml g 2 (crpr 0 (loop3 0 15 3) 0 (loop3 0 15 4)))
-  (grin g 2 (loop3 0 15 -2))
-  (setf rslt (loop3 0 31 1))
-  (setf hat (mapcar #'(lambda (i) (face g i 3 rslt))
-                    (<a-b> 0 3)))
-  (dotimes (i 4)
-    (print (kfll g i 3 (remove (nth i hat) hat :test #'equal)))
-    (check-kan g i 3 (remove (nth i hat) hat :test #'equal)))
-
-  (setf g (loop-space (sphere 2)))
-  (setf rslt (loop3 3 's2 2 5 's2 -2 6 's2 2))
-  (setf hat (mapcar #'(lambda (i) (face g i 3 rslt))
-                    (<a-b> 0 3)))
-  (dotimes (i 4)
-    (print (kfll g i 3 (remove (nth i hat) hat :test #'equal)))
-    (check-kan g i 3 (remove (nth i hat) hat :test #'equal)))
-
-  (setf g (loop-space (sphere 3) 2))
-  (setf x (first (basis (echcm g) 4)))
-  (setf efhm (efhm g))
-  (setf x (lf efhm (rg efhm 4 x)))
-  (setf rslt (gnrt (first (cmbn-list x))))
-  (setf hat (mapcar #'(lambda (i) (face g i 4 rslt))
-                    (<a-b> 0 4)))
-  (dotimes (i 5)
-    (print (kfll g i 4 (remove (nth i hat) hat :test #'equal)))
-    (check-kan g i 4 (remove (nth i hat) hat :test #'equal)))
-
-  (setf rslt (gnrt (third (cmbn-list x))))
-  (setf hat (mapcar #'(lambda (i) (face g i 4 rslt))
-                    (<a-b> 0 4)))
-  (dotimes (i 5)
-    (print (kfll g i 4 (remove (nth i hat) hat :test #'equal)))
-    (check-kan g i 4 (remove (nth i hat) hat :test #'equal)))
-
-  (setf g (loop-space (sphere 3) 2))
-  (setf efhm (efhm g))
-  (setf echcm (rbcc efhm))
-  (setf basis (basis echcm 4))
-  (setf cmbn (cmbn 4 1 (first basis) 10 (second basis)
-                     100 (third basis)))
-  (setf cmbn2 (lf efhm (rg efhm cmbn)))
-  (setf loop-list (mapcar #'cdr (cmbn-list cmbn2)))
-  (dolist (loop loop-list)
-    (setf hat (mapcar #'(lambda (i) (face g i 4 loop))
-                      (<a-b> 0 4)))
-    (dotimes (i 5)
-      (print (kfll g i 4 (remove (nth i hat) hat)))
-      (check-kan g i 4 (remove (nth i hat) hat))))
-|#
-
-#|
-  (cat-init)
-  (setf p (r-proj-space 3))
-  (setf op (loop-space p))
-  (defun random-apowr (dmns max-expn)
-     (loop
-        (let* ((dgop (random (2-exp (1- dmns))))
-               (gmsm (- dmns (logcount dgop))))
-           (unless (< 0 gmsm 3)
-              (return-from random-apowr
-                 (apowr dgop gmsm (srandom max-expn)))))))
-  (dotimes (i 15) (print (random-apowr 8 3)))
-  (defun random-niloop (dmns max-expn length)
-     (mapcar #'(lambda (dummy)
-                  (random-apowr (1+ dmns) max-expn))
-        (make-list length)))
-  (dotimes (i 20)
-     (print (normalize-loop 7 (random-niloop 7 3 3))))
-  (defun random-loop-cmbn (cmpr degr max-cffc max-expn loop-length cmbn-length)
-     (do ((rslt +empty-list+ (cons term rslt))
-          (i cmbn-length (1- i))
-          (term))
-         ((zerop i)
-          (apply #'nterm-add cmpr degr rslt))
-        (setf term
-              (term (srandom max-cffc)
-                 (make-loop :list (random-niloop degr max-expn loop-length))))))
-  (setf cmpr (cmpr op))
-  (setf +too-much-time+ -1)
-  (setf c (random-loop-cmbn cmpr 8 10 4 4 100))
-  (time (? op (? op c)))
-  (time (? op (? op c)))
-|#
-  
-#|  ;; in EAT.
-  (DEFUN PR-INFINITY-EQS (gsm1 gsm2)
-     (declare (fixnum gsm1 gsm2))
-     t)
-
-  (DEFUN PR-INFINITY-BASIS (k)
-     (declare (fixnum k))
-     (flet ((rslt (dmns)
-               (declare (fixnum dmns))
-               (if (< 0 dmns k)
-                  empty-list
-                  (list dmns))))
-        (the basis #'rslt)))
-
-  (DEFUN PR-INFINITY-GDL (k)
-     (declare (fixnum k))
-     (flet ((rslt (indx dmns gsm)
-             (declare (fixnum indx dmns gsm))
-             (if (<= dmns k)
-                (asm (nreverse (<a-b< 0 (1- dmns))) 0)
-                (if (or (zerop indx)
-                        (= indx dmns))
-                   (asm nil (1- dmns))
-                   (if (= dmns (1+ k))
-                      (asm (nreverse (<a-b< 0 (1- dmns))) 0)
-                      (asm (list (1- indx)) (- dmns 2)))))))
-        (the function #'rslt)))
-
-  (DEFUN PR-INFINITY (&optional (k 1))
-     (declare (fixnum k))
-     (build-ss
-         :eqs #'pr-infinity-eqs
-         :sbs (pr-infinity-basis k)
-         :bsp 0
-         :gdl (pr-infinity-gdl k)
-         :org `(pr-infinity ,k)))
-
-  (setf p (pr-infinity))
-  (sbs p 4)
-  (dotimes (i 5)
-     (print (gdl p i 4 4)))
-  (setf cc (ss-cc p))
-  (dotimes (i 5)
-     (print (d-? cc i i)))
-  (setf dd (cmp-mrp (cc-d cc) (cc-d cc)))
-  (dotimes (i 6)
-     (print (? dd i i)))
-  (setf p (pr-infinity 3))
-  (dotimes (i 7)
-     (print (sbs p i)))
-  (dotimes (i 5)
-     (print (gdl p i 4 4)))
-  (setf d (cc-d (ss-cc p)))
-  (dotimes (i 7)
-     (print (? d i i)))
-  (setf dd (cmp-mrp d d))
-  (dotimes (i 7)
-     (print (? dd i i)))
-
-  (setf p (pr-infinity 3))
-  (setf op (loop-space p))
-  (defun srandom (max)
-     (let ((rslt (- (random (+ max max)) max)))
-        (if (zerop rslt)
-           max
-           rslt)))
-  (dotimes (i 20) (print (srandom 3)))
-  (DEFUN DGOP-INT-EXT (dop)
-     (declare (fixnum dop))
-     (the list
-        (do ((dop dop (ash dop -1))
-             (rslt empty-list)
-             (bmark 0 (1+ bmark)))
-            ((zerop dop) rslt)
-           (declare
-              (fixnum dop bmark)
-              (list rslt))
-           (when (oddp dop)
-              (push bmark rslt)))))
-  (defun random-apowr (dmns max-expn)
-     (let ((dgop (dgop-int-ext (* 2 (random (2-exp (1- dmns)))))))
-        (pwr (asm dgop (- 8 (length dgop))) (srandom max-expn))))
-  (dotimes (i 5) (print (random-apowr 8 3)))
-  (defun random-niloop (dmns max-expn length)
-     (mapcar #'(lambda (dummy)
-                  (random-apowr (1+ dmns) max-expn))
-        (make-list length)))
-  (dotimes (i 20)
-     (print (normalize-loop 7 (make-strloop :lst (random-niloop 7 3 3)))))
-  (defun random-loop-cmbn (degr max-cffc max-expn loop-length cmbn-length)
-     (do ((rslt empty-list (cons mnm rslt))
-          (i cmbn-length (1- i))
-          (term))
-         ((zerop i)
-          (make-cmb :dgr degr :lst rslt))
-        (setf mnm
-              (mnm (srandom max-cffc)
-                 (make-strloop :lst (random-niloop degr max-expn loop-length))))))
-  (setf d (cc-d (ss-cc op)))
-  (setf c (random-loop-cmbn 8 10 4 4 100))
-  (time (??? d (??? d c)))
-  (time (??? d (??? d c)))
-|#
-
diff --git a/archive/Kenzo-2/Kenzo-2-Acl8/lp-space-efhm.cl b/archive/Kenzo-2/Kenzo-2-Acl8/lp-space-efhm.cl
deleted file mode 100644
index e8ba2b5..0000000
--- a/archive/Kenzo-2/Kenzo-2-Acl8/lp-space-efhm.cl
+++ /dev/null
@@ -1,644 +0,0 @@
-;;;  LP-SPACE-EFHM  LP-SPACE-EFHM  LP-SPACE-EFHM  LP-SPACE-EFHM
-;;;  LP-SPACE-EFHM  LP-SPACE-EFHM  LP-SPACE-EFHM  LP-SPACE-EFHM
-;;;  LP-SPACE-EFHM  LP-SPACE-EFHM  LP-SPACE-EFHM  LP-SPACE-EFHM
-
-(IN-PACKAGE "CAT")
-
-(PROVIDE "lp-space-efhm")
-
-(DEFUN LS-HAT-U-U (space
-                  &aux (cobar (cobar space))
-                       (loop-space (loop-space space))
-                       (spac-tnsr-lpsp (tnsr-prdc space loop-space)))
-   (declare
-      (type simplicial-set space)
-      (type chain-complex cobar spac-tnsr-lpsp)
-      (type simplicial-group loop-space))
-   (the chain-complex
-      (tnsr-prdc cobar spac-tnsr-lpsp)))
-
-(DEFUN LS-HAT-LEFT-PERTURBATION-INTR (space)
-   (declare (type simplicial-set space))
-   (let ((cprd (cprd space)))
-      (flet ((rslt (degr tnpr)
-                (declare
-                   (fixnum degr)
-                   (type tnpr tnpr))
-                (with-tnpr (degr1 allp1 nil tnpr2) tnpr
-                (with-tnpr (degr21 gmsm21 degr22 loop22) tnpr2
-                   (let ((cprd (cmbn-list (gnrt-? cprd degr21 gmsm21))))
-                      (declare (list cprd))
-                      (setf cprd (rest cprd))    ;;; because \bar{A}
-                      (make-cmbn :degr (1- degr)
-                         :list
-                         (mapcar
-                            #'(lambda (term)
-                                 (declare (type term term))
-                                 (with-term (cffc tnpr21) term
-                                 (with-tnpr (degr211 gmsm211 degr212 gmsm212) tnpr21
-                                    (decf degr211)
-                                    (term cffc
-                                       (tnpr
-                                          (+ degr1 degr211)
-                                          (make-allp
-                                             :list (append
-                                                      (allp-list allp1)
-                                                      (list (cbgn degr211 gmsm211))))
-                                          (+ degr212 degr22)
-                                          (tnpr degr212 gmsm212 degr22 loop22))))))
-                            cprd)))))))
-         (the intr #'rslt))))
-
-(DEFUN LS-HAT-LEFT-PERTURBATION (space)
-   (declare (type simplicial-set space))
-   (the morphism
-      (let ((ls-hat-u-u (ls-hat-u-u space)))
-         (morphism
-            :sorc ls-hat-u-u
-            :trgt ls-hat-u-u
-            :degr -1
-            :intr (ls-hat-left-perturbation-intr space)
-            :strt :gnrt
-            :dfnt `(ls-hat-left-perturbation ,space)))))
-
-(DEFUN LS-HAT-T-U (space
-                  &aux (ls-hat-u-u (ls-hat-u-u space))
-                       (ls-hat-left-perturbation
-                          (ls-hat-left-perturbation space)))
-   (declare
-      (type simplicial-set space)
-      (type chain-complex ls-hat-u-u)
-      (type morphism ls-hat-left-perturbation))
-   (the chain-complex
-      (progn
-         (setf (slot-value ls-hat-left-perturbation 'sorc) ls-hat-u-u
-               (slot-value ls-hat-left-perturbation 'trgt) ls-hat-u-u)
-         ;; because maybe these slots have been modified when constructing
-         ;;   the ls-left-eqvl-right-reduction
-         (add ls-hat-u-u ls-hat-left-perturbation))))
-
-#|
-  (cat-init)
-  (setf c (ls-hat-t-u (deltab)))
-  (defun random-allp (length)
-     (let ((rslt nil))
-        (dotimes (i length)
-           (let* ((gmsm (random (mask 9)))
-                  (dmns (1- (logcount gmsm))))
-              (when (plusp dmns)
-                 (push (cbgn (1- dmns) gmsm) rslt))))
-        (make-allp :list rslt)))
-  (dotimes (i 10) (print (random-allp 5)))
-  (setf allp (random-allp 4))  ;; the degree could be too big
-                               ;; then redo
-  (setf allp-degr (apply #'+ (mapcar #'car (allp-list allp))))
-  (setf gnrt (tnpr allp-degr allp 4 (tnpr 2 7 2 (loop3 0 15 2))))
-  (? c (+ 4 allp-degr) gnrt)
-  (? c *)
-  (dotimes (i 10)
-     (let ((allp (random-allp 3)))
-        (setf allp-degr (apply #'+ (mapcar #'car (allp-list allp))))
-        (setf gnrt (tnpr allp-degr allp 4 (tnpr 2 7 2 (loop3 0 15 2))))
-        (unless (>= allp-degr 11)
-           (print (? c (+ 4 allp-degr) gnrt))
-           (print (? c (? c (+ 4 allp-degr) gnrt))))))
-  (dotimes (i 20)
-     (let ((allp (random-allp 3)))
-        (setf allp-degr (apply #'+ (mapcar #'car (allp-list allp))))
-        (setf gnrt (tnpr allp-degr allp 5 (tnpr 3 15 2 (loop3 0 15 2))))
-        (unless (>= allp-degr 10)
-           (print (? c (+ 5 allp-degr) gnrt))
-           (print (? c (? c (+ 5 allp-degr) gnrt))))))
-  (dotimes (i 20)
-     (let ((allp (random-allp 3)))
-        (setf allp-degr (apply #'+ (mapcar #'car (allp-list allp))))
-        (setf gnrt (tnpr allp-degr allp 5 (tnpr 2 7 3 (loop3 0 31 2))))
-        (unless (>= allp-degr 10)
-           (print (? c (+ 5 allp-degr) gnrt))
-           (print (? c (? c (+ 5 allp-degr) gnrt))))))
-|#
-
-(DEFUN LS-HAT-RIGHT-PERTURBATION (space
-                                 &aux (cobar (cobar space))
-                                      (ls-hat-t-u (ls-hat-t-u space)))
-   (declare
-      (type simplicial-set space)
-      (type chain-complex cobar ls-hat-t-u))
-   (the morphism
-      (multiple-value-bind (szczarba bottom-perturbation)
-                           (szczarba space)
-         (declare
-            (ignore szczarba)
-            (type morphism bottom-perturbation))
-         (let ((rslt (tnsr-prdc (idnt-mrph cobar) bottom-perturbation)))
-	    (declare (type morphism rslt))
-            (setf (slot-value rslt 'sorc) ls-hat-t-u
-                  (slot-value rslt 'trgt) ls-hat-t-u)
-            rslt))))
-
-(DEFUN LS-HAT-U-T (space
-                  &aux (cobar (cobar space))
-                       (twisted-tnsr-prdc (twisted-tnsr-prdc space))
-                       (ls-hat-u-u (ls-hat-u-u space)))
-   (declare
-      (type simplicial-set space)
-      (type chain-complex cobar twisted-tnsr-prdc ls-hat-u-u))
-   (the chain-complex
-      (let ((rslt (tnsr-prdc cobar twisted-tnsr-prdc)))
-         (declare (type chain-complex rslt))
-         (setf (slot-value rslt 'grmd) ls-hat-u-u)
-         rslt)))
-
-#|
-  (cat-init)
-  (setf c (ls-hat-u-t (deltab)))
-  (defun random-allp (length)
-     (let ((rslt nil))
-        (dotimes (i length)
-           (let* ((gmsm (random (mask 9)))
-                  (dmns (1- (logcount gmsm))))
-              (when (plusp dmns)
-                 (push (cbgn (1- dmns) gmsm) rslt))))
-        (make-allp :list rslt)))
-  (dotimes (i 10) (print (random-allp 5)))
-  (setf allp (random-allp 3))
-  (setf allp-degr (apply #'+ (mapcar #'car (allp-list allp))))
-  (setf gnrt (tnpr allp-degr allp 4 (tnpr 2 7 2 (loop3 0 15 2))))
-  (? c (+ 4 allp-degr) gnrt)
-  (? c *)
-  (dotimes (i 10)
-     (let ((allp (random-allp 3)))
-        (setf allp-degr (apply #'+ (mapcar #'car (allp-list allp))))
-        (setf gnrt (tnpr allp-degr allp 4 (tnpr 2 7 2 (loop3 0 15 2))))
-        (unless (>= allp-degr 11)
-           (print (? c (+ 4 allp-degr) gnrt))
-           (print (? c (? c (+ 4 allp-degr) gnrt))))))
-  (dotimes (i 20)
-     (let ((allp (random-allp 3)))
-        (setf allp-degr (apply #'+ (mapcar #'car (allp-list allp))))
-        (setf gnrt (tnpr allp-degr allp 5 (tnpr 3 15 2 (loop3 0 15 2))))
-        (unless (>= allp-degr 10)
-           (print (? c (+ 5 allp-degr) gnrt))
-           (print (? c (? c (+ 5 allp-degr) gnrt))))))
-  (dotimes (i 20)
-     (let ((allp (random-allp 3)))
-        (setf allp-degr (apply #'+ (mapcar #'car (allp-list allp))))
-        (setf gnrt (tnpr allp-degr allp 5 (tnpr 2 7 3 (loop3 0 31 2))))
-        (unless (>= allp-degr 10)
-           (print (? c (+ 5 allp-degr) gnrt))
-           (print (? c (? c (+ 5 allp-degr) gnrt))))))
-|#
-
-(DEFUN LS-LEFT-EQVL-HAT (space
-                    &aux
-                    (ls-hat-u-t (ls-hat-u-t space))
-                    (ls-hat-left-perturbation
-                       (ls-hat-left-perturbation space)))
-   (declare
-      (type simplicial-set space)
-      (type chain-complex ls-hat-u-t)
-      (type morphism ls-hat-left-perturbation))
-   (the chain-complex
-      (add ls-hat-u-t ls-hat-left-perturbation)))
-
-#|
-  (cat-init)
-  (setf c (ls-left-eqvl-hat (deltab)))
-  (defun random-allp (length)
-     (let ((rslt nil))
-        (dotimes (i length)
-           (let* ((gmsm (random (mask 9)))
-                  (dmns (1- (logcount gmsm))))
-              (when (plusp dmns)
-                 (push (cbgn (1- dmns) gmsm) rslt))))
-        (make-allp :list rslt)))
-  (dotimes (i 10) (print (random-allp 5)))
-  (setf allp (random-allp 3))
-  (setf allp-degr (apply #'+ (mapcar #'car (allp-list allp))))
-  (setf gnrt (tnpr allp-degr allp 4 (tnpr 2 7 2 (loop3 0 15 2))))
-  (? c (+ 4 allp-degr) gnrt)
-  (? c *)
-  (dotimes (i 10)
-     (let ((allp (random-allp 3)))
-        (setf allp-degr (apply #'+ (mapcar #'car (allp-list allp))))
-        (setf gnrt (tnpr allp-degr allp 4 (tnpr 2 7 2 (loop3 0 15 2))))
-        (unless (>= allp-degr 11)
-           (print (? c (+ 4 allp-degr) gnrt))
-           (print (? c (? c (+ 4 allp-degr) gnrt))))))
-  (dotimes (i 20)
-     (let ((allp (random-allp 3)))
-        (setf allp-degr (apply #'+ (mapcar #'car (allp-list allp))))
-        (setf gnrt (tnpr allp-degr allp 5 (tnpr 3 15 2 (loop3 0 15 2))))
-        (unless (>= allp-degr 10)
-           (print (? c (+ 5 allp-degr) gnrt))
-           (print (? c (? c (+ 5 allp-degr) gnrt))))))
-  (dotimes (i 20)
-     (let ((allp (random-allp 3)))
-        (setf allp-degr (apply #'+ (mapcar #'car (allp-list allp))))
-        (setf gnrt (tnpr allp-degr allp 5 (tnpr 2 7 3 (loop3 0 31 2))))
-        (unless (>= allp-degr 10)
-           (print (? c (+ 5 allp-degr) gnrt))
-           (print (? c (? c (+ 5 allp-degr) gnrt))))))
-|#
-
-(DEFUN LS-PRE-LEFT-EQVL-LEFT-REDUCTION-INTR-F (cmbn)
-   (declare (type cmbn cmbn))
-   (the cmbn
-      (let ((rslt +empty-list+))
-         (declare (list rslt))
-         (dolist (term (cmbn-list cmbn))
-            (declare (type term term))
-            (with-term (cffc tnpr) term
-            (with-tnpr (degr1 nil nil tnpr2) tnpr
-               (if (zerop degr1)
-                  (with-tnpr (degr21 nil nil loop22) tnpr2
-                     (if (zerop degr21)
-                        (push (term cffc loop22) rslt)
-                        (return)))
-                  (return)))))
-         (make-cmbn :degr (cmbn-degr cmbn)
-            :list (nreverse rslt)))))
-
-#|
-  (ls-pre-left-eqvl-left-reduction-intr-f
-    (cmbn 6 100 (tnpr 0 'a 6 (tnpr 0 'b 6 'c))
-            50 (tnpr 0 'a 6 (tnpr 0 'b 6 'cc))
-            10 (tnpr 0 'a 6 (tnpr 2 'b 4 'c))
-            1 (tnpr 2 'a 4 (tnpr 2 'b 2 'cc))))            
-|#
-
-(DEFUN LS-PRE-LEFT-EQVL-LEFT-REDUCTION-F (space
-                                         &aux (ls-hat-t-u (ls-hat-t-u space))
-                                              (loop-space (loop-space space)))
-   (declare
-      (type simplicial-set space loop-space)
-      (type chain-complex ls-hat-t-u))      
-   (the morphism
-      (morphism  
-         :sorc ls-hat-t-u
-         :trgt loop-space
-         :degr 0
-         :intr #'ls-pre-left-eqvl-left-reduction-intr-f
-         :strt :cmbn
-         :dfnt `(ls-pre-left-eqvl-left-reduction-f ,space))))
-
-(DEFUN LS-LEFT-EQVL-LEFT-REDUCTION-G-INTR (bsgn)
-   (declare (type gmsm bsgn))
-   (flet ((rslt (cmbn)
-             (declare (type cmbn cmbn))
-             (the cmbn
-                (with-cmbn (degr list) cmbn
-                   (make-cmbn :degr degr
-                      :list (mapcar
-                               #'(lambda (term)
-                                    (declare (type term term))
-                                    (with-term (cffc loop) term
-                                       (term cffc
-                                          (tnpr
-                                             0 +null-allp+
-                                             degr (tnpr 0 bsgn degr loop)))))
-                               list))))))
-      (the intr #'rslt)))
-
-#|
-  (setf r (ls-left-eqvl-left-reduction-g-intr '*))
-  (funcall r (cmbn 3 4 'loop))
-|#
-
-(DEFUN LS-LEFT-EQVL-LEFT-REDUCTION-G (space
-                                     &aux (bsgn (bsgn space))
-                                          (ls-hat-t-u (ls-hat-t-u space))
-                                          (loop-space (loop-space space)))
-   (declare
-      (type simplicial-set space loop-space)
-      (type gmsm bsgn)
-      (type chain-complex ls-hat-t-u))      
-   (the morphism
-      (morphism  
-         :sorc loop-space
-         :trgt ls-hat-t-u
-         :degr 0
-         :intr (ls-left-eqvl-left-reduction-g-intr bsgn)
-         :strt :cmbn
-         :dfnt `(ls-left-eqvl-left-reduction-g ,space))))
-
-(DEFUN LS-PRE-LEFT-EQVL-LEFT-REDUCTION-H-INTR (space
-                                          &aux (ls-hat-t-u (ls-hat-t-u space))
-                                               (cmpr (cmpr ls-hat-t-u)))
-   (declare
-      (type simplicial-set space)
-      (type chain-complex ls-hat-t-u)
-      (type cmprf cmpr))
-   (flet ((rslt (cmbn)
-             (declare (type cmbn cmbn))
-             (the cmbn
-                (with-cmbn (degr list) cmbn
-                   (let ((rslt (zero-cmbn (1+ degr))))
-                      (declare (type cmbn rslt))
-                      (dolist (term list)
-                         (declare (type term term))
-                         (with-term (cffc tnpr) term
-                            (with-tnpr (degr1 allp1 degr2 tnpr2) tnpr
-                               (unless (zerop degr1)
-                                  (with-tnpr (degr21 nil degr22 loop22) tnpr2
-                                     (when (zerop degr21)
-                                        (let ((last-cbgn (car (last allp1))))
-                                           (declare (type cbgn last-cbgn))
-                                           (with-cbgn (degrl gmsml) last-cbgn
-                                              (dstr-add-term-to-cmbn cmpr
-                                                 cffc
-                                                 (tnpr
-                                                    (- degr1 degrl)
-                                                    (butlast allp1)
-                                                    (+ degr2 degrl 1)
-                                                    (tnpr
-                                                       (1+ degrl)
-                                                       gmsml
-                                                       degr22
-                                                       loop22))
-                                                 rslt)))))))))
-                      rslt)))))
-      (the intr #'rslt)))
-
-#|
-  (setf r (ls-pre-left-eqvl-left-reduction-h-intr (deltab)))
-  (setf *tnpr-with-degrees* t)
-  (funcall r (cmbn 10 1 (tnpr 3 (allp 2 'a 1 'b) 7 (tnpr 5 'c 2 'd)) 
-                      1 (tnpr 7 (allp 2 'a 5 'b) 3 (tnpr 0 '* 3 'c))
-                      10 (tnpr 8 (allp 4 'aa 4 'bb) 2 (tnpr 0 '* 2 'cc))))
-  (funcall r (cmbn 10 1 (tnpr 3 (allp 2 'a 1 'b) 7 (tnpr 5 'c 2 'd)) 
-                      1 (tnpr 7 (allp 4 'a 3 'b) 3 (tnpr 0 '* 3 'c))
-                      10 (tnpr 8 (allp 3 'aa 5 'bb) 2 (tnpr 0 '* 2 'cc))))
-  (setf *tnpr-with-degrees* nil)
-|#
-
-(DEFUN LS-PRE-LEFT-EQVL-LEFT-REDUCTION-H (space
-                                     &aux (ls-hat-t-u (ls-hat-t-u space)))
-   (declare
-      (type simplicial-set space)
-      (type chain-complex ls-hat-t-u))      
-   (the morphism
-      (morphism
-         :sorc ls-hat-t-u
-         :trgt ls-hat-t-u
-         :degr +1
-         :intr (ls-pre-left-eqvl-left-reduction-h-intr space)
-         :strt :cmbn
-         :dfnt `(ls-pre-left-eqvl-left-reduction-h ,space))))
-
-(DEFUN LS-PRE-LEFT-EQVL-LEFT-REDUCTION (space)
-   (declare (type simplicial-set space))
-   (the reduction
-      (reduction
-         :f (ls-pre-left-eqvl-left-reduction-f space)
-         :g (ls-left-eqvl-left-reduction-g space)
-         :h (ls-pre-left-eqvl-left-reduction-h space)
-         :dfnt `(ls-pre-left-eqvl-left-reduction ,space))))
-
-#|
-  (cat-init)
-  (setf rdct (ls-pre-left-eqvl-left-reduction (deltab)))
-  (pre-check-rdct rdct)
-  (defun random-allp (length)
-     (let ((rslt nil))
-        (dotimes (i length)
-           (let* ((gmsm (random (mask 9)))
-                  (dmns (1- (logcount gmsm))))
-              (when (plusp dmns)
-                 (push (cbgn (1- dmns) gmsm) rslt))))
-        (make-allp :list rslt)))
-  (setf allp (random-allp 3))
-  (setf allp-degr (apply #'+ (mapcar #'car (allp-list allp))))
-  (setf gnrt (tnpr allp-degr allp 4 (tnpr 2 7 2 (loop3 0 15 2))))
-  (setf *tc* (cmbn (+ 4 allp-degr) 1 gnrt))
-  (setf *bc* (cmbn 2 1 (loop3 0 15 2)))
-  (check-rdct)
-  (setf gnrt (tnpr allp-degr allp 4 (tnpr 0 1 4 (loop3 0 (mask 6) 2))))
-  (setf *tc* (cmbn (+ 4 allp-degr) 1 gnrt))
-  (check-rdct)
-  (setf *bc* (cmbn 0 1 (bsgn (bcc rdct)))
-  (setf *tc* (cmbn 0 1 (bsgn (tcc rdct)))
-  (check-rdct)
-|#
-
-(DEFUN LS-LEFT-EQVL-LEFT-REDUCTION (space
-                                   &aux (ls-pre-left-eqvl-left-reduction
-                                           (ls-pre-left-eqvl-left-reduction space))
-                                        (ls-hat-right-perturbation
-                                           (ls-hat-right-perturbation space)))			            
-   (declare
-      (type simplicial-set space)
-      (type reduction ls-pre-left-eqvl-left-reduction)
-      (type morphism ls-hat-right-perturbation))
-   (the reduction
-      (progn
-	 (dstr-change-sorc-trgt ls-hat-right-perturbation
-	    :new-sorc (tcc ls-pre-left-eqvl-left-reduction)
-	    :new-trgt (tcc ls-pre-left-eqvl-left-reduction))
-         (let ((rslt (special-bpl ls-pre-left-eqvl-left-reduction
-                        ls-hat-right-perturbation)))
-            (declare (type reduction rslt))
-            (with-slots (tcc f g h) rslt
-               (setf tcc (ls-left-eqvl-hat space)
-                     (slot-value f 'sorc) tcc
-                     (slot-value g 'trgt) tcc
-                     (slot-value h 'sorc) tcc
-                     (slot-value h 'trgt) tcc)
-               rslt)))))
-
-#|
-  (cat-init)
-  (setf rdct (ls-left-eqvl-left-reduction (deltab2)))
-  (pre-check-rdct rdct)
-  (defun a (d1 d2 d3)
-     (setf *tc* (cmbn (+ d1 d2 d3)
-                 1 (tnpr d1 (allp d1 (mask (+ d1 2)))
-                         (+ d2 d3)
-                      (tnpr d2 (mask (1+ d2))
-                            d3 (loop3 0 (mask (+ d3 2)) 1))))
-           *bc* (cmbn d3 1
-                  (loop3 0 (mask (+ d3 2)) -1)))
-      (check-rdct))
-  (a 1 0 1)
-  (a 1 1 1)  ;; error because 3 does not exist in deltab2
-  (a 1 2 1)
-  (a 2 2 1)
-|#
- 
-(DEFUN LS-PRE-LEFT-EQVL-RIGHT-REDUCTION-INTR-F (cmbn)
-   (declare (type cmbn cmbn))
-   (the cmbn
-      (with-cmbn (degr list) cmbn
-         (let ((tail (member 0 list :test #'= :key #'cadddr)))
-            (make-cmbn :degr degr
-               :list (mapcar
-                        #'(lambda (term)
-                             (declare (type term term))
-                             (with-term (cffc tnpr) term
-                                (term cffc (gnrt1 tnpr))))
-                        tail))))))
-
-#|
-  (ls-pre-left-eqvl-right-reduction-intr-f
-     (cmbn 3 12 (tnpr 2 'a 1 'b) 14 (tnpr 3 'aa 0 '*))))
-|#
-
-(DEFUN LS-PRE-LEFT-EQVL-RIGHT-REDUCTION-F (space
-                                          &aux (ls-hat-u-t (ls-hat-u-t space))
-                                               (cobar (cobar space)))
-   (declare
-      (type simplicial-set space)
-      (type chain-complex ls-hat-u-t cobar))
-   (the morphism
-      (morphism
-         :sorc ls-hat-u-t :trgt cobar :degr 0
-         :intr #'ls-pre-left-eqvl-right-reduction-intr-f
-         :strt :cmbn
-         :dfnt `(ls-pre-left-eqvl-right-reduction-f ,space))))
-
-(DEFUN LS-PRE-LEFT-EQVL-RIGHT-REDUCTION-INTR-G (bsgn)
-   (declare (type gmsm bsgn))
-   (flet ((rslt (cmbn)
-             (declare (type cmbn cmbn))
-             (the cmbn
-                (with-cmbn (degr list) cmbn
-                   (let ((bsgn (tnpr 0 bsgn 0 +null-loop+)))
-                      (declare (type tnpr bsgn))
-                      (make-cmbn :degr degr
-                         :list (mapcar
-                                  #'(lambda (term)
-                                       (declare (type term term))
-                                       (with-term (cffc gnrt) term
-                                          (term cffc (tnpr degr gnrt 0 bsgn))))
-                                  list)))))))
-      (the intr #'rslt)))
-
-#|
-  (setf r (ls-pre-left-eqvl-right-reduction-intr-g '*))
-  (funcall r (cmbn 3 4 'a))
-|#
-
-(DEFUN LS-PRE-LEFT-EQVL-RIGHT-REDUCTION-G (space
-                                          &aux (ls-hat-u-t (ls-hat-u-t space))
-                                               (cobar (cobar space))
-                                               (bsgn (bsgn space)))
-   (declare
-      (type simplicial-set space)
-      (type chain-complex ls-hat-u-t cobar)
-      (type gmsm bsgn))
-   (the morphism
-      (morphism
-         :sorc cobar :trgt ls-hat-u-t :degr 0
-         :intr (ls-pre-left-eqvl-right-reduction-intr-g bsgn)
-         :strt :cmbn
-         :dfnt `(ls-pre-left-eqvl-right-reduction-g ,space))))
-
-(DEFUN LS-PRE-LEFT-EQVL-RIGHT-REDUCTION-H (space
-                                          &aux (cobar (cobar space))
-                                               (tnpr-contraction (tnpr-contraction space)))
-   (declare
-      (type simplicial-set space)
-      (type chain-complex cobar)
-      (type morphism tnpr-contraction))
-   (the morphism
-      (tnsr-prdc (idnt-mrph cobar) tnpr-contraction)))
-
-(DEFUN LS-PRE-LEFT-EQVL-RIGHT-REDUCTION (space)
-   (declare (type simplicial-set space))
-   (the reduction
-      (reduction
-         :f (ls-pre-left-eqvl-right-reduction-f space)
-         :g (ls-pre-left-eqvl-right-reduction-g space)
-         :h (ls-pre-left-eqvl-right-reduction-h space)
-         :dfnt `(ls-pre-left-eqvl-right-reduction ,space))))
-
-#|
-  (cat-init)
-  (setf r (ls-pre-left-eqvl-right-reduction (deltab2)))
-  (pre-check-rdct r)
-  (setf *tc* (cmbn 0 1 (bsgn (tcc r))))
-  (setf *bc* (cmbn 0 1 (bsgn (bcc r))))
-  (check-rdct)
-  (setf *tc* (cmbn 3 1 (tnpr 3 (allp 3 (mask 5)) 0 (tnpr 0 1 0 +null-loop+))))
-  (setf *bc* (cmbn 3 1 (allp 1 7 2 15)))
-  (check-rdct)
-  (setf *tc* (cmbn 6 1 (tnpr 3 (allp 1 7 2 15) 3 (tnpr 2 7 1 (loop3 0 7 2)))))
-  (check-rdct)
-  (setf *tc* (cmbn 6 1 (tnpr 3 (allp 1 7 2 15) 3 (tnpr 0 1 3 (loop3 0 (mask 5) 2)))))
-  (check-rdct)
-|#
-
-(DEFUN LS-LEFT-EQVL-RIGHT-REDUCTION (space
-                                    &aux (pre-reduction
-                                            (ls-pre-left-eqvl-right-reduction space))
-                                         (perturbation
-                                            (ls-hat-left-perturbation space)))                                    
-   (declare
-     (type simplicial-set space)
-     (type reduction pre-reduction)
-     (type morphism perturbation))
-   (the reduction
-      (progn
-         (setf (slot-value perturbation 'sorc) (tcc pre-reduction)
-               (slot-value perturbation 'trgt) (tcc pre-reduction))
-         (special-bpl pre-reduction perturbation))))
-
-#|
-  (cat-init)
-  (setf r (ls-left-eqvl-right-reduction (deltab2)))
-  (pre-check-rdct r)
-  (setf *tc* (cmbn 0 1 (bsgn (tcc r))))
-  (setf *bc* (cmbn 0 1 (bsgn (bcc r))))
-  (check-rdct)
-  (setf *tc* (cmbn 3 1 (tnpr 3 (allp 3 (mask 5)) 0 (tnpr 0 1 0 +null-loop+))))
-  (setf *bc* (cmbn 3 1 (allp 1 7 2 15)))
-  (check-rdct)
-  (setf *tc* (cmbn 6 1 (tnpr 3 (allp 1 7 2 15) 3 (tnpr 2 7 1 (loop3 0 7 2)))))
-  (check-rdct)
-  (setf *tc* (cmbn 6 1 (tnpr 3 (allp 1 7 2 15) 3 (tnpr 0 1 3 (loop3 0 (mask 5) 2)))))
-  (check-rdct)
-|#
-
-(DEFUN LS-LEFT-EQVL (space)
-   (declare (type simplicial-set space))
-   (the equivalence
-      (equivalence 
-       :lrdct (ls-left-eqvl-left-reduction space)
-       :rrdct (ls-left-eqvl-right-reduction space)
-       :dfnt `(ls-left-eqvl ,space))))
-
-#|
-  (cat-init)
-  (setf h (ls-left-eqvl (deltab2)))
-  (setf loop (loop3 0 (mask 5) 2))
-  (lg h 3 loop)
-  (rf h *)
-  (rg h *)
-  (lf h *)
-  (setf allp (allp 2 (mask 4) 3 (mask 5)))
-  (rg h 5 allp)
-  (lf h *)
-  (lg h *)
-  (rf h *)  ;; = allp, but why ?
-|#
-
-(DEFUN LOOP-SPACE-EFHM (space)
-  (declare (type simplicial-set space))
-  (let ((ls-left-eqvl (ls-left-eqvl space))
-	(right-eqvl (cobar (efhm space))))
-    (declare (type equivalence ls-left-eqvl right-eqvl))
-    (cmps ls-left-eqvl right-eqvl)))
-
-(DEFMETHOD SEARCH-EFHM (loop-space (dfnt (eql 'loop-space)))
-  (declare (type simplicial-set loop-space))
-  (loop-space-efhm (second (dfnt loop-space))))
-
-#|
-  (cat-init)
-  (setf l (loop-space (sphere 2)))
-  (homology l 6)
-  (setf oos3 (loop-space (loop-space (sphere 3))))
-  (homology oos3 3)
-  (setf ooos4 (loop-space (loop-space (loop-space (sphere 4)))))
-  (homology ooos4 2)
-|#
diff --git a/archive/Kenzo-2/Kenzo-2-Acl8/ls-twisted-products.cl b/archive/Kenzo-2/Kenzo-2-Acl8/ls-twisted-products.cl
deleted file mode 100644
index d21cec0..0000000
--- a/archive/Kenzo-2/Kenzo-2-Acl8/ls-twisted-products.cl
+++ /dev/null
@@ -1,521 +0,0 @@
-;;;  LS-TWISTED-PRODUCTS  LS-TWISTED-PRODUCTS  LS-TWISTED-PRODUCTS
-;;;  LS-TWISTED-PRODUCTS  LS-TWISTED-PRODUCTS  LS-TWISTED-PRODUCTS
-;;;  LS-TWISTED-PRODUCTS  LS-TWISTED-PRODUCTS  LS-TWISTED-PRODUCTS
-
-(IN-PACKAGE "CAT")
-
-(PROVIDE "ls-twisted-products")
-
-;; ABSM-LOOPABSM is the "twisted" product of ABSM, a simplex of the base
-;;   space of dimension DMNS by LOOP-ABSM, a simplex of the corresponding
-;;   loop-space, of dimension (1- DMNS). The returned object is
-;;   a loop-absm of dimension (1- DMNS).
-
-(DEFUN ABSM-LOOPABSM (cmpr dmns absm loop-absm)
-   (declare
-      (type cmprf cmpr)
-      (fixnum dmns)  ;; dimension of ABSM
-      (type absm absm loop-absm))
-   (the absm
-      (with-absm (dgop1 gmsm1) absm
-         (when (logbitp (1- dmns) dgop1)
-            (return-from absm-loopabsm loop-absm))                  
-         (with-absm (dgop2 loop2) loop-absm
-            (let ((iloop2 (loop-list loop2)))
-               (declare (list iloop2))
-               (unless iloop2
-                  (return-from absm-loopabsm
-                     (absm dgop1 (make-loop :list (list (apowr 0 gmsm1 +1))))))
-               (let ((apowr (first iloop2)))
-                  (declare (type apowr apowr))
-                  (with-apowr (dgop22 gmsm2 expn2) apowr
-                     (if (and (= dgop1 (dgop*dgop dgop2 dgop22))
-                              (eq :equal (funcall cmpr gmsm1 gmsm2)))
-                        ;; the absm is eaten by the first component of the loop
-                        (if (= -1 expn2)
-                           ;; the first item of the loop disappears.
-                           (let ((iloop2-rest (rest iloop2)))
-                              (if iloop2-rest
-                                 (let ((loop-rest (normalize-loop (1- dmns) iloop2-rest)))
-                                    (declare (type absm loop-rest))
-                                    (absm (dgop*dgop dgop2 (dgop loop-rest)) (gmsm loop-rest)))
-                                 (absm (mask (1- dmns)) +null-loop+)))
-                           ;; the exponent of the first item is increased by 1
-                           (absm dgop2 (make-loop :list (cons (apowr dgop22 gmsm2 (1+ expn2))
-                                                           (rest iloop2)))))
-                        ;; a concatenation must be done
-                        (multiple-value-bind (dgop dgop1 dgop2) (extract-common-dgop dgop1 dgop2)
-                           (declare (fixnum dgop dgop1 dgop2))
-                           (absm dgop
-                              (make-loop
-                                 :list (cons (apowr dgop1 gmsm1 +1)
-                                          (if (zerop dgop2)
-                                             iloop2
-                                             (mapcar #'(lambda (apowr)
-                                                          (declare (type apowr apowr))
-                                                          (cons (dgop*dgop dgop2 (apdgop apowr))
-                                                             (cdr apowr)))
-                                                iloop2))))))))))))))
-
-#|
-  (setf cmpr (cmpr (deltab)))
-  (absm-loopabsm cmpr 3 (absm 4 7) (absm 7 +null-loop+))
-  (absm-loopabsm cmpr 3 (absm 0 15) (absm 7 +null-loop+))
-  (absm-loopabsm cmpr 3 (absm 2 7) (absm 2 (loop3 0 7 4)))
-  (absm-loopabsm cmpr 3 (absm 2 7) (absm 2 (loop3 0 7 4 1 12 -1)))
-  (absm-loopabsm cmpr 3 (absm 2 7) (absm 2 (loop3 0 7 -1)))
-  (absm-loopabsm cmpr 3 (absm 2 7) (absm 2 (loop3 0 7 -1 1 12 -1)))
-  (absm-loopabsm cmpr 3 (absm 2 7) (absm 2 (loop3 0 7 4)))
-  (absm-loopabsm cmpr 3 (absm 2 7) (absm 0 (loop3 2 7 4 1 14 -1)))
-  (absm-loopabsm cmpr 3 (absm 2 7) (absm 0 (loop3 2 7 -1)))  ;; in principle illegal but works
-  (absm-loopabsm cmpr 3 (absm 2 7) (absm 0 (loop3 2 7 -1 1 14 -1)))
-  (absm-loopabsm cmpr 3 (absm 2 7) (absm 0 (loop3 0 15 -1 1 14 -1)))
-  (absm-loopabsm cmpr 3 (absm 0 15) (absm 2 (loop3 0 7 -1 0 14 -1)))
-  (absm-loopabsm cmpr 3 (absm 2 7) (absm 2 (loop3 0 28 -1 0 14 -1))))
-|#
-
-(DEFUN TWISTED-CRTS-PRDC-FACE (cmpr space-face loop-space-face non-twisted-face)
-   (declare
-      (type cmprf cmpr)
-      (type face space-face loop-space-face non-twisted-face))
-   (flet ((rslt (indx dmns crpr)
-             (declare
-                (fixnum indx dmns)
-                (type crpr crpr))
-             (the absm
-                (progn
-                   (unless (= indx dmns)
-                      (return-from rslt
-                         (funcall non-twisted-face indx dmns crpr)))
-                   (with-crpr (absm1 absm2) crpr
-                      (let ((face1 (a-face4 space-face dmns dmns absm1))
-                            (face2 (a-face4 loop-space-face dmns dmns absm2)))
-                         (declare (type absm face1 face2))
-                         (setf face2 (absm-loopabsm cmpr dmns absm1 face2))
-                         (2absm-acrpr face1 face2)))))))
-      (the face #'rslt)))
-
-(DEFUN TWISTED-CRTS-PRDC (space
-                          &aux
-                          (loop-space (loop-space space))
-                          (crts-prdc (crts-prdc space loop-space)))
-  (declare (type simplicial-set space loop-space crts-prdc))
-  (the simplicial-set
-    (with-slots ((space-cmpr cmpr) (space-face face)) space
-      (declare
-       (type cmprf space-cmpr)
-       (type face space-face))
-      (with-slots ((loop-space-face face)) loop-space
-        (declare (type face loop-space-face))
-        (with-slots ((crts-prdc-cmpr cmpr) basis bsgn (crts-prdc-face face)) crts-prdc
-          (declare
-           (type cmprf crts-prdc-cmpr)
-           (type basis basis)
-           (type face non-twisted-face)
-           (type gmsm bsgn))
-          (let ((rslt (simplicial-set
-                       :cmpr crts-prdc-cmpr
-                       :basis basis
-                       :bsgn bsgn
-                       :face (twisted-crts-prdc-face
-                              space-cmpr space-face loop-space-face crts-prdc-face)
-                       :dfnt `(twisted-crts-prdc ,space))))
-            (setf (slot-value rslt 'grmd) crts-prdc)
-            rslt))))))
-
-#|
-  (setf p (r-proj-space 3))
-  (setf tw (twisted-crts-prdc p))
-  (defun random-apowr (dmns max-expn)
-     (loop
-        (let* ((dgop (random (2-exp (1- dmns))))
-               (gmsm (- dmns (logcount dgop))))
-           (unless (< 0 gmsm 3)
-              (return-from random-apowr
-                 (apowr dgop gmsm (srandom max-expn)))))))
-  (defun random-niloop (dmns max-expn length)
-     (mapcar #'(lambda (dummy)
-                  (random-apowr (1+ dmns) max-expn))
-        (make-list length)))
-  (defun random-crpr (dmns max-expn length)
-     (loop
-        (let ((loop (normalize-loop dmns (random-niloop dmns max-expn length)))
-              (dgop (random (2-exp dmns))))
-           (let ((absm (2absm-acrpr (absm dgop (- dmns (logcount dgop))) loop)))
-              (when (and (zerop (dgop absm))
-                         (not (< (gmsm1 (gmsm absm)) 3)))
-                 (return (gmsm absm)))))))
-  (setf cmpr (cmpr tw))
-  (defun random-cmbn (degr max-cffc max-expn loop-length cmbn-length)
-     (apply #'nterm-add cmpr degr
-        (mapcar #'(lambda (dummy)
-                     (term (srandom max-cffc) (random-crpr degr max-expn loop-length)))
-           (make-list cmbn-length))))
-  (setf c (random-cmbn 8 10 4 4 100))
-  (time (? tw (? tw c)))
-  (time (? tw (? tw c)))
-|#
-
-(DEFUN DTAU-D-INTR (crts-prdc-cmpr crts-prdc-face twisted-crts-prdc-face)
-   (declare
-      (type cmprf crts-prdc-cmpr)
-      (type face crts-prdc-face twisted-crts-prdc-face))
-   (flet ((rslt (dmns crpr)
-             (declare
-                (fixnum indx dmns)
-                (type crpr crpr))
-             (when (zerop dmns)
-                (return-from rslt +zero-negative-cmbn+))
-             (the cmbn
-                (let ((dmns-1 (1- dmns)))
-                   (declare (fixnum dmns-1))
-                   (when (logbitp dmns-1 (dgop1 crpr))
-                      (return-from rslt (zero-cmbn dmns-1)))
-                   (let ((face-tau (funcall twisted-crts-prdc-face dmns dmns crpr))
-                         (face (funcall crts-prdc-face dmns dmns crpr))
-                         (sign (-1-expt-n dmns)))
-                      (declare
-                         (type absm face-tau face)
-                         (fixnum sign))
-                      (with-absm (dgop-tau gmsm-tau) face-tau
-                      (with-absm (dgop gmsm) face
-                         (if (plusp dgop-tau)
-                            (if (plusp dgop)
-                               (zero-cmbn dmns-1)
-                               (term-cmbn dmns-1 (- sign) gmsm))
-                            (if (plusp dgop)
-                               (term-cmbn dmns-1 sign gmsm-tau)
-                               (ecase (funcall crts-prdc-cmpr gmsm-tau gmsm)
-                                  (:less
-                                   (cmbn dmns-1 sign gmsm-tau (- sign) gmsm))
-                                  (:greater
-                                   (cmbn dmns-1 (- sign) gmsm sign gmsm-tau))
-                                  (:equal
-                                   (error "Surprise in DTAU-D-INTR.~@
-                                           Crpr = ~A~@
-                                           D-tau = ~A~@
-                                           D = ~A"
-                                      crpr gmsm-tau gmsm))))))))))))
-      (the intr #'rslt)))
-
-#|
-  (setf d (deltab))
-  (setf p (crts-prdc d (loop-space d)))
-  (setf tw (twisted-crts-prdc d))
-  (setf crts-prdc-cmpr (cmpr p)
-        crts-prdc-face (face p)
-        twisted-crts-prdc-face (face tw))
-  (setf delta (dtau-d-intr crts-prdc-cmpr crts-prdc-face twisted-crts-prdc-face))
-  (funcall delta 3 (crpr 0 15 0 (loop3 0 (- 2048 64) 1)))
-  (funcall delta 5 (crpr 10 15 5 (loop3 0 (- 2048 64) 1)))
-  (funcall delta 5 (crpr 5 15 10 (loop3 0 (- 2048 64) 1)))
-|#
-
-(DEFUN DTAU-D (space
-                 &aux (loop-space (loop-space space))
-                      (crts-prdc (crts-prdc space loop-space))
-                      (crts-prdc-cmpr (cmpr crts-prdc))
-                      (crts-prdc-face (face crts-prdc))
-                      (twisted-crts-prdc (twisted-crts-prdc space))
-                      (twisted-crts-prdc-face (face twisted-crts-prdc)))
-   (declare
-      (type simplicial-set space loop-space crts-prdc twisted-crts-prdc)
-      (type cmprf crts-prdc-cmpr)
-      (type face crts-prdc-face twisted-crts-prdc-face))
-   (the morphism
-      (morphism
-         :sorc crts-prdc :trgt crts-prdc :degr -1
-         :intr (dtau-d-intr crts-prdc-cmpr crts-prdc-face twisted-crts-prdc-face)
-         :strt :gnrt
-         :dfnt `(dtau-d ,space))))
-
-(DEFUN SZCZARBA (space
-                   &aux (loop-space (loop-space space))
-                        (twisted-crts-prdc (twisted-crts-prdc space))
-                        (ez (ez space loop-space))
-                        (dtau-d (dtau-d space)))
-   (declare
-      (type simplicial-set space loop-space)
-      (type reduction ez szczarba)
-      (type morphism dtau-d))
-   (the (values reduction morphism)
-      (multiple-value-bind (szczarba bottom-perturbation)
-                           (add ez dtau-d)
-         (with-slots (tcc f g h) szczarba
-            (setf tcc twisted-crts-prdc
-                  (slot-value f 'sorc) twisted-crts-prdc
-                  (slot-value g 'trgt) twisted-crts-prdc
-                  (slot-value h 'sorc) twisted-crts-prdc
-                  (slot-value h 'trgt) twisted-crts-prdc))
-         (values szczarba bottom-perturbation))))
- 
-#|
-  (cat-init)
-  (setf rdct (szczarba (deltab)))
-  (pre-check-rdct rdct)
-  (setf *tc* (cmbn 2 1 (crpr 0 7 0 (loop3 0 (- 512 32) 1)))
-        *bc* (cmbn 2 1 (tnpr 0 1 2 (loop3 0 (- 512 32) 1))
-                     10 (tnpr 1 (- 4096 1024) 1 (loop3 0 7 1))
-                     100 (tnpr 2 7 0 (loop3 0 (- 4096 1024) 1))))
-  (check-rdct) 
-  (setf bcc (bcc rdct))
-  (time (? bcc 5 (tnpr 5 (mask 6) 0 +null-loop+)))
-  (time (? bcc 6 (tnpr 6 (mask 7) 0 +null-loop+)))
-|#
-
-(DEFUN TWISTED-TNSR-PRDC (space
-                            &aux (szczarba (szczarba space)))
-   (declare
-      (type simplicial-set space)
-      (type reduction szczarba))
-   (the chain-complex
-      (bcc szczarba)))
-
-;;;
-;;;  The important contraction.
-;;;
-
-(DEFUN POP-FIRST-ABSM (dmns iloop)
-   (declare (type iloop iloop))
-   (the (values (member -1 0 1) (or nil absm) absm)
-      (progn
-         (unless iloop
-            (return-from pop-first-absm
-               (values 0 nil iloop)))
-         (let ((apowr (first iloop))
-               (niloop-rest (rest iloop)))
-            (declare
-               (type apowr apowr)
-               (type iloop niloop-rest))
-            (with-apowr (dgop gmsm expn) apowr
-               (let ((popped-absm (absm dgop gmsm)))
-                  (declare (type absm popped-absm))
-                  (cond ((< expn -1)
-                         (values -1 popped-absm
-                            (absm 0
-                               (make-loop
-                                  :list (cons (apowr dgop gmsm (1+ expn)) niloop-rest)))))
-                        ((> expn +1)
-                         (values +1 popped-absm
-                            (absm 0
-                               (make-loop
-                                  :list (cons (apowr dgop gmsm (1- expn)) niloop-rest)))))
-                        (t
-                           (values expn popped-absm
-                              (normalize-loop dmns niloop-rest))))))))))
-
-#|
-  (pop-first-absm 4 (cdr +null-loop+))
-  (pop-first-absm 4 (cdr (loop3 0 'a -2)))
-  (pop-first-absm 4 (cdr (loop3 0 'a +2)))
-  (pop-first-absm 4 (cdr (loop3 0 'a -1)))
-  (pop-first-absm 4 (cdr (loop3 0 'a +1)))
-  (pop-first-absm 4 (cdr (loop3 1 'a -2 2 'b 3)))
-  (pop-first-absm 4 (cdr (loop3 0 'a +2 2 'b -3)))
-  (pop-first-absm 4 (cdr (loop3 1 'a -1 2 'b 3)))
-  (pop-first-absm 4 (cdr (loop3 0 'a +1 2 'b 5)))
-  (pop-first-absm 4 (cdr (loop3 2 'a -1 1 'b 3)))
-  (pop-first-absm 4 (cdr (loop3 2 'a +1 1 'b 3))))
-|#
-
-(DEFUN CRTS-CONTRACTION-INTR (base-cmpr base-bsgn base-face crts-cmpr)
-   (declare
-      (type cmprf base-cmpr crts-cmpr)
-      (type gmsm base-bsgn)
-      (type face base-face))
-   
-   (flet ((rslt (n crpr)
-             (declare
-                (fixnum n)
-                (type crpr crpr))
-             (the cmbn
-                (let ((n+1 (1+ n)))
-                   (declare (fixnum n+1))
- (labels (
-  (hh (x-n g-n)
-     (declare (type absm x-n g-n))
-     (if (bsgn-p base-cmpr base-bsgn n x-n)
-        (if (degenerate-p g-n)
-           (zero-cmbn n+1)
-           (h-hat (loop-list (gmsm g-n))))
-        (if (degenerate-p g-n)
-           (h-tilde (1dgnr n x-n) g-n)
-           (2cmbn-add crts-cmpr (h-hat (loop-list (gmsm g-n)))
-              (h-tilde (1dgnr n x-n) g-n)))))
-  (h-tilde (x-n+1 g-n)
-     (declare (type absm x-n+1 g-n))
-     (when (bsgn-p base-cmpr base-bsgn n+1 x-n+1)
-        (return-from h-tilde
-           (zero-cmbn n+1)))
-     (do ((i n (1- i))
-          (dgop 0 (+ dgop (2-exp i)))
-          (sign (-1-expt-n+1 n) (- sign))
-          (del-i x-n+1  (a-face4 base-face i (1+ i) del-i))
-          (rslt (zero-cmbn n+1)))
-         ((minusp i) rslt)
-        (declare
-           (fixnum i dgop sign)
-           (type absm del-i)
-           (type cmbn rslt))
-        (let ((absm1 (ndgnr dgop del-i))
-              (loop-absm2 (1dgnr i g-n)))
-           (declare (type absm absm1 loop-absm2))
-           (unless (plusp (logand (dgop absm1) (dgop loop-absm2)))
-              (dstr-add-term-to-cmbn
-                 crts-cmpr
-                 sign (crpr absm1 loop-absm2)
-                 rslt)))))
-  (h-hat (g-n)
-     (declare (type iloop g-n))  ;;; ***
-     (multiple-value-bind (expn y-n+1 gp-n) (pop-first-absm n g-n)
-        (declare
-           (fixnum expn)
-           (type absm y-n+1)
-           (type loop gp-n))  ;;; ***
-        (ecase expn
-           (0 (zero-cmbn (1+ n)))
-           (+1
-            (let ((h-tildes (2cmbn-sbtr crts-cmpr
-                               (h-tilde y-n+1 gp-n)
-                               (h-tilde
-                                  (1dgnr n (a-face4 base-face (1+ n) (1+ n) y-n+1))
-                                  (absm 0 (make-loop :list g-n))))))
-               (declare (type cmbn h-tildes))
-               (if (degenerate-p gp-n)
-                  h-tildes 
-                  (2cmbn-add crts-cmpr (h-hat (loop-list (gmsm gp-n))) h-tildes))))
-           (-1
-            (let ((next-x-n (a-face4 base-face (1+ n) (1+ n) y-n+1))
-                  (h-tilde (h-tilde y-n+1 (absm 0 (make-loop :list g-n)))))
-               (declare
-                  (type absm next-x-n)
-                  (type cmbn h-tilde))
-               (if (zerop (logand (dgop next-x-n) (dgop gp-n)))
-                  (2cmbn-sbtr crts-cmpr
-                     (hh next-x-n gp-n) h-tilde)
-                  (cmbn-opps h-tilde))))))))
-    
-    (with-crpr (absm1 loop-absm2) crpr
-       (hh absm1 loop-absm2)))))))
-    
-    (the intr #'rslt)))
-
-#|
-  (cat-init)
-  (setf delta (deltab))
-  (setf tw (twisted-crts-prdc delta))
-  (setf d (dffr tw))
-  (setf base-cmpr (cmpr delta)
-        base-bsgn (bsgn delta)
-        base-face (face delta)
-        crts-cmpr (cmpr tw))
-  (setf r (crts-contraction-intr base-cmpr base-bsgn base-face crts-cmpr))
-  (setf h (morphism :sorc tw :trgt tw :degr +1
-             :intr r :strt :gnrt :dfnt `(crts-contraction ,delta)))
-  (setf z (i-sbtr (idnt-mrph tw) (cmps d h) (cmps h d)))
-  (? z 0 (crpr 0 1 0 +null-loop+))
-  (? z 0 (crpr 0 1 0 (loop3 0 96 1)))
-  (? z 0 (crpr 0 1 0 (loop3 0 96 1 0 (+ 256 128) 1)))
-  (? z 0 (crpr 0 1 0 (loop3 0 96 1 0 (+ 256 128) 1 0 (+ 512 1024) 1)))
-  (? z 0 (crpr 0 1 0 (loop3 0 96 2)))
-  (? z 1 (crpr 0 3 0 (loop3 0 (+ 32 64 128) 1)))
-  (? z 2 (crpr 0 7 0 (loop3 0 (+ 32 64 128 256) 1)))
-  (? z 3 (crpr 2 7 1 (loop3 2 (+ 32 64 128) 2 4 (+ 32 64 128) -2)))
-  (? z 3 (crpr 2 7 4 (loop3 2 (+ 32 64 128) 2 1 (+ 32 64 128) -2)))
-  (? z 3 (crpr 2 7 1 (loop3 2 (+ 32 64 128) -2 4 (+ 32 64 128) 2)))
-  (? z 3 (crpr 2 7 4 (loop3 2 (+ 32 64 128) -2 1 (+ 32 64 128) 2)))
-  (? z 3 (crpr 1 7 2 (loop3 2 (+ 32 64 128) 2 4 (+ 32 64 128) -2)))
-  (? z 3 (crpr 4 7 2 (loop3 2 (+ 32 64 128) 2 1 (+ 32 64 128) -2)))
-  (? z 3 (crpr 1 7 2 (loop3 2 (+ 32 64 128) -2 4 (+ 32 64 128) 2)))
-  (? z 3 (crpr 4 7 2 (loop3 2 (+ 32 64 128) -2 1 (+ 32 64 128) 2)))
-|#
- 
-
-#|
-  (cat-init)
-  (setf p (r-proj-space 3))
-  (setf tw (twisted-crts-prdc p))
-  (setf r (crts-contraction-intr (cmpr p) (bsgn p) (face p) (cmpr tw)))
-  (defun random-apowr (dmns max-expn)
-     (loop
-        (let* ((dgop (random (2-exp (1- dmns))))
-               (gmsm (- dmns (logcount dgop))))
-           (unless (< 0 gmsm 3)
-              (return-from random-apowr
-                 (apowr dgop gmsm (srandom max-expn)))))))
-  (defun random-niloop (dmns max-expn length)
-     (mapcar #'(lambda (dummy)
-                  (random-apowr (1+ dmns) max-expn))
-        (make-list length)))
-  (defun random-crpr (dmns max-expn length)
-     (loop
-        (let ((loop (normalize-loop dmns (random-niloop dmns max-expn length)))
-              (dgop (random (2-exp dmns))))
-           (let ((absm (2absm-acrpr (absm dgop (- dmns (logcount dgop))) loop)))
-              (when (and (zerop (dgop absm))
-                         (not (< (gmsm1 (gmsm absm)) 3)))
-                 (return (gmsm absm)))))))
-  (setf cmpr (cmpr tw))
-  (defun random-cmbn (degr max-cffc max-expn loop-length cmbn-length)
-     (apply #'nterm-add cmpr degr
-        (mapcar #'(lambda (dummy)
-                     (term (srandom max-cffc) (random-crpr degr max-expn loop-length)))
-           (make-list cmbn-length))))
-  (setf h (morphism :sorc tw :trgt tw :degr +1
-             :intr r :strt :gnrt :dfnt `(crts-contraction ,p)))
-  (setf d (dffr tw))
-  (setf z (i-sbtr (idnt-mrph tw) (cmps h d) (cmps d h)))
-  (setf c (random-cmbn 5 10 2 2 1))
-  (? z c)
-  (setf c (random-cmbn 6 10 3 3 3))
-  (? z c)
-  (setf c (random-cmbn 7 10 4 4 6))
-  (? z c)
-  (setf c (random-cmbn 8 10 4 4 20))
-  (? z c)
-  (? h c)
-  (? d *)
-  (length *)
-|#
-
-(DEFUN CRTS-CONTRACTION (space
-                           &aux (twisted-crts-prdc (twisted-crts-prdc space)))
-   (declare (type simplicial-set space twisted-crts-prdc))
-   (the morphism
-      (morphism
-         :sorc twisted-crts-prdc :trgt twisted-crts-prdc :degr +1
-         :intr (crts-contraction-intr (cmpr space) (bsgn space) (face space)
-                  (cmpr twisted-crts-prdc))
-         :strt :gnrt
-         :dfnt `(crts-contraction ,space))))
-
-#|
-  (setf h (crts-contraction (deltab)))
-  (setf d (dffr (twisted-crts-prdc (deltab))))
-  (setf z (i-sbtr (idnt-mrph (sorc d)) (cmps d h) (cmps h d)))
-  (? z 3 (crpr 4 7 2 (loop3 2 (+ 32 64 128) -2 1 (+ 32 64 128) 2)))
-|#
-
-(DEFUN TNPR-CONTRACTION (space
-                           &aux
-                           (szczarba (szczarba space))
-                           (f (f szczarba))
-                           (g (g szczarba))
-                           (crts-contraction (crts-contraction space)))
-   (declare
-      (type simplicial-set space)
-      (type reduction szczarba)
-      (type morphism f g crts-contraction))
-   (the morphism
-      (i-cmps f crts-contraction g)))
-
-#|
-  (cat-init)
-  (setf delta (deltab))
-  (setf sz (szczarba (deltab)))
-  (setf tw (bcc sz))
-  (setf h (tnpr-contraction delta))
-  (setf z (i-sbtr (idnt-mrph tw) (cmps tw h) (cmps h tw)))
-  (time (? z 3 (tnpr 0 1 3 (loop3 0 (mask 5) 2 0 (* 32 (mask 5)) -1))))
-  (? h 4 (tnpr 0 1 0 (loop3 0 (mask 6) 1)))
-|#
diff --git a/archive/Kenzo-2/Kenzo-2-Acl8/macros.cl b/archive/Kenzo-2/Kenzo-2-Acl8/macros.cl
deleted file mode 100644
index 4a534f8..0000000
--- a/archive/Kenzo-2/Kenzo-2-Acl8/macros.cl
+++ /dev/null
@@ -1,816 +0,0 @@
-;;;  MACROS  MACROS  MACROS  MACROS  MACROS  MACROS  MACROS
-;;;  MACROS  MACROS  MACROS  MACROS  MACROS  MACROS  MACROS
-;;;  MACROS  MACROS  MACROS  MACROS  MACROS  MACROS  MACROS
-
-(IN-PACKAGE "CAT")
-
-(PROVIDE "macros")
-
-;;;
-;;;  VARIOUS
-;;;
-
-(DEFMACRO -1-EXPT-N (n)
-  `(the fixnum (if (evenp (the fixnum ,n)) 1 -1)))
-
-(DEFMACRO -1-EXPT-N+1 (n)
-  `(the fixnum (if (evenp (the fixnum ,n)) -1 1)))
-
-(DEFMACRO -1-EXPT-N-1 (n)
-  `(-1-expt-n+1 ,n))
-
-#|
-  (-1-expt-n 5)
-  (-1-expt-n 6)
-  (-1-expt-n+1 5)
-  (-1-expt-n+1 6)
-  (-1-expt-n-1 5)
-  (-1-expt-n-1 6))
-|#
-
-;;; (DEFCONSTANT +2-EXP+ (make-array (integer-length most-positive-fixnum)
-;;;                         :element-type 'fixnum))
-;;; 
-;;; (dotimes (i (integer-length most-positive-fixnum))
-;;;    (setf (aref +2-exp+ i) (the fixnum (expt 2 i))))
-
-
-(DEFCONSTANT +2-EXP+
-  (let ((rslt (make-array (integer-length most-positive-fixnum)
-                        :element-type 'fixnum)))
-    (declare (type (array fixnum 1) rslt))
-    (dotimes (i (integer-length most-positive-fixnum) rslt)
-      (setf (aref rslt i) (the fixnum (expt 2 i))))))
-
-(DEFMACRO 2-EXP (n)
-   `(aref +2-exp+ ,n))
-
-;;; (DEFCONSTANT +MASK+ (make-array (1+ (integer-length most-positive-fixnum))
-;;;                         :element-type 'fixnum))
-;;; 
-;;; (dotimes (i (1+ (integer-length most-positive-fixnum)))
-;;;    (setf (aref +mask+ i) (the fixnum (1- (expt 2 i)))))
-
-(DEFCONSTANT +MASK+
-  (let ((rslt (make-array (integer-length most-positive-fixnum)
-                        :element-type 'fixnum)))
-    (declare (type (array fixnum 1) rslt))
-    (dotimes (i (integer-length most-positive-fixnum) rslt)
-      (setf (aref rslt i) (the fixnum (1- (expt 2 i)))))))
-
-
-(DEFMACRO MASK (n)
-   `(aref +mask+ ,n))
-
-(DEFMACRO BINOMIAL-P-Q (p q)
-  `(binomial-n-p (+ ,p ,q) ,p))
-
-;;;
-;;;  COMBINATIONS
-;;;
-
-(DEFMACRO LEXICO (&rest rest)
-   (unless (cdr rest)
-      (return-from lexico (first rest)))
-   (let ((vrslt (gensym)))
-      `(let ((,vrslt ,(first rest)))
-          (declare (type cmpr ,vrslt))
-          (if (eq ,vrslt :equal)
-             (lexico ,@(rest rest))
-             ,vrslt))))
-
-#|
-  (let ((#+ACLPC allegro:*top-print-level*
-         #-ACLPC     *print-level* nil))
-    (declare (special
-                #+aclpc allegro:*top-print-level*
-                #-aclpc *print-level*))
-     (pprint (macroexpand-1
-               '(lexico
-                   comparison1
-                   comparison2
-                   comparison3
-                   comparison4)))))
-|#
-
-(DEFMACRO TERM (cffc gnrt)
-  `(cons ,cffc ,gnrt))
-
-(DEFMACRO -TERM (mark)
-   `(car ,mark))
-
-(DEFMACRO CFFC (term)
-   `(car ,term))
-
-(DEFMACRO -CFFC (mark)
-   `(caar ,mark))
-
-(DEFMACRO GNRT (term)
-  `(cdr ,term))
-
-(DEFMACRO -GNRT (mark)
-   `(cdar ,mark))
-
-(DEFMACRO WITH-TERM ((cffc gnrt) term . body)
-   `(let (,@(if cffc `((,cffc (cffc ,term))) nil)
-          ,@(if gnrt `((,gnrt (gnrt ,term))) nil))
-       (declare
-          (fixnum ,@(if cffc `(,cffc) nil))
-          (type gnrt ,@(if gnrt `(,gnrt) nil)))
-       ,@body))
-
-#|
-  (macroexpand-1 '(with-term (cffc gnrt) term
-                     (statement-1)
-                     (statement-2)))
-  (macroexpand-1 '(with-term (nil gnrt) term
-                     (statement-1)
-                     (statement-2)))
-|#
-
-(DEFMACRO WITH--TERM ((cffc gnrt) mark . body)
-   `(let ((,cffc (-cffc ,mark))
-          (,gnrt (-gnrt ,mark)))
-       (declare
-          (fixnum ,cffc)
-          (type gnrt ,gnrt))
-       ,@body))
-
-#|
-  (macroexpand-1 '(with--term (cffc gnrt) mark
-                     (statement-1)
-                     (statement-2)))
-|#
-
-(DEFMACRO MAKE-CMBN (&key degr list)
-   `(cons :cmbn
-       (cons ,degr ,list)))
-
-#|
-  (make-cmbn :degr 3 :list '((1 . a) (2 . b)))
-|#          
-
-(DEFMACRO CMBN-DEGR (cmbn)
-   `(cadr ,cmbn))
-
-(DEFMACRO CMBN-LIST (cmbn)
-   `(cddr ,cmbn))
-
-#|
-  (cmbn-degr (cons :cmbn (cons 5 nil)))
-  (cmbn-list (cons :cmbn (cons 5 nil)))
-|#
-
-(DEFMACRO WITH-CMBN ((degr list) cmbn . body)
-   `(let ((,degr (cmbn-degr ,cmbn))
-          (,list (cmbn-list ,cmbn)))
-       (declare
-          (fixnum ,degr)
-          (list ,list))
-       ,@body))
-
-#|
-  (macroexpand-1 '(with-cmbn (degr list) cmbn
-                     (statement-1)
-                     (statement-2)))
-|#
-
-(DEFMACRO TERM-CMBN (degr cffc gnrt)
-   `(cons :cmbn (cons ,degr (cons (cons ,cffc ,gnrt) nil))))
-
-(DEFMACRO CMBN-NON-ZERO-P (cmbn)
-   `(cmbn-list ,cmbn)) 
-
-(DEFMACRO CMBN-ZERO-P (cmbn)
-  `(null (cmbn-list ,cmbn)))
-
-
-;;;
-;;;  CHAIN COMPLEXES
-;;;
-
-(DEFMACRO CMPR (&rest rest)
-   (ecase (length rest)
-      (1 `(cmpr1 ,@rest))
-      (3 `(cmpr3 ,@rest))))
-
-(DEFMACRO CMPR3 (object item1 item2)
-   `(funcall (cmpr1 ,object) ,item1 ,item2))
-
-#|
-  (macroexpand '(cmpr chcm))
-  (macroexpand '(cmpr chcm item1 item2))
-|#
-
-(DEFMACRO BASIS (&rest rest)
-   (ecase (length rest)
-      (1 `(basis1 ,@rest))
-      (2 `(basis2 ,@rest))
-      (3 `(basis3 ,@rest))))
-
-(DEFUN BASIS2 (object n)         ;;;
-   (declare
-      (type t object)
-      (fixnum n))
-   (the list
-      (with-slots (basis) object
-         (declare (type basis basis))
-         (when (eq :locally-effective basis)
-            (error "The object ~A is locally-effective." object))
-         (funcall basis n))))
-
-(DEFMACRO BASIS3 (smst dmns keyword)
-  (declare (ignore keyword))  
-  `(a-basis2 (basis ,smst) ,dmns))
-
-(DEFMACRO DFFR (&rest rest)
-   (ecase (length rest)
-      (1 `(dffr1 ,@rest))
-      ((2 3) `(? (dffr1 ,(first rest)) ,@(rest rest)))))
-
-#|
-  (macroexpand '(dffr chcm))
-  (macroexpand '(dffr chcm cmbn))
-  (macroexpand '(dffr chcm degr gnrt))
-|#
-
-;;; Result = (:rslt gnrt value clnm rntm . prpr)
-
-(DEFMACRO MAKE-RSLT (&key gnrt value clnm rntm)
-   `(list :rslt ,gnrt ,value ,clnm ,rntm))
-
-(DEFMACRO RSLT-GNRT (rslt)
-   `(second ,rslt))
-
-(DEFMACRO RSLT-VALUE (rslt)
-   `(third ,rslt))
-
-(DEFMACRO RSLT-CLNM (rslt)
-   `(fourth ,rslt))
-
-(DEFMACRO RSLT-RNTM (rslt)
-   `(fifth ,rslt))
-
-(DEFMACRO ? (&rest rest)
-   (ecase (length rest)
-      (2 `(?2 ,@rest))
-      (3 `(?3 ,@rest))))
-
-(DEFMACRO CONTROL (cmpr cmbn)
-   (if *cmbn-control*
-      `(do-control ,cmpr ,cmbn)
-      cmbn))
-
-(DEFMACRO CONTROLN (cmpr cmbn)
-   (if *cmbn-control*
-      `(do-control ,cmpr ,cmbn)
-      nil))
-
-(DEFVAR *WRONG-CMBN*)
-
-
-;;;
-;;;  CHCM-ELEMENTARY-OP
-;;;
-
-(DEFMACRO I-CMPS (mrph1 &rest rest)
-   (if rest
-      `(cmps ,mrph1 (i-cmps ,@rest))
-      mrph1))
-
-#|
-  (macroexpand '(i-cmps m1))
-  (macroexpand '(i-cmps m1 m2))
-  (macroexpand '(i-cmps m1 m2 m3))
-|#
-
-(DEFMACRO I-ADD (mrph1 &rest rest)
-   (if rest
-      `(add ,mrph1 (i-add ,@rest))
-      mrph1))
-
-#|
-  (macroexpand '(i-add m1))
-  (macroexpand '(i-add m1 m2))
-  (macroexpand '(i-add m1 m2 m3))
-|#
-
-(DEFMACRO I-SBTR (mrph1 mrph2 &rest rest)
-   `(sbtr ,mrph1 (i-add ,mrph2 ,@rest)))
-   
-#|
-  (macroexpand '(i-sbtr m1 m2))
-  (macroexpand '(i-sbtr m1 m2 m3))
-|#
-
-;;;
-;;;  EFFECTIVE HOMOLOGY
-;;;
-
-(DEFMACRO BCC (&rest rest)
-   (case (length rest)
-      (1 `(bcc1 ,@rest))
-      (otherwise
-         `(? (bcc1 ,(first rest)) ,@(rest rest)))))
-
-(DEFMACRO TCC (&rest rest)
-   (case (length rest)
-      (1 `(tcc1 ,@rest))
-      (otherwise
-         `(? (tcc1 ,(first rest)) ,@(rest rest)))))
-
-(DEFMACRO F (&rest rest)
-   (case (length rest)
-      (1 `(f1 ,@rest))
-      (otherwise
-         `(? (f1 ,(first rest)) ,@(rest rest)))))
-
-#|
-  (macroexpand '(f rdct))
-  (macroexpand '(f rdct cmbn))
-  (macroexpand '(f rdct degr gnrt))
-|#
-
-(DEFMACRO G (&rest rest)
-   (case (length rest)
-      (1 `(g1 ,@rest))
-      (otherwise
-         `(? (g1 ,(first rest)) ,@(rest rest)))))
-
-(DEFMACRO H (&rest rest)
-   (case (length rest)
-      (1 `(h1 ,@rest))
-      (otherwise
-         `(? (h1 ,(first rest)) ,@(rest rest)))))
-
-(DEFMACRO LBCC (&rest rest)
-   (case (length rest)
-      (1 `(lbcc1 ,@rest))
-      (otherwise
-         `(? (lbcc1 ,(first rest)) ,@(rest rest)))))
-
-(DEFMACRO RBCC (&rest rest)
-   (case (length rest)
-      (1 `(rbcc1 ,@rest))
-      (otherwise
-         `(? (rbcc1 ,(first rest)) ,@(rest rest)))))
-
-(DEFMACRO LF (&rest rest)
-   (case (length rest)
-      (1 `(lf1 ,@rest))
-      (otherwise
-         `(? (lf1 ,(first rest)) ,@(rest rest)))))
-
-(DEFMACRO LG (&rest rest)
-   (case (length rest)
-      (1 `(lg1 ,@rest))
-      (otherwise
-         `(? (lg1 ,(first rest)) ,@(rest rest)))))
-
-(DEFMACRO LH (&rest rest)
-   (case (length rest)
-      (1 `(lh1 ,@rest))
-      (otherwise
-         `(? (lh1 ,(first rest)) ,@(rest rest)))))
-
-(DEFMACRO RF (&rest rest)
-   (case (length rest)
-      (1 `(rf1 ,@rest))
-      (otherwise
-         `(? (rf1 ,(first rest)) ,@(rest rest)))))
-
-(DEFMACRO RG (&rest rest)
-   (case (length rest)
-      (1 `(rg1 ,@rest))
-      (otherwise
-         `(? (rg1 ,(first rest)) ,@(rest rest)))))
-
-(DEFMACRO RH (&rest rest)
-   (case (length rest)
-      (1 `(rh1 ,@rest))
-      (otherwise
-         `(? (rh1 ,(first rest)) ,@(rest rest)))))
-
-;;;
-;;;  CONES
-;;;
-
-(DEFMACRO BCNX (bicn)
-   `(car ,bicn))
-
-(DEFMACRO IBICN (bicn)
-   `(cdr ,bicn))
-
-(DEFMACRO BCNB (gnrt)
-   `(cons :bcnb ,gnrt))
-
-(DEFMACRO BCNC (gnrt)
-   `(cons :bcnc ,gnrt))
-
-(DEFMACRO BCND (gnrt)
-   `(cons :bcnd ,gnrt))
-
-(DEFMACRO WITH-BICN ((bcnx ibicn) bicn . body)
-   `(let ((,bcnx (bcnx ,bicn))
-          (,ibicn (ibicn ,bicn)))
-       (declare
-          (type (member :bcnb :bcnc :bcnd) ,bcnx)
-          (type gnrt ,ibicn))
-       ,@body))
-
-
-;;;
-;;;  TENSOR PRODUCTS
-;;;
-
-(DEFMACRO TNPR (degr1 gnrt1 degr2 gnrt2)
-   `(cons :tnpr (cons (cons ,degr1 ,gnrt1) (cons ,degr2 ,gnrt2))))
-
-(DEFMACRO DEGR1 (tnpr)
-   `(caadr ,tnpr))
-
-(DEFMACRO GNRT1 (tnpr)
-   `(cdadr ,tnpr))
-
-(DEFMACRO DEGR2 (tnpr)
-   `(caddr ,tnpr))
-
-(DEFMACRO GNRT2 (tnpr)
-   `(cdddr ,tnpr))
-
-(DEFMACRO WITH-TNPR ((degr1 gnrt1 degr2 gnrt2) tnpr . body)
-   `(let (,@(if degr1 `((,degr1 (degr1 ,tnpr))) nil)
-          ,@(if gnrt1 `((,gnrt1 (gnrt1 ,tnpr))) nil)
-          ,@(if degr2 `((,degr2 (degr2 ,tnpr))) nil)
-          ,@(if gnrt2 `((,gnrt2 (gnrt2 ,tnpr))) nil))
-       (declare
-          (fixnum ,@(if degr1 `(,degr1) nil) ,@(if degr2 `(,degr2) nil))
-          (type gnrt ,@(if gnrt1 `(,gnrt1) nil) ,@(if gnrt2 `(,gnrt2) nil)))
-       ,@body))
-
-#|
-  (macroexpand '(tnpr 1 a 2 b))
-            1 (tnpr 2 'a 4 (tnpr 2 'b 2 'c))
-  (macroexpand-1 '(with-tnpr (degr1 gnrt1 degr2 gnrt2) tnpr
-                    (statement-1)
-                    (statement-2)))
-  (macroexpand-1 '(with-tnpr (nil gnrt1 degr2 gnrt2) tnpr
-                    (statement-1)
-                    (statement-2)))
-|#
-
-;;;
-;;;  COALGEBRAS
-;;;
-
-(DEFMACRO CPRD (&rest rest)
-   (case (length rest)
-      (1 `(cprd1 ,@rest))
-      ((2 3) `(? (cprd1 ,(first rest)) ,@(rest rest)))))
-
-;;;
-;;;  COBAR
-;;;
-
-(DEFMACRO CBGN (degr gnrt)
-   `(cons ,degr ,gnrt))
-
-(DEFMACRO CDEGR (cbgn)
-   `(car ,cbgn))
-
-(DEFMACRO CGNRT (cbgn)
-   `(cdr ,cbgn))
-
-(DEFMACRO -CDEGR (cbgn)
-   `(caar ,cbgn))
-
-(DEFMACRO -CGNRT (cbgn)
-   `(cdar ,cbgn))
-
-(DEFMACRO WITH-CBGN ((cdegr cgnrt) cbgn . body)
-   `(let ((,cdegr (cdegr ,cbgn))
-          (,cgnrt (cgnrt ,cbgn)))
-       (declare
-          (fixnum ,cdegr)
-          (type gnrt ,cgnrt))
-       ,@body))
-
-(DEFMACRO WITH--CBGN ((cdegr cgnrt) cbgn . body)
-   `(let ((,cdegr (-cdegr ,cbgn))
-          (,cgnrt (-cgnrt ,cbgn)))
-       (declare
-          (fixnum ,cdegr)
-          (type gnrt ,cgnrt))
-       ,@body))
-
-(DEFMACRO MAKE-ALLP (&key list)
-   `(cons :allp ,list))
-
-(DEFMACRO ALLP-LIST (allp)
-   `(cdr ,allp))
-
-(DEFMACRO WITH-ALLP ((list) allp . body)
-   `(let ((,list (allp-list ,allp)))
-       (declare (list ,list))
-       ,@body))
-
-(DEFMACRO GNRT-ALLP-TNPR (degr gnrt allp)
-   `(make-allp :list (cons (cbgn (1- ,degr) ,gnrt) ,allp)))
-
-
-;;;
-;;;  ALGEBRAS
-;;;
-
-(DEFMACRO APRD (&rest rest)
-   (case (length rest)
-      (1 `(aprd1 ,@rest))
-      ((2 3) `(? (aprd1 ,(first rest)) ,@(rest rest)))))
-
-;;;
-;;;  BAR
-;;;
-
-(DEFMACRO BRGN (degr gnrt)
-   `(cons ,degr ,gnrt))
-
-(DEFMACRO BDEGR (brgn)
-   `(car ,brgn))
-
-(DEFMACRO BGNRT (brgn)
-   `(cdr ,brgn))
-
-(DEFMACRO -BDEGR (brgn)
-   `(caar ,brgn))
-
-(DEFMACRO -BGNRT (brgn)
-   `(cdar ,brgn))
-
-(DEFMACRO WITH-BRGN ((bdegr bgnrt) brgn . body)
-   `(let ((,bdegr (bdegr ,brgn))
-          (,bgnrt (bgnrt ,brgn)))
-       (declare
-          (fixnum ,bdegr)
-          (type gnrt ,bgnrt))
-       ,@body))
-
-(DEFMACRO WITH--BRGN ((bdegr bgnrt) brgn . body)
-   `(let ((,bdegr (-bdegr ,brgn))
-          (,bgnrt (-bgnrt ,brgn)))
-       (declare
-          (fixnum ,bdegr)
-          (type gnrt ,bgnrt))
-       ,@body))
-
-(DEFMACRO MAKE-ABAR (&key list)
-   `(cons :abar ,list))
-
-(DEFMACRO ABAR-LIST (abar)
-   `(cdr ,abar))
-
-(DEFMACRO WITH-ABAR ((list) abar . body)
-   `(let ((,list (abar-list ,abar)))
-       (declare (list ,list))
-       ,@body))
-
-(DEFMACRO MAKE-GBAR (&key dmns list)
-   `(cons :gbar (cons ,dmns ,list)))
-
-(DEFMACRO GBAR-DMNS (gbar)
-   `(cadr ,gbar))
-
-(DEFMACRO GBAR-LIST (gbar)
-   `(cddr ,gbar))
-
-(DEFMACRO WITH-GBAR ((dmns list) gbar . body)
-   `(let ((,dmns (gbar-dmns ,gbar))
-	  (,list (gbar-list ,gbar)))
-       (declare
-	 (fixnum ,dmns)
-	 (list ,list))
-       ,@body))
-
-(DEFMACRO GNRT-GBAR-TNPR (degr gnrt gbar)
-   `(make-gbar :list (cons (brgn (1- ,degr) ,gnrt) ,gbar)))
-
-;;;
-;;;  SIMPLICIAL SETS
-;;;
-
-(DEFMACRO ABSM (dgop gmsm)
-   `(cons :absm (cons ,dgop ,gmsm)))
-
-(DEFMACRO DGOP (absm)
-   `(cadr ,absm))
-
-(DEFMACRO GMSM (absm)
-   `(cddr ,absm))
-
-(DEFMACRO WITH-ABSM ((dgop-var gmsm-var) absm . body)
-   `(let ((,dgop-var (dgop ,absm))
-          (,gmsm-var (gmsm ,absm)))
-       (declare
-          (fixnum ,dgop-var)
-          (type gmsm ,gmsm-var))
-       ,@body))
-
-(DEFMACRO DEGENERATE-P (absm)
-   `(plusp (dgop ,absm)))
-
-(DEFMACRO NON-DEGENERATE-P (absm)
-   `(zerop (dgop ,absm)))
-
-(DEFMACRO FACE (&rest rest)
-   (ecase (length rest)
-      (1 `(face1 ,@rest))
-      (4 `(face4 ,@rest))))
-
-(DEFMACRO A-FACE4 (face indx dmns absm)
-   `(ia-face4 ,face ,indx ,dmns (cdr ,absm)))
-
-;;;
-;;;  DELTA
-;;;
-
-(DEFMACRO D (igmsm)
-   `(cons :delt ,igmsm))
-
-;;;
-;;;  SPECIAL-SMSTS
-;;;
-
-;;; GMSM-FACES-INFO = (gmsm (simple-vector absm) . dffr)
-;;;                         faces
-       
-(DEFMACRO MAKE-GMSM-FACES-INFO (&key gmsm faces dffr)
-   `(cons ,gmsm (cons ,faces ,dffr)))
-
-(DEFMACRO INFO-GMSM (gmsm-faces-info)
-   `(car ,gmsm-faces-info))
-
-(DEFMACRO INFO-FACES (gmsm-faces-info)
-   `(cadr ,gmsm-faces-info))
-
-(DEFMACRO INFO-FACE-I (gmsm-faces-info i)
-   `(svref (cadr ,gmsm-faces-info) ,i))
-
-(DEFMACRO INFO-DFFR (gmsm-faces-info)
-   `(cddr ,gmsm-faces-info))
-
-;;;
-;;;  CARTESIAN PRODUCTS
-;;;
-
-(DEFMACRO CRPR (&rest rest)
-   (ecase (length rest)
-      (2 `(cons :crpr (cons (cdr ,(first rest)) (cdr ,(second rest)))))
-      (4 `(cons :crpr (cons
-                         (cons ,(first rest) ,(second rest))
-                         (cons ,(third rest) ,(fourth rest)))))))
-
-#|
-  (macroexpand '(crpr absm1 absm2))
-  (macroexpand '(crpr dgop1 gmsm1 dgop2 gmsm2))
-|#
-
-(DEFMACRO DGOP1 (crpr)
-   `(caadr ,crpr))
-
-(DEFMACRO GMSM1 (crpr)
-   `(cdadr ,crpr))
-
-(DEFMACRO DGOP2 (crpr)
-   `(caddr ,crpr))
-
-(DEFMACRO GMSM2 (crpr)
-   `(cdddr ,crpr))
-
-(DEFMACRO ABSM1 (crpr)
-   `(cons :absm (cadr ,crpr)))
-
-(DEFMACRO ABSM2 (crpr)
-   `(cons :absm (cddr ,crpr)))
-
-#|
-  (setf c (crpr 1 'a 2 'b))
-  (dgop1 c)
-  (gmsm1 c)
-  (dgop2 c)
-  (gmsm2 c)
-  (absm1 c)
-  (absm2 c)
-|#
-
-(DEFMACRO WITH-CRPR (&rest rest)
-   (ecase (length (first rest))
-      (2 `(with-crpr-2 ,@rest))
-      (4 `(with-crpr-4 ,@rest))))
-
-(DEFMACRO WITH-CRPR-2 ((absm1 absm2) crpr . body)
-   `(let ((,absm1 (cons :absm (cadr ,crpr)))
-          (,absm2 (cons :absm (cddr ,crpr))))
-       (declare (type absm ,absm1 ,absm2))
-       ,@body))
-
-(DEFMACRO WITH-CRPR-4 ((dgop1 gmsm1 dgop2 gmsm2) crpr . body)
-   `(let ((,dgop1 (dgop1 ,crpr))
-          (,gmsm1 (gmsm1 ,crpr))
-          (,dgop2 (dgop2 ,crpr))
-          (,gmsm2 (gmsm2 ,crpr)))
-       (declare
-          (fixnum ,dgop1 ,dgop2)
-          (type gmsm ,gmsm1 ,gmsm2))
-       ,@body))
-
-#|
-  (macroexpand-1
-  (macroexpand-1 '(with-crpr (dgop1 gmsm1 dgop2 gmsm2) crpr
-                     (statement-1)
-                     (statement-2))))
-  (macroexpand-1
-  (macroexpand-1 '(with-crpr (absm1 absm2) crpr
-                     (statement-1)
-                     (statement-2))))
-|#
-
-;;;
-;;;  EILENBERG-ZILBER
-;;;
-
-(DEFMACRO EILENBERG-ZILBER (&rest rest)
-   `(ez ,@rest))
-
-;;;
-;;;  LOOP SPACES
-;;;
-
-(DEFMACRO POWR (gmsm expn)
-   `(cons ,gmsm ,expn))
-
-(DEFMACRO PGMSM (powr)
-   `(car ,powr))
-
-(DEFMACRO EXPN (powr)
-   `(cdr ,powr))
-
-(DEFMACRO WITH-POWR ((gmsm expn) powr . body)
-   `(let ((,gmsm (car ,powr))
-          (,expn (cdr ,powr)))
-       (declare
-          (type gmsm ,gmsm)
-          (fixnum expn))
-       ,@body))
-
-(DEFMACRO WITH-APOWR ((dgop gmsm expn) apowr . body)
-   `(let ((,dgop (apdgop ,apowr))
-          (,gmsm (cadr ,apowr))
-          (,expn (cddr ,apowr)))
-       (declare
-          (fixnum ,dgop ,expn)
-          (type gmsm ,gmsm))
-       ,@body))
-
-(DEFMACRO APOWR (dgop gmsm expn)
-   `(cons ,dgop (cons ,gmsm ,expn)))
-   
-(DEFMACRO APDGOP (apowr)
-   `(car ,apowr))
-
-(DEFMACRO APGMSM (apowr)
-   `(cadr ,apowr))
-
-(DEFMACRO APEXPN (apowr)
-   `(cddr ,apowr))
-
-(DEFMACRO MAKE-LOOP (&key list)
-   `(cons :loop ,list))
-
-(DEFMACRO LOOP-LIST (loop)
-   `(cdr ,loop))
-
-;; CONSTRUCTOR
-
-(DEFMACRO WHEN-SLOT (slot-name . body)
-  `(when (or (eq slot-names t)
-             (member ',slot-name slot-names))
-     ,@body))
-
-#|
-(pprint
- (macroexpand-1
-  '(when-slot dfnt (statement-1) (statement-2))))
-|#
-
-(DEFMACRO ALREADY (object dfnt)
-  (let ((sfound (gensym)))
-  `(let ((,sfound (find ,dfnt *k-list* :key #'dfnt :test #'equal)))
-     (declare (type (or kenzo-object null) ,sfound))
-     (when ,sfound
-       (return-from ,object ,sfound)))))
-
-#|
-(pprint
- (macroexpand-1
-  '(already chain-complex '(z-chcm))))
-|#
-
diff --git a/archive/Kenzo-2/Kenzo-2-Acl8/searching-homology.cl b/archive/Kenzo-2/Kenzo-2-Acl8/searching-homology.cl
deleted file mode 100644
index fa3e863..0000000
--- a/archive/Kenzo-2/Kenzo-2-Acl8/searching-homology.cl
+++ /dev/null
@@ -1,43 +0,0 @@
-;;;  SEARCHING-HOMOLOGY  SEARCHING-HOMOLOGY  SEARCHING-HOMOLOGY
-;;;  SEARCHING-HOMOLOGY  SEARCHING-HOMOLOGY  SEARCHING-HOMOLOGY
-;;;  SEARCHING-HOMOLOGY  SEARCHING-HOMOLOGY  SEARCHING-HOMOLOGY
-
-(IN-PACKAGE "CAT")
-
-(PROVIDE "searching-homology")
-
-(DEFUN ECHCM (chcm)
-   (rbcc (efhm chcm)))
-
-(DEFMETHOD HOMOLOGY ((chcm chain-complex) degr1 &optional (degr2 (1+ degr1)))
-   (declare (fixnum degr1 degr2))
-   (do ((degr degr1 (1+ degr)))
-       ((>= degr degr2))
-      (declare (fixnum degr))
-      (chcm-homology (echcm chcm) degr)
-      (terpri) (clock) (terpri)))
-
-(DEFGENERIC SEARCH-EFHM (chcm dfnt))
-
-(DEFMETHOD SEARCH-EFHM (chcm dfnt)
-  (declare (ignore chcm dfnt))
-  nil)
-
-(DEFMETHOD SLOT-UNBOUND (class (chcm chain-complex) (slot-name (eql 'efhm)))
-  (declare (ignore class))
-  (the equivalence
-    (let ((efhm (search-efhm chcm (first (dfnt chcm)))))
-      (declare (type (or null equivalence) efhm))
-      (setf (efhm chcm)
-        (or efhm
-            (when (functionp (basis chcm))
-              (trivial-eqvl chcm))
-            (error "I don't know how to determine ~
-                    the effective homology of:~@
-                    ~A (Origin: ~A)." chcm (dfnt chcm)))))))
-
-#|
-  (cat-init)
-  (setf d (delta 3))
-  (homology d 0)
-|#
diff --git a/archive/Kenzo-2/Kenzo-2-Acl8/serre.cl b/archive/Kenzo-2/Kenzo-2-Acl8/serre.cl
deleted file mode 100644
index ba175ad..0000000
--- a/archive/Kenzo-2/Kenzo-2-Acl8/serre.cl
+++ /dev/null
@@ -1,288 +0,0 @@
-;;;  SERRE  SERRE  SERRE  SERRE  SERRE  SERRE  SERRE  SERRE  SERRE
-;;;  SERRE  SERRE  SERRE  SERRE  SERRE  SERRE  SERRE  SERRE  SERRE
-;;;  SERRE  SERRE  SERRE  SERRE  SERRE  SERRE  SERRE  SERRE  SERRE
-
-(IN-PACKAGE "CAT")
-
-(PROVIDE "serre")
-
-(DEFUN FIBRATION-DTAU-D-INTR
-  (fibration &aux (base (sorc fibration))
-	          (bface (face base))
-	          (fibre (trgt fibration))
-		  (fface (face fibre))
-		  (grml-sintr (sintr (grml fibre)))
-		  (fbsgn (bsgn fibre))
-		  (sintr-twist (sintr fibration))
-		  (total (fibration-total fibration))
-		  (total-cmpr (cmpr total)))
-  (declare
-     (type fibration fibration)
-     (type simplicial-set base total)
-     (type face bface fface)
-     (type simplicial-group fibre)
-     (type gmsm fbsgn)
-     (type sintr grml-sintr sintr-twist)
-     (type cmprf total-cmpr))
-  (flet ((rslt (dmns crpr
-		     &aux (dmns-1 (1- dmns)))
-	    (declare
-	       (fixnum dmns dmns-1)
-	       (type crpr crpr))
-	    (unless (plusp dmns)
-	       (return-from rslt
-		  (zero-cmbn dmns-1)))
-	    (with-crpr (b-absm f-absm) crpr
-	       (let ((tau-b
-		      (tw-a-sintr3 sintr-twist dmns
-				   b-absm fbsgn)))
-		 (declare (type absm tau-b))
-		 (when (= (dgop tau-b) (mask dmns-1))
-		    (return-from rslt
-				 (zero-cmbn dmns-1)))
-		 (let ((deln-b
-			(a-face4 bface dmns dmns
-				 b-absm))
-		       (deln-f
-			(a-face4 fface dmns dmns
-				 f-absm)))
-		   (declare
-                      (type absm deln-b deln-f tau-b))
-		   (let ((acrpr1 (2absm-acrpr deln-b deln-f))
-			 (acrpr2 
-			  (2absm-acrpr
-			     deln-b
-			     (a-grml4 grml-sintr (1- dmns)
-				      tau-b deln-f))))
-		      (declare (type absm crpr1 crpr2))
-		      (with-absm (dgop1 crpr1) acrpr1
-		      (with-absm (dgop2 crpr2) acrpr2
-			 (if (zerop dgop1)
-			    (if (zerop dgop2)
-			       (dstr-add-term-to-cmbn
-				  total-cmpr
-				  (-1-expt-n+1 dmns) crpr1
-				  (term-cmbn dmns-1
-					     (-1-expt-n dmns)
-					     crpr2))
-			       (term-cmbn dmns-1
-					  (-1-expt-n+1 dmns)
-					  crpr1))
-			    (if (zerop dgop2)
-			       (term-cmbn dmns-1
-					  (-1-expt-n dmns)
-					  crpr2)
-			       (zero-cmbn dmns-1)))))))))))
-	(the intr #'rslt)))
-
-#|
-  (cat-init)
-  (setf s2 (sphere 2))
-  (setf k (k-z2-1))
-  (setf tw (simplicial-mrph
-             :sorc s2
-	     :trgt k
-	     :degr -1
-	     :sintr #'(lambda (dmns gmsm)
-			(absm 0 1))
-	     :dfnt '(s2-tw-kz2)))
-  (setf dt-d (fibration-dtau-d-intr tw))
-  (funcall dt-d 0 (crpr 0 '* 0 0))
-  (funcall dt-d 3 (crpr 4 's2 0 3))
-  (funcall dt-d 3 (crpr 2 's2 0 3))
-  (funcall dt-d 3 (crpr 2 's2 5 1))
-  (funcall dt-d 2 (crpr 0 's2 0 2))
-  (cat-init)
-  (setf s2 (sphere 2))
-  (setf k (k-z-1))
-  (setf tw (simplicial-mrph
-             :sorc s2
-	     :trgt k
-	     :degr -1
-	     :sintr #'(lambda (dmns gmsm)
-			(absm 0 (list 1)))
-	     :dfnt '(s2-tw-kz)))
-  (setf dt-d (fibration-dtau-d-intr tw))
-  (funcall dt-d 0 (crpr 0 '* 0 nil))
-  (funcall dt-d 3 (crpr 4 's2 0 '(2 3 4)))
-  (funcall dt-d 3 (crpr 2 's2 0 '(2 3 4)))
-  (funcall dt-d 3 (crpr 2 's2 5 '(5)))
-  (funcall dt-d 2 (crpr 0 's2 0 '(3 -2)))
-|#
-
-(DEFUN FIBRATION-DTAU-D (fibration
-			   &aux (base (sorc fibration))
-			        (fibre (trgt fibration))
-				(utotal (crts-prdc base fibre)))
-  (declare (type fibration fibration))
-  (the morphism
-     (morphism
-        :sorc utotal
-	:trgt utotal
-	:degr -1
-	:intr (fibration-dtau-d-intr fibration)
-	:strt :gnrt
-	:dfnt `(fibration-dtau-d ,fibration))))
-
-#|
-  (cat-init)
-  (setf s2 (sphere 2))
-  (setf k (k-z-1))
-  (setf tw (simplicial-mrph
-             :sorc s2
-	     :trgt k
-	     :degr -1
-	     :sintr #'(lambda (dmns gmsm)
-			(absm 0 (list 1)))
-	     :dfnt '(s2-tw-kz)))
-  (setf dt-d (fibration-dtau-d tw))
-  (? dt-d 0 (crpr 0 '* 0 nil))
-  (? dt-d 3 (crpr 4 's2 0 '(2 3 4)))
-  (? dt-d 3 (crpr 2 's2 0 '(2 3 4)))
-  (? dt-d 3 (crpr 2 's2 5 '(5)))
-  (? dt-d 2 (crpr 0 's2 0 '(3 -2)))
-|#
-
-(DEFUN BROWN-REDUCTION (fibration
-		        &aux (base (sorc fibration))
-			      (fibre (trgt fibration))
-			      (total (fibration-total fibration))
-			      (ez (eilenberg-zilber base fibre))
-			      (t-perturbation (fibration-dtau-d fibration)))
-  (declare
-     (type fibration fibration)
-     (type simplicial-set base fibre total)
-     (type reduction ez)
-     (type morphism t-perturbation))
-  (the (values reduction morphism)
-     (multiple-value-bind (rslt b-perturbation) (add ez t-perturbation)
-	(declare
-	   (type reduction rslt)
-	   (type morphism b-perturbation))
-        (with-slots (f g h tcc) rslt
-	   (setf tcc total)
-	   (dstr-change-sorc-trgt f :new-sorc total)
-	   (dstr-change-sorc-trgt g :new-trgt total)
-	   (dstr-change-sorc-trgt h :new-sorc total :new-trgt total)
-	   (values rslt b-perturbation)))))
-
-#|
-  (cat-init)
-  (setf s2 (sphere 2))
-  (setf k (k-z2-1))
-  (setf tw (simplicial-mrph
-             :sorc s2
-	     :trgt k
-	     :degr -1
-	     :sintr #'(lambda (dmns gmsm)
-			(absm 0 1))
-	     :dfnt '(s2-tw-kz2)))
-  (setf brown (brown-reduction tw))
-  (setf tcc (tcc brown) bcc (bcc brown))
-  (homology bcc 3)
-  (homology tcc 1 8)
-  (homology bcc 1 8)
-  (cat-init)
-  (setf s2 (sphere 2))
-  (setf k (k-z-1))
-  (setf tw (simplicial-mrph
-             :sorc s2
-	     :trgt k
-	     :degr -1
-	     :sintr #'(lambda (dmns gmsm)
-			(absm 0 (list 1)))
-	     :dfnt '(s2-tw-kz1)))
-  (setf brown (brown-reduction tw))
-  (homology (tcc brown) 1 5)
-  (homology (bcc brown) 1 5)
-|#
-
-(DEFUN LEFT-SERRE-EFHM (fibration)
-  (declare (type fibration fibration))
-  (the equivalence
-     (equivalence
-      :lrdct (trivial-rdct (fibration-total fibration))
-      :rrdct (brown-reduction fibration)
-      :dfnt `(left-serre-efhm ,fibration))))
-
-(DEFUN RIGHT-SERRE-EFHM (fibration &aux
-                                   (base (sorc fibration))
-                                   (fibre (trgt fibration))
-                                   (base-efhm (efhm base))
-                                   (fibre-efhm (efhm fibre))
-                                   (uprdc-efhm (tnsr-prdc base-efhm fibre-efhm)))
-  (declare
-   (type fibration fibration)
-   (type simplicial-set base fibre)
-   (type equivalence base-efhm fibre-efhm uprdc-efhm))
-  (the equivalence
-     (multiple-value-bind (brown b-perturbation) (brown-reduction fibration)
-       (declare
-        (type reduction brown)
-        (type morphism b-perturbation))
-       (let ((rslt (add uprdc-efhm b-perturbation)))
-         (declare (type equivalence rslt))
-         (with-slots (lbcc lf lg lrdct) rslt
-           (declare
-            (type chain-complex lbcc)
-            (type morphism lf lg)
-            (type reduction lrdct))
-           (setf lbcc (bcc brown))
-           (dstr-change-sorc-trgt lf :new-trgt lbcc)
-           (dstr-change-sorc-trgt lg :new-sorc lbcc)
-           (with-slots (bcc f g) lrdct
-             (declare
-              (type chain-complex bcc)
-              (type morphism f g))
-             (setf bcc lbcc)
-             (dstr-change-sorc-trgt f :new-trgt lbcc)
-             (dstr-change-sorc-trgt g :new-sorc lbcc)))
-         rslt))))
-
-#|
-(cat-init)
-(setf s2 (sphere 2))
-(setf k (k-z-1))
-(setf tw (simplicial-mrph
-          :sorc s2
-          :trgt k
-          :degr -1
-          :sintr #'(lambda (dmns gmsm)
-                     (absm 0 (list 1)))
-          :dfnt '(s2-tw-kz1)))
-(setf rh (right-serre-efhm tw))
-(setf rbcc (rbcc rh))
-(homology rbcc 0 5)  
-|#
-
-(DEFUN FIBRATION-TOTAL-EFHM (fibration)
-  (declare (type fibration fibration))
-  (the equivalence
-    (cmps
-     (left-serre-efhm fibration)
-     (right-serre-efhm fibration))))
-
-(DEFMETHOD SEARCH-EFHM (smst (dfnt (eql 'fibration-total)))
-  (declare
-     (type simplicial-set smst))
-  (the equivalence
-     (fibration-total-efhm (second (dfnt smst)))))
-
-#|
-  (cat-init)
-  (setf s2 (sphere 2))
-  (setf k (k-z-1))
-  (setf tw (simplicial-mrph
-             :sorc s2
-	     :trgt k
-	     :degr -1
-	     :sintr #'(lambda (dmns gmsm)
-			(absm 0 (list 2)))
-	     :dfnt '(s2-tw-kz1)))
-  (setf p3r (fibration-total tw))
-  (homology p3r 1 )
-|#
-
-
-     
-  
\ No newline at end of file
diff --git a/archive/Kenzo-2/Kenzo-2-Acl8/simplicial-groups.cl b/archive/Kenzo-2/Kenzo-2-Acl8/simplicial-groups.cl
deleted file mode 100644
index 5addaf2..0000000
--- a/archive/Kenzo-2/Kenzo-2-Acl8/simplicial-groups.cl
+++ /dev/null
@@ -1,175 +0,0 @@
-;;;  SIMPLICIAL-GROUPS  SIMPLICIAL-GROUPS  SIMPLICIAL-GROUPS
-;;;  SIMPLICIAL-GROUPS  SIMPLICIAL-GROUPS  SIMPLICIAL-GROUPS
-;;;  SIMPLICIAL-GROUPS  SIMPLICIAL-GROUPS  SIMPLICIAL-GROUPS
-
-(IN-PACKAGE "CAT")
-
-(PROVIDE "simplicial-groups")
-
-(DEFMETHOD PRINT-OBJECT ((smgr simplicial-group) stream)
-  (the simplicial-group
-     (progn
-       (format stream "[K~D Simplicial-Group]" (idnm smgr))
-       smgr)))
-
-(DEFMETHOD PRINT-OBJECT ((smgr ab-simplicial-group) stream)
-  (the simplicial-group
-     (progn
-       (format stream "[K~D Abelian-Simplicial-Group]" (idnm smgr))
-       smgr)))
-
-(DEFUN SIMPLICIAL-GROUP (&rest rest &key dfnt &allow-other-keys)
-  (declare (type list dfnt))
-  (already simplicial-group dfnt)
-  (the simplicial-group
-    (apply #'make-instance 'simplicial-group rest)))
-
-(DEFMETHOD SHARED-INITIALIZE ((smgr simplicial-group) slot-names
-                              &key grml-sintr grin-sintr)
-  (declare
-   (type (or (eql t) list) slot-names)
-   (type sintr grml grin))
-  (call-next-method)
-  (when-slot grml
-             (when grml-sintr
-               (setf (slot-value smgr 'grml)
-                 (simplicial-mrph
-                  :sorc (crts-prdc smgr smgr) :trgt smgr :degr 0
-                  :sintr grml-sintr :dfnt `(group-multiplication ,smgr))))
-             (when grin-sintr
-               (setf (slot-value smgr 'grin)
-                 (simplicial-mrph
-                  :sorc smgr :trgt smgr :degr 0
-                  :sintr grin-sintr :dfnt `(group-inversion ,smgr)))))
-  smgr)
-
-(DEFUN AB-SIMPLICIAL-GROUP (&rest rest &key dfnt &allow-other-keys)
-  (declare (type list dfnt))
-  (already ab-simplicial-group dfnt)
-  (the ab-simplicial-group
-    (apply #'make-instance 'ab-simplicial-group rest)))
-  
-(DEFMETHOD SHARED-INITIALIZE ((asmgr ab-simplicial-group) slot-names &rest rest)
-  (declare (ignore slot-names rest))
-  (call-next-method))
-
-(DEFMETHOD SLOT-UNBOUND (class (smgr simplicial-group)
-			       (name (eql 'kfll)))
-  (declare (ignore class))
-  (the kfll
-     (progn
-       (setf (slot-value smgr 'kfll) (smgr-kfll smgr)))))
-
-(DEFMETHOD SLOT-UNBOUND (class (smgr simplicial-group)
-			       (name (eql 'aprd)))
-  (declare (ignore class))
-  (the morphism
-     (progn
-       (setf (slot-value smgr 'aprd) (smgr-aprd smgr)))))
-
-(DEFUN A-GRML4 (grml-sintr dmns absm1 absm2)
-  (declare
-     (fixnum dmns)
-     (type absm absm1 absm2))
-  (the absm
-     (let ((acrpr (2absm-acrpr absm1 absm2)))
-       (declare (type absm acrpr))
-       (with-absm (dgop crpr) acrpr
-          (ndgnr dgop
-		 (funcall grml-sintr
-			  (- dmns (logcount dgop))
-			  crpr))))))
-
-(DEFUN A-GRIN4 (grin-sintr dmns absm)
-  (declare
-     (type sintr grin-sintr)
-     (fixnum dmns)
-     (type absm absm))
-  (the absm
-     (with-absm (dgop gmsm) absm
-	(absm dgop
-	      (gmsm
-	       (funcall grin-sintr (- dmns (logcount dgop)) gmsm))))))
-
-(DEFUN SMGR-KFLL-INTR (face grml-sintr grin-sintr)
-  (flet ((rslt (indx dmns hat
-		     &aux (dmns-1 (1- dmns)))
-	    (declare
-	       (fixnum indx dmns dmns-1)
-	       (list hat))
-	    (the absm
-	      (let ((rslt (absm 0 nil)))
-		(declare (type absm rslt))
-		(when (plusp indx)
-		   (setf rslt (1dgnr 0 (pop hat)))
-		   (do ((i 1 (1+ i)))
-		       ((= i indx))
-		      (declare (fixnum i))
-		      (setf rslt
-			    (a-grml4
-			     grml-sintr dmns
-			     rslt
-			     (1dgnr i
-				    (a-grml4
-				     grml-sintr dmns-1
-				     (a-grin4
-				      grin-sintr dmns-1
-				      (a-face4 face
-					i dmns rslt))
-				     (pop hat)))))))
-		(when (< indx dmns)
-		  (setf hat (reverse hat))
-                  (when (zerop indx) 
-		  (setf rslt (1dgnr dmns-1 (pop hat))))
-		  (do ((i (if (zerop indx)
-			      dmns-1
-			      dmns)
-			  (1- i)))
-		      ((endp hat) rslt)
-		     (declare
-		        (type absm rslt)
-			(fixnum i))
-		     (setf rslt
-			   (a-grml4
-			    grml-sintr dmns
-			    rslt
-			    (1dgnr (1- i)
-				   (a-grml4
-				    grml-sintr dmns-1
-				    (a-grin4
-				     grin-sintr dmns-1
-				     (a-face4
-				      face
-				      i dmns rslt))
-				    (pop hat)))))))
-		rslt))))
-     (the kfll #'rslt)))
-
-(DEFUN SMGR-KFLL (smgr)
-  (declare (type simplicial-group smgr))
-  (with-slots (face grml grin) smgr
-     (declare
-        (type face face)
-	(type simplicial-mrph grml grin))
-     (smgr-kfll-intr face (sintr grml) (sintr grin))))
-
-#|
-  (cat-init)
-  (setf k (k-z-1))
-  (setf rslt '(1 10 100))
-  (setf hat (mapcar #'(lambda (i) (face k i 3 rslt)) (<a-b> 0 3)))
-  (dotimes (i 4)
-    (check-kan k i 3 (remove (nth i hat) hat :test #'equal)))
-|#
-
-(DEFUN SMGR-APRD (smgr)
-  (declare (type simplicial-group smgr))
-  (the morphism
-    (let ((eml (eml smgr smgr))
-	  (grml (grml smgr)))
-      (declare
-        (type morphism eml)
-	(type simplicial-mrph grml))
-      (cmps grml eml))))
-
-       
\ No newline at end of file
diff --git a/archive/Kenzo-2/Kenzo-2-Acl8/simplicial-mrphs.cl b/archive/Kenzo-2/Kenzo-2-Acl8/simplicial-mrphs.cl
deleted file mode 100644
index 04f2eb7..0000000
--- a/archive/Kenzo-2/Kenzo-2-Acl8/simplicial-mrphs.cl
+++ /dev/null
@@ -1,143 +0,0 @@
-;;;  SIMPLICIAL-MRPHS  SIMPLICIAL-MRPHS  SIMPLICIAL-MRPHS
-;;;  SIMPLICIAL-MRPHS  SIMPLICIAL-MRPHS  SIMPLICIAL-MRPHS
-;;;  SIMPLICIAL-MRPHS  SIMPLICIAL-MRPHS  SIMPLICIAL-MRPHS
-
-(IN-PACKAGE "CAT")
-
-(PROVIDE "simplicial-mrphs")
-
-(DEFMETHOD ?3 ((smmr simplicial-mrph) dmns absm-or-gmsm)
-  (declare
-     (fixnum dmns)
-     (type (or absm gmsm) absm-or-gmsm))
-  (typecase absm-or-gmsm
-     (absm
-      (with-absm (dgop gmsm) absm-or-gmsm
-         (let ((gmsm-smmr (funcall (sintr smmr)
-			     (- dmns (logcount dgop)) gmsm)))
-	   (declare (type absm gmsm-smmr))
-	   (ndgnr dgop gmsm-smmr))))
-     (otherwise
-      (funcall (sintr smmr) dmns absm-or-gmsm))))  
-
-(DEFMETHOD PRINT-OBJECT ((smmr simplicial-mrph) stream)
-  (the simplicial-mrph
-     (progn
-       (if (= -1 (degr smmr))
-	   (format stream "[K~D Fibration K~D -> K~D]"
-		   (idnm smmr) (idnm (sorc smmr)) (idnm (trgt smmr)))
-	 (format stream "[K~D Simplicial-Morphism K~D -> K~D]"
-		 (idnm smmr) (idnm (sorc smmr)) (idnm (trgt smmr))))
-       smmr)))
-
-(DEFUN SINTR-INTR (sintr)
-   (declare (type sintr sintr))
-   (flet ((rslt (dmns gmsm)
-	     (declare
-	        (fixnum dmns)
-		(type gmsm gmsm))
-	     (when (minusp dmns)
-		(return-from rslt (zero-cmbn dmns)))
-	     (let ((rslt (funcall sintr dmns gmsm)))
-	        (declare (type absm rslt))
-		(if (degenerate-p rslt)
-		   (zero-cmbn dmns)
-		   (term-cmbn dmns 1 (gmsm rslt))))))
-       (the intr #'rslt)))
-
-(DEFUN SIMPLICIAL-MRPH (&rest rest &key dfnt &allow-other-keys)
-  (declare (type list dfnt))
-  (already simplicial-mrph dfnt)
-  (the simplicial-mrph
-    (apply #'make-instance 'simplicial-mrph rest)))
-
-(DEFMETHOD SHARED-INITIALIZE ((smmr simplicial-mrph) slot-names &key sintr)
-  (declare
-   (type (or (eql t) list) slot-names)
-   (type sintr sintr))
-  (call-next-method)
-  (when-slot sintr
-             (when sintr (setf (slot-value smmr 'sintr) sintr)))
-  smmr)
-
-(DEFMETHOD SLOT-UNBOUND (class (smmr simplicial-mrph) slot-name)
-  (declare
-   (ignore class)
-   (type symbol slot-name))
-  (let ((name (symbol-name slot-name)))
-    (declare (type string name))
-    (unless (member name '("INTR" "STRT") :test #'string=)
-      (call-next-method))
-    (the (or intr strt)
-      (with-slots ((ssintr intr) strt sintr) smmr
-        (declare
-         (type intr ssintr)
-         (type strt strt)
-         (type sintr sintr))
-        (setf
-         ssintr (sintr-intr sintr)
-         strt :gnrt)
-        (if (string= name "INTR") ssintr strt)))))
-        
-#|
-  (setf d (delta 3))
-  (setf m (simplicial-mrph
-            :sorc d :trgt d :degr 0
-            :sintr #'(lambda (dmns gmsm)
-                        (absm 0 gmsm))
-            :dfnt '(identity delta-3)))
-  (setf m2 (simplicial-mrph
-            :sorc d :trgt d :degr 0
-            :sintr #'(lambda (dmns gmsm)
-                       (absm (mask dmns) 1))
-            :dfnt '(null delta-3)))
-  (? m2 2 7)
-;;  (s? m2 2 7)
-|#
-
-(DEFMACRO WITH-IABSM ((dgop gmsm) iabsm . body)
-  `(let ((,dgop (car ,iabsm))
-	 (,gmsm (cdr ,iabsm)))
-     (declare
-        (fixnum ,dgop)
-	(type gmsm ,gmsm))
-     ,@body))
-
-#|
-  (macroexpand-1 '(with-iabsm (dgop gmsm) iabsm
-                    (statement-1)
-                    (statement-2)))
-|#
-                 
-(DEFMACRO A-SINTR3 (sintr dmns absm)
-  ;; BE CAREFUL: works only if  degr (sintr) = 0.
-  ;; if degr = -1 (fibration), use tw-a-sintr3
-  `(ia-sintr3 ,sintr ,dmns (cdr ,absm)))
-
-(DEFUN IA-SINTR3 (sintr dmns iabsm)
-  (declare
-     (type sintr sintr)
-     (fixnum dmns)
-     (type iabsm iabsm))
-  (the absm
-     (with-iabsm (dgop gmsm) iabsm
-	(ndgnr dgop (funcall sintr (- dmns (logcount dgop)) gmsm)))))
-
-(DEFMACRO TW-A-SINTR3 (sintr dmns absm bsgn)
-  `(tw-ia-sintr3 ,sintr ,dmns (cdr ,absm) ,bsgn))
-
-(DEFUN TW-IA-SINTR3 (sintr dmns iabsm bsgn)
-  (declare
-     (type sintr sintr)
-     (fixnum dmns)
-     (type iabsm iabsm)
-     (type gmsm bsgn))
-  (the absm
-     (with-iabsm (dgop gmsm) iabsm
-	(let ((dmns-1 (1- dmns)))
-	  (declare (fixnum dmns-1))
-	  (if (logbitp dmns-1 dgop)
-	     (absm (mask dmns-1) bsgn)
-	     (ndgnr dgop (funcall sintr
-			    (- dmns (logcount dgop))
-			    gmsm)))))))
\ No newline at end of file
diff --git a/archive/Kenzo-2/Kenzo-2-Acl8/simplicial-sets.cl b/archive/Kenzo-2/Kenzo-2-Acl8/simplicial-sets.cl
deleted file mode 100644
index fe96a65..0000000
--- a/archive/Kenzo-2/Kenzo-2-Acl8/simplicial-sets.cl
+++ /dev/null
@@ -1,679 +0,0 @@
-;;;  SIMPLICIAL-SETS  SIMPLICIAL-SETS  SIMPLICIAL-SETS
-;;;  SIMPLICIAL-SETS  SIMPLICIAL-SETS  SIMPLICIAL-SETS
-;;;  SIMPLICIAL-SETS  SIMPLICIAL-SETS  SIMPLICIAL-SETS
-
-(IN-PACKAGE "CAT")
-
-(PROVIDE "simplicial-sets")
-
-(DEFUN DGOP-EXT-INT (ext-dgop)
-   (declare (list ext-dgop))
-          ;; (list fixnum)
-   (when ext-dgop   
-      (unless (apply #'> ext-dgop)
-         (error "In DGOP-EXT-INT, the external dgop ~A is not decreasing." ext-dgop)))
-   (the fixnum
-      (apply #'logxor (mapcar
-                         #'(lambda (item)
-                              (declare (fixnum item))
-                              (the fixnum (2-exp item)))
-                         ext-dgop))))
-#|
-  (dgop-ext-int '())
-  (dgop-ext-int '(2 2))
-  (dgop-ext-int '(4 0))
-|#
-
-(DEFUN DGOP-INT-EXT (dgop)
-   (declare (fixnum dgop))
-   (unless (typep dgop 'dgop)
-      (error "In DXOP-INT-EXT, ~A is not a dxop." dgop))
-   (the list
-      (do ((dgop dgop (ash dgop -1))
-           (rslt +empty-list+)
-           (bmark 0 (1+ bmark)))
-          ((zerop dgop) rslt)
-         (declare
-            (fixnum dgop bmark)
-            (list rslt))
-         (when (oddp dgop)
-            (push bmark rslt)))))
-
-#|
-  (dgop-int-ext 0)
-  (dgop-int-ext 4)
-  (dgop-int-ext 63)
-  (dotimes (i 33)
-     (print (dgop-ext-int (dgop-int-ext i)))))
-|#
-
-(DEFUN HYPHENIZE-LIST (list)
-   (declare (list list))
-   (if list
-      (format nil "~D~{-~D~}" (first list) (rest list))
-      (format nil "-")))
-
-#|
-  (hyphenize-list '())
-  (hyphenize-list '(3))
-  (hyphenize-list '(5 3 1)))
-|#
-
-
-#|
-  (absm-p 1)
-  (absm-p '(1))
-  (absm-p '(:absm nil))  ;; printer-error
-  (absm-p '(:absm 5 . a))
-  (absm-p '(:absm -5 . a)) ;; printer-error
-|#
-      
-(DEFMETHOD PRINT-KEYCONS ((key (eql :absm)) cdr stream)
-   (setf cdr (cons :absm cdr))
-   (format stream
-      "<AbSm ~A ~A>"
-      (hyphenize-list (dgop-int-ext (dgop cdr)))
-      (gmsm cdr))
-   cdr)
-
-#|
-  (absm 5 'a)
-|#
-
-#|
-  (degenerate-p (absm 0 'a))
-  (degenerate-p (absm 4 'a))
-  (non-degenerate-p (absm 0 'a))
-  (non-degenerate-p (absm 4 'a)))
-|#
-
-(DEFUN FACE4 (smst indx dmns gmsm-or-absm)
-   (if (typep gmsm-or-absm 'absm)
-      (a-face4 (face1 smst) indx dmns gmsm-or-absm)
-      (funcall (face1 smst) indx dmns gmsm-or-absm)))
-
-(DEFMETHOD PRINT-OBJECT ((smst simplicial-set) stream)
-   (the simplicial-set
-      (progn
-         (format stream "[K~D Simplicial-Set]" (idnm smst))
-         smst)))
-
-(DEFUN SIMPLICIAL-SET (&rest rest &key dfnt &allow-other-keys)
-  (declare (type list dfnt))
-  (already simplicial-set dfnt)
-  (the simplicial-set
-    (apply #'make-instance 'simplicial-set rest)))
-
-(DEFMETHOD SHARED-INITIALIZE
-    ((smst simplicial-set) slot-names &key face face*)
-  (declare
-   (type (or (eql t) list) slot-names)
-   (type face face)
-   (type (or face* null) face*))
-  (call-next-method)
-  (when-slot face
-             (when face (setf (slot-value smst 'face) face))
-             (when face*
-               (if (slot-boundp smst 'dffr)
-                   (error "IN SIMPLICIAL-SET, an FACE* initial-argument is given, ~
-                         but the DFFR slot is elsewhere defined.")
-                 (setf (slot-value smst 'dffr)
-                   (morphism :dfnt `(dffr ,smst)
-                             :sorc smst :trgt smst :degr -1
-                             :intr (face*-dffr (cmpr smst) face*) :strt :gnrt))))))
-
-(DEFMETHOD SLOT-UNBOUND (class (smst simplicial-set) (slot (eql 'dffr)))
-  (declare (ignore class))
-  (the morphism
-    (setf (slot-value smst 'dffr)
-      (morphism :dfnt `(dffr ,smst)
-                :sorc smst :trgt smst :degr -1
-                :intr (face-dffr-intr (cmpr smst) (face smst))
-                :strt :gnrt))))
-
-(DEFMETHOD SLOT-UNBOUND (class (smst simplicial-set) (slot (eql 'cprd)))
-  (declare (ignore class))
-  (the morphism
-    (setf (slot-value smst 'cprd)
-      (morphism :dfnt `(cprd ,smst)
-                :sorc smst :trgt (tnsr-prdc smst smst) :degr 0
-                :intr (face-cprd-intr (face smst)) :strt :gnrt))))
-
-(DEFUN A-BASIS2 (basis dmns)
-  (declare
-     (type basis basis)
-     (fixnum dmns))
-  (the list
-    (let ((basis-array (make-array (1+ dmns) :element-type 'list)))
-      (declare (type (vector list) basis-array))
-      (dotimes (i (1+ dmns))
-	(declare (fixnum i))
-	(setf (aref basis-array i) (funcall basis i)))
-      (do ((dgop (mask dmns) (1- dgop))
-	   (rslt +empty-list+
-		 (nconc (mapcar
-			 #'(lambda (gmsm)
-			     (declare (type gmsm gmsm))
-			     (absm dgop gmsm))
-			 (aref basis-array (- dmns (logcount dgop))))
-			rslt)))
-	  ((minusp dgop) rslt)))))
-
-#|
-  (setf m (moore 2 2))
-  (dotimes (i 4)
-    (print (basis m i :dgnr)))
-|#
-
-(DEFUN FACE-CPRD-INTR (face)
-   (declare (type face face))
-   (flet ((rslt (dmns gmsm)
-             (declare
-                (fixnum dmns)
-                (type gmsm gmsm))
-             (the cmbn
-                (let ((del-0-s +empty-list+)
-                      (rslt +empty-list+))
-                   (declare (list del-0-s rslt))
-                   (do ((dmns dmns (1- dmns))
-                        (iabsm (cons 0 gmsm) (cdr (ia-face4 face 0 dmns iabsm))))
-                       ((zerop dmns) (push iabsm del-0-s))
-                      (declare
-                         (fixnum dmns)
-                         (cons iabsm))
-                      (push iabsm del-0-s))
-                   (do ((ldmns dmns (1- ldmns))
-                        (rdmns 0 (1+ rdmns))
-                        (iabsm (cons 0 gmsm) (cdr (ia-face4 face ldmns ldmns iabsm)))
-                        (mark-del-0 del-0-s (cdr mark-del-0)))
-                       ((zerop ldmns) (push (term 1 (tnpr 0 (cdr iabsm) dmns gmsm))
-                                        rslt))
-                      (declare
-                         (fixnum ldmns rdmns)
-                         (type gmsm gmsm)
-                         (list mark-del-0))
-                      (unless (or (plusp (car iabsm))
-                                  (plusp (caar mark-del-0)))
-                         (push (term 1 (tnpr ldmns (cdr iabsm) rdmns (cdar mark-del-0)))
-                            rslt)))
-                   (make-cmbn :degr dmns :list rslt)))))
-      (the intr #'rslt)))
-
-#|
-  (setf cmpr #'f-cmpr
-        face #'delta-face)
-  (setf diag (face-cprd-intr face))
-  (funcall diag 4 (mask 5))
-  (funcall diag 0 4)
-  (setf cmpr #'s-cmpr
-        face (sphere-face 4))
-  (setf diag (face-cprd-intr face))
-  (funcall diag 4 's4)
-  (funcall diag 0 '*)
-  (setf s4 (sphere 4))
-  (cprd s4 4 's4)
-|#                 
-
-(DEFUN FACE-DFFR-INTR (cmpr face)
-   (declare
-      (type cmprf cmpr)
-      (type face face))
-   (flet ((rslt (dmns gmsm)
-             (declare
-                (fixnum dmns)
-                (type gmsm gmsm))
-             (the cmbn
-                (progn
-                   (when (zerop dmns)
-                      (return-from rslt +zero-negative-cmbn+))
-                   (let ((pre-rslt +empty-list+))
-                      (declare (list pre-rslt))
-                             ;; (list (cons cffc face))
-                      (dotimes (indx (1+ dmns))
-                         (declare (fixnum indx))
-                         (let ((face (funcall face indx dmns gmsm)))
-                            (declare (type absm face))
-                            (unless (degenerate-p face)
-                               (push (term (-1-expt-n indx) (gmsm face))
-                                  pre-rslt))))
-                      (apply #'nterm-add cmpr (1- dmns) pre-rslt))))))
-      (the intr #'rslt)))
-
-#|
-  (setf face #'(lambda (indx dmns gmsm)
-                  (absm 0 (append
-                             (subseq gmsm 0 indx)
-                             (subseq gmsm (1+ indx))))))
-  (setf dffr (face-dffr-intr #'l-cmpr face))
-  (funcall dffr 0 '(a))
-  (funcall dffr 1 '(a b))
-  (funcall dffr 2 '(a b c))
-  (funcall dffr 3 '(a b c d))
-  (funcall dffr 3 '(d c b a))
-  (funcall dffr 1 '(a a))
-  (funcall dffr 2 '(a a a))
-  (funcall dffr 3 '(a a a a))
-  (setf face #'(lambda (index dmns gmsm)
-                  (absm (dgop-ext-int (nreverse (<a-b< 0 (1- dmns)))) 'a)))
-  (setf dffr (face-dffr-intr #'s-cmpr face))
-  (funcall dffr 1 '(a b))
-  (funcall dffr 2 '(a b c)))
-|#
-
-(DEFUN FACE*-DFFR (cmpr face*)
-  (declare
-   (type cmprf cmpr)
-   (type face* face*))
-  (flet ((rslt (dmns gmsm)
-               (declare
-                (fixnum dmns)
-                (type gmsm gmsm))
-               (the cmbn
-                 (progn
-                   (when (zerop dmns)
-                     (return-from rslt +zero-negative-cmbn+))
-                   (let ((pre-rslt +empty-list+))
-                     (declare (list pre-rslt))
-                     ;; (list (list gmsm fixnum))
-                     (dotimes (indx (1+ dmns))
-                       (declare (fixnum indx))
-                       (let ((face (funcall face* indx dmns gmsm)))
-                         (declare (type (or gmsm (eql :degenerate)) face))
-                         (unless (eq face :degenerate)
-                           (push (term (-1-expt-n indx) face) pre-rslt))))
-                     (apply #'nterm-add cmpr (1- dmns) pre-rslt))))))
-    (the intr #'rslt)))
-
-#|
-  (setf face* 
-        #'(lambda (indx dmns gmsm)
-             (if (and (= dmns 3) (evenp indx))
-                'm2
-                :degenerate)))
-  (setf dffr (face*-dffr #'s-cmpr face*))
-  (funcall dffr 3 'm3)
-  (funcall dffr 2 'm2)
-  (funcall dffr 0 '*)
-  (setf face* 
-        #'(lambda (indx dmns gmsm)
-             (if (and (= dmns 3) (< indx 2))
-                'm2
-                :degenerate)))
-  (setf dffr (face*-dffr #'s-cmpr face*))
-  (funcall dffr 3 'm3)
-  (funcall dffr 2 'm2)
-  (funcall dffr 0 '*))
-|#
-
-(DEFUN A-CMPR3 (cmpr absm1 absm2)
-   (declare
-      (type cmprf cmpr)
-      (type absm absm1 absm2))
-   (the cmpr
-      (with-absm (dgop1 gmsm1) absm1
-      (with-absm (dgop2 gmsm2) absm2
-         (lexico
-            (f-cmpr dgop1 dgop2)
-            (funcall cmpr gmsm1 gmsm2))))))
-
-#|
-  (a-cmpr3 #'s-cmpr (absm 0 'a) (absm 1 'b))
-  (a-cmpr3 #'s-cmpr (absm 2 'a) (absm 1 'b))
-  (a-cmpr3 #'s-cmpr (absm 1 'a) (absm 1 'b))
-  (a-cmpr3 #'s-cmpr (absm 1 'c) (absm 1 'b))
-  (a-cmpr3 #'s-cmpr (absm 1 'a) (absm 1 'a))
-|#
-
-(DEFUN BSGN-P (cmpr bsgn dmns absm)
-   ;; this function makes sense only in the simplicial context
-   ;; so that the basg (= base-generator) is called bsgn (= base-point)
-   (declare
-      (type gmsm bsgn)
-      (fixnum dmns)
-      (type absm absm))
-   (the boolean
-      (with-absm (dgop gmsm) absm
-         (and (= dgop (mask dmns))
-              (eq :equal (funcall cmpr bsgn gmsm))))))
-
-#|
-  (setf d (delta-infinity))
-  (setf cmpr (cmpr d))
-  (bsgn-p cmpr 1 5 (absm (mask 5) 1))
-  (bsgn-p cmpr 1 5 (absm (mask 5) 2))
-  (bsgn-p cmpr 1 5 (absm (mask 4) 3))
-|#
-
-(DEFUN DLOP-EXT-INT (ext-dlop)
-   (declare (list ext-dlop))
-          ;; (list fixnum)
-   (when ext-dlop   
-      (unless (apply #'< ext-dlop)
-         (error "In DLOP-EXT-INT, the external dlop ~A is not increasing." ext-dlop)))
-   (the fixnum
-      (apply #'logxor
-         (mapcar #'(lambda (item)
-                      (declare (fixnum item))
-                      (the fixnum (2-exp item)))
-            ext-dlop))))
-#|
-  (dlop-ext-int '())
-  (dlop-ext-int '(2 2))
-  (dlop-ext-int '(0 4)))
-|#
-
-(DEFUN DLOP-INT-EXT (dlop)
-   (declare (fixnum dlop))
-   (the list
-      (nreverse (dgop-int-ext dlop))))
-
-#|
-  (dlop-int-ext 0)
-  (dlop-int-ext 4)
-  (dlop-int-ext 63)
-  (dotimes (i 33)
-     (print (dlop-ext-int (dlop-int-ext i)))))
-|#
-
-(DEFUN 1DGOP*DGOP (1dgop dgop)
-   (declare (fixnum 1dgop dgop))
-   ;; 1dgop is an ordinary integer
-   ;; dgop is a bit string
-   (the fixnum
-      (let ((share (ash -1 1dgop)))
-         (declare (fixnum share))
-         (logxor
-            (ash (logand share dgop) 1)
-            (2-exp 1dgop)
-            (logandc1 share dgop)))))
-      
-#|
-  (dotimes (i 20)
-     (dotimes (j 5)
-       (format t "~% (~D) o ~A = ~A"
-                 j (dgop-int-ext i) (dgop-int-ext (1dgop*dgop j i))))))
-|#
-
-(DEFUN DGOP*DGOP (dgop1 dgop2)
-   (declare (type fixnum dgop1 dgop2))
-   (let ((dgop 0)
-         (bmark 0))
-      (declare (fixnum dgop bmark))
-      (loop
-         (when (zerop dgop1)
-            (return-from dgop*dgop
-               (logxor dgop (ash dgop2 bmark))))
-         (when (zerop dgop2)
-            (return-from dgop*dgop
-               (logxor dgop (ash dgop1 bmark))))
-         (cond ((evenp dgop1)
-                (when (oddp dgop2)
-                   (incf dgop (2-exp bmark)))
-                (setf dgop2 (ash dgop2 -1)))
-               (t
-                  (incf dgop (2-exp bmark))))
-         (setf dgop1 (ash dgop1 -1))
-         (incf bmark))))
-
-#|
-  (dotimes (i 10)
-     (dotimes (j 10)
-        (format t "~%~A o ~A = ~A"
-                  (dgop-int-ext i) (dgop-int-ext j)
-                  (dgop-int-ext (dgop*dgop i j))))))
-|#
-
-(DEFUN REMOVE-BIT (n indx)
-   (declare (fixnum n indx))
-   (the fixnum
-      (let ((cut (2-exp indx)))
-         (multiple-value-bind (quotient remainder) (truncate n cut)
-            (declare (fixnum quotient remainder))
-            (+ (ash (ash quotient -1) indx) remainder)))))
-
-#|
-  (remove-bit 107 3)  ;; 51
-|#
-
-(DEFUN DGOP/DGOP (dgop1 dgop2)
-   (declare (fixnum dgop1 dgop2))
-   (the fixnum
-      (do ((indx (1- (integer-length dgop2)) (1- indx)))
-          ((minusp indx) dgop1)
-         (declare (fixnum indx))
-         (when (logbitp indx dgop2)
-            (setf dgop1 (remove-bit dgop1 indx))))))
-
-#|
-  (dgop/dgop 67 0)
-  (dgop/dgop 68 4)
-  (dgop/dgop 31 5)
-|#      
-
-(DEFUN 1DLOP-DGOP (1dlop dgop)
-   (declare (fixnum 1dlop dgop))
-   ;; 1dlop is an ordinary fixnum
-   ;; dgop is a bit string
-   (the (values fixnum (or fixnum null))
-      (progn
-         (when (logbitp 1dlop dgop)
-            (let ((share (ash -1 1dlop)))
-               (declare (fixnum share))
-               (return-from 1dlop-dgop
-                  (values
-                     (logxor
-                        (logand share (ash dgop -1))
-                        (logandc1 share dgop))
-                     nil))))
-         (when (and (plusp 1dlop)
-                    (logbitp (1- 1dlop) dgop))
-            (let ((share (ash -1 1dlop)))   ;;;
-               (declare (fixnum share))
-	       (setf share (ash share -1))  ;;; because of the compiler bug
-               (return-from 1dlop-dgop
-                  (values
-                     (logxor
-                        (logand share (ash dgop -1))
-                        (logandc1 share dgop))
-                     nil))))
-         (let ((share (ash -1 1dlop)))
-            (declare (fixnum share))
-            (let ((right (logandc1 share dgop)))
-               (declare (fixnum right))
-               (values
-                  (logxor right (logand share (ash dgop -1)))
-                  (- 1dlop (logcount right))))))))
-
-#|
-  (dotimes (i 5)
-     (dotimes (j 17)
-        (multiple-value-bind (dgop 1dlop) (1dlop-dgop i j)
-           (format t "~% del-~D o ~A = ~A o del-~A"
-                     i (dgop-int-ext j) (dgop-int-ext dgop) 1dlop)))))
-|#
-
-(DEFUN IA-FACE4 (face indx dmns iabsm) 
-   ;; iabsm = "internal" absm, that is an absm without the keyword :absm.
-   ;; absm = (cons :absm (cons dgop gmsm))
-   ;; iabsm =            (cons dgop gmsm)
-   (declare
-      (type face face)
-      (fixnum indx dmns)
-      (type absm absm))
-   (the absm
-      (let ((dgop (car iabsm))
-            (gmsm (cdr iabsm)))
-         (declare
-            (fixnum dgop)
-            (type gmsm gmsm))
-         (multiple-value-bind (dgop2 1dlop) (1dlop-dgop indx dgop)
-            (declare
-               (fixnum dgop2)
-               (type (or fixnum nil) 1dlop))
-            (unless 1dlop
-               (return-from ia-face4 (absm dgop2 gmsm)))
-            (locally (declare (fixnum 1dlop))
-               (let ((gmsm-face (funcall face 1dlop (- dmns (logcount dgop)) gmsm)))
-                  (declare (type absm gmsm-face))
-                  (with-absm (dgop3 gmsm3) gmsm-face
-                     (absm (dgop*dgop dgop2 dgop3) gmsm3))))))))
-
-#|
-  (require "special-smsts"
-            #-ACLPC "special-smsts"
-            #+ACLPC "special-smsts.fsl")
-  (let ((simp (dlop-ext-int '(0 1 2 3 4 5 6))))
-     (dotimes (i 5)
-        (dotimes (j 17)
-           (let ((face (a-face4 (face (delta-infinity))
-                          i (+ 6 (logcount j)) (absm j simp))))
-              (format t "~%del-~D o ~A (0 1 2 3 4 5 6) = ~A ~A"
-                        i (dgop-int-ext j)
-                        (dgop-int-ext (dgop face))
-                        (dlop-int-ext (gmsm face)))))))
-|#
-
-(DEFUN 1DGNR (indx absm)
-   (declare
-      (fixnum indx)
-      (type absm absm))
-   (the absm
-      (with-absm (dgop gmsm) absm
-         (absm (1dgop*dgop indx dgop) gmsm))))
-
-#|
-  (1dgnr 2 (absm 17 'a))
-|#
-
-(DEFUN NDGNR (dgop absm)
-   (declare
-      (fixnum dgop)
-      (type absm absm))
-   (the absm
-      (with-absm (dgop2 gmsm) absm
-         (absm (dgop*dgop dgop dgop2) gmsm))))
-
-#|
-  (ndgnr 2 (absm 17 'a))
-|#
-
-(DEFMACRO NVERTICES (face dlop-bar dmns gmsm)
-  `(nface ,face (- (mask (1+ ,dmns)) ,dlop-bar) ,dmns ,gmsm))
-
-#|
-  (setf f (face (delta-infinity)))
-  (dotimes (dlop 31)
-    (print (dlop-int-ext (gmsm (nvertices f (1+ dlop) 4 31)))))
-  (setf p (r-proj-space))
-  (setf f (face p))
-  (dotimes (dlop 31)
-    (format t "~%~A ~A"
-       (hyphenize-list (dlop-int-ext (1+ dlop)))
-       (nvertices f (1+ dlop) 4 4)))
-|#
-
-(DEFUN NFACE (face dlop dmns gmsm)
-  (declare
-     (type face face)
-     (type dlop dlop)
-     (fixnum dmns)
-     (type gmsm gmsm))
-  (do* ((gmsm gmsm)
-	(dmns dmns)
-	(dgop 0)
-	(dlop dlop (- dlop (2-exp bark)))
-	(bark (1- (integer-length dlop))
-	      (1- (integer-length dlop))))
-       ((zerop dlop) (absm dgop gmsm))
-      (declare
-         (type gmsm gmsm)
-	 (fixnum dgop dlop bark))
-      (multiple-value-bind (dgop2 indx) (1dlop-dgop bark dgop)
-	 (declare
-	    (fixnum dgop2)
-	    (type (or null fixnum) indx))
-	 (if indx
-	    (locally (declare (fixnum indx))
-	       (let ((new-absm (funcall face indx dmns gmsm)))
-		  (declare (type absm new-absm))
-		  (with-absm (dgop3 gmsm2) new-absm
-		     (setf gmsm gmsm2
-			   dmns (- dmns 1
-				   (logcount dgop3))
-			   dgop (dgop*dgop dgop2 dgop3)))))
-  	     (setf dgop dgop2)))))
-
-#|
-  (setf f (face (delta-infinity)))
-  (dotimes (dlop 31)
-    (print (dlop-int-ext (gmsm (nface f dlop 4 31)))))
-  (setf p (r-proj-space))
-  (setf f (face p))
-  (dotimes (dlop 31)
-    (format t "~%~A ~A"
-       (hyphenize-list (dlop-int-ext dlop))
-       (nface f dlop 4 4)))
-|#
-
-(DEFUN CHECK-FACES (cmpr face dmns gmsm)
-   (declare
-      (type cmprf cmpr)
-      (type face face)
-      (fixnum dmns)
-      (type gmsm gmsm))
-   (the boolean
-      (progn      
-         (when (> dmns 1)
-            (let ((dmns-1 (1- dmns)))
-               (declare (fixnum dmns-1))
-               (dotimes (i dmns)
-                  (declare (fixnum i))
-                  (dotimes (j (1+ i))
-                     (declare (fixnum j))
-                     (let ((rslt1 (a-face4 face i dmns-1 (funcall face j dmns gmsm)))
-                           (rslt2 (a-face4 face j dmns-1 (funcall face (1+ i) dmns gmsm))))
-                        (declare (type absm rslt1 rslt2))
-                        (unless (eq (a-cmpr3 cmpr rslt1 rslt2) :equal)
-                           (cerror "CHECK-FACES will return NIL."
-                              "Noncoherent boundary operators detected by CHECK-FACES :~@
-                               Simplex => ~A~@
-                               del_~D o del_~D => ~A~@
-                               del_~D o del_~D => ~A"
-                              gmsm i j rslt1 j (1+ i) rslt2)
-                              (return-from check-faces nil)))))))
-         t)))
-
-#|
-  (setf d (delta-infinity))
-  (check-faces #'f-cmpr (face d) 4 31)
-|#
-
-(DEFUN CHECK-SMST (smst dmns1 &optional (dmns2 (1+ dmns1)))
-   (declare
-      (type simplicial-set smst)
-      (fixnum dmns1 dmns2))
-   (with-slots (cmpr basis face) smst
-      (declare
-         (type cmprf cmpr)
-         (type face face))
-   (when (eq basis :locally-effective)
-      (error "In CHECK-SMST, the locally-effective simplicial-set ~A~@
-              cannot be checked." smst))
-      (do ((rslt t)
-           (dmns dmns1 (1+ dmns)))
-          ((>= dmns dmns2) rslt)
-         (declare
-            (type boolean rslt)
-            (fixnum dmns))
-         (format t "~%Checking the ~D-simplices..." dmns)
-         (dolist (gmsm (funcall basis dmns))
-            (declare (type gmsm gmsm))
-            (unless (check-faces cmpr face dmns gmsm)
-               (setf rslt nil))))))
-
-#|
-  (check-smst (delta-infinity) 5)
-  (check-smst (delta 3) 2)
-  (check-smst (delta 3) 2 4)
-|#
-
diff --git a/archive/Kenzo-2/Kenzo-2-Acl8/smith.cl b/archive/Kenzo-2/Kenzo-2-Acl8/smith.cl
deleted file mode 100644
index 4b5c6b0..0000000
--- a/archive/Kenzo-2/Kenzo-2-Acl8/smith.cl
+++ /dev/null
@@ -1,1239 +0,0 @@
-;;;  SMITH  SMITH  SMITH  SMITH  SMITH  SMITH  SMITH  SMITH
-;;;  SMITH  SMITH  SMITH  SMITH  SMITH  SMITH  SMITH  SMITH
-;;;  SMITH  SMITH  SMITH  SMITH  SMITH  SMITH  SMITH  SMITH
-
-(IN-PACKAGE "CAT")
-
-(PROVIDE "smith")
-
-(DEFTYPE MATRIX () '(array fixnum (* *)))
-
-(DEFMACRO LINE-NUMBER (mtrx)
-  `(first (array-dimensions ,mtrx)))
-
-(DEFMACRO COLUMN-NUMBER (mtrx)
-  `(second (array-dimensions ,mtrx)))
-
-(DEFUN RANDOM-MATRIX (line-n column-n max)
-  (declare (fixnum line-n column-n max))
-  (the matrix
-    (let ((rslt (make-array (list line-n column-n)
-			    :element-type 'fixnum))
-	  (2max+1 (+ max max 1)))
-      (declare
-        (type matrix rslt)
-	(fixnum 2max+1))
-      (dotimes (i line-n)
-	(declare (fixnum i))
-	(dotimes (j column-n)
-	  (declare (fixnum j))
-	  (setf (aref rslt i j)
-		(- (random 2max+1) max))))
-      rslt)))
-
-#|
-  (random-matrix 2 3 10)
-|#
-
-(DEFUN IDNT-MTRX (n)
-  (declare (fixnum n))
-  (the matrix
-    (let ((rslt
-            #-ACLPC (make-array (list n n)
-		        :element-type 'fixnum
-		        :initial-element 0)
-            #+ACLPC (if (zerop n)
-                       (make-array '(0 0)
-                          :element-type 'fixnum)
-                       (make-array (list n n)
-		          :element-type 'fixnum
-		          :initial-element 0))))
-      (declare (type matrix rslt))
-      (dotimes (i n)
-	(declare (fixnum i))
-	(setf (aref rslt i i) 1))
-      rslt)))
-
-#|
-(idnt-mtrx 3)
-|#
-
-(DEFUN COPY-MTRX (mtrx)
-  (declare (type matrix mtrx))
-  (the matrix
-    (let ((line-n (line-number mtrx))
-	  (column-n (column-number mtrx)))
-      (declare (fixnum line-n column-n))
-      (let ((rslt (make-array (list line-n column-n)
-			      :element-type 'fixnum)))
-	(declare (type matrix rslt))
-	(dotimes (il line-n)
-	  (declare (fixnum il))
-	(dotimes (ic column-n)
-	  (declare (fixnum ic))
-	  (setf (aref rslt il ic) (aref mtrx il ic))))
-	rslt))))
-
-#|
-(setf m (random-matrix 3 4 10))
-(equalp m (copy-mtrx m))
-|#
-
-(DEFUN LEFT-SUBMATRIX (mtrx k)
-  (declare (type matrix mtrx))
-  (the matrix
-    (let ((line-n (line-number mtrx))
-	  (column-n (column-number mtrx)))
-      (declare (fixnum line-n column-n))
-      (assert (<= k column-n))
-      (let ((rslt (make-array (list line-n k)
-			      :element-type 'fixnum)))
-	(declare (type matrix rslt))
-	(dotimes (il line-n)
-	  (declare (fixnum il))
-	(dotimes (ic k)
-	  (declare (fixnum ic))
-	  (setf (aref rslt il ic) (aref mtrx il ic))))
-	rslt))))
-
-#|
-(setf m (random-matrix 3 4 10))
-(left-submatrix m 2)
-|#
-
-(DEFUN MTRX-PRDC (mtrx1 mtrx2)
-  (declare (type matrix mtrx1 mtrx2))
-  (the matrix
-    (let ((rslt-line-n (line-number mtrx1))
-	  (mtrx1-column-n (column-number mtrx1))
-	  (mtrx2-line-n (line-number mtrx2))
-	  (rslt-column-n (column-number mtrx2)))
-      (declare (fixnum rslt-line-n mtrx1-column-n
-		       mtrx2-line-n rslt-column-n))
-      (unless (= mtrx1-column-n mtrx2-line-n)
-	(error "In MTRX-PRDC, bad line or column number."))
-      (let ((rslt (make-array (list rslt-line-n rslt-column-n)
-			      :element-type 'fixnum)))
-	(declare (type matrix rslt))
-	(dotimes (il rslt-line-n)
-	  (declare (fixnum il))
-	(dotimes (ic rslt-column-n)
-	  (declare (fixnum ic))
-	  (do ((k 0 (1+ k))
-	       (sum 0 (+ sum
-			 (* (aref mtrx1 il k) (aref mtrx2 k ic)))))
-	      ((= k mtrx1-column-n) (setf (aref rslt il ic) sum)))))
-	rslt))))
-
-#|
-(setf m1 (random-matrix 2 3 10))
-(setf m2 (random-matrix 3 2 10))
-(mtrx-prdc m1 m2)
-(mtrx-prdc m2 m1)
-|#
-
-(DEFUN CHCM-MTRX (chcm degr)
-  (declare
-    (type chain-complex chcm)
-    (fixnum degr))
-  (the matrix
-    (let ((cmpr (cmpr1 chcm))
-	  (dffr (dffr chcm))
-	  (sbasis (basis chcm degr))
-	  (tbasis (basis chcm (1- degr))))
-      (declare
-        (type cmprf cmpr)
-	(type morphism dffr)
-	(list sbasis tbasis))
-      (let ((srank (length sbasis))
-	    (trank (length tbasis)))
-	(declare (fixnum srank trank))
-	(let ((rslt 
-               #-ACLPC
-                    (make-array (list trank srank)
-				:element-type 'fixnum
-				:initial-element 0)
-               #+ACLPC
-                    (if (or (zerop srank) (zerop trank))
-                       (make-array (list trank srank)
-                          :element-type 'fixnum)
-                       (make-array (list trank srank)
-                          :element-type 'fixnum
-                          :initial-element 0))
-               ))               
-	  (declare (type matrix rslt))
-	  (do ((j 0 (1+ j))
-	       (mark sbasis (cdr mark)))
-	      ((endp mark))
-	      (declare
-	        (fixnum j)
-		(list mark))
-	      (let ((cmbn (gnrt-? dffr degr (car mark))))
-		(declare (type cmbn cmbn))
-		(do ((mark1 (cmbn-list cmbn) (cdr mark1))
-		     (mark2 tbasis)
-		     (i 0))
-		    ((endp mark1))
-		    (declare
-		      (list mark1 mark2)
-		      (fixnum i))
-		  (with--term (cffc gnrt) mark1
-		    (loop
-		     (cond ((eq :equal (funcall cmpr gnrt (car mark2)))
-			    (setf (aref rslt i j) cffc)
-			    (incf i)
-			    (pop mark2)
-			    (return))
-			   (t (incf i)
-			      (pop mark2))))))))
-	  rslt)))))
-
-#|
-  (setf d (delta 5))
-  (chcm-mtrx d 3))
-  (setf m (moore 2 2))
-  (dotimes (i 5)
-    (print (chcm-mtrx m i)))
-  (dotimes (i 6)
-    (print (array-dimensions (chcm-mtrx m i))))
-|#
-
-(DEFUN LINE-OP (mtrx begin lambda line1 line2)
-  ;; line2 := line2 + lambda * line1
-  (declare
-    (type matrix mtrx)
-    (fixnum begin lambda line1 line2))
-  (the matrix
-  (progn
-  (do ((column-number (column-number mtrx))
-       (j begin (1+ j)))
-      ((= j column-number))
-      (declare (fixnum column-number j))
-    (incf (aref mtrx line2 j)
-	  (* lambda (aref mtrx line1 j))))
-  mtrx)))
-	
-#|
-(setf m (random-matrix 3 4 10))
-(line-op m 1 3 2 0)
-|#
-
-;; mtrx-list = (P P^-1 M Q Q^-1)
-
-(DEFMACRO LINE-OP-5 (mtrx-list begin lambda line1 line2)
-  (let ((slambda (gensym)))
-    `(let ((,slambda ,lambda))
-       (column-op (first ,mtrx-list) 0 (- ,slambda) ,line2 ,line1)
-       (line-op (second ,mtrx-list) 0 ,slambda ,line1 ,line2)
-       (line-op (third ,mtrx-list) ,begin ,slambda ,line1 ,line2))))
-     
-#|
-(setf p (idnt-mtrx 4) p-1 (idnt-mtrx 4)
-      m (random-matrix 4 5 10)
-      q (idnt-mtrx 5) q-1 (idnt-mtrx 5))
-(setf list (list p p-1 m q q-1))
-(setf t1 (mtrx-prdc p (mtrx-prdc m q-1)))
-(line-op-5 list 0 3 1 3)
-(equalp t1 (mtrx-prdc p (mtrx-prdc m q-1)))
-(mtrx-prdc p p-1)
-|#
-
-(DEFUN COLUMN-OP (mtrx begin lambda column1 column2)
-  (declare
-    (type matrix mtrx)
-    (fixnum begin lambda column1 column2))
-  (the matrix
-  (progn
-  (do ((line-number (line-number mtrx))
-       (i begin (1+ i)))
-      ((= i line-number))
-      (declare (fixnum line-number i))
-    (incf (aref mtrx i column2)
-	  (* lambda (aref mtrx i column1))))
-  mtrx)))
-	
-#|
-(setf m (random-matrix 3 4 10))
-(column-op m 1 3 2 0)
-|#
-
-(DEFMACRO COLUMN-OP-5 (mtrx-list begin lambda column1 column2)
-  (let ((slambda (gensym)))
-    `(let ((,slambda ,lambda))
-       (column-op (third ,mtrx-list) ,begin ,slambda ,column1 ,column2)
-       (column-op (fourth ,mtrx-list) 0 ,slambda ,column1 ,column2)
-       (line-op (fifth ,mtrx-list) 0 (- ,slambda) ,column2 ,column1))))
-
-#|
-(setf p (idnt-mtrx 4) p-1 (idnt-mtrx 4)
-      m (random-matrix 4 5 10)
-      q (idnt-mtrx 5) q-1 (idnt-mtrx 5))
-(setf list (list p p-1 m q q-1))
-(setf t1 (mtrx-prdc p (mtrx-prdc m q-1)))
-(column-op-5 list 0 3 1 3)
-(equalp t1 (mtrx-prdc p (mtrx-prdc m q-1)))
-(mtrx-prdc p p-1)
-(mtrx-prdc q q-1)
-|#
-
-
-(DEFUN LINE-SWAP (mtrx begin line1 line2)
-  (declare
-    (type matrix mtrx)
-    (fixnum begin line1 line2))
-  (the matrix
-  (progn
-  (do ((column-number (column-number mtrx))
-       (j begin (1+ j)))       
-      ((= j column-number))
-      (declare (fixnum column-number j))
-    (rotatef (aref mtrx line1 j) (aref mtrx line2 j)))
-  mtrx)))
-
-#|
-(setf m (random-matrix 3 4 10))
-(line-swap m 1 0 2)
-|#
-
-(DEFMACRO LINE-SWAP-5 (mtrx-list begin line1 line2)
-  `(progn
-     (column-swap (first ,mtrx-list) 0 ,line1 ,line2)
-     (line-swap (second ,mtrx-list) 0 ,line1 ,line2)
-     (line-swap (third ,mtrx-list) ,begin ,line1 ,line2)))
-
-
-#|
-(setf p (idnt-mtrx 4) p-1 (idnt-mtrx 4)
-      m (random-matrix 4 5 10)
-      q (idnt-mtrx 5) q-1 (idnt-mtrx 5))
-(setf list (list p p-1 m q q-1))
-(setf t1 (mtrx-prdc p (mtrx-prdc m q-1)))
-(line-swap-5 list 0 1 3)
-(equalp t1 (mtrx-prdc p (mtrx-prdc m q-1)))
-(mtrx-prdc p p-1)
-(mtrx-prdc q q-1)
-|#
-
-(DEFUN COLUMN-SWAP (mtrx begin column1 column2)
-  (declare
-    (type matrix mtrx)
-    (fixnum begin column1 column2))
-  (the matrix (progn
-  (do ((line-number (line-number mtrx))
-       (i begin (1+ i)))       
-      ((= i line-number))
-      (declare (fixnum line-number i))
-    (rotatef (aref mtrx i column1) (aref mtrx i column2)))
-  mtrx)))
-
-#|
-(setf m (random-matrix 3 4 10))
-(column-swap m 1 0 2)
-|#
-
-(DEFMACRO COLUMN-SWAP-5 (mtrx-list begin column1 column2)
-  `(progn
-     (column-swap (third ,mtrx-list) ,begin ,column1 ,column2)
-     (column-swap (fourth ,mtrx-list) 0 ,column1 ,column2)
-     (line-swap (fifth ,mtrx-list) 0 ,column1 ,column2)))
-
-#|
-(setf p (idnt-mtrx 4) p-1 (idnt-mtrx 4)
-      m (random-matrix 4 5 10)
-      q (idnt-mtrx 5) q-1 (idnt-mtrx 5))
-(setf list (list p p-1 m q q-1))
-(setf t1 (mtrx-prdc p (mtrx-prdc m q-1)))
-(column-swap-5 list 0 1 3)
-(equalp t1 (mtrx-prdc p (mtrx-prdc m q-1)))
-(mtrx-prdc p p-1)
-(mtrx-prdc q q-1)
-|#
-
-(DEFUN LINE-MINUS (mtrx begin line)
-  (declare
-    (type matrix mtrx)
-    (fixnum begin line))
-  (the matrix (progn
-  (do ((column-number (column-number mtrx))
-       (j begin (1+ j)))
-      ((= j column-number))
-      (declare (fixnum column-number j))
-    (setf (aref mtrx line j) (- (aref mtrx line j))))
-  mtrx)))
-
-(DEFMACRO LINE-MINUS-5 (mtrx-list begin line)
-  `(progn
-     (column-minus (first ,mtrx-list) 0 ,line)
-     (line-minus (second ,mtrx-list) 0 ,line)
-     (line-minus (third ,mtrx-list) ,begin ,line)))
-
-(DEFUN COLUMN-MINUS (mtrx begin column)
-  (declare
-    (type matrix mtrx)
-    (fixnum begin column))
-  (the matrix (progn
-  (do ((line-number (line-number mtrx))
-       (i begin (1+ i)))
-      ((= i line-number))
-      (declare (fixnum line-number i))
-    (setf (aref mtrx i column) (- (aref mtrx i column))))
-  mtrx)))
-
-(DEFMACRO COLUMN-MINUS-5 (mtrx-list begin column)
-  `(progn
-     (column-minus (third ,mtrx-list) ,begin ,column)
-     (column-minus (fourth ,mtrx-list) 0 ,column)
-     (line-minus (fifth ,mtrx-list) 0 ,column)))
-
-#|
-(setf m (random-matrix 3 4 10))
-(line-minus m 1 2)
-(column-minus m 1 2)
-|#
-
-#|
-(setf p (idnt-mtrx 4) p-1 (idnt-mtrx 4)
-      m (random-matrix 4 5 10)
-      q (idnt-mtrx 5) q-1 (idnt-mtrx 5))
-(setf list (list p p-1 m q q-1))
-(setf t1 (mtrx-prdc p (mtrx-prdc m q-1)))
-(line-minus-5 list 0 3)
-(equalp t1 (mtrx-prdc p (mtrx-prdc m q-1)))
-(mtrx-prdc p p-1)
-(mtrx-prdc q q-1)
-(column-minus-5 list 0 2)
-(equalp t1 (mtrx-prdc p (mtrx-prdc m q-1)))
-(mtrx-prdc p p-1)
-(mtrx-prdc q q-1)
-|#
-
-(DEFUN MINIMAL-TERM (matrix begin)
-  (declare
-    (type matrix matrix)
-    (fixnum begin))
-  (the (values fixnum fixnum fixnum)
-  (do ((line-number (line-number matrix))
-       (column-number (column-number matrix))
-       (min 0)
-       (min-il -1)
-       (min-ic -1)
-       (il begin (1+ il)))
-      ((= il line-number) (values min min-il min-ic))
-      (declare (fixnum line-number column-number
-		       min min-il min-ic il))
-      (do ((ic begin (1+ ic)))
-          ((= ic column-number))
-         (declare (fixnum ic))
-         (let ((term (abs (aref matrix il ic))))
-	   (declare (fixnum term))
-            (when (= term 1)
-               (return-from minimal-term (values 1 il ic)))
-            (when (plusp term)
-               (when (or (< term min)
-                         (zerop min))               
-                  (setf min term
-                        min-il il
-                        min-ic ic))))))))
-
-#|
-(setf m (random-matrix 4 5 10))
-(minimal-term m 1)
-|#
-
-(DEFUN MINIMAL-REST-1 (matrix begin)
-  (declare
-    (type matrix matrix)
-    (fixnum begin))
-  (the (values fixnum fixnum fixnum)
-   (let ((line-number (line-number matrix))
-	 (column-number (column-number matrix))
-	 (corner (aref matrix begin begin))
-         (min 0)
-         (min-il -1)
-         (min-ic -1))
-      (declare (fixnum corner min min-il min-ic))
-      (do ((ic (1+ begin) (1+ ic)))
-          ((= ic column-number))
-         (declare (fixnum ic))
-         (let ((term (abs (second (multiple-value-list (round (aref matrix begin ic) 
-                                                          corner))))))
-            (declare (fixnum term))
-            (when (= term 1)
-               (return-from minimal-rest-1 (values 1 begin ic)))
-            (when (plusp term)
-               (when (or (< term min)
-                         (zerop min))               
-                  (setf min term
-                        min-il begin
-                        min-ic ic)))))
-      (do ((il (1+ begin) (1+ il)))
-          ((= il line-number))
-         (declare (fixnum il))
-         (let ((term (abs (second (multiple-value-list (round (aref matrix il begin)
-                                                          corner))))))
-            (declare (fixnum term))
-            (when (= term 1)
-               (return-from minimal-rest-1 (values 1 il begin)))
-            (when (plusp term)
-               (when (or (< term min)
-                         (zerop min))               
-                  (setf min term
-                        min-il il
-                        min-ic begin)))))
-      (values min min-il min-ic))))
-
-#|
-(setf m (random-matrix 4 5 10))
-(minimal-rest-1 m 1)
-|#
-
-(DEFUN MINIMAL-REST-2 (matrix begin)
-  (declare
-    (type matrix matrix)
-    (fixnum begin))
-  (the (values fixnum fixnum fixnum)
-   (let ((line-number (line-number matrix))
-	 (column-number (column-number matrix))		      
-	 (corner (aref matrix begin begin))
-         (min 0)
-         (min-il  -1)
-         (min-ic -1))
-      (declare (fixnum corner min min-il min-ic))
-      (do ((il (1+ begin) (1+ il)))
-          ((= il line-number))
-         (declare (fixnum il))
-         (do ((ic (1+ begin) (1+ ic)))
-             ((= ic column-number))
-            (declare (fixnum il))
-            (let ((term (abs (second (multiple-value-list (round (aref matrix il ic)
-                                                             corner))))))
-               (declare (fixnum term))
-               (when (= 1 term)
-                  (return-from minimal-rest-2 (values 1 il ic)))
-               (when (plusp term)
-                  (when (or (< term min)
-                            (zerop min))
-                     (setf min term
-                           min-il il
-                           min-ic ic))))))
-      (values min min-il min-ic))))
-
-#|
-(setf m (random-matrix 4 5 10))
-(minimal-rest-2 m 1)
-|#
-
-(DEFUN MINIMAL-TERM-TOP-LEFT (mtrx-list begin il ic)
-  (declare
-   (list mtrx-list)
-   (fixnum begin il ic))
-  (the list
-    (progn
-      (when (< begin il)
-        (line-swap-5 mtrx-list begin begin il))
-      (when (< begin ic)
-        (column-swap-5 mtrx-list begin begin ic))
-      (when (minusp (aref (third mtrx-list) begin begin))
-        (line-minus-5 mtrx-list begin begin))
-      mtrx-list)))
-
-#|
-(setf p (idnt-mtrx 4) p-1 (idnt-mtrx 4)
-      m (random-matrix 4 5 10)
-      q (idnt-mtrx 5) q-1 (idnt-mtrx 5))
-(setf list (list p p-1 m q q-1))
-(setf t1 (mtrx-prdc p (mtrx-prdc m q-1)))
-(minimal-term-top-left list 0 1 3)
-(equalp t1 (mtrx-prdc p (mtrx-prdc m q-1)))
-(mtrx-prdc p p-1)
-(mtrx-prdc q q-1))
-|#
-
-(DEFUN PIVOTT (mtrx-list begin)
-  (declare
-    (list mtrx-list)
-    (fixnum begin))
-  (the list (progn
-  (let ((line-number (line-number (third mtrx-list)))
-	(column-number (column-number (third mtrx-list)))
-	(corner (aref (third mtrx-list) begin begin)))
-    (declare (fixnum line-number column-number corner))
-    (do ((il (1+ begin) (1+ il)))
-	((= il line-number))
-	(declare (fixnum il))
-      (line-op-5 mtrx-list begin
-		 (- (round (aref (third mtrx-list) il begin) corner))
-		 begin il))
-    (do ((ic (1+ begin) (1+ ic)))
-	((= ic column-number))
-	(declare (fixnum ic))
-      (column-op-5 mtrx-list begin
-		   (- (round (aref (third mtrx-list) begin ic) corner))
-		   begin ic)))
-  mtrx-list)))
-
-#|
-(setf p (idnt-mtrx 4) p-1 (idnt-mtrx 4)
-      m (random-matrix 4 5 10)
-      q (idnt-mtrx 5) q-1 (idnt-mtrx 5))
-(setf (aref m 0 0) -1)
-(setf list (list p p-1 m q q-1))
-(setf t1 (mtrx-prdc p (mtrx-prdc m q-1)))
-(pivott list 0)
-(equalp t1 (mtrx-prdc p (mtrx-prdc m q-1)))
-(mtrx-prdc p p-1)
-(mtrx-prdc q q-1)
-|#
-
-(DEFUN MATRIX-MODULO (mtrx modulo)
-  (declare (type matrix mtrx) (type fixnum modulo))
-  (the matrix
-    (let ((line-number (line-number mtrx))
-          (column-number (column-number mtrx)))
-      (declare (type fixnum line-number column-number))
-      (do ((il 0 (1+ il)))
-          ((= il line-number))
-        (declare (type fixnum il))
-        (do ((ic 0 (1+ ic)))
-            ((= ic column-number))
-          (declare (type fixnum ic))
-          (setf (aref mtrx il ic)
-            (mod (aref mtrx il ic) modulo))))
-      mtrx)))
-
-#|
-()
-(setf m (random-matrix 3 4 100))
-(matrix-modulo m 10)
-|#
-
-(DEFUN MATRIX-MODULO-5 (list modulo)
-  (declare (type list list))
-  (the list
-    (mapcar #'(lambda (item)
-                (matrix-modulo item modulo))
-      list)))
-
-(DEFUN LIST-SMITH (mtrx-list modulo) 
-  (declare (list mtrx-list) (type fixnum modulo))
-  (the list (progn
-  (let ((matrix (third mtrx-list))
-	(begin 0))
-    (declare
-      (type matrix matrix)
-      (fixnum begin))
-    (loop
-      (when (plusp modulo)
-        (matrix-modulo-5 mtrx-list modulo))
-      (multiple-value-bind (term il ic) (minimal-term matrix begin)
-	(declare (fixnum term il ic))
-        ;; (format t "~%*BEGIN* = ~D ; MIN = ~D." begin term)
-	(when (zerop term)
-	  (return-from list-smith mtrx-list))
-	(minimal-term-top-left mtrx-list begin il ic))
-      (loop
-        (when (plusp modulo)
-          (matrix-modulo-5 mtrx-list modulo))
-        (multiple-value-bind (term il ic) (minimal-rest-1 matrix begin)
-          (declare (fixnum term il ic))
-          (cond ((zerop term)
-                 (pivott mtrx-list begin)
-                 (multiple-value-bind (term il ic) (minimal-rest-2 matrix begin)
-                   (declare
-                    (fixnum term il)
-                    (ignore ic))
-                   (if (zerop term)
-                       (return)
-                     (line-op-5 mtrx-list begin 1 il begin))))
-                ((= il begin)
-                 (column-op-5 mtrx-list begin
-                              (- (round (aref matrix begin ic)
-                                        (aref matrix begin begin)))
-                              begin ic)
-                 (column-swap-5 mtrx-list begin begin ic)
-                 (when (minusp (aref matrix begin begin))
-                   (column-minus-5 mtrx-list begin begin)))
-                (t
-                 (line-op-5 mtrx-list begin
-                            (- (round (aref matrix il begin)
-                                      (aref matrix begin begin)))
-                            begin il)
-                 (line-swap-5 mtrx-list begin begin il)
-                 (when (minusp (aref matrix begin begin))
-                   (column-minus-5 mtrx-list begin begin))))))
-      ;; (Format t "~%  Finally the diagonal term is ~D." (aref matrix begin begin))
-      (incf begin)))
-              mtrx-list)))
-
-#|
-()
-(setf p (idnt-mtrx 4) p-1 (idnt-mtrx 4)
-      m (random-matrix 4 5 10)
-      q (idnt-mtrx 5) q-1 (idnt-mtrx 5))
-(setf list (list p p-1 m q q-1))
-(setf t1 (mtrx-prdc p (mtrx-prdc m q-1)))
-(third (list-smith list 0))
-(equalp t1 (mtrx-prdc p (mtrx-prdc m q-1)))
-(mtrx-prdc p p-1)
-(mtrx-prdc q q-1)
-(setf p (idnt-mtrx 4) p-1 (idnt-mtrx 4)
-      m (random-matrix 4 5 10)
-      q (idnt-mtrx 5) q-1 (idnt-mtrx 5))
-(setf list (list p p-1 m q q-1))
-(setf t1 (matrix-modulo (mtrx-prdc p (mtrx-prdc m q-1)) 10))
-(third (list-smith list 10))
-(equalp t1 (matrix-modulo (mtrx-prdc p (mtrx-prdc m q-1)) 10))
-(matrix-modulo (mtrx-prdc p p-1) 10)
-(matrix-modulo (mtrx-prdc q q-1) 10)
-
-(setf p (idnt-mtrx 10) p-1 (idnt-mtrx 10)
-      m (random-matrix 10 15 40)
-      q (idnt-mtrx 15) q-1 (idnt-mtrx 15))
-(setf list (list p p-1 m q q-1))
-(setf t1 (matrix-modulo (mtrx-prdc p (mtrx-prdc m q-1)) 10000))
-(third (list-smith list 10000))
-(equalp t1 (matrix-modulo (mtrx-prdc p (mtrx-prdc m q-1)) 10000))
-(matrix-modulo (mtrx-prdc p p-1) 10000)
-(matrix-modulo (mtrx-prdc q q-1) 10000)
-
-(setf m (random-matrix 5 5 10))
-(setf mm (copy-mtrx m))
-(third (smith m))
-(third (smith mm 1000))
-|#
-
-(DEFUN SMITH (matrix &optional (modulo 0))
-  (declare (type matrix matrix))
-  (the list
-  (let ((line-n (line-number matrix))
-	(column-n (column-number matrix)))
-    (declare (fixnum line-n column-n))
-    (list-smith
-     (list (idnt-mtrx line-n) (idnt-mtrx line-n)
-	   matrix
-           (idnt-mtrx column-n) (idnt-mtrx column-n))
-     modulo))))
-
-;;; ECHCM -> The same without the first epimorphism
-;;;
-;;; epi: C_f <- C_{f+1}
-;;  rank(C_f) = n
-;;  rank(C_{f+1}) = m
-;;  f = first
-
-(eval-when (:compile-toplevel :load-toplevel :execute)
-  (UNLESS (FIND-PACKAGE "GNRTS")
-    (make-package "GNRTS"))
-  (DEFCONSTANT +GNRTS-PCKG+
-    (find-package "GNRTS")))
-
-(DEFMACRO GNRT-NAME (i)
-  `(intern (format nil "GN-~D" ,i) +gnrts-pckg+))
-
-(DEFUN GNRT-NAME-BASIS (n)
-  (declare (fixnum n))
-  (the list
-  (do ((i (1- n) (1- i))
-       (rslt +empty-list+ (cons (gnrt-name i) rslt)))
-      ((minusp i) rslt)
-      (declare
-        (fixnum i)
-	(list rslt)))))
-
-#|
-(gnrt-name 4)
-(gnrt-name-basis 4)
-|#
-
-(DEFUN ECHCM-KILL-EPI-F-INTR (cmpr first n m f+1-basis mtrx-list)
-  (declare
-    (type cmprf cmpr)
-    (fixnum first n m)
-    (list f+1-basis mtrx-list))
-  (let ((f+1 (1+ first))
-	(m-n (- m n))
-	(q-1 (fifth mtrx-list)))
-    (declare
-      (fixnum f+1 m-n)
-      (type matrix q-1))
-    (flet ((rslt (cmbn)
-	     (declare (type cmbn cmbn))
-	     (with-cmbn (degr list) cmbn
-	       (when (= degr first)
-		 (return-from rslt (zero-cmbn degr)))
-	       (unless (= degr f+1)
-		 (return-from rslt cmbn))
-	       (let ((rslt-cffcs
-                      #-ACLPC (make-array m-n :element-type 'fixnum
-			         :initial-element 0)
-                      #+ACLPC (if (zerop m-n)
-                                 (make-array 0 :element-type 'fixnum)
-                                 (make-array m-n :element-type 'fixnum
-                                   :initial-element 0))
-                      ))
-		 (declare (type (array fixnum *) rslt-cffcs))
-		 (do ((cmbn-mark list (cdr cmbn-mark))
-		      (basis-mark f+1-basis)
-		      (ic 0))
-		     ((endp cmbn-mark))
-		     (declare
-		       (list cmbn-mark basis-mark)
-		       (fixnum ic))
-		   (with--term (cffc gnrt) cmbn-mark
-		     (loop (when (eq :equal (funcall cmpr gnrt (car basis-mark)))
-			     (return))
-			   (pop basis-mark)
-			   (incf ic))
-		     (dotimes (il m-n)
-		       (incf (aref rslt-cffcs il)
-			     (* cffc (aref q-1 (+ n il) ic))))
-		     (pop basis-mark)
-		     (incf ic)))
-		 (do ((term-list +empty-list+)
-		      (il (1- m-n) (1- il)))
-		     ((minusp il) (make-cmbn :degr degr
-					     :list term-list))
-		     (declare
-		       (list term-list)
-		       (fixnum il))
-		   (let ((cffc (aref rslt-cffcs il)))
-		     (declare (fixnum cffc))
-		     (unless (zerop cffc)
-		       (push (term cffc (gnrt-name il)) term-list))))))))
-      (the intr #'rslt))))
-	      
-#|
-(setf q-1 (random-matrix 5 5 10))
-(setf f (echcm-kill-epi-f-intr #'s-cmpr 2 2 5 '(a b c d e)
-		      (list 0 0 0 0 q-1)))
-(funcall f (cmbn 2 1 'a))
-(funcall f (cmbn 4 1 'a))
-(funcall f (cmbn 3 1 'a 10 'b 100 'c 1000 'd 10000 'e))
-|#
-
-(DEFUN ECHCM-KILL-EPI-G-INTR (first n m f+1-basis mtrx-list)
-  (declare
-    (fixnum first n m)
-    (list f+1-basis mtrx-list))
-  (let ((f+1 (1+ first))
-	(m-n (- m n))
-	(q (fourth mtrx-list)))
-    (declare
-      (fixnum f+1 m-n)
-      (type matrix q))
-    (flet ((rslt (cmbn)
-	     (declare (type cmbn cmbn))
-	     (with-cmbn (degr list) cmbn
-	       (unless (= degr f+1)
-		 (return-from rslt cmbn))
-	       (let ((rslt-cffcs
-                      #-ACLPC (make-array m :element-type 'fixnum
-			         :initial-element 0)
-                      #+ACLPC (if (zerop m)
-                                 (make-array 0 :element-type 'fixnum)
-                                 (make-array m :element-type 'fixnum
-                                   :initial-element 0))
-                      ))
-		 (declare (type (array fixnum *) rslt-cffcs))
-		 (do ((cmbn-mark list (cdr cmbn-mark))
-		      (basis-mark (gnrt-name-basis m-n))
-		      (ic 0))
-		     ((endp cmbn-mark))
-		     (declare
-		       (list cmbn-mark basis-mark)
-		       (fixnum ic))
-		   (with--term (cffc gnrt) cmbn-mark
-		     (loop (when (eq :equal (s-cmpr gnrt (car basis-mark)))
-			     (return))
-			   (pop basis-mark)
-			   (incf ic))
-		     (dotimes (il m)
-		       (incf (aref rslt-cffcs il)
-			     (* cffc (aref q il (+ n ic)))))
-		     (pop basis-mark)
-		     (incf ic)))
-		 (do ((term-list +empty-list+)
-		      (il (1- m) (1- il)))
-		     ((minusp il) (make-cmbn :degr degr
-					     :list term-list))
-		     (declare
-		       (list term-list)
-		       (fixnum il))
-		   (let ((cffc (aref rslt-cffcs il)))
-		     (declare (fixnum cffc))
-		     (unless (zerop cffc)
-		       (push (term cffc (nth il f+1-basis)) term-list))))))))
-      (the intr #'rslt))))
-    
-#|
-(setf q (random-matrix 5 5 10))
-(setf g (echcm-kill-epi-g-intr 2 2 5 '(a b c d e)
-		      (list 0 0 0 q 0)))
-(funcall g (cmbn 2))
-(funcall g (cmbn 4 1 'a))
-(funcall g (cmbn 3 1 :gn-0 10 :gn-1 100 :gn-2))
-|#
-
-(DEFUN ECHCM-KILL-EPI-H-INTR (cmpr first n m f-basis f+1-basis mtrx-list)
-  (declare
-    (type cmprf cmpr)
-    (fixnum first n m)
-    (list f-basis f+1-basis mtrx-list))
-  (let ((lqxp-1 (mtrx-prdc (left-submatrix (fourth mtrx-list) n)
-			   (second mtrx-list))))
-    (declare (type matrix lqxp-1))
-    (flet ((rslt (cmbn)
-	     (declare (type cmbn cmbn))
-	     (with-cmbn (degr list) cmbn
-	       (unless (= degr first)
-		 (return-from rslt (zero-cmbn (1+ degr))))
-	       (let ((rslt-cffcs
-                      #-ACLPC (make-array m :element-type 'fixnum
-			        :initial-element 0)
-                      #+ACLPC (if (zerop m)
-                                 (make-array 0 :element-type 'fixnum)
-                                 (make-array m :element-type 'fixnum
-                                   :initial-element 0))
-                      ))
-		 (declare (type (array fixnum *) rslt-cffcs))
-		 (do ((cmbn-mark list (cdr cmbn-mark))
-		      (basis-mark f-basis)
-		      (ic 0))
-		     ((endp cmbn-mark))
-		     (declare
-		       (list cmbn-mark basis-mark)
-		       (fixnum ic))
-		   (with--term (cffc gnrt) cmbn-mark
-		     (loop (when (eq :equal (funcall cmpr gnrt (car basis-mark)))
-			     (return))
-			   (pop basis-mark)
-			   (incf ic))
-		     (dotimes (il m)
-		       (incf (aref rslt-cffcs il)
-			     (* cffc (aref lqxp-1 il ic))))
-		     (pop basis-mark)
-		     (incf ic)))
-		 (do ((term-list +empty-list+)
-		      (il (1- m) (1- il)))
-		     ((minusp il) (make-cmbn :degr (1+ degr)
-					     :list term-list))
-		     (declare
-		       (list term-list)
-		       (fixnum il))
-		   (let ((cffc (aref rslt-cffcs il)))
-		     (declare (fixnum cffc))
-		     (unless (zerop cffc)
-		       (push (term cffc (nth il f+1-basis)) term-list))))))))
-      (the intr #'rslt))))
-	      
-#|
-(setf p-1 (random-matrix 2 2 10))
-(setf q (random-matrix 5 5 10))
-(setf h (echcm-kill-epi-h-intr #'s-cmpr 2 2 5 '(a b) '(a b c d e)
-		      (list 0 p-1 0 q 0)))
-(funcall h (cmbn 2 1 'a 1000 'b))
-(funcall h (cmbn 4 1 'a))
-|#
-
-(DEFUN ECHCM-WITHOUT-EPI (echcm first n m intr-f)
-  (declare
-    (type chain-complex echcm)
-    (fixnum first n m)
-    (type intr intr-f))
-  (the chain-complex
-  (with-slots (cmpr basis dffr dfnt) echcm
-    (declare
-      (type cmprf cmpr)
-      (type basis basis)
-      (type morphism dffr)
-      (list dfnt))
-    (chain-complex
-     :cmpr #'(lambda (gnrt1 gnrt2)
-	       (if (and (symbolp gnrt1)
-			(eq (symbol-package gnrt1)
-			    +gnrts-pckg+))
-		   (s-cmpr gnrt1 gnrt2)
-		 (funcall cmpr gnrt1 gnrt2)))
-     :basis #'(lambda (degr)
-		(declare (fixnum degr))
-		(cond ((= degr first)
-		       +empty-list+)
-		      ((= degr (1+ first))
-		       (gnrt-name-basis (- m n)))
-		      (t
-		       (funcall basis degr))))
-     :dffr-intr #'(lambda (cmbn)
-		    (declare (type cmbn cmbn))
-		    (case (- (cmbn-degr cmbn) first)
-		      (1 (zero-cmbn first))
-		      (2 (funcall intr-f
-			   (cmbn-? dffr cmbn)))
-		      (otherwise
-		         (cmbn-? dffr cmbn))))
-     :dffr-strt :cmbn
-     :dfnt `(echcm-without-epi ,echcm)))))
-
-(DEFUN ECHCM-KILL-EPI (echcm first)
-  (declare
-    (type chain-complex echcm)
-    (fixnum first))
-  (the reduction
-  (with-slots (cmpr basis) echcm
-    (declare
-      (type cmprf cmpr)
-      (type basis basis))
-    (assert (not (eq basis :locally-effective)))
-    (let* ((f-basis (funcall basis first))
-	   (f+1-basis (funcall basis (1+ first)))
-	   (mtrx-list (smith (chcm-mtrx echcm (1+ first))))
-	   (smith (third mtrx-list))
-	   (m (column-number smith))
-	   (n (line-number smith))
-	   (intr-f (echcm-kill-epi-f-intr cmpr first n m
-				    f+1-basis
-				    mtrx-list))
-	   (intr-g (echcm-kill-epi-g-intr first n m f+1-basis mtrx-list))
-	   (intr-h (echcm-kill-epi-h-intr cmpr first n m
-				    f-basis f+1-basis
-				    mtrx-list))
-	   (echcm2 (echcm-without-epi echcm first n m intr-f)))				      
-      (declare
-        (list mtrx-list)
-	(type matrix smith)
-	(fixnum m n)
-	(type intr intr-f intr-g intr-h)
-	(type chain-complex echcm2))
-      (assert (dotimes (i n +true+)
-		(unless (= 1 (aref smith i i))
-		  (return +false+))))
-      (reduction
-       :f (morphism
-	    :sorc echcm :trgt echcm2 :degr 0
-	    :intr intr-f :strt :cmbn
-	    :dfnt `(echcm-kill-epi-f ,echcm))
-       :g (morphism
-	    :sorc echcm2 :trgt echcm :degr 0
-	    :intr intr-g :strt :cmbn
-	    :dfnt `(echcm-kill-epi-g ,echcm))
-       :h (morphism
-	    :sorc echcm :trgt echcm :degr +1
-	    :intr intr-h :strt :cmbn
-	    :dfnt `(echcm-kill-epi-h ,echcm))
-       :dfnt `(echcm-kill-epi ,echcm))))))
-
-#|
-(cat-init)
-(setf s3 (sphere 3))
-(setf s3-chml-clss (chml-clss 's3))
-(setf s3-fibration (z-whitehead s3 3 s3-chml-clss))
-(setf s3-4 (fibration-total s3-fibration))
-(setf ecc (echcm s3-4))
-(setf rdct (echcm-kill-epi ecc 2))
-(pre-check-rdct rdct)
-(setf *tc* (cmbn 0 1 (bsgn ecc))
-      *bc* *tc*)
-(check-rdct)
-(setf *tc* (cmbn 2 1 (first (basis ecc 2))))
-(check-rdct)
-(setf *tc* (cmbn 3 1 (first (basis ecc 3))))
-(check-rdct)
-(setf *tc* (cmbn 4 1 (first (basis ecc 4)))
-      *bc* *tc*)
-(check-rdct)
-(setf s3-4-chml-clss (chml-clss 's3-4))
-(setf s3-4-fibration (z2-whitehead s3-4 4 s3-4-chml-clss))
-(setf s3-5 (fibration-total s3-4-fibration))
-(setf ecc (echcm s3-5))
-(dotimes (i 7)
-  (format t "~%DIM = ~D ; LENGTH = ~D" i (length (basis ecc i))))
-(setf rdct1 (echcm-kill-epi ecc 2))
-(setf rdct2 (echcm-kill-epi (bcc rdct1) 3))
-(setf rdct3 (echcm-kill-epi (bcc rdct2) 4))
-(setf rdct12 (cmps rdct2 rdct1))
-(setf rdct123 (cmps rdct3 rdct12))
-(pre-check-rdct rdct123)
-(setf *tc* (cmbn 0 1 (bsgn ecc)) *bc* *tc*)
-(check-rdct)
-(setf *tc* (cmbn 2 1 (first (basis ecc 2))))
-(check-rdct)
-(let ((b3 (basis ecc 3)))
-  (setf *tc* (cmbn 3 1 (first b3) 10 (second b3))))
-(check-rdct)
-(let ((b4 (basis ecc 4)))
-  (setf *tc* (cmbn 4 1 (first b4) 10 (second b4))))
-(check-rdct)
-(let ((b5 (basis ecc 5)))
-  (setf *tc* (cmbn 5 1 (first b5)
-		     10 (second b5)
-		     100 (third b5)
-		     1000 (fourth b5))))
-(check-rdct)
-(let ((b6 (basis ecc 6)))
-  (setf *tc* (cmbn 6 1 (first b6)
-		     10 (second b6)
-		     100 (third b6)
-		     1000 (fourth b6)
-		     10000 (fifth b6)
-		     100000 (sixth b6)
-		     1000000 (seventh b6))))
-(check-rdct)
-|#
- 
-(DEFUN KILL-EPI (chcm first)
-  (declare
-   (type chain-complex chcm)
-   (fixnum first))
-  (the equivalence
-    (let ((efhm (efhm chcm))
-          (echcm (echcm chcm)))
-      (declare
-       (type equivalence efhm)
-       (type chain-complex echcm))
-      (let ((last-rdct (echcm-kill-epi echcm first)))
-        (declare (type reduction last-rdct))
-        (setf (slot-value chcm 'efhm)
-          (equivalence
-           :lrdct (lrdct efhm)
-           :rrdct (cmps last-rdct (rrdct efhm))
-           :dfnt `(kill-epi ,chcm ,first)))))))
-
-(DEFUN KILL-EPIS (chcm first end)
-  (declare
-    (type chain-complex chcm)
-    (fixnum first end))
-  (the equivalence (progn
-    (do ((indx first (1+ indx)))
-	((= indx end))
-        (declare (fixnum indx))
-      (kill-epi chcm indx))
-    (efhm chcm))))
-
-#|
-(cat-init)
-(setf s3 (sphere 3))
-(setf s3-chml-clss (chml-clss 's3))
-(setf s3-fibration (z-whitehead s3 3 s3-chml-clss))
-(setf s3-4 (fibration-total s3-fibration))
-(setf s3-4-chml-clss (chml-clss 's3-4))
-(setf s3-4-fibration (z2-whitehead s3-4 4 s3-4-chml-clss))
-(setf s3-5 (fibration-total s3-4-fibration))
-(time (homology s3-5 6))
-(kill-epis s3-5 2 5)
-(homology s3-5 0 7)
-
-(cat-init)
-(setf s3 (sphere 3))
-(setf s3-chml-clss (chml-clss 's3))
-(setf s3-fibration (z-whitehead s3 3 s3-chml-clss))
-(setf s3-4 (fibration-total s3-fibration))
-(kill-epi s3-4 2)
-(setf s3-4-chml-clss (chml-clss 's3-4))
-(setf s3-4-fibration (z2-whitehead s3-4 4 s3-4-chml-clss))
-(setf s3-5 (fibration-total s3-4-fibration))
-(time (homology s3-5 6))
-|#
-
-(DEFUN CHML-CLSS-INTR (chcm first)
-  (declare
-    (type chain-complex chcm)
-    (fixnum first))
-  (let* ((echcm (echcm chcm))
-	 (cmpr (cmpr echcm))
-	 (basis (basis echcm))
-	 (f-basis (funcall basis first))
-	 (mtrx-list (smith (chcm-mtrx echcm (1+ first))))
-	 (p-1 (second mtrx-list))
-	 (smith (third mtrx-list))
-	 (n (line-number smith))
-	 (m (column-number smith))
-         (diag-indx (dotimes (indx (min n m)
-			       (if (> n m)
-				   m
-				 (error "In CHML-CLSS, the cohomology-ring ~@
-                                      is null.")))
-		      (declare (fixnum indx))
-		      (unless (= 1 (aref smith indx indx))
-			(return indx)))))
-    (declare
-      (type chain-complex echcm)
-      (type cmprf cmpr)
-      (type basis basis)
-      (fixnum n m diag-indx)
-      (list f-basis mtrx-list)
-      (type matrix p-1 smith))
-    (flet ((rslt (cmbn)
-	     (declare (type cmbn cmbn))
-	     (with-cmbn (degr list) cmbn
-	       (unless (= degr first)
-		 (return-from rslt (zero-cmbn (- degr first))))
-	       (do ((rslt 0)
-		    (bmark f-basis)
-		    (ic 0)
-		    (cmark list (cdr cmark)))
-		   ((endp cmark)
-		    (if (zerop rslt)
-			(zero-cmbn 0)
-		      (term-cmbn 0 rslt :z-gnrt)))
-		   (declare
-		     (fixnum rslt)
-		     (list bmark cmark))
-		 (with--term (cffc gnrt) cmark
-		   (loop
-		    (when (eq :equal (funcall cmpr gnrt (car bmark)))
-		      (return))
-		    (pop bmark)
-		    (incf ic))
-		   (incf rslt (* cffc (aref p-1 diag-indx ic)))
-		   (pop bmark)
-		   (incf ic))))))
-      (the intr #'rslt))))
-
-#|
-(cat-init)
-(setf s3 (sphere 3))
-(setf c (chml-clss-intr s3 3))
-(funcall c (cmbn 3 5 's3))
-(setf s3-chml-clss (chml-clss 's3))
-(setf s3-fibration (z-whitehead s3 3 s3-chml-clss))
-(setf s3-4 (fibration-total s3-fibration))
-(kill-epi s3-4 2)
-(setf c (chml-clss-intr s3-4 4))
-(funcall c (cmbn 4 5 (first (basis (echcm s3-4) 4))))
-(setf s3-4-chml-clss (chml-clss 's3-4))
-(setf s3-4-fibration (z2-whitehead s3-4 4 s3-4-chml-clss))
-(setf s3-5 (fibration-total s3-4-fibration))
-(kill-epis s3-5 3 5)
-(setf c (chml-clss-intr s3-5 5))
-(let ((b5 (basis (echcm s3-5) 5)))
-  (funcall c (cmbn 5 1 (first b5) 10 (second b5))))
-|#
-
-(DEFUN CHML-CLSS (chcm first)
-  (declare
-    (type chain-complex chcm)
-    (fixnum first))
-  (the morphism
-    (morphism
-      :sorc (echcm chcm) :trgt (z-chcm) :degr (- first)
-      :intr (chml-clss-intr chcm first)
-      :strt :cmbn
-      :dfnt `(chml-clss ,chcm ,first))))
-
-#|
-(cat-init)
-(setf s3 (sphere 3))
-(setf s3-chml-clss (chml-clss s3 3))
-(setf s3-fibration (z-whitehead s3 3 s3-chml-clss))
-(setf s3-4 (fibration-total s3-fibration))
-(homology s3-4 0 6)
-(kill-epi s3-4 2)
-(setf s3-4-chml-clss (chml-clss s3-4 4))
-(setf s3-4-fibration (z2-whitehead s3-4 4 s3-4-chml-clss))
-(setf s3-5 (fibration-total s3-4-fibration))
-(homology s3-5 0 6)
-(kill-epis s3-5 3 5)
-(setf s3-5-chml-clss (chml-clss s3-5 5))
-(setf s3-5-fibration (z2-whitehead s3-5 5 s3-5-chml-clss))
-(setf s3-6 (fibration-total s3-5-fibration))
-(homology s3-6 0 7)
-|#
diff --git a/archive/Kenzo-2/Kenzo-2-Acl8/special-smsts.cl b/archive/Kenzo-2/Kenzo-2-Acl8/special-smsts.cl
deleted file mode 100644
index c7e1780..0000000
--- a/archive/Kenzo-2/Kenzo-2-Acl8/special-smsts.cl
+++ /dev/null
@@ -1,551 +0,0 @@
-;;;  SPECIAL-SMSTS  SPECIAL-SMSTS  SPECIAL-SMSTS  SPECIAL-SMSTS  SPECIAL-SMSTS
-;;;  SPECIAL-SMSTS  SPECIAL-SMSTS  SPECIAL-SMSTS  SPECIAL-SMSTS  SPECIAL-SMSTS
-;;;  SPECIAL-SMSTS  SPECIAL-SMSTS  SPECIAL-SMSTS  SPECIAL-SMSTS  SPECIAL-SMSTS
-
-(IN-PACKAGE "CAT")
-
-(PROVIDE "special-smsts")
-
-;;; GMSM-FACES-INFO = (gmsm (simple-vector absm) . dffr)
-;;;                         faces
-
-(DEFUN FINITE-SS-PRE-TABLE (list)
-   (declare (list list))
-   (the list
-      (let ((pre-rslt +empty-list+)
-            (dmns-mark nil)
-            (gmsm-mark nil))
-         (declare (list pre-rslt dmns-mark gmsm-mark))
-         (dolist (item list)
-            (declare (type (or fixnum symbol list) item))
-            (cond ((typep item 'fixnum)
-                   (let ((found (assoc item pre-rslt)))
-                      (declare (list found))
-                      (setf dmns-mark 
-                            (or found
-                                (car (push (list item) pre-rslt)))
-                            gmsm-mark nil)))
-                  ((symbolp item)
-                   (when (assoc item (cdr dmns-mark))
-                      (error "In BUILD-FINITE-SS, the symbol ~A is present two times."
-                         item))
-                   (setf gmsm-mark (car (push (list item) (cdr dmns-mark)))))
-                  ((listp item)
-                   (unless gmsm-mark
-                      (error "In BUILD-FINITE-SS, the face list ~A~@
-                              is not after a symbol." item))
-                   (nconc gmsm-mark item)
-                   (setf gmsm-mark nil))
-                  (t
-                     (error "In BUILD-FINITE-SS, the argument ~A does not make sense." item))))         
-         (do ((mark1 pre-rslt (cdr mark1)))
-             ((endp mark1))
-             (declare (list mark1))
-            (do ((mark2 (rest mark1) (cdr mark2)))
-                ((endp mark2))
-               (declare (list mark2))
-               (let ((inter (intersection (cdar mark1) (cdar mark2) :key #'first)))
-                  (declare (list inter))
-                  (when inter
-                     (error "In BUILD-FINITE-SS, the symbol ~A is present two times."
-                        (caar inter))))))
-         pre-rslt)))
-
-#|
-  (setf p (finite-ss-pre-table '(0 v0 v1 v2)))
-  (finite-ss-pre-table '(0 v0 v0 v2))
-  (setf p (finite-ss-pre-table '(0 v0 v1 1 e0 e1 e2)))
-  (finite-ss-pre-table '(0 v0 v1 1 e0 e1 v1))
-  (setf p (finite-ss-pre-table '(0 v0 (v0 v0))))
-  (setf p (finite-ss-pre-table '(0 v0 v1 v2 0 v3)))
-  (finite-ss-pre-table '(0 v0 (v0 v0) (v1 v1)))
-  (finite-ss-pre-table '(0 (v0 v0) (v1 v1)))
-  (finite-ss-pre-table '(0 v0 (v0 v0) #(1 2))))
-|#
-
-(DEFUN FINITE-SS-PRE-TABLE-TABLE (pre-table)
-   (declare (list pre-table))
-   (let* ((maxdim (1+ (apply #'max (mapcar #'first pre-table))))
-          (table (make-array maxdim :initial-element +empty-list+)))
-      (declare
-         (fixnum maxdim)
-         (simple-vector table))
-      (dolist (item pre-table)
-         (declare (list item))
-         (setf (svref table (first item))
-               (sort (rest item) #'string< :key #'first)))
-      table))
-
-#|
-  (setf p (finite-ss-pre-table-table
-             (finite-ss-pre-table '(2 v0 (e1 e2) v1 1 e0 e1 e2)))))
-|#
-
-(DEFUN FINITE-SS-FIND-GMSM (table gmsm dmns &optional (max-dmns (1+ dmns)))
-   (declare
-      (type gmsm gmsm)
-      (fixnum dmns max-dmns))
-   (do ((dmns dmns (1+ dmns)))
-       ((>= dmns max-dmns) nil)
-      (declare (fixnum dmns))
-      (let ((found (find gmsm (svref table dmns) :test #'eq :key #'car)))
-         (declare (type (or cons null) found))
-         (when found
-            (return-from finite-ss-find-gmsm dmns)))))
- 
-(DEFUN FINITE-SS-FINISH-TABLE (table bsgn)
-   (declare (simple-vector table))
-   (dotimes (dmns (length table))
-      (declare (fixnum dmns))
-      (finite-ss-finish-line table dmns bsgn))
-   table)
-
-(DEFUN FINITE-SS-FINISH-LINE (table dmns bsgn)
-   (declare
-      (simple-vector table)
-      (fixnum dmns))
-   (setf (svref table dmns)
-         (mapcar
-            #'(lambda (entry)
-                 (finite-ss-finish-entry table entry dmns bsgn))
-            (svref table dmns))))
-
-(DEFUN FINITE-SS-FINISH-ENTRY (table entry dmns bsgn)
-   (declare
-      (simple-vector table)
-      (list entry)
-      (fixnum dmns)
-      (symbol bsgn))
-   (let ((simplex (first entry))
-         (faces (rest entry)))
-      (declare
-         (symbol simplex)
-         (list faces))
-      (when (zerop dmns)
-         (return-from finite-ss-finish-entry
-            (make-gmsm-faces-info
-               :gmsm simplex :faces +s-empty-vector+
-               :dffr +zero-negative-cmbn+)))
-      (setf faces (nconc faces (make-list (1+ (- dmns (length faces)))
-                                  :initial-element bsgn)))
-      (let ((rslt (make-gmsm-faces-info :gmsm simplex)))
-         (declare (cons rslt))
-         (flet ((process-face (face)
-                 (declare (type (or symbol list) face))
-                 (when (symbolp face)
-                    (setf face (list face)))
-                 (let* ((gmsm2 (car (last face)))
-                        (dgop-ext (nbutlast face))
-                        (dmns2 (finite-ss-find-gmsm table gmsm2 0 dmns)))
-                    (declare
-                       (symbol gmsm2)
-                       (list dgop-ext)
-                       (type (or fixnum null) dmns2))
-                    (unless dmns2
-                       (error "In BUILD-FINITE-SS, the face ~A is absent." gmsm2))
-                    (when (zerop (length dgop-ext))
-                       (setf dgop-ext (nreverse (<a-b< dmns2 (1- dmns)))))
-                    (unless (= (+ (length dgop-ext) dmns2 1) dmns)
-                       (error "In BUILD-FINITE-SS, the face ~A has a wrong dimension."
-                          (append dgop-ext (list gmsm2))))
-                    (absm (dgop-ext-int dgop-ext) gmsm2))))
-            (setf (info-faces rslt)
-                  (map 'simple-vector #'process-face faces))
-            (setf (info-dffr rslt)
-                  (apply #'nterm-add #'s-cmpr (1- dmns)
-                     (do ((rslt +empty-list+)
-                          (faces (info-faces rslt))
-                          (indx dmns (1- indx)))
-                         ((minusp indx) rslt)
-                        (declare
-                           (list rslt)
-                           (simple-vector faces)
-                           (fixnum indx))
-                        (let ((face (svref faces indx)))
-                           (declare (type absm face))
-                           (unless (degenerate-p face)
-                              (push (term (-1-expt-n indx) (gmsm face))
-                                 rslt))))))
-            rslt))))
-
-(DEFUN FINITE-SS-TABLE (list)
-   (declare (list list))
-   (setf list (cons 0 list))
-   (let* ((bsgn (second list))
-          (pre-table (finite-ss-pre-table list))
-          (table (finite-ss-pre-table-table pre-table)))
-      (declare
-         (symbol bsgn)
-         (list pre-table)
-         (simple-vector table))
-      ;; (vector (vector gmsm-faces-info))
-      (finite-ss-finish-table table bsgn)))
-
-#|
-  (finite-ss-table '(*))
-  (finite-ss-table '(a b))
-  (finite-ss-table '(a b 1 c (b a)))
-  (finite-ss-table '(* 2 s2 3 s3))
-  (finite-ss-table '(s0 s1 s2 1 s01 (s1 s0) s02 (s2 s0) s12 (s2 s1) 2 s012 (s12 s02 s01)))
-  (finite-ss-table '(* 4 s4 ((2 1 0 *))))
-  (finite-ss-table '(* 4 s4 ((1 1 0 *))))
-  (finite-ss-table '(* 1 s (t)))
-  (finite-ss-table '(* 4 s4 ((1 0 *)))))
-|#
-
-(DEFUN FINITE-SS-BASIS (table)
-   (declare (simple-vector table))
-   (flet ((rslt (dmns)
-             (declare (fixnum dmns))
-             (the list
-                (if (< -1 dmns (length table))
-                   (mapcar #'car (svref table dmns))
-                   +empty-list+))))
-      #'rslt))
-
-(DEFUN FINITE-SS-FACE (ind-smst table)
-   (declare
-      (symbol ind-smst)
-      (simple-vector table))
-   (flet ((rslt (indx dmns gmsm)
-           (declare
-              (fixnum indx dmns)
-              (symbol gmsm))
-           (let ((found (find gmsm (svref table dmns) :key #'car)))
-              (unless found
-                 (error "In the finite simplicial set ~A,~@
-                         the simplex ~A is absent in dimension ~D." (eval ind-smst) gmsm dmns))
-              (svref (info-faces found) indx))))
-      #'rslt))
-
-(DEFUN FINITE-SS-DFFR-INTR (ind-smst table)
-   (declare
-      (symbol ind-smst)
-      (simple-vector table))
-   (flet ((rslt (dmns gmsm)
-           (declare
-              (fixnum dmns)
-              (symbol gmsm))
-           (let ((found (find gmsm (svref table dmns) :key #'car)))
-              (unless found
-                 (error "In the finite simplicial set ~A,~@
-                         the simplex ~A is absent in dimension ~D." (eval ind-smst) gmsm dmns))
-              (info-dffr found))))
-      #'rslt))
-
-(DEFUN BUILD-FINITE-SS (list)
-  (declare (list list))
-  (let ((bsgn (first list))
-        (table (finite-ss-table list))
-        (ind-smst (gensym)))
-    (declare
-     (symbol bsgn ind-smst)
-     (simple-vector table))
-    ;;  (vector (vector gmsm-faces-info))
-    (let ((rslt (simplicial-set
-                 :cmpr #'s-cmpr
-                 :basis (finite-ss-basis table)
-                 :bsgn bsgn
-                 :face (finite-ss-face ind-smst table)
-                 :dffr-intr (finite-ss-dffr-intr ind-smst table)
-                 :dffr-strt :gnrt
-                 :dfnt `(build-finite-ss ,list))))
-      (set ind-smst rslt)
-      (unless (check-smst rslt 0 (length table))
-        ;; ???            (pop *k-list*)
-        ;; ???            (pop *k-list*)
-        (return-from build-finite-ss nil))
-      rslt)))
-
-#|
-  (cat-init)
-  (setf tr (build-finite-ss '(s0 s1 s2
-                            1 s01 (s1 s0) s02 (s2 s0) s12 (s2 s1)
-                            2 s012 (s12 s02 s01))))
-  (cmpr tr 's01 's02)
-  (basis tr 2)
-  (bsgn tr)
-  (face tr 1 2 's012)
-  (? tr 2 's012)
-  (? tr *)
-  (inspect tr)
-  (mapcar #'(lambda (s) (length (eval s))) *k-list*)
-  (setf tr (build-finite-ss '(s0 s1 s2
-                            1 s01 (s1 s1) s02 (s2 s0) s12 (s2 s1)
-                            2 s012 (s12 s02 s01))))
-  (mapcar #'(lambda (s) (length (eval s))) *k-list*))
-|#
-
-(DEFUN SPHERE-CMPR (gmsm1 gmsm2)
-   (declare (ignore gmsm1 gmsm2))
-   (the cmpr :equal))
-
-(DEFUN SPHERE-BASIS (dmns)
-   (declare (fixnum dmns))
-   (let ((fund-gmsm (intern (format nil "S~D" dmns))))
-      (declare (symbol fund-gmsm))
-      (flet ((rslt (dmns2)
-                (declare (fixnum dmns2))
-                (cond ((zerop dmns2)
-                       (list '*))
-                      ((= dmns2 dmns)
-                       (list fund-gmsm))
-                      (t
-                         +empty-list+))))
-         (the basis #'rslt))))
-
-(DEFUN SPHERE-FACE (dmns)
-   (declare (fixnum dmns))
-   (let ((face (absm (mask (1- dmns)) '*)))
-      (declare (type absm absm))
-      (flet ((rslt (indx dmns2 gmsm)
-                (declare (ignore indx dmns2 gmsm))
-                (the absm face)))
-         #'rslt)))
-
-(DEFUN SPHERE (dmns)
-  (declare (fixnum dmns))
-  (unless (plusp dmns)
-    (error "In SPHERE, the dimension ~D should be positive." dmns))
-  (unless (< dmns +maximal-dimension+)
-    (error "In SPHERE, the dimension ~D should be < ~D."
-      dmns +maximal-dimension+))
-  (the simplicial-set
-    (let ((rslt (simplicial-set
-                 :cmpr #'sphere-cmpr
-                 :basis (sphere-basis dmns)
-                 :bsgn '*
-                 :face (sphere-face dmns)
-                 :dffr-intr #'zero-dffr-intr
-                 :dffr-strt :cmbn
-                 :dfnt `(sphere ,dmns))))
-      (declare (type simplicial-set rslt))
-      (setf (slot-value (dffr rslt) 'dfnt)
-        `(zero-mrph ,rslt ,rslt -1))
-      rslt)))
-
-#|
-  (cat-init)
-  (setf s3 (sphere 3))
-  (funcall (cmpr s3) 's3 's3)
-  (dotimes (i 5)
-     (print (funcall (basis s3) i)))
-  (mapcar #'(lambda (i) (funcall (face s3) i 3 's3)) (<a-b> 0 3))
-  (? s3 3 's3)
-  (smst (idnm s3))
-  (chcm (idnm s3))
-  (setf d (dffr s3))
-  (add d d))
-|#
-
-(DEFUN SPHERE-WEDGE-BASIS (dmns-list)
-   (declare (list dmns-list))
-   (flet ((rslt (dmns)
-             (declare (fixnum dmns))
-             (when (zerop dmns)
-                (return-from rslt '(*)))
-             (do ((i (count dmns dmns-list) (1- i))
-                  (basis +empty-list+
-                         (cons (intern (format nil "S~D-~D" dmns i))
-                               basis)))
-                 ((zerop i) basis)
-                (declare
-                   (fixnum i)
-                   (list basis)))))
-      (the basis #'rslt)))
-
-(DEFUN SPHERE-WEDGE-FACE (indx dmns gmsm)
-   (declare
-      (ignore indx gmsm)
-      (fixnum dmns))
-   (the absm
-      (absm (mask (1- dmns)) '*)))
-
-(DEFUN SPHERE-WEDGE (&rest dmns-list)
-  (declare (list dmns-list))
-  (the simplicial-set
-    (let ((rslt (simplicial-set
-                 :cmpr #'s-cmpr
-                 :basis (sphere-wedge-basis dmns-list)
-                 :face #'sphere-wedge-face
-                 :dffr-intr #'zero-dffr-intr
-                 :dffr-strt :cmbn
-                 :dfnt `(sphere-wedge ,@dmns-list))))
-      (declare (type simplicial-set rslt))
-      (setf (slot-value (dffr rslt) 'dfnt)
-        `(zero-mrph ,rslt ,rslt -1))
-      rslt)))
-
-#|
-  (cat-init)
-  (setf w (sphere-wedge 3 2 3))
-  (funcall (cmpr w) 's3-1 's3-2)
-  (dotimes (i 5) (print (funcall (basis w) i)))
-  (funcall (face w) 2 3 's3-1)
-  (gnrt-? (dffr w) 3 's3-2))
-|#
-
-(DEFUN MOORE-CMPR (gmsm1 gmsm2)
-   (declare (ignore gmsm1 gmsm2))
-   (the cmpr :equal))
-
-(DEFUN MOORE-BASIS (dmns)
-   (declare (fixnum dmns))
-   (let ((lgmsm1 (list (intern (format nil "M~D" dmns))))
-         (lgmsm2 (list (intern (format nil "N~D" (1+ dmns))))))
-      (declare (symbol gmsm1 gmsm2))
-      (flet ((rslt (dmns2)
-                (declare (fixnum dmns2))
-                (cond ((zerop dmns2) '(*))
-                      ((= dmns dmns2) lgmsm1)
-                      ((= (1+ dmns) dmns2) lgmsm2)
-                      (t +empty-list+))))
-         (the basis #'rslt))))
-
-(DEFUN MOORE-FACE (pii dmns)
-   (declare (fixnum pii dmns))
-   (let ((face (absm 0 (intern (format nil "M~D" dmns))))
-         (bsgn1 (absm (mask (1- dmns)) '*))
-         (bsgn2 (absm (mask dmns) '*))
-         (2pii (ash pii 1)))
-      (declare
-         (type absm face)
-         (type absm bsgn1 bsgn2)
-         (fixnum 2pii))
-      (flet ((rslt (indx dmns2 gmsm)
-                (declare
-                   (fixnum indx dmns2)
-                   (ignore gmsm))
-                (the absm
-                   (if (= dmns dmns2)
-                      bsgn1
-                      (if (oddp indx)
-                         bsgn2
-                         (if (< indx 2pii)
-                            face
-                            bsgn2))))))
-         (the face #'rslt))))
-
-(DEFUN MOORE-DFFR-INTR (pii dmns)
-   (declare (fixnum pii dmns))
-   (let ((1+dmns (1+ dmns))
-         (gmsm1 (intern (format nil "M~D" dmns))))
-      (declare
-         (fixnum 1+dmns)
-         (type symbol gmsm1))
-      (flet ((rslt (cmbn)
-                (declare
-                   (type cmbn cmbn))
-                (with-cmbn (degr list) cmbn
-                   (unless list
-                      (return-from rslt (zero-cmbn (1- (cmbn-degr cmbn)))))
-                   (if (= degr 1+dmns)
-                      (term-cmbn dmns (* (cffc (first list)) pii) gmsm1)
-                      (zero-cmbn (1- (cmbn-degr cmbn)))))))
-         (the intr #'rslt))))
-
-(DEFUN MOORE (pii dmns)
-  (declare (fixnum pii dmns))
-  (the simplicial-set
-    (simplicial-set
-     :bsgn '*
-     :cmpr #'moore-cmpr
-     :basis (moore-basis dmns)
-     :face (moore-face pii dmns)
-     :dffr-intr (moore-dffr-intr pii dmns)
-     :dffr-strt :cmbn
-     :dfnt `(moore ,pii ,dmns))))
-
-#|
-  (cat-init)
-  (setf m4 (moore 2 4))
-  (cmpr m4 'n5 'n5)
-  (dotimes (i 7)
-     (print (basis m4 i)))
-  (mapcar #'(lambda (i) (face m4 i 5 'n5)) (<a-b> 0 5))
-  (? m4 4 'm4)
-  (? m4 5 'n5))
-|#
-
-(DEFUN R-PROJ-SPACE-CMPR (gmsm1 gmsm2)
-   (declare (ignore gmsm1 gmsm2))
-   (the cmpr :equal))
-
-(DEFUN R-PROJ-SPACE-BASIS (k &optional (l 15))
-   (declare (fixnum k))
-   (flet ((rslt (dmns)
-             (declare (fixnum dmns))
-             (the list
-                (if (or (minusp dmns)
-                        (< 0 dmns k)
-		        (>= dmns l))
-                   +empty-list+
-                   (list dmns)))))
-      (the basis #'rslt)))
-
-(DEFUN R-PROJ-SPACE-FACE (k)
-   (declare (fixnum k))
-   (flet ((rslt (indx dmns gmsm)
-           (declare
-	      (fixnum indx dmns)
-	      (ignore gmsm))
-           (if (<= dmns k)
-              (absm (mask (1- dmns)) 0)
-              (if (or (zerop indx)
-                      (= indx dmns))
-                 (absm 0 (1- dmns))
-                 (if (= dmns (1+ k))
-                    (absm (mask (1- dmns)) 0)
-                    (absm (2-exp (1- indx)) (- dmns 2)))))))
-      (the face #'rslt)))
-
-(DEFUN R-PROJ-SPACE-DFFR-INTR (k)
-   (declare (fixnum k))
-   (flet ((rslt (cmbn)
-           (declare (type cmbn cmbn))
-           (with-cmbn (degr list) cmbn
-              (unless list
-                 (return-from rslt (zero-cmbn (1- degr))))
-              (if (<= degr k)
-                 (zero-cmbn (1- degr))
-                 (if (evenp degr)
-                    (make-cmbn
-                       :degr (1- degr)
-                       :list (list (term (* 2 (-cffc list)) (1- degr))))
-                    (zero-cmbn (1- degr)))))))
-      (the intr #'rslt)))
-
-(DEFUN R-PROJ-SPACE (&optional (k 1) (l 15))
-  (declare (fixnum k))
-  (the simplicial-set
-    (simplicial-set
-     :cmpr #'R-proj-space-cmpr
-     :basis (R-proj-space-basis k l)
-     :bsgn 0
-     :face (R-proj-space-face k)
-     :dffr-intr (R-proj-space-dffr-intr k)
-     :dffr-strt :cmbn
-     :dfnt `(R-proj-space ,k))))
-
-#|
-  (cat-init)
-  (setf p (R-proj-space))
-  (basis p 4)
-  (dotimes (i 5)
-     (print (face p i 4 4)))
-  (dotimes (i 5)
-     (print (? p i i)))
-  (setf dd (cmps p p))
-  (dotimes (i 6)
-     (print (? dd i i)))
-  (setf p (R-proj-space 3))
-  (dotimes (i 7)
-     (print (basis p i)))
-  (dotimes (i 5)
-     (print (face p i 4 4)))
-  (dotimes (i 7)
-     (print (? p i i)))
-  (setf dd (cmps p p))
-  (dotimes (i 7)
-     (print (? dd i i)))
-|#
diff --git a/archive/Kenzo-2/Kenzo-2-Acl8/suspensions.cl b/archive/Kenzo-2/Kenzo-2-Acl8/suspensions.cl
deleted file mode 100644
index 8997ff1..0000000
--- a/archive/Kenzo-2/Kenzo-2-Acl8/suspensions.cl
+++ /dev/null
@@ -1,321 +0,0 @@
-;;;  SUSPENSIONS  SUSPENSIONS  SUSPENSIONS  SUSPENSIONS
-;;;  SUSPENSIONS  SUSPENSIONS  SUSPENSIONS  SUSPENSIONS
-;;;  SUSPENSIONS  SUSPENSIONS  SUSPENSIONS  SUSPENSIONS
-
-(IN-PACKAGE "CAT")
-
-(PROVIDE "suspensions")
-
-(DEFUN SUSPENSION-CMPR (cmpr)
-  (declare (type cmprf cmpr))
-  (flet ((rslt (gnrt1 gnrt2)
-	   (declare (type gnrt gnrt1 gnrt2))
-	   (if (eq gnrt1 :s-bsgn)
-	       :equal
-	     (funcall cmpr gnrt1 gnrt2))))
-    (the cmprf #'rslt)))
-
-#|
-  (setf cc (deltab))
-  (setf cmpr (suspension-cmpr (cmpr cc)))
-  (funcall cmpr :s-bsgn :s-bsgn)
-  (funcall cmpr 6 5)
-|#
-
-(DEFUN SUSPENSION-BASIS (basis)
-  (declare (type basis basis))
-  (when (eq basis :locally-effective)
-    (return-from suspension-basis :locally-effective))
-  (flet ((rslt (degr)
-	   (declare (fixnum degr))
-	   (case degr
-	     (0 (list :s-bsgn))
-	     (1 +empty-list+)
-	     (otherwise (funcall basis (1- degr))))))
-    (the basis #'rslt)))
-
-#|
-  (setf cc (sphere 2))
-  (setf basis (suspension-basis (basis cc)))
-  (dotimes (i 6)
-    (print (funcall basis i)))
-  (suspension-basis :locally-effective)
-|#
-
-(DEFUN SUSPENSION-DFFR-INTR (dffr)
-  (declare (type morphism dffr))
-  (flet ((rslt (cmbn)
-	   (declare (type cmbn cmbn))
-	   (with-cmbn (degr list) cmbn
-	     (decf degr)
-	     (if (<= degr 0)
-		 (zero-cmbn degr)
-	       (make-cmbn :degr degr
-			  :list (cmbn-list
-				 (cmbn-? dffr
-				   (make-cmbn :degr degr
-					      :list list))))))))
-    (the intr #'rslt)))
-
-#|
-  (setf cc (deltab))
-  (setf intr (suspension-dffr-intr (dffr cc)))
-  (funcall intr (cmbn 0 3 :s-bsgn))
-  (funcall intr (cmbn 3 66 7))
-|#
-
-(DEFUN SUSPENSION (obj &optional (n 1))
-  (declare (type (or chain-complex morphism reduction
-		     equivalence) obj)
-	   (fixnum n))
-  (if (= n 0)
-      obj
-    (suspension-1 (suspension obj (1- n)))))    
-
-(DEFMETHOD SUSPENSION-1 ((chcm chain-complex))
-  (the chain-complex
-    (with-slots (cmpr basis dffr) chcm
-      (chain-complex
-        :cmpr (suspension-cmpr cmpr)
-	:basis (suspension-basis basis)
-	:bsgn :s-bsgn
-	:dffr-intr (suspension-dffr-intr dffr)
-	:dffr-strt :cmbn
-	:dfnt `(suspension ,chcm)))))
-
-#|
-  (cat-init)
-  (setf cc (deltab))
-  (setf scc (suspension cc))
-  (cmpr scc 7 11)
-  (basis scc 3)  ;; error
-  (bsgn scc)
-  (? scc 3 11)
-  (setf scc (suspension cc 2))
-  (? scc 4 11)
-|#
-
-(DEFUN SUSPENSION-CPRD-INTR (cmbn)
-  (declare (type cmbn cmbn))
-  (the cmbn
-    (with-cmbn (degr list) cmbn
-      (if (zerop degr)
-	  (make-cmbn :degr 0
-		     :list (if list
-			       (list (term (-cffc list)
-					   (tnpr 0 :s-bsgn
-						 0 :s-bsgn)))
-			     +empty-list+))
-	(make-cmbn :degr degr
-		   :list (let ((list1 +empty-list+)
-			       (list2 +empty-list+))
-			   (declare (list list1 list2))
-			   (mapc
-			    #'(lambda (term)
-				(declare (type term term))
-				(with-term (cffc gnrt) term
-				  (push (term cffc
-					      (tnpr 0 :s-bsgn
-						    degr gnrt))
-					list1)
-				  (push (term cffc
-					      (tnpr degr gnrt
-						    0 :s-bsgn))
-					list2)))
-			    list)
-			   (nreconc list1 (nreverse list2))))))))
-
-#|
-(suspension-cprd-intr (cmbn 0))
-(suspension-cprd-intr (cmbn 0 5 :s-bsgn))
-(suspension-cprd-intr (cmbn 3 4 7 5 11))
-|#
-
-(DEFMETHOD SUSPENSION-1 ((clgb coalgebra))
-  (the coalgebra
-    (let ((irslt (call-next-method)))
-      (declare (type (or chain-complex coalgebra) irslt))
-      (when (typep irslt 'coalgebra)
-        (return-from suspension-1 irslt))
-      (change-chcm-to-clgb irslt :cprd-intr #'suspension-cprd-intr
-                           :cprd-strt :cmbn)
-      (setf (slot-value irslt 'dfnt) `(suspension ,clgb))
-      (setf (slot-value (slot-value irslt 'cprd) 'dfnt)
-        `(coproduct ,irslt))
-      irslt)))
-
-#|
-  (cat-init)
-  (setf coal (deltab))
-  (setf scoal (suspension coal))
-  (setf scoal (suspension coal))
-  (? scoal 3 7)
-  (cprd scoal 3 7)
-|#
-
-(DEFUN SUSPENSION-FACE (face)
-  (declare (type face face))
-  (flet ((rslt (indx dmns gmsm)
-	   (declare
-	     (fixnum indx dmns)
-	     (type gmsm gmsm))
-	   (assert (> dmns 1))
-	   (if (= indx dmns)
-	       (absm (mask (1- dmns)) :s-bsgn)
-	     (let ((irslt (funcall face indx (1- dmns) gmsm)))
-	       (declare (type absm irslt))
-	       (if (= (dgop irslt) (mask (- dmns 2)))
-		   (absm (mask (1- dmns)) :s-bsgn)
-		 irslt)))))
-     (the face #'rslt)))
-
-#|
-  (setf ss (deltab))
-  (setf face (suspension-face (face ss)))
-  (funcall face 4 4 15)
-  (funcall face 0 4 15)
-  (check-faces #'f-cmpr face 4 15)
-  (check-faces #'f-cmpr face 3 7)
-  (check-faces #'f-cmpr face 2 3)
-  (setf m (moore 2 3))
-  (setf face (suspension-face (face m)))
-  (dotimes (i 5) (print (funcall face i 4 'm3)))
-  (dotimes (i 6) (print (funcall face i 5 'mm4)))
-  (check-faces #'s-cmpr face 4 'm3)
-  (check-faces #'s-cmpr face 5 'mm4)
-|#
-
-(DEFMETHOD SUSPENSION-1 ((smst simplicial-set))
-  (the simplicial-set
-    (let ((irslt (call-next-method)))
-      (declare (type coalgebra irslt))
-      (when (typep irslt 'simplicial-set)
-	(return-from suspension-1 irslt))
-      (change-class irslt 'simplicial-set)
-      (setf (slot-value irslt 'face)
-	    (suspension-face (face smst)))
-      (setf (slot-value (slot-value irslt 'cprd) 'dfnt)
-	    `(diagonal ,irslt))
-      irslt)))
-
-#|
-  (cat-init)
-  (setf d (deltab))
-  (setf sd (suspension d))
-  (setf sd (suspension d))
-  (inspect sd)
-  (? sd 3 7)
-  (cprd sd 3 7)
-  (face sd 3 3 7)
-  (face sd 2 3 7)
-  (setf m (moore 2 1))
-  (setf sm (suspension m))
-  (homology sm 0 5)
-  (setf ssm (suspension sm))
-  (homology ssm 0 6)
-|#
-
-(DEFUN SUSPENSION-INTR (mrph)
-  (declare (type morphism mrph))
-  (let ((mdegr (degr mrph)))
-    (declare (fixnum mdegr))
-    (flet ((rslt (cmbn)
-	     (declare (type cmbn cmbn))
-	     (with-cmbn (cdegr list) cmbn
-	       (when (zerop cdegr)
-		 (return-from rslt
-		   (if (zerop mdegr)
-		       cmbn
-		     (zero-cmbn (+ mdegr cdegr)))))
-	       (make-cmbn :degr (+ mdegr cdegr)
-			  :list (cmbn-list
-				 (cmbn-? mrph (make-cmbn :degr (1- cdegr)
-							 :list list)))))))
-    (the intr #'rslt))))
-
-#|
-  (setf f (idnt-mrph (deltab)))
-  (setf sf (suspension-intr f))
-  (funcall sf (cmbn 0 3 :s-bsgn))
-  (funcall sf (cmbn 2 4 3))
-  (setf d (dffr (deltab)))
-  (setf sd (suspension-intr d))
-  (funcall sd (cmbn 0 3 :s-bsgn))
-  (funcall sd (cmbn 2 4 3))
-  (funcall sd (cmbn 3 4 7))
-|#
-	 
-(DEFMETHOD SUSPENSION-1 ((mrph morphism))
-  (the morphism
-    (let ((dfnt (dfnt mrph)))
-      (declare (list dfnt))
-      (when (eq (first dfnt) 'zero-mrph)
-	(return-from suspension-1
-	  (zero-mrph (suspension (sorc mrph))
-		     (suspension (trgt mrph))
-		     (degr mrph))))
-      (when (eq (first dfnt) 'idnt-mrph)
-	(return-from suspension-1
-	  (idnt-mrph (suspension (sorc mrph)))))
-      (morphism
-       :sorc (suspension (sorc mrph))
-       :trgt (suspension (trgt mrph))
-       :degr (degr mrph)
-       :intr (suspension-intr mrph)
-       :strt :cmbn
-       :dfnt `(suspension ,mrph)))))
-
-#|
-  (setf f (idnt-mrph (deltab)))
-  (setf sf (suspension f))
-  (? sf (cmbn 0 3 :s-bsgn))
-  (? sf (cmbn 2 4 3))
-  (setf d (dffr (deltab)))
-  (setf sd (suspension d))
-  (? sd (cmbn 0 3 :s-bsgn))
-  (? sd (cmbn 2 4 3))
-  (? sd (cmbn 3 4 7))
-|#
-
-(DEFMETHOD SUSPENSION-1 ((rdct reduction))
-  (the reduction (progn
-    (when (eq (first (dfnt rdct)) 'trivial-rdct)
-      (return-from suspension-1
-	(trivial-rdct (suspension (second (dfnt rdct))))))
-    (reduction
-      :f (suspension (f rdct))
-      :g (suspension (g rdct))
-      :h (suspension (h rdct))
-      :dfnt `(suspension ,rdct)))))
-
-#|
-  (setf rdct (ez (deltab) (deltab)))
-  (setf srdct (suspension rdct))
-  (pre-check-rdct srdct)
-  (setf *tc* (cmbn 4 1 (crpr 0 15 0 15)))
-  (setf *bc* (cmbn 4 1 (tnpr 0 1 3 15)
-                     5 (tnpr 1 3 2 7)
-                     10 (tnpr 2 7 1 3)
-                     100 (tnpr 3 15 0 1)))
-  (check-rdct)
-|#
-
-(DEFMETHOD SUSPENSION-1 ((eqvl equivalence))
-  (the equivalence (progn
-    (when (eq (first (dfnt eqvl)) 'trivial-eqvl)
-      (return-from suspension-1
-	(trivial-eqvl (suspension (second (dfnt eqvl))))))
-    (equivalence
-     :lrdct (suspension (lrdct eqvl))
-     :rrdct (suspension (rrdct eqvl))
-     :dfnt `(suspension ,eqvl)))))
-
-(DEFMETHOD SEARCH-EFHM (suspension (dfnt (eql 'suspension)))
-  (declare (type chain-complex suspension))
-  (suspension (efhm (second (dfnt suspension)))))
-
-#|
-  (setf sk (suspension (k-z 2)))
-  (homology sk 0 10)
-|#
-  
\ No newline at end of file
diff --git a/archive/Kenzo-2/Kenzo-2-Acl8/tensor-products.cl b/archive/Kenzo-2/Kenzo-2-Acl8/tensor-products.cl
deleted file mode 100644
index eec5b67..0000000
--- a/archive/Kenzo-2/Kenzo-2-Acl8/tensor-products.cl
+++ /dev/null
@@ -1,354 +0,0 @@
-;;;  TENSOR-PRODUCTS  TENSOR-PRODUCTS  TENSOR-PRODUCTS  TENSOR-PRODUCTS  TENSOR-PRODUCTS
-;;;  TENSOR-PRODUCTS  TENSOR-PRODUCTS  TENSOR-PRODUCTS  TENSOR-PRODUCTS  TENSOR-PRODUCTS
-;;;  TENSOR-PRODUCTS  TENSOR-PRODUCTS  TENSOR-PRODUCTS  TENSOR-PRODUCTS  TENSOR-PRODUCTS
-
-(IN-PACKAGE "CAT")
-
-(PROVIDE "tensor-products")
-
-(DEFVAR *TNPR-WITH-DEGREES* nil)
-
-(DEFMETHOD PRINT-KEYCONS ((car (eql :tnpr)) cdr stream)
-   (declare
-      (cons cdr)
-      (stream stream))
-   (the (eql t)
-      (progn
-         (setf cdr (cons car cdr))
-         (with-tnpr (degr1 gnrt1 degr2 gnrt2) cdr
-            (format stream
-               "<TnPr~:[~*~; ~D~] ~A~:[~*~; ~D~] ~A>"
-               *tnpr-with-degrees* degr1 gnrt1
-               *tnpr-with-degrees* degr2 gnrt2))
-         t)))
-
-#|
-  (tnpr 2 'a 3 'b)
-  (setf *tnpr-with-degrees* t)    
-  (tnpr 2 'a 3 'b)
-  (setf *tnpr-with-degrees* nil)
-|#
-
-(DEFUN 2CMBN-TNPR (cmbn1 cmbn2)
-   (declare (type cmbn cmbn1 cmbn2))
-   (the cmbn
-      (with-cmbn (degr1 list1) cmbn1
-      (with-cmbn (degr2 list2) cmbn2
-         (make-cmbn
-            :degr (+ degr1 degr2)
-            :list (mapcan
-                     #'(lambda (term1)
-                          (declare (type term term1))
-                          (the list
-                             (with-term (cffc1 gnrt1) term1
-                                (mapcar
-                                   #'(lambda (term2)
-                                        (declare (type term term2))
-                                        (the term
-                                           (term
-                                              (* cffc1 (cffc term2))
-                                              (tnpr degr1 gnrt1 degr2 (gnrt term2)))))
-                                   list2))))
-                     list1))))))
-#|
-  (setf *tnpr-with-degrees* t)
-  (2cmbn-tnpr (cmbn 2 3 'a 4 'b -5 'c) (cmbn 3 4 'x -3 'y 2 'z)))
-|#
-
-(DEFUN TNSR-PRDC-CMPR (cmpr1 cmpr2)
-   (declare (type cmprf cmpr1 cmpr2))
-   (flet ((rslt (tnpr1 tnpr2)
-             (declare (type tnpr tnpr1 tnpr2))
-             (let ((left-cons-1 (cadr tnpr1))
-                   (left-cons-2 (cadr tnpr2)))
-                (declare (cons left-cons-1 left-cons-2))
-                (lexico
-                   (f-cmpr (car left-cons-1) (car left-cons-2))
-                   (funcall cmpr1 (cdr left-cons-1) (cdr left-cons-2))
-                   (funcall cmpr2 (gnrt2 tnpr1) (gnrt2 tnpr2))))))
-      (the cmprf #'rslt)))
-
-#|
-  (setf cmpr (tnsr-prdc-cmpr #'s-cmpr #'s-cmpr))
-  (funcall cmpr (tnpr 2 'a 3 'b) (tnpr 3 'a 2 'b))
-  (funcall cmpr (tnpr 3 'a 2 'b) (tnpr 2 'a 3 'b))
-  (funcall cmpr (tnpr 2 'a 3 'b) (tnpr 2 'b 3 'b))
-  (funcall cmpr (tnpr 2 'b 3 'b) (tnpr 2 'a 3 'b))
-  (funcall cmpr (tnpr 2 'a 3 'a) (tnpr 2 'a 3 'b))
-  (funcall cmpr (tnpr 2 'a 3 'c) (tnpr 2 'a 3 'b))
-  (funcall cmpr (tnpr 2 'a 3 'b) (tnpr 2 'a 3 'b)))
-|#
-
-(DEFUN TNSR-PRDC-BASIS (basis1 basis2)
-   (declare (type basis basis1 basis2))
-   (when (or (eq basis1 :locally-effective)
-             (eq basis2 :locally-effective))
-      (return-from tnsr-prdc-basis :locally-effective))
-   (flet ((rslt (degr)
-             (declare (fixnum degr))
-             (the list
-                (progn
-                   (when (minusp degr)
-                      (return-from rslt +empty-list+))
-                   (mapcan
-                      #'(lambda (degr1)
-                           (declare (fixnum degr1))
-                           (let* ((basis1 (funcall basis1 degr1))
-                                  (degr2 (- degr degr1))
-                                  (basis2 (funcall basis2 degr2)))
-                              (declare
-                                 (fixnum degr2)
-                                 (list basis1 basis2))
-                              (the list
-                                 (mapcan
-                                    #'(lambda (gnrt1)
-                                         (declare (type gnrt gnrt1))
-                                         (the list
-                                            (mapcar
-                                               #'(lambda (gnrt2)
-                                                    (declare (type gnrt gnrt2))
-                                                    (the tnpr
-                                                       (tnpr degr1 gnrt1 degr2 gnrt2)))
-                                               basis2)))
-                                    basis1))))
-                      (<a-b> 0 degr))))))
-      (the basis #'rslt)))
-
-#|
-  (defun bas (degr)
-     (case degr
-        (0 '(a b c))
-        (1 '(d))
-        (2 nil)
-        (3 '(x y))))
-  (setf bas (tnsr-prdc-basis #'bas #'bas))
-  (dotimes (i 8)
-     (print (funcall bas i))))
-|#
-
-(DEFUN TNSR-PRDC-DFFR-INTR (dffr1 dffr2)
-   (declare (type morphism dffr1 dffr2))
-   (flet ((rslt (degr tnpr)
-             (declare
-                (fixnum degr)
-                (type tnpr tnpr))
-             (the cmbn
-                (with-tnpr (degr1 gnrt1 degr2 gnrt2) tnpr
-                   (let ((degr1-1 (1- degr1))
-                         (degr2-1 (1- degr2))
-                         (sign (oddp degr1))
-                         (list1 (cmbn-list (gnrt-? dffr1 degr1 gnrt1)))
-                         (list2 (cmbn-list (gnrt-? dffr2 degr2 gnrt2))))
-                      (declare
-                         (fixnum degr1-1 degr2-1 sign)
-                         (list list1 list2))
-                      (make-cmbn
-                         :degr (1- degr)
-                         :list (nconc
-                                  (mapcar
-                                     #'(lambda (term1)
-                                          (declare (type term term1))
-                                          (with-term (cffc1 gnrt1) term1
-                                             (term cffc1
-                                                (tnpr degr1-1 gnrt1 degr2 gnrt2))))
-                                     list1)
-                                  (mapcar
-                                     #'(lambda (term2)
-                                          (declare (type term term2))
-                                          (with-term (cffc2 gnrt2) term2
-                                             (term (if sign (- cffc2) cffc2)
-                                                (tnpr degr1 gnrt1 degr2-1 gnrt2))))
-                                     list2))))))))
-      (the intr #'rslt)))
-
-#|
-  (cat-init)
-  (setf chcm (chain-complex :cmpr #'s-cmpr :dffr-strt :gnrt :dfnt '(test-1)))
-  (setf dffr (morphism :sorc chcm :trgt chcm :degr -1
-                         :intr #'(lambda (degr gnrt)
-                                    (ecase gnrt
-                                       (a (cmbn (1- degr) 2 'd1a -3 'd2a))
-                                       (b (cmbn (1- degr) 3 'd1b -4 'd2b))))
-                         :strt :gnrt :dfnt '(test-2)))
-  (setf rslt (tnsr-prdc-dffr-intr dffr dffr))
-  (funcall rslt 4 (tnpr 2 'a 2 'b))
-  (funcall rslt 5 (tnpr 3 'a 2 'b))
-  (funcall rslt 5 (tnpr 2 'a 3 'b))
-  (funcall rslt 6 (tnpr 3 'a 3 'b)))
-|#
-
-(DEFMETHOD TNSR-PRDC ((chcm1 chain-complex) (chcm2 chain-complex))
-  (the chain-complex
-    (with-slots ((cmpr1 cmpr) (basis1 basis) (dffr1 dffr)) chcm1
-      (declare
-       (type cmprf cmpr1)
-       (type basis basis1)
-       (type morphism dffr1))
-      (with-slots ((cmpr2 cmpr) (basis2 basis) (dffr2 dffr)) chcm2
-        (declare
-         (type cmprf cmpr2)
-         (type basis basis2)
-         (type morphism dffr2))
-        (let ((rslt
-               (chain-complex
-                :cmpr (tnsr-prdc-cmpr cmpr1 cmpr2)
-                :basis (tnsr-prdc-basis basis1 basis2)
-                :dffr-intr (tnsr-prdc-dffr-intr dffr1 dffr2)
-                :dffr-strt :gnrt
-                :dfnt `(tnsr-prdc ,chcm1 ,chcm2))))
-          (declare (type chain-complex rslt))
-          (if (and (slot-boundp chcm1 'bsgn)
-                   (slot-boundp chcm2 'bsgn))
-              (setf (slot-value rslt 'bsgn)
-                (tnpr 0 (bsgn chcm1) 0 (bsgn chcm2)))
-            (slot-makunbound rslt 'bsgn))
-          rslt)))))
-
-#|
-  (setf dd (tnsr-prdc (delta 2) (delta 3)))
-  (cmpr dd (tnpr 2 7 2 11) (tnpr 2 7 2 14))
-  (basis dd 3)
-  (? dd 4 (tnpr 2 7 2 14))
-  (? dd 3 (tnpr 1 6 2 14))
-  (? dd (? dd 4 (tnpr 2 7 2 14)))
-  (? dd (? dd 3 (tnpr 1 6 2 14))))
-|#
-
-(DEFUN TNSR-PRDC-INTR (mrph1 mrph2)
-   (declare
-      (type morphism mrph1 mrph2))
-   (let ((mrph2-sign (oddp (degr mrph2))))
-      (declare (type boolean mrph2-sign))         
-      (flet ((rslt (degr tnpr)
-              (declare
-                 (ignore degr)
-                 (type tnpr tnpr))
-              (with-tnpr (degr1 gnrt1 degr2 gnrt2) tnpr
-                 (let ((rslt (2cmbn-tnpr
-                                (gnrt-? mrph1 degr1 gnrt1)
-                                (gnrt-? mrph2 degr2 gnrt2))))
-                    (declare (type cmbn rslt))
-                    (when (and mrph2-sign
-                               (oddp degr1))
-                       (mapc #'(lambda (term)
-                                  (declare (type term term))
-                                  (setf (the fixnum (cffc term))
-                                        (the fixnum (- (cffc term)))))
-                          (cmbn-list rslt)))
-                    rslt))))
-         (the intr #'rslt))))
-
-#|
-  (cat-init)
-  (setf chcm (chain-complex :cmpr #'s-cmpr :dffr-strt :gnrt :dfnt '(test-1)))
-  (setf mrph (morphism :sorc chcm :trgt chcm :degr 0
-                         :intr #'(lambda (degr gnrt)
-                                    (ecase gnrt
-                                       (a (cmbn degr 2 'd1a -3 'd2a))
-                                       (b (cmbn degr 3 'd1b -4 'd2b))))
-                         :strt :gnrt :dfnt '(test-2)))
-  (setf rslt (tnsr-prdc-intr mrph mrph))
-  (funcall rslt 6 (tnpr 2 'a 4 'b))
-  (funcall rslt 5 (tnpr 3 'a 2 'b))
-  (setf mrph (morphism :sorc chcm :trgt chcm :degr 1
-                         :intr #'(lambda (degr gnrt)
-                                    (ecase gnrt
-                                       (a (cmbn (1+ degr) 2 'd1a -3 'd2a))
-                                       (b (cmbn (1+ degr) 3 'd1b -4 'd2b))))
-                         :strt :gnrt :dfnt '(test-3)))
-  (setf rslt (tnsr-prdc-intr mrph mrph))
-  (funcall rslt 6 (tnpr 2 'a 4 'b))
-  (funcall rslt 5 (tnpr 3 'a 2 'b)))
-|#
-
-(DEFMETHOD TNSR-PRDC ((mrph1 morphism) (mrph2 morphism))
-  (the morphism
-   (with-slots ((sorc1 sorc) (trgt1 trgt) (degr1 degr)) mrph1
-   (with-slots ((sorc2 sorc) (trgt2 trgt) (degr2 degr)) mrph2
-      (the morphism
-	 (progn
-	   (when (and (eq 'idnt-mrph (first (dfnt mrph1)))
-		      (eq 'idnt-mrph (first (dfnt mrph2))))
-	      (return-from tnsr-prdc
-		 (idnt-mrph (tnsr-prdc sorc1 sorc2))))
-	   (when (or (eq 'zero-mrph (first (dfnt mrph1)))
-		     (eq 'zero-mrph (first (dfnt mrph2))))
-	      (return-from tnsr-prdc
-		 (zero-mrph (tnsr-prdc sorc1 sorc2)
-			    (tnsr-prdc trgt1 trgt2)
-			    (+ degr1 degr2))))
-	   (morphism
-              :sorc (tnsr-prdc sorc1 sorc2)
-	      :trgt (tnsr-prdc trgt1 trgt2)
-	      :degr (+ degr1 degr2)
-	      :intr (tnsr-prdc-intr mrph1 mrph2)
-	      :strt :gnrt
-	      :dfnt `(tnsr-prdc ,mrph1 ,mrph2))))))))
-
-#|
-  (cat-init)
-  (setf d (dffr (delta-infinity)))
-  (setf dd (tnsr-prdc d d))
-  (eq (sorc dd) (tnsr-prdc (delta-infinity) (delta-infinity)))
-  (? dd 5 (tnpr 2 7 3 15))
-  (? dd 5 (tnpr 3 15 2 7))
-  (? dd (? dd 5 (tnpr 2 7 3 15)))
-  (? dd (? dd 5 (tnpr 3 15 2 7)))
-  (setf ddd (cmps dd dd))
-  (? ddd 5 (tnpr 2 7 3 15))
-  (? ddd 5 (tnpr 3 15 2 7))
-|#
-
-(DEFMETHOD TNSR-PRDC ((rdct1 reduction) (rdct2 reduction))
-  (the reduction
-     (progn
-       (when (and (eq 'trivial-rdct (first (dfnt rdct1)))
-		  (eq 'trivial-rdct (first (dfnt rdct2))))
-          (return-from tnsr-prdc
-	     (trivial-rdct (tnsr-prdc (bcc rdct1) (bcc rdct2)))))
-       (with-slots ((tcc1 tcc) (bcc1 bcc) (f1 f) (g1 g) (h1 h)) rdct1
-          (declare
-             (type chain-complex tcc1 bcc1)
-	     (type morphism f1 g1 h1))
-       (with-slots ((tcc2 tcc) (bcc2 bcc) (f2 f) (g2 g) (h2 h)) rdct2
-          (declare
-             (type chain-complex tcc2 bcc2)
-	     (type morphism f2 g2 h2))
-	  (reduction
-	     :f (tnsr-prdc f1 f2)
-	     :g (tnsr-prdc g1 g2)
-	     :h (add
-	         (tnsr-prdc h1 (cmps g2 f2))
-		 (tnsr-prdc (idnt-mrph tcc1) h2))
-	     :dfnt `(tnsr-prdc ,rdct1 ,rdct2)))))))
-
-#|
-  (cat-init)
-  (setf r (ez (delta-infinity) (delta-infinity)))
-  (setf r2 (tnsr-prdc r r))
-  (setf *bc* (cmbn 4 1 (tnpr 2 (tnpr 1 3 1 3) 2 (tnpr 1 3 1 3)))
-        *tc* (cmbn 2 1 (tnpr 1 (crpr 0 3 0 3) 1 (crpr 0 3 0 3))))
-  (pre-check-rdct r2)
-  (check-rdct)
-|#
-
-(DEFMETHOD TNSR-PRDC ((eqvl1 equivalence)
-		      (eqvl2 equivalence))
-  (the equivalence
-     (equivalence
-      :lrdct (tnsr-prdc (lrdct eqvl1) (lrdct eqvl2))
-      :rrdct (tnsr-prdc (rrdct eqvl1) (rrdct eqvl2))
-      :dfnt `(tnsr-prdc ,eqvl1 ,eqvl2))))
-
-(DEFMETHOD SEARCH-EFHM (chcm (dfnt (eql 'tnsr-prdc)))
-  (declare (type chain-complex chcm))
-  (the equivalence
-       (tnsr-prdc (efhm (second (dfnt chcm)))
-		  (efhm (third (dfnt chcm))))))
-
-#|
-(cat-init)
-(setf k (k-z 2))
-(setf k2 (tnsr-prdc k k))
-(homology k2 0 10)
-|#
\ No newline at end of file
diff --git a/archive/Kenzo-2/Kenzo-2-Acl8/test.cl b/archive/Kenzo-2/Kenzo-2-Acl8/test.cl
deleted file mode 100644
index bb81a58..0000000
--- a/archive/Kenzo-2/Kenzo-2-Acl8/test.cl
+++ /dev/null
@@ -1,42 +0,0 @@
-(in-package "CAT")
-(load "file-list")
-(load-cfiles)
-
-(cat-init)
-
-(setf s3 (sphere 3))
-(setf oos3 (loop-space s3 2))
-(homology oos3 5)
-
-(cat-init)
-
-(setf p (r-proj-space 4))
-(setf oop (loop-space p 2))
-(setf faces
-  (list (loop3 0 (loop3 0 'p 1) 2)
-        +null-loop+ +null-loop+ +null-loop+ ))
-(setf doop (disk-pasting oop 3 'D3 faces))
-(setf odoop (loop-space doop))
-(homology odoop 4)
-
-(cat-init)
-
-(setf s3 (sphere 3))
-(setf ch3 (chml-clss s3 3))
-(setf f3 (z-whitehead s3 ch3))
-(setf x4 (fibration-total f3))
-(homology x4 4)
-
-(setf ch4 (chml-clss x4 4))
-(setf f4 (z2-whitehead x4 ch4))
-(setf x5 (fibration-total f4))
-(homology x5 5)
-
-(setf ch5 (chml-clss x5 5))
-(setf f5 (z2-whitehead x5 ch5))
-
-(right-serre-efhm f5)
-
-(setf x6 (fibration-total f5))
-(homology x6 6)
-
diff --git a/archive/Kenzo-2/Kenzo-2-Acl8/various.cl b/archive/Kenzo-2/Kenzo-2-Acl8/various.cl
deleted file mode 100644
index 4cde7e7..0000000
--- a/archive/Kenzo-2/Kenzo-2-Acl8/various.cl
+++ /dev/null
@@ -1,130 +0,0 @@
-;;;  VARIOUS  VARIOUS  VARIOUS  VARIOUS  VARIOUS  VARIOUS
-;;;  VARIOUS  VARIOUS  VARIOUS  VARIOUS  VARIOUS  VARIOUS
-;;;  VARIOUS  VARIOUS  VARIOUS  VARIOUS  VARIOUS  VARIOUS
-
-(IN-PACKAGE "CAT")
-
-(PROVIDE "various")
-
-(DEFCONSTANT +EMPTY-LIST+ '())
-
-(DEFCONSTANT +F-EMPTY-VECTOR+
-   (make-array 0 :element-type 'fixnum))
-
-(DEFCONSTANT +S-EMPTY-VECTOR+
-   #())
-
-(DEFCONSTANT +TRUE+ t)
-
-(DEFCONSTANT +FALSE+ nil)
-
-(DEFUN BINOMIAL-N-P (n p)
-  (declare (fixnum n p))
-  (when (> (2-exp p) n)
-     (setf p (- n p)))
-  (the fixnum
-     (do ((nn n (1- nn))
-	  (pp 1 (1+ pp))
-	  (rslt 1 (/ (* rslt nn) pp)))
-	 ((> pp p) rslt)
-	(declare (fixnum nn pp rslt)))))
-
-#|
-  (dotimes (i 6)
-     (print (binomial-n-p 5 i)))
-  (dotimes (i 6)
-     (print (binomial-p-q (- 5 i) i))))
-|#
-
-(SETF #-ACLPC *PRINT-LEVEL* #+ACLPC ALLEGRO:*TOP-PRINT-LEVEL* 5
-      #-ACLPC *PRINT-LENGTH* #+ACLPC ALLEGRO:*TOP-PRINT-LENGTH* 10)
-
-(DEFUN <A-B< (a b)
-   (declare (fixnum a b))
-   (the list
-      (do ((i (1- b) (1- i))
-           (rslt +empty-list+ (cons i rslt)))
-          ((< i a) rslt)
-         (declare (fixnum i) (list rslt)))))
- 
-(DEFUN <A-B> (a b)
-  (declare (fixnum a b))
- (the list
-   (do ((i b (1- i))
-       (rslt +empty-list+ (cons i rslt)))
-      ((< i a) rslt)
-    (declare (fixnum i) (list rslt)))))
-
-(DEFUN >A-B< (a b)
-  (declare (fixnum a b))
- (the list
-  (do ((i (1- b) (1- i))
-       (rslt +empty-list+ (cons i rslt)))
-      ((= i a) rslt)
-    (declare (fixnum i) (list rslt)))))
-
-(DEFUN >A-B> (a b)
-  (declare (fixnum a b))
- (the list
-  (do ((i b (1- i))
-       (rslt +empty-list+ (cons i rslt)))
-      ((= i a) rslt)
-    (declare (fixnum i) (list rslt)))))
-
-#|
-  (<a-b< 0 5)
-  (<a-b> 0 5)
-  (>a-b< 0 5)
-  (>a-b> 0 5))
-|#
-
-(DEFUN V<A-B> (a b)
-   (declare (fixnum a b))
- (the (vector fixnum)
-    (let ((rslt (make-array (1+ (- b a)) :element-type 'fixnum)))
-       (declare (type (vector fixnum) rslt))
-       (do ((i a (1+ i))
-            (mark 0 (1+ mark)))
-           ((> i b))
-          (declare (fixnum i mark))
-          (setf (aref rslt mark) i))
-       rslt)))
-
-#|
-  (v<a-b> -5 5))
-|#
-
-(DEFUN SRANDOM (max)
-   (declare (fixnum max))
-   (the fixnum
-      (let ((rslt (- (random (+ max max)) max)))
-         (declare (fixnum rslt))
-         (if (zerop rslt)
-            max
-            rslt))))
-
-#|
-  (dotimes (i 20) (print (srandom 3))))
-|#
-
-(DEFUN CLOCK ()
-  (multiple-value-bind (sec min hour day month year)
-		       (get-decoded-time)
-    (format t "~%;; Clock -> ~4D-~2,'0D-~2,'0D, ~Dh ~Dm ~Ds.~%"
-	      year month day hour min sec))
-  (values))
-
-#|
-  (clock))
-|#
-
-(DEFUN DONE ()
-   (format t "~%---done---")
-   (values))
-   
-#|
-  (done))
-|#
-
-
-
diff --git a/archive/Kenzo-2/Kenzo-2-Acl8/whitehead.cl b/archive/Kenzo-2/Kenzo-2-Acl8/whitehead.cl
deleted file mode 100644
index b22fef9..0000000
--- a/archive/Kenzo-2/Kenzo-2-Acl8/whitehead.cl
+++ /dev/null
@@ -1,338 +0,0 @@
-;;;  WHITEHEAD  WHITEHEAD  WHITEHEAD  WHITEHEAD  WHITEHEAD  WHITEHEAD  WHITEHEAD
-;;;  WHITEHEAD  WHITEHEAD  WHITEHEAD  WHITEHEAD  WHITEHEAD  WHITEHEAD  WHITEHEAD
-;;;  WHITEHEAD  WHITEHEAD  WHITEHEAD  WHITEHEAD  WHITEHEAD  WHITEHEAD  WHITEHEAD
-
-(IN-PACKAGE "CAT")
-
-(provide "whitehead")
-
-;;;
-;;; Z
-;;;
-
-(DEFUN Z-WWHITEHEAD-SINTR (smst n chml-clss
-				&aux (face (face smst))
-				     (k-z-n (k-z n))
-				     (idnt (bsgn k-z-n))
-				     (efhm (efhm smst)))
-   (declare
-      (type simplicial-set smst)
-      (fixnum n)
-      (type morphism chml-clss)
-      (type face face)
-      (type ab-simplicial-group k-z-n)
-      (type gmsm idnt)
-      (type equivalence efhm))
-   (setf chml-clss
-	 (i-cmps chml-clss (rf efhm) (lg efhm)))
-   (flet ((rslt (dmns gmsm)
-	    (declare
-	      (fixnum dmns)
-	      (type gmsm gmsm))
-	    (if (< dmns n)
-	        (absm (mask dmns) idnt)
-	      (z-cocycle-gbar n dmns
-		(gmsm-cocycle face n dmns gmsm chml-clss)))))
-     (the sintr #'rslt)))
-
-#|
-(cat-init)
-(setf k (k-z 2))
-(setf ecc (echcm k))
-(setf chml-clss
-      (morphism
-        :sorc ecc :trgt (z-chcm) :degr 2
-	:intr #'(lambda (degr gnrt)
-		  (if (= degr 2)
-		      (term-cmbn 0 1 :z-gnrt)
-		    (zero-cmbn (- degr 2))))
-	:strt :gnrt :dfnt '(fundamental-class k-z-2)))
-(setf tw (z-wwhitehead-sintr k 2 chml-clss))
-(a-sintr3 tw 1 (absm 1 +null-gbar+))
-(a-sintr3 tw 2 (absm 3 +null-gbar+))
-(funcall tw 2 (gbar 2 0 '(55) 0 '()))
-(funcall tw 3 (gbar 3 0 '(12 23)
-                      0 '(34)
-                      0 '()))
-(funcall tw 4 (gbar 4 0 '(12 23 34)
-                      2 '(45)
-                      0 '(56)
-                      0 '()))
-(setf k (k-z 3))
-(setf ecc (echcm k))
-(setf chml-clss
-      (morphism
-        :sorc ecc :trgt (z-chcm) :degr 3
-	:intr #'(lambda (degr gnrt)
-		  (if (= degr 3)
-		      (term-cmbn 0 -1 :z-gnrt)
-		    (zero-cmbn (- degr 3))))
-	:strt :gnrt :dfnt '(fundamental-class k-z-3)))
-(setf tw (z-wwhitehead-sintr k 3 chml-clss))
-(a-sintr3 tw 1 (absm 1 +null-gbar+))
-(a-sintr3 tw 2 (absm 3 +null-gbar+))
-(a-sintr3 tw 3 (absm 7 +null-gbar+))
-(funcall tw 3 (z-fundamental-gmsm 3 55))
-(equal (funcall tw 3 (z-fundamental-gmsm 3 55))
-       (absm 0 (z-fundamental-gmsm 3 55)))
-(funcall tw 4 (gbar 4 0 (gbar 3 0 '(12 23) 0 '(34) 0 '())
-                      0 (gbar 2 0 '(45) 0 '())
-                      1 (gbar 0)
-                      0 (gbar 0)))
-|#
-
-(DEFUN Z-WHITEHEAD-SINTR (smst n chml-clss
-				&aux (face (face smst))
-				     (k-z-n-1 (k-z (1- n)))
-				     (idnt (bsgn k-z-n-1))
-				     (efhm (efhm smst)))
-   (declare
-      (type simplicial-set smst)
-      (fixnum n)
-      (type morphism chml-clss)
-      (type face face)
-      (type ab-simplicial-group k-z-n-1)
-      (type gmsm idnt)
-      (type equivalence efhm))
-   (setf chml-clss
-	 (i-cmps chml-clss (rf efhm) (lg efhm)))
-   (flet ((rslt (dmns gmsm)
-	    (declare
-	      (fixnum dmns)
-	      (type gmsm gmsm))
-	    (if (< dmns n)
-	        (absm (mask (1- dmns)) idnt)
-	      (z-cocycle-gbar-head n dmns
-		(gmsm-cocycle face n dmns gmsm chml-clss)))))
-     (the sintr #'rslt)))
-
-#|
-(cat-init)
-(setf k (k-z 2))
-(setf ecc (echcm k))
-(setf chml-clss
-      (morphism
-        :sorc ecc :trgt (z-chcm) :degr 2
-	:intr #'(lambda (degr gnrt)
-		  (if (= degr 2)
-		      (term-cmbn 0 1 :z-gnrt)
-		    (zero-cmbn (- degr 2))))
-	:strt :gnrt :dfnt '(fundamental-class k-z-2)))
-(setf tw (z-whitehead-sintr k 2 chml-clss))
-(tw-a-sintr3 tw 1 (absm 1 +null-gbar+) '())
-(tw-a-sintr3 tw 2 (absm 3 +null-gbar+) '())
-(funcall tw 2 (gbar 2 0 '(55) 0 '()))
-(funcall tw 3 (gbar 3 0 '(12 23)
-                      0 '(34)
-                      0 '()))
-(funcall tw 4 (gbar 4 0 '(12 23 34)
-                      2 '(45)
-                      0 '(56)
-                      0 '()))
-(setf k (k-z 3))
-(setf ecc (echcm k))
-(setf chml-clss
-      (morphism
-        :sorc ecc :trgt (z-chcm) :degr 3
-	:intr #'(lambda (degr gnrt)
-		  (if (= degr 3)
-		      (term-cmbn 0 -1 :z-gnrt)
-		    (zero-cmbn (- degr 3))))
-	:strt :gnrt :dfnt '(fundamental-class k-z-3)))
-(setf tw (z-whitehead-sintr k 3 chml-clss))
-(tw-a-sintr3 tw 1 (absm 1 +null-gbar+) +null-gbar+)
-(tw-a-sintr3 tw 2 (absm 3 +null-gbar+) +null-gbar+)
-(tw-a-sintr3 tw 3 (absm 7 +null-gbar+) +null-gbar+)
-(funcall tw 3 (z-fundamental-gmsm 3 55))
-(equal (funcall tw 3 (z-fundamental-gmsm 3 55))
-       (absm 0 (z-fundamental-gmsm 2 55)))
-(funcall tw 4 (gbar 4 0 (gbar 3 0 '(12 23) 0 '(34) 0 '())
-                      0 (gbar 2 0 '(45) 0 '())
-                      1 (gbar 0)
-                      0 (gbar 0)))
-|#
-
-(DEFUN Z-WHITEHEAD (smst chml-clss &aux (n (- (degr chml-clss))))
-   (declare
-      (type simplicial-set smst)
-      (fixnum n)
-      (type morphism chml-clss))
-   (the fibration
-      (simplicial-mrph
-         :sorc smst :trgt (k-z (1- n)) :degr -1
-         :sintr (z-whitehead-sintr smst n chml-clss)
-         :dfnt `(z-whitehead ,smst))))
-
-;;;
-;;; Z/2Z
-;;;
-
-(DEFUN Z2-WWHITEHEAD-SINTR (smst n chml-clss
-				&aux (face (face smst))
-				     (k-z2-n (k-z2 n))
-				     (idnt (bsgn k-z2-n))
-				     (efhm (efhm smst)))
-   (declare
-      (type simplicial-set smst)
-      (fixnum n)
-      (type morphism chml-clss)
-      (type face face)
-      (type ab-simplicial-group k-z2-n)
-      (type gmsm idnt)
-      (type equivalence efhm))
-   (setf chml-clss
-	 (i-cmps chml-clss (rf efhm) (lg efhm)))
-   (flet ((rslt (dmns gmsm)
-	    (declare
-	      (fixnum dmns)
-	      (type gmsm gmsm))
-	    (if (< dmns n)
-	        (absm (mask dmns) idnt)
-	      (z2-cocycle-gbar n dmns
-		(gmsm-cocycle face n dmns gmsm chml-clss)))))
-     (the sintr #'rslt)))
-
-#|
-(cat-init)
-(setf k (k-z2 2))
-(setf ecc (echcm k))
-(setf chml-clss
-      (morphism
-        :sorc ecc :trgt (z-chcm) :degr 2
-	:intr #'(lambda (degr gnrt)
-		  (if (= degr 2)
-		      (term-cmbn 0 1 :z-gnrt)
-		    (zero-cmbn (- degr 2))))
-	:strt :gnrt :dfnt '(fundamental-class k-z-2)))
-(setf tw (Z2-wwhitehead-sintr k 2 chml-clss))
-(a-sintr3 tw 1 (absm 1 +null-gbar+))
-(a-sintr3 tw 2 (absm 3 +null-gbar+))
-(funcall tw 2 (gbar 2 0 1 0 0))
-(funcall tw 3 (gbar 3 0 2
-                      0 1
-                      0 0))
-(funcall tw 4 (gbar 4 0 3
-                      2 1
-                      0 1
-                      0 0))
-(setf k (k-z2 3))
-(setf ecc (echcm k))
-(setf chml-clss
-      (morphism
-        :sorc ecc :trgt (z-chcm) :degr 3
-	:intr #'(lambda (degr gnrt)
-		  (if (= degr 3)
-		      (term-cmbn 0 -1 :z-gnrt)
-		    (zero-cmbn (- degr 3))))
-	:strt :gnrt :dfnt '(fundamental-class k-z-3)))
-(setf tw (Z2-wwhitehead-sintr k 3 chml-clss))
-(a-sintr3 tw 1 (absm 1 +null-gbar+))
-(a-sintr3 tw 2 (absm 3 +null-gbar+))
-(a-sintr3 tw 3 (absm 7 +null-gbar+))
-(funcall tw 3 (Z2-fundamental-gmsm 3 1))
-(equal (funcall tw 3 (Z2-fundamental-gmsm 3 1))
-       (absm 0 (Z2-fundamental-gmsm 3 1)))
-(funcall tw 4 (gbar 4 0 (gbar 3 0 2 0 1 0 0)
-                      0 (gbar 2 0 1 0 0)
-                      1 (gbar 0)
-                      0 (gbar 0)))
-|#
-
-(DEFUN Z2-WHITEHEAD-SINTR (smst n chml-clss
-				&aux (face (face smst))
-				     (k-z2-n-1 (k-z2 (1- n)))
-				     (idnt (bsgn k-z2-n-1))
-				     (efhm (efhm smst)))
-   (declare
-      (type simplicial-set smst)
-      (fixnum n)
-      (type morphism chml-clss)
-      (type face face)
-      (type ab-simplicial-group k-z2-n-1)
-      (type gmsm idnt)
-      (type equivalence efhm))
-   (setf chml-clss
-	 (i-cmps chml-clss (rf efhm) (lg efhm)))
-   (flet ((rslt (dmns gmsm)
-	    (declare
-	      (fixnum dmns)
-	      (type gmsm gmsm))
-	    (if (< dmns n)
-	        (absm (mask (1- dmns)) idnt)
-	      (z2-cocycle-gbar-head n dmns
-		(gmsm-cocycle face n dmns gmsm chml-clss)))))     
-     (the sintr #'rslt)))
-
-#|
-(cat-init)
-(setf k (k-z2 2))
-(setf ecc (echcm k))
-(setf chml-clss
-      (morphism
-        :sorc ecc :trgt (z-chcm) :degr 2
-	:intr #'(lambda (degr gnrt)
-		  (if (= degr 2)
-		      (term-cmbn 0 1 :z-gnrt)
-		    (zero-cmbn (- degr 2))))
-	:strt :gnrt :dfnt '(fundamental-class k-z-2)))
-(setf tw (Z2-whitehead-sintr k 2 chml-clss))
-(tw-a-sintr3 tw 1 (absm 1 +null-gbar+) 0)
-(tw-a-sintr3 tw 2 (absm 3 +null-gbar+) 0)
-(funcall tw 2 (gbar 2 0 1 0 '()))
-(funcall tw 3 (gbar 3 0 2
-                      0 1
-                      0 0))
-(funcall tw 4 (gbar 4 0 3
-                      2 1
-                      0 1
-                      0 0))
-(setf k (k-z2 3))
-(setf ecc (echcm k))
-(setf chml-clss
-      (morphism
-        :sorc ecc :trgt (z-chcm) :degr 3
-	:intr #'(lambda (degr gnrt)
-		  (if (= degr 3)
-		      (term-cmbn 0 -1 :z-gnrt)
-		    (zero-cmbn (- degr 3))))
-	:strt :gnrt :dfnt '(fundamental-class k-z-3)))
-(setf tw (Z2-whitehead-sintr k 3 chml-clss))
-(tw-a-sintr3 tw 1 (absm 1 +null-gbar+) 0)
-(tw-a-sintr3 tw 2 (absm 3 +null-gbar+) 0)
-(tw-a-sintr3 tw 3 (absm 7 +null-gbar+) 0)
-(funcall tw 3 (Z2-fundamental-gmsm 3 1))
-(equal (funcall tw 3 (Z2-fundamental-gmsm 3 1))
-       (absm 0 (Z2-fundamental-gmsm 2 1)))
-(funcall tw 4 (gbar 4 0 (gbar 3 0 2 0 1 0 0)
-                      0 (gbar 2 0 1 0 0)
-                      1 (gbar 0)
-                      0 (gbar 0)))
-|#
-
-(DEFUN Z2-WHITEHEAD (smst chml-clss &aux (n (- (degr chml-clss))))
-   (declare
-      (type simplicial-set smst)
-      (fixnum n)
-      (type morphism chml-clss))
-   (the fibration
-      (simplicial-mrph
-         :sorc smst :trgt (k-z2 (1- n)) :degr -1
-         :sintr (Z2-whitehead-sintr smst n chml-clss)
-         :dfnt `(Z2-whitehead ,smst))))
-
-#|
-(setf m (moore 2 4))
-(setf chml-clss
-      (morphism
-         :sorc m :trgt (z-chcm) :degr -4
-         :intr #'(lambda (dmns gmsm)
-                    (if (= 4 dmns)
-                       (cmbn 0 1 :z-gnrt)
-                       (zero-cmbn (- dmns 4))))
-         :strt :gnrt
-         :dfnt '(chml-clss moore 2 4)))
-(setf mf (z2-whitehead m 4 chml-clss))
-(setf mt (fibration-total mf))
-(homology mt 0 10)
-|#
-         
\ No newline at end of file
diff --git a/examples/00_Overview.ipynb b/examples/00_Overview.ipynb
deleted file mode 100644
index 6834689..0000000
--- a/examples/00_Overview.ipynb
+++ /dev/null
@@ -1,2606 +0,0 @@
-{
- "cells": [
-  {
-   "cell_type": "code",
-   "execution_count": 1,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "To load \"kenzo\":\n",
-      "  Load 1 ASDF system:\n",
-      "    kenzo\n",
-      "; Loading \"kenzo\"\n",
-      "\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "#<PACKAGE \"CAT\">"
-      ]
-     },
-     "execution_count": 1,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(ql:quickload \"kenzo\")\n",
-    "(in-package :cat)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "# Overview"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "In this overview we try to  show, without entering in detailed explanations, various possibilities of `Kenzo` in algebraic topology.\n",
-    "\n",
-    "The material is arranged in a sequence of cells. Cells marked with `In [*]` represent (editable) input expressions, which in a traditional REPL (Read-Evaluate-Print Loop) would be typed by the user in a Lisp session. Only the `In [*]` mark is visible if the Lisp statement is not yet run; if run, another `Out [*]` mark is displayed with the corresponding object returned by the execution. Finally, there might be additional, non-editable, diagnostic output printed before the output component, most often a side-effect of the input form evaluation.\n",
-    "\n",
-    "Other cells are the `text` cells, giving various explanations about the Lisp statements and their evaluations. Not editable by the user."
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "## `Kenzo` in Action\n",
-    "\n",
-    "Let us begin by the space $\\mathrm{Moore}(\\mathbb{Z}/2\\mathbb{Z}, 3)$ described as a simplicial set having only three non-degenerate simplices, namely in dimension $0$, $3$ and $4$. In the  representation created by the software, the 0-simplex (base point), the 3-simplex and the 4-simplex are respectively labelled `*`, `M3` and `N4`. The faces 0 and 2 of the 4-simplex `N4` are identified with (pasted to) the 3-simplex `M3`, the others being contracted on the base point. To create the simplicial set one types simply:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 2,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K1 Simplicial-Set]"
-      ]
-     },
-     "execution_count": 2,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def m23 (moore 2 3))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "The system answers that a `Kenzo` object has been created, with number 1 and type `SIMPLICIAL SET`. This object may be referenced  by the symbol `m23`."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 3,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K1 Simplicial-Set]"
-      ]
-     },
-     "execution_count": 3,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "m23"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "We may compute the homology groups of this space, using the underlying chain complex induced by the simplicial set description. Here we compute the $H_i$ from 0 to 4 included. When in the answer the component part is void, it means that the corresponding homology group is null."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 4,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "Computing boundary-matrix in dimension 0.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 0) :\n",
-      "* \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 1.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 0 :\n",
-      "\n",
-      "\n",
-      "Component Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 1.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 2.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 1 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 2.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 3.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 3) :\n",
-      "M3 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 2 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 3.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 3) :\n",
-      "M3 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 4.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 4) :\n",
-      "N4 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 3 :\n",
-      "\n",
-      "\n",
-      "Component Z/2Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 4.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 4) :\n",
-      "N4 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 5.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 4 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 4,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(homology m23 0 5)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "The homology of `m23` is $(Z,0,0,Z/2,0,\\ldots)$; the reduced homology is only $Z/2$ in dimension 3, defining the Moore space up to homotopy.\n",
-    "\n",
-    "As `m23` is a simplicial set, it is possible to create the cartesian product $\\texttt{m23}\\times\\texttt{m23}$ by the function `crts-prdc` (= CaRTeSian PRoDuCt). This is a new simplicial set."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 5,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K10 Simplicial-Set]"
-      ]
-     },
-     "execution_count": 5,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def m23xm23 (crts-prdc m23 m23))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Being a simplicial set, $\\texttt{m23xm23}$ is also a chain complex object and we may for instance ask for the basis in dimension 6."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 6,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(<CrPr 1-0 N4 3-2 N4> <CrPr 1-0 N4 4-2 N4> <CrPr 1-0 N4 4-3 N4> <CrPr 1-0 N4 4-3-2 M3> <CrPr 1-0 N4 5-2 N4> <CrPr 1-0 N4 5-3 N4> <CrPr 1-0 N4 5-3-2 M3> <CrPr 1-0 N4 5-4 N4> <CrPr 1-0 N4 5-4-2 M3> <CrPr 1-0 N4 5-4-3 M3> ...)"
-      ]
-     },
-     "execution_count": 6,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(basis m23xm23 6)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 7,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "230"
-      ]
-     },
-     "execution_count": 7,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(length *)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "As shown by the last command, the number of elements of the basis is quite large (230). The user will note that the basis elements are in this particular case formed by cartesian products of *degenerated simplices*. In the list, an element like `<CrPr 1-0 N4 5-3-2 M3>` means $\\eta_1\\eta_0\\mathrm{N4}\\times\\eta_5\\eta_3\\eta_2\\mathrm{M3}$.\n",
-    "\n",
-    "We may construct also the tensor product $\\mathrm{m23}\\otimes\\mathrm{m23}$ from the underlying chain complex of the simplicial set `m23`. The tensor product of two simplicial sets do not make sense, and Kenzo understands to work on the underlying chain complex `m23`. This tensor product is a new chain complex and we see that the basis in dimension 6 has only one element:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 8,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K3 Chain-Complex]"
-      ]
-     },
-     "execution_count": 8,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def t2m23 (tnsr-prdc m23 m23))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 9,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(<TnPr M3 M3>)"
-      ]
-     },
-     "execution_count": 9,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(basis t2m23 6)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "The Eilenberg-Zilber theorem is used to compute the homology groups of the cartesian product space: as chain complexes, `m23xm23` and `t2m23` have the same homology groups, but the computations using the tensor product are considerably faster. The user can check Künneth's theorem."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 10,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "Computing boundary-matrix in dimension 0.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 0) :\n",
-      "<TnPr * *> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 1.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 0 :\n",
-      "\n",
-      "\n",
-      "Component Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 1.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 2.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 1 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 2.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 3.\n",
-      "Rank of the source-module : 2.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "Computing the boundary of the generator 1/2 (dimension 3) :\n",
-      "<TnPr * M3> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "Computing the boundary of the generator 2/2 (dimension 3) :\n",
-      "<TnPr M3 *> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 2 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 3.\n",
-      "Rank of the source-module : 2.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "Computing the boundary of the generator 1/2 (dimension 3) :\n",
-      "<TnPr * M3> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "Computing the boundary of the generator 2/2 (dimension 3) :\n",
-      "<TnPr M3 *> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 4.\n",
-      "Rank of the source-module : 2.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "Computing the boundary of the generator 1/2 (dimension 4) :\n",
-      "<TnPr * N4> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "Computing the boundary of the generator 2/2 (dimension 4) :\n",
-      "<TnPr N4 *> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 3 :\n",
-      "\n",
-      "\n",
-      "Component Z/2Z\n",
-      "\n",
-      "Component Z/2Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 4.\n",
-      "Rank of the source-module : 2.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "Computing the boundary of the generator 1/2 (dimension 4) :\n",
-      "<TnPr * N4> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "Computing the boundary of the generator 2/2 (dimension 4) :\n",
-      "<TnPr N4 *> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 5.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 4 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 5.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 6.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 6) :\n",
-      "<TnPr M3 M3> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 5 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 6.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 6) :\n",
-      "<TnPr M3 M3> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 7.\n",
-      "Rank of the source-module : 2.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "Computing the boundary of the generator 1/2 (dimension 7) :\n",
-      "<TnPr M3 N4> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "Computing the boundary of the generator 2/2 (dimension 7) :\n",
-      "<TnPr N4 M3> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 6 :\n",
-      "\n",
-      "\n",
-      "Component Z/2Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 7.\n",
-      "Rank of the source-module : 2.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "Computing the boundary of the generator 1/2 (dimension 7) :\n",
-      "<TnPr M3 N4> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "Computing the boundary of the generator 2/2 (dimension 7) :\n",
-      "<TnPr N4 M3> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 8.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 8) :\n",
-      "<TnPr N4 N4> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 7 :\n",
-      "\n",
-      "\n",
-      "Component Z/2Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 10,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(homology m23xm23 0 8)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Let us consider now the space $\\mathrm{K}(\\mathbb{Z}, 1)$. This is an Abelian simplicial group created  in `Kenzo` by the function `k-z`. In this simplicial group, a simplex in dimension $n$ is mathematically represented by a sequence of integers, known as a *bar* object: $$ [a_1 \\mid a_2 \\mid \\ldots \\mid a_n].$$\n",
-    "In `Kenzo`, a non-degenerate simplex of $\\mathrm{K}(\\mathbb{Z}, 1)$ in dimension $n$ will be simply a list of $n$ non-null integers, for instance: `(2 3 4 5)`. In dimension 0, the only simplex is `NIL` (the base point)."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 11,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K38 Abelian-Simplicial-Group]"
-      ]
-     },
-     "execution_count": 11,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def kz1 (k-z 1))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "But this object is also a *coalgebra* and an *algebra*, and we may \n",
-    "see the effect of the respective induced *coproduct* and *product*: "
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 12,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 4}\n",
-       "<1 * <TnPr NIL (2 3 4 5)>>\n",
-       "<1 * <TnPr (2) (3 4 5)>>\n",
-       "<1 * <TnPr (2 3) (4 5)>>\n",
-       "<1 * <TnPr (2 3 4) (5)>>\n",
-       "<1 * <TnPr (2 3 4 5) NIL>>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 12,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(cprd kz1 4 '(2 3 4 5))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 13,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 6}\n",
-       "<1 * (1 2 3 4 5 6)>\n",
-       "<-1 * (1 3 2 4 5 6)>\n",
-       "<1 * (1 3 4 2 5 6)>\n",
-       "<-1 * (1 3 4 5 2 6)>\n",
-       "<1 * (1 3 4 5 6 2)>\n",
-       "<1 * (3 1 2 4 5 6)>\n",
-       "<-1 * (3 1 4 2 5 6)>\n",
-       "<1 * (3 1 4 5 2 6)>\n",
-       "<-1 * (3 1 4 5 6 2)>\n",
-       "<1 * (3 4 1 2 5 6)>\n",
-       "... ...\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 13,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(aprd kz1 6 (tnpr 2 '(1 2) 4 '(3 4 5 6)))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "The printed results are the printed representation of *combinations*, i.e., integer linear combinations of generators resulting from the application of the morphisms. The degree of the combination is indicated by the information: `CMBN n`. \n",
-    "\n",
-    "In the same way, we may create the Abelian simplicial groups $\\mathrm{K}(\\mathbb{Z}/2\\mathbb{Z}, n)$:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 14,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K64 Abelian-Simplicial-Group]"
-      ]
-     },
-     "execution_count": 14,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def k-z2-2 (k-z2 2))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 15,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "Computing boundary-matrix in dimension 4.\n",
-      "Rank of the source-module : 2.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "Computing the boundary of the generator 1/2 (dimension 4) :\n",
-      "<<Abar[4 3]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "Computing the boundary of the generator 2/2 (dimension 4) :\n",
-      "<<Abar[2 1][2 1]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 5.\n",
-      "Rank of the source-module : 3.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "Computing the boundary of the generator 1/3 (dimension 5) :\n",
-      "<<Abar[5 4]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "Computing the boundary of the generator 2/3 (dimension 5) :\n",
-      "<<Abar[2 1][3 2]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "Computing the boundary of the generator 3/3 (dimension 5) :\n",
-      "<<Abar[3 2][2 1]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 4 :\n",
-      "\n",
-      "\n",
-      "Component Z/4Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 15,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(homology k-z2-2 4)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Let us play now with the sphere $S^3$ and its loop spaces. $S^3$ and $\\Omega^2 S^3$ are created by \n",
-    "respective calls to the functions `sphere` and `loop-space`. Then we compute the $H_4$ and $H_5$ of $\\Omega^2 S^3$:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 16,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K174 Simplicial-Set]"
-      ]
-     },
-     "execution_count": 16,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def s3 (sphere 3))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 17,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K191 Simplicial-Group]"
-      ]
-     },
-     "execution_count": 17,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def o2s3 (loop-space s3 2))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 18,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "Computing boundary-matrix in dimension 4.\n",
-      "Rank of the source-module : 3.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "Computing the boundary of the generator 1/3 (dimension 4) :\n",
-      "<<AlLp[1 <<AlLp[2 S3]>>][3 <<AlLp[2 S3][2 S3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "Computing the boundary of the generator 2/3 (dimension 4) :\n",
-      "<<AlLp[3 <<AlLp[2 S3][2 S3]>>][1 <<AlLp[2 S3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "Computing the boundary of the generator 3/3 (dimension 4) :\n",
-      "<<AlLp[1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 5.\n",
-      "Rank of the source-module : 5.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "Computing the boundary of the generator 1/5 (dimension 5) :\n",
-      "<<AlLp[5 <<AlLp[2 S3][2 S3][2 S3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "Computing the boundary of the generator 2/5 (dimension 5) :\n",
-      "<<AlLp[1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][3 <<AlLp[2 S3][2 S3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "Computing the boundary of the generator 3/5 (dimension 5) :\n",
-      "<<AlLp[1 <<AlLp[2 S3]>>][3 <<AlLp[2 S3][2 S3]>>][1 <<AlLp[2 S3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "Computing the boundary of the generator 4/5 (dimension 5) :\n",
-      "<<AlLp[3 <<AlLp[2 S3][2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "Computing the boundary of the generator 5/5 (dimension 5) :\n",
-      "<<AlLp[1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 4 :\n",
-      "\n",
-      "\n",
-      "Component Z/3Z\n",
-      "\n",
-      "Component Z/2Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 5.\n",
-      "Rank of the source-module : 5.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "Computing the boundary of the generator 1/5 (dimension 5) :\n",
-      "<<AlLp[5 <<AlLp[2 S3][2 S3][2 S3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "Computing the boundary of the generator 2/5 (dimension 5) :\n",
-      "<<AlLp[1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][3 <<AlLp[2 S3][2 S3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "Computing the boundary of the generator 3/5 (dimension 5) :\n",
-      "<<AlLp[1 <<AlLp[2 S3]>>][3 <<AlLp[2 S3][2 S3]>>][1 <<AlLp[2 S3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "Computing the boundary of the generator 4/5 (dimension 5) :\n",
-      "<<AlLp[3 <<AlLp[2 S3][2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "Computing the boundary of the generator 5/5 (dimension 5) :\n",
-      "<<AlLp[1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 6.\n",
-      "Rank of the source-module : 8.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "Computing the boundary of the generator 1/8 (dimension 6) :\n",
-      "<<AlLp[1 <<AlLp[2 S3]>>][5 <<AlLp[2 S3][2 S3][2 S3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "Computing the boundary of the generator 2/8 (dimension 6) :\n",
-      "<<AlLp[3 <<AlLp[2 S3][2 S3]>>][3 <<AlLp[2 S3][2 S3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "Computing the boundary of the generator 3/8 (dimension 6) :\n",
-      "<<AlLp[5 <<AlLp[2 S3][2 S3][2 S3]>>][1 <<AlLp[2 S3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "Computing the boundary of the generator 4/8 (dimension 6) :\n",
-      "<<AlLp[1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][3 <<AlLp[2 S3][2 S3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "Computing the boundary of the generator 5/8 (dimension 6) :\n",
-      "<<AlLp[1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][3 <<AlLp[2 S3][2 S3]>>][1 <<AlLp[2 S3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "Computing the boundary of the generator 6/8 (dimension 6) :\n",
-      "<<AlLp[1 <<AlLp[2 S3]>>][3 <<AlLp[2 S3][2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "Computing the boundary of the generator 7/8 (dimension 6) :\n",
-      "<<AlLp[3 <<AlLp[2 S3][2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "Computing the boundary of the generator 8/8 (dimension 6) :\n",
-      "<<AlLp[1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 5 :\n",
-      "\n",
-      "\n",
-      "Component Z/3Z\n",
-      "\n",
-      "Component Z/2Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 18,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(homology o2s3 4 6)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Let us take now the first loop space $\\Omega^1 S^3$"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 19,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K179 Simplicial-Group]"
-      ]
-     },
-     "execution_count": 19,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def os3 (loop-space s3))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "In the following instruction, we locate in the symbol `L1` the canonical generator of $\\pi_2 (\\Omega^1S^3)$, that is the 2-simplex coming from the original sphere. In fact, the object created by the command $\\texttt{(loop3 0 's3 1)}$ is the \"word\" $S3^1$ belonging to the Kan simplicial version $G(S^3)$ (a simplicial group) of the loop space $\\Omega S^3$."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 20,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "<<Loop[S3]>>"
-      ]
-     },
-     "execution_count": 20,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def L1 (loop3 0 's3 1))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Let us consider also the 2-degeneracy of the base point of the loop space. In the printed result, the user will recognize the degeneracy $\\eta_1\\eta_0$ of the null loop, base point of $\\Omega^1 S^3$: "
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 21,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "<AbSm 1-0 <<Loop>>>"
-      ]
-     },
-     "execution_count": 21,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def null-simp (absm 3 +null-loop+))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "We may  build now a new space by pasting a disk $D3$ as indicated by the following call. It means that we \"paste\" to the space `os3` a 3-simplex named `D3`, the attaching map being described by the list of its faces in dimension 2. The faces 0 and 2 of D3 are pasted to L1, the faces 1 and 3 are collapsed on the base point; in this way the attaching map $(S^2 \\rightarrow \\Omega S^3)$ has degree 2."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 22,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K435 Simplicial-Set]"
-      ]
-     },
-     "execution_count": 22,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def dos3 (disk-pasting os3 3 '<D3>\n",
-    "                        (list L1 null-simp L1 null-simp)))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Let us compute a few homology groups of the new space `dos3`:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 23,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "Computing boundary-matrix in dimension 2.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 2) :\n",
-      "<<AlLp[2 S3]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 3.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 3) :\n",
-      "<D3> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 2 :\n",
-      "\n",
-      "\n",
-      "Component Z/2Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 3.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 3) :\n",
-      "<D3> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 4.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 4) :\n",
-      "<<AlLp[2 S3][2 S3]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 3 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 23,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(homology dos3 2 4)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "But more interesting, let us  build the  loop space of the object `dos3` and let us compute the homology in dimension 5:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 24,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K453 Simplicial-Group]"
-      ]
-     },
-     "execution_count": 24,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def odos3 (loop-space dos3))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 25,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "Computing boundary-matrix in dimension 5.\n",
-      "Rank of the source-module : 14.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "Computing the boundary of the generator 1/14 (dimension 5) :\n",
-      "<<AlLp[5 <<AlLp[2 S3][2 S3][2 S3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "Computing the boundary of the generator 2/14 (dimension 5) :\n",
-      "<<AlLp[2 <D3>][3 <<AlLp[2 S3][2 S3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "Computing the boundary of the generator 3/14 (dimension 5) :\n",
-      "<<AlLp[3 <<AlLp[2 S3][2 S3]>>][2 <D3>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "Computing the boundary of the generator 4/14 (dimension 5) :\n",
-      "<<AlLp[1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][3 <<AlLp[2 S3][2 S3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "Computing the boundary of the generator 5/14 (dimension 5) :\n",
-      "<<AlLp[1 <<AlLp[2 S3]>>][2 <D3>][2 <D3>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "Computing the boundary of the generator 6/14 (dimension 5) :\n",
-      "<<AlLp[1 <<AlLp[2 S3]>>][3 <<AlLp[2 S3][2 S3]>>][1 <<AlLp[2 S3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "Computing the boundary of the generator 7/14 (dimension 5) :\n",
-      "<<AlLp[2 <D3>][1 <<AlLp[2 S3]>>][2 <D3>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "Computing the boundary of the generator 8/14 (dimension 5) :\n",
-      "<<AlLp[2 <D3>][2 <D3>][1 <<AlLp[2 S3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "Computing the boundary of the generator 9/14 (dimension 5) :\n",
-      "<<AlLp[3 <<AlLp[2 S3][2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "Computing the boundary of the generator 10/14 (dimension 5) :\n",
-      "<<AlLp[1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][2 <D3>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "Computing the boundary of the generator 11/14 (dimension 5) :\n",
-      "<<AlLp[1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][2 <D3>][1 <<AlLp[2 S3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "Computing the boundary of the generator 12/14 (dimension 5) :\n",
-      "<<AlLp[1 <<AlLp[2 S3]>>][2 <D3>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "Computing the boundary of the generator 13/14 (dimension 5) :\n",
-      "<<AlLp[2 <D3>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "Computing the boundary of the generator 14/14 (dimension 5) :\n",
-      "<<AlLp[1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 6.\n",
-      "Rank of the source-module : 26.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "Computing the boundary of the generator 1/26 (dimension 6) :\n",
-      "<<AlLp[1 <<AlLp[2 S3]>>][5 <<AlLp[2 S3][2 S3][2 S3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "Computing the boundary of the generator 2/26 (dimension 6) :\n",
-      "<<AlLp[3 <<AlLp[2 S3][2 S3]>>][3 <<AlLp[2 S3][2 S3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "Computing the boundary of the generator 3/26 (dimension 6) :\n",
-      "<<AlLp[5 <<AlLp[2 S3][2 S3][2 S3]>>][1 <<AlLp[2 S3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "Computing the boundary of the generator 4/26 (dimension 6) :\n",
-      "<<AlLp[1 <<AlLp[2 S3]>>][2 <D3>][3 <<AlLp[2 S3][2 S3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "Computing the boundary of the generator 5/26 (dimension 6) :\n",
-      "<<AlLp[1 <<AlLp[2 S3]>>][3 <<AlLp[2 S3][2 S3]>>][2 <D3>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "Computing the boundary of the generator 6/26 (dimension 6) :\n",
-      "<<AlLp[2 <D3>][1 <<AlLp[2 S3]>>][3 <<AlLp[2 S3][2 S3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "Computing the boundary of the generator 7/26 (dimension 6) :\n",
-      "<<AlLp[2 <D3>][2 <D3>][2 <D3>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "Computing the boundary of the generator 8/26 (dimension 6) :\n",
-      "<<AlLp[2 <D3>][3 <<AlLp[2 S3][2 S3]>>][1 <<AlLp[2 S3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "Computing the boundary of the generator 9/26 (dimension 6) :\n",
-      "<<AlLp[3 <<AlLp[2 S3][2 S3]>>][1 <<AlLp[2 S3]>>][2 <D3>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "Computing the boundary of the generator 10/26 (dimension 6) :\n",
-      "<<AlLp[3 <<AlLp[2 S3][2 S3]>>][2 <D3>][1 <<AlLp[2 S3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "Computing the boundary of the generator 11/26 (dimension 6) :\n",
-      "<<AlLp[1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][3 <<AlLp[2 S3][2 S3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "Computing the boundary of the generator 12/26 (dimension 6) :\n",
-      "<<AlLp[1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][2 <D3>][2 <D3>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "Computing the boundary of the generator 13/26 (dimension 6) :\n",
-      "<<AlLp[1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][3 <<AlLp[2 S3][2 S3]>>][1 <<AlLp[2 S3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "Computing the boundary of the generator 14/26 (dimension 6) :\n",
-      "<<AlLp[1 <<AlLp[2 S3]>>][2 <D3>][1 <<AlLp[2 S3]>>][2 <D3>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "Computing the boundary of the generator 15/26 (dimension 6) :\n",
-      "<<AlLp[1 <<AlLp[2 S3]>>][2 <D3>][2 <D3>][1 <<AlLp[2 S3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "Computing the boundary of the generator 16/26 (dimension 6) :\n",
-      "<<AlLp[1 <<AlLp[2 S3]>>][3 <<AlLp[2 S3][2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "Computing the boundary of the generator 17/26 (dimension 6) :\n",
-      "<<AlLp[2 <D3>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][2 <D3>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "Computing the boundary of the generator 18/26 (dimension 6) :\n",
-      "<<AlLp[2 <D3>][1 <<AlLp[2 S3]>>][2 <D3>][1 <<AlLp[2 S3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "Computing the boundary of the generator 19/26 (dimension 6) :\n",
-      "<<AlLp[2 <D3>][2 <D3>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "Computing the boundary of the generator 20/26 (dimension 6) :\n",
-      "<<AlLp[3 <<AlLp[2 S3][2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "Computing the boundary of the generator 21/26 (dimension 6) :\n",
-      "<<AlLp[1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][2 <D3>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "Computing the boundary of the generator 22/26 (dimension 6) :\n",
-      "<<AlLp[1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][2 <D3>][1 <<AlLp[2 S3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "Computing the boundary of the generator 23/26 (dimension 6) :\n",
-      "<<AlLp[1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][2 <D3>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "Computing the boundary of the generator 24/26 (dimension 6) :\n",
-      "<<AlLp[1 <<AlLp[2 S3]>>][2 <D3>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "Computing the boundary of the generator 25/26 (dimension 6) :\n",
-      "<<AlLp[2 <D3>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "Computing the boundary of the generator 26/26 (dimension 6) :\n",
-      "<<AlLp[1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 5 :\n",
-      "\n",
-      "\n",
-      "Component Z/2Z\n",
-      "\n",
-      "Component Z/2Z\n",
-      "\n",
-      "Component Z/2Z\n",
-      "\n",
-      "Component Z/2Z\n",
-      "\n",
-      "Component Z/2Z\n",
-      "\n",
-      "Component Z/2Z\n",
-      "\n",
-      "Component Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 25,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(homology odos3 5)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Let us continue with the Kan theory. First, we check that $S^3$ is not of type Kan and that $\\Omega S^3$ is indeed of type Kan and a non-Abelian simplicial group."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 26,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 26,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(typep s3 'kan)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 27,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "T"
-      ]
-     },
-     "execution_count": 27,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(typep os3 'kan)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 28,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "T"
-      ]
-     },
-     "execution_count": 28,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(typep os3 'simplicial-group)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 29,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 29,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(typep os3 'ab-simplicial-group)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Let us create the word $L2=(S3)^2$, i.e an object belonging to $\\Omega S^3$ and let us apply the product of the underlying algebra upon $L2 \\otimes L2$:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 30,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "<<Loop[S3\\2]>>"
-      ]
-     },
-     "execution_count": 30,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def L2 (loop3 0 's3 2))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 31,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 4}\n",
-       "<1 * <<Loop[1-0 S3\\2][3-2 S3\\2]>>>\n",
-       "<-1 * <<Loop[2-0 S3\\2][3-1 S3\\2]>>>\n",
-       "<1 * <<Loop[2-1 S3\\2][3-0 S3\\2]>>>\n",
-       "<1 * <<Loop[3-0 S3\\2][2-1 S3\\2]>>>\n",
-       "<-1 * <<Loop[3-1 S3\\2][2-0 S3\\2]>>>\n",
-       "<1 * <<Loop[3-2 S3\\2][1-0 S3\\2]>>>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 31,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def square (aprd os3 4 (tnpr 2 L2 2 L2)))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "We see that the result is a linear combination of words composed from degeneracies of `L2`. The following instruction selects the generator part of the \n",
-    "second element of the previous combination."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 32,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "<<Loop[2-0 S3\\2][3-1 S3\\2]>>"
-      ]
-     },
-     "execution_count": 32,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def L4 (gnrt (second (cmbn-list square))))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Let us use the lisp function `mapcar` (one among the various iteration functions of Lisp) to create the list of the faces 1, 2, 3 and 4 of the object `L4`, this list is a \"Kan horn\"."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 33,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(<AbSm - <<Loop[1 S3\\2][2 S3\\2]>>> <AbSm - <<Loop[0 S3\\2][2 S3\\2]>>> <AbSm - <<Loop[0 S3\\2][1 S3\\2]>>> <AbSm 1 <<Loop[S3\\2]>>>)"
-      ]
-     },
-     "execution_count": 33,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def horn (mapcar #'(lambda (i) (face os3 i 4 l4)) '(1 2 3 4)))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "The function `kfll` tries to find a filling of this \"Kan horn\", and we see that the face 2 of the resulting simplex (which is very different from `L4`) is  the same as the face 2 of `L4`."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 34,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "<AbSm - <<Loop[3-1 S3\\2][2-1 S3\\-2][2-0 S3\\2][1-0 S3\\-2][2-1 S3\\2][3-1 S3\\-2][1-0 S3\\2][3-1 S3\\2][3-0 S3\\-2][1-0 S3\\-2][3-0 S3\\2][2-0 S3\\-2][1-0 S3\\2][3-0 S3\\-2][2-0 S3\\2][3-0 S3\\2]>>>"
-      ]
-     },
-     "execution_count": 34,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def kan-simplex (kfll os3 0 4 horn))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 35,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "<AbSm - <<Loop[0 S3\\2][2 S3\\2]>>>"
-      ]
-     },
-     "execution_count": 35,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(face os3 2 4 kan-simplex)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 36,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "<AbSm - <<Loop[0 S3\\2][2 S3\\2]>>>"
-      ]
-     },
-     "execution_count": 36,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(second horn)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Let ${\\cal G}$ be a simplicial group 0-reduced. $\\Omega S^3$ is such a group. The program `Kenzo` allows the construction of the universal bundle $\\mathcal{WG}$ and in particular of its base space $\\overline{\\mathcal{W}} \\mathcal{G}$, i.e. the classifying space of ${\\cal G}$. In our case, as $\\Omega S^3$ in non-Abelian, the result is not a simplicial group but only a simplicial set. We verify that the $H_4$, which in principle should be isomorphic to $H_4 S^3 = 0$, is really null."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 37,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K598 Simplicial-Set]"
-      ]
-     },
-     "execution_count": 37,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def cls-os3 (classifying-space os3))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 38,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 38,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(typep cls-os3 'simplicial-group)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 39,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "Computing boundary-matrix in dimension 4.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 5.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 5) :\n",
-      "<<Abar[5 <<AlLp[2 S3][2 S3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 4 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 39,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(homology cls-os3 4)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Let us end this short overview with an example of computation of homotopy groups. The method used in `Kenzo` is the Whitehead tower. An extended version of the Kenzo program due to Ana Romero is more general, but in this present version only the case where the first non-null homology group (in non-null dimension) is $\\mathbb{Z}$ or $\\mathbb{Z}/{2\\mathbb{Z}}$ can be processed; however if this homology group is a direct sum of several copies of $\\mathbb{Z}$ or $\\mathbb{Z}/{2 \\mathbb{Z}}$, then the corresponding stage of the Whitehead tower may also be constructed step by step.\n",
-    "\n",
-    "We take again $\\mathrm{Moore}(\\mathbb{Z}/2\\mathbb{Z}, 3)$ whose $H_3$ is $\\mathbb{Z}/2\\mathbb{Z}$. First the fundamental cohomology class is constructed:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 40,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K729 Cohomology-Class on K1 of degree 3]"
-      ]
-     },
-     "execution_count": 40,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def ch3 (chml-clss m23 3))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Then the function `z2-whitehead` is called to build a fibration over the simplicial set `m23` canonically associated to the cohomology class `ch3`."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 41,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K730 Fibration K1 -> K64]"
-      ]
-     },
-     "execution_count": 41,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def f3 (z2-whitehead m23 ch3))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Then the total space of the fibration is built:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 42,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K736 Simplicial-Set]"
-      ]
-     },
-     "execution_count": 42,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def x4 (fibration-total f3))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "The $H_4$ of this total space is the $\\pi_4$ of $\\mathrm{Moore}(\\mathbb{Z}/2\\mathbb{Z})$:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 43,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "Computing boundary-matrix in dimension 3.\n",
-      "Rank of the source-module : 2.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "Computing the boundary of the generator 1/2 (dimension 3) :\n",
-      "<TnPr * <<Abar[3 2]>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "Computing the boundary of the generator 2/2 (dimension 3) :\n",
-      "<TnPr M3 <<Abar>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 4.\n",
-      "Rank of the source-module : 3.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "Computing the boundary of the generator 1/3 (dimension 4) :\n",
-      "<TnPr * <<Abar[4 3]>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "Computing the boundary of the generator 2/3 (dimension 4) :\n",
-      "<TnPr * <<Abar[2 1][2 1]>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "Computing the boundary of the generator 3/3 (dimension 4) :\n",
-      "<TnPr N4 <<Abar>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 3 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 4.\n",
-      "Rank of the source-module : 3.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "Computing the boundary of the generator 1/3 (dimension 4) :\n",
-      "<TnPr * <<Abar[4 3]>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "Computing the boundary of the generator 2/3 (dimension 4) :\n",
-      "<TnPr * <<Abar[2 1][2 1]>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "Computing the boundary of the generator 3/3 (dimension 4) :\n",
-      "<TnPr N4 <<Abar>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 5.\n",
-      "Rank of the source-module : 4.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "Computing the boundary of the generator 1/4 (dimension 5) :\n",
-      "<TnPr * <<Abar[5 4]>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "Computing the boundary of the generator 2/4 (dimension 5) :\n",
-      "<TnPr * <<Abar[2 1][3 2]>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "Computing the boundary of the generator 3/4 (dimension 5) :\n",
-      "<TnPr * <<Abar[3 2][2 1]>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "Computing the boundary of the generator 4/4 (dimension 5) :\n",
-      "<TnPr M3 <<Abar[2 1]>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 4 :\n",
-      "\n",
-      "\n",
-      "Component Z/2Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 43,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(homology x4 3 5)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "We may now iterate the process, to compute the $\\pi_5$ of $\\mathrm{Moore}(\\mathbb{Z}/2\\mathbb{Z})$:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 44,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K817 Cohomology-Class on K802 of degree 4]"
-      ]
-     },
-     "execution_count": 44,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def ch4 (chml-clss x4 4))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 45,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K832 Fibration K736 -> K818]"
-      ]
-     },
-     "execution_count": 45,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def f4 (z2-whitehead x4 ch4))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 46,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K838 Simplicial-Set]"
-      ]
-     },
-     "execution_count": 46,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def x5 (fibration-total f4))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 47,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "Computing boundary-matrix in dimension 4.\n",
-      "Rank of the source-module : 4.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "Computing the boundary of the generator 1/4 (dimension 4) :\n",
-      "<TnPr <TnPr * <<Abar>>> <<Abar[4 <<Abar[3 2]>>]>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "Computing the boundary of the generator 2/4 (dimension 4) :\n",
-      "<TnPr <TnPr * <<Abar[4 3]>>> <<Abar>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "Computing the boundary of the generator 3/4 (dimension 4) :\n",
-      "<TnPr <TnPr * <<Abar[2 1][2 1]>>> <<Abar>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "Computing the boundary of the generator 4/4 (dimension 4) :\n",
-      "<TnPr <TnPr N4 <<Abar>>> <<Abar>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 5.\n",
-      "Rank of the source-module : 7.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "Computing the boundary of the generator 1/7 (dimension 5) :\n",
-      "<TnPr <TnPr * <<Abar>>> <<Abar[5 <<Abar[4 3]>>]>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "Computing the boundary of the generator 2/7 (dimension 5) :\n",
-      "<TnPr <TnPr * <<Abar>>> <<Abar[5 <<Abar[2 1][2 1]>>]>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "Computing the boundary of the generator 3/7 (dimension 5) :\n",
-      "<TnPr <TnPr * <<Abar[2 1]>>> <<Abar[3 <<Abar[2 1]>>]>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "Computing the boundary of the generator 4/7 (dimension 5) :\n",
-      "<TnPr <TnPr * <<Abar[5 4]>>> <<Abar>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "Computing the boundary of the generator 5/7 (dimension 5) :\n",
-      "<TnPr <TnPr * <<Abar[2 1][3 2]>>> <<Abar>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "Computing the boundary of the generator 6/7 (dimension 5) :\n",
-      "<TnPr <TnPr * <<Abar[3 2][2 1]>>> <<Abar>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "Computing the boundary of the generator 7/7 (dimension 5) :\n",
-      "<TnPr <TnPr M3 <<Abar[2 1]>>> <<Abar>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 4 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 5.\n",
-      "Rank of the source-module : 7.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "Computing the boundary of the generator 1/7 (dimension 5) :\n",
-      "<TnPr <TnPr * <<Abar>>> <<Abar[5 <<Abar[4 3]>>]>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "Computing the boundary of the generator 2/7 (dimension 5) :\n",
-      "<TnPr <TnPr * <<Abar>>> <<Abar[5 <<Abar[2 1][2 1]>>]>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "Computing the boundary of the generator 3/7 (dimension 5) :\n",
-      "<TnPr <TnPr * <<Abar[2 1]>>> <<Abar[3 <<Abar[2 1]>>]>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "Computing the boundary of the generator 4/7 (dimension 5) :\n",
-      "<TnPr <TnPr * <<Abar[5 4]>>> <<Abar>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "Computing the boundary of the generator 5/7 (dimension 5) :\n",
-      "<TnPr <TnPr * <<Abar[2 1][3 2]>>> <<Abar>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "Computing the boundary of the generator 6/7 (dimension 5) :\n",
-      "<TnPr <TnPr * <<Abar[3 2][2 1]>>> <<Abar>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "Computing the boundary of the generator 7/7 (dimension 5) :\n",
-      "<TnPr <TnPr M3 <<Abar[2 1]>>> <<Abar>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 6.\n",
-      "Rank of the source-module : 14.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "Computing the boundary of the generator 1/14 (dimension 6) :\n",
-      "<TnPr <TnPr * <<Abar>>> <<Abar[6 <<Abar[5 4]>>]>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "Computing the boundary of the generator 2/14 (dimension 6) :\n",
-      "<TnPr <TnPr * <<Abar>>> <<Abar[6 <<Abar[2 1][3 2]>>]>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "Computing the boundary of the generator 3/14 (dimension 6) :\n",
-      "<TnPr <TnPr * <<Abar>>> <<Abar[6 <<Abar[3 2][2 1]>>]>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "Computing the boundary of the generator 4/14 (dimension 6) :\n",
-      "<TnPr <TnPr * <<Abar>>> <<Abar[3 <<Abar[2 1]>>][3 <<Abar[2 1]>>]>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "Computing the boundary of the generator 5/14 (dimension 6) :\n",
-      "<TnPr <TnPr * <<Abar[2 1]>>> <<Abar[4 <<Abar[3 2]>>]>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "Computing the boundary of the generator 6/14 (dimension 6) :\n",
-      "<TnPr <TnPr * <<Abar[3 2]>>> <<Abar[3 <<Abar[2 1]>>]>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "Computing the boundary of the generator 7/14 (dimension 6) :\n",
-      "<TnPr <TnPr M3 <<Abar>>> <<Abar[3 <<Abar[2 1]>>]>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "Computing the boundary of the generator 8/14 (dimension 6) :\n",
-      "<TnPr <TnPr * <<Abar[6 5]>>> <<Abar>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "Computing the boundary of the generator 9/14 (dimension 6) :\n",
-      "<TnPr <TnPr * <<Abar[2 1][4 3]>>> <<Abar>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "Computing the boundary of the generator 10/14 (dimension 6) :\n",
-      "<TnPr <TnPr * <<Abar[3 2][3 2]>>> <<Abar>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "Computing the boundary of the generator 11/14 (dimension 6) :\n",
-      "<TnPr <TnPr * <<Abar[4 3][2 1]>>> <<Abar>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "Computing the boundary of the generator 12/14 (dimension 6) :\n",
-      "<TnPr <TnPr * <<Abar[2 1][2 1][2 1]>>> <<Abar>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "Computing the boundary of the generator 13/14 (dimension 6) :\n",
-      "<TnPr <TnPr M3 <<Abar[3 2]>>> <<Abar>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "Computing the boundary of the generator 14/14 (dimension 6) :\n",
-      "<TnPr <TnPr N4 <<Abar[2 1]>>> <<Abar>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 5 :\n",
-      "\n",
-      "\n",
-      "Component Z/4Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 48m 17s.\n",
-      "\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 47,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(homology x5 4 6)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "So $\\pi_5(\\mathrm{Moore}(\\mathbb{Z}/2\\mathbb{Z}))$ is $\\mathbb{Z}/4\\mathbb{Z}$."
-   ]
-  }
- ],
- "metadata": {
-  "kernelspec": {
-   "display_name": "SBCL Lisp",
-   "language": "lisp",
-   "name": "lisp"
-  },
-  "language_info": {
-   "codemirror_mode": "text/x-common-lisp",
-   "mimetype": "text/x-common-lisp",
-   "name": "common-lisp",
-   "pygments_lexer": "common-lisp",
-   "version": "X3J13"
-  }
- },
- "nbformat": 4,
- "nbformat_minor": 1
-}
diff --git a/examples/01_Chain_Complexes.ipynb b/examples/01_Chain_Complexes.ipynb
deleted file mode 100644
index 66e7264..0000000
--- a/examples/01_Chain_Complexes.ipynb
+++ /dev/null
@@ -1,2582 +0,0 @@
-{
- "cells": [
-  {
-   "cell_type": "code",
-   "execution_count": 1,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "To load \"kenzo\":\n",
-      "  Load 1 ASDF system:\n",
-      "    kenzo\n",
-      "; Loading \"kenzo\"\n",
-      "\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "#<PACKAGE \"CAT\">"
-      ]
-     },
-     "execution_count": 1,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(ql:quickload \"kenzo\")\n",
-    "(in-package :cat)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "# Chain Complexes\n",
-    "\n",
-    "## Introduction\n",
-    "\n",
-    "In the Kenzo program, a *chain complex* $(C_p, d_p)$ is a collection of free $\\mathbb{Z}$-modules $(C_p)$, one for each\n",
-    "$p \\in \\mathbb{Z}$, together with a homomorphism $d_p : C_p \\rightarrow C_{p-1}$, such\n",
-    "that, for all $p$, $d_{p-1} \\circ d_p = 0$. (See, for example, __P.J. Giblin__ in *Graph, Surface and Homology*, Chapman and Hall Math. series, 1981.)\n",
-    "\n",
-    "In the Kenzo program, a *morphism* $f=(f_p)$, of degree $k$, from a chain complex $(C_p, d_p)$ to another $(C'_p, d'_p)$ is a collection of homomorphisms\n",
-    "\n",
-    "$$f_p : C_p \\rightarrow C'_{p+k}.$$\n",
-    "\n",
-    "This is expressed by the following diagram, generally not assumend commutative .\n",
-    "\n",
-    "$$\n",
-    "\\begin{aligned}\n",
-    "\\cdots & \\leftarrow & C_{p-1} & \\quad\\xleftarrow{d_p} & C_p & \\quad\\xleftarrow{d_{p+1}} & C_{p+1}  & \\quad\\leftarrow & \\cdots \\\\\n",
-    "       &    & f_{p-1} \\Bigg\\downarrow &    & f_p \\Bigg\\downarrow &    & f_{p+1} \\Bigg\\downarrow \\\\\n",
-    "\\cdots & \\leftarrow & C'_{p+k-1} & \\quad\\xleftarrow{d'_{p+k}} & C'_{p+k} & \\quad\\xleftarrow{d'_{p+k+1}} & C'_{p+k+1} & \\quad\\leftarrow & \\cdots \\end{aligned}\n",
-    "$$\n",
-    "\n",
-    "Three types of   morphisms are most generally considered.\n",
-    "\n",
-    "1. $k=0$. If the commutativity relation $d'_p\\circ f_p=f_{p-1}\\circ d_p$ holds for every $p$, then the morphism $f$ is an ordinary chain complex morphism or *chain map*.\n",
-    "2. $k=-1$. If $(C_p,d_p)=(C'_p,d'_p)$ and $f_p=d_p$, then $f$ is the *differential* of the chain complex $(C_p,d_p)$ and, in fact, this differential is implemented in the ${\\tt Kenzo}$ program as a morphism of degree $-1$. Also, if $d_p \\neq f_p$ and $(d_{p-1}+f_{p-1})(d_p+f_p) = 0$ for every $p$, then $f_\\ast$ is a perturbation of the differential $d_\\ast$.\n",
-    "3. $k=+1$. In this case, $f$ is usually a *homotopy operator*, that is, some relation $$d'_{p+1}\\circ f_p+f_{p-1}\\circ d_p=g_p-g'_p$$ is satisfied for two (ordinary) chain complex morphisms $g_\\ast$ and $g'_\\ast$, and $f_\\ast$ is a homotopy between $g_\\ast$ and $g'_\\ast$.\n",
-    "\n",
-    "For technical reasons, these three types of morphisms have been implemented in the `Kenzo` program\n",
-    "in a unique type.\n",
-    "\n",
-    "\n",
-    "## Generators, terms, and combinations\n",
-    "\n",
-    "To become familiar with the Lisp functions implementing the chain complexes, the best is to begin with an example. *Simplicial complexes* are good candidates for this purpose, and we shall take as a typical example the following simplicial complex."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 2,
-   "metadata": {
-    "scrolled": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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NJ3lCAHZK/xCOlAwGh9tL3DB4o9/v9/v98PGTHPB0Os2yTAAD9i7sSr/46leW5eYpRHme53n+0DfRyrI8nBf8LegfwvGSwaDRONReYhRFaZquu7e6MOzxqakoinUBrCzLo1gbBE5Amqbtdvvi4qLb7bbb7Xa7PRwO8zwfDocrF/zLshwOh8+fP+92u91uN3xQFMU9v12YMfukP0FN9A/h2Mlg8F8OrZfYbDazLFt3PlEd3iN38SqKIkmSxfH3iw4kjgInL0mS4XAY3hG7vb29vb0djUZ5nne73XUBrNvtTqfTOI4Hg0F4JQyPv8/WHSHdPf2PsXv6h3AC/rLvA4DDEnqJvV4v/Cc3mUz2OKI9nFL0er3r6+vlgBTOHprNZlVK3EJRFN1udzAYrEx6WZY1m03tRGDXQh06BLDqNSeO4ziOkyTJsmw5VvV6vU6nszijKMuyMKYoTdPNs4WKotjQMjhkw+EwHPnl5aXlLzheMhjcFU4Cwv9zIZ/sa1B7q9VqNBrz+fzi4mI8Hi+mwTRNw1T68Xi8ISNVa2VlWS4/LASwUOZZ9wzX19eP+REA7iO8oEVRtPxKNR6Pi6K4U0zI87zVat15ce73+9PpNM/zzXXEsiyTJBkMBscVw8J+JHmeP3v27OrqyvIXHDVdRFjtEHqJIYMNBoPwTnC73Q7XPIRrJDqdzvX1dRzHy18YLp9YvC7i4uJi+YKKj861j6LokUVHgPsIy1zrXpFGo9GddbCyLFe+OxZesjav3qdp2ul0jmsbev1DODHWwWCtQ+glTiaTkLJGo1FRFPP5vCiKOI47nU5IaCvd8/TCGhdwIEJqChMRl1++lm9Z+fZTZcObR2Gh7Pr6+oguBtM/hNMjg8Eme+8lLp5nhFWpzWceAMeoelOp1+utfMNrMpnc53mm02kURYPBYOW9oYU4m80ec6h10j+EU6WLCB93CL1EgBNWpaZqg5A7r7T36UUnSRJF0YZ9DpMk6ff7x1Kx1j+EEyaDwb0c7D7OACeg1WotTjJM0/Ti4iIM6riPsF4UxieuG8iRpum6q8gOkP2X4bTJYHBfh7mPM8Bp6Pf7ixsVzufzsIfy5s2+wg6Hz58/D4EtjHtdHng4n8+zLNs8sP5A2H8ZzoEMBg+jlwiwI3Ec39zcLF7Nlef55gWxZrMZx/FsNhuPx9VFZcv7L/d6vcFgsGGU0YHQP4QzIYPBg+klAuxIs9kcjUbhNTbcEnqG62JYq9UKk2D7/f7NzU21Z/3i44fDYavVesx29vXQP4TzIYPBNvQSAXan1WrNZrPFa7c+up9hUK2GVVeF5Xl++C1E/UM4NzIYbE8vEWB3BoNBlZ3Ksryzy/w6Yb2rymBhFMfz588/+X91u93wgOqWHfwE96J/CGdIBoNH0UsEeKQNgzf6/X7VIbznC2wYPX+ffeoPgf4hnCcZDB5LLxHgMaIoWp5kWKnS1Lpdv1aqxm/MZrPbVaqdmqtbtj38LekfwjmTweBp6CUCbKfZbGZZtm5fr+rl9J57K4flsjiOn+rwdkH/EM6cDAZPRi8RYAshXPV6vZXvXoXX0mazuTjYsCzLPM+XHx8uGxsMBofcRdQ/BGQweEp6iQAPFXqD8/n84uLizrtXaZqGKfPj8Xixi5gkSbfbbbfbiy+z8/m82+32+/3FgYoHRf8QCP6y7wOAEzQajTqdTq/XS9O0KIrJZPKgyxgAzkrIYGFr5iRJGgupbD6fdzqd0Wh0p4jY6XSm02lZlmmaZlkW7g17ix3sClie52GtL4qiq6sry19wzmQw2InQS+z1eqGXOJlMDva0AGDvJpNJuIJrNBoVRTGfz4uiiOO40+lU0zUW9fv9TqdTFEVRFK1Wq9VqRVH0oHe7Op1OnXM4hsNhmDtyeXlp+QuQwWBXQi8x/L/b7XYHg8HB1mMA9mtxhEYURVEUfXSoRoheBz57o9FolGUZ3o979uzZ1dWV8RtAw/VgsGvmJQKcLfMPgZVkMNg58xIBzpD5h8A6MhjUwbxEgPNh/iGwmQwG9dFLBDh5+ofAR8lgUCu9RIATpn8I3IcMBnXTSwQ4PfqHwP3JYLAfeokAJ0P/EHgQGQz2Ri8R4AToHwIPJYPBPuklAhwv/UNgOzIY7J9eIsDR0T8EtiaDwUHQSwQ4IvqHwGPIYHAo9BIBDp/+IfB4MhgcFr1EgIOlfwg8CRkMDo5eIsAB0j8EnooMBodILxHgcOgfAk9LBoPDpZcIsHf6h8CTk8HgoOklAuyR/iGwCzIYHDq9RID66R8CuyODwXHQSwSojf4hsFMyGBwNvUSAGugfArsmg8Ex0UsE2B39Q6AeMhgcH71EgCenfwjURgaDo6SXCPCE9A+BOslgcKz0EgEeT/8QqJ8MBsdNLxFga/qHwF7IYHD09BIBtqB/COyLDAanQC8R4P70D4H9ksHgdOglAnyU/iGwdzIYnBS9RIAN9A+BQyCDwanRSwRYpn8IHA4ZDE6TXiJARf8QOCgyGJwsvUSAhv4hcHhkMDhleonAOdM/BA6TDAanTy8ROEP6h8DBksHgLOglAmdF/xA4ZDIYnAu9ROAc6B8Ch08Gg/OilwicMP1D4CjIYHB29BKBk6R/CBwLGQzOkV4icEr0D4HjIoPB+dJLBE6A/iFwdGQwOGt6icBR0z8EjpEMBudOLxE4RvqHwPGSwYBGQy8ROCr6h8BRk8GA/6SXCBwF/UPg2MlgwH/RSwQOmf4hcBpkMOAuvUTgAOkfAidDBgNW0EsEDor+IXBKZDBgNb1E4BDoHwKnRwYDNtFLBPZI/xA4STIY8BF6icBe6B8Cp0oGAz5OLxGok/4hcNpkMOC+9BKBGugfAidPBgMe4Bx6iUVR5Hk+n8+rW8qyXPx0WZ7neZ4LpWzNb11F/xA4BzIY8DAn3EtM07Tdbl9cXHS73Xa73W63h8NhnufD4TDLsuXHl2WZJMknn3zS7Xa73e7z58+73W5RFPUfOcdri9+64XAYftlO7LdO/xA4HzIYsI3T6yUmSTIcDkPCvL29vb29HY1GeZ53u92Vp8JFUbTb7Tt35Xl+cXExnU7rOmqO20N/60JKmU6ncRwPBoMoihqNRnj85kWzw6d/CJwVGQzY0in1EqfTaZZl4VS40+mEG+M4vr6+7vf7jUZj+QQ3SZIoiq6vr8Op82QyCSfE4a4TCKXs2ha/db1eL/y7G4/Ho9Ho+vp6PB43Go2yLNM0rfn4n5D+IXBuZDBgeyfTSwwrV1EUNZvNO3eNx+Moiu5kqrBGMZvNqtwVTp3DmXRZlisXMWDRQ3/r8jxvtVqj0Wjxxn6/H37rjrSOqH8InCcZDHisE+glhgWHdUc+Go3urEhMp9M7p8LVI8MHR3pCTJ0e+ltXluXK37rwRsBykDt8+ofA2ZLBgCdw7L3EcP4aZtMt31v1xCqtVmv5xsa/zoYb60+sofLQ37o4jjcErep371joHwLnTAYDnsZR9xJbrVb4oNfrrTwhnkwmi5+Gi3A2OLoTYur30N+6dabTaRRFg8HgKQ9ul/QPAWQw4CkdaS+xOn+tAuSdI39oporj+MkOjhP1JL91YTZM+Ee3k6N8avqHAA0ZDHhyx9hLbLVai0tbaZpuN2I+fEmn07EOxkc98reuLMter5dl2Xw+P5brD/UPAQIZDHh6x9hL7Pf7k8mkWkyYz+e9Xu+h2y6FE+gjaoWxX9v91hVFkSTJ8+fPw+9bURSh2lfHEW9L/xBgkQwG7MrR9RLjOL65uVlMUA/ac7koiul0OhgMVo7rgJW2+K1rNptxHM9ms/F4XF1UNhwOD3bNWf8Q4A4ZDNiho+slNpvN0WgUjjncEhpf94lhSZLEcbxyejhs8NDfujCWs9Pp9Pv9m5ubsKFz41/LsIdG/xBgmQwG7NYx9hJbrdZsNltMU0mSbF7HCz/XR+clwjpb/NYF1WrYoV0Vpn8IsI4MBtTh6HqJjUZjMBhUmaosyyzL1j0yy7I8z49oNh0H6/6/dYvCUthBZTD9Q4ANZDCgJgfbS9wwAqHf71dFr3UHPJ1OsywTwHiQR/7W3RHmcB7OhYj6hwCbyWBAfQ6zlxhF0YaZctV57cqIVRTFugBWluVRLPexF4/5rVunms+xR/qHAPchgwF1O7ReYrPZzLJsXY+rOrzlLb/CiPDF2eKLDiRhcpi2/q1bKSyX7X1ncP1DgHv6y74PADhHoZfY6/XCSdtkMtljjSqc5vZ6vevr6+U0Fc5um81mVQ8LwqZMg8Fg5Wl0lmXNZlM7kXW2+K0ry7IoiiiK7jw+XDa2900RhsNhWNm7vLy0/AWwmQwG7EfoJYbzthBm9jXVPTS45vP5xcXFeDxePJFN0zTM+x6Px4snviGAlWW5YbHr+vp6l0fNcdvity5Jkul0GoJZ9Y8lbOu8eEv9wiT9PM+fPXt2dXVl+Qvgo2QwYJ9Go1Gn0+n1emmaFkWxrte3U+FsOGySmyRJY+H8eD6fdzqd0Wh0pxL20aHhURTds0XGedrit67T6Uyn07Is0zTNsizcG/YW2+MKWJ7nvV6vLMsoiq6urozfALgPGQzYs0PoJU4mk3AtzWg0KopiPp8XRRHHcafTWTnnwBoXj/fQ37p+v9/pdIqiKIqi1Wq1Wq3lXmLN9A8BtiODAfu3917i4jCDsIS19/EGnLwtfutC9DqEX079Q4DHMBcROBSHNi8RWMn8Q4BHksGAA3Kw+zgDgf2XAR5PBgMOy2Hu4wzYfxngqchgwCHSS4SDon8I8IRkMOBA6SXCgdA/BHhaMhhwuPQSYb/0DwF2QQYDDp1eIuyF/iHAjshgB6coijzP5/N5dUtZlouf3udLPupBD4a900uEmukfAuyODHZA0jRtt9sXFxfdbrfdbrfb7eFwmOf5cDjMsmzll0yn03a7nSRJnue9Xq/dbk+n083fZT6fJ0nSbrd38BPADuklQj30DwF2TQY7FEmSDIfDcJZ5e3t7e3s7Go3yPO92u+sCWJIkvV6v3+9fX1+PRqPr6+s4jnu93rrHV+lr3QPg8Oklwk7pHwLUQAY7CNPpNMuyEMA6nU64MY7j6+vrfr/fWFUdDF/SarUGg0F142g0arVaSZIsr4ZlWTadTuM4brVau/xRYOf0EmFH9A8B6iGDHYQQmaIoajabd+4aj8dRFC2/2R+KWIsBLAiZbbmm1e/3B4NBp9ORwTgBeonwtPQPAeokgx2EsMy1rlU1Go3urINNp9NwS7VoVgm3zOfzj14YBsdOLxGehP4hQM1ksIMQlr/CeMPle5eDVnhYs9lcXtSKomjxMXDa9BLhkfQPAeongx2EKkr1er2VJ5GTyWTx06q7uPLZQmZzMsqZ0EuE7egfAuyLDHYQqsu6qpPIO62qxbhVluV9Old2AOOs6CXCg+gfAuyRDHYQWq3WeDyuPk3T9OLiYt0FXUVRhA+WB3jcYSmMs6KXCPekfwiwXzLYoej3+5PJpIpV8/m81+t1u90Ny1kmHMIdeomwmf4hwCGQwQ5IHMc3NzeL4+bzPN+wIAaspJcIK+kfAhwIGeywNJvN0WgU+lThlrIse72eGAYPopcId+gfAhwOGewQtVqt2Ww2Go2qW5Ikqd7Lr+ZzVBeGrbM81B7Oh14iBPqHAIdGBjtcg8GgGtRRlmWWZeHjZrP50WkcjXtM7IBzoJfImdM/BDhAMtj+bRi80e/3+/1++HixTBUWuNZ9VVgfswgGgV4iZ0v/sDa///7727dv//zzz+qWDx8+LH667O3bt2/fvv3w4cODvtGHDx/evn27xeE99EvOTVEUeZ4vnlmVZXnPbX7Kstzif5aPtpk4bX/Z9wHQiKIoTdPF2fSLOp1OWAFbXNfqdDrT6XQ+n5dleWe9q9o9TAaDSuglDofDsBo2GAwWu75wesK1xHmeP3v27OrqyvLX7vz888+//PLLH3/8ET79/PPPv/nmmyiKfvvtt2fPni03Pz98+PDzzz+/fv36/fv34ZYoivr9/hdffHGfb3d1dVUUxT//+c91D/jhhx9W3v7jjz/e5/nPUJqmWZZVcavVasVxHE60wlX6H32G8G/t9vZ23QO63e7K22ez2XbHzAmQwfYvtKT6/f7iRsyV5cvAGo1GHMdhH+c8z8Fd5igAACAASURBVOM4Xnx8mN7RbDarBTQgGI1GnU6n1+ulaVoUxeJuEHBK8jzv9XplWUZRdHV1Zflrd/7xj3+8fv36yy+/fPnyZQi6b968+fnnn1+9etVoNC4vL+88/sOHDz/88MP79++/+eabZ8+eFUXx7t27oih++OGH8Xj82Wefbf52P/300+bFk19++WXlA66urh70c52PJEmyLIuiaDabhTevp9NpmqZpmjYajcVR1esMh8PNi2BZlq18wGQy2faoOQUy2P6FcNXr9a6vr5fPCMO/2zuZKnyapul0Ol2Zwe7zqgFnKPQSw3uW7XZ7MplYMebEhPXeRqNxeXlp/MZOvXnz5vXr18+ePVvseX799ddff/11yGbV4ljl6uoqiqLq7+X777//5ZdfXr58+f79+59//vlvf/vbhm/3+++/h2i3wc8///zNN998/vnnd27/+uuvH/CDnY3pdJplWShKVCdgcRzHcRyy2Ue7iEVRhH9uG6RpGsfx8p6ud87fODcy2P6Ff5bz+fzi4mI8Hi+eEYaU1Wg0xuPxnXg2Go3yPJ9Op4sxLLzX0u/3N2SwamFtuccI5+BOL/Hf/u3f/uf//J/7Pih4Ah8+fPjxxx//7//9v/qH9fjtt98ajcYXX3yxvNL4t7/97ffff6/ahsHbt28///zzO8H422+//e2334qi2HzJ1ocPH/7xj39cXl5uiGFv3rx5//79ixcvrHzeUzjFiqJo+XRoPB4XRbF5jFNZlkmSDAaDDTFsOp2WZbl8Fgcy2P6FDBZSU5IkjYVUNp/PO53OaDRaWVOczWZpmvZ6vcFg0Gq15vN5mqbrLnTJ8zzP86IoqpbCxcVFeGNGa5EzFP6ZpGn6+vXr//2///e+Dwee0n1abTxeGLmxbqhGv99/+fLl4i3v379f+R/ul19+WRTF5uD0888/R1EUhluue8zr16+/++47Aez+wjLXuqA1Go3CWdk6aZp2Op1Op7Mhg2VZ1u/3BTCWyWAHYTKZhLWs0WhUFMV8Pi+KIlwSurx4XQmXig4GgxCuoij6j//4j3X/zsPLxK5+ADg2VV/ru+++sw7GaajWwZIksQ5Wg5B23r179/bt2+U/7eVbNhcCv/zyy3V3vXnzpiiK//W//teGiYhv374tiuLDhw/v37//7LPPvvnmGzn8o8IpU5iIuHyOtPmsaTqd5nl+fX294WKw8PZ3WC4Loz42nNRxbmSwg7DYCQ5vdN2/JdxsNkN3eTeHBqemmhfXbDZdD8aJ+R//43+E9xdevHjherBd+/zzz0O15OrqamXo/fd///f7PM9vv/325Zdf/vWvf11574cPH16+fPnRqYavX79uNBrv3r179+5do9EIcyYuLy9F8Q2qRNTr9Vb+d7BubEaIVR+dahjmWlcVpOFw2Ol0BoOB/3do2B8MOCvVFmHVpmH7PiJ4YtW+5K9evfrhhx8euv0U91elpnAV1k8//XTnT/s+4+b/8Y9/fPHFFxt2b3v58uV333330ad6//79ncsWiqJ48eLFL7/88tFjOFvVxfNlWXa73TBxevEBK68EaTQaSZKsG2e9qCzLO//L5Hne7XZDNuPMyWDAuaj2qx0MBotTsODEhLcY/vt//+9FUVxeXm6xpS/38dlnn7148aL69NWrV0mSvHnz5p5f/uHDh7///e+vX7/+888/1w3k+Pnnn9+/f3+f9cwff/zxxx9//Oc//zkej7/77rtnz56F21++fCmGrdNqtRZ3Z03T9OLiIgzq2CBN07Is77Nv2Gw2m81mt7e319fXi1eFhaGLjzlyToAMBpy+8B5nmqZhKKINmjl5zWYzz/PBYFAt0ez7iE7Tt99+e3V1VQWeP/744+rq6ocffgjjOtb5/fff//GPf3z33XdhsuK7d+9evHjx888/33nYn3/++csvvyzGvPv44osv/va3v7169eqbb74Jt2RZZjl0nX6/v7hX5Hw+7/V63W533VT6+XyeZdlicruPKIrG4/HNzU115cjymhvnRgYDTpz+IWdLL7EGX3/99atXrxa3Yy6KYvOC2LNnz7755puXL1++ePGi2ssry7I7K5Z///vf//rXv243WuPTTz/993//9++++67RaLx//z5cLcZKcRzf3NwsbuqT5/m6BbFqGPUW3yhchBxmY5ZlaSnszMlgwCnTP+TM6SXW4NNPP/3+++9fvXpVXSD0/v37q6urdTHss88+++qrr7766qtvv/32//yf/xOSUuNfG44FP/3002efffbtt98+5sD6/X5Yo9u8+Rhh0PTim3RhetOdGDYcDh+/o89oNKrmMT7meTh2MhhwmvQPIdBLrMdnn332448/Lp6gv3z58j5rj3/729/CaliVlN6+ffv69euHthCXffrpp9VS2COf6hy0Wq07/1kkSVI1BvM836KFuKzZbFZLYY98Ko6a2fTACcrzvNfrhZlUi11/OFuj0ajT6fR6vVevXr179+7q6spmvrvw17/+9dmzZ2F35lACXDd0ftG3336bZVkYK99oNF69evX+/ftqfWzZf/tv/y188M9//nPzM/tbfqjBYNBsNsPuzKExGGqKYRTH8+fP133hJ598Ej64vb3d/C38l0TDOhhwevQPYSW9xCe0YfDGt99+W8Wne/bNwgbNH511voXQRayuOqOyYfBGv9+v1jM3bMG8tfC/kv2az5wMBpwO/UPYTC/xqXz55ZfLkwwrVZqqRibeR5WUwpT5ZWF5rdFoVLd89DlDULzPTmXnJoqiNE3X3VtdGFa9ixemzC+rdmqubvnotw7ZbxeRmyMigwEnwvxDuCfzEh/v008/ff369bpZF9X1V/cMP2G5rJom/4SKovj8888fOdvjJDWbzSzL1i1UVhdr7SIp5Xn++NkeHDsZDDgF+ofwIHqJjxTag3//+99XJthwZv/s2bPFa7o+fPjw9u3b5cd/+PDh9evXl5eXX3311XYH8+bNm59++mn5L/HNmzfv3r1zrr9SCFfhyuHle0MFsZqfsYXpdDocDperjNPptCgKNQ1kMOC46R/CdvQSHyNs2/XHH38kSXIn/Pz8889hyvyLFy8WR2KEDcEuLy8X/6j//PPPH3744bvvvvv++++3Ppirq6tXr16Fv8Qq47158ybLshcvXnz99ddbP/MJC5djzefzi4uLO0kpTdMwlX48Hm/9jl6v10vTtNvtLm7HHILZeDyuNmvmbJmLCBwx8w/hkcxL3E7IYGFr5nCZVrjlzz///OOPP6Io6vf7d4qIURT99ttv79+/f/Xq1evXr8O9z5496/f7W6+ABd99913YhfnVq1e//fbbZ5999ueff0ZR9OOPP263xfM5CBkszDwMUxCrVDafzzudzmg0ekwRsd/vh12YQ6JrtVrhaWezmWkcNBqNT5avHczzvNvtho/vc2UhZ2U4HKZpOpvNXGzD3oXfxkajMRgMLH/BY5RlGcfxr7/++uzZs6urq0dGgjPx5s2baonp999///PPP3///ffPPvssiqJ1ySc8Jjzs888//+KLL54q8d555hP4G/zpp59evXq10/ON6XRarUcVRTGfz4uiaLVanU7nSWJSeMLwnOFpH/+cHKOV2UoG42FkMA5BWZa9Xi/P82azOZlM/DbCk6je17i8vHxMNQ4er4YMBvVYma1cDwYcGfMPYUfMSwSohwwGHBPzD2GnzEsEqIEMBhwH8w+hHuYlAuyaDAYcAf1DqJleIsDuyGDAodM/hL3QSwTYERkMOFz6h7BfeokAuyCDAQdK/xAOhF4iwNOSwYBDpH+4O0VR5Hk+n8+rW8qyXPx0WZ7neZ6XZXmf53/QgzkWeokAT0gGAw6L/uHupGnabrcvLi663W673W6328PhMM/z4XCYZdny48uyTJLkk08+6Xa73W73+fPn3W63KIqVT16W5XA4DI/56IM5RnqJAE9FBgMOiP7h7iRJMhwOQ7K9vb29vb0djUZ5nne73ZUBrCiKdrt95648zy8uLqbT6Z0Hh+Q8nU7jOB4MBlEUhQd3u93NK2wcHb1EgMeTwYBDoX+4O9PpNMuyEMCqZBvH8fX1db/fbzQay0kpSZIoiq6vr0Ngm0wmIVmFu+5UDXu9XojN4/F4NBpdX1+Px+NGo1GWZZqmO//xqJdeIsAjyWDA/ukf7lpYuYqiaDnZjsfjKIruZKqw/DWbzarcFQJbyG9lWS6uj+V53mq17vyt9fv98GB1xJOklwjwGDIYsGf6hzUIy1zr5mSMRqM762DT6XRlEq5uXExWZVmufHDIb9YzT5heIsB2ZDBgn/QP6xH+YMNExOV7l3Nvq9VaGYarZbHFOBfH8Ya/uOpLOEl6iQBbkMGA/dA/rFOr1Qof9Hq9lTFsMpksfhqu5trgPslqOp1GUTQYDO59mBwlvUSAh5LBgD3QP6xZFYRC9B0Oh3d6iQ9drYrjePMDwkgPa5vnQy8R4P5kMKBu+of1a7Vai0tbaZquHDH/UeFLOp3OhsxWlmWv18uybD6fG8hxVvQSAe5JBgPqo3+4R/1+fzKZVIl3Pp/3er2H7t8VMti6emFRFEmSPH/+PDysKIrw1/3oY+do6CUC3IcMBtRE/3Dv4ji+ublZTFDr9lxeqSiK6XQ6GAzW/d01m804jmez2Xg8rq5AGw6HK69A44TpJQJsJoMBddA/PBDNZnM0Gi1m4FAdvE8MS5IkjuMNq5dhmmKn0+n3+zc3N2H358a/Vs84K3qJABvIYMBu6R8eoFardefvIkmSdbuHBcPhsHGPeYmLqtUwV4WdJ71EgHVkMGCH9A8P2WAwqDJVWZZZlq17ZJZleZ5vsYAZlsJksHOmlwiwTAYDdkX/8EBsGLzR7/erxuC6q7am02mWZdv9DYbxibL3mdNLBLhDBgOenv7hQYmiaMNwwiogrYxYRVGsC2BlWW6uL1aq+RycLb1EgEUyGPDE9A8PTbPZzLJsXSGwylHLW36FWfOLE+0XhSvENgtrax/d0JkzoZcIEPxl3wcAnJThcBiWXAaDgeWvAxHCVa/Xu76+Xk5TISY1m82qlBiE3b0Gg8HK8JZlWbPZDM9WlmVRFFEU3XnycI3Zhln2nKHw1kwcx7/++uvl5eXV1dVXX32174MCqJsMBjyNMOI8z/NmszmZTJx2H45QBZzP5xcXF+PxePGvJk3TMDh+PB4vJqgQwMqy3LDYdX19HT5IkmQ6nYYUVwXvsAf04i0QhF5ieL/mxYsXl5eX33///b4PCqBWMhjwBPI87/V6ZVl2Op111TX2JWSwsDVzkiSNhVQ2n887nc5oNLpTRPzoqPooiqov6XQ60+m0LMs0TbMsC7eHjchEcdYJvx69Xu/Vq1fv3r27urr69NNP931QADWRwYDH0j88fJPJJFyUNRqNiqKYz+dFUcRx3Ol0Vg7MqNa47qPf73c6naIoiqJotVqtVmu5lwjL9BKBsyWDAdvTPzwWi1MxwhLW087JCNHL7A0eSi8ROE/mIgJbMv8QeBLmJQLnRgYDtmH/ZeAJ2ccZOCsyGPAw9l8GdsE+zsD5kMGAB9A/BHZKLxE4BzIYcF/6h0AN9BKBkyeDAR+nfwjUSS8ROG0yGPAR+ofAXuglAqdKBgM20T8E9kgvEThJMhiwmv4hcAj0EoHTI4MBK+gfAgdFLxE4JTIYcJf+IXCA9BKBkyGDAf9F/xA4ZHqJwGmQwYD/pH8IHAW9RODYyWBAo6F/CBwVvUTgqMlgcO70D4FjpJcIHC8ZDM6a/iFw1PQSgWMkg8H50j8EToBeInB0ZDA4R/qHwCnRSwSOiwwGZ0f/EDhJeonAsZDB4LzoHwInTC8ROAoyGJwL/UPgHOglAodPBoOzoH8InBW9ROCQyWBw+vQPgTOklwgcLBkMTpn+IXDO9BKBwySDwcnSPwRo6CUCh0cGg9OkfwhQ0UsEDooMBqdG/xBgmV4icDhkMDgp+ocAG+glAodABoPToX8I8FF6icDeyWBwCvQPAe5PLxHYLxkMjp7+IcAW9BKBfZHB4LjpHwJsTS8R2AsZDI6V/iHA4+klAvWTweAo6R8CPCG9RKBOMhgcH/1DgCenlwjURgaDY6J/CLA7eolAPWQwOBr6hwA10EsEdk0Gg+OgfwhQG71EYKdkMDh0+ocA9dNLBHZHBoODpn8IsEd6icAuyGBwuPQPAfZOLxF4cjIYHCL9Q4DDoZcIPC0ZDA6O/iHAAdJLBJ6KDAaHRf8Q4GDpJQJPQgaDQ6F/CHD49BKBx5PB4CDoHwIcEb1E4DFkMNg//UOAo6OXCGxNBoN90j8EOF56icB2ZDDYG/1DgBOglwg8lAwG+6F/CHAy9BKBB5HBoG76hwCnRy8RuD8ZDGqlfwhwwvQSgfuQwaA++ocAH1UURZ7n8/m8uqUsy8VPl+V5nud5WZZbf8ftvnAlvUTgo/6y7wOAs1CWZa/Xy/O82WxOJhPLXwDL0jTNsqyKW61WK47jTqcznU6bzeZyc7ssy/AlVfrqdDqj0SiKonXfotvtrrx9Nps9xU/wn0IvcTgcpmn64sWLy8vL77///gmfHzh2MhjsXJ7nvV6vLMtOpzOZTCx/ASxLkiTLsiiKZrNZeKNqOp2maZqmaaPRGAwGdx4frq0tyzKO45B5wgJat9u9vr5utVrL3yLLsjzPl2+fTCY7+IEao9Go0+n0er1Xr169e/fu6urq008/3cU3Ao6ODAa7Fd4HbTQag8HA+A2AlabTaZZlYVJR9UZVHMdxHIdsttxF7PV6YdWruiXLsiRJwuLYeDxe/i5pmsZxvBzP4jh+0p/mv4ReYhzHv/766+Xl5dXV1VdffbWj7wUcERkMdkX/EOCeptNpo9GIomi5KTAej4uiuHOtV57nrVbrzhtb/X5/Op2GBbGV36Isy/F4XHMZQS8RWGYmB+yE+YcA9xeWudYN1RiNRnfWwcqyXNksCFeCrUxZWZb1+/19tcHNSwQWyWDw9Mw/BHiQ8DoZLuhavnf5baxwDdi6Z1ueyZH/S5IkaZpunrK4I+YlAhUZDJ6S/ZcBtlBdoxUq3MsPuOfYjOl0GkXR8gCPLMsajUZRFFmWDYfDdrvd7XZXfqOdso8zEMhg8GT0DwG2U6Wm8E7WcDi800vcMG6+kiRJGKu4vEQWJtMu3hImKIZsVjO9REAGg6ehfwiwtVartTjJME3Ti4uLMKjjPsIMpDA+ceVAjtlsNpvNbm9vr6+vF68KC0MXH3/8D6WXCGdOBoPH0j8EeLx+v7+4g+J8Pu/1et1ud/O1W0VRJEny/PnzENiKoggvyOseH0XReDwO8+LDLctrbvXQS4RzJoPBo+gfAjyVOI5vbm4Wr+bK83zzgliz2YzjeDabjcfj6qKy4XC4+VqvsGVIv99vNBplWe5lKSzQS4TzJIPB9vQPAZ5Ws9kcjUaLb2mFnuG6GNZqtTqdTqfT6ff7Nzc3IVY1/rXh2Gaj0aiax/hEh78NvUQ4QzIYbEP/EGB3Wq3WnZfWJEnu0xisVsPuE6uazWa1FPaIg30CeolwbmQweDD9Q4AaDAaDalDH/RuDIVbdc2nroPoLeolwPmQweJg99g/D7qWLl6eXZfnRq9XvfMkGYQPTvb8fDJybDYM3+v1+VS+853ZeYYr9Pd8dC6/h1YVke6eXCGdCBoP72mP/ME3Tdrt9cXHR7Xbb7Xa73Q5XnA+Hw3VvDE+n03a7nSRJnue9Xq/dbq+7OqIsyyRJPvnkk2632+12nz9/3u1293t1BHBWoijaMMmwSlMPes/rnrEqZL/7bD5WG71EOAcyGNzLHvuHSZIMh8MQ/G5vb29vb0ej0ebdRZMk6fV6/X7/+vp6NBpdX1/HcRw2z7nzyKIo2u32nds/OogM4Ak1m80sy9a99VMtzt8zKYXlsmr0/Ecf3Gq1qqW2w6GXCKdNBoOP22P/cDqdZlkWAlgV/OI4DtuMNv71Ju7yl7RarcX5zqPRqNVqJUlyJ1klSRJF0fX1dUh3k8mkOsu55xXwAI8UXnZ6vd7K15yQqar5GUFZliu70+GyscFgsPhO2XQ6XTmtfjqdFkVxsEOV9BLhhMlgsMne5x+GyBRF0XLwG4/HURQtn4IMh8NGo7EYwIJw+hLuDcLy12w2q3JXSHfh3GW/e+YA5yP0Bufz+cXFxZ2klKZpeBkcj8eLL4NJkoRu9uJr2nw+73a7/X7/zmt1r9dL07Tb7S5uxxyC2Xg8vueK2V7oJcKpksFgrUOYfxiWudatR41GozvrYNPpNNyyfLThlvl8Xi2FTafTlamyutFVYUANQgYbDAZxHCdJ0m63w+WpIWJ1Op1QqF78kuqtojRNw1WsIWKNRqPll7VqAS1N0+rC2jzPZ7PZAbYQl+klwun5y74PAA7UcDgM14gPBoM9NlWq/UNDFLxz7/ItVWln+Xr0arErz/NwNhP2Nl3+ptUjdRGBekwmk/C6NBqNiqKYz+dFUcRx3Ol0Vk7X6Pf7nU6nKIqiKFqtVqvVWtkXCMbj8WAwWHzw0e0pEt4KjOP4119/vby8vLq6+uqrr/Z9UMD2ZDC4qyzLXq+X53mz2ZxMJvv9r7o6+ej1eisPZjKZLH5adRdXPlun0wkD6MOn1cY76xzUrDDghC0uc0VRFEXRRyuCIU3ds0n4oAcfptBLDO8Pvnjx4vLy8vvvv9/3QQFb0kWE/8ch9A8XVZd1hSvTFi9mCBZjUlmW91m5uud2YY17DxYDoB56iXAaZDD4L3ucf7hOq9VaXK0KFzOsmxpfXb710SPfvNVpeP5Op2MdDODQmJcIJ0AGg0bjAOYfbtDv9yeTSRWr5vN5r9frdrsblrPuuTnpOiGDLU9WBOAQmJcIx04Gg4PrHy6L4/jm5mYxFO1uG+WiKKbT6Z3ddQA4NHqJcLxkMM7dAfYPV2o2m6PRaDEihtkhTx7DkiSJ4/igVgIBWEkvEY6UDMb5OuT+4TqtVuvOoSZJUs3hqC7f+ui+XuvWuMJupx+dlwjAgdBLhGMkg3GmDr9/uMFgMKhiUlmWWZaFj5vN5n3W8dY9JsuysGnpwS4GArCSXiIcFxmMc3Qs/cMNgzf6/X6/3w8fLw45DGFy3VeF9bGVgXM6nWZZdsh/GgBsoJcIR0QG47wcV/8wiqI0TdfdW0WpxdRUZbDljcKq3cOWM1hRFOsC2D33HANg7/QS4VjIYJyRo+sfNpvNLMvWXdy1fBlYo9GI4zjkqOUdwML0jmazWS2gBUVRJEmyOP5+UbhCDIBjoZcIh08G41wcS/9wUQhXvV5v5UpUSFl3MlX16fK8xJW7fhVF0e124zguiiJf0uv1GvfY8RmAg6KXCAfuL/s+ANi5MMM9z/NmszmZTA5/+asStlqez+cXFxfj8XjxyNM0DZlqPB7fyUij0SjP8+l0Op1O4zgON4Z5G/1+fzGDhQBWluWGxa7r6+un/aEAqEHoJQ6HwzRNX7x4cXl5+f333+/7oID/JINx4sJiTlmWnU5nXd3uYIUMFlJTkiSNhVQ2n887nc5oNFosIlZms1mapr1ebzAYtFqt+XyepulgMLhz/dviXPuVoiha+fwAHIXRaNTpdHq93qtXr969e3d1dfXpp5/u+6AAGYyTFt7/azQay/HjWEwmk7CWNRqNiqKYz+dFUcRx3Ol0Qh5bKWzoPBgM8jwviiKKov/4j/9Yzp/WuABOXuglxnH866+/Xl5eXl1dffXVV/s+KDh3Mhin6Xj7h3dUZcLGv1alFm/ZrNlsxnF8/8cDcJL0EuHQmMnBCTq6+YcAsGvmJcLhkME4Ncc4/xAAamBeIhwIGYzTcVz7LwNA/ezjDIdABuNE6B8CwD3pJcJ+yWCcAv1DAHgQvUTYIxmM46Z/CADb0UuEfZHBOGL6hwDwSHqJUD8ZjGOlfwgAT0IvEWomg3F89A8B4GnpJUKdZDCOjP4hAOyIXiLUQwbjmOgfAsBO6SVCDWQwjoP+IQDUQy8Rdk0G4wjoHwJAzfQSYXdkMA6d/iEA7IVeIuyIDMbh0j8EgP3SS4RdkME4UPqHAHAg9BLhaclgHCL9QwA4KHqJ8IRkMA6L/iEAHCa9RHgqMhgHRP8QAA6cXiI8ngzGodA/BICjoJcIjySDsX/6hwBwXPQS4TFkMPZM/xAAjpReImxHBmOf9A8B4KjpJcIWZDD2Q/8QAE6DXiI8lAzGHugfAsCJ0UuE+5PBqJv+IQCcJL1EuCcZjProHwLAadNLhPuQwaiJ/iEAnAm9RNhMBqMO+ocAcFb0EmEDGYzd0j8EgPOklwjryGDskP4hAJw5vURYJoOxK/qHAEBDLxGWyGA8Pf1DAGCRXiIsksF4YvqHAMBKeokQyGA8Jf1DAGADvURoyGA8Ff1DAOA+9BJBBuMJ6B8CAA+il8g5k8F4LP1DAGALeomcLRmM7ekfAgCPoZfIeZLB2JL+IQDwJPQSOTcyGNvIskz/EAB4Knd6iX/88ce+jwh2SAZjG9PpVP8QAHhCi73E3377bd+HAzskg7EN/UMAYBeqXuK+DwR2SAbjwfQPAYDd8VYvJ+8v+z4AjozyIQCwa+GSh30fBeyKdTAAAID6yGAAAAD1kcEAAADqI4MBAADURwYDAACojwwGAABQHxkMAACgPjIYAABAfWQwAACA+shgAAAA9ZHBAAAA6iODAQAA1EcGAwAAqI8MBgAAUB8ZDAAAoD4yGAAAQH1kMAAAgPrIYAAAAPWRwQAAAOojgwEAANRHBgMAAKiPDAYAAFAfGYwnUBRFnufz+by6pSzLxU/v8yUAABtscb6x8kme+rjgwf6y7wPguKVpmmVZ9fLXarXiOO50OtPptNlsjkaj5S+ZTqfD4bDZbHY6nTzPy7IcjUZxHNd74ADA0djifKPRaHS73ZW3z2azXR0o3I8MxvaSJMmyLIqi2WzW6XQajcZ0Ok3TNE3TRqMxGAzWfcloNKruHQ6HvV5vPB73+/06Dx4AOApbnG80Go0sy/I8X759Mpns9Gjhl9+s8wAAC71JREFUPj65vb29c1Oe59XbBsv3QjCdTnu9XrPZvLm5aTabi3eF18o4ju+8zIUvabVaNzc3i7e32+35fD6ZTKyGAQCLtjjfCNrtdhRFrVbrzu3rFs1gR1ZmK+tgbGk6nTYajSiK7rwgNhqN8XhcFEVZlnduHw6HjVXvV/X7/eFwOBwOZTAAYNEW5xvhq8qyHI/Hy18Fh8BMDrYUOtkrX/gajcZoNLpzjex0Og23hBbBonDLfD4Pr7MAAMFDzzeCLMv6/b4AxsGSwdhSeF0LE4qW710OWuFhzWZzuRUQRdHiYwAAgoeebzQajfxfkiRJ09QQZg6QDMaWqijV6/Xuc81r1SVY+WzhNVQGAwAWPfR8o9FoZFnWaDSKosiybDgcttvtbrfrHIODIoOxpeqyrrIsu93ucDi80xNYjFtlWa5rESzyThUAsOhB5xvVI++sj4WhCCGbwSGQwdhSq9Uaj8fVp2maXlxcrLugq9oP8f9v746uFEUWAAwz52wCbAh0CBiChoAhYAgQgoQgIUgIEMIQQpMCIfR9qL2Mq7bdY2vN7O73Pdlqlzx5+K2i+HBltp+pAIDFT51vBH3f933/9vb2/fv306vCwj6Kzz1c+BwNxv3Ksjwej8tX2zRN2+12s9ncmM66vBgMAOCGO843gjzPD4fD6+vrsvHy5TQa/BIajC8piuL19fV0u/lhGD78gQoA4PO+cr6RpunxeCzLMkmSeZ5NhfE70GB8VZqm+/3+9fV1WXs9z/N2u5VhAMCjfPF8Y7/fL1ssPvEo4XM0GI+RZVnf96f3nt/tdst0/3K97IdffFc3mQUASD4637ghTdNlKuyJxwefo8F4pKqqlgtnT6f70zT9zH0S3UsRAPjQe+cbtznN4PehwbjHjQthy7IMvzMlf9/kMExwvfdfYX7MJBgAsLjjfOOG0GC2B+N3oMG4R57nTdO89+qSUqc/OC0NdrkGYLl7mAYDABZ3nG/cEHLu8n5iEJ8G4x5pmrZt+97FXZeXgSVJUhRF+Iq8/LEqXE27LNQGAEjuOt+4YRiGLMucbPA70GDcI3zZbbfbqxe2hso6a6rlz8v9i8IzpxvOAgDccb7RdV1d11d/8B3H8XQzD/iFNBj3CGupp2larVZnX3NN04SmOhwOZ2sD9vt9nudd151mWNu2wzCUZanBAIBTd5xvbLfbpmk2m83p7ZhDmB0Oh+VmzfBr/fGrD4B/pPCdGKppt9slJ9+S0zSt1+uQW5f/2Pd90zTb7baqqizLpmlqmqaqKr9LAQBn7jjfKMsybJMYIi2cbKzX677v7cbB7+Pb29vb2VPDMGw2m/D48lUIuq5bfkwax3GapnEcsyxbr9cffsfN8zwMwziOeZ6v12t7xQIAV91xvhHeE94W3hnxeOHc1bbSYAAAAE9xta1cDwYAABCPBgMAAIhHgwEAAMSjwQAAAOLRYAAAAPFoMAAAgHg0GAAAQDwaDAAAIB4NBgAAEI8GAwAAiEeDAQAAxKPBAAAA4tFgAAAA8WgwAACAeDQYAABAPBoMAAAgHg0GAAAQjwYDAACIR4MBAADEo8EAAADi0WAAAADxaDAAAIB4NBgAAEA8GgwAACAeDQYAABCPBgMAAIhHgwEAAMSjwQAAAOLRYAAAAPFoMAAAgHg0GAAAQDwaDAAAIB4NBgAAEI8GAwAAiEeDAQAAxKPBAAAA4tFgAAAA8WgwAD5lGIa2bb8ywjRN4zg+6njOjOP4vMEB4IH++NUHAMATDcPQdd00Te+9Ic/zNE3X63We5zfG6bpuu90mSTLPc1VVP3sMwTiOVVXd/qCfMk1TGHYYhmmaHjs4ADyJBgP4N1uv1+v1eimoJEnKsiyKIkmSaZqWhkmSJMuyqqrKsrw6zjzPZw9+1pMmqbIsG8fxRmQCwO9GgwH8+4XoWh6v1+vTV6dpquu667rdbte27eFwuJxNKstynuc7JsGS/3dg0zT3HfwNWZZlWZbn+RcXSQJATK4HA/ivy7LseDzu9/skScZx3Gw2V+esqqra7/dpmkY/wA/8hocEADdoMACSJEmqqgpzXPM8b7fbu9ccAgC3aTAA/rLf77MsS5JkmqZnLB0EABLXgwFwqizLuq6TJGnbNqxOXMzz3LZtmqZn+3aE58dxDFNneZ6XZRla7j3Lbo1hS8b3NgKZpqnrumEYwp/r9booitsjP2kQAHgg82AA/LDs3jHPc+iWkFjb7fbPP/+s6/psB8JhGF5eXqZpOhwOfd9XVdW27Wq1urELYl3Xm82mbdtQYrvdbrVaXS59rOv65eVlnufD4XA8HouiaJrm5eUlJOInPWQQAHgsDQbAD1mWLVtcLB0V9h68fPNy5VhRFOG/wqTWPM/vLWUM9/I6Ho993x+PxzDsOI7L1vlBXddN0+z3+7A8Mky+9X2fJEnTNJ8sqIcMAgAPp8EA+Jslt8LcVFgueHVL+mX94aWu664+P03T9+/fw/74RVH0fR8+bhiGZX/5YRiapknT9OxD8zwPzzRNs6wtfM9DBgGAZ9BgANwpz/OiKIqiuDpLdtXpncqSJDltpKWIQoyd3cQsWK4ce6/xFg8ZBACeQYMB8DfL1NaHG1ekaXo8Ho/H47J88XT3i09a1jEu/xgeXP30cFPm5BP59JBBAOAZNBgAf7NcBvb52a15nsNOG/M8X516ui180NJ+t29NFvLpw9uXPWQQAHgGDQbADx/uw3GpruvVapWmad/37+0y/5Uj+eWDAMBjuT8YAD8sG2OcXbh11TzPm81mHMe+7++Y/jpzlny3J6mW1Y+3PWQQAHgs82AA/GUcx9Bgl9sJXtU0zTiOeZ5/PcCSk/0zlg3rz+5FdvXN73nIIADwDBoMgCRJknmed7tdeHy6zcYNYd+Lr88mhRWDyzrGZQru6vYeZ29+z0MGAYBn0GAAJMMwrFarcRzDVoefnCAKK/1O7xI2z/ONeaer2rad57mqqmUPw6qqwizW5Y2eu64Lt4T+8AgfMggAPIMGA/j3O92aYhiGUErDMAzDEHbU2Gw20zSVZRluoHw5wlJWp0OFhglXhdV1HYZaLuva7XZ1XS/TUCGxwqefHkxd12VZ7vf70487HA5pmk7TtEzNhWOo6zrP88PhcPrm93bD/6lBACCab29vb2dPDcOw2WzC48tXAfgHGYahbduz8jm1Xq/DFojLfbrOTNPUtm3XdUuGlWWZ53lZlsueHMvzIaVeXl7Cx1VVtcTVNE1N04Q5qCXewnuuVl/Y775t2yzLiqKY53kYhqIoTmstZGSYSQvPhPm0ZZHhZwYBgOe52lYaDIAvCWsRlxsfJ0kyz/M4jqfPXL4/OblX8m3LNNdXlg4+ZBAA+FkaDAAAIJ6rbeV6MAAAgHg0GAAAQDwaDAAAIB4NBgAAEI8GAwAAiEeDAQAAxKPBAAAA4tFgAAAA8WgwAACAeDQYAABAPBoMAAAgHg0GAAAQjwYDAACIR4MBAADEo8EAAADi0WAAAADxaDAAAIB4NBgAAEA8GgwAACAeDQYAABCPBgMAAIhHgwEAAMSjwQAAAOLRYAAAAPFoMAAAgHg0GAAAQDwaDAAAIB4NBgAAEI8GAwAAiEeDAQAAxKPBAAAA4tFgAAAA8WgwAACAeDQYAABAPBoMAAAgHg0GAAAQjwYDAACIR4MBAADEo8EAAADi0WAAAADxaDAAAIB4NBgAAEA8GgwAACAeDQYAABCPBgMAAIhHgwEAAMSjwQAAAOLRYAAAAPFoMAAAgHg0GAAAQDwaDAAAIB4NBgAAEI8GAwAAiEeDAQAAxKPBAAAA4tFgAAAA8WgwAACAeDQYAABAPBoMAAAgHg0GAAAQjwYDAACIR4MBAADEo8EAAADi0WAAAADxaDAAAIB4NBgAAEA8GgwAACAeDQYAABCPBgMAAIhHgwEAAMSjwQAAAOL54/bL3759i3McAAAA/wXmwQAAAOLRYAAAAPF8e3t7+9XHAAAA8F9hHgwAACAeDQYAABCPBgMAAIhHgwEAAMSjwQAAAOL5H7oZG+f4o4OfAAAAAElFTkSuQmCC",
-      "text/plain": [
-       "#<CL-JUPYTER-USER::PNG-BYTES {1001A24463}>"
-      ]
-     },
-     "execution_count": 2,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(cl-jupyter-user:png-from-file \"diabolo.png\")"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "In this simplicial complex, called here *diabolo*, there are 3 non-null chain groups.\n",
-    "\n",
-    "* $C_0$, the free $\\mathbb{Z}$-module on the set of vertices $\\{s_0,s_1,s_2,s_3,s_4,s_5\\}$\n",
-    "* $C_1$, the free $\\mathbb{Z}$-module on the set of edges $\\{s_{01},s_{02},s_{12},s_{23},s_{34},s_{35}, s_{45}\\}$\n",
-    "* $C_2$, the free $\\mathbb{Z}$-module on the set of triangles (here a singleton) $\\{s_{345}\\}$\n",
-    "\n",
-    "The elements of either of those groups $C_p$ are linear integer combinations of the corresponding basis $\\beta_p$, i.e. elements of the form:\n",
-    "$$\n",
-    "\\sum_{b \\in \\beta_p} \\lambda_b b.\n",
-    "$$\n",
-    "For example $2 s_{02} - 3 s_{34} \\in C_1$. An element $b$ of the basis $\\beta_p$ of $C_p$ is called a *generator* of $C_p$ and in our specific case this generator will be represented by a Lisp symbol. For instance, $s_{45}$ will be translated into `s45`. However, the user should be aware that in more realistic usage of the software, generators may be of any type. A product such as $\\lambda_i\\sigma_i$ is called a *term* and a sum of terms, a *combination*.\n",
-    "\n",
-    "### Representation of a combination\n",
-    "\n",
-    "A combination is represented internally in the system by a structure having the following general form:\n",
-    "\n",
-    "$$\\#\\texttt{S(CMBN}\\quad\\texttt{DEGREE P}\\quad\\texttt{LIST (}\\texttt{(}\\lambda_1\\cdot\\sigma_1\\texttt{)}\\dots\\texttt{(}\\lambda_k\\cdot\\sigma_k\\texttt{)))}$$\n",
-    "and containing\n",
-    "\n",
-    "1. The degree of the combination corresponding to the index $p\\in\\mathbb{Z}$ of the group $C_p$ to which this combination belongs.\n",
-    "2. The list of the internal representation of the terms, namely the list of pairs $(\\lambda_i\\cdot\\sigma_i)$.\n",
-    "\n",
-    "This choice of representation implies that only homogeneous combinations will be considered. The type `CMBN` and a printing method are provided with this internal representation. The external form of a combination is shown in the examples.\n",
-    "\n",
-    "### Ordering the generators\n",
-    "\n",
-    "In order to speed up the execution of algorithms involving combinations, the list of pairs $(\\lambda_i.\\sigma_i)$ is ordered by an adequate ordering function (ex: the lexicographical ordering on the symbols). For programming convenience, an enumerated type `CMPR` has been defined:\n",
-    "``lisp\n",
-    "(deftype cmpr() '(member :less :equal :greater))\n",
-    "``\n",
-    "A number of macros, functions and methods have been defined on usual sets (symbols, numbers, lists, etc.) taking their value in the set `[:less, :equal, :greater]`. Of course, the user may define its own function for a particular case. There exists functions to compare various couples of usual items:\n",
-    "\n",
-    "`(f-cmpr`  *n1 n2*`)` *[Function]* \n",
-    "> Return `:less`, `:equal`, `:greater`, according to the result of the canonical comparison of both integers *n1* and *n2*.\n",
-    "\n",
-    "`(s-cmpr` *symbol1 symbol2*`)` *[Function]* \n",
-    "> Return  `:less`, `:equal`, `:greater`, according to the result of the lisp comparison functions on the strings `(symbol-name` *symbol1*`)` and `(symbol-name` *symbol2*`)`\n",
-    "\n",
-    "`(l-cmpr ` *list1 list2*`)` *[Function]* \n",
-    "> Return `:less`, `:equal`, `:greater`, according to the lexicographical ordering of the two lists *list1*\n",
-    "and *list2*, making sense only if *list1* and *list2* are lists made of integers, symbols and/or lists; in the last case, the qualifier *list* is to be understood recursively.\n",
-    "\n",
-    "#### Examples"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 3,
-   "metadata": {
-    "scrolled": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       ":LESS"
-      ]
-     },
-     "execution_count": 3,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(f-cmpr 123 789)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 4,
-   "metadata": {
-    "scrolled": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       ":GREATER"
-      ]
-     },
-     "execution_count": 4,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(s-cmpr 'circulation 'circular)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 5,
-   "metadata": {
-    "scrolled": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       ":EQUAL"
-      ]
-     },
-     "execution_count": 5,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(s-cmpr 'qwerty 'qwerty)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 6,
-   "metadata": {
-    "scrolled": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       ":GREATER"
-      ]
-     },
-     "execution_count": 6,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(l-cmpr '(1 a b) '(1 a))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "1.2.3 Functions handling combinations\n",
-    "\n",
-    "The software provides a set of functions, methods, and macros to create or modify combinations.\n",
-    "\n",
-    "`(term-cmbn` *dgr cf gnr*`)` *[Macro]* \n",
-    "> Construct the combination of degree `dgr` with unique term `cf * gnr`.\n",
-    "\n",
-    "`(cmbn` *dgr cf1 gnr1 cf2 gnr2 ... cfn gnrn*`)` *[Function]* \n",
-    "> Construct a combination of degree `dgr`, sum of the terms $cf_i *  gnr_i$. The sequence of pairs $\\lbrace cf_i\\ gnr_i\\rbrace$ has an undefinite length and may be void. In this case, the combination is a null combination of degree `dgr`. It is the responsability of the user to properly order the terms of the combination, otherwise later calculations with this combination could work erroneously. This point can be checked by the `do-control` function. **[I suggest to insert here two appropriate examples.]**\n",
-    "\n",
-    "`(cmbn-p` *object*`)` *[Function]* \n",
-    "> Test is `object` is a legal combination.\n",
-    "\n",
-    "`(cmbn-degr` *cmbn*`)` *[Macro]* \n",
-    "> Get the degree (an integer) of the combination `cmbn`.\n",
-    "\n",
-    "`(cmbn-list` *cmbn*`)` *[Macro]* \n",
-    "> Get the list of the terms  of the combination `cmbn`. Beware: a term is not a structure object, it is a simple `cons` `(cffc . gnrt)`, a pair coefficient - generator. Given a term, one may select the coefficient (an integer) or the generator - a `Kenzo` object - respectively by the macros `cffc` and `gnrt`.\n",
-    "\n",
-    "`(zero-cmbn` *dgr*`)` *[Function]* \n",
-    "> Create an instance of a null combination in the degree `dgr`.\n",
-    "\n",
-    "`(cmbn-zero-p` *cmbn*`)` *[Macro]* \n",
-    "> Test if `cmbn` is a null combination in any degree.\n",
-    "\n",
-    "`(cmbn-non-zero-p` *cmbn*`)` *[Macro]* \n",
-    "> Test if `cmbn` is a non-null combination in any degree.\n",
-    "\n",
-    "`(cmbn-opps` *cmbn*`)` *[Function]*\n",
-    "> Create a combination opposite to `cmbn`.\n",
-    "\n",
-    "`(n-cmbn` *n cmbn*`)` *[Function]* \n",
-    "> Create a  combination multiple of `cmbn` by the factor `n`.\n",
-    "\n",
-    "`(2cmbn-add cmpr` *cmbn1 cmbn2*`)` *[Function]*\n",
-    "> Create a combination, sum of both combinations `cmbn1` and `cmbn2`. The first argument, `cmpr`, must be the comparison function available in the slot `cmpr` of the underlying chain complex, required to properly merge the terms of both combinations.\n",
-    "\n",
-    "`(ncmbn-add` *cmpr cmbn1 cmbn2 ... cmbnk*`)` *[Function]* \n",
-    "> Create a combination, sum of the indefinite number of combinations $cmbn_i$. As to the first argument, `cmpr`, see the function `2cmbn-add`.\n",
-    "\n",
-    "`(2n-2cmbn` *cmpr n1 cmbn1 n2 cmbn2*`)` *[Function]* \n",
-    "> Build the combination `n1 * cmbn1 + n2 * cmbn2`. Both integers `n1` and `n2` must be\n",
-    "non null. As to the first argument, `cmpr`, see the function `2cmbn-add`.\n",
-    "\n",
-    "`(2cmbn-sbtr` *cmpr cmbn1 cmbn2*`)` *[Function]* \n",
-    "> Create a combination, difference of `cmbn1` and `cmbn2`. As to the first argument, `cmpr`, see the function `2cmbn-add`.\n",
-    "\n",
-    "#### Examples"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 7,
-   "metadata": {
-    "scrolled": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 1}\n",
-       "<1 * U>\n",
-       "<2 * V>\n",
-       "<3 * W>\n",
-       "<4 * Z>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 7,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def comb1 (cmbn 1 1 'u 2 'v 3 'w 4 'z))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 8,
-   "metadata": {
-    "scrolled": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "T"
-      ]
-     },
-     "execution_count": 8,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(cmbn-non-zero-p comb1)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 9,
-   "metadata": {
-    "scrolled": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "((1 . U) (2 . V) (3 . W) (4 . Z))"
-      ]
-     },
-     "execution_count": 9,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(cmbn-list comb1)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 10,
-   "metadata": {
-    "scrolled": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(3 . W)"
-      ]
-     },
-     "execution_count": 10,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def term3 (third *))  ;; a simple cons!"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 11,
-   "metadata": {
-    "scrolled": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "3"
-      ]
-     },
-     "execution_count": 11,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(cffc term3)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 12,
-   "metadata": {
-    "scrolled": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "W"
-      ]
-     },
-     "execution_count": 12,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(gnrt term3)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 13,
-   "metadata": {
-    "scrolled": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 1}\n",
-       "<-1 * U>\n",
-       "<-2 * V>\n",
-       "<-3 * W>\n",
-       "<-4 * Z>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 13,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def mcomb1 (cmbn-opps comb1))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 14,
-   "metadata": {
-    "scrolled": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 1}\n",
-       "<10 * U>\n",
-       "<20 * V>\n",
-       "<30 * W>\n",
-       "<40 * Z>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 14,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def comb2 (n-cmbn 10 comb1))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 15,
-   "metadata": {
-    "scrolled": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 1}\n",
-       "<11 * U>\n",
-       "<22 * V>\n",
-       "<33 * W>\n",
-       "<44 * Z>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 15,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def cmb12 (2cmbn-add #'s-cmpr comb1 comb2))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 16,
-   "metadata": {
-    "scrolled": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 1}\n",
-       "<-10 * U>\n",
-       "<-20 * V>\n",
-       "<-30 * W>\n",
-       "<-40 * Z>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 16,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(2cmbn-sbtr #'s-cmpr comb1 cmb12)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 17,
-   "metadata": {
-    "scrolled": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 1}\n",
-       "<55 * U>\n",
-       "<110 * V>\n",
-       "<165 * W>\n",
-       "<220 * Z>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 17,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(ncmbn-add #'s-cmpr\n",
-    "           comb1 comb2 comb1 comb2 comb1 comb2 comb1 comb2 comb1 comb2)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "## Representation of a chain complex\n",
-    "\n",
-    "A chain complex is implemented as an instance of a `CLOS` class, \n",
-    "the class `CHAIN-COMPLEX`, whose definition is\n",
-    "\n",
-    "```commonlisp\n",
-    "(DEFCLASS CHAIN-COMPLEX ()\n",
-    "    ((cmpr  :type cmprf :initarg :cmpr  :reader cmpr1)\n",
-    "     (basis :type basis :initarg :basis :reader basis1)\n",
-    "     ;; BaSe GeNerator\n",
-    "     (bsgn :type gnrt :initarg :bsgn :reader bsgn)\n",
-    "     ;; DiFFeRential\n",
-    "     (dffr :type morphism :initarg :dffr :reader dffr1)\n",
-    "     ;; GRound MoDule\n",
-    "     (grmd :type chain-complex :initarg :grmd :reader grmd)\n",
-    "     ;; EFfective HoMology\n",
-    "     (efhm :type homotopy-equivalence :initarg :efhm :reader efhm)\n",
-    "     ;; IDentification NuMber\n",
-    "     (idnm :type fixnum :initform (incf *idnm-counter*) :reader idnm)\n",
-    "     ;; ORiGiN\n",
-    "     (orgn :type list :initarg :orgn :reader orgn)))\n",
-    "```\n",
-    "\n",
-    "This class has 8 slots:\n",
-    "\n",
-    "1. `cmpr`, a comparison function or method for  generators with a range in the set `[:less, :equal, :greater]`. It is very important to note that the generators to be compared are assumed to be of the *same degree*, i.e. they must belong to the same group $C_p$. As an exception with the general policy of the program, this degree is not explicitly precised. The implementor has chosen to avoid additional tests because in real problems the program spends a lot of time comparing generators.\n",
-    "2. `basis`, a lisp function giving the distinguished **ordered** basis of the free $\\mathbb{Z}$-modules ($C_p$). (Recall that in the program, only free chain complexes are considered.) When some  components of the chain complex are not finitely generated, we say that the chain complex is *locally effective*. In this case the value of this slot must be the keyword `locally-effective`.\n",
-    "3. `bsgn`, a lisp object of any type representing a distinguished generator in dimension 0, the base generator. \n",
-    "4. `dffr`, the differential morphism, instance of the class `MORPHISM`, defined hereafter. The pure lisp function corresponding to the differential homomorphism for each $p$ ($d_p : C_p \\rightarrow C_{p-1}$) is defined in the instance morphism object and not directly in the instance chain complex object.\n",
-    "5. `idnm`, an integer, number plate for this object. This is generated by the system in a sequential way, each time a new `Kenzo` object is created.\n",
-    "6. `orgn`, a list containing a comment to recall to the user the *origin* of the object. This comment must be chosen with care because, when the user creates a new chain complex instance, the  system `Kenzo` uses the comment list information to search in a specific list (here `*chcm-list*`) if the object has not been already built. So, one avoids the  duplication of instances of the same object.\n",
-    "\n",
-    "The two slots `grmd` and `efhm` will be explained later. The accessors of the slots are the functions whose name appears after the specifier `:reader` in the class definition. A printing method has been associated to the class `CHAIN-COMPLEX` and the external representation of a chain complex instance is a string like `[Kn Chain-Complex]`, \n",
-    "where `n` is the number plate of this `Kenzo` object.\n",
-    "\n",
-    "\n",
-    "### The function `build-chcm`\n",
-    "\n",
-    "To facilitate the construction of instances of the class `CHAIN-COMPLEX` and to free the user to call\n",
-    "the standard constructor `make-instance`, the software provides the function\n",
-    "\n",
-    "`build-chcm`\n",
-    "> `:cmpr` *cmpr* `:basis` *basis* `:bsgn` *bsgn* `:intr-dffr` *intr-dffr* `:strt` *strt* `:orgn` *orgn*\n",
-    "\n",
-    "defined with keyword parameters. The returned value is an instance of the class `CHAIN-COMPLEX`. In particular, this function frees the user to build himself the instance of the class `MORPHISM` corresponding to the differential homomorphism. The keyword arguments of `build-chcm` are:\n",
-    "\n",
-    "- `cmpr`, the comparison function for generators.\n",
-    "- `basis`, the function defining the distinguished  basis of the free $\\mathbb{Z}$-modules $C_p$ or the keyword `:locally-effective`.\n",
-    "- `bsgn`, a generator, the base point of the underlying set.\n",
-    "- `intr-dffr`, a **lisp function** defining the differential homomorphism for each $p$ ($d_p : C_p \\rightarrow C_{p-1}$).\n",
-    "- `strt`, one of the two values: `:gnrt` or `:cmbn`, defining the mapping *strategy* of the differential homomorphism, either by generator or by combination. The default is `:gnrt`. The real connection between the  arguments `intr-dffr` and `strt`will be detailed hereafter through typical examples. The general idea is the following: if the strategy is `:gnrt`, the `:intr-dffr` argument function  uses two arguments, namely a degree and a generator of this degree and computes the boundary combination of this generator. If the strategy is `:cmbn`, the `:intr-dffr` argument function uses a combination as argument and computes the boundary combination of this argument. We recall that a combination contains its own degree.\n",
-    "- `orgn`, a list containing  a relevant and carefully chosen  comment about the `origin` of the chain complex. If, during a Lisp session, the user wishes to  modify any slot of an existing chain complex, by calling again `build-chcm`, he must change also the comment, otherwise the new version of the object will not be created. This remark is valid for any kind of instantiation of `Kenzo` objects. The function `cat-init` reinitializes the environment, that is, the previous relations `orgn` $\\rightarrow$ Kenzo objects are deleted.\n",
-    "\n",
-    "\n",
-    "After creation of an instance of chain complex, the function `build-chcm` pushes this\n",
-    "object in the list of already created chain complexes `*chcm-list*`.\n",
-    "\n",
-    "#### A first example of a chain complex\n",
-    "\n",
-    "Let us consider our small example *diabolo*. We shall give the same name to the corresponding chain complex  instance. Let us define, one by one, the values of the key parameters, though it is possible to put them directly in the `build-chcm` call. First, the function `s-cmpr`, already seen above, is  the natural choice to compare generators, which are here, lisp symbols:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 18,
-   "metadata": {
-    "scrolled": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "#<FUNCTION S-CMPR>"
-      ]
-     },
-     "execution_count": 18,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def diabolo-cmpr #'s-cmpr)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "The function for the basis consists in enumerating the distinguished basis as lisp lists according to the degree:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 19,
-   "metadata": {
-    "scrolled": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "#<FUNCTION (LAMBDA (DMN) :IN \"/root/cl-jupyter/cl-jupyter.lisp\") {1001FA0ADB}>"
-      ]
-     },
-     "execution_count": 19,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def diabolo-basis #'(lambda (dmn)\n",
-    "                             (case dmn\n",
-    "                                 (0 '(s0 s1 s2 s3 s4 s5))\n",
-    "                                 (1 '(s01 s02 s12 s23 s34 s35 s45))\n",
-    "                                 (2 '(s345))\n",
-    "                                 (otherwise nil))))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "For the base point, we may choose any vertex:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 20,
-   "metadata": {
-    "scrolled": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "S0"
-      ]
-     },
-     "execution_count": 20,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def diabolo-bspn 's0)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "The lisp function for the differential homomorphism, also called boundary homomorphism, computes the boundary of each generator, in this case, according to the classical (simplicial) rule:\n",
-    "\n",
-    "$$ {\\bf d}[{s_0s_1\\ldots s_n}] = \\sum_{i=0}^n{(-1)^is_0s_1\\ldots\\widehat{s_i}\\ldots s_n}.$$\n",
-    "\n",
-    "It must be noted that our differential uses a predefined choice for the order of the vertices."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 21,
-   "metadata": {
-    "scrolled": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "#<FUNCTION (LAMBDA (DMN GNR) :IN \"/root/cl-jupyter/cl-jupyter.lisp\") {10021380BB}>"
-      ]
-     },
-     "execution_count": 21,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def diabolo-pure-dffr\n",
-    "         #'(lambda (dmn gnr)\n",
-    "                   (unless (<= 0 dmn 2)\n",
-    "                       (error \"Incorrect dimension for diabolo-dp.\"))\n",
-    "                   (case dmn\n",
-    "                       (0 (cmbn -1))  ; Note the null combination of degree -1\n",
-    "                       (1 (case gnr\n",
-    "                              (s01 (cmbn 0 -1 's0 1 's1))\n",
-    "                              (s02 (cmbn 0 -1 's0 1 's2))\n",
-    "                              (s12 (cmbn 0 -1 's1 1 's2))\n",
-    "                              (s23 (cmbn 0 -1 's2 1 's3))\n",
-    "                              (s34 (cmbn 0 -1 's3 1 's4))\n",
-    "                              (s35 (cmbn 0 -1 's3 1 's5))\n",
-    "                              (s45 (cmbn 0 -1 's4 1 's5))))\n",
-    "                       (2 (case gnr\n",
-    "                              (s345 (cmbn 1 1 's34 -1 's35 1 's45))))\n",
-    "                       (otherwise (error \"Bad generator for complex diabolo\")))))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "The  strategy is by generator and the comment recalls the name of the problem:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 22,
-   "metadata": {
-    "scrolled": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       ":GNRT"
-      ]
-     },
-     "execution_count": 22,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def diabolo-strt :GNRT)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 23,
-   "metadata": {
-    "scrolled": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(DIABOLO-FOR-EXAMPLE)"
-      ]
-     },
-     "execution_count": 23,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def diabolo-orgn '(diabolo-for-example))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "The effective call to `build-chcm` is now reduced to:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 24,
-   "metadata": {
-    "scrolled": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K1 Chain-Complex]"
-      ]
-     },
-     "execution_count": 24,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def diabolo (build-chcm :cmpr diabolo-cmpr :basis diabolo-basis\n",
-    "                         :bsgn diabolo-bspn :intr-dffr diabolo-pure-dffr\n",
-    "                         :strt diabolo-strt :orgn diabolo-orgn))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "The value of the symbol `diabolo` is the `CHAIN-COMPLEX` instance which is here the first created `Kenzo` object. The string `[K1 Chain-Complex]` is printed by the printing method associated to the class.\n",
-    "\n",
-    "### Simple functions handling chain complexes\n",
-    "\n",
-    "`(cat-init)` *[Function]*\n",
-    "> Clear among others, the list `*chcm-list*`, list of user created chain complexes  and reset the global counter to 1. The existing objects and in particular here the chain complexes, are not destroyed but they will not enter any more in account during the search process for duplicated objects. This remark is general for the other types of objects saved in specific lists. \n",
-    "\n",
-    "`(chcm` *n*`)` *[Function]*\n",
-    "> Return from the list `*chcm-list*` the chain complex instance whose the Kenzo identification is `n`; if it does not exist, return `NIL`.\n",
-    "\n",
-    "`(cmpr` *object item1 item2*`)` *[Macro]*\n",
-    "> Apply the comparison function associated to the chain complex `object` to the two generators `item1` and `item2`.\n",
-    "\n",
-    "`(basis` *object n*`)` *[Macro]*\n",
-    "> With only one argument (`object`), get the  function attached to the slot `basis` of the chain complex object. With two arguments, get the distinguished basis of the group of degree `n` in the chain complex `object`. If the chain complex is locally effective, this function returns an error because, in some degrees, the corresponding set of generators is probably infinite.\n",
-    "\n",
-    "`(dffr` *chcm* `&rest)` *[Macro]* \n",
-    "> Versatile macro to apply the differential morphism of the chain complex `chcm` either to a combination or a generator with a degree, respectively `(dffr chcm cmbn)` or `(dffr chcm degr gnrt)`. The macro `?`, described later, may be used for the same purpose.\n",
-    "\n",
-    "`(z-chcm)` *[Function]* \n",
-    "> Build the unit chain complex (see hereafter).\n",
-    "\n",
-    "#### Examples\n",
-    "\n",
-    "Let us apply some accessors functions and the simple  functions above to the chain complex `diabolo`. First, we see that the list `*chcm-list*` contains only one element, namely the chain complex just created."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 25,
-   "metadata": {
-    "scrolled": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "([K1 Chain-Complex])"
-      ]
-     },
-     "execution_count": 25,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "*chcm-list*"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 26,
-   "metadata": {
-    "scrolled": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K1 Chain-Complex]"
-      ]
-     },
-     "execution_count": 26,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(chcm 1)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 27,
-   "metadata": {
-    "scrolled": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(DIABOLO-FOR-EXAMPLE)"
-      ]
-     },
-     "execution_count": 27,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(orgn diabolo)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 28,
-   "metadata": {
-    "scrolled": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "1"
-      ]
-     },
-     "execution_count": 28,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(idnm diabolo)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 29,
-   "metadata": {
-    "scrolled": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(S0 S1 S2 S3 S4 S5)"
-      ]
-     },
-     "execution_count": 29,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(basis diabolo 0)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 30,
-   "metadata": {
-    "scrolled": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(S01 S02 S12 S23 S34 S35 S45)"
-      ]
-     },
-     "execution_count": 30,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(basis diabolo 1)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 31,
-   "metadata": {
-    "scrolled": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(S345)"
-      ]
-     },
-     "execution_count": 31,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(basis diabolo 2)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 32,
-   "metadata": {
-    "scrolled": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 32,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(basis diabolo 10)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 33,
-   "metadata": {
-    "scrolled": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 1}\n",
-       "<1 * S34>\n",
-       "<-1 * S35>\n",
-       "<1 * S45>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 33,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(dffr diabolo 2 's345)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 34,
-   "metadata": {
-    "scrolled": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 0}\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 34,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(dffr diabolo *)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "#### An important trivial case: the unit chain complex, $\\mathbb{Z}$\n",
-    "\n",
-    "The unit chain complex, has a unique non null component, namely a $\\mathbb{Z}$-module of degree 0 generated by a unique generator, called here `:Z-gnrt`. It is defined by the following call to `build-chcm`:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 35,
-   "metadata": {
-    "scrolled": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K3 Chain-Complex]"
-      ]
-     },
-     "execution_count": 35,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def ZCC\n",
-    "    (the chain-complex\n",
-    "         (build-chcm\n",
-    "          :cmpr #'(lambda (gnrt1 gnrt2)\n",
-    "                          (declare (ignore gnrt1 gnrt2))\n",
-    "                          (the cmpr :equal))\n",
-    "          :basis #'(lambda (n)\n",
-    "                           (the list\n",
-    "                                (if (zerop n) '(:Z-gnrt) +empty-list+)))\n",
-    "          :bsgn :Z-gnrt\n",
-    "          :intr-dffr #'(lambda (cmbn)\n",
-    "                               (the cmbn (zero-cmbn (1- (cmbn-degr cmbn)))))\n",
-    "          :strt :cmbn\n",
-    "          :orgn '(zcc-constant))))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "In this definition,\n",
-    "\n",
-    "1. The `:cmpr` keyword argument is a function  returning `:equal` on any pair on generators (because there is a unique generator!).\n",
-    "2. The `:basis` keyword argument is a lisp function returning the null basis (the constant `+empty-list+ = ()`) for $p \\not= 0$ and the list `(:Z-gnrt)`, for $p=0$.\n",
-    "3. The base generator is of course `Z-gnrt`.\n",
-    "4. The `:intr-dffr` keyword argument is a lisp function defining the differential  which, to any combination of degre $p$ of the chain complex, returns a *null combination* of degree $p-1$. This simple lisp function is also provided in `Kenzo` and is called `#'zero-intr-dffr`.\n",
-    "5. The `:strt` keyword argument is the combination strategy (`:cmbn`).\n",
-    "6. The `:orgn` keyword argument is the comment list `(zcc-constant)`.\n",
-    "\n",
-    "In the program `Kenzo`, the chain complex instance `ZCC` may be built, when needed, by the lisp statement: `(z-chcm)`. This statement may be used freely each time one needs this chain complex, since the system  recognizes if it has already been created.\n",
-    "\n",
-    "#### The chain complex `circle`\n",
-    "\n",
-    "On the model of the previous chain complex, one may define a function `circle` for building the chain complex associated to the standard model of the circle as a simplicial set."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 36,
-   "metadata": {
-    "scrolled": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "MY-CIRCLE"
-      ]
-     },
-     "execution_count": 36,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(defun MY-CIRCLE ()\n",
-    "    (the chain-complex\n",
-    "         (build-chcm\n",
-    "          :cmpr #'(lambda (gnrt1 gnrt2)\n",
-    "                          (declare (ignore gnrt1 gnrt2))\n",
-    "                          (the cmpr :equal))\n",
-    "          :basis #'(lambda (dmns)\n",
-    "                           (the list\n",
-    "                                (case dmns (0 '(*)) (1 '(s1))\n",
-    "                                    (otherwise +empty-list+))))\n",
-    "          :bsgn '*\n",
-    "          :intr-dffr #'zero-intr-dffr\n",
-    "          :strt :cmbn\n",
-    "          :orgn '(circle))))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "## Morphisms\n",
-    "\n",
-    "Algebraic Topology uses morphisms between chain complexes and the differential homomorphism may be considered as a particular case of  morphism. A morphism is implemented in the system as an instance of the class `MORPHISM`, whose definition is:\n",
-    "\n",
-    "```commonlisp\n",
-    "(DEFCLASS MORPHISM ()\n",
-    "     ;; SOuRCe\n",
-    "    ((sorc :type chain-complex :initarg :sorc :reader sorc)\n",
-    "     ;; TaRGeT\n",
-    "     (trgt :type chain-complex :initarg :trgt :reader trgt)\n",
-    "     ;; DEGRee\n",
-    "     (degr :type fixnum :initarg :degr :reader degr)\n",
-    "     ;; INTeRnal\n",
-    "     (intr :type intr-mrph :initarg :intr :reader intr)\n",
-    "     ;; STRaTegy\n",
-    "     (strt :type strt :initarg :strt :reader strt)\n",
-    "     ;; CaLl NuMber\n",
-    "     (???-clnm :type fixnum :initform 0 :accessor ???-clnm)\n",
-    "     (?-clnm :type fixnum :initform 0 :accessor ?-clnm)\n",
-    "     ;; ReSuLTS\n",
-    "     (rslts :type simple-vector  :reader rslts)\n",
-    "     ;; IDentification NuMber\n",
-    "     (idnm :type fixnum :initform (incf *idnm-counter*) :reader idnm)\n",
-    "     ;; ORiGiN\n",
-    "     (orgn :type list :initarg :orgn :reader orgn)))\n",
-    "```\n",
-    "\n",
-    "This class has 10 slots:\n",
-    "\n",
-    "1. `sorc`, an object of the class `CHAIN-COMPLEX`, namely the *source* chain complex of this morphism.\n",
-    "2. `trgt`, an object of the class `CHAIN-COMPLEX`, namely the *target* chain complex of this morphism.\n",
-    "3. `degr`, an integer, the degree of the morphism. A morphism is supposed to associate to any element of degree $k$ of the source chain complex, an element of degree $k + degr$ of the target chain complex. For instance, a differential homomorphism is of degree -1.\n",
-    "4. `intr`, a **pure lisp function** implementing the mathematical algorithm of the morphism and taking in account the strategy (`strt`).\n",
-    "5. `strt`, one of the two symbols `:gnrt`, `:cmbn`. What has already been said about the strategy of the differential morphism is generalized to any morphism: according  to the value of the argument, `:gnrt` or `:cmbn`, the lisp function attached to the keyword just above, works respectively with 2 arguments (a degree and a generator) or only one (a combination) and must return a combination, image of the generator or the combination argument. \n",
-    "6. `???-clnm`, an integer updated by the system for statistics (number of times the morphism has been called on combinations - Internal use)\n",
-    "7. `?-clnm`, analogous to the previous field, but for generators.\n",
-    "8. `rslts`, an array of dimension `*maxdim*` reserved by the system to save  computed results in order to avoid  re-computing, for instance, the differential of the same generator. - Internal use.\n",
-    "9. `idnm`, an integer, number plate for this object. This is generated by the system.\n",
-    "10. `orgn`, a relevant comment list.\n",
-    "\n",
-    "The accessors of the slots are the functions whose name appears after the specifier `:reader` or after the specifier `:accessor` in the class definition. A printing method has been associated to the class `MORPHISM` and the external representation of an instance is a string like `[Kn Morphism (degree d): Kp -> Kq]` or `[Kn Cohomology-Class (degree d)]` when the chain complex target is the unit $\\mathbb{Z}$. In this string, `n` is the number plate of the `Kenzo` object, `d` is the degree of the morphism, `Kp` is the `Kenzo` object source of the morphism and `Kq` the target. In all the  examples of this manual, the last part of the string will not be necessarily printed."
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "### The function `build-mprh`\n",
-    "\n",
-    "To facilitate the construction of instances of the class `MORPHISM` and to free  the user to call the standard constructor `make-instance`, the software provides the function `build-mrph`\n",
-    "\n",
-    "`build-mrph`\n",
-    "> `:sorc` *sorc* `:trgt` *trgt* `:degr` *degr* `:intr` *intr* `:strt` *strt* `:orgn` *orgn*\n",
-    "\n",
-    "\n",
-    "defined with keyword parameters. The returned value is an instance of the class `MORPHISM`. The keyword arguments of `build-mrph` are:\n",
-    "\n",
-    "- *sorc*, the source object, a `CHAIN-COMPLEX` type object.\n",
-    "- *trgt*, the target object, a `CHAIN-COMPLEX` type object.\n",
-    "- *degr*, the degree of the morphism, an integer.\n",
-    "- *intr*, the pure lisp function defining the effective mapping.\n",
-    "- *strt*, the strategy, i.e. `:gnrt` or `:cmbn`.\n",
-    "- *orgn*, a relevant comment list.\n",
-    "\n",
-    "After a call to `build-mrph`, the morphism instance is added to a list of previously constructed  ones (`*mrph-list*`).\n",
-    "\n",
-    "#### The differential homomorphism in a chain complex instance\n",
-    "\n",
-    "In a  chain complex instance, the differential homomorphism is defined as a morphism with identical source and target, and degree -1. The user must know that the function `build-chcm` calls internally the function `build-mrph` and passes it the keyword argument `intr-dffr`. The function `build-mrph` builds the  morphism instance which will be then inserted into the slot `:dffr` of the chain complex instance to be constructed.\n",
-    "\n",
-    "##### Example\n",
-    "\n",
-    "Let us define respectively a *zero--morphism* of degree -1 and an *identity-morphism* (degree 0)  between  the *unit chain complex* `ZCC` and itself."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 37,
-   "metadata": {
-    "scrolled": false
-   },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "---done---"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 37,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(cat-init)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 38,
-   "metadata": {
-    "scrolled": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K1 Chain-Complex]"
-      ]
-     },
-     "execution_count": 38,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def ZCC (z-chcm))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 39,
-   "metadata": {
-    "scrolled": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K3 Cohomology-Class on K1 of degree 1]"
-      ]
-     },
-     "execution_count": 39,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def zero-morphism (build-mrph :sorc ZCC\n",
-    "                               :trgt ZCC\n",
-    "                               :degr -1\n",
-    "                               :intr #'(lambda (comb)\n",
-    "                                               (cmbn (1- (degr comb))))\n",
-    "                               :strt :cmbn\n",
-    "                               :orgn '(zero morphism on ZCC)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 40,
-   "metadata": {
-    "scrolled": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K4 Cohomology-Class on K1 of degree 0]"
-      ]
-     },
-     "execution_count": 40,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def id-morphism (build-mrph :sorc ZCC\n",
-    "                             :trgt ZCC\n",
-    "                             :degr 0\n",
-    "                             :intr #'identity\n",
-    "                             :strt :cmbn\n",
-    "                             :orgn '(identity morphism on ZCC)))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "On the first morphism, we see that the  `:intr` keyword argument is a lisp function taking any combination of degree `p` of the  unit chain complex and generating a null combination of degree `p-1` of the same chain complex. The second morphism uses the lisp function `identity`.\n",
-    "\n",
-    "### Applying morphisms\n",
-    "\n",
-    "To apply an already constructed morphism on a generator, one uses the function `gnrt-?`, the usage of which is described hereafter. On a similar way, to apply a morphism on a combination, one uses the function `cmbn-?`. It is very important to note that these functions can be used with the underlying morphism, **whatever strategy had been decided\n",
-    "at creation time by the user for the morphism mapping**. In other words, a morphism defined with the strategy `:gnrt` (resp. `:cmbn`) may be applied to a combination (resp. generator). These functions are mainly used inside the software. For a practical usage, one may use the versatile macro `?`.\n",
-    "\n",
-    "`(gnrt-? mrph degr gnrt)` *[Function]*\n",
-    "> Apply the morphism `mrph` on the generator `gnrt` of degree `degr`.\n",
-    "\n",
-    "`(cmbn-? mrph cmbn)` *[Function]*\n",
-    "> Apply the morphism `mrph` on the combination `cmbn`.\n",
-    "\n",
-    "`(? &rest args)` *[Macro]*\n",
-    "> Versatile macro for applying a morphism  in both cases above, i.e. indifferently as `(? mrph degr gnrt)` or  `(? mrph cmbn)`. If the first argument is a chain complex object, as in `(? chcm degr gnrt)` or in  `(? chcm cmbn)`, then the differential morphism of the chain complex `chcm` is applied to the arguments.\n",
-    "\n",
-    "### Functions defining morphisms\n",
-    "\n",
-    "The following functions are useful to work on morphisms, particularly to define new morphisms from already defined ones.\n",
-    "\n",
-    "`(cat-init)` *[Function]*\n",
-    "> Clear in particular `*mrph-list*`, the list of user created morphisms and reset the global counter to 1.\n",
-    "\n",
-    "`(mrph` *n*`)` *[Function]*\n",
-    "> Retrieve in the list `*mrph-list*` the morphism instance whose identification is `n`. If it does not exist, return `NIL`. \n",
-    "\n",
-    "`(zero-mrph` *chcm1* `&optional (`*chcm2 chcm1*`) (`*degr* `0))` *[Function]*\n",
-    "> Construct the null morphism between the chain complexes `chcm1` and `chcm2` of degree `degr`. The parameters `chcm2` and `degr` are optional and if omitted the default values (respectively `chcm1` and 0) are taken.\n",
-    "\n",
-    "`(idnt-mrph` *chcm*`)` *[Function]*\n",
-    "> Construct the identity morphism (degree 0) between the chain complex `chcm` and itself.\n",
-    "\n",
-    "`(opps` *mrph*`)` *[Function]*\n",
-    "> Construct the opposite morphism of `mrph`, i.e. $-1 \\times mrph$; such a function, as well as the following ones, installs the right source and target.\n",
-    "\n",
-    "`(cmps` *mrph1 mrph2* `&optional` *strt*`)` *[Method]*\n",
-    "> Construct the  composite of the morphisms, i.e. $mrph_1 \\circ\\, mrph_2$. Of course, the target of $mrph_2$ must be the same as the source of $mrph_1$, otherwise the system signals an error. The new instance inherits its source slot from $mrph_2$ and its target slot from $mrph_1$. This function optimizes the compositions in which appear zero morphisms or identity morphisms. Unless the user gives explicitly the  strategy (`strt`), the resulting strategy is determined by the respective strategy of the two morphisms.\n",
-    "\n",
-    "`(cmps` *chcm1 chcm2* `&optional` *strt*`)` *[Method]*\n",
-    "Construct the composite of the differential of the chain complexes `chcm1` and `chcm2`, i.e. $d_1 \\circ d_2$.\n",
-    "\n",
-    "`(cmps` *chcm1 mrph2* `&optional` *strt*`)` *[Method]*\n",
-    "> Construct the composite of the differential of the chain complex `chcm1` and the morphism  `mrph2`, i.e. $d_1 \\circ mrph_2$.\n",
-    "\n",
-    "`(cmps` *mrph1 chcm2* `&optional` *strt*`)` *[Method]*\n",
-    "> Construct the composite of the morphism `mrph1` and the differential of the chain complex `chcm2`, i.e. $mrph_1 \\circ d_2$.\n",
-    "\n",
-    "`(i-cmps` *mrph1 mrph2 ... mrphk*`)` *[Macro]*\n",
-    "> Construct the  composite of the morphisms, i.e. $mrph_1 \\circ\\, mrph2 \\circ\\, \\cdots\\, \\circ\\, mrph_k$. Of course, the target of $mrph_i$ must be the same as the source of $mrph_{i-1}$, otherwise the system signals an error. The new instance inherits its source slot from $mrph_k$ and its target slot from $mrph_1$. This function optimizes the compositions in which appear zero morphisms or identity morphisms.\n",
-    "\n",
-    "`(add` *mrph1 mrph2* `&optional` *strt*`)` *[Method]*\n",
-    "> Construct a morphism, sum  of the  morphisms $mrph_1$ and  $mrph_2$.  The result of the mapping of the morphism sum is the sum of the results of the mappings of the morphisms. The respective definitions of the morphisms $mrph_1$ and  $mrph_2$  must be coherent, in particular they must have the same  source, target and degree. The user may impose its strategy, otherwise it is defined in the program according to the respective strategy of the arguments.\n",
-    "\n",
-    "`(i-add` *mrph1 mrph2 ... mrphk*`)` *[Macro]*\n",
-    "> Construct a morphism, sum  of the  morphism $mrph_1$,  $mrph_2$, $\\ldots$, $mrph_k$. The result of the mapping of the morphism sum is the sum of the results of the mappings of the $mrph_i$. The respective definitions of $mrph_i$ must be coherent, in particular they must have the same source, target and degree. The macro `i-add` has an undefinite number of arguments. With one argument, the macro returns that argument.\n",
-    "\n",
-    "`(sbtr` *mrph1 mrph2* `&optional` *strt*`)` *[Method]*\n",
-    "> Construct a morphism, difference  of the  morphisms $mrph_1$ and  $mrph_2$. The conditions of validity are similar to those of the method `add`.\n",
-    "\n",
-    "`(i-sbtr` *mrph1 mrph2 ... mrphk*`)` *[Macro]*\n",
-    "> Construct a morphism, difference  of the  morphisms $mrph_1$,  $mrph_2$, $\\ldots$, $mrph_k$, in the sense $mrph_1 -  mrph_2 - \\cdots - mrph_k$. The conditions of validity are similar to those of the method `add` for the morphisms. The macro `i-sbtr` must have at least 2 arguments.\n",
-    "\n",
-    "`(change-sorc-trgt` *mrph* `&key` *sorc trgt*`)` *[Function]*\n",
-    "> Build from the morphism `mrph` a new morphism inheriting from `mrph` the slots `:degr` (degree), `:intr` (mapping) and `:strt` (strategy). The source  and target slots of this new morphism are given by the key parameters `sorc` and `trgt`. If any key parameter is omitted, the corresponding slot is inherited from `mrph` (default value). This function is most often used when the old and new sources and/or targets are chain complexes with the same underlying graded modules, but with different differentials. Important to have this tool when handling perturbations of differentials.\n",
-    "\n",
-    "`(dstr-change-sorc-trgt` *mrph* `&key` *sorc trgt*`)` *[Function]*\n",
-    "> Modify **destructively** the morphism `mrph`. The source  and target slots of the first argument are replaced respectively by the key parameters `sorc` and `trgt`.\n",
-    "\n",
-    "`(add` *chcm perturbation* `&optional` *strt*`)` *[Method]*\n",
-    "> Create from the chain complex `chcm` a new chain complex inheriting from `chcm` the slots `cmpr` and `basis`. The boundary morphism attached to this new chain complex  is the sum of the boundary morphism $d$ of `chcm` (slot `dffr`) and a perturbation morphism $\\delta$ represented by the `MORPHISM` instance `perturbation`. Of course, the new boundary operator must satisfy $(d+\\delta)\\circ (d+\\delta)=0$.\n",
-    "\n",
-    "#### Examples\n",
-    "\n",
-    "In the following examples, we first construct a chain complex instance `ccn` where the groups $C_p$ are freely generated by numerical basis taken formally. These basis are sets of 10 numbers or *decades* produced by the fonction `<a-b<`. For instance, in dimension 0, the basis is $\\lbrace 0,1,2,3,4,5,6,7,8,9 \\rbrace$, in dimension 1, $\\lbrace 10,11,\\ldots,19 \\rbrace$ and so on.\n",
-    "The differential is defined as follows: for an even dimension $p$ of the group, a generator $k$ is sent to the combination $cmbn (p-1, 1, k-10)$ if $k$ is even and to the null combination of degree $p-1$ if $k$ is odd. The reverse action is taken if $p$ is odd. So, from the programming point of view, it is sufficient to test the parity of $p+k$.\n",
-    "\n",
-    "Then, we construct two simple morphisms `upper-shift` and `lower-shift` which respectively apply bijectively a decade on the following one and on the previous one. The generators being integers, the comparative function is of course `f-cmpr`."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 41,
-   "metadata": {
-    "scrolled": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "#<FUNCTION (LAMBDA (DGR GNR) :IN \"/root/cl-jupyter/cl-jupyter.lisp\") {1002BB447B}>"
-      ]
-     },
-     "execution_count": 41,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def ccn-boundary #'(lambda (dgr gnr)\n",
-    "                            (if (evenp (+ dgr gnr))\n",
-    "                                (cmbn (1- dgr) 1 (- gnr 10))\n",
-    "                                (cmbn (1- dgr)))))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 42,
-   "metadata": {
-    "scrolled": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K5 Chain-Complex]"
-      ]
-     },
-     "execution_count": 42,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def ccn (build-chcm :cmpr #'f-cmpr\n",
-    "                     :basis #'(lambda (n) (<a-b< (* 10 n) (* 10 (1+ n))))\n",
-    "                     :bsgn 0\n",
-    "                     :intr-dffr ccn-boundary\n",
-    "                     :strt :gnrt\n",
-    "                     :orgn '(ccn)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 43,
-   "metadata": {
-    "scrolled": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K7 Morphism (degree 1): K5 -> K5]"
-      ]
-     },
-     "execution_count": 43,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def upper-shift (build-mrph\n",
-    "                  :sorc ccn :trgt ccn :strt :gnrt :degr +1\n",
-    "                  :intr #'(lambda (d gn) (cmbn (1+ d) 1 (+ gn 10)))\n",
-    "                  :orgn '(ccn shift +10)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 44,
-   "metadata": {
-    "scrolled": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K8 Morphism (degree -1): K5 -> K5]"
-      ]
-     },
-     "execution_count": 44,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def lower-shift (build-mrph\n",
-    "                  :sorc ccn :trgt ccn :strt :gnrt :degr -1\n",
-    "                  :intr #'(lambda (d gn) (cmbn (1- d) 1 (- gn 10)))\n",
-    "                  :orgn '(ccn shift -10)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 45,
-   "metadata": {
-    "scrolled": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 1}\n",
-       "<1 * 12>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 45,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? ccn 2 22)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 46,
-   "metadata": {
-    "scrolled": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 0}\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 46,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? ccn *)  ;(* means the result of the previous command)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 47,
-   "metadata": {
-    "scrolled": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 5}\n",
-       "<1 * 50>\n",
-       "<5 * 55>\n",
-       "<9 * 59>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 47,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def combn (cmbn 5 1 50 5 55 9 59))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 48,
-   "metadata": {
-    "scrolled": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 4}\n",
-       "<5 * 45>\n",
-       "<9 * 49>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 48,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? ccn combn)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 49,
-   "metadata": {
-    "scrolled": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 3}\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 49,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? ccn *)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Then, let us test the morphisms on generators and combinations."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 50,
-   "metadata": {
-    "scrolled": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 1}\n",
-       "<1 * 16>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 50,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? upper-shift 0 6)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 51,
-   "metadata": {
-    "scrolled": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 4}\n",
-       "<1 * 41>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 51,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? lower-shift 5 51)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "We may iterate the mapping  upon the previous result (symbol \\*). Note that now, though `lower-shift` has been constructed with \n",
-    "the strategy `:gnrt`, its works also on a combination."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 52,
-   "metadata": {
-    "scrolled": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 3}\n",
-       "<1 * 31>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 52,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? lower-shift *)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Let us construct new morphisms from `upper-shift` and `lower-shift`. The tests are made upon the degree 1 combination $1*10 + 2*11 + 3*12 +4*13$."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 53,
-   "metadata": {
-    "scrolled": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 1}\n",
-       "<1 * 10>\n",
-       "<2 * 11>\n",
-       "<3 * 12>\n",
-       "<4 * 13>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 53,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def comb1 (cmbn 1 1 10 2 11 3 12 4 13))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "The composition of the two morphisms  must be an identity operation. The degree of `identity?` is in the `degr` slot of the morphism object instance and may be read by the function `degr`:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 54,
-   "metadata": {
-    "scrolled": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K9 Morphism (degree 0): K5 -> K5]"
-      ]
-     },
-     "execution_count": 54,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def identity? (cmps upper-shift lower-shift))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 55,
-   "metadata": {
-    "scrolled": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "0"
-      ]
-     },
-     "execution_count": 55,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(degr identity?)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "We see now that `identity?` applied on `comb1` returns a combination mathematically equal to `comb1`. No simple lisp comparison can prove this, nevertheless, their mathematical difference is the null combination, as shown by a call to the function `2cmbn-sbtr` applied to two combinations. Note that the function `2cmbn-sbtr` needs the comparison function of the chain complex `ccn`."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 56,
-   "metadata": {
-    "scrolled": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 1}\n",
-       "<1 * 10>\n",
-       "<2 * 11>\n",
-       "<3 * 12>\n",
-       "<4 * 13>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 56,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? identity? comb1)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 57,
-   "metadata": {
-    "scrolled": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 1}\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 57,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(2cmbn-sbtr (cmpr ccn) comb1 *)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "We may compose `upper-shift` with itself:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 58,
-   "metadata": {
-    "scrolled": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K10 Morphism (degree 2): K5 -> K5]"
-      ]
-     },
-     "execution_count": 58,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def upper-shift2 (cmps upper-shift upper-shift))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 59,
-   "metadata": {
-    "scrolled": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "2"
-      ]
-     },
-     "execution_count": 59,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(degr upper-shift2)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 60,
-   "metadata": {
-    "scrolled": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 3}\n",
-       "<1 * 30>\n",
-       "<2 * 31>\n",
-       "<3 * 32>\n",
-       "<4 * 33>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 60,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? upper-shift2 comb1)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Adding `upper-shift` with itself gives a very different result:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 61,
-   "metadata": {
-    "scrolled": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K11 Morphism (degree 1): K5 -> K5]"
-      ]
-     },
-     "execution_count": 61,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def twice-up-shift (add upper-shift upper-shift))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 62,
-   "metadata": {
-    "scrolled": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "1"
-      ]
-     },
-     "execution_count": 62,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(degr twice-up-shift)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 63,
-   "metadata": {
-    "scrolled": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 2}\n",
-       "<2 * 20>\n",
-       "<4 * 21>\n",
-       "<6 * 22>\n",
-       "<8 * 23>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 63,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? twice-up-shift comb1)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Let us compose `upper-shift` and the differential in both ways. Recall that the differential is a morphism structure, and may be obtained from the `dffr` slot  of the chain complex `ccn` by the reader accessor function `dffr1`. This morphism has been built by `build-chcm` from the lisp function `ccn-boundary`. One can see that the operators do not commute; in other words, `upper-shift` is not a chain complex morphism."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 64,
-   "metadata": {
-    "scrolled": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K12 Morphism (degree 0): K5 -> K5]"
-      ]
-     },
-     "execution_count": 64,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def up-d (cmps upper-shift (dffr1 ccn)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 65,
-   "metadata": {
-    "scrolled": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K13 Morphism (degree 0): K5 -> K5]"
-      ]
-     },
-     "execution_count": 65,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def d-up (cmps (dffr1 ccn) upper-shift))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 66,
-   "metadata": {
-    "scrolled": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 1}\n",
-       "<1 * 11>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 66,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? up-d 1 11)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 67,
-   "metadata": {
-    "scrolled": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 1}\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 67,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? d-up 1 11)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 68,
-   "metadata": {
-    "scrolled": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 1}\n",
-       "<1 * 10>\n",
-       "<2 * 11>\n",
-       "<3 * 12>\n",
-       "<4 * 13>\n",
-       "<5 * 14>\n",
-       "<6 * 15>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 68,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def comb3 (cmbn 1 1 10 2 11 3 12 4 13 5 14 6 15))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 69,
-   "metadata": {
-    "scrolled": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 1}\n",
-       "<2 * 11>\n",
-       "<4 * 13>\n",
-       "<6 * 15>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 69,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? up-d comb3)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 70,
-   "metadata": {
-    "scrolled": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 1}\n",
-       "<1 * 10>\n",
-       "<3 * 12>\n",
-       "<5 * 14>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 70,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? d-up comb3)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "### Accessing `Kenzo` objects\n",
-    "\n",
-    "Up to now, we have seen two kinds of `Kenzo` objects stored in specific lists and retrievable by a number, namely the chain complexes and the morphisms. The retrieval functions are specific to the object: `chcm` for a chain complex, `mrph` for a morphism. The same scheme will be applied for others kinds of objects: reductions, homotopy equivalences, \n",
-    "coalgebras, algebras, simplicial morphisms, etc., each having its specific list. But, in fact the numbering is independent\n",
-    "of the type of the object and is incremented each time an object is created. Three general functions are at the disposal of the user to get information about the `n`-th `Kenzo` object: `K`, `KD`, and `KD2`. They may be useful for debugging purpose.\n",
-    "\n",
-    "`(k` *n*`)` *[Function]*\n",
-    "> Get the `n`-th `Kenzo` object.\n",
-    "\n",
-    "`(kd` *n*`)` *[Function]*\n",
-    "> Give the type of the `Kenzo` objet number `n` and print the comment list (slot `:orgn`) of the object.\n",
-    "\n",
-    "`(kd2` *n*`)` *[Function]*\n",
-    "> Give the type of the `Kenzo` objet number `n`, print the comment list (slot `:orgn`) of the object and recursively, give the same kind of informations about all the `Kenzo` objects of the same type in relation with this `n`-th object. Return the list of numbers of all those objects. See in the following example, the case of composition of morphisms.\n",
-    "\n",
-    "#### Examples"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 71,
-   "metadata": {
-    "scrolled": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K1 Chain-Complex]"
-      ]
-     },
-     "execution_count": 71,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(k 1)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "#### Function `KD`"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 72,
-   "metadata": {
-    "scrolled": false
-   },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "Object: [K1 Chain-Complex]\n",
-      "   Origin: (Z-CHCM)\n",
-      "\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 72,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(kd 1)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 73,
-   "metadata": {
-    "scrolled": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K3 Cohomology-Class on K1 of degree 1]"
-      ]
-     },
-     "execution_count": 73,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(k 3)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 74,
-   "metadata": {
-    "scrolled": false
-   },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "Object: [K3 Cohomology-Class on K1 of degree 1]\n",
-      "   Origin: (ZERO MORPHISM ON ZCC)\n",
-      "\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 74,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(kd 3)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 75,
-   "metadata": {
-    "scrolled": false
-   },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "Object: [K8 Morphism (degree -1): K5 -> K5]\n",
-      "   Origin: (CCN SHIFT -10)\n",
-      "\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 75,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(kd 8)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 76,
-   "metadata": {
-    "scrolled": false
-   },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "Object: [K5 Chain-Complex]\n",
-      "   Origin: (CCN)\n",
-      "\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 76,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(kd 5)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 77,
-   "metadata": {
-    "scrolled": false
-   },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "Object: [K9 Morphism (degree 0): K5 -> K5]\n",
-      "   Origin: (2MRPH-CMPS [K7 Morphism (degree 1): K5 -> K5] [K8 Morphism (degree -1): K5 -> K5] GNRT)\n",
-      "\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 77,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(kd 9)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 78,
-   "metadata": {
-    "scrolled": false
-   },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "Object: [K9 Morphism (degree 0): K5 -> K5]\n",
-      "   Origin: (2MRPH-CMPS [K7 Morphism (degree 1): K5 -> K5] [K8 Morphism (degree -1): K5 -> K5] GNRT)\n",
-      "\n",
-      "\n",
-      "Object: [K8 Morphism (degree -1): K5 -> K5]\n",
-      "   Origin: (CCN SHIFT -10)\n",
-      "\n",
-      "\n",
-      "Object: [K7 Morphism (degree 1): K5 -> K5]\n",
-      "   Origin: (CCN SHIFT 10)\n",
-      "\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "(9 8 7)"
-      ]
-     },
-     "execution_count": 78,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(kd2 9)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "#### Lisp files concerned in this chapter\n",
-    "\n",
-    "`combinations.lisp`, `chain-complexes.lisp`, `chcm-elementary-op.lisp`.\n",
-    "\n",
-    "[`classes.lisp`, `macros.lisp`, `various.lisp`]."
-   ]
-  }
- ],
- "metadata": {
-  "kernelspec": {
-   "display_name": "SBCL Lisp",
-   "language": "lisp",
-   "name": "lisp"
-  },
-  "language_info": {
-   "codemirror_mode": "text/x-common-lisp",
-   "mimetype": "text/x-common-lisp",
-   "name": "common-lisp",
-   "pygments_lexer": "common-lisp",
-   "version": "X3J13"
-  }
- },
- "nbformat": 4,
- "nbformat_minor": 1
-}
diff --git a/examples/02_Objects_with_effective_homology.ipynb b/examples/02_Objects_with_effective_homology.ipynb
deleted file mode 100644
index c84112f..0000000
--- a/examples/02_Objects_with_effective_homology.ipynb
+++ /dev/null
@@ -1,2666 +0,0 @@
-{
- "cells": [
-  {
-   "cell_type": "code",
-   "execution_count": 1,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "To load \"kenzo\":\n",
-      "  Load 1 ASDF system:\n",
-      "    kenzo\n",
-      "; Loading \"kenzo\"\n",
-      "\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "#<PACKAGE \"CAT\">"
-      ]
-     },
-     "execution_count": 1,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(ql:quickload \"kenzo\")\n",
-    "(in-package :cat)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "# Objects with effective homology\n",
-    "\n",
-    "## Introduction\n",
-    "\n",
-    "The present chapter describes the set of programming tools for handling *objects with effective homology*. The theoretical material may be found in the paper *Constructive Algebraic Topology* by Julio Rubio Garcia and Francis Sergeraert (Available at the web site\n",
-    "[**https://www-fourier.ujf-grenoble.fr/~sergerar/**](https://www-fourier.ujf-grenoble.fr/~sergerar/)). The terminology used in this chapter is compatible with this reference. The terminology used in this chapter is compatible with this reference.\n",
-    "\n",
-    "## Reduction\n",
-    "\n",
-    "A *reduction* in `Kenzo` is a 5-tuple $(\\hat C, C, f, g, h)$:\n",
-    "$$\n",
-    "\\begin{aligned}\n",
-    "\\hat{C}\\quad & \\qquad\\stackrel{h}{\\longrightarrow} & \\mbox{$^s\\hat{C}$} \\\\\n",
-    "{\\scriptstyle f} \\downarrow \\uparrow {\\scriptstyle g} & & \\\\\n",
-    "C\\quad & &\n",
-    "\\end{aligned}\n",
-    "$$\n",
-    "where $\\hat C$ and $C$ are chain complexes, $f$ and $g$  chain complex morphisms and\n",
-    "$h$ a homotopy operator. Hereafter, $\\hat C$ is called the *top chain complex* and $C$ the *bottom chain complex*. ${}^s\\hat C$ is $\\hat C$ shifted, i.e. $h$ has degree $1$. The mappings $f$, $g$, $h$, together with the differential operator $d$ on $\\hat C$, must verify the following relations:\n",
-    "$$\n",
-    "\\begin{aligned}\n",
-    "f \\circ g & = & 1_C \\\\\n",
-    "h \\circ d + d \\circ h & = & 1_{\\hat C} - g \\circ f \\\\\n",
-    "f \\circ h & = & 0   \\\\\n",
-    "h \\circ g & = & 0   \\\\\n",
-    "h \\circ h & = & 0 \n",
-    "\\end{aligned}\n",
-    "$$\n",
-    "The morphisms $f$ and $g$ and the homotopy operator $h$ describe the (big) chain complex $\\hat C$ as the direct sum\n",
-    "$$ \\hat C= \\hat C_1 \\oplus \\hat C_2$$\n",
-    "where $\\hat C_1 = Im(g) \\simeq C$ and  $\\hat C_2= Ker(f)$. The summands $\\hat{C}_1$ and $\\hat{C}_2$ are sub-chain complexes of $\\hat{C}$ and the second one is acyclic, provided with an explicit contraction, namely the restriction of $h$ to $\\hat{C}_2$.\n",
-    "\n",
-    "\n",
-    "### Representation of a reduction\n",
-    "\n",
-    "A reduction is implemented as an instance of the `CLOS` class `REDUCTION`, whose definition is:\n",
-    "\n",
-    "```commonlisp\n",
-    "(DEFCLASS REDUCTION ()\n",
-    "     ;; Top Chain Complex\n",
-    "    ((tcc :type chain-complex :initarg :tcc :reader tcc1)\n",
-    "     ;; Bottom Chain Complex\n",
-    "     (bcc :type chain-complex :initarg :bcc :reader bcc1)\n",
-    "     (f :type morphism :initarg :f :reader f1)\n",
-    "     (g :type morphism :initarg :g :reader g1)\n",
-    "     (h :type morphism :initarg :h :reader h1)\n",
-    "     ;; IDentification NuMber\n",
-    "     (idnm :type fixnum :initform (incf *idnm-counter*) :reader idnm)\n",
-    "     ;; ORiGiN\n",
-    "     (orgn :type list :initarg :orgn :reader orgn)))\n",
-    "```\n",
-    "\n",
-    "This class has 7 slots:\n",
-    "\n",
-    "1. `tcc`, the object of type `chain-complex` representing the chain complex $\\hat C$ (top chain complex).\n",
-    "2. `bcc`,  the object of type `chain-complex` representing the chain complex $C$ (bottom chain complex).\n",
-    "3. `f`, the object of type `morphism` representing the morphism $f$.\n",
-    "4. `g`, the object of type `morphism` representing the morphism $g$.\n",
-    "5. `h`, the object of type `morphism`  representing the morphism $h$.\n",
-    "6. `idmn`, an integer, number plate for the object.\n",
-    "7. `orgn`, a comment list carefully chosen.\n",
-    "\n",
-    "The accessors of the slots are the functions whose name appears after the specifier `:reader` in the class definition. A printing method has been associated to the class `REDUCTION` and the external representation of an instance is a string like `[Kn Reduction K n' => Kn'']`, where `n` is the identification number of the reduction, `n'` (resp. `n''`) is the identification number of the top (resp. bottom) chain complex.\n",
-    "\n",
-    "\n",
-    "### The function `build-rdct`\n",
-    "\n",
-    "To facilitate the construction of instances of the `REDUCTION` class, the\n",
-    "software provides the function `build-rdct`.\n",
-    "\n",
-    "```commonlisp\n",
-    "build-rdct :f f :g g :h h :orgn orgn\n",
-    "```\n",
-    "\n",
-    "defined with keyword parameters. The returned value is an instance of the class `REDUCTION`. \n",
-    "The keyword arguments are:\n",
-    "\n",
-    "- *f*, the object of type `morphism` representing the morphism $f$.\n",
-    "- *g*, the object of type `morphism` representing the morphism $g$.\n",
-    "- *h*, the object of type `morphism` representing the morphism $h$.\n",
-    "- *orgn*, the comment list carefully chosen since the system does not build a new instance of the class if it finds in the list of already built reductions, `*rdct-list*`, a reduction  with the same comment list.\n",
-    "\n",
-    "The `tcc` slot and the `bcc` slot of the instance are taken respectively from the `sorc` slot (source slot) and the `trgt` slot (target slot) of the morphism $f$. The function `build-rdct` controls the validity of the degrees of the morphisms and pushes the new created instance on the list `*rdct-list*`.\n",
-    "\n",
-    "### Useful macros and functions\n",
-    "\n",
-    "`(cat-init)` *[Function]*\n",
-    "> Clear among others, the list `*rdct-list*`, list of user created reductions  and reset the global counter to 1. See also the description of this function in chapter 1.\n",
-    "\n",
-    "`(rdct` *n*`)` *[Function]*\n",
-    "> Retrieve in the list `*rdct-list*` the reduction instance whose identification (as `Kenzo` object) is *n*. If it does not exist, return `NIL`.\n",
-    "\n",
-    "`(bcc` *rdct* `&rest` *args*`)` *[Macro]*\n",
-    "> With only one argument (a reduction *rdct*) this macro selects the bottom chain complex of the reduction. Otherwise, it applies  the differential of the bottom chain complex of the reduction *rdct* on the arguments *args*, (either *degree generator* or *cmb*).\n",
-    "\n",
-    "`(tcc` *rdct* `&rest` *args*`)` *[Macro]*\n",
-    "> With only one argument (a reduction *rdct*) this macro selects the top chain complex of the reduction. Otherwise, it applies  the differential of the top chain complex of the reduction *rdct* on the arguments *args*, (either *degree generator* or *cmb*).\n",
-    "\n",
-    "`(f` *rdct* `&rest` *args*`)` *[Macro]*\n",
-    "> With only one argument (a reduction *rdct*) this macro selects the morphism $f$ of the reduction. Otherwise, it applies the morphism $f$ of the reduction *rdct* on the arguments *args*, (either *degree generator* or *cmb*).\n",
-    "\n",
-    "`(g` *rdct* `&rest` *args*`)` *[Macro]*\n",
-    "> With only one argument (a reduction *rdct* this macro selects the morphism $g$ of the reduction. Otherwise, it applies  the morphism $g$ of the reduction *rdc* on the arguments *args*, (either *degree generator* or *cmb*).\n",
-    "\n",
-    "`(h` *rdct* `&rest` *args*`)` *[Macro]*\n",
-    "> With only one argument (a reduction *rdct*) this macro selects the morphism $h$ of the reduction. Otherwise, it applies the morphism $h$ of the reduction *rdc* on the arguments *args*, (either *degree generator* or *cmb*).\n",
-    "\n",
-    "`(trivial-rdct` *chcm*`)` *[Function]*\n",
-    "> Build the trivial reduction involving only the chain complex chcm, as shown in the following diagram,\n",
-    "$$\n",
-    "\\begin{aligned}\n",
-    " C \\quad & \\quad\\stackrel{Zero} {\\longrightarrow} & {}^s C \\\\\n",
-    " {\\scriptstyle {Id}} \\downarrow \\uparrow {\\scriptstyle {Id}} & &  \\\\\n",
-    "  C \\quad & &\n",
-    "\\end{aligned}\n",
-    "$$\n",
-    "where the morphism *Zero* is the zero morphism of degree 1 in the chain complex $C$ and *Id* is the identity morphism in that chain complex (see the functions `zero-mrph` and `idnt-mrph` in the chain complex chapter).\n",
-    "\n",
-    "`(cmps` *brdct trdct*`)` *[Method]*\n",
-    "> Build a new reduction from the two reductions $b$ and $t$ (here, respectively *brdct* and *trdct*). This is done by a call to `build-rdct` with the following parameters:\n",
-    "$$\n",
-    "\\begin{aligned}\n",
-    "f & = & f_{b}\\circ f_{t}, \\\\\n",
-    "g & = & g_{t}\\circ g_{b}, \\\\\n",
-    "h & = &  h_{t}  + g_{t} \\circ h_{b} \\circ f_{t}.\n",
-    "\\end{aligned}\n",
-    "$$\n",
-    "The compositions and additions of morphisms are realized respectively by the methods `cmps`, `i-cmps` and `add` (see chapter 1). We recall that the `tcc` and the `bcc` slots of this new created reduction are respectively the source and target slots of the new morphim $f$.\n",
-    "\n",
-    "### Verification functions\n",
-    "\n",
-    "The two following functions are very helpful to verify the coherence of the the various mappings involved in a reduction. Let us recall the diagram of a reduction:\n",
-    "$$\n",
-    "\\begin{aligned}\n",
-    "\\hat{C} \\quad & \\quad\\stackrel{h}{\\longrightarrow} & \\mbox{$^s\\hat{C}$} \\\\\n",
-    "{\\scriptstyle f} \\downarrow \\uparrow {\\scriptstyle g} & & \\\\\n",
-    "C \\quad & &\n",
-    "\\end{aligned}\n",
-    "$$\n",
-    "\n",
-    "`(pre-check-rdct` *rdct*`)` *[Function]*\n",
-    "> Assign to the following lisp global variables, the morphism instances computed from the morphisms of the reduction *rdct*, according to the  formulas:\n",
-    "$$\n",
-    "\\begin{aligned}\n",
-    "  \\mathtt{*tdd*} & = & d_{\\hat C} \\circ d_{\\hat C},\\\\\n",
-    "  \\mathtt{*bdd*} & = & d_C \\circ d_C , \\\\\n",
-    "  \\mathtt{*id-fg*} & = &  f \\circ g - Id_C, \\\\\n",
-    "  \\mathtt{*id-gf-dh-hd*} & = & Id_{\\hat C} - g \\circ f - (d_{\\hat C} \\circ h + h \\circ d_{\\hat C}),\\\\\n",
-    "  \\mathtt{*hh*} & = & h \\circ h, \\\\\n",
-    "  \\mathtt{*fh*} & = & f \\circ h, \\\\\n",
-    "  \\mathtt{*hg*} & = & h \\circ g, \\\\\n",
-    "  \\mathtt{*df-fd*} & = & d_C \\circ f - f \\circ d_{\\hat C}, \\\\\n",
-    "  \\mathtt{*dg-gd*} & = & d_{\\hat C} \\circ g - g \\circ d_C.\n",
-    "\\end{aligned}\n",
-    "$$\n",
-    "In these formulas  $d_C$ and $d_{\\hat C}$ are the respective boundary operators of the\n",
-    "chain complexes $C$ and $\\hat C$. $Id_C$ and $Id_{\\hat C}$ are the identity morphisms\n",
-    "on the chain complexes $C$ and $\\hat C$  built by the function `idnt-mrph`\n",
-    "\n",
-    "`(check-rdct)` *[Function]*\n",
-    "> Map  all the morphisms prepared by the function *pre-check-rdct* on chosen combinations.\n",
-    "This function having no parameters, the user must  assign to  the two lisp global variables:\n",
-    "`*tc*` and `*bc*`,  valid combinations belonging respectively to $\\hat C$ and $C$. The call to this function is simply `(check-rdct)`. This function knows what morphism to apply\n",
-    "to the combinations and pauses after each evaluation to allow the user to inspect each result.\n",
-    "To resume the execution, the user must enter a blank character. If the morphisms are coherent, the result of each mapping is a null combination.\n",
-    "\n",
-    "#### Example\n",
-    "\n",
-    "To show an example about the verification functions, we first define a locally effective version\n",
-    "of the standard simplex $\\Delta^n$. The following function `cdelta` builds the standard simplex\n",
-    "in dimension *dmns*. In using the created chain complex, the user must bear in mind that\n",
-    "the only valid vertices are the vertices numbered from $(0)$ to $(dmns)$."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 2,
-   "metadata": {
-    "scrolled": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "CDELTA"
-      ]
-     },
-     "execution_count": 2,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(defun cdelta (dmns)\n",
-    "    (build-chcm\n",
-    "     :cmpr #'l-cmpr\n",
-    "     :basis :locally-effective\n",
-    "     :bsgn '(0)\n",
-    "     :intr-dffr\n",
-    "         #'(lambda (degr gmsm)\n",
-    "            (make-cmbn\n",
-    "             :degr (1- degr)\n",
-    "             :list (do ((rslt +empty-list+\n",
-    "                              (cons (cons sign\n",
-    "                                          (append\n",
-    "                                           (subseq gmsm 0 nark)\n",
-    "                                           (subseq gmsm (1+ nark))))\n",
-    "                                    rslt))\n",
-    "                        (sign 1 (- sign))\n",
-    "                        (nark 0 (1+ nark)))\n",
-    "                       ((> nark degr) rslt))))\n",
-    "     :strt :gnrt\n",
-    "     :orgn `(locally effective version of C_* delta ,dmns)))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Now, let us define 3 functions `make-f`, `make-g` and `make-h` which build the following respective morphisms between $\\Delta^m$ and $\\Delta^n$:\n",
-    "\n",
-    "- `(make-f tdms bdms)` builds a projection morphism $f$ from $\\Delta^{tdms}$ to $\\Delta^{bdms}$, $tdms>=bdms$, where the vertices $(0)$ to $(dms)$ of $\\Delta^{tdms}$ are applied on the vertices of the same number in $\\Delta^{bdms}$ and the vertices $(bdms+1)$ to $(tdms)$ are applied on the vertex $(bdms)$ of $\\Delta^{bdms}$.\n",
-    "- `(make-g tdms bdms)` builds the injection morphism $g$ from $\\Delta^{bdms}$ to $\\Delta^{tdms}$ (the slot `:intr` is the identity function).\n",
-    "- `(make-h tdms bdms)` builds a homotopy morphism of degree 1, $h$, from $\\Delta^{tdms}$ to itself, connecting w.r.t. the homotopy relation, the chain map $g \\circ f$ with the identity morphism $Id$."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 3,
-   "metadata": {
-    "scrolled": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "MAKE-F"
-      ]
-     },
-     "execution_count": 3,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(defun make-f (tdmns bdmns)\n",
-    "    (build-mrph\n",
-    "     :sorc (cdelta tdmns) :trgt (cdelta bdmns) :degr 0\n",
-    "     :intr #'(lambda (degr gmsm)\n",
-    "                (let ((pos (position-if #'(lambda (vertex) (>= vertex bdmns))\n",
-    "                                        gmsm)))\n",
-    "                     (if pos\n",
-    "                         (if (< pos degr)\n",
-    "                             (zero-cmbn degr)\n",
-    "                             (cmbn degr 1 (nconc (butlast gmsm) (list bdmns))))\n",
-    "                         (cmbn degr 1 gmsm))))\n",
-    "     :strt :gnrt\n",
-    "     :orgn `(projection delta ,tdmns => delta ,bdmns)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 4,
-   "metadata": {
-    "scrolled": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "MAKE-G"
-      ]
-     },
-     "execution_count": 4,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(defun make-g (tdmns bdmns)\n",
-    "    (build-mrph\n",
-    "     :sorc (cdelta bdmns) :trgt (cdelta tdmns) :degr 0\n",
-    "     :intr #'identity\n",
-    "     :strt :cmbn\n",
-    "     :orgn `(injection delta ,bdmns => delta ,tdmns)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 5,
-   "metadata": {
-    "scrolled": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "MAKE-H"
-      ]
-     },
-     "execution_count": 5,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(defun make-h (tdmns bdmns)\n",
-    "    (build-mrph\n",
-    "     :sorc (cdelta tdmns) :trgt (cdelta tdmns) :degr +1\n",
-    "     :intr #'(lambda (degr gmsm)\n",
-    "                (let ((pos (position-if #'(lambda (vertex) (>= vertex bdmns))\n",
-    "                                        gmsm)))\n",
-    "                     (if pos\n",
-    "                         (if (member bdmns gmsm)\n",
-    "                             (zero-cmbn (1+ degr))\n",
-    "                             (cmbn (1+ degr) (-1-expt-n pos)\n",
-    "                                       (append (subseq gmsm 0 pos) (list bdmns)\n",
-    "                                               (subseq gmsm pos))))\n",
-    "                         (zero-cmbn (1+ degr)))))\n",
-    "     :strt :gnrt\n",
-    "     :orgn `(homotopy for delta ,tdmns => ,bdmns)))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "We may now define a function to build a reduction. One has not to define a priori the standard\n",
-    "simplices: this is done  in  all the functions and we know that there is no duplication, because\n",
-    "before creation, the system checks, owing to the comment list, if the instance of a class (here a chain complex) already exists."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 6,
-   "metadata": {
-    "scrolled": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "MAKE-RDCT"
-      ]
-     },
-     "execution_count": 6,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(defun make-rdct (tdmns bdmns)\n",
-    "    (let ((rdct (build-rdct\n",
-    "                 :f (make-f tdmns bdmns)\n",
-    "                 :g (make-g tdmns bdmns)\n",
-    "                 :h (make-h tdmns bdmns)\n",
-    "                 :orgn `(reduction delta ,tdmns ,bdmns))))\n",
-    "         rdct))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "We now build with a simple call to the function `make-rdct` the chain complexes corresponding \n",
-    "to $\\Delta^6$ and $\\Delta^3$, the 3 morphisms $f$, $g$, $h$ and the reduction. The lisp utility function `inspect` gives an idea of the organisation of the class instance. Then we verify the coherency of the reduction with the functions `pre-check-rdct` and `check-rdct`."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 7,
-   "metadata": {
-    "scrolled": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K8 Reduction K1 => K3]"
-      ]
-     },
-     "execution_count": 7,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def rdct (make-rdct 6 3))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 8,
-   "metadata": {
-    "scrolled": false
-   },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "The object is a STANDARD-OBJECT of type REDUCTION.\n",
-      "0. TCC: [K1 Chain-Complex]\n",
-      "1. BCC: [K3 Chain-Complex]\n",
-      "2. F: [K5 Morphism (degree 0): K1 -> K3]\n",
-      "3. G: [K6 Morphism (degree 0): K3 -> K1]\n",
-      "4. H: [K7 Morphism (degree 1): K1 -> K1]\n",
-      "5. IDNM: 8\n",
-      "6. ORGN: (REDUCTION DELTA 6 3)\n",
-      "> "
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 8,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(inspect rdct)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 9,
-   "metadata": {
-    "scrolled": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(REDUCTION DELTA 6 3)"
-      ]
-     },
-     "execution_count": 9,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(orgn rdct)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 10,
-   "metadata": {
-    "scrolled": false
-   },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "---done---"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 10,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(pre-check-rdct rdct)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 11,
-   "metadata": {
-    "scrolled": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 2}\n",
-       "<1 * (0 1 2)>\n",
-       "<10 * (1 2 3)>\n",
-       "<100 * (1 2 4)>\n",
-       "<1000 * (2 3 4)>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 11,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(setf *tc* (cmbn 2 1 '(0 1 2) 10 '(1 2 3) 100 '(1 2 4) 1000 '(2 3 4)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 12,
-   "metadata": {
-    "scrolled": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 3}\n",
-       "<4 * (0 1 2 3)>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 12,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(setf *bc* (cmbn 3 4 '(0 1 2 3)))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "In this documentation, we use the non-interactive function `check-rdct-no-wait` which does the whole check at once without waiting the newline input between two elementary checks."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 13,
-   "metadata": {
-    "scrolled": false
-   },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "*TC* => \n",
-      "----------------------------------------------------------------------{CMBN 2}\n",
-      "<1 * (0 1 2)>\n",
-      "<10 * (1 2 3)>\n",
-      "<100 * (1 2 4)>\n",
-      "<1000 * (2 3 4)>\n",
-      "------------------------------------------------------------------------------\n",
-      "\n",
-      "*BC* => \n",
-      "----------------------------------------------------------------------{CMBN 3}\n",
-      "<4 * (0 1 2 3)>\n",
-      "------------------------------------------------------------------------------\n",
-      "\n",
-      "Checking *TDD* = 0\n",
-      "Result: \n",
-      "----------------------------------------------------------------------{CMBN 0}\n",
-      "------------------------------------------------------------------------------\n",
-      "\n",
-      "Checking *BDD* = 0\n",
-      "Result: \n",
-      "----------------------------------------------------------------------{CMBN 1}\n",
-      "------------------------------------------------------------------------------\n",
-      "\n",
-      "Checking *DF-FD* = 0\n",
-      "Result: \n",
-      "----------------------------------------------------------------------{CMBN 1}\n",
-      "------------------------------------------------------------------------------\n",
-      "\n",
-      "Checking *DG-GD* = 0\n",
-      "Result: \n",
-      "----------------------------------------------------------------------{CMBN 2}\n",
-      "------------------------------------------------------------------------------\n",
-      "\n",
-      "Checking *ID-FG* = 0\n",
-      "Result: \n",
-      "----------------------------------------------------------------------{CMBN 3}\n",
-      "------------------------------------------------------------------------------\n",
-      "\n",
-      "Checking *ID-GF-DH-HD* = 0\n",
-      "Result: \n",
-      "----------------------------------------------------------------------{CMBN 2}\n",
-      "------------------------------------------------------------------------------\n",
-      "\n",
-      "Checking *HH* = 0\n",
-      "Result: \n",
-      "----------------------------------------------------------------------{CMBN 4}\n",
-      "------------------------------------------------------------------------------\n",
-      "\n",
-      "Checking *FH* = 0\n",
-      "Result: \n",
-      "----------------------------------------------------------------------{CMBN 3}\n",
-      "------------------------------------------------------------------------------\n",
-      "\n",
-      "Checking *HG* = 0\n",
-      "Result: \n",
-      "----------------------------------------------------------------------{CMBN 4}\n",
-      "------------------------------------------------------------------------------\n",
-      "\n",
-      "---done---"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 13,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(check-rdct-no-wait)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "We do now the same thing with a more complicated reduction which is the\n",
-    "composition of the two following reductions:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 14,
-   "metadata": {
-    "scrolled": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K35 Reduction K1 => K30]"
-      ]
-     },
-     "execution_count": 14,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def trdct (make-rdct 6 4))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 15,
-   "metadata": {
-    "scrolled": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K39 Reduction K30 => K3]"
-      ]
-     },
-     "execution_count": 15,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def brdct (make-rdct 4 3))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 16,
-   "metadata": {
-    "scrolled": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K45 Reduction K1 => K3]"
-      ]
-     },
-     "execution_count": 16,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(setf rdct (cmps brdct trdct))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 17,
-   "metadata": {
-    "scrolled": false
-   },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "---done---"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 17,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(pre-check-rdct rdct)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 18,
-   "metadata": {
-    "scrolled": false
-   },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "*TC* => \n",
-      "----------------------------------------------------------------------{CMBN 2}\n",
-      "<1 * (0 1 2)>\n",
-      "<10 * (1 2 3)>\n",
-      "<100 * (1 2 4)>\n",
-      "<1000 * (2 3 4)>\n",
-      "------------------------------------------------------------------------------\n",
-      "\n",
-      "*BC* => \n",
-      "----------------------------------------------------------------------{CMBN 3}\n",
-      "<4 * (0 1 2 3)>\n",
-      "------------------------------------------------------------------------------\n",
-      "\n",
-      "Checking *TDD* = 0\n",
-      "Result: \n",
-      "----------------------------------------------------------------------{CMBN 0}\n",
-      "------------------------------------------------------------------------------\n",
-      "\n",
-      "Checking *BDD* = 0\n",
-      "Result: \n",
-      "----------------------------------------------------------------------{CMBN 1}\n",
-      "------------------------------------------------------------------------------\n",
-      "\n",
-      "Checking *DF-FD* = 0\n",
-      "Result: \n",
-      "----------------------------------------------------------------------{CMBN 1}\n",
-      "------------------------------------------------------------------------------\n",
-      "\n",
-      "Checking *DG-GD* = 0\n",
-      "Result: \n",
-      "----------------------------------------------------------------------{CMBN 2}\n",
-      "------------------------------------------------------------------------------\n",
-      "\n",
-      "Checking *ID-FG* = 0\n",
-      "Result: \n",
-      "----------------------------------------------------------------------{CMBN 3}\n",
-      "------------------------------------------------------------------------------\n",
-      "\n",
-      "Checking *ID-GF-DH-HD* = 0\n",
-      "Result: \n",
-      "----------------------------------------------------------------------{CMBN 2}\n",
-      "------------------------------------------------------------------------------\n",
-      "\n",
-      "Checking *HH* = 0\n",
-      "Result: \n",
-      "----------------------------------------------------------------------{CMBN 4}\n",
-      "------------------------------------------------------------------------------\n",
-      "\n",
-      "Checking *FH* = 0\n",
-      "Result: \n",
-      "----------------------------------------------------------------------{CMBN 3}\n",
-      "------------------------------------------------------------------------------\n",
-      "\n",
-      "Checking *HG* = 0\n",
-      "Result: \n",
-      "----------------------------------------------------------------------{CMBN 4}\n",
-      "------------------------------------------------------------------------------\n",
-      "\n",
-      "---done---"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 18,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(check-rdct-no-wait)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "## Homotopy equivalence\n",
-    "\n",
-    "A *homotopy equivalence* between two chain complexes $C$ and $EC$ is a pair of reductions:\n",
-    "\n",
-    "$$\n",
-    "\\begin{aligned}\n",
-    "  & \\qquad\\hat{C} & \\\\\n",
-    " \\rho_1\\swarrow\\nearrow   & & \\nwarrow\\searrow \\rho_2 \\\\\n",
-    "C \\quad & & EC\\quad\n",
-    "\\end{aligned}\n",
-    "$$\n",
-    "\n",
-    "If $C$ and $EC$ are *free* $\\mathbb{Z}$-chain complexes, a usual chain equivalence between them can be\n",
-    "organized in this way. Frequently the chain complexes $C$ and $\\hat C$ are *locally effective*\n",
-    "and on the contrary, the chain complex $EC$ is *effective*, so that $EC$ can be understood\n",
-    "as a description of the homology of $C$. More precisely, $EC$ is a tool allowing one to compute the\n",
-    "homology of $C$. The chain complexe $\\hat C$ is only an intermediate object.\n",
-    "\n",
-    "### Representation of a homotopy equivalence\n",
-    "\n",
-    "A homotopy equivalence is implemented as an instance of the `CLOS` class `HOMOTOPY-EQUIVALENCE`,\n",
-    "whose definition is\n",
-    "\n",
-    "```commonlisp\n",
-    "(DEFCLASS HOMOTOPY-EQUIVALENCE ()\n",
-    "     ;; Left Bottom Chain Complex\n",
-    "    ((lbcc :type chain-complex :initarg :lbcc :reader lbcc1)\n",
-    "     ;; Top Chain Complex\n",
-    "     (tcc  :type chain-complex :initarg :tcc  :reader tcc1)\n",
-    "     ;; Bottom Right Chain Complex\n",
-    "     (rbcc :type chain-complex :initarg :rbcc :reader rbcc1)\n",
-    "     ;; Left f\n",
-    "     (lf   :type morphism      :initarg :lf   :reader lf1)\n",
-    "     ;; Left g\n",
-    "     (lg   :type morphism      :initarg :lg   :reader lg1)\n",
-    "     ;; Left h\n",
-    "     (lh   :type morphism      :initarg :lh   :reader lh1)\n",
-    "     ;; Right f\n",
-    "     (rf   :type morphism      :initarg :rf   :reader rf1)\n",
-    "     ;; Right g\n",
-    "     (rg   :type morphism      :initarg :rg   :reader rg1)\n",
-    "     ;; Right h\n",
-    "     (rh   :type morphism      :initarg :rh   :reader rh1)\n",
-    "     ;; Left ReDuCTion\n",
-    "     (lrdct :type reduction    :initarg :lrdct :reader lrdct)\n",
-    "     ;; Right ReDuCTion\n",
-    "     (rrdct :type reduction    :initarg :rrdct :reader rrdct)\n",
-    "     ;; IDentification NuMber\n",
-    "     (idnm :type fixnum :initform (incf *idnm-counter*) :reader idnm)\n",
-    "     (orgn :type list          :initarg :orgn :reader orgn)))\n",
-    "```\n",
-    "\n",
-    "This class has 13 slots:\n",
-    "\n",
-    "- `lbcc`, the object of type `chain complex` representing the chain complex $C$  (**l**eft **b**ottom **c**hain **c**omplex on the diagram).\n",
-    "- `tcc`,  the object of type `chain complex`  representing the chain complex $\\hat C$ (**t**op **c**hain **c**omplex).\n",
-    "- `rbcc`, the object of type `chain complex`  representing the chain complex $EC$ (**r**ight **b**ottom **c**hain **c**omplex on the diagram).\n",
-    "- `lf`, the object of type `morphism` representing the morphism $f$ of the (**l**eft) reduction $\\rho_1$.\n",
-    "- `lg`, the object of type `morphism` representing the morphism $g$ of the (**l**eft) reduction $\\rho_1$.\n",
-    "- `lh`, the object of type `morphism`  representing the morphism $h$ of the (**l**eft) reduction $\\rho_1$.\n",
-    "- `rf`, the object of type `morphism`  representing the morphism $f$ of the (**r**ight) reduction $\\rho_2$.\n",
-    "- `rg`, the object of type `morphism` representing the morphism $g$ of the (**r**ight) reduction $\\rho_2$.\n",
-    "- `rh`, the object of type `morphism` representing the morphism $h$ of the (**r**ight) reduction $\\rho_2$.\n",
-    "- `lrdc`, the object of type `reduction` representing the (**l**eft) reduction $\\rho_1$.\n",
-    "- `rrdc`, the object of type `reduction` representing the (**r**ight) reduction $\\rho_2$.\n",
-    "- `idn`, an integer, number plate for the object, set by the system.\n",
-    "- `orgn`, an adequate comment list.\n",
-    "\n",
-    "When an instance is created, the  printing method associated to the class `HOMOTOPY EQUIVALENCE` prints a string like `[Kn Homotopy-Equivalence Ka <= Kb => Kc]`, where `n` is the number plate of the equivalence, `a` is the id number of $C$, `b` the id number of $\\hat C$, `c` the id number of $EC$.\n",
-    "\n",
-    "\n",
-    "### The function `build-hmeq`\n",
-    "\n",
-    "To facilitate the construction of instances of the `HOMOTOPY-EQUIVALENCE` class, the program provides the function, (in fact a method), `build-hmeq` which may be used in the following ways:\n",
-    "either with the two reductions $\\rho_1$ and $\\rho_2$ or explicitly with the morphisms.\n",
-    "The selection of the adequate method is done by inspecting the first keyword, which is \n",
-    "`:lrdct` in the first case and `:lf` in the second one. In both cases the returned value is an instance of the class `HOMOTOPY-EQUIVALENCE`.\n",
-    "\n",
-    "1) `(build-hmeq :lrdct` *lrdct* `:rrdct` *rrdc* `:orgn` *orgn*`)` *[Method]*\n",
-    "> The keyword arguments are:\n",
-    "- *lrdct*, the object of type `reduction` representing the reduction $\\rho_1$.\n",
-    "- *rrdct*, the object of type `reduction` representing the reduction $\\rho_2$.\n",
-    "- *org*, the comment list.\n",
-    "The function `build-heq-from-rdc` calls internally the standard constructor `make-instance`. All the needed information is contained in the two reductions.\n",
-    "\n",
-    "2) `(build-hmeq :lf` *lf* `:lg` *lg* `:lh` *lh* `:rf` *rf* `:rg` *rg* `:rh` *rh* `:orgn` *orgn*`)` *[Method]*\n",
-    "> The keyword arguments are:\n",
-    "- *lf*, the  object of type `morphism` representing the morphism $f$ of the reduction $\\rho_1$.\n",
-    "- *lg*, the  object of type `morphism`  representing the morphism $g$ of the reduction $\\rho_1$.\n",
-    "- *lh*, the object of type  `morphism` representing the morphism $h$ of the reduction $\\rho_1$.\n",
-    "- *rf*, the object of type `morphism` representing the morphism $f$ of the reduction $\\rho_2$.\n",
-    "- *rg*, the object of type `morphism` representing the morphism $g$ of the reduction $\\rho_2$.\n",
-    "- *rh*, the object of type `morphism` representing the morphism $h$ of the reduction $\\rho_2$.\n",
-    "- *org*, the comment list.\n",
-    "\n",
-    "All the needed information is contained in the morphism structures.\n",
-    "In both cases, the method  pushes the created instance onto the list `*hmeq-list*`.\n",
-    "\n",
-    "### Useful macros and functions\n",
-    "\n",
-    "`(cat-init)` *[Function]*\n",
-    "> Clear among others, the list `*hmeq-list*`, list of user created homotopy equivalences and reset the global counter to 1.\n",
-    "\n",
-    "`(hmeq` *n*`)` *[Function]*\n",
-    "> Retrieve in the list `*hmeq-list*` the  homotopy equivalence instance whose identification is $n$. If it does not exist, return `NIL`.\n",
-    "\n",
-    "`(lbcc` *hmeq* `&rest` *args*`)` *[Macro]*\n",
-    "> With only one argument (a homotopy equivalence *hmeq*) this macro selects the left bottom chain complex of the homotopy equivalence. Otherwise, it applies  the differential of the left bottom chain complex of *hmeq* on the arguments *args*, (either *degree generator* or *cmb*).\n",
-    "\n",
-    "`(rbcc` *hmeq* `&rest` *args*`)` *[Macro]*\n",
-    "> With only one argument (a homotopy equivalence *hmeq*) this macro selects the right bottom chain complex of the homotopy equivalence. Otherwise, it applies  the differential of the right  bottom chain complex of *hmeq* on the arguments *args*, (either *degree generator* or *cmb*).\n",
-    "\n",
-    "`(lf` *hmeq* `&rest` *args*`)` *[Macro]*\n",
-    "> With only one argument (a homotopy equivalence *hmeq*) this macro selects the morphism $f$ of the left reduction of *hmeq*. Otherwise, it applies  the morphism $f$ of the left reduction of *hmeq* on the arguments *args*, (either *degree generator* or *cmb*).\n",
-    "\n",
-    "`(lg` *hmeq* `&rest` *args*`)` *[Macro]*\n",
-    "> With only one argument (a homotopy equivalence *hmeq*) this macro selects the morphism $g$ of the left reduction of *hmeq*. Otherwise, it applies  the morphism $g$ of the left reduction of *hmeq* on the arguments *args*, (either *degree generator* or *cmb*).\n",
-    "\n",
-    "`(lh` *hmeq* `&rest` *args*`)` *[Macro]*\n",
-    "> With only one argument (a homotopy equivalence *hmeq*) this macro selects the morphism $h$ of the left reduction of *hmeq*. Otherwise, it applies  the morphism $h$ of the left reduction of *hmeq* on the arguments *args*, (either *degree generator* or *cmb*).\n",
-    "\n",
-    "`(rf` *hmeq* `&rest` *args*`)` *[Macro]*\n",
-    "> With only one argument (a homotopy equivalence *hmeq*) this macro selects the morphism $f$ of the right reduction of *hmeq*. Otherwise, it applies  the morphism $f$ of the right reduction of *hmeq* on the arguments *args*, (either *degree generator* or *cmb*).\n",
-    "\n",
-    "`(rg` *hmeq* `&rest` *args*`)` *[Macro]*\n",
-    "> With only one argument (a homotopy equivalence *hmeq*) this macro selects the morphism $g$ of the right reduction of *hmeq*. Otherwise, it applies  the morphism $g$ of the right reduction of *hmeq* on the arguments *args*, (either *degree generator* or *cmb*).\n",
-    "\n",
-    "`(rh` *hmeq* `&rest` *args*`)` *[Macro]*\n",
-    "> With only one argument (a homotopy equivalence *hmeq*) this macro selects the morphism $h$ of the right reduction of *hmeq*. Otherwise, it applies  the morphism $h$ of the right reduction of *hmeq* on the arguments *args*, (either *degree generator* or *cmb*).\n",
-    "\n",
-    "`(trivial-hmeq` *chcm*`)` *[Function]*\n",
-    "> Build the trivial homotopy equivalence involving only the chain complex *chcm*. In that case,\n",
-    "the 3 chain complexes $C$, $EC$ and $\\hat C$ are  the chain complex *chcm* itself and the reductions $\\rho_1$ and $\\rho_2$ are, of course, the trivial reductions on *chcm* built by the statement `(trivial-rdct chcm)`."
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "## The perturbation lemma machinery\n",
-    "\n",
-    "For a good understanding of the lisp functions involved in the machinery in question,\n",
-    "we recall the *perturbation lemma* (**Ronald Brown**. *The twisted Eilenberg--Zilber theorem*.\n",
-    "Celebrazioni Arch. Secolo XX Simp. Top., 1967, pp 34-37.). In the basic (resp. trivial) perturbation lemma, the given perturbation concerns the **top** (resp. **bottom**) chain complex.\n",
-    "\n",
-    "**Theorem 1 (Basic perturbation lemma)** - Let\n",
-    "$\\rho=(\\hat{C},C,f,g,h)$ a reduction and $\\hat{\\delta}$ a *perturbation* of $d_{\\hat{C}}$, that is, an operator defined on $\\hat{C}$ of degree -1 satisfying the relation $(d_{\\hat{C}}+\\hat{\\delta})\\circ(d_{\\hat{C}}+\\hat{\\delta})=0$. Furthermore, the composite function $h\\circ\\hat{\\delta}$ is assumed *locally nilpotent*, that is, $\\forall x \\in \\hat{C}$, $(h\\circ\\hat{\\delta})^nx=0$, for $n$ sufficiently large. Then a new reduction $\\rho'=(\\hat{C}',C',f',g',h')$ can be constructed where:\n",
-    "1. $\\hat{C}'$ is the chain complex obtained from $C$ by replacing the old differential $d_{\\hat{C}}$ by $(d_{\\hat{C}}+\\hat{\\delta}),$\n",
-    "2. the new chain complex $C'$ is obtained from the chain complex $C$ only by replacing  the old differential $d_C$ by $(d_C + \\delta),$ with $\\delta = f \\circ {\\hat \\delta} \\circ \\phi \\circ g =\n",
-    "               f \\circ \\psi \\circ {\\hat \\delta} \\circ g,$\n",
-    "3. $f'= f \\circ \\psi = f \\circ (Id - {\\hat \\delta} \\circ \\phi \\circ h),$\n",
-    "4. $g'= \\phi \\circ g,$\n",
-    "5. $h'= \\phi \\circ h = h \\circ \\psi$,\n",
-    "with \n",
-    "$$\n",
-    "\\phi=\\sum_{i=0}^{\\infty}{(-1)^i(h \\circ  \\hat{\\delta})^i}\n",
-    "$$\n",
-    "and\n",
-    "$$\n",
-    "\\psi=\\sum_{i=0}^{\\infty}{(-1)^i(\\hat{\\delta}\\circ h)^i} = Id - {\\hat \\delta} \\circ \\phi \\circ h,\n",
-    "$$\n",
-    "the convergence being ensured by the locally nilpotency of $h \\circ \\hat{\\delta}$ and $\\hat{\\delta} \\circ h$.\n",
-    "\n",
-    "**Theorem 2 (Trivial perturbation lemma)** - Let\n",
-    "$\\rho=(\\hat{C},C,f,g,h)$ a reduction and ${\\check\\delta}$ a *perturbation* of $d_C$, that is, an operator defined on $C$ of degree -1 satisfying the relation $(d_C+{\\check\\delta})\\circ (d_C+{\\check\\delta})=0$. Then a new reduction $\\rho'=(\\hat{C}',C',f',g',h')$ can be constructed where:\n",
-    "1. $\\hat{C}'$ is the chain complex obtained from $C$ by replacing the old differential $d_{\\hat{C}}$ by $(d_{\\hat{C}}+ g \\circ {\\check\\delta} \\circ f),$\n",
-    "2. the new chain complex $C'$ is obtained from the chain complex $C$ only by replacing  the old differential $d_C$ by $(d_C +{\\check \\delta}),$ \n",
-    "3. $f'= f,$\n",
-    "4. $g'= g,$\n",
-    "5. $h'= h.$\n",
-    "\n",
-    "### Useful functions related to the perturbation lemma\n",
-    "\n",
-    "The functions implementing the perturbation-lemma are actually the heart of the program. They allow us\n",
-    "to implement the effective versions of the classical spectral sequences (Serre, Eilenberg-Moore, ...). \n",
-    "\n",
-    "`(add` *rdct perturbation*`)` *[Method]*\n",
-    "> Build a new reduction from the  object of type `reduction`, *rdct* and \n",
-    "the  object of type `morphism`,  *perturbation*, applying the formulas given in the perturbation lemma. In fact, this method calls  one or the other of the two following functions according as the perturbation is on the top or on the bottom chain complex and returns the values of the called function.\n",
-    "\n",
-    "`(basic-perturbation-lemma` *reduction top-perturbation*`)` *[Function]*\n",
-    "> Return a double value: the perturbed reduction and the computed bottom-perturbation (a morphism)\n",
-    "$f \\circ {\\hat \\delta}\\circ  \\phi \\circ g$. Of course, to avoid unuseful computations when the morphisms are effectively applied, the function takes in account the simplifications involved for instance when some morphisms are the null morphism.\n",
-    "\n",
-    "`(easy-perturbation-lemma` *reduction bottom-perturbation*`)` *[Function]*\n",
-    "> Return a double value: the perturbed reduction and the computed top-perturbation (a morphism) $g \\circ {\\check \\delta} \\circ f$. Of course, to avoid useless computation when the morphisms will be applied, the function takes in account the simplifications involved for instance when some morphisms are the null morphism.\n",
-    "\n",
-    "`(special-bpl` *reduction top-perturbation*`)` *[Function]*\n",
-    "> This function is analogous to `basic-perturbation-lemma` and is used in some special cases when the morphism $g$ is invariant.\n",
-    "\n",
-    "`(special-bpl2` *reduction top-perturbation*`)` *[Function]*\n",
-    "> [analogous to special-bpl when $f$ is invariant.]\n",
-    "\n",
-    "`(bpl-*-sigma` *homotopy perturbation*`)` *[Function]*\n",
-    "> Construct the principal series $\\phi=\\sum_{i=0}^{\\infty}{(-1)^i(h \\circ  \\hat{\\delta})^i}$ of the basic perturbation lemma.\n",
-    "\n",
-    "`(add` *hmeq lb-perturbation*`)` *[Method]*\n",
-    "> Build a homotopy equivalence from the `homotopy-equivalence` *hmeq* and  the `morphism` *lb-perturbation*, a perturbation  of the differential of the left bottom chain complex of *hmeq*. From *hmeq*:\n",
-    "$$\n",
-    "\\begin{aligned}\n",
-    "  & \\qquad\\hat{C} & \\\\\n",
-    " \\rho_1\\swarrow\\nearrow   & & \\nwarrow\\searrow \\rho_2 \\\\\n",
-    "C\\quad  & & EC\n",
-    "\\end{aligned}\n",
-    "$$\n",
-    "the method `add` builds the new homotopy equivalence:\n",
-    "$$\n",
-    "\\begin{aligned}\n",
-    "  & \\qquad\\hat{C}' & \\\\\n",
-    " \\rho'_1\\swarrow\\nearrow   & & \\nwarrow\\searrow \\rho'_2 \\\\\n",
-    "C'\\quad  & & EC'\n",
-    "\\end{aligned}\n",
-    "$$\n",
-    "where the  construction steps are the following:\n",
-    "- The reduction $\\rho'_1$ is computed with the  method `add` for a reduction with arguments: the left  reduction of *hmeq* and the perturbation *lb-perturbation*. The trivial perturbation lemma is applied. As a bonus, this returns also the top perturbation, say $\\delta$ to be applied to $\\hat{C}$.\n",
-    "- The reduction $\\rho'_2$ is computed with the previous method `add` with arguments: the right reduction of *hmeq* and the top perturbation $\\delta$ just computed. That time, the basic perturbation lemma is applied.\n",
-    "- The function `build-hmeq` is called with parameters $\\rho'_1$ and $\\rho'_2$.\n",
-    "\n",
-    "#### Example\n",
-    "\n",
-    "We shall apply these methods and functions in the following chapters. Let us show on a trivial example\n",
-    "how this machinery works. First, we build a trivial homotopy equivalence on $\\Delta^4$. Then we build a new one by perturbing the differential of the left bottom chain complex with its opposite. The last call shows how this perturbation has been propagated."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 19,
-   "metadata": {
-    "scrolled": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K66 Homotopy-Equivalence K30 <= K30 => K30]"
-      ]
-     },
-     "execution_count": 19,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def hmeq (trivial-hmeq (cdelta 4)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 20,
-   "metadata": {
-    "scrolled": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K74 Homotopy-Equivalence K69 <= K69 => K69]"
-      ]
-     },
-     "execution_count": 20,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(setf hmeq (add hmeq (opps (dffr (cdelta 4)))))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 21,
-   "metadata": {
-    "scrolled": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 2}\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 21,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(gnrt-? (dffr (rbcc hmeq)) 3 '(0 1 2 3))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "## Bicones\n",
-    "\n",
-    "Given 3 chain complexes $B$, $C$ and $D$, together with 2 chain homomorphisms $f_1$ and $f_2$ of degree $0$ (commuting with the differentials), as shown in the following diagram, a bicone on these chain complexes is a chain complex, $BCN(f_1,f_2)$ where the $n$-th chain group $[BCN(f_1,f_2)]$ is $B_n \\oplus C_{n+1} \\oplus D_n$.\n",
-    "$$\n",
-    "\\begin{aligned}\n",
-    "B & & & \\qquad D & \\\\\n",
-    "& f_1 \\searrow & & \\swarrow f_2 & \\\\\n",
-    "& & C \\qquad& &\n",
-    "\\end{aligned}\n",
-    "$$\n",
-    "\n",
-    "### Representation of a combination in a bicone\n",
-    "\n",
-    "To distinguish to which chain complex belongs a generator in a combination of a bicone, the following convention has been adopted: if `gb` is a generator of any degree of $B$, it will be represented in the bicone by the list `(:BcnB gb)` and printed as `<BcnB gb>`. The symbols for $C$ and $D$ are respectively `:BcnC` and `:BcnD`. The 3 macros `bcnb`, `bcnc` and `bcnd` may be used to build such a generator. The building function for combinations, `cmbn`, may be used in the following way:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 22,
-   "metadata": {
-    "scrolled": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 3}\n",
-       "<2 * <BcnB B1>>\n",
-       "<4 * <BcnB B1>>\n",
-       "<6 * <BcnB B3>>\n",
-       "<3 * <BcnB C1>>\n",
-       "<5 * <BcnB C1>>\n",
-       "<7 * <BcnB D1>>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 22,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def comb-bic (cmbn 3 2 (bcnb 'b1) 4 (bcnb 'b1) 6 (bcnb 'b3)\n",
-    "                      3 (bcnb 'c1) 5 (bcnb 'c1) 7 (bcnb 'd1)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 23,
-   "metadata": {
-    "scrolled": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "((2 . <BcnB B1>) (4 . <BcnB B1>) (6 . <BcnB B3>) (3 . <BcnB C1>) (5 . <BcnB C1>) (7 . <BcnB D1>))"
-      ]
-     },
-     "execution_count": 23,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(cmbn-list comb-bic)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "### Useful functions and macros for bicones\n",
-    "\n",
-    "`(bcnb` *gnrt*`)` *[Macro]*\n",
-    "> Build the representation of the generator *gnrt* belonging to the chain complex $B$.\n",
-    "\n",
-    "`(bcnc` *gnrt*`)` *[Macro]*\n",
-    "> Build the representation of the generator *gnrt* belonging to the chain complex $C$.\n",
-    "\n",
-    "`(bcnd` *gnrt*`)` *[Macro]*\n",
-    "> Build the representation of the generator *gnrt* belonging to the chain complex $D$.\n",
-    "\n",
-    "`(make-bicn-cmbn` *cmbnb cmbnc cmbnd*`)` *[Function]*\n",
-    "> Build a bicone combination from the 3 combinations *cmbnb*, *cmbnc* and *cmbnd* belonging respectively and in that order to $B$, $C$ and $D$. The degrees of the combinations *cmbnb* and *cmbnd* must be the same, say $n$. The degree of *cmbnc* must be $n+1$. The degree of the new created combination is $n$.\n",
-    "\n",
-    "`(bicn-cmbn-cmbnb` *cmbn*`)` *[Function]*\n",
-    "> Extract from the bicone combination of degree $n$, *cmbn*, the combination relative to $B$ as a legal combination of degree $n$ in $B$. If there is no $B$-component, return the null combination of degree $n$.\n",
-    "\n",
-    "`(bicn-cmbn-cmbnc` *cmbn*`)` *[Function]*\n",
-    "> Extract from the bicone combination of degree $n$, *cmbn*, the combination relative to $C$ as a legal combination of degree $n+1$ in $C$. If there is no $C$-component, return the null combination of degree $n+1$.\n",
-    "\n",
-    "`(bicn-cmbn-cmbnd` *cmbn*`)` *[Function]*\n",
-    "> Extract from the bicone combination of degree $n$, *cmbn*, the combination relative to $D$ as a legal combination of degree $n$ in $D$. If there is no $D$-component, return the null combination of degree $n$\n",
-    "\n",
-    "`(dispatch-bicn-cmbn` *cmbn*`)` *[Function]*\n",
-    "> Give the 3-values result made of the 3 combinations components of the bicone combination *cmbn*. These combinations are valid combinations in their respective chain complexes.\n",
-    "\n",
-    "#### Examples"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 24,
-   "metadata": {
-    "scrolled": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 3}\n",
-       "<2 * B1>\n",
-       "<4 * B2>\n",
-       "<6 * B3>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 24,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def comb-b (cmbn 3 2 'b1 4 'b2 6 'b3))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 25,
-   "metadata": {
-    "scrolled": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 4}\n",
-       "<3 * C1>\n",
-       "<5 * C2>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 25,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def comb-c (cmbn 4 3 'c1 5 'c2))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 26,
-   "metadata": {
-    "scrolled": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 3}\n",
-       "<7 * D1>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 26,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def comb-d (cmbn 3 7 'd1))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 27,
-   "metadata": {
-    "scrolled": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 3}\n",
-       "<2 * <BcnB B1>>\n",
-       "<4 * <BcnB B2>>\n",
-       "<6 * <BcnB B3>>\n",
-       "<3 * <BcnC C1>>\n",
-       "<5 * <BcnC C2>>\n",
-       "<7 * <BcnD D1>>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 27,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def comb-bic (make-bicn-cmbn comb-b comb-c comb-d))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 28,
-   "metadata": {
-    "scrolled": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 3}\n",
-       "<2 * B1>\n",
-       "<4 * B2>\n",
-       "<6 * B3>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 28,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(bicn-cmbn-cmbnb comb-bic)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 29,
-   "metadata": {
-    "scrolled": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 4}\n",
-       "<3 * C1>\n",
-       "<5 * C2>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 29,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(bicn-cmbn-cmbnc comb-bic)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 30,
-   "metadata": {
-    "scrolled": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 3}\n",
-       "<7 * D1>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 30,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(bicn-cmbn-cmbnd comb-bic)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 31,
-   "metadata": {
-    "scrolled": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(\n",
-       "----------------------------------------------------------------------{CMBN 3}\n",
-       "<2 * B1>\n",
-       "<4 * B2>\n",
-       "<6 * B3>\n",
-       "------------------------------------------------------------------------------\n",
-       " \n",
-       "----------------------------------------------------------------------{CMBN 4}\n",
-       "<3 * C1>\n",
-       "<5 * C2>\n",
-       "------------------------------------------------------------------------------\n",
-       " \n",
-       "----------------------------------------------------------------------{CMBN 3}\n",
-       "<7 * D1>\n",
-       "------------------------------------------------------------------------------\n",
-       ")"
-      ]
-     },
-     "execution_count": 31,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(multiple-value-bind (b c d)\n",
-    "    (dispatch-bicn-cmbn comb-bic)\n",
-    "    (list b c d))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "## Construction of a bicone from 2 reductions\n",
-    "\n",
-    "From the slots of the respective chain complexes $B$, $C$ and $D$, it is possible to build the bicone chain complex. The 3 essential functions are the following:\n",
-    "\n",
-    "`(bicone-cmpr cmprb cmprc cmprd)` *[Function]*\n",
-    "> From the 3 comparison functions *cmprb*, *cmprc* and *cmprd*, build a comparison function adequate to compare the generators as represented in the bicone.\n",
-    "\n",
-    "`(bicone-basis basisb basisc basisd)` *[Function]*\n",
-    "> From the 3 basis function *basisb*, *basisc* and *basisd*, build a basis function for the bicone. If at least one of the chain complex component of the bicone is *locally effective*, the function returns the symbol `:locally-effective`.\n",
-    "\n",
-    "`(bicone-intr-dffr cmprc dffrb dffrc dffrd f1 f2)` *[Function]*\n",
-    "Define the differential in the bicone according to the formula:\n",
-    "$$\n",
-    "d(cb, cc, cd)= (d_B(cb), f_1(cb) + f_2(cd) - d_C(cc), d_D(cd)),\n",
-    "$$\n",
-    "where the notation is self explanatory. One sees that one needs the comparison operator *cmprc* of $C$, to order correctly the second combination of the resulting triple.\n",
-    "\n",
-    "Let us consider now 2 reductions $(\\hat C_1, C_1, f1, g1, h1)$ and $(\\hat C_2, C_2, f2, g2, h2)$\n",
-    "in which $C_1 = C_2$. It is possible to define a bicone, with the identification $\\hat C_1=B, C_1=C_2=C, \\hat C_2=D$. This is realised by the following function:\n",
-    "\n",
-    "`(bicone rdct1 rdct2)` *[Function]*\n",
-    "> Build the bicone chain complex from the objects ot type `reduction` *rdct1* and *rdct2*.\n",
-    "The bicone is built with the following identification: $B$ is the top chain complex of *rdct1*,\n",
-    "$D$ is the top chain complex of *rdct2*. The bottom chain complexes of both *rdct1* and *rdct2*\n",
-    "must be the same and $C$ is  that chain complex. Of course, both chain morphisms $f_1$ and\n",
-    "$f_2$ are respectively the morphism $f$ of the reductions. The construction of the bicone is realised\n",
-    "by a call to the building function `build-chcm` using the 3 functions `bicone-cmpr`, `bicone-basis` and `bicone-intr-dffr` with arguments coming from *rdct1* an *rdct2*. \n",
-    "The slot `bsgn` (base point) is let undefined and the strategy is by combination.\n",
-    "\n",
-    "#### Example\n",
-    "\n",
-    "Let us take again the example with the standard simplex $\\Delta^n$. The following function defines an effective version of ${\\cal C}_*(\\Delta^n)$, so we may ask for the basis in some dimensions."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 32,
-   "metadata": {
-    "scrolled": false
-   },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "---done---"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 32,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(cat-init)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 33,
-   "metadata": {
-    "scrolled": false
-   },
-   "outputs": [
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "REDEFINITION-WITH-DEFUN: \n",
-      "  redefining CAT::CDELTA in DEFUN\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "CDELTA"
-      ]
-     },
-     "execution_count": 33,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(defun cdelta (dmns)\n",
-    "    (build-chcm\n",
-    "     :cmpr #'l-cmpr\n",
-    "     :basis #'(lambda (n)\n",
-    "                      (mapcar #'dlop-int-ext (funcall (delta-n-basis dmns) n)))\n",
-    "     :bsgn '(0)\n",
-    "     :intr-dffr\n",
-    "         #'(lambda (degr gmsm)\n",
-    "            (make-cmbn\n",
-    "             :degr (1- degr)\n",
-    "             :list (do ((rslt +empty-list+\n",
-    "                              (cons (cons sign\n",
-    "                                          (append\n",
-    "                                           (subseq gmsm 0 nark)\n",
-    "                                           (subseq gmsm (1+ nark))))\n",
-    "                                    rslt))\n",
-    "                        (sign 1 (- sign))\n",
-    "                        (nark 0 (1+ nark)))\n",
-    "                       ((> nark degr) rslt))))\n",
-    "     :strt :gnrt\n",
-    "     :orgn `(Effective version of C_* delta ,dmns)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 34,
-   "metadata": {
-    "scrolled": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K1 Chain-Complex]"
-      ]
-     },
-     "execution_count": 34,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def delta3 (cdelta 3))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 35,
-   "metadata": {
-    "scrolled": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "((0) (1) (2) (3))"
-      ]
-     },
-     "execution_count": 35,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(basis delta3 0)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 36,
-   "metadata": {
-    "scrolled": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "((0 1) (0 2) (1 2) (0 3) (1 3) (2 3))"
-      ]
-     },
-     "execution_count": 36,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(basis delta3 1)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 37,
-   "metadata": {
-    "scrolled": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "((0 1 2) (0 1 3) (0 2 3) (1 2 3))"
-      ]
-     },
-     "execution_count": 37,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(basis delta3 2)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 38,
-   "metadata": {
-    "scrolled": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "((0 1 2 3))"
-      ]
-     },
-     "execution_count": 38,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(basis delta3 3)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 39,
-   "metadata": {
-    "scrolled": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 39,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(basis delta3 4)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Using the function `make-rdct` defined in previous example which builds a reduction between \n",
-    "$\\Delta^m$ and $\\Delta^n$, we may create a bicone chain complex with the function `bicone` and ask for basis in some dimensions."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 40,
-   "metadata": {
-    "scrolled": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K15 Chain-Complex]"
-      ]
-     },
-     "execution_count": 40,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def bic (bicone (make-rdct 3 2) (make-rdct 4 2)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 41,
-   "metadata": {
-    "scrolled": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(<BcnB (0)> <BcnB (1)> <BcnB (2)> <BcnB (3)> <BcnC (0 1)> <BcnC (0 2)> <BcnC (1 2)> <BcnD (0)> <BcnD (1)> <BcnD (2)> ...)"
-      ]
-     },
-     "execution_count": 41,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(basis bic 0)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 42,
-   "metadata": {
-    "scrolled": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(<BcnB (0 1)> <BcnB (0 2)> <BcnB (1 2)> <BcnB (0 3)> <BcnB (1 3)> <BcnB (2 3)> <BcnC (0 1 2)> <BcnD (0 1)> <BcnD (0 2)> <BcnD (1 2)> ...)"
-      ]
-     },
-     "execution_count": 42,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(basis bic 1)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 43,
-   "metadata": {
-    "scrolled": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(<BcnD (0 1 2 3 4)>)"
-      ]
-     },
-     "execution_count": 43,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(basis bic 4)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "We verify the validity of the differential in the bicone `bic`."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 44,
-   "metadata": {
-    "scrolled": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 1}\n",
-       "<3 * <BcnB (0 1)>>\n",
-       "<-3 * <BcnB (0 3)>>\n",
-       "<3 * <BcnB (1 3)>>\n",
-       "<12 * <BcnC (0 1 2)>>\n",
-       "<-4 * <BcnC (0 1 3)>>\n",
-       "<4 * <BcnC (0 2 3)>>\n",
-       "<-4 * <BcnC (1 2 3)>>\n",
-       "<5 * <BcnD (0 1)>>\n",
-       "<-5 * <BcnD (0 4)>>\n",
-       "<5 * <BcnD (1 4)>>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 44,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? bic (cmbn 2 3 (bcnb '(0 1 3)) 4 (bcnc '(0 1 2 3)) 5 (bcnd '(0 1 4))))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 45,
-   "metadata": {
-    "scrolled": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 0}\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 45,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? bic *)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "## Composition of homotopy equivalences\n",
-    "\n",
-    "Let us consider 2 homotopy equivalences, as in the following diagram.\n",
-    "$$\n",
-    "\\begin{aligned}\n",
-    "& \\qquad B & & & & \\qquad D \\\\\n",
-    "  \\rho_1 \\swarrow\\nearrow  & & \\nwarrow\\searrow \\rho_2 & \n",
-    "& \\rho'_1\\swarrow\\nearrow  & & \\nwarrow\\searrow\\rho'_2 \\\\\n",
-    "A \\quad &                & C &  & C \\quad & & E \\quad\n",
-    "\\end{aligned}\n",
-    "$$\n",
-    "where the right bottom complex of the first one is the same as the left bottom complex of the second. We may use then the bicone concept to build a bicone chain complex with $B$, $C$ and $D$, say $BCN$, and finally build a new homotopy equivalence between $A$, $BCN$ and $E$.\n",
-    "\n",
-    "$$\n",
-    "\\begin{aligned}\n",
-    "  & \\qquad BCN & \\\\\n",
-    " \\rho''_1 \\swarrow\\nearrow  & & \\nwarrow\\searrow \\rho''_2 \\\\\n",
-    "A \\quad & &  E\\quad\n",
-    "\\end{aligned}\n",
-    "$$\n",
-    "\n",
-    "This is realized by the method `cmps`.\n",
-    "\n",
-    "`(cmps` *hmeq1 hmeq2*`)` *[Method]*\n",
-    "> Build a homotopy equivalence by composition of both homotopy equivalences *hmeq1*, *hmeq2*. The system controls the validity of the composition.\n",
-    "\n",
-    "### Example\n",
-    "\n",
-    "Starting with a very simple chain complex and the trivial homotopy equivalence on the chain complex, we verify the correctness of various compositions. The chain complex `c` has only one vertex `(a)` in every dimension and the differential is the null morphism."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 46,
-   "metadata": {
-    "scrolled": false
-   },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "---done---"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 46,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(cat-init)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 47,
-   "metadata": {
-    "scrolled": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K1 Chain-Complex]"
-      ]
-     },
-     "execution_count": 47,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def c (build-chcm\n",
-    "            :cmpr #'s-cmpr\n",
-    "            :basis #'(lambda (dmns) (declare (ignore dmns)) '(a))\n",
-    "            :bsgn 'a\n",
-    "            :intr-dffr #'zero-intr-dffr\n",
-    "            :strt :cmbn\n",
-    "            :orgn '(c)))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "We build the trivial homotopy equivalence on `c` and we compose it with itself."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 48,
-   "metadata": {
-    "scrolled": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K6 Homotopy-Equivalence K1 <= K1 => K1]"
-      ]
-     },
-     "execution_count": 48,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def h1 (trivial-hmeq c))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 49,
-   "metadata": {
-    "scrolled": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K17 Homotopy-Equivalence K1 <= K7 => K1]"
-      ]
-     },
-     "execution_count": 49,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def h2 (cmps h1 h1))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "We verify the coherency of the morphisms in the left and right reduction of `h2`. The combination `*tc*` must belong to a bicone whereas `*bc*` belongs to `c`."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 50,
-   "metadata": {
-    "scrolled": false
-   },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "---done---"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 50,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(pre-check-rdct (lrdct h2))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 51,
-   "metadata": {
-    "scrolled": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 3}\n",
-       "<1 * <BcnB A>>\n",
-       "<10 * <BcnC A>>\n",
-       "<100 * <BcnD A>>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 51,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(setf *tc* (cmbn 3 1 (bcnb 'a) 10 (bcnc 'a) 100 (bcnd 'a)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 52,
-   "metadata": {
-    "scrolled": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 3}\n",
-       "<1 * A>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 52,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(setf *bc* (cmbn 3 1 'a))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 53,
-   "metadata": {
-    "scrolled": false
-   },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "*TC* => \n",
-      "----------------------------------------------------------------------{CMBN 3}\n",
-      "<1 * <BcnB A>>\n",
-      "<10 * <BcnC A>>\n",
-      "<100 * <BcnD A>>\n",
-      "------------------------------------------------------------------------------\n",
-      "\n",
-      "*BC* => \n",
-      "----------------------------------------------------------------------{CMBN 3}\n",
-      "<1 * A>\n",
-      "------------------------------------------------------------------------------\n",
-      "\n",
-      "Checking *TDD* = 0\n",
-      "Result: \n",
-      "----------------------------------------------------------------------{CMBN 1}\n",
-      "------------------------------------------------------------------------------\n",
-      "\n",
-      "Checking *BDD* = 0\n",
-      "Result: \n",
-      "----------------------------------------------------------------------{CMBN 1}\n",
-      "------------------------------------------------------------------------------\n",
-      "\n",
-      "Checking *DF-FD* = 0\n",
-      "Result: \n",
-      "----------------------------------------------------------------------{CMBN 2}\n",
-      "------------------------------------------------------------------------------\n",
-      "\n",
-      "Checking *DG-GD* = 0\n",
-      "Result: \n",
-      "----------------------------------------------------------------------{CMBN 2}\n",
-      "------------------------------------------------------------------------------\n",
-      "\n",
-      "Checking *ID-FG* = 0\n",
-      "Result: \n",
-      "----------------------------------------------------------------------{CMBN 3}\n",
-      "------------------------------------------------------------------------------\n",
-      "\n",
-      "Checking *ID-GF-DH-HD* = 0\n",
-      "Result: \n",
-      "----------------------------------------------------------------------{CMBN 3}\n",
-      "------------------------------------------------------------------------------\n",
-      "\n",
-      "Checking *HH* = 0\n",
-      "Result: \n",
-      "----------------------------------------------------------------------{CMBN 5}\n",
-      "------------------------------------------------------------------------------\n",
-      "\n",
-      "Checking *FH* = 0\n",
-      "Result: \n",
-      "----------------------------------------------------------------------{CMBN 4}\n",
-      "------------------------------------------------------------------------------\n",
-      "\n",
-      "Checking *HG* = 0\n",
-      "Result: \n",
-      "----------------------------------------------------------------------{CMBN 4}\n",
-      "------------------------------------------------------------------------------\n",
-      "\n",
-      "---done---"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 53,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(check-rdct-no-wait)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 54,
-   "metadata": {
-    "scrolled": false
-   },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "---done---"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 54,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(pre-check-rdct (rrdct h2))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 55,
-   "metadata": {
-    "scrolled": false
-   },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "*TC* => \n",
-      "----------------------------------------------------------------------{CMBN 3}\n",
-      "<1 * <BcnB A>>\n",
-      "<10 * <BcnC A>>\n",
-      "<100 * <BcnD A>>\n",
-      "------------------------------------------------------------------------------\n",
-      "\n",
-      "*BC* => \n",
-      "----------------------------------------------------------------------{CMBN 3}\n",
-      "<1 * A>\n",
-      "------------------------------------------------------------------------------\n",
-      "\n",
-      "Checking *TDD* = 0\n",
-      "Result: \n",
-      "----------------------------------------------------------------------{CMBN 1}\n",
-      "------------------------------------------------------------------------------\n",
-      "\n",
-      "Checking *BDD* = 0\n",
-      "Result: \n",
-      "----------------------------------------------------------------------{CMBN 1}\n",
-      "------------------------------------------------------------------------------\n",
-      "\n",
-      "Checking *DF-FD* = 0\n",
-      "Result: \n",
-      "----------------------------------------------------------------------{CMBN 2}\n",
-      "------------------------------------------------------------------------------\n",
-      "\n",
-      "Checking *DG-GD* = 0\n",
-      "Result: \n",
-      "----------------------------------------------------------------------{CMBN 2}\n",
-      "------------------------------------------------------------------------------\n",
-      "\n",
-      "Checking *ID-FG* = 0\n",
-      "Result: \n",
-      "----------------------------------------------------------------------{CMBN 3}\n",
-      "------------------------------------------------------------------------------\n",
-      "\n",
-      "Checking *ID-GF-DH-HD* = 0\n",
-      "Result: \n",
-      "----------------------------------------------------------------------{CMBN 3}\n",
-      "------------------------------------------------------------------------------\n",
-      "\n",
-      "Checking *HH* = 0\n",
-      "Result: \n",
-      "----------------------------------------------------------------------{CMBN 5}\n",
-      "------------------------------------------------------------------------------\n",
-      "\n",
-      "Checking *FH* = 0\n",
-      "Result: \n",
-      "----------------------------------------------------------------------{CMBN 4}\n",
-      "------------------------------------------------------------------------------\n",
-      "\n",
-      "Checking *HG* = 0\n",
-      "Result: \n",
-      "----------------------------------------------------------------------{CMBN 4}\n",
-      "------------------------------------------------------------------------------\n",
-      "\n",
-      "---done---"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 55,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(check-rdct-no-wait)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "We compose now `h2` with itself. We let `*bc*` unchanged, but `*tc*` is a little more complicated because the chain complexes $B$ and $D$  are themselves bicones."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 56,
-   "metadata": {
-    "scrolled": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K65 Homotopy-Equivalence K1 <= K55 => K1]"
-      ]
-     },
-     "execution_count": 56,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def h3 (cmps h2 h2))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 57,
-   "metadata": {
-    "scrolled": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 3}\n",
-       "<1 * <BcnB <BcnB A>>>\n",
-       "<10 * <BcnB <BcnC A>>>\n",
-       "<100 * <BcnB <BcnD A>>>\n",
-       "<1000 * <BcnC A>>\n",
-       "<10000 * <BcnD <BcnB A>>>\n",
-       "<5234 * <BcnD <BcnC A>>>\n",
-       "<223 * <BcnD <BcnD A>>>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 57,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(setf *tc* (cmbn 3 1 (bcnb (bcnb 'a)) 10 (bcnb (bcnc 'a)) 100 (bcnb (bcnd 'a))\n",
-    "                      1000 (bcnc 'a) 10000 (bcnd (bcnb 'a)) 5234 (bcnd (bcnc 'a))\n",
-    "                       223 (bcnd (bcnd 'a))))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 58,
-   "metadata": {
-    "scrolled": false
-   },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "---done---"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 58,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(pre-check-rdct (lrdct h3))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 59,
-   "metadata": {
-    "scrolled": false
-   },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "*TC* => \n",
-      "----------------------------------------------------------------------{CMBN 3}\n",
-      "<1 * <BcnB <BcnB A>>>\n",
-      "<10 * <BcnB <BcnC A>>>\n",
-      "<100 * <BcnB <BcnD A>>>\n",
-      "<1000 * <BcnC A>>\n",
-      "<10000 * <BcnD <BcnB A>>>\n",
-      "<5234 * <BcnD <BcnC A>>>\n",
-      "<223 * <BcnD <BcnD A>>>\n",
-      "------------------------------------------------------------------------------\n",
-      "\n",
-      "*BC* => \n",
-      "----------------------------------------------------------------------{CMBN 3}\n",
-      "<1 * A>\n",
-      "------------------------------------------------------------------------------\n",
-      "\n",
-      "Checking *TDD* = 0\n",
-      "Result: \n",
-      "----------------------------------------------------------------------{CMBN 1}\n",
-      "------------------------------------------------------------------------------\n",
-      "\n",
-      "Checking *BDD* = 0\n",
-      "Result: \n",
-      "----------------------------------------------------------------------{CMBN 1}\n",
-      "------------------------------------------------------------------------------\n",
-      "\n",
-      "Checking *DF-FD* = 0\n",
-      "Result: \n",
-      "----------------------------------------------------------------------{CMBN 2}\n",
-      "------------------------------------------------------------------------------\n",
-      "\n",
-      "Checking *DG-GD* = 0\n",
-      "Result: \n",
-      "----------------------------------------------------------------------{CMBN 2}\n",
-      "------------------------------------------------------------------------------\n",
-      "\n",
-      "Checking *ID-FG* = 0\n",
-      "Result: \n",
-      "----------------------------------------------------------------------{CMBN 3}\n",
-      "------------------------------------------------------------------------------\n",
-      "\n",
-      "Checking *ID-GF-DH-HD* = 0\n",
-      "Result: \n",
-      "----------------------------------------------------------------------{CMBN 3}\n",
-      "------------------------------------------------------------------------------\n",
-      "\n",
-      "Checking *HH* = 0\n",
-      "Result: \n",
-      "----------------------------------------------------------------------{CMBN 5}\n",
-      "------------------------------------------------------------------------------\n",
-      "\n",
-      "Checking *FH* = 0\n",
-      "Result: \n",
-      "----------------------------------------------------------------------{CMBN 4}\n",
-      "------------------------------------------------------------------------------\n",
-      "\n",
-      "Checking *HG* = 0\n",
-      "Result: \n",
-      "----------------------------------------------------------------------{CMBN 4}\n",
-      "------------------------------------------------------------------------------\n",
-      "\n",
-      "---done---"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 59,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(check-rdct-no-wait)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 60,
-   "metadata": {
-    "scrolled": false
-   },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "---done---"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 60,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(pre-check-rdct (rrdct h3))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 61,
-   "metadata": {
-    "scrolled": false
-   },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "*TC* => \n",
-      "----------------------------------------------------------------------{CMBN 3}\n",
-      "<1 * <BcnB <BcnB A>>>\n",
-      "<10 * <BcnB <BcnC A>>>\n",
-      "<100 * <BcnB <BcnD A>>>\n",
-      "<1000 * <BcnC A>>\n",
-      "<10000 * <BcnD <BcnB A>>>\n",
-      "<5234 * <BcnD <BcnC A>>>\n",
-      "<223 * <BcnD <BcnD A>>>\n",
-      "------------------------------------------------------------------------------\n",
-      "\n",
-      "*BC* => \n",
-      "----------------------------------------------------------------------{CMBN 3}\n",
-      "<1 * A>\n",
-      "------------------------------------------------------------------------------\n",
-      "\n",
-      "Checking *TDD* = 0\n",
-      "Result: \n",
-      "----------------------------------------------------------------------{CMBN 1}\n",
-      "------------------------------------------------------------------------------\n",
-      "\n",
-      "Checking *BDD* = 0\n",
-      "Result: \n",
-      "----------------------------------------------------------------------{CMBN 1}\n",
-      "------------------------------------------------------------------------------\n",
-      "\n",
-      "Checking *DF-FD* = 0\n",
-      "Result: \n",
-      "----------------------------------------------------------------------{CMBN 2}\n",
-      "------------------------------------------------------------------------------\n",
-      "\n",
-      "Checking *DG-GD* = 0\n",
-      "Result: \n",
-      "----------------------------------------------------------------------{CMBN 2}\n",
-      "------------------------------------------------------------------------------\n",
-      "\n",
-      "Checking *ID-FG* = 0\n",
-      "Result: \n",
-      "----------------------------------------------------------------------{CMBN 3}\n",
-      "------------------------------------------------------------------------------\n",
-      "\n",
-      "Checking *ID-GF-DH-HD* = 0\n",
-      "Result: \n",
-      "----------------------------------------------------------------------{CMBN 3}\n",
-      "------------------------------------------------------------------------------\n",
-      "\n",
-      "Checking *HH* = 0\n",
-      "Result: \n",
-      "----------------------------------------------------------------------{CMBN 5}\n",
-      "------------------------------------------------------------------------------\n",
-      "\n",
-      "Checking *FH* = 0\n",
-      "Result: \n",
-      "----------------------------------------------------------------------{CMBN 4}\n",
-      "------------------------------------------------------------------------------\n",
-      "\n",
-      "Checking *HG* = 0\n",
-      "Result: \n",
-      "----------------------------------------------------------------------{CMBN 4}\n",
-      "------------------------------------------------------------------------------\n",
-      "\n",
-      "---done---"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 61,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(check-rdct-no-wait)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "#### Lisp files concerned in this chapter\n",
-    "\n",
-    "`effective-homology.lisp`, `cones.lisp`.\n",
-    "\n",
-    "[`classes.lisp`, `macros.lisp`, `various.lisp`]."
-   ]
-  }
- ],
- "metadata": {
-  "kernelspec": {
-   "display_name": "SBCL Lisp",
-   "language": "lisp",
-   "name": "lisp"
-  },
-  "language_info": {
-   "codemirror_mode": "text/x-common-lisp",
-   "mimetype": "text/x-common-lisp",
-   "name": "common-lisp",
-   "pygments_lexer": "common-lisp",
-   "version": "X3J13"
-  }
- },
- "nbformat": 4,
- "nbformat_minor": 1
-}
diff --git a/examples/03_The_Homology_module.ipynb b/examples/03_The_Homology_module.ipynb
deleted file mode 100644
index c64355b..0000000
--- a/examples/03_The_Homology_module.ipynb
+++ /dev/null
@@ -1,2338 +0,0 @@
-{
- "cells": [
-  {
-   "cell_type": "code",
-   "execution_count": 1,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "To load \"kenzo\":\n",
-      "  Load 1 ASDF system:\n",
-      "    kenzo\n",
-      "; Loading \"kenzo\"\n",
-      "\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "#<PACKAGE \"CAT\">"
-      ]
-     },
-     "execution_count": 1,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(ql:quickload \"kenzo\")\n",
-    "(in-package :cat)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "# The Homology Module\n",
-    "\n",
-    "This chapter is devoted to the description of the functions for computing the homology groups of a chain complex.\n",
-    "\n",
-    "## List of functions\n",
-    "\n",
-    "`chcm-homology` *chcm dim* *[Function]*\n",
-    "> Return a description of the $\\mathbb{Z}$-homology group in dimension *dim* of the chain complex *chcm* in terms of *components* of the form $\\mathbb{Z}$ or $\\mathbb{Z}/{n\\, \\mathbb{Z}}$. The desired homology group is the direct sum of these  components. No canonical presentation is looked for, so that, if for instance, a homology group is $\\mathbb{Z}/{6\\, \\mathbb{Z}}$, it can be displayed as one component $\\mathbb{Z}/{6\\, \\mathbb{Z}}$ or two components $\\mathbb{Z}/{2\\, \\mathbb{Z}}$ and $\\mathbb{Z}/{3\\, \\mathbb{Z}}$. On the other hand, if the component part  is void, this  means  the homology group is the null group. The function `chcm-homology` implements the usual algorithms to compute the homology group associated to two integer matrices, the composite of which is null. The current version is verbose: for each group asked for, the program displays the rank of each integer matrix and each generator of the source module. Timing indications are also given. In the examples, only the  components are printed.\n",
-    "\n",
-    "`chcm-homology-gen` *chcm n* *[Function]*\n",
-    "> This function computes the homology group in dimension $n$ of the chain complex *chcm* and prints a generator of degree $n$ in *chcm* for each component of the group, that is, a combination of the  basis elements of degree $n$ of the chain complex, some cycle representing the corresponding homology class.\n",
-    "\n",
-    "`chcm-mat` *chcm n* *[Function]*\n",
-    "> Return the matrix of the linear homomorphism  $d_n: C_n \\rightarrow C_{n-1}$, where $C_n$ is the $n$-th chain group of the chain complex *chcm*. More precisely, each column  of this matrix contains the integer coefficients in the basis of $C_{n-1}$ of the image by $d_n$ of each basis element of $C_n$. So the number of rows (resp. columns) of the matrix is the number of elements of the basis of $C_{n-1}$ (resp. $C_n$). The homology group ${\\cal H}_n={\\cal Z}_n/{\\cal B}_n$ is computed from the two matrices `MZ` $=$ `chcm-mat` *(chcm,n)* and `NB` $=$ `chcm-mat` *(chcm, n+1)*. By well known algorithms on matrix reduction (**S. MacLane & G. Birkhoff**, *Algebra*, The MacMillan Company, 1967), the matrix `MZ` is used to find a basis for the kernel ${\\cal Z}_n$ and the matrix `NB`, to find in ${\\cal Z}_n$ a presentation of the group ${\\cal H}_n={\\cal Z}_n/{\\cal B}_n$ by generators and relations. This is performed by the internal function `homologie` (beware: not `homology`!).\n",
-    "\n",
-    "`homology` *chcm degr1* `&optional (`*degr2* `(1+` *degr1*`))` *[Method]*\n",
-    "> Compute the homology groups from $degr_1$ to $degr_2-1$ (default: only $degr_1$, if *degr2* is omitted) of the right chain complex of the homotopy equivalence contained in the slot `:efhm` of the\n",
-    "chain complex instance *chcm*. At the creation of the chain complex, this slot is unbound and is set during execution by an adequate CLOS method. If this slot cannot be  bound, an error is returned and the homology groups cannot be computed. A more elaborated explanation of the mechanism used by the function `homology` is given in the  section: **The general method for computing homology groups.**\n",
-    "\n",
-    "\n",
-    "## Example\n",
-    "\n",
-    "Let us get the homology groups for the example `diabolo` of the chapter 1."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 2,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K1 Chain-Complex]"
-      ]
-     },
-     "execution_count": 2,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def diabolo (build-chcm\n",
-    "              :cmpr #'s-cmpr\n",
-    "              :basis #'(lambda (dmn)\n",
-    "                               (case dmn\n",
-    "                                   (0 '(s0 s1 s2 s3 s4 s5))\n",
-    "                                   (1 '(s01 s02 s12 s23 s34 s35 s45))\n",
-    "                                   (2 '(s345))\n",
-    "                                   (otherwise nil)))\n",
-    "              :bsgn 's0\n",
-    "              :intr-dffr #'(lambda (dmn gnr)\n",
-    "                                   (unless (<= 0 dmn 2)\n",
-    "                                       (error \"Incorrect dimension for diabolo-dp.\"))\n",
-    "                                   (case dmn\n",
-    "                                       (0 (cmbn -1))  ; Note the null combination of degree -1\n",
-    "                                       (1 (case gnr\n",
-    "                                              (s01 (cmbn 0 -1 's0 1 's1))\n",
-    "                                              (s02 (cmbn 0 -1 's0 1 's2))\n",
-    "                                              (s12 (cmbn 0 -1 's1 1 's2))\n",
-    "                                              (s23 (cmbn 0 -1 's2 1 's3))\n",
-    "                                              (s34 (cmbn 0 -1 's3 1 's4))\n",
-    "                                              (s35 (cmbn 0 -1 's3 1 's5))\n",
-    "                                              (s45 (cmbn 0 -1 's4 1 's5))))\n",
-    "                                        (2 (case gnr\n",
-    "                                               (s345 (cmbn 1 1 's34 -1 's35 1 's45))))\n",
-    "                                       (otherwise (error \"Bad generator for complex diabolo\"))))\n",
-    "              :strt :GNRT\n",
-    "              :orgn '(diabolo-for-example)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 3,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "Computing boundary-matrix in dimension 0.\n",
-      "Rank of the source-module : 6.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 1/6 (dimension 0) :\n",
-      "S0 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 2/6 (dimension 0) :\n",
-      "S1 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 3/6 (dimension 0) :\n",
-      "S2 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 4/6 (dimension 0) :\n",
-      "S3 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 5/6 (dimension 0) :\n",
-      "S4 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 6/6 (dimension 0) :\n",
-      "S5 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 1.\n",
-      "Rank of the source-module : 7.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 1/7 (dimension 1) :\n",
-      "S01 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 2/7 (dimension 1) :\n",
-      "S02 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 3/7 (dimension 1) :\n",
-      "S12 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 4/7 (dimension 1) :\n",
-      "S23 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 5/7 (dimension 1) :\n",
-      "S34 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 6/7 (dimension 1) :\n",
-      "S35 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 7/7 (dimension 1) :\n",
-      "S45 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 0 :\n",
-      "\n",
-      "\n",
-      "Component Z\n",
-      "\n",
-      "\n",
-      "---done---"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 3,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(chcm-homology diabolo 0)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 4,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "Computing boundary-matrix in dimension 1.\n",
-      "Rank of the source-module : 7.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 1/7 (dimension 1) :\n",
-      "S01 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 2/7 (dimension 1) :\n",
-      "S02 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 3/7 (dimension 1) :\n",
-      "S12 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 4/7 (dimension 1) :\n",
-      "S23 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 5/7 (dimension 1) :\n",
-      "S34 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 6/7 (dimension 1) :\n",
-      "S35 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 7/7 (dimension 1) :\n",
-      "S45 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 2.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 2) :\n",
-      "S345 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 1 :\n",
-      "\n",
-      "\n",
-      "Component Z\n",
-      "\n",
-      "\n",
-      "---done---"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 4,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(chcm-homology diabolo 1)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 5,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "Computing boundary-matrix in dimension 2.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 2) :\n",
-      "S345 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 3.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 2 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 5,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(chcm-homology diabolo 2)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Another simple example is the following  2-chain  complex  corresponding to the well known *dunce hat*. We shall see later in the chapter `Simplicial Sets` a much more elegant method to describe this object."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 6,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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",
-      "text/plain": [
-       "#<CL-JUPYTER-USER::PNG-BYTES {1002094463}>"
-      ]
-     },
-     "execution_count": 6,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(cl-jupyter-user:png-from-file \"dunce.png\")"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "The diagram shows a permissible triangulation. For the generators, we have  chosen lists rather symbols: a vertex $s_i$ is represented as `(i)`, an edge $s_is_j$ as `(i j)` and a triangle $s_is_js_k$ as `(i j k)`. The enumeration of the elements of the basis is a little  cumbersome but defining  the boundary homomorphism is very easy, bearing in mind the boundary rule:\n",
-    "\n",
-    "$$\n",
-    "\\mathbf{d}[s_0s_1\\ldots s_n] = \\sum_{i=0}^n{(-1)^is_0s_1\\ldots\\widehat{s_i}\\ldots s_n}.\n",
-    "$$\n",
-    "\n",
-    "As for diabolo, the vertices are implicitly ordered."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 7,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "#<FUNCTION (LAMBDA (DMN) :IN \"/root/cl-jupyter/cl-jupyter.lisp\") {10022917FB}>"
-      ]
-     },
-     "execution_count": 7,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def duncehat-basis #'(lambda (dmn)\n",
-    "                              (case dmn\n",
-    "                                  (0 '((0) (1) (2) (3) (4) (5) (6) (7)))\n",
-    "                                  (1 '((0 1) (0 2) (0 3)\n",
-    "                                       (0 4) (0 5) (0 6)\n",
-    "                                       (0 7) (1 2) (1 3)\n",
-    "                                       (1 4) (1 5) (1 6)\n",
-    "                                       (1 7) (2 3) (2 4)\n",
-    "                                       (2 6) (2 7) (3 4)\n",
-    "                                       (3 5) (4 5) (4 6)\n",
-    "                                       (5 6) (5 7) (6 7)))\n",
-    "                                  (2 '((0 1 5) (0 1 6) (0 1 7)\n",
-    "                                       (0 2 3) (0 2 4) (0 2 6)\n",
-    "                                       (0 3 4) (0 5 7) (1 2 3)\n",
-    "                                       (1 2 4) (1 2 7) (1 3 5)\n",
-    "                                       (1 4 6) (2 6 7) (3 4 5)\n",
-    "                                       (4 5 6) (5 6 7)))\n",
-    "                                  (otherwise nil))))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 8,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "#<FUNCTION (LAMBDA (DMN GNR) :IN \"/root/cl-jupyter/cl-jupyter.lisp\") {10023AC59B}>"
-      ]
-     },
-     "execution_count": 8,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def duncehat-df #'(lambda (dmn gnr)\n",
-    "                           (case dmn\n",
-    "                               (0 (cmbn -1))\n",
-    "                               (1 (cmbn 0 -1 (list (first gnr)) 1 (rest gnr)))\n",
-    "                               (2 (cmbn 1 1 (list (first gnr) (second gnr))\n",
-    "                                         -1 (list (first gnr) (third gnr))\n",
-    "                                          1 (rest gnr)))\n",
-    "                               (otherwise nil))))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 9,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K3 Chain-Complex]"
-      ]
-     },
-     "execution_count": 9,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def duncehat (build-chcm :cmpr #'l-cmpr\n",
-    "                          :basis duncehat-basis\n",
-    "                          :bsgn '(0)\n",
-    "                          :intr-dffr duncehat-df\n",
-    "                          :strt :gnrt\n",
-    "                          :orgn '(dunce hat)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 10,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "Computing boundary-matrix in dimension 0.\n",
-      "Rank of the source-module : 8.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 1/8 (dimension 0) :\n",
-      "(0) \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 2/8 (dimension 0) :\n",
-      "(1) \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 3/8 (dimension 0) :\n",
-      "(2) \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 4/8 (dimension 0) :\n",
-      "(3) \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 5/8 (dimension 0) :\n",
-      "(4) \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 6/8 (dimension 0) :\n",
-      "(5) \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 7/8 (dimension 0) :\n",
-      "(6) \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 8/8 (dimension 0) :\n",
-      "(7) \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 1.\n",
-      "Rank of the source-module : 24.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 1/24 (dimension 1) :\n",
-      "(0 1) \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 2/24 (dimension 1) :\n",
-      "(0 2) \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 3/24 (dimension 1) :\n",
-      "(0 3) \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 4/24 (dimension 1) :\n",
-      "(0 4) \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 5/24 (dimension 1) :\n",
-      "(0 5) \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 6/24 (dimension 1) :\n",
-      "(0 6) \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 7/24 (dimension 1) :\n",
-      "(0 7) \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 8/24 (dimension 1) :\n",
-      "(1 2) \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 9/24 (dimension 1) :\n",
-      "(1 3) \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 10/24 (dimension 1) :\n",
-      "(1 4) \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 11/24 (dimension 1) :\n",
-      "(1 5) \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 12/24 (dimension 1) :\n",
-      "(1 6) \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 13/24 (dimension 1) :\n",
-      "(1 7) \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 14/24 (dimension 1) :\n",
-      "(2 3) \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 15/24 (dimension 1) :\n",
-      "(2 4) \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 16/24 (dimension 1) :\n",
-      "(2 6) \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 17/24 (dimension 1) :\n",
-      "(2 7) \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 18/24 (dimension 1) :\n",
-      "(3 4) \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 19/24 (dimension 1) :\n",
-      "(3 5) \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 20/24 (dimension 1) :\n",
-      "(4 5) \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 21/24 (dimension 1) :\n",
-      "(4 6) \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 22/24 (dimension 1) :\n",
-      "(5 6) \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 23/24 (dimension 1) :\n",
-      "(5 7) \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 24/24 (dimension 1) :\n",
-      "(6 7) \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 0 :\n",
-      "\n",
-      "\n",
-      "Component Z\n",
-      "\n",
-      "\n",
-      "---done---"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 10,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(chcm-homology duncehat 0)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 11,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "Computing boundary-matrix in dimension 1.\n",
-      "Rank of the source-module : 24.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 1/24 (dimension 1) :\n",
-      "(0 1) \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 2/24 (dimension 1) :\n",
-      "(0 2) \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 3/24 (dimension 1) :\n",
-      "(0 3) \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 4/24 (dimension 1) :\n",
-      "(0 4) \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 5/24 (dimension 1) :\n",
-      "(0 5) \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 6/24 (dimension 1) :\n",
-      "(0 6) \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 7/24 (dimension 1) :\n",
-      "(0 7) \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 8/24 (dimension 1) :\n",
-      "(1 2) \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 9/24 (dimension 1) :\n",
-      "(1 3) \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 10/24 (dimension 1) :\n",
-      "(1 4) \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 11/24 (dimension 1) :\n",
-      "(1 5) \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 12/24 (dimension 1) :\n",
-      "(1 6) \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 13/24 (dimension 1) :\n",
-      "(1 7) \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 14/24 (dimension 1) :\n",
-      "(2 3) \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 15/24 (dimension 1) :\n",
-      "(2 4) \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 16/24 (dimension 1) :\n",
-      "(2 6) \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 17/24 (dimension 1) :\n",
-      "(2 7) \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 18/24 (dimension 1) :\n",
-      "(3 4) \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 19/24 (dimension 1) :\n",
-      "(3 5) \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 20/24 (dimension 1) :\n",
-      "(4 5) \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 21/24 (dimension 1) :\n",
-      "(4 6) \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 22/24 (dimension 1) :\n",
-      "(5 6) \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 23/24 (dimension 1) :\n",
-      "(5 7) \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 24/24 (dimension 1) :\n",
-      "(6 7) \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 2.\n",
-      "Rank of the source-module : 17.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 1/17 (dimension 2) :\n",
-      "(0 1 5) \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 2/17 (dimension 2) :\n",
-      "(0 1 6) \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 3/17 (dimension 2) :\n",
-      "(0 1 7) \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 4/17 (dimension 2) :\n",
-      "(0 2 3) \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 5/17 (dimension 2) :\n",
-      "(0 2 4) \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 6/17 (dimension 2) :\n",
-      "(0 2 6) \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 7/17 (dimension 2) :\n",
-      "(0 3 4) \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 8/17 (dimension 2) :\n",
-      "(0 5 7) \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 9/17 (dimension 2) :\n",
-      "(1 2 3) \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 10/17 (dimension 2) :\n",
-      "(1 2 4) \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 11/17 (dimension 2) :\n",
-      "(1 2 7) \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 12/17 (dimension 2) :\n",
-      "(1 3 5) \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 13/17 (dimension 2) :\n",
-      "(1 4 6) \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 14/17 (dimension 2) :\n",
-      "(2 6 7) \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 15/17 (dimension 2) :\n",
-      "(3 4 5) \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 16/17 (dimension 2) :\n",
-      "(4 5 6) \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 17/17 (dimension 2) :\n",
-      "(5 6 7) \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 1 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 11,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(chcm-homology duncehat 1)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 12,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "Computing boundary-matrix in dimension 2.\n",
-      "Rank of the source-module : 17.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 1/17 (dimension 2) :\n",
-      "(0 1 5) \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 2/17 (dimension 2) :\n",
-      "(0 1 6) \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 3/17 (dimension 2) :\n",
-      "(0 1 7) \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 4/17 (dimension 2) :\n",
-      "(0 2 3) \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 5/17 (dimension 2) :\n",
-      "(0 2 4) \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 6/17 (dimension 2) :\n",
-      "(0 2 6) \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 7/17 (dimension 2) :\n",
-      "(0 3 4) \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 8/17 (dimension 2) :\n",
-      "(0 5 7) \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 9/17 (dimension 2) :\n",
-      "(1 2 3) \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 10/17 (dimension 2) :\n",
-      "(1 2 4) \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 11/17 (dimension 2) :\n",
-      "(1 2 7) \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 12/17 (dimension 2) :\n",
-      "(1 3 5) \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 13/17 (dimension 2) :\n",
-      "(1 4 6) \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 14/17 (dimension 2) :\n",
-      "(2 6 7) \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 15/17 (dimension 2) :\n",
-      "(3 4 5) \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 16/17 (dimension 2) :\n",
-      "(4 5 6) \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 17/17 (dimension 2) :\n",
-      "(5 6 7) \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 3.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 2 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 12,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(chcm-homology duncehat 2)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "We remark the homology of this \"dunce hat\" is the homology of  one point. Good exercise: compute the $\\pi_1$. A maximal \"tree\" is the path $01234567$, and the standard reduction process, for example $35~345$, etc., shows the $\\pi_1$ is generated by the loop $0120$. The same sort of argument shows this loop is homotopic to its double, and therefore null-homotopic, so that finally $\\pi_1 = 0$. A famous theorem of Whitehead then asserts our \"dunce hat\" is contractible, which is not really intuitive. The same result via the minimal triangulation of the dunce hat as a simplicial set is much easier.\n",
-    "\n",
-    "Let us take again  the chain complex `duncehat`. The two matrices of the homomorphisms $d_1: C_1 \\rightarrow C_0$ and $d_2: C_2 \\rightarrow C_1$ are obtained by calling `chcm-mat`."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 13,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "Computing boundary-matrix in dimension 1.\n",
-      "Rank of the source-module : 24.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 1/24 (dimension 1) :\n",
-      "(0 1) \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 2/24 (dimension 1) :\n",
-      "(0 2) \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 3/24 (dimension 1) :\n",
-      "(0 3) \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 4/24 (dimension 1) :\n",
-      "(0 4) \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 5/24 (dimension 1) :\n",
-      "(0 5) \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 6/24 (dimension 1) :\n",
-      "(0 6) \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 7/24 (dimension 1) :\n",
-      "(0 7) \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 8/24 (dimension 1) :\n",
-      "(1 2) \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 9/24 (dimension 1) :\n",
-      "(1 3) \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 10/24 (dimension 1) :\n",
-      "(1 4) \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 11/24 (dimension 1) :\n",
-      "(1 5) \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 12/24 (dimension 1) :\n",
-      "(1 6) \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 13/24 (dimension 1) :\n",
-      "(1 7) \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 14/24 (dimension 1) :\n",
-      "(2 3) \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 15/24 (dimension 1) :\n",
-      "(2 4) \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 16/24 (dimension 1) :\n",
-      "(2 6) \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 17/24 (dimension 1) :\n",
-      "(2 7) \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 18/24 (dimension 1) :\n",
-      "(3 4) \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 19/24 (dimension 1) :\n",
-      "(3 5) \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 20/24 (dimension 1) :\n",
-      "(4 5) \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 21/24 (dimension 1) :\n",
-      "(4 6) \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 22/24 (dimension 1) :\n",
-      "(5 6) \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 23/24 (dimension 1) :\n",
-      "(5 7) \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 24/24 (dimension 1) :\n",
-      "(6 7) \n",
-      "End of computing.\n",
-      "\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "========== MATRIX 8 lines + 24 columns =====\n",
-       "L1=[C1=-1][C2=-1][C3=-1][C4=-1][C5=-1][C6=-1][C7=-1]\n",
-       "L2=[C1=1][C8=-1][C9=-1][C10=-1][C11=-1][C12=-1][C13=-1]\n",
-       "L3=[C2=1][C8=1][C14=-1][C15=-1][C16=-1][C17=-1]\n",
-       "L4=[C3=1][C9=1][C14=1][C18=-1][C19=-1]\n",
-       "L5=[C4=1][C10=1][C15=1][C18=1][C20=-1][C21=-1]\n",
-       "L6=[C5=1][C11=1][C19=1][C20=1][C22=-1][C23=-1]\n",
-       "L7=[C6=1][C12=1][C16=1][C21=1][C22=1][C24=-1]\n",
-       "L8=[C7=1][C13=1][C17=1][C23=1][C24=1]\n",
-       "========== END-MATRIX"
-      ]
-     },
-     "execution_count": 13,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def mz (chcm-mat duncehat 1))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 14,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "Computing boundary-matrix in dimension 2.\n",
-      "Rank of the source-module : 17.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 1/17 (dimension 2) :\n",
-      "(0 1 5) \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 2/17 (dimension 2) :\n",
-      "(0 1 6) \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 3/17 (dimension 2) :\n",
-      "(0 1 7) \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 4/17 (dimension 2) :\n",
-      "(0 2 3) \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 5/17 (dimension 2) :\n",
-      "(0 2 4) \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 6/17 (dimension 2) :\n",
-      "(0 2 6) \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 7/17 (dimension 2) :\n",
-      "(0 3 4) \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 8/17 (dimension 2) :\n",
-      "(0 5 7) \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 9/17 (dimension 2) :\n",
-      "(1 2 3) \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 10/17 (dimension 2) :\n",
-      "(1 2 4) \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 11/17 (dimension 2) :\n",
-      "(1 2 7) \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 12/17 (dimension 2) :\n",
-      "(1 3 5) \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 13/17 (dimension 2) :\n",
-      "(1 4 6) \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 14/17 (dimension 2) :\n",
-      "(2 6 7) \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 15/17 (dimension 2) :\n",
-      "(3 4 5) \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 16/17 (dimension 2) :\n",
-      "(4 5 6) \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 17/17 (dimension 2) :\n",
-      "(5 6 7) \n",
-      "End of computing.\n",
-      "\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "========== MATRIX 24 lines + 17 columns =====\n",
-       "L1=[C1=1][C2=1][C3=1]\n",
-       "L2=[C4=1][C5=1][C6=1]\n",
-       "L3=[C4=-1][C7=1]\n",
-       "L4=[C5=-1][C7=-1]\n",
-       "L5=[C1=-1][C8=1]\n",
-       "L6=[C2=-1][C6=-1]\n",
-       "L7=[C3=-1][C8=-1]\n",
-       "L8=[C9=1][C10=1][C11=1]\n",
-       "L9=[C9=-1][C12=1]\n",
-       "L10=[C10=-1][C13=1]\n",
-       "L11=[C1=1][C12=-1]\n",
-       "L12=[C2=1][C13=-1]\n",
-       "L13=[C3=1][C11=-1]\n",
-       "L14=[C4=1][C9=1]\n",
-       "L15=[C5=1][C10=1]\n",
-       "L16=[C6=1][C14=1]\n",
-       "L17=[C11=1][C14=-1]\n",
-       "L18=[C7=1][C15=1]\n",
-       "L19=[C12=1][C15=-1]\n",
-       "L20=[C15=1][C16=1]\n",
-       "L21=[C13=1][C16=-1]\n",
-       "L22=[C16=1][C17=1]\n",
-       "L23=[C8=1][C17=-1]\n",
-       "L24=[C14=1][C17=1]\n",
-       "========== END-MATRIX"
-      ]
-     },
-     "execution_count": 14,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def nb (chcm-mat duncehat 2))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 15,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 15,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(homologie mz nb)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "## The general method for computing homology\n",
-    "\n",
-    "Among the slots of the instance of an object inheriting the `CHAIN COMPLEX` class, a slot `efhm`\n",
-    "has been reserved to point (possibly) to a homotopy equivalence where the right bottom chain complex is effective. The function `homology` is designed to get the right bottom chain complex of the homotopy equivalence value of the slot. If the slot has been bound, then the homology groups are computed by the function `chcm-homology` as shown in the following definition:\n",
-    "\n",
-    "```commonlisp\n",
-    "(DEFMETHOD HOMOLOGY ((chcm chain-complex) degr1 &optional (degr2 (1+ degr1)))\n",
-    "   (do ((degr degr1 (1+ degr)))\n",
-    "       ((>= degr degr2))\n",
-    " -->   (chcm-homology (rbcc (efhm chcm)) degr)\n",
-    "       (terpri) (clock) (terpri)))\n",
-    "```\n",
-    "\n",
-    "But, at the creation of the object, the slot `efhm` is  unbound and as soon as the `homology`\n",
-    "function tries to get the content of the slot `efhm` via the call `(efchm chcm)`, the *slot-unbound* mechanism of CLOS is triggered, calling at its turn a method `search-efhm` depending on the object. If no method is available for this object, `NIL` is returned. In the following chapters, we shall see that cases have been written for cartesian products, tensor products, suspensions, disk pasting, fibrations, loop spaces, and classifying spaces. The selection of the case is done thanks to the information contained in the comment list of the object (slot `orgn`). In each case, the `search-efhm` method builds - in general with a complex machinery, including a possible recursivity - a homotopy equivalence where the right bottom chain complex is *effective*. The slot `efhm` of the object is then settled and the homology group computation may begin. If `NIL` is returned, then  and only at this moment, the slot-unbound mechanism looks if the chain complex is finite (checking if a basis function exists). If this is the case, then the *trivial homotopy equivalence* is built upon the chain complex and this gives the value of the slot `efhm`. If there is no basis function,  meaning that probably the chain complex is locally effective, an error is returned.\n",
-    "\n",
-    "*Remark.* The user may wonder why one does not  look first if the given object is effective. We recall simply that even in the case of an effective chain complex, it is sometimes possible to find another effective chain complex, homotopic to the first and whose number of basis elements, in any dimensions, is considerably smaller in comparison with the first one. A striking case will be shown in a further chapter, showing the application of the Eilenberg-Zilber theorem to a cartesian product.\n",
-    "\n",
-    "\n",
-    "### Example\n",
-    "\n",
-    "*The reading of this subsection may be postponed until a full reading of this user's guide.* The following examples  show how are filled the slots `efhm` of the various objects. Starting from the sphere $S^2$, we  verify first that the *efhm* slot is unbound. Then we ask for ${\\cal H}_1$ and verify that, though there is a finite basis, `Kenzo` has nevertheless built a trivial homotopy equivalence on this object."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 16,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "---done---"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 16,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(cat-init)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 17,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K1 Simplicial-Set]"
-      ]
-     },
-     "execution_count": 17,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def s2 (sphere 2))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 18,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "The object is a STANDARD-OBJECT of type SIMPLICIAL-SET.\n",
-      "0. CMPR: #<FUNCTION SPHERE-CMPR>\n",
-      "1. BASIS: #<CLOSURE (FLET RSLT :IN SPHERE-BASIS) {100276F5AB}>\n",
-      "2. BSGN: *\n",
-      "3. DFFR: [K2 Morphism (degree -1): K1 -> K1]\n",
-      "4. GRMD: [K1 Simplicial-Set]\n",
-      "5. EFHM: \"unbound\"\n",
-      "6. IDNM: 1\n",
-      "7. ORGN: (SPHERE 2)\n",
-      "8. CPRD: [K5 Morphism (degree 0): K1 -> K3]\n",
-      "9. FACE: #<CLOSURE (FLET RSLT :IN SPHERE-FACE) {100276F5EB}>\n",
-      "> "
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 18,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(inspect s2)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 19,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "Computing boundary-matrix in dimension 1.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 2.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 2) :\n",
-      "S2 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 1 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 0h 52m 47s.\n",
-      "\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 19,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(homology s2 1)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 20,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "The object is a STANDARD-OBJECT of type SIMPLICIAL-SET.\n",
-      "0. CMPR: #<FUNCTION SPHERE-CMPR>\n",
-      "1. BASIS: #<CLOSURE (FLET RSLT :IN SPHERE-BASIS) {100276F5AB}>\n",
-      "2. BSGN: *\n",
-      "3. DFFR: [K2 Morphism (degree -1): K1 -> K1]\n",
-      "4. GRMD: [K1 Simplicial-Set]\n",
-      "5. EFHM: [K9 Homotopy-Equivalence K1 <= K1 => K1]\n",
-      "6. IDNM: 1\n",
-      "7. ORGN: (SPHERE 2)\n",
-      "8. CPRD: [K5 Morphism (degree 0): K1 -> K3]\n",
-      "9. FACE: #<CLOSURE (FLET RSLT :IN SPHERE-FACE) {100276F5EB}>\n",
-      "> "
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 20,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(inspect s2)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 21,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(TRIVIAL-HMEQ [K1 Simplicial-Set])"
-      ]
-     },
-     "execution_count": 21,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(orgn (hmeq 9))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Now, we create $\\Omega^1(S^2)$. Getting  the value of the slot `efhm` by a call to the accessor function `efhm`, triggers the search-efhm method for a loop space. A homotopy equivalence is built and the slot is set."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 22,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K10 Simplicial-Group]"
-      ]
-     },
-     "execution_count": 22,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def os2 (loop-space s2))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 23,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "The object is a STANDARD-OBJECT of type SIMPLICIAL-GROUP.\n",
-      "0. CMPR: #<CLOSURE (FLET RSLT :IN LOOP-SPACE-CMPR) {10033B487B}>\n",
-      "1. BASIS: :LOCALLY-EFFECTIVE\n",
-      "2. BSGN: <<Loop>>\n",
-      "3. DFFR: [K11 Morphism (degree -1): K10 -> K10]\n",
-      "4. GRMD: [K10 Simplicial-Group]\n",
-      "5. EFHM: \"unbound\"\n",
-      "6. IDNM: 10\n",
-      "7. ORGN: (LOOP-SPACE [K1 Simplicial-Set])\n",
-      "8. APRD: \"unbound\"\n",
-      "9. CPRD: [K14 Morphism (degree 0): K10 -> K12]\n",
-      "10. FACE: #<CLOSURE (FLET RSLT :IN LOOP-SPACE-FACE) {10033B4C8B}>\n",
-      "11. KFLL: \"unbound\"\n",
-      "12. GRML: [K20 Simplicial-Morphism K15 -> K10]\n",
-      "13. GRIN: [K21 Simplicial-Morphism K10 -> K10]\n",
-      "> "
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 23,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(inspect os2)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 24,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(LOOP-SPACE [K1 Simplicial-Set])"
-      ]
-     },
-     "execution_count": 24,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(orgn os2)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 25,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K118 Homotopy-Equivalence K10 <= K108 => K25]"
-      ]
-     },
-     "execution_count": 25,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(efhm os2)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 26,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "The object is a STANDARD-OBJECT of type SIMPLICIAL-GROUP.\n",
-      "0. CMPR: #<CLOSURE (FLET RSLT :IN LOOP-SPACE-CMPR) {10033B487B}>\n",
-      "1. BASIS: :LOCALLY-EFFECTIVE\n",
-      "2. BSGN: <<Loop>>\n",
-      "3. DFFR: [K11 Morphism (degree -1): K10 -> K10]\n",
-      "4. GRMD: [K10 Simplicial-Group]\n",
-      "5. EFHM: [K118 Homotopy-Equivalence K10 <= K108 => K25]\n",
-      "6. IDNM: 10\n",
-      "7. ORGN: (LOOP-SPACE [K1 Simplicial-Set])\n",
-      "8. APRD: \"unbound\"\n",
-      "9. CPRD: [K14 Morphism (degree 0): K10 -> K12]\n",
-      "10. FACE: #<CLOSURE (FLET RSLT :IN LOOP-SPACE-FACE) {10033B4C8B}>\n",
-      "11. KFLL: \"unbound\"\n",
-      "12. GRML: [K20 Simplicial-Morphism K15 -> K10]\n",
-      "13. GRIN: [K21 Simplicial-Morphism K10 -> K10]\n",
-      "> "
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 26,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(inspect os2)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "The following example shows the recursion mechanism when one wants to get the value of the slot `efhm` of an iterated loop space, namely $\\Omega^3(S^4)$."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 27,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K119 Simplicial-Set]"
-      ]
-     },
-     "execution_count": 27,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def s4 (sphere 4))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 28,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "The object is a STANDARD-OBJECT of type SIMPLICIAL-SET.\n",
-      "0. CMPR: #<FUNCTION SPHERE-CMPR>\n",
-      "1. BASIS: #<CLOSURE (FLET RSLT :IN SPHERE-BASIS) {1003593C0B}>\n",
-      "2. BSGN: *\n",
-      "3. DFFR: [K120 Morphism (degree -1): K119 -> K119]\n",
-      "4. GRMD: [K119 Simplicial-Set]\n",
-      "5. EFHM: \"unbound\"\n",
-      "6. IDNM: 119\n",
-      "7. ORGN: (SPHERE 4)\n",
-      "8. CPRD: [K123 Morphism (degree 0): K119 -> K121]\n",
-      "9. FACE: #<CLOSURE (FLET RSLT :IN SPHERE-FACE) {1003593C4B}>\n",
-      "> "
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 28,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(inspect s4)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 29,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K148 Simplicial-Group]"
-      ]
-     },
-     "execution_count": 29,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def ooos4 (loop-space (loop-space (loop-space s4))))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 30,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(LOOP-SPACE [K136 Simplicial-Group])"
-      ]
-     },
-     "execution_count": 30,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(orgn ooos4)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 31,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(LOOP-SPACE [K124 Simplicial-Group])"
-      ]
-     },
-     "execution_count": 31,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(orgn (second *))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 32,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(LOOP-SPACE [K119 Simplicial-Set])"
-      ]
-     },
-     "execution_count": 32,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(orgn (second *))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 33,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(SPHERE 4)"
-      ]
-     },
-     "execution_count": 33,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(orgn (second *))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 34,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "The object is a STANDARD-OBJECT of type SIMPLICIAL-GROUP.\n",
-      "0. CMPR: #<CLOSURE (FLET RSLT :IN LOOP-SPACE-CMPR) {100362A2AB}>\n",
-      "1. BASIS: :LOCALLY-EFFECTIVE\n",
-      "2. BSGN: <<Loop>>\n",
-      "3. DFFR: [K149 Morphism (degree -1): K148 -> K148]\n",
-      "4. GRMD: [K148 Simplicial-Group]\n",
-      "5. EFHM: \"unbound\"\n",
-      "6. IDNM: 148\n",
-      "7. ORGN: (LOOP-SPACE [K136 Simplicial-Group])\n",
-      "8. APRD: \"unbound\"\n",
-      "9. CPRD: [K152 Morphism (degree 0): K148 -> K150]\n",
-      "10. FACE: #<CLOSURE (FLET RSLT :IN LOOP-SPACE-FACE) {100362A2CB}>\n",
-      "11. KFLL: \"unbound\"\n",
-      "12. GRML: [K158 Simplicial-Morphism K153 -> K148]\n",
-      "13. GRIN: [K159 Simplicial-Morphism K148 -> K148]\n",
-      "> "
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 34,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(inspect ooos4)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 35,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "The object is a STANDARD-OBJECT of type SIMPLICIAL-GROUP.\n",
-      "0. CMPR: #<CLOSURE (FLET RSLT :IN LOOP-SPACE-CMPR) {100362128B}>\n",
-      "1. BASIS: :LOCALLY-EFFECTIVE\n",
-      "2. BSGN: <<Loop>>\n",
-      "3. DFFR: [K125 Morphism (degree -1): K124 -> K124]\n",
-      "4. GRMD: [K124 Simplicial-Group]\n",
-      "5. EFHM: \"unbound\"\n",
-      "6. IDNM: 124\n",
-      "7. ORGN: (LOOP-SPACE [K119 Simplicial-Set])\n",
-      "8. APRD: \"unbound\"\n",
-      "9. CPRD: [K128 Morphism (degree 0): K124 -> K126]\n",
-      "10. FACE: #<CLOSURE (FLET RSLT :IN LOOP-SPACE-FACE) {10036212AB}>\n",
-      "11. KFLL: \"unbound\"\n",
-      "12. GRML: [K134 Simplicial-Morphism K129 -> K124]\n",
-      "13. GRIN: [K135 Simplicial-Morphism K124 -> K124]\n",
-      "> "
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 35,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(inspect (smgr 124))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 36,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "The object is a STANDARD-OBJECT of type SIMPLICIAL-SET.\n",
-      "0. CMPR: #<FUNCTION SPHERE-CMPR>\n",
-      "1. BASIS: #<CLOSURE (FLET RSLT :IN SPHERE-BASIS) {1003593C0B}>\n",
-      "2. BSGN: *\n",
-      "3. DFFR: [K120 Morphism (degree -1): K119 -> K119]\n",
-      "4. GRMD: [K119 Simplicial-Set]\n",
-      "5. EFHM: \"unbound\"\n",
-      "6. IDNM: 119\n",
-      "7. ORGN: (SPHERE 4)\n",
-      "8. CPRD: [K123 Morphism (degree 0): K119 -> K121]\n",
-      "9. FACE: #<CLOSURE (FLET RSLT :IN SPHERE-FACE) {1003593C4B}>\n",
-      "> "
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 36,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(inspect (smst 119))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 37,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K522 Homotopy-Equivalence K148 <= K512 => K508]"
-      ]
-     },
-     "execution_count": 37,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(efhm ooos4)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 38,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "The object is a STANDARD-OBJECT of type SIMPLICIAL-GROUP.\n",
-      "0. CMPR: #<CLOSURE (FLET RSLT :IN LOOP-SPACE-CMPR) {100362128B}>\n",
-      "1. BASIS: :LOCALLY-EFFECTIVE\n",
-      "2. BSGN: <<Loop>>\n",
-      "3. DFFR: [K125 Morphism (degree -1): K124 -> K124]\n",
-      "4. GRMD: [K124 Simplicial-Group]\n",
-      "5. EFHM: [K426 Homotopy-Equivalence K124 <= K416 => K329]\n",
-      "6. IDNM: 124\n",
-      "7. ORGN: (LOOP-SPACE [K119 Simplicial-Set])\n",
-      "8. APRD: \"unbound\"\n",
-      "9. CPRD: [K128 Morphism (degree 0): K124 -> K126]\n",
-      "10. FACE: #<CLOSURE (FLET RSLT :IN LOOP-SPACE-FACE) {10036212AB}>\n",
-      "11. KFLL: \"unbound\"\n",
-      "12. GRML: [K134 Simplicial-Morphism K129 -> K124]\n",
-      "13. GRIN: [K135 Simplicial-Morphism K124 -> K124]\n",
-      "> "
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 38,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(inspect (smgr 124))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 39,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "The object is a STANDARD-OBJECT of type SIMPLICIAL-SET.\n",
-      "0. CMPR: #<FUNCTION SPHERE-CMPR>\n",
-      "1. BASIS: #<CLOSURE (FLET RSLT :IN SPHERE-BASIS) {1003593C0B}>\n",
-      "2. BSGN: *\n",
-      "3. DFFR: [K120 Morphism (degree -1): K119 -> K119]\n",
-      "4. GRMD: [K119 Simplicial-Set]\n",
-      "5. EFHM: [K412 Homotopy-Equivalence K119 <= K119 => K119]\n",
-      "6. IDNM: 119\n",
-      "7. ORGN: (SPHERE 4)\n",
-      "8. CPRD: [K123 Morphism (degree 0): K119 -> K121]\n",
-      "9. FACE: #<CLOSURE (FLET RSLT :IN SPHERE-FACE) {1003593C4B}>\n",
-      "> "
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 39,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(inspect (smst 119))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "#### Lisp files concerned in this chapter}\n",
-    "\n",
-    "`homology-groups.lisp`, `searching-homology` and files containing a `search-efhm` method."
-   ]
-  }
- ],
- "metadata": {
-  "kernelspec": {
-   "display_name": "SBCL Lisp",
-   "language": "lisp",
-   "name": "lisp"
-  },
-  "language_info": {
-   "codemirror_mode": "text/x-common-lisp",
-   "mimetype": "text/x-common-lisp",
-   "name": "common-lisp",
-   "pygments_lexer": "common-lisp",
-   "version": "X3J13"
-  }
- },
- "nbformat": 4,
- "nbformat_minor": 1
-}
diff --git a/examples/04_Tensor_product_of_chain_complexes.ipynb b/examples/04_Tensor_product_of_chain_complexes.ipynb
deleted file mode 100644
index 3bd1571..0000000
--- a/examples/04_Tensor_product_of_chain_complexes.ipynb
+++ /dev/null
@@ -1,847 +0,0 @@
-{
- "cells": [
-  {
-   "cell_type": "code",
-   "execution_count": 1,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "To load \"kenzo\":\n",
-      "  Load 1 ASDF system:\n",
-      "    kenzo\n",
-      "; Loading \"kenzo\"\n",
-      "\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "#<PACKAGE \"CAT\">"
-      ]
-     },
-     "execution_count": 1,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(ql:quickload \"kenzo\")\n",
-    "(in-package :cat)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "# Tensor product of chain complexes\n",
-    "\n",
-    "## Introduction\n",
-    "\n",
-    "One knows that the homology groups of a cartesian product of two spaces $K$ and $L$ may be obtained by considering a chain complex derived from respective chain complexes of $K$ and $L$ by taking their *tensor product*. The connection between this tensor product and the chain complex of $K \\times L$ is the *Eilenberg-Zilber reduction*, a central point in *constructive* Algebraic Topology. This reduction is implemented in the `eilenberg-zilber` module of this program.\n",
-    "\n",
-    "Let us recall that chain complexes are free $\\mathbb{Z}$-modules with distinguished basis. A tensor product of chain complexes \n",
-    "is itself a free $\\mathbb{Z}$-module with a natural basis formed by the tensor products of the generators of the chain complex factors.\n",
-    "\n",
-    "## Tensor product of generators and combinations\n",
-    "\n",
-    "An elementary tensor product of two generators is represented, in the program, by an object of the structure-class `TNPR`. There are four slots to define such an object:\n",
-    "1. *degr1* is an integer, the degree of the generator *gnrt1*.\n",
-    "2. *gnrt1* is the first generator of the pair.\n",
-    "3. *degr2* is an integer, the degree of the generator *gnrt2*.\n",
-    "4. *gnrt2* is  the second generator of the pair.\n",
-    "To construct such an object, one may use the macro `tnpr`. The corresponding type is `TNPR`. The printing method prints the  tensor product under the form:\n",
-    ">`<TnPr` *gnrt1 gnrt2*`>` or `<TnPr` *degr1 gnrt1 degr2 gnrt2*`>`\n",
-    "\n",
-    "according to the boolean value, `NIL` (default) or `T`  of the system variable  `*tnpr-with-degrees*` (see the examples).\n",
-    "\n",
-    "### Simple functions for the tensor product\n",
-    "\n",
-    "\n",
-    "`(tnpr degr1 gnrt1 degr2 gnrt2)` *[Macro]*\n",
-    "> Build a tensor product $gnrt1 \\otimes gnrt2$, the factors being of respective degree `degr1` and `degr2`.\n",
-    "\n",
-    "`(tnpr-p object)` *[Predicate]*\n",
-    "> Test if *object* is of type `TNPR`.\n",
-    "\n",
-    "`(degr1 tnpr)` *[Macro]*\n",
-    "> Select the degree of the first generator in the tensor product *tnpr*.\n",
-    "\n",
-    "`(gnrt1 tnpr)` *[Macro]*\n",
-    "> Select the first generator from the object *tnpr*.\n",
-    "\n",
-    "`(degr2 tnpr)` *[Macro]*\n",
-    "> Select the degree of the second generator in the tensor product *tnpr*.\n",
-    "\n",
-    "`(gnrt2 tnpr)` *[Macro]*\n",
-    "> Select the second generator from the object *tnpr*.\n",
-    "\n",
-    "`(2cmbn-tnpr cmbn1 cmbn2)` *[Function]*\n",
-    "> Create, from two combinations *cmbn1* and *cmbn2* with respective degree *degr1* and *degr2*, a combination of degree $dgr1 + dgr2$  by applying the tensorial distributive law on the two sums of terms of the combinations.\n",
-    "\n",
-    "#### Example"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 2,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "<TnPr A B>"
-      ]
-     },
-     "execution_count": 2,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(tnpr 1 'a 2 'b)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 3,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "The object is a STRUCTURE-OBJECT of type TNPR.\n",
-      "0. DEGR1: 1\n",
-      "1. GNRT1: A\n",
-      "2. DEGR2: 2\n",
-      "3. GNRT2: B\n",
-      "> "
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 3,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(inspect *)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 4,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "T"
-      ]
-     },
-     "execution_count": 4,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(tnpr-p **)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 5,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 5,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(tnpr-p (cmbn 0 1 'a 2 'b))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 6,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "T"
-      ]
-     },
-     "execution_count": 6,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(setf *tnpr-with-degrees* t)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 7,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 5}\n",
-       "<12 * <TnPr 2 A 3 X>>\n",
-       "<-9 * <TnPr 2 A 3 Y>>\n",
-       "<6 * <TnPr 2 A 3 Z>>\n",
-       "<16 * <TnPr 2 B 3 X>>\n",
-       "<-12 * <TnPr 2 B 3 Y>>\n",
-       "<8 * <TnPr 2 B 3 Z>>\n",
-       "<-20 * <TnPr 2 C 3 X>>\n",
-       "<15 * <TnPr 2 C 3 Y>>\n",
-       "<-10 * <TnPr 2 C 3 Z>>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 7,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(2cmbn-tnpr (cmbn 2 3 'a 4 'b -5 'c) (cmbn 3 4 'x -3 'y 2 'z))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 8,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 8,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(setf *tnpr-with-degrees* nil)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 9,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 5}\n",
-       "<12 * <TnPr A X>>\n",
-       "<-9 * <TnPr A Y>>\n",
-       "<6 * <TnPr A Z>>\n",
-       "<16 * <TnPr B X>>\n",
-       "<-12 * <TnPr B Y>>\n",
-       "<8 * <TnPr B Z>>\n",
-       "<-20 * <TnPr C X>>\n",
-       "<15 * <TnPr C Y>>\n",
-       "<-10 * <TnPr C Z>>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 9,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "**"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "## Tensor product of chain complexes\n",
-    "\n",
-    "The program implements the tensor product of chain complexes according to the classical following definition. Let $C$ and $C'$ be two chain complexes. The tensor product $C\\otimes C'$ is the chain complex $D$ such that:\n",
-    "$$\n",
-    "D_p=\\bigoplus_{m+n=p}C_m\\otimes C_n',\n",
-    "$$\n",
-    "$C_m\\otimes C_n'$ being the tensor product of the two modules $C_m$ and $C_n'$. A basis for $D_p$ is the union of the basis of $C_m\\otimes C_n'$, with $m+n=p$.\n",
-    "\n",
-    "The boundary operator $d^{\\otimes}$ is defined, according to the Koszul rule, by:\n",
-    "\n",
-    "$$d^{\\otimes}(c_m\\otimes c_n')=d(c_m)\\otimes c_n' +(-1)^m c_m\\otimes d'(c_n'),$$\n",
-    "\n",
-    "with $c_m\\in C_m,\\ c_n'\\in C_n'$ and $d$, $d'$ being the respective boundary operators\n",
-    "of $C$ and $C'$.\n",
-    "\n",
-    "In the program, this is realized by the function `tnsr-prdc`. \n",
-    "\n",
-    "`(tnsr-prdc chcm1 chcm2)` *[Method]*\n",
-    "> Build a chain complex, tensor product of the two chain complexes *chcm1* and *chcm2*. The elements\n",
-    "of this new chain complex are integer combinations of generators of *TNPR* type. The creation of this\n",
-    "new chain complex is done by a call to the function *build-chcm* with actual parameters defined from the constituting elements  of *chcm1* and *chcm2*, according to the mathematical definitions above. If both arguments are *effective*, the function constructs an *effective* chain complex. On the other hand, if at least one of the chain complex is *locally effective*, the tensor product is also *locally effective*. In fact, the construction is correct only if both chain complexes are null in negative degrees, otherwise the result is undefined.\n",
-    "\n",
-    "#### Examples\n",
-    "\n",
-    "Let us take the standard 2-simplex, $\\Delta^2$ and let us build $C_*(\\Delta^2) \\otimes C_*(\\Delta^2)$. To build the corresponding chain complex, we use the function `cdelta`, defined in a previous chapter."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 10,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "---done---"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 10,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(cat-init)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 11,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "CDELTA"
-      ]
-     },
-     "execution_count": 11,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(defun cdelta (dmns)\n",
-    "    (build-chcm\n",
-    "     :cmpr #'l-cmpr\n",
-    "     :basis #'(lambda (n)\n",
-    "                      (mapcar #'dlop-int-ext (funcall (delta-n-basis dmns) n)))\n",
-    "     :bsgn '(0)\n",
-    "     :intr-dffr\n",
-    "         #'(lambda (degr gmsm)\n",
-    "            (make-cmbn\n",
-    "             :degr (1- degr)\n",
-    "             :list (do ((rslt +empty-list+\n",
-    "                              (cons (cons sign\n",
-    "                                          (append\n",
-    "                                           (subseq gmsm 0 nark)\n",
-    "                                           (subseq gmsm (1+ nark))))\n",
-    "                                    rslt))\n",
-    "                        (sign 1 (- sign))\n",
-    "                        (nark 0 (1+ nark)))\n",
-    "                       ((> nark degr) rslt))))\n",
-    "     :strt :gnrt\n",
-    "     :orgn `(Effective version of C_* delta ,dmns)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 12,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K1 Chain-Complex]"
-      ]
-     },
-     "execution_count": 12,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def triangle (cdelta 2))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 13,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "((0 1) (0 2) (1 2))"
-      ]
-     },
-     "execution_count": 13,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(basis triangle 1)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 14,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K3 Chain-Complex]"
-      ]
-     },
-     "execution_count": 14,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def tpr-triangles (tnsr-prdc triangle triangle))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Let us inspect some basis of this newly created chain complex."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 15,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(<TnPr (0) (0)> <TnPr (0) (1)> <TnPr (0) (2)> <TnPr (1) (0)> <TnPr (1) (1)> <TnPr (1) (2)> <TnPr (2) (0)> <TnPr (2) (1)> <TnPr (2) (2)>)"
-      ]
-     },
-     "execution_count": 15,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(basis tpr-triangles 0)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 16,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(<TnPr (0) (0 1)> <TnPr (0) (0 2)> <TnPr (0) (1 2)> <TnPr (1) (0 1)> <TnPr (1) (0 2)> <TnPr (1) (1 2)> <TnPr (2) (0 1)> <TnPr (2) (0 2)> <TnPr (2) (1 2)> <TnPr (0 1) (0)> ...)"
-      ]
-     },
-     "execution_count": 16,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(basis tpr-triangles 1)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 17,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(<TnPr (0) (0 1 2)> <TnPr (1) (0 1 2)> <TnPr (2) (0 1 2)> <TnPr (0 1) (0 1)> <TnPr (0 1) (0 2)> <TnPr (0 1) (1 2)> <TnPr (0 2) (0 1)> <TnPr (0 2) (0 2)> <TnPr (0 2) (1 2)> <TnPr (1 2) (0 1)> ...)"
-      ]
-     },
-     "execution_count": 17,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(basis tpr-triangles 2)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 18,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(<TnPr (0 1) (0 1 2)> <TnPr (0 2) (0 1 2)> <TnPr (1 2) (0 1 2)> <TnPr (0 1 2) (0 1)> <TnPr (0 1 2) (0 2)> <TnPr (0 1 2) (1 2)>)"
-      ]
-     },
-     "execution_count": 18,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(basis tpr-triangles 3)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 19,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(<TnPr (0 1 2) (0 1 2)>)"
-      ]
-     },
-     "execution_count": 19,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(basis tpr-triangles 4)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Let us consider now the  chain complex, $ccn$, that we used in the chain complex chapter. The basis in any degree are decades produced by the function `<a-b<`. We build $ccn\\otimes ccn$ and we verify the fundamental property of the associated boundary operator:\n",
-    "\n",
-    "$$d^\\otimes \\circ d^\\otimes=0.$$"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 20,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "#<FUNCTION (LAMBDA (DGR GNR) :IN \"/root/cl-jupyter/cl-jupyter.lisp\") {100222C5BB}>"
-      ]
-     },
-     "execution_count": 20,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def ccn-boundary #'(lambda (dgr gnr)\n",
-    "     (if (evenp (+ dgr gnr))\n",
-    "         (cmbn (1- dgr) 1 (- gnr 10))\n",
-    "         (cmbn (1- dgr)))))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 21,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K5 Chain-Complex]"
-      ]
-     },
-     "execution_count": 21,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def ccn (build-chcm :cmpr #'f-cmpr\n",
-    "                     :basis #'(lambda (n) (<a-b< (* 10 n) (* 10 (1+ n))))\n",
-    "                     :intr-dffr  ccn-boundary\n",
-    "                     :strt :gnrt\n",
-    "                     :orgn '(ccn) ))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 22,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(30 31 32 33 34 35 36 37 38 39)"
-      ]
-     },
-     "execution_count": 22,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(basis ccn 3)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 23,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K7 Chain-Complex]"
-      ]
-     },
-     "execution_count": 23,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def tpr-ccn-ccn (tnsr-prdc ccn ccn))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 24,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 2}\n",
-       "<1 * 21>\n",
-       "<5 * 25>\n",
-       "<9 * 29>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 24,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def comb2 (cmbn 2 1 21 5 25 9 29))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 25,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 3}\n",
-       "<2 * 32>\n",
-       "<3 * 33>\n",
-       "<-4 * 34>\n",
-       "<-6 * 36>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 25,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def comb3 (cmbn 3 2 32 3 33 -4 34 -6 36))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 26,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 5}\n",
-       "<2 * <TnPr 21 32>>\n",
-       "<3 * <TnPr 21 33>>\n",
-       "<-4 * <TnPr 21 34>>\n",
-       "<-6 * <TnPr 21 36>>\n",
-       "<10 * <TnPr 25 32>>\n",
-       "<15 * <TnPr 25 33>>\n",
-       "<-20 * <TnPr 25 34>>\n",
-       "<-30 * <TnPr 25 36>>\n",
-       "<18 * <TnPr 29 32>>\n",
-       "<27 * <TnPr 29 33>>\n",
-       "... ...\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 26,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def tcmb (2cmbn-tnpr comb2 comb3))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 27,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 4}\n",
-       "<3 * <TnPr 21 23>>\n",
-       "<15 * <TnPr 25 23>>\n",
-       "<27 * <TnPr 29 23>>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 27,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? tpr-ccn-ccn *)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 28,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 3}\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 28,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? tpr-ccn-ccn *)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "## Tensor product of morphisms, reductions, homotopy equivalences.\n",
-    "\n",
-    "Let $f:A_1 \\longrightarrow A_2$ and $g:B_1 \\longrightarrow B_2$ two morphisms between \n",
-    "two chain complexes. The tensor product $f \\otimes g$ is the morphism\n",
-    "\n",
-    "$$f\\otimes g : A_1\\otimes B_1 \\longrightarrow A_2\\otimes B_2$$ \n",
-    "\n",
-    "defined by the following formula respecting the Koszul rule:\n",
-    "\n",
-    "$$ (f\\otimes g) (a_1 \\otimes b_1)= (-1)^{deg(g)*deg(a1)}f(a_1) \\otimes g(b_1).$$\n",
-    "\n",
-    "The method `tnsr-prdc` already defined for chain complexes, may be also used for that purpose. \n",
-    "\n",
-    "`(tnsr-prdc mrph1 mrph2)` *[Method]*\n",
-    "> Return the morphism, tensor product of the two morphisms *mrph1* and *mrph2*. The source and target of this new morphism are respectively the tensor product of the chain complexes source and target of *mrph1* and *mrph2*. The degree is the sum of the degrees of the parameters and the lisp function (the `:intr` keyword argument of the function `build-mrph`) conforms to the mathematical definition above. The internal strategy is by generator, i.e. the morphism is designed to work with 2 arguments: a degree and a generator which must be an object of type `TNPR`.\n",
-    "\n",
-    "`(tnsr-prdc rdct1 rdct2)` *[Method]*\n",
-    "> Return the reduction,  tensor product of the two reductions *rdct1* and *rdct2*. The algorithm consists essentially in defining\n",
-    "$$f=f1 \\otimes f2,\\, g=g1 \\otimes g2,\\, h= h1 \\otimes (g2 \\circ g2) + Id_{tcc1} \\otimes h2,$$\n",
-    "where $Id_{tcc1}$ is the identity morphism in the top chain complex of the reduction *rdct1*.\n",
-    "The returned reduction is then built by a call to the method `build-rdct`. This defines completely the chain complexes involved in the reduction.\n",
-    "\n",
-    "`(tnsr-prdc hmeq1 hmeq2)` *[Method]*\n",
-    "> Return the homotopy equivalence, tensor product of the two homotopy equivalences *heqm1* and *heqm2*. This is a homotopy equivalence where the new reductions are the tensor products of the arguments reductions (See the lisp definition just above).\n",
-    "\n",
-    "### Searching homology for tensor products\n",
-    "\n",
-    "The comment list of a tensor product of two chain complexes has the form \n",
-    "`(TNSR-PRDC` *chcm1 chcm2*`)`. The `search-efhm` method applied to a tensor product, looks for the value of the respective `efhm` slots of the chain complexes *chcm1* and *chcm2*, (i.e. two homotopy equivalences) or tries to settle these slots if they are still unbound. Then it builds the tensor product of both homotopy equivalences, as shown in the following lisp listing. In turn, the resulting homotopy equivalence will become the value of the `efhm` slot of the initial tensor product chain complex.\n",
-    "\n",
-    "```commonlisp\n",
-    "(defmethod SEARCH-EFHM (chcm (orgn (eql 'tnsr-prdc)))\n",
-    "  (declare (type chain-complex chcm))\n",
-    "  (the homotopy-equivalence\n",
-    "       (tnsr-prdc (efhm (second (orgn chcm)))\n",
-    "                  (efhm (third (orgn chcm))))))\n",
-    "\n",
-    "(defmethod TNSR-PRDC ((hmeq1 homotopy-equivalence)\n",
-    "\t\t      (hmeq2 homotopy-equivalence))\n",
-    "  (the homotopy-equivalence\n",
-    "     (build-hmeq\n",
-    "        :lrdct (tnsr-prdc (lrdct hmeq1) (lrdct hmeq2))\n",
-    "        :rrdct (tnsr-prdc (rrdct hmeq1) (rrdct hmeq2))\n",
-    "        :orgn `(tnsr-prdc ,hmeq1 ,hmeq2))))\n",
-    "```\n",
-    "\n",
-    "#### Lisp file concerned in this chapter\n",
-    "\n",
-    "`tensor-products.lisp`, `searching-homology.lisp`."
-   ]
-  }
- ],
- "metadata": {
-  "kernelspec": {
-   "display_name": "SBCL Lisp",
-   "language": "lisp",
-   "name": "lisp"
-  },
-  "language_info": {
-   "codemirror_mode": "text/x-common-lisp",
-   "mimetype": "text/x-common-lisp",
-   "name": "common-lisp",
-   "pygments_lexer": "common-lisp",
-   "version": "X3J13"
-  }
- },
- "nbformat": 4,
- "nbformat_minor": 1
-}
diff --git a/examples/05_Coalgebras_and_cobars.ipynb b/examples/05_Coalgebras_and_cobars.ipynb
deleted file mode 100644
index 89911e0..0000000
--- a/examples/05_Coalgebras_and_cobars.ipynb
+++ /dev/null
@@ -1,1177 +0,0 @@
-{
- "cells": [
-  {
-   "cell_type": "code",
-   "execution_count": 1,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "To load \"kenzo\":\n",
-      "  Load 1 ASDF system:\n",
-      "    kenzo\n",
-      "; Loading \"kenzo\"\n",
-      "\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "#<PACKAGE \"CAT\">"
-      ]
-     },
-     "execution_count": 1,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(ql:quickload \"kenzo\")\n",
-    "(in-package :cat)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "# Coalgebras and cobars\n",
-    "\n",
-    "## Introduction\n",
-    "\n",
-    "The implementation of coalgebras and cobars follows closely the section 9 of the paper *Constructive Homological Algebra and Applications* (available at [**http://arxiv.org/pdf/1208.3816**](http://arxiv.org/pdf/1208.3816)).\n",
-    "\n",
-    "## Coalgebras\n",
-    "\n",
-    "A coalgebra  is a pair $(C, \\chi)$ where\n",
-    "1. $C$ is a chain complex.\n",
-    "2. $\\chi$ (the *coproduct*) is a chain complex morphism $$\\chi: C \\rightarrow C \\otimes C.$$\n",
-    "\n",
-    "These components must satisfy the usual structural properties of the coalgebras (**Mac Lane**, Homology, section VI-9. Springer 1970.).\n",
-    "\n",
-    "### Implementation of a coalgebra\n",
-    "\n",
-    "A coalgebra is represented as an instance of the CLOS class `COALGEBRA`, subclass of the `CHAIN COMPLEX` class. The definition of this new class is simply:\n",
-    "\n",
-    "```commonlisp\n",
-    "(DEFCLASS COALGEBRA (chain-complex)\n",
-    "    ((cprd :type morphism :initarg :cprd :reader cprd1)))   ;; coproduct\n",
-    "```\n",
-    "\n",
-    "So, this new class inherits the slots of the `CHAIN COMPLEX` class and has a slot of its own, namely `cprd`, a morphism  object representing the coproduct. The user will note the important following fact that, **once a coalgebra has been defined, one may use on it any\n",
-    "function or method applicable to a chain complex**.\n",
-    "\n",
-    "### The function `build-clgb`\n",
-    "\n",
-    "To facilitate the construction of instances of the `COALGEBRA` class, the program provides the function `build-clgb`,\n",
-    "```commonlisp\n",
-    "(build-clgb :cmpr cmpr :basis basis :bsgn bsgn :intr-dffr intr-dffr :dffr-strt dffr-strt  \n",
-    "            :intr-cprd intr-cprd :cprd-strt cprd-strt :orgn orgn)\n",
-    "```\n",
-    "defined with keyword parameters. The returned value is an instance of type `COALGEBRA`. The keyword arguments are:\n",
-    "\n",
-    "- *cmpr*, a comparison function for generators.\n",
-    "- *basis*, the basis function for the underlying chain complex.\n",
-    "- *bsgn*, the  base point, a generator of any type.\n",
-    "- *intr-dffr*, the differential lisp function for the chain complex.\n",
-    "- *dffr-strt*, the strategy (`:gnrt` or `:cmbn`) for the differential.\n",
-    "- *intr-cprd*, the lisp function for the coproduct of the coalgebra.\n",
-    "- *cprd-strt*, the strategy (`:gnrt` or `:cmbn`) for the coproduct.\n",
-    "- *orgn*, an adequate comment list.\n",
-    "\n",
-    "The function `build-clgb` calls  the function `build-chcm` and with the help of the function\n",
-    "`build-mrph` builds the coproduct morphism of degree 0, to settle the slot `crpd` of the instance. According to the definition, the source slot of the coproduct morphism `cprd` is the underlying chain complex and the target slot is the tensor product of this chain complex with itself. As to the other objects, an identification number $n$ (slot `idnm`) is assigned to this Kenzo object and the `COALGEBRA` instance is  pushed  onto the list `*clgb-list*`. The  associated printing method prints a string like `[K`*n* `Coalgebra]`.\n",
-    "\n",
-    "\n",
-    "\n",
-    "### Miscellaneous functions and macros for coalgebras\n",
-    "\n",
-    "`cat-init` *[Function]*\n",
-    "> Clear among others, the list `*clgb-list*`, list of user created coalgebras  and reset the global counter to 1.\n",
-    "\n",
-    "`clgb` *n* *[Function]*\n",
-    "> Retrieve in the list `*clgb-list*` the coalgebra instance whose identification is $n$. If it does not exist, return `NIL`.\n",
-    "\n",
-    "`cprd` *clgb* `&rest` *[Macro]*\n",
-    "> Versatile macro relative to the coproduct of a coalgebra. The first argument is a `COALGEBRA` instance. With only one argument, this macro returns the coproduct morphism of the coalgebra.\n",
-    "With more arguments, it applies the coproduct morphism on a combination (`(cprd` *clgb cmbn*`)`)\n",
-    "or on a pair *degree, generator* (`(cprd` *clgb degr gnrt*`)`).\n",
-    "\n",
-    "`change-chcm-to-clgb` *chcm* `:intr-cprd` *intr-cprd* `:cprd-strt` *cprd-strt* `:orgn` *orgn* *[Function]*\n",
-    "> Build a coalgebra instance from the already created chain complex *chcm*. The user must give via key parameters a lisp function for the coproduct, the strategy and a comment list.\n",
-    "\n",
-    "## Cobar of a coalgebra\n",
-    "\n",
-    "Let ${\\cal A}$ be a coalgebra, ${\\cal M}$ a  right ${\\cal A}$-comodule, ${\\cal N}$ a left ${\\cal A}$-comodule. It means that there exist coproducts $\\chi_{\\cal M}$ and $\\chi_{\\cal N}$:\n",
-    "\n",
-    "$$\\chi_{\\cal M}: {\\cal M} \\longrightarrow {\\cal M}\\otimes {\\cal A},\\quad\n",
-    "  \\chi_{\\cal N}: {\\cal N} \\longrightarrow {\\cal A}\\otimes {\\cal N}.  $$\n",
-    "  \n",
-    "It is possible to build a chain complex denoted $Cobar^{\\cal A}({\\cal M}, {\\cal N})$, \n",
-    "\n",
-    "$$Cobar^{\\cal A}({\\cal M}, {\\cal N}) = \\bigoplus_p\n",
-    "{\\cal M}\\otimes {\\bar{\\cal A}}^{\\otimes p} \\otimes {\\cal N}.$$\n",
-    "\n",
-    "This section is devoted to the particular case ${\\cal M}={\\cal N}=\\mathbb{Z}$.\n",
-    "\n",
-    "So, let ${\\cal A}$ be  a coalgebra , assumed 1-connected, i.e. ${\\cal A}_1 = 0$ and  ${\\cal A}_0 \\simeq \\mathbb{Z}$, we consider the chain complex, $Cobar^{{\\cal A}}(\\mathbb{Z}, \\mathbb{Z})$, noted more simply  $Cobar({\\cal A})$, whose $n$-th component is:\n",
-    "\n",
-    "$$ [Cobar({\\cal A})]_n = \\bigoplus ({\\bar{\\cal A}}_{i_1} \\otimes \\cdots \\otimes {\\bar{\\cal A}}_{i_k}),\\quad i_j >0, \\quad\n",
-    "i_1 + \\cdots + i_k= n+k.$$\n",
-    "\n",
-    "A tensor product $g_1 \\otimes \\cdots \\otimes g_k$, where $g_i$ is a generator of ${\\bar{\\cal A}}_{i}$ is called, in the program `Kenzo`, an **algebraic loop**. The reason is the following: if $X$ is a 1-connected simplicial set, we shall see in a next chapter that the program `Kenzo` constructs a homotopy equivalence between the chain complex of the loop space ${\\cal C}_*(GX)$ and $Cobar({\\cal C}_*(X)) = Cobar^{{\\cal C}_*(X)}(\\mathbb{Z}, \\mathbb{Z})$, so that a generator of the last chain complex is a kind of \"algebraic\" version of a generator of a loop space. The definition of  differential of the Cobar is recalled hereafter.\n",
-    "\n",
-    "\n",
-    "### Representation of an algebraic loop\n",
-    "\n",
-    "An algebraic loop is represented by a lisp object of the form:\n",
-    "\n",
-    "> `#S(:ALLP :LIST` (($i_1\\,.\\, g_1$) ... ($i_k\\,.\\, g_k$))`)`\n",
-    "\n",
-    "where the $i_j$ are the degrees *in the cobar chain complex* of the generators $g_j$. In the original coalgebra $\\cal A$, the generators $g_j$ had the degree $i_j+1$. The corresponding type is `ALLP`.\n",
-    "The function to build such an object is also called `allp`\n",
-    "\n",
-    "`allp` *degr1 gnr1 degr2 gnr2 ... degrk gnrk* *[Function]*\n",
-    "> Construct an algebraic loop, i.e. a tensorial product of degree $\\sum degr_i$. The sequence of pairs $\\lbrace degr_i,\\,  gnr_i \\rbrace$ has an undefinite length and  may be void. In this case, the algebraic loop is the null algebraic loop, also defined in the system as the constant `+null-allp+`. \n",
-    "The function `allp` accepts also as unique argument a list of the form `(`*degr1 gnr1 degr2 gnr2 ... degrk gnrk*`)`\n",
-    "\n",
-    "`allp-p` *object* *[Function]*\n",
-    "> Test if *object* is an algebraic loop.\n",
-    "\n",
-    "The associated printing  method prints the object under the form:\n",
-    "> `<<AlLp [` $i_1$ $g_1$ `] ... [` $i_k$ $g_k$ `]>>`\n",
-    "\n",
-    "The user will have noted that in the Cobar, each generator $g_i$ appears with its own degree in the underlying chain complex, **lowered by 1**.\n",
-    "\n",
-    "\n",
-    "### Definition of the chain complex Cobar\n",
-    "\n",
-    "The definition of the differential in the Cobar, will be done in three steps. This is better understood, if we consider the following diagram. We recall that the elements of $({\\bar{\\cal A}}_*^{\\otimes_p})_q$ are by convention of degree $q-p$ in the Cobar, if $q$ is the ordinary total degree in the tensor product $\\overline{\\mathcal{A}}_\\ast^{\\otimes p}$, that is, the sum of the degrees of the factors.\n",
-    "\n",
-    "- A chain complex called `vertical-cobar` is defined with the *vertical differential* $d_v$. In this case, only the underlying  chain complex structure is used.\n",
-    "- A horizontal differential $d_h$ is defined. This uses the coproduct structure.\n",
-    "- The final chain complex `cobar` is created with the differential $d_v+d_h$.\n",
-    "\n",
-    "$$\n",
-    "\\begin{aligned}\n",
-    "       &             & \\downarrow\\quad  &  & \\downarrow\\qquad & &\\\\\n",
-    "\\cdots & \\quad\\rightarrow & ({\\bar{\\cal A}}_*^{\\otimes p})_q & \\qquad\\buildrel {d_h} \\over \\longrightarrow\n",
-    "                     & ({\\bar{\\cal A}}_*^{\\otimes {p+1}})_q  & \\qquad\\rightarrow & \\cdots \\\\\n",
-    "       &             &  \\downarrow {\\scriptstyle d}_v  &  &  \\downarrow {\\scriptstyle d}_v\\quad  & & \\\\\n",
-    "\\cdots & \\quad\\rightarrow &\\quad({\\bar{\\cal A}}_*^{\\otimes p})_{q-1} & \\qquad \\buildrel {d_h} \\over \\longrightarrow \n",
-    "                     & \\quad({\\bar{\\cal A}}_*^{\\otimes {p+1}})_{q-1}  & \\qquad\\rightarrow & \\cdots \\\\ \n",
-    "       &             & \\downarrow\\quad  &  & \\downarrow\\qquad & &\n",
-    "\\end{aligned}\n",
-    "$$\n",
-    "\n",
-    "#### Definition of the vertical cobar\n",
-    "\n",
-    "To define the vertical cobar chain complex from a chain complex ${\\cal C}$, the following functions are provided:\n",
-    "\n",
-    "`cobar-cmpr` *cmpr* *[Function]*\n",
-    "> From the comparison function *cmpr*, build a comparison function for objects of algebraic loop type. \n",
-    "\n",
-    "`cobar-basis` *basis* *[Function]*\n",
-    "> From the function *basis* of a  chain complex ${\\cal C}$, build a basis function for the vertical cobar chain complex defined on ${\\cal C}$. In dimension 0, there is only one basis element, namely the null algebraic loop. If ${\\cal C}$ is locally effective, this function returns the symbol `:locally-effective`.\n",
-    "\n",
-    "`cobar-intr-vrtc-dffr` *dffr* *[Function]*\n",
-    "> From the `lisp` function *dffr* of a chain complex  ${\\cal C}$, build a lisp function for the differential of the vertical cobar chain complex, according to the formula\n",
-    "$$d_v(g_1 \\otimes \\cdots \\otimes g_n)=\n",
-    "\\sum_{i=1}^n{(-1)^{n-i+1+{\\sum_{j=1}^{i-1}{\\mid g_j \\mid}}}\n",
-    "  g_1 \\otimes \\cdots \\otimes g_{i-1} \\otimes {\\bf dg_i} \\otimes g_{i+1} \\otimes \\cdots \\otimes g_n},$$\n",
-    "where $dg_i$ is the differential of the generator $g_i$ in the original chain complex (function *dffr*) and $\\mid g_i \\mid$ is the degree of the generator $g_i$ *in the cobar chain complex*.\n",
-    "In general, the differential $dg_i$ is a sum of tensor products. So, applying the distribution law, the right member is a sum of tensor products, represented by a combination.\n",
-    "\n",
-    "`vrtc-cobar` *chcm* *[Method]*\n",
-    "> Build the vertical cobar chain complex with underlying chain complex *chcm*. This is simply done by the following call to `build-chcm`:\n",
-    "```commonlisp\n",
-    "(build-chcm\n",
-    "   :cmpr (cobar-cmpr cmpr)\n",
-    "   :basis (cobar-basis basis)\n",
-    "   :bsgn +null-allp+\n",
-    "   :intr-dffr (cobar-intr-vrtc-dffr dffr)\n",
-    "   :strt :gnrt\n",
-    "   :orgn `(vrtc-cobar ,chcm))\n",
-    "```\n",
-    "where, *cmpr*, *basis* and *dffr* are extracted from the chain complex *chcm*. Note that the base generator is the null algebraic loop.\n",
-    "\n",
-    "### Example\n",
-    "\n",
-    "We  are going to build a coalgebra  which will be reconsidered in a next chapter (Simplicial sets). It is the coalgebra canonicaly associated to the simplicial set $\\Delta_2^\\mathbb{N}$. This simplicial set is the quotient of $\\Delta^\\mathbb{N}$ - the standard simplex spanned by the non-negative integers - by the relation identifying, firstly all the vertices with a unique one and then any 1-simplex of $\\Delta^\\mathbb{N}$ with the unique degeneracy of this unique vertex. In other words, $\\Delta_2^\\mathbb{N}$ is 1-reduced: 1 vertex, no edges.\n",
-    "\n",
-    "Our implementation represents any non--degenerate $n$--simplex as an integer increasing list of length $n+1$. In dimension 0, for every non-negative $m$ and $n$, the vertices `(m)` and `(n)` are identified; in dimension 1, the list $(m\\, n)$ is always an *illegal* 1-simplex. This coalgebra will be located through the symbol `smp-deltab2`. The lisp definition uses the function `build-smst` that will be described in the simplicial set chapter. For the moment, it is sufficient to know, that the function `build-smst` allows us to create a coalgebra suitable for the tests. The definition  of $\\Delta_2^\\mathbb{N}$ given here, is only for pedagogical purpose, an efficient definition using another representation for the simplices is provided in the program `Kenzo`."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 2,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K1 Simplicial-Set]"
-      ]
-     },
-     "execution_count": 2,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def smp-deltab2\n",
-    "    (build-smst\n",
-    "     :cmpr #'(lambda (gsm1 gsm2)\n",
-    "                       (if (rest gsm1) (l-cmpr gsm1 gsm2) :equal))\n",
-    "     :basis :locally-effective\n",
-    "     :bspn '(0)\n",
-    "     :face #'(lambda (i dmn gsm)\n",
-    "                     (case dmn\n",
-    "                         (0 (error \"No face in dimension 0\"))\n",
-    "                         (1 (error \"No non-degenerate simplex in dimension 1\"))\n",
-    "                         (2 (absm 1 '(0)))\n",
-    "                         (otherwise (absm 0 (append (subseq gsm 0 i)\n",
-    "                                                    (subseq gsm (1+ i)))))))\n",
-    "     :orgn '(simple-deltab2)))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "The following statements show the identification of vertices and that the boundary of a 2-simplex is null."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 3,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       ":EQUAL"
-      ]
-     },
-     "execution_count": 3,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(cmpr smp-deltab2 '(5) '(0))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 4,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 1}\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 4,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? smp-deltab2 2 '(0 1 2))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 5,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 2}\n",
-       "<-1 * (0 1 2)>\n",
-       "<1 * (0 1 3)>\n",
-       "<-1 * (0 2 3)>\n",
-       "<1 * (1 2 3)>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 5,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? smp-deltab2 3 '(0 1 2 3))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Let us build the vertical cobar on the coalgebra `smp-deltab2` and apply the comparison function and the differential on some algebraic loops."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 6,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K6 Chain-Complex]"
-      ]
-     },
-     "execution_count": 6,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def precobar (vrtc-cobar smp-deltab2))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 7,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "<<AlLp>>"
-      ]
-     },
-     "execution_count": 7,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(bsgn precobar)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 8,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "<<AlLp[2 (0 1 2 3)]>>"
-      ]
-     },
-     "execution_count": 8,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def loop-1 (allp 2 '(0 1 2 3)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 9,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "<<AlLp[2 (1 2 3 4)]>>"
-      ]
-     },
-     "execution_count": 9,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def loop-2 (allp '(2 (1 2 3 4))))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 10,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       ":LESS"
-      ]
-     },
-     "execution_count": 10,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(cmpr precobar loop-1 loop-2)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 11,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 1}\n",
-       "<1 * <<AlLp[1 (0 1 2)]>>>\n",
-       "<-1 * <<AlLp[1 (0 1 3)]>>>\n",
-       "<1 * <<AlLp[1 (0 2 3)]>>>\n",
-       "<-1 * <<AlLp[1 (1 2 3)]>>>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 11,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? precobar 2 loop-1)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 12,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 0}\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 12,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? precobar *)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 13,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "<<AlLp[3 (0 1 2 3 4)][3 (1 3 5 7 9)]>>"
-      ]
-     },
-     "execution_count": 13,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def loop-3 (allp 3 '(0 1 2 3 4) 3 '(1 3 5 7 9)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 14,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 5}\n",
-       "<1 * <<AlLp[2 (0 1 2 3)][3 (1 3 5 7 9)]>>>\n",
-       "<-1 * <<AlLp[2 (0 1 2 4)][3 (1 3 5 7 9)]>>>\n",
-       "<1 * <<AlLp[2 (0 1 3 4)][3 (1 3 5 7 9)]>>>\n",
-       "<-1 * <<AlLp[2 (0 2 3 4)][3 (1 3 5 7 9)]>>>\n",
-       "<1 * <<AlLp[2 (1 2 3 4)][3 (1 3 5 7 9)]>>>\n",
-       "<1 * <<AlLp[3 (0 1 2 3 4)][2 (1 3 5 7)]>>>\n",
-       "<-1 * <<AlLp[3 (0 1 2 3 4)][2 (1 3 5 9)]>>>\n",
-       "<1 * <<AlLp[3 (0 1 2 3 4)][2 (1 3 7 9)]>>>\n",
-       "<-1 * <<AlLp[3 (0 1 2 3 4)][2 (1 5 7 9)]>>>\n",
-       "<1 * <<AlLp[3 (0 1 2 3 4)][2 (3 5 7 9)]>>>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 14,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? precobar 6 loop-3)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 15,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 4}\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 15,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? precobar *)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 16,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "<<AlLp[3 (0 1 4 5 6)][4 (2 3 4 5 6 8)][4 (0 4 5 6 7 8)]>>"
-      ]
-     },
-     "execution_count": 16,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def loop-4 (allp 3 '(0 1 4 5 6) 4 '(2 3 4 5 6 8) 4 '(0 4 5 6 7 8)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 17,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 10}\n",
-       "<-1 * <<AlLp[2 (0 1 4 5)][4 (2 3 4 5 6 8)][4 (0 4 5 6 7 8)]>>>\n",
-       "<1 * <<AlLp[2 (0 1 4 6)][4 (2 3 4 5 6 8)][4 (0 4 5 6 7 8)]>>>\n",
-       "<-1 * <<AlLp[2 (0 1 5 6)][4 (2 3 4 5 6 8)][4 (0 4 5 6 7 8)]>>>\n",
-       "<1 * <<AlLp[2 (0 4 5 6)][4 (2 3 4 5 6 8)][4 (0 4 5 6 7 8)]>>>\n",
-       "<-1 * <<AlLp[2 (1 4 5 6)][4 (2 3 4 5 6 8)][4 (0 4 5 6 7 8)]>>>\n",
-       "<1 * <<AlLp[3 (0 1 4 5 6)][3 (2 3 4 5 6)][4 (0 4 5 6 7 8)]>>>\n",
-       "<-1 * <<AlLp[3 (0 1 4 5 6)][3 (2 3 4 5 8)][4 (0 4 5 6 7 8)]>>>\n",
-       "<1 * <<AlLp[3 (0 1 4 5 6)][3 (2 3 4 6 8)][4 (0 4 5 6 7 8)]>>>\n",
-       "<-1 * <<AlLp[3 (0 1 4 5 6)][3 (2 3 5 6 8)][4 (0 4 5 6 7 8)]>>>\n",
-       "<1 * <<AlLp[3 (0 1 4 5 6)][3 (2 4 5 6 8)][4 (0 4 5 6 7 8)]>>>\n",
-       "... ...\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 17,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? precobar 11 loop-4)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 18,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 9}\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 18,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? precobar *)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "#### Definition of the horizontal differential\n",
-    "\n",
-    "So far, the coalgebra structure has not been used but now it will be the main ingredient. The so-called \"horizontal\" differential is an operator $d_h$ defined on the tensor algebra $\\bigoplus_p \\widehat{\\mathcal{A}}_ast^{\\otimes p}$ as follows:\n",
-    "\n",
-    "$$d_h:({\\bar{\\cal A}}_*^{\\otimes p})_q \\longrightarrow ({\\bar{\\cal A}}_*^{\\otimes {p+1}})_q,$$\n",
-    "\n",
-    "$$\n",
-    "\\begin{aligned}\n",
-    "d_h( g_1 \\otimes \\cdots \\otimes g_p) = & (-1)^p \\Delta g_1 \\otimes g_2 \\otimes \\cdots \\otimes g_p \\\\\n",
-    "                    & + (-1)^{p-1} g_1 \\otimes \\Delta g_2 \\otimes \\cdots \\otimes g_p \\\\\n",
-    "                    &  \\cdots  \\\\\n",
-    "                    & - g_1 \\otimes g_2 \\otimes \\cdots \\otimes g_{p-1} \\otimes \\Delta g_p,\n",
-    "\\end{aligned}\n",
-    "$$\n",
-    "\n",
-    "where $\\Delta$ is the coproduct of the coalgebra. The fact that every component of $\\Delta g_i$ is split in a tensor product decreases the degree by 1. Two functions are designed for that:\n",
-    "\n",
-    "`cobar-intr-hrzn-dffr` *cprd* *[Function]*\n",
-    "> From the coproduct morphism *cprd*, build the lisp function with 2 arguments: a degree and an algebraic loop (i.e. a generator) implementing the algorithm for $d_h$.\n",
-    "\n",
-    "`cobar-hrzn-dffr` *clbg* *[Function]*\n",
-    "> Build the horizontal differential morphism of the cobar construction, using the slot coproduct *cprd* of the coalgebra *clbg* and the previous function. Note that when called, this function creates, if not already created, the vertical cobar chain complex on *clbg*:\n",
-    "```commonlisp\n",
-    "(build-mrph\n",
-    "  :sorc (vrtc-cobar clgb) \n",
-    "  :trgt (vrtc-cobar clgb) \n",
-    "  :degr -1\n",
-    "  :intr (cobar-intr-hrzn-dffr cprd) \n",
-    "  :strt :gnrt\n",
-    "  :orgn `(cobar-hrzn-dffr ,clgb))\n",
-    "```\n",
-    "\n",
-    "### Example\n",
-    "\n",
-    "We still use our simple coalgebra `smp-deltab2`. The horizontal differential uses the coproduct of the coalgebra. The following examples show the application of the coproduct (note that there are no 1-simplices in the tensor products). We check also the property $d_h^2 = 0$ of the horizontal differential for some generators. "
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 19,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 2}\n",
-       "<1 * <TnPr (0) (0 1 2)>>\n",
-       "<1 * <TnPr (0 1 2) (0)>>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 19,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(cprd smp-deltab2 2 '(0 1 2))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 20,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 3}\n",
-       "<1 * <TnPr (0) (1 2 3 4)>>\n",
-       "<1 * <TnPr (1 2 3 4) (0)>>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 20,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(cprd smp-deltab2 3 '(1 2 3 4))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 21,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 4}\n",
-       "<1 * <TnPr (0) (0 1 2 3 4)>>\n",
-       "<1 * <TnPr (0 1 2) (2 3 4)>>\n",
-       "<1 * <TnPr (0 1 2 3 4) (0)>>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 21,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(cprd smp-deltab2 4 '(0 1 2 3 4))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 22,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K8 Morphism (degree -1): K6 -> K6]"
-      ]
-     },
-     "execution_count": 22,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def dh-mrph (cobar-hrzn-dffr smp-deltab2))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 23,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "<<AlLp[2 (0 1 2 3)]>>"
-      ]
-     },
-     "execution_count": 23,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "loop-1"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 24,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 1}\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 24,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? dh-mrph 2 loop-1)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 25,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "<<AlLp[3 (0 1 2 3 4)][3 (1 3 5 7 9)]>>"
-      ]
-     },
-     "execution_count": 25,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "loop-3"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 26,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 5}\n",
-       "<1 * <<AlLp[1 (0 1 2)][1 (2 3 4)][3 (1 3 5 7 9)]>>>\n",
-       "<-1 * <<AlLp[3 (0 1 2 3 4)][1 (1 3 5)][1 (5 7 9)]>>>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 26,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? dh-mrph 6 loop-3)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 27,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 4}\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 27,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? dh-mrph *)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 28,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "<<AlLp[3 (0 1 4 5 6)][4 (2 3 4 5 6 8)][4 (0 4 5 6 7 8)]>>"
-      ]
-     },
-     "execution_count": 28,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "loop-4"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 29,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 10}\n",
-       "<-1 * <<AlLp[1 (0 1 4)][1 (4 5 6)][4 (2 3 4 5 6 8)][4 (0 4 5 6 7 8)]>>>\n",
-       "<1 * <<AlLp[3 (0 1 4 5 6)][1 (2 3 4)][2 (4 5 6 8)][4 (0 4 5 6 7 8)]>>>\n",
-       "<1 * <<AlLp[3 (0 1 4 5 6)][2 (2 3 4 5)][1 (5 6 8)][4 (0 4 5 6 7 8)]>>>\n",
-       "<-1 * <<AlLp[3 (0 1 4 5 6)][4 (2 3 4 5 6 8)][1 (0 4 5)][2 (5 6 7 8)]>>>\n",
-       "<-1 * <<AlLp[3 (0 1 4 5 6)][4 (2 3 4 5 6 8)][2 (0 4 5 6)][1 (6 7 8)]>>>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 29,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? dh-mrph 11 loop-4)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 30,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 9}\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 30,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? dh-mrph *)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "#### Final definition of the cobar of a coalgebra\n",
-    "\n",
-    "To define completely the cobar chain complex, we have to provide the lisp function for the differential $d_v + d_h$ and, once created the vertical cobar chain complex, to call the building function `build-chcm` with adequate arguments.\n",
-    "\n",
-    "`cobar-intr-dffr` *vrtc-dffr hrzn-dffr* *[Function]*\n",
-    "> Define the lisp function for the differential $d_v+d_h$ from the two morphisms *vrtc-dffr* and *hrzn-dffr*. For efficiency reasons, the implementor has chosen to define this new function rather than to use simply the addition of two morphisms.\n",
-    "\n",
-    "`cobar` *coalgebra* *[Method]*\n",
-    "> Build first the vertical cobar chain complex on the coalgebra. Then return a chain complex with the same slots as the vertical cobar chain complex but with new `:intr-dffr` and `:orgn` slots, as shown in the following definition:\n",
-    "```commonlisp\n",
-    "(defmethod COBAR ((coalgebra coalgebra))\n",
-    "   (let ((vrtc-cobar (vrtc-cobar coalgebra))\n",
-    "         (cobar-hrzn-dffr (cobar-hrzn-dffr coalgebra)))\n",
-    "        (declare (type chain-complex vrtc-coabr hrzn-cobar))\n",
-    "        (the chain-complex\n",
-    "            (build-chcm\n",
-    "               :cmpr (cmpr vrtc-cobar)\n",
-    "               :basis (basis vrtc-cobar)\n",
-    "               :bsgn +null-allp+\n",
-    "               :intr-dffr (cobar-intr-dffr (dffr vrtc-cobar) \n",
-    "                                           cobar-hrzn-dffr)\n",
-    "               :strt :gnrt\n",
-    "               :orgn `(add ,vrtc-cobar ,cobar-hrzn-dffr)))))\n",
-    "```\n",
-    "\n",
-    "### Example\n",
-    "\n",
-    "We may now build the cobar of `smp-deltab2` and test the differential."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 31,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K9 Chain-Complex]"
-      ]
-     },
-     "execution_count": 31,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def cobar-deltab2 (cobar smp-deltab2))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 32,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "<<AlLp[3 (0 1 2 3 4)][3 (1 3 5 7 9)]>>"
-      ]
-     },
-     "execution_count": 32,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "loop-3"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 33,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 5}\n",
-       "<1 * <<AlLp[2 (0 1 2 3)][3 (1 3 5 7 9)]>>>\n",
-       "<-1 * <<AlLp[2 (0 1 2 4)][3 (1 3 5 7 9)]>>>\n",
-       "<1 * <<AlLp[2 (0 1 3 4)][3 (1 3 5 7 9)]>>>\n",
-       "<-1 * <<AlLp[2 (0 2 3 4)][3 (1 3 5 7 9)]>>>\n",
-       "<1 * <<AlLp[2 (1 2 3 4)][3 (1 3 5 7 9)]>>>\n",
-       "<1 * <<AlLp[3 (0 1 2 3 4)][2 (1 3 5 7)]>>>\n",
-       "<-1 * <<AlLp[3 (0 1 2 3 4)][2 (1 3 5 9)]>>>\n",
-       "<1 * <<AlLp[3 (0 1 2 3 4)][2 (1 3 7 9)]>>>\n",
-       "<-1 * <<AlLp[3 (0 1 2 3 4)][2 (1 5 7 9)]>>>\n",
-       "<1 * <<AlLp[3 (0 1 2 3 4)][2 (3 5 7 9)]>>>\n",
-       "... ...\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 33,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? cobar-deltab2 6 loop-3)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 34,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 4}\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 34,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? cobar-deltab2 *)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 35,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "<<AlLp[3 (0 1 4 5 6)][4 (2 3 4 5 6 8)][4 (0 4 5 6 7 8)]>>"
-      ]
-     },
-     "execution_count": 35,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "loop-4"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 36,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 10}\n",
-       "<-1 * <<AlLp[2 (0 1 4 5)][4 (2 3 4 5 6 8)][4 (0 4 5 6 7 8)]>>>\n",
-       "<1 * <<AlLp[2 (0 1 4 6)][4 (2 3 4 5 6 8)][4 (0 4 5 6 7 8)]>>>\n",
-       "<-1 * <<AlLp[2 (0 1 5 6)][4 (2 3 4 5 6 8)][4 (0 4 5 6 7 8)]>>>\n",
-       "<1 * <<AlLp[2 (0 4 5 6)][4 (2 3 4 5 6 8)][4 (0 4 5 6 7 8)]>>>\n",
-       "<-1 * <<AlLp[2 (1 4 5 6)][4 (2 3 4 5 6 8)][4 (0 4 5 6 7 8)]>>>\n",
-       "<1 * <<AlLp[3 (0 1 4 5 6)][3 (2 3 4 5 6)][4 (0 4 5 6 7 8)]>>>\n",
-       "<-1 * <<AlLp[3 (0 1 4 5 6)][3 (2 3 4 5 8)][4 (0 4 5 6 7 8)]>>>\n",
-       "<1 * <<AlLp[3 (0 1 4 5 6)][3 (2 3 4 6 8)][4 (0 4 5 6 7 8)]>>>\n",
-       "<-1 * <<AlLp[3 (0 1 4 5 6)][3 (2 3 5 6 8)][4 (0 4 5 6 7 8)]>>>\n",
-       "<1 * <<AlLp[3 (0 1 4 5 6)][3 (2 4 5 6 8)][4 (0 4 5 6 7 8)]>>>\n",
-       "... ...\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 36,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? cobar-deltab2 11 loop-4)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 37,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 9}\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 37,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? cobar-deltab2 *)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "## Other functions for the cobar construction\n",
-    "\n",
-    "The vertical cobar construction is *natural* and therefore defines a functor. Consequently, the `Kenzo` program contains the following methods.\n",
-    "\n",
-    "`vrtc-cobar` *mrph* *[Method]*\n",
-    "> From the morphism *mrph*, build a new morphism between the vertical-cobar of the source of *mrph* and the vertical cobar of the target of *mrph*, the morphism itself being induced in a natural way by the underlying morphism.\n",
-    "\n",
-    "`vrtc-cobar` *rdct* *[Method]*\n",
-    "> From the reduction *rdct*, build a new reduction, by applying the vertical cobar method to the functions $f$ and $g$. The new homotopy cannot be obtained so simply, being a function of the $f$, $g$ and $h$ of *rdct*. Nevertheless, the source and target of the new homotopy are the vertical cobar of the underlying homotopy.\n",
-    "\n",
-    "`vrtc-cobar` *hmeq* *[Method]*\n",
-    "> Build a homotopy equivalence by applying the vertical cobar construction to the left and right reductions of the homotopy equivalence *hmeq*.\n",
-    "\n",
-    "`cobar` *hmeq* *[Method]*\n",
-    "> Build a  homotopy equivalence where the cobar construction is applied to the underlying homotopy equivalence in the following way. First this construction is limited to the case where the left bottom chain complex of *hmeq* is a **coalgebra**. Then the vertical cobar construction is applied to *hmeq* and the horizontal differential of the left bottom chain complex is propagated upon the new homotopy equivalence with the help of the method `add`. In other words, starting from the left bottom chain complex, firstly the easy pertubation lemma is applied to obtain a new differential on the top chain complex; then the basic perturbation lemma is applied to the right reduction. If *hmeq* is a trivial homotopy equivalence, this function returns a trivial one, built on the cobar of the left bottom chain complex of *hmeq*.\n",
-    "\n",
-    "### Lisp files concerned in this chapter\n",
-    "\n",
-    "`coalgebras.lisp`, `cobar.lisp`.\n",
-    "\n",
-    "[`classes.lisp`, `macros.lisp`, `various.lisp`]."
-   ]
-  }
- ],
- "metadata": {
-  "kernelspec": {
-   "display_name": "SBCL Lisp",
-   "language": "lisp",
-   "name": "lisp"
-  },
-  "language_info": {
-   "codemirror_mode": "text/x-common-lisp",
-   "mimetype": "text/x-common-lisp",
-   "name": "common-lisp",
-   "pygments_lexer": "common-lisp",
-   "version": "X3J13"
-  }
- },
- "nbformat": 4,
- "nbformat_minor": 1
-}
diff --git a/examples/06_Algebras_and_bars.ipynb b/examples/06_Algebras_and_bars.ipynb
deleted file mode 100644
index 54c8525..0000000
--- a/examples/06_Algebras_and_bars.ipynb
+++ /dev/null
@@ -1,897 +0,0 @@
-{
- "cells": [
-  {
-   "cell_type": "code",
-   "execution_count": 1,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "To load \"kenzo\":\n",
-      "  Load 1 ASDF system:\n",
-      "    kenzo\n",
-      "; Loading \"kenzo\"\n",
-      "\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "#<PACKAGE \"CAT\">"
-      ]
-     },
-     "execution_count": 1,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(ql:quickload \"kenzo\")\n",
-    "(in-package :cat)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "# Algebras and Bars\n",
-    "\n",
-    "## Algebra\n",
-    "\n",
-    "An algebra  is a pair $(A, \\varpi)$ where\n",
-    "\n",
-    "1. $A$ is a chain complex.\n",
-    "2. $\\varpi$ (the *product*) is a chain complex morphism \n",
-    "$$\\varpi:  A \\otimes A  \\rightarrow A.$$\n",
-    "\n",
-    "These components must satisfy the usual structural properties of the algebras.\n",
-    "\n",
-    "### Implementation of an algebra\n",
-    "\n",
-    "An algebra  is represented as an instance of the CLOS class `ALGEBRA`, subclass of the ` CHAIN COMPLEX` class. The definition of this new class is simply:\n",
-    "\n",
-    "```commonlisp\n",
-    "(DEFCLASS ALGEBRA (chain-complex)\n",
-    "    ((aprd :type morphism :initarg :aprd :reader aprd1)))   ;; product\n",
-    "```\n",
-    "\n",
-    "So, this new class inherits the slots of the `CHAIN COMPLEX` class and has a slot of its own, namely `aprd`, an  object of type `MORPHISM` representing the product. Like in a coalgebra, the user will note the important following fact that, **once an algebra has been defined, one may use on it any function or method applicable to a chain complex**.\n",
-    "\n",
-    "### The function `build-algb`\n",
-    "\n",
-    "To facilitate the construction of instances of the `ALGEBRA` class, the program **Kenzo** provides the function `build-algb`:\n",
-    "\n",
-    "```commonlisp\n",
-    "build-algb :cmpr cmpr :basis basis :bsgn bsgn :intr-dffr intr-dffr\n",
-    "           :dffr-strt dffr-strt :intr-aprd intr-aprd\n",
-    "           :aprd-strt aprd-strt :orgn orgn\n",
-    "```\n",
-    "\n",
-    "defined with keyword parameters. The returned value is an instance of type `ALGEBRA`. \n",
-    "The keyword arguments are:\n",
-    "\n",
-    "- *cmpr*, a comparison function for generators.\n",
-    "- *basis*, the basis function for the underlying chain complex.\n",
-    "- *bsgn*, the  base point, a generator of any type.\n",
-    "- *intr-dffr*, the differential lisp function for the chain complex.\n",
-    "- *dffr-strt*, the strategy (`:gnrt` or `:cmbn`) for the differential.\n",
-    "- *intr-aprd*, the lisp function for the product of the algebra.\n",
-    "- *aprd-strt*, the strategy (`:gnrt` or `:cmbn`) for the product.\n",
-    "- *orgn*, an adequate comment list.\n",
-    "\n",
-    "The function `build-algb` calls  the function `build-chcm` and with the help of the function `build-mrph` builds the product morphism of degree 0 to settle the slot `aprd` of the instance. According to the definition, the source slot of the product morphism is the tensor product of this chain complex with itself and the target slot is the underlying chain complex. An identification number $n$ (slot `idnm`) is assigned to this Kenzo object and the `ALGEBRA` instance is  pushed  onto the list `*algb-list*`. The  associated printing method prints a string like `[K`*n* `Algebra]`.\n",
-    "\n",
-    "### Miscellaneous functions and macros for algebras\n",
-    "\n",
-    "`cat-init` *[Function]*\n",
-    "> Clear among others, the list `*algb-list*`, list of user created algebras  and reset the global counter to 1.\n",
-    "\n",
-    "`algb` *n* *[Function]*\n",
-    "> Retrieve in the list `*algb-list*` the algebra instance whose identification is $n$. If it does not exist, return `NIL`.\n",
-    "\n",
-    "`aprd` *algb* `&rest` *[Macro]*\n",
-    "> Versatile macro relative to the product of an algebra. The first argument is an `ALGEBRA`\n",
-    "instance. With only one argument, this macro returns the product morphism of the algebra.\n",
-    "With more arguments, it applies the product morphism on a combination (`(aprd` *algb cmbn*`)`)\n",
-    "or on a pair *degree, tensor-product* (`(aprd` *algb degr tensor-product*`)`).\n",
-    "\n",
-    "`change-chcm-to-algb` *chcm* `:intr-aprd` *intr-aprd* `:aprd-strt` *aprd-strt* `:orgn` *orgn* *[Function]*\n",
-    "> Build an algebra instance from the already created chain complex *chcm*. The user must give via key arguments a lisp function for the product, its strategy and a comment list.\n",
-    "\n",
-    "## Hopf Algebra\n",
-    "\n",
-    "In **Kenzo**, a Hopf Algebra is an instance of the class `HOPF-ALGEBRA`, the definition of which being simply:\n",
-    "\n",
-    "```commonlisp\n",
-    "(DEFCLASS HOPF-ALGEBRA (coalgebra algebra)\n",
-    "  ())\n",
-    "```\n",
-    "\n",
-    "So, this class (multi-) inherits the slots of the `COALGEBRA` and `ALGEBRA` classes. The  associated printing method prints a string like `[K`*n* `Hopf-Algebra]`, and the function `hopf` may be used to retrieve the Hopf instance, in the list `*hopf-list*`. As usual, it is the responsability of the user to be sure the standard coherence properties between product, coproduct, differential and base generator are satisfied.\n",
-    "\n",
-    "### Example of algebra\n",
-    "\n",
-    "We shall see later important examples of algebras. Let us content ourself for the moment\n",
-    "to define the trivial algebra on a given chain complex *having only one generator in degree* 0.  If  this chain complex *chcm* already exists, we use simply the function `change-chcm-to-algb` and we have to provide for the keyword `:intr-aprd`, a lisp function for the product morphism. We recall that the argument of the product in the algebra is a tensor product.\n",
-    "This function must obey the rule of the multiplication by the unit and otherwise will return a null combination of degree the sum of the two degrees in the tensor product."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 2,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "TRIVIAL-ALGEBRA"
-      ]
-     },
-     "execution_count": 2,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(defun trivial-algebra (chcm)\n",
-    "   (change-chcm-to-algb  \n",
-    "      chcm\n",
-    "      :intr-aprd #'(lambda (degr tnpr)\n",
-    "                           (declare (ignore degr))\n",
-    "                           (with-tnpr (degr1 gnrt1 degr2 gnrt2) tnpr\n",
-    "                               (if (zerop degr1)\n",
-    "                                   (cmbn degr2 1 gnrt2)\n",
-    "                                   (if (zerop degr2)\n",
-    "                                       (cmbn degr1 1 gnrt1)\n",
-    "                                       (zero-cmbn (+ degr1 degr2))))))\n",
-    "      :aprd-strt :gnrt\n",
-    "      :orgn `(trivial-algebra ,chcm)))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "A good example of a chain complex to be given as argument to the previous function, is the simplicial set `smp-deltab2` that we used as simple example in the coalgebra chapter:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 3,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K1 Simplicial-Set]"
-      ]
-     },
-     "execution_count": 3,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def smp-deltab2\n",
-    "   (build-smst\n",
-    "        :cmpr #'(lambda(gsm1 gsm2)\n",
-    "                       (if(rest gsm1) (l-cmpr gsm1 gsm2) :equal))\n",
-    "        :basis :locally-effective\n",
-    "        :bspn '(0)\n",
-    "        :face #'(lambda (i dmn gsm)\n",
-    "                        (case dmn\n",
-    "                         (0 (error \"No face in dimension 0\"))\n",
-    "                         (1 (error \"No non-degenerate simplex in dimension 1\"))\n",
-    "                         (2 (absm 1 '(0)))\n",
-    "                         (otherwise (absm 0 (append (subseq gsm 0 i)\n",
-    "                                                    (subseq gsm (1+ i))))) ))\n",
-    "        :orgn '(simple-deltab2)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 4,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K1 Algebra]"
-      ]
-     },
-     "execution_count": 4,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(trivial-algebra smp-deltab2)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Note that now `smp-deltab2` is of type `ALGEBRA` and has kept its Kenzo numbering."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 5,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K1 Algebra]"
-      ]
-     },
-     "execution_count": 5,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "smp-deltab2"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 6,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "The object is a STANDARD-OBJECT of type ALGEBRA.\n",
-      "0. CMPR: #<FUNCTION (LAMBDA (GSM1 GSM2) :IN \"/root/cl-jupyter/cl-jupyter.lisp\") {1001AEC60B}>\n",
-      "1. BASIS: :LOCALLY-EFFECTIVE\n",
-      "2. BSGN: (0)\n",
-      "3. DFFR: [K2 Morphism (degree -1): K1 -> K1]\n",
-      "4. GRMD: [K1 Algebra]\n",
-      "5. EFHM: \"unbound\"\n",
-      "6. IDNM: 1\n",
-      "7. ORGN: (SIMPLE-DELTAB2)\n",
-      "8. APRD: [K6 Morphism (degree 0): K3 -> K1]\n",
-      "> "
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 6,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(inspect smp-deltab2)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Note the simplicial structure has been lost: the `face` component is no longer present in the object. We will see later the CLASS `simplicial-group` where the group structure automatically induces an algebra structure: the class `simplicial-group` is a subclass of the classes `simplicial-set` and `algebra`.\n",
-    "\n",
-    "Let us test now the product in this trivial algebra:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 7,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 3}\n",
-       "<1 * (1 2 3 4)>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 7,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(aprd smp-deltab2 3 (tnpr 0 '(0) 3 '(1 2 3 4)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 8,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 3}\n",
-       "<1 * (1 2 3 4)>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 8,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(aprd smp-deltab2 3 (tnpr  3 '(1 2 3 4) 0 '(0)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 9,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 5}\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 9,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(aprd smp-deltab2 5 (tnpr 2 '(0 1 2) 3 '(6 7 8 9)))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "## The Bar construction\n",
-    "\n",
-    "Let $\\cal A$ be an associative algebra, assumed connected, that is, ${\\cal A}_0 \\simeq \\mathbb{Z}$. Furthermore let us suppose that ${\\cal A}$ is a free $\\mathbb{Z}$-module, more precisely, for every $i \\geq 0$, a \"distinguished\" basis is chosen for $\\mathcal{A}_i$, the elements of which will be called the (distinguished) *generators* of $\\mathcal{A}_i$. Then it is possible to define a chain complex, $Bar^{\\cal A}(\\mathbb{Z}, \\mathbb{Z})$ - simply denoted here by $Bar({\\cal A})$ - whose $n$-th component is the free $\\mathbb{Z}$-module generated by the \"bars\":\n",
-    "$$ [Bar({\\cal A})]_n = \\{ [g_1 \\mid g_2 \\mid \\ldots \\mid g_k] \\}, \\quad \\sum_{j=1}^{k} [deg(g_j)+1] =n. $$\n",
-    "where the $g_i$'s are distinguished generators of arbitrary *positive* degree.\n",
-    "\n",
-    "The object denoted $[g_1 \\mid g_2 \\mid \\ldots \\mid g_k]$ \n",
-    "with $\\sum_{j=1}^{k} [deg(g_j)+1] =n$, is traditionally called a *bar* and is in fact,  an element of the $n$-th iterated suspension of ${\\cal A}^{\\otimes n}$. The integer $n$ is the *total degree*. The structure of the bar of the algebra ${\\cal A}$ is recalled in the following figure, where $\\bar{\\cal A}$ is ${\\cal A}$ without its component of degree 0. In the vertical sense, we have the *tensorial degree*, whereas in the horizontal one, we have the *simplicial degree*. The *total degree* $n$ is the sum of both degrees.\n",
-    "\n",
-    "$$\n",
-    "\\begin{array}{|ccccc}\n",
-    "  \\vdots & \\vdots & \\vdots &\\vdots & \\vdots \\\\\n",
-    "  0 & \\bar{\\cal A}_3 & (\\bar{\\cal A} \\otimes \\bar{\\cal A})_3 & \n",
-    "  (\\bar{\\cal A}\\otimes \\bar{\\cal A}\\otimes\\bar{\\cal A})_3 & \\cdots \\\\\n",
-    "  0 & \\bar{\\cal A}_2 & (\\bar{\\cal A}\\otimes\\bar{\\cal A})_2 & 0 & \\cdots \\\\\n",
-    "  0 & \\bar{\\cal A}_1 & 0 & 0 & \\cdots \\\\\n",
-    "  \\mathbb{Z} & 0 & 0 & 0 & \\cdots \\\\ \\hline\n",
-    "    &   &   &   &    \\\\\n",
-    "  \\bar{\\cal A}^{\\otimes 0} & \\bar{\\cal A}^{\\otimes 1} & \\bar{\\cal A}^{\\otimes 2} &\n",
-    "  \\bar{\\cal A}^{\\otimes 3} & \\cdots \n",
-    "\\end{array}\n",
-    "$$\n",
-    "\n",
-    "### Representation of a bar object\n",
-    "\n",
-    "An elementary bar object - not to be confused with the chain complex $Bar({\\cal A})$ - is represented in `Kenzo` by a lisp object of the structure class `ABAR`:\n",
-    "\n",
-    "`(:ABAR :LIST` (($i_1\\, . \\, a_1$) $\\ldots$ ($i_k\\, . \\, a_k$))`)`\n",
-    "\n",
-    "where the $i_j$ are the degrees *in the bar chain complex* of the generators $a_j$. In the original algebra $\\cal A$, the generators $a_j$ had the degree $i_j-1$. The corresponding type is `ABAR`. The function  building such an object is also called `abar`\n",
-    "\n",
-    "`abar` *degr1 gnr1 degr2 gnr2 ... degrk gnrk* *[Function]*\n",
-    "> Construct an elementary bar object, i.e. a \"suspended tensorial product\" of degree $\\sum degr_i$. The sequence of pairs $\\lbrace degr_i,\\,  gnr_i \\rbrace$ has an undefinite length and  may be void. In this case, the bar is the null bar object, also located in the system through the constant `+null-abar+`. The function `abar` accepts also as unique argument a list of the form `(`*degr1 gnr1 degr2 gnr2 ... degrk gnrk*`)`.\n",
-    "\n",
-    "`abar-p` *object* *[Function]*\n",
-    "> Test if *object* is an elementary bar object.\n",
-    "\n",
-    "The associated printing  method prints the object under the form:\n",
-    "\n",
-    "`<<Abar [`$i_1\\quad a_1$ `]` ... `[` $i_k\\quad a_k$ `] >>`\n",
-    "\n",
-    "#### Examples\n",
-    "\n",
-    "These simple commands show the two different ways to create bar objects\n",
-    "from elements of an algebra (or a chain complex)."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 10,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "<<Abar[2 A][3 B][5 C]>>"
-      ]
-     },
-     "execution_count": 10,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(abar 2 'a 3 'b 5 'c)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 11,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "<<Abar[2 A][3 B][5 C]>>"
-      ]
-     },
-     "execution_count": 11,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(abar '(2 a 3 b 5 c))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 12,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "<<Abar>>"
-      ]
-     },
-     "execution_count": 12,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(abar)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "### Definition of the chain complex Bar\n",
-    "\n",
-    "The definition of the differential in the bar chain complex, will be done in three steps. This is better understood,\n",
-    "if we consider the following diagram.\n",
-    "\n",
-    "$$\n",
-    "\\begin{aligned}\n",
-    "       &             & \\downarrow\\quad  &  & \\downarrow\\quad \\cr\n",
-    "\\cdots\\quad & \\leftarrow & ({\\bar{\\cal A}}_*^{\\otimes p})_q & \\qquad\\buildrel {d_h} \\over \\longleftarrow \n",
-    "                     & ({\\bar{\\cal A}}_*^{\\otimes {p+1}})_q  & \\quad\\leftarrow & \\cdots \\cr\n",
-    "       &             &  \\downarrow {\\scriptstyle d}_v  &  &  \\downarrow {\\scriptstyle d}_v \\cr\n",
-    "\\cdots\\quad & \\leftarrow &({\\bar{\\cal A}}_*^{\\otimes p})_{q-1} & \\qquad\\buildrel {d_h} \\over \\longleftarrow \n",
-    "                     & ({\\bar{\\cal A}}_*^{\\otimes {p+1}})_{q-1}  & \\quad\\leftarrow & \\cdots \\cr \n",
-    "       &             & \\downarrow\\quad  &  & \\downarrow\\quad \\cr\n",
-    "\\end{aligned}\n",
-    "$$\n",
-    "\n",
-    "- A chain complex called `vertical-bar` is defined with the *vertical differential* $d_v$. In this case, only the  underlying chain complex structure of the $\\mathcal{A}i$'s is used.\n",
-    "- A horizontal differential $d_h$ is defined. This uses  the product structure.\n",
-    "- The final chain complex `bar` is created with differential $d_v+d_h$.\n",
-    "\n",
-    "#### Definition of the vertical bar\n",
-    "\n",
-    "To define the vertical bar chain complex from the chain complex ${\\cal A}$, the following functions are provided:\n",
-    "\n",
-    "`bar-cmpr` *cmpr* *[Function]*\n",
-    "> From the comparison function *cmpr*, build a comparison function for objects of type `abar`.\n",
-    "\n",
-    "`bar-basis` *basis* *[Function]*\n",
-    "> From the function *basis* of a  chain complex ${\\cal A}$, build a basis function for the vertical bar chain complex defined on ${\\cal A}$. In dimension 0, there is only one basis element, namely the null abar object. If ${\\cal A}$ is locally effective, this function returns the symbol `:locally-effective`.\n",
-    "\n",
-    "`bar-intr-vrtc-dffr` *dffr* *[Function]*\n",
-    "> From the `lisp` function *dffr* of a chain complex  ${\\cal A}$, build a lisp function for the differential of the vertical bar chain complex, according to the formula:\n",
-    "$$d_v [a_1 \\mid \\cdots \\mid a_n]=\n",
-    "-\\sum_{i=1}^n{(-1)^{\\sum_{j=1}^{i-1}{\\mid a_j \\mid}}}\n",
-    " {[a_1 \\mid \\cdots \\mid a_{i-1} \\mid {\\bf da_i} \\mid a_{i+1} \\mid \\cdots \\mid a_n]},$$\n",
-    "where $da_i$ is the differential of the generator $a_i$ in the original chain complex (function *dffr*) and $\\mid a_i \\mid$ is in the exponent of $(-1)$ the degree of the generator $a_i$ *in the bar chain complex*.\n",
-    "In general, the differential $da_i$ is a sum of  objects. So, applying the distributive law, the right member is a sum of bar objects, represented by a combination.\n",
-    "\n",
-    "`vrtc-bar` *chcm* *[Method]*\n",
-    "> Build the vertical bar chain complex from the underlying chain complex *chcm*. This is simply done by the call to `build-chcm`:\n",
-    "```commonlisp\n",
-    "         (build-chcm\n",
-    "            :cmpr  (bar-cmpr cmpr)\n",
-    "            :basis (bar-basis basis)\n",
-    "            :bsgn +null-abar+\n",
-    "            :intr-dffr (bar-intr-vrtc-dffr dffr)\n",
-    "            :strt :gnrt\n",
-    "            :orgn `(vrtc-bar ,chcm))\n",
-    "```\n",
-    "where, *cmpr*, *basis* and *dffr* are extracted from the chain complex *chcm*. Note that the base generator is the null bar object.\n",
-    "\n",
-    "#### Examples\n",
-    "\n",
-    "First, let us test the functions `bar-cmpr` and `bar-basis`. With the first one, applied to the elementary comparison function `s-cmpr`, we create a comparison function suitable for algebras where the generators are symbols."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 13,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "#<CLOSURE (FLET RSLT :IN BAR-CMPR) {10022131CB}>"
-      ]
-     },
-     "execution_count": 13,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def cmpr-for-bar (bar-cmpr #'s-cmpr))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 14,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       ":EQUAL"
-      ]
-     },
-     "execution_count": 14,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(funcall cmpr-for-bar (abar)(abar))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 15,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       ":LESS"
-      ]
-     },
-     "execution_count": 15,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(funcall cmpr-for-bar (abar 3 'a 7 'q) (abar 4 'b 2 'p 4 'q))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 16,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       ":EQUAL"
-      ]
-     },
-     "execution_count": 16,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(funcall cmpr-for-bar (abar '(1 x 2 y 3 z) )(abar 1 'x 2 'y 3 'z))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Let us suppose now that the function `simple-basis` is the basis function for a certain algebra (chain complex): in degree $i$, the basis is only the list $(a_i)$."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 17,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "#<FUNCTION (LAMBDA (DEGR) :IN \"/root/cl-jupyter/cl-jupyter.lisp\") {100238964B}>"
-      ]
-     },
-     "execution_count": 17,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def simple-basis #'(lambda(degr) \n",
-    "    (list (intern(format nil \"A~D\" degr)))))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 18,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(A5)"
-      ]
-     },
-     "execution_count": 18,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(funcall simple-basis 5)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "The function `bar-basis` creates the function for the basis of the corresponding bar chain complex. Note that when this new  function is applied, it returns a priori the null abar in dimension 0 and a null basis in dimension 1. Note also that the basis elements of the underlying algebra (the $a_i$'s) are suspended."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 19,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "#<CLOSURE (FLET RSLT :IN BAR-BASIS) {1002416CEB}>"
-      ]
-     },
-     "execution_count": 19,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def basis-for-bar (bar-basis simple-basis))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 20,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "0 (<<Abar>>)\n",
-      "1 NIL\n",
-      "2 (<<Abar[2 A1]>>)\n",
-      "3 (<<Abar[3 A2]>>)\n",
-      "4 (<<Abar[4 A3]>> <<Abar[2 A1][2 A1]>>)\n",
-      "5 (<<Abar[5 A4]>> <<Abar[2 A1][3 A2]>> <<Abar[3 A2][2 A1]>>)\n",
-      "6 (<<Abar[6 A5]>> <<Abar[2 A1][4 A3]>> <<Abar[3 A2][3 A2]>> <<Abar[4 A3][2 A1]>> <<Abar[2 A1][2 A1][2 A1]>>)"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 20,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(dotimes (i 7)\n",
-    "   (format t \"~%~D ~A\" i (funcall basis-for-bar i)))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "To test the vertical differential, let us take the simplicial set `smp-deltab2` which is also a chain complex. We may use it for testing the function `vrtc-bar` which defines a chain complex independently of the product of the algebra. We recall that, in dimension $n$, the elements of the chain complex `smp-deltab2` are represented by lists of increasing $n+1$  integers. So, in the abar objects, the degree of such elements are $n+1$."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 21,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K7 Chain-Complex]"
-      ]
-     },
-     "execution_count": 21,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def vrt-bar (vrtc-bar smp-deltab2))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 22,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 8}\n",
-       "<1 * <<Abar[3 (0 1 2)][5 (4 5 6 7 8)]>>>\n",
-       "<-1 * <<Abar[3 (0 1 3)][5 (4 5 6 7 8)]>>>\n",
-       "<1 * <<Abar[3 (0 2 3)][5 (4 5 6 7 8)]>>>\n",
-       "<-1 * <<Abar[3 (1 2 3)][5 (4 5 6 7 8)]>>>\n",
-       "<-1 * <<Abar[4 (0 1 2 3)][4 (4 5 6 7)]>>>\n",
-       "<1 * <<Abar[4 (0 1 2 3)][4 (4 5 6 8)]>>>\n",
-       "<-1 * <<Abar[4 (0 1 2 3)][4 (4 5 7 8)]>>>\n",
-       "<1 * <<Abar[4 (0 1 2 3)][4 (4 6 7 8)]>>>\n",
-       "<-1 * <<Abar[4 (0 1 2 3)][4 (5 6 7 8)]>>>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 22,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? vrt-bar 9 (abar 4 '(0 1 2 3) 5 '(4 5 6 7 8)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 23,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 7}\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 23,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? vrt-bar *)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "#### Definition of the horizontal differential\n",
-    "\n",
-    "So far, the algebra structure has not been used but now it will be the main ingredient.\n",
-    "The canonical \"horizontal\"  differential $d_h$ is defined as follows:\n",
-    "\n",
-    "$$d_h:({\\bar{\\cal A}}_*^{\\otimes p})_q \\longrightarrow ({\\bar{\\cal A}}_*^{\\otimes {p-1}})_q,$$\n",
-    "\n",
-    "$$d_h [a_1 \\mid \\cdots \\mid a_k] = \\sum_{i=2}^n{(-1)^{\\sum_{j=1}^{i-1}{\\mid a_j \\mid}}}\n",
-    "      [a_1 \\mid \\cdots \\mid a_{i-2} \\mid {\\bf a_{i-1}a_i} \\mid a_{i+1} \\mid \\cdots \\mid a_k]$$\n",
-    "\n",
-    "where the product in the algebra is noted simply by the concatenation and $\\mid a_i \\mid$  in the exponent of $(-1)$ is the degree of $a_i$ in $Bar({\\cal A})$. In `Kenzo`, two functions are designed for building the horizontal differential:\n",
-    "\n",
-    "`bar-intr-hrzn-dffr` *aprd* *[Function]*\n",
-    "> From the product morphism *aprd*, build the lisp function with 2 arguments: a degree and an `abar` object (i.e. a generator) realizing the algorithm for $d_h$.\n",
-    "\n",
-    "`bar-hrzn-dffr` *algb* *[Function]*\n",
-    "Build the horizontal differential morphism, using the slot product *aprd* of the algebra *algb* and the previous function. Note that when called, this function creates, if not already created, the vertical bar chain complex on *algb*:\n",
-    "```commonlisp\n",
-    "           (build-mrph\n",
-    "             :sorc (vrtc-bar algb) \n",
-    "             :trgt (vrtc-bar algb) \n",
-    "             :degr -1\n",
-    "             :intr (bar-intr-hrzn-dffr aprd) \n",
-    "             :strt :gnrt\n",
-    "             :orgn `(bar-hrzn-dffr ,algb))\n",
-    "```\n",
-    "\n",
-    "#### Final definition of the bar of an algebra\n",
-    "\n",
-    "To define completely the bar chain complex, we have to provide the lisp function for the differential $d_v + d_h$ and, once created the vertical bar chain complex, we have to call the building function `build-chcm` with adequate arguments.\n",
-    "\n",
-    "`bar-intr-dffr` *vrtc-dffr hrzn-dffr* *[Function]*\n",
-    "> Define the lisp function for the differential $d_v+d_h$ from the two morphisms *vrtc-dffr* and *hrzn-dffr*. For efficiency reasons, the implementor has chosen to define this new function rather than to use simply\n",
-    "the addition of two morphisms.\n",
-    "\n",
-    "`bar` *algebra* *[Method]*\n",
-    "> Build first the vertical bar chain complex on the algebra. Then return a chain complex with the same slots as the vertical bar chain complex but with new `:intr-dffr` and `:orgn` slots, as shown in the following definition:\n",
-    "```commonlisp\n",
-    "            (defmethod BAR ((algebra algebra))\n",
-    "                (let ((vrtc-bar (vrtc-bar algebra))\n",
-    "                      (bar-hrzn-dffr (bar-hrzn-dffr algebra)))\n",
-    "                (declare (type chain-complex vrtc-abr hrzn-bar))\n",
-    "                (the chain-complex\n",
-    "                    (build-chcm\n",
-    "                       :cmpr (cmpr vrtc-bar)\n",
-    "                       :basis (basis vrtc-bar)\n",
-    "                       :bsgn +null-abar+\n",
-    "                       :intr-dffr (bar-intr-dffr (dffr vrtc-bar) \n",
-    "                                                   bar-hrzn-dffr)\n",
-    "                       :strt :gnrt\n",
-    "                       :orgn `(add ,vrtc-bar ,bar-hrzn-dffr)))))\n",
-    "```\n",
-    "\n",
-    "We postpone the examples for the bar of an algebra, up to the chapter on simplicial groups where we shall  build interesting examples of algebras.\n",
-    "\n",
-    "## Other functions for the bar construction\n",
-    "\n",
-    "The vertical bar construction is *natural* and therefore defines a functor. Consequently, the `Kenzo` program contains the following methods.\n",
-    "\n",
-    "`vrtc-bar` *mrph* *[Method]*\n",
-    "> From the morphism *mrph*, build a new morphism between the vertical-bar of the source of *mrph* and the vertical bar of the target of *mrph*, the morphism itself being induced in a natural way by the underlying morphism.\n",
-    "\n",
-    "`vrtc-bar` *rdct* *[Method]*\n",
-    "> From the reduction *rdct*, build a new reduction, by applying the vertical bar method to the functions $f$ and $g$. The new homotopy cannot be obtained so simply, being a function of the $f$, $g$ and $h$ of *rdct*. Nevertheless, the source and target of the new homotopy are the vertical bar of the underlying homotopy.\n",
-    "\n",
-    "`vrtc-bar` *hmeq* *[Method]*\n",
-    "> Build a homotopy equivalence by applying the vertical bar construction to the left and right reductions of the homotopy equivalence *hmeq*.\n",
-    "\n",
-    "`bar` *hmeq* *[Method]*\n",
-    "> Build a  homotopy equivalence where the bar construction is applied to the underlying homotopy equivalence in the following way. First this construction is limited to the case where the left bottom chain complex of *hmeq* is an ** algebra**. Then the vertical bar construction is applied to *hmeq* and the horizontal differential of the left bottom chain complex is propagated upon the new homotopy equivalence with the help of the method `add`. In other words,\n",
-    "starting from the left bottom chain complex, firstly the easy pertubation lemma is applied to obtain a new differential on the top chain complex; then the basic perturbation lemma is applied to the right reduction. If *hmeq* is a trivial homotopy equivalence, this function returns a trivial one, built on the bar of the left bottom chain complex of * hmeq*.\n",
-    "\n",
-    "### Lisp files concerned in this chapter\n",
-    "\n",
-    "`algebras.lisp`, `bar.lisp`.\n",
-    "\n",
-    "[`classes.lisp`, `macros.lisp`, `various.lisp`]."
-   ]
-  }
- ],
- "metadata": {
-  "kernelspec": {
-   "display_name": "SBCL Lisp",
-   "language": "lisp",
-   "name": "lisp"
-  },
-  "language_info": {
-   "codemirror_mode": "text/x-common-lisp",
-   "mimetype": "text/x-common-lisp",
-   "name": "common-lisp",
-   "pygments_lexer": "common-lisp",
-   "version": "X3J13"
-  }
- },
- "nbformat": 4,
- "nbformat_minor": 1
-}
diff --git a/examples/07_Simplicial_Sets.ipynb b/examples/07_Simplicial_Sets.ipynb
deleted file mode 100644
index a984de4..0000000
--- a/examples/07_Simplicial_Sets.ipynb
+++ /dev/null
@@ -1,5684 +0,0 @@
-{
- "cells": [
-  {
-   "cell_type": "code",
-   "execution_count": 1,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "To load \"kenzo\":\n",
-      "  Load 1 ASDF system:\n",
-      "    kenzo\n",
-      "; Loading \"kenzo\"\n",
-      "\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "#<PACKAGE \"CAT\">"
-      ]
-     },
-     "execution_count": 1,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(ql:quickload \"kenzo\")\n",
-    "(in-package :cat)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "# Simplicial Sets\n",
-    "\n",
-    "## Introduction\n",
-    "\n",
-    "A *simplicial set* (**J. Peter May**, Simplicial objects in Algebrac Topology, University of Chicago press, 2nd edition, 1992) $K$ is a union $K={\\displaystyle{\\bigcup_{q\\ge 0}{K^q}}}$, where the $K^q$ are disjoints sets, together with functions\n",
-    "\n",
-    "$$\\partial_i^q: K^q \\longrightarrow K^{q-1},\\quad q>0,\\quad i=0,\\ldots , q,$$\n",
-    "\n",
-    "$$\\eta_i^q: K^q \\longrightarrow K^{q+1},\\quad q\\ge 0,\\quad i=0,\\ldots ,q,$$\n",
-    "\n",
-    "subject to the relations\n",
-    "\n",
-    "$$\n",
-    "\\begin{aligned}\n",
-    "\\partial_i^{q-1}\\partial_j^q & = & \\partial_{j-1}^{q-1}\\partial_i^q, & &   i < j \\cr\n",
-    "\\eta_i^{q+1}\\eta_j^q         & = & \\eta_j^{q+1}\\eta_{i-1}^q,         & & i > j    \\cr\n",
-    "\\partial_i^{q+1}\\eta_j^q     & = & \\eta_{j-1}^{q-1}\\partial_i^q,     & & i < j  \\cr\n",
-    "\\partial_i^{q+1}\\eta_i^q     & = & \\partial_{i+1}^{q+1}\\eta_i^q  & = \\mbox{Identity}, & \\cr\n",
-    "\\partial_i^{q+1}\\eta_j^q     & = & \\eta_j^{q-1}\\partial_{i-1}^q,     & &  i > j+1.\\cr \n",
-    "\\end{aligned}\n",
-    "$$\n",
-    "\n",
-    "An element of $K^q$ is an (*abstract*) $q$-simplex of $K$ and the functions $\\partial$ and $\\eta$ are respectively the *face operators* and the *degeneracy operators*. Formally, their action on a simplex is very simple. For instance, if a $q$-simplex is an ordered set of vertices, like $\\lbrace v_0, v_1, \\ldots,v_i,\\ldots, v_q \\rbrace$, the rules are the following (we omit the indication of the dimension of the simplex):\n",
-    "\n",
-    "$$\n",
-    "\\begin{aligned}\n",
-    "\\partial_i \\lbrace v_0, v_1, \\ldots,v_i,\\ldots, v_q \\rbrace & = &\n",
-    "           \\lbrace v_0, v_1, \\ldots,{\\bf v_{i-1}}, {\\bf v_{i+1}},\\ldots, v_q \\rbrace, \\\\\n",
-    "\\eta_i \\lbrace v_0, v_1, \\ldots,v_i,\\ldots, v_q \\rbrace & = &\n",
-    "      \\lbrace v_0, v_1, \\ldots,{\\bf v_i},{\\bf v_i},\\ldots, v_q \\rbrace.\n",
-    "\\end{aligned}\n",
-    "$$\n",
-    "\n",
-    "The operators $\\partial_i^q$ will be used hereafter to define the boundary operator $d^q$ for the $q$-component of the associated chain complex:\n",
-    "\n",
-    "$$d^q = \\sum_{i=0}^q { (-1)^i \\partial_i^q}.$$\n",
-    "\n",
-    "The image of a simplex under some $\\eta$ is called *degenerate*, because it\n",
-    "is not directly implied  in the realization of the simplicial set.\n",
-    "\n",
-    "### Example\n",
-    "\n",
-    "Let us take the small example *diabolo* from the chapter 1. For a better understanding, it is convenient to use a list representation for the simplices. So the set $K^0$ of 0-simplices (vertices) is:\n",
-    "\n",
-    "$$\\lbrace (0), (1),\\ldots (5) \\rbrace.$$\n",
-    "\n",
-    "The set $K^1$ of 1-simplices contains the set of regular simplices:\n",
-    "\n",
-    "$$\\lbrace (0\\  1), (0\\  2), (1\\  2), (2\\  3), (3\\  4), (3\\  5), (4\\  5) \\rbrace,$$\n",
-    "\n",
-    "but also the degenerate 1-simplices:\n",
-    "\n",
-    "$$\\lbrace (0\\ 0), (1\\ 1), (2\\ 2),\\ldots,(5 \\ 5) \\rbrace.$$\n",
-    "\n",
-    "The set $K^2$ of 2-simplices contains the regular singleton:  \n",
-    "\n",
-    "$$\\lbrace ( 3\\  4\\  5) \\rbrace$$\n",
-    "\n",
-    "but also the degenerate 2-simplices:\n",
-    "\n",
-    "$$\\lbrace (0\\ 0\\ 0), \\ldots, (5\\ 5\\ 5), (0\\ 0\\ 1), (0\\ 0\\  2), (1\\ 1\\ 2),\\ldots, (4\\ 5\\ 5)\\rbrace.$$\n",
-    "\n",
-    "The sets $K^q$ ($q >2$) contain only degenerate simplices. With this  naming of the elements of a $q$-simplex, the action of $\\partial$ and $\\eta$ is now clear. For instance\n",
-    "\n",
-    "$$\\partial_0 (0\\  1) = (1),\\  \\partial_1 (0\\  1) = (0),$$\n",
-    "\n",
-    "$$\\eta_0 (0\\  1) = (0\\  0\\  1),\\ \n",
-    "  \\eta_1 (1\\  2)= (1\\  2\\  2),\\ \\eta_2(3\\ 4\\ 5)=(3\\ 4\\ 5\\ 5). $$\n",
-    "\n",
-    "By the way, we see that, in this case, a simplex is non-degenerate if the list is strictly increasing.\n",
-    "\n",
-    "## Notion of abstract simplex in this Lisp implementation\n",
-    "\n",
-    "In this implementation, on account of the essential following property: *any simplex\n",
-    "may be expressed in an unique way as a possibly iterated degeneracy of a non-degenerate simplex*, we call an **abstract simplex**, (in short **absm**), a pair consisting of:\n",
-    "- a (possibly iterated) degeneracy operator,\n",
-    "- a \"geometric\" simplex, i.e. a non-degenerate simplex.\n",
-    "For instance, if $\\sigma$ is a non-degenerate simplex, and $\\sigma'$ is the degenerate simplex  $\\eta_3\\eta_1\\sigma$, the corresponding abstract simplices are respectively $\\lbrace \\emptyset, \\sigma \\rbrace$ and $\\lbrace \\eta_3\\eta_1, \\sigma \\rbrace$.\n",
-    "\n",
-    "An abstract simplex is represented internally in the system by the following lisp object:\n",
-    "```commonlisp\n",
-    "#S(ABSM :DGOP n :GMSM any)\n",
-    "```\n",
-    "where,\n",
-    "\n",
-    "1. *dgop* is a non-negative integer coding a *strictly decreasing integer list*. This strictly  decreasing list of integers represents a sequence of $\\eta$ operators and is coded as a **unique** integer as follows. The iterated degeneracy operator $\\eta_{i_k} \\ldots \\eta_{i_1}$ is coded as the integer $\\sum_{j = 1}^k 2^{i_j}$; in other words we use a binary number where the binary digits 1 correspond to the indices of the $\\eta_i$'s. This is made possible by the *strictly* decreasing  property of the indices. For example the degeneracy operator $\\eta_6 \\eta_3 \\eta_0$ is coded by the integer 73, for $73 = 2^6 + 2^3 + 2^0$. This leads to a compact coding, replacing the numerous operations about degeneracy operators by efficient handlings of bits of fixnums. In particular, 0 codes the void composition of degeneracy operator, that is, the identity operator. Two functions are provided to help the user for the transformation in both directions.\n",
-    "2. *gmsm* is a geometric simplex,  i.e. any kind of lisp object modelizing a non-degenerate simplex. For practical reason, a  type `GMSM`, (any kind of lisp object), has been defined.\n",
-    "\n",
-    "The simplest constructor is the macro `(absm (dgop-ext-int` *dgop-list*`)`  *gmsm*`)`, where *dgop-list* is a strictly decreasing integer list. A structure class `ABSM` has been defined. The associated printing method prints such an object under the form:\n",
-    "$$\\texttt{<AbSm}\\quad\\mathit{ext-dgop}\\quad\\mathit{gmsm}{\\texttt >}$$\n",
-    "where *ext-dgop* shows clearly the sequence of the operators $\\eta_i$ (see the examples). The accessor functions for the components are the macros `dgop` and `gmsm`.\n",
-    "\n",
-    "### Simple functions for abstract simplices\n",
-    "\n",
-    "`dgop-ext-int` *ext-dgop* *[Function]*\n",
-    "> Code on an integer the valid list representing the degeneracy operator *ext-dgop*.\n",
-    "\n",
-    "`dgop-int-ext` *dgop* *[Function]*\n",
-    "> Give the list representing a degeneracy operator from the integer *dgop*.\n",
-    "\n",
-    "`absm` *dgop gmsm* *[Macro]*\n",
-    "> Create an abstract simplex, using directly the coded representation, *dgop*, of the degeneracy operator.\n",
-    "\n",
-    "`dgop` *absm* *[Macro]*\n",
-    "> Get the integer code of the internal representation of the degeneracy operator of the abstract simplex *absm*.\n",
-    " \n",
-    "`gmsm` *absm* *[Macro]*\n",
-    "> Get the basic non-degenerate simplex part of the abstract simplex `absm`.\n",
-    "\n",
-    "`absm-p` *object* *[Predicate]*\n",
-    "> Test if *object* is an abstract simplex.\n",
-    "\n",
-    "### Examples\n",
-    "\n",
-    "Let us suppose that `:sigma` \"is\" a geometric simplex, we may construct the abstract simplices of the beginning of the section."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 2,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "1"
-      ]
-     },
-     "execution_count": 2,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(dgop-ext-int '(0))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 3,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "17"
-      ]
-     },
-     "execution_count": 3,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(dgop-ext-int '(4 0))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 4,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(5 4 3 2 1 0)"
-      ]
-     },
-     "execution_count": 4,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(dgop-int-ext 63)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 5,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "SIMPLE-ERROR: \n",
-      "In DGOP-EXT-INT, the external dgop (2 2) is not decreasing.\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 5,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(dgop-ext-int '(2 2))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 6,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "<AbSm - SIGMA>"
-      ]
-     },
-     "execution_count": 6,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def asigma (absm 0 :sigma))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 7,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "<AbSm 3-1 SIGMA>"
-      ]
-     },
-     "execution_count": 7,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def asigma-prime (absm (dgop-ext-int '(3 1)) :sigma))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 8,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "T"
-      ]
-     },
-     "execution_count": 8,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(absm-p asigma-prime)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "The following  command gives the sixth degeneracy of the vertex 0 represented as `(0)`."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 9,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "<AbSm 5-4-3-2-1-0 (0)>"
-      ]
-     },
-     "execution_count": 9,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def deg-6 (absm (dgop-ext-int '(5 4 3 2 1 0)) '(0)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 10,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "63"
-      ]
-     },
-     "execution_count": 10,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(dgop deg-6)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 11,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(0)"
-      ]
-     },
-     "execution_count": 11,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(gmsm deg-6)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "## Representation of a simplicial set\n",
-    "\n",
-    "A simplicial set is implemented as an instance of the class `SIMPLICIAL-SET`, subclass of the class `COALGEBRA`.\n",
-    "\n",
-    "```commonlisp\n",
-    "(DEFCLASS SIMPLICIAL-SET (coalgebra)\n",
-    "    ((face :type face :initarg :face :reader face1)))\n",
-    "\n",
-    "```\n",
-    "\n",
-    "This class inherits also from the class `CHAIN-COMPLEX` and has one slot of its own:\n",
-    "\n",
-    ">`face`, a lisp function  computing any face of any geometric simplex of the simplicial set.\n",
-    "This is a function with 3 arguments: a face index (a non--negative integer, `indx`), a simplex dimension (a positive integer, `dmns`) and a geometric simplex (`gmsm`), the $indx$-th face of which is looked for. Whatever the face simplex is, degenerate or not, the simplex returned by this function must be an **abstract** simplex, i.e. an `ABSM` object.\n",
-    "\n",
-    "A printing method has been associated to the class `SIMPLICIAL-SET` and the external representation of  an instance is a string like `[K`*n* `Simplicial-Set]`, where $n$ is the number plate of the Kenzo object.\n",
-    "\n",
-    "## The function `build-smst`\n",
-    "\n",
-    "To facilitate the construction of instances of the class `SIMPLICIAL-SET`, the program `Kenzo` provides the function `build-smst` defined with keyword parameters:\n",
-    "\n",
-    "```commonlisp\n",
-    "(build-smst :cmpr cmpr :basis basis :bspn bspn :face face\n",
-    "            :face* face* :intr-bndr intr-bndr :bndr-strt bndr-strt\n",
-    "            :intr-dgnl intr-dgnl :dgnl-strt dgnl-strt :orgn orgn\n",
-    "```\n",
-    "\n",
-    "The returned value is an object of type `SIMPLICIAL-SET`. This function assigns an identification number `idnm` to the Kenzo object instance in a sequential way and pushes this object on the list of already  created simplicial sets instances, `*smst-list*`.\n",
-    "\n",
-    "The keywords parameters are:\n",
-    "- *cmpr*, a comparison function for generators. \n",
-    "- *basis*, if the simplicial set is effective, this argument must be the lisp function returning the  list of non-degenerate simplices  of the simplicial set, in a given dimension; if the simplicial set is locally effective, this argument must be the keyword `:locally-effective`.\n",
-    "- *bspn*, the lisp representation of the base point (an item of type `GMSM`). This is in fact the slot `bsgn` of the associated chain complex.\n",
-    "- *face*, a lisp function for the face operators.\n",
-    "- $face*$, a lisp function for the face operators, returning the symbol `:degenerate` if the corresponding face is degenerate.\n",
-    "- *intr-bndr*, a lisp function for the differential of the associated chain complex.\n",
-    "- *bndr-strt*, the strategy (`:cmbn` or `:gnrt`) for the function *intr-bndr*.\n",
-    "- *intr-dgnl*, a lisp function for the coproduct of the coalgebra.\n",
-    "- *dngl-strt*, the strategy (`:cmbn` or `:gnrt`) for the function *intr-dgnl*.\n",
-    "- *org*, the comment list, adequately chosen.\n",
-    "\n",
-    "The three arguments $face*$,  *intr-bndr* and *intr-dgnl* are not mandatory. Only the function *face* is necessary to define precisely the simplicial set. From the function *face*, we know that we may construct:\n",
-    "- The differential for the associated chain complex, according to the formula:\n",
-    "$$d^q = \\sum_{i=0}^q { (-1)^i \\partial_i^q}.$$\n",
-    "- The coproduct of the underlying coalgebra (the Alexander-Whitney diagonal, $\\Delta$) according to the formula:\n",
-    "$$\\Delta(\\sigma)= \\sum_{i=0}^{n}{{\\tilde{\\delta}}^{(i)}\\sigma \\otimes \\delta_0^{(i)} \\sigma},$$\n",
-    "where the power $(i)$ denotes the $i$-th composition of the operator and $\\tilde{\\delta}$ is the\n",
-    "*last face* operator, so that\n",
-    "$$\n",
-    "\\widetilde{\\delta}^{(i)} = \\partial_{n-i+1} \\circ \\cdots \\circ \\partial_n \\\\\n",
-    "\\widetilde{\\delta}_0^{(i)} = \\partial_0 \\circ \\cdots \\circ \\partial_{i-1}\n",
-    "$$\n",
-    "\n",
-    "But, as the differential ignore degenerate faces, it could be interesting for the user to provide a face function, weaker than the function *face* but sufficient and more efficient to compute the boundary of a simplex. It is the raison d'etre of the parameter $face*$ which may be used as an alternative to *face*. In both cases, the strategy is set to `:gnrt` by the system. It may also arrive that the user knows a particularly simple form for the differential, he may then use the parameter *intr-bndr*. In the computation of differentials in the associated chain complex, this function will be used instead of the canonical differential computed from the face function. In this last case, the user is required to provide the strategy. Same remark for the parameter *intr-dgnl*.\n",
-    "\n",
-    "### Examples\n",
-    "\n",
-    "As first example, we give the construction of the simplicial set $\\Delta^n$  corresponding to the \n",
-    "standard $n$-simplex. This is given only as example. The program `Kenzo` provides a function\n",
-    "for the same purpose which will be described later. For every simplex, we shall use a list representation as in our first example `diabolo`. The various keyword arguments for the call to `build-smst`, are:\n",
-    "\n",
-    "1. *bspn*, the list `(0)`, i.e. the representation of the vertex 0.\n",
-    "2. *cmpr*, the lisp function  `#'l-cmpr`, since this function is adequate to compare the lists representing the simplices.\n",
-    "3. *basis*, the lisp function returning the list of all possible non-degenerate simplices in some dimension. Here, this is the combinatory function returning the set of all the lists of $p+1$ objects taken among $n+1$. Such a function is for instance the function  (`delta-inj` *p n*) whose definition is given hereafter. So, the `:basis` keyword argument is simply: `#'(lambda(dmn) (delta-inj dmn n))`. Note that here the binding of `n` is defined outside the $\\lambda$-expression, which requires a *closure* for the implementation of this $\\lambda$-expression.\n",
-    "4. *face*, the lisp function for the face operators (`face-delta-n`). It consists simply in removing the $i$-th element of the list describing a simplex ($i$ starting at 0).\n",
-    "5. *org* will be a comment."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 12,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "DELTA-INJ"
-      ]
-     },
-     "execution_count": 12,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(defun delta-inj (m n)\n",
-    "  (declare (type fixnum m n))\n",
-    "  (cond ((> m n) +empty-list+)\n",
-    "        ((zerop m) (mapcar #'list (<a-b> 0 n)))\n",
-    "        (t (mapcan #'(lambda (list)\n",
-    "                       (declare (type list list))\n",
-    "                       (mapcar #'(lambda (k)\n",
-    "                                   (declare (type fixnum k))\n",
-    "                                   (cons k list))\n",
-    "                                 (<a-b< 0 (first list))))\n",
-    "                     (delta-inj (1- m) n)))))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 13,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "((0) (1) (2) (3))"
-      ]
-     },
-     "execution_count": 13,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(delta-inj 0 3)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 14,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "((0 1) (0 2) (1 2) (0 3) (1 3) (2 3))"
-      ]
-     },
-     "execution_count": 14,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(delta-inj 1 3)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 15,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "((0 1 2 3))"
-      ]
-     },
-     "execution_count": 15,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(delta-inj 3 3)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 16,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "#<FUNCTION (LAMBDA (I DMN GSM) :IN \"/root/cl-jupyter/cl-jupyter.lisp\") {1001F1A81B}>"
-      ]
-     },
-     "execution_count": 16,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def face-delta-n\n",
-    "  #'(lambda (i dmn gsm)\n",
-    "      (declare (ignore dmn))\n",
-    "      (absm 0 (append (subseq gsm 0 i)\n",
-    "                      (subseq gsm (1+ i))) )))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "To create $\\Delta^n$ for any order $n$, we embed the call of `build-smst` in a function having $n$ as parameter."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 17,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "DELTA-N"
-      ]
-     },
-     "execution_count": 17,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(defun delta-n (n)\n",
-    "  (declare (type fixnum n))\n",
-    "        (build-smst :cmpr #'l-cmpr\n",
-    "                    :basis #'(lambda(dmn)(delta-inj dmn n))\n",
-    "                    :bspn '(0)\n",
-    "                    :face face-delta-n\n",
-    "                    :orgn `(delta-n ,n)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 18,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K1 Simplicial-Set]"
-      ]
-     },
-     "execution_count": 18,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def delta4 (delta-n 4))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 19,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(0)"
-      ]
-     },
-     "execution_count": 19,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(bspn delta4)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 20,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "((0) (1) (2) (3) (4))"
-      ]
-     },
-     "execution_count": 20,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(basis delta4 0)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 21,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "((0 1 2 3) (0 1 2 4) (0 1 3 4) (0 2 3 4) (1 2 3 4))"
-      ]
-     },
-     "execution_count": 21,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(basis delta4 3)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "A second example is the contruction of the simplicial complex  $\\Delta^\\mathbb{N}$ freely generated by the positive integers. The construction of the `SIMPLICIAL-SET` instance to implement this simplicial set is quite similar to that of $\\Delta^n$, but in this case the `:basis` keyword argument is  the keyword `:locally-effective`, since the sets $K^q$ are infinite. Whence, the definition of $\\Delta^\\mathbb{N}$:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 22,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K6 Simplicial-Set]"
-      ]
-     },
-     "execution_count": 22,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def delta-infty\n",
-    "        (build-smst :cmpr #'l-cmpr\n",
-    "                    :basis :locally-effective\n",
-    "                    :bspn '(0)\n",
-    "                    :face face-delta-n\n",
-    "                    :orgn `(delta-infinity)))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "A third example is the construction of the simplicial set corresponding to `diabolo`. This simplicial set is a  sub-complex of $\\Delta^5$. The `:face` function is exactly the same as in the examples above and the `:basis` function returns the sub-simplices of `diabolo`, by enumeration. "
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 23,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K11 Simplicial-Set]"
-      ]
-     },
-     "execution_count": 23,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def diabolo-ss \n",
-    "        (build-smst :cmpr #'l-cmpr\n",
-    "                    :basis  #'(lambda (dmn)\n",
-    "                                (case dmn\n",
-    "                                      (0 '((0)(1)(2)(3)(4)(5)))\n",
-    "                                      (1 '((0 1)(0 2)(1 2)(2 3)(3 4)(3 5)(4 5)))\n",
-    "                                      (2 '((3 4 5)))))\n",
-    "                    :bspn '(0)\n",
-    "                    :face face-delta-n\n",
-    "                    :orgn '(simplicial set for diabolo)))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "## A first set of helpful functions on simplicial sets\n",
-    "\n",
-    "We give now a first set of functions, methods or macros acting on  simplicial set instances. \n",
-    "\n",
-    "`cat-init` *[Function]*\n",
-    "> Clear in particular `*smst-list*`, the list of user created simplicial sets  and reset the global counter to 1.\n",
-    "\n",
-    "`smst` *n* *[Function]*\n",
-    "> Retrieve in the list `*smst-list*` the simplicial set instance whose the Kenzo identification\n",
-    "is $n$. If it does not exist, return `NIL`.\n",
-    "\n",
-    "`a-cmpr3` *smst absm1 absm2* *[Function]*\n",
-    "> Compare the abstract simplices *absm1* and *absm2* with the comparison function associated with the simplicial set *smst*.\n",
-    "\n",
-    "`bspn` *smst* *[Macro]*\n",
-    "> Return the base point of the simplicial set *smst*.\n",
-    "\n",
-    "`bndr`  *smst* `&rest` *[Macro]*\n",
-    "> Identical to the macro `dffr` (see the chain complex chapter). For simplicial sets, it is more traditional to use the term *boundary*.\n",
-    "\n",
-    "`dgnl` *smst* `&rest` *[Macro]*\n",
-    "> Identical to  the macro `cprd` (see the coalgebra chapter). For simplicial sets, this recalls the \n",
-    "Alexander-Witney diagonal.\n",
-    "\n",
-    "`face` *smst i k  gmsm-or-absm* *[Macro]*\n",
-    "> Versatile macro to apply the face operator $\\partial_i^k$ on the simplex *gmsm-or-absm* of the simplicial set *smst*. The name of the simplex parameter shows clearly that it may be either a geometric simplex or an abstract simplex. With only one argument (*smst*), return the function *face*. \n",
-    "In any other case, we recall that this application   returns always  an object of type `ABSM`.\n",
-    "\n",
-    "`degenerate-p` *absm* *[Macro]*\n",
-    "> Return `t` if the abstract simplex *absm* is degenerate, `nil` otherwise.\n",
-    "\n",
-    "`non-degenerate-p` *absm* *[Macro]*\n",
-    "> Return `t` if the abstract simplex *absm* is non-degenerate, `nil` otherwise.\n",
-    "\n",
-    "`check-smst` *smst dmns1* `&optional` *dmns2 (1+ dmns1)* *[Function]*\n",
-    "> Return `t` if the fundamental relations between the face operators $\\partial_i^k$\n",
-    "with $k=dmns1,\\ldots, dmns2-1$, applied on the effective simplicial set *smst*, are satisfied, otherwise `nil`. If the optional parameter *dmns2* is omitted, the test is done only for\n",
-    "$k=dmns1$.\n",
-    "\n",
-    "## Examples\n",
-    "\n",
-    "After having created instances of the standard simplicial sets $\\Delta^2$ and $\\Delta^3$ ($\\Delta^\\mathbb{N}$ has been defined previously), let us test some simple functions. Note that, since the class of simplicial sets is a sub-class of the class of coalgebras, itself subclass of chain complexes, the functions defined on these classes are available."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 24,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K16 Simplicial-Set]"
-      ]
-     },
-     "execution_count": 24,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def delta2 (delta-n 2))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 25,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K21 Simplicial-Set]"
-      ]
-     },
-     "execution_count": 25,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def delta3 (delta-n 3))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 26,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 26,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(degenerate-p (absm 0 '(1 2 3)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 27,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "T"
-      ]
-     },
-     "execution_count": 27,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(degenerate-p (absm 5 '(0 1 2 3 4)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 28,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "((0 1 2) (0 1 3) (0 2 3) (1 2 3))"
-      ]
-     },
-     "execution_count": 28,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(basis delta3 2)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 29,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "((0) (1) (2))"
-      ]
-     },
-     "execution_count": 29,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(basis delta2 0)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "  The set of simplices in any dimension for the simplicial set $\\Delta^\\mathbb{N}$ is infinite:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 30,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "SIMPLE-ERROR: \n",
-      "The object [K6 Simplicial-Set] is locally-effective.\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 30,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(basis delta-infty 1)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Let us test the face function. We see that, though `delta-infty` is locally effective, nevertheless, we may work with its simplices:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 31,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "<AbSm - (0 1 3 4)>"
-      ]
-     },
-     "execution_count": 31,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(face delta-infty 2 4 '(0 1 2 3 4))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 32,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "<AbSm - (0 1 3 4)>"
-      ]
-     },
-     "execution_count": 32,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(face delta-infty 2 4 (absm 0 '(0 1 2 3 4)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 33,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "<AbSm - (0 1 2 3 4)>"
-      ]
-     },
-     "execution_count": 33,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(face delta-infty 2 5 (absm (dgop-ext-int '(1)) '(0 1 2 3 4)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 34,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "<AbSm 2 (0 1 3 4)>"
-      ]
-     },
-     "execution_count": 34,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(face delta-infty 2 5 (absm (dgop-ext-int '(3)) '(0 1 2 3 4)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 35,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(0)"
-      ]
-     },
-     "execution_count": 35,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(bspn delta-infty)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "The two following statement show that `delta-infty` may be considered also as a coalgebra and a chain complex."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 36,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 4}\n",
-       "<1 * <TnPr (0) (0 1 2 3 4)>>\n",
-       "<1 * <TnPr (0 1) (1 2 3 4)>>\n",
-       "<1 * <TnPr (0 1 2) (2 3 4)>>\n",
-       "<1 * <TnPr (0 1 2 3) (3 4)>>\n",
-       "<1 * <TnPr (0 1 2 3 4) (4)>>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 36,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(cprd delta-infty 4 '(0 1 2 3 4))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 37,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 3}\n",
-       "<1 * (0 1 2 3)>\n",
-       "<-1 * (0 1 2 4)>\n",
-       "<1 * (0 1 3 4)>\n",
-       "<-1 * (0 2 3 4)>\n",
-       "<1 * (1 2 3 4)>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 37,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? delta-infty 4 '(0 1 2 3 4))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "The simplicial set `diabolo-ss`,  has also all the properties of a coalgebra and of a chain complex."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 38,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "((0 1) (0 2) (1 2) (2 3) (3 4) (3 5) (4 5))"
-      ]
-     },
-     "execution_count": 38,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(basis diabolo-ss 1)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 39,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "((3 4 5))"
-      ]
-     },
-     "execution_count": 39,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(basis diabolo-ss 2)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 40,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 1}\n",
-       "<1 * (3 4)>\n",
-       "<-1 * (3 5)>\n",
-       "<1 * (4 5)>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 40,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? diabolo-ss 2 (first *))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 41,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 0}\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 41,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? diabolo-ss *)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 42,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 1}\n",
-       "<1 * <TnPr (3) (3 4)>>\n",
-       "<-1 * <TnPr (3) (3 5)>>\n",
-       "<1 * <TnPr (4) (4 5)>>\n",
-       "<1 * <TnPr (3 4) (4)>>\n",
-       "<-1 * <TnPr (3 5) (5)>>\n",
-       "<1 * <TnPr (4 5) (5)>>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 42,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(dgnl diabolo-ss **)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "## The function `build-finite-ss`\n",
-    "\n",
-    "The function `build-finite-ss` is a powerful function simplifying the creation of a finite simplicial set. From the lisp point of view, it accepts only one argument, the structured list of the simplices and their faces. In this list, every non--degenerate simplex must be coded as a symbol given by the user.  The  structure of the list is the following:\n",
-    "\n",
-    "- **0**    (in fact, optional)\n",
-    "- $<$Sequence of the vertices, the first item being the base point$>$,\n",
-    "- **1**\n",
-    "- $<$Sequence of description of simplices in dimension 1$>$,\n",
-    "- **2**\n",
-    "- $<$Sequence of description of simplices in dimension 2$>$,\n",
-    "-   ... ... ... ... ... ...\n",
-    "- **n**\n",
-    "- $<$Sequence of description of simplices in dimension n$>$.\n",
-    "\n",
-    "where $<$Sequence of description of simplices in dimension k$>$ is a sequence of the following items:\n",
-    "\n",
-    "1. A symbol, the symbolic name of the simplex.\n",
-    "2. A list of  faces of this simplex, describing the faces of the simplex. A face can be described in two ways:\n",
-    "  - a symbol, the symbolic name of a **non-degenerate** simplex composing itself the face.\n",
-    "  - or a list of the form  ($i_k\\ i_{k-1}\\ \\ldots \\ i_1 \\ i_0$ `symbol`) meaning that the degeneracy $\\eta_{i_k}\\eta_{i_{k-1}}\\ldots\\eta_{i_1}\\eta_{i_0}$ is to be applied to the non-degenerate simplex of name `symbol`  to produce the actual (possibly degenerate) face. If the simplex face has dimension 0 (a vertex), the name of this vertex is sufficient in the face description because the program computes itself the unique possible degeneracy of the vertex, i.e. $\\eta_{k-2}\\ldots\\eta_0$. \n",
-    "\n",
-    "### Examples\n",
-    "\n",
-    "Let us give some examples to clarify the use of `build-finite-ss`. In the first example, we use  `build-finite-ss` to create a simplicial complex, corresponding to a triangulation of the torus. As the faces are never degenerated, the description of the faces is of simplified form."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 43,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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",
-      "text/plain": [
-       "#<CL-JUPYTER-USER::PNG-BYTES {1002B0C463}>"
-      ]
-     },
-     "execution_count": 43,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(cl-jupyter-user:png-from-file \"torus2.png\")"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "The vertices will be named `v0`, `v1`, ..., `v6`, `v0` being the base point. The edges\n",
-    "will be named `e01`, `e02`, ...,  `e56`, the list of faces of the edge $e_{ij}$ being\n",
-    "$(v_j\\  v_i)$. The triangles will be named `t013`, `t015`, ..., `t456`, the list of faces of\n",
-    "the triangle $t_{ijk}$ being $(e_{jk}\\  e_{ik}\\  e_{ij})$. With this convention of describing the simplices, the call to `build-finite-ss` is in simplified form:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 44,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "The object is a STANDARD-OBJECT of type SIMPLICIAL-SET.\n",
-      "0. CMPR: #<FUNCTION S-CMPR>\n",
-      "1. BASIS: #<CLOSURE (FLET RSLT :IN FINITE-SS-BASIS) {1002C32A0B}>\n",
-      "2. BSGN: V0\n",
-      "3. DFFR: [K27 Morphism (degree -1): K26 -> K26]\n",
-      "4. GRMD: [K26 Simplicial-Set]\n",
-      "5. EFHM: \"unbound\"\n",
-      "6. IDNM: 26\n",
-      "7. ORGN: (BUILD-FINITE-SS (V0 V1 V2 V3 V4 V5 V6 1 E01 (V1 V0) ...))\n",
-      "8. CPRD: [K30 Morphism (degree 0): K26 -> K28]\n",
-      "9. FACE: #<CLOSURE (FLET RSLT :IN FINITE-SS-FACE) {1002C32A2B}>\n",
-      "> \n",
-      "Checking the 0-simplices...\n",
-      "Checking the 1-simplices...\n",
-      "Checking the 2-simplices..."
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "[K26 Simplicial-Set]"
-      ]
-     },
-     "execution_count": 44,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def torus2\n",
-    "    (build-finite-ss \n",
-    "       '(v0  v1  v2  v3  v4  v5  v6 \n",
-    "\n",
-    "         1 e01  (v1 v0)   e02  (v2 v0)   e03  (v3 v0)\n",
-    "           e04  (v4 v0)   e05  (v5 v0)   e06  (v6 v0)\n",
-    "           e12  (v2 v1)   e13  (v3 v1)   e14  (v4 v1)\n",
-    "           e15  (v5 v1)   e16  (v6 v1)   e23  (v3 v2)\n",
-    "           e24  (v4 v2)   e25  (v5 v2)   e26  (v6 v2)\n",
-    "           e34  (v4 v3)   e35  (v5 v3)   e36  (v6 v3)\n",
-    "           e45  (v5 v4)   e46  (v6 v4)   e56  (v6 v5)\n",
-    "\n",
-    "         2 t013  (e13 e03 e01)  t015  (e15 e05 e01)  t024  (e24 e04 e02)\n",
-    "           t026  (e26 e06 e02)  t036  (e36 e06 e03)  t045  (e45 e05 e04)\n",
-    "           t125  (e25 e15 e12)  t126  (e26 e16 e12)  t134  (e34 e14 e13)\n",
-    "           t146  (e46 e16 e14)  t234  (e34 e24 e23)  t235  (e35 e25 e23)\n",
-    "           t356  (e56 e36 e35)  t456  (e56 e46 e45)  )))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "After verification of the coherence of the description of the faces, the function `build-finite-ss` calls adequately the function `build-smst` to create an instance of the class `SIMPLICIAL SET` subclass of the class `CHAIN COMPLEX`. So that, it is easy for the user  to obtain the homology groups of the torus, for instance in dimension 1:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 45,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "Computing boundary-matrix in dimension 1.\n",
-      "Rank of the source-module : 21.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 18m 30s.\n",
-      "Computing the boundary of the generator 1/21 (dimension 1) :\n",
-      "E01 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 18m 30s.\n",
-      "Computing the boundary of the generator 2/21 (dimension 1) :\n",
-      "E02 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 18m 30s.\n",
-      "Computing the boundary of the generator 3/21 (dimension 1) :\n",
-      "E03 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 18m 30s.\n",
-      "Computing the boundary of the generator 4/21 (dimension 1) :\n",
-      "E04 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 18m 30s.\n",
-      "Computing the boundary of the generator 5/21 (dimension 1) :\n",
-      "E05 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 18m 30s.\n",
-      "Computing the boundary of the generator 6/21 (dimension 1) :\n",
-      "E06 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 18m 30s.\n",
-      "Computing the boundary of the generator 7/21 (dimension 1) :\n",
-      "E12 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 18m 30s.\n",
-      "Computing the boundary of the generator 8/21 (dimension 1) :\n",
-      "E13 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 18m 30s.\n",
-      "Computing the boundary of the generator 9/21 (dimension 1) :\n",
-      "E14 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 18m 30s.\n",
-      "Computing the boundary of the generator 10/21 (dimension 1) :\n",
-      "E15 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 18m 30s.\n",
-      "Computing the boundary of the generator 11/21 (dimension 1) :\n",
-      "E16 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 18m 30s.\n",
-      "Computing the boundary of the generator 12/21 (dimension 1) :\n",
-      "E23 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 18m 30s.\n",
-      "Computing the boundary of the generator 13/21 (dimension 1) :\n",
-      "E24 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 18m 30s.\n",
-      "Computing the boundary of the generator 14/21 (dimension 1) :\n",
-      "E25 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 18m 30s.\n",
-      "Computing the boundary of the generator 15/21 (dimension 1) :\n",
-      "E26 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 18m 30s.\n",
-      "Computing the boundary of the generator 16/21 (dimension 1) :\n",
-      "E34 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 18m 30s.\n",
-      "Computing the boundary of the generator 17/21 (dimension 1) :\n",
-      "E35 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 18m 30s.\n",
-      "Computing the boundary of the generator 18/21 (dimension 1) :\n",
-      "E36 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 18m 30s.\n",
-      "Computing the boundary of the generator 19/21 (dimension 1) :\n",
-      "E45 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 18m 30s.\n",
-      "Computing the boundary of the generator 20/21 (dimension 1) :\n",
-      "E46 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 18m 30s.\n",
-      "Computing the boundary of the generator 21/21 (dimension 1) :\n",
-      "E56 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 2.\n",
-      "Rank of the source-module : 14.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 18m 30s.\n",
-      "Computing the boundary of the generator 1/14 (dimension 2) :\n",
-      "T013 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 18m 30s.\n",
-      "Computing the boundary of the generator 2/14 (dimension 2) :\n",
-      "T015 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 18m 30s.\n",
-      "Computing the boundary of the generator 3/14 (dimension 2) :\n",
-      "T024 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 18m 30s.\n",
-      "Computing the boundary of the generator 4/14 (dimension 2) :\n",
-      "T026 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 18m 30s.\n",
-      "Computing the boundary of the generator 5/14 (dimension 2) :\n",
-      "T036 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 18m 30s.\n",
-      "Computing the boundary of the generator 6/14 (dimension 2) :\n",
-      "T045 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 18m 30s.\n",
-      "Computing the boundary of the generator 7/14 (dimension 2) :\n",
-      "T125 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 18m 30s.\n",
-      "Computing the boundary of the generator 8/14 (dimension 2) :\n",
-      "T126 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 18m 30s.\n",
-      "Computing the boundary of the generator 9/14 (dimension 2) :\n",
-      "T134 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 18m 30s.\n",
-      "Computing the boundary of the generator 10/14 (dimension 2) :\n",
-      "T146 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 18m 30s.\n",
-      "Computing the boundary of the generator 11/14 (dimension 2) :\n",
-      "T234 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 18m 30s.\n",
-      "Computing the boundary of the generator 12/14 (dimension 2) :\n",
-      "T235 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 18m 30s.\n",
-      "Computing the boundary of the generator 13/14 (dimension 2) :\n",
-      "T356 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 18m 30s.\n",
-      "Computing the boundary of the generator 14/14 (dimension 2) :\n",
-      "T456 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 1 :\n",
-      "\n",
-      "\n",
-      "Component Z\n",
-      "\n",
-      "Component Z\n",
-      "\n",
-      "\n",
-      "---done---"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 45,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(chcm-homology  torus2 1)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "The function `build-finite-ss` calls internally some verification functions mentioned above to verify the coherence of the description of the simplicial set and gives an error message if the description of the simplicial set is incorrect. For instance:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 46,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "The object is a STANDARD-OBJECT of type SIMPLICIAL-SET.\n",
-      "0. CMPR: #<FUNCTION S-CMPR>\n",
-      "1. BASIS: #<CLOSURE (FLET RSLT :IN FINITE-SS-BASIS) {1002D2FA0B}>\n",
-      "2. BSGN: S0\n",
-      "3. DFFR: [K32 Morphism (degree -1): K31 -> K31]\n",
-      "4. GRMD: [K31 Simplicial-Set]\n",
-      "5. EFHM: \"unbound\"\n",
-      "6. IDNM: 31\n",
-      "7. ORGN: (BUILD-FINITE-SS (S0 S1 S2 S3 1 |0-1| (S1 S0) |1-2| (S2 S1) |2-3| ...))\n",
-      "8. CPRD: [K35 Morphism (degree 0): K31 -> K33]\n",
-      "9. FACE: #<CLOSURE (FLET RSLT :IN FINITE-SS-FACE) {1002D2FA2B}>\n",
-      "> \n",
-      "Checking the 0-simplices...\n",
-      "Checking the 1-simplices...\n",
-      "Checking the 2-simplices..."
-     ]
-    },
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "SIMPLE-ERROR: \n",
-      "Noncoherent boundary operators detected by CHECK-FACES :\n",
-      "Simplex => 0-1-2\n",
-      "del_0 o del_0 => <AbSm - S3>\n",
-      "del_0 o del_1 => <AbSm - S2>\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 46,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def mm (build-finite-ss \n",
-    "   '(s0 s1 s2 s3 \n",
-    "     1 0-1 (s1 s0)  1-2 (s2 s1)  2-3 (s3 s2)\n",
-    "     2 0-1-2 (2-3 1-2 0-1))\n",
-    "  ))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "In the following examples, we show the power of `build-finite-ss` for the description of classical surfaces as simplicial sets, and in each case we  verify the well known homology groups of those surfaces. The examples of the torus or the dunce-hat must be compared, as to the simplicity of the definition, to the respective ones in the previous page and in the Homology chapter."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 47,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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",
-      "text/plain": [
-       "#<CL-JUPYTER-USER::PNG-BYTES {1002DB7103}>"
-      ]
-     },
-     "execution_count": 47,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(cl-jupyter-user:png-from-file \"cylinss.png\")"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 48,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "The object is a STANDARD-OBJECT of type SIMPLICIAL-SET.\n",
-      "0. CMPR: #<FUNCTION S-CMPR>\n",
-      "1. BASIS: #<CLOSURE (FLET RSLT :IN FINITE-SS-BASIS) {1002EDAEDB}>\n",
-      "2. BSGN: V0\n",
-      "3. DFFR: [K37 Morphism (degree -1): K36 -> K36]\n",
-      "4. GRMD: [K36 Simplicial-Set]\n",
-      "5. EFHM: \"unbound\"\n",
-      "6. IDNM: 36\n",
-      "7. ORGN: (BUILD-FINITE-SS (V0 V1 1 E0 (V1 V0) E1 (V1 V1) E2 (V0 V0) E3 ...))\n",
-      "8. CPRD: [K40 Morphism (degree 0): K36 -> K38]\n",
-      "9. FACE: #<CLOSURE (FLET RSLT :IN FINITE-SS-FACE) {1002EDAEFB}>\n",
-      "> \n",
-      "Checking the 0-simplices...\n",
-      "Checking the 1-simplices...\n",
-      "Checking the 2-simplices..."
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "[K36 Simplicial-Set]"
-      ]
-     },
-     "execution_count": 48,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def cylinss (build-finite-ss \n",
-    "    '(v0 v1 \n",
-    "      1 e0 (v1 v0) e1 (v1 v1) e2 (v0 v0) e3 (v1 v0)\n",
-    "      2 t0 (e1 e3 e0) t1 (e0 e3 e2)) ))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 49,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "Computing boundary-matrix in dimension 0.\n",
-      "Rank of the source-module : 2.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 18m 30s.\n",
-      "Computing the boundary of the generator 1/2 (dimension 0) :\n",
-      "V0 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 18m 30s.\n",
-      "Computing the boundary of the generator 2/2 (dimension 0) :\n",
-      "V1 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 1.\n",
-      "Rank of the source-module : 4.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 18m 30s.\n",
-      "Computing the boundary of the generator 1/4 (dimension 1) :\n",
-      "E0 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 18m 30s.\n",
-      "Computing the boundary of the generator 2/4 (dimension 1) :\n",
-      "E1 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 18m 30s.\n",
-      "Computing the boundary of the generator 3/4 (dimension 1) :\n",
-      "E2 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 18m 30s.\n",
-      "Computing the boundary of the generator 4/4 (dimension 1) :\n",
-      "E3 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 0 :\n",
-      "\n",
-      "\n",
-      "Component Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "Computing boundary-matrix in dimension 1.\n",
-      "Rank of the source-module : 4.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 18m 30s.\n",
-      "Computing the boundary of the generator 1/4 (dimension 1) :\n",
-      "E0 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 18m 30s.\n",
-      "Computing the boundary of the generator 2/4 (dimension 1) :\n",
-      "E1 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 18m 30s.\n",
-      "Computing the boundary of the generator 3/4 (dimension 1) :\n",
-      "E2 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 18m 30s.\n",
-      "Computing the boundary of the generator 4/4 (dimension 1) :\n",
-      "E3 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 2.\n",
-      "Rank of the source-module : 2.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 18m 30s.\n",
-      "Computing the boundary of the generator 1/2 (dimension 2) :\n",
-      "T0 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 18m 30s.\n",
-      "Computing the boundary of the generator 2/2 (dimension 2) :\n",
-      "T1 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 1 :\n",
-      "\n",
-      "\n",
-      "Component Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "Computing boundary-matrix in dimension 2.\n",
-      "Rank of the source-module : 2.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 18m 30s.\n",
-      "Computing the boundary of the generator 1/2 (dimension 2) :\n",
-      "T0 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 18m 30s.\n",
-      "Computing the boundary of the generator 2/2 (dimension 2) :\n",
-      "T1 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 3.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 2 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 49,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(dotimes (i 3) (chcm-homology cylinss i))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 50,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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",
-      "text/plain": [
-       "#<CL-JUPYTER-USER::PNG-BYTES {1002FDC333}>"
-      ]
-     },
-     "execution_count": 50,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(cl-jupyter-user:png-from-file \"moebiuss.png\")"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 51,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "The object is a STANDARD-OBJECT of type SIMPLICIAL-SET.\n",
-      "0. CMPR: #<FUNCTION S-CMPR>\n",
-      "1. BASIS: #<CLOSURE (FLET RSLT :IN FINITE-SS-BASIS) {10031030EB}>\n",
-      "2. BSGN: V0\n",
-      "3. DFFR: [K42 Morphism (degree -1): K41 -> K41]\n",
-      "4. GRMD: [K41 Simplicial-Set]\n",
-      "5. EFHM: \"unbound\"\n",
-      "6. IDNM: 41\n",
-      "7. ORGN: (BUILD-FINITE-SS (V0 V1 1 E0 (V1 V0) E1 (V0 V1) E2 (V1 V0) E3 ...))\n",
-      "8. CPRD: [K45 Morphism (degree 0): K41 -> K43]\n",
-      "9. FACE: #<CLOSURE (FLET RSLT :IN FINITE-SS-FACE) {100310310B}>\n",
-      "> \n",
-      "Checking the 0-simplices...\n",
-      "Checking the 1-simplices...\n",
-      "Checking the 2-simplices..."
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "[K41 Simplicial-Set]"
-      ]
-     },
-     "execution_count": 51,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def moebiuss (build-finite-ss \n",
-    "  '(v0 v1 \n",
-    "    1 e0 (v1 v0) e1 (v0 v1) e2 (v1 v0) e3 (v0 v0)\n",
-    "    2 t0 (e1 e3 e0) t1 (e0 e2 e3)) ))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 52,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "Computing boundary-matrix in dimension 0.\n",
-      "Rank of the source-module : 2.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 18m 30s.\n",
-      "Computing the boundary of the generator 1/2 (dimension 0) :\n",
-      "V0 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 18m 30s.\n",
-      "Computing the boundary of the generator 2/2 (dimension 0) :\n",
-      "V1 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 1.\n",
-      "Rank of the source-module : 4.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 18m 30s.\n",
-      "Computing the boundary of the generator 1/4 (dimension 1) :\n",
-      "E0 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 18m 30s.\n",
-      "Computing the boundary of the generator 2/4 (dimension 1) :\n",
-      "E1 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 18m 30s.\n",
-      "Computing the boundary of the generator 3/4 (dimension 1) :\n",
-      "E2 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 18m 30s.\n",
-      "Computing the boundary of the generator 4/4 (dimension 1) :\n",
-      "E3 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 0 :\n",
-      "\n",
-      "\n",
-      "Component Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "Computing boundary-matrix in dimension 1.\n",
-      "Rank of the source-module : 4.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 18m 30s.\n",
-      "Computing the boundary of the generator 1/4 (dimension 1) :\n",
-      "E0 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 18m 30s.\n",
-      "Computing the boundary of the generator 2/4 (dimension 1) :\n",
-      "E1 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 18m 30s.\n",
-      "Computing the boundary of the generator 3/4 (dimension 1) :\n",
-      "E2 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 18m 30s.\n",
-      "Computing the boundary of the generator 4/4 (dimension 1) :\n",
-      "E3 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 2.\n",
-      "Rank of the source-module : 2.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 18m 30s.\n",
-      "Computing the boundary of the generator 1/2 (dimension 2) :\n",
-      "T0 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 18m 30s.\n",
-      "Computing the boundary of the generator 2/2 (dimension 2) :\n",
-      "T1 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 1 :\n",
-      "\n",
-      "\n",
-      "Component Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "Computing boundary-matrix in dimension 2.\n",
-      "Rank of the source-module : 2.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 18m 30s.\n",
-      "Computing the boundary of the generator 1/2 (dimension 2) :\n",
-      "T0 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 18m 30s.\n",
-      "Computing the boundary of the generator 2/2 (dimension 2) :\n",
-      "T1 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 3.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 2 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 52,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(dotimes (i 3) (chcm-homology moebiuss i))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 53,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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",
-      "text/plain": [
-       "#<CL-JUPYTER-USER::PNG-BYTES {10031FBBF3}>"
-      ]
-     },
-     "execution_count": 53,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(cl-jupyter-user:png-from-file \"toruss.png\")"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 54,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "The object is a STANDARD-OBJECT of type SIMPLICIAL-SET.\n",
-      "0. CMPR: #<FUNCTION S-CMPR>\n",
-      "1. BASIS: #<CLOSURE (FLET RSLT :IN FINITE-SS-BASIS) {100333210B}>\n",
-      "2. BSGN: V0\n",
-      "3. DFFR: [K47 Morphism (degree -1): K46 -> K46]\n",
-      "4. GRMD: [K46 Simplicial-Set]\n",
-      "5. EFHM: \"unbound\"\n",
-      "6. IDNM: 46\n",
-      "7. ORGN: (BUILD-FINITE-SS (V0 1 E0 (V0 V0) E1 (V0 V0) E2 (V0 V0) 2 T0 ...))\n",
-      "8. CPRD: [K50 Morphism (degree 0): K46 -> K48]\n",
-      "9. FACE: #<CLOSURE (FLET RSLT :IN FINITE-SS-FACE) {100333212B}>\n",
-      "> \n",
-      "Checking the 0-simplices...\n",
-      "Checking the 1-simplices...\n",
-      "Checking the 2-simplices..."
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "[K46 Simplicial-Set]"
-      ]
-     },
-     "execution_count": 54,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def toruss (build-finite-ss \n",
-    "  '(v0\n",
-    "    1 e0 (v0 v0) e1 (v0 v0) e2 (v0 v0)\n",
-    "    2 t0 (e1 e2 e0) t1 (e0 e2 e1)) ))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 55,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "Computing boundary-matrix in dimension 0.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 18m 30s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 0) :\n",
-      "V0 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 1.\n",
-      "Rank of the source-module : 3.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 18m 30s.\n",
-      "Computing the boundary of the generator 1/3 (dimension 1) :\n",
-      "E0 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 18m 30s.\n",
-      "Computing the boundary of the generator 2/3 (dimension 1) :\n",
-      "E1 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 18m 30s.\n",
-      "Computing the boundary of the generator 3/3 (dimension 1) :\n",
-      "E2 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 0 :\n",
-      "\n",
-      "\n",
-      "Component Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "Computing boundary-matrix in dimension 1.\n",
-      "Rank of the source-module : 3.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 18m 30s.\n",
-      "Computing the boundary of the generator 1/3 (dimension 1) :\n",
-      "E0 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 18m 30s.\n",
-      "Computing the boundary of the generator 2/3 (dimension 1) :\n",
-      "E1 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 18m 30s.\n",
-      "Computing the boundary of the generator 3/3 (dimension 1) :\n",
-      "E2 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 2.\n",
-      "Rank of the source-module : 2.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 18m 30s.\n",
-      "Computing the boundary of the generator 1/2 (dimension 2) :\n",
-      "T0 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 18m 30s.\n",
-      "Computing the boundary of the generator 2/2 (dimension 2) :\n",
-      "T1 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 1 :\n",
-      "\n",
-      "\n",
-      "Component Z\n",
-      "\n",
-      "Component Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "Computing boundary-matrix in dimension 2.\n",
-      "Rank of the source-module : 2.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 18m 30s.\n",
-      "Computing the boundary of the generator 1/2 (dimension 2) :\n",
-      "T0 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 18m 30s.\n",
-      "Computing the boundary of the generator 2/2 (dimension 2) :\n",
-      "T1 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 3.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 2 :\n",
-      "\n",
-      "\n",
-      "Component Z\n",
-      "\n",
-      "\n",
-      "---done---"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 55,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(dotimes (i 3) (chcm-homology toruss i))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 56,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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",
-      "text/plain": [
-       "#<CL-JUPYTER-USER::PNG-BYTES {1003424023}>"
-      ]
-     },
-     "execution_count": 56,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(cl-jupyter-user:png-from-file \"bottless.png\")"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 57,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "The object is a STANDARD-OBJECT of type SIMPLICIAL-SET.\n",
-      "0. CMPR: #<FUNCTION S-CMPR>\n",
-      "1. BASIS: #<CLOSURE (FLET RSLT :IN FINITE-SS-BASIS) {100352A60B}>\n",
-      "2. BSGN: V0\n",
-      "3. DFFR: [K52 Morphism (degree -1): K51 -> K51]\n",
-      "4. GRMD: [K51 Simplicial-Set]\n",
-      "5. EFHM: \"unbound\"\n",
-      "6. IDNM: 51\n",
-      "7. ORGN: (BUILD-FINITE-SS (V0 1 E0 (V0 V0) E1 (V0 V0) E2 (V0 V0) 2 T0 ...))\n",
-      "8. CPRD: [K55 Morphism (degree 0): K51 -> K53]\n",
-      "9. FACE: #<CLOSURE (FLET RSLT :IN FINITE-SS-FACE) {100352A62B}>\n",
-      "> \n",
-      "Checking the 0-simplices...\n",
-      "Checking the 1-simplices...\n",
-      "Checking the 2-simplices..."
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "[K51 Simplicial-Set]"
-      ]
-     },
-     "execution_count": 57,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def bottless (build-finite-ss \n",
-    "  '(v0\n",
-    "    1 e0 (v0 v0) e1 (v0 v0) e2 (v0 v0)\n",
-    "    2 t0 (e1 e2 e0) t1 (e0 e1 e2)) ))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 58,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "Computing boundary-matrix in dimension 0.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 18m 30s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 0) :\n",
-      "V0 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 1.\n",
-      "Rank of the source-module : 3.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 18m 30s.\n",
-      "Computing the boundary of the generator 1/3 (dimension 1) :\n",
-      "E0 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 18m 30s.\n",
-      "Computing the boundary of the generator 2/3 (dimension 1) :\n",
-      "E1 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 18m 30s.\n",
-      "Computing the boundary of the generator 3/3 (dimension 1) :\n",
-      "E2 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 0 :\n",
-      "\n",
-      "\n",
-      "Component Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "Computing boundary-matrix in dimension 1.\n",
-      "Rank of the source-module : 3.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 18m 30s.\n",
-      "Computing the boundary of the generator 1/3 (dimension 1) :\n",
-      "E0 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 18m 30s.\n",
-      "Computing the boundary of the generator 2/3 (dimension 1) :\n",
-      "E1 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 18m 30s.\n",
-      "Computing the boundary of the generator 3/3 (dimension 1) :\n",
-      "E2 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 2.\n",
-      "Rank of the source-module : 2.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 18m 30s.\n",
-      "Computing the boundary of the generator 1/2 (dimension 2) :\n",
-      "T0 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 18m 30s.\n",
-      "Computing the boundary of the generator 2/2 (dimension 2) :\n",
-      "T1 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 1 :\n",
-      "\n",
-      "\n",
-      "Component Z/2Z\n",
-      "\n",
-      "Component Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "Computing boundary-matrix in dimension 2.\n",
-      "Rank of the source-module : 2.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 18m 30s.\n",
-      "Computing the boundary of the generator 1/2 (dimension 2) :\n",
-      "T0 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 18m 30s.\n",
-      "Computing the boundary of the generator 2/2 (dimension 2) :\n",
-      "T1 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 3.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 2 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 58,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(dotimes (i 3) (chcm-homology bottless i))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 59,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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1A+8kocI1Mh3FxezX+kNLCcCbJFS4OqajuKTZbBYOmlLrB44nocLVMR3FhRVFEWr92+029JYAvE5ChetiOopBqPUD7yKhwhUxHcVQwrdc+FitH3iThArXwnQUw8rzPHSVqPUDb5JQ4SqYjiIGZVmGt0ZVVTVNM/RygHhJqHAVTEcRg26uP0mS5XIZ3jIBPCehwvSZjiIeXa2/bVt7+AMvkVBh4kxHEZuyLLMsS9T6gZdJqDBlpqOIkFo/8CYJFSbLdBTRyrKsq/Wb6week1BhskxHEbPb29tQ699sNnVdD70cIC4SKkyT6Sjip9YPvERChQkyHcUodLX+3W7noClgn4QKU2M6ihHpOqTrulbrBzoSKkyK6ShGZ71eh8v8av1AR0KFSTEdxeikadrV+rvL/8CVk1BhOkxHMVJlWYbr/U3TOGgKSCRUmAzTUYxaV+uvqqpt26GXAwxMQoUpMB3F2KVpGi78m+sHEgkVJsB0FNOwWCyKokjU+gEJFSbAdBSTsV/rD9/VwHWSUGHcTEcxJbPZLBw0pdYPV05ChREzHcX0FEURav3b7TZ8ewNXSEKFsTIdxVSp9QMSKoyS6SgmLNQEwsdq/XCdJFQYJdNRTFue5+EbW60frpOECuNjOoprUJZl6F2pqqppmqGXA1yUhAojYzqKK9HN9SdJslwuQ08LcCUkVBgT01Fcla7W37atPfzhqkioMBqmo7hCZVlmWZao9cOVkVBhNExHcYXU+uE6SagwDqajuFpZlnW1fnP9cCUkVBgB01Fcudvb21Dr32w2dV0PvRzg7CRUiJ3pKEiSRK0froqEClEzHQVBV+vf7XYOmoLJk1AhaqajoNO9SavrWq0fpk1ChXiZjoKe9Xod+rDV+mHaJFSIlOkoeC5N067W3/VnA9MjoUKMTEfBS8qyDLX+pmkcNAVTJaFCdExHweu6Wn9VVW3bDr0c4PQkVIiO6Sh4XZqmoTPbXD9MlYQKcTEdBcdYLBZFUSRq/TBREipExHQUHG+/1h/KDsBkSKgQC9NR8C6z2SwcNKXWD9MjoUIUTEfBBxRFEWr92+021B+AaZBQIQqmo+Bj1PphkiRUGJ7pKPiw0LQdPlbrh8mQUGFgpqPgk/I8D5UHtX6YDAkVhmQ6Ck6iLMvw41NVVdM0Qy8H+CwJFQZjOgpOpZvrT5JkuVyGHytgvCRUGIzpKDihrtbftq09/GHsJFQYhukoOLmyLLMsS9T6YfwkVBiA6Sg4B7V+mAwJFS7NdBScT5ZlXa3fXD+Ml4QKF2U6Cs7t9vY21Po3m01d10MvB/gICRUuynQUXMC7av06ViFCEipcjukouIyu1r/b7d48aErHKkRIQoULMR0Fl9R10dR1/Uqtv67rtm3DW0cgHhIqXILpKLi89Xod3gq+cpU0dN1IqBAbCRXOznQUDCJN067W371F7AmXV9u21Y0KUZFQ4exMR8FQyrIM7wmbpnl+0NR2u23bNnxs6h+iIqHCeZmOGpftdjvfo/g7AV2tv6qqLo8G+6l0s9n0/hYYkIQKZ2Q6anR2u12zR2SZgDRNw5vD53P9vcq+NyQQDwkVzsV0FERisVgURZF8v9bftm1ov+ko9EM8JFQ4C9NREJX9Wn8Ips/zqG2nIB4/GHoB8HFh/DbUYWezWZZl8QRB01EQldlstl6vw/vG5XL58PBw8IppXdeLxeLyyzso5pc4OLunp6enp6f7+/vuY4jfw8PDwVfq0HA29OqeuomoLMu+ffs29HI4ynq9zvM8nOe+/x2V53me5w8PD0MvkBMItf4kSX7v937vpV+Lj4+PQy8z9pc4OIdeFv3u6ekpSZKmaebzefgYIrfZbF4/xjDP8wHHksJPU5Iks9ns4eFB++lYrFar57sRde7v712+il8o06dpGn7uwnXH/RvsdrsvX768fsZpWZbDbrsR+UscnEkvi6ryMzJ1Xb95ynbTNDc3N+Hd2IWZjoIBpWn6fGA/6N5g/Kf/9J/+1//6X6/cyWazKctyqPwX+UscXIxJKUYmbN7UKcvy8fHx27dv6/V6Pw42TXP5iQfTUaO2WCzu7+97F8/CJ+/v73uX4ojWer0+2Eja7SD2ejxNkmS32w041B/zSxxc1MHaP8RpvV7vf/f2+rEeHx/3L3ukaXrh5XW/FxeLxYW/NKfSuy5VluXQK+IjPjntlGXZIMuO/CUOzqqXRV1DZUz2L2x0J27vf2b/19LzzQ7PytlREI/1et1Le++y3W4v+erRifklDi5MQmVM9g+AOVh17X2yd2DM+Tg7CmKzWCw+E1IHqaFH+xIHl2dSitHonT8Zzk/v3aY3ovv6xO6pmI6COIUrjm8OHh202Wxub28v+W4z2pc4GISEymj0Xr7btn3zzPQLlMBMR0HMPhlSL3ncRpwvcTAUVX74FGdHQeQ+XO43LA8Dcg2VsVosFt3xMC85d4XOdBSMwseupLZtW9f1m68zZxLDSxwMSEJlNHojArPZbNiSuukoGJGPhdRLJtTYXuJgWBIqozGbzdI07RqzDnZo7Xa7/cas7vDDkzMdBaOzWCzSNO0ax49R13Xbtpf5AY/qJQ4Gpw+VMdm/ohB+c/RuUFXVfM+ZxghMR8FI5Xl+f3//rorHJbtRI3mJgxhIqIxJbxTp5uam2w5wt9utVquqqrq/zbLsTOU501HXQwKYnizL3hVSL5lQI3mJgygcPGkKovU8Eb7UrfXw8HCOBXQTUVmWffv27RxfggE9Pj72vpGyLAsX3oZeGqf08PBwfEhdr9cXW9jgL3EwFKeeMm5lWfbmCXa7Xe9gldlstl6vD57I8kmmoybveWPfdrt1cs/0vOtK6v5hpOc27EscxENCZWRms9nDw8MrtfVwuWv/9OpTadv2d37nd8LHpqMmbL1ee+9xDY4PqU3TXKzfY8CXOIjKd09PT0mSNE0zn8/DxzAKYavC7XYbJpbCGGxRFOe7rvD169fwW+qP/uiP/vRP//RMX4UYtG272Wy6UJJlWRgDH3ZVnEM4XPTN6f4Pb/v/YZd/iYNh9bKohApH6WYUiqK4u7sbejnAyWy32+Vy+fpV0tls9vj46OI6nE8vi6ryw9vqug7xNE3TC19HAc4tlPtfvza52+0u2Y0KSKjwhrZtf/d3fzd8bDoKJmk2m70ZUvd3egLOTUKFN/zGb/zGP/7jPyZJcnt7qwMMpurNkNq2rV0d4GIkVHjNr//6r//d3/1dkiT/+T//Z5vzw7S9GVIV+uFiJFQ4bLfbffny5ac//WmSJP/+3//7//k//+fQKwLO7vWQutls3pz6B05CQoUDdrvdb/7mb3aHYv+3//bftJ/ClXg9pOpGhcuQUKFvu91++fLlb/7mb8Iff/VXf/X3f//3h10ScEkhpB48a1ShHy5DQoXvCfux7Rfy/uzP/mzA9QCDCCH1+dFNYSP9QZYEV0VChX+z2Wx68fRXfuVXiqIYcEnAgNbr9fOQutlsBlkMXBUJFX6mqqrlctn75B/+4R8OshggEs9DatM0XZM6cCYSKiRJkiyXy9Vq1ftkmqbPL58A1+Z5SP3v//2/D7UYuBISKtdut9stl8uDZTv1fSDohdT/8T/+x4CLgWsgoXLVdrvdfD4/GE9ns5kt+oHOfkj9p3/6p+dNQcAJSahcr7Zt5/P5drs9+LeLxcIeqMC+9Xr9W7/1W+Hjv/iLv7B7P5yPhMqV2m63X79+fSmeJkniAirw3F/91V/9x//4H5Mk+Zd/+Zebm5uhlwOTJaFyjZ5vetrjAirwkv/9v//3r/3aryVJ0jSNvVHhTCRUrs7zTU+fcwEVeMVf//Vf//zP/3ySJIvFQq0fzkFC5bqsVqs35xsWi0WappdZDzBGaZr+8R//cZIkf//3f6/WD+cgoXJFlstlVVVv3swmU8CbyrLM8zxJkqZpjnlhAd5FQuUq7Ha7m5ubY84qzPM8/NYBeN16vQ4N63/+53/+05/+dOjlwKRIqExf2PT0yIEGHajAkdI0vb29/dGPfvQP//APf/AHfzD0cmBSJFQmbrvdvrLpaU+WZS6gAsdbLBZfv35NkqRpmmOqNMCRJFSm7F3xNEmS3tHbAG/qav2r1cpcP5yKhMpk1XX95q5S+9I0lVCB90rTNHQH7XY7R6HCqUioTNNms7m5uXnX9QwdqMDHdHP9dV3bwx9OQkJlgo7Z9LRnNpvZZAr4sNvb2/CBWj+chITK1By56WmPY06Bz8iyLNRh2ra1PSp8noTKdIRdpT4wTjubzZT4gU+6vb3NsixJkqqqmqYZejkwbhIqExHi6cd+K7iACpxEV+s3MgWfJKEyBdvt9uvXr8fvKtVjhB84iTzPu1r/arUaejkwYhIqoxc2PW3b9mP/+2KxSNP0tEsCrlZZluElpaqqD79tBiRUxm2z2bxr09PndKACJzSbzdbrdfhYrR8+TEJlxDabzXK5/Ew8zfPcBVTgtPI8D7vXbbdbc/3wMRIqY/WBTU+fcwEVOIfuKNSqqj7cgwTX7AdDLwA+YrVaNU0TDnHppGm6P5L/l3/5l//v//2/V+4kz/PePQCcRKj1h5Ptlsvl/f390CuCkZFQGaVuS5eXrFarEE9/8Rd/8W//9m8P3sYIP3A+RVHked40TdM0m83GCw68iyo/E1TXdej9StP0t3/7tw/eJk1Tx5wCZ9XV+h2FCu8loTI1bdt2/al3d3f/5b/8l4M304EKnFuapuGlJtT6h14OjImEytSExq/kX08gPNhpmqapihtwAWVZhlehuq7ruh56OTAaEiqTslqtwhbZRVF0V0mfh1T1feBiur55tX44noTKdOy3n3Y7ZidJkmXZ/s1ms5kSP3AxWZZ1R6HaHhWOJKEyEb320/1tp3rXUBeLxf7fApxbaDpKkqSqqqZphl4OjICEykT02k/3/6qXUF1ABS6vq/UbmYJjSKhMwcH2031dSHUBFRhEnuddrX+1Wg29HIidhMrovdR+uq+7quoCKjCUsizTNE2SpKqq8KYaeImEyri90n66L1xDXSwW4dcDwOWFo1DDx2r98DoJlXF7pf10X5dQL7cygGfyPA+73W23W3P98AoJlRF7s/103+sRFuAyuqNQq6pq23bo5UCkJFTG6pj20306UIEYdLV+R6HCKyRURunI9lOACBVFEVqPmqbZbDZDLwdiJKEySke2nwLEqav1OwoVDpJQGZ93tZ8CRChN0/DypdYPB0mojMx7208B4lSWZaj113Vd1/XQy4G4SKiMifZTYEq6o1DV+qFHQmVMtJ8CU5JlWXcUqu1RYZ+EymhoPwWmp3u/XVVV0zRDLwdiIaEyDtpPganqav1GpqAjoTIC2k+BCcvzvKv1r1aroZcDUZBQGQHtp8C0lWWZpmmSJFVVhXYmuHISKrHTfgpMXncUaqLWD0mSSKhETvspcCXyPC+KIkmS7XZrrh8kVOKl/RS4Kt1RqFVVtW079HJgSBIq8dJ+ClyVrtbvKFSQUImU9lPgChVFEY5CbZpms9kMvRwYjIRKjLSfAlerq/U7CpVrJqESHe2nwDVL0zQUjtT6uWYSKtHRfgpcubIsQ62/ruu6rodeDgxAQiUu2k8Bkr2jUNX6uU4SKhHRfgoQZFnWHYVqe1SukIRKLLSfAuzrOp2qqmqaZujlwEVJqMRC+ylAT1frNzLFtZFQiYL2U4Dn8jzvav2r1Wro5cDlSKgMT/spwEvKskzTNEmSqqrCO3m4BhIqA9N+CvCK7ijURK2fayKhMjDtpwCvy/O8KIokSbbbrbl+roSEypC0nwIcozsKtaqqtm2HXg6cnYTKYLSfAhypq/U7CpUrIaEyDO2nAO9SFEU4CrVpms1mM/Ry4LwkVIah/RTgvbpav6NQmTwJlQFoPwX4gDRNw2umWj+TJ6FyadpPAT6sLMtQ66/ruq7roZcD5yKhclHaTwE+qTsKVa2fCZNQuSjtpwCflGVZdxSq7VGZKgmVy9F+CnAS3Zv8qqqaphl6OXB6EioXov0U4IS6Wr+RKSZJQuUStJ8CnFae512tf7VaDb0cODEJlUvQfgpwcmVZpmmaJElVVaGHCiZDQuXstJ8CnEN3FGqi1s/kSKicl/ZTgPPJ87woiiRJttutuX6mRELljL0cVosAABjCSURBVLSfApxbdxRqVVVt2w69HDgNCZUz0n4KcG5drd9RqEyJhMq5aD8FuIyiKMJRqE3TbDaboZcDJyChchbaTwEuqav1OwqVaZBQOT3tpwAXlqZpqFap9TMNEiqnp/0U4PLKsgy1/rqu67oeejnwKRIqJ6b9FGAo3VGoav2MnYTKKWk/BRhQlmXdUai2R2XUJFRORvspwOC69qqqqpqmGXo58EESKiej/RQgBl2t38gU4yWhchraTwEiked5V+tfrVZDLwc+QkLlBLSfAkSlLMs0TZMkqaoqXD6AcZFQ+SztpwCx6Y5CTdT6GScJlc/SfgoQoTzPi6JIkmS73ZrrZ3QkVD5F+ylAtLqjUKuqatt26OXAO0iofJz2U4CYdbV+R6EyOhIqH6T9FCB+RVGEo1CbptlsNkMvB44lofJB2k8BRqGr9TsKlRGRUPkI7acAY5GmaXihVutnRCRU3k37KcC4lGUZav11Xdd1PfRy4G0SKu+j/RRgjLqjUNX6GQUJlffRfgowRlmWdUeh2h6V+EmovIP2U4Dx6q4sVFXVNM3Qy4HXSKgcS/spwNh1tX4jU0ROQuUo2k8BJiDP867Wv1qthl4OvEhC5SjaTwGmoSzLNE2TJKmqKjRuQYQkVN6m/RRgMrqjUBO1fiImofIG7acAE5PneVEUSZJst1tz/cRJQuU12k8BJqk7CrWqqrZth14O9EmovEb7KcAkdbV+R6ESJwmVF2k/BZiwoijCUahN02w2m6GXA98joXKY9lOAyetq/Y5CJTYSKgdoPwW4BmmahhKZWj+xkVA5QPspwJUoyzLU+uu6rut66OXAz0io9Gk/Bbgq3VGoav3EQ0Lle7SfAlybLMu6o1Btj0okJFT+jfZTgOvU9XRVVdU0zdDLAQmVPdpPAa5WV+s3MkUMJFR+RvspwDXL87yr9a9Wq6GXw7WTUEkS7acAJElZlmmaJklSVVW4ZgFDkVDRfgpAkuwdhZqo9TO0Hwy9AIY3YPtp0zTb7Xa322VZlmVZeO8OQJIkbdu2bRvmlsIr5AVeovM8L4qiruvtdltVlaYvhiKhXrtB2k93u11VVZvNprfxXuiCCntHA1ytpmkOztTPZrPFYlGW5VmLXev1umma8EJdFIVrBwxClf+qDdJ+utvt5vN5VVXP94VummY+n282m8usBCBCm81mPp8f3PIppMb5fH7WJtGu1u8oVAYkoV6vQdpPQzx9/bV1uVw6eQ+4TnVdvxkKt9tt1511JkVRhHJW0zSuGjAICfV6DdJ+2psPTdO0LMuyLIui2L/Zcrl08h5whXrbPHUvkovFYv/zFzj8ab1ehysXjkJlGE9PT09PT/f3993HXIOu5bQoikt+3f0rtWmafvv27fmSgvV6fcmFAQwu/C7uZFm2/yL58PCw/7ez2ezc6+n28L/wbwquUy+LuoZ6jYba/bSu6/034r1m/9vb2/0/KvQD16bXe9p7VcyybP9K6m63O/fxpN3oal3XXpO5MAn16gy4+2mv/bRX2U+SZH+K38HQwLVp23b/j883Nrn8WH13GVWtnwuTUK/OgLuf9hLq83Dce/F1oglwVd6MgBd+0Q5fsTsK9dydr7DPfqjXZZDdTzv7L77HvM56vw5claIoXn9tHKS4dHt7G05Xqaoqz3NbVnMZEuoVGar9tLN/TfRgd0HvpVlCBa5Kb2D/uV5l6WKXVG9vb+fzeZIky+Xy8fHxMl+UK6fKfy0GbD89Xm9VqvwAnc1ms38NtSiKi72ShwP/kiRp27a3HxaciYR6LQZsPwXgkzabzf5O/rPZrJthuoyyLMOoQG9bazgTCfUqDNt+CsBnrFar3kFT6/X6wnP93VGoSZI4CpULkFCnb/D2UwA+JpwUvT9EP5vN7u7unu/WdwF5noevG6amLr8AroqEOnGjaD99ybhWC3BadV1/+fJlv/c0y7L7+/tB4mnQHYVaVVVv91Y4LQl14qJqP32zJtXbSGXwBQMMZbVadS/gwWKxuL+/H/aFsav173Y7tX7OSkKdstjaT/cTqiOjAA7a7XZfv37tVfbX63V3/XJYRVGELVGbptlsNkMvh8mSUCcrwvbT3jXU59ud9j5jX2jgCs3n8/1h+TRN7+/v39wq9ZK6rOwoVM5HQp2mONtPewn1+WXUXrvVJdYEEJOu9hXMZrOHh4fYXg/TNA11ObV+zseZUtMUVftppyiK/a2ewwF6XXru9d27gApcm7ZtezPyi8Xilc1Hsywb6gJEWZZN0zRNU9d1XdcDDm8xVd89PT0lSdI0zXw+Dx8zdqvVKrzGFUVxd3c39HK+Zz6f9y6ULhaLNE3ruu71Mz0+Pl54tz+AYVVV9a4Tm+7v7wd8M7/dbr9+/ZokSZqmDw8PkRTrGK9eFlXln5oI20/39Q5B2W63y+VyPp/34ml3eAnA9RjXWU1ZlnVHodoelZOTUCclzvbTfVmWvZmbsyy78Gl+ADEYV0JN9hrJqqqyQwunJaFOSpztpz1hS7+XLpGWZfnw8HDhJQHEYIx74HcXFIxMcVompaYjtt1PX5Hn+ePjY13X2+02rHk2m2VZVhSF4j5wtcY4DZLneVmWYdR1tVqpgHEqJqUmoq7rm5ubRMc6AJcVjhgIF4Aj3BuLsTApNUHxt58CMFXdUaiJWj+nI6FOwSjaTwGYqjzPw5ao2+3WXD8nIaGO3ojaTwGYqu4o1N7xK/AxEuq4Rb77KQBXoqv1OwqVk5BQR0z7KQDxKIoinHHVNE3vHBZ4Lwl1xLSfAhCVrta/Wq3Cbyj4GAl1rLSfAhCbNE3DryS1fj5JQh0l7acAxKksy1Drr+u6ruuhl8NYSajjo/0UgJh1J0up9fNhEur4aD8FIGZZloVaf9u2tkflY34w9AJ4H+2nXK3w3izLsjRNsyzz9gxidnt72zRN2MA/z/NQ94fjfRfOP+2dhUqc6rq+ublJkiRN04eHB/V9rsput5vP5+EdWpIks9ks25Om6bDLA3pCtEiSJE3Tx8fHoZdD7HpZVJV/NLSfcuXCfuDdd/5ut2uapqqqm5ubL1++/PjHP765uVmtVk3T6HuDGOR53tX6V6vV0MthZFxDHY2vX7+Gq0e3t7fq+1ytrpLwuq4TIMsy5UUYym63+/r1azgE9eHhQXMOr+hlUQl1HFarVWg2L4ri7u5u6OXAkLofh+N1nQB5nvsdCZfU1fqzLHt4eBh6OcRLQh0f7afQc3Nz85l9FkNONXEFl9H9wKoB8goJdWTatv369Wvoq1MigaA3NfUZJq7g3Ha73ZcvX3a73Ww2e3h48FPGQb0sarep2Nn9FJ4LU1Pz+fzzQ1Fh4qppmu6e8zzv+gGULODzwg9s+HW2XC7v7++HXhEj4Bpq1LSfwiuOnJr6DBNXcCrz+Ty8FVyv14vFYujlEB1V/tHofvv+6Ec/+q//9b/+8Ic/fP3279oSebPZhOHKY7hn9xztPX9gauozfvKTn/zkJz/50Y9+9JOf/OSXf/mXe3/7z//8zz/3cz935F0N/tS5Z/d84Xvumtb+w3/4D//3//5fBQp6+ln06enp6ekpXHJ/Iibr9fpd/7RlWR5/5++6GuSe3XPM91wUxfF3e1a/8iu/cvyNY3jq3LN7vvA9397eJknyS7/0Sw8PD8evhCvRy6L6UOO1WCz+4i/+4v/8n/8z9EIgXrvd7iTzUsAFlGU5m81+4Rd+wVgFb1LlB0as62w7NxNUAGdllh+YiHDG6Znu3C5UAAOSUIFR2mw2J5+RspM/QCQkVGB8ttvtarX6/P04DRUgThIqMDK73a47yeK97G8KMAoSKjAyNzc3x2/TaMIJYIwkVGBM3pyOMuEEMAESKjAaL01HmXACmBgJFRiH/ekoE04A0yahAuNQ13VZliacAK6BhAqMQzjRG4Br8O+GXgB93/2ry5zlCADT4BfolEioAADERUIFACAuEurwttvtm7dp2/ZjJ+gAwFT5BTphEurAttvt169fv3z5slqtnv+ktW1bVVW4QV3Xg6wQACLkF+i0fff09JQkSdM08/k8fMwlrVar/R3I0zTtjnPc/zhJkqIo7u7uLr0+AIiSX6AT08uirqEOrDdvuP8T1Tt53GQiAHT8Ap02CXVgDw8Pd3d3i8ViNpsdvMFsNiuKYr1ePz4+XnhtABAtv0CnTZU/Ir2CRZIkZVnapRwAXucX6ASo8kdqt9s9L0NsNhsTiADwCr9AJ0lCjUVVVd0oYnfs+G63Wy6Xwy0KAGLnF+gkSahRaJqmK0/keX5/f1+WZfhjXde9ygUAEPgFOlX6UKPw5cuXMHg4m80eHx9ns9lut5vP5+FNYffJoZcJAHHxC3Qy9KHG6O7uLsuyJEnW63X4QZrNZuv1OkmSNE3v7+/9dAHAc36BTpVrqBGp67ooit5n8jz30wUAr/ALdAJ6WVRCBQBgYKr8AABETUIFACAuEioAAHGRUAEAiIuECgBAXCRUAADiIqECABAXCRUAgLhIqAAAxEVCBQAgLhIqAABxkVABAIiLhAoAQFwkVAAA4iKhAgAQFwkVAIC4SKgAAMRFQgUAIC4SKgAAcZFQAQCIi4QKAEBcJFQAAOIioQIAEBcJFQCAuEioAADERUIFACAuEioAAHGRUAEAiIuECgBAXCRUAADiIqECABAXCRUAgLhIqAAAxEVCBQAgLhIqAABxkVABAIiLhAoAQFwkVAAA4iKhAgAQFwkVAIC4SKgAAMRFQgUAIC4SKgAAcZFQAQCIi4QKAEBcJFQAAOIioQIAEBcJFQCAuEioAADERUIFACAuEioAAHGRUAEAiIuECgBAXCRUAADiIqECABAXCRUAgLhIqAAAxEVCBQAgLhIqAABxkVABAIiLhAoAQFwkVAAA4iKhAgAQFwkVAIC4SKgAAMRFQgUAIC4SKgAAcZFQAQCIi4QKAEBcJFQAAOIioQIAEBcJFQCAuEioAADERUIFACAuEioAAHGRUAEAiIuECgBAXCRUAADiIqECABAXCRUAgLhIqAAAxEVCBQAgLj8YegEwSk3TNE3z5s1ms1me51mWXWBJL9lsNm3bdn+8vb0dcDFvGstqT/INMJYHC3B53z09PSVJ0jTNfD4PHwNvWq1WVVUdeeM0TdfrdZ7nZ13SS+bz+X6WivzHfCyrPck3wFgeLMAF9LKoKj+cXdu28/l8s9kMvZCBbbfb+Z7reUJ8AwC8lyo/XMhyuUzTdKgrqTHY7Xb7lwyHbX64PN8AAMeTUOEE0jQtimL/M9vtdrvd7na7/U9WVXX5gFIUxYiy4LhW24n5GwBgjCRUOIE0TZ+Puex2u9VqtV/bbZpmt9vNZrNLrm2xWFzyy33SuFbbifkbAGCMJFQ4l9lsdnt72+s+3G633VW0/ZL3bDbrrh3WdR1udvB623a7DUEn/DGMir8SenpX8l66hte2bdM0YbQ8LObIq3273S4sKfwxFLLTND3m/z1ytW3b7s+8p2l68P57w/UH1//hh/kBb34DHKP39CZJkmVZlmUvPcMHv6lCf8V2uw2ff+lba98lnyiAA56enp6enu7v77uPgTeVZbn/c5Tn+Uu37P1ev7+/7/7q+T08PDx0ObUsy95drdfrl3LJYrF4fHw8ZgHPb/Dw8HAwfITrgq88Cd++fXvpkmee5/uPNEyy98r3Icvmef7w8PD6au/u7vY/WRTF88U8Pj727vxUD/Ogk3wDvP5P88rTmyRJlmX7d9V5vqr1ev38DUyapvtP+/meKIAj9bKohAofcY6E+vj4uJ8k9hPqt2/f3ryCNZvN7u7u3lxA72/X6/Xrd5vn+bdv357f7cPDw5sXStfr9cGnq+eY0Lb/zMxms+fr6T2QXr7/8MN8ybkT6rdv347px+2e4U5vVa888Nls9jyknvyJAjhSL4vabQrOqzcr84rlcvnSjXsbZ770hW5ubrpK7jHqul4ul6/fpmmam5ubg19rv/J+0HK5PGZb+2PsX03c7XZ1Xfdu0Hvg+7f/8MM8ieO/AfYd+U+5Wq1e+VfYbrevPPDQJrv/mWGfKIB9Eiqc0X7zX/DShbFer+G+1WrVu5Nwbez+/r4sy14B913poRdQyrJ8fHz89u1br52gaZpeM2UvGIWGy/v7+7u7u951wZB4FovF/f19b5YofPL+/v6Yi4XPJ+V7N9jPrL02zQ8/zM87/htgX++bYTablWUZnqvb29v9NR8M6/t/G/73xWJRlmVZlr3L3l2naTDgEwXQd/DKKvC6N4u84fd6Lz5mWbZ/m+c/j3me393dhSzS9ZX27qRX2H14eHj9Bi+Vknv13F6LYa/lYL+t89u3b/v/42w265V9e2myKyWH15nO80bbV1b79PS0H5J6baYPDw8vPZYPP8zXneQb4KUH27vzXr9pr+O29zQm35dl2f6/zrdv33ohtesMOdMTBXAkVX44vaZpvvu+H//4x8+r9q9vpVQUxf39fVEUYX4oJIm6rnuz7b07ybKsd23yyML6/rW3NE17qShN0/0v1LZtdy2wd9FusVj0cljvrl65yPcu+8F3fz3Pv8T+LT/8MN/lJN8Andlsln9f72+PX9jd3V2vhbe3hoP/rOd7ogCOZLcpuJDn4bLn+YaayavtlfufrKqqK9cemVDfPN6p98mmacJnekvqXTEN/+N+vjnVLkVFUVRV9Xw9vSX1Svwffpgn9+Y3QCdU5A/+1eutpT0Ht+V66dHF80QBJBIqXEYo379yg9lsdnA0/nkH6sH/PcuyLqHudrs3t4Xvjddst9v5fN67Te/6X/fH3v97MKYcTNufFPYB7Z6QpmlCjOsdptq71Lp/D+96mKf15jfAS5qmCdvfhg1K3/X/Hr8rbTxPFEAgocJ5ZVm2WCzevHh25OWol3JnL4u8uS18L5H0tsQ/KIaqblEU+wk1BPFebnsloQ7yMI/8BngunEd1mSAYwxMFsE9ChRN43gzafd4RlydUFMX+vHld14vFYj8qFUXx4eOsPuPk3wA3NzcH+3fDMQdG6YHJk1DhBMJoy4AL6F1pe28qWiwWz9tJe2KI2mma7hf6wwf7Se71f4XzPczTfgNUVbX/oMJ40/7xtudOqGP5fgAmTEKFqD3fwPJgEnrvppu9G3wmYLVt+/yy5X7l/eC8zoftF/rrui7Lcr8e3ctVJ3yYl9SLp72dns5R9x/pEwVMmIQKUetFh7qun0eH3rbwx7S0hsGsLtsdbDrc7Xb7d9sFzSzL9gNo0zS9Jsu2bffnbMqyPOHg1GKx6Ar9vVORiqLoXdj7zMMcUO9fs/egTnVM176RPlHAhNkPFaLWuyi42Wx6l0ufn135Zn022E+6dV0/DyVVVc33dF+3d/9VVfWu6u3vCZWcbrepYDabvbTd6cEv9OGHGYnnV0zPVOIf+xMFTIyEClF7vsX6fD7vDh2t67qXFZ7f/iW9HTdvbm66i3Mh9e4HzSzLulyYZdl+mglXTENSbNs2TKB3fxsmew4u4MMR56U7PBjNP/wwB7R/0XS73Xb/3Nvtdn/9pzXGJwqYsoMnTQGve/PQy2MceQ/fvn07fiqld+Tp06vniD7fFv6lBsTu5NKgd37pK7pDNZ+eHdeZ/GvY3T/V85XV7j8hz79QURQvPYEffpivOMk3wEsP9l3hb7FY7N/nm6t65ezZczxRAEdy6imMzGw2u7+/Pyakrtfrd+27WZZlr2m1t/t9+Orr9bp3szzPe8e4v3T/+2Hreefidrv9wBXBXqE/eCXVffhhDuWlA6WC3j9x2Bf2VF93XE8UMGESKoxAlmWPj4+vpM80Te/u7t67LfxsNnt4eHglD4ULnC8dtXp/f//SrMxsNru7u3s+ILVer0+yS1Evjx7MrPt/++GHOYgsyw4+UbPZrCzL9Xrd67I4/hzU143uiQIm7Lunp6ckSZqmmc/nT9+vEAGxadu2ruvtdttdNgtngb6Sz+bz+f5lsIM/5r27DZPdRVEcc6ks/I9dU2nYsvSVENO27f68V7jxZabCP/MwL2+32202m+7fLs/zi51HMK4nCpiGXhaVUGHijkmoADCsXhZV5QcAIC527IfJ2mw2bdueaXMiADgfCRUmq65r8RSAMVLlhytil3UARkFChWsR9jAaehUA8DZVfpis29vbblOq2WxmqyAAxkJChckSSQEYKVV+AADiIqECABAXCRUAgLhIqAAAxEVCBQAgLhIqAABxkVABAIiLhAoAQFwkVAAA4iKhAgAQFwkVAIC4SKgAAMRFQgUAIC4SKgAAcZFQAQCIi4QKAEBcJFQAAOIioQIAEBcJFQCAuEioAADERUIFACAuEioAAHGRUAEAiIuECgBAXCRUAADiIqECABAXCRUAgLhIqAAAxEVCBQAgLhIqAABxkVABAIiLhAoAQFwkVAAA4iKhAgAQFwkVAIC4/GD/D/P5fKh1AABwtXa73f4ff5ZQ0zQty3KI9QAAQJLneffxd09PTwMuBQAAevShAgAQFwkVAIC4/H+3yZcCrbnTpgAAAABJRU5ErkJggg==",
-      "text/plain": [
-       "#<CL-JUPYTER-USER::PNG-BYTES {100362BDF3}>"
-      ]
-     },
-     "execution_count": 59,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(cl-jupyter-user:png-from-file \"ppss.png\")"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 60,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "The object is a STANDARD-OBJECT of type SIMPLICIAL-SET.\n",
-      "0. CMPR: #<FUNCTION S-CMPR>\n",
-      "1. BASIS: #<CLOSURE (FLET RSLT :IN FINITE-SS-BASIS) {100373162B}>\n",
-      "2. BSGN: *\n",
-      "3. DFFR: [K57 Morphism (degree -1): K56 -> K56]\n",
-      "4. GRMD: [K56 Simplicial-Set]\n",
-      "5. EFHM: \"unbound\"\n",
-      "6. IDNM: 56\n",
-      "7. ORGN: (BUILD-FINITE-SS (* 1 E (* *) 2 T (E * E)))\n",
-      "8. CPRD: [K60 Morphism (degree 0): K56 -> K58]\n",
-      "9. FACE: #<CLOSURE (FLET RSLT :IN FINITE-SS-FACE) {100373164B}>\n",
-      "> \n",
-      "Checking the 0-simplices...\n",
-      "Checking the 1-simplices...\n",
-      "Checking the 2-simplices..."
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "[K56 Simplicial-Set]"
-      ]
-     },
-     "execution_count": 60,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def ppss (build-finite-ss \n",
-    "  '( *\n",
-    "     1 e (* *)\n",
-    "     2 t (e * e)) ))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 61,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "Computing boundary-matrix in dimension 0.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 18m 30s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 0) :\n",
-      "* \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 1.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 18m 30s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 1) :\n",
-      "E \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 0 :\n",
-      "\n",
-      "\n",
-      "Component Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "Computing boundary-matrix in dimension 1.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 18m 30s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 1) :\n",
-      "E \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 2.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 18m 30s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 2) :\n",
-      "T \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 1 :\n",
-      "\n",
-      "\n",
-      "Component Z/2Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "Computing boundary-matrix in dimension 2.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 18m 30s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 2) :\n",
-      "T \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 3.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 2 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 61,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(dotimes (i 3) (chcm-homology ppss i))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "The user will note that the list of faces for the 2-simplex `t`, is in simplified form. In particular, as the face 1 of `t` is the 0-degeneracy of the base point \"$*$\", it is sufficient to code the  face 1 of `t` by \"`*`\" instead of the complete form `(0 *)`."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 62,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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",
-      "text/plain": [
-       "#<CL-JUPYTER-USER::PNG-BYTES {1003816D83}>"
-      ]
-     },
-     "execution_count": 62,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(cl-jupyter-user:png-from-file \"duncess.png\")"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 63,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "The object is a STANDARD-OBJECT of type SIMPLICIAL-SET.\n",
-      "0. CMPR: #<FUNCTION S-CMPR>\n",
-      "1. BASIS: #<CLOSURE (FLET RSLT :IN FINITE-SS-BASIS) {100391929B}>\n",
-      "2. BSGN: *\n",
-      "3. DFFR: [K62 Morphism (degree -1): K61 -> K61]\n",
-      "4. GRMD: [K61 Simplicial-Set]\n",
-      "5. EFHM: \"unbound\"\n",
-      "6. IDNM: 61\n",
-      "7. ORGN: (BUILD-FINITE-SS (* 1 E (* *) 2 T (E E E)))\n",
-      "8. CPRD: [K65 Morphism (degree 0): K61 -> K63]\n",
-      "9. FACE: #<CLOSURE (FLET RSLT :IN FINITE-SS-FACE) {10039192BB}>\n",
-      "> \n",
-      "Checking the 0-simplices...\n",
-      "Checking the 1-simplices...\n",
-      "Checking the 2-simplices..."
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "[K61 Simplicial-Set]"
-      ]
-     },
-     "execution_count": 63,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def duncess (build-finite-ss \n",
-    "  '( *\n",
-    "     1 e (* *)\n",
-    "     2 t (e e e)) ))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 64,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "Computing boundary-matrix in dimension 0.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 18m 30s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 0) :\n",
-      "* \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 1.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 18m 30s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 1) :\n",
-      "E \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 0 :\n",
-      "\n",
-      "\n",
-      "Component Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "Computing boundary-matrix in dimension 1.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 18m 30s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 1) :\n",
-      "E \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 2.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 18m 30s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 2) :\n",
-      "T \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 1 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "Computing boundary-matrix in dimension 2.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 18m 30s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 2) :\n",
-      "T \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 3.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 2 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 64,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(dotimes (i 3) (chcm-homology duncess i))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "## Special simplicial sets\n",
-    "\n",
-    "The system provides useful functions to create interesting simplicial sets of constant usage. In particular, the user is advised from now to use the following version of the standard simplex implemented in `Kenzo` and not the one given previously for simplicity reason.\n",
-    "\n",
-    "### The standard simplex\n",
-    "\n",
-    "`delta` *dmns* *[Function]*\n",
-    "> Create the standard simplex $\\Delta^n$ with vertices $0,1,\\ldots,n$, where *dmns* is the parameter for $n$. This simplicial set is so important in the applications that the implementor has decided to code the simplices in a  way similar to the coding\n",
-    "of the degeneracy operators. An increasing sequence of non-negative integers describing a simplex, is coded on a binary integer with the following convention: a number $i$ representing the vertex $i$ is the $(i+1)$--th binary bit of a machine word. The base point $0$ is the bit 1 in position 1 of the word. This representation is very efficient for saving memory space but somehow awkward to read.\n",
-    "\n",
-    "`delta-infinity` *[Function]*\n",
-    "> Create the locally effective standard simplex $\\Delta^\\mathbb{N}$ freely generated by the positive integers.\n",
-    "\n",
-    "`deltab` *[Function]*\n",
-    "> Create the locally effective *reduced* simplicial set $\\bar \\Delta$, built from $\\Delta^\\mathbb{N}$ by identifying all the vertices to the base point.\n",
-    "\n",
-    "`deltab2` *[Function]*\n",
-    "> Create the locally effective *1-reduced* simplicial set $\\Delta_2^\\mathbb{N}$, obtained from the above $\\bar \\Delta$, by identification of all the edges with the base point. This is the efficient version of the coalgebra that is used as example in the cobar chapter.\n",
-    "\n",
-    "`dlop-ext-int` *ext-dlop* *[Function]*\n",
-    "> Code on an integer the valid list (increasing order) representing the simplex *ext-dlop* of the standard simplex.\n",
-    "\n",
-    "`dlop-int-ext` *dgop* *[Function]*\n",
-    "> Give the list representing a simplex of the standard simplex from the integer *dgop*.\n",
-    "\n",
-    "`vertex-i` *absm i* *[Function]*\n",
-    "> Give the $i$-th vertex of the (coded, degenerate or not) abstract simplex `absm` belonging to a simplicial set of the $\\Delta$ family.\n",
-    "\n",
-    "`absm-ext-int` *vlist* *[Function]*\n",
-    "> Create a valid abstract simplex of the $\\Delta$ family from the simplex *vlist* written as a non-decreasing list of non-negative integers (i.e coding of any degenerate or non--degenerate simplex of the $\\Delta$ family).\n",
-    "\n",
-    "`absm-int-ext` *absm* *[Function]*\n",
-    "> From an internal coded form of an abstract simplex of the $\\Delta$ family, create the  non-decreasing list\n",
-    "of non--negative integers representing the canonical external form of such a simplex.\n",
-    "\n",
-    "`soft-delta` *dmns* *[Function]*\n",
-    "> Create another version of the standard simplex $\\Delta^n$ designed for a better clarity in the printing of the results at testing time. More precisely, the simplices are represented internally by a list of the form `(:delt` *binary-code*`)`. With this representation, the system is able to recognize a coded simplex and to print it in a readable form. For the user, the only\n",
-    "requirement is to write a simplex coded $n$ as `(d` *n*`)`, where `d` is the macro building the internal representation (see the examples). Attention: the above conversion functions do not work with this representation.\n",
-    "\n",
-    "`soft-delta-infinity` *[Function]*\n",
-    "\n",
-    "### Examples"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 65,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K66 Simplicial-Set]"
-      ]
-     },
-     "execution_count": 65,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def d3 (delta 3))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "The simplices $2$, $4$ and  $8$ are the coded representation of the vertices $1$, $2$ and $3$:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 66,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       ":LESS"
-      ]
-     },
-     "execution_count": 66,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(cmpr d3 2 4)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 67,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       ":EQUAL"
-      ]
-     },
-     "execution_count": 67,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(cmpr d3 4 4)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 68,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       ":GREATER"
-      ]
-     },
-     "execution_count": 68,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(cmpr d3 8 4)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "The list returned by the following statement  getting the basis of $\\Delta^3$ in dimension 2, namely `(7 11 13 14)` is in fact the coded list of the following simplices `((0 1 2) (0 1 3) (0 2 3) (1 2 3))`."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 69,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(7 11 13 14)"
-      ]
-     },
-     "execution_count": 69,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(basis d3 2)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "In the following statement, the integer $21$ represents the simplex in dimension $2$, `(0 1 4)`, $1$ represents the operator $\\partial_1$ and the face is therefore `(0 4)` represented as the integer $17$."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 70,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "<AbSm - 17>"
-      ]
-     },
-     "execution_count": 70,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(face d3 1 2 21)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "We may obtain the same result, using:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 71,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "<AbSm - 17>"
-      ]
-     },
-     "execution_count": 71,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(face d3 1 2 (dlop-ext-int '(0 1 4)))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Let us test the conversion functions."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 72,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "0"
-      ]
-     },
-     "execution_count": 72,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(vertex-i (absm 0 1) 0)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 73,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "0"
-      ]
-     },
-     "execution_count": 73,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(vertex-i (absm 1 1) 0)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 74,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "0"
-      ]
-     },
-     "execution_count": 74,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(vertex-i (absm 1 1) 1)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 75,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "2"
-      ]
-     },
-     "execution_count": 75,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(vertex-i (absm 0 7) 2)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 76,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "<AbSm 6-5-1-0 15>"
-      ]
-     },
-     "execution_count": 76,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(absm-ext-int '(0 0 0 1 2 3 3 3))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 77,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "<AbSm 2-1 7>"
-      ]
-     },
-     "execution_count": 77,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(absm-ext-int '(0 1 1 1 2))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 78,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(0 0 0 1 2 3 3 3)"
-      ]
-     },
-     "execution_count": 78,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(absm-int-ext (absm-ext-int '(0 0 0 1 2 3 3 3)))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "The following  call to the macro `?` returns the boundary of the simplex `(0 2 3)` of $\\Delta^3$, the integers $5$, $9$ and $12$ representing respectively the simplices `(0 2)`, `(0 3)` and `(2 3)`. The application of the coproduct `dgnl` to the simplex `(0 1 2 3)`, coded $15$, is also easily interpreted:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 79,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 1}\n",
-       "<1 * 5>\n",
-       "<-1 * 9>\n",
-       "<1 * 12>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 79,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? d3 2 13)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 80,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 3}\n",
-       "<1 * <TnPr 1 15>>\n",
-       "<1 * <TnPr 3 14>>\n",
-       "<1 * <TnPr 7 12>>\n",
-       "<1 * <TnPr 15 8>>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 80,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(dgnl d3 3 15)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "We may show now some examples with the *soft* version of the standard simplex. Using the macro `d` and the function `dlop-ext-int` the user may work with a readable form of the simplices and the degeneracy operators."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 81,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K71 Simplicial-Set]"
-      ]
-     },
-     "execution_count": 81,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def d3 (soft-delta 3))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 82,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       ":LESS"
-      ]
-     },
-     "execution_count": 82,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(cmpr d3 (d 2) (d 4))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 83,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "((:DELT . 3) (:DELT . 5) (:DELT . 6) (:DELT . 9) (:DELT . 10) (:DELT . 12))"
-      ]
-     },
-     "execution_count": 83,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(basis d3 1)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 84,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 3}\n",
-       "<1 * <TnPr (DELT . 1) (DELT . 15)>>\n",
-       "<1 * <TnPr (DELT . 3) (DELT . 14)>>\n",
-       "<1 * <TnPr (DELT . 7) (DELT . 12)>>\n",
-       "<1 * <TnPr (DELT . 15) (DELT . 8)>>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 84,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(dgnl d3 3 (d (dlop-ext-int '(0 1 2 3))))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 85,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "<AbSm - (DELT . 17)>"
-      ]
-     },
-     "execution_count": 85,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(face d3 1 2 (d (dlop-ext-int '(0 2 4))))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 86,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 1}\n",
-       "<1 * (DELT . 5)>\n",
-       "<-1 * (DELT . 9)>\n",
-       "<1 * (DELT . 12)>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 86,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? d3 2 (d (dlop-ext-int '(0 2 3))))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "### Spheres, Moore spaces and projective spaces\n",
-    "\n",
-    "`sphere` *n* *[Function]*\n",
-    "> Create a simplicial set, a model  for the sphere of dimension $n$, ($n \\geq 0$). This is a typical example where the differential is known a priori to be null, so the `:intr-bndr` keyword parameter is set to function `zero-pure-dffr`. This function generates a name `S`*n* for the **unique** simplex of dimension $n$ whose faces are the degeneracies of the base point labelled \"`*`\".\n",
-    "\n",
-    "`sphere-wedge` *dmns1 ... dmnsn* *[Function]*\n",
-    "> Create a simplicial set for a wedge of spheres. Here, the $dmns_i$ are integers, namely the dimensions of the spheres to be wedged. The differential is null. In the representation created by the program, the 0-simplex (base point) is labelled \"`*`\" and in dimension $p$ the simplices are labelled `S`*p*`-`*1*, ...,  `S`*p*`-`*s*,  where *s* is the number of spheres of dimension $p$ in the wedge. (See the example).\n",
-    "\n",
-    "`moore` *p n* *[Function]*\n",
-    "> Construct a simplicial set, a model for  ${\\rm Moore}(\\mathbb{Z}/{p\\mathbb{Z}},n)$. The integers $p$ and $n$ must satisfy  the conditions $p>1,\\ n> 2p-4$, otherwise the result is undefined. ${\\rm Moore}(\\mathbb{Z}/{p\\mathbb{Z}},n)$ is a space, whose the only non-null homology groups are $H_0=\\mathbb{Z}$ and $H_n=\\mathbb{Z}/{p\\mathbb{Z}}$. A Moore space has only three non-degenerate simplices, namely in dimension $0$, $n$ and $n+1$. A number $p$ of faces of the  $(n+1)$-simplex are identified with the $n$-simplex, the others faces being contracted on the base point. In the  representation created by the software, the 0-simplex (base point), the $n$-simplex and the $(n+1)$-simplex are respectively labelled \"`*`\", `M`$n$ and `N`$n'$, where $n'=n+1$.\n",
-    "\n",
-    "`R-proj-space &rest` *[Function]*\n",
-    "> Accepts zero, one or two arguments for parameters $k$ and $l$. A single positive `FIXNUM` argument is interpreted as a value for *k*. Two positive `FIXNUM` arguments will be assigned to parameters $k$ and $l$, such that $k\\leq l$. If $k=1$ or omitted, build a simplicial set model of $K(\\mathbb{Z}_2,1)= P^\\infty\\mathbb{R}$. In dimension $n$, this simplicial set has only one non-degenerate simplex, namely the integer $n$. The faces of this non-degenerate simplex $n$ are given by the following formulas: $\\partial_0 n = \\partial_n n = n-1$ and for $i \\not= 0$ and $i \\not=n$,  $\\partial_i n= \\eta_{i-1} (n-2)$. If $k >1$, build an analogous simplicial set but with no simplices in dimensions $1 \\leq m < k$. If in addition to an argument for $k$ an argument for $l$ ($l \\geq k$) is provided, build an analogous simplicial set but with no simplices in dimensions $m \\geq l$.\n",
-    "\n",
-    "### Examples\n",
-    "\n",
-    "Let us define first, an auxiliary function `show-structure` with 2 arguments *ss* and *dmn*, to show the structure (i.e. generators and faces) of the simplicial set *ss*, from the dimension 0 up to the dimension *dmn* included.\n",
-    "\n",
-    "```commonlisp\n",
-    "(defun show-structure (ss dmn)\n",
-    " (dotimes (i (1+ dmn))\n",
-    "   (format t \"~2%Dimension = ~D :\" i)\n",
-    "   (case i\n",
-    "     (0 (format t \"~2%~8TVertices : ~8T~A\" (basis ss 0)))\n",
-    "     (otherwise\n",
-    "        (dolist (s (basis ss i))\n",
-    "            (format t \"~2%~8TSimplex : ~A~2%~16TFaces : ~A\"\n",
-    "                    s (mapcar #'(lambda (j) (face ss j i s))\n",
-    "                                (<a-b> 0 i)))))\n",
-    "  )))\n",
-    "```\n",
-    "\n",
-    "In these elementary examples, we show the structure of some simplicial sets built\n",
-    "from the functions above. Let us begin with $S^2$."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 87,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K76 Simplicial-Set]"
-      ]
-     },
-     "execution_count": 87,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def s2 (sphere 2))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 88,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "*"
-      ]
-     },
-     "execution_count": 88,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(bspn s2)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Applying the function `basis`, we see that the only non-null simplices are in dimension 0 and 2."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 89,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "(*) \n",
-      "NIL \n",
-      "(S2) \n",
-      "NIL "
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 89,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(dotimes (i 4) (print (basis s2 i)))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "In dimension 2, the 3 faces of the simplicial set are all the degeneracy $\\eta_0$ of the base point."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 90,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(<AbSm 0 *> <AbSm 0 *> <AbSm 0 *>)"
-      ]
-     },
-     "execution_count": 90,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(mapcar #'(lambda(i)(face s2 i 2 's2)) '(0 1 2))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 91,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "<AbSm 3-1-0 S2>"
-      ]
-     },
-     "execution_count": 91,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(face s2 5 7 (absm (dgop-ext-int '(5 3 1 0)) 's2))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 92,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "<AbSm 4-2-0 S2>"
-      ]
-     },
-     "execution_count": 92,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(face s2 2 7 (absm (dgop-ext-int '(5 3 1 0)) 's2))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "The differential of the simplex `s2` in dimension 2 is of course the null combination of degree 1:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 93,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 1}\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 93,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? s2 2 's2)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Now, let us see the stucture of $S^3$, using our auxiliary function `show-structure`."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 94,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K81 Simplicial-Set]"
-      ]
-     },
-     "execution_count": 94,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def s3 (sphere 3))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 95,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "\n",
-      "Dimension = 0:\n",
-      "\n",
-      "        Vertices :  (*)\n",
-      "\n",
-      "Dimension = 1:\n",
-      "\n",
-      "Dimension = 2:\n",
-      "\n",
-      "Dimension = 3:\n",
-      "\n",
-      "        Simplex : S3\n",
-      "\n",
-      "                Faces : (<AbSm 1-0 *> <AbSm 1-0 *> <AbSm 1-0 *> <AbSm 1-0 *>)"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 95,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(show-structure s3 3)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "The space ${\\rm Moore}(2,1)$ is the projective plane:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 96,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K86 Simplicial-Set]"
-      ]
-     },
-     "execution_count": 96,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def p2 (moore 2 1)) "
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 97,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "\n",
-      "Dimension = 0:\n",
-      "\n",
-      "        Vertices :  (*)\n",
-      "\n",
-      "Dimension = 1:\n",
-      "\n",
-      "        Simplex : M1\n",
-      "\n",
-      "                Faces : (<AbSm - *> <AbSm - *>)\n",
-      "\n",
-      "Dimension = 2:\n",
-      "\n",
-      "        Simplex : N2\n",
-      "\n",
-      "                Faces : (<AbSm - M1> <AbSm 0 *> <AbSm - M1>)"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 97,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(show-structure p2 2)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "In the following example, note the identification of $p$ faces of the $(n+1)$-simplex with the $n$-simplex."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 98,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K91 Simplicial-Set]"
-      ]
-     },
-     "execution_count": 98,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def sp2r (moore 2 2))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 99,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "\n",
-      "Dimension = 0:\n",
-      "\n",
-      "        Vertices :  (*)\n",
-      "\n",
-      "Dimension = 1:\n",
-      "\n",
-      "Dimension = 2:\n",
-      "\n",
-      "        Simplex : M2\n",
-      "\n",
-      "                Faces : (<AbSm 0 *> <AbSm 0 *> <AbSm 0 *>)\n",
-      "\n",
-      "Dimension = 3:\n",
-      "\n",
-      "        Simplex : N3\n",
-      "\n",
-      "                Faces : (<AbSm - M2> <AbSm 1-0 *> <AbSm - M2> <AbSm 1-0 *>)"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 99,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(show-structure sp2r 3)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Let us see an example of a wedge of spheres:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 100,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K96 Simplicial-Set]"
-      ]
-     },
-     "execution_count": 100,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def w (sphere-wedge 3 2 3))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 101,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "\n",
-      "Dimension = 0:\n",
-      "\n",
-      "        Vertices :  (*)\n",
-      "\n",
-      "Dimension = 1:\n",
-      "\n",
-      "Dimension = 2:\n",
-      "\n",
-      "        Simplex : S2-1\n",
-      "\n",
-      "                Faces : (<AbSm 0 *> <AbSm 0 *> <AbSm 0 *>)\n",
-      "\n",
-      "Dimension = 3:\n",
-      "\n",
-      "        Simplex : S3-1\n",
-      "\n",
-      "                Faces : (<AbSm 1-0 *> <AbSm 1-0 *> <AbSm 1-0 *> <AbSm 1-0 *>)\n",
-      "\n",
-      "        Simplex : S3-2\n",
-      "\n",
-      "                Faces : (<AbSm 1-0 *> <AbSm 1-0 *> <AbSm 1-0 *> <AbSm 1-0 *>)\n",
-      "\n",
-      "Dimension = 4:\n",
-      "\n",
-      "Dimension = 5:"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 101,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(show-structure w 5)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 102,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       ":LESS"
-      ]
-     },
-     "execution_count": 102,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(cmpr w 's3-1 's3-2)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 103,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "<AbSm 1-0 *>"
-      ]
-     },
-     "execution_count": 103,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(face w 2 3 's3-1)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 104,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 2}\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 104,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? w 3 's3-2)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Let us show now some examples with the simplicial sets generated by the function `R-proj-space`."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 105,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K101 Simplicial-Set]"
-      ]
-     },
-     "execution_count": 105,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def p1 (R-proj-space))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 106,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "(0) \n",
-      "(1) \n",
-      "(2) \n",
-      "(3) \n",
-      "(4) \n",
-      "(5) \n",
-      "(6) "
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 106,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(dotimes (i 7)(print(basis p1 i)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 107,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "\n",
-      "Dimension = 0:\n",
-      "\n",
-      "        Vertices :  (0)\n",
-      "\n",
-      "Dimension = 1:\n",
-      "\n",
-      "        Simplex : 1\n",
-      "\n",
-      "                Faces : (<AbSm - 0> <AbSm - 0>)\n",
-      "\n",
-      "Dimension = 2:\n",
-      "\n",
-      "        Simplex : 2\n",
-      "\n",
-      "                Faces : (<AbSm - 1> <AbSm 0 0> <AbSm - 1>)\n",
-      "\n",
-      "Dimension = 3:\n",
-      "\n",
-      "        Simplex : 3\n",
-      "\n",
-      "                Faces : (<AbSm - 2> <AbSm 0 1> <AbSm 1 1> <AbSm - 2>)\n",
-      "\n",
-      "Dimension = 4:\n",
-      "\n",
-      "        Simplex : 4\n",
-      "\n",
-      "                Faces : (<AbSm - 3> <AbSm 0 2> <AbSm 1 2> <AbSm 2 2> <AbSm - 3>)\n",
-      "\n",
-      "Dimension = 5:\n",
-      "\n",
-      "        Simplex : 5\n",
-      "\n",
-      "                Faces : (<AbSm - 4> <AbSm 0 3> <AbSm 1 3> <AbSm 2 3> <AbSm 3 3> <AbSm - 4>)"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 107,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(show-structure p1 5)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 108,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "Computing boundary-matrix in dimension 0.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 18m 30s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 0) :\n",
-      "0 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 1.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 18m 30s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 1) :\n",
-      "1 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 0 :\n",
-      "\n",
-      "\n",
-      "Component Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "Computing boundary-matrix in dimension 1.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 18m 30s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 1) :\n",
-      "1 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 2.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 18m 30s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 2) :\n",
-      "2 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 1 :\n",
-      "\n",
-      "\n",
-      "Component Z/2Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "Computing boundary-matrix in dimension 2.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 18m 30s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 2) :\n",
-      "2 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 3.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 18m 30s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 3) :\n",
-      "3 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 2 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "Computing boundary-matrix in dimension 3.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 18m 30s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 3) :\n",
-      "3 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 4.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 18m 30s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 4) :\n",
-      "4 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 3 :\n",
-      "\n",
-      "\n",
-      "Component Z/2Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "Computing boundary-matrix in dimension 4.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 18m 30s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 4) :\n",
-      "4 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 5.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 18m 30s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 5) :\n",
-      "5 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 4 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 108,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(dotimes (i 5)(chcm-homology p1 i))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 109,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K106 Simplicial-Set]"
-      ]
-     },
-     "execution_count": 109,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def p2 (R-proj-space 2))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 110,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "\n",
-      "Dimension = 0:\n",
-      "\n",
-      "        Vertices :  (0)\n",
-      "\n",
-      "Dimension = 1:\n",
-      "\n",
-      "Dimension = 2:\n",
-      "\n",
-      "        Simplex : 2\n",
-      "\n",
-      "                Faces : (<AbSm 0 0> <AbSm 0 0> <AbSm 0 0>)\n",
-      "\n",
-      "Dimension = 3:\n",
-      "\n",
-      "        Simplex : 3\n",
-      "\n",
-      "                Faces : (<AbSm - 2> <AbSm 1-0 0> <AbSm 1-0 0> <AbSm - 2>)\n",
-      "\n",
-      "Dimension = 4:\n",
-      "\n",
-      "        Simplex : 4\n",
-      "\n",
-      "                Faces : (<AbSm - 3> <AbSm 0 2> <AbSm 1 2> <AbSm 2 2> <AbSm - 3>)\n",
-      "\n",
-      "Dimension = 5:\n",
-      "\n",
-      "        Simplex : 5\n",
-      "\n",
-      "                Faces : (<AbSm - 4> <AbSm 0 3> <AbSm 1 3> <AbSm 2 3> <AbSm 3 3> <AbSm - 4>)"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 110,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(show-structure p2 5)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 111,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "Computing boundary-matrix in dimension 0.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 18m 30s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 0) :\n",
-      "0 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 1.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 0 :\n",
-      "\n",
-      "\n",
-      "Component Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "Computing boundary-matrix in dimension 1.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 2.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 18m 30s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 2) :\n",
-      "2 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 1 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "Computing boundary-matrix in dimension 2.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 18m 30s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 2) :\n",
-      "2 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 3.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 18m 30s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 3) :\n",
-      "3 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 2 :\n",
-      "\n",
-      "\n",
-      "Component Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "Computing boundary-matrix in dimension 3.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 18m 30s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 3) :\n",
-      "3 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 4.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 18m 30s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 4) :\n",
-      "4 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 3 :\n",
-      "\n",
-      "\n",
-      "Component Z/2Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "Computing boundary-matrix in dimension 4.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 18m 30s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 4) :\n",
-      "4 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 5.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 18m 30s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 5) :\n",
-      "5 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 4 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 111,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(dotimes (i 5)(chcm-homology p2 i))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 112,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K111 Simplicial-Set]"
-      ]
-     },
-     "execution_count": 112,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def pr3 (R-proj-space 3))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 113,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "\n",
-      "Dimension = 0:\n",
-      "\n",
-      "        Vertices :  (0)\n",
-      "\n",
-      "Dimension = 1:\n",
-      "\n",
-      "Dimension = 2:\n",
-      "\n",
-      "Dimension = 3:\n",
-      "\n",
-      "        Simplex : 3\n",
-      "\n",
-      "                Faces : (<AbSm 1-0 0> <AbSm 1-0 0> <AbSm 1-0 0> <AbSm 1-0 0>)\n",
-      "\n",
-      "Dimension = 4:\n",
-      "\n",
-      "        Simplex : 4\n",
-      "\n",
-      "                Faces : (<AbSm - 3> <AbSm 2-1-0 0> <AbSm 2-1-0 0> <AbSm 2-1-0 0> <AbSm - 3>)"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 113,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(show-structure pr3 4)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 114,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "\n",
-      "----------------------------------------------------------------------{CMBN -1}\n",
-      "------------------------------------------------------------------------------\n",
-      " \n",
-      "\n",
-      "----------------------------------------------------------------------{CMBN 0}\n",
-      "------------------------------------------------------------------------------\n",
-      " \n",
-      "\n",
-      "----------------------------------------------------------------------{CMBN 1}\n",
-      "------------------------------------------------------------------------------\n",
-      " \n",
-      "\n",
-      "----------------------------------------------------------------------{CMBN 2}\n",
-      "------------------------------------------------------------------------------\n",
-      " \n",
-      "\n",
-      "----------------------------------------------------------------------{CMBN 3}\n",
-      "<2 * 3>\n",
-      "------------------------------------------------------------------------------\n",
-      " \n",
-      "\n",
-      "----------------------------------------------------------------------{CMBN 4}\n",
-      "------------------------------------------------------------------------------\n",
-      " \n",
-      "\n",
-      "----------------------------------------------------------------------{CMBN 5}\n",
-      "<2 * 5>\n",
-      "------------------------------------------------------------------------------\n",
-      " "
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 114,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(dotimes (i 7)  (print (? pr3 i i)))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Let us use now the parameter *l*, allowing the truncation in the upper dimensions."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 115,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K116 Simplicial-Set]"
-      ]
-     },
-     "execution_count": 115,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def p12 (R-proj-space 1 2))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 116,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "\n",
-      "Dimension = 0:\n",
-      "\n",
-      "        Vertices :  (0)\n",
-      "\n",
-      "Dimension = 1:\n",
-      "\n",
-      "        Simplex : 1\n",
-      "\n",
-      "                Faces : (<AbSm - 0> <AbSm - 0>)\n",
-      "\n",
-      "Dimension = 2:"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 116,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(show-structure p12 2)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Setting $k=l$ does not creates something amazing!"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 117,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K121 Simplicial-Set]"
-      ]
-     },
-     "execution_count": 117,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def p22 (R-proj-space 2 2))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 118,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "\n",
-      "Dimension = 0:\n",
-      "\n",
-      "        Vertices :  (0)\n",
-      "\n",
-      "Dimension = 1:\n",
-      "\n",
-      "Dimension = 2:"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 118,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(show-structure p22 2)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 119,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K126 Simplicial-Set]"
-      ]
-     },
-     "execution_count": 119,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def p47 (R-proj-space 4 7))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 120,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "\n",
-      "Dimension = 0:\n",
-      "\n",
-      "        Vertices :  (0)\n",
-      "\n",
-      "Dimension = 1:\n",
-      "\n",
-      "Dimension = 2:\n",
-      "\n",
-      "Dimension = 3:\n",
-      "\n",
-      "Dimension = 4:\n",
-      "\n",
-      "        Simplex : 4\n",
-      "\n",
-      "                Faces : (<AbSm 2-1-0 0> <AbSm 2-1-0 0> <AbSm 2-1-0 0> <AbSm 2-1-0 0> <AbSm 2-1-0 0>)\n",
-      "\n",
-      "Dimension = 5:\n",
-      "\n",
-      "        Simplex : 5\n",
-      "\n",
-      "                Faces : (<AbSm - 4> <AbSm 3-2-1-0 0> <AbSm 3-2-1-0 0> <AbSm 3-2-1-0 0> <AbSm 3-2-1-0 0> <AbSm - 4>)\n",
-      "\n",
-      "Dimension = 6:\n",
-      "\n",
-      "        Simplex : 6\n",
-      "\n",
-      "                Faces : (<AbSm - 5> <AbSm 0 4> <AbSm 1 4> <AbSm 2 4> <AbSm 3 4> <AbSm 4 4> <AbSm - 5>)\n",
-      "\n",
-      "Dimension = 7:\n",
-      "\n",
-      "Dimension = 8:"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 120,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(show-structure p47 8)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "## Cartesian product of  simplicials sets\n",
-    "\n",
-    "Let $X$ and $Y$ be two simplicial sets, the construction of $X\\times Y$ is based on the very definition $(X\\times Y)_n =X_n\\times Y_n$ where $X_n$, $Y_n$ and $(X\\times Y)_n$ are the *possibly degenerate* simplices of $X$, $Y$ and $X\\times Y$\n",
-    "respectively. A simplex of the product $X\\times Y$ is characterized  by its projections on the factors $X$ and $Y$.\n",
-    "\n",
-    "The *non-degenerate* simplices of $X\\times Y$  are represented internally in the system by a lisp object of the form:\n",
-    "\n",
-    "```commonlisp\n",
-    "#S(CRPR :DGOP1 n1 :GMSM1 a1 :DGOP2 n2 :GMSM2 a2)\n",
-    "```\n",
-    "\n",
-    "where,\n",
-    "1. `n1` is an integer representing a coded degeneracy operator.\n",
-    "2. `a1` is a non-degenerate simplex of $X$, to which is applied the degeneracy operator `dgop1`.\n",
-    "3. `n2` is an integer representing a coded degeneracy operator.\n",
-    "4. `a2` is a non-degenerate simplex of $Y$, to which is applied the degeneracy operator `dgop2`.\n",
-    "\n",
-    "This object must be a *non-degenerate* simplex of $X \\times Y$, that is to say, the degeneracy operators *dgop1* and *dgop2* must not have a common $\\eta_j$, and therefore their list representations must have a void intersection.\n",
-    "The coded representation by  binary bit positions, has the same property. The corresponding type is `CRPR`.\n",
-    "To construct such an object, one may use the macro `crpr`. As usual, a printing method has been defined to reflect the structure of the product under the form:\n",
-    "\n",
-    "> `<CrPr` *ext-dgop1 gmsm1 ext-dgop2 gmsm2*`>`\n",
-    "\n",
-    "where  the sequence of the operators $\\eta_i$ is printed in explicit form (this is the meaning of *ext-dgop*).\n",
-    "If this sequence of $\\eta_i$  is void, i.e. if the simplex *gmsm* is not degenerate, the symbol `-` is printed instead.\n",
-    "\n",
-    "### Functions and macros for the product of simplicial sets\n",
-    "\n",
-    "`crpr` *dgop1 gmsm1 dgop2 gmsm2* *[Macro]*\n",
-    "> Build an object of type `CRPR`, using directly the integer coding for the degeneracy operators. The arguments *gmsm1* and *gmsm2* are non-degenerate simplices.\n",
-    "\n",
-    "`crpr` *absm1 absm2* *[Macro]*\n",
-    "> Build an object of type `CRPR`, using two abstract simplices *absm1* and *absm2*. If these abstract simplices are degenerate, the degeneracy operators must verify the condition of the definition, i.e. no common $\\eta_i$.\n",
-    "\n",
-    "`2absm-acrpr` *absm1 absm2* *[Function]*\n",
-    "> Build an abstract simplex, i.e. object of type `ABSM`, cartesian product of both abstract simplices *absm1* and *absm2*. In contrast with the previous function, there is no condition upon the degeneracy operators of the abstract simplices. Of course, the function `2absm-acrpr` returns a legal abstract simplex in normalized form.\n",
-    "\n",
-    "`crpr-p` *object* *[Predicate]*\n",
-    ">Test if *object* is of type `CRPR`.\n",
-    "\n",
-    "`dgop1` *crpr* *[Macro]*\n",
-    "> Select the degeneracy operator *dgop1* from the object `crpr`.\n",
-    "\n",
-    "`gmsm1` *crpr* *[Macro]*\n",
-    "> Select the geometric simplex *gmsm1* from the object `crpr`.\n",
-    "\n",
-    "`dgop2` *crpr* *[Macro]*\n",
-    "> Select the degeneracy operator *dgop2* from the object `crpr`.\n",
-    "\n",
-    "`gmsm2` *crpr* *[Macro]*\n",
-    "> Select the geometric simplex *gmsm2* from the object `crpr`.\n",
-    "\n",
-    "`absm1` *crpr* *[Macro]*\n",
-    "> Build the abstract simplex `(absm` *dgop1 gmsm1*`)` from *crpr*.\n",
-    "\n",
-    "`absm2` *crpr* *[Macro]*\n",
-    "> Build the abstract simplex `(absm` *dgop2 gmsm2*`)` from *crpr*.\n",
-    "\n",
-    "`crts-prdc` *smst1 smst2* *[Function]*\n",
-    "> Build the simplicial set, cartesian product $smst1 \\times smts2$.\n",
-    "\n",
-    "### Examples\n",
-    "\n",
-    "In the first example, note that the coded representations of $\\eta_1$ and $\\eta_2$ are respectively 2 and 4, but these degeneracy operators appear clearly as 1 and 2 in the printed result. In the second statement, the integer 28 is the coded representation of the degeneracy `(4 3 2)`."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 121,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "<CrPr 1 A 2 B>"
-      ]
-     },
-     "execution_count": 121,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(crpr 2 'a 4 'b)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 122,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "<CrPr - (0 1 2 3 4 5) 4-3-2 (0 1 2)>"
-      ]
-     },
-     "execution_count": 122,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(crpr 0 '(0 1 2 3 4 5) 28 '(0 1 2))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "For more clarity, one may also write:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 123,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "<CrPr - (0 1 2 3 4 5) 4-3-2 (0 1 2)>"
-      ]
-     },
-     "execution_count": 123,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(crpr 0 '(0 1 2 3 4 5) (dgop-ext-int '(4 3 2)) '(0 1 2))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "In the following example, we see that both functions `crpr` and `2absm-acrpr` return the same geometric simplex,"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 124,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "<CrPr 2 A 1-0 B>"
-      ]
-     },
-     "execution_count": 124,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(crpr (absm 4 'a)(absm 3 'b))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 125,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "<AbSm - <CrPr 2 A 1-0 B>>"
-      ]
-     },
-     "execution_count": 125,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(2absm-acrpr (absm 4 'a)(absm 3 'b))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "whereas, in the following call to `crpr`, the condition upon the degeneracy operator is not respected and the result is an illegal cartesian product. The function `2absm-acrpr` returns the correct answer."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 126,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "<CrPr 2-0 A 1-0 B>"
-      ]
-     },
-     "execution_count": 126,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(crpr (absm 5 'a)(absm 3 'b))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 127,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "<AbSm 0 <CrPr 1 A 0 B>>"
-      ]
-     },
-     "execution_count": 127,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(2absm-acrpr (absm 5 'a) (absm 3 'b))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "The following example is particularly instructive. The simplicial set whose the realization is homeomorphic to the  square is built by using the product of two segments. A call like `(delta n)` builds  the standard $n$-simplex. So first, we generate two copies `X` and `Y` of the standard 1-simplex and we list the abstract simplices up to dimension 2 for a better understanding of the components of the product `XY`."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 128,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K131 Simplicial-Set]"
-      ]
-     },
-     "execution_count": 128,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def X (delta 1))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 129,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K131 Simplicial-Set]"
-      ]
-     },
-     "execution_count": 129,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def Y X)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 130,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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",
-      "text/plain": [
-       "#<CL-JUPYTER-USER::PNG-BYTES {100530B593}>"
-      ]
-     },
-     "execution_count": 130,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(cl-jupyter-user:png-from-file \"ssquare.png\")"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "In list representation (non-coded simplices), the  abstract simplices of $X$ up to the dimension 2, including the degenerate ones are:\n",
-    "\n",
-    "- Dimension 0: `<AbSm - (0)>, <AbSm - (1)>`. \n",
-    "- Dimension 1: `<AbSm 0 (0)>,  <AbSm 0 (1)>,  <AbSm - (0 1)>`. \n",
-    "- Dimension 2: `<AbSm 1-0 (0)>, <AbSm 1-0 (1)>,  <AbSm 0 (0 1)>, <AbSm 1 (0 1)>`.\n",
-    "\n",
-    "Let us look first at the non-degenerate simplices of the simplicial set $X \\times Y$. Those simplices are objects of type `CRPR`. In dimension 1, we see that some projections are degeneracies of vertices and, in dimension 2, the projections are all degeneracies of the 1-simplex `(0 1)` coded as 3. Nevertheless, all the listed simplices are *geometric* simplices (i.e. non-degenerate ones) of the product `XY`. The diagram above shows the relationship between the 3 simplicial sets. "
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 131,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K136 Simplicial-Set]"
-      ]
-     },
-     "execution_count": 131,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def XY (crts-prdc X Y))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 132,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "\n",
-      "Dimension = 0:\n",
-      "\n",
-      "        Vertices :  (<CrPr - 1 - 1> <CrPr - 1 - 2> <CrPr - 2 - 1> <CrPr - 2 - 2>)\n",
-      "\n",
-      "Dimension = 1:\n",
-      "\n",
-      "        Simplex : <CrPr - 3 - 3>\n",
-      "\n",
-      "                Faces : (<AbSm - <CrPr - 2 - 2>> <AbSm - <CrPr - 1 - 1>>)\n",
-      "\n",
-      "        Simplex : <CrPr - 3 0 1>\n",
-      "\n",
-      "                Faces : (<AbSm - <CrPr - 2 - 1>> <AbSm - <CrPr - 1 - 1>>)\n",
-      "\n",
-      "        Simplex : <CrPr - 3 0 2>\n",
-      "\n",
-      "                Faces : (<AbSm - <CrPr - 2 - 2>> <AbSm - <CrPr - 1 - 2>>)\n",
-      "\n",
-      "        Simplex : <CrPr 0 1 - 3>\n",
-      "\n",
-      "                Faces : (<AbSm - <CrPr - 1 - 2>> <AbSm - <CrPr - 1 - 1>>)\n",
-      "\n",
-      "        Simplex : <CrPr 0 2 - 3>\n",
-      "\n",
-      "                Faces : (<AbSm - <CrPr - 2 - 2>> <AbSm - <CrPr - 2 - 1>>)\n",
-      "\n",
-      "Dimension = 2:\n",
-      "\n",
-      "        Simplex : <CrPr 0 3 1 3>\n",
-      "\n",
-      "                Faces : (<AbSm - <CrPr - 3 0 2>> <AbSm - <CrPr - 3 - 3>> <AbSm - <CrPr 0 1 - 3>>)\n",
-      "\n",
-      "        Simplex : <CrPr 1 3 0 3>\n",
-      "\n",
-      "                Faces : (<AbSm - <CrPr 0 2 - 3>> <AbSm - <CrPr - 3 - 3>> <AbSm - <CrPr - 3 0 1>>)"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 132,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(show-structure XY 2)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "To be more readable we may translate the coded representations of the degeneracy operators and of the simplices in the list representation:"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "```\n",
-    "Dimension 0 :\n",
-    "\n",
-    "        Vertices : (<CrPr - (0) - (0)> \n",
-    "                    <CrPr - (0) - (1)> \n",
-    "                    <CrPr - (1) - (0)> \n",
-    "                    <CrPr - (1) - (1)>)\n",
-    "\n",
-    "Dimension 1 :\n",
-    "\n",
-    "        Simplex : <CrPr 0 (0) - (0 1)>\n",
-    "\n",
-    "                Faces : (<AbSm - <CrPr - (0) - (1)> >\n",
-    "                         <AbSm - <CrPr - (0) - (0)> >)\n",
-    "\n",
-    "        Simplex : <CrPr 0 (1) - (0 1)>\n",
-    "\n",
-    "                Faces : (<AbSm - <CrPr - (1) - (1)> >\n",
-    "                         <AbSm - <CrPr - (1) - (0)> >)\n",
-    "\n",
-    "        Simplex : <CrPr - (0 1) 0 (0)>\n",
-    "\n",
-    "                Faces : (<AbSm - <CrPr - (1) - (0)> >\n",
-    "                         <AbSm - <CrPr - (0) - (0)> >)\n",
-    "\n",
-    "        Simplex : <CrPr - (0 1) 0 (1)>\n",
-    "\n",
-    "                Faces : (<AbSm - <CrPr - (1) - (1)> >\n",
-    "                         <AbSm - <CrPr - (0) - (1)> >)\n",
-    "\n",
-    "        Simplex : <CrPr - (0 1) - (0 1)>\n",
-    "\n",
-    "                Faces : (<AbSm - <CrPr - (1) - (1)> >\n",
-    "                         <AbSm - <CrPr - (0) - (0)> >)\n",
-    "\n",
-    "Dimension 2 :\n",
-    "\n",
-    "        Simplex : <CrPr 0 (0 1) 1 (0 1)>\n",
-    "\n",
-    "                Faces : (<AbSm - <CrPr - (0 1) 0 (1)> >\n",
-    "                         <AbSm - <CrPr - (0 1) - (0 1)> >\n",
-    "                         <AbSm - <CrPr 0 (0) - (0 1)> >)\n",
-    "\n",
-    "        Simplex : <CrPr 1 (0 1) 0 (0 1)>\n",
-    "\n",
-    "                Faces : (<AbSm - <CrPr 0 (1) - (0 1)> >\n",
-    "                         <AbSm - <CrPr - (0 1) - (0 1)> >\n",
-    "                         <AbSm - <CrPr - (0 1) 0 (0)> >)\n",
-    "```\n",
-    "\n",
-    "In an analogous way, let us build the torus as the cartesian product of two 1-spheres. We recall that the base point of the sphere is named `*`."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 133,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K146 Simplicial-Set]"
-      ]
-     },
-     "execution_count": 133,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def s1xs1 (crts-prdc (sphere 1) (sphere 1)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 134,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "\n",
-      "Dimension = 0:\n",
-      "\n",
-      "        Vertices :  (<CrPr - * - *>)\n",
-      "\n",
-      "Dimension = 1:\n",
-      "\n",
-      "        Simplex : <CrPr - S1 - S1>\n",
-      "\n",
-      "                Faces : (<AbSm - <CrPr - * - *>> <AbSm - <CrPr - * - *>>)\n",
-      "\n",
-      "        Simplex : <CrPr - S1 0 *>\n",
-      "\n",
-      "                Faces : (<AbSm - <CrPr - * - *>> <AbSm - <CrPr - * - *>>)\n",
-      "\n",
-      "        Simplex : <CrPr 0 * - S1>\n",
-      "\n",
-      "                Faces : (<AbSm - <CrPr - * - *>> <AbSm - <CrPr - * - *>>)\n",
-      "\n",
-      "Dimension = 2:\n",
-      "\n",
-      "        Simplex : <CrPr 0 S1 1 S1>\n",
-      "\n",
-      "                Faces : (<AbSm - <CrPr - S1 0 *>> <AbSm - <CrPr - S1 - S1>> <AbSm - <CrPr 0 * - S1>>)\n",
-      "\n",
-      "        Simplex : <CrPr 1 S1 0 S1>\n",
-      "\n",
-      "                Faces : (<AbSm - <CrPr 0 * - S1>> <AbSm - <CrPr - S1 - S1>> <AbSm - <CrPr - S1 0 *>>)"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 134,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(show-structure s1xs1 2)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Let us verify that  $S^1\\times S^1$ has  the same  homology groups as the torus."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 135,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "Computing boundary-matrix in dimension 0.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 18m 31s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 0) :\n",
-      "<CrPr - * - *> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 1.\n",
-      "Rank of the source-module : 3.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 18m 31s.\n",
-      "Computing the boundary of the generator 1/3 (dimension 1) :\n",
-      "<CrPr - S1 - S1> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 18m 31s.\n",
-      "Computing the boundary of the generator 2/3 (dimension 1) :\n",
-      "<CrPr - S1 0 *> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 18m 31s.\n",
-      "Computing the boundary of the generator 3/3 (dimension 1) :\n",
-      "<CrPr 0 * - S1> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 0 :\n",
-      "\n",
-      "\n",
-      "Component Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "Computing boundary-matrix in dimension 1.\n",
-      "Rank of the source-module : 3.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 18m 31s.\n",
-      "Computing the boundary of the generator 1/3 (dimension 1) :\n",
-      "<CrPr - S1 - S1> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 18m 31s.\n",
-      "Computing the boundary of the generator 2/3 (dimension 1) :\n",
-      "<CrPr - S1 0 *> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 18m 31s.\n",
-      "Computing the boundary of the generator 3/3 (dimension 1) :\n",
-      "<CrPr 0 * - S1> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 2.\n",
-      "Rank of the source-module : 2.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 18m 31s.\n",
-      "Computing the boundary of the generator 1/2 (dimension 2) :\n",
-      "<CrPr 0 S1 1 S1> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 18m 31s.\n",
-      "Computing the boundary of the generator 2/2 (dimension 2) :\n",
-      "<CrPr 1 S1 0 S1> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 1 :\n",
-      "\n",
-      "\n",
-      "Component Z\n",
-      "\n",
-      "Component Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "Computing boundary-matrix in dimension 2.\n",
-      "Rank of the source-module : 2.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 18m 31s.\n",
-      "Computing the boundary of the generator 1/2 (dimension 2) :\n",
-      "<CrPr 0 S1 1 S1> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 18m 31s.\n",
-      "Computing the boundary of the generator 2/2 (dimension 2) :\n",
-      "<CrPr 1 S1 0 S1> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 3.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 2 :\n",
-      "\n",
-      "\n",
-      "Component Z\n",
-      "\n",
-      "\n",
-      "---done---"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 135,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(dotimes (i 3)(chcm-homology s1xs1 i))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Of course, we may generate more complex products, whose basis are composed of rather long\n",
-    "lists of simplices as shown below. The user will also pay attention to the fact that the composition of the macro `crpr` is not associative. In the following example, the simplicial sets located respectively by `p1` and `p2` are different objects, though being canonically isomorphic."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 136,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K156 Simplicial-Set]"
-      ]
-     },
-     "execution_count": 136,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def p1 (crts-prdc (sphere 2) (crts-prdc (sphere 2) (sphere 3))))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 137,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K166 Simplicial-Set]"
-      ]
-     },
-     "execution_count": 137,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def p2 (crts-prdc (crts-prdc (sphere 2) (sphere 2)) (sphere 3)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 138,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "1 \n",
-      "0 \n",
-      "3 \n",
-      "22 \n",
-      "138 \n",
-      "390 \n",
-      "480 \n",
-      "210 "
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 138,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(dotimes (i 8) (print (length (basis p1 i))))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "### Lisp files concerned in this chapter\n",
-    "\n",
-    "`simplicial-sets.lisp`, `delta.lisp`, `specials-smsts.lisp`, `cartesian-products.lisp`.\n",
-    "\n",
-    "[`classes.lisp`, `macros.lisp`, `various.lisp`]."
-   ]
-  }
- ],
- "metadata": {
-  "kernelspec": {
-   "display_name": "SBCL Lisp",
-   "language": "lisp",
-   "name": "lisp"
-  },
-  "language_info": {
-   "codemirror_mode": "text/x-common-lisp",
-   "mimetype": "text/x-common-lisp",
-   "name": "common-lisp",
-   "pygments_lexer": "common-lisp",
-   "version": "X3J13"
-  }
- },
- "nbformat": 4,
- "nbformat_minor": 1
-}
diff --git a/examples/08_Simplicial_morphisms.ipynb b/examples/08_Simplicial_morphisms.ipynb
deleted file mode 100644
index b4f0168..0000000
--- a/examples/08_Simplicial_morphisms.ipynb
+++ /dev/null
@@ -1,357 +0,0 @@
-{
- "cells": [
-  {
-   "cell_type": "code",
-   "execution_count": 1,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "To load \"kenzo\":\n",
-      "  Load 1 ASDF system:\n",
-      "    kenzo\n",
-      "; Loading \"kenzo\"\n",
-      "\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "#<PACKAGE \"CAT\">"
-      ]
-     },
-     "execution_count": 1,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(ql:quickload \"kenzo\")\n",
-    "(in-package :cat)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "# Simplicial morphisms\n",
-    "\n",
-    "The program `Kenzo` implements simplicial morphisms in a way analogous to chain complex morphisms.\n",
-    "\n",
-    "## Representation of a  simplicial morphism\n",
-    "\n",
-    "A simplicial morphism is  an instance of the class `SIMPLICIAL-MRPH`, subclass of the class `MORPHISM`.\n",
-    "\n",
-    "```commonlisp\n",
-    "(DEFCLASS SIMPLICIAL-MRPH (morphism)\n",
-    "  ((sintr :type sintr :initarg :sintr :reader sintr)))\n",
-    "```\n",
-    "\n",
-    "It has one slot of its own:\n",
-    "> `sintr`, an object of type `SINTR`, in fact a lisp function defining the morphism between the source and target simplicial sets. It must have  2 parameters:  a dimension (an integer) and a geometric simplex of this dimension (a generator of any type) . It must return  an abstract simplex, image in the target simplicial set of this geometric simplex.\n",
-    "\n",
-    "A printing method has been associated to the class `SIMPLICIAL-MRPH`. A string like `[Simplicial-Morphism K`*s* `-> K`*t*`]` is the  external representation of an instance of such a class, where *s* (resp. *t*) is the identification number of the source (resp. target) simplicial set. \n",
-    "\n",
-    "## The function `build-smmr`\n",
-    "\n",
-    "To facilitate the construction of instances of the class `SIMPLICIAL-MRPH` and to free  the user to call the standard constructor `make-instance`, the program provides the function\n",
-    "\n",
-    "```commonlisp\n",
-    "build-smmr :sorc sorc :trgt trgt :degr degr :sintr sintr :intr intr :strt strt :orgn orgn\n",
-    "```\n",
-    "\n",
-    "defined with keyword parameters and returning an instance of the class `SIMPLICIAL-MRPH`. The keyword arguments of `build-smmr` are:\n",
-    "\n",
-    "- *sorc*, the source object, an object of type `SIMPLICIAL-SET`.\n",
-    "- *trgt*, the target object, an object of type `SIMPLICIAL-SET`.\n",
-    "- *degr*, the degree of the morphism, an integer. In this chapter, we  consider only the 0 degree case (the usual one). The case -1 is particularly important: it allows to implement the notion of twisting operator defining a fibration (See the chapter Fibration).\n",
-    "- *sintr*, the internal lisp function defining the effective mapping between simplicial sets. This argument is mandatory. If the integer *degr* is 0 and if the following keyword argument *intr* is omitted, then the function `build-smmr` builds a lisp function implementing the induced mapping between the underlying source and target chain complexes. This function is installed in the slot `intr`. The strategy is then set to `:gnrt`.\n",
-    "- `intr`, a user defined morphism for the underlying chain complexes. This argument is optional and taken in account only if the degree is 0 and in this case, supersedes the previous derived  mapping. The strategy is then mandatory. If the degree is not null, the implementor has decided  to set the corresponding slot to `NIL`.\n",
-    "- *strt*, the strategy, i.e. `:gnrt` or `:cmbn` attached to the previous function.\n",
-    "- *orgn*, a relevant comment list.\n",
-    "\n",
-    "After a call to `build-smmr`, the simplicial morphism instance is added to a list of previously constructed  ones (`*smmr-list*`). As the other similar lists, the list `*smmr-list*` may be cleared by the function `cat-init`.\n",
-    "\n",
-    "The effective application of a simplicial morphism upon arguments, is realized with the macro `?` which  calls the adequate method defined for this kind of objects.\n",
-    "\n",
-    "`? &rest` *args* *[Macro]*\n",
-    "> Versatile macro for applying a simplicial morphism indifferently as `(?` *smmr dmns absm-or-gmsm*`)` or  `(?` *smmr cmbn*`)`. In the first case, the third argument is either an abstract simplex or a geometric one. In the second case, if the second argument is a combination, *smmr* is then considered as a chain complex  morphism and it is the function in the slot `intr` which is applied, so that it makes sense only if the degree of the mapping is 0.\n",
-    "\n",
-    "### Examples\n",
-    "\n",
-    "In the following examples, we work with $\\Delta^3$. We define three simplicial morphisms, `sm1`, `sm2` and `sm3`. In `sm1`, the mapping is the identity mapping and we can see that this identity mapping has been propagated on the underlying chain complex."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 2,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K1 Simplicial-Set]"
-      ]
-     },
-     "execution_count": 2,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def d3 (delta 3))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 3,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K6 Simplicial-Morphism K1 -> K1]"
-      ]
-     },
-     "execution_count": 3,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def sm1 (build-smmr\n",
-    "            :sorc d3 :trgt d3 :degr 0\n",
-    "            :sintr #'(lambda (dmns gmsm)\n",
-    "                             (declare (ignore dmns))\n",
-    "                             (absm 0 gmsm))\n",
-    "            :orgn '(identity delta-3)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 4,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "<AbSm - 7>"
-      ]
-     },
-     "execution_count": 4,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? sm1 2 7)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 5,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "<AbSm 0 1>"
-      ]
-     },
-     "execution_count": 5,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? sm1 1 (absm 1 1))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 6,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 2}\n",
-       "<1 * 7>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 6,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? sm1 (cmbn 2 1 7))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "In the simplicial morphism `sm2`, the mapping is the \"null\" mapping. In fact, it consists in  applying any abstract simplex in dimension $n$ upon the $n$-degenerate base point. Of course, in terms of chain complex, the corresponding mapping applies any chain complex element upon the null combination of same degree, except in degree 0."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 7,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K7 Simplicial-Morphism K1 -> K1]"
-      ]
-     },
-     "execution_count": 7,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def sm2 (build-smmr\n",
-    "            :sorc d3 :trgt d3 :degr 0\n",
-    "            :sintr #'(lambda (dmns gmsm)\n",
-    "                             (declare (ignore gmsm))\n",
-    "                             (absm (mask dmns) 1))    ;;; mask(n)=2^n - 1 \n",
-    "            :orgn '(null delta-3)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 8,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "<AbSm - 1>"
-      ]
-     },
-     "execution_count": 8,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? sm2 0 4)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 9,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "<AbSm 1-0 1>"
-      ]
-     },
-     "execution_count": 9,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? sm2 2 7)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 10,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "<AbSm 0 1>"
-      ]
-     },
-     "execution_count": 10,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? sm2 1 (absm 1 1))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 11,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "<AbSm 2-1-0 1>"
-      ]
-     },
-     "execution_count": 11,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? sm2 3 15)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 12,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 3}\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 12,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? sm2 (cmbn 3 2 15))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "### Lisp files concerned in this chapter\n",
-    "\n",
-    "`simplicial-mrphs.lisp`.\n",
-    "\n",
-    "[`classes.lisp`, `macros.lisp`, `various.lisp`]."
-   ]
-  }
- ],
- "metadata": {
-  "kernelspec": {
-   "display_name": "SBCL Lisp",
-   "language": "lisp",
-   "name": "lisp"
-  },
-  "language_info": {
-   "codemirror_mode": "text/x-common-lisp",
-   "mimetype": "text/x-common-lisp",
-   "name": "common-lisp",
-   "pygments_lexer": "common-lisp",
-   "version": "X3J13"
-  }
- },
- "nbformat": 4,
- "nbformat_minor": 1
-}
diff --git a/examples/09_The_Eilenberg-Zilber_module.ipynb b/examples/09_The_Eilenberg-Zilber_module.ipynb
deleted file mode 100644
index 60b882b..0000000
--- a/examples/09_The_Eilenberg-Zilber_module.ipynb
+++ /dev/null
@@ -1,2366 +0,0 @@
-{
- "cells": [
-  {
-   "cell_type": "code",
-   "execution_count": 1,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "To load \"kenzo\":\n",
-      "  Load 1 ASDF system:\n",
-      "    kenzo\n",
-      "; Loading \"kenzo\"\n",
-      "\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "#<PACKAGE \"CAT\">"
-      ]
-     },
-     "execution_count": 1,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(ql:quickload \"kenzo\")\n",
-    "(in-package :cat)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "# The Eilenberg-Zilber module\n",
-    "\n",
-    "The functions of this module are related to the chain complex of the product of two simplicial sets. They implement the Eilenberg-Mac Lane morphism (function `eml`) and the Alexander-Whitney morphism  (function `aw`).\n",
-    "\n",
-    "`eml` *ssx ssy* *[Function]*\n",
-    "> build the Eilenberg-Mac Lane homomorphism $\\cal EML$, also called the *shuffle homomorphism*. (**Marvin Greenberg**, *Lectures on Algebraic Topology*, W.A. Benjamin Inc, 1967.) The arguments *ssx* and *ssy* represent some simplicial sets $X$ and $Y$. The homomorphism \n",
-    "$${\\cal EML}:{\\cal C}_*(X) \\otimes {\\cal C}_*(Y) \\longrightarrow {\\cal C}_*(X \\times Y)$$\n",
-    "is defined by:\n",
-    "$${\\cal EML}(\\alpha \\otimes \\beta)= \n",
-    " \\sum{{\\varepsilon(\\varpi)}(\\eta_{j_q}\\ldots \\eta_{j_1}\\alpha,\\, \\eta_{i_p}\\ldots \\eta_{i_1}\\beta)},$$\n",
-    "where $X\\times Y$ is the simplicial cartesian product of the two simplicial sets $X$ and $Y$,  $\\alpha$ (resp. $\\beta$) is a geometric simplex of $X$ (resp. $Y$), $\\eta_k$ is the $k^{th}$ degeneracy operator, the sum is over all permutations $\\varpi = (i_1, \\ldots, i_p, j_1, \\ldots, j_q)$ of $(0, \\ldots, p+q-1)$ such that $$ i_1 < i_2 < \\cdots < i_p,\\quad j_1 < j_2 < \\cdots < j_q, \\quad p+q=n$$\n",
-    "and $\\varepsilon(\\varpi)$ is the signature of the corresponding permutation. The sum at the right hand part determines a decomposition of the geometric product $\\alpha \\times \\beta$ into a combination of generators of the simplicial cartesian product (see the simplicial sets chapter). The combination takes in account the orientation of every simplex. These generators are non-degenerate simplices of the cartesian product but their projections are in general degenerate simplices of $X$ and $Y$ (see the examples).\n",
-    " \n",
-    "`aw` *ssx ssy* *[Function]*\n",
-    "> build the Alexander-Whitney chain homomorphism. The arguments *ssx* and *ssy* represent some simplicial sets $X$ and $Y$. The homomorphism \n",
-    "$${\\cal AW}:{\\cal C}_*(X \\times Y) \\longrightarrow {\\cal C}_*(X) \\otimes {\\cal C}_*(Y)$$\n",
-    "is defined by the following rule: let $\\sigma$ be an $n$-simplex and let us define\n",
-    "two operators, $\\lambda_p$ and $\\rho_q$:\n",
-    "$$\\lambda_p: {\\cal C}_n(X) \\longrightarrow {\\cal C}_{n-p}(X),\\quad (n \\geq p),$$\n",
-    "$$\\rho_q: {\\cal C}_n(Y) \\longrightarrow {\\cal C}_{n-q}(X),\\quad (n \\geq q),$$\n",
-    "respectively by\n",
-    "$$\\lambda_p(\\sigma)=\\partial_{p+1}\\ldots \\partial_n \\sigma$$\n",
-    "and\n",
-    "$$\\rho_q(\\sigma)=\\partial_0\\ldots\\partial_{n-1} \\sigma.$$\n",
-    "Now, for the generator $(\\alpha,\\beta)$  of degree $n$ in ${\\cal C}_*(X \\times Y)$, the Alexander-Whitney morphism is defined  by:\n",
-    "$${\\cal AW}(\\alpha, \\beta)=\\sum_{p=0}^n{\\lambda_p(\\alpha) \\otimes \\rho_{n-p}(\\beta)}.$$\n",
-    "This sum can be interpreted as a decomposition, up to a homotopy, of the simplex $\\alpha \\times \\beta$\n",
-    "($\\alpha$ **and** $\\beta$ can be degenerate even if $\\alpha \\times \\beta$ is not) in terms of (tensor) products of non-degenerate simplices.\n",
-    "\n",
-    "`phi` *ssx ssy* *[Function]*\n",
-    "> build the homotopy chain morphism \n",
-    "$$\\Phi: {\\cal C}_*(X \\times Y) \\longrightarrow {\\cal C}_*(X \\times Y)$$\n",
-    "satisfying the formula\n",
-    "$$d \\circ \\Phi + \\Phi \\circ d = Id - {\\cal EML} \\circ {\\cal AW}.$$\n",
-    "\n",
-    "`ez` *ssx ssy* *[Function]*\n",
-    "> build the Eilenberg--Zilber reduction as shown by the following diagram, where $X={\\mathit ssx}$ \n",
-    "and $Y={\\mathit ssy}$.\n",
-    "$$\n",
-    "\\begin{aligned}\n",
-    "{{\\cal C}_*(X \\times Y)}\\quad & \\quad \\stackrel{\\Phi}{\\longrightarrow} & {}^s{{\\cal C}_*(X \\times Y)} \\cr\n",
-    " {\\scriptstyle {\\cal AW}} \\downarrow \\uparrow {\\scriptstyle {\\cal EML}}  & & \\cr\n",
-    " {{\\cal C}_*(X) \\otimes {\\cal C}_*(Y)} & &\\cr\n",
-    "\\end{aligned}\n",
-    "$$\n",
-    "\n",
-    "## Examples"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 2,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
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",
-      "text/plain": [
-       "#<CL-JUPYTER-USER::PNG-BYTES {1001A24463}>"
-      ]
-     },
-     "execution_count": 2,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(cl-jupyter-user:png-from-file \"eml1.png\")"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "As simplicial sets $X$ and $Y$, let us use two copies of $\\Delta^\\mathbb{N}$, that we may build by the lisp statement `(soft-delta-infinity)` (Though we repeat this statement in the following line, there will be only a simplicial set created). We have chosen the *soft* version, to inspect  the results more easily."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 3,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K11 Morphism (degree 0): K3 -> K6]"
-      ]
-     },
-     "execution_count": 3,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def eml-mrp (eml (soft-delta-infinity)(soft-delta-infinity)))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Let us apply the Eilenberg-Mac Lane homomorphism to the tensor product $(0\\, 1)\\otimes (2\\, 3)$:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 4,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 2}\n",
-       "<-1 * <CrPr 0 (DELT . 3) 1 (DELT . 12)>>\n",
-       "<1 * <CrPr 1 (DELT . 3) 0 (DELT . 12)>>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 4,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? eml-mrp 2 (tnpr 1 (d(dlop-ext-int '(0 1)))\n",
-    "                   1 (d(dlop-ext-int '(2 3)))))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "The decomposition is illustrated by the previous geometric diagram, where for instance a degenerate simplex like $\\eta_1(0\\, 1)$ is noted $(0\\, 1\\, 1)$.\n",
-    "\n",
-    "For the tensor product $(0\\,1\\,2)\\otimes (3\\,4)$, an intuitive description is still possible, as shown in the following diagram, but not in higher dimensions.\n",
-    "\n",
-    "As the input of simplices is sometimes cumbersome, we have defined a macro called `code` to facilitate the input of the simplices."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 5,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "CODE"
-      ]
-     },
-     "execution_count": 5,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(defmacro code (arg) `(d (dlop-ext-int ,arg)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 6,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 3}\n",
-       "<1 * <CrPr 0 (DELT . 7) 2-1 (DELT . 24)>>\n",
-       "<-1 * <CrPr 1 (DELT . 7) 2-0 (DELT . 24)>>\n",
-       "<1 * <CrPr 2 (DELT . 7) 1-0 (DELT . 24)>>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 6,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? eml-mrp 3 (tnpr 2 (code '(0 1 2)) 1 (code '(3 4)) ))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 7,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 6}\n",
-       "<1 * <CrPr 3-2-1-0 (DELT . 41) 5-4 (DELT . 55)>>\n",
-       "<-1 * <CrPr 4-2-1-0 (DELT . 41) 5-3 (DELT . 55)>>\n",
-       "<1 * <CrPr 4-3-1-0 (DELT . 41) 5-2 (DELT . 55)>>\n",
-       "<-1 * <CrPr 4-3-2-0 (DELT . 41) 5-1 (DELT . 55)>>\n",
-       "<1 * <CrPr 4-3-2-1 (DELT . 41) 5-0 (DELT . 55)>>\n",
-       "<1 * <CrPr 5-2-1-0 (DELT . 41) 4-3 (DELT . 55)>>\n",
-       "<-1 * <CrPr 5-3-1-0 (DELT . 41) 4-2 (DELT . 55)>>\n",
-       "<1 * <CrPr 5-3-2-0 (DELT . 41) 4-1 (DELT . 55)>>\n",
-       "<-1 * <CrPr 5-3-2-1 (DELT . 41) 4-0 (DELT . 55)>>\n",
-       "<1 * <CrPr 5-4-1-0 (DELT . 41) 3-2 (DELT . 55)>>\n",
-       "... ...\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 7,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? eml-mrp 6 (tnpr 2 (code '(0 3 5)) 4 (code '(0 1 2 4 5)) ))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 8,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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",
-      "text/plain": [
-       "#<CL-JUPYTER-USER::PNG-BYTES {100213FFC3}>"
-      ]
-     },
-     "execution_count": 8,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(cl-jupyter-user:png-from-file \"eml2.png\")"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "The Alexander-Whitney homomorphism works in the reverse sense:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 9,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K12 Morphism (degree 0): K6 -> K3]"
-      ]
-     },
-     "execution_count": 9,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def aw-mrp (aw (soft-delta-infinity)(soft-delta-infinity)))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "The 2-simplices of the cartesian product $(0\\, 1\\, 2) \\times (3\\, 4)$ are (here, the degeneracy operators are in clear):\n",
-    "\n",
-    "```\n",
-    "      <CrPr 0 (0 1) 1 (3 4)>\n",
-    "      <CrPr 1 (0 1) 0 (3 4)>\n",
-    "      <CrPr 0 (0 2) 1 (3 4)>\n",
-    "      <CrPr 1 (0 2) 0 (3 4)>\n",
-    "      <CrPr 0 (1 2) 1 (3 4)>\n",
-    "      <CrPr 1 (1 2) 0 (3 4)>\n",
-    "      <CrPr * (0 1 2) 1-0 (3)>\n",
-    "      <CrPr * (0 1 2) 1-0 (4)>\n",
-    " -->  <CrPr * (0 1 2) 0 (3 4)>\n",
-    "      <CrPr * (0 1 2) 1 (3 4)>\n",
-    "```\n",
-    "\n",
-    "The last but one line of this list describes the triangle shown in dashed lines in the prism in the previous picture, joining the points $(0,3), (1,3), (2,4)$. Let us apply  the homomorphism $\\cal AW$:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 10,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 2}\n",
-       "<1 * <TnPr (DELT . 3) (DELT . 24)>>\n",
-       "<1 * <TnPr (DELT . 7) (DELT . 16)>>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 10,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? aw-mrp 2 (crpr 0 (code '(0 1 2)) 1 (code '(3 4)) ))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "We see that we obtain  a kind of decomposition, up to a homotopy, of this triangle in terms of the two tensor products $(0\\, 1\\, 2) \\otimes (4)$ (the \"upper\" triangle of the prism) and $(0\\,1) \\otimes (3\\, 4)$ (the \"front\" rectangle of the prism).\n",
-    "\n",
-    "The composition ${\\cal AW} \\circ {\\cal EML}$ is the identity in the tensor product of the two chain complexes."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 11,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "<TnPr (DELT . 7) (DELT . 60)>"
-      ]
-     },
-     "execution_count": 11,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def g (tnpr 2 (code '(0 1 2)) 3 (code '(2 3 4 5)) ))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 12,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 5}\n",
-       "<1 * <CrPr 2-1-0 (DELT . 7) 4-3 (DELT . 60)>>\n",
-       "<-1 * <CrPr 3-1-0 (DELT . 7) 4-2 (DELT . 60)>>\n",
-       "<1 * <CrPr 3-2-0 (DELT . 7) 4-1 (DELT . 60)>>\n",
-       "<-1 * <CrPr 3-2-1 (DELT . 7) 4-0 (DELT . 60)>>\n",
-       "<1 * <CrPr 4-1-0 (DELT . 7) 3-2 (DELT . 60)>>\n",
-       "<-1 * <CrPr 4-2-0 (DELT . 7) 3-1 (DELT . 60)>>\n",
-       "<1 * <CrPr 4-2-1 (DELT . 7) 3-0 (DELT . 60)>>\n",
-       "<1 * <CrPr 4-3-0 (DELT . 7) 2-1 (DELT . 60)>>\n",
-       "<-1 * <CrPr 4-3-1 (DELT . 7) 2-0 (DELT . 60)>>\n",
-       "<1 * <CrPr 4-3-2 (DELT . 7) 1-0 (DELT . 60)>>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 12,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? eml-mrp 5 g)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 13,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 5}\n",
-       "<1 * <TnPr (DELT . 7) (DELT . 60)>>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 13,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? aw-mrp *)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 14,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "T"
-      ]
-     },
-     "execution_count": 14,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(setf *tnpr-with-degrees* t)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 15,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 5}\n",
-       "<1 * <TnPr 2 (DELT . 7) 3 (DELT . 60)>>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 15,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "**"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "But the composition ${\\cal EML} \\circ {\\cal AW}$ is by no means the identity. This composition\n",
-    "is related to the identity via the homotopy morphism $\\Phi$. Let us consider the two following simple simplicial sets `delta-0-1` and `delta-2-3`, where the second is the simplicial set, model of the segment $[2,\\,3]$. To build `delta-2-3`, we have just changed the basis function, the base point and the comment in the system function `soft-delta`."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 16,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K13 Simplicial-Set]"
-      ]
-     },
-     "execution_count": 16,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def delta-0-1 (soft-delta 1))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 17,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K18 Simplicial-Set]"
-      ]
-     },
-     "execution_count": 17,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def delta-2-3 (build-smst \n",
-    "                  :cmpr #'soft-delta-cmpr\n",
-    "                  :basis #'(lambda(dmn) \n",
-    "                             (case dmn\n",
-    "                                  (0 (list (d 4)(d 8)))\n",
-    "                                  (1 (list(d 12)))))   \n",
-    "                  :bspn (d 4)\n",
-    "                  :face #'soft-delta-face\n",
-    "                  :intr-dgnl #'soft-delta-dgnl :dgnl-strt :gnrt\n",
-    "                  :intr-bndr #'soft-delta-bndr :bndr-strt :gnrt\n",
-    "                  :orgn '(my-soft-delta-2-3)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 18,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "\n",
-      "Dimension = 0:\n",
-      "\n",
-      "        Vertices :  ((DELT . 1) (DELT . 2))\n",
-      "\n",
-      "Dimension = 1:\n",
-      "\n",
-      "        Simplex : (DELT . 3)\n",
-      "\n",
-      "                Faces : (<AbSm - (DELT . 2)> <AbSm - (DELT . 1)>)"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 18,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(show-structure delta-0-1 1)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 19,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "\n",
-      "Dimension = 0:\n",
-      "\n",
-      "        Vertices :  ((DELT . 4) (DELT . 8))\n",
-      "\n",
-      "Dimension = 1:\n",
-      "\n",
-      "        Simplex : (DELT . 12)\n",
-      "\n",
-      "                Faces : (<AbSm - (DELT . 8)> <AbSm - (DELT . 4)>)"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 19,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(show-structure delta-2-3 1)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Let us build the cartesian product of these two simplicial sets and let us list, in particular the 0-simplices and the 1-simplices of this new simplicial set:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 20,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K23 Simplicial-Set]"
-      ]
-     },
-     "execution_count": 20,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def carre (crts-prdc delta-0-1 delta-2-3))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 21,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "\n",
-      "Dimension = 0:\n",
-      "\n",
-      "        Vertices :  (<CrPr - (DELT . 1) - (DELT . 4)> <CrPr - (DELT . 1) - (DELT . 8)> <CrPr - (DELT . 2) - (DELT . 4)> <CrPr - (DELT . 2) - (DELT . 8)>)\n",
-      "\n",
-      "Dimension = 1:\n",
-      "\n",
-      "        Simplex : <CrPr - (DELT . 3) - (DELT . 12)>\n",
-      "\n",
-      "                Faces : (<AbSm - <CrPr - (DELT . 2) - (DELT . 8)>> <AbSm - <CrPr - (DELT . 1) - (DELT . 4)>>)\n",
-      "\n",
-      "        Simplex : <CrPr - (DELT . 3) 0 (DELT . 4)>\n",
-      "\n",
-      "                Faces : (<AbSm - <CrPr - (DELT . 2) - (DELT . 4)>> <AbSm - <CrPr - (DELT . 1) - (DELT . 4)>>)\n",
-      "\n",
-      "        Simplex : <CrPr - (DELT . 3) 0 (DELT . 8)>\n",
-      "\n",
-      "                Faces : (<AbSm - <CrPr - (DELT . 2) - (DELT . 8)>> <AbSm - <CrPr - (DELT . 1) - (DELT . 8)>>)\n",
-      "\n",
-      "        Simplex : <CrPr 0 (DELT . 1) - (DELT . 12)>\n",
-      "\n",
-      "                Faces : (<AbSm - <CrPr - (DELT . 1) - (DELT . 8)>> <AbSm - <CrPr - (DELT . 1) - (DELT . 4)>>)\n",
-      "\n",
-      "        Simplex : <CrPr 0 (DELT . 2) - (DELT . 12)>\n",
-      "\n",
-      "                Faces : (<AbSm - <CrPr - (DELT . 2) - (DELT . 8)>> <AbSm - <CrPr - (DELT . 2) - (DELT . 4)>>)\n",
-      "\n",
-      "Dimension = 2:\n",
-      "\n",
-      "        Simplex : <CrPr 0 (DELT . 3) 1 (DELT . 12)>\n",
-      "\n",
-      "                Faces : (<AbSm - <CrPr - (DELT . 3) 0 (DELT . 8)>> <AbSm - <CrPr - (DELT . 3) - (DELT . 12)>> <AbSm - <CrPr 0 (DELT . 1) - (DELT . 12)>>)\n",
-      "\n",
-      "        Simplex : <CrPr 1 (DELT . 3) 0 (DELT . 12)>\n",
-      "\n",
-      "                Faces : (<AbSm - <CrPr 0 (DELT . 2) - (DELT . 12)>> <AbSm - <CrPr - (DELT . 3) - (DELT . 12)>> <AbSm - <CrPr - (DELT . 3) 0 (DELT . 4)>>)"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 21,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(show-structure carre 2)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Let us take the first 1-simplex which corresponds to the diagonal of the square (realisation of the cartesian product) and let us build the three homomorphisms $\\cal AW$, $\\cal EML$ and $\\Phi$:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 22,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "<CrPr - (DELT . 3) - (DELT . 12)>"
-      ]
-     },
-     "execution_count": 22,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def diagonal (crpr 0 (code '(0 1)) 0 (code '(2 3))))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 23,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K30 Morphism (degree 0): K23 -> K28]"
-      ]
-     },
-     "execution_count": 23,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def aw-mrp (aw delta-0-1 delta-2-3)) "
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 24,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K31 Morphism (degree 0): K28 -> K23]"
-      ]
-     },
-     "execution_count": 24,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def eml-mrp (eml delta-0-1 delta-2-3))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 25,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K32 Morphism (degree 1): K23 -> K23]"
-      ]
-     },
-     "execution_count": 25,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def phi-hmy (phi delta-0-1 delta-2-3))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "We see that \n",
-    "$$ {\\cal AW}((0\\, 1), (2\\, 3)) = (0\\, 1)\\otimes (3) + (0) \\otimes (2\\, 3),$$\n",
-    "$$ {\\cal EML}((0\\, 1)\\otimes (3) + (0) \\otimes (2\\, 3))= ((0\\, 1), \\eta_0 (3)) \n",
-    "     + (\\eta_0 (0), (2\\, 3))$$\n",
-    "and that $\\Phi$ applied to the diagonal returns the 2-simplex compatible with the homotopy. \n",
-    "$$\\Phi((0\\, 1), (2\\, 3))= (\\eta_1(2\\, 3),\\eta_0(0\\, 1)).$$\n",
-    "This is illustrated by the following diagram (the 2-simplex is the shaded triangle)."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 26,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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",
-      "text/plain": [
-       "#<CL-JUPYTER-USER::PNG-BYTES {100292EA13}>"
-      ]
-     },
-     "execution_count": 26,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(cl-jupyter-user:png-from-file \"eml3.png\")"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 27,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 1}\n",
-       "<1 * <TnPr 0 (DELT . 1) 1 (DELT . 12)>>\n",
-       "<1 * <TnPr 1 (DELT . 3) 0 (DELT . 8)>>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 27,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? aw-mrp 1 diagonal)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 28,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 1}\n",
-       "<1 * <CrPr - (DELT . 3) 0 (DELT . 8)>>\n",
-       "<1 * <CrPr 0 (DELT . 1) - (DELT . 12)>>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 28,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? eml-mrp *)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 29,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 2}\n",
-       "<-1 * <CrPr 0 (DELT . 3) 1 (DELT . 12)>>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 29,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? phi-hmy 1 diagonal)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Let us inspect now the reduction generated by the function `ez` and verify on reasonably general combinations that the involved morphisms  are coherent."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 30,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K34 Reduction K6 => K3]"
-      ]
-     },
-     "execution_count": 30,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def ez-rdc (ez (soft-delta-infinity) (soft-delta-infinity)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 31,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "The object is a STANDARD-OBJECT of type REDUCTION.\n",
-      "0. TCC: [K6 Simplicial-Set]\n",
-      "1. BCC: [K3 Chain-Complex]\n",
-      "2. F: [K12 Morphism (degree 0): K6 -> K3]\n",
-      "3. G: [K11 Morphism (degree 0): K3 -> K6]\n",
-      "4. H: [K33 Morphism (degree 1): K6 -> K6]\n",
-      "5. IDNM: 34\n",
-      "6. ORGN: (EILENBERG-ZILBER [K1 Simplicial-Set] [K1 Simplicial-Set])\n",
-      "> "
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 31,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(inspect *)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "With the comment slots we see that the morphism *f*, *g* and *h* are respectively *aw*, *eml* and *phi*:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 32,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(EILENBERG-ZILBER [K1 Simplicial-Set] [K1 Simplicial-Set])"
-      ]
-     },
-     "execution_count": 32,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(orgn ez-rdc)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 33,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(AW [K1 Simplicial-Set] [K1 Simplicial-Set])"
-      ]
-     },
-     "execution_count": 33,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(orgn (f ez-rdc))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 34,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(EML [K1 Simplicial-Set] [K1 Simplicial-Set])"
-      ]
-     },
-     "execution_count": 34,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(orgn (g ez-rdc))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 35,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(PHI [K1 Simplicial-Set] [K1 Simplicial-Set])"
-      ]
-     },
-     "execution_count": 35,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(orgn (h ez-rdc))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 36,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 3}\n",
-       "<1 * <TnPr 0 (DELT . 1) 3 (DELT . 30)>>\n",
-       "<10 * <TnPr 1 (DELT . 96) 2 (DELT . 896)>>\n",
-       "<100 * <TnPr 2 (DELT . 7168) 1 (DELT . 24576)>>\n",
-       "<1000 * <TnPr 3 (DELT . 491520) 0 (DELT . 524288)>>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 36,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(setf *bc* (cmbn 3 1 (tnpr 0 (code '(0)) 3 (code '(1 2 3 4)))\n",
-    "                  10 (tnpr 1 (code '(5 6)) 2 (code '(7 8 9)))\n",
-    "                 100 (tnpr 2 (code '(10 11 12)) 1 (code '(13 14)))\n",
-    "                1000 (tnpr 3 (code '(15 16 17 18)) 0 (code '(19)))))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 37,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 3}\n",
-       "<1 * <CrPr - (DELT . 15) - (DELT . 480)>>\n",
-       "<10 * <CrPr - (DELT . 15) 2-0 (DELT . 96)>>\n",
-       "<100 * <CrPr 2-1 (DELT . 3) - (DELT . 480)>>\n",
-       "<1000 * <CrPr 2-1 (DELT . 3) 0 (DELT . 224)>>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 37,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(setf *tc* \n",
-    "     (cmbn 3 1 (crpr 0 (code '(0 1 2 3)) 0 (code '(5 6 7 8)))\n",
-    "            10 (crpr 0 (code '(0 1 2 3)) (dgop-ext-int '(2 0)) (code '(5 6)))\n",
-    "           100 (crpr (dgop-ext-int '(2 1)) (code '(0 1)) 0 (code '(5 6 7 8)))\n",
-    "          1000 (crpr (dgop-ext-int '(2 1)) (code '(0 1)) 1 (code '(5 6 7)))))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 38,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "---done---"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 38,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(pre-check-rdct ez-rdc)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 39,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "*TC* => \n",
-      "----------------------------------------------------------------------{CMBN 3}\n",
-      "<1 * <CrPr - (DELT . 15) - (DELT . 480)>>\n",
-      "<10 * <CrPr - (DELT . 15) 2-0 (DELT . 96)>>\n",
-      "<100 * <CrPr 2-1 (DELT . 3) - (DELT . 480)>>\n",
-      "<1000 * <CrPr 2-1 (DELT . 3) 0 (DELT . 224)>>\n",
-      "------------------------------------------------------------------------------\n",
-      "\n",
-      "*BC* => \n",
-      "----------------------------------------------------------------------{CMBN 3}\n",
-      "<1 * <TnPr 0 (DELT . 1) 3 (DELT . 30)>>\n",
-      "<10 * <TnPr 1 (DELT . 96) 2 (DELT . 896)>>\n",
-      "<100 * <TnPr 2 (DELT . 7168) 1 (DELT . 24576)>>\n",
-      "<1000 * <TnPr 3 (DELT . 491520) 0 (DELT . 524288)>>\n",
-      "------------------------------------------------------------------------------\n",
-      "\n",
-      "Checking *TDD* = 0\n",
-      "Result: \n",
-      "----------------------------------------------------------------------{CMBN 1}\n",
-      "------------------------------------------------------------------------------\n",
-      "\n",
-      "Checking *BDD* = 0\n",
-      "Result: \n",
-      "----------------------------------------------------------------------{CMBN 1}\n",
-      "------------------------------------------------------------------------------\n",
-      "\n",
-      "Checking *DF-FD* = 0\n",
-      "Result: \n",
-      "----------------------------------------------------------------------{CMBN 2}\n",
-      "------------------------------------------------------------------------------\n",
-      "\n",
-      "Checking *DG-GD* = 0\n",
-      "Result: \n",
-      "----------------------------------------------------------------------{CMBN 2}\n",
-      "------------------------------------------------------------------------------\n",
-      "\n",
-      "Checking *ID-FG* = 0\n",
-      "Result: \n",
-      "----------------------------------------------------------------------{CMBN 3}\n",
-      "------------------------------------------------------------------------------\n",
-      "\n",
-      "Checking *ID-GF-DH-HD* = 0\n",
-      "Result: \n",
-      "----------------------------------------------------------------------{CMBN 3}\n",
-      "------------------------------------------------------------------------------\n",
-      "\n",
-      "Checking *HH* = 0\n",
-      "Result: \n",
-      "----------------------------------------------------------------------{CMBN 5}\n",
-      "------------------------------------------------------------------------------\n",
-      "\n",
-      "Checking *FH* = 0\n",
-      "Result: \n",
-      "----------------------------------------------------------------------{CMBN 4}\n",
-      "------------------------------------------------------------------------------\n",
-      "\n",
-      "Checking *HG* = 0\n",
-      "Result: \n",
-      "----------------------------------------------------------------------{CMBN 4}\n",
-      "------------------------------------------------------------------------------\n",
-      "\n",
-      "---done---"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 39,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(check-rdct-no-wait)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "## Application to Homology\n",
-    "\n",
-    "Let us  illustrate the Eilenberg-Zilber theorem by the following example. Let us consider the manifold $P^2\\mathbb{R}\\times S^3$. The theorem says that\n",
-    "$$H_n({\\cal C}_*(P^2\\mathbb{R}\\times S^3)) \\cong H_n({\\cal C}_*(P^2\\mathbb{R}) \\otimes {\\cal C}_*(S^3)).$$"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 40,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "---done---"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 40,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(cat-init)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 41,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K1 Simplicial-Set]"
-      ]
-     },
-     "execution_count": 41,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def p2 (moore 2 1))  ;; Moore(2,1)   generates the projectif plane."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 42,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K6 Simplicial-Set]"
-      ]
-     },
-     "execution_count": 42,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def s3 (sphere 3))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "The simplicial set `p2-X-s3` is obtained from the cartesian product of the two simplicial sets `p2` and `s3`."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 43,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K11 Simplicial-Set]"
-      ]
-     },
-     "execution_count": 43,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def p2-X-s3 (crts-prdc p2 s3))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Now, the chain complex `p2-T-s3` is obtained from the tensor product of the two chain complexes associated to both simplicial sets `p2` and `s3` (don't forget that the class `SIMPLICIAL SET` is a subclass of the class `CHAIN COMPLEX`)."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 44,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K16 Chain-Complex]"
-      ]
-     },
-     "execution_count": 44,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def p2-T-s3 (tnsr-prdc p2 s3))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Applying  successively the  function `chcm-homology` (which computes directly the homology groups without using a homotopy equivalence)  on these chain complexes, shows that  the homology groups are  effectively isomorphic, but the method  of the tensor  product is  much faster than the method of the simple cartesian product, the number of generators being much smaller."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 45,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "Computing boundary-matrix in dimension 0.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 20m 37s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 0) :\n",
-      "<CrPr - * - *> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 1.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 20m 37s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 1) :\n",
-      "<CrPr - M1 0 *> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 0 :\n",
-      "\n",
-      "\n",
-      "Component Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "Computing boundary-matrix in dimension 1.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 20m 37s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 1) :\n",
-      "<CrPr - M1 0 *> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 2.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 20m 37s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 2) :\n",
-      "<CrPr - N2 1-0 *> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 1 :\n",
-      "\n",
-      "\n",
-      "Component Z/2Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "Computing boundary-matrix in dimension 2.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 20m 37s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 2) :\n",
-      "<CrPr - N2 1-0 *> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 3.\n",
-      "Rank of the source-module : 7.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 20m 37s.\n",
-      "Computing the boundary of the generator 1/7 (dimension 3) :\n",
-      "<CrPr 0 N2 - S3> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 20m 37s.\n",
-      "Computing the boundary of the generator 2/7 (dimension 3) :\n",
-      "<CrPr 1 N2 - S3> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 20m 37s.\n",
-      "Computing the boundary of the generator 3/7 (dimension 3) :\n",
-      "<CrPr 1-0 M1 - S3> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 20m 37s.\n",
-      "Computing the boundary of the generator 4/7 (dimension 3) :\n",
-      "<CrPr 2 N2 - S3> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 20m 37s.\n",
-      "Computing the boundary of the generator 5/7 (dimension 3) :\n",
-      "<CrPr 2-0 M1 - S3> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 20m 37s.\n",
-      "Computing the boundary of the generator 6/7 (dimension 3) :\n",
-      "<CrPr 2-1 M1 - S3> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 20m 37s.\n",
-      "Computing the boundary of the generator 7/7 (dimension 3) :\n",
-      "<CrPr 2-1-0 * - S3> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 2 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "Computing boundary-matrix in dimension 3.\n",
-      "Rank of the source-module : 7.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 20m 37s.\n",
-      "Computing the boundary of the generator 1/7 (dimension 3) :\n",
-      "<CrPr 0 N2 - S3> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 20m 37s.\n",
-      "Computing the boundary of the generator 2/7 (dimension 3) :\n",
-      "<CrPr 1 N2 - S3> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 20m 37s.\n",
-      "Computing the boundary of the generator 3/7 (dimension 3) :\n",
-      "<CrPr 1-0 M1 - S3> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 20m 37s.\n",
-      "Computing the boundary of the generator 4/7 (dimension 3) :\n",
-      "<CrPr 2 N2 - S3> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 20m 37s.\n",
-      "Computing the boundary of the generator 5/7 (dimension 3) :\n",
-      "<CrPr 2-0 M1 - S3> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 20m 37s.\n",
-      "Computing the boundary of the generator 6/7 (dimension 3) :\n",
-      "<CrPr 2-1 M1 - S3> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 20m 37s.\n",
-      "Computing the boundary of the generator 7/7 (dimension 3) :\n",
-      "<CrPr 2-1-0 * - S3> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 4.\n",
-      "Rank of the source-module : 16.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 20m 37s.\n",
-      "Computing the boundary of the generator 1/16 (dimension 4) :\n",
-      "<CrPr 1-0 N2 2 S3> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 20m 37s.\n",
-      "Computing the boundary of the generator 2/16 (dimension 4) :\n",
-      "<CrPr 1-0 N2 3 S3> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 20m 37s.\n",
-      "Computing the boundary of the generator 3/16 (dimension 4) :\n",
-      "<CrPr 2-0 N2 1 S3> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 20m 37s.\n",
-      "Computing the boundary of the generator 4/16 (dimension 4) :\n",
-      "<CrPr 2-0 N2 3 S3> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 20m 37s.\n",
-      "Computing the boundary of the generator 5/16 (dimension 4) :\n",
-      "<CrPr 2-1 N2 0 S3> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 20m 37s.\n",
-      "Computing the boundary of the generator 6/16 (dimension 4) :\n",
-      "<CrPr 2-1 N2 3 S3> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 20m 37s.\n",
-      "Computing the boundary of the generator 7/16 (dimension 4) :\n",
-      "<CrPr 2-1-0 M1 3 S3> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 20m 37s.\n",
-      "Computing the boundary of the generator 8/16 (dimension 4) :\n",
-      "<CrPr 3-0 N2 1 S3> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 20m 37s.\n",
-      "Computing the boundary of the generator 9/16 (dimension 4) :\n",
-      "<CrPr 3-0 N2 2 S3> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 20m 37s.\n",
-      "Computing the boundary of the generator 10/16 (dimension 4) :\n",
-      "<CrPr 3-1 N2 0 S3> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 20m 37s.\n",
-      "Computing the boundary of the generator 11/16 (dimension 4) :\n",
-      "<CrPr 3-1 N2 2 S3> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 20m 37s.\n",
-      "Computing the boundary of the generator 12/16 (dimension 4) :\n",
-      "<CrPr 3-1-0 M1 2 S3> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 20m 37s.\n",
-      "Computing the boundary of the generator 13/16 (dimension 4) :\n",
-      "<CrPr 3-2 N2 0 S3> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 20m 37s.\n",
-      "Computing the boundary of the generator 14/16 (dimension 4) :\n",
-      "<CrPr 3-2 N2 1 S3> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 20m 37s.\n",
-      "Computing the boundary of the generator 15/16 (dimension 4) :\n",
-      "<CrPr 3-2-0 M1 1 S3> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 20m 37s.\n",
-      "Computing the boundary of the generator 16/16 (dimension 4) :\n",
-      "<CrPr 3-2-1 M1 0 S3> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 3 :\n",
-      "\n",
-      "\n",
-      "Component Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "Computing boundary-matrix in dimension 4.\n",
-      "Rank of the source-module : 16.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 20m 37s.\n",
-      "Computing the boundary of the generator 1/16 (dimension 4) :\n",
-      "<CrPr 1-0 N2 2 S3> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 20m 37s.\n",
-      "Computing the boundary of the generator 2/16 (dimension 4) :\n",
-      "<CrPr 1-0 N2 3 S3> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 20m 37s.\n",
-      "Computing the boundary of the generator 3/16 (dimension 4) :\n",
-      "<CrPr 2-0 N2 1 S3> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 20m 37s.\n",
-      "Computing the boundary of the generator 4/16 (dimension 4) :\n",
-      "<CrPr 2-0 N2 3 S3> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 20m 37s.\n",
-      "Computing the boundary of the generator 5/16 (dimension 4) :\n",
-      "<CrPr 2-1 N2 0 S3> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 20m 37s.\n",
-      "Computing the boundary of the generator 6/16 (dimension 4) :\n",
-      "<CrPr 2-1 N2 3 S3> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 20m 37s.\n",
-      "Computing the boundary of the generator 7/16 (dimension 4) :\n",
-      "<CrPr 2-1-0 M1 3 S3> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 20m 37s.\n",
-      "Computing the boundary of the generator 8/16 (dimension 4) :\n",
-      "<CrPr 3-0 N2 1 S3> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 20m 37s.\n",
-      "Computing the boundary of the generator 9/16 (dimension 4) :\n",
-      "<CrPr 3-0 N2 2 S3> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 20m 37s.\n",
-      "Computing the boundary of the generator 10/16 (dimension 4) :\n",
-      "<CrPr 3-1 N2 0 S3> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 20m 37s.\n",
-      "Computing the boundary of the generator 11/16 (dimension 4) :\n",
-      "<CrPr 3-1 N2 2 S3> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 20m 37s.\n",
-      "Computing the boundary of the generator 12/16 (dimension 4) :\n",
-      "<CrPr 3-1-0 M1 2 S3> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 20m 37s.\n",
-      "Computing the boundary of the generator 13/16 (dimension 4) :\n",
-      "<CrPr 3-2 N2 0 S3> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 20m 37s.\n",
-      "Computing the boundary of the generator 14/16 (dimension 4) :\n",
-      "<CrPr 3-2 N2 1 S3> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 20m 37s.\n",
-      "Computing the boundary of the generator 15/16 (dimension 4) :\n",
-      "<CrPr 3-2-0 M1 1 S3> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 20m 37s.\n",
-      "Computing the boundary of the generator 16/16 (dimension 4) :\n",
-      "<CrPr 3-2-1 M1 0 S3> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 5.\n",
-      "Rank of the source-module : 10.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 20m 37s.\n",
-      "Computing the boundary of the generator 1/10 (dimension 5) :\n",
-      "<CrPr 2-1-0 N2 4-3 S3> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 20m 37s.\n",
-      "Computing the boundary of the generator 2/10 (dimension 5) :\n",
-      "<CrPr 3-1-0 N2 4-2 S3> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 20m 37s.\n",
-      "Computing the boundary of the generator 3/10 (dimension 5) :\n",
-      "<CrPr 3-2-0 N2 4-1 S3> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 20m 37s.\n",
-      "Computing the boundary of the generator 4/10 (dimension 5) :\n",
-      "<CrPr 3-2-1 N2 4-0 S3> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 20m 37s.\n",
-      "Computing the boundary of the generator 5/10 (dimension 5) :\n",
-      "<CrPr 4-1-0 N2 3-2 S3> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 20m 37s.\n",
-      "Computing the boundary of the generator 6/10 (dimension 5) :\n",
-      "<CrPr 4-2-0 N2 3-1 S3> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 20m 37s.\n",
-      "Computing the boundary of the generator 7/10 (dimension 5) :\n",
-      "<CrPr 4-2-1 N2 3-0 S3> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 20m 37s.\n",
-      "Computing the boundary of the generator 8/10 (dimension 5) :\n",
-      "<CrPr 4-3-0 N2 2-1 S3> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 20m 37s.\n",
-      "Computing the boundary of the generator 9/10 (dimension 5) :\n",
-      "<CrPr 4-3-1 N2 2-0 S3> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 20m 37s.\n",
-      "Computing the boundary of the generator 10/10 (dimension 5) :\n",
-      "<CrPr 4-3-2 N2 1-0 S3> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 4 :\n",
-      "\n",
-      "\n",
-      "Component Z/2Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "Computing boundary-matrix in dimension 5.\n",
-      "Rank of the source-module : 10.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 20m 37s.\n",
-      "Computing the boundary of the generator 1/10 (dimension 5) :\n",
-      "<CrPr 2-1-0 N2 4-3 S3> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 20m 37s.\n",
-      "Computing the boundary of the generator 2/10 (dimension 5) :\n",
-      "<CrPr 3-1-0 N2 4-2 S3> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 20m 37s.\n",
-      "Computing the boundary of the generator 3/10 (dimension 5) :\n",
-      "<CrPr 3-2-0 N2 4-1 S3> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 20m 37s.\n",
-      "Computing the boundary of the generator 4/10 (dimension 5) :\n",
-      "<CrPr 3-2-1 N2 4-0 S3> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 20m 37s.\n",
-      "Computing the boundary of the generator 5/10 (dimension 5) :\n",
-      "<CrPr 4-1-0 N2 3-2 S3> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 20m 37s.\n",
-      "Computing the boundary of the generator 6/10 (dimension 5) :\n",
-      "<CrPr 4-2-0 N2 3-1 S3> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 20m 37s.\n",
-      "Computing the boundary of the generator 7/10 (dimension 5) :\n",
-      "<CrPr 4-2-1 N2 3-0 S3> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 20m 37s.\n",
-      "Computing the boundary of the generator 8/10 (dimension 5) :\n",
-      "<CrPr 4-3-0 N2 2-1 S3> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 20m 37s.\n",
-      "Computing the boundary of the generator 9/10 (dimension 5) :\n",
-      "<CrPr 4-3-1 N2 2-0 S3> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 20m 37s.\n",
-      "Computing the boundary of the generator 10/10 (dimension 5) :\n",
-      "<CrPr 4-3-2 N2 1-0 S3> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 6.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 5 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "\"Evaluation took:\n",
-       "  0.001 seconds of real time\n",
-       "  0.000000 seconds of total run time (0.000000 user, 0.000000 system)\n",
-       "  0.00% CPU\n",
-       "  2,909,834 processor cycles\n",
-       "  256,704 bytes consed\n",
-       "  \n",
-       "\""
-      ]
-     },
-     "execution_count": 45,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(with-output-to-string (*trace-output*)\n",
-    "    (time (dotimes (i 6) (chcm-homology p2-X-s3 i))))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 46,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "Computing boundary-matrix in dimension 0.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 20m 37s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 0) :\n",
-      "<TnPr 0 * 0 *> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 1.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 20m 37s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 1) :\n",
-      "<TnPr 1 M1 0 *> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 0 :\n",
-      "\n",
-      "\n",
-      "Component Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "Computing boundary-matrix in dimension 1.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 20m 37s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 1) :\n",
-      "<TnPr 1 M1 0 *> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 2.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 20m 37s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 2) :\n",
-      "<TnPr 2 N2 0 *> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 1 :\n",
-      "\n",
-      "\n",
-      "Component Z/2Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "Computing boundary-matrix in dimension 2.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 20m 37s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 2) :\n",
-      "<TnPr 2 N2 0 *> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 3.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 20m 37s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 3) :\n",
-      "<TnPr 0 * 3 S3> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 2 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "Computing boundary-matrix in dimension 3.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 20m 37s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 3) :\n",
-      "<TnPr 0 * 3 S3> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 4.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 20m 37s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 4) :\n",
-      "<TnPr 1 M1 3 S3> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 3 :\n",
-      "\n",
-      "\n",
-      "Component Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "Computing boundary-matrix in dimension 4.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 20m 37s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 4) :\n",
-      "<TnPr 1 M1 3 S3> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 5.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 20m 37s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 5) :\n",
-      "<TnPr 2 N2 3 S3> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 4 :\n",
-      "\n",
-      "\n",
-      "Component Z/2Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "Computing boundary-matrix in dimension 5.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 20m 37s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 5) :\n",
-      "<TnPr 2 N2 3 S3> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 6.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 5 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "\"Evaluation took:\n",
-       "  0.000 seconds of real time\n",
-       "  0.000000 seconds of total run time (0.000000 user, 0.000000 system)\n",
-       "  100.00% CPU\n",
-       "  739,383 processor cycles\n",
-       "  30,256 bytes consed\n",
-       "  \n",
-       "\""
-      ]
-     },
-     "execution_count": 46,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(with-output-to-string (*trace-output*)\n",
-    "    (time (dotimes (i 6) (chcm-homology p2-T-s3 i))))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "The following example shows clearly the discrepancy between the length of the basis of two  objects built respectively by cartesian product and tensor product and having the same homology groups."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 47,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "---done---"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 47,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(cat-init)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 48,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K1 Simplicial-Set]"
-      ]
-     },
-     "execution_count": 48,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def s2 (sphere 2))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 49,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K6 Simplicial-Set]"
-      ]
-     },
-     "execution_count": 49,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def s3 (sphere 3))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 50,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K16 Simplicial-Set]"
-      ]
-     },
-     "execution_count": 50,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def s2Xs2Xs3 (crts-prdc (crts-prdc s2 s2) s3))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 51,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(CRTS-PRDC [K11 Simplicial-Set] [K6 Simplicial-Set])"
-      ]
-     },
-     "execution_count": 51,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(orgn s2Xs2Xs3)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 52,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K21 Chain-Complex]"
-      ]
-     },
-     "execution_count": 52,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def s2Ts2Ts3 (tnsr-prdc (tnsr-prdc s2 s2) s3))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 53,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "1 \n",
-      "0 \n",
-      "3 \n",
-      "22 \n",
-      "138 \n",
-      "390 \n",
-      "480 "
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 53,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(dotimes (i 7) (print (length (basis s2Xs2Xs3 i))))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 54,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "1 \n",
-      "0 \n",
-      "2 \n",
-      "1 \n",
-      "1 \n",
-      "2 \n",
-      "0 "
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 54,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(dotimes (i 7) (print (length (basis s2Ts2Ts3 i))))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "### Searching homology process for cartesian products\n",
-    "\n",
-    "When the `search-efhm` method recognizes a cartesian product, by means of the comment list (slot `orgn`) of the object, it builds a homotopy equivalence where the right bottom chain complex is created by the function `ez`. The process may be recursif as shown by the very definition of the method:\n",
-    "\n",
-    "```commonlisp\n",
-    "(defun LEFT-CRTS-PRDC-EFHM (smst1 smst2)\n",
-    "  (declare (type simplicial-set smst1 smst2))\n",
-    "  (the homotopy-equivalence\n",
-    "     (build-hmeq\n",
-    "       :lrdct (trivial-rdct (crts-prdc smst1 smst2))\n",
-    "       :rrdct (ez smst1 smst2))))\n",
-    "\n",
-    "(defmethod SEARCH-EFHM (smst (orgn (eql 'crts-prdc)))\n",
-    "  (declare (type simplicial-set smst))\n",
-    "  (the homotopy-equivalence\n",
-    "    (cmps\n",
-    "      (left-crts-prdc-efhm (second (orgn smst)) \n",
-    "                           (third  (orgn smst)))\n",
-    "      (tnsr-prdc (efhm (second (orgn smst)))\n",
-    "                 (efhm (third  (orgn smst)))))))\n",
-    "```\n",
-    "\n",
-    "### Lisp files concerned in this chapter\n",
-    "\n",
-    "`eilenberg-zilber.lisp`, `searching-homology.lisp`."
-   ]
-  }
- ],
- "metadata": {
-  "kernelspec": {
-   "display_name": "SBCL Lisp",
-   "language": "lisp",
-   "name": "lisp"
-  },
-  "language_info": {
-   "codemirror_mode": "text/x-common-lisp",
-   "mimetype": "text/x-common-lisp",
-   "name": "common-lisp",
-   "pygments_lexer": "common-lisp",
-   "version": "X3J13"
-  }
- },
- "nbformat": 4,
- "nbformat_minor": 1
-}
diff --git a/examples/10_Programming_the_Kan_theory.ipynb b/examples/10_Programming_the_Kan_theory.ipynb
deleted file mode 100644
index 31a7763..0000000
--- a/examples/10_Programming_the_Kan_theory.ipynb
+++ /dev/null
@@ -1,400 +0,0 @@
-{
- "cells": [
-  {
-   "cell_type": "code",
-   "execution_count": 1,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "To load \"kenzo\":\n",
-      "  Load 1 ASDF system:\n",
-      "    kenzo\n",
-      "; Loading \"kenzo\"\n",
-      "\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "#<PACKAGE \"CAT\">"
-      ]
-     },
-     "execution_count": 1,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(ql:quickload \"kenzo\")\n",
-    "(in-package :cat)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "# Programming the Kan theory\n",
-    "\n",
-    "## Introduction\n",
-    "\n",
-    "Let us recall some definitions in relation with the Kan simplicial sets.\n",
-    "\n",
-    "**Definition 1.** A Kan \"horn\" of dimension $n$ and index $i$ is a collection of $n$ simplices of dimension  $(n-1)$, noted  $(\\sigma_0, \\ldots, \\sigma_{i-1}, \\sigma_{i+1}, \\ldots, \\sigma_n)$, such that the following conditions are fulfilled:\n",
-    "$$ \\partial_j\\sigma_k=\\partial_k\\sigma_{j+1},\\quad k \\not= i,\\quad j+1 \\not= i, \\quad 0 \\leq j \\leq n-1, \\quad 0 \\leq k \\leq n-1, \\quad k \\leq j. $$\n",
-    "Note that there is no $\\sigma_i$ term in the list above; in a sense, the Kan process consists in constructing the missing $\\sigma_i$ to be considered as a \"composition\" of the given $\\sigma_j$'s.\n",
-    "\n",
-    "### Example\n",
-    "\n",
-    "We are going to work with the simplices of $\\Delta^\\mathbb{N}$. The set $(\\sigma_1, \\sigma_2) = $ `((0 2), (0 1))` is a Kan horn of dimension 2 and index 0. In effect, $\\partial_1\\sigma_1=\\partial_1\\sigma_2 =$ `(0)`. Likewise, the two sets `((1 2), (0 1))` and `((1 2), (0 2))` are  Kan horns  of dimension 2 and of respective index 1 and 2. Of course, this definition applies equally if the simplices are degenerate.\n",
-    "\n",
-    "**Definition 2.** A *filling* of a Kan horn $(\\sigma_0, \\ldots, \\sigma_{i-1}, \\sigma_{i+1}, \\ldots, \\sigma_n)$, is an $n$-simplex $\\tilde{\\sigma}$, such that for every $j \\not= i$, $\\partial_j\\tilde{\\sigma}=\\sigma_j.$\n",
-    "\n",
-    "### Example\n",
-    "\n",
-    "A filling of `((0 2), (0 1))` is the 2-simplex `(0 1 2)`. A filling of the Kan horn `((1 1), (0 1))` is the degenerate 2-simplex `(0 1 1)`. A filling of the vertex `(0)` is the degenerate 1-simplex `(0 0)`.\n",
-    "\n",
-    "**Definition 3.** A simplicial set is a Kan simplicial set if for every hat there exists a filling.\n",
-    "\n",
-    "In a *constructive* context, an *algorithm* must be provided able to *compute* a solution for the Kan problem. In the Kenzo program, a Kan simplicial-set has an extra slot `kfll` devoted to this problem.\n",
-    "\n",
-    "### Representation of a Kan simplicial set\n",
-    "\n",
-    "A Kan simplicial set is implemented as an instance of the class `KAN`, subclass of the class `SIMPLICIAL-SET`.\n",
-    "\n",
-    "```commonlisp\n",
-    "(DEFCLASS KAN (simplicial-set)\n",
-    "  ((kfll :type kfll :initarg :kfll :reader kfll1)))\n",
-    "```\n",
-    "\n",
-    "We recall that this new class inherits also from the class `CHAIN-COMPLEX`. It has one slot of its own:\n",
-    "\n",
-    "`kfll`\n",
-    "> an object of type `KFLL`, in fact a lisp function with 3 parameters describing a Kan horn: an index (an integer), a dimension (an integer) and the Kan horn (a list of abstract simplices). This function must return a filling of the Kan horn argument, i.e. an abstract simplex satisfying the theoritical definition.\n",
-    "\n",
-    "A printing method has been associated to the class `KAN` and the external representation of  an instance is a string like `[K`*n* `Kan-Simplicial-Set]`, where *n* is the number plate of the Kenzo object.\n",
-    "\n",
-    "### Helpful functions on Kan simplicial sets\n",
-    "\n",
-    "`cat-init` *[Function]*\n",
-    "> Clear in particular `*Kan-list*`, the list of user created Kan simplicial sets  and reset the global counter to 1.\n",
-    "\n",
-    "`Kan` *n* *[Function]*\n",
-    "> Retrieve in the list `*Kan-list*` the Kan object instance whose the Kenzo identification  is n. If it does not exist, return `NIL`.\n",
-    "\n",
-    "`kfll &rest` *args* *[Macro]*\n",
-    "> With only one argument (a Kan instance) return the slot `kfll` of this instance. With 4 arguments like `(kfll` *kan indx dmns horn*`)`, return a filling of the Kan horn *horn*, of dimension *dmns* and of index *indx* by applying the filling function value of the slot `kfll` of the Kan instance *kan*.\n",
-    "\n",
-    "`smst-kan` *smst kfll* *[Function]*\n",
-    "> With the filling lisp function *kfll*, **transform** the simplicial set *smst* in an object of type `KAN` (in other word, *smst* is `modified`). This is the easiest way to build a Kan simplicial set.\n",
-    "\n",
-    "`check-horn` *kan indx dmns horn* *[Function]*\n",
-    "> Useful verification function to check if the collection of simplices `horn` is a valid Kan horn of dimension *dmns* and of index *indx* in the Kan simplicial set *kan*. In fact this works equally if *kan* is a general simplicial set.\n",
-    "\n",
-    "`check-kan` *kan indx dmns horn* *[Function]*\n",
-    "> Useful verification function to check if the collection of simplices *horn* is a valid Kan horn of dimension *dmns* and of index *indx* in the Kan simplicial set *kan*. This verification function applies the filling function of the instance *kan* to the argument *horn* and perform the  verification of the faces relations upon the resulting $dmns$-simplex.\n",
-    "\n",
-    "### Examples\n",
-    "\n",
-    "Let us take again the small examples of the introduction. First we  define a function `dkfll`, a filling function suitable for a  Kan horn in $\\Delta^\\mathbb{N}$. The user will note that in the abstract simplices the degeneracy operators and the geometric simplices are coded in binary."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 2,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "DKFLL"
-      ]
-     },
-     "execution_count": 2,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(defun dkfll (indx dmns horn)\n",
-    "     (cond ((= 1 dmns)\n",
-    "            (absm 1 (gmsm (first horn))))\n",
-    "           ((= 0 indx)\n",
-    "            (let ((del-1 (absm-int-ext (first horn)))\n",
-    "                  (del-2 (absm-int-ext (second horn))))\n",
-    "              (absm-ext-int\n",
-    "                 (cons (first del-1)\n",
-    "                       (cons (second del-2) (rest del-1))))))\n",
-    "           ((= 1 indx)\n",
-    "            (let ((del-0 (absm-int-ext (first horn)))\n",
-    "                  (del-2 (absm-int-ext (second horn))))\n",
-    "              (absm-ext-int\n",
-    "                 (cons (first del-2) del-0))))\n",
-    "           (t\n",
-    "            (let ((del-0 (absm-int-ext (first horn)))\n",
-    "                  (del-1 (absm-int-ext (second horn))))\n",
-    "              (absm-ext-int\n",
-    "                 (cons (first del-1) del-0))))))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 3,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K1 Simplicial-Set]"
-      ]
-     },
-     "execution_count": 3,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def d (delta-infinity))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 4,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K1 Kan-Simplicial-Set]"
-      ]
-     },
-     "execution_count": 4,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(smst-kan d #'dkfll)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 5,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "<AbSm 0 1>"
-      ]
-     },
-     "execution_count": 5,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(kfll d 0 1 (list (absm 0 1)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 6,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "<AbSm - 7>"
-      ]
-     },
-     "execution_count": 6,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(kfll d 0 2 (list (absm 0 5) (absm 0 3)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 7,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "<AbSm - 7>"
-      ]
-     },
-     "execution_count": 7,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(kfll d 1 2 (list (absm 0 6) (absm 0 3)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 8,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "<AbSm - 7>"
-      ]
-     },
-     "execution_count": 8,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(kfll d 2 2 (list (absm 0 6) (absm 0 5)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 9,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "<AbSm 1 3>"
-      ]
-     },
-     "execution_count": 9,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(kfll d 0 2 (list (absm 0 3) (absm 0 3)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 10,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "<AbSm 1 3>"
-      ]
-     },
-     "execution_count": 10,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(kfll d 1 2 (list (absm 1 2) (absm 0 3)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 11,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "T"
-      ]
-     },
-     "execution_count": 11,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(check-hat d 1 2 (list (absm 1 2) (absm 0 3)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 12,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "T"
-      ]
-     },
-     "execution_count": 12,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(check-hat d 0 1 (list (absm 0 1)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 13,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "---done---"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 13,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(check-kan d 0 1 (list (absm 0 1)))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "More elaborate examples with Kan simplicial sets will be given later in the loop spaces chapter.\n",
-    "\n",
-    "### Lisp files concerned in this chapter\n",
-    "\n",
-    "`kan.lisp`.\n",
-    "\n",
-    "[`classes.lisp`, `macros.lisp`, `various.lisp`]."
-   ]
-  }
- ],
- "metadata": {
-  "kernelspec": {
-   "display_name": "SBCL Lisp",
-   "language": "lisp",
-   "name": "lisp"
-  },
-  "language_info": {
-   "codemirror_mode": "text/x-common-lisp",
-   "mimetype": "text/x-common-lisp",
-   "name": "common-lisp",
-   "pygments_lexer": "common-lisp",
-   "version": "X3J13"
-  }
- },
- "nbformat": 4,
- "nbformat_minor": 1
-}
diff --git a/examples/11_Simplicial_Groups.ipynb b/examples/11_Simplicial_Groups.ipynb
deleted file mode 100644
index a076ce4..0000000
--- a/examples/11_Simplicial_Groups.ipynb
+++ /dev/null
@@ -1,1772 +0,0 @@
-{
- "cells": [
-  {
-   "cell_type": "code",
-   "execution_count": 1,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "To load \"kenzo\":\n",
-      "  Load 1 ASDF system:\n",
-      "    kenzo\n",
-      "; Loading \"kenzo\"\n",
-      "\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "#<PACKAGE \"CAT\">"
-      ]
-     },
-     "execution_count": 1,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(ql:quickload \"kenzo\")\n",
-    "(in-package :cat)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "# Simplicial Groups\n",
-    "\n",
-    "## Representation of a  simplicial group\n",
-    "\n",
-    "A simplicial group is  an instance of the class `SIMPLICIAL-GROUP`, subclass of the classes `KAN` and `HOPF-ALGEBRA`.\n",
-    "```commonlisp\n",
-    "(DEFCLASS SIMPLICIAL-GROUP (kan hopf-algebra)\n",
-    "   ((grml :type simplicial-mrph :initarg :grml :reader grml1)\n",
-    "    (grin :type simplicial-mrph :initarg :grin :reader grin1)))\n",
-    "```\n",
-    "We recall that this new class (multi-) inherits from the following classes: `KAN`, `SIMPLICIAL-SET`, `COALGEBRA`,  `ALGEBRA` and `CHAIN-COMPLEX`. It has two slots of its own:\n",
-    "\n",
-    "`grml`, an object of type `SIMPLICIAL-MRPH`, defining in the underlying simplicial set $S$, the group operation as a simplicial morphism from $S \\times S$ onto $S$, compatible with the face and degeneracy operators in $S$, i.e. the $\\partial$'s and $\\eta$'s operators are also group morphisms. In dimension $n$, the neutral element is assumed to be the $n$-th degeneracy of the base point of the underlying simplicial set.\n",
-    "\n",
-    "`grin`, an object of type `SIMPLICIAL-MRPH`, defining the inverse of an element of the Kan simplicial set with respect to the preceding group law.\n",
-    "\n",
-    "A printing method has been associated to the class `SIMPLICIAL GROUP` and the external representation of an instance is a string like `[K`*n* `Simplicial-Group]`, where *n* is the number plate of the Kenzo object.\n",
-    "\n",
-    "## Representation of an Abelian  simplicial group\n",
-    "\n",
-    "The class of Abelian simplicial group, `AB-SIMPLICIAL-GROUP`, inherits  all the properties of the class `SIMPLICIAL-GROUP` and has not slots of its own, as shown by:\n",
-    "```commonlisp\n",
-    "(DEFCLASS AB-SIMPLICIAL-GROUP (simplicial-group) ())\n",
-    "```\n",
-    "The difference is purely mathematical: it is up to the user to provide as slot *grml*, a simplicial morphism which is **commutative**. As expected, the external representation of  an instance of this class, is a string like\n",
-    "`[K`*n* `Abelian-Simplicial-Group]`, where *n* is the number plate of the Kenzo object.\n",
-    "\n",
-    "## The functions `build-smgr` and `build-ab-smrg`\n",
-    "\n",
-    "To facilitate the construction of instances of the classes `SIMPLICIAL-GROUP` and `AB-SIMPLICIAL-GROUP` and to free  the user to call the standard constructor `make-instance`, the software provides the functions *build-smrg* and *build-ab-smrg*.\n",
-    "\n",
-    "`build-smgr`\n",
-    "> `:cmpr` *cmpr* `:basis` *basis* `:bspn` *bspn* `:face` *face* `:face*` *face*$*$  \n",
-    "`:intr-bndr` *intr-bndr* `:bndr-strt` *bndr-strt* `:intr-dgnl` *intr-dgnl*  \n",
-    "`:dgnl-strt` *dgnl-strt* `:sintr-grml` *sintr-grml* `:sintr-grin` *sintr-grin*  \n",
-    "`:orgn` *orgn*\n",
-    "\n",
-    "defined with keyword parameters and returning an instance of the class `SIMPLICIAL-GROUP`. The keyword arguments *cmpr*, *basis*, *bspn*, *face*, *face*$*$, *intr-bndr*, *bndr-strt*, *intr-dgnl* and *dgnl-strt* are the arguments provided to build the underlying simplicial set using the function `build-smst`. Let us call it $S$. As usual, an adequate comment list must be provided for the parameter `:orgn`. The only two new arguments are:\n",
-    "\n",
-    "- *sintr-grml*, a lisp function defining the group operation $S \\times S \\longrightarrow S$. The function `build-smgr` uses this lisp function to build a simplicial morphism of degree 0 between the cartesian product of the newly created simplicial set $S$ and itself. This new simplicial morphism is the value of the slot `grml` of the cartesian square of the simplicial group instance.\n",
-    "- *sintr-grin*, a lisp function defining the inverse w.r.t the preceding group law of an element of $S$. The function `build-smgr` uses this lisp function to build a simplicial morphism of degree 0 between $S$ and itself. This new simplicial morphism is the value of the slot `grin` of the simplicial group instance.\n",
-    "\n",
-    "After a call to `build-smgr`, the simplicial group instance is pushed onto the list of previously constructed  ones (`*smgr-list*`). The simplicial group with Kenzo identification $n$, may be retrieved in the `*smgr-list*`, by a call to the function `sgmr` as `(sgmr` *n*`)`. The list `*smgr-list*` may be cleared by the function `cat-init`.\n",
-    "\n",
-    "Up to now the slot `kfll` has not been filled. As long as the user does not make use of the filling function, directly or indirectly, this slot remains unbound. But as soon as it is needed, the *slot-unbound* mechanism of CLOS enters in action and the filling function is defined by the system with the help of the functions `face`, `sintr-grml` and `sintr-grin`. The automatic creation of the filling function is possible because mathematically, a simplicial group is always a Kan simplicial set. This is realized by the internal function `smgr-kfll-intr`.\n",
-    "\n",
-    "For the user, the two simplicial morphisms, values of the specific slots  of a `SIMPLICIAL-GROUP` are applied via the two following macros:\n",
-    "\n",
-    "`grml` *smgr dmns crpr* *[Macro]*\n",
-    "> Apply the simplicial morphism, value of the slot `grml` of the simplicial group instance *smgr* to the cartesian product *crpr* in dimension *dmns*. Mathematically, this realizes the group operation. In principle, the simplicial morphism must accept the *crpr* argument on both forms: either a geometric cartesian product or an abstract simplex, the geometric part of which is a geometric cartesian product (see the examples). With only one argument (*smgr*) the macro selects the simplicial morphism instance.\n",
-    "\n",
-    "`grin` *smgr dmns absm-or-gsm* *[Macro]*\n",
-    "> Apply the simplicial morphism, value of the slot `grin` of the simplicial group instance *smgr* to the element *absm-or-gsm* in dimension *dmns*. Mathematically this gives the inverse in the group of the element. As suggested by the name of the parameter, this must work with geometric simplices as well as abstract simplices. With only one argument (*smgr*) the macro selects the simplicial morphism.\n",
-    "\n",
-    "`build-ab-smgr`\n",
-    "> `:cmpr` *cmpr* `:basis` *basis* `:bspn` *bspn* `:face` *face* `:face*` *face*$*$  \n",
-    "`:intr-bndr` *intr-bndr* `:bndr-strt` *bndr-strt* `:intr-dgnl` *intr-dgnl*  \n",
-    "`:dgnl-strt` *dgnl-strt* `:sintr-grml` *sintr-grml* `:sintr-grin` *sintr-grin*  \n",
-    "`:orgn` *orgn*\n",
-    "\n",
-    "The description of the parameters is exactly the same as in the previous function, but in this case, the group operation given by the user, (argument *sintr-grml*), must be commutative. The lisp definition of `build-ab-smgr` is simply:\n",
-    "```commonlisp\n",
-    "(DEFMACRO BUILD-AB-SMGR (&rest rest)\n",
-    "  `(change-class (build-smgr ,@rest) 'ab-simplicial-group))\n",
-    "```\n",
-    "\n",
-    "## Two important Abelian simplicial groups: $K(\\mathbb{Z}, 1)$ and $K(\\mathbb{Z}_2, 1)$}\n",
-    "\n",
-    "Let us recall the notion of classifying space in the framework of simplicial sets and in the particular case of discrete groups. Given a discrete group $\\cal G$, we know that we may build a simplicial set $K({\\cal G}, 1)$; in dimension $n$, we have $(K({\\cal G}, 1))_n = {\\cal G}^n$, the simplices or *bar objects* being  conventionally represented  as sequences of elements of $\\cal G$:\n",
-    "$$ [g_1 \\mid g_2 \\mid \\ldots \\mid g_n]. $$\n",
-    "The base point is the void bar object $[\\ ]$, the only vertex of $K(\\mathcal{G},1)$. Let us note the group law multiplicatively.\n",
-    "\n",
-    "The face operators are defined as follows:\n",
-    "$$\n",
-    "\\begin{aligned}\n",
-    "\\partial_0 [g_1 \\mid g_2 \\mid \\ldots \\mid g_n] & = & [g_2 \\mid g_3 \\mid \\ldots \\mid g_n], \\\\\n",
-    "\\partial_1 [g_1 \\mid g_2 \\mid \\ldots \\mid g_n] & = & [{\\bf g_1g_2} \\mid g_3 \\mid \\ldots \\mid g_n], \\\\\n",
-    "\\partial_2 [g_1 \\mid g_2 \\mid \\ldots \\mid g_n] & = & [g_1 \\mid {\\bf g_2g_3} \\mid \\ldots \\mid g_n], \\\\\n",
-    "                        ......                & = &  ......  \\\\\n",
-    "\\partial_{n-1} [g_1 \\mid g_2 \\mid \\ldots \\mid g_n] & = & [g_1 \\mid g_2 \\mid \\ldots \\mid g_{n-2} \\mid {\\bf g_{n-1}g_n}], \\\\\n",
-    "\\partial_n [g_1 \\mid g_2 \\mid \\ldots \\mid g_n] & = & [g_1 \\mid g_2 \\mid \\ldots \\mid g_{n-1}].\n",
-    "\\end{aligned}\n",
-    "$$\n",
-    "The degeneracy operators are defined as follows:\n",
-    "$$ \\eta_i [g_1 \\mid \\ldots \\mid g_{i-1} \\mid g_i \\mid g_{i+1} \\mid \\ldots \\mid g_n] =\n",
-    "          [g_1 \\mid \\ldots \\mid g_{i-1}  \\mid g_i \\mid {\\bf e} \\mid g_{i+1} \\mid \\ldots \\mid g_n],$$\n",
-    "where $e$ is the neutral element of $\\cal G$.\n",
-    "\\par\n",
-    "If, in addition $\\cal G$ is abelian, then  $K({\\cal G}, 1)$ is itself a *simplicial group*, with the\n",
-    "following group law, in dimension $n$:\n",
-    "$$[a_1  \\mid \\cdots \\mid a_n] . [b_1 \\mid \\cdots \\mid b_n] = [a_1+b_1 \\mid \\cdots \\mid a_n+b_n], $$\n",
-    "$$[a_1  \\mid \\cdots \\mid a_n]^{-1}= [-a_1  \\mid \\cdots \\mid -a_n],\\quad a,b \\in {\\cal G}$$\n",
-    "In dimension $n$, the neutral element is the bar object constitued by a sequence of $n$ times the neutral $e$ of ${\\cal G}$; this is also the $n$-th degeneracy of the base point $[\\ ]$ of $K({\\cal G}, 1)$.\n",
-    "\n",
-    "The two important simplicial groups $K(\\mathbb{Z}, 1)$ and $K(\\mathbb{Z}_2, 1)$ may be constructed in `Kenzo`.\n",
-    "\n",
-    "`k-z-1` *[Function]*\n",
-    "> Build the simplicial group $K(\\mathbb{Z},1)$. In this simplicial group, a  simplex  in dimension $n$ is mathematically represented by a sequence of integers, known as a *bar* object:\n",
-    "$$ [a_1 \\mid a_2 \\mid \\ldots \\mid a_n]. $$\n",
-    "Such a simplex of $K(\\mathbb{Z},1)$ is really, mathematically speaking, a *bar* object, but exceptionally is not implemented as a `bar` structure object, as it will be the rule later for arbitrary *classifying spaces*.\n",
-    "The group operation inherits the additive law of $\\mathbb{Z}$:\n",
-    "$$[a_1  \\mid \\cdots \\mid a_n] + [b_1 \\mid \\cdots \\mid b_n] = [a_1+b_1 \\mid \\cdots \\mid a_n+b_n]$$\n",
-    "and the inverse of $[a_1  \\mid \\ldots \\mid a_n]$ is $[-a_1 \\mid \\ldots \\mid -a_n]. $\n",
-    "In `Kenzo`, a non-degenerate simplex of $K(\\mathbb{Z},1)$ in dimension $n$ will be simply a list of $n$ non-null integers. The underlying simplicial set is locally effective and its base point is `NIL`, i.e the void bar object\n",
-    "$[\\ ]$. To be coherent with the general policy of `Kenzo`, a degenerate simplex must be represented by\n",
-    "an abstract simplex of the form `#S(ABSM :dgop` *n* `:gmsm` *list*`)` where *gmsm* is a non-degenerate simplex, here a list of non-null integers. But, for the computations in the simplicial group, the general form of a bar object, including an arbitrary number of 0's, is more natural and more convenient. Consequently, two conversion functions are provided (see below).\n",
-    "\n",
-    "`k-z2-1` *[Function]*\n",
-    "> Build the simplicial group $K(\\mathbb{Z}_2,1)$. Mathematically, in dimension $n$, the only non-degenerate simplex is\n",
-    "a sequence of $n$ 1's. But one may show that as simplicial set, $K(\\mathbb{Z}_2,1)$ is  isomorphic to $P^\\infty \\mathbb{R}$ which may be built by the statement `(R-proj-space)`. This is the representation adopted in `Kenzo`. In dimension $n$, this simplicial set has only one non-degenerate simplex, namely the integer $n$. The formulas for the faces of one non-degenerate simplex conventionally represented by the integer $n$ become:\n",
-    "$$\n",
-    "\\begin{aligned}\n",
-    "\\partial_0 n & = & n-1, \\\\\n",
-    "\\partial_i n & = & \\eta_{i-1} (n-2), \\quad i \\not= 0, i \\not=n,  \\\\\n",
-    "\\partial_n n & = & n-1.\n",
-    "\\end{aligned}\n",
-    "$$\n",
-    "\n",
-    "As a group, in dimension $n$, the non-degenerate element $n$ is its own inverse and the neutral is the $n$-th degeneracy of 0. As in $K(\\mathbb{Z}, 1)$ a degenerate simplex must be represented by a valid abstract simplex, but as the computations are more convenient if the general bar objects are represented by a sequence of mixed 0's and 1's, two conversion functions are\n",
-    "provided.\n",
-    "\n",
-    "`z-bar-absm` *bar* *[Function]*\n",
-    "> Transform a general mathematical bar object *bar* of $K(\\mathbb{Z}, 1)$, represented by a list of integers (including 0's), into a valid abstract simplex (an object of type `ABSM`), `#S(ABSM :dgop` *n* `:gmsm` *list*`)`, where *gmsm*  is a sequence of non-null integers representing a non-degenerate bar object of $K(\\mathbb{Z},1)$ and *dgop* a coded sequence of degeneracy operators $\\eta_i$'s.\n",
-    "\n",
-    "`z-absm-bar` *absm* *[Function]*\n",
-    "> Transform the abstract simplex *absm*,  `#S(ABSM :dgop` *n* `:gmsm` *list*`)`, where *gmsm* is a sequence of non-null integers representing a nondegenerate bar object of $K(\\mathbb{Z},1)$ and *dgop* a coded sequence of degeneracy operators, into a list of integers representing a bar object, degenerate or not, of $K(\\mathbb{Z},1)$, for more convenience in the internal computations or for more clarity in external printing.\n",
-    "\n",
-    "`z2-bar-absm` *bar* *[Function]*\n",
-    "> Function analogous to `z-bar-absm` but for  $K(\\mathbb{Z}_2, 1)$.\n",
-    "\n",
-    "`z2-absm-bar` *absm* *[Function]*\n",
-    "> Function analogous to `z-absm-bar` but for  $K(\\mathbb{Z}_2, 1)$.\n",
-    "\n",
-    "### Examples"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 2,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K1 Abelian-Simplicial-Group]"
-      ]
-     },
-     "execution_count": 2,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def KZ1 (k-z-1))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 3,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(1 10 100)"
-      ]
-     },
-     "execution_count": 3,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def simplex '(1 10 100))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 4,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "<AbSm - (10 100)>"
-      ]
-     },
-     "execution_count": 4,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(face KZ1 0 3 simplex)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Let us build the list of the four faces and by suppressing successively, each face one after the other in this list, let us verify that we have always a Kan horn (we recall that the lisp function `remove`, works on a copy of the list, i.e. the argument `hat` is not modified). In the forth  statement, we verify the property of minimality of this special simplicial group."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 5,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(<AbSm - (10 100)> <AbSm - (11 100)> <AbSm - (1 110)> <AbSm - (1 10)>)"
-      ]
-     },
-     "execution_count": 5,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def hat (mapcar #'(lambda (i) (face KZ1 i 3 simplex)) (<a-b> 0 3)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 6,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "---done---\n",
-      "---done---\n",
-      "---done---\n",
-      "---done---"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 6,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(dotimes (i 4)\n",
-    "    (check-kan KZ1 i 3 (remove (nth i hat) hat)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 7,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(<AbSm - (10 100)> <AbSm - (1 110)> <AbSm - (1 10)>)"
-      ]
-     },
-     "execution_count": 7,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def hat1 (remove (nth 1 hat) hat))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 8,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "<AbSm - (1 10 100)>"
-      ]
-     },
-     "execution_count": 8,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(kfll KZ1 1 3 hat1)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "We test now the two macros `grml` and `grin` related to the group operation."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 9,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "<AbSm - (2 20 200)>"
-      ]
-     },
-     "execution_count": 9,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(grml KZ1 3 (crpr 0 simplex 0 simplex))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 10,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "<AbSm - (-1 -10 -100)>"
-      ]
-     },
-     "execution_count": 10,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def invsimplex (grin KZ1 3 simplex))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 11,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "<AbSm - (1 10 100)>"
-      ]
-     },
-     "execution_count": 11,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(grin KZ1 3 *) "
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 12,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "<AbSm 2-1-0 NIL>"
-      ]
-     },
-     "execution_count": 12,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(grml KZ1 3 (crpr 0 simplex 0 (gmsm invsimplex)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 13,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "<AbSm - <CrPr - (1 10 100) - (-1 -10 -100)>>"
-      ]
-     },
-     "execution_count": 13,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(2absm-acrpr (absm 0 simplex ) (grin KZ1 3 simplex))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 14,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "<AbSm 2-1-0 NIL>"
-      ]
-     },
-     "execution_count": 14,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(grml KZ1 3 *) "
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 15,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K13 Abelian-Simplicial-Group]"
-      ]
-     },
-     "execution_count": 15,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def KZ2 (k-z2-1))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 16,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "<AbSm 2-1-0 0>"
-      ]
-     },
-     "execution_count": 16,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(grml KZ2 3 (crpr 0 3 0 3))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 17,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "<AbSm - 4>"
-      ]
-     },
-     "execution_count": 17,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(grin KZ2 4 4)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 18,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "<AbSm 3-2-1-0 0>"
-      ]
-     },
-     "execution_count": 18,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(grml KZ2 4 (crpr 0 4 0 4))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Let us show some examples of conversions, between general bar objects and valid abstract simplices:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 19,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 19,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(z-absm-bar (absm 0 '()))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 20,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(0)"
-      ]
-     },
-     "execution_count": 20,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(z-absm-bar (absm 1 '()))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 21,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(2)"
-      ]
-     },
-     "execution_count": 21,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(z-absm-bar (absm 0 '(2)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 22,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(0 0 0 1 1 1 1 1 1 1)"
-      ]
-     },
-     "execution_count": 22,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(z2-absm-bar (absm 7 7))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 23,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(1 1 1 1 1 1 1)"
-      ]
-     },
-     "execution_count": 23,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(z2-absm-bar (absm 0 7))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Let us suppose that the value of the symbol `labsms` is a list of abstract simplices built from the simplex `(3 6)` in dimension 1 of $K(\\mathbb{Z}, 1)$. The application of the function `z-absm-bar` on this list gives the representation of the simplices under the classical mathematical representation. Applying then `z-bar-absm` returns the original list. A similar example is given with the symbol `labsm2` in dimension 0."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 24,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(<AbSm - (3 6)> <AbSm 0 (3 6)> <AbSm 1 (3 6)> <AbSm 1-0 (3 6)> <AbSm 2 (3 6)> <AbSm 2-0 (3 6)> <AbSm 2-1 (3 6)> <AbSm 2-1-0 (3 6)>)"
-      ]
-     },
-     "execution_count": 24,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def labsms (mapcar #'(lambda (n) (absm n '(3 6))) '(0 1 2 3 4 5 6 7)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 25,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "((3 6) (0 3 6) (3 0 6) (0 0 3 6) (3 6 0) (0 3 0 6) (3 0 0 6) (0 0 0 3 6))"
-      ]
-     },
-     "execution_count": 25,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(mapcar #'z-absm-bar labsms)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 26,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(<AbSm - (3 6)> <AbSm 0 (3 6)> <AbSm 1 (3 6)> <AbSm 1-0 (3 6)> <AbSm 2 (3 6)> <AbSm 2-0 (3 6)> <AbSm 2-1 (3 6)> <AbSm 2-1-0 (3 6)>)"
-      ]
-     },
-     "execution_count": 26,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(mapcar #'z-bar-absm *)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 27,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(<AbSm - 0> <AbSm - 1> <AbSm - 2> <AbSm - 3> <AbSm 0 0> <AbSm 0 1> <AbSm 0 2> <AbSm 0 3> <AbSm 1-0 0> <AbSm 1-0 1> ...)"
-      ]
-     },
-     "execution_count": 27,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def labsms2 (append (mapcar #'(lambda (n) (absm 0 n)) '(0 1 2 3))\n",
-    "                     (mapcar #'(lambda (n) (absm 1 n)) '(0 1 2 3))\n",
-    "                     (mapcar #'(lambda (n) (absm 3 n)) '(0 1 2 3))))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 28,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(NIL (1) (1 1) (1 1 1) (0) (0 1) (0 1 1) (0 1 1 1) (0 0) (0 0 1) ...)"
-      ]
-     },
-     "execution_count": 28,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(mapcar #'z2-absm-bar labsms2)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 29,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(<AbSm - 0> <AbSm - 1> <AbSm - 2> <AbSm - 3> <AbSm 0 0> <AbSm 0 1> <AbSm 0 2> <AbSm 0 3> <AbSm 1-0 0> <AbSm 1-0 1> ...)"
-      ]
-     },
-     "execution_count": 29,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(mapcar #'z2-bar-absm *)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "## Simplicial Groups as Algebras\n",
-    "\n",
-    "If we consider a simplicial group ${\\cal G}$, with group operation $\\tau$, there is a canonical product for the algebra\n",
-    "$$\\varpi : C_*({\\cal G}) \\otimes C_*({\\cal G}) \\longrightarrow C_*({\\cal G}), $$\n",
-    "defined as the composition $\\tau \\circ {\\cal EML}$, where ${\\cal EML}$ is the Eilenberg-Mac Lane homomorphism or the *shuffle homomorphism* (see the Eilenberg-Zilber chapter):\n",
-    "$$C_*({\\cal G}) \\otimes C_*({\\cal G}) \\buildrel {{\\cal EML}} \\over \\longrightarrow\n",
-    "   C_*({\\cal G} \\times {\\cal G}) \\buildrel {\\tau} \\over \\longrightarrow C_*({\\cal G}). $$\n",
-    "For instance let us look at the simplicial group $K(\\mathbb{Z}, 1)$:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 30,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K1 Abelian-Simplicial-Group]"
-      ]
-     },
-     "execution_count": 30,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def kz1 (k-z-1))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 31,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "The object is a STANDARD-OBJECT of type AB-SIMPLICIAL-GROUP.\n",
-      "0. CMPR: #<FUNCTION K-Z-1-CMPR>\n",
-      "1. BASIS: :LOCALLY-EFFECTIVE\n",
-      "2. BSGN: NIL\n",
-      "3. DFFR: [K2 Morphism (degree -1): K1 -> K1]\n",
-      "4. GRMD: [K1 Abelian-Simplicial-Group]\n",
-      "5. EFHM: \"unbound\"\n",
-      "6. IDNM: 1\n",
-      "7. ORGN: (K-Z-1)\n",
-      "8. APRD: \"unbound\"\n",
-      "9. CPRD: [K5 Morphism (degree 0): K1 -> K3]\n",
-      "10. FACE: #<FUNCTION K-Z-1-FACE>\n",
-      "11. KFLL: #<CLOSURE (FLET RSLT :IN SMGR-KFLL-INTR) {1001E760EB}>\n",
-      "12. GRML: [K11 Simplicial-Morphism K6 -> K1]\n",
-      "13. GRIN: [K12 Simplicial-Morphism K1 -> K1]\n",
-      "> "
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 31,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(inspect kz1)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "We see that  the slot `aprd` has not been filled. As long as the user does not  need, directly or indirectly, the product of the algebra, this slot remains unbound. But as soon as it is needed, the *slot-unbound* mecanism of CLOS enters in action, the canonical algebra product morphism is defined by the system, and the slot\n",
-    "`aprd` is set.\n",
-    "\n",
-    "For instance, let us take the tensor product of two elements of  $K(\\mathbb{Z}, 1)$ and apply the product in the algebra:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 32,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "<TnPr (1 2) (7 8 9)>"
-      ]
-     },
-     "execution_count": 32,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def tnsrp (tnpr 2 '(1 2) 3 '(7 8 9))) "
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 33,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 5}\n",
-       "<1 * (1 2 7 8 9)>\n",
-       "<-1 * (1 7 2 8 9)>\n",
-       "<1 * (1 7 8 2 9)>\n",
-       "<-1 * (1 7 8 9 2)>\n",
-       "<1 * (7 1 2 8 9)>\n",
-       "<-1 * (7 1 8 2 9)>\n",
-       "<1 * (7 1 8 9 2)>\n",
-       "<1 * (7 8 1 2 9)>\n",
-       "<-1 * (7 8 1 9 2)>\n",
-       "<1 * (7 8 9 1 2)>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 33,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(aprd kz1 5 tnsrp)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "The system `Kenzo` has automatically created the needed algebra product morphism  and this is shown in the slot instance `aprd`:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 34,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "The object is a STANDARD-OBJECT of type AB-SIMPLICIAL-GROUP.\n",
-      "0. CMPR: #<FUNCTION K-Z-1-CMPR>\n",
-      "1. BASIS: :LOCALLY-EFFECTIVE\n",
-      "2. BSGN: NIL\n",
-      "3. DFFR: [K2 Morphism (degree -1): K1 -> K1]\n",
-      "4. GRMD: [K1 Abelian-Simplicial-Group]\n",
-      "5. EFHM: \"unbound\"\n",
-      "6. IDNM: 1\n",
-      "7. ORGN: (K-Z-1)\n",
-      "8. APRD: [K26 Morphism (degree 0): K3 -> K1]\n",
-      "9. CPRD: [K5 Morphism (degree 0): K1 -> K3]\n",
-      "10. FACE: #<FUNCTION K-Z-1-FACE>\n",
-      "11. KFLL: #<CLOSURE (FLET RSLT :IN SMGR-KFLL-INTR) {1001E760EB}>\n",
-      "12. GRML: [K11 Simplicial-Morphism K6 -> K1]\n",
-      "13. GRIN: [K12 Simplicial-Morphism K1 -> K1]\n",
-      "> "
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 34,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(inspect kz1)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "An interesting example is to show the associativity of the canonical product of an algebra, by defining in `Kenzo` the morphisms of the following diagram and verifying that this diagram is commutative. In the diagram, $\\nabla$ is the algebra product of ${\\cal A}$, $1$ is the identity morphism on ${\\cal A}$ and\n",
-    "*assoc*, the morphism\n",
-    "$$assoc: ({\\cal A}\\otimes {\\cal A}) \\otimes {\\cal A} \\longrightarrow {\\cal A} \\otimes ({\\cal A}\\otimes {\\cal A}),$$\n",
-    "with:\n",
-    "$$assoc((a\\otimes b)\\otimes c) = a \\otimes (b \\otimes c).$$\n",
-    "\n",
-    "$$\n",
-    "\\begin{aligned}\n",
-    "({\\cal A}\\otimes {\\cal A}) \\otimes {\\cal A} & \\quad\\buildrel {assoc} \\over \\longrightarrow &\n",
-    "  {\\cal A} \\otimes ({\\cal A}\\otimes {\\cal A}) \\cr\n",
-    "{\\scriptstyle \\nabla \\otimes 1}\\downarrow \\qquad&          &  \\downarrow {\\scriptstyle 1 \\otimes \\nabla}\\quad  \\cr\n",
-    "{\\cal A}\\otimes {\\cal A}\\quad    &         &  {\\cal A}\\otimes {\\cal A}\\quad \\cr\n",
-    "{\\scriptstyle \\nabla}\\searrow \\quad   &          &  \\swarrow {\\scriptstyle \\nabla} \\qquad \\cr\n",
-    "                            & \\qquad{\\cal A} &  \\cr\n",
-    "\\end{aligned}\n",
-    "$$\n",
-    "\n",
-    "Let us define two chain complexes with the two ways to compose two tensorial products:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 35,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K1 Abelian-Simplicial-Group]"
-      ]
-     },
-     "execution_count": 35,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def kz1 (k-z-1))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 36,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K27 Chain-Complex]"
-      ]
-     },
-     "execution_count": 36,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def 3-left (tnsr-prdc (tnsr-prdc kz1 kz1) kz1))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 37,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K29 Chain-Complex]"
-      ]
-     },
-     "execution_count": 37,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def 3-right (tnsr-prdc kz1 (tnsr-prdc kz1 kz1)))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Then we define the morphism `assoc` and test it:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 38,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K31 Morphism (degree 0): K27 -> K29]"
-      ]
-     },
-     "execution_count": 38,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def assoc1 (build-mrph\n",
-    "             :sorc 3-left\n",
-    "             :trgt 3-right\n",
-    "             :degr 0\n",
-    "             :intr #'(lambda (degr a2-a)\n",
-    "                             (declare (ignore degr))\n",
-    "                             (with-tnpr (degra2 gnrta2 degra gnrta) a2-a\n",
-    "                                 (declare (ignore degra2))\n",
-    "                                 (with-tnpr (degr1 gnrt1 degr2 gnrt2) gnrta2\n",
-    "                                     (cmbn (+ degr1 degr2 degra) \n",
-    "                                           1 (tnpr degr1 gnrt1 \n",
-    "                                                   (+ degr2 degra) \n",
-    "                                                   (tnpr degr2 gnrt2 degra gnrta))))))\n",
-    "             :strt :gnrt\n",
-    "             :orgn '(assoc-double-tensor-product)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 39,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "T"
-      ]
-     },
-     "execution_count": 39,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(setf *tnpr-with-degrees* t)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 40,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 7}\n",
-       "<1 * <TnPr 2 (1 2) 5 <TnPr 2 (2 3) 3 (4 5 6)>>>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 40,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? assoc1 7 (tnpr 4 (tnpr 2 '(1 2) 2 '(2 3)) 3 '(4 5 6)))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "We define now the other morphisms shown in the diagram:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 41,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K26 Morphism (degree 0): K3 -> K1]"
-      ]
-     },
-     "execution_count": 41,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def nabla (aprd kz1))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 42,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K32 Morphism (degree 0): K1 -> K1]"
-      ]
-     },
-     "execution_count": 42,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def idnt (idnt-mrph kz1))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 43,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K33 Morphism (degree 0): K29 -> K3]"
-      ]
-     },
-     "execution_count": 43,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def 1-t-nabla (tnsr-prdc idnt nabla))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 44,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K34 Morphism (degree 0): K27 -> K3]"
-      ]
-     },
-     "execution_count": 44,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def nabla-t-1 (tnsr-prdc nabla idnt)) "
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Now, if the diagram is commutative, the difference morphism, noted `zero`, between the following morphisms `right` and `left`, must give the null combination if applied to an element of $K(\\mathbb{Z}, 1) \\otimes K(\\mathbb{Z}, 1)) \\otimes K(\\mathbb{Z},1).$"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 45,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K35 Morphism (degree 0): K27 -> K1]"
-      ]
-     },
-     "execution_count": 45,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def left (cmps nabla nabla-t-1))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 46,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K37 Morphism (degree 0): K27 -> K1]"
-      ]
-     },
-     "execution_count": 46,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def right (i-cmps nabla 1-t-nabla assoc1))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 47,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K38 Morphism (degree 0): K27 -> K1]"
-      ]
-     },
-     "execution_count": 47,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def zero (sbtr left right))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 48,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 7}\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 48,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? zero  7 (tnpr 4 (tnpr 2 '(1 2) 2 '(2 3)) 3 '(4 5 6)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 49,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 9}\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 49,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? zero 9 (tnpr 7 (tnpr 3 '(2 3 4) 4 '(5 6 7 8)) 2 '(11 12)))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "It happens the resulting combination of the rather simple double tensor product has 140 terms:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 50,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 7}\n",
-       "<1 * (1 2 3 2 4 5 6)>\n",
-       "<-1 * (1 2 3 4 2 5 6)>\n",
-       "<1 * (1 2 3 4 5 2 6)>\n",
-       "<-1 * (1 2 3 4 5 6 2)>\n",
-       "<1 * (1 2 4 3 2 5 6)>\n",
-       "<-1 * (1 2 4 3 5 2 6)>\n",
-       "<1 * (1 2 4 3 5 6 2)>\n",
-       "<1 * (1 2 4 5 3 2 6)>\n",
-       "<-1 * (1 2 4 5 3 6 2)>\n",
-       "<1 * (1 2 4 5 6 3 2)>\n",
-       "... ...\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 50,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? right  7 (tnpr 4 (tnpr 2 '(1 2) 2 '(2 3)) 3 '(4 5 6)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 51,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "140"
-      ]
-     },
-     "execution_count": 51,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(length (cmbn-list *))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "## Coming back to the Bar of an algebra\n",
-    "\n",
-    "The existence of a canonical product for the underlying algebra of a simplicial group allows us now to generate the bar of this algebra. Let us use again $K(\\mathbb{Z}, 1).$ We begin to test separately the vertical and the horizontal differential."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 52,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K1 Abelian-Simplicial-Group]"
-      ]
-     },
-     "execution_count": 52,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def kz1 (k-z-1))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 53,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "#<CLOSURE (LAMBDA (DEGR ABAR) :IN BAR-INTR-VRTC-DFFR) {10030CE87B}>"
-      ]
-     },
-     "execution_count": 53,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def d-vert (bar-intr-vrtc-dffr (dffr kz1)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 54,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN -1}\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 54,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(funcall d-vert 0 (abar))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 55,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "<<Abar[3 (1 2)][3 (-1 -2)][3 (3 4)]>>"
-      ]
-     },
-     "execution_count": 55,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def abar0 (abar 3 '(1 2) 3 '(-1 -2) 3 '(3 4)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 56,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 8}\n",
-       "<-1 * <<Abar[2 (1)][3 (-1 -2)][3 (3 4)]>>>\n",
-       "<-1 * <<Abar[2 (2)][3 (-1 -2)][3 (3 4)]>>>\n",
-       "<1 * <<Abar[2 (3)][3 (-1 -2)][3 (3 4)]>>>\n",
-       "<-1 * <<Abar[3 (1 2)][2 (-3)][3 (3 4)]>>>\n",
-       "<1 * <<Abar[3 (1 2)][2 (-2)][3 (3 4)]>>>\n",
-       "<1 * <<Abar[3 (1 2)][2 (-1)][3 (3 4)]>>>\n",
-       "<-1 * <<Abar[3 (1 2)][3 (-1 -2)][2 (3)]>>>\n",
-       "<-1 * <<Abar[3 (1 2)][3 (-1 -2)][2 (4)]>>>\n",
-       "<1 * <<Abar[3 (1 2)][3 (-1 -2)][2 (7)]>>>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 56,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(funcall d-vert 9 abar0)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 57,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "#<CLOSURE (LAMBDA (DEGR ABAR) :IN BAR-INTR-HRZN-DFFR) {10031E7E3B}>"
-      ]
-     },
-     "execution_count": 57,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def d-hrz  (bar-intr-hrzn-dffr (aprd kz1)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 58,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 8}\n",
-       "<1 * <<Abar[3 (1 2)][5 (-1 -2 3 4)]>>>\n",
-       "<-1 * <<Abar[3 (1 2)][5 (-1 3 -2 4)]>>>\n",
-       "<1 * <<Abar[3 (1 2)][5 (-1 3 4 -2)]>>>\n",
-       "<1 * <<Abar[3 (1 2)][5 (3 -1 -2 4)]>>>\n",
-       "<-1 * <<Abar[3 (1 2)][5 (3 -1 4 -2)]>>>\n",
-       "<1 * <<Abar[3 (1 2)][5 (3 4 -1 -2)]>>>\n",
-       "<-1 * <<Abar[5 (-1 -2 1 2)][3 (3 4)]>>>\n",
-       "<1 * <<Abar[5 (-1 1 -2 2)][3 (3 4)]>>>\n",
-       "<-1 * <<Abar[5 (-1 1 2 -2)][3 (3 4)]>>>\n",
-       "<-1 * <<Abar[5 (1 -1 -2 2)][3 (3 4)]>>>\n",
-       "... ...\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 58,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(funcall d-hrz 9 abar0)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "We may now construct the bar chain complex of the algebra `kz1` and test the differential, sum of  both previous ones:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 59,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K42 Chain-Complex]"
-      ]
-     },
-     "execution_count": 59,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def bara (bar kz1))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 60,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 8}\n",
-       "<1 * <<Abar[3 (1 2)][5 (-1 -2 3 4)]>>>\n",
-       "<-1 * <<Abar[3 (1 2)][5 (-1 3 -2 4)]>>>\n",
-       "<1 * <<Abar[3 (1 2)][5 (-1 3 4 -2)]>>>\n",
-       "<1 * <<Abar[3 (1 2)][5 (3 -1 -2 4)]>>>\n",
-       "<-1 * <<Abar[3 (1 2)][5 (3 -1 4 -2)]>>>\n",
-       "<1 * <<Abar[3 (1 2)][5 (3 4 -1 -2)]>>>\n",
-       "<-1 * <<Abar[5 (-1 -2 1 2)][3 (3 4)]>>>\n",
-       "<1 * <<Abar[5 (-1 1 -2 2)][3 (3 4)]>>>\n",
-       "<-1 * <<Abar[5 (-1 1 2 -2)][3 (3 4)]>>>\n",
-       "<-1 * <<Abar[5 (1 -1 -2 2)][3 (3 4)]>>>\n",
-       "... ...\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 60,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? bara 9 abar0)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 61,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 7}\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 61,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? bara *)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 62,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "<<Abar[5 (7 11 4 -9)][4 (8 3 2)][5 (-1 -2 -3 -4)]>>"
-      ]
-     },
-     "execution_count": 62,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def abar1 (abar '(5 (7 11  4 -9) 4 (8 3 2) 5 (-1 -2 -3 -4))))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 63,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 13}\n",
-       "<-1 * <<Abar[5 (7 11 4 -9)][8 (-1 -2 -3 -4 8 3 2)]>>>\n",
-       "<1 * <<Abar[5 (7 11 4 -9)][8 (-1 -2 -3 8 -4 3 2)]>>>\n",
-       "<-1 * <<Abar[5 (7 11 4 -9)][8 (-1 -2 -3 8 3 -4 2)]>>>\n",
-       "<1 * <<Abar[5 (7 11 4 -9)][8 (-1 -2 -3 8 3 2 -4)]>>>\n",
-       "<-1 * <<Abar[5 (7 11 4 -9)][8 (-1 -2 8 -3 -4 3 2)]>>>\n",
-       "<1 * <<Abar[5 (7 11 4 -9)][8 (-1 -2 8 -3 3 -4 2)]>>>\n",
-       "<-1 * <<Abar[5 (7 11 4 -9)][8 (-1 -2 8 -3 3 2 -4)]>>>\n",
-       "<-1 * <<Abar[5 (7 11 4 -9)][8 (-1 -2 8 3 -3 -4 2)]>>>\n",
-       "<1 * <<Abar[5 (7 11 4 -9)][8 (-1 -2 8 3 -3 2 -4)]>>>\n",
-       "<-1 * <<Abar[5 (7 11 4 -9)][8 (-1 -2 8 3 2 -3 -4)]>>>\n",
-       "... ...\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 63,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? bara 14 abar1)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 64,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "84"
-      ]
-     },
-     "execution_count": 64,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(length (cmbn-list *))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 65,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 12}\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 65,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? bara **)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "### Lisp files concerned in this chapter\n",
-    "\n",
-    "`simplicial-groups.lisp`, `k-pi-n.lisp`.\n",
-    "\n",
-    "`classes.lisp`, `macros.lisp`, `various.lisp`]."
-   ]
-  }
- ],
- "metadata": {
-  "kernelspec": {
-   "display_name": "SBCL Lisp",
-   "language": "lisp",
-   "name": "lisp"
-  },
-  "language_info": {
-   "codemirror_mode": "text/x-common-lisp",
-   "mimetype": "text/x-common-lisp",
-   "name": "common-lisp",
-   "pygments_lexer": "common-lisp",
-   "version": "X3J13"
-  }
- },
- "nbformat": 4,
- "nbformat_minor": 1
-}
diff --git a/examples/12_Fibrations.ipynb b/examples/12_Fibrations.ipynb
deleted file mode 100644
index 56c3600..0000000
--- a/examples/12_Fibrations.ipynb
+++ /dev/null
@@ -1,2055 +0,0 @@
-{
- "cells": [
-  {
-   "cell_type": "code",
-   "execution_count": 1,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "To load \"kenzo\":\n",
-      "  Load 1 ASDF system:\n",
-      "    kenzo\n",
-      "; Loading \"kenzo\"\n",
-      "\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "#<PACKAGE \"CAT\">"
-      ]
-     },
-     "execution_count": 1,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(ql:quickload \"kenzo\")\n",
-    "(in-package :cat)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "# Fibrations\n",
-    "\n",
-    "In `Kenzo`, the fibration theory is applied in the simplicial frame and limited to the *simplicial principal fiber spaces*.\n",
-    "\n",
-    "## Notion of fibration\n",
-    "\n",
-    "Let $B$ be a simplicial set, called in this context the *base space*, and $\\mathcal{G}$ a simplicial group, the *structural group*. A *simplicial fibration* is defined by a **twisting operator**, $\\tau : B \\longrightarrow {\\cal G}$, of degree -1. For any dimension $n$ and for any element $b \\in B_n$, this twisting operator $\\tau$ must satisfy the following relations with respect to the face and degeneracy operators of the base space $B$ and the structural group $\\mathcal{G}$:\n",
-    "$$\n",
-    "\\begin{aligned}\n",
-    "\\partial_i(\\tau b) & = & \\tau(\\partial_i b), \\qquad i < n-1, \\\\\n",
-    "\\partial_{n-1}(\\tau b) & = & [\\tau(\\partial_n b)]^{-1}.\\tau(\\partial_{n-1} b), \\\\\n",
-    "\\eta_i(\\tau b)  & = & \\tau (\\eta_i b), \\qquad i \\leq n-1, \\\\\n",
-    "e_n             & = & \\tau(\\eta_n b). \n",
-    "\\end{aligned}\n",
-    "$$\n",
-    "where $e_n$ is the neutral element of ${\\cal G}_n$.\n",
-    "\n",
-    "Now, the twisting operator $\\tau$ defines a fibration of base space $B$, of fiber space $\\mathcal{G}$, of total space $B \\times_\\tau \\mathcal{G}$ and of structural group $\\mathcal{G}$. The simplicial components $(B \\times_\\tau \\mathcal{G})_n$ of the total space $B \\times\\tau \\mathcal{G}$ are:\n",
-    "$$ (B \\times_{\\tau} {\\cal G})_n = (B \\times {\\cal G})_n = (B_n \\times {\\cal G}_n), $$\n",
-    "and whose  face operators are defined, in any dimension $n$ and for any pair $(b,g),\\, b \\in B_n,\\, g \\in {\\cal G}_n$ by:\n",
-    "$$\n",
-    "\\begin{aligned}\n",
-    "\\partial_i(b,g) & = & (\\partial_i b, \\partial_i g), \\quad i < n, \\\\\n",
-    "\\partial_n(b,g) & = & (\\partial_n b, \\tau(b).\\partial_n g), \\\\\n",
-    "\\eta_i(b,g) & = & (\\eta_i b, \\eta_i g)\n",
-    "\\end{aligned}\n",
-    "$$\n",
-    "As it is well known, there are 4 natural choices for such a definition. The action of the group can be from the right or from the left and the critical index can be the last one ($n$) or the first one (0). In `Kenzo`, the implementor has chosen the non-usual one (i.e. action on the right hand and, as critical index, the last one), leading to the Szczarba formulas, the best choice in the case of the loop spaces.\n",
-    "\n",
-    "## Building a twisting operator\n",
-    "\n",
-    "To build a twisting operator, one uses the function `build-smmr` designed as a convenient tool to build a simplicial morphism. The source (keyword `:sorc`) is the base space, a **reduced** simplicial set, the target (keyword `:trgt`) is the fiber space, a simplicial group. The degree is -1 and the morphism (keyword `:sintr`) is the internal lisp function implementing $\\tau$. See the example below, where $\\tau$ is a simple twisting operator, applying in particular the only (geometrical) simplex of degree 2  of $S^2$ upon the bar object  $[1] \\in (K(\\mathbb{Z}_2,1))_1$.\n",
-    "\n",
-    "In `Kenzo`, the type `FIBRATION` is defined. An object of this type must be of type `SIMPLICIAL-MRPH`, the degree of the corresponding morphism being  -1. To apply the morphism, one uses the macro `?` or the special macro `tw-a-sintr3`.\n",
-    "\n",
-    "`?` *twop dmns gmsm* *[Macro]*\n",
-    "> Apply the twisting operator *twop* to the geometrical simplex *gmsm* in dimension *dmns*. One may also make `?` work with a combination of geometric simplices as in  `(?` *twop cmbn*`)`.\n",
-    "\n",
-    "`tw-a-sintr3` *sintr dmns absm bspn* *[Macro]*\n",
-    "> Apply the internal lisp function *sintr* implementing a twisting operator to the *abstract* simplex *absm* in dimension *dmns*. The base point *bspn* of the target simplicial set (a simplicial group) must be given, since the function may return the neutral element in dimension $dmns - 1$.\n",
-    "\n",
-    "## Constructing the total space\n",
-    "\n",
-    "The total space associated to a twisting operator is constructed  by the function `fibration-total`.\n",
-    "\n",
-    "`fibration-total` *fibration* *[Function]*\n",
-    "> Build the simplicial set, total space of the fibration. This function extracts from the simplicial morphism *fibration* (a previously defined twisting operator), the base space (a simplicial set) and the fiber space (a simplicial group) and constructs the corresponding twisted cartesian product of these simplicial sets. The face function is built using the internal function `fibration-total-face`. The non-degenerate simplices of the total space are coded exactly as those of the non-twisted product ($B \\times {\\cal G}$) obtained by the lisp call `(crts-prdc` *base* *fiber*`)`. This non-twisted cartesian product is saved into the slot `grmd` (graded module) of the instance object. If the base space and the fiber space are both of type `KAN`, then the filling function is computed y the internal function `fibration-kfll` and  the function `fibration-total` returns  an object of type `KAN`.\n",
-    "\n",
-    "### Examples"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 2,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K1 Simplicial-Set]"
-      ]
-     },
-     "execution_count": 2,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def s2 (sphere 2))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 3,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K6 Abelian-Simplicial-Group]"
-      ]
-     },
-     "execution_count": 3,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def kz2 (k-z2-1))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 4,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K18 Fibration K1 -> K6]"
-      ]
-     },
-     "execution_count": 4,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def tw2 (build-smmr\n",
-    "             :sorc s2\n",
-    "             :trgt kz2\n",
-    "             :degr -1\n",
-    "             :sintr #'(lambda (dmns gmsm)\n",
-    "                              (declare (ignore dmns gmsm))\n",
-    "                              (absm 0 1))\n",
-    "             :orgn '(s2-tw-kz2)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 5,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "The object is a STANDARD-OBJECT of type SIMPLICIAL-MRPH.\n",
-      "0. SORC: [K1 Simplicial-Set]\n",
-      "1. TRGT: [K6 Abelian-Simplicial-Group]\n",
-      "2. DEGR: -1\n",
-      "3. INTR: NIL\n",
-      "4. STRT: :GNRT\n",
-      "5. ???-CLNM: 0\n",
-      "6. ?-CLNM: 0\n",
-      "7. RSLTS: #(#() #() #() #() #() #() #() #() #() #() ...)\n",
-      "8. IDNM: 18\n",
-      "9. ORGN: (S2-TW-KZ2)\n",
-      "10. SINTR: #<FUNCTION (LAMBDA (DMNS GMSM) :IN \"/root/cl-jupyter/cl-jupyter.lisp\") {1001CE90AB}>\n",
-      "> "
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 5,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(inspect tw2)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "The following statement show how to apply the twisting operator to a *geometrical* simplex. But if we have an abstract simplex, one must use the special function `tw-a-sintr3`."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 6,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "<AbSm - 1>"
-      ]
-     },
-     "execution_count": 6,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? tw2 2 's2)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 7,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "<AbSm 0 1>"
-      ]
-     },
-     "execution_count": 7,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(tw-a-sintr3 (sintr tw2) 3 (absm 1 's2) 0)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 8,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "<AbSm 1-0 0>"
-      ]
-     },
-     "execution_count": 8,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(tw-a-sintr3 (sintr tw2) 3 (absm 7 '*) 0)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 9,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "<AbSm - 1> \n",
-      "<AbSm 0 1> \n",
-      "<AbSm 1 1> "
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 9,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(dotimes (i 3) (print (tw-a-sintr3 (sintr tw2) 3 \n",
-    "                                   (absm i 's2) 0)))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Let us build the total space of the fibration (a simplicial set). We show some bases and compute some homology groups. The method to compute the homology groups will be explained in a following chapter."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 10,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K24 Simplicial-Set]"
-      ]
-     },
-     "execution_count": 10,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def tot-spc2 (fibration-total tw2))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 11,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "The object is a STANDARD-OBJECT of type SIMPLICIAL-SET.\n",
-      "0. CMPR: #<CLOSURE (FLET RSLT :IN CRTS-PRDC-CMPR) {100206417B}>\n",
-      "1. BASIS: #<CLOSURE (FLET RSLT :IN CRTS-PRDC-BASIS) {10020648EB}>\n",
-      "2. BSGN: <CrPr - * - 0>\n",
-      "3. DFFR: [K25 Morphism (degree -1): K24 -> K24]\n",
-      "4. GRMD: [K19 Simplicial-Set]\n",
-      "5. EFHM: \"unbound\"\n",
-      "6. IDNM: 24\n",
-      "7. ORGN: (FIBRATION-TOTAL [K18 Fibration K1 -> K6])\n",
-      "8. CPRD: [K28 Morphism (degree 0): K24 -> K26]\n",
-      "9. FACE: #<CLOSURE (FLET RSLT :IN FIBRATION-TOTAL-FACE) {1002069A9B}>\n",
-      "> "
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 11,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(inspect tot-spc2)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 12,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(<CrPr - * - 0>)"
-      ]
-     },
-     "execution_count": 12,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(basis tot-spc2 0)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 13,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(<CrPr 0 * - 1>)"
-      ]
-     },
-     "execution_count": 13,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(basis tot-spc2 1)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 14,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(<CrPr - S2 - 2> <CrPr - S2 0 1> <CrPr - S2 1 1> <CrPr - S2 1-0 0> <CrPr 1-0 * - 2>)"
-      ]
-     },
-     "execution_count": 14,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(basis tot-spc2 2)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 15,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(<CrPr 0 S2 - 3> <CrPr 0 S2 1 2> <CrPr 0 S2 2 2> <CrPr 0 S2 2-1 1> <CrPr 1 S2 - 3> <CrPr 1 S2 0 2> <CrPr 1 S2 2 2> <CrPr 1 S2 2-0 1> <CrPr 2 S2 - 3> <CrPr 2 S2 0 2> ...)"
-      ]
-     },
-     "execution_count": 15,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(basis tot-spc2 3)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 16,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "Computing boundary-matrix in dimension 0.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 23m 32s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 0) :\n",
-      "<TnPr * 0> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 1.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 23m 32s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 1) :\n",
-      "<TnPr * 1> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 0 :\n",
-      "\n",
-      "\n",
-      "Component Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 23m 32s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 1.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 23m 32s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 1) :\n",
-      "<TnPr * 1> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 2.\n",
-      "Rank of the source-module : 2.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 23m 32s.\n",
-      "Computing the boundary of the generator 1/2 (dimension 2) :\n",
-      "<TnPr * 2> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 23m 32s.\n",
-      "Computing the boundary of the generator 2/2 (dimension 2) :\n",
-      "<TnPr S2 0> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 1 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 23m 32s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 2.\n",
-      "Rank of the source-module : 2.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 23m 32s.\n",
-      "Computing the boundary of the generator 1/2 (dimension 2) :\n",
-      "<TnPr * 2> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 23m 32s.\n",
-      "Computing the boundary of the generator 2/2 (dimension 2) :\n",
-      "<TnPr S2 0> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 3.\n",
-      "Rank of the source-module : 2.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 23m 32s.\n",
-      "Computing the boundary of the generator 1/2 (dimension 3) :\n",
-      "<TnPr * 3> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 23m 32s.\n",
-      "Computing the boundary of the generator 2/2 (dimension 3) :\n",
-      "<TnPr S2 1> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 2 :\n",
-      "\n",
-      "\n",
-      "Component Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 23m 32s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 3.\n",
-      "Rank of the source-module : 2.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 23m 32s.\n",
-      "Computing the boundary of the generator 1/2 (dimension 3) :\n",
-      "<TnPr * 3> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 23m 32s.\n",
-      "Computing the boundary of the generator 2/2 (dimension 3) :\n",
-      "<TnPr S2 1> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 4.\n",
-      "Rank of the source-module : 2.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 23m 32s.\n",
-      "Computing the boundary of the generator 1/2 (dimension 4) :\n",
-      "<TnPr * 4> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 23m 32s.\n",
-      "Computing the boundary of the generator 2/2 (dimension 4) :\n",
-      "<TnPr S2 2> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 3 :\n",
-      "\n",
-      "\n",
-      "Component Z/4Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 23m 32s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 4.\n",
-      "Rank of the source-module : 2.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 23m 32s.\n",
-      "Computing the boundary of the generator 1/2 (dimension 4) :\n",
-      "<TnPr * 4> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 23m 32s.\n",
-      "Computing the boundary of the generator 2/2 (dimension 4) :\n",
-      "<TnPr S2 2> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 5.\n",
-      "Rank of the source-module : 2.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 23m 32s.\n",
-      "Computing the boundary of the generator 1/2 (dimension 5) :\n",
-      "<TnPr * 5> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 23m 32s.\n",
-      "Computing the boundary of the generator 2/2 (dimension 5) :\n",
-      "<TnPr S2 3> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 4 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 23m 32s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 5.\n",
-      "Rank of the source-module : 2.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 23m 32s.\n",
-      "Computing the boundary of the generator 1/2 (dimension 5) :\n",
-      "<TnPr * 5> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 23m 32s.\n",
-      "Computing the boundary of the generator 2/2 (dimension 5) :\n",
-      "<TnPr S2 3> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 6.\n",
-      "Rank of the source-module : 2.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 23m 32s.\n",
-      "Computing the boundary of the generator 1/2 (dimension 6) :\n",
-      "<TnPr * 6> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 23m 32s.\n",
-      "Computing the boundary of the generator 2/2 (dimension 6) :\n",
-      "<TnPr S2 4> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 5 :\n",
-      "\n",
-      "\n",
-      "Component Z/4Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 23m 32s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 6.\n",
-      "Rank of the source-module : 2.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 23m 32s.\n",
-      "Computing the boundary of the generator 1/2 (dimension 6) :\n",
-      "<TnPr * 6> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 23m 32s.\n",
-      "Computing the boundary of the generator 2/2 (dimension 6) :\n",
-      "<TnPr S2 4> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 7.\n",
-      "Rank of the source-module : 2.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 23m 32s.\n",
-      "Computing the boundary of the generator 1/2 (dimension 7) :\n",
-      "<TnPr * 7> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 23m 32s.\n",
-      "Computing the boundary of the generator 2/2 (dimension 7) :\n",
-      "<TnPr S2 5> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 6 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 23m 32s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 7.\n",
-      "Rank of the source-module : 2.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 23m 32s.\n",
-      "Computing the boundary of the generator 1/2 (dimension 7) :\n",
-      "<TnPr * 7> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 23m 32s.\n",
-      "Computing the boundary of the generator 2/2 (dimension 7) :\n",
-      "<TnPr S2 5> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 8.\n",
-      "Rank of the source-module : 2.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 23m 32s.\n",
-      "Computing the boundary of the generator 1/2 (dimension 8) :\n",
-      "<TnPr * 8> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 23m 32s.\n",
-      "Computing the boundary of the generator 2/2 (dimension 8) :\n",
-      "<TnPr S2 6> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 7 :\n",
-      "\n",
-      "\n",
-      "Component Z/4Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 23m 32s.\n",
-      "\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 16,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(homology tot-spc2 0 8)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "In the following example, we take $K(\\mathbb{Z},1)$ and build a similar twisting operator. Note that in $(K(\\mathbb{Z},1))_1$, the bar object $[1]$ is represented as `(1)` whereas in $K(\\mathbb{Z}_2,1)$ it is `1`. In this case, it is known that the total space is a model of the sphere $S^3$  (Hopf fibration - see below)."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 17,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K1 Simplicial-Set]"
-      ]
-     },
-     "execution_count": 17,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def s2 (sphere 2))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 18,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K84 Abelian-Simplicial-Group]"
-      ]
-     },
-     "execution_count": 18,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def kz1 (k-z-1))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 19,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K96 Fibration K1 -> K84]"
-      ]
-     },
-     "execution_count": 19,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def tw1 (build-smmr\n",
-    "             :sorc s2\n",
-    "             :trgt kz1\n",
-    "             :degr -1\n",
-    "             :sintr #'(lambda (dmns gmsm)\n",
-    "                              (declare (ignore dmns gmsm))\n",
-    "                              (absm 0 (list 1)))\n",
-    "             :orgn '(s2-tw-kz1)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 20,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K102 Simplicial-Set]"
-      ]
-     },
-     "execution_count": 20,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def tot-spc1 (fibration-total tw1))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 21,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "Computing boundary-matrix in dimension 0.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 23m 32s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 0) :\n",
-      "<TnPr * *> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 1.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 23m 32s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 1) :\n",
-      "<TnPr * S1> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 0 :\n",
-      "\n",
-      "\n",
-      "Component Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 23m 32s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 1.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 23m 32s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 1) :\n",
-      "<TnPr * S1> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 2.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 23m 32s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 2) :\n",
-      "<TnPr S2 *> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 1 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 23m 32s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 2.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 23m 32s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 2) :\n",
-      "<TnPr S2 *> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 3.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 23m 32s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 3) :\n",
-      "<TnPr S2 S1> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 2 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 23m 32s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 3.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 23m 32s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 3) :\n",
-      "<TnPr S2 S1> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 4.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 3 :\n",
-      "\n",
-      "\n",
-      "Component Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 23m 32s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 4.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 5.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 4 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 23m 32s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 5.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 6.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 5 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 23m 32s.\n",
-      "\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 21,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(homology tot-spc1 0 6)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "We may also obtain the boundary and faces of elements of the total space:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 22,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "<CrPr - S2 - (1 2)>"
-      ]
-     },
-     "execution_count": 22,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def elem (crpr 0 's2 0 '(1 2)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 23,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 1}\n",
-       "<2 * <CrPr 0 * - (2)>>\n",
-       "<-1 * <CrPr 0 * - (3)>>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 23,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? tot-spc1 2 elem)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 24,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 0}\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 24,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? tot-spc1 *)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 25,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "<AbSm - <CrPr 0 * - (2)>> \n",
-      "<AbSm - <CrPr 0 * - (3)>> \n",
-      "<AbSm - <CrPr 0 * - (2)>> "
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 25,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(dotimes (i 3) (print (face tot-spc1 i 2 elem)))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "The program `Kenzo` provides the function `hopf-fibration` to build Hopf fibrations. The lisp definition is the following:\n",
-    "\n",
-    "```commonlisp\n",
-    "(defun HOPF-FIBRATION-SINTR (n)\n",
-    "  (declare (fixnum n))\n",
-    "  (flet ((rslt (dmns gmsm)\n",
-    "         (declare (ignore dmns gmsm))\n",
-    "         (if (zerop n)\n",
-    "             (absm 1 +empty-list+)\n",
-    "             (absm 0 (list n)))))\n",
-    "         (the sintr #'rslt)))\n",
-    "\n",
-    "(defun HOPF-FIBRATION (n)\n",
-    "  (declare (fixnum n))\n",
-    "  (the simplicial-mrph\n",
-    "     (build-smmr\n",
-    "        :sorc (sphere 2)\n",
-    "        :trgt (k-z-1)\n",
-    "        :degr -1\n",
-    "        :sintr (hopf-fibration-sintr n)\n",
-    "        :orgn `(hopf ,n))))\n",
-    "```"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "In the definition of the lisp function for the slot `sintr`, we see that the simplicial morphism applies in particular the only geometric simplex in dimension 2 of $S^2$ onto the bar object $[n] \\in (K(\\mathbb{Z},1))_1$. If $n=0$, this is $\\eta_0 [\\ ]$, i.e. the 0-degeneracy of the base point `NIL`. We give some examples of some fibrations and of the corresponding total spaces in function of the parameter `n`. First we generate 4 fibrations and apply the twisting operator on the geometrical simplex `s2`."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 26,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K187 Fibration K1 -> K84]"
-      ]
-     },
-     "execution_count": 26,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def h1 (hopf-fibration 1))\n",
-    "(def h2 (hopf-fibration 2))\n",
-    "(def h3 (hopf-fibration 3))\n",
-    "(def h10 (hopf-fibration 10))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 27,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(<AbSm - (1)> <AbSm - (2)> <AbSm - (3)> <AbSm - (10)>)"
-      ]
-     },
-     "execution_count": 27,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(mapcar #'(lambda (h) (funcall (sintr (eval h)) 2 's2)) '(h1 h2 h3 h10))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Then we generate the corresponding total space and get some homology groups. As already seen, `t1` is a strange simplicial model for the 3-sphere $S^3$. Also, `t2` is a simplcial model for the real projective space $P^3\\mathbb{R} = S^3 / (\\mathbb{Z}/2)$."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 28,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K203 Simplicial-Set]"
-      ]
-     },
-     "execution_count": 28,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def t1 (fibration-total h1))\n",
-    "(def t2  (fibration-total h2))\n",
-    "(def t3 (fibration-total h3))\n",
-    "(def t10 (fibration-total h10))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 29,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "Computing boundary-matrix in dimension 0.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 23m 32s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 0) :\n",
-      "<TnPr * *> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 1.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 23m 32s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 1) :\n",
-      "<TnPr * S1> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 0 :\n",
-      "\n",
-      "\n",
-      "Component Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 23m 32s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 1.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 23m 32s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 1) :\n",
-      "<TnPr * S1> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 2.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 23m 32s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 2) :\n",
-      "<TnPr S2 *> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 1 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 23m 32s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 2.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 23m 32s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 2) :\n",
-      "<TnPr S2 *> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 3.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 23m 32s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 3) :\n",
-      "<TnPr S2 S1> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 2 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 23m 32s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 3.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 23m 32s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 3) :\n",
-      "<TnPr S2 S1> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 4.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 3 :\n",
-      "\n",
-      "\n",
-      "Component Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 23m 32s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 4.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 5.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 4 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 23m 32s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 5.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 6.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 5 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 23m 32s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 6.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 7.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 6 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 23m 32s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 7.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 8.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 7 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 23m 32s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 8.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 9.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 8 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 23m 32s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 9.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 10.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 9 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 23m 32s.\n",
-      "\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 29,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(homology t1 0 10)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 30,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "Computing boundary-matrix in dimension 0.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 23m 32s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 0) :\n",
-      "<TnPr * *> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 1.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 23m 32s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 1) :\n",
-      "<TnPr * S1> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 0 :\n",
-      "\n",
-      "\n",
-      "Component Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 23m 32s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 1.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 23m 32s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 1) :\n",
-      "<TnPr * S1> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 2.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 23m 32s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 2) :\n",
-      "<TnPr S2 *> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 1 :\n",
-      "\n",
-      "\n",
-      "Component Z/2Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 23m 32s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 2.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 23m 32s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 2) :\n",
-      "<TnPr S2 *> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 3.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 23m 32s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 3) :\n",
-      "<TnPr S2 S1> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 2 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 23m 32s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 3.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 23m 32s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 3) :\n",
-      "<TnPr S2 S1> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 4.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 3 :\n",
-      "\n",
-      "\n",
-      "Component Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 23m 32s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 4.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 5.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 4 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 23m 32s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 5.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 6.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 5 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 23m 32s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 6.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 7.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 6 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 23m 32s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 7.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 8.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 7 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 23m 32s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 8.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 9.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 8 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 23m 32s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 9.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 10.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 9 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 23m 32s.\n",
-      "\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 30,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(homology t2 0 10)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 31,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "Computing boundary-matrix in dimension 0.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 23m 32s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 0) :\n",
-      "<TnPr * *> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 1.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 23m 32s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 1) :\n",
-      "<TnPr * S1> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 0 :\n",
-      "\n",
-      "\n",
-      "Component Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 23m 32s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 1.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 23m 32s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 1) :\n",
-      "<TnPr * S1> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 2.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 23m 32s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 2) :\n",
-      "<TnPr S2 *> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 1 :\n",
-      "\n",
-      "\n",
-      "Component Z/3Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 23m 32s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 2.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 23m 32s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 2) :\n",
-      "<TnPr S2 *> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 3.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 23m 32s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 3) :\n",
-      "<TnPr S2 S1> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 2 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 23m 32s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 3.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 23m 32s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 3) :\n",
-      "<TnPr S2 S1> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 4.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 3 :\n",
-      "\n",
-      "\n",
-      "Component Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 23m 32s.\n",
-      "\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 31,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(homology t3 0 4)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 32,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "Computing boundary-matrix in dimension 1.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 23m 32s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 1) :\n",
-      "<TnPr * S1> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 2.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 23m 32s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 2) :\n",
-      "<TnPr S2 *> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 1 :\n",
-      "\n",
-      "\n",
-      "Component Z/10Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 23m 32s.\n",
-      "\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 32,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(homology t10 1)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "## Lisp file concerned in this chapter\n",
-    "\n",
-    "`fibrations.lisp`."
-   ]
-  }
- ],
- "metadata": {
-  "kernelspec": {
-   "display_name": "SBCL Lisp",
-   "language": "lisp",
-   "name": "lisp"
-  },
-  "language_info": {
-   "codemirror_mode": "text/x-common-lisp",
-   "mimetype": "text/x-common-lisp",
-   "name": "common-lisp",
-   "pygments_lexer": "common-lisp",
-   "version": "X3J13"
-  }
- },
- "nbformat": 4,
- "nbformat_minor": 1
-}
diff --git a/examples/13_Loop_Spaces.ipynb b/examples/13_Loop_Spaces.ipynb
deleted file mode 100644
index ccf8197..0000000
--- a/examples/13_Loop_Spaces.ipynb
+++ /dev/null
@@ -1,919 +0,0 @@
-{
- "cells": [
-  {
-   "cell_type": "code",
-   "execution_count": 1,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "To load \"kenzo\":\n",
-      "  Load 1 ASDF system:\n",
-      "    kenzo\n",
-      "; Loading \"kenzo\"\n",
-      "\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "#<PACKAGE \"CAT\">"
-      ]
-     },
-     "execution_count": 1,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(ql:quickload \"kenzo\")\n",
-    "(in-package :cat)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "# Loop Spaces\n",
-    "\n",
-    "## Introduction\n",
-    "\n",
-    "Let us recall the definition of the  *free group* generated by a set ${\\cal A}$. Consider the set ${\\cal A}\\times \\lbrace +1, -1 \\rbrace$ and make, as long as there is no ambiguity, the identification $a_i= (a_i,1)$ and $a_i^{-1}= (a_i,-1)$ for all $a_i\\in{\\cal A}$.\n",
-    "\n",
-    "**Definition.**  $a_i$ and its formal inverse $a_i^{-1}$ are *letters*.\n",
-    "\n",
-    "**Definition.** A word is a *finite* sequence of letters, possibly repeated, without any pair of the form $a_ja_j^{-1}$ and $a_k^{-1}a_k$. The word is said *reduced*.\n",
-    "\n",
-    "Now, let $F(\\cal A)$ the set of *words* on $\\cal A$. It is easy to show that if we define in $F(\\cal A)$ an internal law of composition as the formal *concatenation* of two words, on which the cancelation rule is applied, i.e. any pair of the form $a_ja_j^{-1}$ and $a_k^{-1}a_k$ is replaced by the *void sequence*, then $F(\\cal A)$ is a group (non-commutative in general). The void word is the neutral element for that law. If we consider the concatenation as a  *product*, then, as usual in group theory, a sequence of $k$ times the same letter $a$ will be written $a^k$ and a sequence of $k$ times the same letter $a^{-1}$, $a^{-k}$. So a word formed from letters by the  concatenation product together with the cancellation rule, will be written under the reduced form:\n",
-    "$$a_1^{n_1}a_2^{n_2}\\ldots a_k^{n_k},\\ n_i\\in \\mathbb{Z}^*,\\ a_i\\in {\\cal A},\\  a_i \\not= a_{i+1}$$\n",
-    "and its inverse is\n",
-    "$$a_k^{-n_k}\\ldots a_2^{-n_2}a_1^{-n_1}.$$\n",
-    "Now let $X$ be a reduced simplicial set (i.e. having only one 0-simplex, namely its base point). The Kan simplicial version $GX$ of the loop space $\\Omega(|X|)$ is defined as follows. The set of $n$-simplices $GX_n$ is the free group generated by the $(n+1)$-simplices $\\sigma \\in X_{n+1}$ except those which are $n$-degenerate. In other words:\n",
-    "$$ GX_n=F(X^+_{n+1}),\\ X^+_{n+1}=X_{n+1}-\\eta_n X_n. $$\n",
-    "In fact, from a strictly mathematical point of view, the right definition is \n",
-    "$$ GX_n = F(X^+_{n+1}) / {\\overline{\\eta_n X_n}},$$\n",
-    "i.e. the quotient group of $F(X^+_{n+1})$, the free group generated by **all** the $n+1$-simplices, the $n$-degenerate ones included, by the normal subgroup ${\\overline{\\eta_n X_n}}$ generated by the $n$-degenerate simplices. Both definitions are equivalent, the second is mathematicaly correct but only the first one is visible in the program.\n",
-    "\n",
-    "For a better understanding, we may distinguish carefully a generator $\\sigma$ belonging to  $X_{n+1}$ and the corresponding letter  $\\tau (\\sigma) \\in GX_n$. So a word, element of $GX_n$ will be written \n",
-    "$${\\tau(\\sigma_1)}^{\\epsilon_1} {\\tau(\\sigma_2)}^{\\epsilon_2} \\ldots {\\tau(\\sigma_p)}^{\\epsilon_p}.$$\n",
-    "Now, let us define two homomorphisms:\n",
-    "$$\\overline{\\partial}_i^n: GX_n \\longrightarrow GX_{n-1},\\ \\overline{\\eta}_i^n: GX_n \\longrightarrow GX_{n+1},$$\n",
-    "by the following relations, keeping in mind that $\\partial_i$ and $\\eta_i$ are respectively the face and degeneracy operators acting on the  simplices of  $X$:\n",
-    "$$\n",
-    "\\begin{aligned}\n",
-    "\\overline{\\partial}_i(\\tau(\\sigma))  & = & \\tau(\\partial_i\\sigma),\\qquad 0 \\leq i < n, \\\\\n",
-    "\\overline{\\partial}_n(\\tau(\\sigma))  & = & \\tau(\\partial_{n+1}\\sigma)^{-1}\\tau(\\partial_n\\sigma), \\\\\n",
-    "\\overline{\\eta}_i(\\tau(\\sigma))    & = & \\tau(\\eta_i\\sigma),\\qquad 0 \\leq i \\leq n.\n",
-    "\\end{aligned}\n",
-    "$$\n",
-    "\n",
-    "These definitions for the generators of $GX_n$ extend to arbitrary elements in a unique way, for example:\n",
-    "$$\n",
-    "\\overline{\\partial}_i(a_1^{n_1} \\cdots a_k^{n_k}) = (\\partial_i(a_1))^{n_1} \\cdots (\\partial_i(a_k))^{n_k}\n",
-    "$$\n",
-    "It is known  that the $\\overline{\\partial}_i$ and the $\\overline{\\eta}_i$ satisfy the fundamental relations between face and degeneracy operators (see the chapter on simplicial sets). So, $GX$ is itself a simplicial set; each $GX_n$ is a group, each face and degeneracy operator is a homomorphism, so that $GX$ is a *simplicial group*. The importance of the simplicial group $GX$ is emphasized by the Kan theorem, stating that if we consider the realization $|X|$ of $X$ and the loop space  $\\Omega(|X|, x_0)$ at the base point $x_0 \\in |X|$,  then $\\Omega(|X|, x_0)$ and the realization $|GX|$ of $GX$ have the same  homotopy type.\n",
-    "\n",
-    "## Representation of letters and words\n",
-    "\n",
-    "In the system, the chosen representation for letters and words follows the very definition of the free group $F(X_{n+1}^+)$. Here, a letter is a generator of $GX_n$ i.e. an **abstract simplex** $\\sigma$ of $X^+_{n+1}$. A word will be implemented  as a sequence of such letters to a certain power (including 1). The chosen terminology is the following:\n",
-    "\n",
-    "- A term like $\\sigma^p$ is a **power**.\n",
-    "- A word ${\\sigma_1}^{\\epsilon_1} {\\sigma_2}^{\\epsilon_2} \\ldots {\\sigma_p}^{\\epsilon_p}$ is a **loop**. \n",
-    "\n",
-    "Note that, in this framework the operator $\\tau$ is not visible.\n",
-    "\n",
-    "### Representation of a power\n",
-    "\n",
-    "A power is internally represented by a lisp object of type  `apowr`. This has the form:\n",
-    "\n",
-    "`(`*dgop* *gmsm* `.` *expn*`)`\n",
-    "\n",
-    "in which we may recognize:\n",
-    "\n",
-    "- the components of the abstract simplex: *dgop* and *gmsm*,\n",
-    "- the exponent of the letter: *expn*, a non-zero integer.\n",
-    "\n",
-    "The associated  constructor is the macro `apowr`.\n",
-    "\n",
-    "`apowr` *dgop gmsm expn* *[Macro]*\n",
-    "> Build an object of type  `apowr`. The accessor macros  are respectively `apdgop`,  `apgmsm` and `apexpn`. There is no special printing function since the real object interesting for the user is not the power but rather the loop.\n",
-    "\n",
-    "### Representation of a loop\n",
-    "\n",
-    "A loop is represented by a lisp object of the form:\n",
-    "\n",
-    "`#S(LOOP` $apower_1$ ... $apower_k$`)`\n",
-    "\n",
-    "The corresponding type is `LOOP`. The  constructor is the macro `make-loop` but the practical one is `loop3` and the associated\n",
-    "printing function prints the object under the form:\n",
-    "\n",
-    "`<<Loop [`*ext-dgop1 gmsm1* *expn1*`] ... [`*ext-dgopk gmsmk* *expnk*`]>>`\n",
-    "\n",
-    "where the *ext-dgop*'s are under the form of a readable sequence of $\\eta$ operators.\n",
-    "\n",
-    "#### Notion of normalized loop\n",
-    "\n",
-    "Normalizing a loop is a matter of factoring the degeneracy operators components (the *dgop*'s) of the *apowr*'s and building an  object of type `ABSM` belonging to the simplicial set $GX$. For instance, the normalized null-loop in dimension 5 is `<AbSm 4-3-2-1-0 <<Loop>>>`. For non-null loops, the following examples show the transformation. We have written the loops under the form printed by the system.\n",
-    "\n",
-    "```\n",
-    "<<Loop [1-0 A\\2]>> ===>  <AbSm 1-0 <<Loop [A\\2]>>>\n",
-    "\n",
-    "<<Loop [3-2-1 A\\2] [4-2 B\\3]>>  ===>  <AbSm 2 <<Loop [2-1 A\\2] [3 B\\3]>>>.\n",
-    "\n",
-    "<<Loop [2-1 A\\2] [2-0 B\\2] [1-0 A\\3]>> ===>  \n",
-    "\n",
-    "       <AbSm - <<Loop [2-1 A\\2] [2-0 B\\2] [1-0 A\\3]>>>\n",
-    "\n",
-    "<<Loop [2-1-0 A\\2] [2-1-0 B\\2] [2-1-0 A\\3]>> ===>  \n",
-    "\n",
-    "       <AbSm 2-1-0 <<Loop [A\\2] [B\\2] [A\\3]>>>\n",
-    "```\n",
-    "\n",
-    "## A set of functions for loops\n",
-    "\n",
-    "To facilitate the construction of objects of `LOOP` type, a set of useful functions is provided by the system.\n",
-    "\n",
-    "`loop3` *dgop1 gmsm1 pwr1 ... dgopk gmsmk pwrk* *[Function]*\n",
-    "> Construct a  loop (a word) corresponding to the product of the abstract simplices $asm_i$, the components of which being $dgop_i$ and $gmsm_i$,  to the power $pwr_i$. The function constructs  itself the  objects of type `apowr`  from the arguments.\n",
-    "It  accepts an indefinite number of arguments, including none. If there is no argument, the null loop is created. It exists in fact in the system the constant `+null-loop+` which is  the base point of the underlying simplicial group. **Warning**: the function `loop3` does return neither a normalized loop nor a reduced word (no automatic simplification), so it is up to the user to give a correct sequence of arguments corresponding to  a reduced word.\n",
-    "\n",
-    "`loop-space-cmpr` *cmpr* *[Function]*\n",
-    "> From the comparison function *cmpr* suitable for comparing the geometrical simplices belonging to the underlying simplicial set, build a comparison function for objects of type `LOOP`.\n",
-    "\n",
-    "`loop-space-face` *cmpr face* *[Function]*\n",
-    "> From the comparison function *cmpr* and the face function *face*, build a face function for an object of type `LOOP` returning the face of such an object  as an `ABSM` type object (a normalized loop)\n",
-    "\n",
-    "`loop-space-face*` *cmpr face* *[Function]*\n",
-    "> From the comparison function *cmpr* and the face function *face*, build a *face*$*$ function.\n",
-    "See the description of the slot `face*` in the simplicial sets chapter.\n",
-    "\n",
-    "`loop-space-grml-sintr` *cmpr* *[Function]*\n",
-    "> From the comparison function *cmpr*, build a function for the group operation of the loop space (a simplicial group).\n",
-    "\n",
-    "`loop-space-grin-sintr` *dmns loop* *[Function]*\n",
-    "> Build the inverse of the object *loop* in the simplicial group. The first argument *dmns* is mandatory but ignored.\n",
-    "\n",
-    "`loop-space` *smst* `&optional (n 1)` *[Function]*\n",
-    "> If the second argument is `1` or omitted, construct, from the **reduced** simplicial set $X$, here the argument *smst*, the  corresponding simplicial group $GX$. The new created simplicial set is of course locally effective and its base point is the null loop. For any other positive integer value $n$ of the second argument, build the $n$-th iterated loop space of $X$. The basic construction is given by the following call to the function `build-smgr`:\n",
-    "```\n",
-    "                  (build-smgr   :cmpr (loop-space-cmpr cmpr)\n",
-    "                                :basis :locally-effective\n",
-    "                                :bspn +null-loop+\n",
-    "                                :face (loop-space-face cmpr face)\n",
-    "                                :face* (loop-space-face* cmpr face)\n",
-    "                                :sintr-grml (loop-space-grml-sintr cmpr)\n",
-    "                                :sintr-grin #'loop-space-grin-sintr\n",
-    "                                :orgn `(loop-space ,smst))\n",
-    "```\n",
-    "\n",
-    "`gdeltab` *[Function]*\n",
-    "> Build $\\Omega^1(\\bar{\\Delta})$. This is simply `(loop-space(deltab))`. We recall that $\\bar{\\Delta}$ is the reduced and locally effective simplicial set obtained from ${\\Delta}^\\mathbb{N}$,  by identifying all the vertices to the base point.\n",
-    "$\\Delta^\\mathbb{N}$ is the locally effective simplicial set freely generated by the positive integers.\n",
-    "\n",
-    "### Examples"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 2,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "<<Loop>>"
-      ]
-     },
-     "execution_count": 2,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(loop3)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 3,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "<<Loop[A\\2][4-2 B\\-3][3-2 C]>>"
-      ]
-     },
-     "execution_count": 3,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(loop3 0 'a 2 20 'b -3 12 'c 1)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 4,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "<<Loop[A\\2][4-2 B\\-3][3-2 C][A\\3]>>"
-      ]
-     },
-     "execution_count": 4,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(loop3 0 'a 2 20 'b -3 12 'c 1 0 'a 3)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 5,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "<<Loop[2-1-0 P\\2][5-4-3-2-1 Q\\5]>>"
-      ]
-     },
-     "execution_count": 5,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(loop3 (dgop-ext-int '(2 1 0)) 'p 2 \n",
-    "       (dgop-ext-int '(5 4 3 2 1)) 'q 5)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Let us consider now a true reduced simplicial set, namely $Moore(\\mathbb{Z}/{2\\mathbb{Z}}, 3)$, \n",
-    "whose structure is shown using the function `show-structure` defined in the Simplicial Sets chapter."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 6,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K1 Simplicial-Set]"
-      ]
-     },
-     "execution_count": 6,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def moore23 (moore 2 3))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 7,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "\n",
-      "Dimension = 0:\n",
-      "\n",
-      "        Vertices :  (*)\n",
-      "\n",
-      "Dimension = 1:\n",
-      "\n",
-      "Dimension = 2:\n",
-      "\n",
-      "Dimension = 3:\n",
-      "\n",
-      "        Simplex : M3\n",
-      "\n",
-      "                Faces : (<AbSm 1-0 *> <AbSm 1-0 *> <AbSm 1-0 *> <AbSm 1-0 *>)\n",
-      "\n",
-      "Dimension = 4:\n",
-      "\n",
-      "        Simplex : N4\n",
-      "\n",
-      "                Faces : (<AbSm - M3> <AbSm 2-1-0 *> <AbSm - M3> <AbSm 2-1-0 *> <AbSm 2-1-0 *>)"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 7,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(show-structure moore23 4)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Let us build now $\\Omega^1(Moore(\\mathbb{Z}/{2\\mathbb{Z}}, 3))$ and ask for faces of some loops. The user will note that the function face admits either `LOOP` type objects or `ABSM` type objects (normalized loop) but always returns normalized loops, i.e. an abstract simplex, according to the normal behaviour of the face function in a simplicial set."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 8,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K6 Simplicial-Group]"
-      ]
-     },
-     "execution_count": 8,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def o-moore23 (loop-space moore23))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 9,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "<AbSm 2-1-0 <<Loop>>>"
-      ]
-     },
-     "execution_count": 9,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(face o-moore23 0 4 +null-loop+)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 10,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "<AbSm - <<Loop[M3\\2]>>>"
-      ]
-     },
-     "execution_count": 10,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(face o-moore23 0 3 (loop3 0 'N4 2))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 11,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "<AbSm 1-0 <<Loop>>>"
-      ]
-     },
-     "execution_count": 11,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(face o-moore23 1 3 (loop3 0 'N4 2))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 12,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "<AbSm - <<Loop[N4\\2]>>>"
-      ]
-     },
-     "execution_count": 12,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(face o-moore23 1 4 (loop3 1 'N4 2))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 13,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "<AbSm 0 <<Loop>>>"
-      ]
-     },
-     "execution_count": 13,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(face o-moore23 0 2 (loop3 0 'M3 2))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Let us do the same with the following reduced simplicial set (`ss2`) and with $\\Omega^1(\\bar{\\Delta})$."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 14,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "The object is a STANDARD-OBJECT of type SIMPLICIAL-SET.\n",
-      "0. CMPR: #<FUNCTION S-CMPR>\n",
-      "1. BASIS: #<CLOSURE (FLET RSLT :IN FINITE-SS-BASIS) {1001EE2CFB}>\n",
-      "2. BSGN: *\n",
-      "3. DFFR: [K19 Morphism (degree -1): K18 -> K18]\n",
-      "4. GRMD: [K18 Simplicial-Set]\n",
-      "5. EFHM: \"unbound\"\n",
-      "6. IDNM: 18\n",
-      "7. ORGN: (BUILD-FINITE-SS (* 2 S2 (* * *) 3 S3 (S2 S2 S2 S2)))\n",
-      "8. CPRD: [K22 Morphism (degree 0): K18 -> K20]\n",
-      "9. FACE: #<CLOSURE (FLET RSLT :IN FINITE-SS-FACE) {1001EE2D1B}>\n",
-      "> \n",
-      "Checking the 0-simplices...\n",
-      "Checking the 1-simplices...\n",
-      "Checking the 2-simplices...\n",
-      "Checking the 3-simplices..."
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "[K18 Simplicial-Set]"
-      ]
-     },
-     "execution_count": 14,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def ss2 (build-finite-ss '( * \n",
-    "                              2 s2 (* * *) \n",
-    "                              3 s3 (s2 s2 s2 s2))))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 15,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K23 Simplicial-Group]"
-      ]
-     },
-     "execution_count": 15,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def o-ss2 (loop-space ss2))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 16,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "<AbSm - <<Loop>>>"
-      ]
-     },
-     "execution_count": 16,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(face o-ss2 0 1 (loop3 0 's2 1))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 17,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "<AbSm - <<Loop[S2\\2]>>>"
-      ]
-     },
-     "execution_count": 17,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(face o-ss2 0 2 (loop3 0 's3 2))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 18,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "<AbSm - <<Loop[S2\\2]>>>"
-      ]
-     },
-     "execution_count": 18,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(face o-ss2 1 2 (loop3 0 's3 2))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 19,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "<AbSm - <<Loop[S2\\2]>>>"
-      ]
-     },
-     "execution_count": 19,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(face o-ss2 1 2 (loop3 0 's3 2))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 20,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K40 Simplicial-Group]"
-      ]
-     },
-     "execution_count": 20,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def db (gdeltab))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 21,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "<AbSm 1-0 <<Loop>>>"
-      ]
-     },
-     "execution_count": 21,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(face db 3 3 (loop3 12 7 3))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 22,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "<AbSm 0 <<Loop[7\\3]>>>"
-      ]
-     },
-     "execution_count": 22,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(face db 3 3 (loop3 5 7 3))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 23,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "<AbSm - <<Loop[1 7\\3][0 7\\3][1-0 3\\-1][1-0 5][1-0 3\\-1][1-0 5][1-0 3\\-1][1-0 5]>>>"
-      ]
-     },
-     "execution_count": 23,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(face db 3 3 (loop3 6 7 3 5 7 3 3 7 3))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 24,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "<AbSm - <<Loop[7\\3][0 3\\-1][0 5][0 3\\-1][0 5][0 3\\-1][0 5][0 3\\-1][0 5][0 3\\-1][0 5][0 3\\-1][0 5]>>>"
-      ]
-     },
-     "execution_count": 24,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(face db 3 2 *)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "The last  statement shows that the boundary operator attached to the chain complex derived from all this machinery satisfies its fundamental property ($d\\circ d=0$)."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 25,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 1}\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 25,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? db (? db 3 (loop3 (dgop-ext-int '(3 2)) (dlop-ext-int '(0 1 2)) 3\n",
-    "                     (dgop-ext-int '(3 1)) (dlop-ext-int '(0 1 2)) 3\n",
-    "                     (dgop-ext-int '(2 1)) (dlop-ext-int '(0 1 2)) 3)))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "The loop spaces of reduced simplicial sets, provide us with new examples of algebras. So, we may apply the functor `bar`."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 26,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K52 Simplicial-Set]"
-      ]
-     },
-     "execution_count": 26,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def moore-22 (moore 2 2)) "
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 27,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "(<AbSm - *>) \n",
-      "(<AbSm 0 *>) \n",
-      "(<AbSm - M2> <AbSm 1-0 *>) \n",
-      "(<AbSm - N3> <AbSm 0 M2> <AbSm 1 M2> <AbSm 2 M2> <AbSm 2-1-0 *>) "
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 27,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(dotimes (i 4) (print (basis moore-22  i :dgnr)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 28,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K57 Simplicial-Group]"
-      ]
-     },
-     "execution_count": 28,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def o-moore-22 (loop-space moore-22))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 29,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 3}\n",
-       "<1 * <<Loop[1-0 M2][2 N3]>>>\n",
-       "<-1 * <<Loop[2-0 M2][1 N3]>>>\n",
-       "<1 * <<Loop[2-1 M2][0 N3]>>>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 29,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(aprd o-moore-22 3 (tnpr 1 (loop3 0 'm2 1) 2 (loop3 0 'n3 1)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 30,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K74 Chain-Complex]"
-      ]
-     },
-     "execution_count": 30,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def bar-om (bar o-moore-22))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 31,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 4}\n",
-       "<1 * <<Abar[4 <<Loop[1-0 M2][2 N3]>>]>>>\n",
-       "<-1 * <<Abar[4 <<Loop[2-0 M2][1 N3]>>]>>>\n",
-       "<1 * <<Abar[4 <<Loop[2-1 M2][0 N3]>>]>>>\n",
-       "<-2 * <<Abar[2 <<Loop[M2]>>][2 <<Loop[M2]>>]>>>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 31,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? bar-om 5 (abar 2 (loop3 0 'm2 1) 3 (loop3 0 'n3 1)))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "### Lisp file concerned in this chapter\n",
-    "\n",
-    "`loop-spaces.lisp`."
-   ]
-  }
- ],
- "metadata": {
-  "kernelspec": {
-   "display_name": "SBCL Lisp",
-   "language": "lisp",
-   "name": "lisp"
-  },
-  "language_info": {
-   "codemirror_mode": "text/x-common-lisp",
-   "mimetype": "text/x-common-lisp",
-   "name": "common-lisp",
-   "pygments_lexer": "common-lisp",
-   "version": "X3J13"
-  }
- },
- "nbformat": 4,
- "nbformat_minor": 1
-}
diff --git a/examples/14_Disk_pasting_and_suspension.ipynb b/examples/14_Disk_pasting_and_suspension.ipynb
deleted file mode 100644
index 724f602..0000000
--- a/examples/14_Disk_pasting_and_suspension.ipynb
+++ /dev/null
@@ -1,3803 +0,0 @@
-{
- "cells": [
-  {
-   "cell_type": "code",
-   "execution_count": 1,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "To load \"kenzo\":\n",
-      "  Load 1 ASDF system:\n",
-      "    kenzo\n",
-      "; Loading \"kenzo\"\n",
-      "\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "#<PACKAGE \"CAT\">"
-      ]
-     },
-     "execution_count": 1,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(ql:quickload \"kenzo\")\n",
-    "(in-package :cat)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "# Disk pasting and suspension\n",
-    "\n",
-    "## Introduction\n",
-    "\n",
-    "Let us recall the technique of space construction by *attaching maps* (**Marvin Greenberg** in\n",
-    "*Lectures on Algebraic Topology.* Benjamin Inc, 1967.). Let $A$ be a subspace of a space $X$ and a map $f$ of $A$ into a space $Y$. In the space $X \\coprod Y$, the disjoint union of $X$ and $Y$, let us identify each $x$ in $A$ with its image $f(x)$ in $Y$. The quotient space $Z=X\\bigcup_f Y$ of the space $X\\coprod Y$ by the equivalence relation that the identification above determines, is called the *adjunction space* of the system $(X \\supset A), (Y\\supset f(A))$. The quotient map $g: X\\coprod Y \\rightarrow Z$ sends $Y$ onto a subspace of $Z$. \n",
-    "\n",
-    "In this section, we shall take as pair $(X,A)$ the pair $(D^n, S^{n-1})$, where $D^n$ is the  unit disc of $\\mathbb{R}^n$ and  $S^{n-1}$ is the sphere of dimension ${n-1}$, boundary of $D^n$. In this case, the space $Z=D^n\\bigcup_f Y$ is said to be obtained from $Y$ by *attaching an n-disc via* $f$, or *disk pasting*.\n",
-    "\n",
-    "## The functions for  disk pasting\n",
-    "\n",
-    "The **Kenzo** program implements the previous technique of  space construction, via simplicial sets. We know that $D^n$ is homeomorphic to the standard simplex $\\Delta^n$. The method used by the implementor is the following:\n",
-    "\n",
-    "Starting from a simplicial set *ss* representing $Y$, build a new one having the same simplices as *ss* and in dimension $n$, a new added simplex described by the user. This description consists of:\n",
-    "- a name (a symbol) for this new generator,\n",
-    "- the list of all its $n+1$ faces.\n",
-    "\n",
-    "`disk-pasting` *smst dmns new faces* *[Function]*\n",
-    "> Construct, from the  simplicial set  smst, a new simplicial set by attaching the unit disc of dimension *dmns*. The argument *faces* is the list of  $dmn+1$  simplices corresponding to the faces of the new simplex attached to *smst*. These simplices are, in principle, written as abstract simplices (*absm*), nevertheless it is possible to write them as geometric simplices (*gmsm*). In this case, the corresponding geometric simplices must have the correct dimension. The program will transform these possible *gmsm*s into *absm*s in the *faces* argument. The argument *new* allows the user to name this new added simplex by a symbol. The program verifies the coherence of the addition of the new simplex by calling internally the function `check-faces`.\n",
-    "\n",
-    "`chcm-disk-pasting` *chcm dmns new  bndr* *[Function]*\n",
-    "> Construct, from the chain complex  *chcm* (chain groups ${\\cal C}_*$), a new chain complex (chain groups ${\\cal C}_*'$), where:\n",
-    "$$C'_p=C_p,\\quad \\forall p \\not= dmns,$$\n",
-    "$$C'_{dmns}= C_{dmns} \\oplus \\mathbb{Z}\\, new.$$\n",
-    "The symbol `new` is the name given by the user to a new generator in dimension $dmns$ and *bndr* is a combination of degree $dmns-1$ representing the  boundary of the generator *new*. Of course, one must have $d_{dmns-1}(bndr)=0.$\n",
-    "\n",
-    "`hmeq-disk-pasting` *hmeq dmns new bndr* `&key` *new-lbcc* *[Function]*\n",
-    "> Construct a homotopy equivalence by attaching  the  generator *new* of dimension *dmns* with boundary *bndr* to the left bottom chain complex of the homotopy equivalence *hmeq*. This modification of the left bottom chain complex is propagated along the whole new homotopy equivalence.\n",
-    "The key parameter *new-lbcc* is for internal use.\n",
-    "\n",
-    "### Example\n",
-    "\n",
-    "Let us begin by a trivial example corresponding to the well known following result: if $f$ maps $S^{n-1}$ onto a point $Y$, then by disk pasting we obtain a space homeomorphic to $S^n$. Here, the point $Y$ will be represented by the trivial simplicial set:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 2,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "The object is a STANDARD-OBJECT of type SIMPLICIAL-SET.\n",
-      "0. CMPR: #<FUNCTION S-CMPR>\n",
-      "1. BASIS: #<CLOSURE (FLET RSLT :IN FINITE-SS-BASIS) {1001988EEB}>\n",
-      "2. BSGN: *\n",
-      "3. DFFR: [K2 Morphism (degree -1): K1 -> K1]\n",
-      "4. GRMD: [K1 Simplicial-Set]\n",
-      "5. EFHM: \"unbound\"\n",
-      "6. IDNM: 1\n",
-      "7. ORGN: (BUILD-FINITE-SS (*))\n",
-      "8. CPRD: [K5 Morphism (degree 0): K1 -> K3]\n",
-      "9. FACE: #<CLOSURE (FLET RSLT :IN FINITE-SS-FACE) {1001988F0B}>\n",
-      "> \n",
-      "Checking the 0-simplices..."
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "[K1 Simplicial-Set]"
-      ]
-     },
-     "execution_count": 2,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def s0 (build-finite-ss '(*)))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "In the identification process, the 1-simplices boundaries of the 2-simplex $\\Delta^2$ are applied on the 0--degeneracy of the base point $*$."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 3,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K6 Simplicial-Set]"
-      ]
-     },
-     "execution_count": 3,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def s2 (disk-pasting s0 \n",
-    "                        2 \n",
-    "                       's2 \n",
-    "                       (list (absm 1 '*) (absm 1 '*) (absm 1 '*))  )) "
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 4,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "\n",
-      "Dimension = 0:\n",
-      "\n",
-      "        Vertices :  (*)\n",
-      "\n",
-      "Dimension = 1:\n",
-      "\n",
-      "Dimension = 2:\n",
-      "\n",
-      "        Simplex : S2\n",
-      "\n",
-      "                Faces : (<AbSm 0 *> <AbSm 0 *> <AbSm 0 *>)"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 4,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(show-structure s2 2)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "More interesting is the construction of the successive projectives spaces $P^i\\mathbb{R}$. Let us begin by $P^1\\mathbb{R}$. We start from a point (the simplicial set `s0`) and we identify the two boundary points of $\\Delta^1$ to the base point of `s0`. The new simplex to be added to `s0` is of dimension 1 and its 2 faces  are the base point itself. It is well known that the resulting corresponding  space is homeomorphic to the circle $S^1$."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 5,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K11 Simplicial-Set]"
-      ]
-     },
-     "execution_count": 5,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def p1r (disk-pasting s0 1 'd1 (list (absm 0 '*)(absm 0 '*))))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 6,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "\n",
-      "Dimension = 0:\n",
-      "\n",
-      "        Vertices :  (*)\n",
-      "\n",
-      "Dimension = 1:\n",
-      "\n",
-      "        Simplex : D1\n",
-      "\n",
-      "                Faces : (<AbSm - *> <AbSm - *>)"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 6,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(show-structure p1r 1)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 7,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "Computing boundary-matrix in dimension 0.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 0) :\n",
-      "* \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 1.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 1) :\n",
-      "D1 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 0 :\n",
-      "\n",
-      "\n",
-      "Component Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 1.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 1) :\n",
-      "D1 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 2.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 1 :\n",
-      "\n",
-      "\n",
-      "Component Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 2.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 3.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 2 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 7,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(dotimes (i 3) (homology p1r i))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "The projective spaces $P^n\\mathbb{R}$ of higher degree may be constructed by the following iterative rule. Suppose we have built a simplicial set corresponding to $P^{n-1}\\mathbb{R}$ and that we have named the  additional simplex $d_{n-1}$. Suppose also that $d_{n-2}$ has been previously defined in the same process ($d_0$ is the base point). Then the simplicial set corresponding to $P^n\\mathbb{R}$ is obtained by pasting $\\Delta^n$ with the following description of the additional simplex: \n",
-    "\n",
-    "- the name of the new simplex is  $d_n$,\n",
-    "- the  faces of $d_n$ are:\n",
-    "$$\n",
-    "\\begin{aligned}\n",
-    "\\partial_0 d_n & = & d_{n-1},\\\\\n",
-    "\\partial_1 d_n & = & \\eta_0 d_{n-2},\\\\\n",
-    "\\partial_2 d_n & = & \\eta_1 d_{n-2},\\\\\n",
-    "\\cdots         & = & \\cdots , \\\\\n",
-    "\\partial_{n-1} d_n & = & \\eta_{n-2} d_{n-2},\\\\\n",
-    "\\partial_n d_n & = & d_{n-1}.\n",
-    "\\end{aligned}\n",
-    "$$\n",
-    "\n",
-    "So, applying this rule, we may construct a  model for  $P^i\\mathbb{R},\\, i=2,3,4$ and verify  the well known results about their respective homology groups."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 8,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K31 Simplicial-Set]"
-      ]
-     },
-     "execution_count": 8,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def p2r (disk-pasting p1r 2 'd2\n",
-    "                        (list (absm 0 'd1)\n",
-    "                              (absm 1 '*)\n",
-    "                              (absm 0 'd1)) ))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 9,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "\n",
-      "Dimension = 0:\n",
-      "\n",
-      "        Vertices :  (*)\n",
-      "\n",
-      "Dimension = 1:\n",
-      "\n",
-      "        Simplex : D1\n",
-      "\n",
-      "                Faces : (<AbSm - *> <AbSm - *>)\n",
-      "\n",
-      "Dimension = 2:\n",
-      "\n",
-      "        Simplex : D2\n",
-      "\n",
-      "                Faces : (<AbSm - D1> <AbSm 0 *> <AbSm - D1>)"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 9,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(show-structure p2r 2)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 10,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "Computing boundary-matrix in dimension 0.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 0) :\n",
-      "* \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 1.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 1) :\n",
-      "D1 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 0 :\n",
-      "\n",
-      "\n",
-      "Component Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 1.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 1) :\n",
-      "D1 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 2.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 2) :\n",
-      "D2 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 1 :\n",
-      "\n",
-      "\n",
-      "Component Z/2Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 2.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 2) :\n",
-      "D2 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 3.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 2 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 10,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(dotimes (i 3) (homology p2r i))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 11,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K49 Simplicial-Set]"
-      ]
-     },
-     "execution_count": 11,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def p3r (disk-pasting p2r 3 'd3\n",
-    "                        (list (absm 0 'd2) \n",
-    "                              (absm 1 'd1)\n",
-    "                              (absm 2 'd1)\n",
-    "                              (absm 0 'd2))))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 12,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "\n",
-      "Dimension = 0:\n",
-      "\n",
-      "        Vertices :  (*)\n",
-      "\n",
-      "Dimension = 1:\n",
-      "\n",
-      "        Simplex : D1\n",
-      "\n",
-      "                Faces : (<AbSm - *> <AbSm - *>)\n",
-      "\n",
-      "Dimension = 2:\n",
-      "\n",
-      "        Simplex : D2\n",
-      "\n",
-      "                Faces : (<AbSm - D1> <AbSm 0 *> <AbSm - D1>)\n",
-      "\n",
-      "Dimension = 3:\n",
-      "\n",
-      "        Simplex : D3\n",
-      "\n",
-      "                Faces : (<AbSm - D2> <AbSm 0 D1> <AbSm 1 D1> <AbSm - D2>)"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 12,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(show-structure p3r 3)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 13,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "Computing boundary-matrix in dimension 0.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 0) :\n",
-      "* \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 1.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 1) :\n",
-      "D1 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 0 :\n",
-      "\n",
-      "\n",
-      "Component Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 1.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 1) :\n",
-      "D1 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 2.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 2) :\n",
-      "D2 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 1 :\n",
-      "\n",
-      "\n",
-      "Component Z/2Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 2.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 2) :\n",
-      "D2 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 3.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 3) :\n",
-      "D3 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 2 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 3.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 3) :\n",
-      "D3 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 4.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 3 :\n",
-      "\n",
-      "\n",
-      "Component Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 13,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(dotimes (i 4)(homology p3r i))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 14,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K67 Simplicial-Set]"
-      ]
-     },
-     "execution_count": 14,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def p4r (disk-pasting p3r 4 'd4 \n",
-    "                        (list (absm 0 'd3)\n",
-    "                              (absm 1 'd2)\n",
-    "                              (absm 2 'd2) \n",
-    "                              (absm 4 'd2)\n",
-    "                              (absm 0 'd3))))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 15,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "Computing boundary-matrix in dimension 0.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 0) :\n",
-      "* \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 1.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 1) :\n",
-      "D1 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 0 :\n",
-      "\n",
-      "\n",
-      "Component Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 1.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 1) :\n",
-      "D1 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 2.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 2) :\n",
-      "D2 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 1 :\n",
-      "\n",
-      "\n",
-      "Component Z/2Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 2.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 2) :\n",
-      "D2 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 3.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 3) :\n",
-      "D3 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 2 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 3.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 3) :\n",
-      "D3 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 4.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 4) :\n",
-      "D4 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 3 :\n",
-      "\n",
-      "\n",
-      "Component Z/2Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 4.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 4) :\n",
-      "D4 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 5.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 4 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 15,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(dotimes (i 5) (homology p4r i))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Let us give now some examples with the function `chcm-disk-pasting`. We are going to work with the unit chain complex (obtained by the function `z-chcm`, see chapter 1), having a unique non null component, namely a $\\mathbb{Z}$-module of degree 0 generated by the unique generator `:Z-gnrt`."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 16,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K85 Chain-Complex]"
-      ]
-     },
-     "execution_count": 16,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def *ccz* (z-chcm))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Using the function `chcm-disk-pasting`, let us construct from `*ccz*` a new chain complex  having in dimension 1 a unique  new generator `gen-1` whose boundary  is 5 times the unique generator in dimension 0. In this new chain complex the homology group in dimension 0 is $\\mathbb{Z}/5\\,\\mathbb{Z}$."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 17,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K87 Chain-Complex]"
-      ]
-     },
-     "execution_count": 17,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def newcc-0 (chcm-disk-pasting *ccz* 1 'gen-1 (cmbn 0 5 :Z-gnrt)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 18,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "Computing boundary-matrix in dimension 0.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 0) :\n",
-      ":Z-GNRT \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 1.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 1) :\n",
-      "GEN-1 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 0 :\n",
-      "\n",
-      "Component Z/5Z\n",
-      "\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "(\n",
-       "----------------------------------------------------------------------{CMBN 0}\n",
-       "<1 * Z-GNRT>\n",
-       "------------------------------------------------------------------------------\n",
-       ")"
-      ]
-     },
-     "execution_count": 18,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(chcm-homology-gen newcc-0 0)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 19,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "Computing boundary-matrix in dimension 1.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 1) :\n",
-      "GEN-1 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 2.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 1 :\n",
-      "\n",
-      "\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 19,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(chcm-homology-gen newcc-0 1)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Let us do the same with a generator whose boundary is  165 times the generator `:Z-gnrt`:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 20,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K89 Chain-Complex]"
-      ]
-     },
-     "execution_count": 20,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def newcc-1 (chcm-disk-pasting *ccz* 1 'gen-1 (cmbn 0 165 :Z-gnrt)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 21,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "Computing boundary-matrix in dimension 0.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 0) :\n",
-      ":Z-GNRT \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 1.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 1) :\n",
-      "GEN-1 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 0 :\n",
-      "\n",
-      "Component Z/165Z\n",
-      "\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "(\n",
-       "----------------------------------------------------------------------{CMBN 0}\n",
-       "<1 * Z-GNRT>\n",
-       "------------------------------------------------------------------------------\n",
-       ")"
-      ]
-     },
-     "execution_count": 21,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(chcm-homology-gen newcc-1 0)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Now from the chain complex `newcc-1`, let us build a new one, `newcc-2`, by adding in dimension 1 a second generator whose boundary  is 182 times the generator `:Z-gnrt`. The homology group in dimension 0 of this new chain complex is  the null group, since 165 and 182 are relatively prime integers."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 22,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K91 Chain-Complex]"
-      ]
-     },
-     "execution_count": 22,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def newcc-2 (chcm-disk-pasting newcc-1 1 'gen-2 (cmbn 0 182 :Z-gnrt)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 23,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "Computing boundary-matrix in dimension 0.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 0) :\n",
-      ":Z-GNRT \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 1.\n",
-      "Rank of the source-module : 2.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 1/2 (dimension 1) :\n",
-      "GEN-2 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 2/2 (dimension 1) :\n",
-      "GEN-1 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 0 :\n",
-      "\n",
-      "\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 23,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(chcm-homology-gen newcc-2 0)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 24,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "Computing boundary-matrix in dimension 1.\n",
-      "Rank of the source-module : 2.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 1/2 (dimension 1) :\n",
-      "GEN-2 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 2/2 (dimension 1) :\n",
-      "GEN-1 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 2.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 1 :\n",
-      "\n",
-      "Component Z\n",
-      "\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "(\n",
-       "----------------------------------------------------------------------{CMBN 1}\n",
-       "<-165 * GEN-2>\n",
-       "<182 * GEN-1>\n",
-       "------------------------------------------------------------------------------\n",
-       ")"
-      ]
-     },
-     "execution_count": 24,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(chcm-homology-gen newcc-2 1)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "As a second example, let us start from $\\Omega^1(S^3)$."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 25,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K93 Simplicial-Set]"
-      ]
-     },
-     "execution_count": 25,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def s3 (sphere 3))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 26,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K98 Simplicial-Group]"
-      ]
-     },
-     "execution_count": 26,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def os3 (loop-space s3))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "In the following instruction, we locate in the symbol `fund-simp` the canonical generator of $\\pi_2 (\\Omega^1S^3)$, that is the 2-simplex coming from the original sphere:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 27,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "<AbSm - <<Loop[S3]>>>"
-      ]
-     },
-     "execution_count": 27,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def fund-simp (absm 0 (loop3 0 's3 1)))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "We need also the 2-degeneracy of the base point of the loop space:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 28,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "<AbSm 1-0 <<Loop>>>"
-      ]
-     },
-     "execution_count": 28,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def null-simp (absm 3 +null-loop+))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "We may  build now a new  object by pasting a disk $D^3$ as indicated by the following call:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 29,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K110 Simplicial-Set]"
-      ]
-     },
-     "execution_count": 29,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def dos3 (disk-pasting os3 3 '<D3> \n",
-    "                        (list fund-simp null-simp fund-simp null-simp)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 30,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "Computing boundary-matrix in dimension 2.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 2) :\n",
-      "<<AlLp[2 S3]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 3.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 3) :\n",
-      "<D3> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 2 :\n",
-      "\n",
-      "\n",
-      "Component Z/2Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 30,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(homology dos3 2)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 31,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "Computing boundary-matrix in dimension 3.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 3) :\n",
-      "<D3> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 4.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 4) :\n",
-      "<<AlLp[2 S3][2 S3]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 3 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 31,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(homology dos3 3)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Then, let us  build the  loop space of the object `dos3` and show the homology in dimension 5:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 32,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K229 Simplicial-Group]"
-      ]
-     },
-     "execution_count": 32,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def odos3 (loop-space dos3))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 33,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "Computing boundary-matrix in dimension 5.\n",
-      "Rank of the source-module : 14.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 1/14 (dimension 5) :\n",
-      "<<AlLp[5 <<AlLp[2 S3][2 S3][2 S3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 2/14 (dimension 5) :\n",
-      "<<AlLp[2 <D3>][3 <<AlLp[2 S3][2 S3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 3/14 (dimension 5) :\n",
-      "<<AlLp[3 <<AlLp[2 S3][2 S3]>>][2 <D3>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 4/14 (dimension 5) :\n",
-      "<<AlLp[1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][3 <<AlLp[2 S3][2 S3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 5/14 (dimension 5) :\n",
-      "<<AlLp[1 <<AlLp[2 S3]>>][2 <D3>][2 <D3>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 6/14 (dimension 5) :\n",
-      "<<AlLp[1 <<AlLp[2 S3]>>][3 <<AlLp[2 S3][2 S3]>>][1 <<AlLp[2 S3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 7/14 (dimension 5) :\n",
-      "<<AlLp[2 <D3>][1 <<AlLp[2 S3]>>][2 <D3>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 8/14 (dimension 5) :\n",
-      "<<AlLp[2 <D3>][2 <D3>][1 <<AlLp[2 S3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 9/14 (dimension 5) :\n",
-      "<<AlLp[3 <<AlLp[2 S3][2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 10/14 (dimension 5) :\n",
-      "<<AlLp[1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][2 <D3>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 11/14 (dimension 5) :\n",
-      "<<AlLp[1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][2 <D3>][1 <<AlLp[2 S3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 12/14 (dimension 5) :\n",
-      "<<AlLp[1 <<AlLp[2 S3]>>][2 <D3>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 13/14 (dimension 5) :\n",
-      "<<AlLp[2 <D3>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 14/14 (dimension 5) :\n",
-      "<<AlLp[1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 6.\n",
-      "Rank of the source-module : 26.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 1/26 (dimension 6) :\n",
-      "<<AlLp[1 <<AlLp[2 S3]>>][5 <<AlLp[2 S3][2 S3][2 S3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 2/26 (dimension 6) :\n",
-      "<<AlLp[3 <<AlLp[2 S3][2 S3]>>][3 <<AlLp[2 S3][2 S3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 3/26 (dimension 6) :\n",
-      "<<AlLp[5 <<AlLp[2 S3][2 S3][2 S3]>>][1 <<AlLp[2 S3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 4/26 (dimension 6) :\n",
-      "<<AlLp[1 <<AlLp[2 S3]>>][2 <D3>][3 <<AlLp[2 S3][2 S3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 5/26 (dimension 6) :\n",
-      "<<AlLp[1 <<AlLp[2 S3]>>][3 <<AlLp[2 S3][2 S3]>>][2 <D3>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 6/26 (dimension 6) :\n",
-      "<<AlLp[2 <D3>][1 <<AlLp[2 S3]>>][3 <<AlLp[2 S3][2 S3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 7/26 (dimension 6) :\n",
-      "<<AlLp[2 <D3>][2 <D3>][2 <D3>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 8/26 (dimension 6) :\n",
-      "<<AlLp[2 <D3>][3 <<AlLp[2 S3][2 S3]>>][1 <<AlLp[2 S3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 9/26 (dimension 6) :\n",
-      "<<AlLp[3 <<AlLp[2 S3][2 S3]>>][1 <<AlLp[2 S3]>>][2 <D3>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 10/26 (dimension 6) :\n",
-      "<<AlLp[3 <<AlLp[2 S3][2 S3]>>][2 <D3>][1 <<AlLp[2 S3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 11/26 (dimension 6) :\n",
-      "<<AlLp[1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][3 <<AlLp[2 S3][2 S3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 12/26 (dimension 6) :\n",
-      "<<AlLp[1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][2 <D3>][2 <D3>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 13/26 (dimension 6) :\n",
-      "<<AlLp[1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][3 <<AlLp[2 S3][2 S3]>>][1 <<AlLp[2 S3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 14/26 (dimension 6) :\n",
-      "<<AlLp[1 <<AlLp[2 S3]>>][2 <D3>][1 <<AlLp[2 S3]>>][2 <D3>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 15/26 (dimension 6) :\n",
-      "<<AlLp[1 <<AlLp[2 S3]>>][2 <D3>][2 <D3>][1 <<AlLp[2 S3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 16/26 (dimension 6) :\n",
-      "<<AlLp[1 <<AlLp[2 S3]>>][3 <<AlLp[2 S3][2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 17/26 (dimension 6) :\n",
-      "<<AlLp[2 <D3>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][2 <D3>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 18/26 (dimension 6) :\n",
-      "<<AlLp[2 <D3>][1 <<AlLp[2 S3]>>][2 <D3>][1 <<AlLp[2 S3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 19/26 (dimension 6) :\n",
-      "<<AlLp[2 <D3>][2 <D3>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 20/26 (dimension 6) :\n",
-      "<<AlLp[3 <<AlLp[2 S3][2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 21/26 (dimension 6) :\n",
-      "<<AlLp[1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][2 <D3>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 22/26 (dimension 6) :\n",
-      "<<AlLp[1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][2 <D3>][1 <<AlLp[2 S3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 23/26 (dimension 6) :\n",
-      "<<AlLp[1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][2 <D3>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 24/26 (dimension 6) :\n",
-      "<<AlLp[1 <<AlLp[2 S3]>>][2 <D3>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 25/26 (dimension 6) :\n",
-      "<<AlLp[2 <D3>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 26/26 (dimension 6) :\n",
-      "<<AlLp[1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>][1 <<AlLp[2 S3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 5 :\n",
-      "\n",
-      "\n",
-      "Component Z/2Z\n",
-      "\n",
-      "Component Z/2Z\n",
-      "\n",
-      "Component Z/2Z\n",
-      "\n",
-      "Component Z/2Z\n",
-      "\n",
-      "Component Z/2Z\n",
-      "\n",
-      "Component Z/2Z\n",
-      "\n",
-      "Component Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 33,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(homology odos3 5)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "### Searching Homology for objects created by disk pasting\n",
-    "\n",
-    "The comment list of an object created by disk pasting contains various informations as shown by the simple following example"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 34,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "The object is a STANDARD-OBJECT of type SIMPLICIAL-SET.\n",
-      "0. CMPR: #<FUNCTION S-CMPR>\n",
-      "1. BASIS: #<CLOSURE (FLET RSLT :IN FINITE-SS-BASIS) {1001988EEB}>\n",
-      "2. BSGN: *\n",
-      "3. DFFR: [K2 Morphism (degree -1): K1 -> K1]\n",
-      "4. GRMD: [K1 Simplicial-Set]\n",
-      "5. EFHM: [K19 Homotopy-Equivalence K1 <= K1 => K1]\n",
-      "6. IDNM: 1\n",
-      "7. ORGN: (BUILD-FINITE-SS (*))\n",
-      "8. CPRD: [K5 Morphism (degree 0): K1 -> K3]\n",
-      "9. FACE: #<CLOSURE (FLET RSLT :IN FINITE-SS-FACE) {1001988F0B}>\n",
-      "> \n",
-      "Checking the 0-simplices..."
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "[K1 Simplicial-Set]"
-      ]
-     },
-     "execution_count": 34,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def s0 (build-finite-ss '(*)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 35,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K372 Simplicial-Set]"
-      ]
-     },
-     "execution_count": 35,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def s2 (disk-pasting s0 \n",
-    "                        2 \n",
-    "                       's2 \n",
-    "                       (list (absm 1 '*) (absm 1 '*) (absm 1 '*))  ))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 36,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(DISK-PASTING [K1 Simplicial-Set] 2 S2 (<AbSm 0 *> <AbSm 0 *> <AbSm 0 *>))"
-      ]
-     },
-     "execution_count": 36,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(orgn s2)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "In fact, the comment list contains the very arguments used to realize the attaching. The method retrieves those arguments, gets the homotopy equivalence value of the `efhm` slot of the old object -creating it if necessary - then build a new homotopy equivalence, by calling the function `hmeq-disk-pasting` *hmeq* which takes into account the attaching.\n",
-    "\n",
-    "```commonlisp\n",
-    "(DEFMETHOD SEARCH-EFHM (smst (orgn (eql 'disk-pasting)))\n",
-    "  (declare (type simplicial-set smst))\n",
-    "  (the homotopy-equivalence\n",
-    "   (destructuring-bind (old-smst dmns new faces) (rest (orgn smst))\n",
-    "       (declare\n",
-    "          (type simplicial-set old-smst)\n",
-    "          (fixnum dmns)\n",
-    "          (symbol new)\n",
-    "          (ignore faces))\n",
-    "       (hmeq-disk-pasting \n",
-    "               (efhm old-smst)\n",
-    "               dmns new (? smst dmns new)\n",
-    "               :new-lbcc smst))))\n",
-    "```\n",
-    "\n",
-    "## The functions for the suspension\n",
-    "\n",
-    "In **Kenzo** the suspension process is realized by the function `suspension`. This function has one argument, a reduced  object (chain complex, simplicial set, etc.). **If the object is not reduced, the result is undefined**. The CLOS mechanism is used to apply an adequate method for building the suspension of the object. For a chain complex, a new base point is created with name `:s-bsgn` and the degree of the generators is increased by 1. If the suspension process is applied to a homotopy equivalence, then firstly, the left bottom chain complex is suspended and secondly, the modification is propagated along the  whole homotopy equivalence.\n",
-    "\n",
-    "`suspension-cmpr` *cmpr* *[Function]*\n",
-    "> From the comparison function *cmpr*, build a comparison function to compare two generators of a suspension.\n",
-    "\n",
-    "`suspension-basis` *basis* *[Function]*\n",
-    "> From the function *basis* of  a chain complex, build a basis function for the suspension of this chain complex. In degree 0, the only generator is `:s-bsgn`, in degree 1, the basis is void and in degree $k,\\,k\\ge 2$, the elements of the basis of the suspension are the elements of the initial chain complex in degree $k-1$.\n",
-    "\n",
-    "`suspension-intr-dffr` *dffr* *[Function]*\n",
-    "> From the lisp differential function *dffr* of a chain complex, build the lisp differential function for the suspension of this chain complex.\n",
-    "\n",
-    "`suspension-intr-cprd` *cmbn* *[Function]*\n",
-    "> Return the result of the  application of the coproduct of a suspension (considered as a coalgebra) upon the combination *cmbn*. Note that this function does not need any other argument than the combination.\n",
-    "\n",
-    "`suspension-face` *face* *[Function]*\n",
-    "> From the function face of a simplicial set, build the face function for the suspension of this simplicial set.\n",
-    "\n",
-    "`suspension-intr` *mrph* *[Function]*\n",
-    "> From a **Kenzo** morphism *mrph*, build an internal function  corresponding to the suspension of the initial morphism. This function will be applied to a combination assumed to belong to a suspension of a chain complex.\n",
-    "\n",
-    "`suspension` *obj* `&optional` *(n 1)* *[Function]*\n",
-    "> Construct a new object, the suspension of the **reduced** object *obj*. The (geometrical) base point of the suspension of a chain complex (or simplicial set) is named  `:s-bsgn`. The optional parameter *n* (default: 1) allows to create in one instruction iterated suspensions. This function calls the adequate method (`suspension-1`) for the object *obj*.\n",
-    "\n",
-    "`suspension-1` *chcm* *[Method]*\n",
-    "> Build the chain complex suspension of the chain complex *chcm*, using the basic functions above, as shown in the following call to `build-chcm`:\n",
-    "```commonlisp\n",
-    "           (build-chcm\n",
-    "             :cmpr (suspension-cmpr cmpr)\n",
-    "             :basis (suspension-basis basis)\n",
-    "             :bsgn :s-bsgn\n",
-    "             :intr-dffr (suspension-intr-dffr dffr)\n",
-    "             :strt :cmbn\n",
-    "             :orgn `(suspension ,chcm))\n",
-    "```\n",
-    "\n",
-    "`suspension-1` *clbg* *[Method]*\n",
-    "> Return the coalgebra associated to the suspension of the coalgebra *clbg*. This calls internally the method for the suspension of the chain complex *clbg* then assigns the function `suspension-intr-cprd` to the value of the slot `cprd`.\n",
-    "\n",
-    "`suspension-1` *smst* *[Method]*\n",
-    "> Return the simplicial set, suspension of the simplicial set *smst*. This function uses the previous basic function `suspension-face`. The resulting object is also a coalgebra with a coproduct defined by the function `suspension-intr-cprd`.\n",
-    "\n",
-    "`suspension-1` *mrph* *[Method]*\n",
-    "> Build the suspension of the morphism *mrph*. This is a morphism of the same degree as *mrph*. If *mrph* is the zero morphism, return the zero morphism between the suspensions of the source and target of *mrph*. If *mrph* is the identity morphim, return the identity morphism upon the suspension of the source of *mrph*. Otherwise, return the morphism built by the following call to `build-mrph`:\n",
-    "```commonlisp\n",
-    "              (build-mrph\n",
-    "                 :sorc (suspension (sorc mrph))\n",
-    "                 :trgt (suspension (trgt mrph))\n",
-    "                 :degr (degr mrph)\n",
-    "                 :intr (suspension-intr mrph)\n",
-    "                 :strt :cmbn\n",
-    "                 :orgn `(suspension ,mrph))\n",
-    "```\n",
-    "\n",
-    "`suspension-1` *rdct* *[Method]*\n",
-    "> Build the suspension of the reduction *rdct*. If *rdct* is the trivial reduction upon a chain complex ${\\cal C}$, return the trivial reduction upon the suspension of ${\\cal C}$. Otherwise, return the reduction built by the following call to the function `build-rdct`:\n",
-    "```commonlisp\n",
-    "              (build-rdct\n",
-    "                 :f (suspension (f rdct))\n",
-    "                 :g (suspension (g rdct))\n",
-    "                 :h (suspension (h rdct))\n",
-    "                 :orgn `(suspension ,rdct))\n",
-    "```\n",
-    "\n",
-    "`suspension-1` *hmeq* *[Method]*\n",
-    "> Build the suspension of the  homotopy equivalence *hmeq*. If *hmeq* is the trivial \n",
-    "homotopy equivalence  upon a chain complex ${\\cal C}$, return the trivial homotopy equivalence upon\n",
-    "the suspension of ${\\cal C}$. Otherwise, return the homotopy equivalence built by the following call to the function `build-hmeq`:\n",
-    "```commonlisp\n",
-    "              (build-hmeq\n",
-    "                 :lrdct (suspension (lrdct hmeq))\n",
-    "                 :rrdct (suspension (rrdct hmeq))\n",
-    "                 :orgn `(suspension ,hmeq))\n",
-    "```\n",
-    "\n",
-    "### Examples\n",
-    "\n",
-    "Firstly we test  the coproduct of the suspension of $\\bar\\Delta$. In the third statement, the generators 7 and 11 are the binary coded representation of the simplices `(0 1 2)` and  `(0 1 3)` in dimension 3 of ${\\cal S}\\bar\\Delta$,"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 37,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 0}\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 37,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(suspension-intr-cprd (cmbn 0))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 38,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 0}\n",
-       "<5 * <TnPr S-BSGN S-BSGN>>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 38,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(suspension-intr-cprd (cmbn 0 5 :s-bsgn))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 39,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 3}\n",
-       "<4 * <TnPr S-BSGN 7>>\n",
-       "<5 * <TnPr S-BSGN 11>>\n",
-       "<4 * <TnPr 7 S-BSGN>>\n",
-       "<5 * <TnPr 11 S-BSGN>>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 39,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(suspension-intr-cprd (cmbn 3 4 7 5 11))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Let us verify now the classical result ${\\cal S}(S^n)=S^{n+1}$."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 40,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K377 Simplicial-Set]"
-      ]
-     },
-     "execution_count": 40,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def s1 (sphere 1))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 41,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K382 Simplicial-Set]"
-      ]
-     },
-     "execution_count": 41,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def ss1 (suspension s1))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 42,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(SUSPENSION [K377 Simplicial-Set])"
-      ]
-     },
-     "execution_count": 42,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(orgn ss1)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 43,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "\n",
-      "Dimension = 0:\n",
-      "\n",
-      "        Vertices :  (S-BSGN)\n",
-      "\n",
-      "Dimension = 1:\n",
-      "\n",
-      "Dimension = 2:\n",
-      "\n",
-      "        Simplex : S1\n",
-      "\n",
-      "                Faces : (<AbSm 0 S-BSGN> <AbSm 0 S-BSGN> <AbSm 0 S-BSGN>)"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 43,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(show-structure ss1 2)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "For comparison, let us recall the simplicial set model of $S^2$:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 44,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "\n",
-      "Dimension = 0:\n",
-      "\n",
-      "        Vertices :  (*)\n",
-      "\n",
-      "Dimension = 1:\n",
-      "\n",
-      "Dimension = 2:\n",
-      "\n",
-      "        Simplex : S2\n",
-      "\n",
-      "                Faces : (<AbSm 0 *> <AbSm 0 *> <AbSm 0 *>)"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 44,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(show-structure (sphere 2) 2)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Let us iterate twice the operation of suspension on $S^2$:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 45,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K397 Simplicial-Set]"
-      ]
-     },
-     "execution_count": 45,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def ss22 (suspension (sphere 2) 2))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 46,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "\n",
-      "Dimension = 0:\n",
-      "\n",
-      "        Vertices :  (S-BSGN)\n",
-      "\n",
-      "Dimension = 1:\n",
-      "\n",
-      "Dimension = 2:\n",
-      "\n",
-      "Dimension = 3:\n",
-      "\n",
-      "Dimension = 4:\n",
-      "\n",
-      "        Simplex : S2\n",
-      "\n",
-      "                Faces : (<AbSm 2-1-0 S-BSGN> <AbSm 2-1-0 S-BSGN> <AbSm 2-1-0 S-BSGN> <AbSm 2-1-0 S-BSGN> <AbSm 2-1-0 S-BSGN>)"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 46,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(show-structure ss22 4)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "To test the suspension of a less simple chain complex, let us take a Moore space that we have seen in the simplicial set chapter. We know that the corresponding  chain complex  is connected. Let us compare the basis elements, in various degrees, of this chain complex and its suspension:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 47,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K402 Simplicial-Set]"
-      ]
-     },
-     "execution_count": 47,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def m23 (moore 2 3))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 48,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "(*) \n",
-      "NIL \n",
-      "NIL \n",
-      "(M3) \n",
-      "(N4) \n",
-      "NIL \n",
-      "NIL "
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 48,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(dotimes (i 7) (print (basis m23 i)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 49,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K407 Simplicial-Set]"
-      ]
-     },
-     "execution_count": 49,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def sm23 (suspension m23))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 50,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "(:S-BSGN) \n",
-      "NIL \n",
-      "NIL \n",
-      "NIL \n",
-      "(M3) \n",
-      "(N4) \n",
-      "NIL "
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 50,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(dotimes (i 7) (print (basis sm23 i)))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Let us   apply  now the function `suspension` to objects built from $S^2$, namely $\\Omega(S^2)$, $S\\Omega(S^2)$, and finally $\\Omega S \\Omega(S^2)$ and let us have a look upon the homology groups. For $S^2$, we know that the only non-null homology groups are in dimension 0 and 2:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 51,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "Computing boundary-matrix in dimension 0.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 0) :\n",
-      "* \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 1.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 0 :\n",
-      "\n",
-      "\n",
-      "Component Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 1.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 2.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 2) :\n",
-      "S2 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 1 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 2.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 2) :\n",
-      "S2 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 3.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 2 :\n",
-      "\n",
-      "\n",
-      "Component Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 3.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 4.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 3 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 4.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 5.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 4 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 51,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(homology (sphere 2) 0 5)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "For ${\\cal S}(S^2)$, the non--null homology groups are of course in dimension 0 and 3:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 52,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K392 Simplicial-Set]"
-      ]
-     },
-     "execution_count": 52,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def ss2 (suspension (sphere 2)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 53,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "Computing boundary-matrix in dimension 0.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 0) :\n",
-      ":S-BSGN \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 1.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 0 :\n",
-      "\n",
-      "\n",
-      "Component Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 1.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 2.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 1 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 2.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 3.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 3) :\n",
-      "S2 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 2 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 3.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 3) :\n",
-      "S2 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 4.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 3 :\n",
-      "\n",
-      "\n",
-      "Component Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 4.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 5.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 4 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 53,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(homology ss2 0 5)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Let us verify now that, for the space $\\Omega(S^2)$, the homology groups are organized as the tensor algebra over one generator in degree 1:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 54,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K387 Simplicial-Set]"
-      ]
-     },
-     "execution_count": 54,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def s2 (sphere 2))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 55,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K420 Simplicial-Group]"
-      ]
-     },
-     "execution_count": 55,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def os2 (loop-space s2))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 56,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "Computing boundary-matrix in dimension 0.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 0) :\n",
-      "<<AlLp>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 1.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 1) :\n",
-      "<<AlLp[1 S2]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 0 :\n",
-      "\n",
-      "\n",
-      "Component Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 1.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 1) :\n",
-      "<<AlLp[1 S2]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 2.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 2) :\n",
-      "<<AlLp[1 S2][1 S2]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 1 :\n",
-      "\n",
-      "\n",
-      "Component Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 2.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 2) :\n",
-      "<<AlLp[1 S2][1 S2]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 3.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 3) :\n",
-      "<<AlLp[1 S2][1 S2][1 S2]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 2 :\n",
-      "\n",
-      "\n",
-      "Component Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 3.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 3) :\n",
-      "<<AlLp[1 S2][1 S2][1 S2]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 4.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 4) :\n",
-      "<<AlLp[1 S2][1 S2][1 S2][1 S2]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 3 :\n",
-      "\n",
-      "\n",
-      "Component Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 4.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 4) :\n",
-      "<<AlLp[1 S2][1 S2][1 S2][1 S2]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 5.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 5) :\n",
-      "<<AlLp[1 S2][1 S2][1 S2][1 S2][1 S2]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 4 :\n",
-      "\n",
-      "\n",
-      "Component Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 56,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(homology os2 0 5)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "And, in the suspension of the previous space, we verify that the homology groups are suspended (in particular, there is no homology in dimension 1)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 57,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K529 Simplicial-Set]"
-      ]
-     },
-     "execution_count": 57,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def sos2 (suspension os2))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 58,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "Computing boundary-matrix in dimension 0.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 0) :\n",
-      ":S-BSGN \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 1.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 0 :\n",
-      "\n",
-      "\n",
-      "Component Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 1.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 2.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 2) :\n",
-      "<<AlLp[1 S2]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 1 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 2.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 2) :\n",
-      "<<AlLp[1 S2]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 3.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 3) :\n",
-      "<<AlLp[1 S2][1 S2]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 2 :\n",
-      "\n",
-      "\n",
-      "Component Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 3.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 3) :\n",
-      "<<AlLp[1 S2][1 S2]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 4.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 4) :\n",
-      "<<AlLp[1 S2][1 S2][1 S2]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 3 :\n",
-      "\n",
-      "\n",
-      "Component Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 4.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 4) :\n",
-      "<<AlLp[1 S2][1 S2][1 S2]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 5.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 5) :\n",
-      "<<AlLp[1 S2][1 S2][1 S2][1 S2]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 4 :\n",
-      "\n",
-      "\n",
-      "Component Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 58,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(homology sos2 0 5)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "At last, taking the loop space of the previous suspension, we recognize the tensor algebra over the previous tensor algebra, ${\\cal H}_*\\Omega S^2$. In each dimension, the number of generators is $2^n$:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 59,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K547 Simplicial-Group]"
-      ]
-     },
-     "execution_count": 59,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def osos2 (loop-space sos2))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 60,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "Computing boundary-matrix in dimension 0.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 0) :\n",
-      "<<AlLp>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 1.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 1) :\n",
-      "<<AlLp[1 <<AlLp[1 S2]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 0 :\n",
-      "\n",
-      "\n",
-      "Component Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 1.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 1) :\n",
-      "<<AlLp[1 <<AlLp[1 S2]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 2.\n",
-      "Rank of the source-module : 2.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 1/2 (dimension 2) :\n",
-      "<<AlLp[2 <<AlLp[1 S2][1 S2]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 2/2 (dimension 2) :\n",
-      "<<AlLp[1 <<AlLp[1 S2]>>][1 <<AlLp[1 S2]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 1 :\n",
-      "\n",
-      "\n",
-      "Component Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 2.\n",
-      "Rank of the source-module : 2.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 1/2 (dimension 2) :\n",
-      "<<AlLp[2 <<AlLp[1 S2][1 S2]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 2/2 (dimension 2) :\n",
-      "<<AlLp[1 <<AlLp[1 S2]>>][1 <<AlLp[1 S2]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 3.\n",
-      "Rank of the source-module : 4.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 1/4 (dimension 3) :\n",
-      "<<AlLp[3 <<AlLp[1 S2][1 S2][1 S2]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 2/4 (dimension 3) :\n",
-      "<<AlLp[1 <<AlLp[1 S2]>>][2 <<AlLp[1 S2][1 S2]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 3/4 (dimension 3) :\n",
-      "<<AlLp[2 <<AlLp[1 S2][1 S2]>>][1 <<AlLp[1 S2]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 4/4 (dimension 3) :\n",
-      "<<AlLp[1 <<AlLp[1 S2]>>][1 <<AlLp[1 S2]>>][1 <<AlLp[1 S2]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 2 :\n",
-      "\n",
-      "\n",
-      "Component Z\n",
-      "\n",
-      "Component Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 3.\n",
-      "Rank of the source-module : 4.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 1/4 (dimension 3) :\n",
-      "<<AlLp[3 <<AlLp[1 S2][1 S2][1 S2]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 2/4 (dimension 3) :\n",
-      "<<AlLp[1 <<AlLp[1 S2]>>][2 <<AlLp[1 S2][1 S2]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 3/4 (dimension 3) :\n",
-      "<<AlLp[2 <<AlLp[1 S2][1 S2]>>][1 <<AlLp[1 S2]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 4/4 (dimension 3) :\n",
-      "<<AlLp[1 <<AlLp[1 S2]>>][1 <<AlLp[1 S2]>>][1 <<AlLp[1 S2]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 4.\n",
-      "Rank of the source-module : 8.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 1/8 (dimension 4) :\n",
-      "<<AlLp[4 <<AlLp[1 S2][1 S2][1 S2][1 S2]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 2/8 (dimension 4) :\n",
-      "<<AlLp[1 <<AlLp[1 S2]>>][3 <<AlLp[1 S2][1 S2][1 S2]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 3/8 (dimension 4) :\n",
-      "<<AlLp[2 <<AlLp[1 S2][1 S2]>>][2 <<AlLp[1 S2][1 S2]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 4/8 (dimension 4) :\n",
-      "<<AlLp[3 <<AlLp[1 S2][1 S2][1 S2]>>][1 <<AlLp[1 S2]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 5/8 (dimension 4) :\n",
-      "<<AlLp[1 <<AlLp[1 S2]>>][1 <<AlLp[1 S2]>>][2 <<AlLp[1 S2][1 S2]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 6/8 (dimension 4) :\n",
-      "<<AlLp[1 <<AlLp[1 S2]>>][2 <<AlLp[1 S2][1 S2]>>][1 <<AlLp[1 S2]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 7/8 (dimension 4) :\n",
-      "<<AlLp[2 <<AlLp[1 S2][1 S2]>>][1 <<AlLp[1 S2]>>][1 <<AlLp[1 S2]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 8/8 (dimension 4) :\n",
-      "<<AlLp[1 <<AlLp[1 S2]>>][1 <<AlLp[1 S2]>>][1 <<AlLp[1 S2]>>][1 <<AlLp[1 S2]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 3 :\n",
-      "\n",
-      "\n",
-      "Component Z\n",
-      "\n",
-      "Component Z\n",
-      "\n",
-      "Component Z\n",
-      "\n",
-      "Component Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 4.\n",
-      "Rank of the source-module : 8.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 1/8 (dimension 4) :\n",
-      "<<AlLp[4 <<AlLp[1 S2][1 S2][1 S2][1 S2]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 2/8 (dimension 4) :\n",
-      "<<AlLp[1 <<AlLp[1 S2]>>][3 <<AlLp[1 S2][1 S2][1 S2]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 3/8 (dimension 4) :\n",
-      "<<AlLp[2 <<AlLp[1 S2][1 S2]>>][2 <<AlLp[1 S2][1 S2]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 4/8 (dimension 4) :\n",
-      "<<AlLp[3 <<AlLp[1 S2][1 S2][1 S2]>>][1 <<AlLp[1 S2]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 5/8 (dimension 4) :\n",
-      "<<AlLp[1 <<AlLp[1 S2]>>][1 <<AlLp[1 S2]>>][2 <<AlLp[1 S2][1 S2]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 6/8 (dimension 4) :\n",
-      "<<AlLp[1 <<AlLp[1 S2]>>][2 <<AlLp[1 S2][1 S2]>>][1 <<AlLp[1 S2]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 7/8 (dimension 4) :\n",
-      "<<AlLp[2 <<AlLp[1 S2][1 S2]>>][1 <<AlLp[1 S2]>>][1 <<AlLp[1 S2]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 8/8 (dimension 4) :\n",
-      "<<AlLp[1 <<AlLp[1 S2]>>][1 <<AlLp[1 S2]>>][1 <<AlLp[1 S2]>>][1 <<AlLp[1 S2]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 5.\n",
-      "Rank of the source-module : 16.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 1/16 (dimension 5) :\n",
-      "<<AlLp[5 <<AlLp[1 S2][1 S2][1 S2][1 S2][1 S2]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 2/16 (dimension 5) :\n",
-      "<<AlLp[1 <<AlLp[1 S2]>>][4 <<AlLp[1 S2][1 S2][1 S2][1 S2]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 3/16 (dimension 5) :\n",
-      "<<AlLp[2 <<AlLp[1 S2][1 S2]>>][3 <<AlLp[1 S2][1 S2][1 S2]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 4/16 (dimension 5) :\n",
-      "<<AlLp[3 <<AlLp[1 S2][1 S2][1 S2]>>][2 <<AlLp[1 S2][1 S2]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 5/16 (dimension 5) :\n",
-      "<<AlLp[4 <<AlLp[1 S2][1 S2][1 S2][1 S2]>>][1 <<AlLp[1 S2]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 6/16 (dimension 5) :\n",
-      "<<AlLp[1 <<AlLp[1 S2]>>][1 <<AlLp[1 S2]>>][3 <<AlLp[1 S2][1 S2][1 S2]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 7/16 (dimension 5) :\n",
-      "<<AlLp[1 <<AlLp[1 S2]>>][2 <<AlLp[1 S2][1 S2]>>][2 <<AlLp[1 S2][1 S2]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 8/16 (dimension 5) :\n",
-      "<<AlLp[1 <<AlLp[1 S2]>>][3 <<AlLp[1 S2][1 S2][1 S2]>>][1 <<AlLp[1 S2]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 9/16 (dimension 5) :\n",
-      "<<AlLp[2 <<AlLp[1 S2][1 S2]>>][1 <<AlLp[1 S2]>>][2 <<AlLp[1 S2][1 S2]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 10/16 (dimension 5) :\n",
-      "<<AlLp[2 <<AlLp[1 S2][1 S2]>>][2 <<AlLp[1 S2][1 S2]>>][1 <<AlLp[1 S2]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 11/16 (dimension 5) :\n",
-      "<<AlLp[3 <<AlLp[1 S2][1 S2][1 S2]>>][1 <<AlLp[1 S2]>>][1 <<AlLp[1 S2]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 12/16 (dimension 5) :\n",
-      "<<AlLp[1 <<AlLp[1 S2]>>][1 <<AlLp[1 S2]>>][1 <<AlLp[1 S2]>>][2 <<AlLp[1 S2][1 S2]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 13/16 (dimension 5) :\n",
-      "<<AlLp[1 <<AlLp[1 S2]>>][1 <<AlLp[1 S2]>>][2 <<AlLp[1 S2][1 S2]>>][1 <<AlLp[1 S2]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 14/16 (dimension 5) :\n",
-      "<<AlLp[1 <<AlLp[1 S2]>>][2 <<AlLp[1 S2][1 S2]>>][1 <<AlLp[1 S2]>>][1 <<AlLp[1 S2]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 15/16 (dimension 5) :\n",
-      "<<AlLp[2 <<AlLp[1 S2][1 S2]>>][1 <<AlLp[1 S2]>>][1 <<AlLp[1 S2]>>][1 <<AlLp[1 S2]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "Computing the boundary of the generator 16/16 (dimension 5) :\n",
-      "<<AlLp[1 <<AlLp[1 S2]>>][1 <<AlLp[1 S2]>>][1 <<AlLp[1 S2]>>][1 <<AlLp[1 S2]>>][1 <<AlLp[1 S2]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 4 :\n",
-      "\n",
-      "\n",
-      "Component Z\n",
-      "\n",
-      "Component Z\n",
-      "\n",
-      "Component Z\n",
-      "\n",
-      "Component Z\n",
-      "\n",
-      "Component Z\n",
-      "\n",
-      "Component Z\n",
-      "\n",
-      "Component Z\n",
-      "\n",
-      "Component Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 25m 31s.\n",
-      "\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 60,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(homology osos2 0 5)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "### Searching homology for suspensions\n",
-    "\n",
-    "The comment list of a suspension has the form `(SUSPENSION` *suspended-object*`)`. The `search-efhm` method applied to a suspension, looks for the value of the `efhm` slot of the *suspended-object*, (i.e. a homotopy equivalence), then builds the suspension of this homotopy equivalence (see the method `suspension` applied to a homotopy equivalence). Of course, this may imply a recursive process.\n",
-    "```commonlisp\n",
-    "(DEFMETHOD SEARCH-EFHM (suspension (orgn (eql 'suspension)))\n",
-    "  (declare (type chain-complex suspension))\n",
-    "  (suspension (efhm (second (orgn suspension)))))\n",
-    "```\n",
-    "\n",
-    "### Lisp files concerned in this chapter\n",
-    "\n",
-    "`disk-pasting.lisp`, `suspensions.lisp`, `searching-homology.lisp`"
-   ]
-  }
- ],
- "metadata": {
-  "kernelspec": {
-   "display_name": "SBCL Lisp",
-   "language": "lisp",
-   "name": "lisp"
-  },
-  "language_info": {
-   "codemirror_mode": "text/x-common-lisp",
-   "mimetype": "text/x-common-lisp",
-   "name": "common-lisp",
-   "pygments_lexer": "common-lisp",
-   "version": "X3J13"
-  }
- },
- "nbformat": 4,
- "nbformat_minor": 1
-}
diff --git a/examples/15_Loop_spaces_fibrations.ipynb b/examples/15_Loop_spaces_fibrations.ipynb
deleted file mode 100644
index d8a3d92..0000000
--- a/examples/15_Loop_spaces_fibrations.ipynb
+++ /dev/null
@@ -1,4037 +0,0 @@
-{
- "cells": [
-  {
-   "cell_type": "code",
-   "execution_count": 1,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "To load \"kenzo\":\n",
-      "  Load 1 ASDF system:\n",
-      "    kenzo\n",
-      "; Loading \"kenzo\"\n",
-      "\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "#<PACKAGE \"CAT\">"
-      ]
-     },
-     "execution_count": 1,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(ql:quickload \"kenzo\")\n",
-    "(in-package :cat)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "# Loop spaces fibrations\n",
-    "\n",
-    "## The canonical loop space fibration\n",
-    "\n",
-    "Let $X$ be a  simplicial set. The program `Kenzo` implements the *canonical* twisted cartesian product of $X$ by its loop space $GX$, denoted $X \\times_\\tau GX$, giving the Kan (**Daniel M. Kan**. *A combinatorial definition of homotopy groups*, Ann. of Math., 1958, vol. 67, pp 282-312.) model of the contractible path space of $X$. The *canonical fibration*\n",
-    "$$ GX\\quad \\hookrightarrow\\quad X \\times_\\tau GX  \\hskip 1.2em \\longrightarrow \\hskip -1.2em \\longrightarrow  \n",
-    "   \\quad X,$$\n",
-    "is defined by the application $\\tau$, where $\\tau(x)$ is the *letter* $x$ in $GX$. This twisted cartesian product has the same simplices as the non-twisted one. So both associated chain complexes are equal as graded modules. The essential difference  resides in the differential morphism. More precisely, the face operator $\\partial_n$ behaves differently in the twisted cartesian product. Let $(x,g) \\in (X \\times_\\tau GX)_n$, then the rules for the face operators are:\n",
-    "$$\n",
-    "\\begin{aligned}\n",
-    "\\partial_i(x,g) & =  & (\\partial_i x, \\partial_i g), \\qquad i<n, \\\\\n",
-    "\\partial_n(x,g) & =  & (\\partial_n x, \\tau(x).\\partial_n g), \\qquad i=n,\n",
-    "\\end{aligned}\n",
-    "$$\n",
-    "where $\\tau(x)$ is the *letter* $x$ in $GX$ and '**.**' is the group product in $GX$. Let us recall that, from the mathematical definition of $GX$, if $x \\in X_{n+1}$ is $n$-degenerate, for instance $x=\\eta_n x'$, then $\\tau(x)$ is the neutral element of $GX_n$.\n",
-    "The behaviour of $\\partial_n$ induces a change in the differential morphism of the chain complex associated to the twisted cartesian product.\n",
-    "\n",
-    "## The associated tensor twisted product\n",
-    "\n",
-    "We recall that about the cartesian product $X \\times GX$,  the Eilenberg-Zilber theorem allows to build the reduction (see the function `ez`):\n",
-    "$$\n",
-    "\\begin{aligned}\n",
-    "{{\\cal C}_*(X \\times GX)} \\quad& \\stackrel{h}{\\longrightarrow} & {}^s{{\\cal C}_*(X \\times GX)} \\cr\n",
-    " {\\scriptstyle f} \\downarrow \\uparrow {\\scriptstyle g} \\qquad& & \\cr\n",
-    " \\qquad{{\\cal C}_*(X) \\otimes {\\cal C}_*(GX)} & &\\cr\n",
-    "\\end{aligned}\n",
-    "$$\n",
-    "On the other hand, the differential morphism $d_\\tau$ of the chain complex ${\\cal C}_*(X \\times_\\tau GX)$ may be considered as a perturbed differential morphism $d$ of the chain complex ${\\cal C}_*(X \\times GX)$, the perturbation $\\delta$ being: $\\delta= d_\\tau - d$. Using the basic perturbation lemma, we may construct a new reduction:\n",
-    "$$\n",
-    "\\begin{aligned}\n",
-    "{{\\cal C}_*(X \\times_\\tau GX)} \\quad& \\stackrel{h}{\\longrightarrow} & {}^s{{\\cal C}_*(X \\times_\\tau GX)} \\cr\n",
-    " {\\scriptstyle f} \\downarrow \\uparrow {\\scriptstyle g} \\qquad& & \\cr\n",
-    " \\qquad{{\\cal C}_*(X) \\otimes_t {\\cal C}_*(GX)} & & \\cr\n",
-    "\\end{aligned}\n",
-    "$$\n",
-    "In fact, the interesting object produced by this machinery is the bottom chain complex ${\\cal C}_*(X) \\otimes_t {\\cal C}_*(GX)$, the (algebraic) twisted tensor-product of the \"base space\" $C_\\ast(X)$ by the \"fibre space\" $C_\\ast(GX)$, the twist being defined by a *canonical* twisting cochain $t \\in C^1(X ; C_\\ast(GX))$ (**Edgar H. Brown Jr.** *Twisted tensor products, I*,\n",
-    "Ann. of Math., 1959, vol. 69, pp. 223-246.).\n",
-    "\n",
-    "## Main functions for the twisted products\n",
-    "\n",
-    "`twisted-crts-prdc` *space* *[Function]*\n",
-    "> From the simplicial set $X$, here the argument *space*,  return  the twisted cartesian product $X \\times_\\tau GX$ (a simplicial set). This function calls internally the functions `loop-space` and `crts-prdc` described in preceding chapters. The slot `grmd` of the resulting instance is set with the ordinary cartesian product $X \\times GX$.\n",
-    "\n",
-    "`dtau-d` *space* *[Function]*\n",
-    "> From the simplicial set $X$, here the argument *space*, build the morphism perturbation (degree -1)\n",
-    "$$d_\\tau - d : C_\\ast(X \\times GX) \\longrightarrow C_\\ast(X \\times GX).$$\n",
-    "The work is essentialy done by the  lisp function `dtau-d-intr` which computes the difference between  the differential morphisms taking in account the discrepancy between the last face operator ($\\partial_n$) in both chain complexes, $C_\\ast(X \\times_\\tau GX)$ and $C_\\ast(X \\times GX)$.\n",
-    "\n",
-    "`szczarba` *space* *[Function]*\n",
-    "> Starting from the simplicial set $X$, (the argument *space*), return two values:  \n",
-    "1- The reduction\n",
-    "$$\n",
-    "\\begin{aligned}\n",
-    "{{\\cal C}_*(X \\times_\\tau GX)}\\quad & \\stackrel{h}{\\longrightarrow} & {}^s{{\\cal C}_*(X \\times_\\tau GX)} \\cr\n",
-    " {\\scriptstyle f} \\downarrow \\uparrow {\\scriptstyle g}\\qquad  \\cr\n",
-    " \\quad{{\\cal C}_*(X) \\otimes_t {\\cal C}_*(GX)} \\cr\n",
-    "\\end{aligned}\n",
-    "$$\n",
-    "obtained by perturbing by $d_\\tau-d$ the top chain complex of the reduction \n",
-    "$$\n",
-    "\\begin{aligned}\n",
-    "{{\\cal C}_*(X \\times GX)}\\quad & \\stackrel{h}{\\longrightarrow} & {}^s{{\\cal C}_*(X \\times GX)} \\cr\n",
-    " {\\scriptstyle f} \\downarrow \\uparrow {\\scriptstyle g}\\qquad  \\cr\n",
-    " \\quad{{\\cal C}_*(X) \\otimes {\\cal C}_*(GX)} \\cr\n",
-    "\\end{aligned}\n",
-    "$$\n",
-    "2- The morphism corresponding to the perturbation of the bottom chain complex induced by the perturbation $d_\\tau-d$ upon the top chain complex of the above reduction.\n",
-    "\n",
-    "This algorithm implements in particular  in a very efficient way the formulas of Szczarba (**R.H. Szczarba.** *The homology of twisted cartesian products.* Transactions of the American Math. Society, 1961, vol. 100, pp. 197-216).\n",
-    "\n",
-    "`twisted-tnsr-prdc` *space* *[Function]*\n",
-    "> Return the twisted tensor product (a chain complex)  $C_\\ast(X) \\otimes_t C_\\ast(GX)$. This is done simply by extraction of the bottom chain complex from the reduction  `(szczarba` *space*`)`.\n",
-    "\n",
-    "### Examples\n",
-    "\n",
-    "For testing the functions above, we shall use a \"soft\" version of $\\bar{\\Delta}$ analogous to `soft-delta` or `soft-delta-infinity`. The input of the simplices will be done in clear with the help of the macro `code`. As this version does not exist in `Kenzo`, we have modified some functions of `soft-delta`, as indicated."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 2,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "SOFT-DELTAB-CMPR"
-      ]
-     },
-     "execution_count": 2,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(DEFUN SOFT-DELTAB-CMPR (gmsm1 gmsm2)\n",
-    "    (if (= 1 (logcount (cdr gmsm1))) \n",
-    "        :EQUAL\n",
-    "        (f-cmpr (cdr gmsm1)(cdr gmsm2)) ))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 3,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "SOFT-DELTAB-BNDR"
-      ]
-     },
-     "execution_count": 3,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(DEFUN SOFT-DELTAB-BNDR (dmns gmsm)\n",
-    "   (declare\n",
-    "      (fixnum dmns)\n",
-    "      (type soft-dlop gmsm))\n",
-    "   (the cmbn\n",
-    "      (if (< dmns 2)\n",
-    "         (zero-cmbn (1- dmns))\n",
-    "         (make-cmbn\n",
-    "         :degr (1- dmns)\n",
-    "         :list (mapcar #'(lambda (term)\n",
-    "                         (with-term (cffc gmsm) term\n",
-    "                            (term cffc (d gmsm))))\n",
-    "               (cmbn-list (delta-bndr dmns (cdr gmsm))))))))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 4,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "SOFT-DELTAB"
-      ]
-     },
-     "execution_count": 4,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(DEFUN SOFT-DELTAB ()\n",
-    "   (the simplicial-set\n",
-    "      (build-smst\n",
-    "         :cmpr #'soft-deltab-cmpr\n",
-    "         :basis :locally-effective\n",
-    "         :bspn (d 1)\n",
-    "         :face #'soft-delta-face\n",
-    ";;;      :intr-dgnl #'soft-delta-dgnl :dgnl-strt :gnrt\n",
-    "         :intr-bndr #'soft-deltab-bndr :bndr-strt :gnrt\n",
-    "         :orgn `(soft-deltab))))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 5,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "CODE"
-      ]
-     },
-     "execution_count": 5,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(defmacro code (arg) `(d (dlop-ext-int ,arg)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 6,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K1 Simplicial-Set]"
-      ]
-     },
-     "execution_count": 6,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def db (soft-deltab))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 7,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K6 Simplicial-Group]"
-      ]
-     },
-     "execution_count": 7,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def gdb (loop-space db))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Let us compare the faces of a cartesian product in $\\bar{\\Delta} \\times \\Omega(\\bar{\\Delta})$ and the faces of the same object in $\\bar{\\Delta} \\times_\\tau \\Omega(\\bar{\\Delta})$:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 8,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K18 Simplicial-Set]"
-      ]
-     },
-     "execution_count": 8,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def crts-pr (crts-prdc db gdb))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 9,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K23 Simplicial-Set]"
-      ]
-     },
-     "execution_count": 9,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def tw-crts-pr (twisted-crts-prdc db))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 10,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "<CrPr - (DELT . 31) - <<Loop[(DELT . 63)]>>>"
-      ]
-     },
-     "execution_count": 10,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def smpx (crpr 0 (code '(0 1 2 3 4)) \n",
-    "                 0 (loop3 0 (code '(0 1 2 3 4 5)) 1)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 11,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "<AbSm - <CrPr - (DELT . 30) - <<Loop[(DELT . 62)]>>>> \n",
-      "<AbSm - <CrPr - (DELT . 29) - <<Loop[(DELT . 61)]>>>> \n",
-      "<AbSm - <CrPr - (DELT . 27) - <<Loop[(DELT . 59)]>>>> \n",
-      "<AbSm - <CrPr - (DELT . 23) - <<Loop[(DELT . 55)]>>>> \n",
-      "<AbSm - <CrPr - (DELT . 15) - <<Loop[(DELT . 31)\\-1][(DELT . 47)]>>>> "
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 11,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(dotimes (j 5)\n",
-    "         (print (face crts-pr j 4 smpx)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 12,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "<AbSm - <CrPr - (DELT . 30) - <<Loop[(DELT . 62)]>>>> \n",
-      "<AbSm - <CrPr - (DELT . 29) - <<Loop[(DELT . 61)]>>>> \n",
-      "<AbSm - <CrPr - (DELT . 27) - <<Loop[(DELT . 59)]>>>> \n",
-      "<AbSm - <CrPr - (DELT . 23) - <<Loop[(DELT . 55)]>>>> \n",
-      "<AbSm - <CrPr - (DELT . 15) - <<Loop[(DELT . 47)]>>>> "
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 12,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(dotimes (j 5)\n",
-    "         (print (face tw-crts-pr j 4 smpx)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 13,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "<CrPr - (DELT . 62) - <<Loop[(DELT . 2016)]>>>"
-      ]
-     },
-     "execution_count": 13,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def smpx2 (crpr 0 (code '(1 2 3 4 5)) \n",
-    "                  0 (loop3 0 (code '(5 6 7 8 9 10)) 1)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 14,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "<AbSm - <CrPr - (DELT . 60) - <<Loop[(DELT . 1984)]>>>> \n",
-      "<AbSm - <CrPr - (DELT . 58) - <<Loop[(DELT . 1952)]>>>> \n",
-      "<AbSm - <CrPr - (DELT . 54) - <<Loop[(DELT . 1888)]>>>> \n",
-      "<AbSm - <CrPr - (DELT . 46) - <<Loop[(DELT . 1760)]>>>> \n",
-      "<AbSm - <CrPr - (DELT . 30) - <<Loop[(DELT . 992)\\-1][(DELT . 1504)]>>>> "
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 14,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(dotimes (j 5)\n",
-    "         (print (face crts-pr j 4 smpx2)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 15,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "<AbSm - <CrPr - (DELT . 60) - <<Loop[(DELT . 1984)]>>>> \n",
-      "<AbSm - <CrPr - (DELT . 58) - <<Loop[(DELT . 1952)]>>>> \n",
-      "<AbSm - <CrPr - (DELT . 54) - <<Loop[(DELT . 1888)]>>>> \n",
-      "<AbSm - <CrPr - (DELT . 46) - <<Loop[(DELT . 1760)]>>>> \n",
-      "<AbSm - <CrPr - (DELT . 30) - <<Loop[(DELT . 62)][(DELT . 992)\\-1][(DELT . 1504)]>>>> "
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 15,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(dotimes (j 5)\n",
-    "         (print (face tw-crts-pr j 4 smpx2)))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "The user will have noted that we may obtain the same twisted cartesian product by the fibration theory. Let us define a general function `loop-fbr` with  a reduced simplicial set, *space*, as argument. This function uses the function `fibration-total` that we have seen in the  chapter about fibrations. Here, we see that the lisp function for the simplicial morphism, (keyword `:sintr`), implements straightforwardly the canonical twisting operator which applies a simplex of $X$ to the corresponding 1-letter word of $GX$."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 16,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "LOOP-FBR"
-      ]
-     },
-     "execution_count": 16,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(defun loop-fbr (space)\n",
-    "             (fibration-total\n",
-    "                (build-smmr\n",
-    "                  :sorc space \n",
-    "                  :trgt (loop-space space) \n",
-    "                  :degr -1\n",
-    "                  :sintr #'(lambda (dmns gmsm) (declare (ignore dmns))\n",
-    "                               (absm 0 (loop3 0 gmsm 1)))\n",
-    "                  :orgn `(total-fibration ,space))))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 17,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K29 Simplicial-Set]"
-      ]
-     },
-     "execution_count": 17,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def fb-tt-db (loop-fbr db))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 18,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "<AbSm - <CrPr - (DELT . 60) - <<Loop[(DELT . 1984)]>>>> \n",
-      "<AbSm - <CrPr - (DELT . 58) - <<Loop[(DELT . 1952)]>>>> \n",
-      "<AbSm - <CrPr - (DELT . 54) - <<Loop[(DELT . 1888)]>>>> \n",
-      "<AbSm - <CrPr - (DELT . 46) - <<Loop[(DELT . 1760)]>>>> \n",
-      "<AbSm - <CrPr - (DELT . 30) - <<Loop[(DELT . 62)][(DELT . 992)\\-1][(DELT . 1504)]>>>> "
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 18,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(dotimes (j 5)\n",
-    "         (print(face fb-tt-db j 4 smpx2)))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "The four following statements show the relationship between the differentials:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 19,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K34 Morphism (degree -1): K18 -> K18]"
-      ]
-     },
-     "execution_count": 19,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def perturb (dtau-d db))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 20,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 3}\n",
-       "<1 * <CrPr - (DELT . 30) - <<Loop[(DELT . 62)][(DELT . 992)\\-1][(DELT . 1504)]>>>>\n",
-       "<-1 * <CrPr - (DELT . 30) - <<Loop[(DELT . 992)\\-1][(DELT . 1504)]>>>>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 20,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? perturb 4 smpx2)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 21,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 3}\n",
-       "<1 * <CrPr - (DELT . 30) - <<Loop[(DELT . 992)\\-1][(DELT . 1504)]>>>>\n",
-       "<-1 * <CrPr - (DELT . 46) - <<Loop[(DELT . 1760)]>>>>\n",
-       "<1 * <CrPr - (DELT . 54) - <<Loop[(DELT . 1888)]>>>>\n",
-       "<-1 * <CrPr - (DELT . 58) - <<Loop[(DELT . 1952)]>>>>\n",
-       "<1 * <CrPr - (DELT . 60) - <<Loop[(DELT . 1984)]>>>>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 21,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? crts-pr 4 smpx2)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 22,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 3}\n",
-       "<1 * <CrPr - (DELT . 30) - <<Loop[(DELT . 62)][(DELT . 992)\\-1][(DELT . 1504)]>>>>\n",
-       "<-1 * <CrPr - (DELT . 46) - <<Loop[(DELT . 1760)]>>>>\n",
-       "<1 * <CrPr - (DELT . 54) - <<Loop[(DELT . 1888)]>>>>\n",
-       "<-1 * <CrPr - (DELT . 58) - <<Loop[(DELT . 1952)]>>>>\n",
-       "<1 * <CrPr - (DELT . 60) - <<Loop[(DELT . 1984)]>>>>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 22,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? tw-crts-pr 4 smpx2)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "The same type of tests may be done with another reduced simplicial set, namely $P^3\\mathbb{R}$."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 23,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K35 Simplicial-Set]"
-      ]
-     },
-     "execution_count": 23,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def pri3 (R-proj-space 3))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 24,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K57 Simplicial-Set]"
-      ]
-     },
-     "execution_count": 24,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def tw-pri3 (twisted-crts-prdc pri3))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 25,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       ":LOCALLY-EFFECTIVE"
-      ]
-     },
-     "execution_count": 25,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(basis tw-pri3)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 26,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K52 Simplicial-Set]"
-      ]
-     },
-     "execution_count": 26,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def crt-pri3 (crts-prdc pri3 (loop-space pri3)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 27,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "<CrPr - 4 - <<Loop[5]>>>"
-      ]
-     },
-     "execution_count": 27,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def s (crpr 0 4 0 (loop3 0 5 1)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 28,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "<AbSm - <CrPr - 3 - <<Loop[4]>>>> \n",
-      "<AbSm 0 <CrPr 1-0 0 - <<Loop[3]>>>> \n",
-      "<AbSm 1 <CrPr 1-0 0 - <<Loop[3]>>>> \n",
-      "<AbSm 2 <CrPr 1-0 0 - <<Loop[3]>>>> \n",
-      "<AbSm - <CrPr - 3 - <<Loop[4\\-1]>>>> "
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 28,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(dotimes (i 5) (print (face crt-pri3 i 4 s)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 29,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "<AbSm - <CrPr - 3 - <<Loop[4]>>>> \n",
-      "<AbSm 0 <CrPr 1-0 0 - <<Loop[3]>>>> \n",
-      "<AbSm 1 <CrPr 1-0 0 - <<Loop[3]>>>> \n",
-      "<AbSm 2 <CrPr 1-0 0 - <<Loop[3]>>>> \n",
-      "<AbSm - <CrPr - 3 2-1-0 <<Loop>>>> "
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 29,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(dotimes (i 5) (print (face tw-pri3 i 4 s)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 30,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K63 Simplicial-Set]"
-      ]
-     },
-     "execution_count": 30,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def fb-tt-pri3 (loop-fbr pri3))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 31,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "<AbSm - <CrPr - 3 - <<Loop[4]>>>> \n",
-      "<AbSm 0 <CrPr 1-0 0 - <<Loop[3]>>>> \n",
-      "<AbSm 1 <CrPr 1-0 0 - <<Loop[3]>>>> \n",
-      "<AbSm 2 <CrPr 1-0 0 - <<Loop[3]>>>> \n",
-      "<AbSm - <CrPr - 3 2-1-0 <<Loop>>>> "
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 31,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(dotimes (j 5) (print (face fb-tt-pri3 j 4 s)))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Let us check now the Szczarba reduction, with the simplicial set $\\bar{\\Delta}$."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 32,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K90 Reduction K23 => K88]"
-      ]
-     },
-     "execution_count": 32,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def szc-reduc (szczarba db))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 33,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "---done---"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 33,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(pre-check-rdct szc-reduc)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 34,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 2}\n",
-       "<1 * <CrPr - (DELT . 7) - <<Loop[(DELT . 480)]>>>>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 34,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(setf *tc* (cmbn 2 1 (crpr 0 (code '(0 1 2)) \n",
-    "                           0 (loop3 0 (code '(5 6 7 8)) 1))))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 35,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 2}\n",
-       "<1 * <TnPr (DELT . 1) <<Loop[(DELT . 480)]>>>>\n",
-       "<10 * <TnPr (DELT . 3072) <<Loop[(DELT . 7)]>>>>\n",
-       "<100 * <TnPr (DELT . 7) <<Loop[(DELT . 3072)]>>>>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 35,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(setf *bc* (cmbn 2 1 (tnpr 0 (code '(0)) 2 (loop3 0 (code '(5 6 7 8)) 1))\n",
-    "                  10 (tnpr 1 (code '(10 11)) 1 (loop3 0 (code '(0 1 2)) 1))\n",
-    "                 100 (tnpr 2 (code '(0 1 2)) 0 (loop3 0 (code '(10 11)) 1))))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 36,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "---done---"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 36,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(pre-check-rdct szc-reduc)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 37,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "*TC* => \n",
-      "----------------------------------------------------------------------{CMBN 2}\n",
-      "<1 * <CrPr - (DELT . 7) - <<Loop[(DELT . 480)]>>>>\n",
-      "------------------------------------------------------------------------------\n",
-      "\n",
-      "*BC* => \n",
-      "----------------------------------------------------------------------{CMBN 2}\n",
-      "<1 * <TnPr (DELT . 1) <<Loop[(DELT . 480)]>>>>\n",
-      "<10 * <TnPr (DELT . 3072) <<Loop[(DELT . 7)]>>>>\n",
-      "<100 * <TnPr (DELT . 7) <<Loop[(DELT . 3072)]>>>>\n",
-      "------------------------------------------------------------------------------\n",
-      "\n",
-      "Checking *TDD* = 0\n",
-      "Result: \n",
-      "----------------------------------------------------------------------{CMBN 0}\n",
-      "------------------------------------------------------------------------------\n",
-      "\n",
-      "Checking *BDD* = 0\n",
-      "Result: \n",
-      "----------------------------------------------------------------------{CMBN 0}\n",
-      "------------------------------------------------------------------------------\n",
-      "\n",
-      "Checking *DF-FD* = 0\n",
-      "Result: \n",
-      "----------------------------------------------------------------------{CMBN 1}\n",
-      "------------------------------------------------------------------------------\n",
-      "\n",
-      "Checking *DG-GD* = 0\n",
-      "Result: \n",
-      "----------------------------------------------------------------------{CMBN 1}\n",
-      "------------------------------------------------------------------------------\n",
-      "\n",
-      "Checking *ID-FG* = 0\n",
-      "Result: \n",
-      "----------------------------------------------------------------------{CMBN 2}\n",
-      "------------------------------------------------------------------------------\n",
-      "\n",
-      "Checking *ID-GF-DH-HD* = 0\n",
-      "Result: \n",
-      "----------------------------------------------------------------------{CMBN 2}\n",
-      "------------------------------------------------------------------------------\n",
-      "\n",
-      "Checking *HH* = 0\n",
-      "Result: \n",
-      "----------------------------------------------------------------------{CMBN 4}\n",
-      "------------------------------------------------------------------------------\n",
-      "\n",
-      "Checking *FH* = 0\n",
-      "Result: \n",
-      "----------------------------------------------------------------------{CMBN 3}\n",
-      "------------------------------------------------------------------------------\n",
-      "\n",
-      "Checking *HG* = 0\n",
-      "Result: \n",
-      "----------------------------------------------------------------------{CMBN 3}\n",
-      "------------------------------------------------------------------------------\n",
-      "\n",
-      "---done---"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 37,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(check-rdct-no-wait)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "## Exercice with the twisting cochain.\n",
-    "\n",
-    "Let $B$ be a reduced simplicial set and its loop space $GB$ (a simplicial group). In the following examples, we shall use the efficient `Kenzo` version of the simplicial set $\\bar{\\Delta}$, i.e. the simplices are input and printed under their binary form coding.\n",
-    "\n",
-    "### The twisting cochain.\n",
-    "\n",
-    "The twisting cochain $t$ is the morphism\n",
-    "$$t: aug \\circ d_{\\otimes t} \\circ coaug$$\n",
-    "where,\n",
-    "- $coaug$ is the morphism \n",
-    "$$ coaug: B \\rightarrow B \\otimes GB,$$\n",
-    "$$ coaug(b) = b \\otimes 1_{GB}. $$\n",
-    "- $d_{\\otimes t}$ is the differential morphism of the twisted tensor product $B \\otimes_t GB$.\n",
-    "- $aug$ is the morphism\n",
-    "$$aug: B \\otimes GB  \\longrightarrow GB ,  $$\n",
-    "$$\n",
-    "\\begin{aligned}\n",
-    "aug(b_i \\otimes g_j)&  = g_j, & b_i \\in B_0, \\\\\n",
-    "aug(b_i \\otimes g_j)&  = 0, & b_i \\in B_k,\\, k\\not=0.\n",
-    "\\end{aligned}\n",
-    "$$\n",
-    "We recall that, as graded modules, $B\\otimes GB$ and $B \\otimes_t GB$ are identical.\n",
-    "\n",
-    "First, we create $\\bar{\\Delta}$ and $G\\bar{\\Delta}$. The function `twisted-tnsr-prdc` extracts the twisted tensor product $\\bar{\\Delta} \\otimes_t G\\bar{\\Delta}$ from the reduction obtained by a call to the function `szczarba`."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 38,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K112 Simplicial-Set]"
-      ]
-     },
-     "execution_count": 38,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def d (deltab))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 39,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K117 Simplicial-Group]"
-      ]
-     },
-     "execution_count": 39,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def gd (loop-space d))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 40,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K160 Chain-Complex]"
-      ]
-     },
-     "execution_count": 40,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def d-twtp-gd (twisted-tnsr-prdc d))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Let us define the  coaugmentation and augmentation morphisms. As usual, it is sufficient to define the algorithm on a generator."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 41,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K163 Morphism (degree 0): K112 -> K160]"
-      ]
-     },
-     "execution_count": 41,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def coaug (build-mrph \n",
-    "               :sorc d \n",
-    "               :trgt d-twtp-gd \n",
-    "               :degr 0\n",
-    "               :intr #'(lambda (degr gnrt)\n",
-    "                         (term-cmbn degr 1 (tnpr degr gnrt 0 +null-loop+)))\n",
-    "               :strt :gnrt \n",
-    "               :orgn '(coaug. d --> d-twtp-gd)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 42,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 3}\n",
-       "<1 * <TnPr 15 <<Loop>>>>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 42,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? coaug 3 15)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 43,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 4}\n",
-       "<1 * <TnPr 31 <<Loop>>>>\n",
-       "<1 * <TnPr 62 <<Loop>>>>\n",
-       "<1 * <TnPr 124 <<Loop>>>>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 43,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? coaug (cmbn 4 1 31 1 62 1 124))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 44,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K164 Morphism (degree 0): K160 -> K117]"
-      ]
-     },
-     "execution_count": 44,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def aug (build-mrph\n",
-    "             :sorc d-twtp-gd\n",
-    "             :trgt gd\n",
-    "             :degr 0\n",
-    "             :intr #'(lambda (degr tnpr)\n",
-    "                        (with-tnpr (degr1 gmsm1 degr2 loop2) tnpr\n",
-    "                            (declare (ignore gmsm1 degr2))\n",
-    "                            (if (zerop degr1)\n",
-    "                                (term-cmbn degr 1 loop2)\n",
-    "                                (zero-cmbn degr))))\n",
-    "             :strt :gnrt\n",
-    "             :orgn '(aug. of d-twtp-gd)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 45,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 2}\n",
-       "<9 * <<Loop[15]>>>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 45,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? aug (cmbn 2 9 (tnpr 0 1 2 (loop3 0 15 1))\n",
-    "               3 (tnpr 1 3 1 (loop3 0 7 1))))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "The morphism `cochain` is simply a composition of morphisms. We apply it upon the simplices `(0)`, `(0 1 2)`, `(0 1 2 3)`, ..., coded as the integers $1,7,15,\\ldots$."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 46,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K166 Morphism (degree -1): K112 -> K117]"
-      ]
-     },
-     "execution_count": 46,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def cochain (i-cmps aug (dffr d-twtp-gd) coaug))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 47,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN -1}\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 47,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? cochain 0 1)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 48,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 1}\n",
-       "<1 * <<Loop[0 3][7]>>>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 48,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? cochain 2 7)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 49,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 2}\n",
-       "<1 * <<Loop[1-0 3][0 7][1 13]>>>\n",
-       "<-1 * <<Loop[1-0 3][1 7][15]>>>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 49,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? cochain 3 15)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 50,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 3}\n",
-       "<-1 * <<Loop[2-1-0 3][1-0 7][2-0 13][2-1 25]>>>\n",
-       "<1 * <<Loop[2-1-0 3][1-0 7][2-1 13][2 29]>>>\n",
-       "<1 * <<Loop[2-1-0 3][2-0 7][0 15][2-1 25]>>>\n",
-       "<-1 * <<Loop[2-1-0 3][2-0 7][2-1 13][1 29]>>>\n",
-       "<-1 * <<Loop[2-1-0 3][2-1 7][1 15][2 27]>>>\n",
-       "<1 * <<Loop[2-1-0 3][2-1 7][2 15][31]>>>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 50,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? cochain 4 31)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 51,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 4}\n",
-       "<-1 * <<Loop[3-2-1-0 3][2-1-0 7][3-1-0 13][3-2-0 25][3-2-1 49]>>>\n",
-       "<1 * <<Loop[3-2-1-0 3][2-1-0 7][3-1-0 13][3-2-1 25][3-2 57]>>>\n",
-       "<1 * <<Loop[3-2-1-0 3][2-1-0 7][3-2-0 13][3-0 29][3-2-1 49]>>>\n",
-       "<-1 * <<Loop[3-2-1-0 3][2-1-0 7][3-2-0 13][3-2-1 25][3-1 57]>>>\n",
-       "<-1 * <<Loop[3-2-1-0 3][2-1-0 7][3-2-1 13][3-1 29][3-2 53]>>>\n",
-       "<1 * <<Loop[3-2-1-0 3][2-1-0 7][3-2-1 13][3-2 29][3 61]>>>\n",
-       "<1 * <<Loop[3-2-1-0 3][3-1-0 7][1-0 15][3-2-0 25][3-2-1 49]>>>\n",
-       "<-1 * <<Loop[3-2-1-0 3][3-1-0 7][1-0 15][3-2-1 25][3-2 57]>>>\n",
-       "<-1 * <<Loop[3-2-1-0 3][3-1-0 7][3-2-0 13][2-0 29][3-2-1 49]>>>\n",
-       "<1 * <<Loop[3-2-1-0 3][3-1-0 7][3-2-0 13][3-2-1 25][2-1 57]>>>\n",
-       "... ...\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 51,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? cochain 5 63)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "We verify, that for a simplex in dimension $n$, the length of the resulting combination is $(n-1)!$."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 52,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "24"
-      ]
-     },
-     "execution_count": 52,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(length(cmbn-list *))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 53,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 5}\n",
-       "<1 * <<Loop[4-3-2-1-0 3][3-2-1-0 7][4-2-1-0 13][4-3-1-0 25][4-3-2-0 49][4-3-2-1 97]>>>\n",
-       "<-1 * <<Loop[4-3-2-1-0 3][3-2-1-0 7][4-2-1-0 13][4-3-1-0 25][4-3-2-1 49][4-3-2 113]>>>\n",
-       "<-1 * <<Loop[4-3-2-1-0 3][3-2-1-0 7][4-2-1-0 13][4-3-2-0 25][4-3-0 57][4-3-2-1 97]>>>\n",
-       "<1 * <<Loop[4-3-2-1-0 3][3-2-1-0 7][4-2-1-0 13][4-3-2-0 25][4-3-2-1 49][4-3-1 113]>>>\n",
-       "<1 * <<Loop[4-3-2-1-0 3][3-2-1-0 7][4-2-1-0 13][4-3-2-1 25][4-3-1 57][4-3-2 105]>>>\n",
-       "<-1 * <<Loop[4-3-2-1-0 3][3-2-1-0 7][4-2-1-0 13][4-3-2-1 25][4-3-2 57][4-3 121]>>>\n",
-       "<-1 * <<Loop[4-3-2-1-0 3][3-2-1-0 7][4-3-1-0 13][4-1-0 29][4-3-2-0 49][4-3-2-1 97]>>>\n",
-       "<1 * <<Loop[4-3-2-1-0 3][3-2-1-0 7][4-3-1-0 13][4-1-0 29][4-3-2-1 49][4-3-2 113]>>>\n",
-       "<1 * <<Loop[4-3-2-1-0 3][3-2-1-0 7][4-3-1-0 13][4-3-2-0 25][4-2-0 57][4-3-2-1 97]>>>\n",
-       "<-1 * <<Loop[4-3-2-1-0 3][3-2-1-0 7][4-3-1-0 13][4-3-2-0 25][4-3-2-1 49][4-2-1 113]>>>\n",
-       "... ...\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 53,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? cochain 6 127)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 54,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "120"
-      ]
-     },
-     "execution_count": 54,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(length(cmbn-list *))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "## Expression of the differential $d_{\\otimes t}$\n",
-    "\n",
-    "The differential $d_{\\otimes t}$ of the twisted tensor product $B \\otimes_t GB$ may be expressed as the sum of the differential of the simple tensor product $B \\otimes GB$ and the following morphism of degree -1,\n",
-    "$$\\nabla: B \\otimes GB \\longrightarrow B \\otimes GB,$$\n",
-    "where $\\nabla$ is the composition of the morphisms of the following sequence:\n",
-    "$$B\\otimes GB \\buildrel {\\Delta\\otimes 1_{GB}} \\over \\longrightarrow  (B\\otimes B) \\otimes GB\n",
-    "              \\buildrel {assoc} \\over \\longrightarrow  B \\otimes (B \\otimes GB)\n",
-    "              \\buildrel {1_B \\otimes (t \\otimes 1_{GB})} \\over \\longrightarrow  B \\otimes (GB \\otimes GB)\n",
-    "              \\buildrel {1_B \\otimes \\varpi} \\over \\longrightarrow B \\otimes GB.$$\n",
-    "In the previous formula, $\\Delta$ is the coproduct in the coalgebra $B$, $\\varpi$ is the product in the algebra $GB$, $1_B$ is the identity morphism in $B$ and $1_{GB}$ the identity morphism in $GB$. We need also, as in a previous example, an \"assoc\" morphism for the compound tensor product. The user will note the easiness for coding in `Kenzo` such a long composition of morphisms."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 55,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K167 Chain-Complex]"
-      ]
-     },
-     "execution_count": 55,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def 3-left (tnsr-prdc (tnsr-prdc d d) gd))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 56,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K169 Chain-Complex]"
-      ]
-     },
-     "execution_count": 56,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def 3-right (tnsr-prdc d (tnsr-prdc d gd)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 57,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K171 Morphism (degree 0): K167 -> K169]"
-      ]
-     },
-     "execution_count": 57,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def assoc1 (build-mrph\n",
-    "               :sorc 3-left\n",
-    "               :trgt 3-right\n",
-    "               :degr 0\n",
-    "               :intr #'(lambda (degr a2-a) (declare (ignore degr))\n",
-    "                         (with-tnpr (degra2 gnrta2 degra gnrta) a2-a\n",
-    "                             (declare (ignore degra2))\n",
-    "                            (with-tnpr (degr1 gnrt1 degr2 gnrt2) gnrta2\n",
-    "                               (cmbn (+ degr1 degr2 degra) \n",
-    "                                     1 (tnpr degr1 \n",
-    "                                             gnrt1 \n",
-    "                                             (+ degr2 degra) \n",
-    "                                             (tnpr degr2 gnrt2 degra gnrta))))))\n",
-    "               :strt :gnrt\n",
-    "               :orgn '(assoc-double-tensor-product)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 58,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K172 Morphism (degree 0): K112 -> K112]"
-      ]
-     },
-     "execution_count": 58,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def id-d (idnt-mrph d))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 59,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K173 Morphism (degree 0): K117 -> K117]"
-      ]
-     },
-     "execution_count": 59,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def id-gd (idnt-mrph gd))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 60,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K185 Morphism (degree -1): K139 -> K139]"
-      ]
-     },
-     "execution_count": 60,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def nabla \n",
-    " (add (dffr (tnsr-prdc d gd))\n",
-    "      (i-cmps (tnsr-prdc id-d (aprd gd))\n",
-    "              (tnsr-prdc id-d (tnsr-prdc cochain id-gd))\n",
-    "              assoc1\n",
-    "              (tnsr-prdc (cprd d) id-gd))))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "We verify that the morphism `nabla` and the differential of the  twisted tensor product (accessible through the symbol `d-twtp-gd`) return the same results:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 61,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 1}\n",
-       "<1 * <TnPr 1 <<Loop[7]>>>>\n",
-       "<-1 * <TnPr 1 <<Loop[0 3][7]>>>>\n",
-       "<1 * <TnPr 3 <<Loop[3\\-1][5]>>>>\n",
-       "<-1 * <TnPr 3 <<Loop[6]>>>>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 61,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? (dffr d-twtp-gd) 2 (tnpr 1 3 1 (loop3 0 7 1)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 62,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 1}\n",
-       "<1 * <TnPr 1 <<Loop[7]>>>>\n",
-       "<-1 * <TnPr 1 <<Loop[0 3][7]>>>>\n",
-       "<1 * <TnPr 3 <<Loop[3\\-1][5]>>>>\n",
-       "<-1 * <TnPr 3 <<Loop[6]>>>>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 62,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? nabla 2 (tnpr 1 3 1 (loop3 0 7 1)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 63,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K186 Morphism (degree -1): K139 -> K139]"
-      ]
-     },
-     "execution_count": 63,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def zero (sbtr nabla (dffr d-twtp-gd)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 64,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 1}\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 64,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? zero 2 (tnpr 1 3 1 (loop3 0 7 1)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 65,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 4}\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 65,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? zero 5 (tnpr  3 15 2 (loop3 0 15 1)))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "### The cup product of the twisting cochain\n",
-    "\n",
-    "The cup product $t \\sqcup t$ of the twisting cochain $t$,\n",
-    "$$t\\sqcup t: B \\longrightarrow GB$$\n",
-    "is defined by the following composition of morphisms:\n",
-    "$$B \\buildrel {\\Delta} \\over \\longrightarrow B \\otimes B\n",
-    "    \\buildrel {t \\otimes t} \\over \\longrightarrow GB \\otimes GB \n",
-    "    \\buildrel {\\varpi} \\over \\longrightarrow GB.$$\n",
-    "We may now verify the formula\n",
-    "$$ d_{GB} \\circ t + t \\circ d_B + t\\sqcup t =0,$$\n",
-    "where $d_B$ and $d_{GB}$ are  the respective differential morphisms in $B$ and $GB$."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 66,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K189 Morphism (degree -2): K112 -> K117]"
-      ]
-     },
-     "execution_count": 66,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def t-cup-t (i-cmps (aprd gd) (tnsr-prdc cochain cochain) (cprd d)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 67,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K190 Morphism (degree -2): K112 -> K117]"
-      ]
-     },
-     "execution_count": 67,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def dt (cmps (dffr gd) cochain))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 68,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K191 Morphism (degree -2): K112 -> K117]"
-      ]
-     },
-     "execution_count": 68,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def td (cmps cochain (dffr d)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 69,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K193 Morphism (degree -2): K112 -> K117]"
-      ]
-     },
-     "execution_count": 69,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def zero-2 (i-add dt td t-cup-t))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 70,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 1}\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 70,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? zero-2 3 15)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 71,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 2}\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 71,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? zero-2 4 31)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 72,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 3}\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 72,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? zero-2 5 63)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 73,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 4}\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 73,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? zero-2 6 127)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "So the user has easily verified the *cochain condition* for the twisting cochain $t$.\n",
-    "\n",
-    "## The essential contraction\n",
-    "\n",
-    "It is known that if $B$ is a reduced simplicial set, the space $B \\times_\\tau GB$ is contractible. So it is possible to build a reduction of this space over $\\mathbb{Z}$. This reduction depends of the important contraction\n",
-    "$$\\chi_{\\times\\tau}:  {{\\cal C}_*(B) \\times_\\tau {\\cal C}_*(GB)} \\longrightarrow \n",
-    "                      {{\\cal C}_*(B) \\times_\\tau {\\cal C}_*(GB)}, $$\n",
-    "which is a homotopy operator (degree: $+1$) satisfying the relation\n",
-    "$$d \\circ \\chi_{\\times\\tau} + \\chi_{\\times\\tau} \\circ d =1.$$\n",
-    "Now, from the reduction\n",
-    "$$\n",
-    "\\begin{aligned}\n",
-    "{{\\cal C}_*(X \\times_\\tau GX)} \\quad& \\stackrel{h}{\\longrightarrow} & {}^s{{\\cal C}_*(X \\times_\\tau GX)} \\cr\n",
-    " {\\scriptstyle f} \\downarrow \\uparrow {\\scriptstyle g} \\qquad \\cr\n",
-    " {{\\cal C}_*(X) \\otimes_t {\\cal C}_*(GX)} \\cr\n",
-    "\\end{aligned}\n",
-    "$$\n",
-    "there is also  an induced contraction \n",
-    "$$\\chi_{\\otimes t}:  {{\\cal C}_*(B) \\otimes_t {\\cal C}_*(GB)} \\longrightarrow \n",
-    "                      {{\\cal C}_*(B) \\otimes_t {\\cal C}_*(GB)}, $$\n",
-    "defined by $\\chi_{\\otimes t}= f \\circ \\chi_{\\times\\tau} \\circ g$.\n",
-    "This implies that the twisted tensor product is also contractible over $\\mathbb{Z}$.\n",
-    "\n",
-    "The two functions of `Kenzo` for this construction are:\n",
-    "\n",
-    "`crts-contraction` *space* *[Function]*\n",
-    "> Return the homotopy morphism corresponding to the contraction $\\chi_{\\times\\tau}$. The lisp definition is:\n",
-    "```commonlisp\n",
-    "          (defun CRTS-CONTRACTION \n",
-    "             (space\n",
-    "                &aux (twisted-crts-prdc (twisted-crts-prdc space)))\n",
-    "             (the morphism\n",
-    "                (build-mrph\n",
-    "                   :sorc twisted-crts-prdc \n",
-    "                   :trgt twisted-crts-prdc \n",
-    "                   :degr +1\n",
-    "                   :intr (crts-contraction-intr \n",
-    "                               (cmpr space)\n",
-    "                               (bspn space) \n",
-    "                               (face space) \n",
-    "                               (cmpr twisted-crts-prdc))\n",
-    "                   :strt :gnrt\n",
-    "                   :orgn `(crts-contraction ,space))))\n",
-    "```\n",
-    "At execution time, the work is essentialy done by the function put in the slot `:intr`.\n",
-    "\n",
-    "`tnpr-contraction` *space* *[Function]*\n",
-    "> Return the induced morphism $\\chi_{\\otimes t}= f \\circ \\chi_{\\times\\tau} \\circ g$, as shown by the lisp definition:\n",
-    "```commonlisp\n",
-    "          (defun TNPR-CONTRACTION \n",
-    "             (space\n",
-    "                &aux (szczarba (szczarba space))\n",
-    "                     (f (f szczarba))\n",
-    "                     (g (g szczarba))\n",
-    "                     (crts-contraction (crts-contraction space)))\n",
-    "             (the morphism\n",
-    "                (i-cmps f crts-contraction g)))\n",
-    "```\n",
-    "\n",
-    "### Examples\n",
-    "\n",
-    "Let us use again our familiar simplicial set $\\bar\\Delta$. First we apply  the homotopy operator $\\chi_{\\times t}$   upon various generators. Note that the binary coding of the simplices allows normal arithmetic operators to generate them."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 74,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K112 Simplicial-Set]"
-      ]
-     },
-     "execution_count": 74,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def delta (deltab))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 75,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K194 Morphism (degree 1): K134 -> K134]"
-      ]
-     },
-     "execution_count": 75,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def chi-x (crts-contraction delta))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 76,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 1}\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 76,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? chi-x 0 (crpr 0 1 0 +null-loop+))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 77,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 1}\n",
-       "<-1 * <CrPr - 96 0 <<Loop>>>>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 77,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? chi-x 0 (crpr 0 1 0 (loop3 0 96 1)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 78,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 1}\n",
-       "<-1 * <CrPr - 96 0 <<Loop[384]>>>>\n",
-       "<-1 * <CrPr - 384 0 <<Loop>>>>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 78,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? chi-x 0 (crpr 0 1 0 (loop3 0 96 1 0 (+ 256 128) 1)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 79,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 1}\n",
-       "<-1 * <CrPr - 96 0 <<Loop[384][1536]>>>>\n",
-       "<-1 * <CrPr - 384 0 <<Loop[1536]>>>>\n",
-       "<-1 * <CrPr - 1536 0 <<Loop>>>>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 79,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? chi-x 0 (crpr 0 1 0 (loop3 0 96 1 0 (+ 256 128) 1 0 (+ 512 1024) 1)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 80,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 1}\n",
-       "<-1 * <CrPr - 96 0 <<Loop>>>>\n",
-       "<-1 * <CrPr - 96 0 <<Loop[96]>>>>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 80,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? chi-x 0 (crpr 0 1 0 (loop3 0 96 2)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 81,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 2}\n",
-       "<1 * <CrPr - 224 1-0 <<Loop>>>>\n",
-       "<-1 * <CrPr 1 3 0 <<Loop[224]>>>>\n",
-       "<1 * <CrPr 1 96 0 <<Loop[224]>>>>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 81,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? chi-x 1 (crpr 0 3 0 (loop3 0 (+ 32 64 128) 1)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 82,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 3}\n",
-       "<-1 * <CrPr - 480 2-1-0 <<Loop>>>>\n",
-       "<1 * <CrPr 2 7 1 <<Loop[480]>>>>\n",
-       "<-1 * <CrPr 2 224 1 <<Loop[480]>>>>\n",
-       "<-1 * <CrPr 2-1 5 0 <<Loop[480]>>>>\n",
-       "<1 * <CrPr 2-1 160 0 <<Loop[480]>>>>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 82,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? chi-x 2 (crpr 0 7 0 (loop3 0 (+ 32 64 128 256) 1)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 83,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 4}\n",
-       "<-1 * <CrPr 3-1 7 2-0 <<Loop[1 224\\2][2 224\\-2]>>>>\n",
-       "<1 * <CrPr 3-2 7 1-0 <<Loop[1 224\\2][2 224\\-2]>>>>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 83,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? chi-x 3 (crpr 2 7 1 (loop3 2 (+ 32 64 128) 2 4 (+ 32 64 128) -2)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 84,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 4}\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 84,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? chi-x 3 (crpr 2 7 4 (loop3 2 (+ 32 64 128) 2 1 (+ 32 64 128) -2)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 85,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 4}\n",
-       "<-1 * <CrPr 3-1 7 2-0 <<Loop[1 224\\-2][2 224\\2]>>>>\n",
-       "<1 * <CrPr 3-2 7 1-0 <<Loop[1 224\\-2][2 224\\2]>>>>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 85,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? chi-x 3 (crpr 2 7 1 (loop3 2 (+ 32 64 128) -2 4 (+ 32 64 128) 2)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 86,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 4}\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 86,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? chi-x 3 (crpr 2 7 4 (loop3 2 (+ 32 64 128) -2 1 (+ 32 64 128) 2)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 87,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 4}\n",
-       "<-1 * <CrPr 3-0 7 2-1 <<Loop[1 224\\2][2 224\\-2]>>>>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 87,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? chi-x 3 (crpr 1 7 2 (loop3 2 (+ 32 64 128) 2 4 (+ 32 64 128) -2)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 88,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 4}\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 88,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? chi-x 3 (crpr 4 7 2 (loop3 2 (+ 32 64 128) 2 1 (+ 32 64 128) -2)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 89,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 4}\n",
-       "<-1 * <CrPr 3-0 7 2-1 <<Loop[1 224\\-2][2 224\\2]>>>>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 89,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? chi-x 3 (crpr 1 7 2 (loop3 2 (+ 32 64 128) -2 4 (+ 32 64 128) 2)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 90,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 4}\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 90,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? chi-x 3 (crpr 4 7 2 (loop3 2 (+ 32 64 128) -2 1 (+ 32 64 128) 2)))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Then, for testing  $\\chi_{\\otimes t}$ we use the image of all those generators by the function `f` of the Brown reduction.\n",
-    "$$\n",
-    "\\begin{aligned}\n",
-    "    {{\\cal C}_*(X \\times_\\tau GX)} \\quad& \\stackrel{h}{\\longrightarrow} & {}^s{{\\cal C}_*(X \\times_\\tau GX)} \\cr\n",
-    " {\\scriptstyle f} \\downarrow \\uparrow {\\scriptstyle g}\\qquad  \\cr\n",
-    " {{\\cal C}_*(X) \\otimes_t {\\cal C}_*(GX)} \\cr\n",
-    "\\end{aligned}\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 91,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "T"
-      ]
-     },
-     "execution_count": 91,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(setf *tnpr-with-degrees* t)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 92,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K196 Morphism (degree 1): K160 -> K160]"
-      ]
-     },
-     "execution_count": 92,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def chi-t (tnpr-contraction delta))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 93,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K162 Reduction K134 => K160]"
-      ]
-     },
-     "execution_count": 93,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def reduc (szczarba delta))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 94,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K152 Morphism (degree 0): K134 -> K160]"
-      ]
-     },
-     "execution_count": 94,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def f (f reduc))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 95,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 0}\n",
-       "<1 * <TnPr 0 1 0 <<Loop>>>>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 95,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? f 0 (crpr 0 1 0 +null-loop+))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 96,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 1}\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 96,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? chi-t *)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 97,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 0}\n",
-       "<1 * <TnPr 0 32 0 <<Loop[96]>>>>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 97,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? f 0 (crpr 0 1 0 (loop3 0 96 1)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 98,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 1}\n",
-       "<-1 * <TnPr 1 96 0 <<Loop>>>>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 98,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? chi-t *)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 99,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 0}\n",
-       "<1 * <TnPr 0 1 0 <<Loop[96][384]>>>>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 99,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? f 0 (crpr 0 1 0 (loop3 0 96 1 0 (+ 256 128) 1)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 100,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 1}\n",
-       "<-1 * <TnPr 1 96 0 <<Loop[384]>>>>\n",
-       "<-1 * <TnPr 1 384 0 <<Loop>>>>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 100,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? chi-t *)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 101,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 0}\n",
-       "<1 * <TnPr 0 1 0 <<Loop[96][384][1536]>>>>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 101,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? f 0 (crpr 0 1 0 (loop3 0 96 1 0 (+ 256 128) 1 0 (+ 512 1024) 1)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 102,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 1}\n",
-       "<-1 * <TnPr 1 96 0 <<Loop[384][1536]>>>>\n",
-       "<-1 * <TnPr 1 384 0 <<Loop[1536]>>>>\n",
-       "<-1 * <TnPr 1 1536 0 <<Loop>>>>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 102,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? chi-t *)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 103,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 0}\n",
-       "<1 * <TnPr 0 1 0 <<Loop[96\\2]>>>>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 103,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? f 0 (crpr 0 1 0 (loop3 0 96 2)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 104,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 1}\n",
-       "<-1 * <TnPr 1 96 0 <<Loop>>>>\n",
-       "<-1 * <TnPr 1 96 0 <<Loop[96]>>>>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 104,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? chi-t *)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 105,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 1}\n",
-       "<1 * <TnPr 0 1 1 <<Loop[0 3][224]>>>>\n",
-       "<1 * <TnPr 1 3 0 <<Loop[192]>>>>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 105,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? f 1 (crpr 0 3 0 (loop3 0 (+ 32 64 128) 1)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 106,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 2}\n",
-       "<-1 * <TnPr 1 3 1 <<Loop[224]>>>>\n",
-       "<1 * <TnPr 1 96 1 <<Loop[224]>>>>\n",
-       "<1 * <TnPr 2 224 0 <<Loop>>>>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 106,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? chi-t *)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 107,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 2}\n",
-       "<-1 * <TnPr 0 1 2 <<Loop[1-0 3][0 7][1 416]>>>>\n",
-       "<1 * <TnPr 0 1 2 <<Loop[1-0 3][1 7][480]>>>>\n",
-       "<1 * <TnPr 1 3 1 <<Loop[0 6][448]>>>>\n",
-       "<1 * <TnPr 2 7 0 <<Loop[384]>>>>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 107,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? f 2 (crpr 0 7 0 (loop3 0 (+ 32 64 128 256) 1)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 108,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 3}\n",
-       "<1 * <TnPr 0 1 3 <<Loop[2-1-0 3][1-0 7][2 480]>>>>\n",
-       "<-1 * <TnPr 0 1 3 <<Loop[2-1-0 3][2-0 7][1 480]>>>>\n",
-       "<-1 * <TnPr 0 32 3 <<Loop[2-1-0 96][1-0 224][2 480]>>>>\n",
-       "<1 * <TnPr 0 32 3 <<Loop[2-1-0 96][2-0 224][1 480]>>>>\n",
-       "<-1 * <TnPr 1 5 2 <<Loop[480]>>>>\n",
-       "<1 * <TnPr 1 160 2 <<Loop[480]>>>>\n",
-       "<1 * <TnPr 2 7 1 <<Loop[448]>>>>\n",
-       "<-1 * <TnPr 2 224 1 <<Loop[448]>>>>\n",
-       "<-1 * <TnPr 3 480 0 <<Loop>>>>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 108,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? chi-t *)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 109,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 3}\n",
-       "<1 * <TnPr 0 1 3 <<Loop[2-1-0 3][2-1 7][2-0 224\\2][3-0 224\\-2]>>>>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 109,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? f 3 (crpr 2 7 1 (loop3 2 (+ 32 64 128) 2 4 (+ 32 64 128) -2)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 110,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 4}\n",
-       "<1 * <TnPr 2 7 2 <<Loop[1 224\\2][2 224\\-2]>>>>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 110,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? chi-t *)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 111,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 3}\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 111,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? f 3 (crpr 2 7 4 (loop3 2 (+ 32 64 128) 2 1 (+ 32 64 128) -2)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 112,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 4}\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 112,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? chi-t *)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 113,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 3}\n",
-       "<1 * <TnPr 0 1 3 <<Loop[2-1-0 3][2-1 7][2-0 224\\-2][3-0 224\\2]>>>>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 113,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? f 3 (crpr 2 7 1 (loop3 2 (+ 32 64 128) -2 4 (+ 32 64 128) 2)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 114,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 4}\n",
-       "<1 * <TnPr 2 7 2 <<Loop[1 224\\-2][2 224\\2]>>>>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 114,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? chi-t *)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 115,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 3}\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 115,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? f 3 (crpr 2 7 4 (loop3 2 (+ 32 64 128) -2 1 (+ 32 64 128) 2)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 116,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 4}\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 116,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? chi-t *)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 117,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 3}\n",
-       "<-1 * <TnPr 0 1 3 <<Loop[2-1-0 3][1-0 7][2-1 224\\2][3-2 224\\-2]>>>>\n",
-       "<1 * <TnPr 0 1 3 <<Loop[2-1-0 3][2-0 7][2-1 224\\2][3-1 224\\-2]>>>>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 117,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? f 3 (crpr 1 7 2 (loop3 2 (+ 32 64 128) 2 4 (+ 32 64 128) -2)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 118,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 4}\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 118,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? chi-t *)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 119,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 3}\n",
-       "<1 * <TnPr 0 1 3 <<Loop[2-1-0 3][1-0 7][2-1 224\\2][2-0 224\\-2]>>>>\n",
-       "<-1 * <TnPr 0 1 3 <<Loop[2-1-0 3][2-0 7][2-1 224\\2][1-0 224\\-2]>>>>\n",
-       "<1 * <TnPr 2 7 1 <<Loop[0 192\\2][224\\-2]>>>>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 119,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? f 3 (crpr 4 7 2 (loop3 2 (+ 32 64 128) 2 1 (+ 32 64 128) -2)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 120,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 4}\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 120,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? chi-t *)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 121,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 3}\n",
-       "<-1 * <TnPr 0 1 3 <<Loop[2-1-0 3][1-0 7][2-1 224\\-2][3-2 224\\2]>>>>\n",
-       "<1 * <TnPr 0 1 3 <<Loop[2-1-0 3][2-0 7][2-1 224\\-2][3-1 224\\2]>>>>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 121,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? f 3 (crpr 1 7 2 (loop3 2 (+ 32 64 128) -2 4 (+ 32 64 128) 2)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 122,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 4}\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 122,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? chi-t *)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 123,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 3}\n",
-       "<1 * <TnPr 0 1 3 <<Loop[2-1-0 3][1-0 7][2-1 224\\-2][2-0 224\\2]>>>>\n",
-       "<-1 * <TnPr 0 1 3 <<Loop[2-1-0 3][2-0 7][2-1 224\\-2][1-0 224\\2]>>>>\n",
-       "<1 * <TnPr 2 7 1 <<Loop[0 192\\-2][224\\2]>>>>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 123,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? f 3 (crpr 4 7 2 (loop3 2 (+ 32 64 128) -2 1 (+ 32 64 128) 2)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 124,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 4}\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 124,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? chi-t *)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "We verify now the required property of the homotopy operator $\\chi_{\\times\\tau}$. As usual, we build by composition a morphism `zero`."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 125,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K135 Morphism (degree -1): K134 -> K134]"
-      ]
-     },
-     "execution_count": 125,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def dfr (bndr (twisted-crts-prdc delta)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 126,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K201 Morphism (degree 0): K134 -> K134]"
-      ]
-     },
-     "execution_count": 126,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def zero (i-sbtr (idnt-mrph (sorc dfr)) (cmps dfr chi-x) \n",
-    "                   (cmps chi-x dfr)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 127,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "<CrPr 2 7 1 <<Loop[1 224\\-2][0 224\\2]>>>"
-      ]
-     },
-     "execution_count": 127,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def simplx (crpr 4 7 2 (loop3 2 (+ 32 64 128) -2 1 (+ 32 64 128) 2)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 128,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 3}\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 128,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? zero 3 simplx)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Then, we do the same test for the homotopy operator $\\chi_{\\otimes t}$."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 129,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K160 Chain-Complex]"
-      ]
-     },
-     "execution_count": 129,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def tw (twisted-tnsr-prdc d))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 130,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K206 Morphism (degree 0): K160 -> K160]"
-      ]
-     },
-     "execution_count": 130,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def zero-2  (i-sbtr (idnt-mrph tw) (cmps tw chi-t) (cmps chi-t tw)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 131,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "<TnPr 0 1 3 <<Loop[31\\2][992\\-1]>>>"
-      ]
-     },
-     "execution_count": 131,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def simpx2 (tnpr 0 1 3 (loop3 0 (mask 5) 2 0 (* 32 (mask 5)) -1)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 132,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 3}\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 132,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(time (? zero-2 3 simpx2))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Note nevertheless that the relation is not satisfied for the base generator $*\\otimes *$, namely the tensor product of both base generators. This is due to the fact that both contractions,  $\\chi_{\\times t}$ and  $\\chi_{\\otimes t}$, correspond to  reductions over  $\\mathbb{Z}$ and not on 0."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 133,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "<TnPr 0 1 0 <<Loop>>>"
-      ]
-     },
-     "execution_count": 133,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def gnrt-0 (tnpr 0 1 0 +null-loop+))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 134,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 0}\n",
-       "<1 * <TnPr 0 1 0 <<Loop>>>>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 134,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? zero-2 0 gnrt-0)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Let us build, for instance, the reduction of the twisted tensor product over $\\mathbb{Z}$ and check it. In that case, the two homomorphisms $f$ and $g$ are respectively the *augmentation* and *coaugmentation* morphisms.\n",
-    "$$\n",
-    "\\begin{aligned}\n",
-    "{{\\cal C}_*(B) \\otimes_t {\\cal C}_*(GB)} & \\qquad\\stackrel{\\chi_{\\otimes t}}{\\longrightarrow} &\n",
-    "  {}^s{{\\cal C}_*(B) \\otimes_t {\\cal C}_*(GB)} \\cr\n",
-    " {\\scriptstyle aug} \\downarrow \\uparrow {\\scriptstyle coaug}\\quad & &  \\cr\n",
-    " {{\\cal C}_*(\\mathbb{Z})} \\qquad& & \\cr\n",
-    "\\end{aligned}\n",
-    "$$\n",
-    "We recall that, the unit chain complex corresponding to $\\mathbb{Z}$ is built by the function `z-chcm`. The unique generator in degree 0 is `:z-gnrt`."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 135,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K209 Cohomology-Class on K160 of degree 0]"
-      ]
-     },
-     "execution_count": 135,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def aug (build-mrph\n",
-    "            :sorc tw \n",
-    "            :trgt (z-chcm) \n",
-    "            :degr 0\n",
-    "            :intr #'(lambda (degr gnrt) (declare (ignore gnrt))\n",
-    "                       (if (zerop degr)\n",
-    "                           (term-cmbn 0 1 :z-gnrt)\n",
-    "                           (zero-cmbn degr)))\n",
-    "            :strt :gnrt \n",
-    "            :orgn '(aug tw)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 136,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K210 Morphism (degree 0): K207 -> K160]"
-      ]
-     },
-     "execution_count": 136,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def coaug (build-mrph\n",
-    "              :sorc (z-chcm) \n",
-    "              :trgt tw \n",
-    "              :degr 0\n",
-    "              :intr #'(lambda (degr gnrt) (declare (ignore gnrt))\n",
-    "                         (if (zerop degr)\n",
-    "                             (term-cmbn 0 1 (tnpr 0 1 0 +null-loop+))\n",
-    "                             (zero-cmbn degr)))\n",
-    "              :strt :gnrt\n",
-    "              :orgn '(coaug tw)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 137,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K211 Reduction K160 => K207]"
-      ]
-     },
-     "execution_count": 137,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def rdct (build-rdct :f aug \n",
-    "                       :g coaug \n",
-    "                       :h Chi-t \n",
-    "                       :orgn '(reduction-tw-Z)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 138,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "---done---"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 138,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(pre-check-rdct rdct)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 139,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 3}\n",
-       "<1 * <TnPr 1 3 2 <<Loop[15\\2]>>>>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 139,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(setf *tc* (cmbn 3 1 (tnpr 1 3 2 (loop3 0 15 2))))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 140,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 0}\n",
-       "<1 * Z-GNRT>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 140,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(setf *bc* (cmbn 0 1 :z-gnrt))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 141,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "*TC* => \n",
-      "----------------------------------------------------------------------{CMBN 3}\n",
-      "<1 * <TnPr 1 3 2 <<Loop[15\\2]>>>>\n",
-      "------------------------------------------------------------------------------\n",
-      "\n",
-      "*BC* => \n",
-      "----------------------------------------------------------------------{CMBN 0}\n",
-      "<1 * Z-GNRT>\n",
-      "------------------------------------------------------------------------------\n",
-      "\n",
-      "Checking *TDD* = 0\n",
-      "Result: \n",
-      "----------------------------------------------------------------------{CMBN 1}\n",
-      "------------------------------------------------------------------------------\n",
-      "\n",
-      "Checking *BDD* = 0\n",
-      "Result: \n",
-      "----------------------------------------------------------------------{CMBN -2}\n",
-      "------------------------------------------------------------------------------\n",
-      "\n",
-      "Checking *DF-FD* = 0\n",
-      "Result: \n",
-      "----------------------------------------------------------------------{CMBN 2}\n",
-      "------------------------------------------------------------------------------\n",
-      "\n",
-      "Checking *DG-GD* = 0\n",
-      "Result: \n",
-      "----------------------------------------------------------------------{CMBN -1}\n",
-      "------------------------------------------------------------------------------\n",
-      "\n",
-      "Checking *ID-FG* = 0\n",
-      "Result: \n",
-      "----------------------------------------------------------------------{CMBN 0}\n",
-      "------------------------------------------------------------------------------\n",
-      "\n",
-      "Checking *ID-GF-DH-HD* = 0\n",
-      "Result: \n",
-      "----------------------------------------------------------------------{CMBN 3}\n",
-      "------------------------------------------------------------------------------\n",
-      "\n",
-      "Checking *HH* = 0\n",
-      "Result: \n",
-      "----------------------------------------------------------------------{CMBN 5}\n",
-      "------------------------------------------------------------------------------\n",
-      "\n",
-      "Checking *FH* = 0\n",
-      "Result: \n",
-      "----------------------------------------------------------------------{CMBN 4}\n",
-      "------------------------------------------------------------------------------\n",
-      "\n",
-      "Checking *HG* = 0\n",
-      "Result: \n",
-      "----------------------------------------------------------------------{CMBN 1}\n",
-      "------------------------------------------------------------------------------\n",
-      "\n",
-      "---done---"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 141,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(check-rdct-no-wait)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "## An unproved property of the algebraic Kan contraction\n",
-    "\n",
-    "Since the early version of the software (1990), and through a host of examples, an amazing algebraic property of the Kan contraction $\\chi_{\\otimes t}$ has been experimentally discovered. Many computations have been done of $\\chi_{\\otimes t}(b \\otimes g)$, for various choices of $b \\otimes g$ and in all these cases,  as soon as $degree(b) > 0$, then the result is null.\n",
-    "In other words, $\\chi_{\\otimes t}$ *is null outside the base fiber.* Up to now, no actual proof of this result has yet  been given.\n",
-    "\n",
-    "We show that, using the \"soft\" version of $\\bar{\\Delta}$."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 142,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K1 Simplicial-Set]"
-      ]
-     },
-     "execution_count": 142,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def db (soft-deltab))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 143,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K231 Morphism (degree 1): K88 -> K88]"
-      ]
-     },
-     "execution_count": 143,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def tt (tnpr-contraction db))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 144,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "<TnPr 3 (DELT . 31) 4 <<Loop[(DELT . 63)\\2]>>>"
-      ]
-     },
-     "execution_count": 144,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def gnrt1 (tnpr 3 (code '(0 1 2 3 4)) \n",
-    "                 4 (loop3 0 (code '(0 1 2 3 4 5)) 2)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 145,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 8}\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 145,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? tt 7 gnrt1)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 146,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "<TnPr 4 (DELT . 5460) 5 <<Loop[(DELT . 10922)\\5]>>>"
-      ]
-     },
-     "execution_count": 146,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def gnrt2 (tnpr 4 (code '(2 4 6 8 10 12))  \n",
-    "                  5 (loop3 0 (code '(1 3 5 7 9 11 13)) 5)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 147,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 10}\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 147,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? tt 9 gnrt2)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "But if $degree(b) = 0$, then the result is non-null in general."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 148,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 3}\n",
-       "<-1 * <TnPr 0 (DELT . 1) 3 <<Loop[2-1-0 (DELT . 3)][1-0 (DELT . 7)][2 (DELT . 15)]>>>>\n",
-       "<1 * <TnPr 0 (DELT . 1) 3 <<Loop[2-1-0 (DELT . 3)][2-0 (DELT . 7)][1 (DELT . 15)]>>>>\n",
-       "<1 * <TnPr 1 (DELT . 5) 2 <<Loop[(DELT . 15)]>>>>\n",
-       "<-1 * <TnPr 2 (DELT . 7) 1 <<Loop[(DELT . 14)]>>>>\n",
-       "<-1 * <TnPr 3 (DELT . 15) 0 <<Loop>>>>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 148,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? tt 2 (tnpr 0 (code '(0)) 2 (loop3 0 (code '(0 1 2 3)) 1)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 149,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 5}\n",
-       "<1 * <TnPr 0 (DELT . 2) 5 <<Loop[4-3-2-1-0 (DELT . 6)][3-2-1-0 (DELT . 14)][4-2-1-0 (DELT . 26)][4-3-1-0 (DELT . 50)][4-3-2 (DELT . 114)]>>>>\n",
-       "<1 * <TnPr 0 (DELT . 2) 5 <<Loop[4-3-2-1-0 (DELT . 6)][3-2-1-0 (DELT . 14)][4-2-1-0 (DELT . 26)][4-3-1-0 (DELT . 50)][4-3-2 (DELT . 114)\\2]>>>>\n",
-       "<1 * <TnPr 0 (DELT . 2) 5 <<Loop[4-3-2-1-0 (DELT . 6)][3-2-1-0 (DELT . 14)][4-2-1-0 (DELT . 26)][4-3-1-0 (DELT . 50)][4-3-2 (DELT . 114)\\3]>>>>\n",
-       "<-1 * <TnPr 0 (DELT . 2) 5 <<Loop[4-3-2-1-0 (DELT . 6)][3-2-1-0 (DELT . 14)][4-2-1-0 (DELT . 26)][4-3-1-0 (DELT . 50)][4-3-2-0 (DELT . 98)][4-3-2-1 (DELT . 98)]>>>>\n",
-       "<-1 * <TnPr 0 (DELT . 2) 5 <<Loop[4-3-2-1-0 (DELT . 6)][3-2-1-0 (DELT . 14)][4-2-1-0 (DELT . 26)][4-3-1-0 (DELT . 50)][4-3-2-0 (DELT . 98)][4-3-2-1 (DELT . 98)\\2]>>>>\n",
-       "<-1 * <TnPr 0 (DELT . 2) 5 <<Loop[4-3-2-1-0 (DELT . 6)][3-2-1-0 (DELT . 14)][4-2-1-0 (DELT . 26)][4-3-1-0 (DELT . 82)][4-3-2 (DELT . 114)]>>>>\n",
-       "<-1 * <TnPr 0 (DELT . 2) 5 <<Loop[4-3-2-1-0 (DELT . 6)][3-2-1-0 (DELT . 14)][4-2-1-0 (DELT . 26)][4-3-1-0 (DELT . 82)][4-3-2 (DELT . 114)\\2]>>>>\n",
-       "<1 * <TnPr 0 (DELT . 2) 5 <<Loop[4-3-2-1-0 (DELT . 6)][3-2-1-0 (DELT . 14)][4-2-1-0 (DELT . 26)][4-3-2-0 (DELT . 50)][4-3-0 (DELT . 114)][4-3-2-1 (DELT . 98)]>>>>\n",
-       "<1 * <TnPr 0 (DELT . 2) 5 <<Loop[4-3-2-1-0 (DELT . 6)][3-2-1-0 (DELT . 14)][4-2-1-0 (DELT . 26)][4-3-2-0 (DELT . 50)][4-3-0 (DELT . 114)][4-3-2-1 (DELT . 98)\\2]>>>>\n",
-       "<-1 * <TnPr 0 (DELT . 2) 5 <<Loop[4-3-2-1-0 (DELT . 6)][3-2-1-0 (DELT . 14)][4-2-1-0 (DELT . 26)][4-3-2-0 (DELT . 50)][4-3-1 (DELT . 114)]>>>>\n",
-       "... ...\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 149,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? tt 4 (tnpr 0 (code '(0)) 4 (loop3 0 (code '(1 2 3 4 5 6)) 3)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 150,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "535"
-      ]
-     },
-     "execution_count": 150,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(length (cmbn-list *))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "### Lisp file concerned in this chapter\n",
-    "\n",
-    "`ls-twisted-products.lisp`."
-   ]
-  }
- ],
- "metadata": {
-  "kernelspec": {
-   "display_name": "SBCL Lisp",
-   "language": "lisp",
-   "name": "lisp"
-  },
-  "language_info": {
-   "codemirror_mode": "text/x-common-lisp",
-   "mimetype": "text/x-common-lisp",
-   "name": "common-lisp",
-   "pygments_lexer": "common-lisp",
-   "version": "X3J13"
-  }
- },
- "nbformat": 4,
- "nbformat_minor": 1
-}
diff --git a/examples/16_Eilenberg-Moore_spectral_sequence_I.ipynb b/examples/16_Eilenberg-Moore_spectral_sequence_I.ipynb
deleted file mode 100644
index b9f954c..0000000
--- a/examples/16_Eilenberg-Moore_spectral_sequence_I.ipynb
+++ /dev/null
@@ -1,2431 +0,0 @@
-{
- "cells": [
-  {
-   "cell_type": "code",
-   "execution_count": 1,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "To load \"kenzo\":\n",
-      "  Load 1 ASDF system:\n",
-      "    kenzo\n",
-      "; Loading \"kenzo\"\n",
-      "\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "#<PACKAGE \"CAT\">"
-      ]
-     },
-     "execution_count": 1,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(ql:quickload \"kenzo\")\n",
-    "(in-package :cat)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "# Eilenberg-Moore spectral sequence I\n",
-    "\n",
-    "## Introduction\n",
-    "\n",
-    "This chapter is devoted to the effective homology version of the spectral sequence of Eilenberg-Moore, in the particular case of loop spaces. More precisely, let $X$ be a **1-reduced** simplicial set with effective homology, the program `Kenzo` constructs a 0-reduced simplicial set $GX$ which is also with effective homology. In particular, if $X$ is $m$-reduced, this process may be iterated $m$ times, producing an effective homology version of $G^kX,\\,k\\leq m$. So, the program builds an object which contains a complete solution of the Adams problem about the iteration of the\n",
-    "cobar construction. The user is advised to consult the paper *Stable homotopy and iterated loop spaces, pp. 545* by **Gunnar Carlsson** and **R.James Milgram** in *Handbook of Algebraic Topology, pp 545* edited by *I.M.James, North-Holland, 1995*. The lovely underlying algorithm is due to Julio Rubio, see *A program computing the homology groups of loop spaces*, SIGSAM Bulletin, 1991, vol. 25, pp. 20-24.\n",
-    "\n",
-    "## The detailed construction\n",
-    "\n",
-    "Let ${\\cal C}_*(X)$ be  a coalgebra with effective homology. This means that  a homotopy equivalence:\n",
-    "$$\n",
-    "\\begin{aligned}\n",
-    "  & \\qquad\\hat{C}_* & \\cr\n",
-    " \\swarrow\\nearrow & & \\searrow\\nwarrow \\quad\\cr\n",
-    "{\\cal C}_*(X)  & & EC_* \\cr\n",
-    "\\end{aligned}\n",
-    "$$\n",
-    "is provided, where  the chain complex $EC_*$ is effective and must be considered as describing the homology of ${\\cal C}_*(X)$. This scheme includes the case where ${\\cal C}_*(X)$ is itself effective; in this case, without any other information, the program  constructs automatically a trivial homotopy equivalence.\n",
-    "\n",
-    "Now, if we apply the  *Cobar* functor to this homotopy equivalence we obtain the homotopy equivalence $H_R$:\n",
-    "$$\n",
-    "\\begin{aligned}\n",
-    "  &\\qquad{\\widetilde{Cobar}}^{{\\hat C}_*}(\\mathbb{Z},\\mathbb{Z}) & \\cr\n",
-    " \\swarrow\\nearrow & & \\searrow\\nwarrow \\qquad\\cr\n",
-    "Cobar^{{\\cal C}_*(X)}(\\mathbb{Z}, \\mathbb{Z})  & & {\\widetilde{Cobar}}^{EC_*}(\\mathbb{Z}, \\mathbb{Z}) \\cr\n",
-    "\\end{aligned}\n",
-    "$$\n",
-    "in which the $\\widetilde{Cobar}$'s are cobars construction with respect to the $A_\\infty$-coalgebras structure on ${\\hat C}_*$ and $EC_*$ defined by the initial homotopy equivalence.\n",
-    "\n",
-    "Secondly, Julio Rubio (**J.J. Rubio-Garcia**. *Homologie effective des espaces de lacets iteres: un logiciel*, These, Institut Fourier, 1991.} has shown that it is possible to construct another homotopy equivalence, $H_L$:\n",
-    "$$\n",
-    "\\begin{aligned}\n",
-    "  & \\qquad Cobar^{{\\cal C}_*(X)}(\\mathbb{Z}, {\\cal C}_*(X)\\otimes_t {\\cal C_*}(GX)) \\cr\n",
-    " \\swarrow\\nearrow & & \\searrow\\nwarrow\\qquad \\cr\n",
-    " {\\cal C_*}(GX)  & & Cobar^{{\\cal C}_*(X)}(\\mathbb{Z}, \\mathbb{Z}) \\cr\n",
-    "\\end{aligned}\n",
-    "$$\n",
-    "Both reductions of $H_L$ are obtained by the basic perturbation lemma, as explained in the following section. The composition of both homotopy equivalences, $H_L$ and $H_R$, makes the link between $GX$, i.e. the loop space of $X$ and the effective right bottom chain complex of $H_R$.\n",
-    "\n",
-    "### Obtaining the left reduction $H_L$\n",
-    "\n",
-    "The homotopy equivalence  $H_L$ is obtained by a sequence of intermediate constructions based mainly upon two applications of the basic perturbation lemma. We are led to consider the two following comodules:\n",
-    "\n",
-    "* ${\\cal C}_*(X)$ comodule on itself, with the canonical coproduct.\n",
-    "$${\\cal C}_*(X)\\stackrel {\\Delta}{\\longrightarrow} {\\cal C}_*(X)\\otimes {\\cal C}_*(X).$$\n",
-    "* ${\\check{\\cal C}}_*(X)$, comodule on ${\\cal C}_*(X)$, with a \"trivial\" coproduct \n",
-    "$${\\check{\\cal C}}_*(X) \\stackrel {\\check{\\Delta}}{\\longrightarrow}  {\\cal C}_*(X)\\otimes{\\check{\\cal C}}_*(X),\\quad\n",
-    "\\sigma \\rightarrow 1\\otimes\\sigma,\\,\\sigma \\in {\\check{\\cal C}}_*(X).$$\n",
-    "\n",
-    "Now, we consider the set of the followings cobars (where $u$ means *\"untwisted\"* and $t$ *\"twisted\"*):\n",
-    "$$\n",
-    "\\begin{aligned}\n",
-    "{\\rm Hat}_{uu} &=& Cobar^{{\\cal C}_*(X)}(\\mathbb{Z}, {\\check{\\cal C}}_*(X)\\otimes {\\cal C_*}(GX)),\\\\\n",
-    "{\\rm Hat}_{ut} &=& Cobar^{{\\cal C}_*(X)}(\\mathbb{Z}, {\\check{\\cal C}}_*(X)\\otimes_t {\\cal C_*}(GX)),\\\\\n",
-    "{\\rm Hat}_{tu} &=& Cobar^{{\\cal C}_*(X)}(\\mathbb{Z}, {\\cal C}_*(X)\\otimes {\\cal C_*}(GX)),\\\\\n",
-    "{\\rm Hat}_{tt} &=& Cobar^{{\\cal C}_*(X)}(\\mathbb{Z}, {\\cal C}_*(X)\\otimes_t {\\cal C_*}(GX)).\n",
-    "\\end{aligned}\n",
-    "$$\n",
-    "\n",
-    "One may always say that ${\\rm Hat}_{ut}$ is obtained from ${\\rm Hat}_{uu}$ by a perturbation $\\delta_r$ ($r$: right) induced by the twisted tensor product $\\otimes_t$ and that ${\\rm Hat}_{tu}$ is obtained from ${\\rm Hat}_{uu}$ by a perturbation $\\delta_l$ ($l$: left) induced by the discrepancy between the coproducts in ${\\check{\\cal C}}_*(X)$ and ${\\cal C}_*(X)$. After that, ${\\rm Hat}_{tt}$ is obtained from ${\\rm Hat}_{tu}$ by the perturbation $\\delta_r$ as well as, by commutativity, from ${\\rm Hat}_{ut}$ by the perturbation $\\delta_l$.\n",
-    "\n",
-    "This is shown in the following diagram (here, the arrows are not reductions, but denote the  perturbations between  the differential morphisms):\n",
-    "$$\n",
-    "\\begin{aligned} \n",
-    "  & \\qquad{\\rm Hat}_{uu} & \\cr\n",
-    " \\delta_l \\swarrow  & & \\searrow \\delta_r \\cr\n",
-    "{\\rm Hat}_{tu}  & &  {\\rm Hat}_{ut} \\cr\n",
-    " \\delta_r \\searrow  & & \\swarrow \\delta_l \\cr\n",
-    "  & \\qquad{\\rm Hat}_{tt} & \\cr\n",
-    "\\end{aligned}\n",
-    "$$\n",
-    "The underlying graded modules  ${\\rm Hat}_{uu}$, ${\\rm Hat}_{ut}$, ${\\rm Hat}_{tu}$ and ${\\rm Hat}_{tt}$ are the same and the program keeps ${\\rm Hat}_{uu}$ as the underlying graded module for all the chain complexes. The  differential perturbations are given by the formulas:\n",
-    "$$\n",
-    "\\begin{aligned}\n",
-    "\\delta_r({\\bar{c}}_1 \\otimes \\cdots \\otimes {\\bar{c}}_n \\otimes c \\otimes g) &=& \n",
-    " [{\\bar{c}}_1 \\otimes \\cdots \\otimes {\\bar{c}}_n] \\otimes [d_{\\otimes t}(c \\otimes g)-d_\\otimes (c \\otimes g)], \\\\\n",
-    "\\delta_l({\\bar{c}}_1 \\otimes \\cdots \\otimes {\\bar{c}}_n \\otimes c \\otimes g) &=&\n",
-    "{\\bar{c}}_1 \\otimes \\cdots \\otimes {\\bar{c}}_n \\otimes {\\bar{\\Delta}}c \\otimes g, \n",
-    "\\end{aligned}\n",
-    "$$\n",
-    "where ${\\bar{c}}_i, c \\in {\\cal C}_*(X),\\, g \\in {\\cal C_*}(GX))$ and $\\bar{\\Delta}= \\Delta - \\check{\\Delta}$.\n",
-    "\n",
-    "Now, on one hand, we know that there exists a reduction  \n",
-    "$${\\rm Hat}_{tu}=Cobar^{{\\cal C}_*(X)}(\\mathbb{Z}, {\\cal C}_*(X)\\otimes {\\cal C_*}(GX)) \\Longrightarrow {\\cal C}_*(GX),$$ \n",
-    "so,  perturbing this reduction by $\\delta_r$, one obtains the Rubio reduction \n",
-    "$${\\rm Hat}_{tt}=Cobar^{{\\cal C}_*(X)}(\\mathbb{Z}, {\\cal C}_*(X)\\otimes_t {\\cal C_*}(GX)) \\Longrightarrow{\\cal C}_*(GX).$$\n",
-    "On the other hand, we know also that there exists a reduction \n",
-    "$${\\rm Hat}_{ut}=Cobar^{{\\cal C}_*(X)}(\\mathbb{Z}, {\\check{\\cal C}}_*(X)\\otimes_t {\\cal C_*}(GX)) \\Longrightarrow\n",
-    "Cobar^{{\\cal C}_*(X)}(\\mathbb{Z}, \\mathbb{Z}),$$ \n",
-    "so, perturbing this reduction by $\\delta_l$, one obtains the reduction \n",
-    "$${\\rm Hat}_{tt}=Cobar^{{\\cal C}_*(X)}(\\mathbb{Z}, {\\cal C}_*(X)\\otimes_t {\\cal C_*}(GX)) \\Longrightarrow \n",
-    "Cobar^{{\\cal C}_*(X)}(\\mathbb{Z}, \\mathbb{Z}).$$\n",
-    "Finally, we have obtained the wished left homotopy equivalence $H_L$:\n",
-    "$$\n",
-    "\\begin{aligned}\n",
-    "  & \\qquad Cobar^{{\\cal C}_*(X)}(\\mathbb{Z}, {\\cal C}_*(X)\\otimes_t {\\cal C_*}(GX)) & \\cr\n",
-    "    \\swarrow\\nearrow & & \\searrow\\nwarrow\\qquad\\qquad \\cr\n",
-    " {\\cal C_*}(GX)  & & Cobar^{{\\cal C}_*(X)}(\\mathbb{Z}, \\mathbb{Z}) \\cr\n",
-    "\\end{aligned}\n",
-    "$$\n",
-    "\n",
-    "### The useful functions\n",
-    "\n",
-    "For the applications, the only function that the user must know is the function `loop-space-efhm` which builds the final homotopy equivalence. But for the interested user, we give nevertheless a short description of all the functions involved in the described process.\n",
-    "\n",
-    "`loop-space-efhm` *space* *[Function]*\n",
-    "> From the space $X$ (1-reduced) with effective homology (here the argument *space*), build a homotopy equivalence giving an effective homology version  of the space $GX$. This homotopy equivalence will be used by the homology function to compute the homology groups. In fact, due to the slot-unbound mechanism of CLOS, this function will be automatically called, as soon as the user requires a homology group of a loop-space. If $X$ is $n$-reduced and if the wished loop space is $\\Omega^k X, \\, k \\leq n$, then the process will be automatically  iterated.\n",
-    "\n",
-    "`ls-hat-u-u` *space* *[Function]*\n",
-    "> Return the chain complex $Cobar^{{\\cal C}_*(X)}(\\mathbb{Z}, {\\check{\\cal C}}_*(X)\\otimes {\\cal C_*}(GX))$. Because of the particular structure of ${\\check{\\cal C}}_*(X)$, this chain complex is nothing but $Cobar^{{\\cal C}_*(X)}(\\mathbb{Z},\\mathbb{Z})\\otimes {\\check{\\cal C}}_*(X)\\otimes {\\cal C_*}(GX).$\n",
-    "\n",
-    "`ls-hat-left-perturbation` *space* *[Function]*\n",
-    "> Return the morphism corresponding to the differential perturbation $\\delta_l$, induced by the discrepancy between the coproducts of  ${\\check{\\cal C}}_*(X)$ and ${\\cal C}_*(X)$.\n",
-    "\n",
-    "`ls-hat-t-u` *space* *[Function]*\n",
-    "> Return the chain complex $Cobar^{{\\cal C}_*(X)}(\\mathbb{Z}, {\\cal C}_*(X)\\otimes {\\cal C_*}(GX))$ by applying the differential perturbation `hat-left-perturbation` upon the chain complex built by the function `hat-u-u`. This is realized by the method `add`.\n",
-    "\n",
-    "`ls-hat-u-t` *space* *[Function]*\n",
-    "> Return the chain complex $Cobar^{{\\cal C}_*(X)}(\\mathbb{Z},{\\check{\\cal C}}_*(X)\\otimes_t {\\cal C_*}(GX))$. Because of the particular structure of ${\\check{\\cal C}}_*(X)$, this chain complex is nothing but $Cobar^{{\\cal C}_*(X)}(\\mathbb{Z},\\mathbb{Z})\\otimes[{\\check{\\cal C}}_*(X)\\otimes_t {\\cal C_*}(GX)],$ where the twisted tensor product is obtained by a call to `twisted-tnsr-prdc` (see loop space fibrations chapter).\n",
-    "\n",
-    "`ls-hat-right-perturbation` *space* *[Function]*\n",
-    "> Return the morphism corresponding to the differential perturbation $\\delta_r$ induced by the twisted tensor product. This morphism is nothing but the tensor product of two morphisms: the identity morphism on $Cobar^{{\\cal C}_*(X)}(\\mathbb{Z},\\mathbb{Z})$ and the perturbation morphism induced by the twisted tensor product. This last morphism is a by-product of the function `szczarba`.\n",
-    "\n",
-    "`ls-left-hmeq-hat` *space*  *[Function]*\n",
-    "Return the chain complex ${\\rm Hat}_{tt}=Cobar^{{\\cal C}_*(X)}(\\mathbb{Z}, {\\cal C}_*(X)\\otimes_t {\\cal C_*}(GX))$ by  perturbing the chain complex ${\\rm Hat}_{ut}$ by the perturbation $\\delta_l$.\n",
-    "\n",
-    "`ls-pre-left-hmeq-left-reduction` *space* *[Function]*\n",
-    "Build the reduction\n",
-    "$${\\rm Hat}_{tu}=Cobar^{{\\cal C}_*(X)}(\\mathbb{Z}, {\\cal C}_*(X)\\otimes {\\cal C_*}(GX)) \\Longrightarrow {\\cal C}_*(GX).$$ \n",
-    "\n",
-    "`ls-pre-left-hmeq-right-reduction` *space* *[Function]*\n",
-    "Build the reduction\n",
-    "$${\\rm Hat}_{ut}=Cobar^{{\\cal C}_*(X)}(\\mathbb{Z},{\\check{\\cal C}}_*(X)\\otimes_t {\\cal C_*}(GX)) \\Longrightarrow\n",
-    "Cobar^{{\\cal C}_*(X)}(\\mathbb{Z}, \\mathbb{Z}).$$\n",
-    "\n",
-    "`ls-left-hmeq-left-reduction` *space* *[Function]*\n",
-    "Build the Rubio reduction \n",
-    "$$Cobar^{{\\cal C}_*(X)}(\\mathbb{Z}, {\\cal C}_*(X)\\otimes_t {\\cal C_*}(GX)) \\Longrightarrow{\\cal C}_*(GX)$$\n",
-    "by perturbing by the perturbation $\\delta_r$ the reduction\n",
-    "$${\\rm Hat}_{tu} \\Longrightarrow {\\cal C}_*(GX)$$ \n",
-    "obtained by the function `pre-left-hmeq-left-reduction`.\n",
-    "\n",
-    "`ls-left-hmeq-right-reduction` *space* *[Function]*\n",
-    "Build the reduction \n",
-    "$$Cobar^{{\\cal C}_*(X)}(\\mathbb{Z}, {\\cal C}_*(X)\\otimes_t {\\cal C_*}(GX)) \\Longrightarrow \n",
-    "Cobar^{{\\cal C}_*(X)}(\\mathbb{Z}, \\mathbb{Z})$$\n",
-    "by perturbing by the perturbation $\\delta_l$ the reduction \n",
-    "$${\\rm Hat}_{ut} \\Longrightarrow Cobar^{{\\cal C}_*(X)}(\\mathbb{Z}, \\mathbb{Z})$$\n",
-    "obtained by the function `pre-left-hmeq-right-reduction`.\n",
-    "\n",
-    "`ls-left-hmeq` *space* *[Function]*\n",
-    "Build the homotopy equivalence\n",
-    "$$\n",
-    "\\begin{aligned}\n",
-    "  & \\qquad Cobar^{{\\cal C}_*(X)}(\\mathbb{Z}, {\\cal C}_*(X)\\otimes_t {\\cal C_*}(GX)) & \\cr\n",
-    "    \\swarrow\\nearrow & & \\searrow\\nwarrow \\qquad\\qquad\\cr\n",
-    " {\\cal C_*}(GX)  & & Cobar^{{\\cal C}_*(X)}(\\mathbb{Z}, \\mathbb{Z}) \\cr\n",
-    "\\end{aligned}\n",
-    "$$\n",
-    "from the above reductions. The function `loop-space-efhm` composes this left homotopy equivalence $H_L$ with a homotopy equivalence $H_R$ which is the cobar of a pre-existing homotopy equivalence (possibly the trivial one) between the coalgebra $X$ and an effective version of it, as described at the beginning of this chapter. The Lisp definition is given in the next subsection.\n",
-    "\n",
-    "### Searching homology for loop spaces\n",
-    "\n",
-    "The origin list of a loop space object has the form `(LOOP-SPACE` *space*`)`. The `search-efhm` method applied to a loop space object consists essentially in a call to the function `loop-space-efhm` described in this chapter.\n",
-    "```commonlisp\n",
-    "(defmethod SEARCH-EFHM (loop-space (orgn (eql 'loop-space)))\n",
-    "  (declare (type simplicial-set loop-space))\n",
-    "  (loop-space-efhm (second (orgn loop-space))))\n",
-    "```\n",
-    "The lisp definition of the function `loop-space-efhm` shows clearly the possible recursivity of the process if *space* is itself a loop space.\n",
-    "```commonlisp\n",
-    "(defun LOOP-SPACE-EFHM (space)\n",
-    "  (declare (type simplicial-set space))\n",
-    "  (let ((left-hmeq (ls-left-hmeq space))\n",
-    "        (right-hmeq (cobar (efhm space))))\n",
-    "    (declare (type homotopy-equivalence left-hmeq right-hmeq))\n",
-    "    (cmps left-hmeq right-hmeq)))\n",
-    "```\n",
-    "\n",
-    "### Examples\n",
-    "\n",
-    "Let us show first how to get the homology groups of some known loop spaces, $\\Omega {\\cal S}^2$, $\\Omega^3 {\\cal S}^4$, $\\Omega^2{\\rm Moore}(\\mathbb{Z}/{2\\mathbb{Z}},3)$."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 2,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K1 Simplicial-Set]"
-      ]
-     },
-     "execution_count": 2,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def s2 (sphere 2))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 3,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K6 Simplicial-Group]"
-      ]
-     },
-     "execution_count": 3,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def os2 (loop-space s2))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 4,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "Computing boundary-matrix in dimension 0.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 54s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 0) :\n",
-      "<<AlLp>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 1.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 54s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 1) :\n",
-      "<<AlLp[1 S2]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 0 :\n",
-      "\n",
-      "\n",
-      "Component Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 54s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 1.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 54s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 1) :\n",
-      "<<AlLp[1 S2]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 2.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 54s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 2) :\n",
-      "<<AlLp[1 S2][1 S2]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 1 :\n",
-      "\n",
-      "\n",
-      "Component Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 54s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 2.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 54s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 2) :\n",
-      "<<AlLp[1 S2][1 S2]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 3.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 54s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 3) :\n",
-      "<<AlLp[1 S2][1 S2][1 S2]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 2 :\n",
-      "\n",
-      "\n",
-      "Component Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 54s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 3.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 54s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 3) :\n",
-      "<<AlLp[1 S2][1 S2][1 S2]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 4.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 54s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 4) :\n",
-      "<<AlLp[1 S2][1 S2][1 S2][1 S2]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 3 :\n",
-      "\n",
-      "\n",
-      "Component Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 54s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 4.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 54s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 4) :\n",
-      "<<AlLp[1 S2][1 S2][1 S2][1 S2]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 5.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 54s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 5) :\n",
-      "<<AlLp[1 S2][1 S2][1 S2][1 S2][1 S2]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 4 :\n",
-      "\n",
-      "\n",
-      "Component Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 54s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 5.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 54s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 5) :\n",
-      "<<AlLp[1 S2][1 S2][1 S2][1 S2][1 S2]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 6.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 54s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 6) :\n",
-      "<<AlLp[1 S2][1 S2][1 S2][1 S2][1 S2][1 S2]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 5 :\n",
-      "\n",
-      "\n",
-      "Component Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 54s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 6.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 54s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 6) :\n",
-      "<<AlLp[1 S2][1 S2][1 S2][1 S2][1 S2][1 S2]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 7.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 54s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 7) :\n",
-      "<<AlLp[1 S2][1 S2][1 S2][1 S2][1 S2][1 S2][1 S2]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 6 :\n",
-      "\n",
-      "\n",
-      "Component Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 54s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 7.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 54s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 7) :\n",
-      "<<AlLp[1 S2][1 S2][1 S2][1 S2][1 S2][1 S2][1 S2]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 8.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 54s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 8) :\n",
-      "<<AlLp[1 S2][1 S2][1 S2][1 S2][1 S2][1 S2][1 S2][1 S2]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 7 :\n",
-      "\n",
-      "\n",
-      "Component Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 54s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 8.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 54s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 8) :\n",
-      "<<AlLp[1 S2][1 S2][1 S2][1 S2][1 S2][1 S2][1 S2][1 S2]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 9.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 54s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 9) :\n",
-      "<<AlLp[1 S2][1 S2][1 S2][1 S2][1 S2][1 S2][1 S2][1 S2][1 S2]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 8 :\n",
-      "\n",
-      "\n",
-      "Component Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 54s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 9.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 54s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 9) :\n",
-      "<<AlLp[1 S2][1 S2][1 S2][1 S2][1 S2][1 S2][1 S2][1 S2][1 S2]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 10.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 54s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 10) :\n",
-      "<<AlLp[1 S2][1 S2][1 S2][1 S2][1 S2][1 S2][1 S2][1 S2][1 S2][1 S2]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 9 :\n",
-      "\n",
-      "\n",
-      "Component Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 54s.\n",
-      "\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 4,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(dotimes (k 10) (homology os2 k))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 5,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "---done---"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 5,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(cat-init)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 6,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K1 Simplicial-Set]"
-      ]
-     },
-     "execution_count": 6,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def s4 (sphere 4)) "
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 7,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K30 Simplicial-Group]"
-      ]
-     },
-     "execution_count": 7,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def ooos4 (loop-space s4 3))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 8,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "Computing boundary-matrix in dimension 0.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 54s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 0) :\n",
-      "<<AlLp>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 1.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 54s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 1) :\n",
-      "<<AlLp[1 <<AlLp[2 <<AlLp[3 S4]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 0 :\n",
-      "\n",
-      "\n",
-      "Component Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 54s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 1.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 54s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 1) :\n",
-      "<<AlLp[1 <<AlLp[2 <<AlLp[3 S4]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 2.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 54s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 2) :\n",
-      "<<AlLp[1 <<AlLp[2 <<AlLp[3 S4]>>]>>][1 <<AlLp[2 <<AlLp[3 S4]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 1 :\n",
-      "\n",
-      "\n",
-      "Component Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 54s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 2.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 54s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 2) :\n",
-      "<<AlLp[1 <<AlLp[2 <<AlLp[3 S4]>>]>>][1 <<AlLp[2 <<AlLp[3 S4]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 3.\n",
-      "Rank of the source-module : 2.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 54s.\n",
-      "Computing the boundary of the generator 1/2 (dimension 3) :\n",
-      "<<AlLp[3 <<AlLp[2 <<AlLp[3 S4]>>][2 <<AlLp[3 S4]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 54s.\n",
-      "Computing the boundary of the generator 2/2 (dimension 3) :\n",
-      "<<AlLp[1 <<AlLp[2 <<AlLp[3 S4]>>]>>][1 <<AlLp[2 <<AlLp[3 S4]>>]>>][1 <<AlLp[2 <<AlLp[3 S4]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 2 :\n",
-      "\n",
-      "\n",
-      "Component Z/2Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 54s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 3.\n",
-      "Rank of the source-module : 2.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 54s.\n",
-      "Computing the boundary of the generator 1/2 (dimension 3) :\n",
-      "<<AlLp[3 <<AlLp[2 <<AlLp[3 S4]>>][2 <<AlLp[3 S4]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 54s.\n",
-      "Computing the boundary of the generator 2/2 (dimension 3) :\n",
-      "<<AlLp[1 <<AlLp[2 <<AlLp[3 S4]>>]>>][1 <<AlLp[2 <<AlLp[3 S4]>>]>>][1 <<AlLp[2 <<AlLp[3 S4]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 4.\n",
-      "Rank of the source-module : 4.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 54s.\n",
-      "Computing the boundary of the generator 1/4 (dimension 4) :\n",
-      "<<AlLp[4 <<AlLp[5 <<AlLp[3 S4][3 S4]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 54s.\n",
-      "Computing the boundary of the generator 2/4 (dimension 4) :\n",
-      "<<AlLp[1 <<AlLp[2 <<AlLp[3 S4]>>]>>][3 <<AlLp[2 <<AlLp[3 S4]>>][2 <<AlLp[3 S4]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 54s.\n",
-      "Computing the boundary of the generator 3/4 (dimension 4) :\n",
-      "<<AlLp[3 <<AlLp[2 <<AlLp[3 S4]>>][2 <<AlLp[3 S4]>>]>>][1 <<AlLp[2 <<AlLp[3 S4]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 54s.\n",
-      "Computing the boundary of the generator 4/4 (dimension 4) :\n",
-      "<<AlLp[1 <<AlLp[2 <<AlLp[3 S4]>>]>>][1 <<AlLp[2 <<AlLp[3 S4]>>]>>][1 <<AlLp[2 <<AlLp[3 S4]>>]>>][1 <<AlLp[2 <<AlLp[3 S4]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 3 :\n",
-      "\n",
-      "\n",
-      "Component Z/2Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 54s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 4.\n",
-      "Rank of the source-module : 4.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 54s.\n",
-      "Computing the boundary of the generator 1/4 (dimension 4) :\n",
-      "<<AlLp[4 <<AlLp[5 <<AlLp[3 S4][3 S4]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 54s.\n",
-      "Computing the boundary of the generator 2/4 (dimension 4) :\n",
-      "<<AlLp[1 <<AlLp[2 <<AlLp[3 S4]>>]>>][3 <<AlLp[2 <<AlLp[3 S4]>>][2 <<AlLp[3 S4]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 54s.\n",
-      "Computing the boundary of the generator 3/4 (dimension 4) :\n",
-      "<<AlLp[3 <<AlLp[2 <<AlLp[3 S4]>>][2 <<AlLp[3 S4]>>]>>][1 <<AlLp[2 <<AlLp[3 S4]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 54s.\n",
-      "Computing the boundary of the generator 4/4 (dimension 4) :\n",
-      "<<AlLp[1 <<AlLp[2 <<AlLp[3 S4]>>]>>][1 <<AlLp[2 <<AlLp[3 S4]>>]>>][1 <<AlLp[2 <<AlLp[3 S4]>>]>>][1 <<AlLp[2 <<AlLp[3 S4]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 5.\n",
-      "Rank of the source-module : 7.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 54s.\n",
-      "Computing the boundary of the generator 1/7 (dimension 5) :\n",
-      "<<AlLp[5 <<AlLp[2 <<AlLp[3 S4]>>][2 <<AlLp[3 S4]>>][2 <<AlLp[3 S4]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 54s.\n",
-      "Computing the boundary of the generator 2/7 (dimension 5) :\n",
-      "<<AlLp[1 <<AlLp[2 <<AlLp[3 S4]>>]>>][4 <<AlLp[5 <<AlLp[3 S4][3 S4]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 54s.\n",
-      "Computing the boundary of the generator 3/7 (dimension 5) :\n",
-      "<<AlLp[4 <<AlLp[5 <<AlLp[3 S4][3 S4]>>]>>][1 <<AlLp[2 <<AlLp[3 S4]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 54s.\n",
-      "Computing the boundary of the generator 4/7 (dimension 5) :\n",
-      "<<AlLp[1 <<AlLp[2 <<AlLp[3 S4]>>]>>][1 <<AlLp[2 <<AlLp[3 S4]>>]>>][3 <<AlLp[2 <<AlLp[3 S4]>>][2 <<AlLp[3 S4]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 54s.\n",
-      "Computing the boundary of the generator 5/7 (dimension 5) :\n",
-      "<<AlLp[1 <<AlLp[2 <<AlLp[3 S4]>>]>>][3 <<AlLp[2 <<AlLp[3 S4]>>][2 <<AlLp[3 S4]>>]>>][1 <<AlLp[2 <<AlLp[3 S4]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 54s.\n",
-      "Computing the boundary of the generator 6/7 (dimension 5) :\n",
-      "<<AlLp[3 <<AlLp[2 <<AlLp[3 S4]>>][2 <<AlLp[3 S4]>>]>>][1 <<AlLp[2 <<AlLp[3 S4]>>]>>][1 <<AlLp[2 <<AlLp[3 S4]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 54s.\n",
-      "Computing the boundary of the generator 7/7 (dimension 5) :\n",
-      "<<AlLp[1 <<AlLp[2 <<AlLp[3 S4]>>]>>][1 <<AlLp[2 <<AlLp[3 S4]>>]>>][1 <<AlLp[2 <<AlLp[3 S4]>>]>>][1 <<AlLp[2 <<AlLp[3 S4]>>]>>][1 <<AlLp[2 <<AlLp[3 S4]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 4 :\n",
-      "\n",
-      "\n",
-      "Component Z/3Z\n",
-      "\n",
-      "Component Z/2Z\n",
-      "\n",
-      "Component Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 54s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 5.\n",
-      "Rank of the source-module : 7.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 54s.\n",
-      "Computing the boundary of the generator 1/7 (dimension 5) :\n",
-      "<<AlLp[5 <<AlLp[2 <<AlLp[3 S4]>>][2 <<AlLp[3 S4]>>][2 <<AlLp[3 S4]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 54s.\n",
-      "Computing the boundary of the generator 2/7 (dimension 5) :\n",
-      "<<AlLp[1 <<AlLp[2 <<AlLp[3 S4]>>]>>][4 <<AlLp[5 <<AlLp[3 S4][3 S4]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 54s.\n",
-      "Computing the boundary of the generator 3/7 (dimension 5) :\n",
-      "<<AlLp[4 <<AlLp[5 <<AlLp[3 S4][3 S4]>>]>>][1 <<AlLp[2 <<AlLp[3 S4]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 54s.\n",
-      "Computing the boundary of the generator 4/7 (dimension 5) :\n",
-      "<<AlLp[1 <<AlLp[2 <<AlLp[3 S4]>>]>>][1 <<AlLp[2 <<AlLp[3 S4]>>]>>][3 <<AlLp[2 <<AlLp[3 S4]>>][2 <<AlLp[3 S4]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 54s.\n",
-      "Computing the boundary of the generator 5/7 (dimension 5) :\n",
-      "<<AlLp[1 <<AlLp[2 <<AlLp[3 S4]>>]>>][3 <<AlLp[2 <<AlLp[3 S4]>>][2 <<AlLp[3 S4]>>]>>][1 <<AlLp[2 <<AlLp[3 S4]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 54s.\n",
-      "Computing the boundary of the generator 6/7 (dimension 5) :\n",
-      "<<AlLp[3 <<AlLp[2 <<AlLp[3 S4]>>][2 <<AlLp[3 S4]>>]>>][1 <<AlLp[2 <<AlLp[3 S4]>>]>>][1 <<AlLp[2 <<AlLp[3 S4]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 54s.\n",
-      "Computing the boundary of the generator 7/7 (dimension 5) :\n",
-      "<<AlLp[1 <<AlLp[2 <<AlLp[3 S4]>>]>>][1 <<AlLp[2 <<AlLp[3 S4]>>]>>][1 <<AlLp[2 <<AlLp[3 S4]>>]>>][1 <<AlLp[2 <<AlLp[3 S4]>>]>>][1 <<AlLp[2 <<AlLp[3 S4]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 6.\n",
-      "Rank of the source-module : 13.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 54s.\n",
-      "Computing the boundary of the generator 1/13 (dimension 6) :\n",
-      "<<AlLp[6 <<AlLp[2 <<AlLp[3 S4]>>][5 <<AlLp[3 S4][3 S4]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 54s.\n",
-      "Computing the boundary of the generator 2/13 (dimension 6) :\n",
-      "<<AlLp[6 <<AlLp[5 <<AlLp[3 S4][3 S4]>>][2 <<AlLp[3 S4]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 54s.\n",
-      "Computing the boundary of the generator 3/13 (dimension 6) :\n",
-      "<<AlLp[1 <<AlLp[2 <<AlLp[3 S4]>>]>>][5 <<AlLp[2 <<AlLp[3 S4]>>][2 <<AlLp[3 S4]>>][2 <<AlLp[3 S4]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 54s.\n",
-      "Computing the boundary of the generator 4/13 (dimension 6) :\n",
-      "<<AlLp[3 <<AlLp[2 <<AlLp[3 S4]>>][2 <<AlLp[3 S4]>>]>>][3 <<AlLp[2 <<AlLp[3 S4]>>][2 <<AlLp[3 S4]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 54s.\n",
-      "Computing the boundary of the generator 5/13 (dimension 6) :\n",
-      "<<AlLp[5 <<AlLp[2 <<AlLp[3 S4]>>][2 <<AlLp[3 S4]>>][2 <<AlLp[3 S4]>>]>>][1 <<AlLp[2 <<AlLp[3 S4]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 54s.\n",
-      "Computing the boundary of the generator 6/13 (dimension 6) :\n",
-      "<<AlLp[1 <<AlLp[2 <<AlLp[3 S4]>>]>>][1 <<AlLp[2 <<AlLp[3 S4]>>]>>][4 <<AlLp[5 <<AlLp[3 S4][3 S4]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 54s.\n",
-      "Computing the boundary of the generator 7/13 (dimension 6) :\n",
-      "<<AlLp[1 <<AlLp[2 <<AlLp[3 S4]>>]>>][4 <<AlLp[5 <<AlLp[3 S4][3 S4]>>]>>][1 <<AlLp[2 <<AlLp[3 S4]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 54s.\n",
-      "Computing the boundary of the generator 8/13 (dimension 6) :\n",
-      "<<AlLp[4 <<AlLp[5 <<AlLp[3 S4][3 S4]>>]>>][1 <<AlLp[2 <<AlLp[3 S4]>>]>>][1 <<AlLp[2 <<AlLp[3 S4]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 54s.\n",
-      "Computing the boundary of the generator 9/13 (dimension 6) :\n",
-      "<<AlLp[1 <<AlLp[2 <<AlLp[3 S4]>>]>>][1 <<AlLp[2 <<AlLp[3 S4]>>]>>][1 <<AlLp[2 <<AlLp[3 S4]>>]>>][3 <<AlLp[2 <<AlLp[3 S4]>>][2 <<AlLp[3 S4]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 54s.\n",
-      "Computing the boundary of the generator 10/13 (dimension 6) :\n",
-      "<<AlLp[1 <<AlLp[2 <<AlLp[3 S4]>>]>>][1 <<AlLp[2 <<AlLp[3 S4]>>]>>][3 <<AlLp[2 <<AlLp[3 S4]>>][2 <<AlLp[3 S4]>>]>>][1 <<AlLp[2 <<AlLp[3 S4]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 55s.\n",
-      "Computing the boundary of the generator 11/13 (dimension 6) :\n",
-      "<<AlLp[1 <<AlLp[2 <<AlLp[3 S4]>>]>>][3 <<AlLp[2 <<AlLp[3 S4]>>][2 <<AlLp[3 S4]>>]>>][1 <<AlLp[2 <<AlLp[3 S4]>>]>>][1 <<AlLp[2 <<AlLp[3 S4]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 55s.\n",
-      "Computing the boundary of the generator 12/13 (dimension 6) :\n",
-      "<<AlLp[3 <<AlLp[2 <<AlLp[3 S4]>>][2 <<AlLp[3 S4]>>]>>][1 <<AlLp[2 <<AlLp[3 S4]>>]>>][1 <<AlLp[2 <<AlLp[3 S4]>>]>>][1 <<AlLp[2 <<AlLp[3 S4]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 55s.\n",
-      "Computing the boundary of the generator 13/13 (dimension 6) :\n",
-      "<<AlLp[1 <<AlLp[2 <<AlLp[3 S4]>>]>>][1 <<AlLp[2 <<AlLp[3 S4]>>]>>][1 <<AlLp[2 <<AlLp[3 S4]>>]>>][1 <<AlLp[2 <<AlLp[3 S4]>>]>>][1 <<AlLp[2 <<AlLp[3 S4]>>]>>][1 <<AlLp[2 <<AlLp[3 S4]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 5 :\n",
-      "\n",
-      "\n",
-      "Component Z/3Z\n",
-      "\n",
-      "Component Z/2Z\n",
-      "\n",
-      "Component Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 55s.\n",
-      "\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 8,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(dotimes (k 6) (homology ooos4 k))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 9,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K405 Simplicial-Set]"
-      ]
-     },
-     "execution_count": 9,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def moore-23 (moore 2 3))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 10,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K422 Simplicial-Group]"
-      ]
-     },
-     "execution_count": 10,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def oo-moore-23 (loop-space moore-23 2))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 11,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "Computing boundary-matrix in dimension 0.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 55s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 0) :\n",
-      "<<AlLp>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 1.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 55s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 1) :\n",
-      "<<AlLp[1 <<AlLp[2 M3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 0 :\n",
-      "\n",
-      "\n",
-      "Component Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 55s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 1.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 55s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 1) :\n",
-      "<<AlLp[1 <<AlLp[2 M3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 2.\n",
-      "Rank of the source-module : 2.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 55s.\n",
-      "Computing the boundary of the generator 1/2 (dimension 2) :\n",
-      "<<AlLp[2 <<AlLp[3 N4]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 55s.\n",
-      "Computing the boundary of the generator 2/2 (dimension 2) :\n",
-      "<<AlLp[1 <<AlLp[2 M3]>>][1 <<AlLp[2 M3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 1 :\n",
-      "\n",
-      "\n",
-      "Component Z/2Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 55s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 2.\n",
-      "Rank of the source-module : 2.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 55s.\n",
-      "Computing the boundary of the generator 1/2 (dimension 2) :\n",
-      "<<AlLp[2 <<AlLp[3 N4]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 55s.\n",
-      "Computing the boundary of the generator 2/2 (dimension 2) :\n",
-      "<<AlLp[1 <<AlLp[2 M3]>>][1 <<AlLp[2 M3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 3.\n",
-      "Rank of the source-module : 4.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 55s.\n",
-      "Computing the boundary of the generator 1/4 (dimension 3) :\n",
-      "<<AlLp[3 <<AlLp[2 M3][2 M3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 55s.\n",
-      "Computing the boundary of the generator 2/4 (dimension 3) :\n",
-      "<<AlLp[1 <<AlLp[2 M3]>>][2 <<AlLp[3 N4]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 55s.\n",
-      "Computing the boundary of the generator 3/4 (dimension 3) :\n",
-      "<<AlLp[2 <<AlLp[3 N4]>>][1 <<AlLp[2 M3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 55s.\n",
-      "Computing the boundary of the generator 4/4 (dimension 3) :\n",
-      "<<AlLp[1 <<AlLp[2 M3]>>][1 <<AlLp[2 M3]>>][1 <<AlLp[2 M3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 2 :\n",
-      "\n",
-      "\n",
-      "Component Z/2Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 55s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 3.\n",
-      "Rank of the source-module : 4.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 55s.\n",
-      "Computing the boundary of the generator 1/4 (dimension 3) :\n",
-      "<<AlLp[3 <<AlLp[2 M3][2 M3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 55s.\n",
-      "Computing the boundary of the generator 2/4 (dimension 3) :\n",
-      "<<AlLp[1 <<AlLp[2 M3]>>][2 <<AlLp[3 N4]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 55s.\n",
-      "Computing the boundary of the generator 3/4 (dimension 3) :\n",
-      "<<AlLp[2 <<AlLp[3 N4]>>][1 <<AlLp[2 M3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 55s.\n",
-      "Computing the boundary of the generator 4/4 (dimension 3) :\n",
-      "<<AlLp[1 <<AlLp[2 M3]>>][1 <<AlLp[2 M3]>>][1 <<AlLp[2 M3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 4.\n",
-      "Rank of the source-module : 9.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 55s.\n",
-      "Computing the boundary of the generator 1/9 (dimension 4) :\n",
-      "<<AlLp[4 <<AlLp[2 M3][3 N4]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 55s.\n",
-      "Computing the boundary of the generator 2/9 (dimension 4) :\n",
-      "<<AlLp[4 <<AlLp[3 N4][2 M3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 55s.\n",
-      "Computing the boundary of the generator 3/9 (dimension 4) :\n",
-      "<<AlLp[1 <<AlLp[2 M3]>>][3 <<AlLp[2 M3][2 M3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 55s.\n",
-      "Computing the boundary of the generator 4/9 (dimension 4) :\n",
-      "<<AlLp[2 <<AlLp[3 N4]>>][2 <<AlLp[3 N4]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 55s.\n",
-      "Computing the boundary of the generator 5/9 (dimension 4) :\n",
-      "<<AlLp[3 <<AlLp[2 M3][2 M3]>>][1 <<AlLp[2 M3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 55s.\n",
-      "Computing the boundary of the generator 6/9 (dimension 4) :\n",
-      "<<AlLp[1 <<AlLp[2 M3]>>][1 <<AlLp[2 M3]>>][2 <<AlLp[3 N4]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 55s.\n",
-      "Computing the boundary of the generator 7/9 (dimension 4) :\n",
-      "<<AlLp[1 <<AlLp[2 M3]>>][2 <<AlLp[3 N4]>>][1 <<AlLp[2 M3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 55s.\n",
-      "Computing the boundary of the generator 8/9 (dimension 4) :\n",
-      "<<AlLp[2 <<AlLp[3 N4]>>][1 <<AlLp[2 M3]>>][1 <<AlLp[2 M3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 55s.\n",
-      "Computing the boundary of the generator 9/9 (dimension 4) :\n",
-      "<<AlLp[1 <<AlLp[2 M3]>>][1 <<AlLp[2 M3]>>][1 <<AlLp[2 M3]>>][1 <<AlLp[2 M3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 3 :\n",
-      "\n",
-      "\n",
-      "Component Z/4Z\n",
-      "\n",
-      "Component Z/2Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 55s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 4.\n",
-      "Rank of the source-module : 9.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 55s.\n",
-      "Computing the boundary of the generator 1/9 (dimension 4) :\n",
-      "<<AlLp[4 <<AlLp[2 M3][3 N4]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 55s.\n",
-      "Computing the boundary of the generator 2/9 (dimension 4) :\n",
-      "<<AlLp[4 <<AlLp[3 N4][2 M3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 55s.\n",
-      "Computing the boundary of the generator 3/9 (dimension 4) :\n",
-      "<<AlLp[1 <<AlLp[2 M3]>>][3 <<AlLp[2 M3][2 M3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 55s.\n",
-      "Computing the boundary of the generator 4/9 (dimension 4) :\n",
-      "<<AlLp[2 <<AlLp[3 N4]>>][2 <<AlLp[3 N4]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 55s.\n",
-      "Computing the boundary of the generator 5/9 (dimension 4) :\n",
-      "<<AlLp[3 <<AlLp[2 M3][2 M3]>>][1 <<AlLp[2 M3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 55s.\n",
-      "Computing the boundary of the generator 6/9 (dimension 4) :\n",
-      "<<AlLp[1 <<AlLp[2 M3]>>][1 <<AlLp[2 M3]>>][2 <<AlLp[3 N4]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 55s.\n",
-      "Computing the boundary of the generator 7/9 (dimension 4) :\n",
-      "<<AlLp[1 <<AlLp[2 M3]>>][2 <<AlLp[3 N4]>>][1 <<AlLp[2 M3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 55s.\n",
-      "Computing the boundary of the generator 8/9 (dimension 4) :\n",
-      "<<AlLp[2 <<AlLp[3 N4]>>][1 <<AlLp[2 M3]>>][1 <<AlLp[2 M3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 55s.\n",
-      "Computing the boundary of the generator 9/9 (dimension 4) :\n",
-      "<<AlLp[1 <<AlLp[2 M3]>>][1 <<AlLp[2 M3]>>][1 <<AlLp[2 M3]>>][1 <<AlLp[2 M3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 5.\n",
-      "Rank of the source-module : 19.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 55s.\n",
-      "Computing the boundary of the generator 1/19 (dimension 5) :\n",
-      "<<AlLp[5 <<AlLp[3 N4][3 N4]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 55s.\n",
-      "Computing the boundary of the generator 2/19 (dimension 5) :\n",
-      "<<AlLp[5 <<AlLp[2 M3][2 M3][2 M3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 55s.\n",
-      "Computing the boundary of the generator 3/19 (dimension 5) :\n",
-      "<<AlLp[1 <<AlLp[2 M3]>>][4 <<AlLp[2 M3][3 N4]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 55s.\n",
-      "Computing the boundary of the generator 4/19 (dimension 5) :\n",
-      "<<AlLp[1 <<AlLp[2 M3]>>][4 <<AlLp[3 N4][2 M3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 55s.\n",
-      "Computing the boundary of the generator 5/19 (dimension 5) :\n",
-      "<<AlLp[2 <<AlLp[3 N4]>>][3 <<AlLp[2 M3][2 M3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 55s.\n",
-      "Computing the boundary of the generator 6/19 (dimension 5) :\n",
-      "<<AlLp[3 <<AlLp[2 M3][2 M3]>>][2 <<AlLp[3 N4]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 55s.\n",
-      "Computing the boundary of the generator 7/19 (dimension 5) :\n",
-      "<<AlLp[4 <<AlLp[2 M3][3 N4]>>][1 <<AlLp[2 M3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 55s.\n",
-      "Computing the boundary of the generator 8/19 (dimension 5) :\n",
-      "<<AlLp[4 <<AlLp[3 N4][2 M3]>>][1 <<AlLp[2 M3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 55s.\n",
-      "Computing the boundary of the generator 9/19 (dimension 5) :\n",
-      "<<AlLp[1 <<AlLp[2 M3]>>][1 <<AlLp[2 M3]>>][3 <<AlLp[2 M3][2 M3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 55s.\n",
-      "Computing the boundary of the generator 10/19 (dimension 5) :\n",
-      "<<AlLp[1 <<AlLp[2 M3]>>][2 <<AlLp[3 N4]>>][2 <<AlLp[3 N4]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 55s.\n",
-      "Computing the boundary of the generator 11/19 (dimension 5) :\n",
-      "<<AlLp[1 <<AlLp[2 M3]>>][3 <<AlLp[2 M3][2 M3]>>][1 <<AlLp[2 M3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 55s.\n",
-      "Computing the boundary of the generator 12/19 (dimension 5) :\n",
-      "<<AlLp[2 <<AlLp[3 N4]>>][1 <<AlLp[2 M3]>>][2 <<AlLp[3 N4]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 55s.\n",
-      "Computing the boundary of the generator 13/19 (dimension 5) :\n",
-      "<<AlLp[2 <<AlLp[3 N4]>>][2 <<AlLp[3 N4]>>][1 <<AlLp[2 M3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 55s.\n",
-      "Computing the boundary of the generator 14/19 (dimension 5) :\n",
-      "<<AlLp[3 <<AlLp[2 M3][2 M3]>>][1 <<AlLp[2 M3]>>][1 <<AlLp[2 M3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 55s.\n",
-      "Computing the boundary of the generator 15/19 (dimension 5) :\n",
-      "<<AlLp[1 <<AlLp[2 M3]>>][1 <<AlLp[2 M3]>>][1 <<AlLp[2 M3]>>][2 <<AlLp[3 N4]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 55s.\n",
-      "Computing the boundary of the generator 16/19 (dimension 5) :\n",
-      "<<AlLp[1 <<AlLp[2 M3]>>][1 <<AlLp[2 M3]>>][2 <<AlLp[3 N4]>>][1 <<AlLp[2 M3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 55s.\n",
-      "Computing the boundary of the generator 17/19 (dimension 5) :\n",
-      "<<AlLp[1 <<AlLp[2 M3]>>][2 <<AlLp[3 N4]>>][1 <<AlLp[2 M3]>>][1 <<AlLp[2 M3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 55s.\n",
-      "Computing the boundary of the generator 18/19 (dimension 5) :\n",
-      "<<AlLp[2 <<AlLp[3 N4]>>][1 <<AlLp[2 M3]>>][1 <<AlLp[2 M3]>>][1 <<AlLp[2 M3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 55s.\n",
-      "Computing the boundary of the generator 19/19 (dimension 5) :\n",
-      "<<AlLp[1 <<AlLp[2 M3]>>][1 <<AlLp[2 M3]>>][1 <<AlLp[2 M3]>>][1 <<AlLp[2 M3]>>][1 <<AlLp[2 M3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 4 :\n",
-      "\n",
-      "\n",
-      "Component Z/2Z\n",
-      "\n",
-      "Component Z/2Z\n",
-      "\n",
-      "Component Z/2Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 55s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 5.\n",
-      "Rank of the source-module : 19.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 55s.\n",
-      "Computing the boundary of the generator 1/19 (dimension 5) :\n",
-      "<<AlLp[5 <<AlLp[3 N4][3 N4]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 55s.\n",
-      "Computing the boundary of the generator 2/19 (dimension 5) :\n",
-      "<<AlLp[5 <<AlLp[2 M3][2 M3][2 M3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 55s.\n",
-      "Computing the boundary of the generator 3/19 (dimension 5) :\n",
-      "<<AlLp[1 <<AlLp[2 M3]>>][4 <<AlLp[2 M3][3 N4]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 55s.\n",
-      "Computing the boundary of the generator 4/19 (dimension 5) :\n",
-      "<<AlLp[1 <<AlLp[2 M3]>>][4 <<AlLp[3 N4][2 M3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 55s.\n",
-      "Computing the boundary of the generator 5/19 (dimension 5) :\n",
-      "<<AlLp[2 <<AlLp[3 N4]>>][3 <<AlLp[2 M3][2 M3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 55s.\n",
-      "Computing the boundary of the generator 6/19 (dimension 5) :\n",
-      "<<AlLp[3 <<AlLp[2 M3][2 M3]>>][2 <<AlLp[3 N4]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 55s.\n",
-      "Computing the boundary of the generator 7/19 (dimension 5) :\n",
-      "<<AlLp[4 <<AlLp[2 M3][3 N4]>>][1 <<AlLp[2 M3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 55s.\n",
-      "Computing the boundary of the generator 8/19 (dimension 5) :\n",
-      "<<AlLp[4 <<AlLp[3 N4][2 M3]>>][1 <<AlLp[2 M3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 55s.\n",
-      "Computing the boundary of the generator 9/19 (dimension 5) :\n",
-      "<<AlLp[1 <<AlLp[2 M3]>>][1 <<AlLp[2 M3]>>][3 <<AlLp[2 M3][2 M3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 55s.\n",
-      "Computing the boundary of the generator 10/19 (dimension 5) :\n",
-      "<<AlLp[1 <<AlLp[2 M3]>>][2 <<AlLp[3 N4]>>][2 <<AlLp[3 N4]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 55s.\n",
-      "Computing the boundary of the generator 11/19 (dimension 5) :\n",
-      "<<AlLp[1 <<AlLp[2 M3]>>][3 <<AlLp[2 M3][2 M3]>>][1 <<AlLp[2 M3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 55s.\n",
-      "Computing the boundary of the generator 12/19 (dimension 5) :\n",
-      "<<AlLp[2 <<AlLp[3 N4]>>][1 <<AlLp[2 M3]>>][2 <<AlLp[3 N4]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 55s.\n",
-      "Computing the boundary of the generator 13/19 (dimension 5) :\n",
-      "<<AlLp[2 <<AlLp[3 N4]>>][2 <<AlLp[3 N4]>>][1 <<AlLp[2 M3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 55s.\n",
-      "Computing the boundary of the generator 14/19 (dimension 5) :\n",
-      "<<AlLp[3 <<AlLp[2 M3][2 M3]>>][1 <<AlLp[2 M3]>>][1 <<AlLp[2 M3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 55s.\n",
-      "Computing the boundary of the generator 15/19 (dimension 5) :\n",
-      "<<AlLp[1 <<AlLp[2 M3]>>][1 <<AlLp[2 M3]>>][1 <<AlLp[2 M3]>>][2 <<AlLp[3 N4]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 55s.\n",
-      "Computing the boundary of the generator 16/19 (dimension 5) :\n",
-      "<<AlLp[1 <<AlLp[2 M3]>>][1 <<AlLp[2 M3]>>][2 <<AlLp[3 N4]>>][1 <<AlLp[2 M3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 55s.\n",
-      "Computing the boundary of the generator 17/19 (dimension 5) :\n",
-      "<<AlLp[1 <<AlLp[2 M3]>>][2 <<AlLp[3 N4]>>][1 <<AlLp[2 M3]>>][1 <<AlLp[2 M3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 55s.\n",
-      "Computing the boundary of the generator 18/19 (dimension 5) :\n",
-      "<<AlLp[2 <<AlLp[3 N4]>>][1 <<AlLp[2 M3]>>][1 <<AlLp[2 M3]>>][1 <<AlLp[2 M3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 55s.\n",
-      "Computing the boundary of the generator 19/19 (dimension 5) :\n",
-      "<<AlLp[1 <<AlLp[2 M3]>>][1 <<AlLp[2 M3]>>][1 <<AlLp[2 M3]>>][1 <<AlLp[2 M3]>>][1 <<AlLp[2 M3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 6.\n",
-      "Rank of the source-module : 41.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 55s.\n",
-      "Computing the boundary of the generator 1/41 (dimension 6) :\n",
-      "<<AlLp[6 <<AlLp[2 M3][2 M3][3 N4]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 55s.\n",
-      "Computing the boundary of the generator 2/41 (dimension 6) :\n",
-      "<<AlLp[6 <<AlLp[2 M3][3 N4][2 M3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 55s.\n",
-      "Computing the boundary of the generator 3/41 (dimension 6) :\n",
-      "<<AlLp[6 <<AlLp[3 N4][2 M3][2 M3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 55s.\n",
-      "Computing the boundary of the generator 4/41 (dimension 6) :\n",
-      "<<AlLp[1 <<AlLp[2 M3]>>][5 <<AlLp[3 N4][3 N4]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 55s.\n",
-      "Computing the boundary of the generator 5/41 (dimension 6) :\n",
-      "<<AlLp[1 <<AlLp[2 M3]>>][5 <<AlLp[2 M3][2 M3][2 M3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 55s.\n",
-      "Computing the boundary of the generator 6/41 (dimension 6) :\n",
-      "<<AlLp[2 <<AlLp[3 N4]>>][4 <<AlLp[2 M3][3 N4]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 55s.\n",
-      "Computing the boundary of the generator 7/41 (dimension 6) :\n",
-      "<<AlLp[2 <<AlLp[3 N4]>>][4 <<AlLp[3 N4][2 M3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 55s.\n",
-      "Computing the boundary of the generator 8/41 (dimension 6) :\n",
-      "<<AlLp[3 <<AlLp[2 M3][2 M3]>>][3 <<AlLp[2 M3][2 M3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 55s.\n",
-      "Computing the boundary of the generator 9/41 (dimension 6) :\n",
-      "<<AlLp[4 <<AlLp[2 M3][3 N4]>>][2 <<AlLp[3 N4]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 55s.\n",
-      "Computing the boundary of the generator 10/41 (dimension 6) :\n",
-      "<<AlLp[4 <<AlLp[3 N4][2 M3]>>][2 <<AlLp[3 N4]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 55s.\n",
-      "Computing the boundary of the generator 11/41 (dimension 6) :\n",
-      "<<AlLp[5 <<AlLp[3 N4][3 N4]>>][1 <<AlLp[2 M3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 55s.\n",
-      "Computing the boundary of the generator 12/41 (dimension 6) :\n",
-      "<<AlLp[5 <<AlLp[2 M3][2 M3][2 M3]>>][1 <<AlLp[2 M3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 55s.\n",
-      "Computing the boundary of the generator 13/41 (dimension 6) :\n",
-      "<<AlLp[1 <<AlLp[2 M3]>>][1 <<AlLp[2 M3]>>][4 <<AlLp[2 M3][3 N4]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 55s.\n",
-      "Computing the boundary of the generator 14/41 (dimension 6) :\n",
-      "<<AlLp[1 <<AlLp[2 M3]>>][1 <<AlLp[2 M3]>>][4 <<AlLp[3 N4][2 M3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 55s.\n",
-      "Computing the boundary of the generator 15/41 (dimension 6) :\n",
-      "<<AlLp[1 <<AlLp[2 M3]>>][2 <<AlLp[3 N4]>>][3 <<AlLp[2 M3][2 M3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 55s.\n",
-      "Computing the boundary of the generator 16/41 (dimension 6) :\n",
-      "<<AlLp[1 <<AlLp[2 M3]>>][3 <<AlLp[2 M3][2 M3]>>][2 <<AlLp[3 N4]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 55s.\n",
-      "Computing the boundary of the generator 17/41 (dimension 6) :\n",
-      "<<AlLp[1 <<AlLp[2 M3]>>][4 <<AlLp[2 M3][3 N4]>>][1 <<AlLp[2 M3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 55s.\n",
-      "Computing the boundary of the generator 18/41 (dimension 6) :\n",
-      "<<AlLp[1 <<AlLp[2 M3]>>][4 <<AlLp[3 N4][2 M3]>>][1 <<AlLp[2 M3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 55s.\n",
-      "Computing the boundary of the generator 19/41 (dimension 6) :\n",
-      "<<AlLp[2 <<AlLp[3 N4]>>][1 <<AlLp[2 M3]>>][3 <<AlLp[2 M3][2 M3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 55s.\n",
-      "Computing the boundary of the generator 20/41 (dimension 6) :\n",
-      "<<AlLp[2 <<AlLp[3 N4]>>][2 <<AlLp[3 N4]>>][2 <<AlLp[3 N4]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 55s.\n",
-      "Computing the boundary of the generator 21/41 (dimension 6) :\n",
-      "<<AlLp[2 <<AlLp[3 N4]>>][3 <<AlLp[2 M3][2 M3]>>][1 <<AlLp[2 M3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 55s.\n",
-      "Computing the boundary of the generator 22/41 (dimension 6) :\n",
-      "<<AlLp[3 <<AlLp[2 M3][2 M3]>>][1 <<AlLp[2 M3]>>][2 <<AlLp[3 N4]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 55s.\n",
-      "Computing the boundary of the generator 23/41 (dimension 6) :\n",
-      "<<AlLp[3 <<AlLp[2 M3][2 M3]>>][2 <<AlLp[3 N4]>>][1 <<AlLp[2 M3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 55s.\n",
-      "Computing the boundary of the generator 24/41 (dimension 6) :\n",
-      "<<AlLp[4 <<AlLp[2 M3][3 N4]>>][1 <<AlLp[2 M3]>>][1 <<AlLp[2 M3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 55s.\n",
-      "Computing the boundary of the generator 25/41 (dimension 6) :\n",
-      "<<AlLp[4 <<AlLp[3 N4][2 M3]>>][1 <<AlLp[2 M3]>>][1 <<AlLp[2 M3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 55s.\n",
-      "Computing the boundary of the generator 26/41 (dimension 6) :\n",
-      "<<AlLp[1 <<AlLp[2 M3]>>][1 <<AlLp[2 M3]>>][1 <<AlLp[2 M3]>>][3 <<AlLp[2 M3][2 M3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 55s.\n",
-      "Computing the boundary of the generator 27/41 (dimension 6) :\n",
-      "<<AlLp[1 <<AlLp[2 M3]>>][1 <<AlLp[2 M3]>>][2 <<AlLp[3 N4]>>][2 <<AlLp[3 N4]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 55s.\n",
-      "Computing the boundary of the generator 28/41 (dimension 6) :\n",
-      "<<AlLp[1 <<AlLp[2 M3]>>][1 <<AlLp[2 M3]>>][3 <<AlLp[2 M3][2 M3]>>][1 <<AlLp[2 M3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 55s.\n",
-      "Computing the boundary of the generator 29/41 (dimension 6) :\n",
-      "<<AlLp[1 <<AlLp[2 M3]>>][2 <<AlLp[3 N4]>>][1 <<AlLp[2 M3]>>][2 <<AlLp[3 N4]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 55s.\n",
-      "Computing the boundary of the generator 30/41 (dimension 6) :\n",
-      "<<AlLp[1 <<AlLp[2 M3]>>][2 <<AlLp[3 N4]>>][2 <<AlLp[3 N4]>>][1 <<AlLp[2 M3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 55s.\n",
-      "Computing the boundary of the generator 31/41 (dimension 6) :\n",
-      "<<AlLp[1 <<AlLp[2 M3]>>][3 <<AlLp[2 M3][2 M3]>>][1 <<AlLp[2 M3]>>][1 <<AlLp[2 M3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 55s.\n",
-      "Computing the boundary of the generator 32/41 (dimension 6) :\n",
-      "<<AlLp[2 <<AlLp[3 N4]>>][1 <<AlLp[2 M3]>>][1 <<AlLp[2 M3]>>][2 <<AlLp[3 N4]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 55s.\n",
-      "Computing the boundary of the generator 33/41 (dimension 6) :\n",
-      "<<AlLp[2 <<AlLp[3 N4]>>][1 <<AlLp[2 M3]>>][2 <<AlLp[3 N4]>>][1 <<AlLp[2 M3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 55s.\n",
-      "Computing the boundary of the generator 34/41 (dimension 6) :\n",
-      "<<AlLp[2 <<AlLp[3 N4]>>][2 <<AlLp[3 N4]>>][1 <<AlLp[2 M3]>>][1 <<AlLp[2 M3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 55s.\n",
-      "Computing the boundary of the generator 35/41 (dimension 6) :\n",
-      "<<AlLp[3 <<AlLp[2 M3][2 M3]>>][1 <<AlLp[2 M3]>>][1 <<AlLp[2 M3]>>][1 <<AlLp[2 M3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 55s.\n",
-      "Computing the boundary of the generator 36/41 (dimension 6) :\n",
-      "<<AlLp[1 <<AlLp[2 M3]>>][1 <<AlLp[2 M3]>>][1 <<AlLp[2 M3]>>][1 <<AlLp[2 M3]>>][2 <<AlLp[3 N4]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 55s.\n",
-      "Computing the boundary of the generator 37/41 (dimension 6) :\n",
-      "<<AlLp[1 <<AlLp[2 M3]>>][1 <<AlLp[2 M3]>>][1 <<AlLp[2 M3]>>][2 <<AlLp[3 N4]>>][1 <<AlLp[2 M3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 55s.\n",
-      "Computing the boundary of the generator 38/41 (dimension 6) :\n",
-      "<<AlLp[1 <<AlLp[2 M3]>>][1 <<AlLp[2 M3]>>][2 <<AlLp[3 N4]>>][1 <<AlLp[2 M3]>>][1 <<AlLp[2 M3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 55s.\n",
-      "Computing the boundary of the generator 39/41 (dimension 6) :\n",
-      "<<AlLp[1 <<AlLp[2 M3]>>][2 <<AlLp[3 N4]>>][1 <<AlLp[2 M3]>>][1 <<AlLp[2 M3]>>][1 <<AlLp[2 M3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 55s.\n",
-      "Computing the boundary of the generator 40/41 (dimension 6) :\n",
-      "<<AlLp[2 <<AlLp[3 N4]>>][1 <<AlLp[2 M3]>>][1 <<AlLp[2 M3]>>][1 <<AlLp[2 M3]>>][1 <<AlLp[2 M3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 55s.\n",
-      "Computing the boundary of the generator 41/41 (dimension 6) :\n",
-      "<<AlLp[1 <<AlLp[2 M3]>>][1 <<AlLp[2 M3]>>][1 <<AlLp[2 M3]>>][1 <<AlLp[2 M3]>>][1 <<AlLp[2 M3]>>][1 <<AlLp[2 M3]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 5 :\n",
-      "\n",
-      "\n",
-      "Component Z/2Z\n",
-      "\n",
-      "Component Z/2Z\n",
-      "\n",
-      "Component Z/2Z\n",
-      "\n",
-      "Component Z/2Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 55s.\n",
-      "\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 11,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(dotimes (k 6) (homology oo-moore-23 k))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "## The solution of the Adams and Carlsson problem\n",
-    "\n",
-    "Let $X$ be an $n$-reduced simplicial set which is not a suspension. The Adams and Carlsson problem (**Gunnar Carlsson, R.James Milgram.** *Stable homotopy and iterated loop spaces* in *Handbook of Algebraic Topology, pp 545* edited by *I.M.James, North-Holland, 1995*.) asks for a finite CW-complex modelizing the iterated loop space $\\Omega^n X$. We show in this section how the `Kenzo` program builds the relevant solution.\n",
-    "\n",
-    "Let us consider for instance the stunted projective space $X=P^\\infty \\mathbb{R}/ P^3 \\mathbb{R}$ (a non-suspended space) and let us build $\\Omega^3 X$."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 12,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "---done---"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 12,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(cat-init)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 13,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K1 Simplicial-Set]"
-      ]
-     },
-     "execution_count": 13,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def p4 (R-proj-space :infinity 4))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 14,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K30 Simplicial-Group]"
-      ]
-     },
-     "execution_count": 14,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def o3p4 (loop-space p4 3))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 15,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K390 Chain-Complex]"
-      ]
-     },
-     "execution_count": 15,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def ecc (rbcc (efhm o3p4)))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "The cellular homology of $\\Omega^3 X$ is now known through the symbol `ecc`. Note that 360 objects ($390-30$) have been built to get the final chain complex `ecc`. From the printing of the length of the basis in dimensions 0 to 5,"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 16,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "1 \n",
-      "1 \n",
-      "2 \n",
-      "5 \n",
-      "13 \n",
-      "33 "
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 16,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(dotimes (i 6) (print (length (basis ecc i))))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "we see that the required CW-complex can be constructed using 1 0-cell, 1 1-cell, 2 2-cells, 5 3-cells, 13 4-cells and 33 5-cells. Let us print the incidence matrix between the 5 and the 4-cells:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 17,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "Computing boundary-matrix in dimension 5.\n",
-      "Rank of the source-module : 33.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 55s.\n",
-      "Computing the boundary of the generator 1/33 (dimension 5) :\n",
-      "<<AlLp[5 <<AlLp[6 <<AlLp[7 8]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 55s.\n",
-      "Computing the boundary of the generator 2/33 (dimension 5) :\n",
-      "<<AlLp[5 <<AlLp[6 <<AlLp[3 4][4 5]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 55s.\n",
-      "Computing the boundary of the generator 3/33 (dimension 5) :\n",
-      "<<AlLp[5 <<AlLp[6 <<AlLp[4 5][3 4]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 55s.\n",
-      "Computing the boundary of the generator 4/33 (dimension 5) :\n",
-      "<<AlLp[5 <<AlLp[2 <<AlLp[3 4]>>][4 <<AlLp[5 6]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 55s.\n",
-      "Computing the boundary of the generator 5/33 (dimension 5) :\n",
-      "<<AlLp[5 <<AlLp[3 <<AlLp[4 5]>>][3 <<AlLp[4 5]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 55s.\n",
-      "Computing the boundary of the generator 6/33 (dimension 5) :\n",
-      "<<AlLp[5 <<AlLp[4 <<AlLp[5 6]>>][2 <<AlLp[3 4]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 55s.\n",
-      "Computing the boundary of the generator 7/33 (dimension 5) :\n",
-      "<<AlLp[5 <<AlLp[2 <<AlLp[3 4]>>][2 <<AlLp[3 4]>>][2 <<AlLp[3 4]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 55s.\n",
-      "Computing the boundary of the generator 8/33 (dimension 5) :\n",
-      "<<AlLp[1 <<AlLp[2 <<AlLp[3 4]>>]>>][4 <<AlLp[5 <<AlLp[6 7]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 55s.\n",
-      "Computing the boundary of the generator 9/33 (dimension 5) :\n",
-      "<<AlLp[1 <<AlLp[2 <<AlLp[3 4]>>]>>][4 <<AlLp[5 <<AlLp[3 4][3 4]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 55s.\n",
-      "Computing the boundary of the generator 10/33 (dimension 5) :\n",
-      "<<AlLp[1 <<AlLp[2 <<AlLp[3 4]>>]>>][4 <<AlLp[2 <<AlLp[3 4]>>][3 <<AlLp[4 5]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 55s.\n",
-      "Computing the boundary of the generator 11/33 (dimension 5) :\n",
-      "<<AlLp[1 <<AlLp[2 <<AlLp[3 4]>>]>>][4 <<AlLp[3 <<AlLp[4 5]>>][2 <<AlLp[3 4]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 55s.\n",
-      "Computing the boundary of the generator 12/33 (dimension 5) :\n",
-      "<<AlLp[2 <<AlLp[3 <<AlLp[4 5]>>]>>][3 <<AlLp[4 <<AlLp[5 6]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 55s.\n",
-      "Computing the boundary of the generator 13/33 (dimension 5) :\n",
-      "<<AlLp[2 <<AlLp[3 <<AlLp[4 5]>>]>>][3 <<AlLp[2 <<AlLp[3 4]>>][2 <<AlLp[3 4]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 55s.\n",
-      "Computing the boundary of the generator 14/33 (dimension 5) :\n",
-      "<<AlLp[3 <<AlLp[4 <<AlLp[5 6]>>]>>][2 <<AlLp[3 <<AlLp[4 5]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 55s.\n",
-      "Computing the boundary of the generator 15/33 (dimension 5) :\n",
-      "<<AlLp[3 <<AlLp[2 <<AlLp[3 4]>>][2 <<AlLp[3 4]>>]>>][2 <<AlLp[3 <<AlLp[4 5]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 55s.\n",
-      "Computing the boundary of the generator 16/33 (dimension 5) :\n",
-      "<<AlLp[4 <<AlLp[5 <<AlLp[6 7]>>]>>][1 <<AlLp[2 <<AlLp[3 4]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 56s.\n",
-      "Computing the boundary of the generator 17/33 (dimension 5) :\n",
-      "<<AlLp[4 <<AlLp[5 <<AlLp[3 4][3 4]>>]>>][1 <<AlLp[2 <<AlLp[3 4]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 56s.\n",
-      "Computing the boundary of the generator 18/33 (dimension 5) :\n",
-      "<<AlLp[4 <<AlLp[2 <<AlLp[3 4]>>][3 <<AlLp[4 5]>>]>>][1 <<AlLp[2 <<AlLp[3 4]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 56s.\n",
-      "Computing the boundary of the generator 19/33 (dimension 5) :\n",
-      "<<AlLp[4 <<AlLp[3 <<AlLp[4 5]>>][2 <<AlLp[3 4]>>]>>][1 <<AlLp[2 <<AlLp[3 4]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 56s.\n",
-      "Computing the boundary of the generator 20/33 (dimension 5) :\n",
-      "<<AlLp[1 <<AlLp[2 <<AlLp[3 4]>>]>>][1 <<AlLp[2 <<AlLp[3 4]>>]>>][3 <<AlLp[4 <<AlLp[5 6]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 56s.\n",
-      "Computing the boundary of the generator 21/33 (dimension 5) :\n",
-      "<<AlLp[1 <<AlLp[2 <<AlLp[3 4]>>]>>][1 <<AlLp[2 <<AlLp[3 4]>>]>>][3 <<AlLp[2 <<AlLp[3 4]>>][2 <<AlLp[3 4]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 56s.\n",
-      "Computing the boundary of the generator 22/33 (dimension 5) :\n",
-      "<<AlLp[1 <<AlLp[2 <<AlLp[3 4]>>]>>][2 <<AlLp[3 <<AlLp[4 5]>>]>>][2 <<AlLp[3 <<AlLp[4 5]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 56s.\n",
-      "Computing the boundary of the generator 23/33 (dimension 5) :\n",
-      "<<AlLp[1 <<AlLp[2 <<AlLp[3 4]>>]>>][3 <<AlLp[4 <<AlLp[5 6]>>]>>][1 <<AlLp[2 <<AlLp[3 4]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 56s.\n",
-      "Computing the boundary of the generator 24/33 (dimension 5) :\n",
-      "<<AlLp[1 <<AlLp[2 <<AlLp[3 4]>>]>>][3 <<AlLp[2 <<AlLp[3 4]>>][2 <<AlLp[3 4]>>]>>][1 <<AlLp[2 <<AlLp[3 4]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 56s.\n",
-      "Computing the boundary of the generator 25/33 (dimension 5) :\n",
-      "<<AlLp[2 <<AlLp[3 <<AlLp[4 5]>>]>>][1 <<AlLp[2 <<AlLp[3 4]>>]>>][2 <<AlLp[3 <<AlLp[4 5]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 56s.\n",
-      "Computing the boundary of the generator 26/33 (dimension 5) :\n",
-      "<<AlLp[2 <<AlLp[3 <<AlLp[4 5]>>]>>][2 <<AlLp[3 <<AlLp[4 5]>>]>>][1 <<AlLp[2 <<AlLp[3 4]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 56s.\n",
-      "Computing the boundary of the generator 27/33 (dimension 5) :\n",
-      "<<AlLp[3 <<AlLp[4 <<AlLp[5 6]>>]>>][1 <<AlLp[2 <<AlLp[3 4]>>]>>][1 <<AlLp[2 <<AlLp[3 4]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 56s.\n",
-      "Computing the boundary of the generator 28/33 (dimension 5) :\n",
-      "<<AlLp[3 <<AlLp[2 <<AlLp[3 4]>>][2 <<AlLp[3 4]>>]>>][1 <<AlLp[2 <<AlLp[3 4]>>]>>][1 <<AlLp[2 <<AlLp[3 4]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 56s.\n",
-      "Computing the boundary of the generator 29/33 (dimension 5) :\n",
-      "<<AlLp[1 <<AlLp[2 <<AlLp[3 4]>>]>>][1 <<AlLp[2 <<AlLp[3 4]>>]>>][1 <<AlLp[2 <<AlLp[3 4]>>]>>][2 <<AlLp[3 <<AlLp[4 5]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 56s.\n",
-      "Computing the boundary of the generator 30/33 (dimension 5) :\n",
-      "<<AlLp[1 <<AlLp[2 <<AlLp[3 4]>>]>>][1 <<AlLp[2 <<AlLp[3 4]>>]>>][2 <<AlLp[3 <<AlLp[4 5]>>]>>][1 <<AlLp[2 <<AlLp[3 4]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 56s.\n",
-      "Computing the boundary of the generator 31/33 (dimension 5) :\n",
-      "<<AlLp[1 <<AlLp[2 <<AlLp[3 4]>>]>>][2 <<AlLp[3 <<AlLp[4 5]>>]>>][1 <<AlLp[2 <<AlLp[3 4]>>]>>][1 <<AlLp[2 <<AlLp[3 4]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 56s.\n",
-      "Computing the boundary of the generator 32/33 (dimension 5) :\n",
-      "<<AlLp[2 <<AlLp[3 <<AlLp[4 5]>>]>>][1 <<AlLp[2 <<AlLp[3 4]>>]>>][1 <<AlLp[2 <<AlLp[3 4]>>]>>][1 <<AlLp[2 <<AlLp[3 4]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 27m 56s.\n",
-      "Computing the boundary of the generator 33/33 (dimension 5) :\n",
-      "<<AlLp[1 <<AlLp[2 <<AlLp[3 4]>>]>>][1 <<AlLp[2 <<AlLp[3 4]>>]>>][1 <<AlLp[2 <<AlLp[3 4]>>]>>][1 <<AlLp[2 <<AlLp[3 4]>>]>>][1 <<AlLp[2 <<AlLp[3 4]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "========== MATRIX 13 lines + 33 columns =====\n",
-       "L1=[C1=-2]\n",
-       "L2=[C1=-1]\n",
-       "L3=[C1=-4][C2=1][C3=-1][C4=-2]\n",
-       "L4=[C2=1][C3=-1][C6=2]\n",
-       "L5=[C1=6][C4=1][C6=1]\n",
-       "L6=[C1=4][C4=4][C6=4][C7=3]\n",
-       "L7=[C1=4][C12=-2][C14=2]\n",
-       "L8=[C1=6][C4=1][C6=1]\n",
-       "L9=[C1=4][C4=4][C6=4][C7=3]\n",
-       "L10=[C8=4][C10=1][C11=-1][C14=-4][C15=-2][C20=-2]\n",
-       "L11=[C1=4][C8=4][C10=1][C11=-1][C16=-4][C18=-1][C19=1][C23=-2]\n",
-       "L12=[C12=4][C13=2][C16=-4][C18=-1][C19=1][C27=-2]\n",
-       "L13=[C1=-1][C20=4][C21=2][C23=-4][C24=-2][C27=4][C28=2]\n",
-       "========== END-MATRIX"
-      ]
-     },
-     "execution_count": 17,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(chcm-mat ecc 5)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "For instance, we see that the first $5$-cell,"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 18,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "<<AlLp[5 <<AlLp[6 <<AlLp[7 8]>>]>>]>>"
-      ]
-     },
-     "execution_count": 18,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(first (basis ecc 5)) "
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "is glued to the 4-cells \\#5 and \\#8 by attaching maps of degree 6. The 5-cell \\#4 is also glued to the 4-cell \\#5 by an attaching map of degree 1, etc.\n",
-    "\n",
-    "### Lisp files concerned in this chapter\n",
-    "\n",
-    "`lp-space-efhm.lisp`, `searching-homology.lisp`."
-   ]
-  }
- ],
- "metadata": {
-  "kernelspec": {
-   "display_name": "SBCL Lisp",
-   "language": "lisp",
-   "name": "lisp"
-  },
-  "language_info": {
-   "codemirror_mode": "text/x-common-lisp",
-   "mimetype": "text/x-common-lisp",
-   "name": "common-lisp",
-   "pygments_lexer": "common-lisp",
-   "version": "X3J13"
-  }
- },
- "nbformat": 4,
- "nbformat_minor": 1
-}
diff --git a/examples/17_Classifying_Spaces.ipynb b/examples/17_Classifying_Spaces.ipynb
deleted file mode 100644
index 386eb90..0000000
--- a/examples/17_Classifying_Spaces.ipynb
+++ /dev/null
@@ -1,1246 +0,0 @@
-{
- "cells": [
-  {
-   "cell_type": "code",
-   "execution_count": 1,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "To load \"kenzo\":\n",
-      "  Load 1 ASDF system:\n",
-      "    kenzo\n",
-      "; Loading \"kenzo\"\n",
-      "\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "#<PACKAGE \"CAT\">"
-      ]
-     },
-     "execution_count": 1,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(ql:quickload \"kenzo\")\n",
-    "(in-package :cat)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "# Classifying Spaces\n",
-    "\n",
-    "## Introduction\n",
-    "\n",
-    "Let ${\\cal G}$ be a simplicial group $0$-reduced. The program `Kenzo` allows the construction of the universal bundle $\\bar{\\cal W}{\\cal G}$, called the classifying space of ${\\cal G}$. It is known that this is the base space of  a principal bundle such that the total space is contractible. We know also that if ${\\cal G}$ is an Abelian simplicial group then $\\bar{\\cal W}{\\cal G}$ is also an Abelian simplicial group, otherwise if ${\\cal G}$ is non-Abelian, then $\\bar{\\cal W}{\\cal G}$ is only a simplicial set. In dimension $n$ the simplices of the classifying space are elements of the  product:\n",
-    "$${\\cal G}_{n-1}\\times {\\cal G}_{n-2}\\times\\cdots\\times{\\cal G}_0,$$\n",
-    "where ${\\cal G}_k$ is the set of the $k$-simplices of the given simplicial group.\n",
-    "\n",
-    "A simplex of $\\bar{\\cal W}{\\cal G}$ is called **gbar** (*geometric* bar) and  may be seen as an $n$-tuple\n",
-    "$$(g_{n-1}, g_{n-2}, \\ldots, g_1, g_0),$$\n",
-    "where the $g_i$'s are elements of ${\\cal G}_i$, possibly *degenerated*.\n",
-    "In `Kenzo` a gbar is represented externally under the form:\n",
-    "\n",
-    "`<<GBar <` $[\\eta_{n-1}, g_{n-1}]$ `><` $[\\eta_{n-2}, g_{n-2}]$ `> ...  <` $[\\eta_1, g_1]$ `> < -` $g_0$`> >>`\n",
-    "\n",
-    "where a term such as $[\\eta_i, g_i]$ is a simplex of ${\\cal G}_i$. Let us recall that our group ${\\cal G}$ is assumed 0-reduced; as a consequence, the $g_0$ compound of a gbar is necessarily the identity element of ${\\cal G}$.\n",
-    "\n",
-    "In the  symbolic expression $[\\eta_i, g_i]$, the operator $\\eta$ represents a sequence (possibly the void one) of degeneracy operators applied coherently upon some element of ${\\cal G}_k$, for $k\\leq i$. For instance $[\\eta_1, g_1]$ can be the pair $((0),g_0)$, internally implemented as an `absm` object, i.e. the 0-degeneracy of the base point and $[\\eta_2, g_2]$ can be $((1 0), g_0)$, that is, the only possible 2-degeneracy of the base point $g_0$ of $mathcal{G}$. In particular, the dimension of the \"geometric\" simplex $g_i$ is $i - \\ell$ with $\\ell$ the length of the integer sequence $\\eta_i$. To be more explicit, let us take the Abelian simplicial group $K(\\mathbb{Z}_2, 1)$ (see the simplicial groups chapter), then some elements of the basis in dimension 4 of its classifying space are, for instance:\n",
-    "```\n",
-    "<<GBar<- 3><- 2><- 1><- 0>>>\n",
-    "<<GBar<- 3><1-0 0><0 0><- 0>>>\n",
-    "<<GBar<1 2><- 2><0 0><- 0>>>\n",
-    "<<GBar<1 2><0 1><0 0><- 0>>>\n",
-    "<<GBar<2 2><1 1><0 0><- 0>>>\n",
-    "<<GBar<2-0 1><1 1><0 0><- 0>>>\n",
-    "<<GBar<2-1 1><1 1><- 1><- 0>>>\n",
-    "<<GBar<2-1 1><0 1><0 0><- 0>>>\n",
-    "```\n",
-    "We recall that the symbol `-`, in front of an element means \"no degeneracy\".\n",
-    "\n",
-    "## Face, degeneracy and group operations\n",
-    "\n",
-    "Let us denote a gbar under the following generic form:\n",
-    "$$\n",
-    "g_{bar}=(g_{n-1}, g_{n-2}, \\ldots, g_j, \\ldots, g_1, g_0).\n",
-    "$$\n",
-    "In this symbolism, $g_0$ is also the base point of the initial simplicial group. The rule for the face operators is the following:\n",
-    "- If $j=n$, $\\delta_n g_{bar}= (g_{n-2}, g_{n-3}, \\ldots, g_1, g_0).$\n",
-    "- If $j \\not=n$, $\\delta_j g_{bar}= (\\delta_j g_{n-1}, \\ldots, \\delta_j g_{j+1}, g_{j-1}.\\delta_j g_j, g_{j-1}, \\ldots, g_1, g_0),$ where in the term $g_{j-1}.\\delta_j g_j$, the dot represents the group composition.\n",
-    "- If $j=0$, $\\delta_0 g_{bar}= (\\delta_0 g_{n-1}, \\ldots, \\delta_0 g_1).$\n",
-    "\n",
-    "The rule for the degeneracy operators is:\n",
-    "\n",
-    "$$\n",
-    "\\eta_j g_{bar}= (\\eta_j g_{n-1}, \\ldots, \\eta_j g_{j+1}, \\eta_{j-1}\\eta_{j-2}\\ldots\\eta_1\\eta_0 g_0, g_{j-1}, \\ldots, g_1, g_0).\n",
-    "$$\n",
-    "\n",
-    "If ${\\cal G}$ is Abelian then $\\bar{\\cal W}{\\cal G}$ is also  Abelian and its composition law is simply:\n",
-    "\n",
-    "$$\n",
-    "(g_{n-1}, \\ldots, g_1, g_0).(g'_{n-1}, g'_1, g'_0)=(g_{n-1}.g'_{n-1},  \\ldots, g_1.g'_1, g_0.g'_0).\n",
-    "$$\n",
-    "\n",
-    "If the initial group is not Abelian then, in general, the previous composition law is not compatible with the simplicial structure.\n",
-    "\n",
-    "## The functions for the classifying spaces\n",
-    "\n",
-    "`gbar` *dmns dop-1 elem-1 ... dop-n elem-n* *[Macro]*\n",
-    "> Build a gbar in dimension *dmns*. The sequence *dop-1 elem-1 ... dop-n elem-n*, is a sequence of pairs (*dop-k, elem-k*), where *dop-k* is  a **binary coded** degeneracy operator and *elem-k* a simplex of the initial simplicial group. The ordering of the pairs in the sequence must conform to the theoritical definition of a gbar. If the sequence of pairs is void, the special call `(gbar 0)`, creates the base point of the classifying space externally represented by `<<GBAR>>`. This base point can be reached through the system symbol `+null-gbar+`.\n",
-    "\n",
-    "`classifying-space-cmpr` *cmpr* *[Function]*\n",
-    "> From a comparison function *cmpr* defined for a simplicial group ${\\cal G}$, build a comparison function for the classifying space of ${\\cal G}$.\n",
-    "\n",
-    "`classifying-space-basis` *basis* *[Function]*\n",
-    "> From the basis function *basis* of a simplicial group ${\\cal G}$, build a basis function for the classifying space of ${\\cal G}$. If ${\\cal G}$ is locally effective, this function returns the symbol `:locally-effective`.\n",
-    "\n",
-    "`classifying-space-face` *face sintr-grml* *[Function]*\n",
-    "> From the face function *face* and the lisp function for the group law, *sintr-grml*, of a simplicial group ${\\cal G}$, build a face function for the classifying space of ${\\cal G}$.\n",
-    "\n",
-    "`classifying-space` *smgr* *[Method]*\n",
-    "> Build the simplicial set, classifying space of the simplicial group *smgr*. The construction uses the three preceding auxiliary functions. The base point of the returned simplicial set is the null gbar `+null-gbar+`.\n",
-    "\n",
-    "`classifying-space` *A-smgr* *[Method]*\n",
-    "> Build the Abelian simplicial group, classifying space of the Abelian simplicial group *A-smgr*. The group law and its inverse (slots `:sintr-grml` and `:sintr-grin`) are built by the two auxiliary functions:  \n",
-    "`classifying-space-grml-sintr` and  \n",
-    "`classifying-space-grin-sintr`,  \n",
-    "defining the laws of this new group from the corresponding laws of *A-smgr*.\n",
-    "\n",
-    "## Eilenberg-Mac Lane spaces $K(\\pi,n)$\n",
-    "\n",
-    "We have already described $K(\\mathbb{Z},1)$ and $K(\\mathbb{Z}_2,1)$ in the chapter on simplicial groups. This section gives some complements about the construction of $K(\\mathbb{Z},n)$ and $K(\\mathbb{Z}_2,n)$. The trivial case for $n=0$ is not implemented in `Kenzo`. For $n > 1$, these simplicial groups are built recursively as the classifying spaces of $K(\\mathbb{Z},n-1)$ and $K(\\mathbb{Z}_2,n-1)$, respectively, as shown in the following description:\n",
-    "\n",
-    "`k-z` *n* *[Function]*\n",
-    "> Build $K(\\mathbb{Z},n)$ recursively from $K(\\mathbb{Z},n-1)$. If $n=1$, return $K(\\mathbb{Z},1)$\n",
-    "```commonlisp\n",
-    "     (defun K-Z (n)\n",
-    "        (the ab-simplicial-group\n",
-    "           (if (= n 1)\n",
-    "               (k-z-1)\n",
-    "               (classifying-space (k-z (1- n))))))\n",
-    "```\n",
-    "\n",
-    "`k-z2` *n* *[Function]*\n",
-    "> Build $K(\\mathbb{Z}_2,n)$ recursively from $K(\\mathbb{Z}_2,n-1)$. If $n=1$, return $K(\\mathbb{Z}_2,1)$\n",
-    "```commonlisp\n",
-    "     (defun K-Z2 (n)\n",
-    "        (the ab-simplicial-group\n",
-    "           (if (= n 1)\n",
-    "               (k-z2-1)\n",
-    "               (classifying-space (k-z2 (1- n))))))\n",
-    "```\n",
-    "\n",
-    "These spaces have an effective homology which is computed via a *search-efhm* method (described in a next chapter). For the case $n=1$, we may recall here that $K(\\mathbb{Z},1)$, though being locally effective, has the homology of $S^1$. The  *search-efhm* method applied to this chain complex does the following:  a reduction between $K(\\mathbb{Z},1)$ and the chain complex `circle` (described in the chain complex chapter) is built using the function `kz1-rdct` and the homotopy equivalence, value of the slot `efhm`, is built between this reduction and the trivial reduction of $K(\\mathbb{Z},1)$ upon itself.\n",
-    "\n",
-    "On the other hand, $K(\\mathbb{Z},2)$ has a very simple finite basis in every dimension (see $\\mathbb{R}$-projective spaces), so its homology is computed directly from its basis. The  homotopy equivalence, value of the slot `efhm`, is the trivial homotopy equivalence of $K(\\mathbb{Z},2)$ upon itself.\n",
-    "\n",
-    "### Examples\n",
-    "\n",
-    "Let us begin by showing some examples of gbars built  from various initial simplicial groups. In the second statement, the initial simplicial group is $K(\\mathbb{Z}_2, 1)$, in the third, it is $\\Omega({\\mathit Moore}(2,2))$. We recall that in the call of the function `gbar`, the degeneracy operators appear as integers, according to the general rule in `Kenzo`, but the printed result shows in clear the sequence of $\\eta_i$'s."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 2,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "<<GBar<0 A><1 B>>>"
-      ]
-     },
-     "execution_count": 2,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(gbar 2 1 'a 2 'b)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 3,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "<<GBar<- 3><1-0 0><0 0><- 0>>>"
-      ]
-     },
-     "execution_count": 3,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(gbar 4 0 3 3 0 1 0 0 0)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 4,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "<<GBar<- <<Loop[1-0 M2][2 N3]>>><- <<Loop[N3]>>><- <<Loop[M2]>>><- <<Loop>>>>>"
-      ]
-     },
-     "execution_count": 4,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def gbar-m22 (gbar 4 0 (loop3 3 'm2 1 4 'n3 1)\n",
-    "                      0 (loop3 0 'n3 1)\n",
-    "                      0 (loop3 0 'm2 1)\n",
-    "                      0 +null-loop+))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Let us test the face function upon this simplex. The user will note that the face function returns an abstract simplex."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 5,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K6 Simplicial-Group]"
-      ]
-     },
-     "execution_count": 5,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def om (loop-space (moore 2 2)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 6,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "#<CLOSURE (FLET RSLT :IN CLASSIFYING-SPACE-FACE) {1001CE47FB}>"
-      ]
-     },
-     "execution_count": 6,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def face (classifying-space-face (face om) (sintr (grml om))))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 7,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "<AbSm - <<GBar<- <<Loop[0 M2][1 M2]>>><- <<Loop[M2]>>><- <<Loop>>>>>> \n",
-      "<AbSm 0 <<GBar<- <<Loop[M2]>>><- <<Loop>>>>>> \n",
-      "<AbSm - <<GBar<- <<Loop[0 M2][N3]>>><- <<Loop[M2\\2]>>><- <<Loop>>>>>> \n",
-      "<AbSm - <<GBar<- <<Loop[N3\\2]>>><- <<Loop[M2]>>><- <<Loop>>>>>> \n",
-      "<AbSm - <<GBar<- <<Loop[N3]>>><- <<Loop[M2]>>><- <<Loop>>>>>> "
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 7,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(dotimes (i 5) (print (funcall face i 4 gbar-m22)))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Let us work now, directly with the classifying space of $K(\\mathbb{Z}_2, 1)$."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 8,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K30 Abelian-Simplicial-Group]"
-      ]
-     },
-     "execution_count": 8,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def cs-kz21 (classifying-space (k-z2-1))) "
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 9,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(CLASSIFYING-SPACE [K18 Abelian-Simplicial-Group])"
-      ]
-     },
-     "execution_count": 9,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(orgn cs-kz21)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 10,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "<<GBar<- 3><- 2><- 1><- 0>>>"
-      ]
-     },
-     "execution_count": 10,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def elem-1 (first (basis cs-kz21 4)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 11,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 3}\n",
-       "<2 * <<GBar<- 2><- 1><- 0>>>>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 11,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? cs-kz21 4 elem-1)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 12,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 2}\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 12,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? cs-kz21 *)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 13,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 4}\n",
-       "<1 * <TnPr <<GBar>> <<GBar<- 3><- 2><- 1><- 0>>>>>\n",
-       "<1 * <TnPr <<GBar<- 1><- 0>>> <<GBar<- 1><- 0>>>>>\n",
-       "<1 * <TnPr <<GBar<- 3><- 2><- 1><- 0>>> <<GBar>>>>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 13,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(cprd cs-kz21  4 elem-1)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 14,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "<AbSm - <<GBar<- 2><- 1><- 0>>>> \n",
-      "<AbSm 0 <<GBar<- 1><- 0>>>> \n",
-      "<AbSm 1 <<GBar<- 1><- 0>>>> \n",
-      "<AbSm 2 <<GBar<- 1><- 0>>>> \n",
-      "<AbSm - <<GBar<- 2><- 1><- 0>>>> "
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 14,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(dotimes (i 5)\n",
-    "    (print (face cs-kz21 i 4 elem-1)))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Let us test the law group with $K(\\mathbb{Z}, 1)$. We recall the simplices of  this Abelian simplicial group are represented as lists of integers. The functions `grml` and `grin` accept also the gbars under the form of abstract simplices (see the last statement)."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 15,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K54 Abelian-Simplicial-Group]"
-      ]
-     },
-     "execution_count": 15,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def cs-kz1 (classifying-space (k-z-1)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 16,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "<AbSm 2-1-0 <<GBar>>>"
-      ]
-     },
-     "execution_count": 16,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(grml cs-kz1 3 (crpr 0 (gbar 3 0 '(1 2) 0 '(3) 0 '())\n",
-    "                     0 (gbar 3 0 '(-1 -2) 0 '(-3) 0 '())))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 17,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "<AbSm - <<GBar<- (1 2)><0 NIL><- NIL>>>>"
-      ]
-     },
-     "execution_count": 17,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(grml cs-kz1 3 (crpr 0 (gbar 3 0 '(1 2) 0 '(3) 0 '())\n",
-    "                     4 (gbar 2 0 '(-3) 0 '()))) "
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 18,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "<AbSm - <<GBar<- (1 -1)><- (3)><- NIL>>>>"
-      ]
-     },
-     "execution_count": 18,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(grml cs-kz1 3 (crpr 0 (gbar 3 0 '(1 2) 0 '(3) 0 '())\n",
-    "                     1 (gbar 2 0 '(-3) 0 '())))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 19,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "<AbSm - <<GBar<- (-1 -2)><0 NIL><- NIL>>>>"
-      ]
-     },
-     "execution_count": 19,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(grin cs-kz1 3 (gbar 3 0 '(1 2) 1 '() 0 '()))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 20,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "<AbSm - <<GBar<- (1 2)><0 NIL><- NIL>>>>"
-      ]
-     },
-     "execution_count": 20,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(grin cs-kz1 3 *)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "As $K(\\mathbb{Z}, 1)$ and $K(\\mathbb{Z}_2, 1)$ are Abelian simplicial groups, we may iterate the classifying space construction and retrieve some known results."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 21,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "---done---"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 21,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(cat-init)    ;; re-initialization"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 22,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K25 Abelian-Simplicial-Group]"
-      ]
-     },
-     "execution_count": 22,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def k-z-3 (k-z 3))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 23,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "Computing boundary-matrix in dimension 0.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 28m 49s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 0) :\n",
-      "<<Abar>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 1.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 0 :\n",
-      "\n",
-      "\n",
-      "Component Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 28m 49s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 1.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 2.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 1 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 28m 49s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 2.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 3.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 28m 49s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 3) :\n",
-      "<<Abar[3 <<Abar[2 S1]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 2 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 28m 49s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 3.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 28m 49s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 3) :\n",
-      "<<Abar[3 <<Abar[2 S1]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 4.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 3 :\n",
-      "\n",
-      "\n",
-      "Component Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 28m 49s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 4.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 5.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 28m 49s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 5) :\n",
-      "<<Abar[5 <<Abar[2 S1][2 S1]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 4 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 28m 49s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 5.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 28m 49s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 5) :\n",
-      "<<Abar[5 <<Abar[2 S1][2 S1]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 6.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 28m 49s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 6) :\n",
-      "<<Abar[3 <<Abar[2 S1]>>][3 <<Abar[2 S1]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 5 :\n",
-      "\n",
-      "\n",
-      "Component Z/2Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 28m 49s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 6.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 28m 49s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 6) :\n",
-      "<<Abar[3 <<Abar[2 S1]>>][3 <<Abar[2 S1]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 7.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 28m 49s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 7) :\n",
-      "<<Abar[7 <<Abar[2 S1][2 S1][2 S1]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 6 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 28m 49s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 7.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 28m 49s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 7) :\n",
-      "<<Abar[7 <<Abar[2 S1][2 S1][2 S1]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 8.\n",
-      "Rank of the source-module : 2.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 28m 49s.\n",
-      "Computing the boundary of the generator 1/2 (dimension 8) :\n",
-      "<<Abar[3 <<Abar[2 S1]>>][5 <<Abar[2 S1][2 S1]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 28m 49s.\n",
-      "Computing the boundary of the generator 2/2 (dimension 8) :\n",
-      "<<Abar[5 <<Abar[2 S1][2 S1]>>][3 <<Abar[2 S1]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 7 :\n",
-      "\n",
-      "\n",
-      "Component Z/3Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 28m 49s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 8.\n",
-      "Rank of the source-module : 2.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 28m 49s.\n",
-      "Computing the boundary of the generator 1/2 (dimension 8) :\n",
-      "<<Abar[3 <<Abar[2 S1]>>][5 <<Abar[2 S1][2 S1]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 28m 49s.\n",
-      "Computing the boundary of the generator 2/2 (dimension 8) :\n",
-      "<<Abar[5 <<Abar[2 S1][2 S1]>>][3 <<Abar[2 S1]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 9.\n",
-      "Rank of the source-module : 2.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 28m 49s.\n",
-      "Computing the boundary of the generator 1/2 (dimension 9) :\n",
-      "<<Abar[9 <<Abar[2 S1][2 S1][2 S1][2 S1]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 28m 49s.\n",
-      "Computing the boundary of the generator 2/2 (dimension 9) :\n",
-      "<<Abar[3 <<Abar[2 S1]>>][3 <<Abar[2 S1]>>][3 <<Abar[2 S1]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 8 :\n",
-      "\n",
-      "\n",
-      "Component Z/2Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 28m 49s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 9.\n",
-      "Rank of the source-module : 2.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 28m 49s.\n",
-      "Computing the boundary of the generator 1/2 (dimension 9) :\n",
-      "<<Abar[9 <<Abar[2 S1][2 S1][2 S1][2 S1]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 28m 49s.\n",
-      "Computing the boundary of the generator 2/2 (dimension 9) :\n",
-      "<<Abar[3 <<Abar[2 S1]>>][3 <<Abar[2 S1]>>][3 <<Abar[2 S1]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 10.\n",
-      "Rank of the source-module : 3.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 28m 49s.\n",
-      "Computing the boundary of the generator 1/3 (dimension 10) :\n",
-      "<<Abar[3 <<Abar[2 S1]>>][7 <<Abar[2 S1][2 S1][2 S1]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 28m 49s.\n",
-      "Computing the boundary of the generator 2/3 (dimension 10) :\n",
-      "<<Abar[5 <<Abar[2 S1][2 S1]>>][5 <<Abar[2 S1][2 S1]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 28m 49s.\n",
-      "Computing the boundary of the generator 3/3 (dimension 10) :\n",
-      "<<Abar[7 <<Abar[2 S1][2 S1][2 S1]>>][3 <<Abar[2 S1]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 9 :\n",
-      "\n",
-      "\n",
-      "Component Z/2Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 28m 49s.\n",
-      "\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 23,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(homology k-z-3 0 10)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 24,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K342 Abelian-Simplicial-Group]"
-      ]
-     },
-     "execution_count": 24,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def k-z2-5 (k-z2 5))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 25,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "Computing boundary-matrix in dimension 0.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 28m 49s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 0) :\n",
-      "<<Abar>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 1.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 0 :\n",
-      "\n",
-      "\n",
-      "Component Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 28m 49s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 1.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 2.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 1 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 28m 49s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 2.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 3.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 2 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 28m 49s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 3.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 4.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 3 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 28m 49s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 4.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 5.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 28m 49s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 5) :\n",
-      "<<Abar[5 <<Abar[4 <<Abar[3 <<Abar[2 1]>>]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 4 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 28m 49s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 5.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 28m 49s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 5) :\n",
-      "<<Abar[5 <<Abar[4 <<Abar[3 <<Abar[2 1]>>]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 6.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 28m 49s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 6) :\n",
-      "<<Abar[6 <<Abar[5 <<Abar[4 <<Abar[3 2]>>]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 5 :\n",
-      "\n",
-      "\n",
-      "Component Z/2Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 28m 49s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 6.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 28m 49s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 6) :\n",
-      "<<Abar[6 <<Abar[5 <<Abar[4 <<Abar[3 2]>>]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 7.\n",
-      "Rank of the source-module : 2.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 28m 49s.\n",
-      "Computing the boundary of the generator 1/2 (dimension 7) :\n",
-      "<<Abar[7 <<Abar[6 <<Abar[5 <<Abar[4 3]>>]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 28m 49s.\n",
-      "Computing the boundary of the generator 2/2 (dimension 7) :\n",
-      "<<Abar[7 <<Abar[6 <<Abar[5 <<Abar[2 1][2 1]>>]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 6 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 28m 49s.\n",
-      "\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 25,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(homology k-z2-5 0 7)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "### Lisp files concerned in this chapter\n",
-    "\n",
-    "`classifying-space.lisp`, `k-pi-n.lisp`."
-   ]
-  }
- ],
- "metadata": {
-  "kernelspec": {
-   "display_name": "SBCL Lisp",
-   "language": "lisp",
-   "name": "lisp"
-  },
-  "language_info": {
-   "codemirror_mode": "text/x-common-lisp",
-   "mimetype": "text/x-common-lisp",
-   "name": "common-lisp",
-   "pygments_lexer": "common-lisp",
-   "version": "X3J13"
-  }
- },
- "nbformat": 4,
- "nbformat_minor": 1
-}
diff --git a/examples/18_Serre_spectral_sequence.ipynb b/examples/18_Serre_spectral_sequence.ipynb
deleted file mode 100644
index 95de69b..0000000
--- a/examples/18_Serre_spectral_sequence.ipynb
+++ /dev/null
@@ -1,1753 +0,0 @@
-{
- "cells": [
-  {
-   "cell_type": "code",
-   "execution_count": 1,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "To load \"kenzo\":\n",
-      "  Load 1 ASDF system:\n",
-      "    kenzo\n",
-      "; Loading \"kenzo\"\n",
-      "\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "#<PACKAGE \"CAT\">"
-      ]
-     },
-     "execution_count": 1,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(ql:quickload \"kenzo\")\n",
-    "(in-package :cat)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "# Serre spectral sequence\n",
-    "\n",
-    "## Introduction\n",
-    "\n",
-    "This chapter is devoted to the `Kenzo` implementation of the Serre spectral sequence with the aim to compute the homology groups of the total space of a fibration. From the programming point of view, this method will be used according to our general scheme of searching homology (generic function `search-efhm`) applied to an object of type `fibration-total`.\n",
-    "\n",
-    "## The topological problem\n",
-    "\n",
-    "Let ${\\cal G}$ be a simplicial group (the fiber space),  $B$, a 1-reduced simplicial set (the base space) and $\\tau$ (the fibration), a simplicial morphism of degree $-1$, and $\\tau: B \\rightarrow \\mathcal{G}$ a fibration, that is, a twisting operator as defined in Chapter 12. In the Kenzo program, this object $\\tau$ is implemented as an object of class `simplicial-mrph` and \"degree\" $-1$ while a genuine simplicial morphism has degree 0. We know the program Kenzo knows how to build the total space of the fibration: $B \\times_\\tau {\\cal G}$, which has the same simplices as $B \\times {\\cal G}$ and the same face operators except the last one, given by:\n",
-    "$$\n",
-    "\\partial_n(b,g)  =  (\\partial_n b, \\tau(b).\\partial_n g), \\quad b\\in B, g \\in {\\cal G},\n",
-    "$$\n",
-    "where the '`.`' denotes the group operation in ${\\cal G}$. This discrepancy between the respective face operators $\\partial_n$ induces a discrepancy between the differential operators. We suppose now, that the base and  fiber  spaces are objects of effective homology type, i.e. there exist homotopy equivalences\n",
-    "$$\n",
-    "\\begin{aligned}\n",
-    "  & \\qquad\\widehat{B}  & & & & \\qquad\\widehat{\\cal G} & & \\cr\n",
-    " \\rho_1 \\swarrow\\nearrow  & & \\searrow\\nwarrow \\rho_2 &\\quad & \\rho'_1\\swarrow\\nearrow & & \\searrow\\nwarrow\\rho'_2 & \\cr\n",
-    "B  & & EB & & {\\cal G}   & & EG \\cr\n",
-    "\\end{aligned}\n",
-    "$$\n",
-    "where the chain complexes $EB$ and $EG$ are effective. The problem consists in finding a homotopy equivalence between $B \\times_\\tau {\\cal G}$ and an effective chain complex noted $EB \\widetilde{\\otimes} EG$; the underlying graded module of $EB \\widetilde{\\otimes} EG$ is $EB \\otimes EG$ but the differential is twisted in a rather complicated way. In fact, the chain complex $EB \\widetilde{\\otimes} EG$ is nothing but the Hirsch complex (**Guy Hirsch.** `Sur les groupes d'homologie des espaces fibres`, Bulletin de la Societe Mathematique de Belgique, 1954, vol. 6, pp. 79-96.).\n",
-    "\n",
-    "### The Ronald Brown reduction\n",
-    "\n",
-    "We start from the Eilenberg-Zilber reduction  (built in `Kenzo` by the function `ez`).\n",
-    "$$\n",
-    "\\begin{aligned}\n",
-    "{{\\cal C}_*(B \\times {\\cal G})} & \\qquad\\stackrel{h}{\\longrightarrow} & {}^s{{\\cal C}_*(B \\times {\\cal G})} \\cr\n",
-    " {\\scriptstyle f} \\downarrow \\uparrow {\\scriptstyle g}  & & \\cr\n",
-    " {{\\cal C}_*(B) \\otimes {\\cal C}_*({\\cal G})} & &\\cr\n",
-    "\\end{aligned}\n",
-    "$$\n",
-    "Using the *basic perturbation lemma*, we then obtain a new reduction between twisted objects:\n",
-    "$$\n",
-    "\\begin{aligned}\n",
-    "{{\\cal C}_*(B \\times_\\tau {\\cal G})} & \\qquad\\stackrel{h}{\\longrightarrow} & {}^s{{\\cal C}_*(B \\times_\\tau {\\cal G})} \\cr\n",
-    " {\\scriptstyle f} \\downarrow \\uparrow {\\scriptstyle g} & &  \\cr\n",
-    " {{\\cal C}_*(B) \\otimes_t {\\cal C}_*({\\cal G})} & &\\cr\n",
-    "\\end{aligned}\n",
-    "$$\n",
-    "where the symbol $\\otimes_t$ represents a *twisted tensor product*, induced by the twisting operator $\\tau$; this twisting operator is nothing but the Shih twisting cochain (**Gugenheim.**, *On the chain complex of a fibration*. Illinois Journal of Mathematics, 1972, vol. 16, pp. 398-414.) determined by Szczarba (**R. H. Szczarba.** *The homology of twisted cartesian products*. Transactions of the American Mathematical Society, 1961, vol. 100, pp. 197-216.). In effect, writing \n",
-    "$$ d_\\tau = d + (d_\\tau -d),$$\n",
-    "one may consider that the differential $d_\\tau$ of $B \\times_\\tau {\\cal G}$ is the differential $d$ of $B \\times {\\cal G}$ modified by the perturbation $d_\\tau - d$. The perturbation morphism $d_\\tau -d$ is deduced from the  difference  between both  $\\partial_n$ face operators. This being done,  a perturbation may possibly be propagated along the Eilenberg-Zilber reduction  (see the method `add` applied to a reduction) and  the perturbation lemma  gives also, as a bonus, the perturbation to be applied to the differential of $B \\otimes {\\cal G}$  to obtain the differential of $B \\otimes_t {\\cal G}$.\n",
-    "\n",
-    "### The Gugenheim algorithm\n",
-    "\n",
-    "On the other hand, from the homotopy equivalences\n",
-    "$$\n",
-    "\\begin{aligned}\n",
-    "  & \\qquad\\widehat{B} & & & & \\qquad\\widehat{\\cal G} & & \\cr\n",
-    " \\rho_1 \\swarrow\\nearrow  & & \\searrow\\nwarrow \\rho_2 &\\quad & \\rho'_1\\swarrow\\nearrow & & \\searrow\\nwarrow\\rho'_2 & \\cr\n",
-    "B  & & EB & & {\\cal G}   & & EG \\cr\n",
-    "\\end{aligned}\n",
-    "$$\n",
-    "it is possible to build their tensor product, i.e. the homotopy equivalence:\n",
-    "$$\n",
-    "\\begin{aligned}\n",
-    "  & \\qquad\\widehat{B}\\otimes \\widehat{\\cal G} &    \\cr\n",
-    " \\swarrow\\nearrow & & \\searrow\\nwarrow \\qquad\\cr\n",
-    "B\\otimes {\\cal G}  & & EB \\otimes EG \\cr\n",
-    "\\end{aligned}\n",
-    "$$\n",
-    "This is done in `Kenzo` by the method  `tnsr-prdc`.\n",
-    "In fact, we are interested in the following one:\n",
-    "$$\n",
-    "\\begin{aligned}\n",
-    "  & \\qquad\\widehat{B}\\widetilde{\\otimes}\\widehat{\\cal G} &    \\cr\n",
-    " \\swarrow\\nearrow & & \\searrow\\nwarrow \\qquad\\cr\n",
-    "B\\otimes_t {\\cal G}  & & EB \\widetilde{\\otimes} EG \\cr\n",
-    "\\end{aligned}\n",
-    "$$\n",
-    "where $\\widehat{B}\\widetilde{\\otimes}\\widehat{\\cal G}$ and $EB \\widetilde{\\otimes} EG$ are appropriate twisted tensor products determined by the perturbation lemma: this last homotopy equivalence is obtained by propagating over the previous one, the perturbation to be applied to the differential of $B \\otimes {\\cal G}$  to obtain the differential of $B \\otimes_t {\\cal G}$. The homotopy equivalence so obtained is called in `Kenzo` the *right Serre homotopy equivalence*.\n",
-    "\n",
-    "### Assembling the puzzle\n",
-    "\n",
-    "Let us build now the so-called *left Serre homotopy equivalence*, \n",
-    "$$\n",
-    "\\begin{aligned}\n",
-    "  & \\qquad B\\times_\\tau{\\cal G} &    \\cr\n",
-    " \\swarrow\\nearrow & & \\searrow\\nwarrow \\qquad\\cr\n",
-    "B\\times_\\tau {\\cal G}  & & B\\otimes_t {\\cal G} \\cr\n",
-    "\\end{aligned}\n",
-    "$$\n",
-    "where the left reduction is the trivial one and the right reduction is the Brown reduction. We may then compose both Serre homotopy equivalences to obtain what we were looking for: \n",
-    "$$\n",
-    "\\begin{aligned}\n",
-    "  & \\qquad B\\times_\\tau {\\cal G}  & & &\\widehat{B}\\otimes_t\\widehat{\\cal G} \\qquad& & \\cr\n",
-    " \\rho_1 \\swarrow\\nearrow  & & \\searrow\\nwarrow \\rho_2\\qquad &\\qquad\\rho'_1\\swarrow\\nearrow & & \\searrow\\nwarrow\\rho'_2 & \\cr\n",
-    "B\\times_\\tau {\\cal G}  & &B\\otimes_t {\\cal G}\\quad &\\quad B\\otimes_t {\\cal G} & &EB \\otimes_t EG \\cr\n",
-    "\\end{aligned}\n",
-    "$$\n",
-    "\n",
-    "## The functions for the Serre spectral sequence\n",
-    "\n",
-    "The following functions are given for information purpose.\n",
-    "\n",
-    "`fibration-dtau-d-intr` *fibration* *[Function]*\n",
-    "> Build the lisp function corresponding to the difference $d_\\tau - d$, where $d$ is the differential in $B \\times {\\cal G}$ and $d_\\tau$ the differential in $B \\times_\\tau {\\cal G}$. This is an internal function and is used in the following one.\n",
-    "\n",
-    "`fibration-dtau-d` *fibration* *[Function]*\n",
-    "> Build the morphism $d_\\tau-d$, which is the perturbation morphism to be added to the differential  $d$ of $B \\times {\\cal G}$  to obtain  $d_\\tau$, the differential in $B \\times_\\tau {\\cal G}$. We recall that both simplicial sets have the same simplices. The source and the target of this morphism is the total space $B \\times_\\tau {\\cal G}$ and the degree is $-1$.\n",
-    "\n",
-    "`Brown-reduction` *fibration* *[Function]*\n",
-    "> Return two values: a) the Brown reduction and b) the  perturbation to be applied to the differential of the tensor product $B \\otimes {\\cal G}$  to obtain the differential of the twisted tensor product $B \\otimes_t {\\cal G}$.\n",
-    "\n",
-    "`left-Serre-efhm` *fibration* *[Function]*\n",
-    "> Build the left Serre homotopy equivalence from the argument *fibration*.\n",
-    "\n",
-    "`right-Serre-efhm` *fibration* *[Function]*\n",
-    "> Build the right Serre homotopy equivalence from the argument *fibration*.\n",
-    "\n",
-    "## Searching homology for fibration total spaces\n",
-    "\n",
-    "The comment list of a `Kenzo` object which is the total space of a fibration has the form `(fibration-total` *fibration*`)`. The `search-efhm` method applied to a simplicial set having this kind of comment list, builds the composition of the left and right Serre homotopy equivalences. The right one needs the homotopy equivalences attached respectively to the base and  fiber spaces. This may involve a recursive call of `search-efhm`. If the base space or the fiber space are locally effective, the total space is locally effective and the method cannot compute the homology.\n",
-    "```commonlisp\n",
-    "(defmethod SEARCH-EFHM (smst (orgn (eql 'fibration-total)))\n",
-    "  (declare\n",
-    "     (type simplicial-set smst))\n",
-    "  (the homotopy-equivalence\n",
-    "     (fibration-total-efhm (second (orgn smst)))))\n",
-    "\n",
-    "(defun FIBRATION-TOTAL-EFHM (fibration)\n",
-    "  (declare (type fibration fibration))\n",
-    "  (the homotopy-equivalence\n",
-    "       (cmps (left-serre-efhm fibration)\n",
-    "             (right-serre-efhm fibration))))\n",
-    "```\n",
-    "\n",
-    "### Examples\n",
-    "\n",
-    "We begin by some examples similar to examples that we have seen in the fibrations chapter. For the user, the delicate point is to write in Lisp a correct twisting operator. There is no check in this version of `Kenzo` for the coherency of the twisting operator. In the first example we define a fibration $\\tau: S^2 \\rightarrow K(\\mathbb{Z},1)$ with $\\tau(s2)= (2)$, then we build the total space of the fibration, namely $P^3\\mathbb{R}$, and we compute some known homology groups."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 2,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K1 Simplicial-Set]"
-      ]
-     },
-     "execution_count": 2,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def sph2 (sphere 2))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 3,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K6 Abelian-Simplicial-Group]"
-      ]
-     },
-     "execution_count": 3,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def kz1 (k-z-1)) "
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 4,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K18 Fibration K1 -> K6]"
-      ]
-     },
-     "execution_count": 4,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def tw2 (build-smmr\n",
-    "          :sorc sph2\n",
-    "          :trgt kz1\n",
-    "          :degr -1\n",
-    "          :sintr #'(lambda (dmns gmsm)\n",
-    "                           (declare (ignore gmsm))\n",
-    "                        (unless (= dmns 2)\n",
-    "                                (error \"Dimension error for \n",
-    "                                        the twisting operator S2-->KZ1\"))\n",
-    "                        (absm 0 (list 2)))\n",
-    "          :orgn '(s2-tw-kz1)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 5,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "<AbSm - (2)>"
-      ]
-     },
-     "execution_count": 5,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? tw2 2 's2)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 6,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "SIMPLE-ERROR: \n",
-      "Dimension error for \n",
-      "                                        the twisting operator S2-->KZ1\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 6,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? tw2 0 '*)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 7,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K24 Simplicial-Set]"
-      ]
-     },
-     "execution_count": 7,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def p3r (fibration-total tw2))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 8,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "Computing boundary-matrix in dimension 0.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 30m 3s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 0) :\n",
-      "<TnPr * *> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 1.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 30m 3s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 1) :\n",
-      "<TnPr * S1> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 0 :\n",
-      "\n",
-      "\n",
-      "Component Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 30m 3s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 1.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 30m 3s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 1) :\n",
-      "<TnPr * S1> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 2.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 30m 3s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 2) :\n",
-      "<TnPr S2 *> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 1 :\n",
-      "\n",
-      "\n",
-      "Component Z/2Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 30m 3s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 2.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 30m 3s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 2) :\n",
-      "<TnPr S2 *> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 3.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 30m 3s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 3) :\n",
-      "<TnPr S2 S1> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 2 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 30m 3s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 3.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 30m 3s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 3) :\n",
-      "<TnPr S2 S1> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 4.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 3 :\n",
-      "\n",
-      "\n",
-      "Component Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 30m 3s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 4.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 5.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 4 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 30m 3s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 5.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 6.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 5 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 30m 3s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 6.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 7.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 6 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 30m 3s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 7.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 8.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 7 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 30m 3s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 8.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 9.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 8 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 30m 3s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 9.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 10.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 9 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 30m 3s.\n",
-      "\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 8,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(homology p3r 0 10)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Let us do the same kind of computations with $\\tau(s2)= (5)$ and $\\tau(s2)= (17)$."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 9,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K110 Fibration K1 -> K6]"
-      ]
-     },
-     "execution_count": 9,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def tw5 (build-smmr\n",
-    "             :sorc sph2\n",
-    "             :trgt kz1\n",
-    "             :degr -1\n",
-    "             :sintr #'(lambda (dmns gmsm)\n",
-    "                              (declare (ignore dmns gmsm))\n",
-    "                        (absm 0 (list 5)))\n",
-    "             :orgn '(s2-tw-kz1-5))) "
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 10,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K111 Simplicial-Set]"
-      ]
-     },
-     "execution_count": 10,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def total-5 (fibration-total tw5))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 11,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "Computing boundary-matrix in dimension 0.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 30m 3s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 0) :\n",
-      "<TnPr * *> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 1.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 30m 3s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 1) :\n",
-      "<TnPr * S1> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 0 :\n",
-      "\n",
-      "\n",
-      "Component Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 30m 3s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 1.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 30m 3s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 1) :\n",
-      "<TnPr * S1> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 2.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 30m 3s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 2) :\n",
-      "<TnPr S2 *> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 1 :\n",
-      "\n",
-      "\n",
-      "Component Z/5Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 30m 3s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 2.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 30m 3s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 2) :\n",
-      "<TnPr S2 *> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 3.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 30m 3s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 3) :\n",
-      "<TnPr S2 S1> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 2 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 30m 3s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 3.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 30m 3s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 3) :\n",
-      "<TnPr S2 S1> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 4.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 3 :\n",
-      "\n",
-      "\n",
-      "Component Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 30m 3s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 4.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 5.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 4 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 30m 3s.\n",
-      "\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 11,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(homology total-5 0 5)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 12,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K165 Fibration K1 -> K6]"
-      ]
-     },
-     "execution_count": 12,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def tw17 (build-smmr\n",
-    "             :sorc sph2\n",
-    "             :trgt kz1\n",
-    "             :degr -1\n",
-    "             :sintr #'(lambda (dmns gmsm)\n",
-    "                              (declare (ignore dmns gmsm))\n",
-    "                        (absm 0 (list 17)))\n",
-    "             :orgn '(s2-tw-kz1-17)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 13,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K166 Simplicial-Set]"
-      ]
-     },
-     "execution_count": 13,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def total-17 (fibration-total tw17)) "
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 14,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "Computing boundary-matrix in dimension 0.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 30m 3s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 0) :\n",
-      "<TnPr * *> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 1.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 30m 3s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 1) :\n",
-      "<TnPr * S1> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 0 :\n",
-      "\n",
-      "\n",
-      "Component Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 30m 3s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 1.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 30m 3s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 1) :\n",
-      "<TnPr * S1> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 2.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 30m 3s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 2) :\n",
-      "<TnPr S2 *> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 1 :\n",
-      "\n",
-      "\n",
-      "Component Z/17Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 30m 3s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 2.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 30m 3s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 2) :\n",
-      "<TnPr S2 *> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 3.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 30m 3s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 3) :\n",
-      "<TnPr S2 S1> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 2 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 30m 3s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 3.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 30m 3s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 3) :\n",
-      "<TnPr S2 S1> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 4.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 3 :\n",
-      "\n",
-      "\n",
-      "Component Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 30m 3s.\n",
-      "\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 14,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(homology total-17 0 4)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Using the last total space (`total-17`), it is instructive to enter in the details of the resulting homotopy equivalence that the system builds to compute the homology groups. First, the function `echcm` selects the **effective** chain complex of the homotopy equivalence, value of the slot `efhm` of the simplicial set `total-17`, and we may print some basis of this chain complex. In fact, all basis in dimension above 3 are null. The presence of the symbol `S1` is due to the fact that the effective chain complex used for the homology of $K(\\mathbb{Z},1)$ is the circle (see the classifying spaces chapter)."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 15,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K205 Chain-Complex]"
-      ]
-     },
-     "execution_count": 15,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def echcm (echcm total-17))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 16,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "(<TnPr * *>) \n",
-      "(<TnPr * S1>) \n",
-      "(<TnPr S2 *>) \n",
-      "(<TnPr S2 S1>) \n",
-      "NIL \n",
-      "NIL "
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 16,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(dotimes (i 6) (print (basis echcm i)))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "The resulting homotopy equivalence built by the system, may be summarized by the diagram:\n",
-    "$$\n",
-    "\\begin{aligned}\n",
-    "  &\\qquad\\qquad \\widehat{S^2\\times_\\tau K(\\mathbb{Z},1)} &    \\cr\n",
-    " f\\swarrow\\nearrow & & \\searrow\\nwarrow g \\qquad\\qquad \\cr\n",
-    "S^2\\times_\\tau K(\\mathbb{Z},1) & & [K205\\, Chain\\, Complex] \\cr\n",
-    "\\end{aligned}\n",
-    "$$\n",
-    "where *f* and *g* are respectively the *descending* and *ascending* morphisms of the left and right reductions of the homotopy equivalence. We recall that these morphisms are obtained respectively by the functions `lf` and `rg`. We may\n",
-    "compose these morphisms to create a morphism `fg` from $[K205]$ to $S^2\\times_\\tau K(\\mathbb{Z},1)$ and see how it acts on the basis  elements in dimension 1 and 2:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 17,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K220 Morphism (degree 0): K205 -> K166]"
-      ]
-     },
-     "execution_count": 17,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def fg (cmps (lf (efhm total-17)) (rg (efhm total-17))))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 18,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "<TnPr * S1>"
-      ]
-     },
-     "execution_count": 18,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def gen1 (first (basis echcm 1)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 19,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 1}\n",
-       "<-1 * <CrPr 0 * - (1)>>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 19,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? fg 1 gen1)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 20,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "<TnPr S2 *>"
-      ]
-     },
-     "execution_count": 20,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def gen2 (first (basis echcm 2)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 21,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 2}\n",
-       "<-1 * <CrPr - S2 1-0 NIL>>\n",
-       "<-1 * <CrPr 1-0 * - (1 1)>>\n",
-       "<-1 * <CrPr 1-0 * - (1 2)>>\n",
-       "<-1 * <CrPr 1-0 * - (1 3)>>\n",
-       "<-1 * <CrPr 1-0 * - (1 4)>>\n",
-       "<-1 * <CrPr 1-0 * - (1 5)>>\n",
-       "<-1 * <CrPr 1-0 * - (1 6)>>\n",
-       "<-1 * <CrPr 1-0 * - (1 7)>>\n",
-       "<-1 * <CrPr 1-0 * - (1 8)>>\n",
-       "<-1 * <CrPr 1-0 * - (1 9)>>\n",
-       "... ...\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 21,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def fg-gen2 (? fg 2 gen2))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "The boundary of this combination in $S^2\\times_\\tau K(\\mathbb{Z},1)$ is"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 22,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 1}\n",
-       "<-17 * <CrPr 0 * - (1)>>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 22,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? total-17 *)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "to which corresponds in the effective chain complex, the boundary of the basis element in dimension 2, $gen2=s2 \\otimes *$:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 23,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 1}\n",
-       "<17 * <TnPr * S1>>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 23,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? echcm 2 gen2)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "The printing of the 3 faces of the 17 simplices of the combination `fg-gen2` shows the geometrical organisation of the twisted product:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 24,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "<AbSm 0 <CrPr - * - NIL>> \n",
-      "<AbSm 0 <CrPr - * - NIL>> \n",
-      "<AbSm - <CrPr 0 * - (17)>> \n",
-      "\n",
-      "<AbSm - <CrPr 0 * - (1)>> \n",
-      "<AbSm - <CrPr 0 * - (2)>> \n",
-      "<AbSm - <CrPr 0 * - (1)>> \n",
-      "\n",
-      "<AbSm - <CrPr 0 * - (2)>> \n",
-      "<AbSm - <CrPr 0 * - (3)>> \n",
-      "<AbSm - <CrPr 0 * - (1)>> \n",
-      "\n",
-      "<AbSm - <CrPr 0 * - (3)>> \n",
-      "<AbSm - <CrPr 0 * - (4)>> \n",
-      "<AbSm - <CrPr 0 * - (1)>> \n",
-      "\n",
-      "<AbSm - <CrPr 0 * - (4)>> \n",
-      "<AbSm - <CrPr 0 * - (5)>> \n",
-      "<AbSm - <CrPr 0 * - (1)>> \n",
-      "\n",
-      "<AbSm - <CrPr 0 * - (5)>> \n",
-      "<AbSm - <CrPr 0 * - (6)>> \n",
-      "<AbSm - <CrPr 0 * - (1)>> \n",
-      "\n",
-      "<AbSm - <CrPr 0 * - (6)>> \n",
-      "<AbSm - <CrPr 0 * - (7)>> \n",
-      "<AbSm - <CrPr 0 * - (1)>> \n",
-      "\n",
-      "<AbSm - <CrPr 0 * - (7)>> \n",
-      "<AbSm - <CrPr 0 * - (8)>> \n",
-      "<AbSm - <CrPr 0 * - (1)>> \n",
-      "\n",
-      "<AbSm - <CrPr 0 * - (8)>> \n",
-      "<AbSm - <CrPr 0 * - (9)>> \n",
-      "<AbSm - <CrPr 0 * - (1)>> \n",
-      "\n",
-      "<AbSm - <CrPr 0 * - (9)>> \n",
-      "<AbSm - <CrPr 0 * - (10)>> \n",
-      "<AbSm - <CrPr 0 * - (1)>> \n",
-      "\n",
-      "<AbSm - <CrPr 0 * - (10)>> \n",
-      "<AbSm - <CrPr 0 * - (11)>> \n",
-      "<AbSm - <CrPr 0 * - (1)>> \n",
-      "\n",
-      "<AbSm - <CrPr 0 * - (11)>> \n",
-      "<AbSm - <CrPr 0 * - (12)>> \n",
-      "<AbSm - <CrPr 0 * - (1)>> \n",
-      "\n",
-      "<AbSm - <CrPr 0 * - (12)>> \n",
-      "<AbSm - <CrPr 0 * - (13)>> \n",
-      "<AbSm - <CrPr 0 * - (1)>> \n",
-      "\n",
-      "<AbSm - <CrPr 0 * - (13)>> \n",
-      "<AbSm - <CrPr 0 * - (14)>> \n",
-      "<AbSm - <CrPr 0 * - (1)>> \n",
-      "\n",
-      "<AbSm - <CrPr 0 * - (14)>> \n",
-      "<AbSm - <CrPr 0 * - (15)>> \n",
-      "<AbSm - <CrPr 0 * - (1)>> \n",
-      "\n",
-      "<AbSm - <CrPr 0 * - (15)>> \n",
-      "<AbSm - <CrPr 0 * - (16)>> \n",
-      "<AbSm - <CrPr 0 * - (1)>> \n",
-      "\n",
-      "<AbSm - <CrPr 0 * - (16)>> \n",
-      "<AbSm - <CrPr 0 * - (17)>> \n",
-      "<AbSm - <CrPr 0 * - (1)>> \n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 24,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(dolist(iterm (cmbn-list fg-gen2))\n",
-    "       (dotimes (i 3)(print (face total-17 i 2 (gnrt iterm)))) \n",
-    "                     (terpri))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "We have seen that for the special case of loop spaces, there is a canonical fibration and that the function `twisted-crts-prdc` builds the total space $X \\times_\\tau \\Omega X$."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 25,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K221 Simplicial-Set]"
-      ]
-     },
-     "execution_count": 25,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def sph3 (sphere 3))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 26,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K243 Simplicial-Set]"
-      ]
-     },
-     "execution_count": 26,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def tw3 (twisted-crts-prdc sph3))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 27,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "<AbSm - <CrPr 1-0 * - <<Loop[S3]>>>>"
-      ]
-     },
-     "execution_count": 27,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(face tw3 3 3 (crpr 0 's3 7 +null-loop+))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "It is of course possible to study, any other fibration, provided one defines a correct fibration $\\tau$. In the following example the fibration $\\tau: S^3 \\longrightarrow \\Omega S^3$, is defined by $\\tau(s3)= s3^{-2},$ where $s3^{-2}$ is a word in the Kan simplicial version of the first loop space of $S^3$. In Kenzo, this object is created by the statement:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 28,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "<AbSm - <<Loop[S3\\-2]>>>"
-      ]
-     },
-     "execution_count": 28,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(absm 0 (loop3 0 's3 -2))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 29,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K248 Fibration K221 -> K226]"
-      ]
-     },
-     "execution_count": 29,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def tws3 (build-smmr   :sorc sph3\n",
-    "                         :trgt (loop-space sph3)\n",
-    "                         :degr -1\n",
-    "                         :sintr #'(lambda (dmns gmsm) (declare (ignore dmns gmsm)) (absm 0 (loop3 0 's3 -2)))\n",
-    "                         :orgn '(s3-tw-lps3)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 30,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K249 Simplicial-Set]"
-      ]
-     },
-     "execution_count": 30,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def total (fibration-total tws3))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 31,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "Computing boundary-matrix in dimension 0.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 30m 3s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 0) :\n",
-      "<TnPr * <<AlLp>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 1.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 0 :\n",
-      "\n",
-      "\n",
-      "Component Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 30m 3s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 1.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 2.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 30m 3s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 2) :\n",
-      "<TnPr * <<AlLp[2 S3]>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 1 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 30m 3s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 2.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 30m 3s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 2) :\n",
-      "<TnPr * <<AlLp[2 S3]>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 3.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 30m 3s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 3) :\n",
-      "<TnPr S3 <<AlLp>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 2 :\n",
-      "\n",
-      "\n",
-      "Component Z/2Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 30m 3s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 3.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 30m 3s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 3) :\n",
-      "<TnPr S3 <<AlLp>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 4.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 30m 3s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 4) :\n",
-      "<TnPr * <<AlLp[2 S3][2 S3]>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 3 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 30m 3s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 4.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 30m 3s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 4) :\n",
-      "<TnPr * <<AlLp[2 S3][2 S3]>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 5.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 30m 3s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 5) :\n",
-      "<TnPr S3 <<AlLp[2 S3]>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 4 :\n",
-      "\n",
-      "\n",
-      "Component Z/2Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 30m 3s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 5.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 30m 3s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 5) :\n",
-      "<TnPr S3 <<AlLp[2 S3]>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 6.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 30m 3s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 6) :\n",
-      "<TnPr * <<AlLp[2 S3][2 S3][2 S3]>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 5 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 30m 3s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 6.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 30m 3s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 6) :\n",
-      "<TnPr * <<AlLp[2 S3][2 S3][2 S3]>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 7.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 30m 3s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 7) :\n",
-      "<TnPr S3 <<AlLp[2 S3][2 S3]>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 6 :\n",
-      "\n",
-      "\n",
-      "Component Z/2Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 30m 3s.\n",
-      "\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 31,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(homology total 0 7)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "### Lisp files concerned in this chapter\n",
-    "\n",
-    "`serre.lisp`, `searching-homology.lisp`."
-   ]
-  }
- ],
- "metadata": {
-  "kernelspec": {
-   "display_name": "SBCL Lisp",
-   "language": "lisp",
-   "name": "lisp"
-  },
-  "language_info": {
-   "codemirror_mode": "text/x-common-lisp",
-   "mimetype": "text/x-common-lisp",
-   "name": "common-lisp",
-   "pygments_lexer": "common-lisp",
-   "version": "X3J13"
-  }
- },
- "nbformat": 4,
- "nbformat_minor": 1
-}
diff --git a/examples/19_Simplicial_groups_fibration.ipynb b/examples/19_Simplicial_groups_fibration.ipynb
deleted file mode 100644
index f09ab63..0000000
--- a/examples/19_Simplicial_groups_fibration.ipynb
+++ /dev/null
@@ -1,2475 +0,0 @@
-{
- "cells": [
-  {
-   "cell_type": "code",
-   "execution_count": 1,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "To load \"kenzo\":\n",
-      "  Load 1 ASDF system:\n",
-      "    kenzo\n",
-      "; Loading \"kenzo\"\n",
-      "\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "#<PACKAGE \"CAT\">"
-      ]
-     },
-     "execution_count": 1,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(ql:quickload \"kenzo\")\n",
-    "(in-package :cat)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "# Simplicial groups fibrations\n",
-    "\n",
-    "## Introduction\n",
-    "\n",
-    "This chapter is analogous to the  Loop spaces fibrations chapter where algorithms have been specially designed for loop spaces. In the present case, we have at our disposal all the tools developped for the fibrations. Let ${\\cal G}$ be a 0-reduced simplicial group and $\\bar{\\cal W}{\\cal G}$, its classifying space.  We recall that if ${\\cal G}$ is an Abelian simplicial group then $\\bar{\\cal W}{\\cal G}$ is also an Abelian simplicial group, otherwise if ${\\cal G}$ is non-Abelian, then $\\bar{\\cal W}{\\cal G}$ is only a simplicial set. The software `Kenzo` implements the **canonical** twisted cartesian product of $\\bar{\\cal W}{\\cal G}$ by  ${\\cal G}$, denoted ${\\cal WG}=\\bar{\\cal W}{\\cal G} \\times_\\tau  {\\cal G}$. The *canonical fibration*\n",
-    "$$ {\\cal G}\\quad \\hookrightarrow\\quad  {\\cal WG} \\hskip 1.2em \\longrightarrow \\hskip -1.2em \\longrightarrow  \n",
-    "   \\quad\\bar{\\cal W}{\\cal G},$$\n",
-    "is defined by the following twisting operator:\n",
-    "$$\\tau[(g_{n-1}, g_{n-2}, \\ldots, g_0)]= g_{n-1}.$$\n",
-    "The total space ${\\cal WG}=\\bar{\\cal W}{\\cal G} \\times_\\tau  {\\cal G}$ is acyclic.\n",
-    "\n",
-    "## The function for the canonical fibration\n",
-    "\n",
-    "`smgr-fibration` *smgr* *[Function]*\n",
-    "> Build the simplicial morphism of degree -1 corresponding to the canonical fibration. The source is the classifying space of the simplicial group *smgr* (built internally by the function), the target is *smgr* and the internal lisp function value of the slot `:sintr` implements\n",
-    "the twisting operator. The returned object is a fibration.\n",
-    "\n",
-    "### Examples\n",
-    "\n",
-    "Let us take the Abelian simplicial group $K(\\mathbb{Z},1)$ and  build the fibration morphism."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 2,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K1 Abelian-Simplicial-Group]"
-      ]
-     },
-     "execution_count": 2,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def k1 (k-z-1))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 3,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K25 Fibration K13 -> K1]"
-      ]
-     },
-     "execution_count": 3,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def tw (smgr-fibration k1))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "If needed, the classifying space may be found in the slot `:sorc` of the fibration:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 4,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K13 Abelian-Simplicial-Group]"
-      ]
-     },
-     "execution_count": 4,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def k2 (sorc tw))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "We may build now the total space of the fibration. We see that `Kenzo` returns a Kan simplicial set because the base and fiber spaces are also of Kan type. Then we test the face and differential operator upon a simplex of degree 4 of the total space `tt`."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 5,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K31 Kan-Simplicial-Set]"
-      ]
-     },
-     "execution_count": 5,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def tt (fibration-total tw)) "
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 6,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "<CrPr - <<GBar<- (10 11 12)><- (20 21)><- (30)><- NIL>>> - (2 4 6 8)>"
-      ]
-     },
-     "execution_count": 6,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def gmsm (crpr 0 (gbar 4 0 '(10 11 12) 0 '(20 21) 0 '(30) 0 '())\n",
-    "                0 '(2 4 6 8)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 7,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "<AbSm - <CrPr - <<GBar<- (11 12)><- (21)><- NIL>>> - (4 6 8)>> \n",
-      "<AbSm - <CrPr - <<GBar<- (21 12)><- (41)><- NIL>>> - (6 6 8)>> \n",
-      "<AbSm - <CrPr - <<GBar<- (10 23)><- (50)><- NIL>>> - (2 10 8)>> \n",
-      "<AbSm - <CrPr - <<GBar<- (30 32)><- (30)><- NIL>>> - (2 4 14)>> \n",
-      "<AbSm - <CrPr - <<GBar<- (20 21)><- (30)><- NIL>>> - (12 15 18)>> "
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 7,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(dotimes (i 5) (print (face tt i 4 gmsm)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 8,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 3}\n",
-       "<1 * <CrPr - <<GBar<- (10 23)><- (50)><- NIL>>> - (2 10 8)>>\n",
-       "<1 * <CrPr - <<GBar<- (11 12)><- (21)><- NIL>>> - (4 6 8)>>\n",
-       "<1 * <CrPr - <<GBar<- (20 21)><- (30)><- NIL>>> - (12 15 18)>>\n",
-       "<-1 * <CrPr - <<GBar<- (21 12)><- (41)><- NIL>>> - (6 6 8)>>\n",
-       "<-1 * <CrPr - <<GBar<- (30 32)><- (30)><- NIL>>> - (2 4 14)>>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 8,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? tt 4 gmsm)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 9,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 2}\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 9,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? tt *)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "We may also build the Ronald Brown reduction and test the differential upon a simplex belonging to the twisted tensor product (slot `:bcc` of the reduction)."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 10,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K59 Reduction K31 => K57]"
-      ]
-     },
-     "execution_count": 10,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def br (brown-reduction tw))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 11,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K57 Chain-Complex]"
-      ]
-     },
-     "execution_count": 11,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def tw-pr (bcc br))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 12,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 3}\n",
-       "<-1 * <TnPr <<GBar>> (111 11000 100000)>>\n",
-       "<1 * <TnPr <<GBar>> (111 101000 10000)>>\n",
-       "<1 * <TnPr <<GBar>> (11011 100 100000)>>\n",
-       "<-1 * <TnPr <<GBar>> (11011 100000 100)>>\n",
-       "<-1 * <TnPr <<GBar>> (101001 110 10000)>>\n",
-       "<1 * <TnPr <<GBar>> (101001 10010 100)>>\n",
-       "<1 * <TnPr <<GBar<- (100000)><- NIL>>> (100)>>\n",
-       "<1 * <TnPr <<GBar<- (1 110)><- (101000)><- NIL>>> NIL>>\n",
-       "<1 * <TnPr <<GBar<- (10 100)><- (10000)><- NIL>>> NIL>>\n",
-       "<-1 * <TnPr <<GBar<- (11 100)><- (11000)><- NIL>>> NIL>>\n",
-       "... ...\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 12,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? tw-pr 4 (tnpr 4 (gbar 4 0 '(1 10 100) 0 '(1000 10000) 0 '(100000) 0 '())\n",
-    "                           0 '()))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 13,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 2}\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 13,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? tw-pr *)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "## The essential contraction for simplicial groups fibrations\n",
-    "\n",
-    "It is known that if ${\\cal G}$ is a 0-reduced simplicial group, the space ${\\cal WG}=\\bar{\\cal W}{\\cal G} \\times_\\tau  {\\cal G}$ is contractible. So it is possible to build a reduction of this space over $\\mathbb{Z}$. This reduction depends on the important contraction\n",
-    "$$\\chi_{\\times\\tau}:  {\\bar{\\cal W}{\\cal G} \\times_\\tau  {\\cal G}} \\longrightarrow \n",
-    "                      {\\bar{\\cal W}{\\cal G} \\times_\\tau  {\\cal G}}, $$\n",
-    "defined by:\n",
-    "$$\\chi_{\\times\\tau}[(g_{n-1}, \\ldots, g_0), g_n] = (-1)^{n+1} (g_n, g_{n-1}, \\ldots, g_0, *),$$\n",
-    "where $g_n \\in {\\cal G}$, $(g_{n-1}, \\ldots, g_0)$ is a gbar in $\\bar{\\cal W}{\\cal G}$,  and\n",
-    "$*$ is the neutral element  of ${\\cal G}_{n+1}$ (in fact the n-th degeneracy of the base point of\n",
-    "${\\cal G}$). We recall also that $\\chi_{\\times\\tau}$\n",
-    "is a homotopy operator (degree: +1) satisfying the relation\n",
-    "$$d \\circ \\chi_{\\times\\tau} + \\chi_{\\times\\tau} \\circ d =1.$$\n",
-    "In addition, if we consider the Brown reduction\n",
-    "$$\n",
-    "\\begin{aligned}\n",
-    "{\\bar{\\cal W}{\\cal G} \\times_\\tau  {\\cal G}} & \\qquad\\stackrel{h}{\\longrightarrow} & \n",
-    " {}^s{\\bar{\\cal W}{\\cal G} \\times_\\tau  {\\cal G}} \\cr\n",
-    " {\\scriptstyle f} \\downarrow \\uparrow {\\scriptstyle g}  \\cr\n",
-    " {\\bar{\\cal W}{\\cal G} \\otimes_\\tau  {\\cal G}} \\cr\n",
-    "\\end{aligned}\n",
-    "$$\n",
-    "there is an induced contraction \n",
-    "$$\\chi_{\\otimes t}:  {\\bar{\\cal W}{\\cal G} \\otimes_\\tau  {\\cal G}} \\longrightarrow \n",
-    "                     {\\bar{\\cal W}{\\cal G} \\otimes_\\tau  {\\cal G}}, $$\n",
-    "defined by $\\chi_{\\otimes t}= f \\circ \\chi_{\\times\\tau} \\circ g$.\n",
-    "This implies that the twisted tensor product is also contractible over $\\mathbb{Z}$.\n",
-    "\n",
-    "The two functions of `Kenzo` for this construction are:\n",
-    "\n",
-    "`smgr-crts-contraction` *smgr* *[Function]*\n",
-    "> Return the homotopy morphism corresponding to the contraction $\\chi_{\\times\\tau}$. The lisp definition is:\n",
-    "```commonlisp\n",
-    "                     (defun SMGR-CRTS-CONTRACTION (smgr)\n",
-    "                         (the morphism\n",
-    "                           (build-mrph\n",
-    "                            :sorc (fibration-total (smgr-fibration smgr))\n",
-    "                            :trgt (fibration-total (smgr-fibration smgr))\n",
-    "                            :degr +1\n",
-    "                            :intr (smgr-crts-contraction-intr (bspn smgr))\n",
-    "                            :strt :gnrt\n",
-    "                            :orgn `(smgr-crts-contraction ,smgr))))\n",
-    "```\n",
-    "At execution time, the work is essentialy done by the function put in the slot `:intr`. This function is itself built by the internal function `smgr-crts-contraction-intr` requiring as argument the base point of the  simplicial group.\n",
-    "\n",
-    "`smgr-tnpr-contraction` *smgr* *[Function]*\n",
-    "> Return the induced morphism $\\chi_{\\otimes t}= f \\circ \\chi_{\\times\\tau} \\circ g$, where $f$ and $g$ are built by the Brown reduction. The lisp definition is:\n",
-    "```commonlisp\n",
-    "                     (defun SMGR-TNPR-CONTRACTION (smgr \n",
-    "                         &aux (fibration (smgr-fibration smgr))\n",
-    "                              (brown (brown-reduction fibration))\n",
-    "                              (f (f brown))\n",
-    "                              (g (g brown))\n",
-    "                              (chi (smgr-crts-contraction smgr)))\n",
-    "                           (the morphism\n",
-    "                              (i-cmps f chi g)))\n",
-    "```\n",
-    "\n",
-    "### Examples\n",
-    "\n",
-    "It is an instructive exercise to build and check the reduction over $\\mathbb{Z}$ of the space\n",
-    "${\\cal WG}=\\bar{\\cal W}{\\cal G} \\times_\\tau  {\\cal G}$ as we did in the loop spaces fibrations chapter. \n",
-    "$$\n",
-    "\\begin{aligned}\n",
-    "\\bar{\\cal W}{\\cal G} \\times_\\tau  {\\cal G} & \\qquad\\stackrel{\\chi_{\\times t}}{\\longrightarrow} &\n",
-    "{}^s\\bar{\\cal W}{\\cal G} \\times_\\tau  {\\cal G} \\cr\n",
-    " {\\scriptstyle aug} \\downarrow \\uparrow {\\scriptstyle coaug}  \\cr\n",
-    " {{\\cal C}_*(\\mathbb{Z})} \\quad& & \\cr\n",
-    "\\end{aligned}\n",
-    "$$\n",
-    "In this case, the two homomorphisms $f$ and $g$ of the reduction, are respectively the *augmentation* and *coaugmentation* morphisms. We define both morphisms according to our previous example based on $K(\\mathbb{Z},1)$. The unit chain complex corresponding to $\\mathbb{Z}$ is built by the function `z-chcm`; its unique generator in degree 0 is `:z-gnrt`. "
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 14,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K1 Abelian-Simplicial-Group]"
-      ]
-     },
-     "execution_count": 14,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def k1 (k-z-1)) "
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 15,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K25 Fibration K13 -> K1]"
-      ]
-     },
-     "execution_count": 15,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def tw (smgr-fibration k1))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 16,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K31 Kan-Simplicial-Set]"
-      ]
-     },
-     "execution_count": 16,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def tt (fibration-total tw)) "
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "The base point of the total space, needed for the coaugmentation, may be obtained by either of the following statements:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 17,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "<CrPr - <<GBar>> - NIL>"
-      ]
-     },
-     "execution_count": 17,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(bspn tt)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 18,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "<CrPr - <<GBar>> - NIL>"
-      ]
-     },
-     "execution_count": 18,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(crpr 0 +null-gbar+ 0 nil)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 19,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K62 Cohomology-Class on K31 of degree 0]"
-      ]
-     },
-     "execution_count": 19,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def aug (build-mrph\n",
-    "              :sorc (fibration-total (smgr-fibration (k-z-1))) \n",
-    "              :trgt (z-chcm) \n",
-    "              :degr 0\n",
-    "              :intr #'(lambda (degr gnrt)\n",
-    "                              (declare (ignore gnrt))\n",
-    "                       (if (zerop degr)\n",
-    "                           (term-cmbn 0 1 :z-gnrt)\n",
-    "                           (zero-cmbn degr)))\n",
-    "              :strt :gnrt \n",
-    "              :orgn '(aug-fibr-tot-smgr-fibr-k-z-1)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 20,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "SIMPLE-STYLE-WARNING: \n",
-      "  undefined function: :TYPE\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "[K63 Morphism (degree 0): K60 -> K31]"
-      ]
-     },
-     "execution_count": 20,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def coaug (build-mrph\n",
-    "              :sorc (z-chcm) \n",
-    "              :trgt (fibration-total (smgr-fibration (k-z-1))) \n",
-    "              :degr 0\n",
-    "              :intr #'(lambda (degr gnrt)\n",
-    "                              (declare (ignore gnrt))\n",
-    "                         (if (zerop degr)\n",
-    "                             (term-cmbn 0 1 (crpr 0 +null-gbar+ 0 '()))\n",
-    "                             (zero-cmbn degr)))\n",
-    "              :strt :gnrt\n",
-    "              :orgn '(coaug-fibr-tot-smgr-fibr-k-z-1)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 21,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 0}\n",
-       "<1 * Z-GNRT>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 21,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? aug 0 (bspn tt))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 22,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 0}\n",
-       "<1 * <CrPr - <<GBar>> - NIL>>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 22,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? coaug 0 :z-gnrt)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 23,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K64 Morphism (degree 1): K31 -> K31]"
-      ]
-     },
-     "execution_count": 23,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def chi-x-tau (smgr-crts-contraction (k-z-1)))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Let us apply the contraction morphism upon some simplices:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 24,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 0}\n",
-       "<1 * <CrPr - <<GBar>> - NIL>>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 24,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(setf *tc* (cmbn 0 1 (crpr 0 +null-gbar+ 0 '())))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 25,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 1}\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 25,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? chi-x-tau *)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 26,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 4}\n",
-       "<1 * <CrPr - <<GBar<- (10 11 12)><- (20 21)><- (30)><- NIL>>> - (2 4 6 8)>>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 26,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(setf *tc* (cmbn 4 1 (crpr 0 (gbar 4 0 '(10 11 12) 0 '(20 21) 0 '(30) 0 '())\n",
-    "                           0 '(2 4 6 8))))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 27,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 5}\n",
-       "<-1 * <CrPr - <<GBar<- (2 4 6 8)><- (10 11 12)><- (20 21)><- (30)><- NIL>>> 4-3-2-1-0 NIL>>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 27,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? chi-x-tau *)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 28,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 3}\n",
-       "<1 * <CrPr - <<GBar<- (10 11)><- (20)><- NIL>>> - (2 4 6)>>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 28,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(setf *tc* (cmbn 3 1 (crpr 0 (gbar 3 0 '(10 11) 0 '(20) 0 '())\n",
-    "                           0 '(2 4 6))))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 29,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 4}\n",
-       "<1 * <CrPr - <<GBar<- (2 4 6)><- (10 11)><- (20)><- NIL>>> 3-2-1-0 NIL>>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 29,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? chi-x-tau *)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "We may build now the reduction over $\\mathbb{Z}$ and test it upon the various simplices above:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 30,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K65 Reduction K31 => K60]"
-      ]
-     },
-     "execution_count": 30,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def rdct (build-rdct :f aug \n",
-    "                      :g coaug \n",
-    "                      :h chi-x-tau \n",
-    "                      :orgn '(reduction-tt-z)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 31,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "---done---"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 31,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(pre-check-rdct rdct)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 32,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 0}\n",
-       "<1 * <CrPr - <<GBar>> - NIL>>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 32,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(setf *tc* (cmbn 0 1 (crpr 0 +null-gbar+ 0 '())))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 33,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 0}\n",
-       "<1 * Z-GNRT>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 33,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(setf *bc* (cmbn 0 1 :z-gnrt))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 34,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "*TC* => \n",
-      "----------------------------------------------------------------------{CMBN 0}\n",
-      "<1 * <CrPr - <<GBar>> - NIL>>\n",
-      "------------------------------------------------------------------------------\n",
-      "\n",
-      "*BC* => \n",
-      "----------------------------------------------------------------------{CMBN 0}\n",
-      "<1 * Z-GNRT>\n",
-      "------------------------------------------------------------------------------\n",
-      "\n",
-      "Checking *TDD* = 0\n",
-      "Result: \n",
-      "----------------------------------------------------------------------{CMBN -2}\n",
-      "------------------------------------------------------------------------------\n",
-      "\n",
-      "Checking *BDD* = 0\n",
-      "Result: \n",
-      "----------------------------------------------------------------------{CMBN -2}\n",
-      "------------------------------------------------------------------------------\n",
-      "\n",
-      "Checking *DF-FD* = 0\n",
-      "Result: \n",
-      "----------------------------------------------------------------------{CMBN -1}\n",
-      "------------------------------------------------------------------------------\n",
-      "\n",
-      "Checking *DG-GD* = 0\n",
-      "Result: \n",
-      "----------------------------------------------------------------------{CMBN -1}\n",
-      "------------------------------------------------------------------------------\n",
-      "\n",
-      "Checking *ID-FG* = 0\n",
-      "Result: \n",
-      "----------------------------------------------------------------------{CMBN 0}\n",
-      "------------------------------------------------------------------------------\n",
-      "\n",
-      "Checking *ID-GF-DH-HD* = 0\n",
-      "Result: \n",
-      "----------------------------------------------------------------------{CMBN 0}\n",
-      "------------------------------------------------------------------------------\n",
-      "\n",
-      "Checking *HH* = 0\n",
-      "Result: \n",
-      "----------------------------------------------------------------------{CMBN 2}\n",
-      "------------------------------------------------------------------------------\n",
-      "\n",
-      "Checking *FH* = 0\n",
-      "Result: \n",
-      "----------------------------------------------------------------------{CMBN 1}\n",
-      "------------------------------------------------------------------------------\n",
-      "\n",
-      "Checking *HG* = 0\n",
-      "Result: \n",
-      "----------------------------------------------------------------------{CMBN 1}\n",
-      "------------------------------------------------------------------------------\n",
-      "\n",
-      "---done---"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 34,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(check-rdct-no-wait)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 35,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 4}\n",
-       "<1 * <CrPr - <<GBar<- (10 11 12)><- (20 21)><- (30)><- NIL>>> - (2 4 6 8)>>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 35,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(setf *tc* (cmbn 4 1 (crpr 0 (gbar 4 0 '(10 11 12) 0 '(20 21) 0 '(30) 0 '())\n",
-    "                           0 '(2 4 6 8))))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 36,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "*TC* => \n",
-      "----------------------------------------------------------------------{CMBN 4}\n",
-      "<1 * <CrPr - <<GBar<- (10 11 12)><- (20 21)><- (30)><- NIL>>> - (2 4 6 8)>>\n",
-      "------------------------------------------------------------------------------\n",
-      "\n",
-      "*BC* => \n",
-      "----------------------------------------------------------------------{CMBN 0}\n",
-      "<1 * Z-GNRT>\n",
-      "------------------------------------------------------------------------------\n",
-      "\n",
-      "Checking *TDD* = 0\n",
-      "Result: \n",
-      "----------------------------------------------------------------------{CMBN 2}\n",
-      "------------------------------------------------------------------------------\n",
-      "\n",
-      "Checking *BDD* = 0\n",
-      "Result: \n",
-      "----------------------------------------------------------------------{CMBN -2}\n",
-      "------------------------------------------------------------------------------\n",
-      "\n",
-      "Checking *DF-FD* = 0\n",
-      "Result: \n",
-      "----------------------------------------------------------------------{CMBN 3}\n",
-      "------------------------------------------------------------------------------\n",
-      "\n",
-      "Checking *DG-GD* = 0\n",
-      "Result: \n",
-      "----------------------------------------------------------------------{CMBN -1}\n",
-      "------------------------------------------------------------------------------\n",
-      "\n",
-      "Checking *ID-FG* = 0\n",
-      "Result: \n",
-      "----------------------------------------------------------------------{CMBN 0}\n",
-      "------------------------------------------------------------------------------\n",
-      "\n",
-      "Checking *ID-GF-DH-HD* = 0\n",
-      "Result: \n",
-      "----------------------------------------------------------------------{CMBN 4}\n",
-      "------------------------------------------------------------------------------\n",
-      "\n",
-      "Checking *HH* = 0\n",
-      "Result: \n",
-      "----------------------------------------------------------------------{CMBN 6}\n",
-      "------------------------------------------------------------------------------\n",
-      "\n",
-      "Checking *FH* = 0\n",
-      "Result: \n",
-      "----------------------------------------------------------------------{CMBN 5}\n",
-      "------------------------------------------------------------------------------\n",
-      "\n",
-      "Checking *HG* = 0\n",
-      "Result: \n",
-      "----------------------------------------------------------------------{CMBN 1}\n",
-      "------------------------------------------------------------------------------\n",
-      "\n",
-      "---done---"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 36,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(check-rdct-no-wait)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 37,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 3}\n",
-       "<1 * <CrPr - <<GBar<- (10 11)><- (20)><- NIL>>> - (2 4 6)>>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 37,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(setf *tc* (cmbn 3 1 (crpr 0 (gbar 3 0 '(10 11) 0 '(20) 0 '())\n",
-    "                             0 '(2 4 6))))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 38,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "*TC* => \n",
-      "----------------------------------------------------------------------{CMBN 3}\n",
-      "<1 * <CrPr - <<GBar<- (10 11)><- (20)><- NIL>>> - (2 4 6)>>\n",
-      "------------------------------------------------------------------------------\n",
-      "\n",
-      "*BC* => \n",
-      "----------------------------------------------------------------------{CMBN 0}\n",
-      "<1 * Z-GNRT>\n",
-      "------------------------------------------------------------------------------\n",
-      "\n",
-      "Checking *TDD* = 0\n",
-      "Result: \n",
-      "----------------------------------------------------------------------{CMBN 1}\n",
-      "------------------------------------------------------------------------------\n",
-      "\n",
-      "Checking *BDD* = 0\n",
-      "Result: \n",
-      "----------------------------------------------------------------------{CMBN -2}\n",
-      "------------------------------------------------------------------------------\n",
-      "\n",
-      "Checking *DF-FD* = 0\n",
-      "Result: \n",
-      "----------------------------------------------------------------------{CMBN 2}\n",
-      "------------------------------------------------------------------------------\n",
-      "\n",
-      "Checking *DG-GD* = 0\n",
-      "Result: \n",
-      "----------------------------------------------------------------------{CMBN -1}\n",
-      "------------------------------------------------------------------------------\n",
-      "\n",
-      "Checking *ID-FG* = 0\n",
-      "Result: \n",
-      "----------------------------------------------------------------------{CMBN 0}\n",
-      "------------------------------------------------------------------------------\n",
-      "\n",
-      "Checking *ID-GF-DH-HD* = 0\n",
-      "Result: \n",
-      "----------------------------------------------------------------------{CMBN 3}\n",
-      "------------------------------------------------------------------------------\n",
-      "\n",
-      "Checking *HH* = 0\n",
-      "Result: \n",
-      "----------------------------------------------------------------------{CMBN 5}\n",
-      "------------------------------------------------------------------------------\n",
-      "\n",
-      "Checking *FH* = 0\n",
-      "Result: \n",
-      "----------------------------------------------------------------------{CMBN 4}\n",
-      "------------------------------------------------------------------------------\n",
-      "\n",
-      "Checking *HG* = 0\n",
-      "Result: \n",
-      "----------------------------------------------------------------------{CMBN 1}\n",
-      "------------------------------------------------------------------------------\n",
-      "\n",
-      "---done---"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 38,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(check-rdct-no-wait)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "We build now the reduction over $\\mathbb{Z}$ of the twisted tensor product. The contraction is obtained by a call to the function `smgr-tnpr-contraction`. \n",
-    "$$\n",
-    "\\begin{aligned}\n",
-    "\\bar{\\cal W}{\\cal G} \\otimes_\\tau  {\\cal G} & \\qquad\\stackrel{\\chi_{\\otimes t}}{\\longrightarrow} &\n",
-    "{}^s\\bar{\\cal W}{\\cal G} \\otimes_\\tau  {\\cal G} \\cr\n",
-    " {\\scriptstyle aug} \\downarrow \\uparrow {\\scriptstyle coaug}  \\cr\n",
-    " {{\\cal C}_*(\\mathbb{Z})}\\quad \\cr\n",
-    "\\end{aligned}\n",
-    "$$\n",
-    "Of course, we have to define the augmentation and coaugmentation morphisms adapted to this new example. The user will note that the twisted tensor product chain complex may be obtained from the slot `:sorc` of the contration $\\chi_{\\otimes t}$."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 39,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K88 Morphism (degree 1): K57 -> K57]"
-      ]
-     },
-     "execution_count": 39,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def chi-t-tau (smgr-tnpr-contraction (k-z-1)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 40,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K89 Cohomology-Class on K57 of degree 0]"
-      ]
-     },
-     "execution_count": 40,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def aug-t (build-mrph\n",
-    "              :sorc (sorc chi-t-tau)\n",
-    "              :trgt (z-chcm) \n",
-    "              :degr 0\n",
-    "              :intr #'(lambda (degr gnrt)\n",
-    "                              (declare (ignore gnrt))\n",
-    "                       (if (zerop degr)\n",
-    "                           (term-cmbn 0 1 :z-gnrt)\n",
-    "                           (zero-cmbn degr)))\n",
-    "              :strt :gnrt \n",
-    "              :orgn '(aug-t-fibr-tot-smgr-fibr-k-z-1)  ))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 41,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K90 Morphism (degree 0): K60 -> K57]"
-      ]
-     },
-     "execution_count": 41,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def coaug-t (build-mrph\n",
-    "                :sorc (z-chcm) \n",
-    "                :trgt (sorc chi-t-tau)\n",
-    "                :degr 0\n",
-    "                :intr #'(lambda (degr gnrt)\n",
-    "                                (declare (ignore gnrt))\n",
-    "                         (if (zerop degr)\n",
-    "                             (term-cmbn 0 1 (tnpr 0 +null-gbar+ 0 '()))\n",
-    "                             (zero-cmbn degr)))\n",
-    "                :strt :gnrt\n",
-    "                :orgn '(coaug-t-fibr-tot-smgr-fibr-k-z-1) ))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 42,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K91 Reduction K57 => K60]"
-      ]
-     },
-     "execution_count": 42,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def rdct-t (build-rdct :f aug-t \n",
-    "                        :g coaug-t \n",
-    "                        :h chi-t-tau\n",
-    "                        :orgn '(reduction-t-tt-z)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 43,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "---done---"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 43,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(pre-check-rdct rdct-t)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 44,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 0}\n",
-       "<1 * <TnPr <<GBar>> NIL>>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 44,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(setf *tc* (cmbn 0 1 (tnpr 0 +null-gbar+ 0 '())))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 45,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 0}\n",
-       "<1 * Z-GNRT>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 45,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(setf *bc* (cmbn 0 1 :z-gnrt))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 46,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "*TC* => \n",
-      "----------------------------------------------------------------------{CMBN 0}\n",
-      "<1 * <TnPr <<GBar>> NIL>>\n",
-      "------------------------------------------------------------------------------\n",
-      "\n",
-      "*BC* => \n",
-      "----------------------------------------------------------------------{CMBN 0}\n",
-      "<1 * Z-GNRT>\n",
-      "------------------------------------------------------------------------------\n",
-      "\n",
-      "Checking *TDD* = 0\n",
-      "Result: \n",
-      "----------------------------------------------------------------------{CMBN -2}\n",
-      "------------------------------------------------------------------------------\n",
-      "\n",
-      "Checking *BDD* = 0\n",
-      "Result: \n",
-      "----------------------------------------------------------------------{CMBN -2}\n",
-      "------------------------------------------------------------------------------\n",
-      "\n",
-      "Checking *DF-FD* = 0\n",
-      "Result: \n",
-      "----------------------------------------------------------------------{CMBN -1}\n",
-      "------------------------------------------------------------------------------\n",
-      "\n",
-      "Checking *DG-GD* = 0\n",
-      "Result: \n",
-      "----------------------------------------------------------------------{CMBN -1}\n",
-      "------------------------------------------------------------------------------\n",
-      "\n",
-      "Checking *ID-FG* = 0\n",
-      "Result: \n",
-      "----------------------------------------------------------------------{CMBN 0}\n",
-      "------------------------------------------------------------------------------\n",
-      "\n",
-      "Checking *ID-GF-DH-HD* = 0\n",
-      "Result: \n",
-      "----------------------------------------------------------------------{CMBN 0}\n",
-      "------------------------------------------------------------------------------\n",
-      "\n",
-      "Checking *HH* = 0\n",
-      "Result: \n",
-      "----------------------------------------------------------------------{CMBN 2}\n",
-      "------------------------------------------------------------------------------\n",
-      "\n",
-      "Checking *FH* = 0\n",
-      "Result: \n",
-      "----------------------------------------------------------------------{CMBN 1}\n",
-      "------------------------------------------------------------------------------\n",
-      "\n",
-      "Checking *HG* = 0\n",
-      "Result: \n",
-      "----------------------------------------------------------------------{CMBN 1}\n",
-      "------------------------------------------------------------------------------\n",
-      "\n",
-      "---done---"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 46,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(check-rdct-no-wait)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "The check is validated also for the following simplices. We see also that, if we apply the contraction $\\chi_{\\otimes t}$ upon various simplices outside the base fiber, the result is in general non--null. The nullity of this contraction  outside the base fiber, which we have verified experimentally in many cases in  loop spaces fibration is not verified in  simplicial group fibrations."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 47,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 3}\n",
-       "<1 * <TnPr <<GBar>> (1 10 100)>>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 47,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(setf *tc* (cmbn 3 1 (tnpr 0 +null-gbar+ 3 '(1 10 100))))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 48,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 4}\n",
-       "<1 * <TnPr <<GBar<- (1 10 100)><1-0 NIL><0 NIL><- NIL>>> NIL>>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 48,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? chi-t-tau *tc*)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 49,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 3}\n",
-       "<1 * <TnPr <<GBar<- (1)><- NIL>>> (10)>>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 49,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(setf *tc* (cmbn 3 1 (tnpr 2 (gbar 2 0 '(1) 0 '()) 1 '(10))))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 50,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 4}\n",
-       "<1 * <TnPr <<GBar<1-0 (10)><1-0 NIL><- (1)><- NIL>>> NIL>>\n",
-       "<-1 * <TnPr <<GBar<2-0 (10)><1 (1)><0 NIL><- NIL>>> NIL>>\n",
-       "<1 * <TnPr <<GBar<2-1 (10)><0 (1)><0 NIL><- NIL>>> NIL>>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 50,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? chi-t-tau *tc*)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 51,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 3}\n",
-       "<1 * <TnPr <<GBar<- (1 10)><- (100)><- NIL>>> NIL>>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 51,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(setf *tc* (cmbn 3 1 (tnpr 3 (gbar 3 0 '(1 10) 0 '(100) 0 '()) 0 '())))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 52,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 4}\n",
-       "<1 * <TnPr <<GBar<2 (1 10)><1 (100)><0 NIL><- NIL>>> NIL>>\n",
-       "<-1 * <TnPr <<GBar<2-1 (11)><0 (100)><0 NIL><- NIL>>> NIL>>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 52,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? chi-t-tau *tc*)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 53,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 4}\n",
-       "<1 * <TnPr <<GBar>> (1 10 100 1000)>>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 53,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(setf *tc* (cmbn 4 1 (tnpr 0 +null-gbar+ 4 '(1 10 100 1000))))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 54,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 5}\n",
-       "<-1 * <TnPr <<GBar<- (1 10 100 1000)><2-1-0 NIL><1-0 NIL><0 NIL><- NIL>>> NIL>>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 54,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? chi-t-tau *tc*)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 55,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 4}\n",
-       "<1 * <TnPr <<GBar<- (1)><- NIL>>> (10 100)>>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 55,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(setf *tc* (cmbn 4 1 (tnpr 2 (gbar 2 0 '(1) 0 '()) 2 '(10 100))))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 56,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 5}\n",
-       "<-1 * <TnPr <<GBar<1-0 (10 100)><2-1-0 NIL><1-0 NIL><- (1)><- NIL>>> NIL>>\n",
-       "<1 * <TnPr <<GBar<2-0 (10 100)><2-1-0 NIL><1 (1)><0 NIL><- NIL>>> NIL>>\n",
-       "<-1 * <TnPr <<GBar<2-1 (10 100)><2-1-0 NIL><0 (1)><0 NIL><- NIL>>> NIL>>\n",
-       "<-1 * <TnPr <<GBar<3-0 (10 100)><2-1 (1)><1-0 NIL><0 NIL><- NIL>>> NIL>>\n",
-       "<1 * <TnPr <<GBar<3-1 (10 100)><2-0 (1)><1-0 NIL><0 NIL><- NIL>>> NIL>>\n",
-       "<-1 * <TnPr <<GBar<3-2 (10 100)><1-0 (1)><1-0 NIL><0 NIL><- NIL>>> NIL>>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 56,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? chi-t-tau *tc*)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 57,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 4}\n",
-       "<1 * <TnPr <<GBar<- (1 10)><- (100)><- NIL>>> (1000)>>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 57,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(setf *tc* (cmbn 4 1 (tnpr 3 (gbar 3 0 '(1 10) 0 '(100) 0 '())\n",
-    "                           1 '(1000)))) "
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 58,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 5}\n",
-       "<-1 * <TnPr <<GBar<2 (1 10 1000)><2-1-0 NIL><1 (100)><0 NIL><- NIL>>> NIL>>\n",
-       "<1 * <TnPr <<GBar<2-1 (11 1000)><2-1-0 NIL><0 (100)><0 NIL><- NIL>>> NIL>>\n",
-       "<-1 * <TnPr <<GBar<2-1-0 (1000)><2-1-0 NIL><- (1 10)><- (100)><- NIL>>> NIL>>\n",
-       "<1 * <TnPr <<GBar<3 (1 10 1000)><2-1 (100)><1-0 NIL><0 NIL><- NIL>>> NIL>>\n",
-       "<-1 * <TnPr <<GBar<3 (1 1000 10)><2-1 (100)><1-0 NIL><0 NIL><- NIL>>> NIL>>\n",
-       "<1 * <TnPr <<GBar<3 (1000 1 10)><2-0 (100)><1-0 NIL><0 NIL><- NIL>>> NIL>>\n",
-       "<-1 * <TnPr <<GBar<3-1 (11 1000)><2-0 (100)><1-0 NIL><0 NIL><- NIL>>> NIL>>\n",
-       "<1 * <TnPr <<GBar<3-1-0 (1000)><2 (1 10)><1-0 NIL><- (100)><- NIL>>> NIL>>\n",
-       "<1 * <TnPr <<GBar<3-2 (11 1000)><1-0 (100)><1-0 NIL><0 NIL><- NIL>>> NIL>>\n",
-       "<-1 * <TnPr <<GBar<3-2 (1000 11)><1-0 (100)><1-0 NIL><0 NIL><- NIL>>> NIL>>\n",
-       "... ...\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 58,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? chi-t-tau *tc*)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 59,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 4}\n",
-       "<1 * <TnPr <<GBar<- (1 10 100)><- (1000 10000)><- (100000)><- NIL>>> NIL>>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 59,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(setf *tc* (cmbn 4 1 (tnpr 4 (gbar 4 0 '(1 10 100)\n",
-    "                                     0 '(1000 10000)\n",
-    "                                     0 '(100000)\n",
-    "                                     0 '())\n",
-    "                              0 '())))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 60,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 5}\n",
-       "<1 * <TnPr <<GBar<2 (1001 10010 100)><2-1-0 NIL><1 (100000)><0 NIL><- NIL>>> NIL>>\n",
-       "<-1 * <TnPr <<GBar<2-1 (11011 100)><2-1-0 NIL><0 (100000)><0 NIL><- NIL>>> NIL>>\n",
-       "<-1 * <TnPr <<GBar<3 (1 10 100)><2 (1000 10000)><1-0 NIL><- (100000)><- NIL>>> NIL>>\n",
-       "<-1 * <TnPr <<GBar<3 (111 1000 10000)><2-0 (100000)><1-0 NIL><0 NIL><- NIL>>> NIL>>\n",
-       "<1 * <TnPr <<GBar<3 (1001 110 10000)><2-1 (100000)><1-0 NIL><0 NIL><- NIL>>> NIL>>\n",
-       "<-1 * <TnPr <<GBar<3 (1001 10010 100)><2-1 (100000)><1-0 NIL><0 NIL><- NIL>>> NIL>>\n",
-       "<1 * <TnPr <<GBar<3-1 (11011 100)><2-0 (100000)><1-0 NIL><0 NIL><- NIL>>> NIL>>\n",
-       "<1 * <TnPr <<GBar<3-2 (1 110)><1 (1000 10000)><1 (100000)><0 NIL><- NIL>>> NIL>>\n",
-       "<1 * <TnPr <<GBar<3-2 (111 11000)><1-0 (100000)><1-0 NIL><0 NIL><- NIL>>> NIL>>\n",
-       "<-1 * <TnPr <<GBar<3-2 (11011 100)><1-0 (100000)><1-0 NIL><0 NIL><- NIL>>> NIL>>\n",
-       "... ...\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 60,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? chi-t-tau *tc*)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Let us verify once again the unproved conjecture signaled in the loop spaces fibrations chapter. In fact, if the conjecture is true, it is sufficient to prove it with $\\bar{\\Delta}$. But the following is also a good test of verifying all the involved machinery. If we take ${\\cal G}= K(\\mathbb{Z},1)$, the space ${\\cal WG}=\\bar{\\cal W}{\\cal G} \\times_\\tau  {\\cal G}$ is 0-reduced. Let us consider its loop space and the induced contraction $\\chi_{\\otimes t}$ over ${\\cal WG} \\otimes_\\tau \\Omega{\\cal WG}$. ${\\cal WG}$ and the contraction $\\chi_{\\otimes t}$ are  built by the two following statements:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 61,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K31 Kan-Simplicial-Set]"
-      ]
-     },
-     "execution_count": 61,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def wgkz1 (fibration-total (smgr-fibration(k-z-1))))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 62,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K159 Morphism (degree 1): K154 -> K154]"
-      ]
-     },
-     "execution_count": 62,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def chi-t-tau (tnpr-contraction wgkz1))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Let us apply successively the contraction upon  a simplex belonging to the base fiber (`gnrt0`) and a simplex out of the base fiber (`gnrt1`). We see that in the second case we obtain a null result. We verify also that $\\chi_{\\otimes t}\\circ \\chi_{\\otimes t}=0$."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 63,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "<TnPr <CrPr - <<GBar>> - NIL> <<Loop[<CrPr - <<GBar<- (1)><- (0)>>> - (1)>\\-3]>>>"
-      ]
-     },
-     "execution_count": 63,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def gnrt0 (tnpr 0 (crpr 0 +null-gbar+  0 nil)\n",
-    "                 0 (loop3 0 (crpr 0 (gbar 2 0 '(1) 0 '(0) ) 0 '(1)) -3)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 64,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 1}\n",
-       "<1 * <TnPr <CrPr - <<GBar<- (1)><- (0)>>> - (1)> <<Loop[<CrPr - <<GBar<- (1)><- (0)>>> - (1)>\\-3]>>>>\n",
-       "<1 * <TnPr <CrPr - <<GBar<- (1)><- (0)>>> - (1)> <<Loop[<CrPr - <<GBar<- (1)><- (0)>>> - (1)>\\-2]>>>>\n",
-       "<1 * <TnPr <CrPr - <<GBar<- (1)><- (0)>>> - (1)> <<Loop[<CrPr - <<GBar<- (1)><- (0)>>> - (1)>\\-1]>>>>\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 64,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? chi-t-tau 0 gnrt0)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 65,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 2}\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 65,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? chi-t-tau *)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 66,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "<TnPr <CrPr - <<GBar<- (10 11 12)><- (20 21)><- (30)><- NIL>>> - (2 4 6 8)> <<Loop[<CrPr - <<GBar<- (1)><- (0)>>> - (1)>\\2]>>>"
-      ]
-     },
-     "execution_count": 66,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def gnrt1 (tnpr 4 (crpr 0 (gbar 4 0 '(10 11 12) 0 '(20 21) 0 '(30) 0 '())\n",
-    "                         0 '(2 4 6 8))\n",
-    "                 0 (loop3 0 (crpr 0 (gbar 2 0 '(1) 0 '(0) ) 0 '(1)) 2)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 67,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "----------------------------------------------------------------------{CMBN 5}\n",
-       "------------------------------------------------------------------------------\n"
-      ]
-     },
-     "execution_count": 67,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(? chi-t-tau 4 gnrt1)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "At last we verify that the total space of the fibration of $K(\\mathbb{Z},1)$ is contractible."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 68,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "Computing boundary-matrix in dimension 0.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 31m 26s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 0) :\n",
-      "<TnPr <<Abar>> *> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 1.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 31m 26s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 1) :\n",
-      "<TnPr <<Abar>> S1> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 0 :\n",
-      "\n",
-      "\n",
-      "Component Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 31m 26s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 1.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 31m 26s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 1) :\n",
-      "<TnPr <<Abar>> S1> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 2.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 31m 26s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 2) :\n",
-      "<TnPr <<Abar[2 S1]>> *> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 1 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 31m 26s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 2.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 31m 26s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 2) :\n",
-      "<TnPr <<Abar[2 S1]>> *> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 3.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 31m 26s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 3) :\n",
-      "<TnPr <<Abar[2 S1]>> S1> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 2 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 31m 26s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 3.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 31m 26s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 3) :\n",
-      "<TnPr <<Abar[2 S1]>> S1> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 4.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 31m 26s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 4) :\n",
-      "<TnPr <<Abar[2 S1][2 S1]>> *> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 3 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 31m 26s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 4.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 31m 26s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 4) :\n",
-      "<TnPr <<Abar[2 S1][2 S1]>> *> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 5.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 31m 26s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 5) :\n",
-      "<TnPr <<Abar[2 S1][2 S1]>> S1> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 4 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 31m 26s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 5.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 31m 26s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 5) :\n",
-      "<TnPr <<Abar[2 S1][2 S1]>> S1> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 6.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 31m 26s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 6) :\n",
-      "<TnPr <<Abar[2 S1][2 S1][2 S1]>> *> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 5 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 31m 26s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 6.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 31m 26s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 6) :\n",
-      "<TnPr <<Abar[2 S1][2 S1][2 S1]>> *> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 7.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 31m 26s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 7) :\n",
-      "<TnPr <<Abar[2 S1][2 S1][2 S1]>> S1> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 6 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 31m 26s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 7.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 31m 26s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 7) :\n",
-      "<TnPr <<Abar[2 S1][2 S1][2 S1]>> S1> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 8.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 31m 26s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 8) :\n",
-      "<TnPr <<Abar[2 S1][2 S1][2 S1][2 S1]>> *> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 7 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 31m 26s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 8.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 31m 26s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 8) :\n",
-      "<TnPr <<Abar[2 S1][2 S1][2 S1][2 S1]>> *> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 9.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 31m 26s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 9) :\n",
-      "<TnPr <<Abar[2 S1][2 S1][2 S1][2 S1]>> S1> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 8 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 31m 26s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 9.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 31m 26s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 9) :\n",
-      "<TnPr <<Abar[2 S1][2 S1][2 S1][2 S1]>> S1> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 10.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 31m 26s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 10) :\n",
-      "<TnPr <<Abar[2 S1][2 S1][2 S1][2 S1][2 S1]>> *> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 9 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 31m 26s.\n",
-      "\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 68,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(homology (fibration-total(smgr-fibration (k-z-1))) 0 10)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Another example is the following: we build the canonical fibration of $\\bar{\\cal W}^2K(\\mathbb{Z}_2, 1)$ and verify that its fibration total  space is contractible:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 69,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K327 Abelian-Simplicial-Group]"
-      ]
-     },
-     "execution_count": 69,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def k22 (classifying-space(classifying-space(k-z2-1))))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 70,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K351 Fibration K339 -> K327]"
-      ]
-     },
-     "execution_count": 70,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def fb (smgr-fibration k22))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 71,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K357 Kan-Simplicial-Set]"
-      ]
-     },
-     "execution_count": 71,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def tt2 (fibration-total fb))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "(homology tt2 0 10)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "### Lisp file concerned in this chapter\n",
-    "\n",
-    "`cs-twisted-products.lisp`."
-   ]
-  }
- ],
- "metadata": {
-  "kernelspec": {
-   "display_name": "SBCL Lisp",
-   "language": "lisp",
-   "name": "lisp"
-  },
-  "language_info": {
-   "codemirror_mode": "text/x-common-lisp",
-   "mimetype": "text/x-common-lisp",
-   "name": "common-lisp",
-   "pygments_lexer": "common-lisp",
-   "version": "X3J13"
-  }
- },
- "nbformat": 4,
- "nbformat_minor": 1
-}
diff --git a/examples/20_Eilenberg-Moore_spectral_sequence_II.ipynb b/examples/20_Eilenberg-Moore_spectral_sequence_II.ipynb
deleted file mode 100644
index 36d4651..0000000
--- a/examples/20_Eilenberg-Moore_spectral_sequence_II.ipynb
+++ /dev/null
@@ -1,1147 +0,0 @@
-{
- "cells": [
-  {
-   "cell_type": "code",
-   "execution_count": 1,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "To load \"kenzo\":\n",
-      "  Load 1 ASDF system:\n",
-      "    kenzo\n",
-      "; Loading \"kenzo\"\n",
-      "\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "#<PACKAGE \"CAT\">"
-      ]
-     },
-     "execution_count": 1,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(ql:quickload \"kenzo\")\n",
-    "(in-package :cat)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "# Eilenberg-Moore spectral sequence II\n",
-    "\n",
-    "## Introduction\n",
-    "\n",
-    "This chapter is devoted to the effective homology version of the spectral sequence of Eilenberg-Moore, in the particular case of classifying spaces. More precisely, let ${\\cal G}$ be a simplicial group; then its classifying space $\\bar{\\cal W}{\\cal G}$ is a simplicial set canonically defined (**J. Peter May**. *Simplicial objects in algebraic topology*, Van Nostrand, 1967.). Furthermore, if ${\\cal G}$ is an Abelian simplicial group, then  $\\bar{\\cal W}{\\cal G}$ is again an Abelian simplicial group with natural structure, so that the $\\bar{\\cal W}$ construction can be iterated. The $\\bar{\\cal W}$ construction is implemented in `Kenzo` only if ${\\cal G}$ is reduced (${\\cal G}_0$ has only one element). In particular if ${\\cal G}$ is a simplicial group with effective homology, then `Kenzo` constructs a version of $\\bar{\\cal W}{\\cal G}$ also with effective homology.\n",
-    "\n",
-    "## The detailed construction\n",
-    "\n",
-    "Let ${\\cal G}$ be a simplicial group with effective homology. This means that a  homotopy equivalence:\n",
-    "$$\\begin{aligned}\n",
-    "  & \\qquad\\hat{C}_* \\cr\n",
-    " \\swarrow\\nearrow & & \\searrow\\nwarrow\\qquad \\cr\n",
-    "{\\cal C}_*({\\cal G})  & & EG_* \\cr\n",
-    "\\end{aligned}$$ \n",
-    "is provided, where  the chain complex $EG_*$ is effective and must be considered as describing the homology of ${\\cal C}_*({\\cal G})$. This scheme includes the case where ${\\cal C}_*({\\cal G})$ itself is  effective; without any other information, the program  constructs automatically a trivial homotopy equivalence.\n",
-    "\n",
-    "Now, if we apply the *Bar* functor to this homotopy equivalence we obtain the homotopy equivalence $H_R$:\n",
-    "$$\\begin{aligned}\n",
-    "  &\\qquad{\\widetilde{Bar}}^{\\hat{ C}_*} \\cr\n",
-    " \\swarrow\\nearrow & & \\searrow\\nwarrow\\qquad \\cr\n",
-    "Bar^{{\\cal C}_*({\\cal G})}(\\mathbb{Z}, \\mathbb{Z})  & & {\\widetilde{Bar}}^{EG_*}(\\mathbb{Z}, \\mathbb{Z}) \\cr\n",
-    "\\end{aligned}$$\n",
-    "in which the $\\widetilde{Bar}$'s are Bars constructions with respect to the $A_\\infty$ structure on $\\hat{C}_*$ and $EG_*$ defined by the initial homotopy equivalence.\n",
-    "\n",
-    "By analogy  with the result of Julio Rubio (**J.J. Rubio-Garcia**. *Homologie effective des espaces de lacets iteres: un logiciel*, These, Institut Fourier, 1991.) one may show  that it is possible to construct another homotopy equivalence, $H_L$:\n",
-    "$$\\begin{aligned}\n",
-    "  & \\qquad Bar^{{\\cal C}_*({\\cal G})}({\\cal C}_*(\\bar{\\cal W}{\\cal G})\\otimes_t {\\cal C}_*({\\cal G}),\\mathbb{Z}) \\cr\n",
-    " \\swarrow\\nearrow & & \\searrow\\nwarrow\\qquad \\cr\n",
-    " {\\cal C}_*(\\bar{\\cal W}{\\cal G})  & & Bar^{{\\cal C}_*({\\cal G})}(\\mathbb{Z}, \\mathbb{Z}) \\cr\n",
-    "\\end{aligned}$$\n",
-    "Both reductions of $H_L$ are obtained by the basic perturbation lemma, as explained in the following section. The composition of both homotopy equivalences, $H_L$ and $H_R$, makes the link between $\\bar{\\cal W}{\\cal G}$, the classifying space of  the simplicial group ${\\cal G}$ and the effective  right bottom  chain complex of $H_R$.\n",
-    "\n",
-    "## Obtaining the left reduction $H_L$\n",
-    "\n",
-    "The homotopy equivalence  $H_L$ is obtained by a sequence of intermediate constructions based mainly upon two applications of the basic perturbation lemma. We are led to consider the two following modules:\n",
-    "- ${\\cal C}_*({\\cal G})$ module on itself, with the canonical product.\n",
-    "$${\\cal C}_*({\\cal G})\\otimes {\\cal C}_*({\\cal G})\\stackrel {\\Pi}{\\longrightarrow} {\\cal C}_*({\\cal G}).$$\n",
-    "- ${\\check{\\cal C}}_*({\\cal G})$, module on ${\\cal C}_*({\\cal G})$, with a \"trivial\" product $${\\check{\\cal C}}_*({\\cal G})\\otimes{\\cal C}_*({\\cal G}) \\stackrel {\\check{\\Pi}}{\\longrightarrow} {\\check{\\cal C}}_*({\\cal G})$$ defined by $$\\sigma \\otimes \\tau \\longmapsto \\sigma . \\varepsilon(\\tau),$$ where $\\varepsilon$ is the traditional augmentation of ${\\cal C}_*({\\cal G})$.\n",
-    "\n",
-    "Now, we consider the set of the followings Bars (where $u$ means *\"untwisted\"* and $t$ *\"twisted\"*):\n",
-    "$$\\begin{aligned}\n",
-    "{\\rm Hat}_{uu} &=& Bar^{{\\cal C}_*({\\cal G})}({\\cal C}_*(\\bar{\\cal W}{\\cal G})\\otimes {\\check{\\cal C}}_*({\\cal G}),\\mathbb{Z}),\\\\\n",
-    "{\\rm Hat}_{ut} &=& Bar^{{\\cal C}_*({\\cal G})}({\\cal C}_*(\\bar{\\cal W}{\\cal G})\\otimes {\\cal C}_*({\\cal G}),\\mathbb{Z}),\\\\\n",
-    "{\\rm Hat}_{tu} &=& Bar^{{\\cal C}_*({\\cal G})}({\\cal C}_*(\\bar{\\cal W}{\\cal G})\\otimes_t{\\check{\\cal C}}_*({\\cal G}),\\mathbb{Z}),\\\\\n",
-    "{\\rm Hat}_{tt} &=& Bar^{{\\cal C}_*({\\cal G})}({\\cal C}_*(\\bar{\\cal W}{\\cal G})\\otimes_t {\\cal C}_*({\\cal G}),\\mathbb{Z}).\n",
-    "\\end{aligned}$$\n",
-    "\n",
-    "One may always say that ${\\rm Hat}_{ut}$ is obtained from ${\\rm Hat}_{uu}$ by a perturbation $\\delta_r$ ($r$: right) induced by the discrepancy between the products in ${\\check{\\cal C}}_*({\\cal G})$ and ${\\cal C}_*({\\cal G})$ and that ${\\rm Hat}_{tu}$ is obtained from ${\\rm Hat}_{uu}$ by a perturbation $\\delta_l$ ($l$: left) induced by the twisted tensor product $\\otimes_t$. After that,\n",
-    "${\\rm Hat}_{tt}$ is obtained from ${\\rm Hat}_{tu}$ by the perturbation $\\delta_r$ as well as, by commutativity, from ${\\rm Hat}_{ut}$ by the perturbation $\\delta_l$.\n",
-    "\n",
-    "This is shown in the following diagram (here, the arrows are not reductions, but denote the  perturbations between  the differential morphisms):\n",
-    "$$\\begin{aligned} \n",
-    "  & \\qquad{\\rm Hat}_{uu} \\cr\n",
-    " \\delta_l \\swarrow  & & \\searrow \\delta_r \\cr\n",
-    "{\\rm Hat}_{tu}  & &  {\\rm Hat}_{ut} \\cr\n",
-    " \\delta_r \\searrow  & & \\swarrow \\delta_l \\cr\n",
-    "  & \\qquad{\\rm Hat}_{tt} \\cr\n",
-    "\\end{aligned}$$\n",
-    "\n",
-    "The underlying graded modules  ${\\rm Hat}_{uu}$, ${\\rm Hat}_{ut}$, ${\\rm Hat}_{tu}$ and ${\\rm Hat}_{tt}$ are the same and the program keeps ${\\rm Hat}_{uu}$ as the underlying graded module for all the chain complexes. The  differential perturbations are given by the formulas:\n",
-    "$$\\begin{aligned}\n",
-    "\\delta_l[(w\\otimes {\\check g}_0)\\otimes (g_1 \\otimes\\cdots\\otimes g_n)] &=&\n",
-    "[d_{\\otimes t}(w\\otimes {\\check g}_0) - d_\\otimes (w\\otimes {\\check g}_0)] \\otimes (g_1 \\otimes\\cdots\\otimes g_n), \\\\\n",
-    "\\delta_r[(w\\otimes {\\check g}_0)\\otimes (g_1 \\otimes\\cdots\\otimes g_n)] &=& \n",
-    "w \\otimes(g_0 . g_1) \\otimes g_2 \\otimes\\cdots\\otimes  g_n,\n",
-    "\\end{aligned}$$\n",
-    "where ${\\check g}_0 \\in {\\check {\\cal G}}_0,\\, g_i \\in {\\cal G},\\, w \\in \\bar{\\cal W}{\\cal G}.$\n",
-    "\n",
-    "Now, on the other hand, we know that there exists a reduction  \n",
-    "$${\\rm Hat}_{ut} = Bar^{{\\cal C}_*({\\cal G})}({\\cal C}_*(\\bar{\\cal W}{\\cal G})\\otimes \n",
-    "{\\cal C}_*({\\cal G}),\\mathbb{Z}) \\Longrightarrow {\\cal C}_*(\\bar{\\cal W}{\\cal G}),$$ \n",
-    "so,  perturbing this reduction by $\\delta_l$, one obtains the Rubio reduction\n",
-    "$${\\rm Hat}_{tt}=Bar^{{\\cal C}_*({\\cal G})}({\\cal C}_*(\\bar{\\cal W}{\\cal G})\\otimes_t \n",
-    "{\\cal C}_*({\\cal G}),\\mathbb{Z}) \\Longrightarrow {\\cal C}_*(\\bar{\\cal W}{\\cal G}).$$\n",
-    "On the other hand, we know also that there exists a reduction \n",
-    "$${\\rm Hat}_{tu} = Bar^{{\\cal C}_*({\\cal G})}({\\cal C}_*(\\bar{\\cal W}{\\cal G})\\otimes_t \n",
-    "{\\check{\\cal C}}_*({\\cal G}),\\mathbb{Z}) \\Longrightarrow\n",
-    "Bar^{{\\cal C}_*({\\cal G})}(\\mathbb{Z}, \\mathbb{Z}),$$ \n",
-    "so, perturbing this reduction by $\\delta_r$, one obtains the reduction \n",
-    "$${\\rm Hat}_{tt}=Bar^{{\\cal C}_*({\\cal G})}({\\cal C}_*(\\bar{\\cal W}{\\cal G})\\otimes_t \n",
-    "{\\cal C}_*({\\cal G}),\\mathbb{Z}) \\Longrightarrow Bar^{{\\cal C}_*({\\cal G})}(\\mathbb{Z}, \\mathbb{Z}).$$\n",
-    "Finally, we have obtained the wished left homotopy equivalence $H_L$:\n",
-    "$$\\begin{aligned}\n",
-    "  & \\qquad Bar^{{\\cal C}_*({\\cal G})}({\\cal C}_*(\\bar{\\cal W}{\\cal G})\\otimes_t {\\cal C}_*({\\cal G}),\\mathbb{Z}) \\cr\n",
-    "    \\swarrow\\nearrow & & \\searrow\\nwarrow \\qquad\\cr\n",
-    " {\\cal C}_*(\\bar{\\cal W}{\\cal G})  & & Bar^{{\\cal C}_*({\\cal G})}(\\mathbb{Z}, \\mathbb{Z}) \\cr\n",
-    "\\end{aligned}$$\n",
-    "\n",
-    "### The useful functions\n",
-    "\n",
-    "For the applications, the only function that the user must know is the function `classifying-space-efhm` which builds the final homotopy equivalence. But for the interested user, we give nevertheless a short description of all the functions involved in the described process.\n",
-    "\n",
-    "`classifying-space-efhm` *smgr* *[Function]*\n",
-    "> From the simplicial group ${\\cal G}$ (0-reduced) with effective homology (here the argument *smgr*), build a homotopy equivalence giving an effective homology version  of the classifying space $\\bar{\\cal W}{\\cal G}$ of ${\\cal G}$. This homotopy equivalence will be used by the homology function to compute the homology groups. In fact, due to the slot-unbound mechanism of CLOS, this function will be automatically called, as soon as the user requires a homology group for a classifying space.\n",
-    "\n",
-    "`cs-hat-u-u` *smgr* *[Function]*\n",
-    "> Return the chain complex $Bar^{{\\cal C}_*({\\cal G})}({\\cal C}_*(\\bar{\\cal W}{\\cal G})\\otimes {\\check{\\cal C}}_*({\\cal G}),\\mathbb{Z})$. Because of the particular structure of ${\\check{\\cal C}}_*({\\cal G})$, this chain complex is nothing but $[{\\cal C}_*(\\bar{\\cal W}{\\cal G})\\otimes {\\check{\\cal C}}_*({\\cal G})]\\otimes Bar^{{\\cal C}_*({\\cal G})}(\\mathbb{Z},\\mathbb{Z}).$\n",
-    "\n",
-    "`cs-hat-right-perturbation` *smgr* *[Function]*\n",
-    "> Return the morphism corresponding to the differential perturbation $\\delta_r$, induced by the discrepancy between the respective products in  ${\\check{\\cal C}}_*({\\cal G})$ and in ${\\cal C}_*({\\cal G})$.\n",
-    "\n",
-    "`cs-hat-u-t` *smgr* *[Function]*\n",
-    "> Return the chain complex $Bar^{{\\cal C}_*({\\cal G})}({\\cal C}_*(\\bar{\\cal W}{\\cal G})\\otimes {\\cal C}_*({\\cal G}),\\mathbb{Z})$ by applying the differential perturbation `hat-right-perturbation` upon the chain complex `hat-u-u` *smgr*. This is realized by the method `add`.\n",
-    "\n",
-    "`cs-hat-t-u` *smgr* *[Function]*\n",
-    "> Return the chain complex $Bar^{{\\cal C}_*({\\cal G})}({\\cal C}_*(\\bar{\\cal W}{\\cal G})\\otimes_t {\\check{\\cal C}}_*({\\cal G}),\\mathbb{Z})$. Because of the particular structure of ${\\check{\\cal C}}_*({\\cal G})$, this chain complex is nothing but $[{\\cal C}_*(\\bar{\\cal W}{\\cal G})\\otimes_t {\\check{\\cal C}}_*({\\cal G})]\\otimes Bar^{{\\cal C}_*({\\cal G})}(\\mathbb{Z},\\mathbb{Z}),$ where the twisted tensor product is the botton chain complex of the Brown reduction of the fibration of the simplicial group.\n",
-    "\n",
-    "`cs-hat-left-perturbation` *smgr* *[Function]*\n",
-    "> Return the morphism corresponding to the differential perturbation $\\delta_l$ induced by the twisted tensor product. This morphism is nothing but the tensor product of two morphisms: the perturbation morphism by-product of the Brown reduction of the fibration of the simplicial group and the identity morphism on $Bar^{{\\cal C}_*({\\cal G})}(\\mathbb{Z},\\mathbb{Z})$.\n",
-    "\n",
-    "`cs-left-hmeq-hat` *smgr* *[Function]*\n",
-    "> Return the chain complex ${\\rm Hat}_{tt}=Bar^{{\\cal C}_*({\\cal G})}({\\cal C}_*(\\bar{\\cal W}{\\cal G})\\otimes_t {\\cal C}_*({\\cal G}),\\mathbb{Z})$ by perturbing the chain complex ${\\rm Hat}_{ut}$ by the perturbation $\\delta_l$.\n",
-    "\n",
-    "`cs-pre-left-hmeq-left-reduction` *smgr* *[Function]*\n",
-    ">Build the reduction $${\\rm Hat}_{tu}=Bar^{{\\cal C}_*({\\cal G})}({\\cal C}_*(\\bar{\\cal W}{\\cal G})\\otimes {\\cal C}_*({\\cal G}),\\mathbb{Z}) \\Longrightarrow {\\cal C}_*(\\bar{\\cal W}{\\cal G}).$$ \n",
-    "\n",
-    "`cs-pre-left-hmeq-right-reduction` *smgr* *[Function]*\n",
-    "> Build the reduction $${\\rm Hat}_{ut}=Bar^{{\\cal C}_*({\\cal G})}({\\check{\\cal C}}_*({\\cal G})\\otimes_t {\\cal C}_*(\\bar{\\cal W}{\\cal G}),\\mathbb{Z}) \\Longrightarrow Bar^{{\\cal C}_*({\\cal G})}(\\mathbb{Z}, \\mathbb{Z}).$$\n",
-    "\n",
-    "`cs-left-hmeq-left-reduction` *smgr* *[Function]*\n",
-    "> Build the Rubio reduction $$Bar^{{\\cal C}_*({\\cal G})}({\\cal C}_*(\\bar{\\cal W}{\\cal G})\\otimes_t {\\cal C}_*({\\cal G}),\\mathbb{Z}) \\Longrightarrow{\\cal C}_*(\\bar{\\cal W}{\\cal G})$$ by perturbing by the perturbation $\\delta_r$ the reduction $${\\rm Hat}_{tu} \\Longrightarrow {\\cal C}_*(\\bar{\\cal W}{\\cal G})$$  obtained by the function {\\tt pre-left-hmeq-left-reduction}.\n",
-    "\n",
-    "`cs-left-hmeq-right-reduction` *smgr* *[Function]*\n",
-    "> Build the reduction $$Bar^{{\\cal C}_*({\\cal G})}({\\cal C}_*(\\bar{\\cal W}{\\cal G})\\otimes_t {\\cal C}_*({\\cal G}),\\mathbb{Z}) \\Longrightarrow Bar^{{\\cal C}_*({\\cal G})}(\\mathbb{Z}, \\mathbb{Z})$$\n",
-    "by perturbing by the perturbation $\\delta_l$ the reduction $${\\rm Hat}_{ut} \\Longrightarrow Bar^{{\\cal C}_*({\\cal G})}(\\mathbb{Z}, \\mathbb{Z})$$ obtained by the function `cs-pre-left-hmeq-right-reduction`.\n",
-    "\n",
-    "`cs-left-hmeq` *smgr* *[Function]*\n",
-    "> Build the homotopy equivalence\n",
-    "$$\\begin{aligned}\n",
-    "  &\\qquad Bar^{{\\cal C}_*({\\cal G})}({\\cal C}_*(\\bar{\\cal W}{\\cal G})\\otimes_t {\\cal C}_*({\\cal G}),\\mathbb{Z}) \\cr\n",
-    "    \\swarrow\\nearrow & & \\searrow\\nwarrow\\qquad \\cr\n",
-    " {\\cal C}_*(\\bar{\\cal W}{\\cal G})    & & Bar^{{\\cal C}_*({\\cal G})}(\\mathbb{Z}, \\mathbb{Z}) \\cr\n",
-    "\\end{aligned}$$\n",
-    "from the above reductions. The function `classifying-space-efhm` composes this left homotopy equivalence $H_L$ with the homotopy equivalence $H_R$ which is the Bar of a pre-existing homotopy equivalence (possibly the trivial one) between the module ${\\cal G}$ and an effective version of it, as described at the beginning of this chapter.\n",
-    "\n",
-    "### Searching homology for classifying spaces\n",
-    "\n",
-    "The origin list of a classifying space object has the form `(CLASSIFYING-SPACE` *smgr*`)`. The `search-efhm` method applied to a classifying space object consists essentially in a call to the function `classifying-space-efhm` described just above.\n",
-    "```commonlisp\n",
-    "(defmethod SEARCH-EFHM (classifying-space (orgn (eql 'classifying-space)))\n",
-    "  (declare (type simplicial-set classifying-space))\n",
-    "  (classifying-space-efhm (second (orgn classifying-space))))\n",
-    "```\n",
-    "The following Lisp definition of the function  `classifying-space-efhm` shows that  the process may be recursive if it happens that *smrg* is itself a classifying space:\n",
-    "```commonlisp\n",
-    "(defun CLASSIFYING-SPACE-EFHM (smgr)\n",
-    "  (declare (type simplicial-group smgr))\n",
-    "  (let ((left-hmeq (cs-left-hmeq smgr))\n",
-    "        (right-hmeq (bar (efhm smgr))))\n",
-    "        (declare (type homotopy-equivalence left-hmeq right-hmeq))\n",
-    "        (cmps left-hmeq right-hmeq)))\n",
-    "```\n",
-    "\n",
-    "### Examples"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 2,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K1 Abelian-Simplicial-Group]"
-      ]
-     },
-     "execution_count": 2,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def kz1 (k-z-1))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 3,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "Computing boundary-matrix in dimension 0.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 33m 7s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 0) :\n",
-      "* \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 1.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 33m 7s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 1) :\n",
-      "S1 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 0 :\n",
-      "\n",
-      "\n",
-      "Component Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 33m 7s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 1.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 33m 7s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 1) :\n",
-      "S1 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 2.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 1 :\n",
-      "\n",
-      "\n",
-      "Component Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 33m 7s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 2.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 3.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 2 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 33m 7s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 3.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 4.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 3 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 33m 7s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 4.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 5.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 4 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 33m 7s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 5.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 6.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 5 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 33m 7s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 6.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 7.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 6 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 33m 7s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 7.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 8.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 7 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 33m 7s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 8.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 9.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 8 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 33m 7s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 9.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 10.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 9 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 33m 7s.\n",
-      "\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 3,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(homology kz1 0 10)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 4,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K23 Abelian-Simplicial-Group]"
-      ]
-     },
-     "execution_count": 4,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def bkz1 (classifying-space kz1))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 5,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "Computing boundary-matrix in dimension 0.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 33m 7s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 0) :\n",
-      "<<Abar>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 1.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 0 :\n",
-      "\n",
-      "\n",
-      "Component Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 33m 7s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 1.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 2.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 33m 7s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 2) :\n",
-      "<<Abar[2 S1]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 1 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 33m 7s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 2.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 33m 7s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 2) :\n",
-      "<<Abar[2 S1]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 3.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 2 :\n",
-      "\n",
-      "\n",
-      "Component Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 33m 7s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 3.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 4.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 33m 7s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 4) :\n",
-      "<<Abar[2 S1][2 S1]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 3 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 33m 7s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 4.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 33m 7s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 4) :\n",
-      "<<Abar[2 S1][2 S1]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 5.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 4 :\n",
-      "\n",
-      "\n",
-      "Component Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 33m 7s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 5.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 6.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 33m 7s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 6) :\n",
-      "<<Abar[2 S1][2 S1][2 S1]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 5 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 33m 7s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 6.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 33m 7s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 6) :\n",
-      "<<Abar[2 S1][2 S1][2 S1]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 7.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 6 :\n",
-      "\n",
-      "\n",
-      "Component Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 33m 7s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 7.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 8.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 33m 7s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 8) :\n",
-      "<<Abar[2 S1][2 S1][2 S1][2 S1]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 7 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 33m 7s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 8.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 33m 7s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 8) :\n",
-      "<<Abar[2 S1][2 S1][2 S1][2 S1]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 9.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 8 :\n",
-      "\n",
-      "\n",
-      "Component Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 33m 7s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 9.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 10.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 33m 7s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 10) :\n",
-      "<<Abar[2 S1][2 S1][2 S1][2 S1][2 S1]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 9 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 33m 7s.\n",
-      "\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 5,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(homology bkz1 0 10)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 6,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K154 Simplicial-Group]"
-      ]
-     },
-     "execution_count": 6,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def obkz1 (loop-space bkz1))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 7,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "Computing boundary-matrix in dimension 0.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 33m 7s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 0) :\n",
-      "<<AlLp>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 1.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 33m 7s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 1) :\n",
-      "<<AlLp[1 <<Abar[2 S1]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 0 :\n",
-      "\n",
-      "\n",
-      "Component Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 33m 7s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 1.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 33m 7s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 1) :\n",
-      "<<AlLp[1 <<Abar[2 S1]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 2.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 33m 7s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 2) :\n",
-      "<<AlLp[1 <<Abar[2 S1]>>][1 <<Abar[2 S1]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 1 :\n",
-      "\n",
-      "\n",
-      "Component Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 33m 7s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 2.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 33m 7s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 2) :\n",
-      "<<AlLp[1 <<Abar[2 S1]>>][1 <<Abar[2 S1]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 3.\n",
-      "Rank of the source-module : 2.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 33m 7s.\n",
-      "Computing the boundary of the generator 1/2 (dimension 3) :\n",
-      "<<AlLp[3 <<Abar[2 S1][2 S1]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 33m 7s.\n",
-      "Computing the boundary of the generator 2/2 (dimension 3) :\n",
-      "<<AlLp[1 <<Abar[2 S1]>>][1 <<Abar[2 S1]>>][1 <<Abar[2 S1]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 2 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 33m 7s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 3.\n",
-      "Rank of the source-module : 2.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 33m 7s.\n",
-      "Computing the boundary of the generator 1/2 (dimension 3) :\n",
-      "<<AlLp[3 <<Abar[2 S1][2 S1]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 33m 7s.\n",
-      "Computing the boundary of the generator 2/2 (dimension 3) :\n",
-      "<<AlLp[1 <<Abar[2 S1]>>][1 <<Abar[2 S1]>>][1 <<Abar[2 S1]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 4.\n",
-      "Rank of the source-module : 3.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 33m 7s.\n",
-      "Computing the boundary of the generator 1/3 (dimension 4) :\n",
-      "<<AlLp[1 <<Abar[2 S1]>>][3 <<Abar[2 S1][2 S1]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 33m 7s.\n",
-      "Computing the boundary of the generator 2/3 (dimension 4) :\n",
-      "<<AlLp[3 <<Abar[2 S1][2 S1]>>][1 <<Abar[2 S1]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 33m 7s.\n",
-      "Computing the boundary of the generator 3/3 (dimension 4) :\n",
-      "<<AlLp[1 <<Abar[2 S1]>>][1 <<Abar[2 S1]>>][1 <<Abar[2 S1]>>][1 <<Abar[2 S1]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 3 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 33m 7s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 4.\n",
-      "Rank of the source-module : 3.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 33m 7s.\n",
-      "Computing the boundary of the generator 1/3 (dimension 4) :\n",
-      "<<AlLp[1 <<Abar[2 S1]>>][3 <<Abar[2 S1][2 S1]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 33m 7s.\n",
-      "Computing the boundary of the generator 2/3 (dimension 4) :\n",
-      "<<AlLp[3 <<Abar[2 S1][2 S1]>>][1 <<Abar[2 S1]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 33m 7s.\n",
-      "Computing the boundary of the generator 3/3 (dimension 4) :\n",
-      "<<AlLp[1 <<Abar[2 S1]>>][1 <<Abar[2 S1]>>][1 <<Abar[2 S1]>>][1 <<Abar[2 S1]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 5.\n",
-      "Rank of the source-module : 5.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 33m 7s.\n",
-      "Computing the boundary of the generator 1/5 (dimension 5) :\n",
-      "<<AlLp[5 <<Abar[2 S1][2 S1][2 S1]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 33m 7s.\n",
-      "Computing the boundary of the generator 2/5 (dimension 5) :\n",
-      "<<AlLp[1 <<Abar[2 S1]>>][1 <<Abar[2 S1]>>][3 <<Abar[2 S1][2 S1]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 33m 7s.\n",
-      "Computing the boundary of the generator 3/5 (dimension 5) :\n",
-      "<<AlLp[1 <<Abar[2 S1]>>][3 <<Abar[2 S1][2 S1]>>][1 <<Abar[2 S1]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 33m 7s.\n",
-      "Computing the boundary of the generator 4/5 (dimension 5) :\n",
-      "<<AlLp[3 <<Abar[2 S1][2 S1]>>][1 <<Abar[2 S1]>>][1 <<Abar[2 S1]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 33m 7s.\n",
-      "Computing the boundary of the generator 5/5 (dimension 5) :\n",
-      "<<AlLp[1 <<Abar[2 S1]>>][1 <<Abar[2 S1]>>][1 <<Abar[2 S1]>>][1 <<Abar[2 S1]>>][1 <<Abar[2 S1]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 4 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 33m 7s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 5.\n",
-      "Rank of the source-module : 5.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 33m 7s.\n",
-      "Computing the boundary of the generator 1/5 (dimension 5) :\n",
-      "<<AlLp[5 <<Abar[2 S1][2 S1][2 S1]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 33m 7s.\n",
-      "Computing the boundary of the generator 2/5 (dimension 5) :\n",
-      "<<AlLp[1 <<Abar[2 S1]>>][1 <<Abar[2 S1]>>][3 <<Abar[2 S1][2 S1]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 33m 7s.\n",
-      "Computing the boundary of the generator 3/5 (dimension 5) :\n",
-      "<<AlLp[1 <<Abar[2 S1]>>][3 <<Abar[2 S1][2 S1]>>][1 <<Abar[2 S1]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 33m 7s.\n",
-      "Computing the boundary of the generator 4/5 (dimension 5) :\n",
-      "<<AlLp[3 <<Abar[2 S1][2 S1]>>][1 <<Abar[2 S1]>>][1 <<Abar[2 S1]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 33m 7s.\n",
-      "Computing the boundary of the generator 5/5 (dimension 5) :\n",
-      "<<AlLp[1 <<Abar[2 S1]>>][1 <<Abar[2 S1]>>][1 <<Abar[2 S1]>>][1 <<Abar[2 S1]>>][1 <<Abar[2 S1]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 6.\n",
-      "Rank of the source-module : 8.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 33m 7s.\n",
-      "Computing the boundary of the generator 1/8 (dimension 6) :\n",
-      "<<AlLp[1 <<Abar[2 S1]>>][5 <<Abar[2 S1][2 S1][2 S1]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 33m 7s.\n",
-      "Computing the boundary of the generator 2/8 (dimension 6) :\n",
-      "<<AlLp[3 <<Abar[2 S1][2 S1]>>][3 <<Abar[2 S1][2 S1]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 33m 7s.\n",
-      "Computing the boundary of the generator 3/8 (dimension 6) :\n",
-      "<<AlLp[5 <<Abar[2 S1][2 S1][2 S1]>>][1 <<Abar[2 S1]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 33m 7s.\n",
-      "Computing the boundary of the generator 4/8 (dimension 6) :\n",
-      "<<AlLp[1 <<Abar[2 S1]>>][1 <<Abar[2 S1]>>][1 <<Abar[2 S1]>>][3 <<Abar[2 S1][2 S1]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 33m 7s.\n",
-      "Computing the boundary of the generator 5/8 (dimension 6) :\n",
-      "<<AlLp[1 <<Abar[2 S1]>>][1 <<Abar[2 S1]>>][3 <<Abar[2 S1][2 S1]>>][1 <<Abar[2 S1]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 33m 7s.\n",
-      "Computing the boundary of the generator 6/8 (dimension 6) :\n",
-      "<<AlLp[1 <<Abar[2 S1]>>][3 <<Abar[2 S1][2 S1]>>][1 <<Abar[2 S1]>>][1 <<Abar[2 S1]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 33m 7s.\n",
-      "Computing the boundary of the generator 7/8 (dimension 6) :\n",
-      "<<AlLp[3 <<Abar[2 S1][2 S1]>>][1 <<Abar[2 S1]>>][1 <<Abar[2 S1]>>][1 <<Abar[2 S1]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 33m 7s.\n",
-      "Computing the boundary of the generator 8/8 (dimension 6) :\n",
-      "<<AlLp[1 <<Abar[2 S1]>>][1 <<Abar[2 S1]>>][1 <<Abar[2 S1]>>][1 <<Abar[2 S1]>>][1 <<Abar[2 S1]>>][1 <<Abar[2 S1]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 5 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 33m 8s.\n",
-      "\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 7,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(homology obkz1 0 6)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "### Lisp files concerned in this chapter\n",
-    "\n",
-    "`cs-space-efhm.lisp`, `searching-homology.lisp`."
-   ]
-  }
- ],
- "metadata": {
-  "kernelspec": {
-   "display_name": "SBCL Lisp",
-   "language": "lisp",
-   "name": "lisp"
-  },
-  "language_info": {
-   "codemirror_mode": "text/x-common-lisp",
-   "mimetype": "text/x-common-lisp",
-   "name": "common-lisp",
-   "pygments_lexer": "common-lisp",
-   "version": "X3J13"
-  }
- },
- "nbformat": 4,
- "nbformat_minor": 1
-}
diff --git a/examples/21_Computing_homotopy_groups.ipynb b/examples/21_Computing_homotopy_groups.ipynb
deleted file mode 100644
index 9127ffc..0000000
--- a/examples/21_Computing_homotopy_groups.ipynb
+++ /dev/null
@@ -1,3179 +0,0 @@
-{
- "cells": [
-  {
-   "cell_type": "code",
-   "execution_count": 1,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "To load \"kenzo\":\n",
-      "  Load 1 ASDF system:\n",
-      "    kenzo\n",
-      "; Loading \"kenzo\"\n",
-      "\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "#<PACKAGE \"CAT\">"
-      ]
-     },
-     "execution_count": 1,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(ql:quickload \"kenzo\")\n",
-    "(in-package :cat)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "# Computing homotopy groups\n",
-    "\n",
-    "## Mathematical aspects\n",
-    "\n",
-    "The method used here to compute the homotopy groups is  known as the **Whitehead tower**. We recall some mathematical points:\n",
-    "\n",
-    "### 1) The Hurewicz theorem.\n",
-    "\n",
-    "**Theorem.** *Let X be a 1-connected space such that all its homology groups $H_r(X)$ are null\n",
-    "for $0<r<n$, then $\\pi_n(X)\\simeq H_n(X)$.*\n",
-    "\n",
-    "### 2) The properties of the classifying spaces.\n",
-    "\n",
-    "Let $X$ such that $\\pi_r(X)=0$ for $0<r<n$. From now on, we shall denote  $\\pi_n(X)$ simply by $\\pi$.\n",
-    "Let us consider the universal coefficients exact sequence:\n",
-    "$$ 0 \\longrightarrow Ext(H_{n-1}(X), \\pi) \\longrightarrow H^n(X,\\pi) \\longrightarrow Hom(H_n(X),\\pi) \\longrightarrow 0.$$\n",
-    "Here $H_{n-1}(X)=0$, so that a canonical isomorphism is given:\n",
-    "$$H^n(X,\\pi) \\buildrel {\\simeq} \\over \\longrightarrow Hom(H_n(X),\\pi),$$\n",
-    "but $H_n(X) \\simeq \\pi$ and this gives us a canonical element $h \\in H^n(X, \\pi)$ which is the fundamental $n$-th cohomology class in this context. A cocycle $\\chi$ representing $h$ is constructed as follows. In the chain complex\n",
-    "$$ \\cdots  \\rightarrow  C_{n+1}  \\buildrel {d_{n+1}} \\over \\longrightarrow C_n\n",
-    "            \\buildrel {d_n} \\over \\longrightarrow  C_{n-1} \\longrightarrow \\cdots,$$\n",
-    "the kernel $Z_n$ of $d_n$ is a summand of $C_n(X)$:\n",
-    "$$ C_n = Z_n \\oplus S$$\n",
-    "and such a decomposition induces a projection $p:C_n(X) \\longrightarrow Z_n$. Finally, we have also the canonical projection $p':Z_n \\longrightarrow H_n=\\pi$. Then, $\\chi$ can be defined by $\\chi = p' \\circ p$ and $\\chi$ *is a cocycle*. If another $p$ is chosen, another $\\chi$ is obtained but the cohomology class is the same.\n",
-    "\n",
-    "Let us fix now a choice for the cocycle $\\chi: C_n(X) \\longrightarrow \\pi$. This cocycle induces in turn a simplicial map:\n",
-    "$$ \\varphi_\\chi: C_n(X) \\longrightarrow K(\\pi,n), $$\n",
-    "where $K(\\pi,n)$ is the classifying group $K(\\pi_n(X),n)$ of the group $\\pi_n(X)=\\pi$. If $\\chi'$ is another choice for the cocycle then $\\varphi_{\\chi'}$ is homotopic to $\\varphi_\\chi$. We recall that the space $K(\\pi,n)$ has the following properties:\n",
-    "\n",
-    "1. $H_r(K(\\pi,n))=0$ for $0 < r < n$,\n",
-    "2. $\\pi_r(K(\\pi,n))=0$ for $r \\not= n$,\n",
-    "3. $\\pi_n(K(\\pi,n))=H_n(K(\\pi,n)= \\pi$.\n",
-    "\n",
-    "On the other hand, a canonical fibration of base space $K(\\pi, n)$ and fibre space $K(\\pi, n-1)$ is deduced from a canonical twisting operator $$\\tau: K(\\pi, n) \\longrightarrow K(\\pi, n-1)$$\n",
-    "\n",
-    "$$\n",
-    "\\begin{gathered}\n",
-    "K(\\pi, n-1)\\cr\n",
-    "\\downarrow \\cr\n",
-    "K(\\pi, n) \\times_\\tau K(\\pi, n-1) \\cr\n",
-    "\\downarrow \\cr\n",
-    "K(\\pi,n)\n",
-    "\\end{gathered}\n",
-    "$$\n",
-    "\n",
-    "So, if a simplicial map $\\varphi_\\chi: X \\longrightarrow K(\\pi,n)$ is given, it is then possible to construct a fibration of base space $X$ and fibre space $K(\\pi, n-1)$, the twisting operator being then defined by: $\\tau_\\chi = \\tau \\circ \\varphi_\\chi $, according to the diagram:\n",
-    "$$\\begin{aligned}\n",
-    "K(\\pi, n-1)\\qquad &\\qquad \\buildrel {=} \\over \\longrightarrow & K(\\pi, n-1)\\qquad \\cr\n",
-    "\\downarrow\\qquad\\qquad  & & \\downarrow\\qquad\\qquad \\cr\n",
-    "X'=X \\times_{\\tau_\\chi} K(\\pi, n-1) & \\qquad \\buildrel {\\psi_\\chi} \\over \\longrightarrow & K(\\pi,n) \\times_\\tau K(\\pi, n-1) \\cr\n",
-    "\\downarrow\\qquad\\qquad  & & \\downarrow\\qquad\\qquad \\cr\n",
-    "   X  \\qquad\\qquad      & \\qquad\\buildrel \\varphi_\\chi \\over \\longrightarrow & K(\\pi,n)\\qquad\\quad\n",
-    "\\end{aligned}$$\n",
-    "\n",
-    "### 3) The Serre exact sequence of the homotopy groups of fibrations.\n",
-    "\n",
-    "Let us consider the fibration\n",
-    "$$F \\quad \\hookrightarrow\\quad  T=X \\otimes_\\tau F \\hskip 1.2em \\longrightarrow \\hskip -1.2em \\longrightarrow \\quad X,$$\n",
-    "The Serre exact sequence establishes a connection between the homotopy groups of the 3 spaces, in any  dimension:\n",
-    "$$\\cdots \\longrightarrow \\pi_{n+1}(F) \\longrightarrow \\pi_{n+1}(T) \\longrightarrow \\pi_{n+1}(X) \\longrightarrow \\pi_n(F) \\longrightarrow$$\n",
-    "$$\\longrightarrow  \\pi_n(T) \\longrightarrow \\pi_n(X)  \\longrightarrow \\pi_{n-1}(F) \\longrightarrow \\cdots $$\n",
-    "In our special case, where the fibration is:\n",
-    "$$K(\\pi, n-1) \\quad \\hookrightarrow\\quad  X' \\hskip 1.2em \\longrightarrow \\hskip -1.2em\\longrightarrow  \\quad X,$$\n",
-    "the Serre sequence may be written:\n",
-    "$$\\cdots \\longrightarrow  \\pi_{n+1}(K(\\pi, n-1)) \\longrightarrow \\pi_{n+1}(X') \\longrightarrow \\pi_{n+1}(X) \\longrightarrow $$\n",
-    "$$\\longrightarrow \\pi_n(K(\\pi, n-1))\\longrightarrow\\pi_n(X')\\longrightarrow \\pi_n(X)\\longrightarrow \\pi_{n-1}(K(\\pi, n-1)) \\longrightarrow 0.$$\n",
-    "But we know that $\\pi_i(K(\\pi,n))=0$ for $i \\not= n$ and that $\\pi_n(K(\\pi, n))=\\pi,$\n",
-    "so the exact sequence may be re-written:\n",
-    "$$0 \\rightarrow \\pi_{n+1}(X') \\rightarrow \\pi_{n+1}(X) \\rightarrow 0 \\rightarrow  \\pi_n(X') \\rightarrow \\pi_n(X) \\rightarrow \\pi \\rightarrow 0.$$\n",
-    "The subsequence:\n",
-    "$$0 \\longrightarrow  \\pi_n(X') \\longrightarrow \\pi_n(X)\\longrightarrow \\pi \\longrightarrow 0.$$\n",
-    "is exact; furthermore, the cocycle $\\chi$ is such that the connection morphism\n",
-    "$\\partial: \\pi_n(X) \\rightarrow \\pi$ is the identity; so that we deduce that $\\pi_n (X')=0$.\n",
-    "\n",
-    "On the other hand, from the exactness of the subsequence\n",
-    "$$0 \\longrightarrow \\pi_{n+1}(X') \\longrightarrow \\pi_{n+1}(X) \\longrightarrow 0$$\n",
-    "we deduce that $\\pi_{n+1}(X') \\simeq \\pi_{n+1}(X)$ and more generally $\\pi_r(X') \\simeq \\pi_r(X)$ for $r \\not= n.$ In particular, $\\pi_r(X')=0$ for $r \\leq n+1$ and the Hurewicz theorem gives again:\n",
-    "$$H_{n+1}(X') \\simeq \\pi_{n+1}(X') \\simeq  \\pi_{n+1}(X).$$\n",
-    "So, if we know how to compute $H_{n+1}(X')$ then we  have obtained $\\pi_{n+1}(X).$\n",
-    "\n",
-    "### 4) The Whitehead tower\n",
-    "\n",
-    "Let us denote for a reason which will be clear in a moment the space $X'$ by $X^{(n+1)}$. Due to the properties of  $X^{(n+1)}$, we may iterate the process, namely, build the following fibrations, where $\\pi_{n+1}(X^{(n+1)})$ is  denoted simply by $\\pi'$:\n",
-    "\n",
-    "$$\\begin{aligned}\n",
-    "K(\\pi', n)\\qquad\\quad &\\qquad\\buildrel {=} \\over \\longrightarrow  & K(\\pi', n)\\qquad\\quad \\cr\n",
-    "\\downarrow\\qquad\\qquad  & & \\downarrow\\qquad\\qquad \\cr\n",
-    "X^{(n+2)}=X^{(n+1)} \\times_{\\tau_\\chi} K(\\pi', n) &\\qquad\\buildrel {\\psi_\\chi} \\over \\longrightarrow & \n",
-    "K(\\pi',n+1) \\times_\\tau K(\\pi', n) \\cr\n",
-    "\\downarrow \\qquad\\qquad & & \\downarrow\\qquad\\qquad \\cr\n",
-    "   X^{(n+1)}\\qquad\\quad  & \\qquad\\buildrel \\varphi_\\chi \\over \\longrightarrow & K(\\pi',n+1)\\qquad\n",
-    "\\end{aligned}$$\n",
-    "\n",
-    "where $X^{(n+2)}= X^{(n+1)} \\times_{\\tau_\\chi} K(\\pi', n)$ has the property\n",
-    "$$H_{n+2}(X^{(n+2)}) \\simeq  \\pi_{n+2}(X^{(n+2)}) \\simeq \\pi_{n+2}(X^{(n+1)}) \\simeq \\pi_{n+2}(X). $$\n",
-    "This construction is known as the Whitehead tower.\n",
-    "\n",
-    "## The functions for computing homotopy groups\n",
-    "\n",
-    "### An important remark\n",
-    "\n",
-    "In this version of Kenzo, only the case where the first non-null homology group (in non-null dimension) is $\\mathbb{Z}$ or $\\mathbb{Z}/{2 \\mathbb{Z}}$ can be processed; however if this homology group is a direct sum of several copies of $\\mathbb{Z}$ or $\\mathbb{Z}/{2 \\mathbb{Z}}$, then the corresponding stage of the Whitehead tower may also be constructed step by step.\n",
-    "\n",
-    "`chml-clss` *chcm first* *[Function]*\n",
-    "> Return a \"fundamental\" cohomology class, more precisely a cocycle $\\chi$ defining it. The first argument *chcm* must be a chain complex $C_*$ with effective homology; in particular, an effective chain complex $EC_*$ is a by-product of the machine object $C_*$. The second argument \"*first*\" is an integer $n$, namely the first non-null dimension from which the chain complex *chcm* has a non-null homology group, which {\\bf must be isomorphic to $\\mathbb{Z}$} or $\\mathbb{Z}/{2 \\mathbb{Z}}$. The reader may be amazed that this argument \"*first*\" must be provided, since it is a consequence of the given $C_*$. But in fact, the same function `chml-class` may also be used in different contexts, for example, the Postnikov tower; in such a case, the argument *first* is not redundant. The returned cocycle $\\chi$ is in any case a chain complex morphism $\\chi: EC_* \\longrightarrow \\mathbb{Z}$, where $\\mathbb{Z}$ is the unit chain complex created by the function `z-chcm`. The degree of the morphism is $-n$. It is important to note that  the chain complex involved in the source of the morphism is the **effective** chain complex of the homotopy equivalence value of the slot `efhm` of the object *chcm*. See the section *The general method for computing homology* in the Homology chapter. Finally, if $H_n(C_*)=\\mathbb{Z}/{2 \\mathbb{Z}}$, the actual cohomology class hoped by the user is the composition $p \\circ \\chi$, where $p$ is the canonical projection $\\mathbb{Z}\\longrightarrow\\mathbb{Z}/{2\\mathbb{Z}}$. But nevertheless, the `chml-clss` lisp function returns $\\chi$ and not $p \\circ \\chi$.\n",
-    "\n",
-    "`z-whitehead` *smst chml-clss* *[Function]*\n",
-    "> Return a fibration  over the simplicial set *smst* (the first argument), canonically associated to the \"cohomology class\" *chml-clss* (the second argument). The simplicial set $X$, i.e. *smst*, is reduced; its homotopy groups $\\pi_r(X)$ are null for $0 \\leq r \\leq n-1$. The first non null homotopy group $\\pi_n(X)$ is assumed to be $\\mathbb{Z}$, i.e. $\\pi_n(X)= H_n(X)= \\mathbb{Z}$. The previous function `chml-clss`, in this situation, returns a cocycle $\\chi$, which may be used as the second argument *chml-clss* of the function `z-whitehead`. The integer  $n$ is determined by the absolute value of the degree of the cohomology class *chcm-clss*. As explained in the previous section, a canonical fibration is induced by $\\chi$ and it is this fibration which is returned by `z-whitehead`. The slot `sintr` of the fibration is set by the internal function `z-whitehead-sintr` which builds in an efficient way the lisp function implementing the twisting operator $\\tau \\circ \\varphi_\\chi$.\n",
-    "\n",
-    "`z2-whitehead` *smst chcm-clss* *[Function]*\n",
-    "> Return a fibration  over the simplicial set *smst* (the first argument), canonically associated to the \"cohomology class\" *chml-clss* (the second argument). The simplicial set $X$, i.e. *smst*, is reduced; its homotopy groups $\\pi_r(X)$ are null for $0 \\leq r \\leq n-1$. The first non null homotopy group $\\pi_n(X)$ is assumed to be $\\mathbb{Z}/2\\mathbb{Z}$, i.e. $\\pi_n(X)= H_n(X)= \\mathbb{Z}/2\\mathbb{Z}$. The previous function `chml-clss`, in this situation, returns a \"cocycle\" $\\chi$, which may be used as the second argument *chml-clss* of the function `z2-whitehead`. The integer $n$ is determined by the absolute value of the degree of the cohomology class *chcm-clss*. In this $\\mathbb{Z}/2\\mathbb{Z}$ case, $\\chi$ is even not a cocycle. The actual cocycle is obtained by the composition $p \\circ \\chi$, $p$ being the canonical projection $\\mathbb{Z} \\longrightarrow \\mathbb{Z}/{2 \\mathbb{Z}}$. But the user is not concerned by these technicalities, because the function `z2-whitehead` makes itself the necessary conversion. The slot `sintr` of the fibration is set by the internal function `z2-whitehead-sintr` which builds in an efficient way the lisp function implementing the twisting operator $\\tau \\circ \\varphi_\\chi$.\n",
-    "\n",
-    "### Examples\n",
-    "\n",
-    "Let us retrieve some known facts about $S^3$, in particular $\\pi_4(S^3) \\simeq \\mathbb{Z}/{2 \\mathbb{Z}}$. We follow the theoritical method exposed above, namely build the fibration\n",
-    "$$K(\\mathbb{Z},2) \\quad \\hookrightarrow\\quad  S^3 \\times_{\\tau_\\chi} K(\\mathbb{Z},2) \\hskip 1.2em \\longrightarrow \\hskip -1.2em \\longrightarrow\\quad S^3,$$\n",
-    "and get the homology group in dimension 4 of the total space."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 2,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K1 Simplicial-Set]"
-      ]
-     },
-     "execution_count": 2,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def s3 (sphere 3))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 3,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "Computing boundary-matrix in dimension 0.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 10s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 0) :\n",
-      "* \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 1.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 0 :\n",
-      "\n",
-      "\n",
-      "Component Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 10s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 1.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 2.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 1 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 10s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 2.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 3.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 10s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 3) :\n",
-      "S3 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 2 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 10s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 3.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 10s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 3) :\n",
-      "S3 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 4.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 3 :\n",
-      "\n",
-      "\n",
-      "Component Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 10s.\n",
-      "\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 3,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(homology s3 0 4)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 4,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K12 Cohomology-Class on K1 of degree 3]"
-      ]
-     },
-     "execution_count": 4,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def s3-chml-clss (chml-clss s3 3))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 5,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K37 Fibration K1 -> K25]"
-      ]
-     },
-     "execution_count": 5,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def s3-fibr (z-whitehead s3 s3-chml-clss))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 6,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K43 Simplicial-Set]"
-      ]
-     },
-     "execution_count": 6,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def s3-total (fibration-total  s3-fibr))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 7,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "Computing boundary-matrix in dimension 0.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 10s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 0) :\n",
-      "<TnPr * <<Abar>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 1.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 0 :\n",
-      "\n",
-      "\n",
-      "Component Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 10s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 1.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 2.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 10s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 2) :\n",
-      "<TnPr * <<Abar[2 S1]>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 1 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 10s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 2.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 10s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 2) :\n",
-      "<TnPr * <<Abar[2 S1]>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 3.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 10s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 3) :\n",
-      "<TnPr S3 <<Abar>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 2 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 10s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 3.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 10s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 3) :\n",
-      "<TnPr S3 <<Abar>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 4.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 10s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 4) :\n",
-      "<TnPr * <<Abar[2 S1][2 S1]>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 3 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 10s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 4.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 10s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 4) :\n",
-      "<TnPr * <<Abar[2 S1][2 S1]>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 5.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 10s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 5) :\n",
-      "<TnPr S3 <<Abar[2 S1]>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 4 :\n",
-      "\n",
-      "\n",
-      "Component Z/2Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 10s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 5.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 10s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 5) :\n",
-      "<TnPr S3 <<Abar[2 S1]>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 6.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 10s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 6) :\n",
-      "<TnPr * <<Abar[2 S1][2 S1][2 S1]>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 5 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 10s.\n",
-      "\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 7,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(homology s3-total 0 6)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Let us show a similar example with the space $Moore(2,4)$. As $H_4 \\simeq \\mathbb{Z}/{2 \\mathbb{Z}}$, the function for building the fibration is `z2-whitehead`.  We verify that $\\pi_5(Moore(2,4))\\simeq \\mathbb{Z}/{2 \\mathbb{Z}}$"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 8,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "---done---"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 8,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(cat-init)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 9,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K1 Simplicial-Set]"
-      ]
-     },
-     "execution_count": 9,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def m24 (moore 2 4))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 10,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "\n",
-      "Dimension = 0:\n",
-      "\n",
-      "        Vertices :  (*)\n",
-      "\n",
-      "Dimension = 1:\n",
-      "\n",
-      "Dimension = 2:\n",
-      "\n",
-      "Dimension = 3:\n",
-      "\n",
-      "Dimension = 4:\n",
-      "\n",
-      "        Simplex : M4\n",
-      "\n",
-      "                Faces : (<AbSm 2-1-0 *> <AbSm 2-1-0 *> <AbSm 2-1-0 *> <AbSm 2-1-0 *> <AbSm 2-1-0 *>)\n",
-      "\n",
-      "Dimension = 5:\n",
-      "\n",
-      "        Simplex : N5\n",
-      "\n",
-      "                Faces : (<AbSm - M4> <AbSm 3-2-1-0 *> <AbSm - M4> <AbSm 3-2-1-0 *> <AbSm 3-2-1-0 *> <AbSm 3-2-1-0 *>)\n",
-      "\n",
-      "Dimension = 6:"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 10,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(show-structure m24 6)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 11,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "Computing boundary-matrix in dimension 0.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 10s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 0) :\n",
-      "* \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 1.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 0 :\n",
-      "\n",
-      "\n",
-      "Component Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 10s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 1.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 2.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 1 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 10s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 2.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 3.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 2 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 10s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 3.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 4.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 10s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 4) :\n",
-      "M4 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 3 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 10s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 4.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 10s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 4) :\n",
-      "M4 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 5.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 10s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 5) :\n",
-      "N5 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 4 :\n",
-      "\n",
-      "\n",
-      "Component Z/2Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 10s.\n",
-      "\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 11,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(homology m24 0 5)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 12,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K12 Cohomology-Class on K1 of degree 4]"
-      ]
-     },
-     "execution_count": 12,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def m24-chml-clss (chml-clss m24 4))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 13,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K49 Fibration K1 -> K37]"
-      ]
-     },
-     "execution_count": 13,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def m24-fibr (z2-whitehead m24 m24-chml-clss))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 14,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K55 Simplicial-Set]"
-      ]
-     },
-     "execution_count": 14,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def m24-total (fibration-total m24-fibr))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 15,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "Computing boundary-matrix in dimension 0.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 10s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 0) :\n",
-      "<TnPr * <<Abar>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 1.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 0 :\n",
-      "\n",
-      "\n",
-      "Component Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 10s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 1.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 2.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 1 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 10s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 2.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 3.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 10s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 3) :\n",
-      "<TnPr * <<Abar[3 <<Abar[2 1]>>]>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 2 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 10s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 3.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 10s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 3) :\n",
-      "<TnPr * <<Abar[3 <<Abar[2 1]>>]>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 4.\n",
-      "Rank of the source-module : 2.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 10s.\n",
-      "Computing the boundary of the generator 1/2 (dimension 4) :\n",
-      "<TnPr * <<Abar[4 <<Abar[3 2]>>]>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 10s.\n",
-      "Computing the boundary of the generator 2/2 (dimension 4) :\n",
-      "<TnPr M4 <<Abar>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 3 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 10s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 4.\n",
-      "Rank of the source-module : 2.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 10s.\n",
-      "Computing the boundary of the generator 1/2 (dimension 4) :\n",
-      "<TnPr * <<Abar[4 <<Abar[3 2]>>]>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 10s.\n",
-      "Computing the boundary of the generator 2/2 (dimension 4) :\n",
-      "<TnPr M4 <<Abar>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 5.\n",
-      "Rank of the source-module : 3.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 10s.\n",
-      "Computing the boundary of the generator 1/3 (dimension 5) :\n",
-      "<TnPr * <<Abar[5 <<Abar[4 3]>>]>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 10s.\n",
-      "Computing the boundary of the generator 2/3 (dimension 5) :\n",
-      "<TnPr * <<Abar[5 <<Abar[2 1][2 1]>>]>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 10s.\n",
-      "Computing the boundary of the generator 3/3 (dimension 5) :\n",
-      "<TnPr N5 <<Abar>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 4 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 10s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 5.\n",
-      "Rank of the source-module : 3.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 10s.\n",
-      "Computing the boundary of the generator 1/3 (dimension 5) :\n",
-      "<TnPr * <<Abar[5 <<Abar[4 3]>>]>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 10s.\n",
-      "Computing the boundary of the generator 2/3 (dimension 5) :\n",
-      "<TnPr * <<Abar[5 <<Abar[2 1][2 1]>>]>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 10s.\n",
-      "Computing the boundary of the generator 3/3 (dimension 5) :\n",
-      "<TnPr N5 <<Abar>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 6.\n",
-      "Rank of the source-module : 4.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 10s.\n",
-      "Computing the boundary of the generator 1/4 (dimension 6) :\n",
-      "<TnPr * <<Abar[6 <<Abar[5 4]>>]>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 10s.\n",
-      "Computing the boundary of the generator 2/4 (dimension 6) :\n",
-      "<TnPr * <<Abar[6 <<Abar[2 1][3 2]>>]>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 10s.\n",
-      "Computing the boundary of the generator 3/4 (dimension 6) :\n",
-      "<TnPr * <<Abar[6 <<Abar[3 2][2 1]>>]>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 10s.\n",
-      "Computing the boundary of the generator 4/4 (dimension 6) :\n",
-      "<TnPr * <<Abar[3 <<Abar[2 1]>>][3 <<Abar[2 1]>>]>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 5 :\n",
-      "\n",
-      "\n",
-      "Component Z/2Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 10s.\n",
-      "\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 15,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(homology m24-total 0 6)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "We may even verify that, up to 9, the homotopy groups of the classifying group $K(\\mathbb{Z},5)$, for instance, are null except $\\pi_5$. This is a far-fetched method to verify this well known result, but\n",
-    "it proves that the software is coherent."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 16,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K410 Abelian-Simplicial-Group]"
-      ]
-     },
-     "execution_count": 16,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def k5 (k-z 5))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 17,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K935 Cohomology-Class on K920 of degree 5]"
-      ]
-     },
-     "execution_count": 17,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def k5-chml-clss (chml-clss k5 5))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 18,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K938 Fibration K410 -> K398]"
-      ]
-     },
-     "execution_count": 18,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def k5-fibr (z-whitehead k5 k5-chml-clss)) "
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 19,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K939 Kan-Simplicial-Set]"
-      ]
-     },
-     "execution_count": 19,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def k5-total (fibration-total k5-fibr))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 20,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "Computing boundary-matrix in dimension 0.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 10s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 0) :\n",
-      "<TnPr <<Abar>> <<Abar>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 1.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 0 :\n",
-      "\n",
-      "\n",
-      "Component Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 10s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 1.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 2.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 1 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 10s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 2.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 3.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 2 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 10s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 3.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 4.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 10s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 4) :\n",
-      "<TnPr <<Abar>> <<Abar[4 <<Abar[3 <<Abar[2 S1]>>]>>]>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 3 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 10s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 4.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 10s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 4) :\n",
-      "<TnPr <<Abar>> <<Abar[4 <<Abar[3 <<Abar[2 S1]>>]>>]>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 5.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 10s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 5) :\n",
-      "<TnPr <<Abar[5 <<Abar[4 <<Abar[3 <<Abar[2 S1]>>]>>]>>]>> <<Abar>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 4 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 10s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 5.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 10s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 5) :\n",
-      "<TnPr <<Abar[5 <<Abar[4 <<Abar[3 <<Abar[2 S1]>>]>>]>>]>> <<Abar>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 6.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 10s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 6) :\n",
-      "<TnPr <<Abar>> <<Abar[6 <<Abar[5 <<Abar[2 S1][2 S1]>>]>>]>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 5 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 10s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 6.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 10s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 6) :\n",
-      "<TnPr <<Abar>> <<Abar[6 <<Abar[5 <<Abar[2 S1][2 S1]>>]>>]>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 7.\n",
-      "Rank of the source-module : 2.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 10s.\n",
-      "Computing the boundary of the generator 1/2 (dimension 7) :\n",
-      "<TnPr <<Abar>> <<Abar[7 <<Abar[3 <<Abar[2 S1]>>][3 <<Abar[2 S1]>>]>>]>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 10s.\n",
-      "Computing the boundary of the generator 2/2 (dimension 7) :\n",
-      "<TnPr <<Abar[7 <<Abar[6 <<Abar[5 <<Abar[2 S1][2 S1]>>]>>]>>]>> <<Abar>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 6 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 10s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 7.\n",
-      "Rank of the source-module : 2.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 10s.\n",
-      "Computing the boundary of the generator 1/2 (dimension 7) :\n",
-      "<TnPr <<Abar>> <<Abar[7 <<Abar[3 <<Abar[2 S1]>>][3 <<Abar[2 S1]>>]>>]>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 10s.\n",
-      "Computing the boundary of the generator 2/2 (dimension 7) :\n",
-      "<TnPr <<Abar[7 <<Abar[6 <<Abar[5 <<Abar[2 S1][2 S1]>>]>>]>>]>> <<Abar>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 8.\n",
-      "Rank of the source-module : 3.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 10s.\n",
-      "Computing the boundary of the generator 1/3 (dimension 8) :\n",
-      "<TnPr <<Abar>> <<Abar[8 <<Abar[7 <<Abar[2 S1][2 S1][2 S1]>>]>>]>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 10s.\n",
-      "Computing the boundary of the generator 2/3 (dimension 8) :\n",
-      "<TnPr <<Abar>> <<Abar[4 <<Abar[3 <<Abar[2 S1]>>]>>][4 <<Abar[3 <<Abar[2 S1]>>]>>]>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 10s.\n",
-      "Computing the boundary of the generator 3/3 (dimension 8) :\n",
-      "<TnPr <<Abar[8 <<Abar[7 <<Abar[3 <<Abar[2 S1]>>][3 <<Abar[2 S1]>>]>>]>>]>> <<Abar>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 7 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 10s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 8.\n",
-      "Rank of the source-module : 3.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 10s.\n",
-      "Computing the boundary of the generator 1/3 (dimension 8) :\n",
-      "<TnPr <<Abar>> <<Abar[8 <<Abar[7 <<Abar[2 S1][2 S1][2 S1]>>]>>]>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 10s.\n",
-      "Computing the boundary of the generator 2/3 (dimension 8) :\n",
-      "<TnPr <<Abar>> <<Abar[4 <<Abar[3 <<Abar[2 S1]>>]>>][4 <<Abar[3 <<Abar[2 S1]>>]>>]>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 10s.\n",
-      "Computing the boundary of the generator 3/3 (dimension 8) :\n",
-      "<TnPr <<Abar[8 <<Abar[7 <<Abar[3 <<Abar[2 S1]>>][3 <<Abar[2 S1]>>]>>]>>]>> <<Abar>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 9.\n",
-      "Rank of the source-module : 5.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 10s.\n",
-      "Computing the boundary of the generator 1/5 (dimension 9) :\n",
-      "<TnPr <<Abar>> <<Abar[9 <<Abar[3 <<Abar[2 S1]>>][5 <<Abar[2 S1][2 S1]>>]>>]>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 10s.\n",
-      "Computing the boundary of the generator 2/5 (dimension 9) :\n",
-      "<TnPr <<Abar>> <<Abar[9 <<Abar[5 <<Abar[2 S1][2 S1]>>][3 <<Abar[2 S1]>>]>>]>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 10s.\n",
-      "Computing the boundary of the generator 3/5 (dimension 9) :\n",
-      "<TnPr <<Abar[5 <<Abar[4 <<Abar[3 <<Abar[2 S1]>>]>>]>>]>> <<Abar[4 <<Abar[3 <<Abar[2 S1]>>]>>]>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 10s.\n",
-      "Computing the boundary of the generator 4/5 (dimension 9) :\n",
-      "<TnPr <<Abar[9 <<Abar[8 <<Abar[7 <<Abar[2 S1][2 S1][2 S1]>>]>>]>>]>> <<Abar>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 10s.\n",
-      "Computing the boundary of the generator 5/5 (dimension 9) :\n",
-      "<TnPr <<Abar[9 <<Abar[4 <<Abar[3 <<Abar[2 S1]>>]>>][4 <<Abar[3 <<Abar[2 S1]>>]>>]>>]>> <<Abar>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 8 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 10s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 9.\n",
-      "Rank of the source-module : 5.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 10s.\n",
-      "Computing the boundary of the generator 1/5 (dimension 9) :\n",
-      "<TnPr <<Abar>> <<Abar[9 <<Abar[3 <<Abar[2 S1]>>][5 <<Abar[2 S1][2 S1]>>]>>]>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 10s.\n",
-      "Computing the boundary of the generator 2/5 (dimension 9) :\n",
-      "<TnPr <<Abar>> <<Abar[9 <<Abar[5 <<Abar[2 S1][2 S1]>>][3 <<Abar[2 S1]>>]>>]>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 10s.\n",
-      "Computing the boundary of the generator 3/5 (dimension 9) :\n",
-      "<TnPr <<Abar[5 <<Abar[4 <<Abar[3 <<Abar[2 S1]>>]>>]>>]>> <<Abar[4 <<Abar[3 <<Abar[2 S1]>>]>>]>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 10s.\n",
-      "Computing the boundary of the generator 4/5 (dimension 9) :\n",
-      "<TnPr <<Abar[9 <<Abar[8 <<Abar[7 <<Abar[2 S1][2 S1][2 S1]>>]>>]>>]>> <<Abar>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 10s.\n",
-      "Computing the boundary of the generator 5/5 (dimension 9) :\n",
-      "<TnPr <<Abar[9 <<Abar[4 <<Abar[3 <<Abar[2 S1]>>]>>][4 <<Abar[3 <<Abar[2 S1]>>]>>]>>]>> <<Abar>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 10.\n",
-      "Rank of the source-module : 7.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 10s.\n",
-      "Computing the boundary of the generator 1/7 (dimension 10) :\n",
-      "<TnPr <<Abar>> <<Abar[10 <<Abar[9 <<Abar[2 S1][2 S1][2 S1][2 S1]>>]>>]>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 10s.\n",
-      "Computing the boundary of the generator 2/7 (dimension 10) :\n",
-      "<TnPr <<Abar>> <<Abar[10 <<Abar[3 <<Abar[2 S1]>>][3 <<Abar[2 S1]>>][3 <<Abar[2 S1]>>]>>]>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 10s.\n",
-      "Computing the boundary of the generator 3/7 (dimension 10) :\n",
-      "<TnPr <<Abar>> <<Abar[4 <<Abar[3 <<Abar[2 S1]>>]>>][6 <<Abar[5 <<Abar[2 S1][2 S1]>>]>>]>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 11s.\n",
-      "Computing the boundary of the generator 4/7 (dimension 10) :\n",
-      "<TnPr <<Abar>> <<Abar[6 <<Abar[5 <<Abar[2 S1][2 S1]>>]>>][4 <<Abar[3 <<Abar[2 S1]>>]>>]>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 11s.\n",
-      "Computing the boundary of the generator 5/7 (dimension 10) :\n",
-      "<TnPr <<Abar[10 <<Abar[9 <<Abar[3 <<Abar[2 S1]>>][5 <<Abar[2 S1][2 S1]>>]>>]>>]>> <<Abar>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 11s.\n",
-      "Computing the boundary of the generator 6/7 (dimension 10) :\n",
-      "<TnPr <<Abar[10 <<Abar[9 <<Abar[5 <<Abar[2 S1][2 S1]>>][3 <<Abar[2 S1]>>]>>]>>]>> <<Abar>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 11s.\n",
-      "Computing the boundary of the generator 7/7 (dimension 10) :\n",
-      "<TnPr <<Abar[5 <<Abar[4 <<Abar[3 <<Abar[2 S1]>>]>>]>>][5 <<Abar[4 <<Abar[3 <<Abar[2 S1]>>]>>]>>]>> <<Abar>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 9 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 12s.\n",
-      "\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 20,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(homology k5-total 0 10)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Let us show now the iteration of the process, to get for instance $\\pi_5(S^3)$ and $\\pi_6(S^3)$:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 21,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "---done---"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 21,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(cat-init)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 22,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K1 Simplicial-Set]"
-      ]
-     },
-     "execution_count": 22,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def s3 (sphere 3))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 23,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K12 Cohomology-Class on K1 of degree 3]"
-      ]
-     },
-     "execution_count": 23,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def s3-chml-clss (chml-clss s3 3))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 24,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K37 Fibration K1 -> K25]"
-      ]
-     },
-     "execution_count": 24,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def s3-fibration (z-whitehead s3 s3-chml-clss))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 25,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K43 Simplicial-Set]"
-      ]
-     },
-     "execution_count": 25,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def s3-4 (fibration-total s3-fibration))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 26,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "Computing boundary-matrix in dimension 4.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 12s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 4) :\n",
-      "<TnPr * <<Abar[2 S1][2 S1]>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 5.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 12s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 5) :\n",
-      "<TnPr S3 <<Abar[2 S1]>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 4 :\n",
-      "\n",
-      "\n",
-      "Component Z/2Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 12s.\n",
-      "\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 26,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(homology s3-4 4)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 27,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K253 Cohomology-Class on K238 of degree 4]"
-      ]
-     },
-     "execution_count": 27,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def s3-4-chml-clss (chml-clss s3-4 4))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 28,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K292 Fibration K43 -> K278]"
-      ]
-     },
-     "execution_count": 28,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def s3-4-fibration (z2-whitehead s3-4 s3-4-chml-clss))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 29,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K298 Simplicial-Set]"
-      ]
-     },
-     "execution_count": 29,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def s3-5 (fibration-total s3-4-fibration))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 30,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "Computing boundary-matrix in dimension 5.\n",
-      "Rank of the source-module : 4.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 12s.\n",
-      "Computing the boundary of the generator 1/4 (dimension 5) :\n",
-      "<TnPr <TnPr * <<Abar>>> <<Abar[5 <<Abar[4 3]>>]>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 12s.\n",
-      "Computing the boundary of the generator 2/4 (dimension 5) :\n",
-      "<TnPr <TnPr * <<Abar>>> <<Abar[5 <<Abar[2 1][2 1]>>]>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 12s.\n",
-      "Computing the boundary of the generator 3/4 (dimension 5) :\n",
-      "<TnPr <TnPr * <<Abar[2 S1]>>> <<Abar[3 <<Abar[2 1]>>]>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 12s.\n",
-      "Computing the boundary of the generator 4/4 (dimension 5) :\n",
-      "<TnPr <TnPr S3 <<Abar[2 S1]>>> <<Abar>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 6.\n",
-      "Rank of the source-module : 7.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 12s.\n",
-      "Computing the boundary of the generator 1/7 (dimension 6) :\n",
-      "<TnPr <TnPr * <<Abar>>> <<Abar[6 <<Abar[5 4]>>]>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 12s.\n",
-      "Computing the boundary of the generator 2/7 (dimension 6) :\n",
-      "<TnPr <TnPr * <<Abar>>> <<Abar[6 <<Abar[2 1][3 2]>>]>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 12s.\n",
-      "Computing the boundary of the generator 3/7 (dimension 6) :\n",
-      "<TnPr <TnPr * <<Abar>>> <<Abar[6 <<Abar[3 2][2 1]>>]>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 12s.\n",
-      "Computing the boundary of the generator 4/7 (dimension 6) :\n",
-      "<TnPr <TnPr * <<Abar>>> <<Abar[3 <<Abar[2 1]>>][3 <<Abar[2 1]>>]>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 12s.\n",
-      "Computing the boundary of the generator 5/7 (dimension 6) :\n",
-      "<TnPr <TnPr * <<Abar[2 S1]>>> <<Abar[4 <<Abar[3 2]>>]>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 12s.\n",
-      "Computing the boundary of the generator 6/7 (dimension 6) :\n",
-      "<TnPr <TnPr S3 <<Abar>>> <<Abar[3 <<Abar[2 1]>>]>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 12s.\n",
-      "Computing the boundary of the generator 7/7 (dimension 6) :\n",
-      "<TnPr <TnPr * <<Abar[2 S1][2 S1][2 S1]>>> <<Abar>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 5 :\n",
-      "\n",
-      "\n",
-      "Component Z/2Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 12s.\n",
-      "\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 30,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(homology s3-5 5)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 31,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K609 Cohomology-Class on K594 of degree 5]"
-      ]
-     },
-     "execution_count": 31,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def s3-5-chml-clss (chml-clss s3-5 5))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 32,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K624 Fibration K298 -> K610]"
-      ]
-     },
-     "execution_count": 32,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def s3-5-fibration (z2-whitehead s3-5 s3-5-chml-clss))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 33,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K630 Simplicial-Set]"
-      ]
-     },
-     "execution_count": 33,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def s3-6 (fibration-total s3-5-fibration))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 34,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "Computing boundary-matrix in dimension 6.\n",
-      "Rank of the source-module : 10.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 12s.\n",
-      "Computing the boundary of the generator 1/10 (dimension 6) :\n",
-      "<TnPr <TnPr <TnPr * <<Abar>>> <<Abar>>> <<Abar[6 <<Abar[5 <<Abar[4 3]>>]>>]>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 12s.\n",
-      "Computing the boundary of the generator 2/10 (dimension 6) :\n",
-      "<TnPr <TnPr <TnPr * <<Abar>>> <<Abar>>> <<Abar[6 <<Abar[5 <<Abar[2 1][2 1]>>]>>]>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 12s.\n",
-      "Computing the boundary of the generator 3/10 (dimension 6) :\n",
-      "<TnPr <TnPr <TnPr * <<Abar[2 S1]>>> <<Abar>>> <<Abar[4 <<Abar[3 <<Abar[2 1]>>]>>]>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 12s.\n",
-      "Computing the boundary of the generator 4/10 (dimension 6) :\n",
-      "<TnPr <TnPr <TnPr * <<Abar>>> <<Abar[6 <<Abar[5 4]>>]>>> <<Abar>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 12s.\n",
-      "Computing the boundary of the generator 5/10 (dimension 6) :\n",
-      "<TnPr <TnPr <TnPr * <<Abar>>> <<Abar[6 <<Abar[2 1][3 2]>>]>>> <<Abar>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 12s.\n",
-      "Computing the boundary of the generator 6/10 (dimension 6) :\n",
-      "<TnPr <TnPr <TnPr * <<Abar>>> <<Abar[6 <<Abar[3 2][2 1]>>]>>> <<Abar>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 12s.\n",
-      "Computing the boundary of the generator 7/10 (dimension 6) :\n",
-      "<TnPr <TnPr <TnPr * <<Abar>>> <<Abar[3 <<Abar[2 1]>>][3 <<Abar[2 1]>>]>>> <<Abar>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 12s.\n",
-      "Computing the boundary of the generator 8/10 (dimension 6) :\n",
-      "<TnPr <TnPr <TnPr * <<Abar[2 S1]>>> <<Abar[4 <<Abar[3 2]>>]>>> <<Abar>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 12s.\n",
-      "Computing the boundary of the generator 9/10 (dimension 6) :\n",
-      "<TnPr <TnPr <TnPr S3 <<Abar>>> <<Abar[3 <<Abar[2 1]>>]>>> <<Abar>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 12s.\n",
-      "Computing the boundary of the generator 10/10 (dimension 6) :\n",
-      "<TnPr <TnPr <TnPr * <<Abar[2 S1][2 S1][2 S1]>>> <<Abar>>> <<Abar>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 7.\n",
-      "Rank of the source-module : 19.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 12s.\n",
-      "Computing the boundary of the generator 1/19 (dimension 7) :\n",
-      "<TnPr <TnPr <TnPr * <<Abar>>> <<Abar>>> <<Abar[7 <<Abar[6 <<Abar[5 4]>>]>>]>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 12s.\n",
-      "Computing the boundary of the generator 2/19 (dimension 7) :\n",
-      "<TnPr <TnPr <TnPr * <<Abar>>> <<Abar>>> <<Abar[7 <<Abar[6 <<Abar[2 1][3 2]>>]>>]>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 12s.\n",
-      "Computing the boundary of the generator 3/19 (dimension 7) :\n",
-      "<TnPr <TnPr <TnPr * <<Abar>>> <<Abar>>> <<Abar[7 <<Abar[6 <<Abar[3 2][2 1]>>]>>]>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 12s.\n",
-      "Computing the boundary of the generator 4/19 (dimension 7) :\n",
-      "<TnPr <TnPr <TnPr * <<Abar>>> <<Abar>>> <<Abar[7 <<Abar[3 <<Abar[2 1]>>][3 <<Abar[2 1]>>]>>]>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 12s.\n",
-      "Computing the boundary of the generator 5/19 (dimension 7) :\n",
-      "<TnPr <TnPr <TnPr * <<Abar[2 S1]>>> <<Abar>>> <<Abar[5 <<Abar[4 <<Abar[3 2]>>]>>]>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 12s.\n",
-      "Computing the boundary of the generator 6/19 (dimension 7) :\n",
-      "<TnPr <TnPr <TnPr * <<Abar>>> <<Abar[3 <<Abar[2 1]>>]>>> <<Abar[4 <<Abar[3 <<Abar[2 1]>>]>>]>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 12s.\n",
-      "Computing the boundary of the generator 7/19 (dimension 7) :\n",
-      "<TnPr <TnPr <TnPr S3 <<Abar>>> <<Abar>>> <<Abar[4 <<Abar[3 <<Abar[2 1]>>]>>]>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 12s.\n",
-      "Computing the boundary of the generator 8/19 (dimension 7) :\n",
-      "<TnPr <TnPr <TnPr * <<Abar>>> <<Abar[7 <<Abar[6 5]>>]>>> <<Abar>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 12s.\n",
-      "Computing the boundary of the generator 9/19 (dimension 7) :\n",
-      "<TnPr <TnPr <TnPr * <<Abar>>> <<Abar[7 <<Abar[2 1][4 3]>>]>>> <<Abar>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 12s.\n",
-      "Computing the boundary of the generator 10/19 (dimension 7) :\n",
-      "<TnPr <TnPr <TnPr * <<Abar>>> <<Abar[7 <<Abar[3 2][3 2]>>]>>> <<Abar>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 12s.\n",
-      "Computing the boundary of the generator 11/19 (dimension 7) :\n",
-      "<TnPr <TnPr <TnPr * <<Abar>>> <<Abar[7 <<Abar[4 3][2 1]>>]>>> <<Abar>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 12s.\n",
-      "Computing the boundary of the generator 12/19 (dimension 7) :\n",
-      "<TnPr <TnPr <TnPr * <<Abar>>> <<Abar[7 <<Abar[2 1][2 1][2 1]>>]>>> <<Abar>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 12s.\n",
-      "Computing the boundary of the generator 13/19 (dimension 7) :\n",
-      "<TnPr <TnPr <TnPr * <<Abar>>> <<Abar[3 <<Abar[2 1]>>][4 <<Abar[3 2]>>]>>> <<Abar>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 12s.\n",
-      "Computing the boundary of the generator 14/19 (dimension 7) :\n",
-      "<TnPr <TnPr <TnPr * <<Abar>>> <<Abar[4 <<Abar[3 2]>>][3 <<Abar[2 1]>>]>>> <<Abar>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 12s.\n",
-      "Computing the boundary of the generator 15/19 (dimension 7) :\n",
-      "<TnPr <TnPr <TnPr * <<Abar[2 S1]>>> <<Abar[5 <<Abar[4 3]>>]>>> <<Abar>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 12s.\n",
-      "Computing the boundary of the generator 16/19 (dimension 7) :\n",
-      "<TnPr <TnPr <TnPr * <<Abar[2 S1]>>> <<Abar[5 <<Abar[2 1][2 1]>>]>>> <<Abar>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 12s.\n",
-      "Computing the boundary of the generator 17/19 (dimension 7) :\n",
-      "<TnPr <TnPr <TnPr S3 <<Abar>>> <<Abar[4 <<Abar[3 2]>>]>>> <<Abar>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 12s.\n",
-      "Computing the boundary of the generator 18/19 (dimension 7) :\n",
-      "<TnPr <TnPr <TnPr * <<Abar[2 S1][2 S1]>>> <<Abar[3 <<Abar[2 1]>>]>>> <<Abar>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 12s.\n",
-      "Computing the boundary of the generator 19/19 (dimension 7) :\n",
-      "<TnPr <TnPr <TnPr S3 <<Abar[2 S1][2 S1]>>> <<Abar>>> <<Abar>>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 6 :\n",
-      "\n",
-      "\n",
-      "Component Z/12Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 15s.\n",
-      "\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 34,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(homology s3-6 6)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "An interesting example is given by the real projective space $P^\\infty\\mathbb{R}/P^1\\mathbb{R}$ which may be built in `Kenzo` by the function `r-proj-space`. We list its first homotopy groups."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 35,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "---done---"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 35,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(cat-init)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 36,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K1 Simplicial-Set]"
-      ]
-     },
-     "execution_count": 36,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def x (r-proj-space 2))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 37,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "Computing boundary-matrix in dimension 0.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 15s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 0) :\n",
-      "0 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 1.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 0 :\n",
-      "\n",
-      "\n",
-      "Component Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 15s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 1.\n",
-      "Rank of the source-module : 0.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 2.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 15s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 2) :\n",
-      "2 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 1 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 15s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 2.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 15s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 2) :\n",
-      "2 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 3.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 15s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 3) :\n",
-      "3 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 2 :\n",
-      "\n",
-      "\n",
-      "Component Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 15s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 3.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 15s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 3) :\n",
-      "3 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 4.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 15s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 4) :\n",
-      "4 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 3 :\n",
-      "\n",
-      "\n",
-      "Component Z/2Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 15s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 4.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 15s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 4) :\n",
-      "4 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 5.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 15s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 5) :\n",
-      "5 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 4 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 15s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 5.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 15s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 5) :\n",
-      "5 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 6.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 15s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 6) :\n",
-      "6 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 5 :\n",
-      "\n",
-      "\n",
-      "Component Z/2Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 15s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 6.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 15s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 6) :\n",
-      "6 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 7.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 15s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 7) :\n",
-      "7 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 6 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 15s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 7.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 15s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 7) :\n",
-      "7 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 8.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 15s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 8) :\n",
-      "8 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 7 :\n",
-      "\n",
-      "\n",
-      "Component Z/2Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 15s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 8.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 15s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 8) :\n",
-      "8 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 9.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 15s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 9) :\n",
-      "9 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 8 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 15s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 9.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 15s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 9) :\n",
-      "9 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 10.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 15s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 10) :\n",
-      "10 \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 9 :\n",
-      "\n",
-      "\n",
-      "Component Z/2Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 15s.\n",
-      "\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 37,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(homology x 0 10)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Using the machinery described in this chapter, we find that the total space of the fibration has the same homology groups as $S^3$. It has been effectively proved that this space is homotopic to $S^3$."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 38,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K12 Cohomology-Class on K1 of degree 2]"
-      ]
-     },
-     "execution_count": 38,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def ch (chml-clss x 2))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 39,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K25 Fibration K1 -> K13]"
-      ]
-     },
-     "execution_count": 39,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def f2 (z-whitehead x ch))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 40,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K31 Simplicial-Set]"
-      ]
-     },
-     "execution_count": 40,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def x3 (fibration-total f2))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 41,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "Computing boundary-matrix in dimension 0.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 15s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 0) :\n",
-      "<TnPr 0 *> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 1.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 15s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 1) :\n",
-      "<TnPr 0 S1> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 0 :\n",
-      "\n",
-      "\n",
-      "Component Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 15s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 1.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 15s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 1) :\n",
-      "<TnPr 0 S1> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 2.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 15s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 2) :\n",
-      "<TnPr 2 *> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 1 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 15s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 2.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 15s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 2) :\n",
-      "<TnPr 2 *> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 3.\n",
-      "Rank of the source-module : 2.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 15s.\n",
-      "Computing the boundary of the generator 1/2 (dimension 3) :\n",
-      "<TnPr 2 S1> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 15s.\n",
-      "Computing the boundary of the generator 2/2 (dimension 3) :\n",
-      "<TnPr 3 *> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 2 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 15s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 3.\n",
-      "Rank of the source-module : 2.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 15s.\n",
-      "Computing the boundary of the generator 1/2 (dimension 3) :\n",
-      "<TnPr 2 S1> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 15s.\n",
-      "Computing the boundary of the generator 2/2 (dimension 3) :\n",
-      "<TnPr 3 *> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 4.\n",
-      "Rank of the source-module : 2.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 15s.\n",
-      "Computing the boundary of the generator 1/2 (dimension 4) :\n",
-      "<TnPr 3 S1> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 15s.\n",
-      "Computing the boundary of the generator 2/2 (dimension 4) :\n",
-      "<TnPr 4 *> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 3 :\n",
-      "\n",
-      "\n",
-      "Component Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 15s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 4.\n",
-      "Rank of the source-module : 2.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 15s.\n",
-      "Computing the boundary of the generator 1/2 (dimension 4) :\n",
-      "<TnPr 3 S1> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 15s.\n",
-      "Computing the boundary of the generator 2/2 (dimension 4) :\n",
-      "<TnPr 4 *> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 5.\n",
-      "Rank of the source-module : 2.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 15s.\n",
-      "Computing the boundary of the generator 1/2 (dimension 5) :\n",
-      "<TnPr 4 S1> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 15s.\n",
-      "Computing the boundary of the generator 2/2 (dimension 5) :\n",
-      "<TnPr 5 *> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 4 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 15s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 5.\n",
-      "Rank of the source-module : 2.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 15s.\n",
-      "Computing the boundary of the generator 1/2 (dimension 5) :\n",
-      "<TnPr 4 S1> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 15s.\n",
-      "Computing the boundary of the generator 2/2 (dimension 5) :\n",
-      "<TnPr 5 *> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 6.\n",
-      "Rank of the source-module : 2.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 15s.\n",
-      "Computing the boundary of the generator 1/2 (dimension 6) :\n",
-      "<TnPr 5 S1> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 15s.\n",
-      "Computing the boundary of the generator 2/2 (dimension 6) :\n",
-      "<TnPr 6 *> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 5 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 15s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 6.\n",
-      "Rank of the source-module : 2.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 15s.\n",
-      "Computing the boundary of the generator 1/2 (dimension 6) :\n",
-      "<TnPr 5 S1> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 15s.\n",
-      "Computing the boundary of the generator 2/2 (dimension 6) :\n",
-      "<TnPr 6 *> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 7.\n",
-      "Rank of the source-module : 2.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 15s.\n",
-      "Computing the boundary of the generator 1/2 (dimension 7) :\n",
-      "<TnPr 6 S1> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 15s.\n",
-      "Computing the boundary of the generator 2/2 (dimension 7) :\n",
-      "<TnPr 7 *> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 6 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 15s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 7.\n",
-      "Rank of the source-module : 2.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 15s.\n",
-      "Computing the boundary of the generator 1/2 (dimension 7) :\n",
-      "<TnPr 6 S1> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 15s.\n",
-      "Computing the boundary of the generator 2/2 (dimension 7) :\n",
-      "<TnPr 7 *> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 8.\n",
-      "Rank of the source-module : 2.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 15s.\n",
-      "Computing the boundary of the generator 1/2 (dimension 8) :\n",
-      "<TnPr 7 S1> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 15s.\n",
-      "Computing the boundary of the generator 2/2 (dimension 8) :\n",
-      "<TnPr 8 *> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 7 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 15s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 8.\n",
-      "Rank of the source-module : 2.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 15s.\n",
-      "Computing the boundary of the generator 1/2 (dimension 8) :\n",
-      "<TnPr 7 S1> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 15s.\n",
-      "Computing the boundary of the generator 2/2 (dimension 8) :\n",
-      "<TnPr 8 *> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 9.\n",
-      "Rank of the source-module : 2.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 15s.\n",
-      "Computing the boundary of the generator 1/2 (dimension 9) :\n",
-      "<TnPr 8 S1> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 16s.\n",
-      "Computing the boundary of the generator 2/2 (dimension 9) :\n",
-      "<TnPr 9 *> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 8 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 16s.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 9.\n",
-      "Rank of the source-module : 2.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 16s.\n",
-      "Computing the boundary of the generator 1/2 (dimension 9) :\n",
-      "<TnPr 8 S1> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 16s.\n",
-      "Computing the boundary of the generator 2/2 (dimension 9) :\n",
-      "<TnPr 9 *> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 10.\n",
-      "Rank of the source-module : 2.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 16s.\n",
-      "Computing the boundary of the generator 1/2 (dimension 10) :\n",
-      "<TnPr 9 S1> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 21s.\n",
-      "Computing the boundary of the generator 2/2 (dimension 10) :\n",
-      "<TnPr 10 *> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 9 :\n",
-      "\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-10-08, 12h 34m 25s.\n",
-      "\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 41,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(homology x3 0 10)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "### Lisp files concerned in this chapter\n",
-    "\n",
-    "`whitehead.lisp`, `smith.lisp`."
-   ]
-  }
- ],
- "metadata": {
-  "kernelspec": {
-   "display_name": "SBCL Lisp",
-   "language": "lisp",
-   "name": "lisp"
-  },
-  "language_info": {
-   "codemirror_mode": "text/x-common-lisp",
-   "mimetype": "text/x-common-lisp",
-   "name": "common-lisp",
-   "pygments_lexer": "common-lisp",
-   "version": "X3J13"
-  }
- },
- "nbformat": 4,
- "nbformat_minor": 1
-}
diff --git a/examples/anromero/bousfield-kan/gamma.lsp b/examples/anromero/bousfield-kan/gamma.lsp
deleted file mode 100644
index 2d1b67e..0000000
--- a/examples/anromero/bousfield-kan/gamma.lsp
+++ /dev/null
@@ -1,1107 +0,0 @@
-;; GAMMA GAMMA GAMMA GAMMA GAMMA GAMMA GAMMA
-;; GAMMA GAMMA GAMMA GAMMA GAMMA GAMMA GAMMA
-;; GAMMA GAMMA GAMMA GAMMA GAMMA GAMMA GAMMA
-
-(IN-PACKAGE "COMMON-LISP-USER")
-
-(provide "gamma")
-
-
-;; TYPES
-
-(DEFUN SGM-P (object)
-   ;; SGM = SiGMa   
-   (declare (type any object))
-   (the boolean
-     (and (consp object)
-          (typep (car object) 'fixnum)
-          (typep (cdr object) 'cmbn))))
-
-(DEFTYPE SGM () '(satisfies sgm-p))
-
-(DEFUN IGAMMA-P (object)
-   ;; IGAMMA = Internal GAMMA,
-   ;;   without the keyword and the degree
-   (declare (type any object))
-   (the boolean
-     (and (listp object)
-          (every #'sgm-p object)))) 
-
-(DEFTYPE IGAMMA () '(satisfies igamma-p))
-
-(DEFUN GAMMA-P (object)
-   (declare (type any object))
-   (the boolean
-     (and (consp object)
-          (eql (car object) :gamma)
-          (consp (cdr object))
-          (typep (second object) 'fixnum)
-          (typep (cddr object) 'igamma))))
-
-(DEFTYPE GAMMA () '(satisfies gamma-p))
-
-
-
-;; MACROS
-
-(DEFMACRO SGM (sgop cmbn)
-   `(cons ,sgop ,cmbn))
-
-(DEFMACRO -SGM (mark)
-   `(car ,mark))
-
-(DEFMACRO SGOP (sgm)
-   `(car ,sgm))
-
-(DEFMACRO -SGOP (mark)
-   `(caar ,mark))
-
-(DEFMACRO SGCM (sgm)
-   `(cdr ,sgm))
-
-(DEFMACRO -SGCM (mark)
-   `(cdar ,mark))
-
-(DEFMACRO WITH-SGM ((sgop-var sgcm-var) sgm . body)
-   `(let ((,sgop-var (sgop ,sgm))
-          (,sgcm-var (sgcm ,sgm)))
-       (declare
-          (fixnum ,sgop-var)
-          (type cmbn ,sgcm-var))
-       ,@body))
-
-(DEFMACRO WITH--SGM ((sgop-var sgcm-var) mark . body)
-   `(let ((,sgop-var (-sgop ,mark))
-          (,sgcm-var (-sgcm ,mark)))
-       (declare
-          (fixnum ,sgop-var)
-          (type cmbn ,sgcm-var))
-       ,@body))
-
-(DEFMACRO SGM-NON-ZERO-P (sgm)
-   `(cmbn-non-zero-p (sgcm ,sgm)))
-
-(DEFMACRO SGM-ZERO-P (sgm)
-  `(cmbn-zero-p (sgcm ,sgm)))
-
-(DEFMACRO MAKE-GAMMA (&key degr list)
-   `(cons :gamma
-       (cons ,degr ,list)))
-
-(DEFMACRO GAMMA-DEGR (gmm)
-   `(cadr ,gmm))
-
-(DEFMACRO GAMMA-LIST (gmm)
-   `(cddr ,gmm))
-
-(DEFMACRO WITH-GAMMA ((degr list) gmm . body)
-   `(let ((,degr (gamma-degr ,gmm))
-          (,list (gamma-list ,gmm)))
-       (declare
-          (fixnum ,degr)
-          (list ,list))
-       ,@body))
-
-(DEFMACRO SGM-GAMMA (degr sgop sgcm)
-   `(cons :gamma (cons ,degr (cons (cons ,sgop ,sgcm) nil))))
-
-(DEFMACRO GAMMA-NON-ZERO-P (gmm)
-   `(gamma-list ,gmm)) 
-
-(DEFMACRO GAMMA-ZERO-P (gmm)
-  `(null (gamma-list ,gmm)))
-
-
-#|(DEFMETHOD PRINT-KEYCONS ((key (eql :sgm)) cdr stream)
-   (setf cdr (cons :sgm cdr))
-   (format stream
-      "<Sgm ~A ~A>"
-      (hyphenize-list (dgop-int-ext (sgop cdr)))
-      (sgcm cdr))
-   cdr)
-|#
-
-
-;; METHODS
-
-(DEFMETHOD PRINT-KEYCONS ((key (eql :gamma)) cdr stream)
-   (declare
-    (list cdr)
-    (stream stream))
-   (the (eql t)
-     (let ((degr (first cdr))
-           (list (rest cdr)))
-        (declare
-         (fixnum degr)
-         (list list))
-        (format stream "<GAMMA ~D" degr)
-        (do ((mark list (cdr mark))
-             (nth 0 (1+ nth)))
-            ((endp mark))
-           (declare
-            (list mark)
-            (fixnum nth))
-           (when (and *print-length* (= nth *print-length*))
-              (format stream "~%... ...")
-              (return))
-           (format stream "~%  <~D  ~A  >" (hyphenize-list (dgop-int-ext (sgop (car mark)))) (sgcm (car mark))))
-        (format stream "~%>" )
-        t)))
-
-
-;; ELEMENTARY OPERATIONS WITH GAMMA ELEMENTS
- 
-(DEFUN GAMMA-ELT (degr &rest rest)
-   (declare (fixnum degr))
-   (the gamma
-     (let ((rslt (list degr :gamma)))
-        (do ((mark rest (cddr mark)))
-            ((endp mark) (nreverse rslt))
-           (declare (list mark))
-           (push (sgm (car mark) (cadr mark)) rslt)))))
-
-(DEFUN CHECK-GAMMA (gmm)
-  (declare
-   (type gamma gmm))
-  (the boolean
-    (with-gamma (degr glist) gmm
-      (declare
-       (fixnum degr)
-       (list glist))
-      (do ((mark2 glist mark1)
-           (mark1 (rest glist) (cdr mark1)))
-          ((endp mark1) t)
-         (declare
-          (list mark1 mark2))
-         (unless (= degr (+ (length (dgop-int-ext (-sgop mark2))) (cmbn-degr (-sgcm mark2))))
-            (error "In CHECK-GAMMA, bad degre; the element:~@
-                ~A~@
-                has a degree different to:~@
-                ~A."
-	       (-sgm mark2) degr))
-         (unless (< (-sgop mark2) (-sgop mark1))
-            (error "In CHECK-GAMMA, bad order; the degeneracy operator:~@
-                ~A~@
-                is not less than the degeneracy operator:~@
-                ~A."
-              (dgop-int-ext (-sgop mark2)) (dgop-int-ext (-sgop mark1))))))))
-
-#|
-(setf g1 (gamma-elt 5 3 (cmbn 3 8 'a) 1 (cmbn 4 3 'b)))
-(check-gamma g1)
-(setf g2 (gamma-elt 5 3 (cmbn 4 3 'b) 1 (cmbn 3 8 'a)))
-(check-gamma g2)
-(setf g3 (gamma-elt 5 1 (cmbn 4 3 'b) 3 (cmbn 3 8 'a)))
-(check-gamma g3)
-(setf g4 (gamma-elt 5))
-(check-gamma g4)
-|#
-
-(DEFUN ZERO-GAMMA (degr)
-   (declare (fixnum degr))
-   (the gamma
-     (make-gamma
-      :degr degr
-      :list +empty-list+)))
-
-#|
-(setf g0 (zero-gamma 3))
-(check-gamma g0) 
-|#
-
-(DEFUN GAMMA-OPPS (gmm)
-   (declare (type gamma gmm))
-   (the gamma
-      (with-gamma (degr glist) gmm
-         (make-gamma
-            :degr degr
-            :list (mapcar #'(lambda (sgm)
-                               (declare (type sgm sgm))
-                               (with-sgm (sgop cmbn) sgm
-                                  (sgm sgop (cmbn-opps cmbn))))
-                     glist)))))
-
-#|
-(setf g (gamma-elt 5 1 (cmbn 4 3 'b 8 'c) 3 (cmbn 3 8 'a -9 'b)))
-(gamma-opps g)
-|# 
-
-(DEFUN 2GAMMA-ADD (cmpr gmm1 gmm2)
-   (declare
-    (type cmprf cmpr)
-    (type gamma gmm1 gmm2))
-   (the gamma
-     (with-gamma (degr1 list1) gmm1
-       (with-gamma (degr2 list2) gmm2
-         (declare
-          (fixnum degr1 degr2)
-          (list list1 list2))
-         (unless (= degr1 degr2)
-            (error "In 2GAMMA-ADD, the gamma elements have different degrees ~D and ~D."
-              degr1 degr2))
-         (unless list1
-            (return-from 2gamma-add gmm2))
-         (unless list2
-            (return-from 2gamma-add gmm1))
-         (let ((pre-rslt +empty-list+))
-            (declare (list pre-rslt))
-            (do ((mark1 list1)
-                 (mark2 list2))
-                ((or (endp mark1) (endp mark2))
-                 (if mark1
-                    (setf pre-rslt (nreconc pre-rslt mark1))
-                    (if mark2
-                       (setf pre-rslt (nreconc pre-rslt mark2))
-                       (setf pre-rslt (nreverse pre-rslt)))))
-               (declare (list mark1 mark2))
-               (with--sgm (sgop1 cmbn1) mark1
-                 (with--sgm (sgop2 cmbn2) mark2
-                   (declare 
-                     (fixnum sgop1 sgop2)
-                     (type cmbn cmbn1 cmbn2))
-                   (if (= sgop1 sgop2)
-                      (let ((cmbn (2cmbn-add cmpr cmbn1 cmbn2)))
-                         (declare (type cmbn cmbn))
-                         (unless (cmbn-zero-p cmbn)
-                            (push (sgm sgop1 cmbn) pre-rslt))
-                         (setf mark1 (cdr mark1)
-                               mark2 (cdr mark2)))
-                      (if (< sgop1 sgop2)
-                         (progn
-                          (push (-sgm mark1) pre-rslt)
-                          (setf mark1 (cdr mark1)))
-                         (progn
-                          (push (-sgm mark2) pre-rslt)
-                          (setf mark2 (cdr mark2))))))))
-            (make-gamma :degr degr1 :list pre-rslt))))))
-
-#|
-(setf g1 (gamma-elt 5 1 (cmbn 4 3 'b -5 'd) 3 (cmbn 3 8 'a -7 'c)))
-(setf g2 (gamma-elt 5 0 (cmbn 5 3 'a 8 'c) 1 (cmbn 4 2 'b 9 'c) 
-           2 (cmbn 4 -5 'a) 3 (cmbn 3 -4 'a 8 'b)))
-(setf g3 (2GAMMA-ADD #'s-cmpr g1 g2))
-(setf g4 (gamma-elt 5 0 (cmbn 5 -3 'a -8 'c) 1 (cmbn 4 -2 'b 8 'c)
-           3 (cmbn 3 5 'a -8 'b 7 'c)))
-(setf g5 (2GAMMA-ADD #'s-cmpr g3 g4))
-(setf g6 (gamma-elt 5 1 (cmbn 4 -3 'b -17 'c 5 'd) 2 (cmbn 4 5 'a) 3 (cmbn 3 -9 'a)))
-(2GAMMA-ADD #'s-cmpr g5 g6)
-|#  
-
-(defun ADD-SGM-TO-GAMMA (cmpr sgm gmm)
-   (declare
-    (type cmprf cmpr)
-    (type sgm sgm)
-    (type gamma gmm))
-   (the gamma
-     (with-sgm (sgop sgcm) sgm
-       (declare 
-         (fixnum sgop)
-         (type cmbn sgcm))
-       (with-gamma (degr glist) gmm
-         (declare 
-           (fixnum degr)
-           (list glist))
-         (let ((pre-rslt +empty-list+))
-            (declare (list pre-rslt))
-            (do ((mark glist (cdr mark)))
-                ((or (endp mark) (equal nil sgop))
-                 (if sgop
-                  (progn
-                   (push sgm pre-rslt)
-                   (setf pre-rslt (nreverse pre-rslt)))
-                    (setf pre-rslt (nreconc pre-rslt mark))))
-               (declare (list mark))
-               (with--sgm (sgop2 sgcm2) mark
-                 (declare 
-                   (fixnum sgop2)
-                   (type cmbn sgcm2))
-                 (if (= sgop sgop2)
-                    (let ((cmbn (2cmbn-add cmpr sgcm sgcm2)))
-                       (declare (type cmbn cmbn))
-                       (unless (cmbn-zero-p cmbn)
-                          (push (sgm sgop cmbn) pre-rslt))
-                       (setf sgop nil))
-                    (if (< sgop sgop2)
-                       (progn 
-                         (push sgm pre-rslt)
-                         (setf sgop nil)
-                         (push (-sgm mark) pre-rslt))
-                       (push (-sgm mark) pre-rslt)))))
-            (make-gamma :degr degr :list pre-rslt))))))
-
- #|
-(setf g1 (gamma-elt 5 1 (cmbn 4 3 'b -5 'd) 3 (cmbn 3 8 'a -7 'c)))
-(setf g2 (add-sgm-to-gamma cmpr (sgm 7 (cmbn 2 -8 'd)) g1))
-(setf g3 (add-sgm-to-gamma cmpr (sgm 7 (cmbn 2 8 'd)) g2))
-(setf g4 (add-sgm-to-gamma cmpr (sgm 3 (cmbn 3 -8 'a 7 'c 8 'd)) g2))
-(setf g5 (add-sgm-to-gamma cmpr (sgm 11 (cmbn 2 9 'a )) g4))
-(setf g6 (add-sgm-to-gamma cmpr (sgm 9 (cmbn 3 8 'b)) g5))
-(setf g7 (add-sgm-to-gamma cmpr (sgm 9 (cmbn 3 -8 'b 8 'c)) g6))
-(setf g8 (add-sgm-to-gamma cmpr (sgm 9 (cmbn 3 -8 'b )) g6))
-|# 
-
-(DEFUN NSGM-ADD (cmpr degr &rest rest)
-   (declare
-      (type cmprf cmpr)
-      (fixnum degr)
-      (list rest))
-   (unless rest
-      (return-from nsgm-add (zero-gamma degr)))
-   (the gamma
-      (let ((rslt (list (first rest))))
-         (declare (list rslt))
-         (dolist (sgm (rest rest))
-            (declare (type sgm sgm))
-            (with-sgm  (sgop sgcm) sgm
-               (do ((mark1 rslt (cdr mark1))
-                    (mark2 nil mark1))
-                   ((endp mark1) 
-                    (setf (cdr mark2) (list sgm)))
-                  (ecase (funcall #'f-cmpr sgop (-sgop mark1))
-                     (:less
-                      (if mark2
-                         (push sgm (cdr mark2))
-                         (push sgm rslt))
-                      (return))                     
-                     (:equal
-                      (let ((cmbn2 (2cmbn-add cmpr (-sgcm mark1) sgcm)))
-                         (setf (-sgcm mark1) cmbn2))
-                      (return))                     
-                     (:greater )))))
-         (make-gamma
-          :degr degr
-          :list (flet ((sgm-zero-p (sgm)
-                        (let ((sgcm (sgcm sgm)))
-                           (cmbn-zero-p sgcm))))
-                  (remove-if #'sgm-zero-p rslt))))))
-
- #|
-(setf cmpr #'s-cmpr)
-(setf degr 5)
-(progn 
-  (setf sgm1 (sgm 7 (cmbn 2 3 'a 5 'b)))
-  (setf sgm2 (sgm 4 (cmbn 4 7 'a 8 'c)))
-  (setf sgm3 (sgm 12 (cmbn 3 -5 'a 8 'b)))
-  (setf sgm4 (sgm 4 (cmbn 4 -7 'a 9 'c 12 'd)))
-  (setf sgm5 (sgm 6 (cmbn 3 8 'a)))
-  (setf sgm6 (sgm 12 (cmbn 3 6 'a)))
-  (nsgm-add cmpr degr sgm1 sgm2 sgm3 sgm4 sgm5 sgm6))
-
-(progn 
-  (setf sgm1 (sgm 7 (cmbn 2 3 'a 5 'b)))
-  (setf sgm2 (sgm 4 (cmbn 4 7 'a 8 'c)))
-  (setf sgm3 (sgm 12 (cmbn 3 -5 'a 8 'b)))
-  (setf sgm4 (sgm 4 (cmbn 4 -7 'a 9 'c 12 'd)))
-  (setf sgm5 (sgm 6 (cmbn 3 8 'a)))
-  (setf sgm6 (sgm 12 (cmbn 3 6 'a)))
-  (setf sgm7 (sgm 12 (cmbn 3 -6 'a)))
-  (nsgm-add cmpr degr sgm1 sgm2 sgm3 sgm4 sgm5 sgm6 sgm7))
-
-(progn 
-  (setf sgm1 (sgm 7 (cmbn 2 3 'a 5 'b)))
-  (setf sgm2 (sgm 4 (cmbn 4 7 'a 8 'c)))
-  (setf sgm3 (sgm 12 (cmbn 3 -5 'a 8 'b)))
-  (setf sgm4 (sgm 4 (cmbn 4 -7 'a 9 'c 12 'd)))
-  (setf sgm5 (sgm 6 (cmbn 3 8 'a)))
-  (setf sgm6 (sgm 12 (cmbn 3 6 'a)))
-  (setf sgm7 (sgm 7 (cmbn 2 -3 'a -5 'b)))
-  (nsgm-add cmpr degr sgm1 sgm2 sgm3 sgm4 sgm5 sgm6 sgm7))
-
-(progn 
-  (setf sgm1 (sgm 7 (cmbn 2 3 'a 5 'b)))
-  (setf sgm2 (sgm 7 (cmbn 2 -3 'a -5 'b)))
-  (nsgm-add cmpr degr sgm1 sgm2))
-
-|#  
-
-
-(DEFUN SGM-NDGNR (dgop sgm)
-   (declare
-      (fixnum dgop)
-      (type sgm sgm))
-   (the sgm
-      (with-sgm (sgop sgcm) sgm
-         (sgm (dgop*dgop dgop sgop) sgcm)))) 
-
-#|
-(setf sgm (sgm 5 (cmbn 2 5 'a)))
-(sgm-ndgnr 2 sgm)
-(sgm-ndgnr 1 sgm)
-(sgm-ndgnr 5 sgm)
-|# 
-
-(DEFUN GAMMA-NDGNR (dgop gmm)
-   (declare
-      (fixnum dgop)
-      (type gamma gmm))
-   (the gamma
-      (with-gamma (degr glist) gmm
-        (let ((pre-rslt (mapcar #'(lambda (sgm)
-                          (sgm-ndgnr dgop sgm))
-                          glist))
-              (degr2 (+ degr (length (dgop-int-ext dgop)))))
-           (make-gamma :degr degr2 :list pre-rslt)))))
-
-#|
-(setf g (gamma-elt 5 3 (cmbn 3 7 'a) 11 (cmbn 2 -4 'b)))
-(gamma-ndgnr 2 g)
-(gamma-ndgnr 8 g)
-(gamma-ndgnr 3 g)
-
-|# 
-        
-
-
- 
-;; FUNCTIONS FOR THE CONSTRUCTION OF THE SIMPLICIAL ABELIAN GROUP
-;; \GAMMA(C) 
- 
-(DEFUN GAMMA-TO-ABSM (gmm)
-   (declare (type gamma gmm))
-   (the absm
-     (with-gamma (degr glist) gmm
-       (declare (fixnum degr)
-         (list glist))
-       (if (endp glist)
-          (let ((dgop (dgop-ext-int (reverse (<a-b< 0 degr)))))
-             (declare (fixnum dgop))
-             (absm dgop (gamma-elt 0)))
-          (let* ((sgop-list (mapcar #'(lambda (sgm)
-                                        (sgop sgm))
-                              glist))
-                 (dgop (first sgop-list)))
-             (declare
-              (type list sgop-list)
-              (fixnum dgop))
-             (progn
-              (do ((mark1 (cdr sgop-list) (cdr mark1)))
-                  ((endp mark1))
-                 (declare (list mark1))
-                 (setf dgop (logand dgop (car mark1))))
-              (let* ((degr2 (- degr (length (dgop-int-ext dgop))))
-                     (pre-rslt +empty-list+))
-                 (declare (fixnum degr2)
-                   (type list pre-rslt))
-                 (do ((mark2 glist (cdr mark2)))
-                     ((endp mark2))
-                    (declare (list mark2))
-                    (with--sgm (sgop sgcm) mark2
-                      (declare (fixnum sgop)
-                        (type cmbn sgcm))
-                      (let ((sgop2 sgop))
-                          (declare (fixnum sgop2))
-                         (progn
-                          (do ((indx (1- (integer-length dgop)) (1- indx)))
-                              ((minusp indx))
-                             (declare (fixnum indx))
-                              (when (logbitp indx dgop)
-                                 (setf sgop2 (remove-bit sgop2 indx))))
-                          (push (sgm sgop2 sgcm) pre-rslt)))))
-                 (absm dgop (make-gamma :degr degr2
-                              :list (nreverse pre-rslt))))))))))
-
-
-
-#|
- (setf gmm (gamma-elt 5 3 (cmbn 3 6 'a) 7 (cmbn 2 -8 'c)))
-(gamma-to-absm gmm)
-
-(setf gmm2 (gamma-elt 5 3 (cmbn 3 6 'a) 7 (cmbn 2 -8 'c) 11 (cmbn 2 6 'a)))
-(gamma-to-absm gmm2)
-|#
-     
-
-(DEFUN CMBN-CMPR (cmpr)
-   (declare (type cmprf cmpr))
-   (flet ((rslt (cmbn1 cmbn2)
-            (declare (type cmbn cmbn1 cmbn2))
-            (let ((degr1 (cmbn-degr cmbn1))
-                  (degr2 (cmbn-degr cmbn2)))
-               (declare (fixnum degr1 degr2))
-               (unless (= degr1 degr2)
-                  (error "In CMBN-CMPR, the two combinations have different degrees ~D and ~D."
-                    degr1 degr2))
-               (flet ((term-cmpr (term1 term2)
-                        (with-term (cffc1 gnrt1) term1
-                          (with-term (cffc2 gnrt2) term2
-                            (declare (fixnum cffc1 cffc2)
-                              (type gnrt gnrt1 gnrt2))
-                            (lexico
-                             (f-cmpr cffc1 cffc2)
-                             (funcall cmpr gnrt1 gnrt2))))))
-                 (maplexico #'term-cmpr (cmbn-list cmbn1) (cmbn-list cmbn2))))))
-     (the cmprf #'rslt)))
- 
-(DEFUN GAMMA-CMPR (cmpr)
-   (declare (type cmprf cmpr))
-   (let ((c-cmpr (cmbn-cmpr cmpr)))
-      (declare (type cmprf c-cmpr))
-      (flet ((rslt (gmm1 gmm2)
-               (declare (type gamma gmm1 gmm2))
-               (flet ((sgm-cmpr (sgm1 sgm2)
-                       (declare (type sgm sgm1 sgm2))
-                       (with-sgm (sgop1 cmbn1) sgm1
-                         (with-sgm (sgop2 cmbn2) sgm2
-                           (declare
-                            (fixnum sgop1 sgop2)
-                            (type cmbn cmbn1 cmbn2))
-                           (lexico
-                            (f-cmpr sgop1 sgop2)
-                            (funcall c-cmpr cmbn1 cmbn2))))))
-                 (maplexico #'sgm-cmpr (gamma-list gmm1) (gamma-list gmm2)))))
-     (the cmprf #'rslt))))   
-
-#|
-(setf g-cmpr (gamma-cmpr #'s-cmpr))
-(setf g1 (gamma-elt 3 1 (cmbn 2 3 'a) 3 (cmbn 1 5 'b)))
-(setf g2 (gamma-elt 3 1 (cmbn 2 3 'a) 3 (cmbn 1 8 'b)))
-(funcall g-cmpr g1 g2)
-(funcall g-cmpr g2 g1)
-(setf g3 (gamma-elt 3 2 (cmbn 2 3 'a) 3 (cmbn 1 5 'b)))
-(funcall g-cmpr g1 g3)
-(funcall g-cmpr g2 g3)
-(funcall g-cmpr g2 g2)
-(setf g4 (gamma-elt 3 2 (cmbn 2 3 'b) 3 (cmbn 1 5 'b)))
-(funcall g-cmpr g4 g3)
-(setf g5 (gamma-elt 3 2 (cmbn 2 3 'b)))
-(funcall g-cmpr g5 g3)
-(funcall g-cmpr g5 g4)
-|# 
-
-
-
-(defun sgm-face (dffr)
-   (declare (type morphism dffr))
-   (flet ((rslt (indx dmns sgm)
-            (declare 
-              (fixnum indx dmns)
-              (type sgm sgm))
-            (the sgm 
-              (with-sgm (sgop sgcm) sgm
-                (declare 
-                  (fixnum sgop)
-                  (type cmbn sgcm))
-                (let* ((ext-sgop (dgop-int-ext sgop))
-                       (k (length ext-sgop))
-                       (r (- dmns k))
-                       (c-degr (cmbn-degr sgcm)))
-                   (declare
-                    (type list ext-sgop)
-                    (fixnum k r c-degr))
-                   (unless (= r c-degr)
-                      (error "In SGM-FACE, the degree of the Sigma element ~D is different to the degree introduced ~D."
-                        (+ c-degr k) dmns))
-                   (multiple-value-bind (dgop 1dlop) (1dlop-dgop indx sgop)
-                      (declare (fixnum dgop 1dlop))                     
-                      (if (not 1dlop)
-                         (SGM dgop sgcm)
-                         (if (= r 1dlop)
-                          (let ((cmbn (? dffr sgcm)))
-                             (declare (type cmbn cmbn))
-                             (SGM dgop cmbn))
-                            (sgm dgop (cmbn (1- r)))
-                            ))))))))
-     (the face #'rslt)))
-
-
- 
-(DEFUN GAMMA-FACE (cmpr dffr)
-   (declare 
-     (type cmprf cmpr)
-     (type morphism dffr))
-   (let ((sgm-f (sgm-face dffr)))
-      (flet ((rslt (indx dmns gmsm)
-               (declare
-                (fixnum indx dmns)
-                (type gamma gmsm))
-               (the absm
-                 (let ((pre-rslt nil))
-                    (do ((mark (gamma-list gmsm) (cdr mark)))
-                        ((endp mark) (setf pre-rslt (nreverse pre-rslt)))
-                       (declare 
-                         (type list mark))
-                       (let ((sgm (-sgm mark)))
-                          (let ((sface (funcall sgm-f indx dmns sgm)))
-                             (if (sgm-non-zero-p sface)
-                                (push sface pre-rslt)))))
-                    (gamma-to-absm (apply #'nsgm-add cmpr (1- dmns) pre-rslt))))))
-        (the face #'rslt))))
-
-
-#|
-(setf d3 (delta 3))
-(setf cmpr (cmpr d3))
-(setf dffr (dffr d3))
-
-(setf sface (sgm-face dffr))
-(setf s1 (sgm 3 (cmbn 2 5 7 -8 13)))
-(dotimes (i 5)
-   (print (funcall sface i 4 s1)))
-
-(setf s2 (sgm 23 (cmbn 3 -7 15)))
-(dotimes (i 8)
-   (print (funcall sface i 7 s2)))
-
-(setf gface (gamma-face cmpr dffr))
-(setf g1 (sgm-gamma 4 3 (cmbn 2 5 7 -8 13)))
-(dotimes (i 5)
-   (print i)
-   (print (funcall gface i 4 g1)))
-
-(setf g2 (sgm-gamma 7 23 (cmbn 3 -7 15)))
-(dotimes (i 8)
-   (print i)
-   (print (funcall gface i 7 g2)))
-
-(setf g3 (sgm-gamma 7 59 (cmbn 2 1 7 -5 13 6 14)))
-(setf g4 (2gamma-add cmpr g2 g3))
-
-(dotimes (i 8)
-   (print i)
-   (print (funcall gface i 7 g3)))
-
-(setf g5 (sgm-gamma 7 27 (cmbn 3 1 15)))
-(setf g6 (2gamma-add cmpr g2 g5))
-(dotimes (i 8)
-   (print i)
-   (print (funcall gface i 7 g6)))
-|# 
-
-(defun gamma-grml (cmpr)
-   (flet ((rslt (dmns crpr)
-            (the absm
-              (with-crpr (dgop1 gmm1 dgop2 gmm2) crpr
-                (let ((sgm-list1 +empty-list+)
-                      (sgm-list2 +empty-list+)
-                      (k1 (length (dgop-int-ext dgop1)))
-                      (k2 (length (dgop-int-ext dgop2)))
-                      (g1 (gamma-elt 0))
-                      (g2 (gamma-elt 0)))
-                   (with-gamma (degr1 glist1) gmm1
-                     (do ((mark1 glist1 (cdr mark1)))
-                         ((endp mark1))
-                        (with--sgm (sgop1 sgcm1) mark1 
-                          (push (sgm (dgop*dgop dgop1 sgop1) sgcm1) sgm-list1)))
-                     (setf g1 (make-gamma :degr (+ degr1 k1)
-                                :list (nreverse sgm-list1))))
-                   (with-gamma (degr2 glist2) gmm2
-                     (do ((mark2 glist2 (cdr mark2)))
-                         ((endp mark2))
-                        (with--sgm (sgop2 sgcm2) mark2 
-                          (push (sgm (dgop*dgop dgop2 sgop2) sgcm2) sgm-list2)))
-                     (setf g2 (make-gamma :degr (+ degr2 k2)
-                                :list (nreverse sgm-list2))))
-                   (gamma-to-absm (2gamma-add cmpr g1 g2)))))))
-     #'rslt))
-
-#|
-(setf ggrml (gamma-grml cmpr))
-(funcall ggrml 9 (crpr 136 g3 9 g4))
-
-(funcall ggrml 7 (crpr 0 g3 0 g4))
-(funcall ggrml 7 (crpr 0 g3 0 (gamma-opps g4)))
-|# 
-
-(defun gamma-grin (dmns gmm)
-   (the absm
-     (absm 0 (gamma-opps gmm))))
-
-
-#|
-(gamma-grin 7 g3)
-(gamma-grin 7 g4)
-|# 
- 
-  
-(defun gamma-chcm (x)
-   (declare (type simplicial-set x))
-   (the ab-simplicial-group
-     (let* ((x-cmpr (cmpr x))
-            (x-dffr (dffr x))
-            (x-orgn (orgn x))
-            (cmpr (gamma-cmpr x-cmpr))
-            (bspn (gamma-elt 0))
-            (face (gamma-face x-cmpr x-dffr))
-            (sintr-grml (gamma-grml x-cmpr)))
-        (build-ab-smgr
-         :cmpr cmpr
-         :basis :locally-effective
-         :bspn bspn
-         :face face
-         :bndr-strt :gnrt
-         :dgnl-strt :gnrt
-         :sintr-grml sintr-grml
-         :sintr-grin #'gamma-grin
-         :orgn `(GAMMA ,x)
-         ))))
-
-
-#|
-(setf d2 (delta 2)) 
-(setf gamma-d2 (gamma-chcm d2))
-(basis gamma-d2 2)
-(orgn gamma-d2)
-(setf g1 (gamma-elt 5 7 (cmbn 2 3 7) 11 (cmbn 2 -9 13)))
-(setf g2 (gamma-elt 5 7 (cmbn 2 -3 7) 9 (cmbn 3 -5 15)))
-(cmpr gamma-d2 g1 g2)
-(cmpr gamma-d2 g2 g1)
-(setf g3 (2gamma-add (cmpr d2) g1 g2))
-(cmpr gamma-d2 g1 g3)
-(cmpr gamma-d2 g2 g3)
-(bspn gamma-d2)
-(dotimes (i 6)
-   (print i)
-   (print (face gamma-d2 i 5 g3)))
-(grml gamma-d2 5 (crpr 0 g2 0 (gamma-opps g3)))
-(grin gamma-d2 5 g1)
-
-|# 
-
-
-
-;; GAMMA APPLIED TO A MORPHISM
-
-(defun gamma-sintr (f)
-   (declare (type morphism f))
-   (flet ((rslt (dmns gmm)
-            (declare 
-              (fixnum dmns)
-              (type gamma gmm))
-            (the absm
-              (with-gamma (degr glist) gmm
-                (declare 
-                  (fixnum degr)
-                  (list glist))
-                (let ((pre-rslt +empty-list+))
-                   (declare (list pre-rslt))
-                   (do ((mark glist (cdr mark)))
-                       ((endp mark))
-                      (declare (list mark))
-                      (with--sgm (sgop sgcm) mark
-                        (declare
-                         (fixnum sgop)
-                         (type cmbn sgcm))
-                        (let ((sgm2 (sgm sgop (? f sgcm))))
-                           (declare (type sgm sgm2))
-                           (if (sgm-non-zero-p sgm2)
-                              (push sgm2 pre-rslt)))))
-                   (gamma-to-absm (make-gamma :degr degr :list (nreverse pre-rslt))))))))
-     #'rslt))
-                    
-#|
-(setf d3 (delta 3))
-(setf f (idnt-mrph d3))
-(setf gamma-f (gamma-sintr f))
-(setf gmm1 (gamma-elt 5 5 (cmbn 3 7 15) 26 (cmbn 2 -3 11)))
-(funcall gamma-f 5 gmm1)
-
-(setf g (opps f))
-(setf gamma-g (gamma-sintr g))
-(funcall gamma-g 5 g1)
-
-(setf f+g (add f g))
-(setf gamma-fg (gamma-sintr f+g))
-(funcall gamma-fg 5 g1)
-
-|#  
-
-(defun gamma-mrph (f)
-   (declare (type morphism f))
-   (the simplicial-mrph
-     (let ((sorc (sorc f))
-           (trgt (trgt f))
-           (degr (degr f)))
-        (unless (= degr 0)
-           (error "In GAMMA-MRPH, the morphism has degree ~D different to zero."
-             degr))
-        (build-smmr
-         :sorc (gamma-chcm sorc)
-         :trgt (gamma-chcm trgt)
-         :degr degr
-         :sintr (gamma-sintr f)
-         :orgn `(GAMMA ,f)))))
-
-#|
-(setf gamma-f (gamma-mrph f))
-(? gamma-f 5 g1)
-(setf g2 (gamma-elt 5 5 (cmbn 3 -7 15) 10 (cmbn 3 7 15)))
-(? gamma-f 5 g2)
-(? gamma-f 5 (2gamma-add (cmpr d3) g1 g2))
-(? gamma-f (cmbn 5 1 g2 1 g1))
-|#
-
-
-(defun sgm-hintr (cmpr h d)
-   (declare 
-     (type cmprf cmpr)
-     (type morphism h d))
-   (labels ((rslt (indx dmns sgm)
-            (declare 
-              (fixnum indx dmns)
-              (type sgm sgm))
-            (the gamma
-              (with-sgm (sgop sgcm) sgm
-                (declare 
-                  (fixnum sgop)
-                  (type cmbn sgcm))
-                (if (= 0 sgop)
-                   (let ((degr (cmbn-degr sgcm)))
-                      (declare (fixnum degr))
-                      (if (= degr indx)
-                         (let* ((sgm1 (sgm 0 (cmbn-opps (? h sgcm))))
-                                (sgm2 (sgm (dgop-ext-int (list indx)) (2cmbn-add cmpr sgcm (cmbn-opps (? h (? d sgcm))))))
-                                (glist +empty-list+))
-                            (declare 
-                              (type sgm sgm1 sgm2)
-                              (list glist))
-                            (if (sgm-non-zero-p sgm2)
-                               (push sgm2 glist))
-                            (if (sgm-non-zero-p sgm1)
-                               (push sgm1 glist))
-                            (make-gamma :degr (1+ dmns)
-                              :list glist))
-                         (if (= (1- degr) indx)
-                            (let* ((sgm1 (sgm (dgop-ext-int (list indx)) sgcm))
-                                   (sgm2 (sgm (dgop-ext-int (list degr)) (cmbn-opps (? h (? d sgcm)))))
-                                   (glist +empty-list+))
-                               (declare 
-                                 (type sgm sgm1 sgm2)
-                                 (list glist))
-                               (if (sgm-non-zero-p sgm2)
-                                  (push sgm2 glist))
-                               (if (sgm-non-zero-p sgm1)
-                                  (push sgm1 glist))
-                               (make-gamma :degr (1+ dmns)
-                                 :list glist))
-                            (sgm-gamma (1+ dmns) (dgop-ext-int (list indx)) sgcm))))
-                   (let* ((dgop1-ext (first (dgop-int-ext sgop)))
-                          (dgop2 (remove-bit sgop dgop1-ext))
-                          (sgm2 (sgm dgop2 sgcm)))
-                      (declare
-                       (fixnum dgop1-ext dgop2)
-                       (type sgm sgm2))
-                      (if (>= dgop1-ext indx)
-                         (let ((smhmt-i (rslt indx (1- dmns)  (sgm dgop2 sgcm))))
-                            (declare (type gamma smhmt-i))
-                            (gamma-ndgnr (dgop-ext-int (list (1+ dgop1-ext))) smhmt-i))
-                         (let ((smhmt-i-1 (rslt (1- indx) (1- dmns)  sgm2)))
-                            (declare (type gamma smhmt-i-1))
-                            (gamma-ndgnr (dgop-ext-int (list dgop1-ext)) smhmt-i-1)))))))))
-     (the hintr #'rslt)))
-     
-#|
-(setf d3 (delta 3))
-(setf d (dffr d3))
-(setf h (lh (efhm d3)))
-(setf cmpr #'f-cmpr)
-
-(setf sgm-smhmt (sgm-hintr cmpr h d))
-(setf sgm (sgm 5 (cmbn 3 -7 15)))
-(dotimes (indx 6)
-   (print (funcall sgm-smhmt indx 5 sgm)))
-
-(setf sgm2 (sgm 11 (cmbn 2 7 7)))
-(dotimes (indx 6)
-   (print (funcall sgm-smhmt indx 5 sgm2)))
-
-
-|# 
-
-
-(defun gamma-hintr (cmpr h d)
-   (declare 
-     (type morphism h d)
-     (type cmprf cmpr))
-   (let ((s-hintr (sgm-hintr cmpr h d)))
-      (flet ((rslt (indx dmns gmsm)
-               (declare 
-                 (type fixnum indx dmns)
-                 (type gamma gmsm))
-               (let ((rslt (gamma-elt (1+ dmns))))
-                  (do ((mark (gamma-list gmsm) (cdr mark)))
-                      ((endp mark) (gamma-to-absm rslt))
-                     (setf rslt (2gamma-add cmpr rslt (funcall s-hintr indx dmns (-sgm mark))))))))
-      (the hintr #'rslt))))
-             
-
-#|
-(setf d3 (delta 3))
-(setf d (dffr d3))
-(setf h (lh (efhm d3)))
-
-(setf gmm (gamma-elt 5 5 (cmbn 3 -7 15) 11 (cmbn 2 7 7)))
-(setf cmpr #'f-cmpr)
-
-(setf g-hintr (gamma-hintr cmpr h d))
-(dotimes (indx 6)
-   (print (funcall g-hintr indx 5 gmm)))
-
-|# 
-           
-
-(defun gamma-hmtp (h)
-   (declare (type morphism h))
-   (the simplicial-hmtp
-     (let* ((cc (sorc h))
-            (gamma-cc (gamma-chcm cc))
-            (degr (degr h))
-            (cmpr (cmpr cc))
-            (dffr (dffr cc))
-            (orgn (orgn cc)))
-        (declare
-         (type chain-complex cc)
-         (type ab-simplicial-group gamma-cc)
-         (fixnum degr)
-         (type cmprf cmpr)
-         (type morphism dffr))
-        (unless (= degr 1)
-           (error "In GAMMA-HMTP, the morphism has degree ~D different to +1."
-             degr))
-        (build-smhmt
-         :sorc gamma-cc
-         :trgt gamma-cc
-         :degr 1
-         :hintr (gamma-hintr cmpr h dffr)
-         :orgn `(GAMMA ,orgn)))))
-
-#|
-(setf d3 (delta 3))
-(setf h (lh (efhm d3)))
-(setf gamma-h (gamma-hmtp h))
-(setf gmm (gamma-elt 5 5 (cmbn 3 -7 15) 11 (cmbn 2 7 7)))
-(dotimes (i 6)
-  (print (? gamma-h i 5 gmm)) )
-
-(setf i 0)
-(? gamma-h i 5 gmm)
-
-(? gamma-h 5 gmm)
-
-|# 
- 
-#|
-(defun deltan-h (n)
-   (the morphism
-     (let ((delta-n (delta n)))
-        (build-mrph
-         :sorc delta-n
-         :trgt delta-n
-         :degr +1
-         :intr #'(lambda (degr gmsm)
-                   (if (oddp gmsm)
-                      (zero-cmbn (1+ degr))
-                      (term-cmbn (1+ degr) 1 (1+ gmsm))))
-                   :strt :gnrt
-                   :orgn `(homotopy for delta ,n)))))
-
-(setf h5 (deltan-h 5))
-(? h5 3 15)
-(? h5 3 30)
-(? h5 3 39)
-
-(setf gmm-d5-h (gamma-hmtp h5))
-
-(setf g1 (gamma-elt 3 0 (cmbn 3 1 15)))
-(dotimes (indx 4)
-   (print (? gmm-d5-h indx 3 g1)))
-
-(setf g2 (gamma-elt 3 0 (cmbn 3 1 46)))
-(dotimes (indx 4)
-   (print (? gmm-d5-h indx 3 g2)))
-
-(setf g3 (gamma-elt 5 5 (cmbn 3 -7 15)))
-(dotimes (indx 6)
-   (print (? gmm-d5-h indx 5 g3)))
-
-(dotimes (i 6)
-   (dotimes (j 7)
-      (format t "i= ~D, j= ~D" i j)
-      (print (? gmm-d5-h j 6 (? gmm-d3-h i 5 g3)))))
-
-(setf g4 (gamma-elt 5 11 (cmbn 2 1 14)))
-(dotimes (indx 6)
-   (print (? gmm-d5-h indx 5 g4)))
-
-(setf g5 (2gamma-add #'f-cmpr g3 g4))
-(dotimes (indx 6)
-   (print (? gmm-d5-h indx 5 g5)))
-
-(setf g6 (2gamma-add #'f-cmpr g5 (gamma-elt 5 0 (cmbn 5 2 63))))
-(dotimes (indx 6)
-   (print (? gmm-d5-h indx 5 g6)))
-|#
-
-
-(defun gamma-rdct (rdct)
-   (declare (type reduction rdct))
-   (the reduction
-     (let ((f (f rdct))
-           (g (g rdct))
-           (h (h rdct))
-           (orgn (orgn rdct)))
-        (declare
-         (type morphism f g h)
-         (list orgn))
-        (build-rdct
-         :f (gamma-mrph f)
-         :g (gamma-mrph g)
-         :h (gamma-hmtp h)
-         :orgn `(gamma ,orgn)))))
-
-#|
-(setf d3 (delta 3))
-(setf rdct (lrdct (efhm d3)))
-(setf grdct (gamma-rdct rdct))
-
-(setf d5 (delta 5))
-(setf z (z-chcm))
-(setf f (build-mrph
-         :sorc d5
-         :trgt z
-         :degr 0
-         :intr #'(lambda (dmns gnrt)
-                   (if (and (= dmns 0) (= gnrt 1))
-                      (cmbn 0 1 :zgnrt)
-                      (cmbn dmns)))
-         :strt :gnrt
-         :orgn `(trivial-morphism from ,d5 to ,z)))
-      
-(setf g (build-mrph
-         :sorc z
-         :trgt d5
-         :degr 0
-         :intr #'(lambda (dmns gnrt)
-                   (if (equal gnrt :z-gnrt)
-                      (cmbn 0 1 1)
-                      (cmbn dmns)))
-         :strt :gnrt
-         :orgn `(trivial-morphism from ,z to ,d5)))
-
-(setf h (deltan-h 5))
-(setf rdct5 (build-rdct :f f :g g :h h :orgn `(contraction-homotopy ,d5)))
-(setf grdct5 (gamma-rdct rdct5))
-
-(pre-check-rdct grdct5)
-(setf *tc* (cmbn 5 1 (gamma-elt 5 0 (cmbn 5 2 63) 5 (cmbn 3 -7 15) 11 (cmbn 2 1 14)))) 
-(setf *bc* (cmbn 0 1 (gamma-elt 0 0 (cmbn 0 1 :z-gnrt))))
-(check-rdct)
-
-(setf *tc* (cmbn 3 1 (gamma-elt 3 0 (cmbn 3 -6 27 2 43) 5 (cmbn 1 8 9) 7 (cmbn 0 7 8 1 32)) 6 
-             (gamma-elt 3 0 (cmbn 3 1 15) 5 (cmbn 1 -7 5 6 18) 6 (cmbn 1 6 12 -3 18 4 20) 7 (cmbn 0 8 16 -3 32))
-))
-
-(check-rdct)
-
-
-
-
-|# 
-   
-
-(DEFMETHOD GAMMA ((chcm chain-complex))
-   (gamma-chcm chcm))
-
-(DEFMETHOD GAMMA ((rdct reduction))
-   (gamma-rdct rdct))
- 
-   
\ No newline at end of file
diff --git a/examples/anromero/bousfield-kan/simplicial-hmtps.lsp b/examples/anromero/bousfield-kan/simplicial-hmtps.lsp
deleted file mode 100644
index 81f4c75..0000000
--- a/examples/anromero/bousfield-kan/simplicial-hmtps.lsp
+++ /dev/null
@@ -1,153 +0,0 @@
-;;;  SIMPLICIAL-HMTPS  SIMPLICIAL-HMTPS  SIMPLICIAL-HMTPS
-;;;  SIMPLICIAL-HMTPS  SIMPLICIAL-HMTPS  SIMPLICIAL-HMTPS
-;;;  SIMPLICIAL-HMTPS  SIMPLICIAL-HMTPS  SIMPLICIAL-HMTPS
-
-(IN-PACKAGE "COMMON-LISP-USER")
-
-(PROVIDE "simplicial-hmtps")
-
-(DEFTYPE HINTR () 'function)
-;; (function (indx dmns gmsm) absm)
- 
-(DEFCLASS SIMPLICIAL-HMTP (morphism)
-    ((hintr :type hintr :initarg :hintr :reader hintr)))
-
-
-(DEFVAR *SMHMT-LIST*)
-(SETF *SMHMT-LIST* +empty-list+)
-(PUSHNEW '*SMHMT-LIST* *LIST-LIST*)
-
-(DEFMETHOD PRINT-OBJECT ((smhmt simplicial-hmtp) stream)
-  (the simplicial-hmtp
-     (progn
-      (format stream "[K~D Simplicial-Homotopy K~D -> K~D]"
-        (idnm smhmt) (idnm (sorc smhmt)) (idnm (trgt smhmt)))
-      smhmt)))
-
-(DEFUN SMHMT (idnm)
-  (declare (fixnum idnm))
-  (the (or null simplicial-hmtp)
-     (find idnm *smhmt-list* :key #'idnm)))
-
-(DEFUN HINTR-INTR (cmpr hintr)
-   (declare (type hintr hintr)
-     (type cmprf cmpr))
-   (flet ((rslt (dmns gmsm)
-            (declare
-             (fixnum dmns)
-             (type gmsm gmsm))
-            (when (minusp dmns) 
-               (return-from rslt (zero-cmbn (1+ dmns))))
-            (let ((cmbn (zero-cmbn (1+ dmns))))
-               (declare (type cmbn cmbn))
-               (do ((indx 0 (1+ indx)))
-                   ((> indx dmns) cmbn)
-                  (declare (fixnum indx))
-                  (let ((hmtp-i (funcall hintr indx dmns gmsm)))
-                     (declare (type absm hmtp-i))
-                     (if (non-degenerate-p hmtp-i)
-                        (setf cmbn (2cmbn-add cmpr cmbn (term-cmbn (1+ dmns) (-1-expt-n indx) (gmsm hmtp-i))))))))))
-     (the intr-mrph #'rslt)))
-
-(DEFUN BUILD-SMHMT (&key sorc trgt degr hintr intr strt orgn)
-   (declare
-      (type simplicial-set sorc trgt)
-      (fixnum degr)
-      (type hintr hint)
-      (type (or intr-mrph null) intr)
-      (type (or strt null) strt)
-      (list orgn))
-   (the simplicial-hmtp
-      (progn
-	 (let ((already (find orgn *smhmt-list* :test #'equal :key #'orgn)))
-	    (declare (type (or simplicial-hmtp null) already))
-	    (when already
-	       (return-from build-smhmt already)))
-       (unless (= 1 degr)
-          (error "In BUILD-SMHMT, the degree ~D is different to +1."
-            degr))
-       (if intr
-          (unless strt
-             (error "In BUILD-SMMR, an intr is given but not its strt"))
-          (let ((cmpr (cmpr sorc)))
-             (declare (type cmprf cmpr))
-             (setf strt :gnrt
-                   intr (hintr-intr cmpr hintr))))
-          (let ((rslt (build-mrph
-		        :sorc sorc :trgt trgt :degr degr
-			:intr intr :strt strt
-			:orgn orgn)))
-          (declare (type morphism rslt))
-          (change-class rslt 'simplicial-hmtp)
-          (setf (slot-value rslt 'hintr) hintr)
-          (push rslt *smhmt-list*)
-	   rslt))))
-
-
-#|
-(setf d (delta 3))
-(setf h (build-smhmt
-         :sorc d :trgt d :degr 1
-         :hintr #'(lambda (indx dmns gmsm)
-                    (absm (dgop-ext-int (list indx)) gmsm))
-         :orgn '(simplicial-homotopy delta-3)))
-(dotimes (indx 5)
-     (print (? h indx 4 (absm 8 15))))
-(dotimes (indx 7)
-     (print (? h indx 6 (absm 45 11))))
-(? h 2 11)
-|#
-
-
-
-(DEFMETHOD ?4 ((smhmt simplicial-hmtp) indx dmns absm-or-gmsm)
-  (declare
-     (fixnum indx dmns)
-     (type (or absm gmsm) absm-or-gmsm))
-   (the absm
-     (typecase absm-or-gmsm
-       (absm
-        (with-absm (dgop gmsm) absm-or-gmsm
-          (declare 
-            (fixnum dgop)
-          (type gmsm gmsm))
-          (if (= 0 dgop) 
-             (funcall (hintr smhmt) indx dmns gmsm)
-             (let* ((dgop1-ext (first (dgop-int-ext dgop)))
-                    (dgop2 (remove-bit dgop dgop1-ext))
-                    (absm2 (absm dgop2 gmsm)))
-                (declare
-                 (fixnum dgop1-ext dgop2)
-                 (type absm sbsm2))
-                (if (>= dgop1-ext indx)
-                   (let ((smhmt-i (?4 smhmt indx (1- dmns)  absm2)))
-                      (declare (type absm smhmt-i))
-                      (ndgnr (dgop-ext-int (list (1+ dgop1-ext))) smhmt-i))
-                   (let ((smhmt-i-1 (?4 smhmt (1- indx) (1- dmns)  absm2)))
-                      (declare (type absm smhmt-i-1))
-                      (ndgnr (dgop-ext-int (list dgop1-ext)) smhmt-i-1)))))))
-       (otherwise
-        (funcall (hintr smhmt) indx dmns absm-or-gmsm)))))
-
-
-;; This macro definition changes the definition of the macro ? in the file macro.lsp
-(DEFMACRO ? (&rest rest)
-   (ecase (length rest)
-     (2 `(?2 ,@rest))
-     (3 `(?3 ,@rest))
-     (4 `(?4 ,@rest))))
-
-
-
-
-
-
-
-             
-      
-   
-   
-    
-
-   
-
diff --git a/examples/anromero/filtered-complexes/bicomplexes.lsp b/examples/anromero/filtered-complexes/bicomplexes.lsp
deleted file mode 100644
index 6ab13a1..0000000
--- a/examples/anromero/filtered-complexes/bicomplexes.lsp
+++ /dev/null
@@ -1,270 +0,0 @@
-;; BICOMPLEXES   BICOMPLEXES   BICOMPLEXES   BICOMPLEXES   BICOMPLEXES   BICOMPLEXES  
-;; BICOMPLEXES   BICOMPLEXES   BICOMPLEXES   BICOMPLEXES   BICOMPLEXES   BICOMPLEXES
-;; BICOMPLEXES   BICOMPLEXES   BICOMPLEXES   BICOMPLEXES   BICOMPLEXES   BICOMPLEXES
-
-
-(IN-PACKAGE "COMMON-LISP-USER")
-
-(PROVIDE "bicomplexes")
-
-(DEFMETHOD PRINT-KEYCONS ((car (eql :BcGnrt)) cdr stream)
-   (declare
-      (cons cdr)
-      (stream stream))
-   (the (eql t)
-       (let* 
-            ((cdr (cons car cdr))
-             (degr1 (BcGnrt-Degr1 cdr))
-             (degr2 (BcGnrt-Degr2 cdr))
-             (gnrt (BcGnrt-gnrt cdr)))
-          (progn
-            (format stream "<BcGnrt ")
-            (format stream "[~D ~D] ~A" degr1 degr2 gnrt)
-            (format stream ">"))
-         t)))
-
-
-
-        ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
-        ;;; TYPES FOR BICOMPLEXES ;;;
-        ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
-
-;; TYPE BcGnrt (a generator in a Bicomplex)
-(DEFUN BcGnrt-p (object)
-   (declare (type any object))
-   (the boolean
-     (and (consp object)
-          (eql :BcGnrt (car object))
-          (consp (cdr object))
-          (consp (cadr object))
-          (typep (caadr object) 'fixnum)
-          (typep (cdadr object) 'fixnum))))
-(DEFTYPE BcGnrt () '(satisfies BcGnrt-p))
-
-#|
-(typep  `(:BcGnrt ,(cons 5 6) u) 'BcGnrt)
-(typep `(:BcGnrt ,(cons 3 2) '(f g)) 'BcGnrt)
-(typep `(:BcGnrt ,(cons 4 5.4) u) 'BcGnrt)
-|#
-
- 
-;; TYPE BcBasis (basis of a Bicomplex, function of the variables p and q or
-;; ":locally-effective")
-(DEFTYPE BcBASIS () '(or function (eql :locally-effective))) 
-                     ;; (function (degr degr) (list gnrt)) 
-
-
-;; TYPE Bicomplex
-(DEFUN OrgnBiCmpl-p (object)
-   (declare (type chain-complex object))
-     (let* ((orgn (orgn object)))
-        (the boolean
-          (and (consp orgn)
-             (eql (car orgn) 'BiCmpl)))))
-(DEFTYPE Bicomplex () '(satisfies OrgnBiCmpl-p))
-
-
- ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
- ;;; FUCTIONS FOR THE REPRESENTATION OF (GENERAL) BICOMPLEXES ;;;
- ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
-
-
-;; Function that builds a generator of a Bicomplex from two degrees and 
-;; a simple generator.
-(DEFUN build-BcGnrt (degr1 degr2 gnrt)
-   (declare 
-     (type fixnum degr1 degr2)
-     (type any gnrt))
-   (list :BcGnrt (cons degr1 degr2) gnrt))
-
-#|
-(build-BcGnrt 2 3 'c)
-(typep  (build-BcGnrt 2 2 'd) 'BcGnrt)
-|#
- 
-
-;; Function that returns the first degree from a bicomplex' generator.
-(DEFUN BcGnrt-Degr1 (BcGnrt)
-   (declare (type BcGnrt BcGnrt))
-   (caadr BcGnrt))
-
-;; Function that returns the second degree from a bicomplex' generator.
-(DEFUN BcGnrt-Degr2 (BcGnrt)
-   (declare (type BcGnrt BcGnrt))
-   (cdadr BcGnrt))
-
-;; Function that returns the original generator from a bicomplex' generator.
-(DEFUN BcGnrt-Gnrt (BcGnrt)
-   (declare (type BcGnrt BcGnrt))
-   (caddr BcGnrt))
-
-#|
-(build-BcGnrt 5 6 8)
-(BcGnrt-Degr1 (build-BcGnrt 5 6 8))
-(BcGnrt-Degr2 (build-BcGnrt 6 4 '(4 6)))
-(BcGnrt-Gnrt (build-BcGnrt 6 4 '(4 6)))
-(BcGnrt-Gnrt (build-BcGnrt 2 8 'u))
-|# 
-
- 
-;; Comparison function of a bicomplex. 
-(defun BC-CMPR (cmpr)
-   (declare (type cmprf cmpr))
-   (flet ((comp (bc1 bc2)
-            (declare (type BcGnrt bc1 bc2))
-            (let ((degr11 (BcGnrt-Degr1 bc1))
-                  (degr21 (BcGnrt-Degr2 bc1))
-                  (degr12 (BcGnrt-Degr1 bc2))
-                  (degr22 (BcGnrt-Degr2 bc2))
-                  (gnrt1 (BcGnrt-Gnrt bc1))
-                  (gnrt2 (BcGnrt-Gnrt bc2)))
-               (declare 
-                 (type fixnum degr11 degr21 degr12 degr22)
-                 (type any gnrt1 gnrt2))
-               (lexico
-                (f-cmpr degr11 degr12)
-                (f-cmpr degr21 degr22)
-                (funcall cmpr gnrt1 gnrt2)))))
-     (the cmprf #'comp)))
-
-#|
-(setf cmpr (BC-CMPR #'s-cmpr)) 
-(funcall cmpr (build-BcGnrt 5 6 'a) (build-BcGnrt 7 8 'b))
-(funcall cmpr (build-BcGnrt 8 6 'a) (build-BcGnrt 7 8 'b))
-(funcall cmpr (build-BcGnrt 8 5 'c) (build-BcGnrt 8 6 'b))
-(funcall cmpr (build-BcGnrt 8 5 'c) (build-BcGnrt 8 5 'b))
-|# 
-      
-;; Basis of a bicomplex (from a function of type BcBasis).
-(DEFUN BC-BASIS (bcbasis)
-   (declare (type BcBasis bcbasis))
-   (when (eq bcbasis :locally-effective)
-      (return-from bc-basis :locally-effective))
-   (flet ((bas (degr)
-            (declare (type fixnum degr))
-            (the list
-              (progn
-               (when (minusp degr)
-                  (return-from bas +empty-list+))
-               (mapcan
-                #'(lambda (degr1)
-                    (declare (type fixnum degr1))
-                    (let* ((degr2 (- degr degr1))
-                           (basis (funcall bcbasis degr1 degr2)))
-                       (declare
-                        (fixnum degr2)
-                        (list basis))
-                       (the list
-                         (mapcar
-                          #'(lambda (gnrt)
-                              (declare (type gnrt gnrt))
-                              (the BcGnrt
-                                (build-BcGnrt degr1 degr2 gnrt)))
-                          basis)))
-                    )
-                (<a-b> 0 degr))))))
-     (the basis #'bas)))
-
-#|
-(defun bas (degr1 degr2)
-   (if (and (= degr1 0) (= degr2 1)) (return-from bas '(a)))
-   (if (and (= degr1 1) (= degr2 0)) (return-from bas '(b)))
-   (if (and (= degr1 1) (= degr2 1)) (return-from bas '(c)))
-   (if (and (= degr1 2) (= degr2 0))  (return-from bas '(d)))
-   (return-from bas nil))
-(setf basis (BC-BASIS #'bas))
-(dotimes (i 5)
-   (print (funcall basis i)))
-|#
-
-;; Differential function of a Bicomplex (from the differential functions,
-;; dffr1=horizontal dffr, dffr2=vertical dffr). 
-(DEFUN BC-INTR-DFFR (dffr1 dffr2)
-   (declare (type function dffr1 dffr2))
-   (flet ((dif (degr bc)
-            (declare
-             (fixnum degr)
-             (type BcGnrt bc))
-            (the cmbn
-              (let* ((degr1 (BcGnrt-Degr1 bc))
-                     (degr2 (BcGnrt-Degr2 bc))
-                     (gnrt (BcGnrt-Gnrt bc))
-                     (degr1-1 (1- degr1))
-                     (degr2-1 (1- degr2))
-                     (list1 (funcall dffr1 degr1 degr2 gnrt))
-                     (list2 (funcall dffr2 degr1 degr2 gnrt)))
-                 (declare (type fixnum degr1 degr2 degr1-1 gegr2-1)
-                   (list list1 list2))
-                 (make-cmbn
-                  :degr (1- degr)
-                  :list (nconc
-                         (mapcar
-                          #'(lambda (term1)
-                              (declare (type term term1))
-                              (let* ((cffc1 (cffc term1))
-                                     (gnrt1 (gnrt term1)))
-                                 (declare (type fixnum cffc1)
-                                   (type gnrt gnrt1))
-                                 (term cffc1 (build-BcGnrt degr1-1 degr2 gnrt1))))
-                          list1)
-                         (mapcar 
-                           #'(lambda (term2)
-                               (declare (type term term2))
-                               (let* ((cffc2 (cffc term2))
-                                      (gnrt2 (gnrt term2)))
-                                  (declare (type fixnum cffc2)
-                                    (type gnrt gnrt2))
-                                  (term cffc2 (build-BcGnrt degr1 degr2-1 gnrt2))))
-                           list2)))))))
-     (the intr-mrph #'dif)))
-
-#|
-(defun dif1 (degr1 degr2 gnrt)
-   (if (and (= degr1 1) (= degr2 1) (eql gnrt 'c)) (return-from dif1 (list (cons 2 'a))))
-   (if (and (= degr1 2) (= degr2 0) (eql gnrt 'd)) (return-from dif1 (list (cons 2 'b))))
-   (return-from dif1 nil))
-(defun dif2 (degr1 degr2 gnrt)
-   (if (and (= degr1 1) (= degr2 1) (eql gnrt 'c)) (return-from dif2 (list (cons 1 'b))))
-   (return-from dif2 nil))
-(setf dif (BC-INTR-DFFR #'dif1 #'dif2))
-(funcall dif 2 (build-BcGnrt 1 1 'c))
-|#
-
-;; Function that builds a bicomplex from a basis function, the two differential
-;; functions and the original comparison. 
-(DEFUN BUILD-BICM (&key bcbasis dffr1 dffr2 cmpr orgn)
-   (declare 
-     (type BCbasis bcbasis)
-     (type function dffr1 dffr2)
-     (type cmprf cmpr)
-     (list (orgn)))
-   (the chain-complex
-     (let ((chcm
-            (build-chcm
-             :cmpr (BC-CMPR cmpr)
-             :basis (BC-BASIS bcbasis)
-             :intr-dffr (BC-INTR-DFFR dffr1 dffr2)
-             :strt :gnrt
-             :orgn orgn)))
-        (declare (type chain-complex chcm))
-        (slot-makunbound chcm 'bsgn)
-        chcm)))
-
-#|
-(setf bc (Build-Bicm :bcbasis #'bas :dffr1 #'dif1 :dffr2 #'dif2 :cmpr 's-cmpr 
-          :orgn '(BC-test)))
-(dotimes (i 5)
-   (print (basis bc i)))
-(cmpr bc (build-BcGnrt 0 1 'a) (build-BcGnrt 1 1 'c))
-
-(? bc (? bc 2 (build-BcGnrt 1 1 'c))) 
-(? bc 2 (build-BcGnrt 2 0 'd))
-(? bc 2 '(:BcGnrt (1 . 1) c))
-(? bc (cmbn 2 3 '(:BcGnrt (1 . 1) c)))
-(? bc 1 (build-bicm 0  1 'a))
-|#
-
-
-
-
-
diff --git a/examples/anromero/filtered-complexes/filtered-complexes.lsp b/examples/anromero/filtered-complexes/filtered-complexes.lsp
deleted file mode 100644
index ab665f7..0000000
--- a/examples/anromero/filtered-complexes/filtered-complexes.lsp
+++ /dev/null
@@ -1,843 +0,0 @@
-;; FILTERED-COMPLEXES   FILTERED-COMPLEXES   FILTERED-COMPLEXES   FILTERED-COMPLEXES
-;; FILTERED-COMPLEXES   FILTERED-COMPLEXES   FILTERED-COMPLEXES   FILTERED-COMPLEXES
-;; FILTERED-COMPLEXES   FILTERED-COMPLEXES   FILTERED-COMPLEXES   FILTERED-COMPLEXES
-
-(IN-PACKAGE "COMMON-LISP-USER")
-
-(provide "filtered-complexes")
-
-(DEFTYPE degr () 'fixnum)
-
-(DEFTYPE CHCM-FLIN () 'function) 
-                     ;; '(function (degr gnrt) degr)
-
-
-(DEFCLASS FILTERED-CHAIN-COMPLEX (chain-complex)
-    ((flin :type chcm-flin :initarg :flin :reader flin1)))
-
-(DEFVAR *flcc-list*)
-(SETF *flcc-list* +empty-list+)
-(PUSHNEW '*flcc-list* *list-list*)
-
-(DEFMETHOD PRINT-OBJECT ((flcm FILTERED-CHAIN-COMPLEX) stream)
-(the FILTERED-CHAIN-COMPLEX
-   (progn
-      (format stream "[K~D Filtered-Chain-Complex]" (idnm flcm))
-     flcm)))
-
-(DEFUN FLCC (idnm)
-   (declare (type fixnum idnm))
-   (the (or FILTERED-CHAIN-COMPLEX null)
-      (find idnm *flcc-list* :key #'idnm)))
-
-
-;; Function that builds a filtered chain complex. 
-(DEFUN BUILD-FLCC
-    (&key cmpr basis bsgn intr-dffr dffr-strt flin orgn)
-   (declare
-      (type cmprf cmpr)
-      (type intr-mrph intr-dffr)
-      (type basis basis)
-      (type gnrt bsgn)
-      (type strt dffr-strt)
-      (type Chcm-Flin flin)
-      (list orgn))
-   (the FILTERED-CHAIN-COMPLEX
-     (progn
-         (let ((already (find orgn *flcc-list* :key #'orgn :test #'equal)))
-            (declare (type (or null FILTERED-CHAIN-COMPLEX) already))
-            (when already
-               (return-from build-flcc already)))
-         (let ((rslt (build-chcm :cmpr cmpr :basis basis :bsgn bsgn
-                        :intr-dffr intr-dffr :strt dffr-strt
-                        :orgn orgn)))
-            (declare (type chain-complex rslt))
-            (change-class rslt 'FILTERED-CHAIN-COMPLEX)
-            (setf (slot-value rslt 'flin) flin)
-            (push rslt *flcc-list*)
-               rslt))))
-
-
-;; Function that changes a chain complex chcm to a filtered complex, with filtration
-;; index of a generator defined by the function flin, and origin orgn. 
-#|(DEFUN CHANGE-CHCM-TO-FLCC (chcm &key flin orgn)
-   (declare
-      (type chain-complex chcm)
-      (type chcm-flin flin)
-      (list orgn))
-   (the FILTERED-CHAIN-COMPLEX
-      (progn
-         (change-class chcm 'FILTERED-CHAIN-COMPLEX)
-         ;;(setf orgn (list (orgn chcm) 'then orgn))
-         (let ((already (find orgn *flcc-list* :key #'orgn :test #'equal)))
-            (declare (type (or null FILTERED-CHAIN-COMPLEX) already))
-            (when already
-               (return-from change-chcm-to-flcc already)))
-         (setf (slot-value chcm 'flin) flin)
-         ;;(setf (slot-value chcm 'orgn) orgn)
-         (push chcm *flcc-list*)
-         chcm)))
-|#
-
-
-(DEFMETHOD CHANGE-CHCM-TO-FLCC ((chcm chain-complex) flin flin-orgn)
-   (declare
-      (type chain-complex chcm)
-      (type chcm-flin flin)
-      (list flin-orgn))
-   (the FILTERED-CHAIN-COMPLEX
-      (progn
-         (change-class chcm 'FILTERED-CHAIN-COMPLEX)
-         (setf orgn (append (orgn chcm) (list 'FILTERED-WITH) flin-orgn))
-         (let ((already (find orgn *flcc-list* :key #'orgn :test #'equal)))
-            (declare (type (or null FILTERED-CHAIN-COMPLEX) already))
-            (when already
-               (return-from change-chcm-to-flcc already)))
-         (setf (slot-value chcm 'flin) flin)
-         (setf (slot-value chcm 'orgn) orgn)
-         (push chcm *flcc-list*)
-         chcm)))
-
-
-(DEFMACRO FLIN (&rest rest)
-   (ecase (length rest)
-      (1 `(flin1 ,@rest))
-      (2 `(flin2 ,@rest))
-      (3 `(flin3 ,@rest))))
-
-(DEFUN FLIN3 (object degr gnrt)         
-   (declare
-      (type FILTERED-CHAIN-COMPLEX object)
-      (fixnum degr)
-      (type gnrt gnrt))
-   (the fixnum
-      (with-slots (flin) object
-         (declare (type chcm-flin flin))
-         (funcall flin degr gnrt))))
-
-(DEFUN FLIN2 (object cmbn)
-   (declare
-    (type FILTERED-CHAIN-COMPLEX object)
-    (type cmbn cmbn))
-   (the fixnum
-      (with-slots (flin) object
-         (declare (type chcm-flin flin))
-        (with-cmbn (degr cmbn-list) cmbn
-          (declare
-           (fixnum degr)
-           (list cmbn-list))
-          (labels ((list-max (list)
-                     (declare (type list list))
-                     (let* ((max-int (car list)))
-                        (do ((mark1 list (cdr mark1)))
-                            ((endp mark1))
-                           (setq max-int (max max-int (car mark1))))
-                        max-int)))
-         (if (endp cmbn-list)
-            0
-            (list-max 
-              (mapcar 
-                #'(lambda (term)
-                    (flin3 object degr (gnrt term)))
-                cmbn-list))))))))
-   
-
-
-;; Function that returns the min and max of the filtration index of the elements of the basis
-;; for degree degr
-(DEFUN FLIN-MIN-MAX (fltrcm degr)
-   (declare (type FILTERED-CHAIN-COMPLEX fltrcm)
-            (type fixnum degr))
-   (when (eq (basis fltrcm) :locally-effective)
-    (error "flin-min-max cannot work with a LOCALLY-EFFECTIVE chain complex."))
-   (the list
-     (let* ((basis (basis fltrcm degr)))
-        (declare (list basis))
-        (if (endp basis)
-           (list 0 0)
-           (let* ((min (flin fltrcm degr (first basis)))
-                  (max min))
-              (declare (type fixnum min max))
-              (dolist (gnrt (cdr basis))
-                 (let ((aux (flin fltrcm degr gnrt)))
-                    (declare (type fixnum aux))
-                    (if (< aux min)
-                       (setf min aux)
-                       (if (> aux max)
-                          (setf max aux)))))
-              (list min max))))))
-           
- 
-   
-;; Function that returns the elements of the basis that have bidegree (p,q).
-(DEFUN BIGRD-BASIS (fltrcm p q)
-   (declare (type FILTERED-CHAIN-COMPLEX fltrcm)
-            (type fixnum p q))
-   (when (eq (basis fltrcm) :locally-effective)
-    (error "Bigrd-Basis cannot work with a LOCALLY-EFFECTIVE chain complex."))
-   (the list
-     (let* ((degr (+ p q))
-            (basis (basis fltrcm degr)))
-        (declare 
-          (type list basis)
-          (fixnum degr))
-        (mapcan 
-          #'(lambda (gnrt)
-              (declare (type gnrt gnrt))
-              (if (= (flin fltrcm degr gnrt) p)
-                 (list gnrt)
-                 nil))
-          basis))))
-
-;; Function that returns the elements of the basis of degree "degr" that have
-;; filtration index <= "fltr-index".
-(DEFUN FLTRD-BASIS (fltrcm degr fltr-index)
-   (declare (type FILTERED-CHAIN-COMPLEX fltrcm)
-            (type fixnum degr fltr-index))
-   (when (eq (basis fltrcm) :locally-effective)
-    (error "Fltrd-Basis cannot work with a LOCALLY-EFFECTIVE chain complex."))
-   (let ((min (first (flin-min-max fltrcm degr))))
-      (declare (type fixnum min))
-      (the list
-        (mapcan
-          #'(lambda (i)
-              (bigrd-basis fltrcm i (- degr i)))
-          (<a-b> min fltr-index)))))
-
-;; Function that returns the elements of the basis with degree "degr",
-;; ordered by the filtration index.
-(DEFUN ORDERED-BASIS (fltrcm degr)
-   (declare
-    (type FILTERED-CHAIN-COMPLEX fltrcm)
-    (fixnum degr))
-   (when (eq (basis fltrcm) :locally-effective)
-    (error "Ordered-Basis cannot work with a LOCALLY-EFFECTIVE chain complex."))
-   (the list
-     (let ((max (second (flin-min-max fltrcm degr))))
-        (declare (type fixnum max))
-        (fltrd-basis fltrcm degr max))))  
-
-;; Matrix of the differential application of degree "degr" of the subcomplex
-;; F_pX, where p=fltr-index and X=fltrcm.
-(defun FLCC-DFFR-MTRX (fltrcm degr fltr-index)
-  (declare
-    (type FILTERED-CHAIN-COMPLEX fltrcm)
-    (fixnum degr fltr-index))
-   (when (eq (basis fltrcm) :locally-effective)
-    (error "flcc-dffr-mtrx cannot work with a LOCALLY-EFFECTIVE chain complex."))
-  (the matrix
-    (let* ((cmpr (cmpr1 fltrcm))
-	     (dffr (dffr fltrcm))
-	     (sbasis (fltrd-basis fltrcm degr fltr-index))
-           (tbasis (ordered-basis fltrcm (1- degr)))
-           ;; If the differential application in the filtered complex respects the filtration,
-           ;; i.e., d(F_pA_n) \in (F_pA)_{n-1}, the target basis is (fltrd-basis fltrcm (1- degr) fltr-index)
-           (srank (length sbasis))
-	     (trank (length tbasis)))
-       (declare
-        (type cmprf cmpr)
-        (type morphism dffr)
-        (fixnum degr)
-        (list sbasis tbasis)
-        (fixnum srank trank))
-       (let ((rslt 
-               #-ACLPC
-                    (make-array (list trank srank)
-				:element-type 'fixnum
-				:initial-element 0)
-               #+ACLPC
-                    (if (or (zerop srank) (zerop trank))
-                       (make-array (list trank srank)
-                          :element-type 'fixnum)
-                       (make-array (list trank srank)
-                          :element-type 'fixnum
-                          :initial-element 0))
-               ))               
-            (declare (type matrix rslt))
-            (do ((j 0 (1+ j))
-	           (mark sbasis (cdr mark)))
-                ((endp mark))
-               (declare
-                (fixnum j)
-                (list mark))
-               (let ((cmbn (gnrt-? dffr degr (car mark))))
-                  (declare (type cmbn cmbn))
-                  (do ((mark1 (cmbn-list cmbn) (cdr mark1)))
-                      ((endp mark1))
-                     (declare (list mark1))
-                     (with--term (cffc gnrt) mark1
-                       (declare 
-                         (fixnum cffc)
-                         (type gnrt gnrt))
-                       (do ((mark2 tbasis (cdr mark2))
-                            (i 0 (1+ i))
-                            (found nil))
-                           ((or (endp mark2) found))
-                          (declare 
-                            (list mark2)
-                            (fixnum i found))
-                          (if (eq :equal (funcall cmpr gnrt (car mark2)))
-                             (progn
-                              (setq found 1)
-                              (setf (aref rslt i j) cffc))))))))
-               rslt))))
-
-
-;; OTHER CLASSES THAT INHERIT FROM FILTERED-CHAIN-COMPLEX
-
-
-(DEFCLASS FILTERED-COALGEBRA (filtered-chain-complex coalgebra)
-    ())
-
-(DEFVAR *FLCLGB-LIST*)
-(SETF *FLCLGB-LIST* +empty-list+)
-(PUSHNEW '*FLCLGB-LIST* *list-list*)
-
-(DEFMETHOD PRINT-OBJECT ((flclgb FILTERED-COALGEBRA) stream)
-(the FILTERED-COALGEBRA
-   (progn
-      (format stream "[K~D FILTERED-COALGEBRA]" (idnm flclgb))
-     flclgb)))
-
-(DEFUN FltrClgb (idnm)
-   (declare (type fixnum idnm))
-   (the (or FILTERED-COALGEBRA null)
-      (find idnm *flclgb-list* :key #'idnm)))
-
-;; Function that builds a filtered coalgebra. 
-(DEFUN BUILD-FltrClgb
-    (&key cmpr basis bsgn intr-dffr dffr-strt intr-cprd cprd-strt flin orgn)
-   (declare
-     (type cmprf cmpr)
-     (type intr-mrph intr-dffr intr-cprd)
-     (type basis basis)
-     (type gnrt bsgn)
-     (type strt dffr-strt cprd-strt)
-     (type chcm-flin flin)
-     (list orgn))
-   (the FILTERED-COALGEBRA
-     (progn
-         (let ((already (find orgn *flclgb-list* :key #'orgn :test #'equal)))
-            (declare (type (or null FILTERED-COALGEBRA) already))
-            (when already
-               (return-from build-FltrClgb already)))
-         (let ((rslt (build-clgb :cmpr cmpr :basis basis :bsgn bsgn
-                        :intr-dffr intr-dffr :dffr-strt dffr-strt
-                       :intr-cprd intr-cprf :cprd-strt cprd-strt
-                        :orgn orgn)))
-            (declare (type coalgebra rslt))
-            (change-class rslt 'FILTERED-COALGEBRA)
-            (setf (slot-value rslt 'flin) flin)
-            (push rslt *flclgb-list*)
-               rslt))))
-
-(defmethod change-chcm-to-flcc ((chcm coalgebra) flin flin-orgn )
-   (declare
-      
-      (type chcm-flin flin)
-      (list flin-orgn))
-   (the FILTERED-COALGEBRA
-      (progn
-         (change-class chcm 'FILTERED-COALGEBRA)
-         (setf orgn (append (orgn chcm) (list 'FILTERED-WITH) flin-orgn))
-         (let ((already (find orgn *flclgb-list* :key #'orgn :test #'equal)))
-            (declare (type (or null FILTERED-COALGEBRA) already))
-            (when already
-               (return-from change-chcm-to-flcc already)))
-         (setf (slot-value chcm 'flin) flin)
-         (setf (slot-value chcm 'orgn) orgn)
-         (push chcm *flCLGB-list*)
-         chcm)))
-
-
-(DEFCLASS FILTERED-ALGEBRA (filtered-chain-complex algebra)
-    ())
-
-(DEFVAR *FLALGB-LIST*)
-(SETF *FLALGB-LIST* +empty-list+)
-(PUSHNEW '*FLALGB-LIST* *list-list*)
-
-(DEFMETHOD PRINT-OBJECT ((flalgb FILTERED-ALGEBRA) stream)
-(the FILTERED-ALGEBRA
-   (progn
-      (format stream "[K~D FILTERED-ALGEBRA]" (idnm flalgb))
-     flalgb)))
-
-(DEFUN FltrAlgb (idnm)
-   (declare (type fixnum idnm))
-   (the (or FILTERED-ALGEBRA null)
-      (find idnm *flalgb-list* :key #'idnm)))
-
-;; Function that builds a filtered algebra. 
-(DEFUN BUILD-FltrAlgb
-    (&key cmpr basis bsgn intr-dffr dffr-strt intr-aprd aprd-strt flin orgn)
-   (declare
-     (type cmprf cmpr)
-     (type intr-mrph intr-dffr intr-aprd)
-     (type basis basis)
-     (type gnrt bsgn)
-     (type strt dffr-strt aprd-strt)
-     (type chcm-flin flin)
-     (list orgn))
-   (the FILTERED-ALGEBRA
-     (progn
-         (let ((already (find orgn *flalgb-list* :key #'orgn :test #'equal)))
-            (declare (type (or null FILTERED-ALGEBRA) already))
-            (when already
-               (return-from build-FltrAlgb already)))
-         (let ((rslt (build-algb :cmpr cmpr :basis basis :bsgn bsgn
-                        :intr-dffr intr-dffr :dffr-strt dffr-strt
-                       :intr-aprd intr-aprf :aprd-strt aprd-strt
-                        :orgn orgn)))
-            (declare (type algebra rslt))
-            (change-class rslt 'FILTERED-ALGEBRA)
-            (setf (slot-value rslt 'flin) flin)
-            (push rslt *flalgb-list*)
-               rslt))))
-
-(defmethod change-chcm-to-flcc ((chcm algebra) flin flin-orgn )
-   (declare
-      
-      (type chcm-flin flin)
-      (list flin-orgn))
-   (the FILTERED-ALGEBRA
-      (progn
-         (change-class chcm 'FILTERED-ALGEBRA)
-         (setf orgn (append (orgn chcm) (list 'FILTERED-WITH) flin-orgn))
-         (let ((already (find orgn *flalgb-list* :key #'orgn :test #'equal)))
-            (declare (type (or null FILTERED-ALGEBRA) already))
-            (when already
-               (return-from change-chcm-to-flcc already)))
-         (setf (slot-value chcm 'flin) flin)
-         (setf (slot-value chcm 'orgn) orgn)
-         (push chcm *flaLGB-list*)
-         chcm)))
-
-
-(DEFCLASS FILTERED-HOPF-ALGEBRA (filtered-chain-complex hopf-algebra)
-    ())
-
-(DEFVAR *FLHOPF-LIST*)
-(SETF *FLHOPF-LIST* +empty-list+)
-(PUSHNEW '*FLHOPF-LIST* *list-list*)
-
-(DEFMETHOD PRINT-OBJECT ((flhopf FILTERED-HOPF-ALGEBRA) stream)
-(the FILTERED-HOPF-ALGEBRA
-   (progn
-      (format stream "[K~D FILTERED-HOPF-ALGEBRA]" (idnm flhopf))
-     flhopf)))
-
-(DEFUN FltrHopf (idnm)
-   (declare (type fixnum idnm))
-   (the (or FILTERED-HOPF-ALGEBRA null)
-      (find idnm *flhopf-list* :key #'idnm)))
-
-(defmethod change-chcm-to-flcc ((chcm hopf-algebra) flin flin-orgn )
-   (declare
-      
-      (type chcm-flin flin)
-      (list flin-orgn))
-   (the FILTERED-hofp-algebra
-      (progn
-         (change-class chcm 'FILTERED-hopf-COALGEBRA)
-        (setf orgn (append (orgn chcm) (list 'FILTERED-WITH) flin-orgn))
-         (let ((already (find orgn *flhopf-list* :key #'orgn :test #'equal)))
-            (declare (type (or null FILTERED-HOPF-COALGEBRA) already))
-            (when already
-               (return-from change-chcm-to-flcc already)))
-         (setf (slot-value chcm 'flin) flin)
-         (setf (slot-value chcm 'orgn) orgn)
-         (push chcm *flhopf-list*)
-         chcm)))
-
-
-(DEFCLASS FILTERED-SIMPLICIAL-SET (FILTERED-CHAIN-COMPLEX simplicial-set )
-    ())
-
-(DEFVAR *FLSMST-LIST*)
-(SETF *FLSMST-LIST* +empty-list+)
-(PUSHNEW '*FLSMST-LIST* *list-list*)
-
-(DEFMETHOD PRINT-OBJECT ((flsmst filtered-simplicial-set) stream)
- (the filtered-simplicial-set
-   (progn
-      (format stream "[K~D Filtered-Simplicial-Set]" (idnm flsmst))
-      flsmst)))
-
-(DEFUN FltrSmSet (idnm)
-   (declare (type fixnum idnm))
-   (the (or filtered-simplicial-set null)
-      (find idnm *flsmst-list* :key #'idnm)))
-
-
-
-;; Function that builds a filtered simplicial set 
-(DEFUN BUILD-FltrSmSt
-    (&key cmpr basis bspn face face* intr-bndr bndr-strt intr-dgnl dgnl-strt flin orgn)
-   (declare
-     (type cmprf cmpr)
-     (type basis basis)
-     (type gmsm bspn)
-     (type face face)
-     (type (or null face*) face*)
-     (type (or intr-mrph null) intr-bndr intr-dgnl)
-        (type (or strt null) bndr-strt dgnl-strt)
-     (type chcm-flin flin)
-     (list orgn))
-   (the FILTERED-SIMPLICIAL-SET
-     (progn
-         (let ((already (find orgn *flsmst-list* :key #'orgn :test #'equal)))
-            (declare (type (or null FILTERED-SIMPLICIAL-SET) already))
-            (when already
-               (return-from build-FltrSmst already)))
-         (let ((rslt (build-smst :cmpr cmpr :basis basis :bspn bspn
-                       :face face :face* face* :intr-bndr intr-bndr 
-                       :bndr-strt bndr-strt :intr-dgnl intr-dgnl 
-                       :dgnl-strt dgnl :orgn orgn)))
-            (declare (type simplicial-set rslt))
-            (change-class rslt 'FILTERED-SIMPLICIAL-SET)
-            (setf (slot-value rslt 'flin) flin)
-            (push rslt *flsmst-list*)
-               rslt))))
-
-(defmethod change-chcm-to-flcc ((chcm simplicial-set) flin flin-orgn )
-   (declare
-      
-      (type chcm-flin flin)
-      (list flin-orgn))
-   (the FILTERED-SIMPLICIAL-SET
-      (progn
-         (change-class chcm 'FILTERED-SIMPLICIAL-SET)
-         (setf orgn (append (orgn chcm) (list 'FILTERED-WITH) flin-orgn))
-         (let ((already (find orgn *flsmst-list* :key #'orgn :test #'equal)))
-            (declare (type (or null FILTERED-SIMPLICIAL-SET) already))
-            (when already
-               (return-from change-chcm-to-flcc already)))
-         (setf (slot-value chcm 'flin) flin)
-         (setf (slot-value chcm 'orgn) orgn)
-         (push chcm *flsmst-list*)
-         chcm)))
-
-
-(DEFCLASS FILTERED-KAN (FILTERED-CHAIN-COMPLEX KAN )
-    ())
-
-(DEFVAR *FLKAN-LIST*)
-(SETF *FLKAN-LIST* +empty-list+)
-(PUSHNEW '*FLKAN-LIST* *list-list*)
-
-(DEFMETHOD PRINT-OBJECT ((flkan filtered-kan) stream)
- (the filtered-kan
-   (progn
-      (format stream "[K~D Filtered-Kan-Simplicial-Set]" (idnm flkan))
-      flkan)))
-
-(DEFUN FltrKan (idnm)
-   (declare (type fixnum idnm))
-   (the (or filtered-kan null)
-      (find idnm *flkan-list* :key #'idnm)))
-
-(defmethod change-chcm-to-flcc ((chcm kan) flin flin-orgn )
-   (declare
-      
-      (type chcm-flin flin)
-      (list flin-orgn))
-   (the FILTERED-KAN
-      (progn
-         (change-class chcm 'FILTERED-KAN)
-         (setf orgn (append (orgn chcm) (list 'FILTERED-WITH) flin-orgn))
-         (let ((already (find orgn *flkan-list* :key #'orgn :test #'equal)))
-            (declare (type (or null FILTERED-KAN) already))
-            (when already
-               (return-from change-chcm-to-flcc already)))
-         (setf (slot-value chcm 'flin) flin)
-         (setf (slot-value chcm 'orgn) orgn)
-         (push chcm *flkan-list*)
-         chcm)))
-
-
-(DEFCLASS FILTERED-SIMPLICIAL-GROUP (FILTERED-CHAIN-COMPLEX SIMPLICIAL-GROUP )
-    ())
-
-(DEFCLASS FILTERED-AB-SIMPLICIAL-GROUP (FILTERED-CHAIN-COMPLEX AB-SIMPLICIAL-GROUP )
-    ())
-
-(DEFVAR *FLSMGR-LIST*)
-(SETF *FLSMGR-LIST* +empty-list+)
-(PUSHNEW '*FLSMGR-LIST* *list-list*)
-
-(DEFMETHOD PRINT-OBJECT ((flsmgr filtered-simplicial-group) stream)
- (the filtered-simplicial-group
-   (progn
-      (format stream "[K~D Filtered-Simplicial-Group]" (idnm flsmgr))
-      flsmgr)))
-
-(DEFMETHOD PRINT-OBJECT ((flsmgr filtered-ab-simplicial-group) stream)
- (the filtered-simplicial-group
-   (progn
-      (format stream "[K~D Filtered-Abelian-Simplicial-Group]" (idnm flsmgr))
-      flsmgr)))
-
-(DEFUN FltrSmgr (idnm)
-   (declare (type fixnum idnm))
-   (the (or filtered-simplicial-group null)
-      (find idnm *flsmgr-list* :key #'idnm)))
-
-(DEFUN BUILD-FltrSmGr
-    (&key cmpr basis bspn face face* intr-bndr bndr-strt intr-dgnl dgnl-strt 
-      sintr-grml sintr-grin flin orgn)
-   (declare
-     (type cmprf cmpr)
-     (type basis basis)
-     (type gmsm bspn)
-     (type face face)
-     (type (or null face*) face*)
-     (type (or intr-mrph null) intr-bndr intr-dgnl)
-        (type (or strt null) bndr-strt dgnl-strt)
-     (type sintr sintr-grml sintr-grin)
-     (type chcm-flin flin)
-     (list orgn))
-   (the FILTERED-SIMPLICIAL-GROUP
-     (progn
-         (let ((already (find orgn *flsmgr-list* :key #'orgn :test #'equal)))
-            (declare (type (or null FILTERED-SIMPLICIAL-GROUP) already))
-            (when already
-               (return-from build-FltrSmgr already)))
-         (let ((rslt (build-smgr :cmpr cmpr :basis basis :bspn bspn
-                       :face face :face* face* :intr-bndr intr-bndr 
-                       :bndr-strt bndr-strt :intr-dgnl intr-dgnl 
-                       :dgnl-strt dgnl :sintr-grml sintr-grml
-                       :sintr-grin sintr-grin :orgn orgn)))
-            (declare (type simplicial-group rslt))
-            (change-class rslt 'FILTERED-SIMPLICIAL-GROUP)
-            (setf (slot-value rslt 'flin) flin)
-            (push rslt *flsmgr-list*)
-               rslt))))
-
-(DEFMACRO BUILD-FlABSMGR (&rest rest)
-  `(change-class (build-flsmgr ,@rest) 'filtered-ab-simplicial-group))
-
-(defmethod change-chcm-to-flcc ((chcm simplicial-group) flin flin-orgn )
-   (declare
-      
-      (type chcm-flin flin)
-      (list flin-orgn))
-   (the FILTERED-SIMPLICIAL-GROUP
-      (progn
-         (change-class chcm 'FILTERED-SIMPLICIAL-GROUP)
-         (setf orgn (append (orgn chcm) (list 'FILTERED-WITH) flin-orgn))
-         (let ((already (find orgn *flsmgr-list* :key #'orgn :test #'equal)))
-            (declare (type (or null FILTERED-SIMPLICIAL-GROUP) already))
-            (when already
-               (return-from change-chcm-to-flcc already)))
-         (setf (slot-value chcm 'flin) flin)
-         (setf (slot-value chcm 'orgn) orgn)
-         (push chcm *flsmgr-list*)
-         chcm)))
-
-(defmethod change-chcm-to-flcc ((chcm ab-simplicial-group) flin flin-orgn )
-   (declare
-      
-      (type chcm-flin flin)
-      (list flin-orgn))
-   (the FILTERED-AB-SIMPLICIAL-GROUP
-      (progn
-         (change-class chcm 'AB-FILTERED-SIMPLICIAL-GROUP)
-         (setf orgn (append (orgn chcm) (list 'FILTERED-WITH) flin-orgn))
-         (let ((already (find orgn *flabsmgr-list* :key #'orgn :test #'equal)))
-            (declare (type (or null FILTERED-AB-SIMPLICIAL-GROUP) already))
-            (when already
-               (return-from change-chcm-to-flcc already)))
-         (setf (slot-value chcm 'flin) flin)
-         (setf (slot-value chcm 'orgn) orgn)
-         (push chcm *flabsmgr-list*)
-         chcm)))
-
-        
-;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;    EXAMPLES    ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
-
-
-;; BICOMPLEXES
-
-;; Filtration index function of a Bicomplex (first degree of a generator).
-(setf BCflin 
-      #'(lambda (degr gnrt)
-       (declare 
-         (type fixnum degr)
-         (type gnrt gnrt))
-       (let* ((degr1 (BcGnrt-Degr1 gnrt))
-              (degr2 (BcGnrt-Degr2 gnrt)))
-          (declare (type fixnum degr1 degr2))
-          (if (=  degr (+ degr1 degr2))
-             degr1
-             0))))
-
-#|
-(funcall BCflin 5 (build-bcgnrt 2 3 'a))
-(funcall BCflin 7 (build-bcgnrt 6 1 'c))
-|# 
-
-;; Function that changes the bicomplex bc to a filtered complex, with filtration
-;; index of a generator defined as its first degree. 
-(defun CHANGE-BICM-TO-FLCC (bc)
-   (declare 
-     (type bicomplex bc))
-   (let* ((orgn (orgn bc))
-          (flin BCflin))
-      (declare
-       (type list orgn)
-       (type chcm-flin flin))
-      (the FILTERED-CHAIN-COMPLEX
-        (change-chcm-to-flcc bc flin '(Bicomplex-Flin)))))
-
-#|
-(defun bas (degr1 degr2)
-   (if (and (= degr1 0) (= degr2 1)) (return-from bas '(a)))
-   (if (and (= degr1 1) (= degr2 0)) (return-from bas '(b)))
-   (if (and (= degr1 1) (= degr2 1)) (return-from bas '(c)))
-   (if (and (= degr1 2) (= degr2 0))  (return-from bas '(d)))
-   (return-from bas nil))
- 
-(defun dif1 (degr1 degr2 gnrt)
-   (if (and (= degr1 1) (= degr2 1) (eql gnrt 'c)) (return-from dif1 (list (cons 2 'a))))
-   (if (and (= degr1 2) (= degr2 0) (eql gnrt 'd)) (return-from dif1 (list (cons 2 'b))))
-   (return-from dif1 nil))
-(defun dif2 (degr1 degr2 gnrt)
-   (if (and (= degr1 1) (= degr2 1) (eql gnrt 'c)) (return-from dif2 (list (cons 1 'b))))
-   (return-from dif2 nil))
-
-(setf bc (Build-Bicm :bcbasis #'bas :dffr1 #'dif1 :dffr2 #'dif2 :cmpr 's-cmpr 
-          :orgn '(BC-test)))
-
-(change-bicm-to-flcc bc)
-(flin bc 1 (build-bcgnrt 0 1 'a))
-(flin bc (cmbn 2 4 (build-bcgnrt 1 1 'c)))
-(flin bc (cmbn 2 4 (build-bcgnrt 1 1 'c) 2 (build-bcgnrt 2 0 'd)))
-(bigrd-basis bc 1 1)
-(bigrd-basis bc 2 0)
-(fltrd-basis bc 2 1)
-(ordered-basis bc 2)
-(flcc-dffr-mtrx bc 2 1)
-(flcc-dffr-mtrx bc 2 2)
-|#
-
-
-;; BARS
-
-(defun abar-bidegree (abar)
-    (declare (type abar abar))
-    (the list
-      (let ((p (1- (length abar)))
-            (q 0))
-        (declare (type fixnum p q))
-        (setf q (apply #'+ (mapcar #'car (rest abar))))
-        (decf q p)
-        (return-from abar-bidegree (list p q)))))
-
-
-(setf abar-flin 
-      #'(lambda (degr abar)
-       (declare (type fixnum degr)
-         (type abar abar))
-       (let* ((abar-bidgr (abar-bidegree abar))
-              (degr1 (first abar-bidgr))
-             (degr2 (second abar-bidgr)))
-         (if (=  degr (+ degr1 degr2))
-           degr1
-          0))))
-
-#|
-(setq kz2 (k-z2-1))
-(setq bar2 (bar kz2))
-
-(change-chcm-to-flcc bar2 abar-flin '(abar-flin))
-
-
-(setf basis7 (basis bar2 7))
-
-(mapcar
- #'(lambda (gnrt)
-     (flin bar2 7 gnrt))
- basis7)
-
-(flin bar2 (cmbn 7 (first basis7) (second basis7))) 
-
-(bigrd-basis bar2 2 5)
-(bigrd-basis bar2 3 4)
-(fltrd-basis bar2 7 2)
-(ordered-basis bar2 7)
-(flcc-dffr-mtrx bar2 7 2)
-(flcc-dffr-mtrx bar2 7 3)
-|#
-
-;; COBAR
-
-(defun allp-bidegree (allp)
-    (declare (type allp allp))
-    (the list
-      (let ((p (1- (length allp)))
-            (q 0))
-        (declare (type fixnum p q))
-        (setf q (apply #'+ (mapcar #'car (rest allp))))
-        (incf q p)
-        (return-from allp-bidegree (list (- p) q)))))
-
-(setf cobar-flin 
-      #'(lambda (degr allp)
-       (declare (type fixnum degr)
-         (type allp allp))
-       (let* ((allp-bidgr (allp-bidegree allp))
-              (degr1 (first allp-bidgr))
-             (degr2 (second allp-bidgr)))
-         (if (=  degr (+ degr1 degr2))
-           degr1
-          0))))
-
-;; TENSOR PRODUCTS 
- 
-(setf tnpr-flin 
-      #'(lambda (degr tnpr)
-       (declare 
-         (type fixnum degr)
-         (type tnpr tnpr))
-       (the fixnum
-          (degr1 tnpr))))
-
-
-;; FIBRATIONS (CARTESIAN PRODUCTS AND TWISTED PRODUCTS)
-
-(setf crpr-flin 
-      #'(lambda (degr crpr)
-          (declare
-           (type fixnum degr)
-           (type crpr crpr))
-          (let* ((b (cadr crpr))
-                 (dgop (car b)))
-             (declare
-              (type iabsm b)
-              (type fixnum dgop))
-             (the fixnum
-               (- degr (length (dgop-int-ext dgop)))))))
-
-#|
-(funcall fbrt-flin 3 '(:crpr (1 . s2) 0 . 3))
-(funcall fbrt-flin 4 '(:crpr (5 . s2) 0 . 3))
-|# 
- 
-
-;; BICONES
- 
-(defun bicone-flin (flinb flinc flind)
-   (declare (type chcm-flin flinb flinc flind))
-   (flet ((rslt (degr bicn)
-            (declare 
-              (type bicn bicn)
-              (type degr degr))
-            (let ((bcnx (bcnx bicn)))
-               (declare (type (member :bcnb :bcnc :bcnd) bcnx))
-               (if (eql :bcnb bcnx)
-                  (funcall flinb degr (ibicn bicn))
-                  (if (eql :bcnc bcnx)
-                     (funcall flinc degr (ibicn bicn))
-                     (funcall flind degr (ibicn bicn)))))))
-     (the chcm-flin #'rslt))) 
\ No newline at end of file
diff --git a/examples/anromero/filtered-complexes/spectral-sequences.lsp b/examples/anromero/filtered-complexes/spectral-sequences.lsp
deleted file mode 100644
index 4b55947..0000000
--- a/examples/anromero/filtered-complexes/spectral-sequences.lsp
+++ /dev/null
@@ -1,1359 +0,0 @@
-;; SPECTRAL-SEQUENCES   SPECTRAL-SEQUENCES   SPECTRAL-SEQUENCES   SPECTRAL-SEQUENCES
-;; SPECTRAL-SEQUENCES   SPECTRAL-SEQUENCES   SPECTRAL-SEQUENCES   SPECTRAL-SEQUENCES
-;; SPECTRAL-SEQUENCES   SPECTRAL-SEQUENCES   SPECTRAL-SEQUENCES   SPECTRAL-SEQUENCES
-
-
-(IN-PACKAGE "COMMON-LISP-USER")
-
-(provide "spectral-sequences")
-
-
-
-;; Auxiliary functions to deal with matrices
-
-(defun submatrix (mtrx first-line last-line first-col last-col)
-   (declare (type matrix mtrx)
-            (type fixnum first-line last-line first-col last-col))
-  (the matrix
-    (let ((line-n (line-number mtrx))
-	  (column-n (column-number mtrx)))
-      (declare (type fixnum line-n column-n))
-      (assert (<= first-line last-line (1- line-n)))
-      (assert (<= first-col last-col (1- column-n)))
-      (let* ((line-num (+ (- last-line first-line) 1))
-             (column-num (+ (- last-col first-col) 1))
-             (rslt (make-array (list line-num column-num)
-			      :element-type 'fixnum)))
-         (declare (type fixnum line-num column-num) 
-                  (type matrix rslt))
-         (dotimes (il line-num)
-            (declare (type fixnum il))
-            (dotimes (ic column-num)
-               (declare (type fixnum ic))
-               (setf (aref rslt il ic)
-                     (aref mtrx (+ il first-line) (+ ic first-col)))))
-         rslt))))
-
-#|
-(setf m (random-matrix 4 6 10))
-(submatrix m 1 3 2 4)
-|#
-
-
-(Defun column-j (mtrx j)
-   (declare (type matrix mtrx)
-            (type fixnum j))
-   (assert (< j (column-number mtrx)))
-   (the list
-     (let ((line-n (line-number mtrx)))
-        (declare (type fixnum line-n))
-        (mapcar
-         #'(lambda (i)
-             (declare (type fixnum i))
-             (aref mtrx i j))
-         (<a-b> 0 (1- line-n))))))
-
-#|
-(setf m (random-matrix 4 6 10))
-(column-j m 2)
-|#
-
-;; Function that concatenates two matrices (if their line number is different, the 
-;; needed zeros are added. 
-(defun mtrx-conc (mtrx1 mtrx2)
-   (declare (type matrix mtrx1 mtrx2))
-   (the matrix
-     (let* ((line-n-1 (line-number mtrx1))
-            (column-n-1 (column-number mtrx1))
-            (line-n-2 (line-number mtrx2))
-            (column-n-2 (column-number mtrx2))
-            (line-n (max line-n-1 line-n-2))
-            (column-n (+ column-n-1 column-n-2)))
-        (declare (type fixnum line-n-1 column-n-1 line-n-2
-                   column-n-2 line-n column-n))
-        (let ((rslt 
-                #-ACLPC
-                (make-array (list line-n column-n)
-                  :element-type 'fixnum
-                  :initial-element 0)
-                #+ACLPC
-                (if (or (zerop line-n) (zerop column-n))
-                   (make-array (list line-n column-n)
-                     :element-type 'fixnum)
-                   (make-array (list line-n column-n)
-                     :element-type 'fixnum
-                     :initial-element 0))))
-           (declare (type matrix rslt))
-           (do ((j 0 (1+ j)))
-               ((>= j column-n-1))
-              (declare (type fixnum j))
-              (do ((i 0 (1+ i)))
-                   ((>= i line-n-1))
-                 (declare (type fixnum i))
-                 (Setf (aref rslt i j) (aref mtrx1 i j))))
-           (do ((j 0 (1+ j)))
-                ((>= j column-n-2))
-              (declare (type fixnum j))
-              (do ((i 0 (1+ i)))
-                   ((>= i line-n-2))
-                 (declare (type fixnum i))
-                 (Setf (aref rslt i (+ column-n-1 j)) (aref mtrx2 i j))))
-            rslt))))
-
-#|
-(setf m1 (random-matrix 3 4 10))
-(setf m2 (random-matrix 4 2 10))
-(mtrx-conc m1 m2)
-(mtrx-conc m2 m1)
-|#
-
- 
-;; Functions related with submodules and matrices
-
-;; Function that returns a list of generators of the kernel of a matrix.
-;; Each generator is a list of integers which represent its coordinates
-;; in the initial basis.
-(defun kernel (mtrx)
-   (declare (type matrix mtrx))
-   (the list
-     (let* ((smith-list (smith mtrx))
-            (m (third smith-list))
-            (q (fourth smith-list))
-            (min (min (line-number mtrx) (column-number mtrx)))
-            (rslt nil))
-        (declare 
-          (type list smith-list rslt)
-          (type matrix m q)
-          (type fixnum min))
-        (progn
-         (do ((j (1- (column-number mtrx)) (1- j)))
-             ((< j min))
-            (declare (type fixnum j))
-            (setq rslt (nconc (list (column-j q j)) rslt)))
-         (do ((i (1- min) (1- i)))
-             ((or (< i 0) (not (eql  0 (aref m i i)))))
-            (declare (type fixnum i))
-            (setq rslt (nconc (list (column-j q i)) rslt)))
-         rslt))))
-
-#|
-(setf m (random-matrix 3 4 10))
-(kernel m)
-|#
-
-
-;; Returns a matrix which has as columns the elements of the list.
-;; (Each element in the list is a list of integers).
-(defun Gnrt-List-to-Mtrx (gnrt-list)
-   (declare (type list gnrt-list))
-   (the matrix
-     (let* ((column-n (length gnrt-list))
-            (line-n (length (car gnrt-list)))
-            (rslt 
-              #-ACLPC
-              (make-array (list line-n column-n)
-                :element-type 'fixnum
-                :initial-element 0)
-              #+ACLPC
-              (if (or (zerop line-n) (zerop column-n))
-                 (make-array (list line-n column-n)
-                   :element-type 'fixnum)
-                 (make-array (list line-n column-n)
-                   :element-type 'fixnum
-                   :initial-element 0))))
-        (declare 
-          (type fixnum column-n line-n)
-          (type matrix rslt))
-        (do ((j 0 (1+ j))
-             (mark2 gnrt-list (cdr mark2)))
-            ((endp mark2))
-           (declare
-            (type fixnum j)
-            (list mark2)) 
-           (if (eql line-n (length (car mark2)))
-              (do ((i 0 (1+ i))
-                   (mark1 (car mark2) (cdr mark1)))
-                  ((endp mark1))
-                 (declare 
-                   (type fixnum i)
-                   (list mark1))
-                 (setf (aref rslt i j) (car mark1)))))
-        rslt)))
-
-#|
-(setq gnrt-list (list '(2 4 6 8) '(0 1 0 0) '(0 3 3 3)))
-(Gnrt-List-to-Mtrx gnrt-list)
-|# 
-
-;; Returns the list of columns of the matrix mtrx.
-(defun gnrt-mtrx-to-list (mtrx)
-   (declare (type matrix mtrx))
-   (the list
-     (let* ((column-n (column-number mtrx)))
-        (declare (type fixnum column-n))
-        (mapcar
-         #'(lambda (j)
-             (declare (type fixnum j))
-             (column-j mtrx j))
-       (<a-b> 0 (1- column-n))))))
-
-#|
-(setf m (random-matrix 3 4 10))
-(gnrt-mtrx-to-list m)
-|#
-
-;; Returns the representation basis-divisors of a quotient of submodules B/C
-;; which are the images of the matrices mtrx1 and mtrx2, where basis=list
-;; of combinations (c_1...c_m) that forms a basis for B and divisors=list of
-;; integers (n_1....n_m) such that (n_1*c_1,...,n_m*c_m) forms a basis for C. 
-(defun mtrx-quotient (mtrx1 mtrx2)
-   (declare (type matrix mtrx1 mtrx2))
-   (the list
-     (let* ((smith-list-1 (smith mtrx1))
-            (p1 (first smith-list-1))
-            (p1-1 (second smith-list-1))
-            (d1 (third smith-list-1))
-            (p1-1Xmtrx2 (mtrx-prdc p1-1 mtrx2))
-            (p1Xd1 (copy-mtrx p1))
-            (d1-1Xp1-1Xmtrx2 (copy-mtrx p1-1Xmtrx2)))
-        (declare
-         (list smith-list-1)
-         (type matrix p1 p1-1 s1 p1-1Xmtrx2 p1Xd1 d1-1Xp1))
-        (progn
-         (let* ((line-n-1 (line-number p1))
-                (column-n-1 (column-number p1)))
-            (declare (type fixnum line-n-1 column-n-1))
-            (dotimes (ic column-n-1)
-               (declare (type fixnum ic))
-               (if (and (< ic (line-number d1)) (< ic (column-number d1)))
-                  (let ((d (aref d1 ic ic)))
-                     (declare (type fixnum d))
-                     (dotimes (il line-n-1)
-                        (declare (type fixnum il))
-                        (if (and (not (eql 1 d)) (not (eql 0 d)))
-                           (setf (aref p1Xd1 il ic) (* d (aref p1Xd1 il ic)))))))))
-         (let* ((line-n-2 (line-number p1-1Xmtrx2))
-                (column-n-2 (column-number p1-1Xmtrx2)))
-            (declare (type fixnum line-n-2 column-n-2))    
-            (dotimes (il line-n-2)
-               (declare (type fixnum il))
-               (if (and (< il (line-number d1)) (< il (column-number d1)))
-                  (let ((d (aref d1 il il)))
-                     (if (and (not (eql 1 d)) (not (eql 0 d)))
-                        (dotimes (ic column-n-2)
-                           (declare (type fixnum ic))
-                           (setf (aref d1-1Xp1-1Xmtrx2 il ic) 
-                                 (floor (aref d1-1Xp1-1Xmtrx2 il ic) d))))))))
-         (let* ((smith-list-2 (smith d1-1Xp1-1Xmtrx2))
-                (p2 (first smith-list-2))
-                (basis-mtrx (mtrx-prdc p1Xd1 p2))
-                (div-mtrx (third smith-list-2))
-                (cmbns nil)
-                (divs nil))
-            (declare 
-              (list smith-list-2 cmbns divs)
-              (type matrix p2 basis-mtrx div-mtrx))
-            (do ((i 0 (1+ i)))
-                ((or (>= i (line-number d1)) (>= i (column-number d1))
-                     (eql 0 (aref d1 i i))))
-               (declare (type fixnum i))
-               (progn
-                (setq cmbns (nconc cmbns (list (column-j basis-mtrx i))))
-                (if (and (< i (line-number div-mtrx)) (< i (column-number div-mtrx))) 
-                   (setq divs (nconc divs (list (aref div-mtrx i i))))
-                   (setq divs (nconc divs (list 0))))))
-            (list cmbns divs))))))
-
-#|
-(setf m1 (gnrt-list-to-mtrx '((1 1 1 1) (0 2 0 3) (1 0 0 0))))
-(setf m2 (gnrt-list-to-mtrx '((2 3 1 4) (0 1 1 1))))
-(mtrx-quotient m1 m2)
-|#
-
-
-
-;; SPECIFIC FUNCTIONS FOR THE COMPUTATION OF SPECTRAL SEQUENCES 
-;; OF EFFECTIVE FILTERED COMPLEXES.
-
-
-;; GROUPS
-
-;; Returns the matrix that defines Z^r_{p,q} (a submatrix of the 
-;; differential matrix M, such that the elements of Z^r_{p,q} are those that
-;; when we apply M to them we obtain zero, i.e. Z^r_{p,q}=Ker M). Only can be applied
-;; to a finitely generated complex. 
-(defun FLTR-CHCM-Z-MTRX (fltrcm r p q)
-  (declare
-    (type filtered-chain-complex fltrcm)
-    (type fixnum r p q))
-  (the matrix
-    (let* ((cmpr (cmpr1 fltrcm))
-	     (dffr (dffr fltrcm))
-	     (degr (+ p q))
-           (sbasis (fltrd-basis fltrcm degr p))
-           (tbasis 
-             (mapcan 
-              #'(lambda (i)
-                  (declare (type fixnum i))
-                  (bigrd-basis fltrcm i (- (1- degr) i)))
-              (<a-b> (1+ (- p r)) p)))) ;; We suppose that the differential
-                                        ;; respects the filtration, i.e., 
-                                        ;; d(F_pX) \in F_p(dX). If not, we must
-                                        ;; consider (<a-b> (1+ (-p r)) t(degr),
-                                        ;; where t(degr)=max{flin(x), x \in X_degr}.
-       (declare
-        (type cmprf cmpr)
-        (type morphism dffr)
-        (type fixnum degr)
-        (list sbasis tbasis))
-      (let ((srank (length sbasis))
-	      (trank (length tbasis)))
-         (declare (type fixnum srank trank))
-         (let ((rslt 
-               #-ACLPC
-                    (make-array (list trank srank)
-				:element-type 'fixnum
-				:initial-element 0)
-               #+ACLPC
-                    (if (or (zerop srank) (zerop trank))
-                       (make-array (list trank srank)
-                          :element-type 'fixnum)
-                       (make-array (list trank srank)
-                          :element-type 'fixnum
-                          :initial-element 0))))               
-            (declare (type matrix rslt))
-            (do ((j 0 (1+ j))
-	           (mark sbasis (cdr mark)))
-                ((endp mark))
-               (declare
-                (type fixnum j)
-                (list mark))
-               (let ((cmbn (gnrt-? dffr degr (car mark))))
-                  (declare (type cmbn cmbn))
-                  (do ((mark1 (cmbn-list cmbn) (cdr mark1)))
-                      ((endp mark1))
-                     (declare (list mark1))
-                     (with--term (cffc gnrt) mark1
-                       (declare 
-                         (type fixnum cffc)
-                         (type gnrt gnrt))
-                       (do ((mark2 tbasis (cdr mark2))
-                            (i 0 (1+ i))
-                            (found nil))
-                           ((or (endp mark2) found))
-                          (declare 
-                            (list mark2)
-                            (type fixnum i found))
-                          (if (eq :equal (funcall cmpr gnrt (car mark2)))
-                             (progn
-                              (setq found 1)
-                              (setf (aref rslt i j) cffc))))))))
-               rslt)))))
-
-#|
-(cat-init)
-(setq kz2 (k-z2-1))
-(setq fcc (bar kz2))
-(Change-Chcm-TO-Flcc fcc abar-flin `(abar-flin))
-(FLTR-CHCM-Z-MTRX fcc 2 3 2)
-(FLTR-CHCM-Z-MTRX fcc 1 2 4)
-|#
- 
-
-;; Returns a list of generators (list of coordinates) of Z^r_{p,q}
-;; (only for finitely generated complexes)
-(defun Fltr-Chcm-Z-Gnrt-List (FltrCm r p q)
-   (declare (type filtered-chain-complex fltrcm)
-     (type fixnum r p q))
-   (the list
-         (let* ((degr (+ p q))
-                (all-basis-gnrt-list (fltr-basis-gnrt-list fltrcm degr p)))
-            (declare
-             (type fixnum degr)
-             (list all-basis-gnrt-list))
-            (if (= 0 r)
-               all-basis-gnrt-list
-               (let* ((mat (FLTR-CHCM-Z-MTRX fltrcm r p q))
-                   (line-n (line-number mat))
-                   (column-n (column-number mat)))
-                  (declare 
-                    (type matrix mat)
-                    (type fixnum line-n column-n))
-                  (if (= 0 column-n) nil
-                     (if (= 0 line-n)
-                     all-basis-gnrt-list
-                     (kernel mat))))))))
-#|
-(Fltr-Chcm-Z-Gnrt-List fcc 2 3 2)
-(Fltr-Chcm-Z-Gnrt-List fcc 1 2 4)
-|# 
-
-;; Returns a list of lists with the coordinates of the elements of
-;; the basis of F_pX_n (with p=fltr-index, n=degr), that are lists with
-;; the form (0...0 i 0...0) (only for finitely generated complexes)
-(defun fltr-basis-gnrt-list (FltrCm degr fltr-index)
-   (declare 
-     (type filtered-chain-complex fltrcm)
-     (type fixnum degr fltr-index))
-   (the list
-     (let* ((all-basis (fltrd-basis fltrcm degr fltr-index))
-            (basis-l (length all-basis))
-            (rslt 
-              (the list
-                (mapcar
-                 #'(lambda (i)
-                     (nconc (make-list (1- i) :initial-element 0) 
-                       (list 1) (make-list (- basis-l i) :initial-element 0)))
-                 (<a-b> 1 basis-l)))))
-        rslt)))
-
-#|
-(fltr-basis-gnrt-list fcc 6 2)
-|#
- 
-
-;; Returns the matrix of the generators of the numerator in E^r_{p,q}
-;; (Only for finitely generated complexes)
-(defun spsq-num-mtrx (FltrCm r p q)
-  (the matrix
-    (let* ((degr (+ p q))
-           (fltr-p-basis (fltrd-basis fltrcm degr p))
-           (p-basis-l (length fltr-p-basis))
-           (z1-list (fltr-chcm-z-gnrt-list fltrcm r p q))
-           (fltr-p-1-list (fltr-basis-gnrt-list fltrcm degr (1- p)))
-           (z1-mtrx (gnrt-list-to-mtrx z1-list))
-           (fltr-p-1-mtrx (gnrt-list-to-mtrx fltr-p-1-list))
-           (num1-mtrx (mtrx-conc z1-mtrx fltr-p-1-mtrx))
-           (num1-line-n (line-number num1-mtrx)))
-       (declare
-        (type fixnum degr num1-line-n)
-        (type list fltr-p-basis p-basis-l z1-list fltr-p-1-list)
-        (type matrix z1-mtrx fltr-p-1-mtrx num1-mtrx))
-       (if (eql num1-line-n p-basis-l)
-          num1-mtrx 
-          (let* ((num-line-n p-basis-l)
-                 (num-column-n (column-number num1-mtrx))
-                 (rslt  
-                   #-ACLPC (make-array (list num-line-n num-column-n)
-                             :element-type 'fixnum
-                             :initial-element 0)
-                   #+ACLPC
-                   (if (or (zerop num-line-n) (zerop num-column-n))
-                      (make-array (list num-line-n num-column-n)
-                        :element-type 'fixnum)
-                      (make-array (list num-line-n num-column-n)
-                        :element-type 'fixnum
-                        :initial-element 0))))
-             (declare
-              (type fixnum num-lin-n num-column-n)
-              (type matrix rslt))
-             (do ((j 0 (1+ j)))
-                 ((>= j num-column-n))
-                (declare (type fixnum j))
-                (do ((i 0 (1+ i)))
-                    ((>= i num1-line-n))
-                   (declare (type fixnum i))
-                   (Setf (aref rslt i j) (aref num1-mtrx i j))))
-             rslt)))))
-
-#|
-(spsq-num-mtrx fcc 2 3 2)
-(spsq-num-mtrx fcc 1 2 4)
-|# 
-
-;; Returns the matrix of the generators of the denominator in E^r_{p,q}
-;; (Only for finitely generated complexes) 
-(defun spsq-den-mtrx (FltrCm r p q)
-   (the matrix
-     (let* ((degr (+ p q))
-            (fltr-p-basis (fltrd-basis fltrcm degr p))
-            (p-basis-l (length fltr-p-basis))
-            (fltr-p-1-list (fltr-basis-gnrt-list fltrcm degr (1- p)))
-            (z2-list (fltr-chcm-z-gnrt-list fltrcm (1- r) (1- (+ p r)) (+ 2 (- q r))))
-            (z2-mtrx (gnrt-list-to-mtrx z2-list))
-            (fltr-p-1-mtrx (gnrt-list-to-mtrx fltr-p-1-list))
-            (dffr-mtrx (flcc-dffr-mtrx fltrcm (1+ degr) (1- (+ p r))))
-            (nil-mtrx 
-              #-ACLPC (make-array (list 0 0)
-                        :element-type 'fixnum
-                        :initial-element 0)
-              #+ACLPC (make-array (list 0 0)
-                        :element-type 'fixnum))
-            (dffr-z2-mtrx 
-              (if (or (= 0 (array-total-size z2-mtrx)) (= 0 (array-total-size dffr-mtrx)))
-                 nil-mtrx
-                 (mtrx-prdc dffr-mtrx z2-mtrx)))
-            (bnd-z2-line-n p-basis-l)
-            (bnd-z2-column-n (column-number dffr-z2-mtrx))
-            (bnd-z2-mtrx
-             (if (or (= 0 bnd-z2-line-n) (= 0 bnd-z2-column-n))
-                nil-mtrx
-                (submatrix dffr-z2-mtrx 0 (1- bnd-z2-line-n) 0 (1- bnd-z2-column-n))))
-            (den1-mtrx (mtrx-conc bnd-z2-mtrx fltr-p-1-mtrx))
-            (den-column-n (column-number den1-mtrx))
-            (den-line-n p-basis-l)
-            (rslt  
-              #-ACLPC (make-array (list den-line-n den-column-n)
-                        :element-type 'fixnum
-                        :initial-element 0)
-              #+ACLPC
-              (if (or (zerop den-line-n) (zerop den-column-n))
-                 (make-array (list den-line-n den-column-n)
-                   :element-type 'fixnum)
-                 (make-array (list den-line-n den-column-n)
-                   :element-type 'fixnum
-                   :initial-element 0))))
-        (declare
-             (list fltr-p-basis fltr-p-1-list z2-list)
-             (type fixnum degr p-basis-l bnd-z2-line-n bnd-z2-column-n den-column-n den-line-n)
-             (type matrix z2-mtrx fltr-p-1-mtrx dffr-mtrx nil-mtrx 
-               dffr-z2-mtrx bnd-z2-mtrx den1-mtrx rslt))
-        (do ((j 0 (1+ j)))
-            ((>= j den-column-n))
-           (declare (type fixnum j))
-           (do ((i 0 (1+ i)))
-               ((>= i (min den-line-n (line-number den1-mtrx))))
-              (declare (type fixnum i))
-              (Setf (aref rslt i j) (aref den1-mtrx i j))))
-        rslt)))
-                   
-#|
-(spsq-den-mtrx fcc 2 3 2)
-(spsq-den-mtrx fcc 1 2 4)
-|#   
-
-;; Function that returns the representation basis-divisors of E^r_{p,q} of a
-;; finitely generated complex. 
-(defun eff-spsq-basis-dvs (FltrCm r p q)
-   (declare 
-     (type filtered-chain-complex fltrcm)
-     (type fixnum r p q))
-   (the list
-     (let* ((degr (+ p q))
-            (fltr-p-basis (fltrd-basis fltrcm degr p))
-            (p-basis-l (length fltr-p-basis))
-            (num-mtrx (spsq-num-mtrx fltrcm r p q))
-            (den-mtrx (spsq-den-mtrx fltrcm r p q)) 
-            (cmbn-list nil)
-            (divs nil))
-        (declare
-         (list fltr-p-basis cmbn-list divs)
-         (type fixnum degr p-basis-l)
-         (type matrix num-mtrx den-mtrx))
-        (progn
-         (if (= 0 (array-total-size num-mtrx))
-            (progn
-             (setq cmbn-list nil)
-             (setq divs nil))
-            (if (= 0 (array-total-size den-mtrx))
-               (progn
-                (setq cmbn-list (gnrt-mtrx-to-list num-mtrx))
-                (setq divs (make-list (length cmbn-list) :initial-element 0)))
-               (let ((quotient-list (mtrx-quotient num-mtrx den-mtrx)))
-                  (declare (list quotient-list))
-                  (setq cmbn-list (first quotient-list)
-                    divs (second quotient-list)))))
-         (list
-          (mapcar 
-            #'(lambda (int-list)
-                (declare (list int-list))
-                (the cmbn
-                  (let* ((cmbn (cmbn degr))
-                         (cmpr (cmpr fltrcm)))
-                     (declare 
-                       (type cmbn cmbn)
-                       (type cmprf cmpr))
-                     (do ((mark1 int-list (cdr mark1))
-                          (mark2 fltr-p-basis (cdr mark2)))
-                         ((or (endp mark1) (endp mark2)))
-                        (declare (type list mark1 mark2))
-                        (if (not (= 0 (car mark1)))
-                           (setq cmbn (2cmbn-add cmpr cmbn 
-                                        (cmbn degr (car mark1) (car mark2))))))
-                     cmbn))) 
-            cmbn-list)
-          divs)))))
-
-#|
-(do ((r 1 (1+ r)))
-    ((> r 3))
-   (dotimes (n 8)
-      (dotimes (p (+ n 1))
-         (let ((q (- n p)))
-            (print (list r p q))
-            (princ (eff-spsq-basis-dvs fcc r p q))
-            ))))
-|# 
-
-
-(defun eff-spsq-gnrts (FltrCm r p q)
-   (declare 
-     (type filtered-chain-complex fltrcm)
-     (type fixnum r p q))
-   (let* ((basis-dvs (eff-spsq-basis-dvs fltrcm r p q))
-         (basis (first basis-dvs))
-         (dvs (second basis-dvs))
-         (rslt nil))
-      (declare (type list basis-dvs basis dvs rslt))
-      (do ((mark1 basis (cdr mark1))
-           (mark2 dvs (cdr mark2)))
-          ((endp mark1))
-         (if (not (eql 1 (car mark2)))
-            (setf rslt (append rslt (list (car mark1))))))
-      rslt))
-      
- 
-;; Function that presents on the screen the components of the E^r_{p,q}
-;; of the spectral sequence of a filtered complex.
-(defun eff-spsq-group (fltrcm r p q)
-   (declare 
-     (type filtered-chain-complex fltrcm)
-     (type fixnum r p q))  
-   (let* ((basis-dvs (eff-spsq-basis-dvs fltrcm r p q))
-          (cmbns (first basis-dvs))
-          (divs (second basis-dvs)))
-      (declare (list basis-dvs cmbns divs))
-      (format t "Spectral sequence E^~D_{~D,~D}" r p q)
-      (dolist (item divs)
-         (declare (type fixnum item))
-         (if (not (eql 1 item))
-            (progn
-             (format t "~2%Component Z")
-             (unless (zerop item) 
-                (format t "/~DZ" item))
-             )))
-      (terpri)))
-
-#|
-(do ((r 1 (1+ r)))
-    ((> r 3))
-   (dotimes (n 8)
-      (dotimes (p (+ n 1))
-         (let ((q (- n p)))
-            (eff-spsq-group fcc r p q)
-            (terpri)
-            (terpri)
-            ))))
-|# 
-
-
-
-;; DIFFERENTIAL FUNCTIONS
-
-;; Auxiliary functions to deal with coefficients of elements with regard to 
-;; some generators or elements of a basis. 
-
-
-;; Function that returns the coordinates of a vector vctr with regard to
-;; the basis whose elements are the columns of the matrix gnrt-mtrx.
-(defun vctr-coordinates (vctr gnrt-mtrx)
-   (declare 
-     (type list vctr)
-     (type matrix gnrt-mtrx))
-   (the list
-     (let* ((C (gnrt-list-to-mtrx (list vctr)))
-            (B (copy-mtrx gnrt-mtrx))
-            (smith-list (smith B))
-            (p-1 (second smith-list))
-            (D (third smith-list))
-            (q (fourth smith-list))
-            (q-1 (fifth smith-list))
-            (C2 (mtrx-prdc p-1 C))
-            (line-n (column-number B))
-            (A2 
-             #-ACLPC
-             (make-array (list line-n 1)
-               :element-type 'fixnum
-               :initial-element 0)
-             #+ACLPC
-             (if (zerop line-n)
-                (make-array (list line-n 1)
-                  :element-type 'fixnum)
-                (make-array (list line-n 1)
-                  :element-type 'fixnum
-                  :initial-element 0)))
-            (end nil))
-        (declare 
-          (type matrix C B p-1 D q q-1 C2 A2)
-          (type list smith-list)
-          (type fixnum line-n end))
-        (do ((i 0 (1+ i)))
-            ((or (>= i (column-number D)) (>= i (line-number D)) end))
-           (declare (type fixnum i))
-           (let* ((di (aref D i i)))
-              (declare (type fixnum di))
-              (if (eql 0 di)
-                 (setq found 1)
-                 (progn
-                  (setf (aref A2 i 0) (floor (aref C2 i 0) di))))))
-        (let* ((A (mtrx-prdc Q A2)))
-           (declare (type matrix A))
-           (column-j A 0)))))
-
-#|
-(setf m (gnrt-list-to-mtrx '((1 0 0 0) (2 3 4 5) (0 1 0 3))))
-(setq vctr '(5 9 8 19))
-(vctr-coordinates vctr m)
-|# 
-
-;; Function that returns the list of coefficients of the combination "cmbn"
-;; in the basis (list of generators) "basis" (with comparison function "cmpr").
-(defun cmbn-cffc-list (cmbn basis cmpr)
-   (declare 
-     (type cmbn cmbn)
-     (type list basis)
-     (type cmprf cmpr))
-   (the list
-     (let* ((rslt nil)
-            (mark1 (cmbn-list cmbn))
-            (term (car mark1))
-            (cffc (cffc term))
-            (gnrt (gnrt term)))
-        (declare
-         (type list rslt mark1)
-         (type term term)
-         (type cffc cffc)
-         (type gnrt gnrt))
-        (do ((mark2 basis (cdr mark2)))
-            ((endp mark2))
-           (declare 
-             (type list mark2))
-           (if (endp mark1)
-              (setq rslt (nconc rslt (list 0)))
-           (if (eq :equal (funcall cmpr gnrt (car mark2)))
-              (progn
-               (setq rslt (nconc rslt (list cffc)))
-               (pop mark1)
-               (setq term (car mark1))
-               (setq cffc (cffc term) gnrt (gnrt term)))
-              (setq rslt (nconc rslt (list 0))))))
-        rslt)))
-
-#|
-(setf basis (list 'a 'b 'c 'd 'e 'f))
-(setq cmbn (cmbn 2 3 'a 5 'c 8 'f))
-(cmbn-cffc-list cmbn basis #'s-cmpr)
-|# 
-
-;; Function that returns the list of coordinates of the combination "cmbn" in the basis
-;; formed by the combinations in the list "gnrt-list". All these combinations are combinations
-;; of the generators in "basis" ("cmpr" is the comparison function). 
-(defun cmbn-coordinates (cmbn gnrt-list basis cmpr)
-   (declare 
-     (type cmbn cmbn)
-     (type list gnrt-list basis)
-     (type cmprf cmpr))
-   (the list
-     (let* ((vctr (cmbn-cffc-list cmbn basis cmpr))
-            (B (gnrt-list-to-mtrx
-                (mapcar
-                 #'(lambda (cmbn2)
-                     (declare (type cmbn cmbn2))
-                     (cmbn-cffc-list cmbn2 basis cmpr))
-                 gnrt-list))))
-        (declare
-         (type list vctr)
-         (type matrix B))
-        (vctr-coordinates vctr B))))
-
-#|
-(setf basis (list 'a 'b 'c 'd 'e 'f))
-(setq cmbn (cmbn 2 3 'a 5 'c 6 'f))
-(setq gnrt-list (list (cmbn 2 1 'a 2 'd 2 'f) (cmbn 2 5 'c -6 'd)))
-(cmbn-coordinates cmbn gnrt-list basis #'s-cmpr)
-|# 
-    
-         
-;; Main function to compute the differential of an element in the spectral sequence          
-
-
-;; Function that returns the list of integers which correspond to the coordinates
-;; on each of the components of E^r_{p-r,q+r-1} of the differential 
-;; d: E^r_{p,q} --> E^r_{p-r,q+r-1} applied to the element of E^r_{p,q}
-;; which has as coordinates the list int-list. (Only for finitely generated complexes)
-(defun eff-spsq-dffr (fltrcm r p q int-list)
-   (declare
-    (type filtered-chain-complex fltrcm)
-    (type fixnum r p q)
-    (list int-list))
-   (the list
-     (let* ((cmpr (cmpr1 fltrcm))
-            (degr (+ p q))
-            (sbasis (fltrd-basis fltrcm degr p))
-            (tbasis (fltrd-basis fltrcm (1- degr) (- p r)))
-            (num-mtrx (spsq-num-mtrx fltrcm r p q))
-            (den-mtrx (spsq-den-mtrx fltrcm r p q))
-            (Z-gnrt-list (Fltr-Chcm-Z-Gnrt-List fltrcm r p q))
-            (s-basis-dvs (mtrx-quotient (copy-mtrx num-mtrx) den-mtrx))
-            (s-gnrt-list (first s-basis-dvs))
-            (s-dvs (second s-basis-dvs))
-            (t-basis-dvs (spsq-basis-dvs fltrcm r (- p r) (1- (+ q r))))
-            (t-gnrt-list (first t-basis-dvs))
-            (t-dvs (second t-basis-dvs))
-            (selement (make-list (length sbasis) :initial-element 0))
-            (cmbn (cmbn degr)))
-        (declare 
-          (type fcmpr cmpr)
-          (type fixnum degr)
-          (type list sbasis tbasis z-gnrt-list s-basis-dvs s-gnrt-list s-dvs
-            t-basis-dvs t-gnrt-list t-dvs selement)
-          (type matrix num-mtrx den-mtrx)
-          (type cmbn cmbn))
-        (progn
-         (labels ((2list-add (list1 list2)
-                    (declare (type list list1 list2))
-                    (the list
-                      (mapcar #'+ list1 list2)))
-                  (n-list (n list)
-                    (declare
-                     (type list list)
-                     (type fixnum n))
-                    (the list
-                      (mapcar #'(lambda (i)
-                                  (* n i))
-                        list))))
-           (do ((mark1 s-gnrt-list (cdr mark1))
-                (mark2 s-dvs (cdr mark2))
-                (mark3 int-list))
-               ((endp mark1))
-              (declare (list mark1 mark2 mark3))
-              (if (not (eql 1 (car mark2)))
-                 (progn
-                  (setq selement (2list-add selement (n-list (car mark3) (car mark1))))
-                  (pop mark3)))))
-         (let* ((selt-coord (vctr-coordinates selement num-mtrx)))
-            (declare (list selt-coord))
-            (do ((mark1 z-gnrt-list (cdr mark1))
-                 (mark2 selt-coord (cdr mark2)))
-                ((endp mark1))
-               (declare (list mark1 mark2))
-               (if (not (eql 0 (car mark2)))
-                  (setq cmbn (2cmbn-add cmpr cmbn (n-cmbn (car mark2)
-                                                    (funcall 
-                                                      #'(lambda (int-list)
-                                                          (declare (list int-list))
-                                                          (the cmbn
-                                                            (let* ((cmbn2 (cmbn degr)))
-                                                               (declare 
-                                                                 (type cmbn cmbn))
-                                                               (do ((mark3 int-list (cdr mark3))
-                                                                    (mark4 sbasis (cdr mark4)))
-                                                                   ((or (endp mark3) (endp mark4)))
-                                                                  (declare (type list mark3 mark4))
-                                                                  (if (not (= 0 (car mark3)))
-                                                                     (setq cmbn2 (2cmbn-add cmpr cmbn2 
-                                                                                   (cmbn degr (car mark3) (car mark4))))))
-                                                               cmbn2)))
-                                                      (car mark1))))))))
-         (let* ((dffr-cmbn (dffr fltrcm cmbn))
-                (crdnt (cmbn-coordinates dffr-cmbn t-gnrt-list tbasis cmpr))
-                (rslt nil))
-            (declare
-             (type cmbn dffr-cmbn)
-             (type list crdnt rslt))
-            (do ((mark1 t-dvs (cdr mark1))
-                 (mark2 crdnt (cdr mark2)))
-                ((endp mark1))
-               (declare (list mark1 mark2))
-               (if (not (eql 1 (car mark1)))
-                  (if (eql 0 (car mark1))
-                     (setq rslt (nconc rslt (list (car mark2))))
-                     (setq rslt (nconc rslt (list (mod (car mark2) (car mark1))))))))
-            rslt)))))          
-                           
-#|
-(eff-spsq-dffr fcc 1 2 3 '(1))
-(eff-spsq-dffr fcc 1 2 5 '(0 1))
-(eff-spsq-dffr fcc 1 2 5 '(1 0))
-(eff-spsq-dffr fcc 1 3 4 '(1 0))
-(eff-spsq-dffr fcc 1 3 4 '(0 1))
-|# 
-
-;; CONVERGENCE OF THE SPECTRAL SEQUENCE            
-
-;; Function that determines if at level r and for degree n the E^r_{p,q} of the
-;; filtered complex fltrcm with p+q=degr are equal to E^\infty_{p,q} (i.e., it 
-;; determines if the convergence of the spectral sequence has been reached at 
-;; level r for the degree n). The list hmlg-cmpns contains the "components" of
-;; the homology group of the complex. It begins with m zeros if the free part of the
-;; group is Z^m and the rest of the list contains the torsion coefficients.
-;; (only for finitely generated complexes). 
-(defun eff-compare-spsq-with-homology (fltrcm r degr hmlg-cmpns)
-   (declare
-    (type filtered-chain-complex fltrcm)
-    (type fixnum r degr)
-    (type list hmlg-cmpns))
-   (let* ((min-max (flin-min-max fltrcm degr))
-          (min (first min-max))
-          (max (second min-max))
-          (spsq-cmpns
-           (mapcan
-           #'(lambda (p)
-               (declare (type fixnum p))
-               (let* ((q (- degr p)))
-                  (declare (type fixnum q))
-                  (second (eff-spsq-basis-dvs fltrcm r p q))))
-            (<a-b> min max)))
-          (mark2 hmlg-cmpns)
-          (hmlg-prdc 1)
-          (spsq-prdc 1))
-      (declare 
-        (type function spsq)
-        (type list spsq-cmpns mark2)
-        (type fixnum hmlg-prdc spsq-prdc))
-      (progn
-       (do ((mark1 spsq-cmpns (cdr mark1)))
-           ((endp mark1))
-          (declare (type list mark1))
-          (if (eql 0 (car mark1))
-             (if (not (eql 0 (car mark2)))
-                (return-from eff-compare-spsq-with-homology nil)
-                (pop mark2))
-             (setq spsq-prdc (* spsq-prdc (car mark1)))))
-       (do ((mark3 mark2 (cdr mark3)))
-           ((endp mark3))
-          (declare (type list mark3))
-          (setq hmlg-prdc (* hmlg-prdc (car mark3))))
-       (if (eql hmlg-prdc spsq-prdc)
-          't
-          nil))))
-   
-#|
-(homology fcc 5) 
-(eff-compare-spsq-with-homology fcc  1 5 '(2))
-(homology fcc 6)
-(eff-compare-spsq-with-homology fcc  1 6 '(2))
-|# 
-
-;; Function that determines the level r at which for degree n the E^r_{p,q} of the
-;; filtered complex fltrcm with p+q=degr are equal to E^\infty_{p,q} (i.e., it 
-;; determines the level r which the convergence of the spectral sequence has been 
-;; reached at for the degree n).            
-(defun eff-spsq-cnvg (fltrcm degr)
-   (declare 
-     (type filtered-chain-complex fltrcm)
-     (type fixnum degr))
-   (the fixnum
-     (let* ((hmlg-dvs-gnrs (homologie (chcm-mat fltrcm degr) (chcm-mat fltrcm (1+ degr))))
-            (hmlg-cmpns (reverse
-                         (mapcar
-                          #'(lambda (l)
-                              (first l))
-                          hmlg-dvs-gnrs)))
-            (cnvg-r 0))
-        (declare 
-          (list hmlg-dvs-gnrs hmlg-cmpns)
-          (type fixnum cnvg-r))
-        (do ((r 1 (1+ r)))
-            ((> cnvg-r 0))
-           (declare (type fixnum r))
-           (if (eff-compare-spsq-with-homology fltrcm r degr hmlg-cmpns)
-              (setq cnvg-r r)))
-        cnvg-r)))
-
-#|
-(eff-spsq-cnvg fcc 5)
-(eff-spsq-cnvg fcc 6)
-|# 
-
-;; EFFECTIVE HOMOLOGY
-
-
-;; Function that returns the order of filtration t (with regard to the filtration in the
-;; left complex, which is translated to the top and right ones) of the homotopy in the right reduction,
-;; which will determine the level r (=t+1) up to which the spectral sequences E^r_p,q 
-;; (with p+q=n) of the left and right complexes are isomorphic. This function can only be used
-;; when the top complex is effective (we need to obtain the elements in the basis of this complex). 
-(defun hmtp-eq-fltr-order (hmtp-eq degr)
-   (declare 
-     (type HOMOTOPY-EQUIVALENCE hmtp-eq)
-     (type fixnum degr))
-   (let* ((lcc (lbcc hmtp-eq))
-          (tcc (tcc hmtp-eq))
-          (lf (lf hmtp-eq))
-          (rh (rh hmtp-eq))
-          (max 0))
-      (declare
-       (type chain-complex lcc tcc)
-       (type morphism lf rh)
-       (type fixnum max))
-      (when (eq (basis tcc) :locally-effective)
-         (error "Hmtp-eq-fltr-order cannot work when the top complex of the homotopy equivalence
-             is a LOCALLY-EFFECTIVE chain complex."))
-      (mapcar 
-        #'(lambda (gnrt)
-            (declare (type gnrt gnrt))
-            (setq max (max max (- (flin lcc (lf hmtp-eq (rh hmtp-eq degr gnrt)))
-                        (flin lcc (lf hmtp-eq degr gnrt))))))
-        (basis tcc degr))
-      max))
-
-#|
-(setf hmtp-eq (efhm fcc)) ;; Trivial homotopy equivalence
-(hmtp-eq-fltr-order hmtp-eq 3)
-
-(setq k3 (k-z2 3))
-(Setq hmtp-eq3 (efhm k3))
-(setq ek3 (rbcc hmtp-eq3))
-(Change-Chcm-TO-Flcc ek3 :flin abar-flin :orgn `(filtered-chain-complex ,ek3))
-(setf k3-flin
-        #'(lambda (degr gnrt)
-            (flin ek3 (rf hmtp-eq3 (lg hmtp-eq3 degr gnrt)))))
-(Change-Chcm-TO-Flcc k3 :flin k3-flin :orgn `(filtered-chain-complex ,k3))
-(hmtp-eq-fltr-order hmtp-eq3 3)
-(hmtp-eq-fltr-order hmtp-eq3 5)
-|#
-
-;; Function that changes the right bottom chain complex in a homotopy equivalence into 
-;; a filtered complex, with a filtration defined translating the filtration in the left complex 
-;; (which must be a filtered complex). 
-(defun translate-filtration (hmtp-eq)
-   (declare
-    (type homotopy-equivalence hmtp-eq))
-   (let ((fltrcm (lbcc hmtp-eq))
-         (eff-chcm (rbcc hmtp-eq)))
-      (declare (type chain-complex fltrcm eff-chcm))
-      (Change-Chcm-TO-Flcc eff-chcm :flin
-                                 #'(lambda (degr gnrt)
-                                     (flin fltrcm (lf hmtp-eq (rg hmtp-eq degr gnrt))))
-                                 :orgn (orgn eff-chcm))))
-     
-  
- 
-;; Function that returns the representation basis-divisors of E^r_{p,q} for a filtered
-;; complex fltrcm with effective homology, computing the E^r_{p,q} of the effective complex
-;; in the right side of the homotopy equivalence. 
-;; If the effective complex is a filtered complex, we supose that both reductions in the equi-
-;; valence are compatible with the filtrations (f and g respect the filtration index and h has
-;; filtration order < r). If not, we define the filtration in the effective
-;; complex translating the filtration in the original filtered complex FltrCm, suposing that the 
-;; homotopy in the right side is compatible with the filtration in the left complex for such r (we 
-;; supose that flin(rh(lf(y)))-flin(lf(y))<r for every y in the top complex). 
-(defun spsq-basis-dvs (FltrCm r p q)
-   (declare 
-     (type filtered-chain-complex fltrcm)
-     (type fixnum r p q))
-   (let* ((hmtp-eq (efhm fltrcm))
-          (eff-chcm (rbcc hmtp-eq))
-          (degr (+ p q)))
-      (declare 
-        (type homotopy-equivalence hmtp-eq)
-        (type chain-complex eff-chcm)
-        (type fixnum degr))
-      (progn
-       (if (not (typep eff-chcm 'filtered-chain-complex))
-          (translate-filtration hmtp-eq))
-       (let ((spsq-list (eff-spsq-basis-dvs eff-chcm r p q)))
-          (declare (list spsq-list))
-          (if (eql fltrcm eff-chcm) spsq-list
-             (list
-              (mapcar
-               #'(lambda (cmbn)
-                   (lf hmtp-eq (rg hmtp-eq cmbn)))
-               (first spsq-list))
-              (second spsq-list)))))))
-
-#|
-(spsq-basis-dvs k3 2 2 2)
-|# 
-
-
-(defun spsq-gnrts (fltrcm r p q)
-   (declare
-    (type filtered-chain-complex fltrcm)
-    (type fixnum r p q))
-   (let* ((hmtp-eq (efhm fltrcm))
-          (eff-chcm (rbcc hmtp-eq))
-          (degr (+ p q)))
-      (declare
-       (type homotopy-equivalence hmtp-eq)
-       (type chain-complex eff-chcm)
-       (type fixnum degr))
-      (progn
-       (if (not (typep eff-chcm 'filtered-chain-complex))
-          (translate-filtration hmtp-eq))
-       (eff-spsq-gnrts eff-chcm r p q))))
-
-;; Function that presents on the screen the components of the E^r_{p,q}
-;; of the spectral sequence of a filtered complex fltrcm with effective homology.
-;; If the effective complex is a filtered complex, we supose that both reductions in the equi-
-;; valence are compatible with the filtrations (f and g respect the filtration index and h has
-;; filtration order < r). If not, we define the filtration in the effective
-;; complex translating the filtration in the original filtered complex FltrCm, suposing that the 
-;; homotopy in the right side is compatible with the filtration in the left complex for such r (we 
-;; supose that flin(rh(lf(y)))-flin(lf(y))<r for every y in the top complex). 
-(defun spsq-group (fltrcm r p q)
-   (declare
-    (type filtered-chain-complex fltrcm)
-    (type fixnum r p q))
-   (let* ((hmtp-eq (efhm fltrcm))
-          (eff-chcm (rbcc hmtp-eq))
-          (degr (+ p q)))
-      (declare
-       (type homotopy-equivalence hmtp-eq)
-       (type chain-complex eff-chcm)
-       (type fixnum degr))
-      (progn
-       (if (not (typep eff-chcm 'filtered-chain-complex))
-          (translate-filtration hmtp-eq))
-       (eff-spsq-group eff-chcm r p q))))
-
-;; Function that returns the list of integers which correspond to the coordinates
-;; on each of the components of E^r_{p-r,q+r-1} of the differential 
-;; d: E^r_{p,q} --> E^r_{p-r,q+r-1} applied to the element of E^r_{p,q}
-;; which has as coordinates the list int-list.
-(defun spsq-dffr (fltrcm r p q int-list)
-   (declare
-    (type filtered-chain-complex fltrcm)
-    (type fixnum p q r)
-    (type list int-list))
-   (let* ((hmtp-eq (efhm fltrcm))
-          (eff-chcm (rbcc hmtp-eq))
-          (degr (+ p q)))
-      (declare
-       (type homotopy-equivalence hmtp-eq)
-       (type chain-complex eff-chcm)
-       (type fixnum degr))
-      (progn
-       (if (not (typep eff-chcm 'filtered-chain-complex))
-          (translate-filtration hmtp-eq))
-       (eff-spsq-dffr eff-chcm r p q int-list))))
-   
-;; Function that determines the level r at which for degree n the E^r_{p,q} (with p+q=degr)
-;; of the filtered complex fltrcm (with effective homology) are equal to E^\infty_{p,q} (i.e., it 
-;; determines the level r which the convergence of the spectral sequence has been 
-;; reached at for the degree n).
-(defun spsq-cnvg (fltrcm degr)
-   (declare
-    (type filtered-chain-complex fltrcm)
-    (type fixnum degr))
-   (let* ((hmtp-eq (efhm fltrcm))
-          (eff-chcm (rbcc hmtp-eq)))
-      (declare
-       (type homotopy-equivalence hmtp-eq)
-       (type chain-complex eff-chcm)
-       (type fixnum degr))
-      (progn
-       (if (not (typep eff-chcm 'filtered-chain-complex))
-          (translate-filtration hmtp-eq))
-       (eff-spsq-cnvg eff-chcm degr))))
-
-
- 
-       
-          
-;; Homology filtration
-
-
-(defun homology-gnrt-list (chcm degr)
-     (declare (type cc chcm) (type fixnum degr))
-     (let ((src (cons :unused (basis chcm degr)))
-           (hom-dvs-gnrts (homologie (chcm-mat chcm degr) (chcm-mat chcm (1+ degr))))
-           (rslt nil))
-        (declare (type list src hom-dvs-gnrts rslt))
-        (mapcar #'(lambda (item)
-                    (declare (type list item))
-                    (let ((cmbn (cmbn degr))
-                          (cmpr (cmpr chcm)))
-                       (dolist (item2 (rest item))
-                          (declare (type cons item2))
-                          (setf cmbn (2cmbn-add cmpr cmbn (cmbn degr (car item2) (nth (cdr item2) src)))))
-                       cmbn))
-          hom-dvs-gnrts)))
-
-
-
-
-(defun homology-fltr1 (fltrcm degr fltr-index)
-   (declare
-    (type filtered-chain-complex fltrcm)
-    (type fixnum degr fltr-index))
-   (let* ((r (spsq-cnvg fltrcm degr))
-          (cmpr (cmpr1 fltrcm))
-          (total-basis (fltrd-basis fltrcm degr fltr-index))
-          (dffr-mtrx (FLTR-CHCM-Z-MTRX fltrcm r fltr-index (- degr fltr-index)))
-          (fltrt-basis 
-           (mapcan #'(lambda (p)
-                       (let* ((q (- degr p))
-                              (num-mtrx (spsq-num-mtrx fltrcm r p q))
-                              (den-mtrx (spsq-den-mtrx fltrcm r p q))
-                              (Z-gnrt-list (Fltr-Chcm-Z-Gnrt-List fltrcm r p q))
-                              (ss-basis-dvs (mtrx-quotient (copy-mtrx num-mtrx) den-mtrx))
-                              (ss-gnrt-list (first ss-basis-dvs))
-                              (ss-dvs (second ss-basis-dvs))
-                              (rslt nil))
-                          (declare 
-                            (type fcmpr cmpr)
-                            (type fixnum r q)
-                            (type list total-basis z-gnrt-list ss-basis-dvs ss-gnrt-list ss-dvs rslt)
-                            (type matrix num-mtrx den-mtrx))
-                          (labels ((2list-add (list1 list2)
-                                     (declare (type list list1 list2))
-                                     (the list
-                                       (mapcar #'+ list1 list2)))
-                                   (n-list (n list)
-                                     (declare
-                                       (type list list)
-                                       (type fixnum n))
-                                     (the list
-                                       (mapcar #'(lambda (i)
-                                                   (* n i))
-                                         list))))
-                            (do ((mark1 ss-gnrt-list (cdr mark1))
-                                 (mark2 ss-dvs (cdr mark2)))
-                                ((endp mark1))
-                               (declare (type list mark1 mark2))
-                               (if (not (eql 1 (car mark2)))
-                                  (let* ((selt (first mark1))
-                                         ;;(coord (cmbn-cffc-list selt total-basis cmpr))
-                                         (cmbn (cmbn degr)))
-                                     (progn
-                                       (let* ((selt-coord (vctr-coordinates selt num-mtrx)))
-                                          (declare (list selt-coord))
-                                          (do ((mark3 z-gnrt-list (cdr mark3))
-                                               (mark4 selt-coord (cdr mark4)))
-                                              ((endp mark3))
-                                             (declare (list mark3 mark4))
-                                             (if (not (eql 0 (car mark4)))
-                                                (setq cmbn (2cmbn-add cmpr cmbn (n-cmbn (car mark4)
-                                                                                  (funcall 
-                                                                                    #'(lambda (int-list)
-                                                                                        (declare (list int-list))
-                                                                                        (the cmbn
-                                                                                          (let* ((cmbn2 (cmbn degr)))
-                                                                                             (declare 
-                                                                                               (type cmbn 
-                                                                                                 cmbn2))
-                                                                                             (do ((
-                                                                                                   mark5 int-list (cdr 
-                                                                                                                    mark5))
-                                                                                                  (mark6 total-basis (cdr mark6)))
-                                                                                                 ((or (endp mark5) (endp mark6)))
-                                                                                                (declare (type list mark5 mark6))
-                                                                                                (if (not (= 0 (car mark5)))
-                                                                                                   (setq cmbn2 (2cmbn-add cmpr cmbn2 
-                                                                                                                 (cmbn degr (car 
-                                                                                                                              mark5) (car 
-                                                                                                                                       mark6))))))
-                                                               cmbn2)))
-                                                      (car mark3))))))))
-                                       (setf rslt (nconc rslt (list cmbn)))
-                                       rslt)))))))
-                          (<a-b> 0 fltr-index))))
-      (if (not (endp fltrt-basis))
-          (let ((fltrt-mtrx
-                  (gnrt-list-to-mtrx
-                    (mapcar #'(lambda (cmbn)
-                                (cmbn-cff-list cmbn total-basis cmpr))
-                      (fltrt-basis))))
-                (num-mtrx (mtrx-conc fltrt-mtrx dffr-mtrx)))
-             (mtrx-quotient num-mtrx dffr-mtrx))
-         nil)))
-
-
-
-(defun eff-hmlg-fltr (fltrcm degr p)
-   (declare
-     (type filtered-chain-complex fltrcm)
-     (type fixnum degr p))
-   (let* ((min-max-1 (flin-min-max fltrcm (1- degr)))
-          (min-1 (first min-max-1))
-          (max-1 (second min-max-1))
-          (min-max+1 (flin-min-max fltrcm (1+ degr)))
-          (min+1 (first min-max+1))
-          (max+1 (second min-max+1))
-          (r (1+ (- p min-1)))
-          (q (- degr p))
-          (Z-gnrts (Fltr-Chcm-Z-Gnrt-List FltrCm r p q))
-          (dffr-mtrx (FLTR-CHCM-Z-MTRX fltrcm (+ 2 (- degr min+1)) (1+ degr) 0))
-          (num-mtrx (mtrx-conc (gnrt-list-to-mtrx z-gnrts) dffr-mtrx))
-          (basis-divs (mtrx-quotient num-mtrx dffr-mtrx))
-          (divs (second basis-divs)))
-      (format t "Filtration F_~D H_~D" p degr)
-      (dolist (item divs)
-         (declare (type fixnum item))
-         (if (not (eql 1 item))
-            (progn
-             (format t "~2%Component Z")
-             (unless (zerop item) 
-                (format t "/~DZ" item))
-             )))))
-     
-
-(defun hmlg-fltr (fltrcm degr p)
-   (declare
-    (type filtered-chain-complex fltrcm)
-    (type fixnum degr))
-   (let* ((hmtp-eq (efhm fltrcm))
-          (eff-chcm (rbcc hmtp-eq)))
-      (declare
-       (type homotopy-equivalence hmtp-eq)
-       (type chain-complex eff-chcm)
-       (type fixnum degr))
-      (progn
-       (if (not (typep eff-chcm 'filtered-chain-complex))
-          (translate-filtration hmtp-eq))
-       (eff-hmlg-fltr eff-chcm degr p))))
-
-
-
-
-(DEFTYPE ss-type () '(member :serre :eilenberg-moore :filtration))
-         
-   
-
-(defclass OUTPUT-SPECTRAL-SEQUENCE ()
-    ((hmeq :type homotopy-equivalence :initarg hmeq :reader hmeq)
-     (eff-flin :type chcm-fltrindex :initarg eff-flin :reader eff-flin)
-     (bgn :type fixnum :initarg bgn :reader bgn)
-     ;; IDentification NuMber

-     (idnm :type fixnum :initform (incf *idnm-counter*) :reader idnm)

-     ;; ORiGiN

-     (orgn :type list :initarg :orgn :reader orgn)))
-
-
-(DEFVAR *oss-list*)
-(SETF *oss-list* +empty-list+)
-(PUSHNEW '*oss-list* *list-list*)
-
-(DEFMETHOD PRINT-OBJECT ((oss OUTPUT-SPECTRAL-SEQUENCE) stream)
-(the output-spectral-sequence
-   (progn
-      (format stream "[K~D output-spectral-sequence]" (idnm oss))
-     oss)))
-
-(DEFUN Oss (idnm)
-   (declare (type fixnum idnm))
-   (the (or OUTPUT-SPECTRAL-SEQUENCE null)
-      (find idnm *oss-list* :key #'idnm)))
-
-
-(DEFUN BUILD-oss (&key hmeq eff-flin bgn orgn)
-   (declare
-      (type homotopy-equivalence hmeq)
-      (type chcm-fltrindex eff-flin)
-      (type fixnum bgn)
-      (type list orgn))
-   (the output-spectral-sequence
-      (progn
-         (let ((already (find orgn *oss-list* :test #'equal :key #'orgn)))
-            (declare (type (or output-spectral-sequence null) already))
-            (when already
-               (return-from build-oss already)))
-         (let ((oss (make-instance 'output-spectral-sequence
-                        :hmeq hmeq
-                        :eff-flin eff-flin
-                        :bgn bgn
-                        :orgn orgn)))
-            (declare (type output-spectral-sequence oss))
-            (push oss *oss-list*)
-            oss))))
-     
-;;(defun serre-ss (fibration)
-
-#|(defun serre-ss (f)
-   (declare (type fibration f))
-   (let* ((X (fibration-total f))
-          (hmeq (efhm X))
-          (eX (rbcc efhm))
-|#
\ No newline at end of file
diff --git a/examples/anromero/homology-of-groups/OMparsers.lisp b/examples/anromero/homology-of-groups/OMparsers.lisp
deleted file mode 100644
index 3467726..0000000
--- a/examples/anromero/homology-of-groups/OMparsers.lisp
+++ /dev/null
@@ -1,464 +0,0 @@
-(in-package :user)
-
-
-
-
-(defun OMgetNextLabel (s)
-   (let* ((p1 (search "<" s)))
-      (delete-if #'(lambda (item) t) s :start 0 :end p1)
-          (let ((p1 (search "<" s))
-                (p2 (if (search " " s) (min (search ">" s) (search " " s))
-                      (search ">" s) )))
-      (subseq s (1+ p1) p2))))
-
-(defun OMgetNextSymbol (s)
-   (let* ((p1 (search "cd=" s))
-          (p2 (search "name=" s))
-          (p3 (search "/>" s))
-          (rslt1 (subseq s (+ 3 p1) p2))
-          (rslt2 (subseq s (+ 5 p2) p3))
-          )
-         (OMLispSymbol (list (delete #\" (delete #\space rslt1)) (delete #\" (delete #\space rslt2))))
-         ))
-
-(defun OMparseNextInteger (s)
-   (if (not (equal (OMgetNextLabel s) "OMI"))
-      (error "The next token is not an integer")
-      (let* ((p1 (search "<OMI>" s))
-             (p2 (search "</OMI>" s))
-             (rslt (parse-integer (subseq s (+ 5 p1) p2))))
-         (delete-if #'(lambda (item) t) s :start 0 :end (+ 6 p2))
-         rslt
-         )))
-
-(defun OMparseNextString (s)
-   (if (not (equal (OMgetNextLabel s) "OMSTR"))
-      (error "The next token is not a string")
-      (let* ((p1 (search "<OMSTR>" s))
-             (p2 (search "</OMSTR>" s))
-             (rslt (subseq s (+ 7 p1) p2)))
-         (delete-if #'(lambda (item) t) s :start 0 :end (+ 8 p2))
-         rslt
-         )))
-
-(defun OMparseNextVar (s)
-   (if (not (equal (OMgetNextLabel s) "OMV"))
-      (error "The next token is not a variable")
-      (let* ((p1 (search "<OMV>" s))
-             (p2 (search "</OMV>" s))
-             (rslt (intern (subseq s (+ 5 p1) p2))))
-         (delete-if #'(lambda (item) t) s :start 0 :end (+ 6 p2))
-         rslt
-         )))
-
-(defun OMparseNextSymbol (s)
-   (if (not (equal (OMgetNextLabel s) "OMS"))
-      (error "The next token is not a symbol")
-      (let* ((rslt (OMgetNextSymbol s))
-             (p (search "/>" s))
-             )
-         (delete-if #'(lambda (item) t) s :start 0 :end (+ 2 p))
-         rslt
-         )))
-  
-(DEFTYPE direct-symbol () '(member list cyclicgroup))
-
-
-(defun OMLispSymbol (list)
-   (let ((cd (first list))
-         (name (second list)))
-      (if (equal cd "list1")
-         (if (equal name "list")
-            'list)
-         (if (equal cd "resolutions")
-            (if (equal name "zgcombination")
-               "zgcombination"
-               (if (equal name "zgterm")
-                  "zgterm"
-                  (if (equal name "zggnrt")
-                     "zggnrt"
-                     (if (equal name "resolution")
-                        "resolution"))))
-            (if (equal cd "group1")
-               (if (equal name "cyclic_group")
-                  'cyclicgroup))))))
-
-(defun OMparseNextApplication (s)
-   (if (not (equal (OMgetNextLabel s) "OMA"))
-      (error "The next token is not an application")
-      (let* ((p1 (search "<OMA>" s)))
-         (delete-if #'(lambda (item) t) s :start 0 :end (+ 5 p1))
-         (let ((head (if (equal (OMgetNextLabel s) "OMS")
-                        (OMparseNextSymbol s)
-                        (OMparseNextObject s)))
-               (rest nil))
-            (if (typep head 'direct-symbol)
-               (do ((rest nil  (append rest (list nextobj))))
-                   ((equal (OMgetNextLabel s) "/OMA") (let ((p (search "</OMA>" s)))
-                                                         (delete-if #'(lambda (item) t) s :start 0 :end (+ 6 p1))
-                                                         (eval (append (list head) rest))))
-                  (setf nextobj (OMparseNextObject s))
-                  )
-               (if (equal head "resolution")
-                  (OMparseResolution s)
-                  (error "imposible to parse")
-            ))))))
-         
-         
-         
-           
-(defun OMparseNextObject (s)
-   (progn 
-     (if (equal (OMgetNextLabel s) "OMOBJ")
-        (delete-if #'(lambda (item) t) s :start 0 :end (+ 7 (search "<OMOBJ>" s))))
-   
-     (if (equal (subseq (OMgetNextLabel s) 0 3) "!--")
-        (delete-if #'(lambda (item) t) s :start 0 :end (+ 4 (search "--/>" s))))
-      
-     (let ((rslt
-            (if (equal (OMgetNextLabel s) "OMI")
-               (OMparseNextInteger s)
-               (if (equal (OMgetNextLabel s) "OMSTR")
-                  (OMparseNextString s)
-                  (if (equal (OMgetNextLabel s) "OMV")
-                     (OMparseNextVar s)
-                     (if (equal (OMgetNextLabel s) "OMS")
-                        (OMLispSymbol(OMparseNextSymbol s))
-                        (if (equal (OMgetNextLabel s) "OMA")
-                           (OMparseNextApplication s)
-                           (error "imposible to parse"))))))))
-        (progn
-         (if (equal (OMgetNextLabel s) "/OMOBJ")
-            (delete-if #'(lambda (item) t) s :start 0 :end (+ 8 (search "</OMOBJ>" s))))
-         rslt))))
-
-
-
-   
-
-
-(defun OMparseZggnrt (s grbasis zgbasis-degr)
-   (if (not (equal (OMgetNextLabel s) "OMA"))
-      (error "The next label is not an application")
-      (progn 
-        (delete-if #'(lambda (item) t) s :start 0 :end (+ 5 (search "<OMA>" s)))
-        (if (not (equal (OMgetNextSymbol s) "zggnrt"))
-           (error "This is not specified as a zggnrt")
-           (progn 
-             (OMparseNextSymbol s)
-             (let* ((i1 (OMparseNextInteger s))
-                    (i2 (OMparseNextInteger s)))
-                (delete-if #'(lambda (item) t) s :start 0 :end (+ 6 (search "</OMA>" s)))
-                (zggnrt (nth (1- i1) grbasis) (nth (1- i2) zgbasis-degr))))))))
-
-
-(defun OMparseZgterm (s degr grbasis zgbasis)
-   (if (not (equal (OMgetNextLabel s) "OMA"))
-      (error "The next label is not an application")
-      (progn 
-        (delete-if #'(lambda (item) t) s :start 0 :end (+ 5 (search "<OMA>" s)))
-        (if (not (equal (OMgetNextSymbol s) "zgterm"))
-           (error "This is not specified as a zgterm")
-           (progn 
-             (OMparseNextSymbol s)
-             (let* ((coeff (OMparseNextInteger s))
-                    (zggnrt (OMparseZggnrt s grbasis (funcall zgbasis degr))))
-                (delete-if #'(lambda (item) t) s :start 0 :end (+ 6 (search "</OMA>" s)))
-                (term-cmbn degr coeff zggnrt )))))))
-
-(defun OMparseZgcmbn (s degr grbasis grcmpr zgbasis zgcmpr)
-   (if (equal (subseq (OMgetNextLabel s) 0 3) "!--")
-      (delete-if #'(lambda (item) t) s :start 0 :end (+ 4 (search "--/>" s))))
-   (if (not (equal (OMgetNextLabel s) "OMA"))
-      (error "The next label is not an application")
-      (progn 
-        (delete-if #'(lambda (item) t) s :start 0 :end (+ 5 (search "<OMA>" s)))
-        (if (not (equal (OMgetNextSymbol s) "zgcombination"))
-           (error "This is not specified as a zgcombination")
-           (progn 
-             (OMparseNextSymbol s)
-             (let ((cmbn-list nil))
-                (do ((term-list nil  (push  (cons 1 nexttermcmbn) term-list)))
-                   ((equal (OMgetNextLabel s) "/OMA") (setf cmbn-list term-list) )
-                  (setf nexttermcmbn (OMparseZgterm s degr grbasis zgbasis))
-                  )
-                (delete-if #'(lambda (item) t) s :start 0 :end (+ 6 (search "</OMA>" s)))
-                (if cmbn-list
-                   (cmbn-cmbn (zggnrt-cmpr grcmpr zgcmpr) cmbn-list)
-                   (zero-cmbn degr))))))))
-
-(defun OMparseZgboundaryList (s grbasis grcmpr zgbasis zgcmpr maxdegr)
-   (if (equal (subseq (OMgetNextLabel s) 0 3) "!--")
-      (delete-if #'(lambda (item) t) s :start 0 :end (+ 4 (search "--/>" s))))
-   (if (not (equal (OMgetNextLabel s) "OMA"))
-      (error "The next label is not an application")
-      (progn 
-        (delete-if #'(lambda (item) t) s :start 0 :end (+ 5 (search "<OMA>" s)))
-        (if (not (equal (OMgetNextSymbol s) 'list))
-           (error "This is not specified as a list")
-           (progn 
-             (OMparseNextSymbol s)
-             (let ((rslt nil))
-                (dotimes (i maxdegr)
-                   (if (equal (subseq (OMgetNextLabel s) 0 3) "!--")
-                      (delete-if #'(lambda (item) t) s :start 0 :end (+ 4 (search "--/>" s))))
-                   (if (not (equal (OMgetNextLabel s) "OMA"))
-                      (error "The next label is not an application")
-                      (progn 
-                        (delete-if #'(lambda (item) t) s :start 0 :end (+ 5 (search "<OMA>" s)))
-                        (if (not (equal (OMgetNextSymbol s) 'list))
-                           (error "This is not specified as a list")
-                           (progn 
-                             (OMparseNextSymbol s)
-                             (let ((rslt-i nil))
-                                (do ((aux nil (push cmbn aux)))
-                                    ((equal (OMgetNextLabel s) "/OMA") (setf rslt-i aux))
-                                   (setf cmbn (OMparseZgcmbn s i grbasis grcmpr zgbasis zgcmpr)))
-                                (delete-if #'(lambda (item) t) s :start 0 :end (+ 6 (search "</OMA>" s)))
-                                (push (nreverse rslt-i) rslt)))))))
-                (delete-if #'(lambda (item) t) s :start 0 :end (+ 6 (search "</OMA>" s)))
-                (nreverse rslt)))))))
-                   
-
-(defun OMparseContractinghmtpList (s grbasis grcmpr zgbasis zgcmpr maxdegr)
-   (if (equal (subseq (OMgetNextLabel s) 0 3) "!--")
-      (delete-if #'(lambda (item) t) s :start 0 :end (+ 4 (search "--/>" s))))
-   (if (not (equal (OMgetNextLabel s) "OMA"))
-      (error "The next label is not an application")
-      (progn 
-        (delete-if #'(lambda (item) t) s :start 0 :end (+ 5 (search "<OMA>" s)))
-        (if (not (equal (OMgetNextSymbol s) 'list))
-           (error "This is not specified as a list")
-           (progn 
-             (OMparseNextSymbol s)
-             (let ((rslt nil))
-                (dotimes (i (1- maxdegr))
-                   (if (equal (subseq (OMgetNextLabel s) 0 3) "!--")
-                      (delete-if #'(lambda (item) t) s :start 0 :end (+ 4 (search "--/>" s))))
-                   (if (not (equal (OMgetNextLabel s) "OMA"))
-                      (error "The next label is not an application")
-                      (progn 
-                        (delete-if #'(lambda (item) t) s :start 0 :end (+ 5 (search "<OMA>" s)))
-                        (if (not (equal (OMgetNextSymbol s) 'list))
-                           (error "This is not specified as a list")
-                           (progn 
-                             (OMparseNextSymbol s)
-                             (let ((rslt-i nil))
-                                (do ((mark1 (funcall zgbasis (1+ i)) (cdr mark1)))
-                                    ((endp mark1) (push (nreverse rslt-i) rslt))
-                                    (if (equal (subseq (OMgetNextLabel s) 0 3) "!--")
-                                       (delete-if #'(lambda (item) t) s :start 0 :end (+ 4 (search "--/>" s))))
-                                   (if (not (equal (OMgetNextLabel s) "OMA"))
-                                      (error "The next label is not an application")
-                                      (progn 
-                                        (delete-if #'(lambda (item) t) s :start 0 :end (+ 5 (search "<OMA>" s)))
-                                        (if (not (equal (OMgetNextSymbol s) 'list))
-                                           (error "This is not specified as a list")
-                                           (progn 
-                                             (OMparseNextSymbol s)
-                                             (let ((rslt-i-g nil))
-                                                
-                                                (do ((mark2 grbasis (cdr mark2)))
-                                                    ((endp mark2) (push (nreverse rslt-i-g) rslt-i))
-                                                   (setf cmbn (OMparseZgcmbn s (1+ i) grbasis grcmpr zgbasis zgcmpr))
-                                                   (push cmbn rslt-i-g))
-                                                (delete-if #'(lambda (item) t) s :start 0 :end (+ 6 (search "</OMA>" s)))
-                                                ))))))
-                                (delete-if #'(lambda (item) t) s :start 0 :end (+ 6 (search "</OMA>" s)))
-                                ))))))
-                (delete-if #'(lambda (item) t) s :start 0 :end (+ 6 (search "</OMA>" s)))
-                (nreverse rslt)))))))
-
-
-
-(defun OMrsltnZgbasis (rank-list maxdegr)
-   (flet ((rslt (degr)
-            (declare (fixnum degr))
-            (if (> degr maxdegr) (error "unknown basis for this degree")
-               (if (< degr 0) nil
-                  (let ((rank (nth degr rank-list))
-                        (list nil))
-                     (dotimes (i rank)
-                        (push (concatenate 'string "g" (Write-to-string degr) (Write-to-string (1+ i))) list))
-                     (nreverse list))))))
-     
-     (the basis #'rslt)))
-
-(defun OMrsltnZgboundary-intr (Zgboundary-list zgbasis maxdegr)
-   (flet ((rslt (degr gnrt)
-            (declare (fixnum degr) (type gnrt gnrt))
-            (if (> degr maxdegr) (error "unknown basis for this degree")
-               (if (< degr 1) (zero-cmbn (1- degr))
-                  (nth (position gnrt (funcall zgbasis degr)  :test #'equal) (nth (1- degr) Zgboundary-list))))))
-          (the intr-mrph #'rslt)))
-
-(defun OMrsltnCntrHmtp-intr (Zgcontractinghmtp-list zgbasis grbasis maxdegr)
-   (flet ((rslt (degr zggnrt)
-            (declare (fixnum degr) (type zggnrt zggnrt))
-            (if (> degr (1- maxdegr)) (error "unknown basis for this degree")
-               (with-zggnrt (gnrt1 gnrt2) zggnrt
-                 (let ((gnrt1-pos (position gnrt1 grbasis :test #'equal))
-                       (gnrt2-pos (position gnrt2 (funcall zgbasis degr) :test #'equal)))
-                    (nth gnrt1-pos (nth gnrt2-pos (nth degr Zgcontractinghmtp-list))))))))
-               (the intr-mrph #'rslt)))
-
-
-
-                             
-                             
-(defun OMparseResolution (s)
-   ;;(if (not (equal (OMgetNextLabel s) "OMA"))
-    ;;  (error "The next label is not an application")
-    ;;  (progn 
-    ;;    (delete-if #'(lambda (item) t) s :start 0 :end (+ 5 (search "<OMA>" s)))
-    ;;    (if (not (equal (OMgetNextSymbol s) "resolution"))
-    ;;       (error "This is not specified as a resolution")
-    ;;       (progn 
-    ;;         (OMparseNextSymbol s)
-             (let* ((group (OMparseNextObject s))
-                    (maxdegr (OMparseNextObject s))
-                    (rank-list (OMparseNextObject s))
-                    (zgbasis (OMrsltnZgbasis rank-list maxdegr)))
-                (with-slots ((grcmpr cmpr) (grbasis elements) nullel) group
-                  (let* ((zgboundary-list (OMparseZgboundaryList s grbasis grcmpr zgbasis #'s-cmpr maxdegr))
-                         (cntrchmtp-list (OMparseContractinghmtpList s grbasis grcmpr zgbasis #'s-cmpr maxdegr))
-                         (zgchcm (BUILD-ZGCHCM :group group :zgcmpr #'s-cmpr :zgbasis zgbasis :zgbsgn "g00" 
-                                   :intr-zgbndr (OMrsltnZgboundary-intr Zgboundary-list zgbasis maxdegr)
-                                   :zgbndr-strt :gnrt :orgn  `(ZG-Chain complex for ,group obtained from HAP)))
-                         (cmpr (cmpr1 zgchcm))
-                         (f-intr #'(lambda (degr zggnrt)
-                                     (if (zerop degr) (cmbn degr 1 :zgnrt) (zero-cmbn degr))))
-                         (g-intr #'(lambda (degr gnrt)
-                                     (if (zerop degr) (cmbn degr 1 (zggnrt nullel "g01")) (zero-cmbn degr))))
-                         (h-intr (OMrsltnCntrHmtp-intr cntrchmtp-list zgbasis grbasis maxdegr))
-
-                         (f (build-mrph :sorc zgchcm :trgt (z-chcm) :degr 0 :intr f-intr :strt :gnrt :orgn `(f-mrph for ,group obtained from HAP)))
-                         (g (build-mrph :sorc (z-chcm) :trgt zgchcm :degr 0 :intr g-intr :strt :gnrt :orgn  `(g-mrph for ,group obtained from HAP)))
-                         (h (build-mrph :sorc zgchcm :trgt zgchcm :degr 1 :intr h-intr :strt :gnrt :orgn `(h-mrph for ,group obtained from HAP))))
-                     (delete-if #'(lambda (item) t) s :start 0 :end (+ 6 (search "</OMA>" s)))
-                     (build-rdct :f f :g g :h h :orgn `(Resolution of ,group obtained from HAP))))))
-;;;))))
-                       
-(defun FileToString (FileName)
-     (with-open-file (f FileName :direction :input)
-       (labels ((getString (f s)
-                 (let* ((aux (read-line f nil 'EOF)))
-                    (if (not (string= aux 'EOF))
-                       (getString f (concatenate 'string s (if (not (string= s "")) (format nil "~%")) aux)) 
-                       s))))
-       (getString f ""))))
-
-                             
-
-#|
-
-
-
-   
-
-(cat-init)
-(load "omparsers.lisp")
-(setf s (filetostring "resolution.log")) 
-(setf rsltn1 (OmparseNextObject s))
-(setf group (group1 (tcc rsltn1)))
-(setf (slot-value group 'resolution) rsltn1)
-(setf k-g-1 (k-g-1 group))
-(setf k-g-2 (k-g group 2))
-(setf k-g-3 (k-g group 3))
-
-(homology k-g-1 0 6)
-(homology k-g-2 0 6)
-(homology k-g-3 0 6)
-
-
-
-(if (equal (OMgetNextLabel s) "OMOBJ")
-        (delete-if #'(lambda (item) t) s :start 0 :end (+ 7 (search "<OMOBJ>" s))))
-   
-     (if (equal (subseq (OMgetNextLabel s) 0 3) "!--")
-        (delete-if #'(lambda (item) t) s :start 0 :end (+ 4 (search "--/>" s))))
-
-
-(if (not (equal (OMgetNextLabel s) "OMA"))
-      (error "The next label is not an application"))
-(delete-if #'(lambda (item) t) s :start 0 :end (+ 5 (search "<OMA>" s)))
-(if (not (equal (OMgetNextSymbol s) "resolution"))
-   (error "This is not specified as a resolution"))
-
-(OMparseNextSymbol s)
-
-(setf group (OMparseNextObject s))
-(setf maxdegr (OMparseNextObject s))
-(setf rank-list (OMparseNextObject s))
-(setf zgbasis (OMrsltnZgbasis rank-list maxdegr))
-
-(setf grcmpr (cmpr1 group) grbasis (elements group) nullel (nullel group))
-(setf zgcmpr #'s-cmpr)
-(setf zgboundary-list (OMparseZgboundaryList s grbasis grcmpr zgbasis #'s-cmpr maxdegr))
-;;(setf cntrchmtp-list (OMparseContractinghmtpList s grbasis grcmpr zgbasis #'s-cmpr maxdegr))                                  
-                         
-(if (not (equal (OMgetNextLabel s) "OMA"))
-      (error "The next label is not an application"))
-
-(delete-if #'(lambda (item) t) s :start 0 :end (+ 5 (search "<OMA>" s)))
-
-(if (not (equal (OMgetNextSymbol s) 'list))
-           (error "This is not specified as a list"))
-(OMparseNextSymbol s)
-
-(setf rslt nil)
-
-(setf i 0)
-(if (not (equal (OMgetNextLabel s) "OMA"))
-                      (error "The next label is not an application"))
-(delete-if #'(lambda (item) t) s :start 0 :end (+ 5 (search "<OMA>" s)))
-(OMparseNextSymbol s)
-(setf rslt-i nil)  
-
-(setf mark1 zgbasis)
-
-
-                (dotimes (i maxdegr)
-                   (if (not (equal (OMgetNextLabel s) "OMA"))
-                      (error "The next label is not an application")
-                      (progn 
-                        (delete-if #'(lambda (item) t) s :start 0 :end (+ 5 (search "<OMA>" s)))
-                        (if (not (equal (OMgetNextSymbol s) 'list))
-                           (error "This is not specified as a list")
-                           (progn 
-                             (OMparseNextSymbol s)
-                             (let ((rslt-i nil))
-                                (do ((mark1 (funcall zgbasis (1+ i)) (cdr mark1)))
-                                    ((endp mark1) (push rslt-i rslt))
-                                    
-                                   (if (not (equal (OMgetNextLabel s) "OMA"))
-                                      (error "The next label is not an application")
-                                      (progn 
-                                        (delete-if #'(lambda (item) t) s :start 0 :end (+ 5 (search "<OMA>" s)))
-                                        (if (not (equal (OMgetNextSymbol s) 'list))
-                                           (error "This is not specified as a list")
-                                           (progn 
-                                             (OMparseNextSymbol s)
-                                             (let ((rslt-i-g nil))
-                                                
-                                                (do ((mark2 grbasis (cdr mark2)))
-                                                    ((endp mark2) (push rslt-i-g rslt-i))
-                                                   (setf cmbn (OMparseZgcmbn s (1+ i) grbasis grcmpr zgbasis zgcmpr))
-                                                   (push cmbn rslt-i-g))
-                                                (delete-if #'(lambda (item) t) s :start 0 :end (+ 6 (search "</OMA>" s)))
-                                                ))))))
-                                (delete-if #'(lambda (item) t) s :start 0 :end (+ 6 (search "</OMA>" s)))
-                                ))))))
-                (delete-if #'(lambda (item) t) s :start 0 :end (+ 6 (search "</OMA>" s)))
-                rslt)))))
-
-
-
-|# 
-
-
-
-
-
-
-
diff --git a/examples/anromero/homology-of-groups/cylinders.lisp b/examples/anromero/homology-of-groups/cylinders.lisp
deleted file mode 100644
index 2f3d3a3..0000000
--- a/examples/anromero/homology-of-groups/cylinders.lisp
+++ /dev/null
@@ -1,462 +0,0 @@
-;;;  CYLIDERS  CYLIDERS  CYLIDERS  CYLIDERS  CYLIDERS  CYLIDERS  CYLIDERS  
-;;;  CYLIDERS  CYLIDERS  CYLIDERS  CYLIDERS  CYLIDERS  CYLIDERS  CYLIDERS 
-;;;  CYLIDERS  CYLIDERS  CYLIDERS  CYLIDERS  CYLIDERS  CYLIDERS  CYLIDERS 
-
-(IN-PACKAGE "COMMON-LISP-USER")
-
-(PROVIDE "CYCLINDERS")
-
-
-(DEFUN CYLN-P (object)
-   (declare (type any object))
-   (the boolean       
-     (and (consp object)            
-          (typep (car object) '(member :CYLNA1 :CYLNB :CYLNA2))
-          (typep (cdr object) 'gnrt))))
-
-(DEFTYPE CYLN () '(satisfies CYLN-P))  
-
-;; MACROS
-
-(DEFMACRO CYLNX (CYLN)
-   `(car ,CYLN))
-
-(DEFMACRO ICYLN (CYLN)
-   `(cdr ,CYLN))
-
-(DEFMACRO CYLNA1 (gnrt)
-   `(cons :CYLNA1 ,gnrt))
-
-(DEFMACRO CYLNB (gnrt)
-   `(cons :CYLNB ,gnrt))
-
-(DEFMACRO CYLNA2 (gnrt)
-   `(cons :CYLNA2 ,gnrt))
-
-(DEFMACRO WITH-CYLN ((CYLNx iCYLN) CYLN . body)
-   `(let ((,CYLNx (CYLNx ,CYLN))
-          (,iCYLN (iCYLN ,CYLN)))
-       (declare
-          (type (member :CYLNA1 :CYLNB :CYLNA2) ,CYLNx)
-          (type gnrt ,iCYLN))
-       ,@body))
-
-
-(DEFUN DISPATCH-CYLN-CMBN (cmbn)
-   (declare (type cmbn cmbn))
-   (the (values cmbn cmbn cmbn)
-      (with-cmbn (degr list) cmbn
-         (let ((listA1 +empty-list+)
-               (listB +empty-list+)
-               (listA2 +empty-list+))
-            (declare (list listA1 listB listA2))
-            (dolist (term list)
-               (declare (type term term))
-               (with-term (cffc cyln) term
-                  (with-cyln (cylnx icyln) cyln
-                     (ecase cylnx
-                        (:cylnA1 (push (term cffc icyln) listA1))
-                        (:cylnB (push (term cffc icyln) listB))
-                        (:cylnA2 (push (term cffc icyln) listA2))))))
-            (values
-               (make-cmbn :degr (1- degr) :list (nreverse listA1))
-               (make-cmbn :degr degr :list (nreverse listB))
-               (make-cmbn :degr degr :list (nreverse listA2)))))))
-
-#|
-  (dispatch-CYLN-cmbn (cmbn 3 3 (cylnA1 'a11) 4 (cylnA1 'a12) 33 (cylnB 'b) 333 (cylnA2 'a2)))
-|#
-
-(DEFUN CYLN-CMBN-CMBNA1 (cmbn)
-   (declare (type cmbn cmbn))
-   (the cmbn
-      (with-cmbn (degr list) cmbn
-         (make-cmbn :degr (1- degr)
-            :list (do ((rslt +empty-list+)
-                       (mark list (cdr mark)))
-                      ((endp mark) (nreverse rslt))
-                     (declare (list rslt mark))
-                     (with--term (cffc CYLN) mark
-                     (with-CYLN (CYLNx gnrtA1) CYLN
-                        (if (eq CYLNx :CYLNA1)
-                           (push (term cffc gnrtA1) rslt)
-                           (return (nreverse rslt))))))))))
-
-(DEFUN CYLN-CMBN-CMBNB (cmbn)
-   (declare (type cmbn cmbn))
-   (the cmbn
-      (with-cmbn (degr list) cmbn
-         (make-cmbn :degr degr
-            :list (do ((rslt +empty-list+)
-                       (mark (member :CYLNb list :key #'cadr) (cdr mark)))
-                      ((endp mark) (nreverse rslt))
-                     (declare (list rslt mark))
-                     (with--term (cffc CYLN) mark
-                     (with-CYLN (CYLNx gnrtB) CYLN
-                        (if (eq CYLNx :CYLNB)
-                           (push (term cffc gnrtB) rslt)
-                           (return (nreverse rslt))))))))))
-
-(DEFUN CYLN-CMBN-CMBNA2 (cmbn)
-   (declare (type cmbn cmbn))
-   (the cmbn
-      (with-cmbn (degr list) cmbn
-         (make-cmbn :degr degr
-            :list (mapcar
-                     #'(lambda (term)
-                          (declare (type term term))
-                          (with-term (cffc CYLN) term
-                             (term cffc (iCYLN CYLN))))
-                     (member :CYLNA2 list :key #'cadr))))))
-
-#|
- 
-  (CYLN-cmbn-cmbnA1 (cmbn 3 1 (CYLNA1 'a) 2 (CYLNB 'b)))
-  (CYLN-cmbn-cmbnA1 (cmbn 3 2 (CYLNB 'b)))
-  (CYLN-cmbn-cmbnB (cmbn 3 1 (CYLNA1 'a) 2 (CYLNB 'b) 3 (CYLNA2 'c)))
-  (CYLN-cmbn-cmbnB (cmbn 3 1 (CYLNA1 'a) 3 (CYLNA2 'c)))
-  (CYLN-cmbn-cmbnA2 (cmbn 3 1 (CYLNA1 'a) 2 (CYLNB 'b) 3 (CYLNA2 'c)))
-  (CYLN-cmbn-cmbnA2 (cmbn 3 2 (CYLNA1 'b)))
-|#
-
-(DEFUN MAKE-CYLN-CMBN (cmbnA1 cmbnB cmbnA2)
-   (declare (type cmbn cmbnA1 cmbnB cmbnA2))
-   (the cmbn
-      (with-cmbn (degrA1 listA1) cmbnA1
-      (with-cmbn (degrB listB) cmbnB
-      (with-cmbn (degrA2 listA2) cmbnA2
-         (unless (= (1+ degrA1) degrB degrA2)
-            (error "In MAKE-CYLN-CMBN, the degrees are not coherent."))
-         (make-cmbn :degr degrB
-            :list (nconc
-                     (mapcar #'(lambda (termA1)
-                                  (declare (type term termA1))
-                                  (with-term (cffc gnrtA1) termA1
-                                     (term cffc (CYLNA1 gnrtA1))))
-                        listA1)
-                     (mapcar #'(lambda (termB)
-                                  (declare (type term termB))
-                                  (with-term (cffc gnrtB) termB
-                                     (term cffc (CYLNB gnrtB))))
-                        listB)
-                     (mapcar #'(lambda (termA2)
-                                  (declare (type term termA2))
-                                  (with-term (cffc gnrtA2) termA2
-                                     (term cffc (CYLNA2 gnrtA2))))
-                        listA2))))))))
-
-#|
-  (multiple-value-call #'make-CYLN-cmbn 
-     (dispatch-CYLN-cmbn (cmbn 3 3 (CYLNA1 'A11) 4 (CYLNA1 'A12) 33 (CYLNB 'B) 333 (CYLNA2 'A2))))
-|#
-
-(DEFMETHOD PRINT-KEYCONS ((car (eql :CYLNA1)) cdr stream)
-   (declare
-      (type gnrt cdr)
-      (stream stream))
-   (the (eql t)
-      (progn
-         (format stream "<CylnA1 ~A>" cdr)
-         t)))
-
-(DEFMETHOD PRINT-KEYCONS ((car (eql :CYLNB)) cdr stream)
-   (declare
-      (type gnrt cdr)
-      (stream stream))
-   (the (eql t)
-      (progn
-         (format stream "<CylnB ~A>" cdr)
-         t)))
-
-(DEFMETHOD PRINT-KEYCONS ((car (eql :CYLNA2)) cdr stream)
-   (declare
-      (type gnrt cdr)
-      (stream stream))
-   (the (eql t)
-      (progn
-         (format stream "<CylnA2 ~A>" cdr)
-         t)))
-
-#|
-  (CYLNa1 'a)
-  (CYLNB 'b)
-  (CYLNA2 'c)
-|#
-
-(DEFUN cylnX-CMPR (s1 s2)
-   (declare (symbol s1 s2))
-   (the cmpr
-      (if (string= s1 s2) :equal
-         (if (string= s1 :cylnA1) :less
-            (if (string= s2 :cylnA1) :greater
-               (if (string= s1 :cylnB) :less
-                  :greater))))))
-         
-
-(DEFUN CYLINDER-CMPR (cmprA cmprB)
-   (declare (type cmprf cmpra cmprb))
-   (flet ((rslt (cyln1 cyln2)
-             (declare (type cyln cyln1 cyln2))
-             (let ((cylnx1 (cylnx cyln1)))
-                (declare (type (member :cylnA1 :cylnB :cylnA2) cylnx))
-                (lexico
-                   (cylnX-CMPR cylnx1 (cylnx cyln2))
-                   (case cylnx1
-                      (:cylnA1 (funcall cmprA (icyln cyln1) (icyln cyln2)))
-                      (:cylnB (funcall cmprB (icyln cyln1) (icyln cyln2)))
-                      (:cylnA2 (funcall cmprA (icyln cyln1) (icyln cyln2))))))))
-      (the cmprf #'rslt)))
-
-#|
-  (setf r (cylinder-cmpr #'f-cmpr #'f-cmpr ))
-  (funcall r (cylnA1 1) (cylnB 0))
-  (funcall r (cylnA1 1) (cylnA1 2))
-  (funcall r (cylnB 0) (cylnA1 1))
-  (funcall r (cylnA1 2) (cylnA1 1)) 
-|#
-
-(DEFUN CYLINDER-BASIS (basisA basisB)
-   (declare (type basis basisA basisB))
-   (the basis
-      (if (or (eq :locally-effective basisA)
-              (eq :locally-effective basisB)
-              )
-         :locally-effective
-         (flet ((rslt (degr)
-                   (declare (fixnum degr))
-                   (append
-                      (mapcar #'(lambda (item)
-                                   (declare (type gnrt item))
-                                   (cylnA1 item))
-                         (funcall basisA (1- degr)))
-                      (mapcar #'(lambda (item)
-                                   (declare (type gnrt item))
-                                   (cylnB item))
-                         (funcall basisB degr))
-                      (mapcar #'(lambda (item)
-                                   (declare (type gnrt item))
-                                   (cylnA2 item))
-                         (funcall basisA degr)))))
-            (the basis #'rslt)))))
-
-#|
-  (CYLINDER-basis :locally-effective :locally-effective )
-  (setf b #'(lambda (degr) (mapcar #'(lambda (item) (cons degr item)) (<a-b> 0 degr))))
-  (setf r (CYLINDER-basis b b))
-  (funcall r 3)
-|#
-
-(DEFUN CYLINDER-INTR-DFFR (cmprA cmprB dffrA dffrB f)
-   (declare
-      (type cmprf cmprA cmprB)
-      (type morphism dffrA dffrB f))
-   (flet ((rslt (cmbn)
-             (declare (type cmbn cmbn))
-             (the cmbn
-                (multiple-value-bind (cmbnA1 cmbnB cmbnA2) (dispatch-cyln-cmbn cmbn)
-                   (declare (type cmbn cmbnA1 cmbnB cmbnA2))
-                   (let ((dffrA1-cmbn (cmbn-? dffrA cmbnA1))
-                         (dffrB-cmbn (cmbn-? dffrB cmbnB))
-                         (dffrA2-cmbn (cmbn-? dffrA cmbnA2))
-                         (f-cmbn (cmbn-? f cmbnA1))
-                         )
-                      (declare (type cmbn dffrA1-cmbn dffrB-cmbn dffrA2-cmbn f-cmbn))
-                      (let ((cmbnB (2cmbn-add cmprB f-cmbn dffrB-cmbn))
-                            (cmbnA2 (2cmbn-sbtr cmprA dffrA2-cmbn cmbnA1)))
-                         (declare (type cmbn cmbnB cmbnA2))
-                         (make-cyln-cmbn (cmbn-opps dffrA1-cmbn) cmbnB cmbnA2)))))))
-      (the intr-mrph #'rslt)))
-
-
-(DEFUN CYLINDER (f)
-   (declare (type morphism f))
-   (the chain-complex
-     (with-slots (sorc trgt) f
-       (declare
-        (type chain-complex sorc trgt ))
-       (let ((rslt (build-chcm
-                    :cmpr (cylinder-cmpr (cmpr sorc) (cmpr trgt))
-                    :basis (cylinder-basis (basis sorc) (basis trgt))
-                    :bsgn :undefined
-                    :intr-dffr (cylinder-intr-dffr (cmpr sorc) (cmpr trgt)
-                                     (dffr sorc) (dffr trgt) f)
-                    :strt :cmbn
-                    :orgn `(cylinder ,f))))
-          (declare (type chain-complex rslt))
-          (slot-makunbound rslt 'bsgn)
-          rslt))))
-
-
-
-
-
-(defun cylinder-rrdct (f)
-   (declare (type morphism f))
-   (the reduction
-     (with-slots (sorc (Bcc trgt)) f
-       (with-slots ((cmprb cmpr)) Bcc
-         (let ((cylinder (cylinder f)))
-            (let ((rf (build-mrph
-                       :sorc cylinder :trgt Bcc :degr 0
-                       :intr #'(lambda (cmbn)
-                                 (declare (type cmbn cmbn))
-                                 (2cmbn-add cmprB (cyln-cmbn-cmbnB cmbn) (cmbn-? f (cyln-cmbn-cmbnA2 cmbn))))
-                       :strt :cmbn
-                       :orgn `(cylinder ,f rf)))
-                  (rg (build-mrph
-                       :sorc Bcc :trgt cylinder :degr 0
-                       :intr #'(lambda (cmbn)
-                                 (declare (type cmbn cmbn))
-                                 (let* ((cmbnA1 (zero-cmbn (1- (cmbn-degr cmbn))))
-                                        (cmbnA2 (zero-cmbn (cmbn-degr cmbn))))
-                                    (declare (type cmbn cmbnA1 cmbnA2))
-                                    (make-cyln-cmbn cmbnA1 cmbn cmbnA2)))
-                       :strt :cmbn
-                       :orgn `(cylinder ,f rg)))
-                  (rh (build-mrph
-                       :sorc cylinder :trgt cylinder :degr +1
-                       :intr #'(lambda (cmbn)
-                                 (declare (type cmbn cmbn))
-                                 (let* ((cmbnA1 (cmbn-opps (cyln-cmbn-cmbnA2 cmbn)))
-                                        (cmbnB (zero-cmbn (1+ (cmbn-degr cmbn))))
-                                        (cmbnA2 (zero-cmbn (1+ (cmbn-degr cmbn)))))
-                                    (declare (type cmbn cmbnA1 cmbnB cmbnA2))
-                                    (make-cyln-cmbn cmbnA1 cmbnB cmbnA2)))
-                       :strt :cmbn
-                       :orgn `(cylinder ,f rh))))
-               (declare
-                (type chain-complex cylinder)
-                (type morphism rf rg rh))
-               (build-rdct :f rf :g rg :h rh :orgn `(cylinder right reduction ,f))))))))
-
-
-(defun cylinder-lrdct (f g h k)
-   (declare (type morphism f g h k))
-   (the reduction
-     (with-slots ((Acc sorc) (Bcc trgt)) f
-       (with-slots ((cmprA cmpr)) Acc
-         (with-slots ((cmprb cmpr)) Bcc
-           (let ((cylinder (cylinder f)))
-              (let ((lf (build-mrph
-                         :sorc cylinder :trgt Acc :degr 0
-                         :intr #'(lambda (cmbn)
-                                   (declare (type cmbn cmbn))
-                                   (2cmbn-sbtr cmprA 
-                                     (2cmbn-add cmpra (cyln-cmbn-cmbnA2 cmbn) (cmbn-? g (cyln-cmbn-cmbnB cmbn)))
-                                     (cmbn-? h (cyln-cmbn-cmbnA1 cmbn))))
-                         :strt :cmbn
-                         :orgn `(cylinder hmtpeq ,f lf)))
-                    (lg (build-mrph
-                         :sorc Acc :trgt cylinder :degr 0
-                         :intr #'(lambda (cmbn)
-                                   (declare (type cmbn cmbn))
-                                   (let* ((cmbnA1 (zero-cmbn (1- (cmbn-degr cmbn))))
-                                          (cmbnB (zero-cmbn (cmbn-degr cmbn)))
-                                          )
-                                      (declare (type cmbn cmbnA1 cmbnB ))
-                                      (make-cyln-cmbn cmbnA1 cmbnB cmbn)))
-                         :strt :cmbn
-                         :orgn `(cylinder hmtpeq ,f lg)))
-                    (lh (build-mrph
-                         :sorc cylinder :trgt cylinder :degr +1
-                         :intr #'(lambda (cmbn)
-                                   (declare (type cmbn cmbn))
-                                   (multiple-value-bind (cmbnA1 cmbnB cmbnA2) 
-                                       (dispatch-cyln-cmbn cmbn)
-                                      (let* ((cmbnA11 (cmbn-opps (cmbn-? h cmbnA1)))
-                                             (cmbnA12 (cmbn-opps (cmbn-? g (cmbn-? k (cmbn-? f cmbnA1)))))
-                                             (cmbnA13 (cmbn-? g (cmbn-? f (cmbn-? h cmbnA1))))
-                                             (cmbnA14 (cmbn-? g cmbnB))
-                                             (cmbnB1 (cmbn-opps (cmbn-? k (cmbn-? k (cmbn-? f cmbnA1)))))
-                                             (cmbnB2 (cmbn-? k (cmbn-? f (cmbn-? h cmbnA1))))
-                                             (cmbnB3 (cmbn-? k cmbnB))
-                                             (cmbnA21 (cmbn-opps (cmbn-? h (cmbn-? h cmbnA1))))
-                                             (cmbnA22 (cmbn-opps (cmbn-? h (cmbn-? g (cmbn-? k (cmbn-? f cmbnA1))))))
-                                             (cmbnA23 (cmbn-? h (cmbn-? g (cmbn-? f (cmbn-? h cmbnA1)))))
-                                             (cmbnA24 (cmbn-? g (cmbn-? k (cmbn-? k (cmbn-? f cmbnA1)))))
-                                             (cmbnA25 (cmbn-opps (cmbn-? g (cmbn-? k (cmbn-? f (cmbn-? h cmbnA1))))))
-                                             (cmbnA26 (cmbn-? h (cmbn-? g cmbnB)))
-                                             (cmbnA27 (cmbn-opps (cmbn-? g (cmbn-? k cmbnB)))))
-                                         (declare (type cmbn cmbnA11 cmbnA12 cmbnA13 cmbnA14
-                                                    cmbnB1 cmbnB2 cmbnB3 
-                                                    cmbnA21 cmbnA22 cmbnA23 cmbnA24 cmbnA25 cmbnA26 cmbnA27))
-                                         (make-cyln-cmbn (ncmbn-add cmprA cmbnA11 cmbnA12 cmbnA13 cmbnA14)
-                                     (ncmbn-add cmprB cmbnB1 cmbnB2 cmbnB3)
-                                     (ncmbn-add cmprA cmbnA21 cmbnA22 cmbnA23 cmbnA24 cmbnA25 cmbnA26 cmbnA27)))))
-                                     
-                         :strt :cmbn
-                         :orgn `(cylinder hmtpeq ,f lh))))
-            (declare
-                     (type chain-complex cylinder)
-                     (type morphism lf lg lh))
-            (build-rdct :f lf :g lg :h lh :orgn `(cylinder left reduction ,f ,g ,h ,k)))))))))
-
-
-#|
- (cat-init) 
- (setf z3 (cyclicgroup 3))
- (setf rsltn1 (cyclicgroup-rsltn 3))
- (setf rsltn2 (bar-rsltn z3))
- (setf f (zgmrph-twi (2rsltn-zgmrph rsltn1 rsltn2)))
- (setf g (zgmrph-twi (2rsltn-zgmrph rsltn2 rsltn1)))
- (setf h (zgmrph-twi (2rsltn-hmtpop rsltn1 rsltn2)))
- (setf k (zgmrph-twi (2rsltn-hmtpop rsltn2 rsltn1)))
- (setf Acc (sorc f) Bcc (trgt f))
-
-
- (setf rrdct (cylinder-rrdct f))
- (setf lrdct (cylinder-lrdct f g h k))
-
- (setf lf (f lrdct) lg (g lrdct) lh (h lrdct))
- (setf rf (f rrdct) rg (g rrdct) rh (h rrdct))
-
- (pre-check-rdct rrdct)
- (setf *tc* (cmbn 3 1 (cylnA1 2) 10 (cylnB '(1 2 1)) 100 (cylnA2 3)))
- (setf *bc* (cmbn 3 1 '(1 1 2)))
- (check-rdct)
- (setf *tc* (cmbn 4 10 (cylnB '(1 2 1 1)) 5 (cylnB '(1 2 2 1)) 100 (cylnA2 4)))
- (setf *bc* (cmbn 2 5 '(1 1) 7 '(2 1) -4 '(2 2)))
- (check-rdct)
-
-
- (pre-check-rdct lrdct)
-
- (setf *tc* (cmbn 3 1 (cylnA1 2) 10 (cylnB '(1 2 1)) 100 (cylnA2 3)))
- (setf *bc* (cmbn 3 1 3))
- (check-rdct)
-
- (setf *tc* (cmbn 4 10 (cylnB '(1 2 1 1)) 5 (cylnB '(1 2 2 1)) 100 (cylnA2 4)))
- (setf *bc* (cmbn 2 1 2))
- (check-rdct)
-|#
-
-
- (DEFMETHOD SEARCH-EFHM (smst (orgn (eql 'k-g-1)))
-   (declare (type simplicial-group smst))
-   (the homotopy-equivalence
-    (let* ((group (second (orgn smst)))
-           (rsltn1 (bar-rsltn group))
-           (rsltn2 (resolution group))
-           (f (zgmrph-twi (2rsltn-zgmrph rsltn1 rsltn2)))
-           (g (zgmrph-twi (2rsltn-zgmrph rsltn2 rsltn1)))
-           (h (zgmrph-twi (2rsltn-hmtpop rsltn1 rsltn2)))
-           (k (zgmrph-twi (2rsltn-hmtpop rsltn2 rsltn1)))
-           (rrdct (cylinder-rrdct f))
-           (lrdct (cylinder-lrdct f g h k)))
-       (build-hmeq :lrdct lrdct :rrdct rrdct :orgn  `(cylinder-hmeq ,f ,g ,h ,k )))))
-
- #|
- (setf z3 (cyclicgroup 3))
- (setf k-z3-1 (k-g-1 z3))
-
- (cat-init)
- (setf z4 (cyclicgroup 4))
- (setf k-z4-1 (k-g-1 z4))
- (setf k-z4-2 (classifying-space k-z4-1))
-
- (cat-init)
- (setf z2 (cyclicgroup 2))
- (setf k-z2-1 (k-g-1 z2))
- (setf k-z2-2 (classifying-space k-z2-1))
- |#
-        
diff --git a/examples/anromero/homology-of-groups/kzs.LSP b/examples/anromero/homology-of-groups/kzs.LSP
deleted file mode 100644
index 9553b29..0000000
--- a/examples/anromero/homology-of-groups/kzs.LSP
+++ /dev/null
@@ -1,52 +0,0 @@
-
-(load "file-list.lisp")
-
-(load-cfiles)
-
-(load "resolutions.lisp")
-
-(load "cylinders.lisp")
-
-
-;;
-
-
-(setf kz22 (k-zp 2 2))
-(setf kz23 (k-zp 2 3))
-(setf kz32 (k-zp 3 2))
-(setf kz33 (k-zp 3 3))
-(setf kz42 (k-zp 4 2))
-(setf kz43 (k-zp 4 3))
-(setf kz52 (k-zp 5 2))
-(setf kz53 (k-zp 5 3))
-
-
-(print "homology of kz22")
-(time (homology kz22 0 7))
-
-(print "homology of kz23")
-(time (homology kz23 0 7))
-
-(print "homology of kz32")
-(time (homology kz32 0 7))
-
-(print "homology of kz33")
-(time (homology kz33 0 7))
-
-(print "homology of kz42")
-(time (homology kz42 0 7))
-
-(print "homology of kz43")
-(time (homology kz43 0 7))
-
-(print "homology of kz52")
-(time (homology kz52 0 7))
-
-(print "homology of kz53")
-(time (homology kz53 0 7))
-
-
-
-
-
-
diff --git a/examples/anromero/homology-of-groups/resolutions.lisp b/examples/anromero/homology-of-groups/resolutions.lisp
deleted file mode 100644
index 418bf31..0000000
--- a/examples/anromero/homology-of-groups/resolutions.lisp
+++ /dev/null
@@ -1,1600 +0,0 @@
-
-
-;; RESOLUTIONS   RESOLUTIONS   RESOLUTIONS   RESOLUTIONS   RESOLUTIONS   RESOLUTIONS   
-;; RESOLUTIONS   RESOLUTIONS   RESOLUTIONS   RESOLUTIONS   RESOLUTIONS   RESOLUTIONS   
-;; RESOLUTIONS   RESOLUTIONS   RESOLUTIONS   RESOLUTIONS   RESOLUTIONS   RESOLUTIONS   
-
-(IN-PACKAGE "COMMON-LISP-USER")
-
-(provide "resolutions")
-
-
-;;;;;;;;;;;;;;;;;;;;;
-;;;;; clases y tipos
-;;;;;;;;;;;;;;;;;;;;;
-
-(DEFUN ZGgnrt-P (object)
-   (declare (type any object))
-   (the boolean
-     (and (consp object)
-          (eql :ZGgnrt (car object))
-          (consp (cdr object))
-          ;;(consp (cadr object))
-          ;;(consp (cddr object))
-          (typep (cadr object) 'gnrt)
-          (typep (cddr object) 'gnrt)
-          )))
-
-(DEFTYPE ZGgnrt () '(satisfies ZGgnrt-p)) 
-
-(DEFUN ZGTERM-P (object)
-   (declare (type any object))
-   (the boolean
-     (and (consp object)
-          (typep (car object) 'fixnum)
-          (typep (cdr object) 'ZGgnrt))))
-
-(DEFTYPE ZGTERM () '(satisfies zgterm-p))
-
-;; IZGCMBN = Internal-ZGCoMBiNation 
-(DEFUN IZGCMBN-P (object)
-;; IZGCMBN = Internal ZGCoMBiNation,    
-;; without the keyword and the degree
-   (declare (type any object))
-   (the boolean
-     (and (listp object)
-          (every #'zgterm-p object))))
-
-(DEFTYPE IZGCMBN () '(satisfies izgcmbn-p)) 
-
-;; ZGCMBN = ZGCoMBiNation 
-(DEFUN ZGCMBN-P (object)
-   (declare (type any object))
-   (the boolean
-     (and (consp object)
-          (eql (car object) :cmbn)
-          (consp (cdr object))
-          (typep (second object) 'fixnum)
-          (typep (cddr object) 'iZGcmbn))))
-
-(DEFTYPE ZGCMBN () '(satisfies ZGcmbn-p)) 
-
-
-
-(DEFTYPE GROUP-BASIS () '(or list (eql :locally-effective))) 
-  
-(DEFCLASS GROUP ()
-   ((elements :type group-basis :initarg :elements :reader elements)
-   (cmpr :type cmprf :initarg :cmpr :reader cmpr1)
-   (mult :type function :initarg :mult :reader mult1)
-   (inv :type function :initarg :inv :reader inv1)
-   (nullel :type gnrt :initarg :nullel :reader nullel)
-   (idnm :type fixnum :initform (incf *idnm-counter*) :reader idnm)
-   (orgn :type list :initarg :orgn :reader orgn)
-   (resolution :type reduction :initarg :resolution :reader resolution))
-  )
-
-(DEFCLASS AB-GROUP (GROUP)
-    ())
-
-
-(DEFTYPE GROUP-MORPHISM () 'function)
-
-(DEFVAR *group-list*)
-(SETF *group-list* +empty-list+)
-(PUSHNEW '*group-list* *list-list*)
-
-(DEFVAR *ab-group-list*)
-(SETF *ab-group-list* +empty-list+)
-(PUSHNEW '*ab-group-list* *list-list*)
-
-(DEFMETHOD PRINT-OBJECT ((group GROUP) stream)
-   (the GROUP
-     (progn
-      (format stream "[K~D Group]" (idnm group))
-      group)))
-
-(DEFMETHOD PRINT-OBJECT ((group ab-GROUP) stream)
-   (the ab-GROUP
-     (progn
-      (format stream "[K~D Abelian-Group]" (idnm group))
-      group)))
-
-(DEFUN GROUP (idnm)
-   (declare (type fixnum idnm))
-   (the (or GROUP null)
-      (find idnm *group-list* :key #'idnm)))
-
-(DEFUN AB-GROUP (idnm)
-   (declare (type fixnum idnm))
-   (the (or AB-GROUP null)
-      (find idnm *ab-group-list* :key #'idnm)))
-
-
-#|
-(DEFCLASS GROUP-WITH-RESOLUTION (GROUP)
-    ((resolution :type reduction :initarg :resolution :reader resolution)))
-
-(DEFVAR *group+res-list*)
-(SETF *group+res-list* +empty-list+)
-(PUSHNEW '*group+res-list* *list-list*)
-
-(DEFMETHOD PRINT-OBJECT ((group GROUP-WITH-RESOLUTION) stream)
-   (the GROUP-WITH-RESOLUTION
-     (progn
-      (format stream "[K~D Group with resolution]" (idnm group))
-      group)))
-
-(DEFUN GROUP-WITH-RESOLUTION (idnm)
-   (declare (type fixnum idnm))
-   (the (or GROUP-WITH-RESOLUTION null)
-      (find idnm *group+res-list* :key #'idnm)))
-|#
-   
-
-;;(DEFCLASS ZG-MORPHISM () ())  ;; will be redefined later.
-
-
-(DEFCLASS ZG-CHAIN-COMPLEX (chain-complex)
-    (
-     (group :type group :initarg :group :reader group1)
-     (zgcmpr :type cmprf :initarg :zgcmpr :reader zgcmpr1)
-     (zgbasis :type basis :initarg :zgbasis :reader zgbasis1)
-     (zgbsgn :type gnrt :initarg :zgbsgn :reader zgbsgn)
-     (zgbndr :type ZG-morphism :initarg :zgbndr :reader zgbndr1)
-     ))
-
-(DEFVAR *zgcc-list*)
-(SETF *zgcc-list* +empty-list+)
-(PUSHNEW '*zgcc-list* *list-list*)
-
-(DEFMETHOD PRINT-OBJECT ((zgcm ZG-CHAIN-COMPLEX) stream)
-   (the ZG-CHAIN-COMPLEX
-     (progn
-      (format stream "[K~D ZG-Chain-Complex]" (idnm zgcm))
-      zgcm)))
-
-(DEFUN ZGCC (idnm)
-   (declare (type fixnum idnm))
-   (the (or ZG-CHAIN-COMPLEX null)
-      (find idnm *zgcc-list* :key #'idnm)))
-
-
-
-
-;; ZGSTRT = ZGSTRaTegy 
-(DEFTYPE ZGSTRT () '(member :gnrt :zggnrt :zgcmbn))
-
-;; INTR-ZGMRPH = INTeRnal-ZGMoRPHism 
-(DEFTYPE INTR-ZGMRPH () 'function)                
-;; (or (function (degr gnrt) zgcmbn)    ;; if :gnrt strategy
-;;     (function (degr zggnrt) zgcmbn)  ;; if :zggnrt strategy                
-;;     (function (zgcmbn) zgcmbn)     ;; if :zgcmbn strategy 
-
-(DEFCLASS ZG-MORPHISM (morphism)
-    (
-     (zgintr :type intr-zgmrph :initarg :zg-intr :reader intr-zgmrph)
-     (zgstrt :type zgstrt :initarg :zgstrt :reader zgstrt) 
-    ))
-
-(DEFVAR *zgmrph-list*)
-(SETF *zgmrph-list* +empty-list+)
-(PUSHNEW '*zgmrph-list* *list-list*)
-
-
-(DEFMETHOD PRINT-OBJECT ((mrph ZG-MORPHISM) stream)
-   (the ZG-MORPHISM
-      (progn
-	(format stream "[K~D ZG-Morphism (degree ~D): K~D -> K~D]"
-		  (idnm mrph) (degr mrph)
-		  (idnm (sorc mrph)) (idnm (trgt mrph)))
-         mrph)))
-
-
-(DEFUN zgmrph (idnm)
-   (declare (type fixnum idnm))
-   (the (or ZG-MORPHISM null)
-      (find idnm *zgmrph-list* :key #'idnm)))
-
-
-
-
-;;;;;;;;;;;;;;;;;;;;;;;;;
-;;;;;;;;;;;;;;;;; macros
-;;;;;;;;;;;;;;;;;;;;;;;;
-
-
-(DEFMACRO ZGgnrt (gnrt1 gnrt2)
-  `(cons  :zggnrt
-     (cons ,gnrt1 ,gnrt2)))
-
-
-(DEFMACRO zggnrt1 (ZGgnrt)
-   `(car (cdr ,ZGgnrt)))
-
-(DEFMACRO zggnrt2 (ZGgnrt)
-  `(cddr ,ZGgnrt))
-
-;; (setf gn1 (zggnrt 'g1 'b1))
-;; (setf gn2 (zggnrt 'g2 'b1))
-;; (setf gn3 (zggnrt 'g1 'b2))
-;; (setf gn4 (zggnrt 'g2 'b2))
-
-(DEFMACRO WITH-ZGgnrt ((zggnrt1 zggnrt2) zggnrt . body)
-   `(let (,@(if zggnrt1 `((,zggnrt1 (zggnrt1 ,zggnrt))) nil)
-          ,@(if zggnrt2 `((,zggnrt2 (zggnrt2 ,zggnrt))) nil))
-       (declare
-         (type gnrt ,@(if zggnrt1 `(,zggnrt1) nil) ,@(if zggnrt2 `(,zggnrt2) nil)))
-       ,@body))
-
-;;(with-zggnrt (gnrt1 gnrt2) gn3
-;;     (progn
-;;      (format t "~D" gnrt1)
-;;      (format t "~D" gnrt2))) 
-
-
-;; Sobra??? podemos usar directamente el macro term
-(DEFMACRO ZGTERM (cffc zggnrt)
-  `(cons ,cffc ,zggnrt))
-
-
-;; Sobra??? podemos usar directamente el macro with-term
-(DEFMACRO WITH-zgTERM ((cffc zggnrt) zgterm . body)
-   `(let (,@(if cffc `((,cffc (cffc ,zgterm))) nil)
-          ,@(if zggnrt `((,zggnrt (gnrt ,zgterm))) nil))
-       (declare
-          (fixnum ,@(if cffc `(,cffc) nil))
-          (type zggnrt ,@(if zggnrt `(,zggnrt) nil)))
-       ,@body))
-
-;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
-;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
-;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
-
-
-(defun build-group 
-    (&key elements cmpr mult inv nullel orgn)
-   (declare 
-     (type group-basis elements)
-     (type cmprf cmpr)
-     (type group-morphism mult)
-     (type function inv)
-     (type gnrt nullel)
-     (list orgn))
-   (the group
-     (progn
-      (let ((already (find orgn *group-list* :test #'equal :key #'orgn)))
-         (declare (type (or group null) already))
-         (when already
-            (return-from build-group already)))
-      (unless elements
-         (setf elements :locally-effective))
-      (let ((group (make-instance 'group
-                     :cmpr cmpr
-                     :elements elements
-                     :mult mult
-                     :inv inv
-                     :nullel nullel
-                     :orgn orgn)))
-         (declare (type group group))   
-         (push group *group-list*)
-         group))))
-
-#|
-(setf elements '(0 1 2 3 4))
-(setf cmpr #'f-cmpr)
-(setf grmult #'(lambda (g1 g2)
-                  (mod (+ g1 g2) 5)))
-(setf inv #'(lambda (g)
-                 (mod (- 5 g) 5)))
-(setf nullel 0)
-(setf orgn '(Z_5))
-(setf gr (build-group :elements elements :cmpr cmpr :mult grmult :inv inv :nullel 0 :orgn orgn))
-|#
-
-(DEFMACRO BUILD-AB-GROUP (&rest rest)
-  `(change-class (build-group ,@rest) 'ab-group))
- 
-#| 
-
-(defun build-group-with-resolution 
-    (&key elements cmpr mult inv nullel resolution orgn)
-   (the group-with-resolution
-     (progn
-         (let ((already (find orgn *group+res-list* :key #'orgn :test #'equal)))
-            (declare (type (or null group-with-resolution) already))
-            (when already
-               (return-from build-group-with-resolution already)))
-         (let ((rslt (build-group :elements elements :cmpr cmpr :mult mult :inv inv :nullel nullel 
-                      :orgn orgn)))
-            (declare (type group rslt))
-            (change-class rslt 'GROUP-WITH-RESOLUTION)
-            (setf (slot-value rslt 'resolution) resolution)
-            (push rslt *group+res-list*)
-               rslt))))
-
-|#
-
-
-
-        
-(DEFUN ZGGNRT-CMPR (grcmpr zgcmpr)
-   (declare (type cmprf grcmpr zgcmpr))
-   (flet ((rslt (gnrt1 gnrt2)
-            (declare (type zggnrt gnrt1 gnrt2))
-            (the cmpr
-              (let ((gnrt12 (zggnrt2 gnrt1))
-                    (gnrt22 (zggnrt2 gnrt2)))
-                 (declare (type gnrt gnrt12 gnrt22))
-                 (lexico
-                  (funcall zgcmpr gnrt12 gnrt22)
-                  (let ((gnrt11 (zggnrt1 gnrt1))
-                        (gnrt21 (zggnrt1 gnrt2)))
-                     (declare (type gnrt gnrt11 gnrt21))
-                     (funcall grcmpr gnrt11 gnrt21)))))))
-     (the cmprf #'rslt)))
-
-
-;;(setf cmpr (zggnrt-cmpr #'s-cmpr #'s-cmpr))
-;;(funcall cmpr gn1 gn2)
-
-(DEFUN ZGCHCM-BASIS (grbasis zgbasis)
-   (declare (type group-basis grbasis)
-            (type basis zgbasis))
-   (when (or (eq grbasis :locally-effective)
-             (eq zgbasis :locally-effective))
-      (return-from ZGCHCM-BASIS :locally-effective))
-   (flet ((rslt (degr)
-             (declare (fixnum degr))
-             (the list
-                (progn
-                   (when (minusp degr)
-                      (return-from rslt +empty-list+))
-                   (the list
-                     (mapcan
-                      #'(lambda (gnrt2)
-                          (declare (type gnrt gnrt2))
-                          (the list
-                            (mapcar
-                             #'(lambda (gnrt1)
-                                 (declare (type gnrt gnrt1))
-                                 (the zggnrt
-                                   (zggnrt gnrt1 gnrt2)))
-                             grbasis)))
-                       (funcall zgbasis degr)))
-                      ))
-                      ))
-      (the basis #'rslt)))
-
-;; (setf basis1 '(0 1 2 3 4))
-;; (setf basis2 
-;;       #'(lambda (degr)
-;;           (<a-b> 0 degr)))
-;; (setf zgbasis (ZGCHCM-BASIS basis1 basis2))
-   
-
-
-(DEFUN ZGMRPH-GNRT-GNRT (intr degr gnrt)
-   (declare
-    (type intr-zgmrph intr)
-    (fixnum degr)
-    (type gnrt gnrt))
-   (funcall intr degr gnrt))
-
-(DEFUN ZGMRPH-GNRT-ZGGNRT (grcmpr zgcmpr grmult intr degr zggnrt)
-   (declare
-    (type cmprf grcmpr zgcmpr)
-    (type group-morphism grmult)
-    (type intr-zgmrph intr)
-    (fixnum degr)
-    (type zggnrt zggnrt))
-   (let* ((zggnrt1 (zggnrt1 zggnrt))
-          (zggnrt2 (zggnrt2 zggnrt))
-          (zgcmbn (ZGMRPH-GNRT-GNRT intr degr zggnrt2))
-          (degr (cmbn-degr zgcmbn))
-          (list (cmbn-list zgcmbn))
-          (n-cmbn-list +empty-list+))
-      (declare (list n-cmbn-list))
-      (if list 
-         (progn 
-           (mapcar #'(lambda (zgterm)
-                  (declare (type zgterm zgterm))
-                  (with-zgterm (cffc gnrt) zgterm
-                   (declare (type fixnum cffc)
-                     (type zggnrt gnrt))
-                   (with-zggnrt (gnrt1 gnrt2) gnrt
-                    (declare (type gnrt gnrt1 gnrt2))
-                    (push (cons 1
-                      (term-cmbn degr cffc (zggnrt (funcall grmult zggnrt1 gnrt1) gnrt2)))
-                      n-cmbn-list))))
-             list)
-           (cmbn-cmbn (zggnrt-cmpr grcmpr zgcmpr) n-cmbn-list))
-         (zero-cmbn degr))))
-
-;; (setf grbasis '(0 1 2 3 4))
-;; (setf zgbasis 
-;;      #'(lambda (degr)
-;;           (<a-b> 0 degr)))
-;; (setf grmult #'(lambda (g1 g2)
-;;                  (mod (+ g1 g2) 5)))
-;; (setf grcmpr #'f-cmpr zgcmpr #'f-cmpr)
-;;(setf intr #'(lambda (degr gnrt)
-;;               (declare
-;;                (fixnum degr)
-;;                (type gnrt gnrt))
-;;               (let ((cmbn (cmbn degr)))
-;;                  (declare (type cmbn cmbn))
-;;                  (mapcar #'(lambda (i)
-;;                              (declare (fixnum i))
-;;                              (setf cmbn
-;;                               (2cmbn-add (zggnrt-cmpr #'f-cmpr #'f-cmpr) cmbn (term-cmbn degr i (zggnrt i gnrt))
-;;                               )))
-;;                    (<a-b> 1 4))
-;;                  cmbn)))
-
-;;(ZGMRPH-GNRT-ZGGNRT grcmpr zgcmpr grmult intr 5 (zggnrt 1 3))
-
-(DEFUN ZGMRPH-GNRT-ZGCMBN (grcmpr zgcmpr grmult intr zgcmbn)
-   (declare
-    (type cmprf grcmpr zgcmpr)
-    (type group-morphism grmult)
-    (type intr-zgmrph intr)
-    (type zgcmbn zgcmbn))
-      (the cmbn
-        (with-cmbn (degr list) zgcmbn
-          (if list
-             (let ((n-cmbn-list +empty-list+))
-                (declare (list n-cmbn-list))
-                (do ((mark list (cdr mark))
-                     )
-                    ((endp mark))
-                   (declare (list mark))
-                   (with-term (cffc gnrt) (car mark) 
-                   (push 
-                     (cons cffc 
-                       (zgmrph-gnrt-zggnrt grcmpr zgcmpr grmult intr degr gnrt))
-                     n-cmbn-list)))
-                (cmbn-cmbn (zggnrt-cmpr grcmpr zgcmpr) n-cmbn-list))
-             (cmbn degr)))))
-
-;;(ZGMRPH-GNRT-ZGCMBN grcmpr zgcmpr grmult intr (cmbn 5 2 (zggnrt 1 3) 3 (zggnrt 2 4)))
-
-
-(DEFUN ZGMRPH-ZGGNRT-ZGGNRT (intr degr zggnrt)
-   (declare
-    (type intr-zgmrph intr)
-    (fixnum degr)
-    (type zggnrt zggnrt))
-   (funcall intr degr zggnrt))
-
-
-
-(DEFUN ZGMRPH-ZGGNRT-ZGCMBN (grcmpr zgcmpr intr zgcmbn)
-   (declare
-    (type intr-zgmrph intr)
-    (type cmprf grcmpr zgcmpr)
-    (type zgcmbn zgcmbn))
-   
-      (the cmbn
-      (with-cmbn (degr list) zgcmbn
-         (let ((n-cmbn-list +empty-list+))
-            (declare (list n-cmbn-list))
-            (do ((mark list (cdr mark))
-                 )
-                ((endp mark))
-               (declare (list mark))
-               (with-term (cffc gnrt) (car mark) 
-                   (push 
-                     (cons cffc 
-                       (zgmrph-zggnrt-zggnrt intr degr gnrt))
-                     n-cmbn-list)))
-	    (cmbn-cmbn (zggnrt-cmpr grcmpr zgcmpr) n-cmbn-list)))))
-
-
-
-(DEFUN ZGmrph-GNRT-? (ZGmrph degr gnrt)
-   (declare
-      (type zg-morphism ZGmrph)
-      (fixnum degr)
-      (type gnrt gnrt))
-   (the cmbn
-     (with-slots (zgintr zgstrt trgt) zgmrph
-       (declare (type ZG-CHAIN-COMPLEX trgt)
-         (type intr-zgmrph zgintr)
-         (type zgstrt zgstr))
-       (with-slots (group) trgt
-            (declare
-             (type group group))
-
-       (with-slots (nullel) group
-         (declare (type gnrt nullel))
-         (prog1
-          (ecase zgstrt
-            (:gnrt
-             (zgmrph-gnrt-gnrt zgintr degr gnrt))
-            (:zggnrt
-             (funcall zgintr degr (zggnrt nullel gnrt)))
-            (:cmbn
-             (funcall zgintr (term-cmbn degr 1 (zggnrt nullel gnrt)))))
-          ))))))
-
-
-(DEFUN ZGmrph-ZGGNRT-? (ZGmrph degr zggnrt)
-   (declare
-      (type ZG-morphism ZGmrph)
-      (fixnum degr)
-      (type zggnrt zggnrt))
-   (the cmbn
-     (with-slots (trgt zgintr zgstrt ) zgmrph
-       (declare (type ZG-CHAIN-COMPLEX trgt)
-         (type intr-zgmrph zgintr)
-         (type zgstrt zgstr))
-       (with-slots (group) trgt
-            (declare
-             (type group group))
-       (with-slots ((grcmpr cmpr) mult nullel) group
-         (declare (type cmprf grcmpr)
-           (type group-morphism mult)
-           (type gnrt nullel))
-         (with-slots (zgcmpr)  trgt
-           (declare (type cmprf zgcmpr ))
-           (prog1
-                     (ecase zgstrt
-                        (:gnrt
-                         (zgmrph-gnrt-zggnrt grcmpr zgcmpr mult zgintr degr zggnrt))
-                        (:zggnrt
-                         (funcall zgintr degr zggnrt))
-                        (:cmbn
-                         (funcall zgintr (term-cmbn degr 1 zggnrt))))
-            )))))))
-
-
-(DEFUN ZGmrph-ZGCMBN-? (ZGmrph zgcmbn)
-   (declare
-      (type ZG-morphism ZGmrph)
-      (fixnum degr)
-      (type zggnrt zggnrt))
-   (the cmbn
-     (with-slots (trgt zgintr zgstrt ) zgmrph
-       (declare
-             (type zg-chain-complex trgt)
-             (type intr-zgmrph zgintr)
-             (type zgstrt zgstrt)
-        )
-       (with-slots (group zgcmpr) trgt
-            (declare (type group group)
-              (type cmprf zgcmpr))
-       (with-slots ((grcmpr cmpr) mult nullel) group
-         (declare
-          (type cmprf grcmpr)
-          (type group-morphism mult)
-          (type gnrt nullel))
-         (prog1
-          (ecase zgstrt
-            (:gnrt
-             (zgmrph-gnrt-zgcmbn grcmpr zgcmpr mult zgintr zgcmbn))
-            (:zggnrt
-             (zgmrph-zggnrt-zgcmbn grcmpr zgcmpr zgintr zgcmbn))
-            (:cmbn
-             (funcall zgintr zgcmbn)))
-            ))))))
-
-(Defun izgmrph-imrph (grcmpr zgcmpr mult intr strt)
-   (declare (type intr-zgmrph intr)
-     (type zgstrt strt)
-     (type group-morphism mult)
-     (type cmprf grcmpr zgcmpr))
-   (flet ((rslt (degr zggnrt)
-             (declare
-                (fixnum degr)
-                (type zggnrt zggnrt))
-             (ecase strt
-                        (:gnrt
-                         (zgmrph-gnrt-zggnrt grcmpr zgcmpr mult intr degr zggnrt))
-                        (:zggnrt
-                         (funcall intr degr zggnrt))
-                        (:cmbn
-                         (funcall intr (term-cmbn degr 1 zggnrt))))))
-     (the intr-mrph #'rslt)))
-
-
-(DEFUN INTR-ZGCHCM-MRPH (zgmrph)
-   (declare (type zg-morphism zgmrph))
-   (flet ((rslt (degr zggnrt)
-             (declare
-                (fixnum degr)
-                (type zggnrt zggnrt))
-             (zgmrph-zggnrt-? zgmrph degr zggnrt)))
-     (the intr-mrph #'rslt)))
-                
-               
-(DEFUN BUILD-ZGCHCM
-    (&key group zgcmpr zgbasis zgbsgn intr-zgbndr zgbndr-strt orgn)
-   (declare
-    (type group group)
-    (type cmprf zgcmpr)
-    (type basis zgbasis)
-    (type gnrt zgbsgn)
-    (type intr-zgmrph intr-zgbndr)
-    (type zgstrt zgbndr-strt)
-    (list orgn))
-   (let ((already (find orgn *zgcc-list* :test #'equal :key #'orgn)))
-      (declare (type (or zg-chain-complex null) already))
-      (when already
-         (return-from build-zgchcm already)))
-   (if intr-zgbndr
-      (unless zgbndr-strt
-            (error "In BUILD-ZGCHCM, an intr-zgbndr is given but not its strategy."))
-      )
-   (the zg-chain-complex
-     (with-slots ((grcmpr cmpr) (grbasis elements) mult nullel) group
-       (declare 
-         (type cmprf grcmpr)
-         (type list grbasis)
-         (type group-morphism mult)
-         (type gnrt nullel))
-       (let* ((cmpr (zggnrt-cmpr grcmpr zgcmpr))
-              (basis (ZGCHCM-BASIS grbasis zgbasis))
-              (bsgn (zggnrt nullel zgbsgn))
-              (intr-dffr (izgmrph-imrph grcmpr zgcmpr mult intr-zgbndr zgbndr-strt))
-              (rslt (build-chcm :cmpr cmpr :basis basis :bsgn bsgn
-                     :intr-dffr intr-dffr :strt :gnrt :orgn orgn)))
-         (change-class rslt 'zg-chain-complex)
-         (setf (slot-value rslt 'group) group)
-         (setf (slot-value rslt 'zgcmpr) zgcmpr)
-         (setf (slot-value rslt 'zgbasis) zgbasis)
-         (setf (slot-value rslt 'zgbsgn) zgbsgn)
-         (setf (slot-value rslt 'zgbndr) (build-zgmrph :sorc rslt :trgt rslt :degr -1
-                                          :zgintr intr-zgbndr :zgstrt zgbndr-strt :orgn `(zgbndr ,rslt)))
-         (push rslt *zgcc-list*)
-         rslt))))
-
-
-(DEFUN BUILD-ZGMRPH (&key sorc trgt degr zgintr zgstrt orgn)
-   (declare
-    (type zg-chain-complex sorc trgt)
-    (fixnum degr)
-    (type intr-zgmrph intr)
-    (type zgstrt strt)
-    (list orgn))
-   (the zg-morphism
-     (with-slots (group zgcmpr) trgt
-       (declare
-        (type group group)
-        (type cmprf zgcmpr))
-       (with-slots ((grcmpr cmpr) (grbasis elements) mult nullel ) group
-         (declare 
-           (type cmprf grcmpr)
-           (type list grbasis)
-           (type group-morphism mult)
-           (type gnrt nullel))
-         (let* ((intr (izgmrph-imrph grcmpr zgcmpr mult zgintr zgstrt))
-                (rslt (build-mrph :sorc sorc :trgt trgt :degr degr
-                        :intr intr :strt :gnrt :orgn orgn)))
-            (change-class rslt 'zg-morphism)
-            (setf (slot-value rslt 'zgintr) zgintr)
-            (setf (slot-value rslt 'zgstrt) zgstrt)
-            (push rslt *zgcc-list*)
-            rslt)))))
-
-
-
-
-
-;;(DEFMETHOD zg-?2 ((zgmrph zg-morphism) zgcmbn)
-;;   (declare (type zgcmbn zgcmbn))
-;;   (the zgcmbn
-;;      (zgmrph-zgcmbn-? zgmrph zgcmbn)))
-
-
-
-;;(DEFMETHOD zg-?3 ((zgmrph zg-morphism) degr gnrt)
-;;   (declare
-;;      (fixnum degr)
-;;      (type gnrt gnrt))
-;;   (the zgcmbn
-;;      (zgmrph-gnrt-? zgmrph degr gnrt)))
-
-
-
-
-;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
-;;;;;;;;;TENSOR WITH INTEGERS
-;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
-
-
-(DEFUN zgcmbn-twi (zgcmpr zgcmbn)
-   (declare (type zgcmbn zgcmbn))
-   (with-cmbn (degr list) zgcmbn
-    (declare (fixnum degr)
-      (type list list))
-     (if list
-        (let* ((cmbn-list +empty-list+))
-           (mapcar #'(lambda (zgterm)
-                       (with-zgterm (cffc zggnrt) zgterm
-                         (let ((gnrt2 (zggnrt2 zggnrt)))
-                            (push (cons 1
-                                    (term-cmbn degr cffc gnrt2))
-                              cmbn-list))))
-             list)
-           (cmbn-cmbn zgcmpr cmbn-list))
-     (zero-cmbn degr))))
-
-;; (setf zgcmbn (cmbn 5 2 (zggnrt 1 3) 3 (zggnrt 2 4)))
-;; (zgcmbn-twi #'f-cmpr zgcmbn)
-;; (setf zgcmbn2 (cmbn 5 2 (zggnrt 1 3) 3 (zggnrt 2 4) -8 (zggnrt 6 3)))
-;; (zgcmbn-twi #'f-cmpr zgcmbn2)
-
-
-(Defun zgmrph-twi-intr (mrph)
-   (declare (type zg-morphism mrph))     
-   (flet ((rslt (degr gnrt)
-             (declare
-                (fixnum degr)
-                (type zggnrt zggnrt))
-            (with-slots (trgt) mrph
-              (with-slots (zgcmpr) trgt
-             (zgcmbn-twi zgcmpr (zgmrph-gnrt-? mrph degr gnrt))))))
-     (the intr-mrph #'rslt)))
-
-(defun zgmrph-twi (mrph)
-   (declare (type zg-morphism mrph))
-   (the morphism
-     (with-slots (sorc trgt degr orgn) mrph
-       (build-mrph :sorc (chcm-twi sorc) :trgt (chcm-twi trgt) :degr degr
-                     :intr (zgmrph-twi-intr mrph) :strt :gnrt :orgn `(tensor-with-integers ,orgn))
-                    )))
-
-(defun chcm-twi (chcm)
-   (declare (type zg-chain-complex chcm))
-   (the chain-complex
-     (if (string= (car (orgn chcm)) 'bar-zgchcm) 
-        (with-slots (group) chcm
-          (k-g-1 group))
-     (with-slots (zgcmpr zgbasis zgbsgn zgbndr orgn) chcm
-       (build-chcm :cmpr zgcmpr :basis zgbasis :bsgn zgbsgn :intr-dffr (zgmrph-twi-intr zgbndr) 
-        :strt :gnrt :orgn `(tensor-with-integers ,orgn))))))
-
-
-
-
-
-
-
-
-
-;;;;; EJEMPLOS
-
-
-#|
-(cat-init) 
-(setf Z3 (build-group :elements '(0 1 2) :cmpr #'f-cmpr :mult #'(lambda (g1 g2)
-                                                                  (mod (+ g1 g2) 3))
-          :inv #'(lambda (g)
-                 (mod (- 3 g) 3)) :nullel 0 :orgn '(Cyclic Group order 3)))
-
-(setf zgbasis #'(lambda (degr) (list degr)))
-(setf zgbspn 0)
-(setf zgcmpr #'f-cmpr)
-(setf intr #'(lambda(degr gnrt)
-               (let ((degr- (1- degr)))
-                  (if (oddp degr)
-                     (cmbn degr- -1 (zggnrt 0 degr-)  1 (zggnrt 1 degr-))
-                     (cmbn degr- 1 (zggnrt 0 degr-)  1 (zggnrt 1 degr-)  1 (zggnrt 2 degr-))))))
-
-(setf zgchcm (BUILD-ZGCHCM
-    :group Z3 :zgcmpr zgcmpr :zgbasis zgbasis :zgbsgn 0 :intr-zgbndr intr :zgbndr-strt :gnrt :orgn '(prueba)
-))
-
-(setf zgmrph (zgbndr1 zgchcm))
-(ZGmrph-GNRT-? zgmrph 4 4)
-(ZGmrph-zgGNRT-? zgmrph 4 (zggnrt 2 4))
-(ZGmrph-zgGNRT-? zgmrph 3 (zggnrt 0 3))
-(ZGmrph-zgGNRT-? zgmrph 3 (zggnrt 1 3))
-(ZGmrph-zgGNRT-? zgmrph 3 (zggnrt 2 3))
-(ZGmrph-zgGNRT-? zgmrph 4 (zggnrt 0 4))
-
-(ZGmrph-zgcmbn-? zgmrph (cmbn 4 1 (zggnrt 2 4) -3 (zggnrt 3 4)))
-(ZGmrph-zgcmbn-? zgmrph (cmbn 4 2 (zggnrt 2 4) -5 (zggnrt 3 4)))
-(ZGmrph-zgcmbn-? zgmrph (cmbn 3 1 (zggnrt 2 3) -3 (zggnrt 3 3)))
-(ZGmrph-zgGNRT-? zgmrph 3 (zggnrt 2 3))
-(ZGmrph-zgGNRT-? zgmrph 3 (zggnrt 3 3))
-
-
-(setf chcm (chcm-twi zgchcm))
-(? chcm 3 3)
-(? chcm 4 4)
-(? chcm 5 5 ))
-
-(homology chcm 0 10)
-
-|#
-
-
-#| 
-(setf ZCC
-      (the chain-complex
-        (build-chcm
-         :cmpr #'(lambda (gnrt1 gnrt2) (the cmpr :equal))
-         :basis #'(lambda (n)
-                    (the list
-                      (if (zerop n) '(:Z-gnrt) +empty-list+)))
-         :bsgn :Z-gnrt
-         :intr-dffr #'(lambda (cmbn)
-                        (the cmbn (zero-cmbn (1- (cmbn-degr cmbn)))))
-         :strt :cmbn
-         :orgn '(zcc-constant))))
-|#
-;; ya est� definido con la funci�n (z-chcm) 
-
-(defun cyclicgroup (n)
-   (declare (fixnum n))
-   (build-ab-group :elements (<a-b> 0 (1- n)) :cmpr #'f-cmpr :mult #'(lambda (g1 g2)
-                                                                  (mod (+ g1 g2) n))
-           :inv #'(lambda (g)
-                 (mod (- n g) n)) :nullel 0 :orgn `(Cyclic-group of order ,n)))
-
-(DEFMETHOD SLOT-UNBOUND (class (group group) (slot-name (eql 'resolution)))
-   (declare (ignore class))
-   (the reduction
-     (let ((rsltn (search-resolution group (first (orgn group)))))
-       (setf (slot-value group 'resolution)
-	     (or rsltn
-          (error "I don't know how to determine ~
-                         a resolution for 
-                         ~A (Origin: ~A)." group (orgn group)))))))
-
-(DEFGENERIC SEARCH-resolution (group orgn))
-
-(DEFMETHOD SEARCH-RESOLUTION (group orgn)
-  (declare (ignore group orgn))
-  nil)
-
-
-
-      
-
-(defun cyclicgroup-zgchcm (n)
-   (let* ((group (cyclicgroup n))
-          (zgbasis #'(lambda (degr) (list degr)))
-          (zgcmpr #'f-cmpr)
-          (intr #'(lambda(degr gnrt)
-               (let ((degr- (1- degr)))
-                  (if (zerop degr) (zero-cmbn -1)
-                     (if (oddp degr)
-                        (cmbn degr- -1 (zggnrt 0 degr-)  1 (zggnrt 1 degr-))
-                        (let ((list +empty-list+))
-                           (mapcar #'(lambda (i)
-                                       (push (cons 1 (zggnrt (- n i) degr-)) list))
-                             (<a-b> 1  n))
-                           (make-cmbn :degr degr- :list list))))))))
-          (BUILD-ZGCHCM
-    :group group :zgcmpr zgcmpr :zgbasis zgbasis :zgbsgn 0 
-           :intr-zgbndr intr :zgbndr-strt :gnrt :orgn  `(ZG-Chain complex for ,group)
-)))
-                     
-#|
-(setf z5 (cyclicgroup 5))
-(setf z5-zgchcm (cyclicgroup-zgchcm 5))
-(? z5-zgchcm 3 (zggnrt 2 3))
-(? z5-zgchcm 4 (zggnrt 2 4))
-|#   
-
-
-(defun cyclicgroup-rsltn (n)
-   (let* ((group (cyclicgroup n))
-          (zgchcm (cyclicgroup-zgchcm n))
-          (cmpr (cmpr1 zgchcm))
-          (f-intr #'(lambda (degr zggnrt)
-                      (if (zerop degr) (cmbn degr 1 :zgnrt) (zero-cmbn degr))))
-          (g-intr #'(lambda (degr gnrt)
-                      (if (zerop degr) (cmbn degr 1 (zggnrt 0 0)) (zero-cmbn degr))))
-          (h-intr #'(lambda (degr zggnrt)
-                      (with-zggnrt (gnrt1 gnrt2) zggnrt
-                        (if (oddp degr)
-                           (if (= gnrt1 (1- n)) (cmbn (1+ degr) 1 (zggnrt 0 (1+ degr)))
-                              (zero-cmbn (1+ degr)))
-                           (let ((list +empty-list+))
-                              (dotimes (i gnrt1)
-                                 (push (cons 1 (zggnrt i (1+ degr))) list ))
-                              (make-cmbn :degr (1+ degr) :list (nreverse list)))))))
-          (f (build-mrph :sorc zgchcm :trgt (z-chcm) :degr 0 :intr f-intr :strt :gnrt :orgn `(f-mrph for ,group)))
-          (g (build-mrph :sorc (z-chcm) :trgt zgchcm :degr 0 :intr g-intr :strt :gnrt :orgn  `(g-mrph for ,group)))
-          (h (build-mrph :sorc zgchcm :trgt zgchcm :degr 1 :intr h-intr :strt :gnrt :orgn `(h-mrph for ,group))))
-      (build-rdct :f f :g g :h h :orgn `(Resolution of ,group)))) 
-                     
-
-(DEFMETHOD SEARCH-RESOLUTION (group (orgn (eql 'Cyclic-group)))
-  (declare
-     (type group group))
-  (the reduction
-    (with-slots (elements) group
-      (let ((n (length elements)))
-         (cyclicgroup-rsltn n)))))
-
-
-
-
-(DEFMETHOD HOMOLOGY ((group group) degr1 &optional (degr2 (1+ degr1)))
-   (declare (fixnum degr1 degr2))
-   (with-slots (resolution) group 
-     (let ((chcm (chcm-twi (tcc resolution))))
-        (homology chcm degr1 degr2))))
-            
-#|
-(setf z3 (cyclicgroup 3))
-(homology z3 0 6)
-(setf g (build-group :elements '(0 1 2) :cmpr #'f-cmpr :mult #'(lambda (g1 g2)
-                                                                  (mod (+ g1 g2) 3))
-          :inv #'(lambda (g)
-                 (mod (- 3 g) 3)) :nullel 0 :orgn '(hola)))
-(homology g 0 6) 
-|#
-
-
-
-;;;; BAR RESOLUTION
-
-
-(defun bar-zgcmpr (grcmpr)
-   (declare (type cmprf grcmpr))
-   (labels ((rslt (gnrt1 gnrt2)
-           (declare (list gnrt1 gnrt2))
-           (unless gnrt1
-              (return-from rslt (if gnrt2 :less :equal)))
-           (unless gnrt2
-              (return-from rslt :greater))
-           (lexico
-            (funcall grcmpr (first gnrt1) (first gnrt2))
-            (rslt (rest gnrt1) (rest gnrt2)))
-         ))
-      (the cmprf #'rslt)))
-
-(defun bar-zgbasis (elements nullel)
-   (declare (type group-basis elements)
-     (type gnrt nullel))
-   (when (eq elements :locally-effective)
-      (return-from bar-zgbasis :locally-effective))
-   (labels ((rslt (degr)
-            (declare (fixnum degr))
-            ;;(the list
-              (progn
-               (when (minusp degr)
-                  (return-from rslt +empty-list+))
-               (when (zerop degr)
-                  (return-from rslt (list (list))))
-               (let ((basis-1 (rslt (1- degr)))
-                     (elements-0 (remove nullel elements)))
-                    (mapcan #'(lambda (gbar)
-                                (mapcar #'(lambda (g)
-                                            (append gbar (list g)))
-                                  elements-0)
-                                )
-                      basis-1)))))
-     ;;)
-     (the basis #'rslt)))
-                    
-                    
-
-(DEFUN bar-bndr-i (grmult nullel indx degr gnrt)
-   (declare
-    (fixnum indx degr)
-    (list gnrt))
-   (the cmbn
-     (cond ((zerop indx) (cmbn (1- degr) 1 (zggnrt (car gnrt) (rest gnrt))))
-           ((= indx degr) (cmbn (1- degr) 1 (zggnrt nullel (butlast gnrt))))
-           (t
-            (do ((rslt +empty-list+ (cons (car mark) rslt))
-                 (mark gnrt (cdr mark))
-                 (i 1 (1+ i)))
-                ((= i indx) (let ((new-k (funcall grmult (car mark) (cadr mark))))
-                                        (declare (type gnrt new-k))
-                               (if (eq nullel new-k)
-                                  (zero-cmbn (1- degr)) 
-                                  (cmbn (1- degr) 1 (zggnrt nullel (nreconc rslt (cons new-k (cddr mark))))))))
-               (declare
-                (list rslt mark)
-                (fixnum i)))))))
-
-
-(defun bar-bndr-intr (grcmpr grmult nullel)
-    #'(lambda (degr gnrt)
-        (if (zerop degr)
-           (zero-cmbn -1)
-           (let ((cmbn-list
-                  (mapcar #'(lambda (indx)
-                              (let ((cmbn (bar-bndr-i grmult nullel indx degr gnrt)))
-                                 (if (oddp indx)
-                                    (cons -1 cmbn)
-                                    (cons 1 cmbn))))
-                    (<a-b> 0 degr))))
-              (cmbn-cmbn (zggnrt-cmpr grcmpr (bar-zgcmpr grcmpr)) cmbn-list)))))
-     
-
-
-(defun bar-zgchcm (group)
-   (declare (type group group))
-  (the zg-chain-complex
-    (with-slots (elements cmpr mult nullel) group
-     (build-zgchcm
-      :group group
-      :zgcmpr (bar-zgcmpr cmpr)
-	:zgbasis (bar-zgbasis elements nullel)
-	:zgbsgn +empty-list+
-	:intr-zgbndr (bar-bndr-intr cmpr mult nullel)
-      :zgbndr-strt :gnrt
-	:orgn  `(bar-zgchcm ,group)))))
-
-(defun bar-cntrhmtp-intr (grcmpr grmult nullel)
-   #'(lambda (degr zggnrt)
-                      (with-zggnrt (gnrt1 gnrt2) zggnrt
-                        (if (eq nullel gnrt1)
-                           (zero-cmbn (1+ degr))
-                           (if (zerop degr)
-                              (cmbn 1 1 (zggnrt nullel (list gnrt1)))
-                              (cmbn (1+ degr) 1 (zggnrt nullel (cons gnrt1 gnrt2))))))))
-   
-
-(defun bar-f-intr ()
-   #'(lambda (degr zggnrt)
-       (if (zerop degr) (cmbn degr 1 :zgnrt) (zero-cmbn degr))))
-
-
-(defun bar-g-intr (nullel)
-   #'(lambda (degr gnrt)
-         (if (zerop degr) (cmbn degr 1 (zggnrt nullel +empty-list+)) (zero-cmbn degr))))
-
-(defun bar-rsltn (group)
-   (declare (type group group))
-   (the reduction
-    (with-slots (cmpr mult nullel) group
-      (let* ((zgchcm (bar-zgchcm group))
-             (f (build-mrph :sorc zgchcm :trgt (z-chcm) :degr 0 :intr (bar-f-intr) :strt :gnrt :orgn `(f-mrph in bar-resolution for ,group)))
-             (g (build-mrph :sorc (z-chcm) :trgt zgchcm :degr 0 :intr (bar-g-intr nullel) :strt :gnrt :orgn  `(g-mrph in bar-resolution for ,group)))
-             (h (build-mrph :sorc zgchcm :trgt zgchcm :degr 1 :intr (bar-cntrhmtp-intr cmpr mult nullel)
-                  :strt :gnrt :orgn `(h-mrph in bar-resolution for ,group))))
-         (build-rdct :f f :g g :h h :orgn `(Bar-resolution of ,group)))))) 
-
-
-                   
-;;; EJEMPLOS
-
-#|
-(setf z5 (cyclicgroup 5))
-(setf bar-chcm-z5 (bar-zgchcm z5))
-
-(setf zgbasis (zgbasis1 bar-chcm-z5))
-(funcall zgbasis 2)
-
-(setf zgmrph (zgbndr1 bar-chcm-z5))
-(ZGmrph-GNRT-? zgmrph 4 '(1 2 3 4))
-(ZGmrph-zgGNRT-? zgmrph 4 (zggnrt 2 '(1 2 3 4)))
-(ZGmrph-zgGNRT-? zgmrph 4 (zggnrt 1 '(1 1 4 4)))
-(ZGmrph-zgcmbn-? zgmrph (cmbn 4 1 (zggnrt 2 '(1 2 3 4)) -3 (zggnrt 1 '(1 1 4 4))))
-
-(setf chcm (chcm-twi bar-chcm-z5))
-(? chcm 4 '(1 2 3 4))
-(? chcm 5 '(1 1 2 3 4))
-
-
-(homology chcm 3)
-
-
-(setf bar-rsltn-z5 (bar-rsltn z5))
-(pre-check-rdct bar-rsltn-z5)
-
-(setf *tc* (cmbn 4 3 (zggnrt 4 '(1 2 1 4)) -3 (zggnrt 2 '(3 1 2 3)) 8 (zggnrt 1 '(4 4 3 2))))
-
-(setf *bc* (cmbn 0 1 :zgnrt))
-
-(check-rdct)
-
-
-
-|# 
-
-
-
-
-
-
-
-
-(defun K-G-1-cmpr (grcmpr)
-   (declare (type cmprf grcmpr))
-   (labels ((rslt (gnrt1 gnrt2)
-           (declare (list gnrt1 gnrt2))
-           (unless gnrt1
-              (return-from rslt (if gnrt2 :less :equal)))
-           (unless gnrt2
-              (return-from rslt :greater))
-           (lexico
-            (funcall grcmpr (first gnrt1) (first gnrt2))
-            (rslt (rest gnrt1) (rest gnrt2)))
-         ))
-      (the cmprf #'rslt)))
-
-(defun K-G-1-basis (elements nullel)
-   (declare (type group-basis elements)
-     (type gnrt nullel))
-   (when (eq elements :locally-effective)
-      (return-from K-G-1-basis :locally-effective))
-   (labels ((rslt (degr)
-            (declare (fixnum degr))
-            ;;(the list
-              (progn
-               (when (minusp degr)
-                  (return-from rslt +empty-list+))
-               (when (zerop degr)
-                  (return-from rslt (list (list))))
-               (let ((basis-1 (rslt (1- degr)))
-                     (elements-0 (remove nullel elements)))
-                    (mapcan #'(lambda (gbar)
-                                (mapcar #'(lambda (g)
-                                            (append gbar (list g)))
-                                  elements-0)
-                                )
-                      basis-1)))))
-     ;;)
-     (the basis #'rslt)))
-                    
-                    
-
-(DEFUN K-G-1-FACE (grmult nullel)
-   (flet ((face (indx dmns gmsm)
-            (declare
-             (fixnum indx dmns)
-             (list gmsm))
-            (the absm
-              (cond ((zerop indx) (absm 0 (rest gmsm)))
-                    ((= indx dmns) (absm 0 (butlast gmsm)))
-                    (t
-                     (do ((rslt +empty-list+ (cons (car mark) rslt))
-                          (mark gmsm (cdr mark))
-                          (i 1 (1+ i)))
-                         ((= i indx) (let ((new-k (funcall grmult (car mark) (cadr mark))))
-                                        (declare (type gnrt new-k))
-                                        (if (eq nullel new-k)
-                                           (absm (2-exp (1- indx)) (nreconc rslt (cddr mark)))
-                                           (absm 0 (nreconc rslt (cons new-k (cddr mark)))))))
-                        (declare
-                         (list rslt mark)
-                         (fixnum i))))))))
-     (the face #'face)))
-         
-   
-(DEFUN G-ABSM-BAR (nullel absm)
-  (declare (type absm absm))
-  (the list
-    (with-absm (dgop bar1) absm
-      (do ((dgop dgop (ash dgop -1))
-	   (rslt +empty-list+))
-	  ((and (zerop dgop) (endp bar1)) (nreverse rslt))
-	  (declare
-	     (fixnum dgop)
-	     (list rslt))
-	  (push (if (oddp dgop)
-		    nullel
-		  (pop bar1))
-		rslt)))))
-
-
-(DEFUN G-BAR-ABSM (nullel bar)
-  (declare (list bar))
-  (the absm
-     (do ((rslt-dgop 0)
-	  (rslt-bar +empty-list+)
-	  (mark bar (cdr mark))
-	  (bark 1 (+ bark bark)))
-	 ((endp mark) (absm rslt-dgop (nreverse rslt-bar)))
-	(declare
-	   (fixnum rslt-dgop bark)
-	   (list rslt-bar mark))
-	(let ((k-i (car mark)))
-	  (declare (fixnum k-i))
-	  (if (eq nullel k-i)
-	     (incf rslt-dgop bark)
-	     (push k-i rslt-bar))))))
-
- 
-
-(DEFUN K-G-1-GRML (grmult nullel)
-   (flet ((grml (dmns crpr)
-            (declare
-             (fixnum dmns)
-             (type crpr crpr))
-            (the absm
-              (with-crpr (dgop1 bar1 dgop2 bar2) crpr
-                (do ((indx 1 (1+ indx))
-                     (dgop1 dgop1 (ash dgop1 -1))
-                     (dgop2 dgop2 (ash dgop2 -1))
-                     (bark 1 (ash bark +1))
-                     (rslt-dgop 0)
-                     (rslt-bar +empty-list+))
-                    ((> indx dmns) (absm rslt-dgop (nreverse rslt-bar)))
-                   (declare
-                    (fixnum indx dgop1 dgop2 bark rslt-dgop)
-		(list rslt-bar))
-                   (let ((item (if (evenp dgop1)
-                                  (if (evenp dgop2)
-                                     (funcall grmult (pop bar1) (pop bar2))
-                                     (pop bar1))
-                                  (if (evenp dgop2)
-                                     (pop bar2)
-                                     nullel))))
-                      (declare (type gnrt item))
-                      (if (eq nullel item)
-                         (incf rslt-dgop bark)
-                         (push item rslt-bar))))))))
-     (the intr-mrph #'grml)))
-
-
-(DEFUN K-G-1-GRIN (grin)
-   (flet ((grin (dmns bar)
-            (declare
-             (ignore dmns)
-             (list bar))
-            (the absm
-              (absm 0 (mapcar #'grin bar)))))
-     (the intr-mrph #'grin)))
-          
-
-
-(DEFMETHOD K-G-1 ((group GROUP))
-   (declare (type group group))
-  (the simplicial-group
-    (with-slots (elements cmpr mult nullel inv) group
-     (build-smgr
-      :cmpr (k-g-1-cmpr cmpr)
-	:basis (k-g-1-basis elements nullel)
-	:bspn +empty-list+
-	:face (k-g-1-face mult nullel)
-	:sintr-grml (k-g-1-grml mult nullel)
-	:sintr-grin (k-g-1-grin inv)
-	:orgn  `(k-g-1 ,group)))
-    ))
-
-(DEFMETHOD K-G-1 ((group AB-GROUP))
-   (declare (type AB-group group))
-  (the AB-simplicial-group
-    (with-slots (elements cmpr mult nullel inv) group
-     (build-AB-smgr
-      :cmpr (k-g-1-cmpr cmpr)
-	:basis (k-g-1-basis elements nullel)
-	:bspn +empty-list+
-	:face (k-g-1-face mult nullel)
-	:sintr-grml (k-g-1-grml mult nullel)
-	:sintr-grin (k-g-1-grin inv)
-	:orgn  `(k-g-1 ,group)))
-    ))
-
-(DEFUN K-G (gROUP n)
-   (declare (fixnum n)
-     (type group group))
-   (the ab-simplicial-group
-      (if (= n 1)
-         (k-g-1 group)
-         (classifying-space (k-g group (1- n))))))
-
-(DEFUN K-ZP-1 (p)
-   (k-g-1 (cyclicgroup p)))
-
-(DEFUN K-Zp (p n)
-   (declare (fixnum p n)
-     )
-   (the ab-simplicial-group
-      (if (= n 1)
-         (k-Zp-1 p)
-         (classifying-space (k-Zp p (1- n))))))
-  
-
-(defun rsltn-zgchcm (rsltn)
-   (declare (type reduction rsltn))
-   (tcc rsltn))
-
-(defun rsltn-cntrhmtp (rsltn)
-   (declare (type reduction rsltn))
-   (h rsltn))
-   
-(defun 2rsltn-zgmrph-intr (rsltn1 rsltn2)
-   (let ((zgchcm1 (rsltn-zgchcm rsltn1))
-         (zgchcm2 (rsltn-zgchcm rsltn2))
-         (h2 (rsltn-cntrhmtp rsltn2))
-         (f1 (f rsltn1))
-         (g2 (g rsltn2))
-         (d1 (zgbndr1 (rsltn-zgchcm rsltn1))))
-      
-      (with-slots (group (zgcmpr2 zgcmpr)) zgchcm2
-        (with-slots ((grcmpr cmpr) mult nullel) group
-          (labels ((rslt (degr gnrt)
-                     (if (zerop degr)
-                        (? g2 (? f1 degr (zggnrt nullel gnrt)))
-                        (? h2 
-                          
-                          (with-cmbn (degr- list) (zgmrph-gnrt-? d1 degr gnrt)
-                            (let ((n-cmbn-list +empty-list+))
-                               (declare (list n-cmbn-list))
-                               (do ((mark list (cdr mark))
-                                    )
-                                   ((endp mark))
-                                  (declare (list mark))
-                                  (with-term (cffc ZGgnrt) (car mark) 
-                                    (push 
-                                      (cons cffc 
-                                        
-                                        (let* ((gnrt1 (zggnrt1 zggnrt))
-                                               (gnrt2 (zggnrt2 zggnrt))
-                                               (zgcmbn (rslt degr- gnrt2))
-                                               (list (cmbn-list zgcmbn))
-                                               (n-cmbn-list2 +empty-list+))
-                                           (declare (list n-cmbn-list2))
-                                           (if list 
-                                              (progn 
-                                                (mapcar #'(lambda (zgterm)
-                                                            (declare (type zgterm zgterm))
-                                                            (with-zgterm (cffc2 zggnrt2) zgterm
-                                                             (declare (type fixnum cffc2)
-                                                               (type zggnrt zggnrt2))
-                                                             (with-zggnrt (gnrt21 gnrt22) zggnrt2
-                                                              (declare (type gnrt gnrt21 gnrt22))
-                                                              (push (cons 1
-                                                                      (term-cmbn degr- cffc2 (zggnrt (funcall mult gnrt1 gnrt21) gnrt22)))
-                                                                n-cmbn-list2))))
-                                                  list)
-                                                (cmbn-cmbn (zggnrt-cmpr grcmpr zgcmpr2) n-cmbn-list2))
-                                              (zero-cmbn degr-))))
-                                        
-
-                                        n-cmbn-list)))
-                               (cmbn-cmbn (zggnrt-cmpr grcmpr zgcmpr2) n-cmbn-list)))))))
-            #'rslt)))))
-                          
-
-
-
-                    
-
-
-(defun 2rsltn-zgmrph (rsltn1 rsltn2)
-   (let ((zgchcm1 (rsltn-zgchcm rsltn1))
-         (zgchcm2 (rsltn-zgchcm rsltn2)))
-      (build-zgmrph :sorc zgchcm1 :trgt zgchcm2 :degr 0 :zgintr (2rsltn-zgmrph-intr rsltn1 rsltn2)
-       :zgstrt :gnrt :orgn `(ZG-morphism from ,rsltn1 to ,rsltn2))))
-
-
-#|
-
-(cat-init) 
-(setf z3 (cyclicgroup 3))
-(setf rsltn1 (cyclicgroup-rsltn 3))
-(setf rsltn2 (bar-rsltn z3))
-(setf f (2rsltn-zgmrph rsltn1 rsltn2))
-(setf g (2rsltn-zgmrph rsltn2 rsltn1))
-
-(setf zgchcm1 (rsltn-zgchcm rsltn1))
-(setf zgchcm2 (rsltn-zgchcm rsltn2))
-(setf f1 (f rsltn1)
-         g2 (g rsltn2))
-(setf d1 (zgbndr1 (rsltn-zgchcm rsltn1)))
-(setf h2 (rsltn-cntrhmtp rsltn2))
-(setf group (group1 zgchcm2) zgcmpr2 (zgcmpr1 zgchcm2))
-(setf grcmpr (cmpr1 group) mult (mult1 group) nullel (nullel group))
-
-(ZGmrph-GNRT-? f 0 0)
-(ZGmrph-zgGNRT-? f 0 (zggnrt 0 0))
-(ZGmrph-zgGNRT-? f 0 (zggnrt 1 0))
-(ZGmrph-zgGNRT-? f 0 (zggnrt 2 0))
-(ZGmrph-zgGNRT-? f 1 (zggnrt 0 1))
-(ZGmrph-zgGNRT-? f 1 (zggnrt 1 1))
-(ZGmrph-zgGNRT-? f 1 (zggnrt 2 1))
-
-(ZGmrph-zgGNRT-? f 2 (zggnrt 2 2))
-(? f 2 (zggnrt 2 2))
-
-
-(zgmrph-gnrt-? f 1 1)
-(setf f-intr (2rsltn-zgmrph-intr rsltn1 rsltn2))
-(funcall f-intr 1 1)
-
-     
-|#
-
-
-
-(defun 2rsltn-hmtpop-intr (rsltn1 rsltn2)
-   (let ((zgchcm1 (rsltn-zgchcm rsltn1))
-         (h1 (rsltn-cntrhmtp rsltn1))
-         (m (2rsltn-zgmrph rsltn1 rsltn2))
-         (n (2rsltn-zgmrph rsltn2 rsltn1))
-         (d1 (zgbndr1 (rsltn-zgchcm rsltn1))))
-      
-      
-      (with-slots (group (zgcmpr1 zgcmpr)) zgchcm1
-        (with-slots ((grcmpr cmpr) mult nullel) group
-          (let ((cmpr (zggnrt-cmpr grcmpr zgcmpr1)))
-             
-             (labels ((rslt (degr gnrt)
-                       (if (zerop degr)
-                        (2cmbn-sbtr cmpr (? h1 degr (zggnrt nullel gnrt)) 
-                                         (? h1 (zgmrph-zgcmbn-? n (zgmrph-gnrt-? m degr gnrt))))
-                          (2cmbn-sbtr cmpr (2cmbn-sbtr cmpr (? h1 degr (zggnrt nullel gnrt)) 
-                                         (? h1 (zgmrph-zgcmbn-? n (zgmrph-gnrt-? m degr gnrt))))
-                           (? h1 
-                             (with-cmbn (degr- list) (zgmrph-gnrt-? d1 degr gnrt)
-                            (let ((n-cmbn-list +empty-list+))
-                               (declare (list n-cmbn-list))
-                               (do ((mark list (cdr mark))
-                                    )
-                                   ((endp mark))
-                                  (declare (list mark))
-                                  (with-term (cffc ZGgnrt) (car mark) 
-                                    (push 
-                                      (cons cffc 
-                                        
-                                        (let* ((gnrt1 (zggnrt1 zggnrt))
-                                               (gnrt2 (zggnrt2 zggnrt))
-                                               (zgcmbn (rslt degr- gnrt2))
-                                               (list (cmbn-list zgcmbn))
-                                               (n-cmbn-list2 +empty-list+))
-                                           (declare (list n-cmbn-list2))
-                                           (if list 
-                                              (progn 
-                                                (mapcar #'(lambda (zgterm)
-                                                            (declare (type zgterm zgterm))
-                                                            (with-zgterm (cffc2 zggnrt2) zgterm
-                                                             (declare (type fixnum cffc2)
-                                                               (type zggnrt zggnrt2))
-                                                             (with-zggnrt (gnrt21 gnrt22) zggnrt2
-                                                              (declare (type gnrt gnrt21 gnrt22))
-                                                              (push (cons 1
-                                                                      (term-cmbn degr cffc2 (zggnrt (funcall mult gnrt1 gnrt21) gnrt22)))
-                                                                n-cmbn-list2))))
-                                                  list)
-                                                (cmbn-cmbn cmpr n-cmbn-list2))
-                                              (zero-cmbn degr))))
-                                        
-
-                                        n-cmbn-list)))
-                               (cmbn-cmbn cmpr n-cmbn-list)))
-                             
-                             
-                             
-                             
-                             
-                             
-                             
-                             
-                             )))))
-                          
-                          
-            #'rslt))))))
-
-(defun 2rsltn-hmtpop (rsltn1 rsltn2)
-   (let ((zgchcm1 (rsltn-zgchcm rsltn1))
-         )
-      (build-zgmrph :sorc zgchcm1 :trgt zgchcm1 :degr 1 :zgintr (2rsltn-hmtpop-intr rsltn1 rsltn2)
-       :zgstrt :gnrt :orgn `(ZG-homotopy-operator from ,rsltn1 to ,rsltn2))))
-
-
-
-#|
-
-(cat-init) 
-(setf z3 (cyclicgroup 3))
-(setf rsltn1 (cyclicgroup-rsltn 3))
-(setf rsltn2 (bar-rsltn z3))
-(setf f (2rsltn-zgmrph rsltn1 rsltn2))
-(setf g (2rsltn-zgmrph rsltn2 rsltn1))
-(setf k1 (2rsltn-hmtpop rsltn1 rsltn2))
-(setf k2 (2rsltn-hmtpop rsltn2 rsltn1))
-
-
-
-(setf zgchcm1 (rsltn-zgchcm rsltn1))
-(setf zgchcm2 (rsltn-zgchcm rsltn2))
-(setf d1 (zgbndr1 zgchcm1))
-(setf d2 (zgbndr1 zgchcm2))
-
-(setf iz1 (add (cmps d1 k1) (cmps k1 d1)))
-(setf drch1 (sbtr (idnt-mrph zgchcm1) (cmps g f)))
-
-(setf iz2 (add (cmps d2 k2) (cmps k2 d2)))
-(setf drch2 (sbtr (idnt-mrph zgchcm2) (cmps f g)))
-
-(? iz1 0 (zggnrt 0 0))
-(? drch1 0 (zggnrt 0 0))
-
-(? iz1 1 (zggnrt 0 1))
-(? drch1 1 (zggnrt 0 1))
-(? iz1 2 (zggnrt 0 2))
-(? drch1 2 (zggnrt 0 2))
-(? iz1 3 (zggnrt 0 3))
-(? drch1 3 (zggnrt 0 3))
-
-(? d1 (? k1 1 (zggnrt 0 1)))
-(? k1 (? d1 1 (zggnrt 0 1)))
-(? (cmps g f) 1 (zggnrt 0 1))
-(? f 1 (zggnrt 0 1))
-(? g (? f 1 (zggnrt 0 1)))
-
-
-(dotimes (i 6)
-   (progn
-    (print (? iz1 i (zggnrt 0 i)))
-    (print (? drch1 i (zggnrt 0 i)))
-))
-
-(? iz2 1 (zggnrt 0 '(1)))
-(? drch2 1 (zggnrt 0 '(1)))
-(? iz2 2 (zggnrt 0 '(2 1)))
-(? drch2 2 (zggnrt 0 '(2 1)))
-(? iz2 2 (zggnrt 0 '(1 1)))
-(? drch2 2 (zggnrt 0 '(1 1)))
-
-
-(? iz2 3 (zggnrt 0 '(1 1 2)))
-(? drch2 3 (zggnrt 0 '(1 1 2)))
-|#
-
-
-#| 
-(cat-init) 
-(setf z4 (cyclicgroup 4))
-(setf rsltn1 (bar-rsltn z4))
-(setf rsltn2 (cyclicgroup-rsltn 4))
-
-(setf f (2rsltn-zgmrph rsltn1 rsltn2))
-(setf g (2rsltn-zgmrph rsltn2 rsltn1))
-(setf h (2rsltn-hmtpop rsltn1 rsltn2))
-(setf k (2rsltn-hmtpop rsltn2 rsltn1))
-
-(setf zgchcm1 (rsltn-zgchcm rsltn1))
-(setf zgchcm2 (rsltn-zgchcm rsltn2))
-(setf d1 (zgbndr1 zgchcm1))
-(setf d2 (zgbndr1 zgchcm2))
-
-(setf h2 (rsltn-cntrhmtp rsltn2)
-         f1 (f rsltn1)
-         g2 (g rsltn2))
-
-(setf group (group1 zgchcm2)
-      zgcmpr2 (zgcmpr1 zgchcm2))
-
-(setf grcmpr (cmpr1 group) mult (mult1 group) nullel (nullel group))
-
-         
-
-
-
-(setf iz1 (add (cmps d1 h) (cmps h d1)))
-(setf drch1 (sbtr (idnt-mrph zgchcm1) (cmps g f)))
-
-(? iz1 0 (zggnrt 0 '()))
-(? drch1 0 (zggnrt 0 '()))
-(? f 0 (zggnrt 0 nil))
-
-(? iz1 1 (zggnrt 0 '(1)))
-(? drch1 1 (zggnrt 0 '(1)))
-(? f 1 (zggnrt 0 '(1)))
-
-
-(? iz1 2 (zggnrt 0 '(1 1)))
-(? drch1 2 (zggnrt 0 '(1 1)))
-
-(? iz1 3 (zggnrt 0 '(1 1 1)))
-(? drch1 3 (zggnrt 0 '(1 1 1)))
-
-(? iz1 4 (zggnrt 0 '(1 1 1 1)))
-(? drch1 4 (zggnrt 0 '(1 1 1 1)))
-
-(setf iz2 (add (cmps d2 k) (cmps k d2)))
-(setf drch2 (sbtr (idnt-mrph zgchcm2) (cmps f g)))
-
-(? iz2 4 (zggnrt 0 4))
-(? drch2 4 (zggnrt 0 4))
-
-
-|# 
-
-
- 
\ No newline at end of file
diff --git a/examples/anromero/persistent-homology/filtered-complexes.lsp b/examples/anromero/persistent-homology/filtered-complexes.lsp
deleted file mode 100644
index ab665f7..0000000
--- a/examples/anromero/persistent-homology/filtered-complexes.lsp
+++ /dev/null
@@ -1,843 +0,0 @@
-;; FILTERED-COMPLEXES   FILTERED-COMPLEXES   FILTERED-COMPLEXES   FILTERED-COMPLEXES
-;; FILTERED-COMPLEXES   FILTERED-COMPLEXES   FILTERED-COMPLEXES   FILTERED-COMPLEXES
-;; FILTERED-COMPLEXES   FILTERED-COMPLEXES   FILTERED-COMPLEXES   FILTERED-COMPLEXES
-
-(IN-PACKAGE "COMMON-LISP-USER")
-
-(provide "filtered-complexes")
-
-(DEFTYPE degr () 'fixnum)
-
-(DEFTYPE CHCM-FLIN () 'function) 
-                     ;; '(function (degr gnrt) degr)
-
-
-(DEFCLASS FILTERED-CHAIN-COMPLEX (chain-complex)
-    ((flin :type chcm-flin :initarg :flin :reader flin1)))
-
-(DEFVAR *flcc-list*)
-(SETF *flcc-list* +empty-list+)
-(PUSHNEW '*flcc-list* *list-list*)
-
-(DEFMETHOD PRINT-OBJECT ((flcm FILTERED-CHAIN-COMPLEX) stream)
-(the FILTERED-CHAIN-COMPLEX
-   (progn
-      (format stream "[K~D Filtered-Chain-Complex]" (idnm flcm))
-     flcm)))
-
-(DEFUN FLCC (idnm)
-   (declare (type fixnum idnm))
-   (the (or FILTERED-CHAIN-COMPLEX null)
-      (find idnm *flcc-list* :key #'idnm)))
-
-
-;; Function that builds a filtered chain complex. 
-(DEFUN BUILD-FLCC
-    (&key cmpr basis bsgn intr-dffr dffr-strt flin orgn)
-   (declare
-      (type cmprf cmpr)
-      (type intr-mrph intr-dffr)
-      (type basis basis)
-      (type gnrt bsgn)
-      (type strt dffr-strt)
-      (type Chcm-Flin flin)
-      (list orgn))
-   (the FILTERED-CHAIN-COMPLEX
-     (progn
-         (let ((already (find orgn *flcc-list* :key #'orgn :test #'equal)))
-            (declare (type (or null FILTERED-CHAIN-COMPLEX) already))
-            (when already
-               (return-from build-flcc already)))
-         (let ((rslt (build-chcm :cmpr cmpr :basis basis :bsgn bsgn
-                        :intr-dffr intr-dffr :strt dffr-strt
-                        :orgn orgn)))
-            (declare (type chain-complex rslt))
-            (change-class rslt 'FILTERED-CHAIN-COMPLEX)
-            (setf (slot-value rslt 'flin) flin)
-            (push rslt *flcc-list*)
-               rslt))))
-
-
-;; Function that changes a chain complex chcm to a filtered complex, with filtration
-;; index of a generator defined by the function flin, and origin orgn. 
-#|(DEFUN CHANGE-CHCM-TO-FLCC (chcm &key flin orgn)
-   (declare
-      (type chain-complex chcm)
-      (type chcm-flin flin)
-      (list orgn))
-   (the FILTERED-CHAIN-COMPLEX
-      (progn
-         (change-class chcm 'FILTERED-CHAIN-COMPLEX)
-         ;;(setf orgn (list (orgn chcm) 'then orgn))
-         (let ((already (find orgn *flcc-list* :key #'orgn :test #'equal)))
-            (declare (type (or null FILTERED-CHAIN-COMPLEX) already))
-            (when already
-               (return-from change-chcm-to-flcc already)))
-         (setf (slot-value chcm 'flin) flin)
-         ;;(setf (slot-value chcm 'orgn) orgn)
-         (push chcm *flcc-list*)
-         chcm)))
-|#
-
-
-(DEFMETHOD CHANGE-CHCM-TO-FLCC ((chcm chain-complex) flin flin-orgn)
-   (declare
-      (type chain-complex chcm)
-      (type chcm-flin flin)
-      (list flin-orgn))
-   (the FILTERED-CHAIN-COMPLEX
-      (progn
-         (change-class chcm 'FILTERED-CHAIN-COMPLEX)
-         (setf orgn (append (orgn chcm) (list 'FILTERED-WITH) flin-orgn))
-         (let ((already (find orgn *flcc-list* :key #'orgn :test #'equal)))
-            (declare (type (or null FILTERED-CHAIN-COMPLEX) already))
-            (when already
-               (return-from change-chcm-to-flcc already)))
-         (setf (slot-value chcm 'flin) flin)
-         (setf (slot-value chcm 'orgn) orgn)
-         (push chcm *flcc-list*)
-         chcm)))
-
-
-(DEFMACRO FLIN (&rest rest)
-   (ecase (length rest)
-      (1 `(flin1 ,@rest))
-      (2 `(flin2 ,@rest))
-      (3 `(flin3 ,@rest))))
-
-(DEFUN FLIN3 (object degr gnrt)         
-   (declare
-      (type FILTERED-CHAIN-COMPLEX object)
-      (fixnum degr)
-      (type gnrt gnrt))
-   (the fixnum
-      (with-slots (flin) object
-         (declare (type chcm-flin flin))
-         (funcall flin degr gnrt))))
-
-(DEFUN FLIN2 (object cmbn)
-   (declare
-    (type FILTERED-CHAIN-COMPLEX object)
-    (type cmbn cmbn))
-   (the fixnum
-      (with-slots (flin) object
-         (declare (type chcm-flin flin))
-        (with-cmbn (degr cmbn-list) cmbn
-          (declare
-           (fixnum degr)
-           (list cmbn-list))
-          (labels ((list-max (list)
-                     (declare (type list list))
-                     (let* ((max-int (car list)))
-                        (do ((mark1 list (cdr mark1)))
-                            ((endp mark1))
-                           (setq max-int (max max-int (car mark1))))
-                        max-int)))
-         (if (endp cmbn-list)
-            0
-            (list-max 
-              (mapcar 
-                #'(lambda (term)
-                    (flin3 object degr (gnrt term)))
-                cmbn-list))))))))
-   
-
-
-;; Function that returns the min and max of the filtration index of the elements of the basis
-;; for degree degr
-(DEFUN FLIN-MIN-MAX (fltrcm degr)
-   (declare (type FILTERED-CHAIN-COMPLEX fltrcm)
-            (type fixnum degr))
-   (when (eq (basis fltrcm) :locally-effective)
-    (error "flin-min-max cannot work with a LOCALLY-EFFECTIVE chain complex."))
-   (the list
-     (let* ((basis (basis fltrcm degr)))
-        (declare (list basis))
-        (if (endp basis)
-           (list 0 0)
-           (let* ((min (flin fltrcm degr (first basis)))
-                  (max min))
-              (declare (type fixnum min max))
-              (dolist (gnrt (cdr basis))
-                 (let ((aux (flin fltrcm degr gnrt)))
-                    (declare (type fixnum aux))
-                    (if (< aux min)
-                       (setf min aux)
-                       (if (> aux max)
-                          (setf max aux)))))
-              (list min max))))))
-           
- 
-   
-;; Function that returns the elements of the basis that have bidegree (p,q).
-(DEFUN BIGRD-BASIS (fltrcm p q)
-   (declare (type FILTERED-CHAIN-COMPLEX fltrcm)
-            (type fixnum p q))
-   (when (eq (basis fltrcm) :locally-effective)
-    (error "Bigrd-Basis cannot work with a LOCALLY-EFFECTIVE chain complex."))
-   (the list
-     (let* ((degr (+ p q))
-            (basis (basis fltrcm degr)))
-        (declare 
-          (type list basis)
-          (fixnum degr))
-        (mapcan 
-          #'(lambda (gnrt)
-              (declare (type gnrt gnrt))
-              (if (= (flin fltrcm degr gnrt) p)
-                 (list gnrt)
-                 nil))
-          basis))))
-
-;; Function that returns the elements of the basis of degree "degr" that have
-;; filtration index <= "fltr-index".
-(DEFUN FLTRD-BASIS (fltrcm degr fltr-index)
-   (declare (type FILTERED-CHAIN-COMPLEX fltrcm)
-            (type fixnum degr fltr-index))
-   (when (eq (basis fltrcm) :locally-effective)
-    (error "Fltrd-Basis cannot work with a LOCALLY-EFFECTIVE chain complex."))
-   (let ((min (first (flin-min-max fltrcm degr))))
-      (declare (type fixnum min))
-      (the list
-        (mapcan
-          #'(lambda (i)
-              (bigrd-basis fltrcm i (- degr i)))
-          (<a-b> min fltr-index)))))
-
-;; Function that returns the elements of the basis with degree "degr",
-;; ordered by the filtration index.
-(DEFUN ORDERED-BASIS (fltrcm degr)
-   (declare
-    (type FILTERED-CHAIN-COMPLEX fltrcm)
-    (fixnum degr))
-   (when (eq (basis fltrcm) :locally-effective)
-    (error "Ordered-Basis cannot work with a LOCALLY-EFFECTIVE chain complex."))
-   (the list
-     (let ((max (second (flin-min-max fltrcm degr))))
-        (declare (type fixnum max))
-        (fltrd-basis fltrcm degr max))))  
-
-;; Matrix of the differential application of degree "degr" of the subcomplex
-;; F_pX, where p=fltr-index and X=fltrcm.
-(defun FLCC-DFFR-MTRX (fltrcm degr fltr-index)
-  (declare
-    (type FILTERED-CHAIN-COMPLEX fltrcm)
-    (fixnum degr fltr-index))
-   (when (eq (basis fltrcm) :locally-effective)
-    (error "flcc-dffr-mtrx cannot work with a LOCALLY-EFFECTIVE chain complex."))
-  (the matrix
-    (let* ((cmpr (cmpr1 fltrcm))
-	     (dffr (dffr fltrcm))
-	     (sbasis (fltrd-basis fltrcm degr fltr-index))
-           (tbasis (ordered-basis fltrcm (1- degr)))
-           ;; If the differential application in the filtered complex respects the filtration,
-           ;; i.e., d(F_pA_n) \in (F_pA)_{n-1}, the target basis is (fltrd-basis fltrcm (1- degr) fltr-index)
-           (srank (length sbasis))
-	     (trank (length tbasis)))
-       (declare
-        (type cmprf cmpr)
-        (type morphism dffr)
-        (fixnum degr)
-        (list sbasis tbasis)
-        (fixnum srank trank))
-       (let ((rslt 
-               #-ACLPC
-                    (make-array (list trank srank)
-				:element-type 'fixnum
-				:initial-element 0)
-               #+ACLPC
-                    (if (or (zerop srank) (zerop trank))
-                       (make-array (list trank srank)
-                          :element-type 'fixnum)
-                       (make-array (list trank srank)
-                          :element-type 'fixnum
-                          :initial-element 0))
-               ))               
-            (declare (type matrix rslt))
-            (do ((j 0 (1+ j))
-	           (mark sbasis (cdr mark)))
-                ((endp mark))
-               (declare
-                (fixnum j)
-                (list mark))
-               (let ((cmbn (gnrt-? dffr degr (car mark))))
-                  (declare (type cmbn cmbn))
-                  (do ((mark1 (cmbn-list cmbn) (cdr mark1)))
-                      ((endp mark1))
-                     (declare (list mark1))
-                     (with--term (cffc gnrt) mark1
-                       (declare 
-                         (fixnum cffc)
-                         (type gnrt gnrt))
-                       (do ((mark2 tbasis (cdr mark2))
-                            (i 0 (1+ i))
-                            (found nil))
-                           ((or (endp mark2) found))
-                          (declare 
-                            (list mark2)
-                            (fixnum i found))
-                          (if (eq :equal (funcall cmpr gnrt (car mark2)))
-                             (progn
-                              (setq found 1)
-                              (setf (aref rslt i j) cffc))))))))
-               rslt))))
-
-
-;; OTHER CLASSES THAT INHERIT FROM FILTERED-CHAIN-COMPLEX
-
-
-(DEFCLASS FILTERED-COALGEBRA (filtered-chain-complex coalgebra)
-    ())
-
-(DEFVAR *FLCLGB-LIST*)
-(SETF *FLCLGB-LIST* +empty-list+)
-(PUSHNEW '*FLCLGB-LIST* *list-list*)
-
-(DEFMETHOD PRINT-OBJECT ((flclgb FILTERED-COALGEBRA) stream)
-(the FILTERED-COALGEBRA
-   (progn
-      (format stream "[K~D FILTERED-COALGEBRA]" (idnm flclgb))
-     flclgb)))
-
-(DEFUN FltrClgb (idnm)
-   (declare (type fixnum idnm))
-   (the (or FILTERED-COALGEBRA null)
-      (find idnm *flclgb-list* :key #'idnm)))
-
-;; Function that builds a filtered coalgebra. 
-(DEFUN BUILD-FltrClgb
-    (&key cmpr basis bsgn intr-dffr dffr-strt intr-cprd cprd-strt flin orgn)
-   (declare
-     (type cmprf cmpr)
-     (type intr-mrph intr-dffr intr-cprd)
-     (type basis basis)
-     (type gnrt bsgn)
-     (type strt dffr-strt cprd-strt)
-     (type chcm-flin flin)
-     (list orgn))
-   (the FILTERED-COALGEBRA
-     (progn
-         (let ((already (find orgn *flclgb-list* :key #'orgn :test #'equal)))
-            (declare (type (or null FILTERED-COALGEBRA) already))
-            (when already
-               (return-from build-FltrClgb already)))
-         (let ((rslt (build-clgb :cmpr cmpr :basis basis :bsgn bsgn
-                        :intr-dffr intr-dffr :dffr-strt dffr-strt
-                       :intr-cprd intr-cprf :cprd-strt cprd-strt
-                        :orgn orgn)))
-            (declare (type coalgebra rslt))
-            (change-class rslt 'FILTERED-COALGEBRA)
-            (setf (slot-value rslt 'flin) flin)
-            (push rslt *flclgb-list*)
-               rslt))))
-
-(defmethod change-chcm-to-flcc ((chcm coalgebra) flin flin-orgn )
-   (declare
-      
-      (type chcm-flin flin)
-      (list flin-orgn))
-   (the FILTERED-COALGEBRA
-      (progn
-         (change-class chcm 'FILTERED-COALGEBRA)
-         (setf orgn (append (orgn chcm) (list 'FILTERED-WITH) flin-orgn))
-         (let ((already (find orgn *flclgb-list* :key #'orgn :test #'equal)))
-            (declare (type (or null FILTERED-COALGEBRA) already))
-            (when already
-               (return-from change-chcm-to-flcc already)))
-         (setf (slot-value chcm 'flin) flin)
-         (setf (slot-value chcm 'orgn) orgn)
-         (push chcm *flCLGB-list*)
-         chcm)))
-
-
-(DEFCLASS FILTERED-ALGEBRA (filtered-chain-complex algebra)
-    ())
-
-(DEFVAR *FLALGB-LIST*)
-(SETF *FLALGB-LIST* +empty-list+)
-(PUSHNEW '*FLALGB-LIST* *list-list*)
-
-(DEFMETHOD PRINT-OBJECT ((flalgb FILTERED-ALGEBRA) stream)
-(the FILTERED-ALGEBRA
-   (progn
-      (format stream "[K~D FILTERED-ALGEBRA]" (idnm flalgb))
-     flalgb)))
-
-(DEFUN FltrAlgb (idnm)
-   (declare (type fixnum idnm))
-   (the (or FILTERED-ALGEBRA null)
-      (find idnm *flalgb-list* :key #'idnm)))
-
-;; Function that builds a filtered algebra. 
-(DEFUN BUILD-FltrAlgb
-    (&key cmpr basis bsgn intr-dffr dffr-strt intr-aprd aprd-strt flin orgn)
-   (declare
-     (type cmprf cmpr)
-     (type intr-mrph intr-dffr intr-aprd)
-     (type basis basis)
-     (type gnrt bsgn)
-     (type strt dffr-strt aprd-strt)
-     (type chcm-flin flin)
-     (list orgn))
-   (the FILTERED-ALGEBRA
-     (progn
-         (let ((already (find orgn *flalgb-list* :key #'orgn :test #'equal)))
-            (declare (type (or null FILTERED-ALGEBRA) already))
-            (when already
-               (return-from build-FltrAlgb already)))
-         (let ((rslt (build-algb :cmpr cmpr :basis basis :bsgn bsgn
-                        :intr-dffr intr-dffr :dffr-strt dffr-strt
-                       :intr-aprd intr-aprf :aprd-strt aprd-strt
-                        :orgn orgn)))
-            (declare (type algebra rslt))
-            (change-class rslt 'FILTERED-ALGEBRA)
-            (setf (slot-value rslt 'flin) flin)
-            (push rslt *flalgb-list*)
-               rslt))))
-
-(defmethod change-chcm-to-flcc ((chcm algebra) flin flin-orgn )
-   (declare
-      
-      (type chcm-flin flin)
-      (list flin-orgn))
-   (the FILTERED-ALGEBRA
-      (progn
-         (change-class chcm 'FILTERED-ALGEBRA)
-         (setf orgn (append (orgn chcm) (list 'FILTERED-WITH) flin-orgn))
-         (let ((already (find orgn *flalgb-list* :key #'orgn :test #'equal)))
-            (declare (type (or null FILTERED-ALGEBRA) already))
-            (when already
-               (return-from change-chcm-to-flcc already)))
-         (setf (slot-value chcm 'flin) flin)
-         (setf (slot-value chcm 'orgn) orgn)
-         (push chcm *flaLGB-list*)
-         chcm)))
-
-
-(DEFCLASS FILTERED-HOPF-ALGEBRA (filtered-chain-complex hopf-algebra)
-    ())
-
-(DEFVAR *FLHOPF-LIST*)
-(SETF *FLHOPF-LIST* +empty-list+)
-(PUSHNEW '*FLHOPF-LIST* *list-list*)
-
-(DEFMETHOD PRINT-OBJECT ((flhopf FILTERED-HOPF-ALGEBRA) stream)
-(the FILTERED-HOPF-ALGEBRA
-   (progn
-      (format stream "[K~D FILTERED-HOPF-ALGEBRA]" (idnm flhopf))
-     flhopf)))
-
-(DEFUN FltrHopf (idnm)
-   (declare (type fixnum idnm))
-   (the (or FILTERED-HOPF-ALGEBRA null)
-      (find idnm *flhopf-list* :key #'idnm)))
-
-(defmethod change-chcm-to-flcc ((chcm hopf-algebra) flin flin-orgn )
-   (declare
-      
-      (type chcm-flin flin)
-      (list flin-orgn))
-   (the FILTERED-hofp-algebra
-      (progn
-         (change-class chcm 'FILTERED-hopf-COALGEBRA)
-        (setf orgn (append (orgn chcm) (list 'FILTERED-WITH) flin-orgn))
-         (let ((already (find orgn *flhopf-list* :key #'orgn :test #'equal)))
-            (declare (type (or null FILTERED-HOPF-COALGEBRA) already))
-            (when already
-               (return-from change-chcm-to-flcc already)))
-         (setf (slot-value chcm 'flin) flin)
-         (setf (slot-value chcm 'orgn) orgn)
-         (push chcm *flhopf-list*)
-         chcm)))
-
-
-(DEFCLASS FILTERED-SIMPLICIAL-SET (FILTERED-CHAIN-COMPLEX simplicial-set )
-    ())
-
-(DEFVAR *FLSMST-LIST*)
-(SETF *FLSMST-LIST* +empty-list+)
-(PUSHNEW '*FLSMST-LIST* *list-list*)
-
-(DEFMETHOD PRINT-OBJECT ((flsmst filtered-simplicial-set) stream)
- (the filtered-simplicial-set
-   (progn
-      (format stream "[K~D Filtered-Simplicial-Set]" (idnm flsmst))
-      flsmst)))
-
-(DEFUN FltrSmSet (idnm)
-   (declare (type fixnum idnm))
-   (the (or filtered-simplicial-set null)
-      (find idnm *flsmst-list* :key #'idnm)))
-
-
-
-;; Function that builds a filtered simplicial set 
-(DEFUN BUILD-FltrSmSt
-    (&key cmpr basis bspn face face* intr-bndr bndr-strt intr-dgnl dgnl-strt flin orgn)
-   (declare
-     (type cmprf cmpr)
-     (type basis basis)
-     (type gmsm bspn)
-     (type face face)
-     (type (or null face*) face*)
-     (type (or intr-mrph null) intr-bndr intr-dgnl)
-        (type (or strt null) bndr-strt dgnl-strt)
-     (type chcm-flin flin)
-     (list orgn))
-   (the FILTERED-SIMPLICIAL-SET
-     (progn
-         (let ((already (find orgn *flsmst-list* :key #'orgn :test #'equal)))
-            (declare (type (or null FILTERED-SIMPLICIAL-SET) already))
-            (when already
-               (return-from build-FltrSmst already)))
-         (let ((rslt (build-smst :cmpr cmpr :basis basis :bspn bspn
-                       :face face :face* face* :intr-bndr intr-bndr 
-                       :bndr-strt bndr-strt :intr-dgnl intr-dgnl 
-                       :dgnl-strt dgnl :orgn orgn)))
-            (declare (type simplicial-set rslt))
-            (change-class rslt 'FILTERED-SIMPLICIAL-SET)
-            (setf (slot-value rslt 'flin) flin)
-            (push rslt *flsmst-list*)
-               rslt))))
-
-(defmethod change-chcm-to-flcc ((chcm simplicial-set) flin flin-orgn )
-   (declare
-      
-      (type chcm-flin flin)
-      (list flin-orgn))
-   (the FILTERED-SIMPLICIAL-SET
-      (progn
-         (change-class chcm 'FILTERED-SIMPLICIAL-SET)
-         (setf orgn (append (orgn chcm) (list 'FILTERED-WITH) flin-orgn))
-         (let ((already (find orgn *flsmst-list* :key #'orgn :test #'equal)))
-            (declare (type (or null FILTERED-SIMPLICIAL-SET) already))
-            (when already
-               (return-from change-chcm-to-flcc already)))
-         (setf (slot-value chcm 'flin) flin)
-         (setf (slot-value chcm 'orgn) orgn)
-         (push chcm *flsmst-list*)
-         chcm)))
-
-
-(DEFCLASS FILTERED-KAN (FILTERED-CHAIN-COMPLEX KAN )
-    ())
-
-(DEFVAR *FLKAN-LIST*)
-(SETF *FLKAN-LIST* +empty-list+)
-(PUSHNEW '*FLKAN-LIST* *list-list*)
-
-(DEFMETHOD PRINT-OBJECT ((flkan filtered-kan) stream)
- (the filtered-kan
-   (progn
-      (format stream "[K~D Filtered-Kan-Simplicial-Set]" (idnm flkan))
-      flkan)))
-
-(DEFUN FltrKan (idnm)
-   (declare (type fixnum idnm))
-   (the (or filtered-kan null)
-      (find idnm *flkan-list* :key #'idnm)))
-
-(defmethod change-chcm-to-flcc ((chcm kan) flin flin-orgn )
-   (declare
-      
-      (type chcm-flin flin)
-      (list flin-orgn))
-   (the FILTERED-KAN
-      (progn
-         (change-class chcm 'FILTERED-KAN)
-         (setf orgn (append (orgn chcm) (list 'FILTERED-WITH) flin-orgn))
-         (let ((already (find orgn *flkan-list* :key #'orgn :test #'equal)))
-            (declare (type (or null FILTERED-KAN) already))
-            (when already
-               (return-from change-chcm-to-flcc already)))
-         (setf (slot-value chcm 'flin) flin)
-         (setf (slot-value chcm 'orgn) orgn)
-         (push chcm *flkan-list*)
-         chcm)))
-
-
-(DEFCLASS FILTERED-SIMPLICIAL-GROUP (FILTERED-CHAIN-COMPLEX SIMPLICIAL-GROUP )
-    ())
-
-(DEFCLASS FILTERED-AB-SIMPLICIAL-GROUP (FILTERED-CHAIN-COMPLEX AB-SIMPLICIAL-GROUP )
-    ())
-
-(DEFVAR *FLSMGR-LIST*)
-(SETF *FLSMGR-LIST* +empty-list+)
-(PUSHNEW '*FLSMGR-LIST* *list-list*)
-
-(DEFMETHOD PRINT-OBJECT ((flsmgr filtered-simplicial-group) stream)
- (the filtered-simplicial-group
-   (progn
-      (format stream "[K~D Filtered-Simplicial-Group]" (idnm flsmgr))
-      flsmgr)))
-
-(DEFMETHOD PRINT-OBJECT ((flsmgr filtered-ab-simplicial-group) stream)
- (the filtered-simplicial-group
-   (progn
-      (format stream "[K~D Filtered-Abelian-Simplicial-Group]" (idnm flsmgr))
-      flsmgr)))
-
-(DEFUN FltrSmgr (idnm)
-   (declare (type fixnum idnm))
-   (the (or filtered-simplicial-group null)
-      (find idnm *flsmgr-list* :key #'idnm)))
-
-(DEFUN BUILD-FltrSmGr
-    (&key cmpr basis bspn face face* intr-bndr bndr-strt intr-dgnl dgnl-strt 
-      sintr-grml sintr-grin flin orgn)
-   (declare
-     (type cmprf cmpr)
-     (type basis basis)
-     (type gmsm bspn)
-     (type face face)
-     (type (or null face*) face*)
-     (type (or intr-mrph null) intr-bndr intr-dgnl)
-        (type (or strt null) bndr-strt dgnl-strt)
-     (type sintr sintr-grml sintr-grin)
-     (type chcm-flin flin)
-     (list orgn))
-   (the FILTERED-SIMPLICIAL-GROUP
-     (progn
-         (let ((already (find orgn *flsmgr-list* :key #'orgn :test #'equal)))
-            (declare (type (or null FILTERED-SIMPLICIAL-GROUP) already))
-            (when already
-               (return-from build-FltrSmgr already)))
-         (let ((rslt (build-smgr :cmpr cmpr :basis basis :bspn bspn
-                       :face face :face* face* :intr-bndr intr-bndr 
-                       :bndr-strt bndr-strt :intr-dgnl intr-dgnl 
-                       :dgnl-strt dgnl :sintr-grml sintr-grml
-                       :sintr-grin sintr-grin :orgn orgn)))
-            (declare (type simplicial-group rslt))
-            (change-class rslt 'FILTERED-SIMPLICIAL-GROUP)
-            (setf (slot-value rslt 'flin) flin)
-            (push rslt *flsmgr-list*)
-               rslt))))
-
-(DEFMACRO BUILD-FlABSMGR (&rest rest)
-  `(change-class (build-flsmgr ,@rest) 'filtered-ab-simplicial-group))
-
-(defmethod change-chcm-to-flcc ((chcm simplicial-group) flin flin-orgn )
-   (declare
-      
-      (type chcm-flin flin)
-      (list flin-orgn))
-   (the FILTERED-SIMPLICIAL-GROUP
-      (progn
-         (change-class chcm 'FILTERED-SIMPLICIAL-GROUP)
-         (setf orgn (append (orgn chcm) (list 'FILTERED-WITH) flin-orgn))
-         (let ((already (find orgn *flsmgr-list* :key #'orgn :test #'equal)))
-            (declare (type (or null FILTERED-SIMPLICIAL-GROUP) already))
-            (when already
-               (return-from change-chcm-to-flcc already)))
-         (setf (slot-value chcm 'flin) flin)
-         (setf (slot-value chcm 'orgn) orgn)
-         (push chcm *flsmgr-list*)
-         chcm)))
-
-(defmethod change-chcm-to-flcc ((chcm ab-simplicial-group) flin flin-orgn )
-   (declare
-      
-      (type chcm-flin flin)
-      (list flin-orgn))
-   (the FILTERED-AB-SIMPLICIAL-GROUP
-      (progn
-         (change-class chcm 'AB-FILTERED-SIMPLICIAL-GROUP)
-         (setf orgn (append (orgn chcm) (list 'FILTERED-WITH) flin-orgn))
-         (let ((already (find orgn *flabsmgr-list* :key #'orgn :test #'equal)))
-            (declare (type (or null FILTERED-AB-SIMPLICIAL-GROUP) already))
-            (when already
-               (return-from change-chcm-to-flcc already)))
-         (setf (slot-value chcm 'flin) flin)
-         (setf (slot-value chcm 'orgn) orgn)
-         (push chcm *flabsmgr-list*)
-         chcm)))
-
-        
-;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;    EXAMPLES    ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
-
-
-;; BICOMPLEXES
-
-;; Filtration index function of a Bicomplex (first degree of a generator).
-(setf BCflin 
-      #'(lambda (degr gnrt)
-       (declare 
-         (type fixnum degr)
-         (type gnrt gnrt))
-       (let* ((degr1 (BcGnrt-Degr1 gnrt))
-              (degr2 (BcGnrt-Degr2 gnrt)))
-          (declare (type fixnum degr1 degr2))
-          (if (=  degr (+ degr1 degr2))
-             degr1
-             0))))
-
-#|
-(funcall BCflin 5 (build-bcgnrt 2 3 'a))
-(funcall BCflin 7 (build-bcgnrt 6 1 'c))
-|# 
-
-;; Function that changes the bicomplex bc to a filtered complex, with filtration
-;; index of a generator defined as its first degree. 
-(defun CHANGE-BICM-TO-FLCC (bc)
-   (declare 
-     (type bicomplex bc))
-   (let* ((orgn (orgn bc))
-          (flin BCflin))
-      (declare
-       (type list orgn)
-       (type chcm-flin flin))
-      (the FILTERED-CHAIN-COMPLEX
-        (change-chcm-to-flcc bc flin '(Bicomplex-Flin)))))
-
-#|
-(defun bas (degr1 degr2)
-   (if (and (= degr1 0) (= degr2 1)) (return-from bas '(a)))
-   (if (and (= degr1 1) (= degr2 0)) (return-from bas '(b)))
-   (if (and (= degr1 1) (= degr2 1)) (return-from bas '(c)))
-   (if (and (= degr1 2) (= degr2 0))  (return-from bas '(d)))
-   (return-from bas nil))
- 
-(defun dif1 (degr1 degr2 gnrt)
-   (if (and (= degr1 1) (= degr2 1) (eql gnrt 'c)) (return-from dif1 (list (cons 2 'a))))
-   (if (and (= degr1 2) (= degr2 0) (eql gnrt 'd)) (return-from dif1 (list (cons 2 'b))))
-   (return-from dif1 nil))
-(defun dif2 (degr1 degr2 gnrt)
-   (if (and (= degr1 1) (= degr2 1) (eql gnrt 'c)) (return-from dif2 (list (cons 1 'b))))
-   (return-from dif2 nil))
-
-(setf bc (Build-Bicm :bcbasis #'bas :dffr1 #'dif1 :dffr2 #'dif2 :cmpr 's-cmpr 
-          :orgn '(BC-test)))
-
-(change-bicm-to-flcc bc)
-(flin bc 1 (build-bcgnrt 0 1 'a))
-(flin bc (cmbn 2 4 (build-bcgnrt 1 1 'c)))
-(flin bc (cmbn 2 4 (build-bcgnrt 1 1 'c) 2 (build-bcgnrt 2 0 'd)))
-(bigrd-basis bc 1 1)
-(bigrd-basis bc 2 0)
-(fltrd-basis bc 2 1)
-(ordered-basis bc 2)
-(flcc-dffr-mtrx bc 2 1)
-(flcc-dffr-mtrx bc 2 2)
-|#
-
-
-;; BARS
-
-(defun abar-bidegree (abar)
-    (declare (type abar abar))
-    (the list
-      (let ((p (1- (length abar)))
-            (q 0))
-        (declare (type fixnum p q))
-        (setf q (apply #'+ (mapcar #'car (rest abar))))
-        (decf q p)
-        (return-from abar-bidegree (list p q)))))
-
-
-(setf abar-flin 
-      #'(lambda (degr abar)
-       (declare (type fixnum degr)
-         (type abar abar))
-       (let* ((abar-bidgr (abar-bidegree abar))
-              (degr1 (first abar-bidgr))
-             (degr2 (second abar-bidgr)))
-         (if (=  degr (+ degr1 degr2))
-           degr1
-          0))))
-
-#|
-(setq kz2 (k-z2-1))
-(setq bar2 (bar kz2))
-
-(change-chcm-to-flcc bar2 abar-flin '(abar-flin))
-
-
-(setf basis7 (basis bar2 7))
-
-(mapcar
- #'(lambda (gnrt)
-     (flin bar2 7 gnrt))
- basis7)
-
-(flin bar2 (cmbn 7 (first basis7) (second basis7))) 
-
-(bigrd-basis bar2 2 5)
-(bigrd-basis bar2 3 4)
-(fltrd-basis bar2 7 2)
-(ordered-basis bar2 7)
-(flcc-dffr-mtrx bar2 7 2)
-(flcc-dffr-mtrx bar2 7 3)
-|#
-
-;; COBAR
-
-(defun allp-bidegree (allp)
-    (declare (type allp allp))
-    (the list
-      (let ((p (1- (length allp)))
-            (q 0))
-        (declare (type fixnum p q))
-        (setf q (apply #'+ (mapcar #'car (rest allp))))
-        (incf q p)
-        (return-from allp-bidegree (list (- p) q)))))
-
-(setf cobar-flin 
-      #'(lambda (degr allp)
-       (declare (type fixnum degr)
-         (type allp allp))
-       (let* ((allp-bidgr (allp-bidegree allp))
-              (degr1 (first allp-bidgr))
-             (degr2 (second allp-bidgr)))
-         (if (=  degr (+ degr1 degr2))
-           degr1
-          0))))
-
-;; TENSOR PRODUCTS 
- 
-(setf tnpr-flin 
-      #'(lambda (degr tnpr)
-       (declare 
-         (type fixnum degr)
-         (type tnpr tnpr))
-       (the fixnum
-          (degr1 tnpr))))
-
-
-;; FIBRATIONS (CARTESIAN PRODUCTS AND TWISTED PRODUCTS)
-
-(setf crpr-flin 
-      #'(lambda (degr crpr)
-          (declare
-           (type fixnum degr)
-           (type crpr crpr))
-          (let* ((b (cadr crpr))
-                 (dgop (car b)))
-             (declare
-              (type iabsm b)
-              (type fixnum dgop))
-             (the fixnum
-               (- degr (length (dgop-int-ext dgop)))))))
-
-#|
-(funcall fbrt-flin 3 '(:crpr (1 . s2) 0 . 3))
-(funcall fbrt-flin 4 '(:crpr (5 . s2) 0 . 3))
-|# 
- 
-
-;; BICONES
- 
-(defun bicone-flin (flinb flinc flind)
-   (declare (type chcm-flin flinb flinc flind))
-   (flet ((rslt (degr bicn)
-            (declare 
-              (type bicn bicn)
-              (type degr degr))
-            (let ((bcnx (bcnx bicn)))
-               (declare (type (member :bcnb :bcnc :bcnd) bcnx))
-               (if (eql :bcnb bcnx)
-                  (funcall flinb degr (ibicn bicn))
-                  (if (eql :bcnc bcnx)
-                     (funcall flinc degr (ibicn bicn))
-                     (funcall flind degr (ibicn bicn)))))))
-     (the chcm-flin #'rslt))) 
\ No newline at end of file
diff --git a/examples/anromero/persistent-homology/persistent-homology.cl b/examples/anromero/persistent-homology/persistent-homology.cl
deleted file mode 100644
index cf9a3dd..0000000
--- a/examples/anromero/persistent-homology/persistent-homology.cl
+++ /dev/null
@@ -1,501 +0,0 @@
-
-
-
-
-
-(defun eff-prst-hmlg-basis-dvs-quotient (FltrCm r p q)
-   (declare 
-     (type filtered-chain-complex fltrcm)
-     (type fixnum r p q))
-   (the list
-     (let* ((degr (+ p q))
-            (fltr-p-basis (fltrd-basis fltrcm degr p))
-            (p-basis-l (length fltr-p-basis))
-            (num-mtrx (spsq-num-mtrx fltrcm (1+ p) p q))
-            (den-mtrx (spsq-den-mtrx fltrcm r p q)) 
-            (cmbn-list nil)
-            (divs nil))
-        (declare
-         (list fltr-p-basis cmbn-list divs)
-         (type fixnum degr p-basis-l)
-         (type matrix num-mtrx den-mtrx))
-        (progn
-         (if (= 0 (array-total-size num-mtrx))
-            (progn
-             (setq cmbn-list nil)
-             (setq divs nil))
-            (if (= 0 (array-total-size den-mtrx))
-               (progn
-                (setq cmbn-list (gnrt-mtrx-to-list num-mtrx))
-                (setq divs (make-list (length cmbn-list) :initial-element 0)))
-               (let ((quotient-list (mtrx-quotient num-mtrx den-mtrx)))
-                  (declare (list quotient-list))
-                  (setq cmbn-list (first quotient-list)
-                    divs (second quotient-list)))))
-         (list
-          (mapcar 
-            #'(lambda (int-list)
-                (declare (list int-list))
-                (the cmbn
-                  (let* ((cmbn (cmbn degr))
-                         (cmpr (cmpr fltrcm)))
-                     (declare 
-                       (type cmbn cmbn)
-                       (type cmprf cmpr))
-                     (do ((mark1 int-list (cdr mark1))
-                          (mark2 fltr-p-basis (cdr mark2)))
-                         ((or (endp mark1) (endp mark2)))
-                        (declare (type list mark1 mark2))
-                        (if (not (= 0 (car mark1)))
-                           (setq cmbn (2cmbn-add cmpr cmbn 
-                                        (cmbn degr (car mark1) (car mark2))))))
-                     cmbn))) 
-            cmbn-list)
-          divs)))))
-
-;; (setf fltrcm triangle r 1 p 5 q -4)
-;; (setf degr (+ p q))
-;; (setf fltr-p-basis (fltrd-basis fltrcm degr p))
-;; (setf p-basis-l (length fltr-p-basis))
-;; (setf z1-list (fltr-chcm-z-gnrt-list fltrcm r p q))
-;;(eff-prst-hmlg-basis-dvs-2 fltrcm r p q)
-;;(eff-prst-hmlg-basis-dvs-2 fltrcm r 1 -1)
-;;(eff-prst-hmlg-basis-dvs-2 fltrcm r 2 -2)
-;;(eff-prst-hmlg-basis-dvs-2 fltrcm r 3 -3)
-;;(eff-prst-hmlg-basis-dvs-2 fltrcm r 4 -4)
-;;(eff-prst-hmlg-basis-dvs-2 fltrcm r 5 -5)
-
-(defun eff-prst-hmlg-basis-dvs-total (FltrCm r p q)
-   (declare 
-     (type filtered-chain-complex fltrcm)
-     (type fixnum r p q))
-   (the list
-     (let* ((degr (+ p q))
-            (fltr-p-basis (fltrd-basis fltrcm degr p))
-            (p-basis-l (length fltr-p-basis))
-            (fltr-p-1-list (fltr-basis-gnrt-list fltrcm degr (1- p)))
-            (z1-list (fltr-chcm-z-gnrt-list fltrcm (1+ p) p q))
-            (z1-mtrx (gnrt-list-to-mtrx z1-list))
-            (z2-list (fltr-chcm-z-gnrt-list fltrcm (1- r) (1- (+ p r)) (+ 2 (- q r))))
-            (z2-mtrx (gnrt-list-to-mtrx z2-list))
-            (fltr-p-1-mtrx (gnrt-list-to-mtrx fltr-p-1-list))
-            (dffr-mtrx (flcc-dffr-mtrx fltrcm (1+ degr) (1- (+ p r))))
-            (nil-mtrx 
-              #-ACLPC (make-array (list 0 0)
-                        :element-type 'fixnum
-                        :initial-element 0)
-              #+ACLPC (make-array (list 0 0)
-                        :element-type 'fixnum))
-            (dffr-z2-mtrx 
-              (if (or (= 0 (array-total-size z2-mtrx)) (= 0 (array-total-size dffr-mtrx)))
-                 nil-mtrx
-                 (mtrx-prdc dffr-mtrx z2-mtrx)))
-            (bnd-z2-line-n p-basis-l)
-            (bnd-z2-column-n (column-number dffr-z2-mtrx))
-            (bnd-z2-mtrx
-             (if (or (= 0 bnd-z2-line-n) (= 0 bnd-z2-column-n))
-                nil-mtrx
-                (submatrix dffr-z2-mtrx 0 (1- bnd-z2-line-n) 0 (1- bnd-z2-column-n))))
-            (num-mtrx z1-mtrx)
-            (den-mtrx bnd-z2-mtrx) 
-            (cmbn-list nil)
-            (divs nil))
-        (declare
-         (list fltr-p-basis cmbn-list divs)
-         (type fixnum degr p-basis-l)
-         (type matrix num-mtrx den-mtrx))
-        (progn
-         (if (= 0 (array-total-size num-mtrx))
-            (progn
-             (setq cmbn-list nil)
-             (setq divs nil))
-            (if (= 0 (array-total-size den-mtrx))
-               (progn
-                (setq cmbn-list (gnrt-mtrx-to-list num-mtrx))
-                (setq divs (make-list (length cmbn-list) :initial-element 0)))
-               (let ((quotient-list (mtrx-quotient num-mtrx den-mtrx)))
-                  (declare (list quotient-list))
-                  (setq cmbn-list (first quotient-list)
-                    divs (second quotient-list)))))
-         (list
-          (mapcar 
-            #'(lambda (int-list)
-                (declare (list int-list))
-                (the cmbn
-                  (let* ((cmbn (cmbn degr))
-                         (cmpr (cmpr fltrcm)))
-                     (declare 
-                       (type cmbn cmbn)
-                       (type cmprf cmpr))
-                     (do ((mark1 int-list (cdr mark1))
-                          (mark2 fltr-p-basis (cdr mark2)))
-                         ((or (endp mark1) (endp mark2)))
-                        (declare (type list mark1 mark2))
-                        (if (not (= 0 (car mark1)))
-                           (setq cmbn (2cmbn-add cmpr cmbn 
-                                        (cmbn degr (car mark1) (car mark2))))))
-                     cmbn))) 
-            cmbn-list)
-          divs)))))
-
-
-(defun eff-prst-hmlg-basis-dvs-bar (FltrCm r p q)
-   (declare 
-     (type filtered-chain-complex fltrcm)
-     (type fixnum r p q))
-   (the list
-     (let* ((degr (+ p q))
-            (fltr-p-basis (fltrd-basis fltrcm degr p))
-            (p-basis-l (length fltr-p-basis))
-            (num-mtrx (spsq-den-mtrx fltrcm r p q))
-            (den-mtrx (spsq-den-mtrx fltrcm (- r 1) p q)) 
-            (cmbn-list nil)
-            (divs nil))
-        (declare
-         (list fltr-p-basis cmbn-list divs)
-         (type fixnum degr p-basis-l)
-         (type matrix num-mtrx den-mtrx))
-        (progn
-         (if (= 0 (array-total-size num-mtrx))
-            (progn
-             (setq cmbn-list nil)
-             (setq divs nil))
-            (if (= 0 (array-total-size den-mtrx))
-               (progn
-                (setq cmbn-list (gnrt-mtrx-to-list num-mtrx))
-                (setq divs (make-list (length cmbn-list) :initial-element 0)))
-               (let ((quotient-list (mtrx-quotient num-mtrx den-mtrx)))
-                  (declare (list quotient-list))
-                  (setq cmbn-list (first quotient-list)
-                    divs (second quotient-list)))))
-         (list
-          (mapcar 
-            #'(lambda (int-list)
-                (declare (list int-list))
-                (the cmbn
-                  (let* ((cmbn (cmbn degr))
-                         (cmpr (cmpr fltrcm)))
-                     (declare 
-                       (type cmbn cmbn)
-                       (type cmprf cmpr))
-                     (do ((mark1 int-list (cdr mark1))
-                          (mark2 fltr-p-basis (cdr mark2)))
-                         ((or (endp mark1) (endp mark2)))
-                        (declare (type list mark1 mark2))
-                        (if (not (= 0 (car mark1)))
-                           (setq cmbn (2cmbn-add cmpr cmbn 
-                                        (cmbn degr (car mark1) (car mark2))))))
-                     cmbn))) 
-            cmbn-list)
-          divs)))))
-
-
-
-
-
-(defun eff-prst-hmlg-gnrts-total (FltrCm r p q)
-   (declare 
-     (type filtered-chain-complex fltrcm)
-     (type fixnum r p q))
-   (let* ((basis-dvs (eff-prst-hmlg-basis-dvs-total fltrcm r p q))
-         (basis (first basis-dvs))
-         (dvs (second basis-dvs))
-         (rslt nil))
-      (declare (type list basis-dvs basis dvs rslt))
-      (do ((mark1 basis (cdr mark1))
-           (mark2 dvs (cdr mark2)))
-          ((endp mark1))
-         (if (not (eql 1 (car mark2)))
-            (setf rslt (append rslt (list (car mark1))))))
-     rslt))
-
-(defun eff-prst-hmlg-gnrts-quotient (FltrCm r p q)
-   (declare 
-     (type filtered-chain-complex fltrcm)
-     (type fixnum r p q))
-   (let* ((basis-dvs (eff-prst-hmlg-basis-dvs-quotient fltrcm r p q))
-         (basis (first basis-dvs))
-         (dvs (second basis-dvs))
-         (rslt nil))
-      (declare (type list basis-dvs basis dvs rslt))
-      (do ((mark1 basis (cdr mark1))
-           (mark2 dvs (cdr mark2)))
-          ((endp mark1))
-         (if (not (eql 1 (car mark2)))
-            (setf rslt (append rslt (list (car mark1))))))
-     rslt))
-
-(defun eff-prst-hmlg-gnrts-bar (FltrCm r p q)
-   (declare 
-     (type filtered-chain-complex fltrcm)
-     (type fixnum r p q))
-   (let* ((basis-dvs (eff-prst-hmlg-basis-dvs-bar fltrcm r p q))
-         (basis (first basis-dvs))
-         (dvs (second basis-dvs))
-         (rslt nil))
-      (declare (type list basis-dvs basis dvs rslt))
-      (do ((mark1 basis (cdr mark1))
-           (mark2 dvs (cdr mark2)))
-          ((endp mark1))
-         (if (not (eql 1 (car mark2)))
-            (setf rslt (append rslt (list (car mark1))))))
-     rslt))
-
-
-(defun eff-prst-hmlg-group-total (fltrcm r p q)
-   (declare 
-     (type filtered-chain-complex fltrcm)
-     (type fixnum r p q))  
-   (let* ((basis-dvs (eff-prst-hmlg-basis-dvs-total fltrcm r p q))
-          (cmbns (first basis-dvs))
-          (divs (second basis-dvs)))
-      (declare (list basis-dvs cmbns divs))
-      
-      (dolist (item divs)
-         (declare (type fixnum item))
-         (if (not (eql 1 item))
-            (progn
-             (format t "~2%Component Z")
-             (unless (zerop item) 
-                (format t "/~DZ" item))
-             )))
-     (terpri)))
-
-(defun eff-prst-hmlg-group-quotient (fltrcm r p q)
-   (declare 
-     (type filtered-chain-complex fltrcm)
-     (type fixnum r p q))  
-   (let* ((basis-dvs (eff-prst-hmlg-basis-dvs-quotient fltrcm r p q))
-          (cmbns (first basis-dvs))
-          (divs (second basis-dvs)))
-      (declare (list basis-dvs cmbns divs))
-      
-      (dolist (item divs)
-         (declare (type fixnum item))
-         (if (not (eql 1 item))
-            (progn
-             (format t "~2%Component Z")
-             (unless (zerop item) 
-                (format t "/~DZ" item))
-             )))
-     (terpri)))
-
-(defun eff-prst-hmlg-group-bar (fltrcm r p q)
-   (declare 
-     (type filtered-chain-complex fltrcm)
-     (type fixnum r p q))  
-   (let* ((basis-dvs (eff-prst-hmlg-basis-dvs-bar fltrcm r p q))
-          (cmbns (first basis-dvs))
-          (divs (second basis-dvs)))
-      (declare (list basis-dvs cmbns divs))
-      
-      (dolist (item divs)
-         (declare (type fixnum item))
-         (if (not (eql 1 item))
-            (progn
-             (format t "~2%Component Z")
-             (unless (zerop item) 
-                (format t "/~DZ" item))
-             )))
-     (terpri)))
-
-(defun prst-hmlg-group-total-rpq (fltrcm r p q)
-   (declare
-    (type filtered-chain-complex fltrcm)
-    (type fixnum r p q))
-   (let* ((hmtp-eq (efhm fltrcm))
-          (eff-chcm (rbcc hmtp-eq))
-          (degr (+ p q)))
-      (declare
-       (type homotopy-equivalence hmtp-eq)
-       (type chain-complex eff-chcm)
-       (type fixnum degr))
-      (progn
-       (if (not (typep eff-chcm 'filtered-chain-complex))
-          (translate-filtration hmtp-eq))
-        (eff-prst-hmlg-group-total eff-chcm r p q))))
-
-(defun prst-hmlg-group-quotient-rpq (fltrcm r p q)
-   (declare
-    (type filtered-chain-complex fltrcm)
-    (type fixnum r p q))
-   (let* ((hmtp-eq (efhm fltrcm))
-          (eff-chcm (rbcc hmtp-eq))
-          (degr (+ p q)))
-      (declare
-       (type homotopy-equivalence hmtp-eq)
-       (type chain-complex eff-chcm)
-       (type fixnum degr))
-      (progn
-       (if (not (typep eff-chcm 'filtered-chain-complex))
-          (translate-filtration hmtp-eq))
-        (eff-prst-hmlg-group-quotient eff-chcm r p q))))
-
-(defun prst-hmlg-group-bar-rpq (fltrcm r p q)
-   (declare
-    (type filtered-chain-complex fltrcm)
-    (type fixnum r p q))
-   (let* ((hmtp-eq (efhm fltrcm))
-          (eff-chcm (rbcc hmtp-eq))
-          (degr (+ p q)))
-      (declare
-       (type homotopy-equivalence hmtp-eq)
-       (type chain-complex eff-chcm)
-       (type fixnum degr))
-      (progn
-       (if (not (typep eff-chcm 'filtered-chain-complex))
-          (translate-filtration hmtp-eq))
-        (eff-prst-hmlg-group-bar eff-chcm r p q))))
-
-(defun prst-hmlg-gnrts-total-rpq (FltrCm r p q)
-   (declare
-    (type filtered-chain-complex fltrcm)
-    (type fixnum r p q))
-   (let* ((hmtp-eq (efhm fltrcm))
-          (eff-chcm (rbcc hmtp-eq))
-          (degr (+ p q)))
-      (declare
-       (type homotopy-equivalence hmtp-eq)
-       (type chain-complex eff-chcm)
-       (type fixnum degr))
-      (progn
-       (if (not (typep eff-chcm 'filtered-chain-complex))
-          (translate-filtration hmtp-eq))
-        (eff-prst-hmlg-gnrts-total eff-chcm r p q))))
-
-(defun prst-hmlg-gnrts-quotient-rpq (FltrCm r p q)
-   (declare
-    (type filtered-chain-complex fltrcm)
-    (type fixnum r p q))
-   (let* ((hmtp-eq (efhm fltrcm))
-          (eff-chcm (rbcc hmtp-eq))
-          (degr (+ p q)))
-      (declare
-       (type homotopy-equivalence hmtp-eq)
-       (type chain-complex eff-chcm)
-       (type fixnum degr))
-      (progn
-       (if (not (typep eff-chcm 'filtered-chain-complex))
-          (translate-filtration hmtp-eq))
-        (eff-prst-hmlg-gnrts-quotient eff-chcm r p q))))
-
-(defun prst-hmlg-gnrts-bar-rpq (FltrCm r p q)
-   (declare
-    (type filtered-chain-complex fltrcm)
-    (type fixnum r p q))
-   (let* ((hmtp-eq (efhm fltrcm))
-          (eff-chcm (rbcc hmtp-eq))
-          (degr (+ p q)))
-      (declare
-       (type homotopy-equivalence hmtp-eq)
-       (type chain-complex eff-chcm)
-       (type fixnum degr))
-      (progn
-       (if (not (typep eff-chcm 'filtered-chain-complex))
-          (translate-filtration hmtp-eq))
-        (eff-prst-hmlg-gnrts-bar eff-chcm r p q))))
-
- (defun total-prst-hmlg-gnrts (fltrcm i j n)
-   (prst-hmlg-gnrts-total-rpq fltrcm (1+ (- j i)) i (- n i) ))
-
-(defun total-prst-hmlg-group (fltrcm i j n)
-  (format t "Persistent Homology H^{~D,~D}_~D" i j n)
-  (prst-hmlg-group-total-rpq fltrcm (1+ (- j i)) i (- n i) ))
-
- (defun prst-hmlg-gnrts-quotient (fltrcm i j n)
-   (prst-hmlg-gnrts-quotient-rpq fltrcm (1+ (- j i)) i (- n i) ))
-
-(defun prst-hmlg-group-quotient (fltrcm i j n)
-  (format t "Persistent Homology H^{~D,~D}_~D" i j n)
-  (prst-hmlg-group-quotient-rpq fltrcm (1+ (- j i)) i (- n i) ))
-
-
- (defun prst-hmlg-gnrts (fltrcm i j n)
-   (prst-hmlg-gnrts-bar-rpq fltrcm (1+ (- j i)) i (- n i) ))
-
-(defun prst-hmlg-group (fltrcm i j n)
-  (format t "Persistent Homology B^{~D,~D}_~D" i j n)
-  (prst-hmlg-group-bar-rpq fltrcm (1+ (- j i)) i (- n i) ))
-
-
-
-
-
-
-;; EXAMPLE: TRIANGLE
-
-
-(defun contains-element (list element)
-  (let ((rslt nil))
-    (dotimes (i (length list))
-      (if (eq element (nth i list))
-          (setf rslt 't)))
-    rslt))
-
-
-
-(setf triangle
-  (build-finite-ss
-   '(a b c
-     1 ab (b a) ac (c a) bc (c b)
-       2 abc (bc ac ab) )))
-
-
-
-(setf triangle-flin 
-      #'(lambda (degr gnrt)
-       (declare 
-         (type fixnum degr)
-        (type gnrt gnrt))
-          (let (
-                (l1 (list 'a))
-                (l2 (list 'b))
-                (l3 (list 'c))
-                (l4 (list 'ab))
-                (l5 (list 'bc))
-                (l6 (list 'ac))
-                (l7 (list 'abc))
-                (rslt -1))
-            
-              (if (contains-element l1 gnrt)  (setf rslt 1)
-                (if (contains-element l2 gnrt)  (setf rslt 2)
-                  (if (contains-element l3 gnrt)  (setf rslt 3)
-                    (if (contains-element l4 gnrt)  (setf rslt 4)
-                      (if (contains-element l5 gnrt)  (setf rslt 5)
-                        (if (contains-element l6 gnrt)  (setf rslt 6)
-                           (if (contains-element l7 gnrt)  (setf rslt 7)
-
-
-                        )))))))
-            rslt)))
-
-
-(setf triangle (change-chcm-to-flcc triangle triangle-flin 'triangle-flin))
-
-
-(dotimes (p 8)
-    (print (spsq-group triangle 1 p (- 0 p)))
-    (print (spsq-group triangle 1 p (- 1 p)))
-    (print (spsq-group triangle 1 p (- 2 p)))
-    (print (spsq-group triangle 1 p (- 3 p))))
-
-
-(dotimes (p 8)
-    (print (spsq-group triangle 2 p (- 0 p)))
-    (print (spsq-group triangle 2 p (- 1 p)))
-    (print (spsq-group triangle 2 p (- 2 p)))
-  (print (spsq-group triangle 2 p (- 3 p))))
-
-
-(dotimes (n 3)
-  (dotimes (p 8)
-    (print (prst-hmlg-group triangle p p n))
-    (print (prst-hmlg-group triangle p (1+ p) n))
-    (print (prst-hmlg-group triangle p (+ 2 p) n))
-    (print (prst-hmlg-group triangle p (+ 3 p) n))
-    (print (prst-hmlg-group triangle p (+ 4 p) n))
-))
-
-
-
-
diff --git a/examples/anromero/persistent-homology/spectral-sequences.lsp b/examples/anromero/persistent-homology/spectral-sequences.lsp
deleted file mode 100644
index 4b55947..0000000
--- a/examples/anromero/persistent-homology/spectral-sequences.lsp
+++ /dev/null
@@ -1,1359 +0,0 @@
-;; SPECTRAL-SEQUENCES   SPECTRAL-SEQUENCES   SPECTRAL-SEQUENCES   SPECTRAL-SEQUENCES
-;; SPECTRAL-SEQUENCES   SPECTRAL-SEQUENCES   SPECTRAL-SEQUENCES   SPECTRAL-SEQUENCES
-;; SPECTRAL-SEQUENCES   SPECTRAL-SEQUENCES   SPECTRAL-SEQUENCES   SPECTRAL-SEQUENCES
-
-
-(IN-PACKAGE "COMMON-LISP-USER")
-
-(provide "spectral-sequences")
-
-
-
-;; Auxiliary functions to deal with matrices
-
-(defun submatrix (mtrx first-line last-line first-col last-col)
-   (declare (type matrix mtrx)
-            (type fixnum first-line last-line first-col last-col))
-  (the matrix
-    (let ((line-n (line-number mtrx))
-	  (column-n (column-number mtrx)))
-      (declare (type fixnum line-n column-n))
-      (assert (<= first-line last-line (1- line-n)))
-      (assert (<= first-col last-col (1- column-n)))
-      (let* ((line-num (+ (- last-line first-line) 1))
-             (column-num (+ (- last-col first-col) 1))
-             (rslt (make-array (list line-num column-num)
-			      :element-type 'fixnum)))
-         (declare (type fixnum line-num column-num) 
-                  (type matrix rslt))
-         (dotimes (il line-num)
-            (declare (type fixnum il))
-            (dotimes (ic column-num)
-               (declare (type fixnum ic))
-               (setf (aref rslt il ic)
-                     (aref mtrx (+ il first-line) (+ ic first-col)))))
-         rslt))))
-
-#|
-(setf m (random-matrix 4 6 10))
-(submatrix m 1 3 2 4)
-|#
-
-
-(Defun column-j (mtrx j)
-   (declare (type matrix mtrx)
-            (type fixnum j))
-   (assert (< j (column-number mtrx)))
-   (the list
-     (let ((line-n (line-number mtrx)))
-        (declare (type fixnum line-n))
-        (mapcar
-         #'(lambda (i)
-             (declare (type fixnum i))
-             (aref mtrx i j))
-         (<a-b> 0 (1- line-n))))))
-
-#|
-(setf m (random-matrix 4 6 10))
-(column-j m 2)
-|#
-
-;; Function that concatenates two matrices (if their line number is different, the 
-;; needed zeros are added. 
-(defun mtrx-conc (mtrx1 mtrx2)
-   (declare (type matrix mtrx1 mtrx2))
-   (the matrix
-     (let* ((line-n-1 (line-number mtrx1))
-            (column-n-1 (column-number mtrx1))
-            (line-n-2 (line-number mtrx2))
-            (column-n-2 (column-number mtrx2))
-            (line-n (max line-n-1 line-n-2))
-            (column-n (+ column-n-1 column-n-2)))
-        (declare (type fixnum line-n-1 column-n-1 line-n-2
-                   column-n-2 line-n column-n))
-        (let ((rslt 
-                #-ACLPC
-                (make-array (list line-n column-n)
-                  :element-type 'fixnum
-                  :initial-element 0)
-                #+ACLPC
-                (if (or (zerop line-n) (zerop column-n))
-                   (make-array (list line-n column-n)
-                     :element-type 'fixnum)
-                   (make-array (list line-n column-n)
-                     :element-type 'fixnum
-                     :initial-element 0))))
-           (declare (type matrix rslt))
-           (do ((j 0 (1+ j)))
-               ((>= j column-n-1))
-              (declare (type fixnum j))
-              (do ((i 0 (1+ i)))
-                   ((>= i line-n-1))
-                 (declare (type fixnum i))
-                 (Setf (aref rslt i j) (aref mtrx1 i j))))
-           (do ((j 0 (1+ j)))
-                ((>= j column-n-2))
-              (declare (type fixnum j))
-              (do ((i 0 (1+ i)))
-                   ((>= i line-n-2))
-                 (declare (type fixnum i))
-                 (Setf (aref rslt i (+ column-n-1 j)) (aref mtrx2 i j))))
-            rslt))))
-
-#|
-(setf m1 (random-matrix 3 4 10))
-(setf m2 (random-matrix 4 2 10))
-(mtrx-conc m1 m2)
-(mtrx-conc m2 m1)
-|#
-
- 
-;; Functions related with submodules and matrices
-
-;; Function that returns a list of generators of the kernel of a matrix.
-;; Each generator is a list of integers which represent its coordinates
-;; in the initial basis.
-(defun kernel (mtrx)
-   (declare (type matrix mtrx))
-   (the list
-     (let* ((smith-list (smith mtrx))
-            (m (third smith-list))
-            (q (fourth smith-list))
-            (min (min (line-number mtrx) (column-number mtrx)))
-            (rslt nil))
-        (declare 
-          (type list smith-list rslt)
-          (type matrix m q)
-          (type fixnum min))
-        (progn
-         (do ((j (1- (column-number mtrx)) (1- j)))
-             ((< j min))
-            (declare (type fixnum j))
-            (setq rslt (nconc (list (column-j q j)) rslt)))
-         (do ((i (1- min) (1- i)))
-             ((or (< i 0) (not (eql  0 (aref m i i)))))
-            (declare (type fixnum i))
-            (setq rslt (nconc (list (column-j q i)) rslt)))
-         rslt))))
-
-#|
-(setf m (random-matrix 3 4 10))
-(kernel m)
-|#
-
-
-;; Returns a matrix which has as columns the elements of the list.
-;; (Each element in the list is a list of integers).
-(defun Gnrt-List-to-Mtrx (gnrt-list)
-   (declare (type list gnrt-list))
-   (the matrix
-     (let* ((column-n (length gnrt-list))
-            (line-n (length (car gnrt-list)))
-            (rslt 
-              #-ACLPC
-              (make-array (list line-n column-n)
-                :element-type 'fixnum
-                :initial-element 0)
-              #+ACLPC
-              (if (or (zerop line-n) (zerop column-n))
-                 (make-array (list line-n column-n)
-                   :element-type 'fixnum)
-                 (make-array (list line-n column-n)
-                   :element-type 'fixnum
-                   :initial-element 0))))
-        (declare 
-          (type fixnum column-n line-n)
-          (type matrix rslt))
-        (do ((j 0 (1+ j))
-             (mark2 gnrt-list (cdr mark2)))
-            ((endp mark2))
-           (declare
-            (type fixnum j)
-            (list mark2)) 
-           (if (eql line-n (length (car mark2)))
-              (do ((i 0 (1+ i))
-                   (mark1 (car mark2) (cdr mark1)))
-                  ((endp mark1))
-                 (declare 
-                   (type fixnum i)
-                   (list mark1))
-                 (setf (aref rslt i j) (car mark1)))))
-        rslt)))
-
-#|
-(setq gnrt-list (list '(2 4 6 8) '(0 1 0 0) '(0 3 3 3)))
-(Gnrt-List-to-Mtrx gnrt-list)
-|# 
-
-;; Returns the list of columns of the matrix mtrx.
-(defun gnrt-mtrx-to-list (mtrx)
-   (declare (type matrix mtrx))
-   (the list
-     (let* ((column-n (column-number mtrx)))
-        (declare (type fixnum column-n))
-        (mapcar
-         #'(lambda (j)
-             (declare (type fixnum j))
-             (column-j mtrx j))
-       (<a-b> 0 (1- column-n))))))
-
-#|
-(setf m (random-matrix 3 4 10))
-(gnrt-mtrx-to-list m)
-|#
-
-;; Returns the representation basis-divisors of a quotient of submodules B/C
-;; which are the images of the matrices mtrx1 and mtrx2, where basis=list
-;; of combinations (c_1...c_m) that forms a basis for B and divisors=list of
-;; integers (n_1....n_m) such that (n_1*c_1,...,n_m*c_m) forms a basis for C. 
-(defun mtrx-quotient (mtrx1 mtrx2)
-   (declare (type matrix mtrx1 mtrx2))
-   (the list
-     (let* ((smith-list-1 (smith mtrx1))
-            (p1 (first smith-list-1))
-            (p1-1 (second smith-list-1))
-            (d1 (third smith-list-1))
-            (p1-1Xmtrx2 (mtrx-prdc p1-1 mtrx2))
-            (p1Xd1 (copy-mtrx p1))
-            (d1-1Xp1-1Xmtrx2 (copy-mtrx p1-1Xmtrx2)))
-        (declare
-         (list smith-list-1)
-         (type matrix p1 p1-1 s1 p1-1Xmtrx2 p1Xd1 d1-1Xp1))
-        (progn
-         (let* ((line-n-1 (line-number p1))
-                (column-n-1 (column-number p1)))
-            (declare (type fixnum line-n-1 column-n-1))
-            (dotimes (ic column-n-1)
-               (declare (type fixnum ic))
-               (if (and (< ic (line-number d1)) (< ic (column-number d1)))
-                  (let ((d (aref d1 ic ic)))
-                     (declare (type fixnum d))
-                     (dotimes (il line-n-1)
-                        (declare (type fixnum il))
-                        (if (and (not (eql 1 d)) (not (eql 0 d)))
-                           (setf (aref p1Xd1 il ic) (* d (aref p1Xd1 il ic)))))))))
-         (let* ((line-n-2 (line-number p1-1Xmtrx2))
-                (column-n-2 (column-number p1-1Xmtrx2)))
-            (declare (type fixnum line-n-2 column-n-2))    
-            (dotimes (il line-n-2)
-               (declare (type fixnum il))
-               (if (and (< il (line-number d1)) (< il (column-number d1)))
-                  (let ((d (aref d1 il il)))
-                     (if (and (not (eql 1 d)) (not (eql 0 d)))
-                        (dotimes (ic column-n-2)
-                           (declare (type fixnum ic))
-                           (setf (aref d1-1Xp1-1Xmtrx2 il ic) 
-                                 (floor (aref d1-1Xp1-1Xmtrx2 il ic) d))))))))
-         (let* ((smith-list-2 (smith d1-1Xp1-1Xmtrx2))
-                (p2 (first smith-list-2))
-                (basis-mtrx (mtrx-prdc p1Xd1 p2))
-                (div-mtrx (third smith-list-2))
-                (cmbns nil)
-                (divs nil))
-            (declare 
-              (list smith-list-2 cmbns divs)
-              (type matrix p2 basis-mtrx div-mtrx))
-            (do ((i 0 (1+ i)))
-                ((or (>= i (line-number d1)) (>= i (column-number d1))
-                     (eql 0 (aref d1 i i))))
-               (declare (type fixnum i))
-               (progn
-                (setq cmbns (nconc cmbns (list (column-j basis-mtrx i))))
-                (if (and (< i (line-number div-mtrx)) (< i (column-number div-mtrx))) 
-                   (setq divs (nconc divs (list (aref div-mtrx i i))))
-                   (setq divs (nconc divs (list 0))))))
-            (list cmbns divs))))))
-
-#|
-(setf m1 (gnrt-list-to-mtrx '((1 1 1 1) (0 2 0 3) (1 0 0 0))))
-(setf m2 (gnrt-list-to-mtrx '((2 3 1 4) (0 1 1 1))))
-(mtrx-quotient m1 m2)
-|#
-
-
-
-;; SPECIFIC FUNCTIONS FOR THE COMPUTATION OF SPECTRAL SEQUENCES 
-;; OF EFFECTIVE FILTERED COMPLEXES.
-
-
-;; GROUPS
-
-;; Returns the matrix that defines Z^r_{p,q} (a submatrix of the 
-;; differential matrix M, such that the elements of Z^r_{p,q} are those that
-;; when we apply M to them we obtain zero, i.e. Z^r_{p,q}=Ker M). Only can be applied
-;; to a finitely generated complex. 
-(defun FLTR-CHCM-Z-MTRX (fltrcm r p q)
-  (declare
-    (type filtered-chain-complex fltrcm)
-    (type fixnum r p q))
-  (the matrix
-    (let* ((cmpr (cmpr1 fltrcm))
-	     (dffr (dffr fltrcm))
-	     (degr (+ p q))
-           (sbasis (fltrd-basis fltrcm degr p))
-           (tbasis 
-             (mapcan 
-              #'(lambda (i)
-                  (declare (type fixnum i))
-                  (bigrd-basis fltrcm i (- (1- degr) i)))
-              (<a-b> (1+ (- p r)) p)))) ;; We suppose that the differential
-                                        ;; respects the filtration, i.e., 
-                                        ;; d(F_pX) \in F_p(dX). If not, we must
-                                        ;; consider (<a-b> (1+ (-p r)) t(degr),
-                                        ;; where t(degr)=max{flin(x), x \in X_degr}.
-       (declare
-        (type cmprf cmpr)
-        (type morphism dffr)
-        (type fixnum degr)
-        (list sbasis tbasis))
-      (let ((srank (length sbasis))
-	      (trank (length tbasis)))
-         (declare (type fixnum srank trank))
-         (let ((rslt 
-               #-ACLPC
-                    (make-array (list trank srank)
-				:element-type 'fixnum
-				:initial-element 0)
-               #+ACLPC
-                    (if (or (zerop srank) (zerop trank))
-                       (make-array (list trank srank)
-                          :element-type 'fixnum)
-                       (make-array (list trank srank)
-                          :element-type 'fixnum
-                          :initial-element 0))))               
-            (declare (type matrix rslt))
-            (do ((j 0 (1+ j))
-	           (mark sbasis (cdr mark)))
-                ((endp mark))
-               (declare
-                (type fixnum j)
-                (list mark))
-               (let ((cmbn (gnrt-? dffr degr (car mark))))
-                  (declare (type cmbn cmbn))
-                  (do ((mark1 (cmbn-list cmbn) (cdr mark1)))
-                      ((endp mark1))
-                     (declare (list mark1))
-                     (with--term (cffc gnrt) mark1
-                       (declare 
-                         (type fixnum cffc)
-                         (type gnrt gnrt))
-                       (do ((mark2 tbasis (cdr mark2))
-                            (i 0 (1+ i))
-                            (found nil))
-                           ((or (endp mark2) found))
-                          (declare 
-                            (list mark2)
-                            (type fixnum i found))
-                          (if (eq :equal (funcall cmpr gnrt (car mark2)))
-                             (progn
-                              (setq found 1)
-                              (setf (aref rslt i j) cffc))))))))
-               rslt)))))
-
-#|
-(cat-init)
-(setq kz2 (k-z2-1))
-(setq fcc (bar kz2))
-(Change-Chcm-TO-Flcc fcc abar-flin `(abar-flin))
-(FLTR-CHCM-Z-MTRX fcc 2 3 2)
-(FLTR-CHCM-Z-MTRX fcc 1 2 4)
-|#
- 
-
-;; Returns a list of generators (list of coordinates) of Z^r_{p,q}
-;; (only for finitely generated complexes)
-(defun Fltr-Chcm-Z-Gnrt-List (FltrCm r p q)
-   (declare (type filtered-chain-complex fltrcm)
-     (type fixnum r p q))
-   (the list
-         (let* ((degr (+ p q))
-                (all-basis-gnrt-list (fltr-basis-gnrt-list fltrcm degr p)))
-            (declare
-             (type fixnum degr)
-             (list all-basis-gnrt-list))
-            (if (= 0 r)
-               all-basis-gnrt-list
-               (let* ((mat (FLTR-CHCM-Z-MTRX fltrcm r p q))
-                   (line-n (line-number mat))
-                   (column-n (column-number mat)))
-                  (declare 
-                    (type matrix mat)
-                    (type fixnum line-n column-n))
-                  (if (= 0 column-n) nil
-                     (if (= 0 line-n)
-                     all-basis-gnrt-list
-                     (kernel mat))))))))
-#|
-(Fltr-Chcm-Z-Gnrt-List fcc 2 3 2)
-(Fltr-Chcm-Z-Gnrt-List fcc 1 2 4)
-|# 
-
-;; Returns a list of lists with the coordinates of the elements of
-;; the basis of F_pX_n (with p=fltr-index, n=degr), that are lists with
-;; the form (0...0 i 0...0) (only for finitely generated complexes)
-(defun fltr-basis-gnrt-list (FltrCm degr fltr-index)
-   (declare 
-     (type filtered-chain-complex fltrcm)
-     (type fixnum degr fltr-index))
-   (the list
-     (let* ((all-basis (fltrd-basis fltrcm degr fltr-index))
-            (basis-l (length all-basis))
-            (rslt 
-              (the list
-                (mapcar
-                 #'(lambda (i)
-                     (nconc (make-list (1- i) :initial-element 0) 
-                       (list 1) (make-list (- basis-l i) :initial-element 0)))
-                 (<a-b> 1 basis-l)))))
-        rslt)))
-
-#|
-(fltr-basis-gnrt-list fcc 6 2)
-|#
- 
-
-;; Returns the matrix of the generators of the numerator in E^r_{p,q}
-;; (Only for finitely generated complexes)
-(defun spsq-num-mtrx (FltrCm r p q)
-  (the matrix
-    (let* ((degr (+ p q))
-           (fltr-p-basis (fltrd-basis fltrcm degr p))
-           (p-basis-l (length fltr-p-basis))
-           (z1-list (fltr-chcm-z-gnrt-list fltrcm r p q))
-           (fltr-p-1-list (fltr-basis-gnrt-list fltrcm degr (1- p)))
-           (z1-mtrx (gnrt-list-to-mtrx z1-list))
-           (fltr-p-1-mtrx (gnrt-list-to-mtrx fltr-p-1-list))
-           (num1-mtrx (mtrx-conc z1-mtrx fltr-p-1-mtrx))
-           (num1-line-n (line-number num1-mtrx)))
-       (declare
-        (type fixnum degr num1-line-n)
-        (type list fltr-p-basis p-basis-l z1-list fltr-p-1-list)
-        (type matrix z1-mtrx fltr-p-1-mtrx num1-mtrx))
-       (if (eql num1-line-n p-basis-l)
-          num1-mtrx 
-          (let* ((num-line-n p-basis-l)
-                 (num-column-n (column-number num1-mtrx))
-                 (rslt  
-                   #-ACLPC (make-array (list num-line-n num-column-n)
-                             :element-type 'fixnum
-                             :initial-element 0)
-                   #+ACLPC
-                   (if (or (zerop num-line-n) (zerop num-column-n))
-                      (make-array (list num-line-n num-column-n)
-                        :element-type 'fixnum)
-                      (make-array (list num-line-n num-column-n)
-                        :element-type 'fixnum
-                        :initial-element 0))))
-             (declare
-              (type fixnum num-lin-n num-column-n)
-              (type matrix rslt))
-             (do ((j 0 (1+ j)))
-                 ((>= j num-column-n))
-                (declare (type fixnum j))
-                (do ((i 0 (1+ i)))
-                    ((>= i num1-line-n))
-                   (declare (type fixnum i))
-                   (Setf (aref rslt i j) (aref num1-mtrx i j))))
-             rslt)))))
-
-#|
-(spsq-num-mtrx fcc 2 3 2)
-(spsq-num-mtrx fcc 1 2 4)
-|# 
-
-;; Returns the matrix of the generators of the denominator in E^r_{p,q}
-;; (Only for finitely generated complexes) 
-(defun spsq-den-mtrx (FltrCm r p q)
-   (the matrix
-     (let* ((degr (+ p q))
-            (fltr-p-basis (fltrd-basis fltrcm degr p))
-            (p-basis-l (length fltr-p-basis))
-            (fltr-p-1-list (fltr-basis-gnrt-list fltrcm degr (1- p)))
-            (z2-list (fltr-chcm-z-gnrt-list fltrcm (1- r) (1- (+ p r)) (+ 2 (- q r))))
-            (z2-mtrx (gnrt-list-to-mtrx z2-list))
-            (fltr-p-1-mtrx (gnrt-list-to-mtrx fltr-p-1-list))
-            (dffr-mtrx (flcc-dffr-mtrx fltrcm (1+ degr) (1- (+ p r))))
-            (nil-mtrx 
-              #-ACLPC (make-array (list 0 0)
-                        :element-type 'fixnum
-                        :initial-element 0)
-              #+ACLPC (make-array (list 0 0)
-                        :element-type 'fixnum))
-            (dffr-z2-mtrx 
-              (if (or (= 0 (array-total-size z2-mtrx)) (= 0 (array-total-size dffr-mtrx)))
-                 nil-mtrx
-                 (mtrx-prdc dffr-mtrx z2-mtrx)))
-            (bnd-z2-line-n p-basis-l)
-            (bnd-z2-column-n (column-number dffr-z2-mtrx))
-            (bnd-z2-mtrx
-             (if (or (= 0 bnd-z2-line-n) (= 0 bnd-z2-column-n))
-                nil-mtrx
-                (submatrix dffr-z2-mtrx 0 (1- bnd-z2-line-n) 0 (1- bnd-z2-column-n))))
-            (den1-mtrx (mtrx-conc bnd-z2-mtrx fltr-p-1-mtrx))
-            (den-column-n (column-number den1-mtrx))
-            (den-line-n p-basis-l)
-            (rslt  
-              #-ACLPC (make-array (list den-line-n den-column-n)
-                        :element-type 'fixnum
-                        :initial-element 0)
-              #+ACLPC
-              (if (or (zerop den-line-n) (zerop den-column-n))
-                 (make-array (list den-line-n den-column-n)
-                   :element-type 'fixnum)
-                 (make-array (list den-line-n den-column-n)
-                   :element-type 'fixnum
-                   :initial-element 0))))
-        (declare
-             (list fltr-p-basis fltr-p-1-list z2-list)
-             (type fixnum degr p-basis-l bnd-z2-line-n bnd-z2-column-n den-column-n den-line-n)
-             (type matrix z2-mtrx fltr-p-1-mtrx dffr-mtrx nil-mtrx 
-               dffr-z2-mtrx bnd-z2-mtrx den1-mtrx rslt))
-        (do ((j 0 (1+ j)))
-            ((>= j den-column-n))
-           (declare (type fixnum j))
-           (do ((i 0 (1+ i)))
-               ((>= i (min den-line-n (line-number den1-mtrx))))
-              (declare (type fixnum i))
-              (Setf (aref rslt i j) (aref den1-mtrx i j))))
-        rslt)))
-                   
-#|
-(spsq-den-mtrx fcc 2 3 2)
-(spsq-den-mtrx fcc 1 2 4)
-|#   
-
-;; Function that returns the representation basis-divisors of E^r_{p,q} of a
-;; finitely generated complex. 
-(defun eff-spsq-basis-dvs (FltrCm r p q)
-   (declare 
-     (type filtered-chain-complex fltrcm)
-     (type fixnum r p q))
-   (the list
-     (let* ((degr (+ p q))
-            (fltr-p-basis (fltrd-basis fltrcm degr p))
-            (p-basis-l (length fltr-p-basis))
-            (num-mtrx (spsq-num-mtrx fltrcm r p q))
-            (den-mtrx (spsq-den-mtrx fltrcm r p q)) 
-            (cmbn-list nil)
-            (divs nil))
-        (declare
-         (list fltr-p-basis cmbn-list divs)
-         (type fixnum degr p-basis-l)
-         (type matrix num-mtrx den-mtrx))
-        (progn
-         (if (= 0 (array-total-size num-mtrx))
-            (progn
-             (setq cmbn-list nil)
-             (setq divs nil))
-            (if (= 0 (array-total-size den-mtrx))
-               (progn
-                (setq cmbn-list (gnrt-mtrx-to-list num-mtrx))
-                (setq divs (make-list (length cmbn-list) :initial-element 0)))
-               (let ((quotient-list (mtrx-quotient num-mtrx den-mtrx)))
-                  (declare (list quotient-list))
-                  (setq cmbn-list (first quotient-list)
-                    divs (second quotient-list)))))
-         (list
-          (mapcar 
-            #'(lambda (int-list)
-                (declare (list int-list))
-                (the cmbn
-                  (let* ((cmbn (cmbn degr))
-                         (cmpr (cmpr fltrcm)))
-                     (declare 
-                       (type cmbn cmbn)
-                       (type cmprf cmpr))
-                     (do ((mark1 int-list (cdr mark1))
-                          (mark2 fltr-p-basis (cdr mark2)))
-                         ((or (endp mark1) (endp mark2)))
-                        (declare (type list mark1 mark2))
-                        (if (not (= 0 (car mark1)))
-                           (setq cmbn (2cmbn-add cmpr cmbn 
-                                        (cmbn degr (car mark1) (car mark2))))))
-                     cmbn))) 
-            cmbn-list)
-          divs)))))
-
-#|
-(do ((r 1 (1+ r)))
-    ((> r 3))
-   (dotimes (n 8)
-      (dotimes (p (+ n 1))
-         (let ((q (- n p)))
-            (print (list r p q))
-            (princ (eff-spsq-basis-dvs fcc r p q))
-            ))))
-|# 
-
-
-(defun eff-spsq-gnrts (FltrCm r p q)
-   (declare 
-     (type filtered-chain-complex fltrcm)
-     (type fixnum r p q))
-   (let* ((basis-dvs (eff-spsq-basis-dvs fltrcm r p q))
-         (basis (first basis-dvs))
-         (dvs (second basis-dvs))
-         (rslt nil))
-      (declare (type list basis-dvs basis dvs rslt))
-      (do ((mark1 basis (cdr mark1))
-           (mark2 dvs (cdr mark2)))
-          ((endp mark1))
-         (if (not (eql 1 (car mark2)))
-            (setf rslt (append rslt (list (car mark1))))))
-      rslt))
-      
- 
-;; Function that presents on the screen the components of the E^r_{p,q}
-;; of the spectral sequence of a filtered complex.
-(defun eff-spsq-group (fltrcm r p q)
-   (declare 
-     (type filtered-chain-complex fltrcm)
-     (type fixnum r p q))  
-   (let* ((basis-dvs (eff-spsq-basis-dvs fltrcm r p q))
-          (cmbns (first basis-dvs))
-          (divs (second basis-dvs)))
-      (declare (list basis-dvs cmbns divs))
-      (format t "Spectral sequence E^~D_{~D,~D}" r p q)
-      (dolist (item divs)
-         (declare (type fixnum item))
-         (if (not (eql 1 item))
-            (progn
-             (format t "~2%Component Z")
-             (unless (zerop item) 
-                (format t "/~DZ" item))
-             )))
-      (terpri)))
-
-#|
-(do ((r 1 (1+ r)))
-    ((> r 3))
-   (dotimes (n 8)
-      (dotimes (p (+ n 1))
-         (let ((q (- n p)))
-            (eff-spsq-group fcc r p q)
-            (terpri)
-            (terpri)
-            ))))
-|# 
-
-
-
-;; DIFFERENTIAL FUNCTIONS
-
-;; Auxiliary functions to deal with coefficients of elements with regard to 
-;; some generators or elements of a basis. 
-
-
-;; Function that returns the coordinates of a vector vctr with regard to
-;; the basis whose elements are the columns of the matrix gnrt-mtrx.
-(defun vctr-coordinates (vctr gnrt-mtrx)
-   (declare 
-     (type list vctr)
-     (type matrix gnrt-mtrx))
-   (the list
-     (let* ((C (gnrt-list-to-mtrx (list vctr)))
-            (B (copy-mtrx gnrt-mtrx))
-            (smith-list (smith B))
-            (p-1 (second smith-list))
-            (D (third smith-list))
-            (q (fourth smith-list))
-            (q-1 (fifth smith-list))
-            (C2 (mtrx-prdc p-1 C))
-            (line-n (column-number B))
-            (A2 
-             #-ACLPC
-             (make-array (list line-n 1)
-               :element-type 'fixnum
-               :initial-element 0)
-             #+ACLPC
-             (if (zerop line-n)
-                (make-array (list line-n 1)
-                  :element-type 'fixnum)
-                (make-array (list line-n 1)
-                  :element-type 'fixnum
-                  :initial-element 0)))
-            (end nil))
-        (declare 
-          (type matrix C B p-1 D q q-1 C2 A2)
-          (type list smith-list)
-          (type fixnum line-n end))
-        (do ((i 0 (1+ i)))
-            ((or (>= i (column-number D)) (>= i (line-number D)) end))
-           (declare (type fixnum i))
-           (let* ((di (aref D i i)))
-              (declare (type fixnum di))
-              (if (eql 0 di)
-                 (setq found 1)
-                 (progn
-                  (setf (aref A2 i 0) (floor (aref C2 i 0) di))))))
-        (let* ((A (mtrx-prdc Q A2)))
-           (declare (type matrix A))
-           (column-j A 0)))))
-
-#|
-(setf m (gnrt-list-to-mtrx '((1 0 0 0) (2 3 4 5) (0 1 0 3))))
-(setq vctr '(5 9 8 19))
-(vctr-coordinates vctr m)
-|# 
-
-;; Function that returns the list of coefficients of the combination "cmbn"
-;; in the basis (list of generators) "basis" (with comparison function "cmpr").
-(defun cmbn-cffc-list (cmbn basis cmpr)
-   (declare 
-     (type cmbn cmbn)
-     (type list basis)
-     (type cmprf cmpr))
-   (the list
-     (let* ((rslt nil)
-            (mark1 (cmbn-list cmbn))
-            (term (car mark1))
-            (cffc (cffc term))
-            (gnrt (gnrt term)))
-        (declare
-         (type list rslt mark1)
-         (type term term)
-         (type cffc cffc)
-         (type gnrt gnrt))
-        (do ((mark2 basis (cdr mark2)))
-            ((endp mark2))
-           (declare 
-             (type list mark2))
-           (if (endp mark1)
-              (setq rslt (nconc rslt (list 0)))
-           (if (eq :equal (funcall cmpr gnrt (car mark2)))
-              (progn
-               (setq rslt (nconc rslt (list cffc)))
-               (pop mark1)
-               (setq term (car mark1))
-               (setq cffc (cffc term) gnrt (gnrt term)))
-              (setq rslt (nconc rslt (list 0))))))
-        rslt)))
-
-#|
-(setf basis (list 'a 'b 'c 'd 'e 'f))
-(setq cmbn (cmbn 2 3 'a 5 'c 8 'f))
-(cmbn-cffc-list cmbn basis #'s-cmpr)
-|# 
-
-;; Function that returns the list of coordinates of the combination "cmbn" in the basis
-;; formed by the combinations in the list "gnrt-list". All these combinations are combinations
-;; of the generators in "basis" ("cmpr" is the comparison function). 
-(defun cmbn-coordinates (cmbn gnrt-list basis cmpr)
-   (declare 
-     (type cmbn cmbn)
-     (type list gnrt-list basis)
-     (type cmprf cmpr))
-   (the list
-     (let* ((vctr (cmbn-cffc-list cmbn basis cmpr))
-            (B (gnrt-list-to-mtrx
-                (mapcar
-                 #'(lambda (cmbn2)
-                     (declare (type cmbn cmbn2))
-                     (cmbn-cffc-list cmbn2 basis cmpr))
-                 gnrt-list))))
-        (declare
-         (type list vctr)
-         (type matrix B))
-        (vctr-coordinates vctr B))))
-
-#|
-(setf basis (list 'a 'b 'c 'd 'e 'f))
-(setq cmbn (cmbn 2 3 'a 5 'c 6 'f))
-(setq gnrt-list (list (cmbn 2 1 'a 2 'd 2 'f) (cmbn 2 5 'c -6 'd)))
-(cmbn-coordinates cmbn gnrt-list basis #'s-cmpr)
-|# 
-    
-         
-;; Main function to compute the differential of an element in the spectral sequence          
-
-
-;; Function that returns the list of integers which correspond to the coordinates
-;; on each of the components of E^r_{p-r,q+r-1} of the differential 
-;; d: E^r_{p,q} --> E^r_{p-r,q+r-1} applied to the element of E^r_{p,q}
-;; which has as coordinates the list int-list. (Only for finitely generated complexes)
-(defun eff-spsq-dffr (fltrcm r p q int-list)
-   (declare
-    (type filtered-chain-complex fltrcm)
-    (type fixnum r p q)
-    (list int-list))
-   (the list
-     (let* ((cmpr (cmpr1 fltrcm))
-            (degr (+ p q))
-            (sbasis (fltrd-basis fltrcm degr p))
-            (tbasis (fltrd-basis fltrcm (1- degr) (- p r)))
-            (num-mtrx (spsq-num-mtrx fltrcm r p q))
-            (den-mtrx (spsq-den-mtrx fltrcm r p q))
-            (Z-gnrt-list (Fltr-Chcm-Z-Gnrt-List fltrcm r p q))
-            (s-basis-dvs (mtrx-quotient (copy-mtrx num-mtrx) den-mtrx))
-            (s-gnrt-list (first s-basis-dvs))
-            (s-dvs (second s-basis-dvs))
-            (t-basis-dvs (spsq-basis-dvs fltrcm r (- p r) (1- (+ q r))))
-            (t-gnrt-list (first t-basis-dvs))
-            (t-dvs (second t-basis-dvs))
-            (selement (make-list (length sbasis) :initial-element 0))
-            (cmbn (cmbn degr)))
-        (declare 
-          (type fcmpr cmpr)
-          (type fixnum degr)
-          (type list sbasis tbasis z-gnrt-list s-basis-dvs s-gnrt-list s-dvs
-            t-basis-dvs t-gnrt-list t-dvs selement)
-          (type matrix num-mtrx den-mtrx)
-          (type cmbn cmbn))
-        (progn
-         (labels ((2list-add (list1 list2)
-                    (declare (type list list1 list2))
-                    (the list
-                      (mapcar #'+ list1 list2)))
-                  (n-list (n list)
-                    (declare
-                     (type list list)
-                     (type fixnum n))
-                    (the list
-                      (mapcar #'(lambda (i)
-                                  (* n i))
-                        list))))
-           (do ((mark1 s-gnrt-list (cdr mark1))
-                (mark2 s-dvs (cdr mark2))
-                (mark3 int-list))
-               ((endp mark1))
-              (declare (list mark1 mark2 mark3))
-              (if (not (eql 1 (car mark2)))
-                 (progn
-                  (setq selement (2list-add selement (n-list (car mark3) (car mark1))))
-                  (pop mark3)))))
-         (let* ((selt-coord (vctr-coordinates selement num-mtrx)))
-            (declare (list selt-coord))
-            (do ((mark1 z-gnrt-list (cdr mark1))
-                 (mark2 selt-coord (cdr mark2)))
-                ((endp mark1))
-               (declare (list mark1 mark2))
-               (if (not (eql 0 (car mark2)))
-                  (setq cmbn (2cmbn-add cmpr cmbn (n-cmbn (car mark2)
-                                                    (funcall 
-                                                      #'(lambda (int-list)
-                                                          (declare (list int-list))
-                                                          (the cmbn
-                                                            (let* ((cmbn2 (cmbn degr)))
-                                                               (declare 
-                                                                 (type cmbn cmbn))
-                                                               (do ((mark3 int-list (cdr mark3))
-                                                                    (mark4 sbasis (cdr mark4)))
-                                                                   ((or (endp mark3) (endp mark4)))
-                                                                  (declare (type list mark3 mark4))
-                                                                  (if (not (= 0 (car mark3)))
-                                                                     (setq cmbn2 (2cmbn-add cmpr cmbn2 
-                                                                                   (cmbn degr (car mark3) (car mark4))))))
-                                                               cmbn2)))
-                                                      (car mark1))))))))
-         (let* ((dffr-cmbn (dffr fltrcm cmbn))
-                (crdnt (cmbn-coordinates dffr-cmbn t-gnrt-list tbasis cmpr))
-                (rslt nil))
-            (declare
-             (type cmbn dffr-cmbn)
-             (type list crdnt rslt))
-            (do ((mark1 t-dvs (cdr mark1))
-                 (mark2 crdnt (cdr mark2)))
-                ((endp mark1))
-               (declare (list mark1 mark2))
-               (if (not (eql 1 (car mark1)))
-                  (if (eql 0 (car mark1))
-                     (setq rslt (nconc rslt (list (car mark2))))
-                     (setq rslt (nconc rslt (list (mod (car mark2) (car mark1))))))))
-            rslt)))))          
-                           
-#|
-(eff-spsq-dffr fcc 1 2 3 '(1))
-(eff-spsq-dffr fcc 1 2 5 '(0 1))
-(eff-spsq-dffr fcc 1 2 5 '(1 0))
-(eff-spsq-dffr fcc 1 3 4 '(1 0))
-(eff-spsq-dffr fcc 1 3 4 '(0 1))
-|# 
-
-;; CONVERGENCE OF THE SPECTRAL SEQUENCE            
-
-;; Function that determines if at level r and for degree n the E^r_{p,q} of the
-;; filtered complex fltrcm with p+q=degr are equal to E^\infty_{p,q} (i.e., it 
-;; determines if the convergence of the spectral sequence has been reached at 
-;; level r for the degree n). The list hmlg-cmpns contains the "components" of
-;; the homology group of the complex. It begins with m zeros if the free part of the
-;; group is Z^m and the rest of the list contains the torsion coefficients.
-;; (only for finitely generated complexes). 
-(defun eff-compare-spsq-with-homology (fltrcm r degr hmlg-cmpns)
-   (declare
-    (type filtered-chain-complex fltrcm)
-    (type fixnum r degr)
-    (type list hmlg-cmpns))
-   (let* ((min-max (flin-min-max fltrcm degr))
-          (min (first min-max))
-          (max (second min-max))
-          (spsq-cmpns
-           (mapcan
-           #'(lambda (p)
-               (declare (type fixnum p))
-               (let* ((q (- degr p)))
-                  (declare (type fixnum q))
-                  (second (eff-spsq-basis-dvs fltrcm r p q))))
-            (<a-b> min max)))
-          (mark2 hmlg-cmpns)
-          (hmlg-prdc 1)
-          (spsq-prdc 1))
-      (declare 
-        (type function spsq)
-        (type list spsq-cmpns mark2)
-        (type fixnum hmlg-prdc spsq-prdc))
-      (progn
-       (do ((mark1 spsq-cmpns (cdr mark1)))
-           ((endp mark1))
-          (declare (type list mark1))
-          (if (eql 0 (car mark1))
-             (if (not (eql 0 (car mark2)))
-                (return-from eff-compare-spsq-with-homology nil)
-                (pop mark2))
-             (setq spsq-prdc (* spsq-prdc (car mark1)))))
-       (do ((mark3 mark2 (cdr mark3)))
-           ((endp mark3))
-          (declare (type list mark3))
-          (setq hmlg-prdc (* hmlg-prdc (car mark3))))
-       (if (eql hmlg-prdc spsq-prdc)
-          't
-          nil))))
-   
-#|
-(homology fcc 5) 
-(eff-compare-spsq-with-homology fcc  1 5 '(2))
-(homology fcc 6)
-(eff-compare-spsq-with-homology fcc  1 6 '(2))
-|# 
-
-;; Function that determines the level r at which for degree n the E^r_{p,q} of the
-;; filtered complex fltrcm with p+q=degr are equal to E^\infty_{p,q} (i.e., it 
-;; determines the level r which the convergence of the spectral sequence has been 
-;; reached at for the degree n).            
-(defun eff-spsq-cnvg (fltrcm degr)
-   (declare 
-     (type filtered-chain-complex fltrcm)
-     (type fixnum degr))
-   (the fixnum
-     (let* ((hmlg-dvs-gnrs (homologie (chcm-mat fltrcm degr) (chcm-mat fltrcm (1+ degr))))
-            (hmlg-cmpns (reverse
-                         (mapcar
-                          #'(lambda (l)
-                              (first l))
-                          hmlg-dvs-gnrs)))
-            (cnvg-r 0))
-        (declare 
-          (list hmlg-dvs-gnrs hmlg-cmpns)
-          (type fixnum cnvg-r))
-        (do ((r 1 (1+ r)))
-            ((> cnvg-r 0))
-           (declare (type fixnum r))
-           (if (eff-compare-spsq-with-homology fltrcm r degr hmlg-cmpns)
-              (setq cnvg-r r)))
-        cnvg-r)))
-
-#|
-(eff-spsq-cnvg fcc 5)
-(eff-spsq-cnvg fcc 6)
-|# 
-
-;; EFFECTIVE HOMOLOGY
-
-
-;; Function that returns the order of filtration t (with regard to the filtration in the
-;; left complex, which is translated to the top and right ones) of the homotopy in the right reduction,
-;; which will determine the level r (=t+1) up to which the spectral sequences E^r_p,q 
-;; (with p+q=n) of the left and right complexes are isomorphic. This function can only be used
-;; when the top complex is effective (we need to obtain the elements in the basis of this complex). 
-(defun hmtp-eq-fltr-order (hmtp-eq degr)
-   (declare 
-     (type HOMOTOPY-EQUIVALENCE hmtp-eq)
-     (type fixnum degr))
-   (let* ((lcc (lbcc hmtp-eq))
-          (tcc (tcc hmtp-eq))
-          (lf (lf hmtp-eq))
-          (rh (rh hmtp-eq))
-          (max 0))
-      (declare
-       (type chain-complex lcc tcc)
-       (type morphism lf rh)
-       (type fixnum max))
-      (when (eq (basis tcc) :locally-effective)
-         (error "Hmtp-eq-fltr-order cannot work when the top complex of the homotopy equivalence
-             is a LOCALLY-EFFECTIVE chain complex."))
-      (mapcar 
-        #'(lambda (gnrt)
-            (declare (type gnrt gnrt))
-            (setq max (max max (- (flin lcc (lf hmtp-eq (rh hmtp-eq degr gnrt)))
-                        (flin lcc (lf hmtp-eq degr gnrt))))))
-        (basis tcc degr))
-      max))
-
-#|
-(setf hmtp-eq (efhm fcc)) ;; Trivial homotopy equivalence
-(hmtp-eq-fltr-order hmtp-eq 3)
-
-(setq k3 (k-z2 3))
-(Setq hmtp-eq3 (efhm k3))
-(setq ek3 (rbcc hmtp-eq3))
-(Change-Chcm-TO-Flcc ek3 :flin abar-flin :orgn `(filtered-chain-complex ,ek3))
-(setf k3-flin
-        #'(lambda (degr gnrt)
-            (flin ek3 (rf hmtp-eq3 (lg hmtp-eq3 degr gnrt)))))
-(Change-Chcm-TO-Flcc k3 :flin k3-flin :orgn `(filtered-chain-complex ,k3))
-(hmtp-eq-fltr-order hmtp-eq3 3)
-(hmtp-eq-fltr-order hmtp-eq3 5)
-|#
-
-;; Function that changes the right bottom chain complex in a homotopy equivalence into 
-;; a filtered complex, with a filtration defined translating the filtration in the left complex 
-;; (which must be a filtered complex). 
-(defun translate-filtration (hmtp-eq)
-   (declare
-    (type homotopy-equivalence hmtp-eq))
-   (let ((fltrcm (lbcc hmtp-eq))
-         (eff-chcm (rbcc hmtp-eq)))
-      (declare (type chain-complex fltrcm eff-chcm))
-      (Change-Chcm-TO-Flcc eff-chcm :flin
-                                 #'(lambda (degr gnrt)
-                                     (flin fltrcm (lf hmtp-eq (rg hmtp-eq degr gnrt))))
-                                 :orgn (orgn eff-chcm))))
-     
-  
- 
-;; Function that returns the representation basis-divisors of E^r_{p,q} for a filtered
-;; complex fltrcm with effective homology, computing the E^r_{p,q} of the effective complex
-;; in the right side of the homotopy equivalence. 
-;; If the effective complex is a filtered complex, we supose that both reductions in the equi-
-;; valence are compatible with the filtrations (f and g respect the filtration index and h has
-;; filtration order < r). If not, we define the filtration in the effective
-;; complex translating the filtration in the original filtered complex FltrCm, suposing that the 
-;; homotopy in the right side is compatible with the filtration in the left complex for such r (we 
-;; supose that flin(rh(lf(y)))-flin(lf(y))<r for every y in the top complex). 
-(defun spsq-basis-dvs (FltrCm r p q)
-   (declare 
-     (type filtered-chain-complex fltrcm)
-     (type fixnum r p q))
-   (let* ((hmtp-eq (efhm fltrcm))
-          (eff-chcm (rbcc hmtp-eq))
-          (degr (+ p q)))
-      (declare 
-        (type homotopy-equivalence hmtp-eq)
-        (type chain-complex eff-chcm)
-        (type fixnum degr))
-      (progn
-       (if (not (typep eff-chcm 'filtered-chain-complex))
-          (translate-filtration hmtp-eq))
-       (let ((spsq-list (eff-spsq-basis-dvs eff-chcm r p q)))
-          (declare (list spsq-list))
-          (if (eql fltrcm eff-chcm) spsq-list
-             (list
-              (mapcar
-               #'(lambda (cmbn)
-                   (lf hmtp-eq (rg hmtp-eq cmbn)))
-               (first spsq-list))
-              (second spsq-list)))))))
-
-#|
-(spsq-basis-dvs k3 2 2 2)
-|# 
-
-
-(defun spsq-gnrts (fltrcm r p q)
-   (declare
-    (type filtered-chain-complex fltrcm)
-    (type fixnum r p q))
-   (let* ((hmtp-eq (efhm fltrcm))
-          (eff-chcm (rbcc hmtp-eq))
-          (degr (+ p q)))
-      (declare
-       (type homotopy-equivalence hmtp-eq)
-       (type chain-complex eff-chcm)
-       (type fixnum degr))
-      (progn
-       (if (not (typep eff-chcm 'filtered-chain-complex))
-          (translate-filtration hmtp-eq))
-       (eff-spsq-gnrts eff-chcm r p q))))
-
-;; Function that presents on the screen the components of the E^r_{p,q}
-;; of the spectral sequence of a filtered complex fltrcm with effective homology.
-;; If the effective complex is a filtered complex, we supose that both reductions in the equi-
-;; valence are compatible with the filtrations (f and g respect the filtration index and h has
-;; filtration order < r). If not, we define the filtration in the effective
-;; complex translating the filtration in the original filtered complex FltrCm, suposing that the 
-;; homotopy in the right side is compatible with the filtration in the left complex for such r (we 
-;; supose that flin(rh(lf(y)))-flin(lf(y))<r for every y in the top complex). 
-(defun spsq-group (fltrcm r p q)
-   (declare
-    (type filtered-chain-complex fltrcm)
-    (type fixnum r p q))
-   (let* ((hmtp-eq (efhm fltrcm))
-          (eff-chcm (rbcc hmtp-eq))
-          (degr (+ p q)))
-      (declare
-       (type homotopy-equivalence hmtp-eq)
-       (type chain-complex eff-chcm)
-       (type fixnum degr))
-      (progn
-       (if (not (typep eff-chcm 'filtered-chain-complex))
-          (translate-filtration hmtp-eq))
-       (eff-spsq-group eff-chcm r p q))))
-
-;; Function that returns the list of integers which correspond to the coordinates
-;; on each of the components of E^r_{p-r,q+r-1} of the differential 
-;; d: E^r_{p,q} --> E^r_{p-r,q+r-1} applied to the element of E^r_{p,q}
-;; which has as coordinates the list int-list.
-(defun spsq-dffr (fltrcm r p q int-list)
-   (declare
-    (type filtered-chain-complex fltrcm)
-    (type fixnum p q r)
-    (type list int-list))
-   (let* ((hmtp-eq (efhm fltrcm))
-          (eff-chcm (rbcc hmtp-eq))
-          (degr (+ p q)))
-      (declare
-       (type homotopy-equivalence hmtp-eq)
-       (type chain-complex eff-chcm)
-       (type fixnum degr))
-      (progn
-       (if (not (typep eff-chcm 'filtered-chain-complex))
-          (translate-filtration hmtp-eq))
-       (eff-spsq-dffr eff-chcm r p q int-list))))
-   
-;; Function that determines the level r at which for degree n the E^r_{p,q} (with p+q=degr)
-;; of the filtered complex fltrcm (with effective homology) are equal to E^\infty_{p,q} (i.e., it 
-;; determines the level r which the convergence of the spectral sequence has been 
-;; reached at for the degree n).
-(defun spsq-cnvg (fltrcm degr)
-   (declare
-    (type filtered-chain-complex fltrcm)
-    (type fixnum degr))
-   (let* ((hmtp-eq (efhm fltrcm))
-          (eff-chcm (rbcc hmtp-eq)))
-      (declare
-       (type homotopy-equivalence hmtp-eq)
-       (type chain-complex eff-chcm)
-       (type fixnum degr))
-      (progn
-       (if (not (typep eff-chcm 'filtered-chain-complex))
-          (translate-filtration hmtp-eq))
-       (eff-spsq-cnvg eff-chcm degr))))
-
-
- 
-       
-          
-;; Homology filtration
-
-
-(defun homology-gnrt-list (chcm degr)
-     (declare (type cc chcm) (type fixnum degr))
-     (let ((src (cons :unused (basis chcm degr)))
-           (hom-dvs-gnrts (homologie (chcm-mat chcm degr) (chcm-mat chcm (1+ degr))))
-           (rslt nil))
-        (declare (type list src hom-dvs-gnrts rslt))
-        (mapcar #'(lambda (item)
-                    (declare (type list item))
-                    (let ((cmbn (cmbn degr))
-                          (cmpr (cmpr chcm)))
-                       (dolist (item2 (rest item))
-                          (declare (type cons item2))
-                          (setf cmbn (2cmbn-add cmpr cmbn (cmbn degr (car item2) (nth (cdr item2) src)))))
-                       cmbn))
-          hom-dvs-gnrts)))
-
-
-
-
-(defun homology-fltr1 (fltrcm degr fltr-index)
-   (declare
-    (type filtered-chain-complex fltrcm)
-    (type fixnum degr fltr-index))
-   (let* ((r (spsq-cnvg fltrcm degr))
-          (cmpr (cmpr1 fltrcm))
-          (total-basis (fltrd-basis fltrcm degr fltr-index))
-          (dffr-mtrx (FLTR-CHCM-Z-MTRX fltrcm r fltr-index (- degr fltr-index)))
-          (fltrt-basis 
-           (mapcan #'(lambda (p)
-                       (let* ((q (- degr p))
-                              (num-mtrx (spsq-num-mtrx fltrcm r p q))
-                              (den-mtrx (spsq-den-mtrx fltrcm r p q))
-                              (Z-gnrt-list (Fltr-Chcm-Z-Gnrt-List fltrcm r p q))
-                              (ss-basis-dvs (mtrx-quotient (copy-mtrx num-mtrx) den-mtrx))
-                              (ss-gnrt-list (first ss-basis-dvs))
-                              (ss-dvs (second ss-basis-dvs))
-                              (rslt nil))
-                          (declare 
-                            (type fcmpr cmpr)
-                            (type fixnum r q)
-                            (type list total-basis z-gnrt-list ss-basis-dvs ss-gnrt-list ss-dvs rslt)
-                            (type matrix num-mtrx den-mtrx))
-                          (labels ((2list-add (list1 list2)
-                                     (declare (type list list1 list2))
-                                     (the list
-                                       (mapcar #'+ list1 list2)))
-                                   (n-list (n list)
-                                     (declare
-                                       (type list list)
-                                       (type fixnum n))
-                                     (the list
-                                       (mapcar #'(lambda (i)
-                                                   (* n i))
-                                         list))))
-                            (do ((mark1 ss-gnrt-list (cdr mark1))
-                                 (mark2 ss-dvs (cdr mark2)))
-                                ((endp mark1))
-                               (declare (type list mark1 mark2))
-                               (if (not (eql 1 (car mark2)))
-                                  (let* ((selt (first mark1))
-                                         ;;(coord (cmbn-cffc-list selt total-basis cmpr))
-                                         (cmbn (cmbn degr)))
-                                     (progn
-                                       (let* ((selt-coord (vctr-coordinates selt num-mtrx)))
-                                          (declare (list selt-coord))
-                                          (do ((mark3 z-gnrt-list (cdr mark3))
-                                               (mark4 selt-coord (cdr mark4)))
-                                              ((endp mark3))
-                                             (declare (list mark3 mark4))
-                                             (if (not (eql 0 (car mark4)))
-                                                (setq cmbn (2cmbn-add cmpr cmbn (n-cmbn (car mark4)
-                                                                                  (funcall 
-                                                                                    #'(lambda (int-list)
-                                                                                        (declare (list int-list))
-                                                                                        (the cmbn
-                                                                                          (let* ((cmbn2 (cmbn degr)))
-                                                                                             (declare 
-                                                                                               (type cmbn 
-                                                                                                 cmbn2))
-                                                                                             (do ((
-                                                                                                   mark5 int-list (cdr 
-                                                                                                                    mark5))
-                                                                                                  (mark6 total-basis (cdr mark6)))
-                                                                                                 ((or (endp mark5) (endp mark6)))
-                                                                                                (declare (type list mark5 mark6))
-                                                                                                (if (not (= 0 (car mark5)))
-                                                                                                   (setq cmbn2 (2cmbn-add cmpr cmbn2 
-                                                                                                                 (cmbn degr (car 
-                                                                                                                              mark5) (car 
-                                                                                                                                       mark6))))))
-                                                               cmbn2)))
-                                                      (car mark3))))))))
-                                       (setf rslt (nconc rslt (list cmbn)))
-                                       rslt)))))))
-                          (<a-b> 0 fltr-index))))
-      (if (not (endp fltrt-basis))
-          (let ((fltrt-mtrx
-                  (gnrt-list-to-mtrx
-                    (mapcar #'(lambda (cmbn)
-                                (cmbn-cff-list cmbn total-basis cmpr))
-                      (fltrt-basis))))
-                (num-mtrx (mtrx-conc fltrt-mtrx dffr-mtrx)))
-             (mtrx-quotient num-mtrx dffr-mtrx))
-         nil)))
-
-
-
-(defun eff-hmlg-fltr (fltrcm degr p)
-   (declare
-     (type filtered-chain-complex fltrcm)
-     (type fixnum degr p))
-   (let* ((min-max-1 (flin-min-max fltrcm (1- degr)))
-          (min-1 (first min-max-1))
-          (max-1 (second min-max-1))
-          (min-max+1 (flin-min-max fltrcm (1+ degr)))
-          (min+1 (first min-max+1))
-          (max+1 (second min-max+1))
-          (r (1+ (- p min-1)))
-          (q (- degr p))
-          (Z-gnrts (Fltr-Chcm-Z-Gnrt-List FltrCm r p q))
-          (dffr-mtrx (FLTR-CHCM-Z-MTRX fltrcm (+ 2 (- degr min+1)) (1+ degr) 0))
-          (num-mtrx (mtrx-conc (gnrt-list-to-mtrx z-gnrts) dffr-mtrx))
-          (basis-divs (mtrx-quotient num-mtrx dffr-mtrx))
-          (divs (second basis-divs)))
-      (format t "Filtration F_~D H_~D" p degr)
-      (dolist (item divs)
-         (declare (type fixnum item))
-         (if (not (eql 1 item))
-            (progn
-             (format t "~2%Component Z")
-             (unless (zerop item) 
-                (format t "/~DZ" item))
-             )))))
-     
-
-(defun hmlg-fltr (fltrcm degr p)
-   (declare
-    (type filtered-chain-complex fltrcm)
-    (type fixnum degr))
-   (let* ((hmtp-eq (efhm fltrcm))
-          (eff-chcm (rbcc hmtp-eq)))
-      (declare
-       (type homotopy-equivalence hmtp-eq)
-       (type chain-complex eff-chcm)
-       (type fixnum degr))
-      (progn
-       (if (not (typep eff-chcm 'filtered-chain-complex))
-          (translate-filtration hmtp-eq))
-       (eff-hmlg-fltr eff-chcm degr p))))
-
-
-
-
-(DEFTYPE ss-type () '(member :serre :eilenberg-moore :filtration))
-         
-   
-
-(defclass OUTPUT-SPECTRAL-SEQUENCE ()
-    ((hmeq :type homotopy-equivalence :initarg hmeq :reader hmeq)
-     (eff-flin :type chcm-fltrindex :initarg eff-flin :reader eff-flin)
-     (bgn :type fixnum :initarg bgn :reader bgn)
-     ;; IDentification NuMber

-     (idnm :type fixnum :initform (incf *idnm-counter*) :reader idnm)

-     ;; ORiGiN

-     (orgn :type list :initarg :orgn :reader orgn)))
-
-
-(DEFVAR *oss-list*)
-(SETF *oss-list* +empty-list+)
-(PUSHNEW '*oss-list* *list-list*)
-
-(DEFMETHOD PRINT-OBJECT ((oss OUTPUT-SPECTRAL-SEQUENCE) stream)
-(the output-spectral-sequence
-   (progn
-      (format stream "[K~D output-spectral-sequence]" (idnm oss))
-     oss)))
-
-(DEFUN Oss (idnm)
-   (declare (type fixnum idnm))
-   (the (or OUTPUT-SPECTRAL-SEQUENCE null)
-      (find idnm *oss-list* :key #'idnm)))
-
-
-(DEFUN BUILD-oss (&key hmeq eff-flin bgn orgn)
-   (declare
-      (type homotopy-equivalence hmeq)
-      (type chcm-fltrindex eff-flin)
-      (type fixnum bgn)
-      (type list orgn))
-   (the output-spectral-sequence
-      (progn
-         (let ((already (find orgn *oss-list* :test #'equal :key #'orgn)))
-            (declare (type (or output-spectral-sequence null) already))
-            (when already
-               (return-from build-oss already)))
-         (let ((oss (make-instance 'output-spectral-sequence
-                        :hmeq hmeq
-                        :eff-flin eff-flin
-                        :bgn bgn
-                        :orgn orgn)))
-            (declare (type output-spectral-sequence oss))
-            (push oss *oss-list*)
-            oss))))
-     
-;;(defun serre-ss (fibration)
-
-#|(defun serre-ss (f)
-   (declare (type fibration f))
-   (let* ((X (fibration-total f))
-          (hmeq (efhm X))
-          (eX (rbcc efhm))
-|#
\ No newline at end of file
diff --git a/examples/anromero/suspended-classifying-spaces-lisp-files/OMparsers.cl b/examples/anromero/suspended-classifying-spaces-lisp-files/OMparsers.cl
deleted file mode 100644
index eca59cd..0000000
--- a/examples/anromero/suspended-classifying-spaces-lisp-files/OMparsers.cl
+++ /dev/null
@@ -1,469 +0,0 @@
-(in-package :user)
-
-
-
-
-(defun OMgetNextLabel (s)
-   (let* ((p1 (search "<" s)))
-      (delete-if #'(lambda (item) t) s :start 0 :end p1)
-          (let ((p1 (search "<" s))
-                (p2 (if (search " " s) (min (search ">" s) (search " " s))
-                      (search ">" s) )))
-      (subseq s (1+ p1) p2))))
-
-(defun OMgetNextSymbol (s)
-   (let* ((p1 (search "cd=" s))
-          (p2 (search "name=" s))
-          (p3 (search "/>" s))
-          (rslt1 (subseq s (+ 3 p1) p2))
-          (rslt2 (subseq s (+ 5 p2) p3))
-          )
-         (OMLispSymbol (list (delete #\" (delete #\space rslt1)) (delete #\" (delete #\space rslt2))))
-         ))
-
-(defun OMparseNextInteger (s)
-   (if (not (equal (OMgetNextLabel s) "OMI"))
-      (error "The next token is not an integer")
-      (let* ((p1 (search "<OMI>" s))
-             (p2 (search "</OMI>" s))
-             (rslt (parse-integer (subseq s (+ 5 p1) p2))))
-         (delete-if #'(lambda (item) t) s :start 0 :end (+ 6 p2))
-         rslt
-         )))
-
-(defun OMparseNextString (s)
-   (if (not (equal (OMgetNextLabel s) "OMSTR"))
-      (error "The next token is not a string")
-      (let* ((p1 (search "<OMSTR>" s))
-             (p2 (search "</OMSTR>" s))
-             (rslt (subseq s (+ 7 p1) p2)))
-         (delete-if #'(lambda (item) t) s :start 0 :end (+ 8 p2))
-         rslt
-         )))
-
-(defun OMparseNextVar (s)
-   (if (not (equal (OMgetNextLabel s) "OMV"))
-      (error "The next token is not a variable")
-      (let* ((p1 (search "<OMV>" s))
-             (p2 (search "</OMV>" s))
-             (rslt (intern (subseq s (+ 5 p1) p2))))
-         (delete-if #'(lambda (item) t) s :start 0 :end (+ 6 p2))
-         rslt
-         )))
-
-(defun OMparseNextSymbol (s)
-   (if (not (equal (OMgetNextLabel s) "OMS"))
-      (error "The next token is not a symbol")
-      (let* ((rslt (OMgetNextSymbol s))
-             (p (search "/>" s))
-             )
-         (delete-if #'(lambda (item) t) s :start 0 :end (+ 2 p))
-         rslt
-         )))
-  
-(DEFTYPE direct-symbol () '(member list cyclicgroup symmetricgroup))
-
-
-(defun OMLispSymbol (list)
-   (let ((cd (first list))
-         (name (second list)))
-      (if (equal cd "list1")
-         (if (equal name "list")
-            'list)
-         (if (equal cd "resolutions")
-            (if (equal name "zgcombination")
-               "zgcombination"
-               (if (equal name "zgterm")
-                  "zgterm"
-                  (if (equal name "zggnrt")
-                     "zggnrt"
-                     (if (equal name "resolution")
-                        "resolution"))))
-            (if (equal cd "group1")
-               (if (equal name "cyclic_group")
-                   'cyclicgroup
-                 (if (equal name "symmetric_group")
-                     'symmetricgroup)
-                 )
-              )))))
-
-(defun OMparseNextApplication (s)
-   (if (not (equal (OMgetNextLabel s) "OMA"))
-      (error "The next token is not an application")
-      (let* ((p1 (search "<OMA>" s)))
-         (delete-if #'(lambda (item) t) s :start 0 :end (+ 5 p1))
-         (let ((head (if (equal (OMgetNextLabel s) "OMS")
-                        (OMparseNextSymbol s)
-                        (OMparseNextObject s)))
-               (rest nil))
-            (if (typep head 'direct-symbol)
-               (do ((rest nil  (append rest (list nextobj))))
-                   ((equal (OMgetNextLabel s) "/OMA") (let ((p (search "</OMA>" s)))
-                                                         (delete-if #'(lambda (item) t) s :start 0 :end (+ 6 p1))
-                                                         (eval (append (list head) rest))))
-                  (setf nextobj (OMparseNextObject s))
-                  )
-               (if (equal head "resolution")
-                  (OMparseResolution s)
-                  (error "imposible to parse")
-            ))))))
-         
-         
-         
-           
-(defun OMparseNextObject (s)
-   (progn 
-     (if (equal (OMgetNextLabel s) "OMOBJ")
-        (delete-if #'(lambda (item) t) s :start 0 :end (+ 7 (search "<OMOBJ>" s))))
-   
-     (if (equal (subseq (OMgetNextLabel s) 0 3) "!--")
-        (delete-if #'(lambda (item) t) s :start 0 :end (+ 4 (search "--/>" s))))
-      
-     (let ((rslt
-            (if (equal (OMgetNextLabel s) "OMI")
-               (OMparseNextInteger s)
-               (if (equal (OMgetNextLabel s) "OMSTR")
-                  (OMparseNextString s)
-                  (if (equal (OMgetNextLabel s) "OMV")
-                     (OMparseNextVar s)
-                     (if (equal (OMgetNextLabel s) "OMS")
-                        (OMLispSymbol(OMparseNextSymbol s))
-                        (if (equal (OMgetNextLabel s) "OMA")
-                           (OMparseNextApplication s)
-                           (error "imposible to parse"))))))))
-        (progn
-         (if (and (not (equal s "")) (equal (OMgetNextLabel s) "/OMOBJ"))
-            (delete-if #'(lambda (item) t) s :start 0 :end (+ 8 (search "</OMOBJ>" s))))
-         rslt))))
-
-
-
-   
-
-
-(defun OMparseZggnrt (s grbasis zgbasis-degr)
-   (if (not (equal (OMgetNextLabel s) "OMA"))
-      (error "The next label is not an application")
-      (progn 
-        (delete-if #'(lambda (item) t) s :start 0 :end (+ 5 (search "<OMA>" s)))
-        (if (not (equal (OMgetNextSymbol s) "zggnrt"))
-           (error "This is not specified as a zggnrt")
-           (progn 
-             (OMparseNextSymbol s)
-             (let* ((i1 (OMparseNextInteger s))
-                    (i2 (OMparseNextInteger s)))
-                (delete-if #'(lambda (item) t) s :start 0 :end (+ 6 (search "</OMA>" s)))
-                (zggnrt (nth (1- i1) grbasis) (nth (1- i2) zgbasis-degr))))))))
-
-
-(defun OMparseZgterm (s degr grbasis zgbasis)
-   (if (not (equal (OMgetNextLabel s) "OMA"))
-      (error "The next label is not an application")
-      (progn 
-        (delete-if #'(lambda (item) t) s :start 0 :end (+ 5 (search "<OMA>" s)))
-        (if (not (equal (OMgetNextSymbol s) "zgterm"))
-           (error "This is not specified as a zgterm")
-           (progn 
-             (OMparseNextSymbol s)
-             (let* ((coeff (OMparseNextInteger s))
-                    (zggnrt (OMparseZggnrt s grbasis (funcall zgbasis degr))))
-                (delete-if #'(lambda (item) t) s :start 0 :end (+ 6 (search "</OMA>" s)))
-                (term-cmbn degr coeff zggnrt )))))))
-
-(defun OMparseZgcmbn (s degr grbasis grcmpr zgbasis zgcmpr)
-   (if (equal (subseq (OMgetNextLabel s) 0 3) "!--")
-      (delete-if #'(lambda (item) t) s :start 0 :end (+ 4 (search "--/>" s))))
-   (if (not (equal (OMgetNextLabel s) "OMA"))
-      (error "The next label is not an application")
-      (progn 
-        (delete-if #'(lambda (item) t) s :start 0 :end (+ 5 (search "<OMA>" s)))
-        (if (not (equal (OMgetNextSymbol s) "zgcombination"))
-           (error "This is not specified as a zgcombination")
-           (progn 
-             (OMparseNextSymbol s)
-             (let ((cmbn-list nil))
-                (do ((term-list nil  (push  (cons 1 nexttermcmbn) term-list)))
-                   ((equal (OMgetNextLabel s) "/OMA") (setf cmbn-list term-list) )
-                  (setf nexttermcmbn (OMparseZgterm s degr grbasis zgbasis))
-                  )
-                (delete-if #'(lambda (item) t) s :start 0 :end (+ 6 (search "</OMA>" s)))
-                (if cmbn-list
-                   (cmbn-cmbn (zggnrt-cmpr grcmpr zgcmpr) cmbn-list)
-                   (zero-cmbn degr))))))))
-
-(defun OMparseZgboundaryList (s grbasis grcmpr zgbasis zgcmpr maxdegr)
-   (if (equal (subseq (OMgetNextLabel s) 0 3) "!--")
-      (delete-if #'(lambda (item) t) s :start 0 :end (+ 4 (search "--/>" s))))
-   (if (not (equal (OMgetNextLabel s) "OMA"))
-      (error "The next label is not an application")
-      (progn 
-        (delete-if #'(lambda (item) t) s :start 0 :end (+ 5 (search "<OMA>" s)))
-        (if (not (equal (OMgetNextSymbol s) 'list))
-           (error "This is not specified as a list")
-           (progn 
-             (OMparseNextSymbol s)
-             (let ((rslt nil))
-                (dotimes (i maxdegr)
-                   (if (equal (subseq (OMgetNextLabel s) 0 3) "!--")
-                      (delete-if #'(lambda (item) t) s :start 0 :end (+ 4 (search "--/>" s))))
-                   (if (not (equal (OMgetNextLabel s) "OMA"))
-                      (error "The next label is not an application")
-                      (progn 
-                        (delete-if #'(lambda (item) t) s :start 0 :end (+ 5 (search "<OMA>" s)))
-                        (if (not (equal (OMgetNextSymbol s) 'list))
-                           (error "This is not specified as a list")
-                           (progn 
-                             (OMparseNextSymbol s)
-                             (let ((rslt-i nil))
-                                (do ((aux nil (push cmbn aux)))
-                                    ((equal (OMgetNextLabel s) "/OMA") (setf rslt-i aux))
-                                   (setf cmbn (OMparseZgcmbn s i grbasis grcmpr zgbasis zgcmpr)))
-                                (delete-if #'(lambda (item) t) s :start 0 :end (+ 6 (search "</OMA>" s)))
-                                (push (nreverse rslt-i) rslt)))))))
-                (delete-if #'(lambda (item) t) s :start 0 :end (+ 6 (search "</OMA>" s)))
-                (nreverse rslt)))))))
-                   
-
-(defun OMparseContractinghmtpList (s grbasis grcmpr zgbasis zgcmpr maxdegr)
-   (if (equal (subseq (OMgetNextLabel s) 0 3) "!--")
-      (delete-if #'(lambda (item) t) s :start 0 :end (+ 4 (search "--/>" s))))
-   (if (not (equal (OMgetNextLabel s) "OMA"))
-      (error "The next label is not an application")
-      (progn 
-        (delete-if #'(lambda (item) t) s :start 0 :end (+ 5 (search "<OMA>" s)))
-        (if (not (equal (OMgetNextSymbol s) 'list))
-           (error "This is not specified as a list")
-           (progn 
-             (OMparseNextSymbol s)
-             (let ((rslt nil))
-                (dotimes (i (1- maxdegr))
-                   (if (equal (subseq (OMgetNextLabel s) 0 3) "!--")
-                      (delete-if #'(lambda (item) t) s :start 0 :end (+ 4 (search "--/>" s))))
-                   (if (not (equal (OMgetNextLabel s) "OMA"))
-                      (error "The next label is not an application")
-                      (progn 
-                        (delete-if #'(lambda (item) t) s :start 0 :end (+ 5 (search "<OMA>" s)))
-                        (if (not (equal (OMgetNextSymbol s) 'list))
-                           (error "This is not specified as a list")
-                           (progn 
-                             (OMparseNextSymbol s)
-                             (let ((rslt-i nil))
-                                (do ((mark1 (funcall zgbasis i) (cdr mark1)))
-                                    ((endp mark1) (push (nreverse rslt-i) rslt))
-                                  (progn
-                                    (if (equal (subseq (OMgetNextLabel s) 0 3) "!--")
-                                       (delete-if #'(lambda (item) t) s :start 0 :end (+ 4 (search "--/>" s))))
-                                   (if (not (equal (OMgetNextLabel s) "OMA"))
-                                      (error "The next label is not an application")
-                                      (progn 
-                                        (delete-if #'(lambda (item) t) s :start 0 :end (+ 5 (search "<OMA>" s)))
-                                        (if (not (equal (OMgetNextSymbol s) 'list))
-                                           (error "This is not specified as a list")
-                                           (progn 
-                                             (OMparseNextSymbol s)
-                                             (let ((rslt-i-g nil))
-                                                
-                                                (do ((mark2 grbasis (cdr mark2)))
-                                                    ((endp mark2) (push (nreverse rslt-i-g) rslt-i))
-                                                   (setf cmbn (OMparseZgcmbn s (1+ i) grbasis grcmpr zgbasis zgcmpr))
-                                                   (push cmbn rslt-i-g))
-                                                (delete-if #'(lambda (item) t) s :start 0 :end (+ 6 (search "</OMA>" s)))
-                                                )))))))
-                                (delete-if #'(lambda (item) t) s :start 0 :end (+ 6 (search "</OMA>" s)))
-                                ))))))
-                (delete-if #'(lambda (item) t) s :start 0 :end (+ 6 (search "</OMA>" s)))
-                (nreverse rslt)))))))
-
-
-
-(defun OMrsltnZgbasis (rank-list maxdegr)
-   (flet ((rslt (degr)
-            (declare (fixnum degr))
-            (if (> degr maxdegr) (error "unknown basis for this degree")
-               (if (< degr 0) nil
-                  (let ((rank (nth degr rank-list))
-                        (list nil))
-                     (dotimes (i rank)
-                        (push (concatenate 'string "g" (Write-to-string degr) (Write-to-string (1+ i))) list))
-                     (nreverse list))))))
-     
-     (the basis #'rslt)))
-
-(defun OMrsltnZgboundary-intr (Zgboundary-list zgbasis maxdegr)
-   (flet ((rslt (degr gnrt)
-            (declare (fixnum degr) (type gnrt gnrt))
-            (if (> degr maxdegr) (error "unknown basis for this degree")
-               (if (< degr 1) (zero-cmbn (1- degr))
-                  (nth (position gnrt (funcall zgbasis degr)  :test #'equal) (nth (1- degr) Zgboundary-list))))))
-          (the intr-mrph #'rslt)))
-
-(defun OMrsltnCntrHmtp-intr (Zgcontractinghmtp-list zgbasis grbasis maxdegr)
-   (flet ((rslt (degr zggnrt)
-            (declare (fixnum degr) (type zggnrt zggnrt))
-            (if (> degr (1- maxdegr)) (error "unknown basis for this degree")
-               (with-zggnrt (gnrt1 gnrt2) zggnrt
-                 (let ((gnrt1-pos (position gnrt1 grbasis :test #'equal))
-                       (gnrt2-pos (position gnrt2 (funcall zgbasis degr) :test #'equal)))
-                    (nth gnrt1-pos (nth gnrt2-pos (nth degr Zgcontractinghmtp-list))))))))
-               (the intr-mrph #'rslt)))
-
-
-
-                             
-                             
-(defun OMparseResolution (s)
-   ;;(if (not (equal (OMgetNextLabel s) "OMA"))
-    ;;  (error "The next label is not an application")
-    ;;  (progn 
-    ;;    (delete-if #'(lambda (item) t) s :start 0 :end (+ 5 (search "<OMA>" s)))
-    ;;    (if (not (equal (OMgetNextSymbol s) "resolution"))
-    ;;       (error "This is not specified as a resolution")
-    ;;       (progn 
-    ;;         (OMparseNextSymbol s)
-             (let* ((group (OMparseNextObject s))
-                    (maxdegr (OMparseNextObject s))
-                    (rank-list (OMparseNextObject s))
-                    (zgbasis (OMrsltnZgbasis rank-list maxdegr)))
-                (with-slots ((grcmpr cmpr) (grbasis elements) nullel) group
-                  (let* ((zgboundary-list (OMparseZgboundaryList s grbasis grcmpr zgbasis #'s-cmpr maxdegr))
-                         (cntrchmtp-list (OMparseContractinghmtpList s grbasis grcmpr zgbasis #'s-cmpr maxdegr))
-                         (zgchcm (BUILD-ZGCHCM :group group :zgcmpr #'s-cmpr :zgbasis zgbasis :zgbsgn "g00" 
-                                   :intr-zgbndr (OMrsltnZgboundary-intr Zgboundary-list zgbasis maxdegr)
-                                   :zgbndr-strt :gnrt :orgn  `(ZG-Chain complex for ,group obtained from HAP)))
-                         (cmpr (cmpr1 zgchcm))
-                         (f-intr #'(lambda (degr zggnrt)
-                                     (if (zerop degr) (cmbn degr 1 :zgnrt) (zero-cmbn degr))))
-                         (g-intr #'(lambda (degr gnrt)
-                                     (if (zerop degr) (cmbn degr 1 (zggnrt nullel "g01")) (zero-cmbn degr))))
-                         (h-intr (OMrsltnCntrHmtp-intr cntrchmtp-list zgbasis grbasis maxdegr))
-
-                         (f (build-mrph :sorc zgchcm :trgt (z-chcm) :degr 0 :intr f-intr :strt :gnrt :orgn `(f-mrph for ,group obtained from HAP)))
-                         (g (build-mrph :sorc (z-chcm) :trgt zgchcm :degr 0 :intr g-intr :strt :gnrt :orgn  `(g-mrph for ,group obtained from HAP)))
-                         (h (build-mrph :sorc zgchcm :trgt zgchcm :degr 1 :intr h-intr :strt :gnrt :orgn `(h-mrph for ,group obtained from HAP))))
-                     (delete-if #'(lambda (item) t) s :start 0 :end (+ 6 (search "</OMA>" s)))
-                     (build-rdct :f f :g g :h h :orgn `(Resolution of ,group obtained from HAP))))))
-;;;))))
-                       
-(defun FileToString (FileName)
-     (with-open-file (f FileName :direction :input)
-       (labels ((getString (f s)
-                 (let* ((aux (read-line f nil 'EOF)))
-                    (if (not (string= aux 'EOF))
-                       (getString f (concatenate 'string s (if (not (string= s "")) (format nil "~%")) aux)) 
-                       s))))
-       (getString f ""))))
-
-                             
-
-#|
-
-
-
-   
-
-(cat-init)
-(load "omparsers.lisp")
-(setf s (filetostring "resolution.log")) 
-(setf rsltn1 (OmparseNextObject s))
-(setf group (group1 (tcc rsltn1)))
-(setf (slot-value group 'resolution) rsltn1)
-(setf k-g-1 (k-g-1 group))
-(setf k-g-2 (k-g group 2))
-(setf k-g-3 (k-g group 3))
-
-(homology k-g-1 0 6)
-(homology k-g-2 0 6)
-(homology k-g-3 0 6)
-
-
-
-(if (equal (OMgetNextLabel s) "OMOBJ")
-        (delete-if #'(lambda (item) t) s :start 0 :end (+ 7 (search "<OMOBJ>" s))))
-   
-     (if (equal (subseq (OMgetNextLabel s) 0 3) "!--")
-        (delete-if #'(lambda (item) t) s :start 0 :end (+ 4 (search "--/>" s))))
-
-
-(if (not (equal (OMgetNextLabel s) "OMA"))
-      (error "The next label is not an application"))
-(delete-if #'(lambda (item) t) s :start 0 :end (+ 5 (search "<OMA>" s)))
-(if (not (equal (OMgetNextSymbol s) "resolution"))
-   (error "This is not specified as a resolution"))
-
-(OMparseNextSymbol s)
-
-(setf group (OMparseNextObject s))
-(setf maxdegr (OMparseNextObject s))
-(setf rank-list (OMparseNextObject s))
-(setf zgbasis (OMrsltnZgbasis rank-list maxdegr))
-
-(setf grcmpr (cmpr1 group) grbasis (elements group) nullel (nullel group))
-(setf zgcmpr #'s-cmpr)
-(setf zgboundary-list (OMparseZgboundaryList s grbasis grcmpr zgbasis #'s-cmpr maxdegr))
-;;(setf cntrchmtp-list (OMparseContractinghmtpList s grbasis grcmpr zgbasis #'s-cmpr maxdegr))                                  
-                         
-(if (not (equal (OMgetNextLabel s) "OMA"))
-      (error "The next label is not an application"))
-
-(delete-if #'(lambda (item) t) s :start 0 :end (+ 5 (search "<OMA>" s)))
-
-(if (not (equal (OMgetNextSymbol s) 'list))
-           (error "This is not specified as a list"))
-(OMparseNextSymbol s)
-
-(setf rslt nil)
-
-(setf i 0)
-(if (not (equal (OMgetNextLabel s) "OMA"))
-                      (error "The next label is not an application"))
-(delete-if #'(lambda (item) t) s :start 0 :end (+ 5 (search "<OMA>" s)))
-(OMparseNextSymbol s)
-(setf rslt-i nil)  
-
-(setf mark1 zgbasis)
-
-
-                (dotimes (i maxdegr)
-                   (if (not (equal (OMgetNextLabel s) "OMA"))
-                      (error "The next label is not an application")
-                      (progn 
-                        (delete-if #'(lambda (item) t) s :start 0 :end (+ 5 (search "<OMA>" s)))
-                        (if (not (equal (OMgetNextSymbol s) 'list))
-                           (error "This is not specified as a list")
-                           (progn 
-                             (OMparseNextSymbol s)
-                             (let ((rslt-i nil))
-                                (do ((mark1 (funcall zgbasis (1+ i)) (cdr mark1)))
-                                    ((endp mark1) (push rslt-i rslt))
-                                    
-                                   (if (not (equal (OMgetNextLabel s) "OMA"))
-                                      (error "The next label is not an application")
-                                      (progn 
-                                        (delete-if #'(lambda (item) t) s :start 0 :end (+ 5 (search "<OMA>" s)))
-                                        (if (not (equal (OMgetNextSymbol s) 'list))
-                                           (error "This is not specified as a list")
-                                           (progn 
-                                             (OMparseNextSymbol s)
-                                             (let ((rslt-i-g nil))
-                                                
-                                                (do ((mark2 grbasis (cdr mark2)))
-                                                    ((endp mark2) (push rslt-i-g rslt-i))
-                                                   (setf cmbn (OMparseZgcmbn s (1+ i) grbasis grcmpr zgbasis zgcmpr))
-                                                   (push cmbn rslt-i-g))
-                                                (delete-if #'(lambda (item) t) s :start 0 :end (+ 6 (search "</OMA>" s)))
-                                                ))))))
-                                (delete-if #'(lambda (item) t) s :start 0 :end (+ 6 (search "</OMA>" s)))
-                                ))))))
-                (delete-if #'(lambda (item) t) s :start 0 :end (+ 6 (search "</OMA>" s)))
-                rslt)))))
-
-
-
-|# 
-
-
-
-
-
-
-
diff --git a/examples/anromero/suspended-classifying-spaces-lisp-files/cylinders.cl b/examples/anromero/suspended-classifying-spaces-lisp-files/cylinders.cl
deleted file mode 100644
index 73d8b3c..0000000
--- a/examples/anromero/suspended-classifying-spaces-lisp-files/cylinders.cl
+++ /dev/null
@@ -1,454 +0,0 @@
-;;;  CYLIDERS  CYLIDERS  CYLIDERS  CYLIDERS  CYLIDERS  CYLIDERS  CYLIDERS  
-;;;  CYLIDERS  CYLIDERS  CYLIDERS  CYLIDERS  CYLIDERS  CYLIDERS  CYLIDERS 
-;;;  CYLIDERS  CYLIDERS  CYLIDERS  CYLIDERS  CYLIDERS  CYLIDERS  CYLIDERS 
-
-(IN-PACKAGE "COMMON-LISP-USER")
-
-(PROVIDE "CYCLINDERS")
-
-
-;; MACROS
-
-(DEFMACRO CYLNX (CYLN)
-   `(car ,CYLN))
-
-(DEFMACRO ICYLN (CYLN)
-   `(cdr ,CYLN))
-
-(DEFMACRO CYLNA1 (gnrt)
-   `(cons :CYLNA1 ,gnrt))
-
-(DEFMACRO CYLNB (gnrt)
-   `(cons :CYLNB ,gnrt))
-
-(DEFMACRO CYLNA2 (gnrt)
-   `(cons :CYLNA2 ,gnrt))
-
-(DEFMACRO WITH-CYLN ((CYLNx iCYLN) CYLN . body)
-   `(let ((,CYLNx (CYLNx ,CYLN))
-          (,iCYLN (iCYLN ,CYLN)))
-       (declare
-          (type (member :CYLNA1 :CYLNB :CYLNA2) ,CYLNx)
-          (type gnrt ,iCYLN))
-       ,@body))
-
-
-(DEFUN DISPATCH-CYLN-CMBN (cmbn)
-   (declare (type cmbn cmbn))
-   (the (values cmbn cmbn cmbn)
-      (with-cmbn (degr list) cmbn
-         (let ((listA1 +empty-list+)
-               (listB +empty-list+)
-               (listA2 +empty-list+))
-            (declare (list listA1 listB listA2))
-            (dolist (term list)
-               (declare (type term term))
-               (with-term (cffc cyln) term
-                  (with-cyln (cylnx icyln) cyln
-                     (ecase cylnx
-                        (:cylnA1 (push (term cffc icyln) listA1))
-                        (:cylnB (push (term cffc icyln) listB))
-                        (:cylnA2 (push (term cffc icyln) listA2))))))
-            (values
-               (make-cmbn :degr (1- degr) :list (nreverse listA1))
-               (make-cmbn :degr degr :list (nreverse listB))
-               (make-cmbn :degr degr :list (nreverse listA2)))))))
-
-#|
-  (dispatch-CYLN-cmbn (cmbn 3 3 (cylnA1 'a11) 4 (cylnA1 'a12) 33 (cylnB 'b) 333 (cylnA2 'a2)))
-|#
-
-(DEFUN CYLN-CMBN-CMBNA1 (cmbn)
-   (declare (type cmbn cmbn))
-   (the cmbn
-      (with-cmbn (degr list) cmbn
-         (make-cmbn :degr (1- degr)
-            :list (do ((rslt +empty-list+)
-                       (mark list (cdr mark)))
-                      ((endp mark) (nreverse rslt))
-                     (declare (list rslt mark))
-                     (with--term (cffc CYLN) mark
-                     (with-CYLN (CYLNx gnrtA1) CYLN
-                        (if (eq CYLNx :CYLNA1)
-                           (push (term cffc gnrtA1) rslt)
-                           (return (nreverse rslt))))))))))
-
-(DEFUN CYLN-CMBN-CMBNB (cmbn)
-   (declare (type cmbn cmbn))
-   (the cmbn
-      (with-cmbn (degr list) cmbn
-         (make-cmbn :degr degr
-            :list (do ((rslt +empty-list+)
-                       (mark (member :CYLNb list :key #'cadr) (cdr mark)))
-                      ((endp mark) (nreverse rslt))
-                     (declare (list rslt mark))
-                     (with--term (cffc CYLN) mark
-                     (with-CYLN (CYLNx gnrtB) CYLN
-                        (if (eq CYLNx :CYLNB)
-                           (push (term cffc gnrtB) rslt)
-                           (return (nreverse rslt))))))))))
-
-(DEFUN CYLN-CMBN-CMBNA2 (cmbn)
-   (declare (type cmbn cmbn))
-   (the cmbn
-      (with-cmbn (degr list) cmbn
-         (make-cmbn :degr degr
-            :list (mapcar
-                     #'(lambda (term)
-                          (declare (type term term))
-                          (with-term (cffc CYLN) term
-                             (term cffc (iCYLN CYLN))))
-                     (member :CYLNA2 list :key #'cadr))))))
-
-#|
- 
-  (CYLN-cmbn-cmbnA1 (cmbn 3 1 (CYLNA1 'a) 2 (CYLNB 'b)))
-  (CYLN-cmbn-cmbnA1 (cmbn 3 2 (CYLNB 'b)))
-  (CYLN-cmbn-cmbnB (cmbn 3 1 (CYLNA1 'a) 2 (CYLNB 'b) 3 (CYLNA2 'c)))
-  (CYLN-cmbn-cmbnB (cmbn 3 1 (CYLNA1 'a) 3 (CYLNA2 'c)))
-  (CYLN-cmbn-cmbnA2 (cmbn 3 1 (CYLNA1 'a) 2 (CYLNB 'b) 3 (CYLNA2 'c)))
-  (CYLN-cmbn-cmbnA2 (cmbn 3 2 (CYLNA1 'b)))
-|#
-
-(DEFUN MAKE-CYLN-CMBN (cmbnA1 cmbnB cmbnA2)
-   (declare (type cmbn cmbnA1 cmbnB cmbnA2))
-   (the cmbn
-      (with-cmbn (degrA1 listA1) cmbnA1
-      (with-cmbn (degrB listB) cmbnB
-      (with-cmbn (degrA2 listA2) cmbnA2
-         (unless (= (1+ degrA1) degrB degrA2)
-            (error "In MAKE-CYLN-CMBN, the degrees are not coherent."))
-         (make-cmbn :degr degrB
-            :list (nconc
-                     (mapcar #'(lambda (termA1)
-                                  (declare (type term termA1))
-                                  (with-term (cffc gnrtA1) termA1
-                                     (term cffc (CYLNA1 gnrtA1))))
-                        listA1)
-                     (mapcar #'(lambda (termB)
-                                  (declare (type term termB))
-                                  (with-term (cffc gnrtB) termB
-                                     (term cffc (CYLNB gnrtB))))
-                        listB)
-                     (mapcar #'(lambda (termA2)
-                                  (declare (type term termA2))
-                                  (with-term (cffc gnrtA2) termA2
-                                     (term cffc (CYLNA2 gnrtA2))))
-                        listA2))))))))
-
-#|
-  (multiple-value-call #'make-CYLN-cmbn 
-     (dispatch-CYLN-cmbn (cmbn 3 3 (CYLNA1 'A11) 4 (CYLNA1 'A12) 33 (CYLNB 'B) 333 (CYLNA2 'A2))))
-|#
-
-(DEFMETHOD PRINT-KEYCONS ((car (eql :CYLNA1)) cdr stream)
-   (declare
-      (type gnrt cdr)
-      (stream stream))
-   (the (eql t)
-      (progn
-         (format stream "<CylnA1 ~A>" cdr)
-         t)))
-
-(DEFMETHOD PRINT-KEYCONS ((car (eql :CYLNB)) cdr stream)
-   (declare
-      (type gnrt cdr)
-      (stream stream))
-   (the (eql t)
-      (progn
-         (format stream "<CylnB ~A>" cdr)
-         t)))
-
-(DEFMETHOD PRINT-KEYCONS ((car (eql :CYLNA2)) cdr stream)
-   (declare
-      (type gnrt cdr)
-      (stream stream))
-   (the (eql t)
-      (progn
-         (format stream "<CylnA2 ~A>" cdr)
-         t)))
-
-#|
-  (CYLNa1 'a)
-  (CYLNB 'b)
-  (CYLNA2 'c)
-|#
-
-(DEFUN cylnX-CMPR (s1 s2)
-   (declare (symbol s1 s2))
-   (the cmpr
-      (if (string= s1 s2) :equal
-         (if (string= s1 :cylnA1) :less
-            (if (string= s2 :cylnA1) :greater
-               (if (string= s1 :cylnB) :less
-                  :greater))))))
-         
-
-(DEFUN CYLINDER-CMPR (cmprA cmprB)
-   (declare (type cmprf cmpra cmprb))
-   (flet ((rslt (cyln1 cyln2)
-             (declare (type cyln cyln1 cyln2))
-             (let ((cylnx1 (cylnx cyln1)))
-                (declare (type (member :cylnA1 :cylnB :cylnA2) cylnx))
-                (lexico
-                   (cylnX-CMPR cylnx1 (cylnx cyln2))
-                   (case cylnx1
-                      (:cylnA1 (funcall cmprA (icyln cyln1) (icyln cyln2)))
-                      (:cylnB (funcall cmprB (icyln cyln1) (icyln cyln2)))
-                      (:cylnA2 (funcall cmprA (icyln cyln1) (icyln cyln2))))))))
-      (the cmprf #'rslt)))
-
-#|
-  (setf r (cylinder-cmpr #'f-cmpr #'f-cmpr ))
-  (funcall r (cylnA1 1) (cylnB 0))
-  (funcall r (cylnA1 1) (cylnA1 2))
-  (funcall r (cylnB 0) (cylnA1 1))
-  (funcall r (cylnA1 2) (cylnA1 1)) 
-|#
-
-(DEFUN CYLINDER-BASIS (basisA basisB)
-   (declare (type basis basisA basisB))
-   (the basis
-      (if (or (eq :locally-effective basisA)
-              (eq :locally-effective basisB)
-              )
-         :locally-effective
-         (flet ((rslt (degr)
-                   (declare (fixnum degr))
-                   (append
-                      (mapcar #'(lambda (item)
-                                   (declare (type gnrt item))
-                                   (cylnA1 item))
-                         (funcall basisA (1- degr)))
-                      (mapcar #'(lambda (item)
-                                   (declare (type gnrt item))
-                                   (cylnB item))
-                         (funcall basisB degr))
-                      (mapcar #'(lambda (item)
-                                   (declare (type gnrt item))
-                                   (cylnA2 item))
-                         (funcall basisA degr)))))
-            (the basis #'rslt)))))
-
-#|
-  (CYLINDER-basis :locally-effective :locally-effective )
-  (setf b #'(lambda (degr) (mapcar #'(lambda (item) (cons degr item)) (<a-b> 0 degr))))
-  (setf r (CYLINDER-basis b b))
-  (funcall r 3)
-|#
-
-(DEFUN CYLINDER-INTR-DFFR (cmprA cmprB dffrA dffrB f)
-   (declare
-      (type cmprf cmprA cmprB)
-      (type morphism dffrA dffrB f))
-   (flet ((rslt (cmbn)
-             (declare (type cmbn cmbn))
-             (the cmbn
-                (multiple-value-bind (cmbnA1 cmbnB cmbnA2) (dispatch-cyln-cmbn cmbn)
-                   (declare (type cmbn cmbnA1 cmbnB cmbnA2))
-                   (let ((dffrA1-cmbn (cmbn-? dffrA cmbnA1))
-                         (dffrB-cmbn (cmbn-? dffrB cmbnB))
-                         (dffrA2-cmbn (cmbn-? dffrA cmbnA2))
-                         (f-cmbn (cmbn-? f cmbnA1))
-                         )
-                      (declare (type cmbn dffrA1-cmbn dffrB-cmbn dffrA2-cmbn f-cmbn))
-                      (let ((cmbnB (2cmbn-add cmprB f-cmbn dffrB-cmbn))
-                            (cmbnA2 (2cmbn-sbtr cmprA dffrA2-cmbn cmbnA1)))
-                         (declare (type cmbn cmbnB cmbnA2))
-                         (make-cyln-cmbn (cmbn-opps dffrA1-cmbn) cmbnB cmbnA2)))))))
-      (the intr-mrph #'rslt)))
-
-
-(DEFUN CYLINDER (f)
-   (declare (type morphism f))
-   (the chain-complex
-     (with-slots (sorc trgt) f
-       (declare
-        (type chain-complex sorc trgt ))
-       (let ((rslt (build-chcm
-                    :cmpr (cylinder-cmpr (cmpr sorc) (cmpr trgt))
-                    :basis (cylinder-basis (basis sorc) (basis trgt))
-                    :bsgn :undefined
-                    :intr-dffr (cylinder-intr-dffr (cmpr sorc) (cmpr trgt)
-                                     (dffr sorc) (dffr trgt) f)
-                    :strt :cmbn
-                    :orgn `(cylinder ,f))))
-          (declare (type chain-complex rslt))
-          (slot-makunbound rslt 'bsgn)
-          rslt))))
-
-
-
-
-
-(defun cylinder-rrdct (f)
-   (declare (type morphism f))
-   (the reduction
-     (with-slots (sorc (Bcc trgt)) f
-       (with-slots ((cmprb cmpr)) Bcc
-         (let ((cylinder (cylinder f)))
-            (let ((rf (build-mrph
-                       :sorc cylinder :trgt Bcc :degr 0
-                       :intr #'(lambda (cmbn)
-                                 (declare (type cmbn cmbn))
-                                 (2cmbn-add cmprB (cyln-cmbn-cmbnB cmbn) (cmbn-? f (cyln-cmbn-cmbnA2 cmbn))))
-                       :strt :cmbn
-                       :orgn `(cylinder ,f rf)))
-                  (rg (build-mrph
-                       :sorc Bcc :trgt cylinder :degr 0
-                       :intr #'(lambda (cmbn)
-                                 (declare (type cmbn cmbn))
-                                 (let* ((cmbnA1 (zero-cmbn (1- (cmbn-degr cmbn))))
-                                        (cmbnA2 (zero-cmbn (cmbn-degr cmbn))))
-                                    (declare (type cmbn cmbnA1 cmbnA2))
-                                    (make-cyln-cmbn cmbnA1 cmbn cmbnA2)))
-                       :strt :cmbn
-                       :orgn `(cylinder ,f rg)))
-                  (rh (build-mrph
-                       :sorc cylinder :trgt cylinder :degr +1
-                       :intr #'(lambda (cmbn)
-                                 (declare (type cmbn cmbn))
-                                 (let* ((cmbnA1 (cmbn-opps (cyln-cmbn-cmbnA2 cmbn)))
-                                        (cmbnB (zero-cmbn (1+ (cmbn-degr cmbn))))
-                                        (cmbnA2 (zero-cmbn (1+ (cmbn-degr cmbn)))))
-                                    (declare (type cmbn cmbnA1 cmbnB cmbnA2))
-                                    (make-cyln-cmbn cmbnA1 cmbnB cmbnA2)))
-                       :strt :cmbn
-                       :orgn `(cylinder ,f rh))))
-               (declare
-                (type chain-complex cylinder)
-                (type morphism rf rg rh))
-               (build-rdct :f rf :g rg :h rh :orgn `(cylinder right reduction ,f))))))))
-
-
-(defun cylinder-lrdct (f g h k)
-   (declare (type morphism f g h k))
-   (the reduction
-     (with-slots ((Acc sorc) (Bcc trgt)) f
-       (with-slots ((cmprA cmpr)) Acc
-         (with-slots ((cmprb cmpr)) Bcc
-           (let ((cylinder (cylinder f)))
-              (let ((lf (build-mrph
-                         :sorc cylinder :trgt Acc :degr 0
-                         :intr #'(lambda (cmbn)
-                                   (declare (type cmbn cmbn))
-                                   (2cmbn-sbtr cmprA 
-                                     (2cmbn-add cmpra (cyln-cmbn-cmbnA2 cmbn) (cmbn-? g (cyln-cmbn-cmbnB cmbn)))
-                                     (cmbn-? h (cyln-cmbn-cmbnA1 cmbn))))
-                         :strt :cmbn
-                         :orgn `(cylinder hmtpeq ,f lf)))
-                    (lg (build-mrph
-                         :sorc Acc :trgt cylinder :degr 0
-                         :intr #'(lambda (cmbn)
-                                   (declare (type cmbn cmbn))
-                                   (let* ((cmbnA1 (zero-cmbn (1- (cmbn-degr cmbn))))
-                                          (cmbnB (zero-cmbn (cmbn-degr cmbn)))
-                                          )
-                                      (declare (type cmbn cmbnA1 cmbnB ))
-                                      (make-cyln-cmbn cmbnA1 cmbnB cmbn)))
-                         :strt :cmbn
-                         :orgn `(cylinder hmtpeq ,f lg)))
-                    (lh (build-mrph
-                         :sorc cylinder :trgt cylinder :degr +1
-                         :intr #'(lambda (cmbn)
-                                   (declare (type cmbn cmbn))
-                                   (multiple-value-bind (cmbnA1 cmbnB cmbnA2) 
-                                       (dispatch-cyln-cmbn cmbn)
-                                      (let* ((cmbnA11 (cmbn-opps (cmbn-? h cmbnA1)))
-                                             (cmbnA12 (cmbn-opps (cmbn-? g (cmbn-? k (cmbn-? f cmbnA1)))))
-                                             (cmbnA13 (cmbn-? g (cmbn-? f (cmbn-? h cmbnA1))))
-                                             (cmbnA14 (cmbn-? g cmbnB))
-                                             (cmbnB1 (cmbn-opps (cmbn-? k (cmbn-? k (cmbn-? f cmbnA1)))))
-                                             (cmbnB2 (cmbn-? k (cmbn-? f (cmbn-? h cmbnA1))))
-                                             (cmbnB3 (cmbn-? k cmbnB))
-                                             (cmbnA21 (cmbn-opps (cmbn-? h (cmbn-? h cmbnA1))))
-                                             (cmbnA22 (cmbn-opps (cmbn-? h (cmbn-? g (cmbn-? k (cmbn-? f cmbnA1))))))
-                                             (cmbnA23 (cmbn-? h (cmbn-? g (cmbn-? f (cmbn-? h cmbnA1)))))
-                                             (cmbnA24 (cmbn-? g (cmbn-? k (cmbn-? k (cmbn-? f cmbnA1)))))
-                                             (cmbnA25 (cmbn-opps (cmbn-? g (cmbn-? k (cmbn-? f (cmbn-? h cmbnA1))))))
-                                             (cmbnA26 (cmbn-? h (cmbn-? g cmbnB)))
-                                             (cmbnA27 (cmbn-opps (cmbn-? g (cmbn-? k cmbnB)))))
-                                         (declare (type cmbn cmbnA11 cmbnA12 cmbnA13 cmbnA14
-                                                    cmbnB1 cmbnB2 cmbnB3 
-                                                    cmbnA21 cmbnA22 cmbnA23 cmbnA24 cmbnA25 cmbnA26 cmbnA27))
-                                         (make-cyln-cmbn (ncmbn-add cmprA cmbnA11 cmbnA12 cmbnA13 cmbnA14)
-                                     (ncmbn-add cmprB cmbnB1 cmbnB2 cmbnB3)
-                                     (ncmbn-add cmprA cmbnA21 cmbnA22 cmbnA23 cmbnA24 cmbnA25 cmbnA26 cmbnA27)))))
-                                     
-                         :strt :cmbn
-                         :orgn `(cylinder hmtpeq ,f lh))))
-            (declare
-                     (type chain-complex cylinder)
-                     (type morphism lf lg lh))
-            (build-rdct :f lf :g lg :h lh :orgn `(cylinder left reduction ,f)))))))))
-
-
-#|
- (cat-init) 
- (setf z3 (cyclicgroup 3))
- 
- (setf rsltn1 (cyclicgroup-rsltn 3))
- (setf rsltn2 (bar-rsltn z3))
- (setf f (zgmrph-twi (2rsltn-zgmrph rsltn1 rsltn2)))
- (setf g (zgmrph-twi (2rsltn-zgmrph rsltn2 rsltn1)))
- (setf h (zgmrph-twi (2rsltn-hmtpop rsltn1 rsltn2)))
- (setf k (zgmrph-twi (2rsltn-hmtpop rsltn2 rsltn1)))
- (setf Acc (sorc f) Bcc (trgt f))
-
-
- (setf rrdct (cylinder-rrdct f))
- (setf lrdct (cylinder-lrdct f g h k))
-
- (setf lf (f lrdct) lg (g lrdct) lh (h lrdct))
- (setf rf (f rrdct) rg (g rrdct) rh (h rrdct))
-
- (pre-check-rdct rrdct)
- (setf *tc* (cmbn 3 1 (cylnA1 2) 10 (cylnB '(1 2 1)) 100 (cylnA2 3)))
- (setf *bc* (cmbn 3 1 '(1 1 2)))
- (check-rdct)
- (setf *tc* (cmbn 4 10 (cylnB '(1 2 1 1)) 5 (cylnB '(1 2 2 1)) 100 (cylnA2 4)))
- (setf *bc* (cmbn 2 5 '(1 1) 7 '(2 1) -4 '(2 2)))
- (check-rdct)
-
-
- (pre-check-rdct lrdct)
-
- (setf *tc* (cmbn 3 1 (cylnA1 2) 10 (cylnB '(1 2 1)) 100 (cylnA2 3)))
- (setf *bc* (cmbn 3 1 3))
- (check-rdct)
-
- (setf *tc* (cmbn 4 10 (cylnB '(1 2 1 1)) 5 (cylnB '(1 2 2 1)) 100 (cylnA2 4)))
- (setf *bc* (cmbn 2 1 2))
- (check-rdct)
-|#
-
-
- (DEFMETHOD SEARCH-EFHM (smst (orgn (eql 'k-g-1)))
-   (declare (type simplicial-group smst))
-   (the homotopy-equivalence
-    (let* ((group (second (orgn smst)))
-           (rsltn1 (bar-rsltn group))
-           (rsltn2 (resolution group))
-           (f (zgmrph-twi (2rsltn-zgmrph rsltn1 rsltn2)))
-           (g (zgmrph-twi (2rsltn-zgmrph rsltn2 rsltn1)))
-           (h (zgmrph-twi (2rsltn-hmtpop rsltn1 rsltn2)))
-           (k (zgmrph-twi (2rsltn-hmtpop rsltn2 rsltn1)))
-           (rrdct (cylinder-rrdct f))
-           (lrdct (cylinder-lrdct f g h k)))
-       (build-hmeq :lrdct lrdct :rrdct rrdct :orgn `(efhm of ,smst)))))
-
- #|
- (setf z3 (cyclicgroup 3))
- (setf k-z3-1 (k-g-1 z3))
-
- (cat-init)
- (setf z4 (cyclicgroup 4))
- (setf k-z4-1 (k-g-1 z4))
- (setf k-z4-2 (classifying-space k-z4-1))
-
- (cat-init)
- (setf z2 (cyclicgroup 2))
- (setf k-z2-1 (k-g-1 z2))
- (setf k-z2-2 (classifying-space k-z2-1))
- |#
-        
diff --git a/examples/anromero/suspended-classifying-spaces-lisp-files/fundamental-classes.cl b/examples/anromero/suspended-classifying-spaces-lisp-files/fundamental-classes.cl
deleted file mode 100644
index b6fdd6e..0000000
--- a/examples/anromero/suspended-classifying-spaces-lisp-files/fundamental-classes.cl
+++ /dev/null
@@ -1,173 +0,0 @@
-;; Fundamental classes
-(IN-PACKAGE "COMMON-LISP-USER")
-
-
-(DEFUN Zp-FUNDAMENTAL-GMSM (p dmns pi-elm)  ;; pi-elm not "equal" to 0
-   (declare (fixnum dmns pi-elm))
-   (the gmsm
-      (if (= 1 dmns)
-         (list pi-elm)
-         (let ((bspn (if (= 2 dmns) nil +null-gbar+)))
-            (declare (type gmsm bspn))
-            (make-gbar :dmns dmns
-               :list (cons (absm 0 (Zp-fundamental-gmsm p (1- dmns) pi-elm))
-                        (mapcar
-                           #'(lambda (k)
-                                (declare (fixnum k))
-                                (absm (mask k) bspn))
-                           (nreverse (<a-b> 0 (- dmns 2))))))))))
-#|
-
-  (Zp-fundamental-gmsm 2 1 1)
-  (Zp-fundamental-gmsm 2 2 1)
-  (Zp-fundamental-gmsm 2 3 1)
-  (Zp-fundamental-gmsm 2 4 1) 
-
-  (Zp-fundamental-gmsm 5 1 1)
-  (Zp-fundamental-gmsm 5 4 1)
-  
-|#
-
-
-(DEFUN Zp-COCYCLE-GBAR (p n dmns cocycle)
-  ;; cocycle \in Z^n(\Delta^{dmns}, \pi) with \pi = Z/pZ
-  (declare
-    (fixnum p n dmns)
-    (list cocycle))
-  (the absm
-    (progn
-      (mapc
-        #'(lambda (cons)
-	    (declare (cons cons))
-            (setf (cdr cons)
-                  (mod (cdr cons) p)))
-       cocycle)
-      (cond ((= n 1)
-	     (g-bar-absm (cyclicgroup p) (nreverse (mapcar #'cdr cocycle))))
-	    ((= n dmns)
-	     (let ((value (cdr (first cocycle))))
-	       (declare (fixnum value))
-	       (if (zerop value)
-		   (absm (mask dmns) +null-gbar+)
-		 (absm 0 (zp-fundamental-gmsm p dmns value)))))
-	    (t
-	     (let ((cocycle1 +empty-list+)
-		   (cocycle2 +empty-list+))
-	       (declare (list cocycle1 cocycle2))
-	       (dolist (cons cocycle)
-		 (declare (cons cons))
-		 (if (evenp (car cons))
-		     (push (cons (ash (car cons) -1) (cdr cons))
-			   cocycle1)
-		   (push (cons (ash (car cons) -1) (cdr cons))
-			 cocycle2)))
-	       (setf cocycle1 (nreverse cocycle1)
-		     cocycle2 (nreverse cocycle2))
-	       (mapc
-		#'(lambda (cons)
-		    (declare (cons cons))
-		    (when (evenp (car cons))
-			  (setf (cdr cons)
-				(mod (- (cdr cons)
-					(cdr (assoc (1+ (car cons)) cocycle1)))
-				     p))))
-		cocycle2)
-	       (let ((head-absm (zp-cocycle-gbar p (1- n) (1- dmns) cocycle2))
-		     (tail-absm (zp-cocycle-gbar p n (1- dmns) cocycle1)))
-		 (declare (type absm head-absm tail-absm))
-		 (normalize-gbar
-		  (cons dmns
-			(cons head-absm
-			      (rest (unnormalize-gbar tail-absm
-						      (if (= n 2) () +null-gbar+)))))))))))))
-
-
-(DEFUN Zp-COCYCLE-GBAR-HEAD (p n dmns cocycle)
-  ;; cocycle \in Z^n(\Delta^{dmns}, \pi) with \pi = Z/pZ
-  (declare
-    (fixnum n dmns)
-    (list cocycle))
-  (the absm
-    (progn
-      (mapc
-        #'(lambda (cons)
-	    (declare (cons cons))
-            (setf (cdr cons)
-                  (mod (cdr cons) p)))
-       cocycle)
-      (cond ((= n 1)
-	     (error "In Zp-COCYCLE-GBAR-HEAD, this point should not have been reached."))
-		 ; (zp-bar-absm (nreverse (mapcar #'cdr cocycle))))
-	    ((= n dmns)
-	     (let ((value (cdr (first cocycle))))
-	       (declare (fixnum value))
-	       (if (zerop value)
-		   (if (= n 2)
-		       (absm 1 +empty-list+)
-		     (absm (mask (1- dmns)) +null-gbar+))
-		 (absm 0 (zp-fundamental-gmsm p (1- dmns) value)))))
-	    (t
-	     (let ((cocycle1 +empty-list+)
-		   (cocycle2 +empty-list+))
-	       (declare (list cocycle1 cocycle2))
-	       (dolist (cons cocycle)
-		 (declare (cons cons))
-		 (if (evenp (car cons))
-		     (push (cons (ash (car cons) -1) (cdr cons))
-			   cocycle1)
-		   (push (cons (ash (car cons) -1) (cdr cons))
-			 cocycle2)))
-	       (setf cocycle1 (nreverse cocycle1)
-		     cocycle2 (nreverse cocycle2))
-	       (mapc
-		#'(lambda (cons)
-		    (declare (cons cons))
-		    (when (evenp (car cons))
-			  (setf (cdr cons)
-				(mod (- (cdr cons)
-					(cdr (assoc (1+ (car cons)) cocycle1)))
-				     p))))
-		cocycle2)
-	       (zp-cocycle-gbar p (1- n) (1- dmns) cocycle2)))))))
-
-
-
-
-
-(DEFUN Zp-WHITEHEAD-SINTR (p smst n chml-clss
-				&aux (face (face smst))
-				     (k-zp-n-1 (k-zp p (1- n)))
-				     (idnt (bspn k-zp-n-1))
-				     (efhm (efhm smst)))
-   (declare
-      (type simplicial-set smst)
-      (fixnum n)
-      (type morphism chml-clss)
-      (type face face)
-      (type ab-simplicial-group k-zp-n-1)
-      (type gmsm idnt)
-      (type homotopy-equivalence efhm))
-   (setf chml-clss
-	 (i-cmps chml-clss (rf efhm) (lg efhm)))
-   (flet ((rslt (dmns gmsm)
-	    (declare
-	      (fixnum dmns)
-	      (type gmsm gmsm))
-	    (if (< dmns n)
-	        (absm (mask (1- dmns)) idnt)
-	      (zp-cocycle-gbar-head p n dmns
-		(gmsm-cocycle face n dmns gmsm chml-clss)))))
-     (the sintr #'rslt)))
-
-(DEFUN Zp-WHITEHEAD (p smst chml-clss &aux (n (- (degr chml-clss))))
-   (declare
-      (type simplicial-set smst)
-      (fixnum p n)
-      (type morphism chml-clss))
-   (the fibration
-      (build-smmr
-         :sorc smst :trgt (k-zp p (1- n)) :degr -1
-         :sintr (Zp-whitehead-sintr p smst n chml-clss)
-         :orgn `(Zp-whitehead ,p ,smst))))
-
-
diff --git a/examples/anromero/suspended-classifying-spaces-lisp-files/permutation-groups.cl b/examples/anromero/suspended-classifying-spaces-lisp-files/permutation-groups.cl
deleted file mode 100644
index 881401e..0000000
--- a/examples/anromero/suspended-classifying-spaces-lisp-files/permutation-groups.cl
+++ /dev/null
@@ -1,153 +0,0 @@
-
-(defun permgr-elements (l)
-  (declare (type 'list l))
-  (let* ((n (length (first l)))
-         (end nil)
-         (rslt (list (<a-b> 1 n))))
-    
-    (while (not end)
-      (progn
-        (setf end t) 
-        (mapcar #'(lambda (p)
-                    (progn
-                      (mapcar #'(lambda (p2)
-                                  (let ((p*p2 (permgr-mult p p2))
-                                        (pos -1))
-                                    (do ((j 0 (1+ j)))
-                                        ((or (not (equal pos -1)) (>= j (length rslt))))
-                                      (if (equal (l-cmpr p*p2 (nth j rslt)) :less)
-                                          (setf pos j)
-                                        (if (equal (l-cmpr p*p2 (nth j rslt)) :equal)
-                                            (setf pos -2)
-                                          (if (and (equal j (1- (length rslt))) (equal pos -1))
-                                              (setf pos (length rslt))))))
-                                    (if (> pos -1)
-                                        (progn
-                                          (setf rslt (append (subseq rslt 0 pos) (list p*p2) (subseq rslt pos (length rslt))))
-                                          (setf end nil))))
-                                    
-                                  (let ((p2*p (permgr-mult p2 p))
-                                        (pos -1))
-                                    (do ((j 0 (1+ j)))
-                                        ((or (not (equal pos -1)) (>= j (length rslt))))
-                                        (if (equal (l-cmpr p2*p (nth j rslt)) :less)
-                                            (setf pos j)
-                                          (if (equal (l-cmpr p2*p (nth j rslt)) :equal)
-                                              (setf pos -2)
-                                            (if (and (equal j (1- (length rslt))) (equal pos -1))
-                                                (setf pos (length rslt))))))
-                                      (if (> pos -1)
-                                          (progn
-                                            (setf rslt (append (subseq rslt 0 pos) (list p2*p) (subseq rslt pos (length rslt))))
-                                            (setf end nil)))
-                                  
-                                  
-                                  ))
-                        rslt)
-                      ))
-      l)))
-    rslt))
-                
-  
-
-#|
-(permgr-elements (list '(2 3 1) '(2 1 3)))
-(permgr-elements (list '(2 3 4 1) '(2 1 3 4)))
-(permgr-elements (list '(2 3 4 5 1) '(2 1 3 4 5)))
-
-|#
-
-
-
-
-
-
-(defun permgr-mult (p1 p2)
-  (declare (type 'list p1 p2))
-  (mapcar #'(lambda (i)
-              (nth (1- i) p2))
-    p1))
-
-#|
-(permgr-mult '(1 3 2) '(1 2 3))
-(permgr-mult '(1 5 4 3 2) '(1 2 3 5 4))
-|#
-
-(defun permgr-inv (p1)
-  (declare (type 'list p1))
-  (mapcar #'(lambda (i)
-              (1+ (position i p1)))
-    (<a-b> 1 (length p1))))
-
-#|
-(permgr-inv '(1 3 2 5 4))
-(permgr-mult '(1 3 2 5 4) '(1 3 2 5 4))
-(permgr-mult '(1 5 2 3 4) (permgr-inv '(1 5 2 3 4)))
-(permgr-mult '(5 4 3 1 2) (permgr-inv '(5 4 3 1 2)))
-|#
-
-
-
-(defun permutationgroup (l)
-  (declare (type 'list l))
-  (build-group :elements (permgr-elements l)
-               :cmpr #'l-cmpr
-               :mult #'permgr-mult
-               :inv #'permgr-inv
-               :nullel (<a-b> 1 (length (first l))) :orgn `(Permutation group generated by ,l)
-               ))
-
-
-#|
-(setf s3 (permutationgroup (list '(2 3 1) '(2 1 3))))
-|#
-
-
-
-(defun symmetricgroup (n)
-  (let* ((l (list (append (<a-b> 2 n) (list 1)) (append (list 2 1) (<a-b> 3 n))))
-         (rslt (permutationgroup l)))
-    (setf (slot-value rslt 'orgn) `(Symmetric group ,n))
-    rslt)) 
-
-#|
-(cat-init)
-(setf s3 (symmetricgroup 3))
-(elements s3)
-
-(setf s4 (symmetricgroup 4))
-(elements s4)
-
-
-
-
-|#
-
-
-
-(defun alternatinggroup (n)
-  (let* ((l (list 
-            (if (or (eq n 1) (eq n 2)) nil
-              (if (eq n 3) (list '(2 3 1))
-                (if (oddp n) (list (append (<a-b> 2 n) (list 1)) (append (<a-b> 1 (- n 3)) (list (1- n) n (- n 2))))
-                  (list (append (<a-b> 2 (1- n)) (list 1 n)) (append (<a-b> 1 (- n 3)) (list (1- n) n (- n 2)))))))))
-         (rslt (permutationgroup l)))
-    (setf (slot-value rslt 'orgn) `(Alternating group ,n))
-    rslt))
-
-
-#|
-(cat-init)
-(setf a3 (alternatinggroup 3))
-(elements a3)
-
-(setf a4 (alternatinggroup 4))
-(elements a4)
-
-
-
-|#
-
-                    
-            
-            
\ No newline at end of file
diff --git a/examples/anromero/suspended-classifying-spaces-lisp-files/resolutions.cl b/examples/anromero/suspended-classifying-spaces-lisp-files/resolutions.cl
deleted file mode 100644
index fef9831..0000000
--- a/examples/anromero/suspended-classifying-spaces-lisp-files/resolutions.cl
+++ /dev/null
@@ -1,1791 +0,0 @@
-
-
-;; RESOLUTIONS   RESOLUTIONS   RESOLUTIONS   RESOLUTIONS   RESOLUTIONS   RESOLUTIONS   
-;; RESOLUTIONS   RESOLUTIONS   RESOLUTIONS   RESOLUTIONS   RESOLUTIONS   RESOLUTIONS   
-;; RESOLUTIONS   RESOLUTIONS   RESOLUTIONS   RESOLUTIONS   RESOLUTIONS   RESOLUTIONS   
-
-(IN-PACKAGE "COMMON-LISP-USER")
-
-(provide "resolutions")
-
-
-;;;;;;;;;;;;;;;;;;;;;
-;;;;; clases y tipos
-;;;;;;;;;;;;;;;;;;;;;
-
-(DEFUN ZGgnrt-P (object)
-   (declare (type any object))
-   (the boolean
-     (and (consp object)
-          (eql :ZGgnrt (car object))
-          (consp (cdr object))
-          ;;(consp (cadr object))
-          ;;(consp (cddr object))
-          (typep (cadr object) 'gnrt)
-          (typep (cddr object) 'gnrt)
-          )))
-
-(DEFTYPE ZGgnrt () '(satisfies ZGgnrt-p)) 
-
-(DEFUN ZGTERM-P (object)
-   (declare (type any object))
-   (the boolean
-     (and (consp object)
-          (typep (car object) 'fixnum)
-          (typep (cdr object) 'ZGgnrt))))
-
-(DEFTYPE ZGTERM () '(satisfies zgterm-p))
-
-;; IZGCMBN = Internal-ZGCoMBiNation 
-(DEFUN IZGCMBN-P (object)
-;; IZGCMBN = Internal ZGCoMBiNation,    
-;; without the keyword and the degree
-   (declare (type any object))
-   (the boolean
-     (and (listp object)
-          (every #'zgterm-p object))))
-
-(DEFTYPE IZGCMBN () '(satisfies izgcmbn-p)) 
-
-;; ZGCMBN = ZGCoMBiNation 
-(DEFUN ZGCMBN-P (object)
-   (declare (type any object))
-   (the boolean
-     (and (consp object)
-          (eql (car object) :cmbn)
-          (consp (cdr object))
-          (typep (second object) 'fixnum)
-          (typep (cddr object) 'iZGcmbn))))
-
-(DEFTYPE ZGCMBN () '(satisfies ZGcmbn-p)) 
-
-
-
-(DEFTYPE GROUP-BASIS () '(or list (eql :locally-effective))) 
-
-;;(DEFCLASS GROUP-MRPH () ()) ;; to be redefined later
-  
-(DEFCLASS GROUP ()
-   ((elements :type group-basis :initarg :elements :reader elements)
-   (cmpr :type cmprf :initarg :cmpr :reader cmpr1)
-   (mult :type function :initarg :mult :reader mult1)
-   (inv :type function :initarg :inv :reader inv1)
-   (nullel :type gnrt :initarg :nullel :reader nullel)
-   (idnm :type fixnum :initform (incf *idnm-counter*) :reader idnm)
-   (orgn :type list :initarg :orgn :reader orgn)
-   (resolution :type reduction :initarg :resolution :reader resolution))
-  )
-
-(DEFCLASS AB-GROUP (GROUP)
-    ())
-
-(DEFCLASS GROUP-MRPH ()
-    ;; SOuRCe     
-    ((sorc :type group :initarg :sorc :reader sorc)
-     ;; TaRGeT 
-     (trgt :type group :initarg :trgt :reader trgt)
-      
-     ;; INTeRnal      
-     (intr :type function :initarg :intr :reader intr)      
-          ;; IDentification NuMber      
-     (idnm :type fixnum :initform (incf *idnm-counter*) :reader idnm)      
-     ;; ORiGiN      
-     (orgn :type list :initarg :orgn :reader orgn)))
-
-
-
-
-(DEFVAR *group-list*)
-(SETF *group-list* +empty-list+)
-(PUSHNEW '*group-list* *list-list*)
-
-(DEFVAR *ab-group-list*)
-(SETF *ab-group-list* +empty-list+)
-(PUSHNEW '*ab-group-list* *list-list*)
-
-(DEFVAR *group-mrph-list*)
-(SETF *group-mrph-list* +empty-list+)
-(PUSHNEW '*group-mrph-list* *list-list*)
-
-
-(DEFMETHOD PRINT-OBJECT ((group GROUP) stream)
-   (the GROUP
-     (progn
-      (format stream "[K~D Group]" (idnm group))
-      group)))
-
-(DEFMETHOD PRINT-OBJECT ((group ab-GROUP) stream)
-   (the ab-GROUP
-     (progn
-      (format stream "[K~D Abelian-Group]" (idnm group))
-      group)))
-
-(DEFMETHOD PRINT-OBJECT ((group-mrph GROUP-MRPH) stream)
-   (the GROUP-MRPH
-     (progn
-      (format stream "[K~D Group-morphism]" (idnm group-mrph))
-      group-mrph)))
-
-
-(DEFUN GROUP (idnm)
-   (declare (type fixnum idnm))
-   (the (or GROUP null)
-      (find idnm *group-list* :key #'idnm)))
-
-(DEFUN AB-GROUP (idnm)
-   (declare (type fixnum idnm))
-   (the (or AB-GROUP null)
-      (find idnm *ab-group-list* :key #'idnm)))
-
-(DEFUN GROUP-MRPH (idnm)
-   (declare (type fixnum idnm))
-   (the (or GROUP-MRPH null)
-      (find idnm *group-mrph-list* :key #'idnm)))
-
-
-
-
-   
-
-;;(DEFCLASS ZG-MORPHISM () ())  ;; will be redefined later.
-
-
-(DEFCLASS ZG-CHAIN-COMPLEX (chain-complex)
-    (
-     (group :type group :initarg :group :reader group1)
-     (zgcmpr :type cmprf :initarg :zgcmpr :reader zgcmpr1)
-     (zgbasis :type basis :initarg :zgbasis :reader zgbasis1)
-     (zgbsgn :type gnrt :initarg :zgbsgn :reader zgbsgn)
-     (zgbndr :type ZG-morphism :initarg :zgbndr :reader zgbndr1)
-     ))
-
-(DEFVAR *zgcc-list*)
-(SETF *zgcc-list* +empty-list+)
-(PUSHNEW '*zgcc-list* *list-list*)
-
-(DEFMETHOD PRINT-OBJECT ((zgcm ZG-CHAIN-COMPLEX) stream)
-   (the ZG-CHAIN-COMPLEX
-     (progn
-      (format stream "[K~D ZG-Chain-Complex]" (idnm zgcm))
-      zgcm)))
-
-(DEFUN ZGCC (idnm)
-   (declare (type fixnum idnm))
-   (the (or ZG-CHAIN-COMPLEX null)
-      (find idnm *zgcc-list* :key #'idnm)))
-
-
-
-
-;; ZGSTRT = ZGSTRaTegy 
-(DEFTYPE ZGSTRT () '(member :gnrt :zggnrt :zgcmbn))
-
-;; INTR-ZGMRPH = INTeRnal-ZGMoRPHism 
-(DEFTYPE INTR-ZGMRPH () 'function)                
-;; (or (function (degr gnrt) zgcmbn)    ;; if :gnrt strategy
-;;     (function (degr zggnrt) zgcmbn)  ;; if :zggnrt strategy                
-;;     (function (zgcmbn) zgcmbn)     ;; if :zgcmbn strategy 
-
-(DEFCLASS ZG-MORPHISM (morphism)
-    (
-     (zgintr :type intr-zgmrph :initarg :zg-intr :reader intr-zgmrph)
-     (zgstrt :type zgstrt :initarg :zgstrt :reader zgstrt) 
-    ))
-
-(DEFVAR *zgmrph-list*)
-(SETF *zgmrph-list* +empty-list+)
-(PUSHNEW '*zgmrph-list* *list-list*)
-
-
-(DEFMETHOD PRINT-OBJECT ((mrph ZG-MORPHISM) stream)
-   (the ZG-MORPHISM
-      (progn
-	(format stream "[K~D ZG-Morphism (degree ~D): K~D -> K~D]"
-		  (idnm mrph) (degr mrph)
-		  (idnm (sorc mrph)) (idnm (trgt mrph)))
-         mrph)))
-
-
-(DEFUN zgmrph (idnm)
-   (declare (type fixnum idnm))
-   (the (or ZG-MORPHISM null)
-      (find idnm *zgmrph-list* :key #'idnm)))
-
-
-
-
-;;;;;;;;;;;;;;;;;;;;;;;;;
-;;;;;;;;;;;;;;;;; macros
-;;;;;;;;;;;;;;;;;;;;;;;;
-
-
-(DEFMACRO ZGgnrt (gnrt1 gnrt2)
-  `(cons  :zggnrt
-     (cons ,gnrt1 ,gnrt2)))
-
-
-(DEFMACRO zggnrt1 (ZGgnrt)
-   `(car (cdr ,ZGgnrt)))
-
-(DEFMACRO zggnrt2 (ZGgnrt)
-  `(cddr ,ZGgnrt))
-
-;; (setf gn1 (zggnrt 'g1 'b1))
-;; (setf gn2 (zggnrt 'g2 'b1))
-;; (setf gn3 (zggnrt 'g1 'b2))
-;; (setf gn4 (zggnrt 'g2 'b2))
-
-(DEFMACRO WITH-ZGgnrt ((zggnrt1 zggnrt2) zggnrt . body)
-   `(let (,@(if zggnrt1 `((,zggnrt1 (zggnrt1 ,zggnrt))) nil)
-          ,@(if zggnrt2 `((,zggnrt2 (zggnrt2 ,zggnrt))) nil))
-       (declare
-         (type gnrt ,@(if zggnrt1 `(,zggnrt1) nil) ,@(if zggnrt2 `(,zggnrt2) nil)))
-       ,@body))
-
-;;(with-zggnrt (gnrt1 gnrt2) gn3
-;;     (progn
-;;      (format t "~D" gnrt1)
-;;      (format t "~D" gnrt2))) 
-
-
-;; Sobra??? podemos usar directamente el macro term
-(DEFMACRO ZGTERM (cffc zggnrt)
-  `(cons ,cffc ,zggnrt))
-
-
-;; Sobra??? podemos usar directamente el macro with-term
-(DEFMACRO WITH-zgTERM ((cffc zggnrt) zgterm . body)
-   `(let (,@(if cffc `((,cffc (cffc ,zgterm))) nil)
-          ,@(if zggnrt `((,zggnrt (gnrt ,zgterm))) nil))
-       (declare
-          (fixnum ,@(if cffc `(,cffc) nil))
-          (type zggnrt ,@(if zggnrt `(,zggnrt) nil)))
-       ,@body))
-
-
-
-
-
-;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
-;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
-;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
-
-
-(defun build-group 
-    (&key elements cmpr mult inv nullel orgn)
-   (declare 
-     (type group-basis elements)
-     (type cmprf cmpr)
-     (type function mult)
-     (type function inv)
-     (type gnrt nullel)
-     (list orgn))
-   (the group
-     (progn
-      (let ((already (find orgn *group-list* :test #'equal :key #'orgn)))
-         (declare (type (or group null) already))
-         (when already
-            (return-from build-group already)))
-      (unless elements
-         (setf elements :locally-effective))
-      (let ((group (make-instance 'group
-                     :cmpr cmpr
-                     :elements elements
-                     :mult mult
-                     :inv inv
-                     :nullel nullel
-                     :orgn orgn)))
-         (declare (type group group))   
-         (push group *group-list*)
-         group))))
-
-(DEFUN BUILD-GRMR (&key sorc trgt intr orgn)
-   (declare
-      (type group sorc trgt)
-      (type (or intr-mrph null) intr)
-      (list orgn))
-   (the group-mrph
-     (progn
-         (let ((already (find orgn *group-mrph-list* :test #'equal :key #'orgn)))
-            (declare (type (or group-mrph null) already))
-            (when already
-               (return-from build-grmr already)))
-         (let ((mrph (make-instance 'group-mrph
-                        :sorc sorc :trgt trgt 
-                        :intr intr 
-                        :orgn orgn)))
-            (declare (type group-mrph mrph))
-            (push mrph *group-mrph-list*)
-            mrph))))
-
-
-(DEFMACRO BUILD-AB-GROUP (&rest rest)
-  `(change-class (build-group ,@rest) 'ab-group))
-
-  
-   
-(DEFMETHOD ?2 ((grmrph group-mrph) grelt)
-   (declare (type gnrt grelt))
-   (the gnrt
-     (with-slots (intr) grmrph
-       (funcall intr grelt))))
-
-
-(DEFMETHOD ?3 ((group group) g1 g2)
-   (declare
-      (type gnrt g1 g2))
-   (the gnrt
-     (with-slots (mult) group
-      (funcall mult g1 g2))))
-
-#|
-(setf elements '(0 1 2 3 4))
-(setf cmpr #'f-cmpr)
-(setf grmult #'(lambda (g1 g2)
-                  (mod (+ g1 g2) 5)))
-(setf inv #'(lambda (g)
-                 (mod (- 5 g) 5)))
-(setf nullel 0)
-(setf orgn '(Z_5))
-(setf gr (build-group :elements elements :cmpr cmpr :mult grmult :inv inv :nullel 0 :orgn orgn))
-(setf intr #'(lambda (g) (funcall grmult g g)))
-(setf grmrph (build-grmr :sorc gr :trgt gr :intr intr :orgn '(grmrph)))
-(? grmrph 3)
-(? gr 1 2)
-|#
-      
-
-
-        
-(DEFUN ZGGNRT-CMPR (grcmpr zgcmpr)
-   (declare (type cmprf grcmpr zgcmpr))
-   (flet ((rslt (gnrt1 gnrt2)
-            (declare (type zggnrt gnrt1 gnrt2))
-            (the cmpr
-              (let ((gnrt12 (zggnrt2 gnrt1))
-                    (gnrt22 (zggnrt2 gnrt2)))
-                 (declare (type gnrt gnrt12 gnrt22))
-                 (lexico
-                  (funcall zgcmpr gnrt12 gnrt22)
-                  (let ((gnrt11 (zggnrt1 gnrt1))
-                        (gnrt21 (zggnrt1 gnrt2)))
-                     (declare (type gnrt gnrt11 gnrt21))
-                     (funcall grcmpr gnrt11 gnrt21)))))))
-     (the cmprf #'rslt)))
-
-
-;;(setf cmpr (zggnrt-cmpr #'s-cmpr #'s-cmpr))
-;;(funcall cmpr gn1 gn2)
-
-(DEFUN ZGCHCM-BASIS (grbasis zgbasis)
-   (declare (type group-basis grbasis)
-            (type basis zgbasis))
-   (when (or (eq grbasis :locally-effective)
-             (eq zgbasis :locally-effective))
-      (return-from ZGCHCM-BASIS :locally-effective))
-   (flet ((rslt (degr)
-             (declare (fixnum degr))
-             (the list
-                (progn
-                   (when (minusp degr)
-                      (return-from rslt +empty-list+))
-                   (the list
-                     (mapcan
-                      #'(lambda (gnrt2)
-                          (declare (type gnrt gnrt2))
-                          (the list
-                            (mapcar
-                             #'(lambda (gnrt1)
-                                 (declare (type gnrt gnrt1))
-                                 (the zggnrt
-                                   (zggnrt gnrt1 gnrt2)))
-                             grbasis)))
-                       (funcall zgbasis degr)))
-                      ))
-                      ))
-      (the basis #'rslt)))
-
-;; (setf basis1 '(0 1 2 3 4))
-;; (setf basis2 
-;;       #'(lambda (degr)
-;;           (<a-b> 0 degr)))
-;; (setf zgbasis (ZGCHCM-BASIS basis1 basis2))
-   
-
-
-(DEFUN ZGMRPH-GNRT-GNRT (intr degr gnrt)
-   (declare
-    (type intr-zgmrph intr)
-    (fixnum degr)
-    (type gnrt gnrt))
-   (funcall intr degr gnrt))
-
-(DEFUN ZGMRPH-GNRT-ZGGNRT (grcmpr zgcmpr grmult intr degr zggnrt)
-   (declare
-    (type cmprf grcmpr zgcmpr)
-    (type function grmult)
-    (type intr-zgmrph intr)
-    (fixnum degr)
-    (type zggnrt zggnrt))
-   (let* ((zggnrt1 (zggnrt1 zggnrt))
-          (zggnrt2 (zggnrt2 zggnrt))
-          (zgcmbn (ZGMRPH-GNRT-GNRT intr degr zggnrt2))
-          (degr (cmbn-degr zgcmbn))
-          (list (cmbn-list zgcmbn))
-          (n-cmbn-list +empty-list+))
-      (declare (list n-cmbn-list))
-      (if list 
-         (progn 
-           (mapcar #'(lambda (zgterm)
-                  (declare (type zgterm zgterm))
-                  (with-zgterm (cffc gnrt) zgterm
-                   (declare (type fixnum cffc)
-                     (type zggnrt gnrt))
-                   (with-zggnrt (gnrt1 gnrt2) gnrt
-                    (declare (type gnrt gnrt1 gnrt2))
-                    (push (cons 1
-                      (term-cmbn degr cffc (zggnrt (funcall grmult zggnrt1 gnrt1) gnrt2)))
-                      n-cmbn-list))))
-             list)
-           (cmbn-cmbn (zggnrt-cmpr grcmpr zgcmpr) n-cmbn-list))
-         (zero-cmbn degr))))
-
-;; (setf grbasis '(0 1 2 3 4))
-;; (setf zgbasis 
-;;      #'(lambda (degr)
-;;           (<a-b> 0 degr)))
-;; (setf grmult #'(lambda (g1 g2)
-;;                  (mod (+ g1 g2) 5)))
-;; (setf grcmpr #'f-cmpr zgcmpr #'f-cmpr)
-;;(setf intr #'(lambda (degr gnrt)
-;;               (declare
-;;                (fixnum degr)
-;;                (type gnrt gnrt))
-;;               (let ((cmbn (cmbn degr)))
-;;                  (declare (type cmbn cmbn))
-;;                  (mapcar #'(lambda (i)
-;;                              (declare (fixnum i))
-;;                              (setf cmbn
-;;                               (2cmbn-add (zggnrt-cmpr #'f-cmpr #'f-cmpr) cmbn (term-cmbn degr i (zggnrt i gnrt))
-;;                               )))
-;;                    (<a-b> 1 4))
-;;                  cmbn)))
-
-;;(ZGMRPH-GNRT-ZGGNRT grcmpr zgcmpr grmult intr 5 (zggnrt 1 3))
-
-(DEFUN ZGMRPH-GNRT-ZGCMBN (grcmpr zgcmpr grmult intr zgcmbn)
-   (declare
-    (type cmprf grcmpr zgcmpr)
-    (type function grmult)
-    (type intr-zgmrph intr)
-    (type zgcmbn zgcmbn))
-      (the cmbn
-        (with-cmbn (degr list) zgcmbn
-          (if list
-             (let ((n-cmbn-list +empty-list+))
-                (declare (list n-cmbn-list))
-                (do ((mark list (cdr mark))
-                     )
-                    ((endp mark))
-                   (declare (list mark))
-                   (with-term (cffc gnrt) (car mark) 
-                   (push 
-                     (cons cffc 
-                       (zgmrph-gnrt-zggnrt grcmpr zgcmpr grmult intr degr gnrt))
-                     n-cmbn-list)))
-                (cmbn-cmbn (zggnrt-cmpr grcmpr zgcmpr) n-cmbn-list))
-             (cmbn degr)))))
-
-;;(ZGMRPH-GNRT-ZGCMBN grcmpr zgcmpr grmult intr (cmbn 5 2 (zggnrt 1 3) 3 (zggnrt 2 4)))
-
-
-(DEFUN ZGMRPH-ZGGNRT-ZGGNRT (intr degr zggnrt)
-   (declare
-    (type intr-zgmrph intr)
-    (fixnum degr)
-    (type zggnrt zggnrt))
-   (funcall intr degr zggnrt))
-
-
-
-(DEFUN ZGMRPH-ZGGNRT-ZGCMBN (grcmpr zgcmpr intr zgcmbn)
-   (declare
-    (type intr-zgmrph intr)
-    (type cmprf grcmpr zgcmpr)
-    (type zgcmbn zgcmbn))
-   
-      (the cmbn
-      (with-cmbn (degr list) zgcmbn
-         (let ((n-cmbn-list +empty-list+))
-            (declare (list n-cmbn-list))
-            (do ((mark list (cdr mark))
-                 )
-                ((endp mark))
-               (declare (list mark))
-               (with-term (cffc gnrt) (car mark) 
-                   (push 
-                     (cons cffc 
-                       (zgmrph-zggnrt-zggnrt intr degr gnrt))
-                     n-cmbn-list)))
-	    (cmbn-cmbn (zggnrt-cmpr grcmpr zgcmpr) n-cmbn-list)))))
-
-
-
-(DEFUN ZGmrph-GNRT-? (ZGmrph degr gnrt)
-   (declare
-      (type zg-morphism ZGmrph)
-      (fixnum degr)
-      (type gnrt gnrt))
-   (the cmbn
-     (with-slots (zgintr zgstrt trgt) zgmrph
-       (with-slots (group) trgt
-            (declare
-             (type intr-zgmrph zgintr)
-             (type zgstrt zgstrt)
-             (type group group))
-
-       (with-slots (nullel) group
-         (prog1
-          (ecase zgstrt
-            (:gnrt
-             (zgmrph-gnrt-gnrt zgintr degr gnrt))
-            (:zggnrt
-             (funcall zgintr degr (zggnrt nullel gnrt)))
-            (:cmbn
-             (funcall zgintr (term-cmbn degr 1 (zggnrt nullel gnrt)))))
-          ))))))
-
-
-(DEFUN ZGmrph-ZGGNRT-? (ZGmrph degr zggnrt)
-   (declare
-      (type ZG-morphism ZGmrph)
-      (fixnum degr)
-      (type zggnrt zggnrt))
-   (the cmbn
-     (with-slots (trgt zgintr zgstrt ) zgmrph
-       (with-slots (group) trgt
-            (declare
-               (type zg-chain-complex trgt)
-               (fixnum mdegr )
-               (type intr-zgmrph zgintr)
-               (type zgstrt zgstrt)
-             (type group group))
-       (with-slots ((grcmpr cmpr) mult nullel) group
-         (with-slots (zgcmpr)  trgt
-            (declare (type cmprf zgcmpr grcmpr))
-           (prog1
-                     (ecase zgstrt
-                        (:gnrt
-                         (zgmrph-gnrt-zggnrt grcmpr zgcmpr mult zgintr degr zggnrt))
-                        (:zggnrt
-                         (funcall zgintr degr zggnrt))
-                        (:cmbn
-                         (funcall zgintr (term-cmbn degr 1 zggnrt))))
-            )))))))
-
-
-(DEFUN ZGmrph-ZGCMBN-? (ZGmrph zgcmbn)
-   (declare
-      (type ZG-morphism ZGmrph)
-      (fixnum degr)
-      (type zggnrt zggnrt))
-   (the cmbn
-     (with-slots (trgt zgintr zgstrt ) zgmrph
-       (with-slots (group zgcmpr) trgt
-            (declare
-             (type zg-chain-complex trgt)
-             (type intr-zgmrph zgintr)
-             (type zgstrt zgstrt)
-             (type group group)
-             )
-       (with-slots ((grcmpr cmpr) mult nullel) group
-         (declare
-          (type cmprf grcmpr)
-          (type function mult)
-          (type gnrt nullel))
-         (prog1
-          (ecase zgstrt
-            (:gnrt
-             (zgmrph-gnrt-zgcmbn grcmpr zgcmpr mult zgintr zgcmbn))
-            (:zggnrt
-             (zgmrph-zggnrt-zgcmbn grcmpr zgcmpr zgintr zgcmbn))
-            (:cmbn
-             (funcall zgintr zgcmbn)))
-            ))))))
-
-(Defun izgmrph-imrph (grcmpr zgcmpr mult intr strt)
-   (declare (type intr-zgmrph intr)
-     (type zgstrt strt))
-   (flet ((rslt (degr zggnrt)
-             (declare
-                (fixnum degr)
-                (type zggnrt zggnrt))
-             (ecase strt
-                        (:gnrt
-                         (zgmrph-gnrt-zggnrt grcmpr zgcmpr mult intr degr zggnrt))
-                        (:zggnrt
-                         (funcall intr degr zggnrt))
-                        (:cmbn
-                         (funcall intr (term-cmbn degr 1 zggnrt))))))
-     (the intr-mrph #'rslt)))
-
-
-(DEFUN INTR-ZGCHCM-MRPH (zgmrph)
-   (declare (type zg-morphism zgmrph))
-   (flet ((rslt (degr zggnrt)
-             (declare
-                (fixnum degr)
-                (type zggnrt zggnrt))
-             (zgmrph-zggnrt-? zgmrph degr zggnrt)))
-     (the intr-mrph #'rslt)))
-                
-               
-(DEFUN BUILD-ZGCHCM
-    (&key group zgcmpr zgbasis zgbsgn intr-zgbndr zgbndr-strt orgn)
-   (declare
-    (type group group)
-    (type cmprf zgcmpr)
-    (type basis zgbasis)
-    (type gnrt zgbsgn)
-    (type intr-zgmrph intr-zgbndr)
-    (type zgstrt zgbndr-strt)
-    (list orgn))
-   (let ((already (find orgn *zgcc-list* :test #'equal :key #'orgn)))
-      (declare (type (or zg-chain-complex null) already))
-      (when already
-         (return-from build-zgchcm already)))
-   (if intr-zgbndr
-      (unless zgbndr-strt
-            (error "In BUILD-ZGCHCM, an intr-zgbndr is given but not its strategy."))
-      )
-   (the zg-chain-complex
-     (with-slots ((grcmpr cmpr) (grbasis elements) mult nullel) group
-       (let* ((cmpr (zggnrt-cmpr grcmpr zgcmpr))
-              (basis (ZGCHCM-BASIS grbasis zgbasis))
-              (bsgn (zggnrt nullel zgbsgn))
-              (intr-dffr (izgmrph-imrph grcmpr zgcmpr mult intr-zgbndr zgbndr-strt))
-              (rslt (build-chcm :cmpr cmpr :basis basis :bsgn bsgn
-                     :intr-dffr intr-dffr :strt :gnrt :orgn orgn)))
-         (change-class rslt 'zg-chain-complex)
-         (setf (slot-value rslt 'group) group)
-         (setf (slot-value rslt 'zgcmpr) zgcmpr)
-         (setf (slot-value rslt 'zgbasis) zgbasis)
-         (setf (slot-value rslt 'zgbsgn) zgbsgn)
-         (setf (slot-value rslt 'zgbndr) (build-zgmrph :sorc rslt :trgt rslt :degr -1
-                                          :zgintr intr-zgbndr :zgstrt zgbndr-strt :orgn `(zgbndr ,rslt)))
-         (push rslt *zgcc-list*)
-         rslt))))
-
-
-(DEFUN BUILD-ZGMRPH (&key sorc trgt degr zgintr zgstrt orgn)
-   (declare
-    (type zg-chain-complex sorc trgt)
-    (fixnum degr)
-    (type intr-zgmrph intr)
-    (type zgstrt strt)
-    (list orgn))
-   (the zg-morphism
-     (with-slots (group zgcmpr) trgt
-       (with-slots ((grcmpr cmpr) (grbasis elements) mult nullel ) group
-         (let* ((intr (izgmrph-imrph grcmpr zgcmpr mult zgintr zgstrt))
-                (rslt (build-mrph :sorc sorc :trgt trgt :degr degr
-                        :intr intr :strt :gnrt :orgn orgn)))
-            (change-class rslt 'zg-morphism)
-            (setf (slot-value rslt 'zgintr) zgintr)
-            (setf (slot-value rslt 'zgstrt) zgstrt)
-            (push rslt *zgcc-list*)
-            rslt)))))
-
-
-
-
-
-;;(DEFMETHOD zg-?2 ((zgmrph zg-morphism) zgcmbn)
-;;   (declare (type zgcmbn zgcmbn))
-;;   (the zgcmbn
-;;      (zgmrph-zgcmbn-? zgmrph zgcmbn)))
-
-
-
-;;(DEFMETHOD zg-?3 ((zgmrph zg-morphism) degr gnrt)
-;;   (declare
-;;      (fixnum degr)
-;;      (type gnrt gnrt))
-;;   (the zgcmbn
-;;      (zgmrph-gnrt-? zgmrph degr gnrt)))
-
-
-
-
-;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
-;;;;;;;;;TENSOR WITH INTEGERS
-;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
-
-
-(DEFUN zgcmbn-twi (zgcmpr zgcmbn)
-   (declare (type zgcmbn zgcmbn))
-   (with-cmbn (degr list) zgcmbn
-     (if list
-        (let* ((cmbn-list +empty-list+))
-           (mapcar #'(lambda (zgterm)
-                       (with-zgterm (cffc zggnrt) zgterm
-                         (let ((gnrt2 (zggnrt2 zggnrt)))
-                            (push (cons 1
-                                    (term-cmbn degr cffc gnrt2))
-                              cmbn-list))))
-             list)
-           (cmbn-cmbn zgcmpr cmbn-list))
-     (zero-cmbn degr))))
-
-;; (setf zgcmbn (cmbn 5 2 (zggnrt 1 3) 3 (zggnrt 2 4)))
-;; (zgcmbn-twi #'f-cmpr zgcmbn)
-;; (setf zgcmbn2 (cmbn 5 2 (zggnrt 1 3) 3 (zggnrt 2 4) -8 (zggnrt 6 3)))
-;; (zgcmbn-twi #'f-cmpr zgcmbn2)
-
-
-(Defun zgmrph-twi-intr (mrph)
-   (declare (type zg-morphism mrph))     
-   (flet ((rslt (degr gnrt)
-             (declare
-                (fixnum degr)
-                (type zggnrt zggnrt))
-            (with-slots (trgt) mrph
-              (with-slots (zgcmpr) trgt
-             (zgcmbn-twi zgcmpr (zgmrph-gnrt-? mrph degr gnrt))))))
-     (the intr-mrph #'rslt)))
-
-(defun zgmrph-twi (mrph)
-   (declare (type zg-morphism mrph))
-   (the morphism
-     (with-slots (sorc trgt degr zgintr zgstrt orgn) mrph
-       (build-mrph :sorc (chcm-twi sorc) :trgt (chcm-twi trgt) :degr degr
-                     :intr (zgmrph-twi-intr mrph) :strt :gnrt :orgn `(tensor-with-integers ,orgn))
-                    )))
-
-(defun chcm-twi (chcm)
-   (declare (type zg-chain-complex chcm))
-   (the chain-complex
-     (if (string= (car (orgn chcm)) 'bar-zgchcm) 
-        (with-slots (group) chcm
-          (k-g-1 group))
-     (with-slots (zgcmpr zgbasis zgbsgn zgbndr orgn) chcm
-       (build-chcm :cmpr zgcmpr :basis zgbasis :bsgn zgbsgn :intr-dffr (zgmrph-twi-intr zgbndr) 
-        :strt :gnrt :orgn `(tensor-with-integers ,orgn))))))
-
-
-
-
-
-
-
-
-
-;;;;; EJEMPLOS
-
-
-#|
-(cat-init) 
-(setf Z3 (build-group :elements '(0 1 2) :cmpr #'f-cmpr :mult #'(lambda (g1 g2)
-                                                                  (mod (+ g1 g2) 3))
-          :inv #'(lambda (g)
-                 (mod (- 3 g) 3)) :nullel 0 :orgn '(Cyclic Group order 3)))
-
-(setf zgbasis #'(lambda (degr) (list degr)))
-(setf zgbspn 0)
-(setf zgcmpr #'f-cmpr)
-(setf intr #'(lambda(degr gnrt)
-               (let ((degr- (1- degr)))
-                  (if (oddp degr)
-                     (cmbn degr- -1 (zggnrt 0 degr-)  1 (zggnrt 1 degr-))
-                     (cmbn degr- 1 (zggnrt 0 degr-)  1 (zggnrt 1 degr-)  1 (zggnrt 2 degr-))))))
-
-(setf zgchcm (BUILD-ZGCHCM
-    :group Z3 :zgcmpr zgcmpr :zgbasis zgbasis :zgbsgn 0 :intr-zgbndr intr :zgbndr-strt :gnrt :orgn '(prueba)
-))
-
-(setf zgmrph (zgbndr1 zgchcm))
-(ZGmrph-GNRT-? zgmrph 4 4)
-(ZGmrph-zgGNRT-? zgmrph 4 (zggnrt 2 4))
-(ZGmrph-zgGNRT-? zgmrph 3 (zggnrt 0 3))
-(ZGmrph-zgGNRT-? zgmrph 3 (zggnrt 1 3))
-(ZGmrph-zgGNRT-? zgmrph 3 (zggnrt 2 3))
-(ZGmrph-zgGNRT-? zgmrph 4 (zggnrt 0 4))
-
-(ZGmrph-zgcmbn-? zgmrph (cmbn 4 1 (zggnrt 2 4) -3 (zggnrt 3 4)))
-(ZGmrph-zgcmbn-? zgmrph (cmbn 4 2 (zggnrt 2 4) -5 (zggnrt 3 4)))
-(ZGmrph-zgcmbn-? zgmrph (cmbn 3 1 (zggnrt 2 3) -3 (zggnrt 3 3)))
-(ZGmrph-zgGNRT-? zgmrph 3 (zggnrt 2 3))
-(ZGmrph-zgGNRT-? zgmrph 3 (zggnrt 3 3))
-
-
-(setf chcm (chcm-twi zgchcm))
-(? chcm 3 3)
-(? chcm 4 4)
-(? chcm 5 5 ))
-
-(homology chcm 0 10)
-
-|#
-
-
-#| 
-(setf ZCC
-      (the chain-complex
-        (build-chcm
-         :cmpr #'(lambda (gnrt1 gnrt2) (the cmpr :equal))
-         :basis #'(lambda (n)
-                    (the list
-                      (if (zerop n) '(:Z-gnrt) +empty-list+)))
-         :bsgn :Z-gnrt
-         :intr-dffr #'(lambda (cmbn)
-                        (the cmbn (zero-cmbn (1- (cmbn-degr cmbn)))))
-         :strt :cmbn
-         :orgn '(zcc-constant))))
-|#
-;; ya est� definido con la funci�n (z-chcm) 
-
-(defun cyclicgroup (n)
-   (declare (fixnum n))
-   (build-ab-group :elements (<a-b> 0 (1- n)) :cmpr #'f-cmpr :mult #'(lambda (g1 g2)
-                                                                  (mod (+ g1 g2) n))
-           :inv #'(lambda (g)
-                 (mod (- n g) n)) :nullel 0 :orgn `(Cyclic-group of order ,n)))
-
-
-(defun z-group ()
-    (build-ab-group :elements :locally-effective :cmpr #'f-cmpr :mult #'(lambda (g1 g2)
-                                                                  (+ g1 g2) )
-           :inv #'(lambda (g)
-                 (- g)) :nullel 0 :orgn `(z-group)))
-
-
-(DEFMETHOD SLOT-UNBOUND (class (group group) (slot-name (eql 'resolution)))
-   (declare (ignore class))
-   (the reduction
-     (let ((rsltn (search-resolution group (first (orgn group)))))
-       (setf (slot-value group 'resolution)
-	     (or rsltn
-          (error "I don't know how to determine ~
-                         a resolution for 
-                         ~A (Origin: ~A)." group (orgn group)))))))
-
-(DEFGENERIC SEARCH-resolution (group orgn))
-
-(DEFMETHOD SEARCH-RESOLUTION (group orgn)
-  (declare (ignore group orgn))
-  nil)
-
-
-
-      
-
-(defun cyclicgroup-zgchcm (n)
-   (let* ((group (cyclicgroup n))
-          (zgbasis #'(lambda (degr) (list degr)))
-          (zgcmpr #'f-cmpr)
-          (intr #'(lambda(degr gnrt)
-               (let ((degr- (1- degr)))
-                  (if (zerop degr) (zero-cmbn -1)
-                     (if (oddp degr)
-                        (cmbn degr- -1 (zggnrt 0 degr-)  1 (zggnrt 1 degr-))
-                        (let ((list +empty-list+))
-                           (mapcar #'(lambda (i)
-                                       (push (cons 1 (zggnrt (- n i) degr-)) list))
-                             (<a-b> 1  n))
-                           (make-cmbn :degr degr- :list list))))))))
-          (BUILD-ZGCHCM
-    :group group :zgcmpr zgcmpr :zgbasis zgbasis :zgbsgn 0 
-           :intr-zgbndr intr :zgbndr-strt :gnrt :orgn  `(ZG-Chain complex for ,group)
-)))
-                     
-#|
-(setf z5 (cyclicgroup 5))
-(setf z5-zgchcm (cyclicgroup-zgchcm 5))
-(? z5-zgchcm 3 (zggnrt 2 3))
-(? z5-zgchcm 4 (zggnrt 2 4))
-|#   
-
-
-(defun cyclicgroup-rsltn (n)
-   (let* ((group (cyclicgroup n))
-          (zgchcm (cyclicgroup-zgchcm n))
-          (cmpr (cmpr1 zgchcm))
-          (f-intr #'(lambda (degr zggnrt)
-                      (with-zggnrt (gnrt1 gnrt2) zggnrt
-                        (if (zerop degr) (cmbn degr 1 :zgnrt) (zero-cmbn degr)))))
-          (g-intr #'(lambda (degr gnrt)
-                      (if (zerop degr) (cmbn degr 1 (zggnrt 0 0)) (zero-cmbn degr))))
-          (h-intr #'(lambda (degr zggnrt)
-                      (with-zggnrt (gnrt1 gnrt2) zggnrt
-                        (if (oddp degr)
-                           (if (= gnrt1 (1- n)) (cmbn (1+ degr) 1 (zggnrt 0 (1+ degr)))
-                              (zero-cmbn (1+ degr)))
-                           (let ((list +empty-list+))
-                              (dotimes (i gnrt1)
-                                 (push (cons 1 (zggnrt i (1+ degr))) list ))
-                              (make-cmbn :degr (1+ degr) :list (nreverse list)))))))
-          (f (build-mrph :sorc zgchcm :trgt (z-chcm) :degr 0 :intr f-intr :strt :gnrt :orgn `(f-mrph for ,group)))
-          (g (build-mrph :sorc (z-chcm) :trgt zgchcm :degr 0 :intr g-intr :strt :gnrt :orgn  `(g-mrph for ,group)))
-          (h (build-mrph :sorc zgchcm :trgt zgchcm :degr 1 :intr h-intr :strt :gnrt :orgn `(h-mrph for ,group))))
-      (build-rdct :f f :g g :h h :orgn `(Resolution of ,group)))) 
-                      
-
-(DEFMETHOD SEARCH-RESOLUTION (group (orgn (eql 'Cyclic-group)))
-  (declare
-     (type group group))
-  (the reduction
-    (with-slots (elements) group
-      (let ((n (length elements)))
-         (cyclicgroup-rsltn n)))))
-
-
-                      
-#|(defun cyclicgroup-with-resolution (n)
-   (let ((group (cyclicgroup n))
-         (rsltn (cyclicgroup-rsltn n)))
-      (setf (slot-value group 'resolution) rsltn)
-      group))
-|#
-
-(DEFMETHOD HOMOLOGY ((group group) degr1 &optional (degr2 (1+ degr1)))
-   (declare (fixnum degr1 degr2))
-   (with-slots (resolution) group 
-     (let ((chcm (chcm-twi (tcc resolution))))
-        (homology chcm degr1 degr2))))
-            
-#|
-(setf z3 (cyclicgroup 3))
-(homology z3 0 6)
-(setf g (build-group :elements '(0 1 2) :cmpr #'f-cmpr :mult #'(lambda (g1 g2)
-                                                                  (mod (+ g1 g2) 3))
-          :inv #'(lambda (g)
-                 (mod (- 3 g) 3)) :nullel 0 :orgn '(hola)))
-(homology g 0 6) 
-|#
-
-
-
-;;;; BAR RESOLUTION
-
-
-(defun bar-zgcmpr (grcmpr)
-   (declare (type cmprf grcmpr))
-   (labels ((rslt (gnrt1 gnrt2)
-           (declare (list gnrt1 gnrt2))
-           (unless gnrt1
-              (return-from rslt (if gnrt2 :less :equal)))
-           (unless gnrt2
-              (return-from rslt :greater))
-           (lexico
-            (funcall grcmpr (first gnrt1) (first gnrt2))
-            (rslt (rest gnrt1) (rest gnrt2)))
-         ))
-      (the cmprf #'rslt)))
-
-(defun bar-zgbasis (elements nullel)
-   (declare (type group-basis elements)
-     (type gnrt nullel))
-   (when (eq elements :locally-effective)
-      (return-from bar-zgbasis :locally-effective))
-   (labels ((rslt (degr)
-            (declare (fixnum degr))
-            ;;(the list
-              (progn
-               (when (minusp degr)
-                  (return-from rslt +empty-list+))
-               (when (zerop degr)
-                  (return-from rslt (list (list))))
-               (let ((basis-1 (rslt (1- degr)))
-                     (elements-0 (remove nullel elements)))
-                    (mapcan #'(lambda (gbar)
-                                (mapcar #'(lambda (g)
-                                            (append gbar (list g)))
-                                  elements-0)
-                                )
-                      basis-1)))))
-     ;;)
-     (the basis #'rslt)))
-                    
-                    
-
-(DEFUN bar-bndr-i (grmult nullel indx degr gnrt)
-   (declare
-    (fixnum indx degr)
-    (list gnrt))
-   (the cmbn
-     (cond ((zerop indx) (cmbn (1- degr) 1 (zggnrt (car gnrt) (rest gnrt))))
-           ((= indx degr) (cmbn (1- degr) 1 (zggnrt nullel (butlast gnrt))))
-           (t
-            (do ((rslt +empty-list+ (cons (car mark) rslt))
-                 (mark gnrt (cdr mark))
-                 (i 1 (1+ i)))
-                ((= i indx) (let ((new-k (funcall grmult (car mark) (cadr mark))))
-                                        (declare (type gnrt new-k))
-                               (if (equal nullel new-k)
-                                  (zero-cmbn (1- degr)) 
-                                  (cmbn (1- degr) 1 (zggnrt nullel (nreconc rslt (cons new-k (cddr mark))))))))
-               (declare
-                (list rslt mark)
-                (fixnum i)))))))
-
-
-(defun bar-bndr-intr (grcmpr grmult nullel)
-    #'(lambda (degr gnrt)
-        (if (zerop degr)
-           (zero-cmbn -1)
-           (let ((cmbn-list
-                  (mapcar #'(lambda (indx)
-                              (let ((cmbn (bar-bndr-i grmult nullel indx degr gnrt)))
-                                 (if (oddp indx)
-                                    (cons -1 cmbn)
-                                    (cons 1 cmbn))))
-                    (<a-b> 0 degr))))
-              (cmbn-cmbn (zggnrt-cmpr grcmpr (bar-zgcmpr grcmpr)) cmbn-list)))))
-     
-
-
-(defun bar-zgchcm (group)
-   (declare (type group group))
-  (the zg-chain-complex
-    (with-slots (elements cmpr mult nullel) group
-     (build-zgchcm
-      :group group
-      :zgcmpr (bar-zgcmpr cmpr)
-	:zgbasis (bar-zgbasis elements nullel)
-	:zgbsgn +empty-list+
-	:intr-zgbndr (bar-bndr-intr cmpr mult nullel)
-      :zgbndr-strt :gnrt
-	:orgn  `(bar-zgchcm ,group)))))
-
-(defun bar-cntrhmtp-intr (grcmpr grmult nullel)
-   #'(lambda (degr zggnrt)
-                      (with-zggnrt (gnrt1 gnrt2) zggnrt
-                        (if (equal nullel gnrt1)
-                           (zero-cmbn (1+ degr))
-                           (if (zerop degr)
-                              (cmbn 1 1 (zggnrt nullel (list gnrt1)))
-                              (cmbn (1+ degr) 1 (zggnrt nullel (cons gnrt1 gnrt2))))))))
-   
-
-(defun bar-f-intr ()
-   #'(lambda (degr zggnrt)
-       (if (zerop degr) (cmbn degr 1 :zgnrt) (zero-cmbn degr))))
-
-
-(defun bar-g-intr (nullel)
-   #'(lambda (degr gnrt)
-         (if (zerop degr) (cmbn degr 1 (zggnrt nullel +empty-list+)) (zero-cmbn degr))))
-
-(defun bar-rsltn (group)
-   (declare (type group group))
-   (the reduction
-    (with-slots (cmpr mult nullel) group
-      (let* ((zgchcm (bar-zgchcm group))
-             (f (build-mrph :sorc zgchcm :trgt (z-chcm) :degr 0 :intr (bar-f-intr) :strt :gnrt :orgn `(f-mrph in bar-resolution for ,group)))
-             (g (build-mrph :sorc (z-chcm) :trgt zgchcm :degr 0 :intr (bar-g-intr nullel) :strt :gnrt :orgn  `(g-mrph in bar-resolution for ,group)))
-             (h (build-mrph :sorc zgchcm :trgt zgchcm :degr 1 :intr (bar-cntrhmtp-intr cmpr mult nullel)
-                  :strt :gnrt :orgn `(h-mrph in bar-resolution for ,group))))
-         (build-rdct :f f :g g :h h :orgn `(Bar-resolution of ,group)))))) 
-
-
-                   
-;;; EJEMPLOS
-
-#|
-(setf z5 (cyclicgroup 5))
-(setf bar-chcm-z5 (bar-zgchcm z5))
-
-(setf zgbasis (zgbasis1 bar-chcm-z5))
-(funcall zgbasis 2)
-
-(setf zgmrph (zgbndr1 bar-chcm-z5))
-(ZGmrph-GNRT-? zgmrph 4 '(1 2 3 4))
-(ZGmrph-zgGNRT-? zgmrph 4 (zggnrt 2 '(1 2 3 4)))
-(ZGmrph-zgGNRT-? zgmrph 4 (zggnrt 1 '(1 1 4 4)))
-(ZGmrph-zgcmbn-? zgmrph (cmbn 4 1 (zggnrt 2 '(1 2 3 4)) -3 (zggnrt 1 '(1 1 4 4))))
-
-(setf chcm (chcm-twi bar-chcm-z5))
-(? chcm 4 '(1 2 3 4))
-(? chcm 5 '(1 1 2 3 4))
-
-
-(homology chcm 3)
-
-
-(setf bar-rsltn-z5 (bar-rsltn z5))
-(pre-check-rdct bar-rsltn-z5)
-
-(setf *tc* (cmbn 4 3 (zggnrt 4 '(1 2 1 4)) -3 (zggnrt 2 '(3 1 2 3)) 8 (zggnrt 1 '(4 4 3 2))))
-
-(setf *bc* (cmbn 0 1 :zgnrt))
-
-(check-rdct)
-
-
-
-|# 
-
-
-
-
-
-
-
-
-(defun K-G-1-cmpr (grcmpr)
-   (declare (type cmprf grcmpr))
-   (labels ((rslt (gnrt1 gnrt2)
-           (declare (list gnrt1 gnrt2))
-           (unless gnrt1
-              (return-from rslt (if gnrt2 :less :equal)))
-           (unless gnrt2
-              (return-from rslt :greater))
-           (lexico
-            (funcall grcmpr (first gnrt1) (first gnrt2))
-            (rslt (rest gnrt1) (rest gnrt2)))
-         ))
-      (the cmprf #'rslt)))
-
-
-#|
-(defun K-G-1-basis (elements nullel)
-   (declare (type group-basis elements)
-     (type gnrt nullel))
-   (when (eq elements :locally-effective)
-      (return-from K-G-1-basis :locally-effective))
-   (labels ((rslt (degr)
-            (declare (fixnum degr))
-            ;;(the list
-              (progn
-               (when (minusp degr)
-                  (return-from rslt +empty-list+))
-               (when (zerop degr)
-                  (return-from rslt (list (list))))
-               (let ((basis-1 (rslt (1- degr)))
-                     (elements-0 (remove nullel elements)))
-                    (mapcan #'(lambda (gbar)
-                                (mapcar #'(lambda (g)
-                                            (append gbar (list g)))
-                                  elements-0)
-                                )
-                      basis-1)))))
-     ;;)
-     (the basis #'rslt)))
-|#
-
-(defun K-G-1-basis (elements nullel)
-   (declare (type group-basis elements)
-     (type gnrt nullel))
-   (when (eq elements :locally-effective)
-      (return-from K-G-1-basis :locally-effective))
-   (labels ((rslt (degr)
-            (declare (fixnum degr))
-            ;;(the list
-              (progn
-               (when (minusp degr)
-                  (return-from rslt +empty-list+))
-               (when (zerop degr)
-                  (return-from rslt (list (list))))
-               (let ((basis-1 (rslt (1- degr)))
-                     (elements-0
-                      
-                  (do ((indx 0 (1+ indx))
-                      (aux +empty-list+))
-                    ((>= indx (length elements)) (nreverse aux))
-                    (if (not (equal nullel (nth indx elements)))
-                       (push (nth indx elements) aux)))))
-                     
-                   
-                    (mapcan #'(lambda (gbar)
-                                (mapcar #'(lambda (g)
-                                            (append gbar (list g)))
-                                  elements-0)
-                                )
-                      basis-1)))))
-     ;;)
-     (the basis #'rslt)))
-                    
-                    
-
-(DEFUN K-G-1-FACE (grmult nullel)
-   (flet ((face (indx dmns gmsm)
-            (declare
-             (fixnum indx dmns)
-             (list gmsm))
-            (the absm
-              (cond ((zerop indx) (absm 0 (rest gmsm)))
-                    ((= indx dmns) (absm 0 (butlast gmsm)))
-                    (t
-                     (do ((rslt +empty-list+ (cons (car mark) rslt))
-                          (mark gmsm (cdr mark))
-                          (i 1 (1+ i)))
-                         ((= i indx) (let ((new-k (funcall grmult (car mark) (cadr mark))))
-                                        (declare (type gnrt new-k))
-                                        (if (equal nullel new-k)
-                                           (absm (2-exp (1- indx)) (nreconc rslt (cddr mark)))
-                                           (absm 0 (nreconc rslt (cons new-k (cddr mark)))))))
-                        (declare
-                         (list rslt mark)
-                         (fixnum i))))))))
-     (the face #'face)))
-         
-   
-(DEFUN G-ABSM-BAR (nullel absm)
-  (declare (type absm absm))
-  (the list
-    (with-absm (dgop bar1) absm
-      (do ((dgop dgop (ash dgop -1))
-	   (rslt +empty-list+))
-	  ((and (zerop dgop) (endp bar1)) (nreverse rslt))
-	  (declare
-	     (fixnum dgop)
-	     (list rslt))
-	  (push (if (oddp dgop)
-		    nullel
-		  (pop bar1))
-		rslt)))))
-
-
-(DEFUN G-BAR-ABSM (nullel bar)
-  (declare (list bar))
-  (the absm
-     (do ((rslt-dgop 0)
-	  (rslt-bar +empty-list+)
-	  (mark bar (cdr mark))
-	  (bark 1 (+ bark bark)))
-	 ((endp mark) (absm rslt-dgop (nreverse rslt-bar)))
-	(declare
-	   (fixnum rslt-dgop bark)
-	   (list rslt-bar mark))
-	(let ((k-i (car mark)))
-	  (declare (fixnum k-i))
-	  (if (equal nullel k-i)
-	     (incf rslt-dgop bark)
-	     (push k-i rslt-bar))))))
-
- 
-
-(DEFUN K-G-1-GRML (grmult nullel)
-   (flet ((grml (dmns crpr)
-            (declare
-             (fixnum dmns)
-             (type crpr crpr))
-            (the absm
-              (with-crpr (dgop1 bar1 dgop2 bar2) crpr
-                (do ((indx 1 (1+ indx))
-                     (dgop1 dgop1 (ash dgop1 -1))
-                     (dgop2 dgop2 (ash dgop2 -1))
-                     (bark 1 (ash bark +1))
-                     (rslt-dgop 0)
-                     (rslt-bar +empty-list+))
-                    ((> indx dmns) (absm rslt-dgop (nreverse rslt-bar)))
-                   (declare
-                    (fixnum indx dgop1 dgop2 bark rslt-dgop)
-		(list rslt-bar))
-                   (let ((item (if (evenp dgop1)
-                                  (if (evenp dgop2)
-                                     (funcall grmult (pop bar1) (pop bar2))
-                                     (pop bar1))
-                                  (if (evenp dgop2)
-                                     (pop bar2)
-                                     nullel))))
-                      (declare (type gnrt item))
-                      (if (equal nullel item)
-                         (incf rslt-dgop bark)
-                         (push item rslt-bar))))))))
-     (the intr-mrph #'grml)))
-
-
-(DEFUN K-G-1-GRIN (grin)
-   (flet ((grin (dmns bar)
-            (declare
-             (ignore dmns)
-             (list bar))
-            (the absm
-              (absm 0 (mapcar #'grin bar)))))
-     (the intr-mrph #'grin)))
-          
-
-
-(DEFMETHOD K-G-1 ((group GROUP))
-   (declare (type group group))
-  (the simplicial-group
-    (if (string= (car (orgn group)) 'z-group) 
-        (k-z-1)
-       
-       (with-slots (elements cmpr mult nullel inv) group
-         (build-smgr
-          :cmpr (k-g-1-cmpr cmpr)
-          :basis (k-g-1-basis elements nullel)
-          :bspn +empty-list+
-          :face (k-g-1-face mult nullel)
-          :sintr-grml (k-g-1-grml mult nullel)
-          :sintr-grin (k-g-1-grin inv)
-          :orgn  `(k-g-1 ,group)))
-       )))
-
-(DEFMETHOD K-G-1 ((group AB-GROUP))
-   (declare (type AB-group group))
-  (the AB-simplicial-group
-    (if (string= (car (orgn group)) 'z-group) 
-        (k-z-1)
-       (with-slots (elements cmpr mult nullel inv) group
-     (build-AB-smgr
-      :cmpr (k-g-1-cmpr cmpr)
-	:basis (k-g-1-basis elements nullel)
-	:bspn +empty-list+
-	:face (k-g-1-face mult nullel)
-	:sintr-grml (k-g-1-grml mult nullel)
-	:sintr-grin (k-g-1-grin inv)
-	:orgn  `(k-g-1 ,group)))
-    )))
-
-
-(defun K-G-0-basis (elements)
-   (declare (type group-basis elements))
-   (when (eq elements :locally-effective)
-      (return-from K-G-0-basis :locally-effective))
-   (labels ((rslt (degr)
-            (declare (fixnum degr))
-            ;;(the list
-              (progn
-               (when (not (equal degr 0))
-                  (return-from rslt +empty-list+))
-               (return-from rslt elements)
-               )))
-     ;;)
-     (the basis #'rslt)))
-
-
-
-(DEFUN K-G-0-FACE ()
-   (flet ((face (indx dmns gmsm)
-            (declare
-             (fixnum indx dmns)
-             (gnrt gmsm))
-            (the absm
-              (absm 0 gmsm))))
-     (the face #'face)))
-
-(DEFUN K-G-0-GRML (grmult)
-   (flet ((grml (dmns crpr)
-            (declare
-             (fixnum dmns)
-             (type crpr crpr))
-            (the absm
-              (with-crpr (dgop1 g1 dgop2 g2) crpr
-               (absm (dgop-ext-int (nreverse (<a-b> 0 (1- dmns)))) (funcall grmult g1 g2)))
-                )))
-     (the intr-mrph #'grml)))
-
-(DEFUN K-G-0-GRIN (grin)
-   (flet ((grin (dmns g)
-            (declare
-             (ignore dmns)
-             (gnrt g))
-            (the absm
-              (absm 0 (funcall grin g)))))
-     (the intr-mrph #'grin)))
-
-
-(DEFMETHOD K-G-0 ((group GROUP))
-   (declare (type group group))
-  (the simplicial-group
-    (with-slots (elements cmpr mult nullel inv) group
-     (build-smgr
-      :cmpr cmpr
-	:basis (k-g-0-basis elements)
-	:bspn nullel
-	:face (k-g-0-face)
-	:sintr-grml (k-g-0-grml mult)
-	:sintr-grin (k-g-0-grin inv)
-	:orgn  `(k-g-0 ,group)))
-    ))
-
-(DEFMETHOD K-G-0 ((group AB-GROUP))
-   (declare (type AB-group group))
-  (the AB-simplicial-group
-    (with-slots (elements cmpr mult nullel inv) group
-     (build-AB-smgr
-      :cmpr cmpr
-	:basis (k-g-0-basis elements)
-	:bspn nullel
-	:face (k-g-0-face)
-	:sintr-grml (k-g-0-grml mult)
-	:sintr-grin (k-g-0-grin inv)
-	:orgn  `(k-g-0 ,group)))
-
-    ))
-
-
-
-
-(DEFMETHOD K-G ((gROUP ab-group) n)
-   (declare (fixnum n)
-     (type AB-group group))
-   (the ab-simplicial-group
-     (if (= n 0)
-        (k-g-0 group)
-        (if (= n 1)
-           (k-g-1 group)
-           (classifying-space (k-g group (1- n)))))))
-
-(DEFMETHOD K-G ((group gROUP) n)
-   (declare (fixnum n)
-     (type group group))
-   (the simplicial-group
-     (if (= n 0)
-        (k-g-0 group)
-        (if (= n 1)
-           (k-g-1 group)
-           (classifying-space (k-g group (1- n)))))))
-
-(DEFUN K-ZP-1 (p)
-   (k-g-1 (cyclicgroup p)))
-
-(DEFUN K-Zp (p n)
-   (declare (fixnum p n)
-     )
-   (the ab-simplicial-group
-     (if (= n 0) 
-        (k-g-0 (cyclicgroup p))
-      (if (= n 1)
-         (k-Zp-1 p)
-         (classifying-space (k-Zp p (1- n)))))))
-
-
-(defun univ-fbrt-intr (G n)
-   (declare
-    (type group G)
-    (fixnum n))
-   (flet ((rslt (degr gmsm)
-            (declare 
-              (fixnum degr)
-              (type gnrt gmsm))
-            (if (equal n 1)
-               (absm (dgop-ext-int (nreverse (<a-b> 0 (- degr 2)))) (first (last gmsm)))
-               (with-gbar (d list) gmsm
-                 (first list)))))
-     (the sintr #'rslt)))
-            
-            
-(defun univ-fbrt-tw (G n)
-   (the fibration
-      (build-smmr
-         :sorc (k-g g n) :trgt (k-g g (1- n)) :degr -1
-         :sintr (univ-fbrt-intr G n)
-         :orgn `(universal fibration ,G ,n))))
-  
-
-(defun rsltn-zgchcm (rsltn)
-   (declare (type reduction rsltn))
-   (tcc rsltn))
-
-(defun rsltn-cntrhmtp (rsltn)
-   (declare (type reduction rsltn))
-   (h rsltn))
-   
-(defun 2rsltn-zgmrph-intr (rsltn1 rsltn2)
-   (let ((zgchcm1 (rsltn-zgchcm rsltn1))
-         (zgchcm2 (rsltn-zgchcm rsltn2))
-         (h2 (rsltn-cntrhmtp rsltn2))
-         (f1 (f rsltn1))
-         (g2 (g rsltn2))
-         (d1 (zgbndr1 (rsltn-zgchcm rsltn1))))
-      
-      (with-slots (group (zgcmpr2 zgcmpr)) zgchcm2
-        (with-slots ((grcmpr cmpr) mult nullel) group
-          (labels ((rslt (degr gnrt)
-                     (if (zerop degr)
-                        (? g2 (? f1 degr (zggnrt nullel gnrt)))
-                        (? h2 
-                          
-                          (with-cmbn (degr- list) (zgmrph-gnrt-? d1 degr gnrt)
-                            (let ((n-cmbn-list +empty-list+))
-                               (declare (list n-cmbn-list))
-                               (do ((mark list (cdr mark))
-                                    )
-                                   ((endp mark))
-                                  (declare (list mark))
-                                  (with-term (cffc ZGgnrt) (car mark) 
-                                    (push 
-                                      (cons cffc 
-                                        
-                                        (let* ((gnrt1 (zggnrt1 zggnrt))
-                                               (gnrt2 (zggnrt2 zggnrt))
-                                               (zgcmbn (rslt degr- gnrt2))
-                                               (list (cmbn-list zgcmbn))
-                                               (n-cmbn-list2 +empty-list+))
-                                           (declare (list n-cmbn-list2))
-                                           (if list 
-                                              (progn 
-                                                (mapcar #'(lambda (zgterm)
-                                                            (declare (type zgterm zgterm))
-                                                            (with-zgterm (cffc2 zggnrt2) zgterm
-                                                             (declare (type fixnum cffc2)
-                                                               (type zggnrt zggnrt2))
-                                                             (with-zggnrt (gnrt21 gnrt22) zggnrt2
-                                                              (declare (type gnrt gnrt21 gnrt22))
-                                                              (push (cons 1
-                                                                      (term-cmbn degr- cffc2 (zggnrt (funcall mult gnrt1 gnrt21) gnrt22)))
-                                                                n-cmbn-list2))))
-                                                  list)
-                                                (cmbn-cmbn (zggnrt-cmpr grcmpr zgcmpr2) n-cmbn-list2))
-                                              (zero-cmbn degr-))))
-                                        
-
-                                        n-cmbn-list)))
-                               (cmbn-cmbn (zggnrt-cmpr grcmpr zgcmpr2) n-cmbn-list)))))))
-            #'rslt)))))
-                          
-
-
-
-                    
-
-
-(defun 2rsltn-zgmrph (rsltn1 rsltn2)
-   (let ((zgchcm1 (rsltn-zgchcm rsltn1))
-         (zgchcm2 (rsltn-zgchcm rsltn2)))
-      (build-zgmrph :sorc zgchcm1 :trgt zgchcm2 :degr 0 :zgintr (2rsltn-zgmrph-intr rsltn1 rsltn2)
-       :zgstrt :gnrt :orgn `(ZG-morphism from ,rsltn1 to ,rsltn2))))
-
-
-#|
-
-(cat-init) 
-(setf z3 (cyclicgroup 3))
-(setf rsltn1 (cyclicgroup-rsltn 3))
-(setf rsltn2 (bar-rsltn z3))
-(setf f (2rsltn-zgmrph rsltn1 rsltn2))
-(setf g (2rsltn-zgmrph rsltn2 rsltn1))
-
-(setf zgchcm1 (rsltn-zgchcm rsltn1))
-(setf zgchcm2 (rsltn-zgchcm rsltn2))
-(setf f1 (f rsltn1)
-         g2 (g rsltn2))
-(setf d1 (zgbndr1 (rsltn-zgchcm rsltn1)))
-(setf h2 (rsltn-cntrhmtp rsltn2))
-(setf group (group1 zgchcm2) zgcmpr2 (zgcmpr1 zgchcm2))
-(setf grcmpr (cmpr1 group) mult (mult1 group) nullel (nullel group))
-
-(ZGmrph-GNRT-? f 0 0)
-(ZGmrph-zgGNRT-? f 0 (zggnrt 0 0))
-(ZGmrph-zgGNRT-? f 0 (zggnrt 1 0))
-(ZGmrph-zgGNRT-? f 0 (zggnrt 2 0))
-(ZGmrph-zgGNRT-? f 1 (zggnrt 0 1))
-(ZGmrph-zgGNRT-? f 1 (zggnrt 1 1))
-(ZGmrph-zgGNRT-? f 1 (zggnrt 2 1))
-
-(ZGmrph-zgGNRT-? f 2 (zggnrt 2 2))
-(? f 2 (zggnrt 2 2))
-
-
-(zgmrph-gnrt-? f 1 1)
-(setf f-intr (2rsltn-zgmrph-intr rsltn1 rsltn2))
-(funcall f-intr 1 1)
-
-     
-|#
-
-
-
-(defun 2rsltn-hmtpop-intr (rsltn1 rsltn2)
-   (let ((zgchcm1 (rsltn-zgchcm rsltn1))
-         (h1 (rsltn-cntrhmtp rsltn1))
-         (m (2rsltn-zgmrph rsltn1 rsltn2))
-         (n (2rsltn-zgmrph rsltn2 rsltn1))
-         (d1 (zgbndr1 (rsltn-zgchcm rsltn1))))
-      
-      
-      (with-slots (group (zgcmpr1 zgcmpr)) zgchcm1
-        (with-slots ((grcmpr cmpr) mult nullel) group
-          (let ((cmpr (zggnrt-cmpr grcmpr zgcmpr1)))
-             
-             (labels ((rslt (degr gnrt)
-                       (if (zerop degr)
-                        (2cmbn-sbtr cmpr (? h1 degr (zggnrt nullel gnrt)) 
-                                         (? h1 (zgmrph-zgcmbn-? n (zgmrph-gnrt-? m degr gnrt))))
-                          (2cmbn-sbtr cmpr (2cmbn-sbtr cmpr (? h1 degr (zggnrt nullel gnrt)) 
-                                         (? h1 (zgmrph-zgcmbn-? n (zgmrph-gnrt-? m degr gnrt))))
-                           (? h1 
-                             (with-cmbn (degr- list) (zgmrph-gnrt-? d1 degr gnrt)
-                            (let ((n-cmbn-list +empty-list+))
-                               (declare (list n-cmbn-list))
-                               (do ((mark list (cdr mark))
-                                    )
-                                   ((endp mark))
-                                  (declare (list mark))
-                                  (with-term (cffc ZGgnrt) (car mark) 
-                                    (push 
-                                      (cons cffc 
-                                        
-                                        (let* ((gnrt1 (zggnrt1 zggnrt))
-                                               (gnrt2 (zggnrt2 zggnrt))
-                                               (zgcmbn (rslt degr- gnrt2))
-                                               (list (cmbn-list zgcmbn))
-                                               (n-cmbn-list2 +empty-list+))
-                                           (declare (list n-cmbn-list2))
-                                           (if list 
-                                              (progn 
-                                                (mapcar #'(lambda (zgterm)
-                                                            (declare (type zgterm zgterm))
-                                                            (with-zgterm (cffc2 zggnrt2) zgterm
-                                                             (declare (type fixnum cffc2)
-                                                               (type zggnrt zggnrt2))
-                                                             (with-zggnrt (gnrt21 gnrt22) zggnrt2
-                                                              (declare (type gnrt gnrt21 gnrt22))
-                                                              (push (cons 1
-                                                                      (term-cmbn degr cffc2 (zggnrt (funcall mult gnrt1 gnrt21) gnrt22)))
-                                                                n-cmbn-list2))))
-                                                  list)
-                                                (cmbn-cmbn cmpr n-cmbn-list2))
-                                              (zero-cmbn degr))))
-                                        
-
-                                        n-cmbn-list)))
-                               (cmbn-cmbn cmpr n-cmbn-list)))
-                             
-                             
-                             
-                             
-                             
-                             
-                             
-                             
-                             )))))
-                          
-                          
-            #'rslt))))))
-
-(defun 2rsltn-hmtpop (rsltn1 rsltn2)
-   (let ((zgchcm1 (rsltn-zgchcm rsltn1))
-         )
-      (build-zgmrph :sorc zgchcm1 :trgt zgchcm1 :degr 1 :zgintr (2rsltn-hmtpop-intr rsltn1 rsltn2)
-       :zgstrt :gnrt :orgn `(ZG-homotopy-operator from ,rsltn1 to ,rsltn2))))
-
-
-
-#|
-
-(cat-init) 
-(setf z3 (cyclicgroup 3))
-(setf rsltn1 (cyclicgroup-rsltn 3))
-(setf rsltn2 (bar-rsltn z3))
-(setf f (2rsltn-zgmrph rsltn1 rsltn2))
-(setf g (2rsltn-zgmrph rsltn2 rsltn1))
-(setf k1 (2rsltn-hmtpop rsltn1 rsltn2))
-(setf k2 (2rsltn-hmtpop rsltn2 rsltn1))
-
-
-
-(setf zgchcm1 (rsltn-zgchcm rsltn1))
-(setf zgchcm2 (rsltn-zgchcm rsltn2))
-(setf d1 (zgbndr1 zgchcm1))
-(setf d2 (zgbndr1 zgchcm2))
-
-(setf iz1 (add (cmps d1 k1) (cmps k1 d1)))
-(setf drch1 (sbtr (idnt-mrph zgchcm1) (cmps g f)))
-
-(setf iz2 (add (cmps d2 k2) (cmps k2 d2)))
-(setf drch2 (sbtr (idnt-mrph zgchcm2) (cmps f g)))
-
-(? iz1 0 (zggnrt 0 0))
-(? drch1 0 (zggnrt 0 0))
-
-(? iz1 1 (zggnrt 0 1))
-(? drch1 1 (zggnrt 0 1))
-(? iz1 2 (zggnrt 0 2))
-(? drch1 2 (zggnrt 0 2))
-(? iz1 3 (zggnrt 0 3))
-(? drch1 3 (zggnrt 0 3))
-
-(? d1 (? k1 1 (zggnrt 0 1)))
-(? k1 (? d1 1 (zggnrt 0 1)))
-(? (cmps g f) 1 (zggnrt 0 1))
-(? f 1 (zggnrt 0 1))
-(? g (? f 1 (zggnrt 0 1)))
-
-
-(dotimes (i 6)
-   (progn
-    (print (? iz1 i (zggnrt 0 i)))
-    (print (? drch1 i (zggnrt 0 i)))
-))
-
-(? iz2 1 (zggnrt 0 '(1)))
-(? drch2 1 (zggnrt 0 '(1)))
-(? iz2 2 (zggnrt 0 '(2 1)))
-(? drch2 2 (zggnrt 0 '(2 1)))
-(? iz2 2 (zggnrt 0 '(1 1)))
-(? drch2 2 (zggnrt 0 '(1 1)))
-
-
-(? iz2 3 (zggnrt 0 '(1 1 2)))
-(? drch2 3 (zggnrt 0 '(1 1 2)))
-|#
-
-
-#| 
-(cat-init) 
-(setf z4 (cyclicgroup 4))
-(setf rsltn1 (bar-rsltn z4))
-(setf rsltn2 (cyclicgroup-rsltn 4))
-
-(setf f (2rsltn-zgmrph rsltn1 rsltn2))
-(setf g (2rsltn-zgmrph rsltn2 rsltn1))
-(setf h (2rsltn-hmtpop rsltn1 rsltn2))
-(setf k (2rsltn-hmtpop rsltn2 rsltn1))
-
-(setf zgchcm1 (rsltn-zgchcm rsltn1))
-(setf zgchcm2 (rsltn-zgchcm rsltn2))
-(setf d1 (zgbndr1 zgchcm1))
-(setf d2 (zgbndr1 zgchcm2))
-
-(setf h2 (rsltn-cntrhmtp rsltn2)
-         f1 (f rsltn1)
-         g2 (g rsltn2))
-
-(setf group (group1 zgchcm2)
-      zgcmpr2 (zgcmpr1 zgchcm2))
-
-(setf grcmpr (cmpr1 group) mult (mult1 group) nullel (nullel group))
-
-         
-
-
-
-(setf iz1 (add (cmps d1 h) (cmps h d1)))
-(setf drch1 (sbtr (idnt-mrph zgchcm1) (cmps g f)))
-
-(? iz1 0 (zggnrt 0 '()))
-(? drch1 0 (zggnrt 0 '()))
-(? f 0 (zggnrt 0 nil))
-
-(? iz1 1 (zggnrt 0 '(1)))
-(? drch1 1 (zggnrt 0 '(1)))
-(? f 1 (zggnrt 0 '(1)))
-
-
-(? iz1 2 (zggnrt 0 '(1 1)))
-(? drch1 2 (zggnrt 0 '(1 1)))
-
-(? iz1 3 (zggnrt 0 '(1 1 1)))
-(? drch1 3 (zggnrt 0 '(1 1 1)))
-
-(? iz1 4 (zggnrt 0 '(1 1 1 1)))
-(? drch1 4 (zggnrt 0 '(1 1 1 1)))
-
-(setf iz2 (add (cmps d2 k) (cmps k d2)))
-(setf drch2 (sbtr (idnt-mrph zgchcm2) (cmps f g)))
-
-(? iz2 4 (zggnrt 0 4))
-(? drch2 4 (zggnrt 0 4))
-
-
-|# 
-
-(defun K-Cm-n (m n)
-   (K-Zp m n))
-
- 
\ No newline at end of file
diff --git a/examples/anromero/suspended-classifying-spaces-lisp-files/suspended-classifying-spaces-examples.cl b/examples/anromero/suspended-classifying-spaces-lisp-files/suspended-classifying-spaces-examples.cl
deleted file mode 100644
index eacd832..0000000
--- a/examples/anromero/suspended-classifying-spaces-lisp-files/suspended-classifying-spaces-examples.cl
+++ /dev/null
@@ -1,10036 +0,0 @@
-International Allegro CL Enterprise Edition
-8.1 [Windows] (Nov 20, 2008 16:34)
-Copyright (C) 1985-2007, Franz Inc., Oakland, CA, USA.  All Rights Reserved.
-
-This development copy of Allegro CL is licensed to:
-   [TC16573] Universidad de La Rioja
-
-CG version 1.103.2.10 / IDE version 1.103.2.15
-Loaded options from C:\Documents and Settings\Ana\Mis documentos\allegro-prefs-8-1.cl.
-
-;; Optimization settings: safety 1, space 1, speed 1, debug 2.
-;; For a complete description of all compiler switches given the current optimization settings evaluate
-;; (EXPLAIN-COMPILER-SETTINGS).
-
-[changing package from "COMMON-LISP-USER" to "COMMON-GRAPHICS-USER"]
-CG-USER(1): (in-package :user)
-#<The COMMON-LISP-USER package>
-CL-USER(2): (progn
-              (load "cat-init")
-              (load-cfiles)
-              (load "resolutions")
-              (load "cylinders")
-              (load "omparsers")
-              (load "fundamental-classes")
-              (load "permutation-groups")
-              (load "homotopy"))
-
-; Loading C:\Archivos de programa\acl81\ana\cat-init.cl
-
- FILE  1: macros
- FILE  2: various
- FILE  3: classes
- FILE  4: combinations
- FILE  5: chain-complexes
- FILE  6: chcm-elementary-op
- FILE  7: effective-homology
- FILE  8: homology-groups
- FILE  9: searching-homology
- FILE 10: cones
- FILE 11: bicones
- FILE 12: tensor-products
- FILE 13: coalgebras
- FILE 14: cobar
- FILE 15: algebras
- FILE 16: bar
- FILE 17: simplicial-sets
- FILE 18: simplicial-mrphs
- FILE 19: delta
- FILE 20: special-smsts
- FILE 21: suspensions
- FILE 22: disk-pasting
- FILE 23: cartesian-products
- FILE 24: eilenberg-zilber
- FILE 25: kan
- FILE 26: simplicial-groups
- FILE 27: fibrations
- FILE 28: loop-spaces
- FILE 29: ls-twisted-products
- FILE 30: lp-space-efhm
- FILE 31: classifying-spaces
- FILE 32: k-pi-n
- FILE 33: serre
- FILE 34: cs-twisted-products
- FILE 35: cl-space-efhm
- FILE 36: whitehead
- FILE 37: smith
-; Fast loading C:\Archivos de programa\acl81\macros.fasl
-; Fast loading C:\Archivos de programa\acl81\various.fasl
-; Fast loading C:\Archivos de programa\acl81\classes.fasl
-; Fast loading C:\Archivos de programa\acl81\combinations.fasl
-; Fast loading C:\Archivos de programa\acl81\chain-complexes.fasl
-; Fast loading C:\Archivos de programa\acl81\chcm-elementary-op.fasl
-; Fast loading C:\Archivos de programa\acl81\effective-homology.fasl
-; Fast loading C:\Archivos de programa\acl81\homology-groups.fasl
-; Fast loading C:\Archivos de programa\acl81\searching-homology.fasl
-; Fast loading C:\Archivos de programa\acl81\cones.fasl
-; Fast loading C:\Archivos de programa\acl81\bicones.fasl
-; Fast loading C:\Archivos de programa\acl81\tensor-products.fasl
-; Fast loading C:\Archivos de programa\acl81\coalgebras.fasl
-; Fast loading C:\Archivos de programa\acl81\cobar.fasl
-; Fast loading C:\Archivos de programa\acl81\algebras.fasl
-; Fast loading C:\Archivos de programa\acl81\bar.fasl
-; Fast loading C:\Archivos de programa\acl81\simplicial-sets.fasl
-; Fast loading C:\Archivos de programa\acl81\simplicial-mrphs.fasl
-; Fast loading C:\Archivos de programa\acl81\delta.fasl
-; Fast loading C:\Archivos de programa\acl81\special-smsts.fasl
-; Fast loading C:\Archivos de programa\acl81\suspensions.fasl
-; Fast loading C:\Archivos de programa\acl81\disk-pasting.fasl
-; Fast loading C:\Archivos de programa\acl81\cartesian-products.fasl
-; Fast loading C:\Archivos de programa\acl81\eilenberg-zilber.fasl
-; Fast loading C:\Archivos de programa\acl81\kan.fasl
-; Fast loading C:\Archivos de programa\acl81\simplicial-groups.fasl
-; Fast loading C:\Archivos de programa\acl81\fibrations.fasl
-; Fast loading C:\Archivos de programa\acl81\loop-spaces.fasl
-; Fast loading C:\Archivos de programa\acl81\ls-twisted-products.fasl
-; Fast loading C:\Archivos de programa\acl81\lp-space-efhm.fasl
-; Fast loading C:\Archivos de programa\acl81\classifying-spaces.fasl
-; Fast loading C:\Archivos de programa\acl81\k-pi-n.fasl
-; Fast loading C:\Archivos de programa\acl81\serre.fasl
-; Fast loading C:\Archivos de programa\acl81\cs-twisted-products.fasl
-; Fast loading C:\Archivos de programa\acl81\cl-space-efhm.fasl
-; Fast loading C:\Archivos de programa\acl81\whitehead.fasl
-; Fast loading C:\Archivos de programa\acl81\smith.fasl
-; Fast loading C:\Archivos de programa\acl81\resolutions.fasl
-; Fast loading C:\Archivos de programa\acl81\cylinders.fasl
-; Fast Loading C:\Archivos de programa\acl81\omparsers.fasl
-; Fast Loading C:\Archivos de programa\acl81\symmetricgroup.fasl
-; Fast Loading C:\Archivos de programa\acl81\fundamental-classes.fasl
-; Fast Loading C:\Archivos de programa\acl81\permutation-groups.fasl
-; Fast Loading C:\Archivos de programa\acl81\homotopy.fasl
-T
-CL-USER(3): (setf z5 (cyclicgroup 5))
-[K1 Abelian-Group]
-CL-USER(4): (setf k-z5-1 (k-g-1 z5))
-[K2 Abelian-Simplicial-Group]
-CL-USER(5): (efhm k-z5-1)
-[K50 Homotopy-Equivalence K2 <= K40 => K31]
-CL-USER(6): (homology k-z5-1 5)
-
-Computing boundary-matrix in dimension 5.
-Rank of the source-module : 1.
-
-
-;; Clock -> 2011-07-12, 10h 48m 45s.
-Computing the boundary of the generator 1/1 (dimension 5) :
-5 
-End of computing.
-
-
-Computing boundary-matrix in dimension 6.
-Rank of the source-module : 1.
-
-
-;; Clock -> 2011-07-12, 10h 48m 45s.
-Computing the boundary of the generator 1/1 (dimension 6) :
-6 
-End of computing.
-
-
-
-
-Homology in dimension 5 :
-
-
-Component Z/5Z
-
-
----done---
-
-;; Clock -> 2011-07-12, 10h 48m 45s.
-
-NIL
-CL-USER(7): (setf s-k-z5-1 (suspension k-z5-1))
-[K51 Simplicial-Set]
-CL-USER(8): (efhm s-k-z5-1)
-[K68 Homotopy-Equivalence K51 <= K56 => K62]
-CL-USER(9): (homotopy s-k-z5-1 5)
-
-Computing boundary-matrix in dimension 1.
-Rank of the source-module : 0.
-
-
-Computing boundary-matrix in dimension 2.
-Rank of the source-module : 1.
-
-
-;; Clock -> 2011-07-12, 10h 50m 9s.
-Computing the boundary of the generator 1/1 (dimension 2) :
-1 
-End of computing.
-
-
-
-;; Clock -> 2011-07-12, 10h 50m 9s.
-
-
-Computing boundary-matrix in dimension 2.
-Rank of the source-module : 1.
-
-
-;; Clock -> 2011-07-12, 10h 50m 9s.
-Computing the boundary of the generator 1/1 (dimension 2) :
-1 
-End of computing.
-
-
-Computing boundary-matrix in dimension 3.
-Rank of the source-module : 1.
-
-
-;; Clock -> 2011-07-12, 10h 50m 9s.
-Computing the boundary of the generator 1/1 (dimension 3) :
-2 
-End of computing.
-
-
-
-;; Clock -> 2011-07-12, 10h 50m 9s.
-
-
-Computing boundary-matrix in dimension 2.
-Rank of the source-module : 1.
-
-
-;; Clock -> 2011-07-12, 10h 50m 9s.
-Computing the boundary of the generator 1/1 (dimension 2) :
-1 
-End of computing.
-
-
-Computing boundary-matrix in dimension 3.
-Rank of the source-module : 1.
-
-
-;; Clock -> 2011-07-12, 10h 50m 9s.
-Computing the boundary of the generator 1/1 (dimension 3) :
-2 
-End of computing.
-
-
-
-;; Clock -> 2011-07-12, 10h 50m 9s.
-
-
-Computing boundary-matrix in dimension 3.
-Rank of the source-module : 3.
-
-
-;; Clock -> 2011-07-12, 10h 50m 9s.
-Computing the boundary of the generator 1/3 (dimension 3) :
-<TnPr S-BSGN 3> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 10h 50m 9s.
-Computing the boundary of the generator 2/3 (dimension 3) :
-<TnPr 1 1> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 10h 50m 9s.
-Computing the boundary of the generator 3/3 (dimension 3) :
-<TnPr 2 0> 
-End of computing.
-
-
-Computing boundary-matrix in dimension 4.
-Rank of the source-module : 4.
-
-
-;; Clock -> 2011-07-12, 10h 50m 9s.
-Computing the boundary of the generator 1/4 (dimension 4) :
-<TnPr S-BSGN 4> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 10h 50m 9s.
-Computing the boundary of the generator 2/4 (dimension 4) :
-<TnPr 1 2> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 10h 50m 9s.
-Computing the boundary of the generator 3/4 (dimension 4) :
-<TnPr 2 1> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 10h 50m 9s.
-Computing the boundary of the generator 4/4 (dimension 4) :
-<TnPr 3 0> 
-End of computing.
-
-
-
-;; Clock -> 2011-07-12, 10h 50m 9s.
-
-
-Computing boundary-matrix in dimension 4.
-Rank of the source-module : 9.
-
-
-;; Clock -> 2011-07-12, 10h 50m 9s.
-Computing the boundary of the generator 1/9 (dimension 4) :
-<TnPr <TnPr S-BSGN 0> <<Abar[4 3]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 10h 50m 9s.
-Computing the boundary of the generator 2/9 (dimension 4) :
-<TnPr <TnPr S-BSGN 0> <<Abar[2 1][2 1]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 10h 50m 9s.
-Computing the boundary of the generator 3/9 (dimension 4) :
-<TnPr <TnPr S-BSGN 1> <<Abar[3 2]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 10h 50m 9s.
-Computing the boundary of the generator 4/9 (dimension 4) :
-<TnPr <TnPr S-BSGN 2> <<Abar[2 1]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 10h 50m 9s.
-Computing the boundary of the generator 5/9 (dimension 4) :
-<TnPr <TnPr 1 0> <<Abar[2 1]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 10h 50m 9s.
-Computing the boundary of the generator 6/9 (dimension 4) :
-<TnPr <TnPr S-BSGN 4> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 10h 50m 9s.
-Computing the boundary of the generator 7/9 (dimension 4) :
-<TnPr <TnPr 1 2> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 10h 50m 9s.
-Computing the boundary of the generator 8/9 (dimension 4) :
-<TnPr <TnPr 2 1> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 10h 50m 9s.
-Computing the boundary of the generator 9/9 (dimension 4) :
-<TnPr <TnPr 3 0> <<Abar>>> 
-End of computing.
-
-
-Computing boundary-matrix in dimension 5.
-Rank of the source-module : 15.
-
-
-;; Clock -> 2011-07-12, 10h 50m 9s.
-Computing the boundary of the generator 1/15 (dimension 5) :
-<TnPr <TnPr S-BSGN 0> <<Abar[5 4]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 10h 50m 9s.
-Computing the boundary of the generator 2/15 (dimension 5) :
-<TnPr <TnPr S-BSGN 0> <<Abar[2 1][3 2]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 10h 50m 10s.
-Computing the boundary of the generator 3/15 (dimension 5) :
-<TnPr <TnPr S-BSGN 0> <<Abar[3 2][2 1]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 10h 50m 10s.
-Computing the boundary of the generator 4/15 (dimension 5) :
-<TnPr <TnPr S-BSGN 1> <<Abar[4 3]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 10h 50m 10s.
-Computing the boundary of the generator 5/15 (dimension 5) :
-<TnPr <TnPr S-BSGN 1> <<Abar[2 1][2 1]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 10h 50m 10s.
-Computing the boundary of the generator 6/15 (dimension 5) :
-<TnPr <TnPr S-BSGN 2> <<Abar[3 2]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 10h 50m 10s.
-Computing the boundary of the generator 7/15 (dimension 5) :
-<TnPr <TnPr 1 0> <<Abar[3 2]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 10h 50m 10s.
-Computing the boundary of the generator 8/15 (dimension 5) :
-<TnPr <TnPr S-BSGN 3> <<Abar[2 1]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 10h 50m 10s.
-Computing the boundary of the generator 9/15 (dimension 5) :
-<TnPr <TnPr 1 1> <<Abar[2 1]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 10h 50m 10s.
-Computing the boundary of the generator 10/15 (dimension 5) :
-<TnPr <TnPr 2 0> <<Abar[2 1]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 10h 50m 10s.
-Computing the boundary of the generator 11/15 (dimension 5) :
-<TnPr <TnPr S-BSGN 5> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 10h 50m 10s.
-Computing the boundary of the generator 12/15 (dimension 5) :
-<TnPr <TnPr 1 3> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 10h 50m 10s.
-Computing the boundary of the generator 13/15 (dimension 5) :
-<TnPr <TnPr 2 2> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 10h 50m 11s.
-Computing the boundary of the generator 14/15 (dimension 5) :
-<TnPr <TnPr 3 1> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 10h 50m 11s.
-Computing the boundary of the generator 15/15 (dimension 5) :
-<TnPr <TnPr 4 0> <<Abar>>> 
-End of computing.
-
-
-
-;; Clock -> 2011-07-12, 10h 50m 11s.
-
-
-Computing boundary-matrix in dimension 5.
-Rank of the source-module : 21.
-
-
-;; Clock -> 2011-07-12, 10h 50m 11s.
-Computing the boundary of the generator 1/21 (dimension 5) :
-<TnPr <TnPr <TnPr S-BSGN 0> <<Abar>>> <<Abar[5 <<Abar[4 3]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 10h 50m 11s.
-Computing the boundary of the generator 2/21 (dimension 5) :
-<TnPr <TnPr <TnPr S-BSGN 0> <<Abar>>> <<Abar[5 <<Abar[2 1][2 1]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 10h 50m 11s.
-Computing the boundary of the generator 3/21 (dimension 5) :
-<TnPr <TnPr <TnPr S-BSGN 1> <<Abar>>> <<Abar[4 <<Abar[3 2]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 10h 50m 11s.
-Computing the boundary of the generator 4/21 (dimension 5) :
-<TnPr <TnPr <TnPr S-BSGN 0> <<Abar[2 1]>>> <<Abar[3 <<Abar[2 1]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 10h 50m 11s.
-Computing the boundary of the generator 5/21 (dimension 5) :
-<TnPr <TnPr <TnPr S-BSGN 2> <<Abar>>> <<Abar[3 <<Abar[2 1]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 10h 50m 11s.
-Computing the boundary of the generator 6/21 (dimension 5) :
-<TnPr <TnPr <TnPr 1 0> <<Abar>>> <<Abar[3 <<Abar[2 1]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 10h 50m 11s.
-Computing the boundary of the generator 7/21 (dimension 5) :
-<TnPr <TnPr <TnPr S-BSGN 0> <<Abar[5 4]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 10h 50m 11s.
-Computing the boundary of the generator 8/21 (dimension 5) :
-<TnPr <TnPr <TnPr S-BSGN 0> <<Abar[2 1][3 2]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 10h 50m 12s.
-Computing the boundary of the generator 9/21 (dimension 5) :
-<TnPr <TnPr <TnPr S-BSGN 0> <<Abar[3 2][2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 10h 50m 12s.
-Computing the boundary of the generator 10/21 (dimension 5) :
-<TnPr <TnPr <TnPr S-BSGN 1> <<Abar[4 3]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 10h 50m 12s.
-Computing the boundary of the generator 11/21 (dimension 5) :
-<TnPr <TnPr <TnPr S-BSGN 1> <<Abar[2 1][2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 10h 50m 12s.
-Computing the boundary of the generator 12/21 (dimension 5) :
-<TnPr <TnPr <TnPr S-BSGN 2> <<Abar[3 2]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 10h 50m 12s.
-Computing the boundary of the generator 13/21 (dimension 5) :
-<TnPr <TnPr <TnPr 1 0> <<Abar[3 2]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 10h 50m 12s.
-Computing the boundary of the generator 14/21 (dimension 5) :
-<TnPr <TnPr <TnPr S-BSGN 3> <<Abar[2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 10h 50m 12s.
-Computing the boundary of the generator 15/21 (dimension 5) :
-<TnPr <TnPr <TnPr 1 1> <<Abar[2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 10h 50m 12s.
-Computing the boundary of the generator 16/21 (dimension 5) :
-<TnPr <TnPr <TnPr 2 0> <<Abar[2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 10h 50m 12s.
-Computing the boundary of the generator 17/21 (dimension 5) :
-<TnPr <TnPr <TnPr S-BSGN 5> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 10h 50m 13s.
-Computing the boundary of the generator 18/21 (dimension 5) :
-<TnPr <TnPr <TnPr 1 3> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 10h 50m 13s.
-Computing the boundary of the generator 19/21 (dimension 5) :
-<TnPr <TnPr <TnPr 2 2> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 10h 50m 19s.
-Computing the boundary of the generator 20/21 (dimension 5) :
-<TnPr <TnPr <TnPr 3 1> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 10h 50m 19s.
-Computing the boundary of the generator 21/21 (dimension 5) :
-<TnPr <TnPr <TnPr 4 0> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-Computing boundary-matrix in dimension 6.
-Rank of the source-module : 39.
-
-
-;; Clock -> 2011-07-12, 10h 50m 19s.
-Computing the boundary of the generator 1/39 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN 0> <<Abar>>> <<Abar[6 <<Abar[5 4]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 10h 50m 19s.
-Computing the boundary of the generator 2/39 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN 0> <<Abar>>> <<Abar[6 <<Abar[2 1][3 2]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 10h 50m 19s.
-Computing the boundary of the generator 3/39 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN 0> <<Abar>>> <<Abar[6 <<Abar[3 2][2 1]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 10h 50m 20s.
-Computing the boundary of the generator 4/39 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN 0> <<Abar>>> <<Abar[3 <<Abar[2 1]>>][3 <<Abar[2 1]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 10h 50m 20s.
-Computing the boundary of the generator 5/39 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN 1> <<Abar>>> <<Abar[5 <<Abar[4 3]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 10h 50m 20s.
-Computing the boundary of the generator 6/39 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN 1> <<Abar>>> <<Abar[5 <<Abar[2 1][2 1]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 10h 50m 20s.
-Computing the boundary of the generator 7/39 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN 0> <<Abar[2 1]>>> <<Abar[4 <<Abar[3 2]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 10h 50m 20s.
-Computing the boundary of the generator 8/39 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN 2> <<Abar>>> <<Abar[4 <<Abar[3 2]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 10h 50m 20s.
-Computing the boundary of the generator 9/39 (dimension 6) :
-<TnPr <TnPr <TnPr 1 0> <<Abar>>> <<Abar[4 <<Abar[3 2]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 10h 50m 20s.
-Computing the boundary of the generator 10/39 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN 0> <<Abar[3 2]>>> <<Abar[3 <<Abar[2 1]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 10h 50m 20s.
-Computing the boundary of the generator 11/39 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN 1> <<Abar[2 1]>>> <<Abar[3 <<Abar[2 1]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 10h 50m 20s.
-Computing the boundary of the generator 12/39 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN 3> <<Abar>>> <<Abar[3 <<Abar[2 1]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 10h 50m 20s.
-Computing the boundary of the generator 13/39 (dimension 6) :
-<TnPr <TnPr <TnPr 1 1> <<Abar>>> <<Abar[3 <<Abar[2 1]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 10h 50m 20s.
-Computing the boundary of the generator 14/39 (dimension 6) :
-<TnPr <TnPr <TnPr 2 0> <<Abar>>> <<Abar[3 <<Abar[2 1]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 10h 50m 20s.
-Computing the boundary of the generator 15/39 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN 0> <<Abar[6 5]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 10h 50m 21s.
-Computing the boundary of the generator 16/39 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN 0> <<Abar[2 1][4 3]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 10h 50m 21s.
-Computing the boundary of the generator 17/39 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN 0> <<Abar[3 2][3 2]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 10h 50m 22s.
-Computing the boundary of the generator 18/39 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN 0> <<Abar[4 3][2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 10h 50m 22s.
-Computing the boundary of the generator 19/39 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN 0> <<Abar[2 1][2 1][2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 10h 50m 22s.
-Computing the boundary of the generator 20/39 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN 1> <<Abar[5 4]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 10h 50m 23s.
-Computing the boundary of the generator 21/39 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN 1> <<Abar[2 1][3 2]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 10h 50m 24s.
-Computing the boundary of the generator 22/39 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN 1> <<Abar[3 2][2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 10h 50m 24s.
-Computing the boundary of the generator 23/39 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN 2> <<Abar[4 3]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 10h 50m 25s.
-Computing the boundary of the generator 24/39 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN 2> <<Abar[2 1][2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 10h 50m 26s.
-Computing the boundary of the generator 25/39 (dimension 6) :
-<TnPr <TnPr <TnPr 1 0> <<Abar[4 3]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 10h 50m 26s.
-Computing the boundary of the generator 26/39 (dimension 6) :
-<TnPr <TnPr <TnPr 1 0> <<Abar[2 1][2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 10h 50m 26s.
-Computing the boundary of the generator 27/39 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN 3> <<Abar[3 2]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 10h 50m 28s.
-Computing the boundary of the generator 28/39 (dimension 6) :
-<TnPr <TnPr <TnPr 1 1> <<Abar[3 2]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 10h 50m 30s.
-Computing the boundary of the generator 29/39 (dimension 6) :
-<TnPr <TnPr <TnPr 2 0> <<Abar[3 2]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 10h 50m 32s.
-Computing the boundary of the generator 30/39 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN 4> <<Abar[2 1]>>> <<Abar>>> 
-*CR* -- Cut = 6.6320505e-4 -- N = 1332
-End of computing.
-
-
-;; Clock -> 2011-07-12, 10h 50m 35s.
-Computing the boundary of the generator 31/39 (dimension 6) :
-<TnPr <TnPr <TnPr 1 2> <<Abar[2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 10h 50m 41s.
-Computing the boundary of the generator 32/39 (dimension 6) :
-<TnPr <TnPr <TnPr 2 1> <<Abar[2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 10h 50m 46s.
-Computing the boundary of the generator 33/39 (dimension 6) :
-<TnPr <TnPr <TnPr 3 0> <<Abar[2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 10h 50m 47s.
-Computing the boundary of the generator 34/39 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN 6> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 10h 50m 50s.
-Computing the boundary of the generator 35/39 (dimension 6) :
-<TnPr <TnPr <TnPr 1 4> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 10h 51m 14s.
-Computing the boundary of the generator 36/39 (dimension 6) :
-<TnPr <TnPr <TnPr 2 3> <<Abar>>> <<Abar>>> 
-*CR* -- Cut = 0.0019053577 -- N = 3747
-*CR* -- Cut = 0.0030287788 -- N = 5565
-*CR* -- Cut = 0.0037655816 -- N = 7046
-End of computing.
-
-
-;; Clock -> 2011-07-12, 10h 52m 42s.
-Computing the boundary of the generator 37/39 (dimension 6) :
-<TnPr <TnPr <TnPr 3 2> <<Abar>>> <<Abar>>> 
-*CR* -- Cut = 0.0045507667 -- N = 8614
-*CR* -- Cut = 0.005675921 -- N = 10577
-End of computing.
-
-
-;; Clock -> 2011-07-12, 10h 53m 42s.
-Computing the boundary of the generator 38/39 (dimension 6) :
-<TnPr <TnPr <TnPr 4 1> <<Abar>>> <<Abar>>> 
-*CR* -- Cut = 0.0063750423 -- N = 11880
-End of computing.
-
-
-;; Clock -> 2011-07-12, 10h 53m 55s.
-Computing the boundary of the generator 39/39 (dimension 6) :
-<TnPr <TnPr <TnPr 5 0> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-
-;; Clock -> 2011-07-12, 10h 53m 56s.
-
-
-Computing boundary-matrix in dimension 5.
-Rank of the source-module : 21.
-
-
-;; Clock -> 2011-07-12, 10h 53m 56s.
-Computing the boundary of the generator 1/21 (dimension 5) :
-<TnPr <TnPr <TnPr S-BSGN 0> <<Abar>>> <<Abar[5 <<Abar[4 3]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 10h 53m 56s.
-Computing the boundary of the generator 2/21 (dimension 5) :
-<TnPr <TnPr <TnPr S-BSGN 0> <<Abar>>> <<Abar[5 <<Abar[2 1][2 1]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 10h 53m 56s.
-Computing the boundary of the generator 3/21 (dimension 5) :
-<TnPr <TnPr <TnPr S-BSGN 1> <<Abar>>> <<Abar[4 <<Abar[3 2]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 10h 53m 56s.
-Computing the boundary of the generator 4/21 (dimension 5) :
-<TnPr <TnPr <TnPr S-BSGN 0> <<Abar[2 1]>>> <<Abar[3 <<Abar[2 1]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 10h 53m 56s.
-Computing the boundary of the generator 5/21 (dimension 5) :
-<TnPr <TnPr <TnPr S-BSGN 2> <<Abar>>> <<Abar[3 <<Abar[2 1]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 10h 53m 56s.
-Computing the boundary of the generator 6/21 (dimension 5) :
-<TnPr <TnPr <TnPr 1 0> <<Abar>>> <<Abar[3 <<Abar[2 1]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 10h 53m 56s.
-Computing the boundary of the generator 7/21 (dimension 5) :
-<TnPr <TnPr <TnPr S-BSGN 0> <<Abar[5 4]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 10h 53m 56s.
-Computing the boundary of the generator 8/21 (dimension 5) :
-<TnPr <TnPr <TnPr S-BSGN 0> <<Abar[2 1][3 2]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 10h 53m 56s.
-Computing the boundary of the generator 9/21 (dimension 5) :
-<TnPr <TnPr <TnPr S-BSGN 0> <<Abar[3 2][2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 10h 53m 56s.
-Computing the boundary of the generator 10/21 (dimension 5) :
-<TnPr <TnPr <TnPr S-BSGN 1> <<Abar[4 3]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 10h 53m 57s.
-Computing the boundary of the generator 11/21 (dimension 5) :
-<TnPr <TnPr <TnPr S-BSGN 1> <<Abar[2 1][2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 10h 53m 57s.
-Computing the boundary of the generator 12/21 (dimension 5) :
-<TnPr <TnPr <TnPr S-BSGN 2> <<Abar[3 2]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 10h 53m 57s.
-Computing the boundary of the generator 13/21 (dimension 5) :
-<TnPr <TnPr <TnPr 1 0> <<Abar[3 2]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 10h 53m 57s.
-Computing the boundary of the generator 14/21 (dimension 5) :
-<TnPr <TnPr <TnPr S-BSGN 3> <<Abar[2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 10h 53m 57s.
-Computing the boundary of the generator 15/21 (dimension 5) :
-<TnPr <TnPr <TnPr 1 1> <<Abar[2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 10h 53m 57s.
-Computing the boundary of the generator 16/21 (dimension 5) :
-<TnPr <TnPr <TnPr 2 0> <<Abar[2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 10h 53m 57s.
-Computing the boundary of the generator 17/21 (dimension 5) :
-<TnPr <TnPr <TnPr S-BSGN 5> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 10h 53m 57s.
-Computing the boundary of the generator 18/21 (dimension 5) :
-<TnPr <TnPr <TnPr 1 3> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 10h 53m 58s.
-Computing the boundary of the generator 19/21 (dimension 5) :
-<TnPr <TnPr <TnPr 2 2> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 10h 54m 1s.
-Computing the boundary of the generator 20/21 (dimension 5) :
-<TnPr <TnPr <TnPr 3 1> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 10h 54m 2s.
-Computing the boundary of the generator 21/21 (dimension 5) :
-<TnPr <TnPr <TnPr 4 0> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-Computing boundary-matrix in dimension 6.
-Rank of the source-module : 39.
-
-
-;; Clock -> 2011-07-12, 10h 54m 2s.
-Computing the boundary of the generator 1/39 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN 0> <<Abar>>> <<Abar[6 <<Abar[5 4]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 10h 54m 2s.
-Computing the boundary of the generator 2/39 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN 0> <<Abar>>> <<Abar[6 <<Abar[2 1][3 2]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 10h 54m 2s.
-Computing the boundary of the generator 3/39 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN 0> <<Abar>>> <<Abar[6 <<Abar[3 2][2 1]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 10h 54m 2s.
-Computing the boundary of the generator 4/39 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN 0> <<Abar>>> <<Abar[3 <<Abar[2 1]>>][3 <<Abar[2 1]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 10h 54m 2s.
-Computing the boundary of the generator 5/39 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN 1> <<Abar>>> <<Abar[5 <<Abar[4 3]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 10h 54m 2s.
-Computing the boundary of the generator 6/39 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN 1> <<Abar>>> <<Abar[5 <<Abar[2 1][2 1]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 10h 54m 2s.
-Computing the boundary of the generator 7/39 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN 0> <<Abar[2 1]>>> <<Abar[4 <<Abar[3 2]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 10h 54m 2s.
-Computing the boundary of the generator 8/39 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN 2> <<Abar>>> <<Abar[4 <<Abar[3 2]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 10h 54m 2s.
-Computing the boundary of the generator 9/39 (dimension 6) :
-<TnPr <TnPr <TnPr 1 0> <<Abar>>> <<Abar[4 <<Abar[3 2]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 10h 54m 2s.
-Computing the boundary of the generator 10/39 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN 0> <<Abar[3 2]>>> <<Abar[3 <<Abar[2 1]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 10h 54m 2s.
-Computing the boundary of the generator 11/39 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN 1> <<Abar[2 1]>>> <<Abar[3 <<Abar[2 1]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 10h 54m 2s.
-Computing the boundary of the generator 12/39 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN 3> <<Abar>>> <<Abar[3 <<Abar[2 1]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 10h 54m 2s.
-Computing the boundary of the generator 13/39 (dimension 6) :
-<TnPr <TnPr <TnPr 1 1> <<Abar>>> <<Abar[3 <<Abar[2 1]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 10h 54m 3s.
-Computing the boundary of the generator 14/39 (dimension 6) :
-<TnPr <TnPr <TnPr 2 0> <<Abar>>> <<Abar[3 <<Abar[2 1]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 10h 54m 3s.
-Computing the boundary of the generator 15/39 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN 0> <<Abar[6 5]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 10h 54m 3s.
-Computing the boundary of the generator 16/39 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN 0> <<Abar[2 1][4 3]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 10h 54m 3s.
-Computing the boundary of the generator 17/39 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN 0> <<Abar[3 2][3 2]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 10h 54m 4s.
-Computing the boundary of the generator 18/39 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN 0> <<Abar[4 3][2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 10h 54m 4s.
-Computing the boundary of the generator 19/39 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN 0> <<Abar[2 1][2 1][2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 10h 54m 4s.
-Computing the boundary of the generator 20/39 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN 1> <<Abar[5 4]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 10h 54m 4s.
-Computing the boundary of the generator 21/39 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN 1> <<Abar[2 1][3 2]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 10h 54m 5s.
-Computing the boundary of the generator 22/39 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN 1> <<Abar[3 2][2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 10h 54m 5s.
-Computing the boundary of the generator 23/39 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN 2> <<Abar[4 3]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 10h 54m 5s.
-Computing the boundary of the generator 24/39 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN 2> <<Abar[2 1][2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 10h 54m 6s.
-Computing the boundary of the generator 25/39 (dimension 6) :
-<TnPr <TnPr <TnPr 1 0> <<Abar[4 3]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 10h 54m 6s.
-Computing the boundary of the generator 26/39 (dimension 6) :
-<TnPr <TnPr <TnPr 1 0> <<Abar[2 1][2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 10h 54m 6s.
-Computing the boundary of the generator 27/39 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN 3> <<Abar[3 2]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 10h 54m 7s.
-Computing the boundary of the generator 28/39 (dimension 6) :
-<TnPr <TnPr <TnPr 1 1> <<Abar[3 2]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 10h 54m 8s.
-Computing the boundary of the generator 29/39 (dimension 6) :
-<TnPr <TnPr <TnPr 2 0> <<Abar[3 2]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 10h 54m 10s.
-Computing the boundary of the generator 30/39 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN 4> <<Abar[2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 10h 54m 10s.
-Computing the boundary of the generator 31/39 (dimension 6) :
-<TnPr <TnPr <TnPr 1 2> <<Abar[2 1]>>> <<Abar>>> 
-*CR* -- Cut = 0.0068156803 -- N = 12771
-End of computing.
-
-
-;; Clock -> 2011-07-12, 10h 54m 14s.
-Computing the boundary of the generator 32/39 (dimension 6) :
-<TnPr <TnPr <TnPr 2 1> <<Abar[2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 10h 54m 17s.
-Computing the boundary of the generator 33/39 (dimension 6) :
-<TnPr <TnPr <TnPr 3 0> <<Abar[2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 10h 54m 17s.
-Computing the boundary of the generator 34/39 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN 6> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 10h 54m 18s.
-Computing the boundary of the generator 35/39 (dimension 6) :
-<TnPr <TnPr <TnPr 1 4> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 10h 54m 27s.
-Computing the boundary of the generator 36/39 (dimension 6) :
-<TnPr <TnPr <TnPr 2 3> <<Abar>>> <<Abar>>> 
-*CR* -- Cut = 0.007411653 -- N = 13953
-*CR* -- Cut = 0.007767046 -- N = 14611
-End of computing.
-
-
-;; Clock -> 2011-07-12, 10h 54m 54s.
-Computing the boundary of the generator 37/39 (dimension 6) :
-<TnPr <TnPr <TnPr 3 2> <<Abar>>> <<Abar>>> 
-*CR* -- Cut = 0.00818243 -- N = 15505
-End of computing.
-
-
-;; Clock -> 2011-07-12, 10h 55m 9s.
-Computing the boundary of the generator 38/39 (dimension 6) :
-<TnPr <TnPr <TnPr 4 1> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 10h 55m 13s.
-Computing the boundary of the generator 39/39 (dimension 6) :
-<TnPr <TnPr <TnPr 5 0> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-
-;; Clock -> 2011-07-12, 10h 55m 13s.
-
-
-
-
-Homotopy in dimension 5 :
-
-
-Component Z/5Z
-
-Component Z/5Z
-
-NIL
-CL-USER(10): (setf z3 (cyclicgroup 3))
-[K627 Abelian-Group]
-CL-USER(11): (setf k-z3-1 (k-g-1 z3))
-[K628 Abelian-Simplicial-Group]
-CL-USER(12): (setf k-z3+3-1 (crts-prdc k-z3-1 k-z3-1))
-[K633 Simplicial-Set]
-CL-USER(13): (setf s-k-z3+3-1 (suspension k-z3+3-1))
-[K640 Simplicial-Set]
-CL-USER(14): (homotopy s-k-z3+3-1 4)
-
-Computing boundary-matrix in dimension 1.
-Rank of the source-module : 0.
-
-
-Computing boundary-matrix in dimension 2.
-Rank of the source-module : 2.
-
-
-;; Clock -> 2011-07-12, 11h 26m 14s.
-Computing the boundary of the generator 1/2 (dimension 2) :
-<TnPr 0 1> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 26m 14s.
-Computing the boundary of the generator 2/2 (dimension 2) :
-<TnPr 1 0> 
-End of computing.
-
-
-
-;; Clock -> 2011-07-12, 11h 26m 14s.
-
-
-Computing boundary-matrix in dimension 2.
-Rank of the source-module : 2.
-
-
-;; Clock -> 2011-07-12, 11h 26m 14s.
-Computing the boundary of the generator 1/2 (dimension 2) :
-<TnPr 0 1> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 26m 14s.
-Computing the boundary of the generator 2/2 (dimension 2) :
-<TnPr 1 0> 
-End of computing.
-
-
-Computing boundary-matrix in dimension 3.
-Rank of the source-module : 3.
-
-
-;; Clock -> 2011-07-12, 11h 26m 14s.
-Computing the boundary of the generator 1/3 (dimension 3) :
-<TnPr 0 2> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 26m 14s.
-Computing the boundary of the generator 2/3 (dimension 3) :
-<TnPr 1 1> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 26m 14s.
-Computing the boundary of the generator 3/3 (dimension 3) :
-<TnPr 2 0> 
-End of computing.
-
-
-
-;; Clock -> 2011-07-12, 11h 26m 14s.
-
-
-Computing boundary-matrix in dimension 2.
-Rank of the source-module : 2.
-
-
-;; Clock -> 2011-07-12, 11h 26m 14s.
-Computing the boundary of the generator 1/2 (dimension 2) :
-<TnPr 0 1> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 26m 14s.
-Computing the boundary of the generator 2/2 (dimension 2) :
-<TnPr 1 0> 
-End of computing.
-
-
-Computing boundary-matrix in dimension 3.
-Rank of the source-module : 3.
-
-
-;; Clock -> 2011-07-12, 11h 26m 14s.
-Computing the boundary of the generator 1/3 (dimension 3) :
-<TnPr 0 2> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 26m 14s.
-Computing the boundary of the generator 2/3 (dimension 3) :
-<TnPr 1 1> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 26m 14s.
-Computing the boundary of the generator 3/3 (dimension 3) :
-<TnPr 2 0> 
-End of computing.
-
-
-
-;; Clock -> 2011-07-12, 11h 26m 14s.
-
-
-Computing boundary-matrix in dimension 3.
-Rank of the source-module : 11.
-
-
-;; Clock -> 2011-07-12, 11h 26m 14s.
-Computing the boundary of the generator 1/11 (dimension 3) :
-<TnPr <TnPr S-BSGN 0> 3> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 26m 14s.
-Computing the boundary of the generator 2/11 (dimension 3) :
-<TnPr <TnPr S-BSGN 1> 2> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 26m 14s.
-Computing the boundary of the generator 3/11 (dimension 3) :
-<TnPr <TnPr S-BSGN 2> 1> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 26m 14s.
-Computing the boundary of the generator 4/11 (dimension 3) :
-<TnPr <TnPr <TnPr 0 1> 0> 1> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 26m 14s.
-Computing the boundary of the generator 5/11 (dimension 3) :
-<TnPr <TnPr <TnPr 1 0> 0> 1> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 26m 14s.
-Computing the boundary of the generator 6/11 (dimension 3) :
-<TnPr <TnPr S-BSGN 3> 0> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 26m 14s.
-Computing the boundary of the generator 7/11 (dimension 3) :
-<TnPr <TnPr <TnPr 0 1> 1> 0> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 26m 14s.
-Computing the boundary of the generator 8/11 (dimension 3) :
-<TnPr <TnPr <TnPr 1 0> 1> 0> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 26m 14s.
-Computing the boundary of the generator 9/11 (dimension 3) :
-<TnPr <TnPr <TnPr 0 2> 0> 0> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 26m 14s.
-Computing the boundary of the generator 10/11 (dimension 3) :
-<TnPr <TnPr <TnPr 1 1> 0> 0> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 26m 14s.
-Computing the boundary of the generator 11/11 (dimension 3) :
-<TnPr <TnPr <TnPr 2 0> 0> 0> 
-End of computing.
-
-
-Computing boundary-matrix in dimension 4.
-Rank of the source-module : 21.
-
-
-;; Clock -> 2011-07-12, 11h 26m 15s.
-Computing the boundary of the generator 1/21 (dimension 4) :
-<TnPr <TnPr S-BSGN 0> 4> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 26m 15s.
-Computing the boundary of the generator 2/21 (dimension 4) :
-<TnPr <TnPr S-BSGN 1> 3> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 26m 15s.
-Computing the boundary of the generator 3/21 (dimension 4) :
-<TnPr <TnPr S-BSGN 2> 2> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 26m 15s.
-Computing the boundary of the generator 4/21 (dimension 4) :
-<TnPr <TnPr <TnPr 0 1> 0> 2> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 26m 15s.
-Computing the boundary of the generator 5/21 (dimension 4) :
-<TnPr <TnPr <TnPr 1 0> 0> 2> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 26m 15s.
-Computing the boundary of the generator 6/21 (dimension 4) :
-<TnPr <TnPr S-BSGN 3> 1> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 26m 15s.
-Computing the boundary of the generator 7/21 (dimension 4) :
-<TnPr <TnPr <TnPr 0 1> 1> 1> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 26m 15s.
-Computing the boundary of the generator 8/21 (dimension 4) :
-<TnPr <TnPr <TnPr 1 0> 1> 1> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 26m 15s.
-Computing the boundary of the generator 9/21 (dimension 4) :
-<TnPr <TnPr <TnPr 0 2> 0> 1> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 26m 15s.
-Computing the boundary of the generator 10/21 (dimension 4) :
-<TnPr <TnPr <TnPr 1 1> 0> 1> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 26m 15s.
-Computing the boundary of the generator 11/21 (dimension 4) :
-<TnPr <TnPr <TnPr 2 0> 0> 1> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 26m 15s.
-Computing the boundary of the generator 12/21 (dimension 4) :
-<TnPr <TnPr S-BSGN 4> 0> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 26m 15s.
-Computing the boundary of the generator 13/21 (dimension 4) :
-<TnPr <TnPr <TnPr 0 1> 2> 0> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 26m 15s.
-Computing the boundary of the generator 14/21 (dimension 4) :
-<TnPr <TnPr <TnPr 1 0> 2> 0> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 26m 15s.
-Computing the boundary of the generator 15/21 (dimension 4) :
-<TnPr <TnPr <TnPr 0 2> 1> 0> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 26m 15s.
-Computing the boundary of the generator 16/21 (dimension 4) :
-<TnPr <TnPr <TnPr 1 1> 1> 0> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 26m 15s.
-Computing the boundary of the generator 17/21 (dimension 4) :
-<TnPr <TnPr <TnPr 2 0> 1> 0> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 26m 15s.
-Computing the boundary of the generator 18/21 (dimension 4) :
-<TnPr <TnPr <TnPr 0 3> 0> 0> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 26m 15s.
-Computing the boundary of the generator 19/21 (dimension 4) :
-<TnPr <TnPr <TnPr 1 2> 0> 0> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 26m 15s.
-Computing the boundary of the generator 20/21 (dimension 4) :
-<TnPr <TnPr <TnPr 2 1> 0> 0> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 26m 15s.
-Computing the boundary of the generator 21/21 (dimension 4) :
-<TnPr <TnPr <TnPr 3 0> 0> 0> 
-End of computing.
-
-
-
-;; Clock -> 2011-07-12, 11h 26m 15s.
-
-
-*CR* -- Cut = 0.008484252 -- N = 16123
-Computing boundary-matrix in dimension 4.
-Rank of the source-module : 63.
-
-
-;; Clock -> 2011-07-12, 11h 26m 26s.
-Computing the boundary of the generator 1/63 (dimension 4) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> 0> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar[4 3]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 26m 26s.
-Computing the boundary of the generator 2/63 (dimension 4) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> 0> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar[2 1][2 1]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 26m 26s.
-Computing the boundary of the generator 3/63 (dimension 4) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> 1> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar[3 2]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 26m 26s.
-Computing the boundary of the generator 4/63 (dimension 4) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 1> 0> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar[3 2]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 26m 26s.
-Computing the boundary of the generator 5/63 (dimension 4) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> 0> <<Abar>>> <<Abar>>> <<Abar[2 1]>>> <<Abar[2 1]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 26m 26s.
-Computing the boundary of the generator 6/63 (dimension 4) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> 0> <<Abar>>> <<Abar[2 1]>>> <<Abar>>> <<Abar[2 1]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 26m 26s.
-Computing the boundary of the generator 7/63 (dimension 4) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> 0> <<Abar[2 1]>>> <<Abar>>> <<Abar>>> <<Abar[2 1]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 26m 26s.
-Computing the boundary of the generator 8/63 (dimension 4) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> 2> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar[2 1]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 26m 26s.
-Computing the boundary of the generator 9/63 (dimension 4) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 1> 1> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar[2 1]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 26m 26s.
-Computing the boundary of the generator 10/63 (dimension 4) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 2> 0> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar[2 1]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 26m 26s.
-Computing the boundary of the generator 11/63 (dimension 4) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 0 1> 0> 0> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar[2 1]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 26m 26s.
-Computing the boundary of the generator 12/63 (dimension 4) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 1 0> 0> 0> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar[2 1]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 26m 26s.
-Computing the boundary of the generator 13/63 (dimension 4) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> 0> <<Abar>>> <<Abar>>> <<Abar[4 3]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 26m 26s.
-Computing the boundary of the generator 14/63 (dimension 4) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> 0> <<Abar>>> <<Abar>>> <<Abar[2 1][2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 26m 26s.
-Computing the boundary of the generator 15/63 (dimension 4) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> 1> <<Abar>>> <<Abar>>> <<Abar[3 2]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 26m 27s.
-Computing the boundary of the generator 16/63 (dimension 4) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 1> 0> <<Abar>>> <<Abar>>> <<Abar[3 2]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 26m 27s.
-Computing the boundary of the generator 17/63 (dimension 4) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> 0> <<Abar>>> <<Abar[2 1]>>> <<Abar[2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 26m 27s.
-Computing the boundary of the generator 18/63 (dimension 4) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> 0> <<Abar[2 1]>>> <<Abar>>> <<Abar[2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 26m 27s.
-Computing the boundary of the generator 19/63 (dimension 4) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> 2> <<Abar>>> <<Abar>>> <<Abar[2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 26m 27s.
-Computing the boundary of the generator 20/63 (dimension 4) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 1> 1> <<Abar>>> <<Abar>>> <<Abar[2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 26m 27s.
-Computing the boundary of the generator 21/63 (dimension 4) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 2> 0> <<Abar>>> <<Abar>>> <<Abar[2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 26m 27s.
-Computing the boundary of the generator 22/63 (dimension 4) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 0 1> 0> 0> <<Abar>>> <<Abar>>> <<Abar[2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 26m 27s.
-Computing the boundary of the generator 23/63 (dimension 4) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 1 0> 0> 0> <<Abar>>> <<Abar>>> <<Abar[2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 26m 27s.
-Computing the boundary of the generator 24/63 (dimension 4) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> 0> <<Abar>>> <<Abar[4 3]>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 26m 27s.
-Computing the boundary of the generator 25/63 (dimension 4) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> 0> <<Abar>>> <<Abar[2 1][2 1]>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 26m 27s.
-Computing the boundary of the generator 26/63 (dimension 4) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> 1> <<Abar>>> <<Abar[3 2]>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 26m 27s.
-Computing the boundary of the generator 27/63 (dimension 4) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 1> 0> <<Abar>>> <<Abar[3 2]>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 26m 28s.
-Computing the boundary of the generator 28/63 (dimension 4) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> 0> <<Abar[2 1]>>> <<Abar[2 1]>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 26m 28s.
-Computing the boundary of the generator 29/63 (dimension 4) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> 2> <<Abar>>> <<Abar[2 1]>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 26m 28s.
-Computing the boundary of the generator 30/63 (dimension 4) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 1> 1> <<Abar>>> <<Abar[2 1]>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 26m 28s.
-Computing the boundary of the generator 31/63 (dimension 4) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 2> 0> <<Abar>>> <<Abar[2 1]>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 26m 28s.
-Computing the boundary of the generator 32/63 (dimension 4) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 0 1> 0> 0> <<Abar>>> <<Abar[2 1]>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 26m 28s.
-Computing the boundary of the generator 33/63 (dimension 4) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 1 0> 0> 0> <<Abar>>> <<Abar[2 1]>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 26m 28s.
-Computing the boundary of the generator 34/63 (dimension 4) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> 0> <<Abar[4 3]>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 26m 28s.
-Computing the boundary of the generator 35/63 (dimension 4) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> 0> <<Abar[2 1][2 1]>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 26m 29s.
-Computing the boundary of the generator 36/63 (dimension 4) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> 1> <<Abar[3 2]>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 26m 29s.
-Computing the boundary of the generator 37/63 (dimension 4) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 1> 0> <<Abar[3 2]>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 26m 29s.
-Computing the boundary of the generator 38/63 (dimension 4) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> 2> <<Abar[2 1]>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 26m 29s.
-Computing the boundary of the generator 39/63 (dimension 4) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 1> 1> <<Abar[2 1]>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 26m 29s.
-Computing the boundary of the generator 40/63 (dimension 4) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 2> 0> <<Abar[2 1]>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 26m 30s.
-Computing the boundary of the generator 41/63 (dimension 4) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 0 1> 0> 0> <<Abar[2 1]>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 26m 30s.
-Computing the boundary of the generator 42/63 (dimension 4) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 1 0> 0> 0> <<Abar[2 1]>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 26m 30s.
-Computing the boundary of the generator 43/63 (dimension 4) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> 4> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 26m 30s.
-Computing the boundary of the generator 44/63 (dimension 4) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 1> 3> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 26m 30s.
-Computing the boundary of the generator 45/63 (dimension 4) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 2> 2> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-*CR* -- Cut = 0.008873884 -- N = 16836
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 26m 32s.
-Computing the boundary of the generator 46/63 (dimension 4) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 0 1> 0> 2> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 26m 34s.
-Computing the boundary of the generator 47/63 (dimension 4) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 1 0> 0> 2> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 26m 36s.
-Computing the boundary of the generator 48/63 (dimension 4) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 3> 1> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 26m 36s.
-Computing the boundary of the generator 49/63 (dimension 4) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 0 1> 1> 1> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 26m 38s.
-Computing the boundary of the generator 50/63 (dimension 4) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 1 0> 1> 1> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 26m 39s.
-Computing the boundary of the generator 51/63 (dimension 4) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 0 2> 0> 1> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 26m 41s.
-Computing the boundary of the generator 52/63 (dimension 4) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 1 1> 0> 1> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 26m 43s.
-Computing the boundary of the generator 53/63 (dimension 4) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 2 0> 0> 1> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 26m 44s.
-Computing the boundary of the generator 54/63 (dimension 4) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 4> 0> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 26m 45s.
-Computing the boundary of the generator 55/63 (dimension 4) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 0 1> 2> 0> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 26m 46s.
-Computing the boundary of the generator 56/63 (dimension 4) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 1 0> 2> 0> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 26m 48s.
-Computing the boundary of the generator 57/63 (dimension 4) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 0 2> 1> 0> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-*CR* -- Cut = 0.009364715 -- N = 17500
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 26m 49s.
-Computing the boundary of the generator 58/63 (dimension 4) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 1 1> 1> 0> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 26m 51s.
-Computing the boundary of the generator 59/63 (dimension 4) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 2 0> 1> 0> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 26m 52s.
-Computing the boundary of the generator 60/63 (dimension 4) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 0 3> 0> 0> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 26m 52s.
-Computing the boundary of the generator 61/63 (dimension 4) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 1 2> 0> 0> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 26m 54s.
-Computing the boundary of the generator 62/63 (dimension 4) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 2 1> 0> 0> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 26m 55s.
-Computing the boundary of the generator 63/63 (dimension 4) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 3 0> 0> 0> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-Computing boundary-matrix in dimension 5.
-Rank of the source-module : 152.
-
-
-;; Clock -> 2011-07-12, 11h 26m 56s.
-Computing the boundary of the generator 1/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> 0> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar[5 4]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 26m 56s.
-Computing the boundary of the generator 2/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> 0> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar[2 1][3 2]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 26m 56s.
-Computing the boundary of the generator 3/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> 0> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar[3 2][2 1]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 26m 56s.
-Computing the boundary of the generator 4/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> 1> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar[4 3]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 26m 56s.
-Computing the boundary of the generator 5/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> 1> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar[2 1][2 1]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 26m 56s.
-Computing the boundary of the generator 6/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 1> 0> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar[4 3]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 26m 56s.
-Computing the boundary of the generator 7/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 1> 0> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar[2 1][2 1]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 26m 56s.
-Computing the boundary of the generator 8/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> 0> <<Abar>>> <<Abar>>> <<Abar[2 1]>>> <<Abar[3 2]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 26m 56s.
-Computing the boundary of the generator 9/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> 0> <<Abar>>> <<Abar[2 1]>>> <<Abar>>> <<Abar[3 2]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 26m 56s.
-Computing the boundary of the generator 10/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> 0> <<Abar[2 1]>>> <<Abar>>> <<Abar>>> <<Abar[3 2]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 26m 56s.
-Computing the boundary of the generator 11/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> 2> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar[3 2]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 26m 56s.
-Computing the boundary of the generator 12/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 1> 1> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar[3 2]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 26m 56s.
-Computing the boundary of the generator 13/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 2> 0> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar[3 2]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 26m 56s.
-Computing the boundary of the generator 14/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 0 1> 0> 0> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar[3 2]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 26m 56s.
-Computing the boundary of the generator 15/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 1 0> 0> 0> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar[3 2]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 26m 56s.
-Computing the boundary of the generator 16/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> 0> <<Abar>>> <<Abar>>> <<Abar[3 2]>>> <<Abar[2 1]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 26m 56s.
-Computing the boundary of the generator 17/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> 1> <<Abar>>> <<Abar>>> <<Abar[2 1]>>> <<Abar[2 1]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 26m 57s.
-Computing the boundary of the generator 18/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 1> 0> <<Abar>>> <<Abar>>> <<Abar[2 1]>>> <<Abar[2 1]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 26m 57s.
-Computing the boundary of the generator 19/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> 0> <<Abar>>> <<Abar[3 2]>>> <<Abar>>> <<Abar[2 1]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 26m 57s.
-Computing the boundary of the generator 20/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> 1> <<Abar>>> <<Abar[2 1]>>> <<Abar>>> <<Abar[2 1]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 26m 57s.
-Computing the boundary of the generator 21/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 1> 0> <<Abar>>> <<Abar[2 1]>>> <<Abar>>> <<Abar[2 1]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 26m 57s.
-Computing the boundary of the generator 22/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> 0> <<Abar[3 2]>>> <<Abar>>> <<Abar>>> <<Abar[2 1]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 26m 57s.
-Computing the boundary of the generator 23/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> 1> <<Abar[2 1]>>> <<Abar>>> <<Abar>>> <<Abar[2 1]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 26m 57s.
-Computing the boundary of the generator 24/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 1> 0> <<Abar[2 1]>>> <<Abar>>> <<Abar>>> <<Abar[2 1]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 26m 57s.
-Computing the boundary of the generator 25/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> 3> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar[2 1]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 26m 57s.
-Computing the boundary of the generator 26/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 1> 2> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar[2 1]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 26m 58s.
-Computing the boundary of the generator 27/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 2> 1> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar[2 1]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 26m 58s.
-Computing the boundary of the generator 28/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 0 1> 0> 1> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar[2 1]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 26m 58s.
-Computing the boundary of the generator 29/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 1 0> 0> 1> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar[2 1]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 26m 58s.
-Computing the boundary of the generator 30/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 3> 0> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar[2 1]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 26m 58s.
-Computing the boundary of the generator 31/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 0 1> 1> 0> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar[2 1]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 26m 59s.
-Computing the boundary of the generator 32/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 1 0> 1> 0> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar[2 1]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 26m 59s.
-Computing the boundary of the generator 33/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 0 2> 0> 0> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar[2 1]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 26m 59s.
-Computing the boundary of the generator 34/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 1 1> 0> 0> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar[2 1]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 26m 59s.
-Computing the boundary of the generator 35/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 2 0> 0> 0> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar[2 1]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 26m 59s.
-Computing the boundary of the generator 36/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> 0> <<Abar>>> <<Abar>>> <<Abar[5 4]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 27m 0s.
-Computing the boundary of the generator 37/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> 0> <<Abar>>> <<Abar>>> <<Abar[2 1][3 2]>>> <<Abar>>> 
-*CR* -- Cut = 0.009671103 -- N = 17912
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 27m 0s.
-Computing the boundary of the generator 38/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> 0> <<Abar>>> <<Abar>>> <<Abar[3 2][2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 27m 0s.
-Computing the boundary of the generator 39/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> 1> <<Abar>>> <<Abar>>> <<Abar[4 3]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 27m 0s.
-Computing the boundary of the generator 40/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> 1> <<Abar>>> <<Abar>>> <<Abar[2 1][2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 27m 0s.
-Computing the boundary of the generator 41/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 1> 0> <<Abar>>> <<Abar>>> <<Abar[4 3]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 27m 1s.
-Computing the boundary of the generator 42/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 1> 0> <<Abar>>> <<Abar>>> <<Abar[2 1][2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 27m 1s.
-Computing the boundary of the generator 43/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> 0> <<Abar>>> <<Abar[2 1]>>> <<Abar[3 2]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 27m 1s.
-Computing the boundary of the generator 44/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> 0> <<Abar[2 1]>>> <<Abar>>> <<Abar[3 2]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 27m 1s.
-Computing the boundary of the generator 45/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> 2> <<Abar>>> <<Abar>>> <<Abar[3 2]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 27m 2s.
-Computing the boundary of the generator 46/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 1> 1> <<Abar>>> <<Abar>>> <<Abar[3 2]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 27m 2s.
-Computing the boundary of the generator 47/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 2> 0> <<Abar>>> <<Abar>>> <<Abar[3 2]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 27m 3s.
-Computing the boundary of the generator 48/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 0 1> 0> 0> <<Abar>>> <<Abar>>> <<Abar[3 2]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 27m 3s.
-Computing the boundary of the generator 49/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 1 0> 0> 0> <<Abar>>> <<Abar>>> <<Abar[3 2]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 27m 4s.
-Computing the boundary of the generator 50/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> 0> <<Abar>>> <<Abar[3 2]>>> <<Abar[2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 27m 4s.
-Computing the boundary of the generator 51/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> 1> <<Abar>>> <<Abar[2 1]>>> <<Abar[2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 27m 5s.
-Computing the boundary of the generator 52/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 1> 0> <<Abar>>> <<Abar[2 1]>>> <<Abar[2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 27m 5s.
-Computing the boundary of the generator 53/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> 0> <<Abar[3 2]>>> <<Abar>>> <<Abar[2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 27m 5s.
-Computing the boundary of the generator 54/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> 1> <<Abar[2 1]>>> <<Abar>>> <<Abar[2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 27m 5s.
-Computing the boundary of the generator 55/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 1> 0> <<Abar[2 1]>>> <<Abar>>> <<Abar[2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 27m 6s.
-Computing the boundary of the generator 56/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> 3> <<Abar>>> <<Abar>>> <<Abar[2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 27m 6s.
-Computing the boundary of the generator 57/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 1> 2> <<Abar>>> <<Abar>>> <<Abar[2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 27m 7s.
-Computing the boundary of the generator 58/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 2> 1> <<Abar>>> <<Abar>>> <<Abar[2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 27m 8s.
-Computing the boundary of the generator 59/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 0 1> 0> 1> <<Abar>>> <<Abar>>> <<Abar[2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 27m 9s.
-Computing the boundary of the generator 60/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 1 0> 0> 1> <<Abar>>> <<Abar>>> <<Abar[2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 27m 10s.
-Computing the boundary of the generator 61/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 3> 0> <<Abar>>> <<Abar>>> <<Abar[2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 27m 10s.
-Computing the boundary of the generator 62/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 0 1> 1> 0> <<Abar>>> <<Abar>>> <<Abar[2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 27m 11s.
-Computing the boundary of the generator 63/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 1 0> 1> 0> <<Abar>>> <<Abar>>> <<Abar[2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 27m 12s.
-Computing the boundary of the generator 64/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 0 2> 0> 0> <<Abar>>> <<Abar>>> <<Abar[2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 27m 13s.
-Computing the boundary of the generator 65/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 1 1> 0> 0> <<Abar>>> <<Abar>>> <<Abar[2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 27m 14s.
-Computing the boundary of the generator 66/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 2 0> 0> 0> <<Abar>>> <<Abar>>> <<Abar[2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 27m 15s.
-Computing the boundary of the generator 67/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> 0> <<Abar>>> <<Abar[5 4]>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 27m 15s.
-Computing the boundary of the generator 68/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> 0> <<Abar>>> <<Abar[2 1][3 2]>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 27m 15s.
-Computing the boundary of the generator 69/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> 0> <<Abar>>> <<Abar[3 2][2 1]>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 27m 16s.
-Computing the boundary of the generator 70/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> 1> <<Abar>>> <<Abar[4 3]>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 27m 16s.
-Computing the boundary of the generator 71/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> 1> <<Abar>>> <<Abar[2 1][2 1]>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 27m 17s.
-Computing the boundary of the generator 72/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 1> 0> <<Abar>>> <<Abar[4 3]>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 27m 17s.
-Computing the boundary of the generator 73/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 1> 0> <<Abar>>> <<Abar[2 1][2 1]>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 27m 18s.
-Computing the boundary of the generator 74/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> 0> <<Abar[2 1]>>> <<Abar[3 2]>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 27m 18s.
-Computing the boundary of the generator 75/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> 2> <<Abar>>> <<Abar[3 2]>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 27m 20s.
-Computing the boundary of the generator 76/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 1> 1> <<Abar>>> <<Abar[3 2]>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 27m 22s.
-Computing the boundary of the generator 77/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 2> 0> <<Abar>>> <<Abar[3 2]>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 27m 23s.
-Computing the boundary of the generator 78/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 0 1> 0> 0> <<Abar>>> <<Abar[3 2]>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 27m 24s.
-Computing the boundary of the generator 79/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 1 0> 0> 0> <<Abar>>> <<Abar[3 2]>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 27m 25s.
-Computing the boundary of the generator 80/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> 0> <<Abar[3 2]>>> <<Abar[2 1]>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 27m 26s.
-Computing the boundary of the generator 81/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> 1> <<Abar[2 1]>>> <<Abar[2 1]>>> <<Abar>>> <<Abar>>> 
-*CR* -- Cut = 0.010428162 -- N = 19091
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 27m 27s.
-Computing the boundary of the generator 82/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 1> 0> <<Abar[2 1]>>> <<Abar[2 1]>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 27m 27s.
-Computing the boundary of the generator 83/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> 3> <<Abar>>> <<Abar[2 1]>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 27m 28s.
-Computing the boundary of the generator 84/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 1> 2> <<Abar>>> <<Abar[2 1]>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 27m 30s.
-Computing the boundary of the generator 85/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 2> 1> <<Abar>>> <<Abar[2 1]>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 27m 32s.
-Computing the boundary of the generator 86/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 0 1> 0> 1> <<Abar>>> <<Abar[2 1]>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 27m 36s.
-Computing the boundary of the generator 87/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 1 0> 0> 1> <<Abar>>> <<Abar[2 1]>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 27m 38s.
-Computing the boundary of the generator 88/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 3> 0> <<Abar>>> <<Abar[2 1]>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 27m 39s.
-Computing the boundary of the generator 89/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 0 1> 1> 0> <<Abar>>> <<Abar[2 1]>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 27m 41s.
-Computing the boundary of the generator 90/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 1 0> 1> 0> <<Abar>>> <<Abar[2 1]>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 27m 43s.
-Computing the boundary of the generator 91/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 0 2> 0> 0> <<Abar>>> <<Abar[2 1]>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 27m 45s.
-Computing the boundary of the generator 92/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 1 1> 0> 0> <<Abar>>> <<Abar[2 1]>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 27m 47s.
-Computing the boundary of the generator 93/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 2 0> 0> 0> <<Abar>>> <<Abar[2 1]>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 27m 49s.
-Computing the boundary of the generator 94/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> 0> <<Abar[5 4]>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 27m 49s.
-Computing the boundary of the generator 95/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> 0> <<Abar[2 1][3 2]>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 27m 50s.
-Computing the boundary of the generator 96/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> 0> <<Abar[3 2][2 1]>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 27m 51s.
-Computing the boundary of the generator 97/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> 1> <<Abar[4 3]>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 27m 52s.
-Computing the boundary of the generator 98/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> 1> <<Abar[2 1][2 1]>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 27m 53s.
-Computing the boundary of the generator 99/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 1> 0> <<Abar[4 3]>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 27m 54s.
-Computing the boundary of the generator 100/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 1> 0> <<Abar[2 1][2 1]>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 27m 55s.
-Computing the boundary of the generator 101/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> 2> <<Abar[3 2]>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 27m 58s.
-Computing the boundary of the generator 102/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 1> 1> <<Abar[3 2]>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 28m 2s.
-Computing the boundary of the generator 103/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 2> 0> <<Abar[3 2]>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 28m 5s.
-Computing the boundary of the generator 104/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 0 1> 0> 0> <<Abar[3 2]>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-*CR* -- Cut = 0.011627681 -- N = 20450
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 28m 7s.
-Computing the boundary of the generator 105/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 1 0> 0> 0> <<Abar[3 2]>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 28m 9s.
-Computing the boundary of the generator 106/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> 3> <<Abar[2 1]>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 28m 11s.
-Computing the boundary of the generator 107/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 1> 2> <<Abar[2 1]>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 28m 15s.
-Computing the boundary of the generator 108/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 2> 1> <<Abar[2 1]>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 28m 20s.
-Computing the boundary of the generator 109/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 0 1> 0> 1> <<Abar[2 1]>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 28m 24s.
-Computing the boundary of the generator 110/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 1 0> 0> 1> <<Abar[2 1]>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 28m 28s.
-Computing the boundary of the generator 111/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 3> 0> <<Abar[2 1]>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 28m 30s.
-Computing the boundary of the generator 112/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 0 1> 1> 0> <<Abar[2 1]>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 28m 34s.
-Computing the boundary of the generator 113/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 1 0> 1> 0> <<Abar[2 1]>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 28m 37s.
-Computing the boundary of the generator 114/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 0 2> 0> 0> <<Abar[2 1]>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 28m 42s.
-Computing the boundary of the generator 115/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 1 1> 0> 0> <<Abar[2 1]>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 28m 46s.
-Computing the boundary of the generator 116/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 2 0> 0> 0> <<Abar[2 1]>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 28m 50s.
-Computing the boundary of the generator 117/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> 5> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 28m 50s.
-Computing the boundary of the generator 118/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 1> 4> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 28m 53s.
-Computing the boundary of the generator 119/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 2> 3> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-*CR* -- Cut = 0.013046071 -- N = 21789
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 29m 1s.
-Computing the boundary of the generator 120/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 0 1> 0> 3> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 29m 15s.
-Computing the boundary of the generator 121/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 1 0> 0> 3> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 29m 27s.
-Computing the boundary of the generator 122/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 3> 2> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 29m 36s.
-Computing the boundary of the generator 123/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 0 1> 1> 2> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-*CR* -- Cut = 0.014317282 -- N = 22849
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 30m 13s.
-Computing the boundary of the generator 124/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 1 0> 1> 2> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-*CR* -- Cut = 0.015753578 -- N = 16408
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 30m 46s.
-Computing the boundary of the generator 125/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 0 2> 0> 2> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-*CR* -- Cut = 0.013701802 -- N = 17436
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 31m 44s.
-Computing the boundary of the generator 126/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 1 1> 0> 2> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-*CR* -- Cut = 0.015032681 -- N = 18066
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 32m 41s.
-Computing the boundary of the generator 127/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 2 0> 0> 2> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-*CR* -- Cut = 0.016601875 -- N = 4967
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 33m 32s.
-Computing the boundary of the generator 128/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 4> 1> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 33m 37s.
-Computing the boundary of the generator 129/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 0 1> 2> 1> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 34m 12s.
-Computing the boundary of the generator 130/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 1 0> 2> 1> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-*CR* -- Cut = 0.011981033 -- N = 6448
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 34m 38s.
-Computing the boundary of the generator 131/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 0 2> 1> 1> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 35m 18s.
-Computing the boundary of the generator 132/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 1 1> 1> 1> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-*CR* -- Cut = 0.014471108 -- N = 7937
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 35m 58s.
-Computing the boundary of the generator 133/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 2 0> 1> 1> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 36m 33s.
-Computing the boundary of the generator 134/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 0 3> 0> 1> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-*CR* -- Cut = 0.01644922 -- N = 6611
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 36m 47s.
-Computing the boundary of the generator 135/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 1 2> 0> 1> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 37m 29s.
-Computing the boundary of the generator 136/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 2 1> 0> 1> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-*CR* -- Cut = 0.017286744 -- N = 7003
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 38m 18s.
-Computing the boundary of the generator 137/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 3 0> 0> 1> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 38m 29s.
-Computing the boundary of the generator 138/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 5> 0> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 38m 30s.
-Computing the boundary of the generator 139/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 0 1> 3> 0> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 38m 42s.
-Computing the boundary of the generator 140/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 1 0> 3> 0> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 38m 50s.
-Computing the boundary of the generator 141/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 0 2> 2> 0> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-*CR* -- Cut = 0.018456804 -- N = 7390
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 39m 23s.
-Computing the boundary of the generator 142/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 1 1> 2> 0> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 39m 55s.
-Computing the boundary of the generator 143/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 2 0> 2> 0> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-*CR* -- Cut = 0.020442575 -- N = 7937
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 40m 21s.
-Computing the boundary of the generator 144/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 0 3> 1> 0> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 40m 31s.
-Computing the boundary of the generator 145/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 1 2> 1> 0> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 41m 1s.
-Computing the boundary of the generator 146/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 2 1> 1> 0> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-*CR* -- Cut = 0.02240238 -- N = 8307
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 41m 33s.
-Computing the boundary of the generator 147/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 3 0> 1> 0> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 41m 39s.
-Computing the boundary of the generator 148/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 0 4> 0> 0> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 41m 43s.
-Computing the boundary of the generator 149/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 1 3> 0> 0> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 41m 54s.
-Computing the boundary of the generator 150/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 2 2> 0> 0> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-*CR* -- Cut = 0.023798611 -- N = 8615
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 42m 29s.
-Computing the boundary of the generator 151/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 3 1> 0> 0> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 42m 37s.
-Computing the boundary of the generator 152/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 4 0> 0> 0> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-
-;; Clock -> 2011-07-12, 11h 42m 40s.
-
-
-Computing boundary-matrix in dimension 4.
-Rank of the source-module : 63.
-
-
-;; Clock -> 2011-07-12, 11h 42m 40s.
-Computing the boundary of the generator 1/63 (dimension 4) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> 0> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar[4 3]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 42m 40s.
-Computing the boundary of the generator 2/63 (dimension 4) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> 0> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar[2 1][2 1]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 42m 40s.
-Computing the boundary of the generator 3/63 (dimension 4) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> 1> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar[3 2]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 42m 40s.
-Computing the boundary of the generator 4/63 (dimension 4) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 1> 0> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar[3 2]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 42m 40s.
-Computing the boundary of the generator 5/63 (dimension 4) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> 0> <<Abar>>> <<Abar>>> <<Abar[2 1]>>> <<Abar[2 1]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 42m 40s.
-Computing the boundary of the generator 6/63 (dimension 4) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> 0> <<Abar>>> <<Abar[2 1]>>> <<Abar>>> <<Abar[2 1]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 42m 40s.
-Computing the boundary of the generator 7/63 (dimension 4) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> 0> <<Abar[2 1]>>> <<Abar>>> <<Abar>>> <<Abar[2 1]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 42m 40s.
-Computing the boundary of the generator 8/63 (dimension 4) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> 2> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar[2 1]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 42m 40s.
-Computing the boundary of the generator 9/63 (dimension 4) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 1> 1> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar[2 1]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 42m 40s.
-Computing the boundary of the generator 10/63 (dimension 4) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 2> 0> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar[2 1]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 42m 40s.
-Computing the boundary of the generator 11/63 (dimension 4) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 0 1> 0> 0> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar[2 1]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 42m 40s.
-Computing the boundary of the generator 12/63 (dimension 4) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 1 0> 0> 0> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar[2 1]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 42m 40s.
-Computing the boundary of the generator 13/63 (dimension 4) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> 0> <<Abar>>> <<Abar>>> <<Abar[4 3]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 42m 40s.
-Computing the boundary of the generator 14/63 (dimension 4) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> 0> <<Abar>>> <<Abar>>> <<Abar[2 1][2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 42m 40s.
-Computing the boundary of the generator 15/63 (dimension 4) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> 1> <<Abar>>> <<Abar>>> <<Abar[3 2]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 42m 40s.
-Computing the boundary of the generator 16/63 (dimension 4) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 1> 0> <<Abar>>> <<Abar>>> <<Abar[3 2]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 42m 41s.
-Computing the boundary of the generator 17/63 (dimension 4) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> 0> <<Abar>>> <<Abar[2 1]>>> <<Abar[2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 42m 41s.
-Computing the boundary of the generator 18/63 (dimension 4) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> 0> <<Abar[2 1]>>> <<Abar>>> <<Abar[2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 42m 41s.
-Computing the boundary of the generator 19/63 (dimension 4) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> 2> <<Abar>>> <<Abar>>> <<Abar[2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 42m 41s.
-Computing the boundary of the generator 20/63 (dimension 4) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 1> 1> <<Abar>>> <<Abar>>> <<Abar[2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 42m 41s.
-Computing the boundary of the generator 21/63 (dimension 4) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 2> 0> <<Abar>>> <<Abar>>> <<Abar[2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 42m 41s.
-Computing the boundary of the generator 22/63 (dimension 4) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 0 1> 0> 0> <<Abar>>> <<Abar>>> <<Abar[2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 42m 41s.
-Computing the boundary of the generator 23/63 (dimension 4) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 1 0> 0> 0> <<Abar>>> <<Abar>>> <<Abar[2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 42m 41s.
-Computing the boundary of the generator 24/63 (dimension 4) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> 0> <<Abar>>> <<Abar[4 3]>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 42m 41s.
-Computing the boundary of the generator 25/63 (dimension 4) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> 0> <<Abar>>> <<Abar[2 1][2 1]>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 42m 41s.
-Computing the boundary of the generator 26/63 (dimension 4) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> 1> <<Abar>>> <<Abar[3 2]>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 42m 42s.
-Computing the boundary of the generator 27/63 (dimension 4) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 1> 0> <<Abar>>> <<Abar[3 2]>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 42m 42s.
-Computing the boundary of the generator 28/63 (dimension 4) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> 0> <<Abar[2 1]>>> <<Abar[2 1]>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 42m 42s.
-Computing the boundary of the generator 29/63 (dimension 4) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> 2> <<Abar>>> <<Abar[2 1]>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 42m 42s.
-Computing the boundary of the generator 30/63 (dimension 4) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 1> 1> <<Abar>>> <<Abar[2 1]>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 42m 42s.
-Computing the boundary of the generator 31/63 (dimension 4) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 2> 0> <<Abar>>> <<Abar[2 1]>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 42m 42s.
-Computing the boundary of the generator 32/63 (dimension 4) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 0 1> 0> 0> <<Abar>>> <<Abar[2 1]>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 42m 42s.
-Computing the boundary of the generator 33/63 (dimension 4) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 1 0> 0> 0> <<Abar>>> <<Abar[2 1]>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 42m 43s.
-Computing the boundary of the generator 34/63 (dimension 4) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> 0> <<Abar[4 3]>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 42m 43s.
-Computing the boundary of the generator 35/63 (dimension 4) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> 0> <<Abar[2 1][2 1]>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 42m 43s.
-Computing the boundary of the generator 36/63 (dimension 4) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> 1> <<Abar[3 2]>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 42m 43s.
-Computing the boundary of the generator 37/63 (dimension 4) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 1> 0> <<Abar[3 2]>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 42m 44s.
-Computing the boundary of the generator 38/63 (dimension 4) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> 2> <<Abar[2 1]>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 42m 44s.
-Computing the boundary of the generator 39/63 (dimension 4) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 1> 1> <<Abar[2 1]>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 42m 45s.
-Computing the boundary of the generator 40/63 (dimension 4) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 2> 0> <<Abar[2 1]>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 42m 45s.
-Computing the boundary of the generator 41/63 (dimension 4) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 0 1> 0> 0> <<Abar[2 1]>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 42m 46s.
-Computing the boundary of the generator 42/63 (dimension 4) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 1 0> 0> 0> <<Abar[2 1]>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 42m 46s.
-Computing the boundary of the generator 43/63 (dimension 4) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> 4> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 42m 46s.
-Computing the boundary of the generator 44/63 (dimension 4) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 1> 3> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 42m 46s.
-Computing the boundary of the generator 45/63 (dimension 4) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 2> 2> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 42m 47s.
-Computing the boundary of the generator 46/63 (dimension 4) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 0 1> 0> 2> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 42m 48s.
-Computing the boundary of the generator 47/63 (dimension 4) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 1 0> 0> 2> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-*CR* -- Cut = 0.024053123 -- N = 8716
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 42m 50s.
-Computing the boundary of the generator 48/63 (dimension 4) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 3> 1> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 42m 50s.
-Computing the boundary of the generator 49/63 (dimension 4) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 0 1> 1> 1> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 42m 51s.
-Computing the boundary of the generator 50/63 (dimension 4) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 1 0> 1> 1> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 42m 51s.
-Computing the boundary of the generator 51/63 (dimension 4) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 0 2> 0> 1> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 42m 52s.
-Computing the boundary of the generator 52/63 (dimension 4) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 1 1> 0> 1> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 42m 53s.
-Computing the boundary of the generator 53/63 (dimension 4) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 2 0> 0> 1> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 42m 53s.
-Computing the boundary of the generator 54/63 (dimension 4) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 4> 0> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 42m 53s.
-Computing the boundary of the generator 55/63 (dimension 4) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 0 1> 2> 0> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 42m 54s.
-Computing the boundary of the generator 56/63 (dimension 4) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 1 0> 2> 0> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 42m 54s.
-Computing the boundary of the generator 57/63 (dimension 4) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 0 2> 1> 0> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 42m 55s.
-Computing the boundary of the generator 58/63 (dimension 4) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 1 1> 1> 0> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 42m 55s.
-Computing the boundary of the generator 59/63 (dimension 4) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 2 0> 1> 0> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 42m 56s.
-Computing the boundary of the generator 60/63 (dimension 4) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 0 3> 0> 0> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 42m 56s.
-Computing the boundary of the generator 61/63 (dimension 4) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 1 2> 0> 0> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 42m 56s.
-Computing the boundary of the generator 62/63 (dimension 4) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 2 1> 0> 0> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 42m 57s.
-Computing the boundary of the generator 63/63 (dimension 4) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 3 0> 0> 0> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-Computing boundary-matrix in dimension 5.
-Rank of the source-module : 152.
-
-
-;; Clock -> 2011-07-12, 11h 42m 57s.
-Computing the boundary of the generator 1/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> 0> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar[5 4]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 42m 57s.
-Computing the boundary of the generator 2/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> 0> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar[2 1][3 2]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 42m 57s.
-Computing the boundary of the generator 3/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> 0> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar[3 2][2 1]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 42m 57s.
-Computing the boundary of the generator 4/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> 1> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar[4 3]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 42m 57s.
-Computing the boundary of the generator 5/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> 1> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar[2 1][2 1]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 42m 57s.
-Computing the boundary of the generator 6/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 1> 0> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar[4 3]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 42m 57s.
-Computing the boundary of the generator 7/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 1> 0> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar[2 1][2 1]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 42m 57s.
-Computing the boundary of the generator 8/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> 0> <<Abar>>> <<Abar>>> <<Abar[2 1]>>> <<Abar[3 2]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 42m 57s.
-Computing the boundary of the generator 9/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> 0> <<Abar>>> <<Abar[2 1]>>> <<Abar>>> <<Abar[3 2]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 42m 58s.
-Computing the boundary of the generator 10/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> 0> <<Abar[2 1]>>> <<Abar>>> <<Abar>>> <<Abar[3 2]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 42m 58s.
-Computing the boundary of the generator 11/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> 2> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar[3 2]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 42m 58s.
-Computing the boundary of the generator 12/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 1> 1> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar[3 2]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 42m 58s.
-Computing the boundary of the generator 13/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 2> 0> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar[3 2]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 42m 58s.
-Computing the boundary of the generator 14/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 0 1> 0> 0> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar[3 2]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 42m 58s.
-Computing the boundary of the generator 15/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 1 0> 0> 0> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar[3 2]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 42m 58s.
-Computing the boundary of the generator 16/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> 0> <<Abar>>> <<Abar>>> <<Abar[3 2]>>> <<Abar[2 1]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 42m 58s.
-Computing the boundary of the generator 17/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> 1> <<Abar>>> <<Abar>>> <<Abar[2 1]>>> <<Abar[2 1]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 42m 58s.
-Computing the boundary of the generator 18/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 1> 0> <<Abar>>> <<Abar>>> <<Abar[2 1]>>> <<Abar[2 1]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 42m 58s.
-Computing the boundary of the generator 19/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> 0> <<Abar>>> <<Abar[3 2]>>> <<Abar>>> <<Abar[2 1]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 42m 59s.
-Computing the boundary of the generator 20/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> 1> <<Abar>>> <<Abar[2 1]>>> <<Abar>>> <<Abar[2 1]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 42m 59s.
-Computing the boundary of the generator 21/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 1> 0> <<Abar>>> <<Abar[2 1]>>> <<Abar>>> <<Abar[2 1]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 42m 59s.
-Computing the boundary of the generator 22/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> 0> <<Abar[3 2]>>> <<Abar>>> <<Abar>>> <<Abar[2 1]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 42m 59s.
-Computing the boundary of the generator 23/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> 1> <<Abar[2 1]>>> <<Abar>>> <<Abar>>> <<Abar[2 1]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 42m 59s.
-Computing the boundary of the generator 24/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 1> 0> <<Abar[2 1]>>> <<Abar>>> <<Abar>>> <<Abar[2 1]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 42m 59s.
-Computing the boundary of the generator 25/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> 3> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar[2 1]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 43m 0s.
-Computing the boundary of the generator 26/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 1> 2> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar[2 1]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 43m 0s.
-Computing the boundary of the generator 27/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 2> 1> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar[2 1]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 43m 0s.
-Computing the boundary of the generator 28/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 0 1> 0> 1> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar[2 1]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 43m 0s.
-Computing the boundary of the generator 29/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 1 0> 0> 1> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar[2 1]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 43m 0s.
-Computing the boundary of the generator 30/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 3> 0> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar[2 1]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 43m 0s.
-Computing the boundary of the generator 31/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 0 1> 1> 0> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar[2 1]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 43m 1s.
-Computing the boundary of the generator 32/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 1 0> 1> 0> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar[2 1]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 43m 1s.
-Computing the boundary of the generator 33/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 0 2> 0> 0> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar[2 1]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 43m 1s.
-Computing the boundary of the generator 34/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 1 1> 0> 0> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar[2 1]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 43m 1s.
-Computing the boundary of the generator 35/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 2 0> 0> 0> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar[2 1]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 43m 1s.
-Computing the boundary of the generator 36/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> 0> <<Abar>>> <<Abar>>> <<Abar[5 4]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 43m 1s.
-Computing the boundary of the generator 37/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> 0> <<Abar>>> <<Abar>>> <<Abar[2 1][3 2]>>> <<Abar>>> 
-*CR* -- Cut = 0.023999266 -- N = 8751
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 43m 2s.
-Computing the boundary of the generator 38/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> 0> <<Abar>>> <<Abar>>> <<Abar[3 2][2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 43m 2s.
-Computing the boundary of the generator 39/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> 1> <<Abar>>> <<Abar>>> <<Abar[4 3]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 43m 2s.
-Computing the boundary of the generator 40/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> 1> <<Abar>>> <<Abar>>> <<Abar[2 1][2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 43m 2s.
-Computing the boundary of the generator 41/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 1> 0> <<Abar>>> <<Abar>>> <<Abar[4 3]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 43m 3s.
-Computing the boundary of the generator 42/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 1> 0> <<Abar>>> <<Abar>>> <<Abar[2 1][2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 43m 3s.
-Computing the boundary of the generator 43/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> 0> <<Abar>>> <<Abar[2 1]>>> <<Abar[3 2]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 43m 3s.
-Computing the boundary of the generator 44/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> 0> <<Abar[2 1]>>> <<Abar>>> <<Abar[3 2]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 43m 3s.
-Computing the boundary of the generator 45/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> 2> <<Abar>>> <<Abar>>> <<Abar[3 2]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 43m 4s.
-Computing the boundary of the generator 46/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 1> 1> <<Abar>>> <<Abar>>> <<Abar[3 2]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 43m 4s.
-Computing the boundary of the generator 47/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 2> 0> <<Abar>>> <<Abar>>> <<Abar[3 2]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 43m 5s.
-Computing the boundary of the generator 48/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 0 1> 0> 0> <<Abar>>> <<Abar>>> <<Abar[3 2]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 43m 5s.
-Computing the boundary of the generator 49/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 1 0> 0> 0> <<Abar>>> <<Abar>>> <<Abar[3 2]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 43m 5s.
-Computing the boundary of the generator 50/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> 0> <<Abar>>> <<Abar[3 2]>>> <<Abar[2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 43m 5s.
-Computing the boundary of the generator 51/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> 1> <<Abar>>> <<Abar[2 1]>>> <<Abar[2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 43m 6s.
-Computing the boundary of the generator 52/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 1> 0> <<Abar>>> <<Abar[2 1]>>> <<Abar[2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 43m 6s.
-Computing the boundary of the generator 53/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> 0> <<Abar[3 2]>>> <<Abar>>> <<Abar[2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 43m 6s.
-Computing the boundary of the generator 54/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> 1> <<Abar[2 1]>>> <<Abar>>> <<Abar[2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 43m 6s.
-Computing the boundary of the generator 55/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 1> 0> <<Abar[2 1]>>> <<Abar>>> <<Abar[2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 43m 7s.
-Computing the boundary of the generator 56/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> 3> <<Abar>>> <<Abar>>> <<Abar[2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 43m 7s.
-Computing the boundary of the generator 57/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 1> 2> <<Abar>>> <<Abar>>> <<Abar[2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 43m 8s.
-Computing the boundary of the generator 58/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 2> 1> <<Abar>>> <<Abar>>> <<Abar[2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 43m 8s.
-Computing the boundary of the generator 59/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 0 1> 0> 1> <<Abar>>> <<Abar>>> <<Abar[2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 43m 9s.
-Computing the boundary of the generator 60/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 1 0> 0> 1> <<Abar>>> <<Abar>>> <<Abar[2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 43m 9s.
-Computing the boundary of the generator 61/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 3> 0> <<Abar>>> <<Abar>>> <<Abar[2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 43m 10s.
-Computing the boundary of the generator 62/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 0 1> 1> 0> <<Abar>>> <<Abar>>> <<Abar[2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 43m 10s.
-Computing the boundary of the generator 63/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 1 0> 1> 0> <<Abar>>> <<Abar>>> <<Abar[2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 43m 11s.
-Computing the boundary of the generator 64/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 0 2> 0> 0> <<Abar>>> <<Abar>>> <<Abar[2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 43m 11s.
-Computing the boundary of the generator 65/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 1 1> 0> 0> <<Abar>>> <<Abar>>> <<Abar[2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 43m 12s.
-Computing the boundary of the generator 66/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 2 0> 0> 0> <<Abar>>> <<Abar>>> <<Abar[2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 43m 12s.
-Computing the boundary of the generator 67/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> 0> <<Abar>>> <<Abar[5 4]>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 43m 12s.
-Computing the boundary of the generator 68/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> 0> <<Abar>>> <<Abar[2 1][3 2]>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 43m 12s.
-Computing the boundary of the generator 69/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> 0> <<Abar>>> <<Abar[3 2][2 1]>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 43m 13s.
-Computing the boundary of the generator 70/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> 1> <<Abar>>> <<Abar[4 3]>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 43m 13s.
-Computing the boundary of the generator 71/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> 1> <<Abar>>> <<Abar[2 1][2 1]>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 43m 13s.
-Computing the boundary of the generator 72/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 1> 0> <<Abar>>> <<Abar[4 3]>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 43m 13s.
-Computing the boundary of the generator 73/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 1> 0> <<Abar>>> <<Abar[2 1][2 1]>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 43m 13s.
-Computing the boundary of the generator 74/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> 0> <<Abar[2 1]>>> <<Abar[3 2]>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 43m 14s.
-Computing the boundary of the generator 75/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> 2> <<Abar>>> <<Abar[3 2]>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 43m 14s.
-Computing the boundary of the generator 76/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 1> 1> <<Abar>>> <<Abar[3 2]>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 43m 15s.
-Computing the boundary of the generator 77/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 2> 0> <<Abar>>> <<Abar[3 2]>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 43m 16s.
-Computing the boundary of the generator 78/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 0 1> 0> 0> <<Abar>>> <<Abar[3 2]>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 43m 17s.
-Computing the boundary of the generator 79/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 1 0> 0> 0> <<Abar>>> <<Abar[3 2]>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 43m 17s.
-Computing the boundary of the generator 80/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> 0> <<Abar[3 2]>>> <<Abar[2 1]>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 43m 17s.
-Computing the boundary of the generator 81/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> 1> <<Abar[2 1]>>> <<Abar[2 1]>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 43m 18s.
-Computing the boundary of the generator 82/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 1> 0> <<Abar[2 1]>>> <<Abar[2 1]>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 43m 18s.
-Computing the boundary of the generator 83/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> 3> <<Abar>>> <<Abar[2 1]>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 43m 19s.
-Computing the boundary of the generator 84/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 1> 2> <<Abar>>> <<Abar[2 1]>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 43m 20s.
-Computing the boundary of the generator 85/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 2> 1> <<Abar>>> <<Abar[2 1]>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 43m 21s.
-Computing the boundary of the generator 86/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 0 1> 0> 1> <<Abar>>> <<Abar[2 1]>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 43m 22s.
-Computing the boundary of the generator 87/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 1 0> 0> 1> <<Abar>>> <<Abar[2 1]>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 43m 23s.
-Computing the boundary of the generator 88/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 3> 0> <<Abar>>> <<Abar[2 1]>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 43m 23s.
-Computing the boundary of the generator 89/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 0 1> 1> 0> <<Abar>>> <<Abar[2 1]>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 43m 24s.
-Computing the boundary of the generator 90/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 1 0> 1> 0> <<Abar>>> <<Abar[2 1]>>> <<Abar>>> <<Abar>>> 
-*CR* -- Cut = 0.024359837 -- N = 8862
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 43m 25s.
-Computing the boundary of the generator 91/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 0 2> 0> 0> <<Abar>>> <<Abar[2 1]>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 43m 25s.
-Computing the boundary of the generator 92/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 1 1> 0> 0> <<Abar>>> <<Abar[2 1]>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 43m 26s.
-Computing the boundary of the generator 93/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 2 0> 0> 0> <<Abar>>> <<Abar[2 1]>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 43m 26s.
-Computing the boundary of the generator 94/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> 0> <<Abar[5 4]>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 43m 26s.
-Computing the boundary of the generator 95/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> 0> <<Abar[2 1][3 2]>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 43m 27s.
-Computing the boundary of the generator 96/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> 0> <<Abar[3 2][2 1]>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 43m 27s.
-Computing the boundary of the generator 97/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> 1> <<Abar[4 3]>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 43m 27s.
-Computing the boundary of the generator 98/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> 1> <<Abar[2 1][2 1]>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 43m 27s.
-Computing the boundary of the generator 99/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 1> 0> <<Abar[4 3]>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 43m 28s.
-Computing the boundary of the generator 100/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 1> 0> <<Abar[2 1][2 1]>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 43m 28s.
-Computing the boundary of the generator 101/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> 2> <<Abar[3 2]>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 43m 29s.
-Computing the boundary of the generator 102/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 1> 1> <<Abar[3 2]>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 43m 29s.
-Computing the boundary of the generator 103/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 2> 0> <<Abar[3 2]>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 43m 30s.
-Computing the boundary of the generator 104/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 0 1> 0> 0> <<Abar[3 2]>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 43m 31s.
-Computing the boundary of the generator 105/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 1 0> 0> 0> <<Abar[3 2]>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 43m 31s.
-Computing the boundary of the generator 106/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> 3> <<Abar[2 1]>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 43m 32s.
-Computing the boundary of the generator 107/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 1> 2> <<Abar[2 1]>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 43m 33s.
-Computing the boundary of the generator 108/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 2> 1> <<Abar[2 1]>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 43m 34s.
-Computing the boundary of the generator 109/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 0 1> 0> 1> <<Abar[2 1]>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 43m 36s.
-Computing the boundary of the generator 110/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 1 0> 0> 1> <<Abar[2 1]>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 43m 37s.
-Computing the boundary of the generator 111/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 3> 0> <<Abar[2 1]>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 43m 37s.
-Computing the boundary of the generator 112/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 0 1> 1> 0> <<Abar[2 1]>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 43m 38s.
-Computing the boundary of the generator 113/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 1 0> 1> 0> <<Abar[2 1]>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 43m 39s.
-Computing the boundary of the generator 114/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 0 2> 0> 0> <<Abar[2 1]>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 43m 40s.
-Computing the boundary of the generator 115/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 1 1> 0> 0> <<Abar[2 1]>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 43m 41s.
-Computing the boundary of the generator 116/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 2 0> 0> 0> <<Abar[2 1]>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 43m 42s.
-Computing the boundary of the generator 117/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> 5> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 43m 42s.
-Computing the boundary of the generator 118/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 1> 4> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 43m 43s.
-Computing the boundary of the generator 119/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 2> 3> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 43m 44s.
-Computing the boundary of the generator 120/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 0 1> 0> 3> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 43m 46s.
-Computing the boundary of the generator 121/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 1 0> 0> 3> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-*CR* -- Cut = 0.024477713 -- N = 8980
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 43m 49s.
-Computing the boundary of the generator 122/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 3> 2> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 43m 49s.
-Computing the boundary of the generator 123/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 0 1> 1> 2> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 43m 56s.
-Computing the boundary of the generator 124/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 1 0> 1> 2> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 43m 57s.
-Computing the boundary of the generator 125/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 0 2> 0> 2> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 44m 4s.
-Computing the boundary of the generator 126/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 1 1> 0> 2> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-*CR* -- Cut = 0.024651775 -- N = 9089
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 44m 15s.
-Computing the boundary of the generator 127/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 2 0> 0> 2> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 44m 16s.
-Computing the boundary of the generator 128/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 4> 1> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 44m 17s.
-Computing the boundary of the generator 129/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 0 1> 2> 1> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 44m 22s.
-Computing the boundary of the generator 130/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 1 0> 2> 1> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 44m 26s.
-Computing the boundary of the generator 131/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 0 2> 1> 1> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-*CR* -- Cut = 0.02475143 -- N = 9176
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 44m 30s.
-Computing the boundary of the generator 132/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 1 1> 1> 1> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 44m 35s.
-Computing the boundary of the generator 133/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 2 0> 1> 1> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 44m 38s.
-Computing the boundary of the generator 134/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 0 3> 0> 1> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 44m 41s.
-Computing the boundary of the generator 135/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 1 2> 0> 1> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 44m 44s.
-Computing the boundary of the generator 136/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 2 1> 0> 1> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 44m 50s.
-Computing the boundary of the generator 137/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 3 0> 0> 1> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-*CR* -- Cut = 0.024916824 -- N = 9269
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 44m 52s.
-Computing the boundary of the generator 138/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 5> 0> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 44m 52s.
-Computing the boundary of the generator 139/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 0 1> 3> 0> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 44m 53s.
-Computing the boundary of the generator 140/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 1 0> 3> 0> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 44m 54s.
-Computing the boundary of the generator 141/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 0 2> 2> 0> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 44m 56s.
-Computing the boundary of the generator 142/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 1 1> 2> 0> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 44m 58s.
-Computing the boundary of the generator 143/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 2 0> 2> 0> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 44m 59s.
-Computing the boundary of the generator 144/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 0 3> 1> 0> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 45m 0s.
-Computing the boundary of the generator 145/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 1 2> 1> 0> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 45m 3s.
-Computing the boundary of the generator 146/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 2 1> 1> 0> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-*CR* -- Cut = 0.024949644 -- N = 9336
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 45m 10s.
-Computing the boundary of the generator 147/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 3 0> 1> 0> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 45m 10s.
-Computing the boundary of the generator 148/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 0 4> 0> 0> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 45m 11s.
-Computing the boundary of the generator 149/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 1 3> 0> 0> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 45m 13s.
-Computing the boundary of the generator 150/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 2 2> 0> 0> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 45m 18s.
-Computing the boundary of the generator 151/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 3 1> 0> 0> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 11h 45m 19s.
-Computing the boundary of the generator 152/152 (dimension 5) :
-<TnPr <TnPr <TnPr <TnPr <TnPr <TnPr <TnPr 4 0> 0> 0> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-
-;; Clock -> 2011-07-12, 11h 45m 19s.
-
-
-
-
-Homotopy in dimension 4 :
-
-
-Component Z/3Z
-
-Component Z/3Z
-
-Component Z/3Z
-
-Component Z/3Z
-
-Component Z/3Z
-
-Component Z/3Z
-
-Component Z/3Z
-
-Component Z/3Z
-
-NIL
-CL-USER(15): (setf z (z-group))
-[K1423 Abelian-Group]
-CL-USER(16): (setf k-z-1 (k-g-1 z))
-[K1424 Abelian-Simplicial-Group]
-CL-USER(17): (setf s-k-z-1 (suspension k-z-1))
-[K1436 Simplicial-Set]
-CL-USER(18): (homotopy s-k-z-1 2)
-
-Computing boundary-matrix in dimension 1.
-Rank of the source-module : 0.
-
-
-Computing boundary-matrix in dimension 2.
-Rank of the source-module : 1.
-
-
-;; Clock -> 2011-07-12, 12h 48m 0s.
-Computing the boundary of the generator 1/1 (dimension 2) :
-S1 
-End of computing.
-
-
-
-;; Clock -> 2011-07-12, 12h 48m 0s.
-
-
-Computing boundary-matrix in dimension 2.
-Rank of the source-module : 1.
-
-
-;; Clock -> 2011-07-12, 12h 48m 0s.
-Computing the boundary of the generator 1/1 (dimension 2) :
-S1 
-End of computing.
-
-
-Computing boundary-matrix in dimension 3.
-Rank of the source-module : 0.
-
-
-
-;; Clock -> 2011-07-12, 12h 48m 0s.
-
-
-Computing boundary-matrix in dimension 2.
-Rank of the source-module : 1.
-
-
-;; Clock -> 2011-07-12, 12h 48m 0s.
-Computing the boundary of the generator 1/1 (dimension 2) :
-S1 
-End of computing.
-
-
-Computing boundary-matrix in dimension 3.
-Rank of the source-module : 0.
-
-
-
-;; Clock -> 2011-07-12, 12h 48m 0s.
-
-
-Computing boundary-matrix in dimension 2.
-Rank of the source-module : 1.
-
-
-;; Clock -> 2011-07-12, 12h 48m 0s.
-Computing the boundary of the generator 1/1 (dimension 2) :
-S1 
-End of computing.
-
-
-Computing boundary-matrix in dimension 3.
-Rank of the source-module : 0.
-
-
-
-;; Clock -> 2011-07-12, 12h 48m 0s.
-
-
-
-
-Homotopy in dimension 2 :
-
-
-Component Z
-
-NIL
-CL-USER(19):  (homotopy s-k-z-1 3)
-
-Computing boundary-matrix in dimension 1.
-Rank of the source-module : 0.
-
-
-Computing boundary-matrix in dimension 2.
-Rank of the source-module : 1.
-
-
-;; Clock -> 2011-07-12, 12h 48m 4s.
-Computing the boundary of the generator 1/1 (dimension 2) :
-S1 
-End of computing.
-
-
-
-;; Clock -> 2011-07-12, 12h 48m 4s.
-
-
-Computing boundary-matrix in dimension 2.
-Rank of the source-module : 1.
-
-
-;; Clock -> 2011-07-12, 12h 48m 4s.
-Computing the boundary of the generator 1/1 (dimension 2) :
-S1 
-End of computing.
-
-
-Computing boundary-matrix in dimension 3.
-Rank of the source-module : 0.
-
-
-
-;; Clock -> 2011-07-12, 12h 48m 4s.
-
-
-Computing boundary-matrix in dimension 2.
-Rank of the source-module : 1.
-
-
-;; Clock -> 2011-07-12, 12h 48m 4s.
-Computing the boundary of the generator 1/1 (dimension 2) :
-S1 
-End of computing.
-
-
-Computing boundary-matrix in dimension 3.
-Rank of the source-module : 0.
-
-
-
-;; Clock -> 2011-07-12, 12h 48m 4s.
-
-
-Computing boundary-matrix in dimension 3.
-Rank of the source-module : 1.
-
-
-;; Clock -> 2011-07-12, 12h 48m 4s.
-Computing the boundary of the generator 1/1 (dimension 3) :
-<TnPr S1 S1> 
-End of computing.
-
-
-Computing boundary-matrix in dimension 4.
-Rank of the source-module : 0.
-
-
-
-;; Clock -> 2011-07-12, 12h 48m 4s.
-
-
-Computing boundary-matrix in dimension 3.
-Rank of the source-module : 1.
-
-
-;; Clock -> 2011-07-12, 12h 48m 4s.
-Computing the boundary of the generator 1/1 (dimension 3) :
-<TnPr S1 S1> 
-End of computing.
-
-
-Computing boundary-matrix in dimension 4.
-Rank of the source-module : 0.
-
-
-
-;; Clock -> 2011-07-12, 12h 48m 4s.
-
-
-
-
-Homotopy in dimension 3 :
-
-
-Component Z
-
-NIL
-CL-USER(20):  (homotopy s-k-z-1 4)
-
-Computing boundary-matrix in dimension 1.
-Rank of the source-module : 0.
-
-
-Computing boundary-matrix in dimension 2.
-Rank of the source-module : 1.
-
-
-;; Clock -> 2011-07-12, 12h 48m 9s.
-Computing the boundary of the generator 1/1 (dimension 2) :
-S1 
-End of computing.
-
-
-
-;; Clock -> 2011-07-12, 12h 48m 9s.
-
-
-Computing boundary-matrix in dimension 2.
-Rank of the source-module : 1.
-
-
-;; Clock -> 2011-07-12, 12h 48m 9s.
-Computing the boundary of the generator 1/1 (dimension 2) :
-S1 
-End of computing.
-
-
-Computing boundary-matrix in dimension 3.
-Rank of the source-module : 0.
-
-
-
-;; Clock -> 2011-07-12, 12h 48m 9s.
-
-
-Computing boundary-matrix in dimension 2.
-Rank of the source-module : 1.
-
-
-;; Clock -> 2011-07-12, 12h 48m 9s.
-Computing the boundary of the generator 1/1 (dimension 2) :
-S1 
-End of computing.
-
-
-Computing boundary-matrix in dimension 3.
-Rank of the source-module : 0.
-
-
-
-;; Clock -> 2011-07-12, 12h 48m 9s.
-
-
-Computing boundary-matrix in dimension 3.
-Rank of the source-module : 1.
-
-
-;; Clock -> 2011-07-12, 12h 48m 9s.
-Computing the boundary of the generator 1/1 (dimension 3) :
-<TnPr S1 S1> 
-End of computing.
-
-
-Computing boundary-matrix in dimension 4.
-Rank of the source-module : 0.
-
-
-
-;; Clock -> 2011-07-12, 12h 48m 9s.
-
-
-Computing boundary-matrix in dimension 4.
-Rank of the source-module : 2.
-
-
-;; Clock -> 2011-07-12, 12h 48m 9s.
-Computing the boundary of the generator 1/2 (dimension 4) :
-<TnPr <TnPr S-BSGN *> <<Abar[2 S1][2 S1]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 48m 9s.
-Computing the boundary of the generator 2/2 (dimension 4) :
-<TnPr <TnPr S1 *> <<Abar[2 S1]>>> 
-End of computing.
-
-
-Computing boundary-matrix in dimension 5.
-Rank of the source-module : 2.
-
-
-;; Clock -> 2011-07-12, 12h 48m 9s.
-Computing the boundary of the generator 1/2 (dimension 5) :
-<TnPr <TnPr S-BSGN S1> <<Abar[2 S1][2 S1]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 48m 9s.
-Computing the boundary of the generator 2/2 (dimension 5) :
-<TnPr <TnPr S1 S1> <<Abar[2 S1]>>> 
-End of computing.
-
-
-
-;; Clock -> 2011-07-12, 12h 48m 10s.
-
-
-Computing boundary-matrix in dimension 4.
-Rank of the source-module : 2.
-
-
-;; Clock -> 2011-07-12, 12h 48m 10s.
-Computing the boundary of the generator 1/2 (dimension 4) :
-<TnPr <TnPr S-BSGN *> <<Abar[2 S1][2 S1]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 48m 10s.
-Computing the boundary of the generator 2/2 (dimension 4) :
-<TnPr <TnPr S1 *> <<Abar[2 S1]>>> 
-End of computing.
-
-
-Computing boundary-matrix in dimension 5.
-Rank of the source-module : 2.
-
-
-;; Clock -> 2011-07-12, 12h 48m 10s.
-Computing the boundary of the generator 1/2 (dimension 5) :
-<TnPr <TnPr S-BSGN S1> <<Abar[2 S1][2 S1]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 48m 10s.
-Computing the boundary of the generator 2/2 (dimension 5) :
-<TnPr <TnPr S1 S1> <<Abar[2 S1]>>> 
-End of computing.
-
-
-
-;; Clock -> 2011-07-12, 12h 48m 10s.
-
-
-
-
-Homotopy in dimension 4 :
-
-
-Component Z/2Z
-
-NIL
-CL-USER(21):  (homotopy s-k-z-1 5)
-
-Computing boundary-matrix in dimension 1.
-Rank of the source-module : 0.
-
-
-Computing boundary-matrix in dimension 2.
-Rank of the source-module : 1.
-
-
-;; Clock -> 2011-07-12, 12h 48m 16s.
-Computing the boundary of the generator 1/1 (dimension 2) :
-S1 
-End of computing.
-
-
-
-;; Clock -> 2011-07-12, 12h 48m 16s.
-
-
-Computing boundary-matrix in dimension 2.
-Rank of the source-module : 1.
-
-
-;; Clock -> 2011-07-12, 12h 48m 16s.
-Computing the boundary of the generator 1/1 (dimension 2) :
-S1 
-End of computing.
-
-
-Computing boundary-matrix in dimension 3.
-Rank of the source-module : 0.
-
-
-
-;; Clock -> 2011-07-12, 12h 48m 16s.
-
-
-Computing boundary-matrix in dimension 2.
-Rank of the source-module : 1.
-
-
-;; Clock -> 2011-07-12, 12h 48m 16s.
-Computing the boundary of the generator 1/1 (dimension 2) :
-S1 
-End of computing.
-
-
-Computing boundary-matrix in dimension 3.
-Rank of the source-module : 0.
-
-
-
-;; Clock -> 2011-07-12, 12h 48m 16s.
-
-
-Computing boundary-matrix in dimension 3.
-Rank of the source-module : 1.
-
-
-;; Clock -> 2011-07-12, 12h 48m 16s.
-Computing the boundary of the generator 1/1 (dimension 3) :
-<TnPr S1 S1> 
-End of computing.
-
-
-Computing boundary-matrix in dimension 4.
-Rank of the source-module : 0.
-
-
-
-;; Clock -> 2011-07-12, 12h 48m 16s.
-
-
-Computing boundary-matrix in dimension 4.
-Rank of the source-module : 2.
-
-
-;; Clock -> 2011-07-12, 12h 48m 16s.
-Computing the boundary of the generator 1/2 (dimension 4) :
-<TnPr <TnPr S-BSGN *> <<Abar[2 S1][2 S1]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 48m 16s.
-Computing the boundary of the generator 2/2 (dimension 4) :
-<TnPr <TnPr S1 *> <<Abar[2 S1]>>> 
-End of computing.
-
-
-Computing boundary-matrix in dimension 5.
-Rank of the source-module : 2.
-
-
-;; Clock -> 2011-07-12, 12h 48m 16s.
-Computing the boundary of the generator 1/2 (dimension 5) :
-<TnPr <TnPr S-BSGN S1> <<Abar[2 S1][2 S1]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 48m 16s.
-Computing the boundary of the generator 2/2 (dimension 5) :
-<TnPr <TnPr S1 S1> <<Abar[2 S1]>>> 
-End of computing.
-
-
-
-;; Clock -> 2011-07-12, 12h 48m 16s.
-
-
-Computing boundary-matrix in dimension 5.
-Rank of the source-module : 7.
-
-
-;; Clock -> 2011-07-12, 12h 48m 16s.
-Computing the boundary of the generator 1/7 (dimension 5) :
-<TnPr <TnPr <TnPr S-BSGN *> <<Abar>>> <<Abar[5 <<Abar[4 3]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 48m 16s.
-Computing the boundary of the generator 2/7 (dimension 5) :
-<TnPr <TnPr <TnPr S-BSGN *> <<Abar>>> <<Abar[5 <<Abar[2 1][2 1]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 48m 16s.
-Computing the boundary of the generator 3/7 (dimension 5) :
-<TnPr <TnPr <TnPr S-BSGN S1> <<Abar>>> <<Abar[4 <<Abar[3 2]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 48m 16s.
-Computing the boundary of the generator 4/7 (dimension 5) :
-<TnPr <TnPr <TnPr S-BSGN *> <<Abar[2 S1]>>> <<Abar[3 <<Abar[2 1]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 48m 16s.
-Computing the boundary of the generator 5/7 (dimension 5) :
-<TnPr <TnPr <TnPr S1 *> <<Abar>>> <<Abar[3 <<Abar[2 1]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 48m 16s.
-Computing the boundary of the generator 6/7 (dimension 5) :
-<TnPr <TnPr <TnPr S-BSGN S1> <<Abar[2 S1][2 S1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 48m 16s.
-Computing the boundary of the generator 7/7 (dimension 5) :
-<TnPr <TnPr <TnPr S1 S1> <<Abar[2 S1]>>> <<Abar>>> 
-End of computing.
-
-
-Computing boundary-matrix in dimension 6.
-Rank of the source-module : 12.
-
-
-;; Clock -> 2011-07-12, 12h 48m 16s.
-Computing the boundary of the generator 1/12 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN *> <<Abar>>> <<Abar[6 <<Abar[5 4]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 48m 16s.
-Computing the boundary of the generator 2/12 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN *> <<Abar>>> <<Abar[6 <<Abar[2 1][3 2]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 48m 16s.
-Computing the boundary of the generator 3/12 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN *> <<Abar>>> <<Abar[6 <<Abar[3 2][2 1]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 48m 16s.
-Computing the boundary of the generator 4/12 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN *> <<Abar>>> <<Abar[3 <<Abar[2 1]>>][3 <<Abar[2 1]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 48m 16s.
-Computing the boundary of the generator 5/12 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN S1> <<Abar>>> <<Abar[5 <<Abar[4 3]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 48m 16s.
-Computing the boundary of the generator 6/12 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN S1> <<Abar>>> <<Abar[5 <<Abar[2 1][2 1]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 48m 16s.
-Computing the boundary of the generator 7/12 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN *> <<Abar[2 S1]>>> <<Abar[4 <<Abar[3 2]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 48m 16s.
-Computing the boundary of the generator 8/12 (dimension 6) :
-<TnPr <TnPr <TnPr S1 *> <<Abar>>> <<Abar[4 <<Abar[3 2]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 48m 16s.
-Computing the boundary of the generator 9/12 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN S1> <<Abar[2 S1]>>> <<Abar[3 <<Abar[2 1]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 48m 16s.
-Computing the boundary of the generator 10/12 (dimension 6) :
-<TnPr <TnPr <TnPr S1 S1> <<Abar>>> <<Abar[3 <<Abar[2 1]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 48m 16s.
-Computing the boundary of the generator 11/12 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN *> <<Abar[2 S1][2 S1][2 S1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 48m 16s.
-Computing the boundary of the generator 12/12 (dimension 6) :
-<TnPr <TnPr <TnPr S1 *> <<Abar[2 S1][2 S1]>>> <<Abar>>> 
-End of computing.
-
-
-
-;; Clock -> 2011-07-12, 12h 48m 17s.
-
-
-Computing boundary-matrix in dimension 5.
-Rank of the source-module : 7.
-
-
-;; Clock -> 2011-07-12, 12h 48m 17s.
-Computing the boundary of the generator 1/7 (dimension 5) :
-<TnPr <TnPr <TnPr S-BSGN *> <<Abar>>> <<Abar[5 <<Abar[4 3]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 48m 17s.
-Computing the boundary of the generator 2/7 (dimension 5) :
-<TnPr <TnPr <TnPr S-BSGN *> <<Abar>>> <<Abar[5 <<Abar[2 1][2 1]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 48m 17s.
-Computing the boundary of the generator 3/7 (dimension 5) :
-<TnPr <TnPr <TnPr S-BSGN S1> <<Abar>>> <<Abar[4 <<Abar[3 2]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 48m 17s.
-Computing the boundary of the generator 4/7 (dimension 5) :
-<TnPr <TnPr <TnPr S-BSGN *> <<Abar[2 S1]>>> <<Abar[3 <<Abar[2 1]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 48m 17s.
-Computing the boundary of the generator 5/7 (dimension 5) :
-<TnPr <TnPr <TnPr S1 *> <<Abar>>> <<Abar[3 <<Abar[2 1]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 48m 17s.
-Computing the boundary of the generator 6/7 (dimension 5) :
-<TnPr <TnPr <TnPr S-BSGN S1> <<Abar[2 S1][2 S1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 48m 17s.
-Computing the boundary of the generator 7/7 (dimension 5) :
-<TnPr <TnPr <TnPr S1 S1> <<Abar[2 S1]>>> <<Abar>>> 
-End of computing.
-
-
-Computing boundary-matrix in dimension 6.
-Rank of the source-module : 12.
-
-
-;; Clock -> 2011-07-12, 12h 48m 17s.
-Computing the boundary of the generator 1/12 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN *> <<Abar>>> <<Abar[6 <<Abar[5 4]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 48m 17s.
-Computing the boundary of the generator 2/12 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN *> <<Abar>>> <<Abar[6 <<Abar[2 1][3 2]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 48m 17s.
-Computing the boundary of the generator 3/12 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN *> <<Abar>>> <<Abar[6 <<Abar[3 2][2 1]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 48m 17s.
-Computing the boundary of the generator 4/12 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN *> <<Abar>>> <<Abar[3 <<Abar[2 1]>>][3 <<Abar[2 1]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 48m 17s.
-Computing the boundary of the generator 5/12 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN S1> <<Abar>>> <<Abar[5 <<Abar[4 3]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 48m 17s.
-Computing the boundary of the generator 6/12 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN S1> <<Abar>>> <<Abar[5 <<Abar[2 1][2 1]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 48m 17s.
-Computing the boundary of the generator 7/12 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN *> <<Abar[2 S1]>>> <<Abar[4 <<Abar[3 2]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 48m 17s.
-Computing the boundary of the generator 8/12 (dimension 6) :
-<TnPr <TnPr <TnPr S1 *> <<Abar>>> <<Abar[4 <<Abar[3 2]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 48m 17s.
-Computing the boundary of the generator 9/12 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN S1> <<Abar[2 S1]>>> <<Abar[3 <<Abar[2 1]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 48m 17s.
-Computing the boundary of the generator 10/12 (dimension 6) :
-<TnPr <TnPr <TnPr S1 S1> <<Abar>>> <<Abar[3 <<Abar[2 1]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 48m 17s.
-Computing the boundary of the generator 11/12 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN *> <<Abar[2 S1][2 S1][2 S1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 48m 17s.
-Computing the boundary of the generator 12/12 (dimension 6) :
-<TnPr <TnPr <TnPr S1 *> <<Abar[2 S1][2 S1]>>> <<Abar>>> 
-End of computing.
-
-
-
-;; Clock -> 2011-07-12, 12h 48m 17s.
-
-
-
-
-Homotopy in dimension 5 :
-
-
-Component Z/2Z
-
-NIL
-CL-USER(22):  (homotopy s-k-z-1 6)
-
-Computing boundary-matrix in dimension 1.
-Rank of the source-module : 0.
-
-
-Computing boundary-matrix in dimension 2.
-Rank of the source-module : 1.
-
-
-;; Clock -> 2011-07-12, 12h 48m 26s.
-Computing the boundary of the generator 1/1 (dimension 2) :
-S1 
-End of computing.
-
-
-
-;; Clock -> 2011-07-12, 12h 48m 26s.
-
-
-Computing boundary-matrix in dimension 2.
-Rank of the source-module : 1.
-
-
-;; Clock -> 2011-07-12, 12h 48m 26s.
-Computing the boundary of the generator 1/1 (dimension 2) :
-S1 
-End of computing.
-
-
-Computing boundary-matrix in dimension 3.
-Rank of the source-module : 0.
-
-
-
-;; Clock -> 2011-07-12, 12h 48m 26s.
-
-
-Computing boundary-matrix in dimension 2.
-Rank of the source-module : 1.
-
-
-;; Clock -> 2011-07-12, 12h 48m 26s.
-Computing the boundary of the generator 1/1 (dimension 2) :
-S1 
-End of computing.
-
-
-Computing boundary-matrix in dimension 3.
-Rank of the source-module : 0.
-
-
-
-;; Clock -> 2011-07-12, 12h 48m 26s.
-
-
-Computing boundary-matrix in dimension 3.
-Rank of the source-module : 1.
-
-
-;; Clock -> 2011-07-12, 12h 48m 26s.
-Computing the boundary of the generator 1/1 (dimension 3) :
-<TnPr S1 S1> 
-End of computing.
-
-
-Computing boundary-matrix in dimension 4.
-Rank of the source-module : 0.
-
-
-
-;; Clock -> 2011-07-12, 12h 48m 26s.
-
-
-Computing boundary-matrix in dimension 4.
-Rank of the source-module : 2.
-
-
-;; Clock -> 2011-07-12, 12h 48m 26s.
-Computing the boundary of the generator 1/2 (dimension 4) :
-<TnPr <TnPr S-BSGN *> <<Abar[2 S1][2 S1]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 48m 26s.
-Computing the boundary of the generator 2/2 (dimension 4) :
-<TnPr <TnPr S1 *> <<Abar[2 S1]>>> 
-End of computing.
-
-
-Computing boundary-matrix in dimension 5.
-Rank of the source-module : 2.
-
-
-;; Clock -> 2011-07-12, 12h 48m 26s.
-Computing the boundary of the generator 1/2 (dimension 5) :
-<TnPr <TnPr S-BSGN S1> <<Abar[2 S1][2 S1]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 48m 26s.
-Computing the boundary of the generator 2/2 (dimension 5) :
-<TnPr <TnPr S1 S1> <<Abar[2 S1]>>> 
-End of computing.
-
-
-
-;; Clock -> 2011-07-12, 12h 48m 26s.
-
-
-Computing boundary-matrix in dimension 5.
-Rank of the source-module : 7.
-
-
-;; Clock -> 2011-07-12, 12h 48m 26s.
-Computing the boundary of the generator 1/7 (dimension 5) :
-<TnPr <TnPr <TnPr S-BSGN *> <<Abar>>> <<Abar[5 <<Abar[4 3]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 48m 26s.
-Computing the boundary of the generator 2/7 (dimension 5) :
-<TnPr <TnPr <TnPr S-BSGN *> <<Abar>>> <<Abar[5 <<Abar[2 1][2 1]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 48m 26s.
-Computing the boundary of the generator 3/7 (dimension 5) :
-<TnPr <TnPr <TnPr S-BSGN S1> <<Abar>>> <<Abar[4 <<Abar[3 2]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 48m 26s.
-Computing the boundary of the generator 4/7 (dimension 5) :
-<TnPr <TnPr <TnPr S-BSGN *> <<Abar[2 S1]>>> <<Abar[3 <<Abar[2 1]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 48m 26s.
-Computing the boundary of the generator 5/7 (dimension 5) :
-<TnPr <TnPr <TnPr S1 *> <<Abar>>> <<Abar[3 <<Abar[2 1]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 48m 26s.
-Computing the boundary of the generator 6/7 (dimension 5) :
-<TnPr <TnPr <TnPr S-BSGN S1> <<Abar[2 S1][2 S1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 48m 26s.
-Computing the boundary of the generator 7/7 (dimension 5) :
-<TnPr <TnPr <TnPr S1 S1> <<Abar[2 S1]>>> <<Abar>>> 
-End of computing.
-
-
-Computing boundary-matrix in dimension 6.
-Rank of the source-module : 12.
-
-
-;; Clock -> 2011-07-12, 12h 48m 26s.
-Computing the boundary of the generator 1/12 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN *> <<Abar>>> <<Abar[6 <<Abar[5 4]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 48m 26s.
-Computing the boundary of the generator 2/12 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN *> <<Abar>>> <<Abar[6 <<Abar[2 1][3 2]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 48m 26s.
-Computing the boundary of the generator 3/12 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN *> <<Abar>>> <<Abar[6 <<Abar[3 2][2 1]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 48m 26s.
-Computing the boundary of the generator 4/12 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN *> <<Abar>>> <<Abar[3 <<Abar[2 1]>>][3 <<Abar[2 1]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 48m 26s.
-Computing the boundary of the generator 5/12 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN S1> <<Abar>>> <<Abar[5 <<Abar[4 3]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 48m 26s.
-Computing the boundary of the generator 6/12 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN S1> <<Abar>>> <<Abar[5 <<Abar[2 1][2 1]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 48m 26s.
-Computing the boundary of the generator 7/12 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN *> <<Abar[2 S1]>>> <<Abar[4 <<Abar[3 2]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 48m 26s.
-Computing the boundary of the generator 8/12 (dimension 6) :
-<TnPr <TnPr <TnPr S1 *> <<Abar>>> <<Abar[4 <<Abar[3 2]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 48m 26s.
-Computing the boundary of the generator 9/12 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN S1> <<Abar[2 S1]>>> <<Abar[3 <<Abar[2 1]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 48m 26s.
-Computing the boundary of the generator 10/12 (dimension 6) :
-<TnPr <TnPr <TnPr S1 S1> <<Abar>>> <<Abar[3 <<Abar[2 1]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 48m 26s.
-Computing the boundary of the generator 11/12 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN *> <<Abar[2 S1][2 S1][2 S1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 48m 26s.
-Computing the boundary of the generator 12/12 (dimension 6) :
-<TnPr <TnPr <TnPr S1 *> <<Abar[2 S1][2 S1]>>> <<Abar>>> 
-End of computing.
-
-
-
-;; Clock -> 2011-07-12, 12h 48m 26s.
-
-
-Computing boundary-matrix in dimension 6.
-Rank of the source-module : 17.
-
-
-;; Clock -> 2011-07-12, 12h 48m 26s.
-Computing the boundary of the generator 1/17 (dimension 6) :
-<TnPr <TnPr <TnPr <TnPr S-BSGN *> <<Abar>>> <<Abar>>> <<Abar[6 <<Abar[5 <<Abar[4 3]>>]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 48m 26s.
-Computing the boundary of the generator 2/17 (dimension 6) :
-<TnPr <TnPr <TnPr <TnPr S-BSGN *> <<Abar>>> <<Abar>>> <<Abar[6 <<Abar[5 <<Abar[2 1][2 1]>>]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 48m 26s.
-Computing the boundary of the generator 3/17 (dimension 6) :
-<TnPr <TnPr <TnPr <TnPr S-BSGN S1> <<Abar>>> <<Abar>>> <<Abar[5 <<Abar[4 <<Abar[3 2]>>]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 48m 26s.
-Computing the boundary of the generator 4/17 (dimension 6) :
-<TnPr <TnPr <TnPr <TnPr S-BSGN *> <<Abar[2 S1]>>> <<Abar>>> <<Abar[4 <<Abar[3 <<Abar[2 1]>>]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 48m 26s.
-Computing the boundary of the generator 5/17 (dimension 6) :
-<TnPr <TnPr <TnPr <TnPr S1 *> <<Abar>>> <<Abar>>> <<Abar[4 <<Abar[3 <<Abar[2 1]>>]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 48m 27s.
-Computing the boundary of the generator 6/17 (dimension 6) :
-<TnPr <TnPr <TnPr <TnPr S-BSGN *> <<Abar>>> <<Abar[6 <<Abar[5 4]>>]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 48m 27s.
-Computing the boundary of the generator 7/17 (dimension 6) :
-<TnPr <TnPr <TnPr <TnPr S-BSGN *> <<Abar>>> <<Abar[6 <<Abar[2 1][3 2]>>]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 48m 27s.
-Computing the boundary of the generator 8/17 (dimension 6) :
-<TnPr <TnPr <TnPr <TnPr S-BSGN *> <<Abar>>> <<Abar[6 <<Abar[3 2][2 1]>>]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 48m 27s.
-Computing the boundary of the generator 9/17 (dimension 6) :
-<TnPr <TnPr <TnPr <TnPr S-BSGN *> <<Abar>>> <<Abar[3 <<Abar[2 1]>>][3 <<Abar[2 1]>>]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 48m 27s.
-Computing the boundary of the generator 10/17 (dimension 6) :
-<TnPr <TnPr <TnPr <TnPr S-BSGN S1> <<Abar>>> <<Abar[5 <<Abar[4 3]>>]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 48m 27s.
-Computing the boundary of the generator 11/17 (dimension 6) :
-<TnPr <TnPr <TnPr <TnPr S-BSGN S1> <<Abar>>> <<Abar[5 <<Abar[2 1][2 1]>>]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 48m 27s.
-Computing the boundary of the generator 12/17 (dimension 6) :
-<TnPr <TnPr <TnPr <TnPr S-BSGN *> <<Abar[2 S1]>>> <<Abar[4 <<Abar[3 2]>>]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 48m 27s.
-Computing the boundary of the generator 13/17 (dimension 6) :
-<TnPr <TnPr <TnPr <TnPr S1 *> <<Abar>>> <<Abar[4 <<Abar[3 2]>>]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 48m 27s.
-Computing the boundary of the generator 14/17 (dimension 6) :
-<TnPr <TnPr <TnPr <TnPr S-BSGN S1> <<Abar[2 S1]>>> <<Abar[3 <<Abar[2 1]>>]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 48m 27s.
-Computing the boundary of the generator 15/17 (dimension 6) :
-<TnPr <TnPr <TnPr <TnPr S1 S1> <<Abar>>> <<Abar[3 <<Abar[2 1]>>]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 48m 27s.
-Computing the boundary of the generator 16/17 (dimension 6) :
-<TnPr <TnPr <TnPr <TnPr S-BSGN *> <<Abar[2 S1][2 S1][2 S1]>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 48m 29s.
-Computing the boundary of the generator 17/17 (dimension 6) :
-<TnPr <TnPr <TnPr <TnPr S1 *> <<Abar[2 S1][2 S1]>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-Computing boundary-matrix in dimension 7.
-Rank of the source-module : 32.
-
-
-;; Clock -> 2011-07-12, 12h 48m 29s.
-Computing the boundary of the generator 1/32 (dimension 7) :
-<TnPr <TnPr <TnPr <TnPr S-BSGN *> <<Abar>>> <<Abar>>> <<Abar[7 <<Abar[6 <<Abar[5 4]>>]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 48m 29s.
-Computing the boundary of the generator 2/32 (dimension 7) :
-<TnPr <TnPr <TnPr <TnPr S-BSGN *> <<Abar>>> <<Abar>>> <<Abar[7 <<Abar[6 <<Abar[2 1][3 2]>>]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 48m 29s.
-Computing the boundary of the generator 3/32 (dimension 7) :
-<TnPr <TnPr <TnPr <TnPr S-BSGN *> <<Abar>>> <<Abar>>> <<Abar[7 <<Abar[6 <<Abar[3 2][2 1]>>]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 48m 29s.
-Computing the boundary of the generator 4/32 (dimension 7) :
-<TnPr <TnPr <TnPr <TnPr S-BSGN *> <<Abar>>> <<Abar>>> <<Abar[7 <<Abar[3 <<Abar[2 1]>>][3 <<Abar[2 1]>>]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 48m 29s.
-Computing the boundary of the generator 5/32 (dimension 7) :
-<TnPr <TnPr <TnPr <TnPr S-BSGN S1> <<Abar>>> <<Abar>>> <<Abar[6 <<Abar[5 <<Abar[4 3]>>]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 48m 29s.
-Computing the boundary of the generator 6/32 (dimension 7) :
-<TnPr <TnPr <TnPr <TnPr S-BSGN S1> <<Abar>>> <<Abar>>> <<Abar[6 <<Abar[5 <<Abar[2 1][2 1]>>]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 48m 29s.
-Computing the boundary of the generator 7/32 (dimension 7) :
-<TnPr <TnPr <TnPr <TnPr S-BSGN *> <<Abar[2 S1]>>> <<Abar>>> <<Abar[5 <<Abar[4 <<Abar[3 2]>>]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 48m 29s.
-Computing the boundary of the generator 8/32 (dimension 7) :
-<TnPr <TnPr <TnPr <TnPr S1 *> <<Abar>>> <<Abar>>> <<Abar[5 <<Abar[4 <<Abar[3 2]>>]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 48m 30s.
-Computing the boundary of the generator 9/32 (dimension 7) :
-<TnPr <TnPr <TnPr <TnPr S-BSGN *> <<Abar>>> <<Abar[3 <<Abar[2 1]>>]>>> <<Abar[4 <<Abar[3 <<Abar[2 1]>>]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 48m 30s.
-Computing the boundary of the generator 10/32 (dimension 7) :
-<TnPr <TnPr <TnPr <TnPr S-BSGN S1> <<Abar[2 S1]>>> <<Abar>>> <<Abar[4 <<Abar[3 <<Abar[2 1]>>]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 48m 30s.
-Computing the boundary of the generator 11/32 (dimension 7) :
-<TnPr <TnPr <TnPr <TnPr S1 S1> <<Abar>>> <<Abar>>> <<Abar[4 <<Abar[3 <<Abar[2 1]>>]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 48m 30s.
-Computing the boundary of the generator 12/32 (dimension 7) :
-<TnPr <TnPr <TnPr <TnPr S-BSGN *> <<Abar>>> <<Abar[7 <<Abar[6 5]>>]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 48m 30s.
-Computing the boundary of the generator 13/32 (dimension 7) :
-<TnPr <TnPr <TnPr <TnPr S-BSGN *> <<Abar>>> <<Abar[7 <<Abar[2 1][4 3]>>]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 48m 30s.
-Computing the boundary of the generator 14/32 (dimension 7) :
-<TnPr <TnPr <TnPr <TnPr S-BSGN *> <<Abar>>> <<Abar[7 <<Abar[3 2][3 2]>>]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 48m 30s.
-Computing the boundary of the generator 15/32 (dimension 7) :
-<TnPr <TnPr <TnPr <TnPr S-BSGN *> <<Abar>>> <<Abar[7 <<Abar[4 3][2 1]>>]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 48m 30s.
-Computing the boundary of the generator 16/32 (dimension 7) :
-<TnPr <TnPr <TnPr <TnPr S-BSGN *> <<Abar>>> <<Abar[7 <<Abar[2 1][2 1][2 1]>>]>>> <<Abar>>> 
-*CR* -- Cut = 0.025002742 -- N = 9372
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 48m 31s.
-Computing the boundary of the generator 17/32 (dimension 7) :
-<TnPr <TnPr <TnPr <TnPr S-BSGN *> <<Abar>>> <<Abar[3 <<Abar[2 1]>>][4 <<Abar[3 2]>>]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 48m 31s.
-Computing the boundary of the generator 18/32 (dimension 7) :
-<TnPr <TnPr <TnPr <TnPr S-BSGN *> <<Abar>>> <<Abar[4 <<Abar[3 2]>>][3 <<Abar[2 1]>>]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 48m 31s.
-Computing the boundary of the generator 19/32 (dimension 7) :
-<TnPr <TnPr <TnPr <TnPr S-BSGN S1> <<Abar>>> <<Abar[6 <<Abar[5 4]>>]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 48m 31s.
-Computing the boundary of the generator 20/32 (dimension 7) :
-<TnPr <TnPr <TnPr <TnPr S-BSGN S1> <<Abar>>> <<Abar[6 <<Abar[2 1][3 2]>>]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 48m 32s.
-Computing the boundary of the generator 21/32 (dimension 7) :
-<TnPr <TnPr <TnPr <TnPr S-BSGN S1> <<Abar>>> <<Abar[6 <<Abar[3 2][2 1]>>]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 48m 32s.
-Computing the boundary of the generator 22/32 (dimension 7) :
-<TnPr <TnPr <TnPr <TnPr S-BSGN S1> <<Abar>>> <<Abar[3 <<Abar[2 1]>>][3 <<Abar[2 1]>>]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 48m 32s.
-Computing the boundary of the generator 23/32 (dimension 7) :
-<TnPr <TnPr <TnPr <TnPr S-BSGN *> <<Abar[2 S1]>>> <<Abar[5 <<Abar[4 3]>>]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 48m 32s.
-Computing the boundary of the generator 24/32 (dimension 7) :
-<TnPr <TnPr <TnPr <TnPr S-BSGN *> <<Abar[2 S1]>>> <<Abar[5 <<Abar[2 1][2 1]>>]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 48m 33s.
-Computing the boundary of the generator 25/32 (dimension 7) :
-<TnPr <TnPr <TnPr <TnPr S1 *> <<Abar>>> <<Abar[5 <<Abar[4 3]>>]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 48m 33s.
-Computing the boundary of the generator 26/32 (dimension 7) :
-<TnPr <TnPr <TnPr <TnPr S1 *> <<Abar>>> <<Abar[5 <<Abar[2 1][2 1]>>]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 48m 33s.
-Computing the boundary of the generator 27/32 (dimension 7) :
-<TnPr <TnPr <TnPr <TnPr S-BSGN S1> <<Abar[2 S1]>>> <<Abar[4 <<Abar[3 2]>>]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 48m 33s.
-Computing the boundary of the generator 28/32 (dimension 7) :
-<TnPr <TnPr <TnPr <TnPr S1 S1> <<Abar>>> <<Abar[4 <<Abar[3 2]>>]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 48m 34s.
-Computing the boundary of the generator 29/32 (dimension 7) :
-<TnPr <TnPr <TnPr <TnPr S-BSGN *> <<Abar[2 S1][2 S1]>>> <<Abar[3 <<Abar[2 1]>>]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 48m 35s.
-Computing the boundary of the generator 30/32 (dimension 7) :
-<TnPr <TnPr <TnPr <TnPr S1 *> <<Abar[2 S1]>>> <<Abar[3 <<Abar[2 1]>>]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 48m 36s.
-Computing the boundary of the generator 31/32 (dimension 7) :
-<TnPr <TnPr <TnPr <TnPr S-BSGN S1> <<Abar[2 S1][2 S1][2 S1]>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 48m 41s.
-Computing the boundary of the generator 32/32 (dimension 7) :
-<TnPr <TnPr <TnPr <TnPr S1 S1> <<Abar[2 S1][2 S1]>>> <<Abar>>> <<Abar>>> 
-*CR* -- Cut = 0.025244262 -- N = 9428
-*CR* -- Cut = 0.026013508 -- N = 9770
-*CR* -- Cut = 0.025819128 -- N = 9868
-End of computing.
-
-
-
-;; Clock -> 2011-07-12, 12h 50m 21s.
-
-
-Computing boundary-matrix in dimension 6.
-Rank of the source-module : 17.
-
-
-;; Clock -> 2011-07-12, 12h 50m 21s.
-Computing the boundary of the generator 1/17 (dimension 6) :
-<TnPr <TnPr <TnPr <TnPr S-BSGN *> <<Abar>>> <<Abar>>> <<Abar[6 <<Abar[5 <<Abar[4 3]>>]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 50m 21s.
-Computing the boundary of the generator 2/17 (dimension 6) :
-<TnPr <TnPr <TnPr <TnPr S-BSGN *> <<Abar>>> <<Abar>>> <<Abar[6 <<Abar[5 <<Abar[2 1][2 1]>>]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 50m 21s.
-Computing the boundary of the generator 3/17 (dimension 6) :
-<TnPr <TnPr <TnPr <TnPr S-BSGN S1> <<Abar>>> <<Abar>>> <<Abar[5 <<Abar[4 <<Abar[3 2]>>]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 50m 21s.
-Computing the boundary of the generator 4/17 (dimension 6) :
-<TnPr <TnPr <TnPr <TnPr S-BSGN *> <<Abar[2 S1]>>> <<Abar>>> <<Abar[4 <<Abar[3 <<Abar[2 1]>>]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 50m 21s.
-Computing the boundary of the generator 5/17 (dimension 6) :
-<TnPr <TnPr <TnPr <TnPr S1 *> <<Abar>>> <<Abar>>> <<Abar[4 <<Abar[3 <<Abar[2 1]>>]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 50m 21s.
-Computing the boundary of the generator 6/17 (dimension 6) :
-<TnPr <TnPr <TnPr <TnPr S-BSGN *> <<Abar>>> <<Abar[6 <<Abar[5 4]>>]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 50m 21s.
-Computing the boundary of the generator 7/17 (dimension 6) :
-<TnPr <TnPr <TnPr <TnPr S-BSGN *> <<Abar>>> <<Abar[6 <<Abar[2 1][3 2]>>]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 50m 21s.
-Computing the boundary of the generator 8/17 (dimension 6) :
-<TnPr <TnPr <TnPr <TnPr S-BSGN *> <<Abar>>> <<Abar[6 <<Abar[3 2][2 1]>>]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 50m 21s.
-Computing the boundary of the generator 9/17 (dimension 6) :
-<TnPr <TnPr <TnPr <TnPr S-BSGN *> <<Abar>>> <<Abar[3 <<Abar[2 1]>>][3 <<Abar[2 1]>>]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 50m 22s.
-Computing the boundary of the generator 10/17 (dimension 6) :
-<TnPr <TnPr <TnPr <TnPr S-BSGN S1> <<Abar>>> <<Abar[5 <<Abar[4 3]>>]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 50m 22s.
-Computing the boundary of the generator 11/17 (dimension 6) :
-<TnPr <TnPr <TnPr <TnPr S-BSGN S1> <<Abar>>> <<Abar[5 <<Abar[2 1][2 1]>>]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 50m 22s.
-Computing the boundary of the generator 12/17 (dimension 6) :
-<TnPr <TnPr <TnPr <TnPr S-BSGN *> <<Abar[2 S1]>>> <<Abar[4 <<Abar[3 2]>>]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 50m 22s.
-Computing the boundary of the generator 13/17 (dimension 6) :
-<TnPr <TnPr <TnPr <TnPr S1 *> <<Abar>>> <<Abar[4 <<Abar[3 2]>>]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 50m 22s.
-Computing the boundary of the generator 14/17 (dimension 6) :
-<TnPr <TnPr <TnPr <TnPr S-BSGN S1> <<Abar[2 S1]>>> <<Abar[3 <<Abar[2 1]>>]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 50m 22s.
-Computing the boundary of the generator 15/17 (dimension 6) :
-<TnPr <TnPr <TnPr <TnPr S1 S1> <<Abar>>> <<Abar[3 <<Abar[2 1]>>]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 50m 22s.
-Computing the boundary of the generator 16/17 (dimension 6) :
-<TnPr <TnPr <TnPr <TnPr S-BSGN *> <<Abar[2 S1][2 S1][2 S1]>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 50m 23s.
-Computing the boundary of the generator 17/17 (dimension 6) :
-<TnPr <TnPr <TnPr <TnPr S1 *> <<Abar[2 S1][2 S1]>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-Computing boundary-matrix in dimension 7.
-Rank of the source-module : 32.
-
-
-;; Clock -> 2011-07-12, 12h 50m 23s.
-Computing the boundary of the generator 1/32 (dimension 7) :
-<TnPr <TnPr <TnPr <TnPr S-BSGN *> <<Abar>>> <<Abar>>> <<Abar[7 <<Abar[6 <<Abar[5 4]>>]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 50m 23s.
-Computing the boundary of the generator 2/32 (dimension 7) :
-<TnPr <TnPr <TnPr <TnPr S-BSGN *> <<Abar>>> <<Abar>>> <<Abar[7 <<Abar[6 <<Abar[2 1][3 2]>>]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 50m 23s.
-Computing the boundary of the generator 3/32 (dimension 7) :
-<TnPr <TnPr <TnPr <TnPr S-BSGN *> <<Abar>>> <<Abar>>> <<Abar[7 <<Abar[6 <<Abar[3 2][2 1]>>]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 50m 23s.
-Computing the boundary of the generator 4/32 (dimension 7) :
-<TnPr <TnPr <TnPr <TnPr S-BSGN *> <<Abar>>> <<Abar>>> <<Abar[7 <<Abar[3 <<Abar[2 1]>>][3 <<Abar[2 1]>>]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 50m 23s.
-Computing the boundary of the generator 5/32 (dimension 7) :
-<TnPr <TnPr <TnPr <TnPr S-BSGN S1> <<Abar>>> <<Abar>>> <<Abar[6 <<Abar[5 <<Abar[4 3]>>]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 50m 23s.
-Computing the boundary of the generator 6/32 (dimension 7) :
-<TnPr <TnPr <TnPr <TnPr S-BSGN S1> <<Abar>>> <<Abar>>> <<Abar[6 <<Abar[5 <<Abar[2 1][2 1]>>]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 50m 23s.
-Computing the boundary of the generator 7/32 (dimension 7) :
-<TnPr <TnPr <TnPr <TnPr S-BSGN *> <<Abar[2 S1]>>> <<Abar>>> <<Abar[5 <<Abar[4 <<Abar[3 2]>>]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 50m 23s.
-Computing the boundary of the generator 8/32 (dimension 7) :
-<TnPr <TnPr <TnPr <TnPr S1 *> <<Abar>>> <<Abar>>> <<Abar[5 <<Abar[4 <<Abar[3 2]>>]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 50m 23s.
-Computing the boundary of the generator 9/32 (dimension 7) :
-<TnPr <TnPr <TnPr <TnPr S-BSGN *> <<Abar>>> <<Abar[3 <<Abar[2 1]>>]>>> <<Abar[4 <<Abar[3 <<Abar[2 1]>>]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 50m 23s.
-Computing the boundary of the generator 10/32 (dimension 7) :
-<TnPr <TnPr <TnPr <TnPr S-BSGN S1> <<Abar[2 S1]>>> <<Abar>>> <<Abar[4 <<Abar[3 <<Abar[2 1]>>]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 50m 23s.
-Computing the boundary of the generator 11/32 (dimension 7) :
-<TnPr <TnPr <TnPr <TnPr S1 S1> <<Abar>>> <<Abar>>> <<Abar[4 <<Abar[3 <<Abar[2 1]>>]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 50m 23s.
-Computing the boundary of the generator 12/32 (dimension 7) :
-<TnPr <TnPr <TnPr <TnPr S-BSGN *> <<Abar>>> <<Abar[7 <<Abar[6 5]>>]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 50m 23s.
-Computing the boundary of the generator 13/32 (dimension 7) :
-<TnPr <TnPr <TnPr <TnPr S-BSGN *> <<Abar>>> <<Abar[7 <<Abar[2 1][4 3]>>]>>> <<Abar>>> 
-*CR* -- Cut = 0.02626452 -- N = 9977
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 50m 24s.
-Computing the boundary of the generator 14/32 (dimension 7) :
-<TnPr <TnPr <TnPr <TnPr S-BSGN *> <<Abar>>> <<Abar[7 <<Abar[3 2][3 2]>>]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 50m 24s.
-Computing the boundary of the generator 15/32 (dimension 7) :
-<TnPr <TnPr <TnPr <TnPr S-BSGN *> <<Abar>>> <<Abar[7 <<Abar[4 3][2 1]>>]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 50m 24s.
-Computing the boundary of the generator 16/32 (dimension 7) :
-<TnPr <TnPr <TnPr <TnPr S-BSGN *> <<Abar>>> <<Abar[7 <<Abar[2 1][2 1][2 1]>>]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 50m 24s.
-Computing the boundary of the generator 17/32 (dimension 7) :
-<TnPr <TnPr <TnPr <TnPr S-BSGN *> <<Abar>>> <<Abar[3 <<Abar[2 1]>>][4 <<Abar[3 2]>>]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 50m 25s.
-Computing the boundary of the generator 18/32 (dimension 7) :
-<TnPr <TnPr <TnPr <TnPr S-BSGN *> <<Abar>>> <<Abar[4 <<Abar[3 2]>>][3 <<Abar[2 1]>>]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 50m 25s.
-Computing the boundary of the generator 19/32 (dimension 7) :
-<TnPr <TnPr <TnPr <TnPr S-BSGN S1> <<Abar>>> <<Abar[6 <<Abar[5 4]>>]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 50m 25s.
-Computing the boundary of the generator 20/32 (dimension 7) :
-<TnPr <TnPr <TnPr <TnPr S-BSGN S1> <<Abar>>> <<Abar[6 <<Abar[2 1][3 2]>>]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 50m 26s.
-Computing the boundary of the generator 21/32 (dimension 7) :
-<TnPr <TnPr <TnPr <TnPr S-BSGN S1> <<Abar>>> <<Abar[6 <<Abar[3 2][2 1]>>]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 50m 26s.
-Computing the boundary of the generator 22/32 (dimension 7) :
-<TnPr <TnPr <TnPr <TnPr S-BSGN S1> <<Abar>>> <<Abar[3 <<Abar[2 1]>>][3 <<Abar[2 1]>>]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 50m 27s.
-Computing the boundary of the generator 23/32 (dimension 7) :
-<TnPr <TnPr <TnPr <TnPr S-BSGN *> <<Abar[2 S1]>>> <<Abar[5 <<Abar[4 3]>>]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 50m 27s.
-Computing the boundary of the generator 24/32 (dimension 7) :
-<TnPr <TnPr <TnPr <TnPr S-BSGN *> <<Abar[2 S1]>>> <<Abar[5 <<Abar[2 1][2 1]>>]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 50m 27s.
-Computing the boundary of the generator 25/32 (dimension 7) :
-<TnPr <TnPr <TnPr <TnPr S1 *> <<Abar>>> <<Abar[5 <<Abar[4 3]>>]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 50m 27s.
-Computing the boundary of the generator 26/32 (dimension 7) :
-<TnPr <TnPr <TnPr <TnPr S1 *> <<Abar>>> <<Abar[5 <<Abar[2 1][2 1]>>]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 50m 28s.
-Computing the boundary of the generator 27/32 (dimension 7) :
-<TnPr <TnPr <TnPr <TnPr S-BSGN S1> <<Abar[2 S1]>>> <<Abar[4 <<Abar[3 2]>>]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 50m 28s.
-Computing the boundary of the generator 28/32 (dimension 7) :
-<TnPr <TnPr <TnPr <TnPr S1 S1> <<Abar>>> <<Abar[4 <<Abar[3 2]>>]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 50m 29s.
-Computing the boundary of the generator 29/32 (dimension 7) :
-<TnPr <TnPr <TnPr <TnPr S-BSGN *> <<Abar[2 S1][2 S1]>>> <<Abar[3 <<Abar[2 1]>>]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 50m 29s.
-Computing the boundary of the generator 30/32 (dimension 7) :
-<TnPr <TnPr <TnPr <TnPr S1 *> <<Abar[2 S1]>>> <<Abar[3 <<Abar[2 1]>>]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 50m 30s.
-Computing the boundary of the generator 31/32 (dimension 7) :
-<TnPr <TnPr <TnPr <TnPr S-BSGN S1> <<Abar[2 S1][2 S1][2 S1]>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-12, 12h 50m 34s.
-Computing the boundary of the generator 32/32 (dimension 7) :
-<TnPr <TnPr <TnPr <TnPr S1 S1> <<Abar[2 S1][2 S1]>>> <<Abar>>> <<Abar>>> 
-*CR* -- Cut = 0.02604392 -- N = 10039
-*CR* -- Cut = 0.02635973 -- N = 10124
-End of computing.
-
-
-
-;; Clock -> 2011-07-12, 12h 51m 35s.
-
-
-
-
-Homotopy in dimension 6 :
-
-
-Component Z/12Z
-
-NIL
-CL-USER(23): (setf s1 (filetostring "resolutions3-8-first-part.txt"))
-
-
-
-CL-USER(25): (setf s2 (filetostring "resolutions3-8-second-part.txt"))
-
-
-
-			
-CL-USER(26): (setf s (concatenate 'string   s1 s2))
-
-
-
-			
-CL-USER(27): (setf rsltn (OMparseNextObject s))
-[K2362 Reduction K2356 => K17]
-CL-USER(28): (setf s3 (group1 (tcc rsltn)))
-[K2355 Group]
-CL-USER(30): (setf (slot-value s3 'resolution) rsltn)
-[K2362 Reduction K2356 => K17]
-CL-USER(31): (setf k-s3-1 (k-g-1 s3))
-[K2363 Simplicial-Group]
-CL-USER(32): (setf s-k-s3-1 (suspension k-s3-1))
-[K2375 Simplicial-Set]
-CL-USER(33): (homotopy s-k-s3-1 3)
-
-Computing boundary-matrix in dimension 1.
-Rank of the source-module : 0.
-
-
-Computing boundary-matrix in dimension 2.
-Rank of the source-module : 2.
-
-
-;; Clock -> 2011-07-14, 9h 54m 34s.
-Computing the boundary of the generator 1/2 (dimension 2) :
-"g11" 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 54m 34s.
-Computing the boundary of the generator 2/2 (dimension 2) :
-"g12" 
-End of computing.
-
-
-
-;; Clock -> 2011-07-14, 9h 54m 34s.
-
-
-Computing boundary-matrix in dimension 2.
-Rank of the source-module : 2.
-
-
-;; Clock -> 2011-07-14, 9h 54m 34s.
-Computing the boundary of the generator 1/2 (dimension 2) :
-"g11" 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 54m 34s.
-Computing the boundary of the generator 2/2 (dimension 2) :
-"g12" 
-End of computing.
-
-
-Computing boundary-matrix in dimension 3.
-Rank of the source-module : 3.
-
-
-;; Clock -> 2011-07-14, 9h 54m 34s.
-Computing the boundary of the generator 1/3 (dimension 3) :
-"g21" 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 54m 34s.
-Computing the boundary of the generator 2/3 (dimension 3) :
-"g22" 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 54m 34s.
-Computing the boundary of the generator 3/3 (dimension 3) :
-"g23" 
-End of computing.
-
-
-
-;; Clock -> 2011-07-14, 9h 54m 34s.
-
-
-Computing boundary-matrix in dimension 2.
-Rank of the source-module : 2.
-
-
-;; Clock -> 2011-07-14, 9h 54m 34s.
-Computing the boundary of the generator 1/2 (dimension 2) :
-"g11" 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 54m 34s.
-Computing the boundary of the generator 2/2 (dimension 2) :
-"g12" 
-End of computing.
-
-
-Computing boundary-matrix in dimension 3.
-Rank of the source-module : 3.
-
-
-;; Clock -> 2011-07-14, 9h 54m 34s.
-Computing the boundary of the generator 1/3 (dimension 3) :
-"g21" 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 54m 34s.
-Computing the boundary of the generator 2/3 (dimension 3) :
-"g22" 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 54m 34s.
-Computing the boundary of the generator 3/3 (dimension 3) :
-"g23" 
-End of computing.
-
-
-
-;; Clock -> 2011-07-14, 9h 54m 34s.
-
-
-Computing boundary-matrix in dimension 3.
-Rank of the source-module : 6.
-
-
-;; Clock -> 2011-07-14, 9h 54m 34s.
-Computing the boundary of the generator 1/6 (dimension 3) :
-<TnPr S-BSGN 3> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 54m 34s.
-Computing the boundary of the generator 2/6 (dimension 3) :
-<TnPr g11 1> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 54m 34s.
-Computing the boundary of the generator 3/6 (dimension 3) :
-<TnPr g12 1> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 54m 34s.
-Computing the boundary of the generator 4/6 (dimension 3) :
-<TnPr g21 0> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 54m 34s.
-Computing the boundary of the generator 5/6 (dimension 3) :
-<TnPr g22 0> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 54m 34s.
-Computing the boundary of the generator 6/6 (dimension 3) :
-<TnPr g23 0> 
-End of computing.
-
-
-Computing boundary-matrix in dimension 4.
-Rank of the source-module : 10.
-
-
-;; Clock -> 2011-07-14, 9h 54m 35s.
-Computing the boundary of the generator 1/10 (dimension 4) :
-<TnPr S-BSGN 4> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 54m 35s.
-Computing the boundary of the generator 2/10 (dimension 4) :
-<TnPr g11 2> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 54m 35s.
-Computing the boundary of the generator 3/10 (dimension 4) :
-<TnPr g12 2> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 54m 35s.
-Computing the boundary of the generator 4/10 (dimension 4) :
-<TnPr g21 1> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 54m 35s.
-Computing the boundary of the generator 5/10 (dimension 4) :
-<TnPr g22 1> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 54m 35s.
-Computing the boundary of the generator 6/10 (dimension 4) :
-<TnPr g23 1> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 54m 35s.
-Computing the boundary of the generator 7/10 (dimension 4) :
-<TnPr g31 0> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 54m 35s.
-Computing the boundary of the generator 8/10 (dimension 4) :
-<TnPr g32 0> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 54m 35s.
-Computing the boundary of the generator 9/10 (dimension 4) :
-<TnPr g33 0> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 54m 35s.
-Computing the boundary of the generator 10/10 (dimension 4) :
-<TnPr g34 0> 
-End of computing.
-
-
-
-;; Clock -> 2011-07-14, 9h 54m 35s.
-
-
-Computing boundary-matrix in dimension 3.
-Rank of the source-module : 6.
-
-
-;; Clock -> 2011-07-14, 9h 54m 35s.
-Computing the boundary of the generator 1/6 (dimension 3) :
-<TnPr S-BSGN 3> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 54m 35s.
-Computing the boundary of the generator 2/6 (dimension 3) :
-<TnPr g11 1> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 54m 35s.
-Computing the boundary of the generator 3/6 (dimension 3) :
-<TnPr g12 1> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 54m 35s.
-Computing the boundary of the generator 4/6 (dimension 3) :
-<TnPr g21 0> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 54m 35s.
-Computing the boundary of the generator 5/6 (dimension 3) :
-<TnPr g22 0> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 54m 35s.
-Computing the boundary of the generator 6/6 (dimension 3) :
-<TnPr g23 0> 
-End of computing.
-
-
-Computing boundary-matrix in dimension 4.
-Rank of the source-module : 10.
-
-
-;; Clock -> 2011-07-14, 9h 54m 35s.
-Computing the boundary of the generator 1/10 (dimension 4) :
-<TnPr S-BSGN 4> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 54m 35s.
-Computing the boundary of the generator 2/10 (dimension 4) :
-<TnPr g11 2> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 54m 35s.
-Computing the boundary of the generator 3/10 (dimension 4) :
-<TnPr g12 2> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 54m 35s.
-Computing the boundary of the generator 4/10 (dimension 4) :
-<TnPr g21 1> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 54m 35s.
-Computing the boundary of the generator 5/10 (dimension 4) :
-<TnPr g22 1> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 54m 35s.
-Computing the boundary of the generator 6/10 (dimension 4) :
-<TnPr g23 1> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 54m 35s.
-Computing the boundary of the generator 7/10 (dimension 4) :
-<TnPr g31 0> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 54m 35s.
-Computing the boundary of the generator 8/10 (dimension 4) :
-<TnPr g32 0> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 54m 35s.
-Computing the boundary of the generator 9/10 (dimension 4) :
-<TnPr g33 0> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 54m 35s.
-Computing the boundary of the generator 10/10 (dimension 4) :
-<TnPr g34 0> 
-End of computing.
-
-
-
-;; Clock -> 2011-07-14, 9h 54m 35s.
-
-
-
-
-Homotopy in dimension 3 :
-
-
-Component Z/2Z
-
-NIL
-CL-USER(34): (homotopy s-k-s3-1 4)
-
-Computing boundary-matrix in dimension 1.
-Rank of the source-module : 0.
-
-
-Computing boundary-matrix in dimension 2.
-Rank of the source-module : 2.
-
-
-;; Clock -> 2011-07-14, 9h 55m 49s.
-Computing the boundary of the generator 1/2 (dimension 2) :
-"g11" 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 55m 49s.
-Computing the boundary of the generator 2/2 (dimension 2) :
-"g12" 
-End of computing.
-
-
-
-;; Clock -> 2011-07-14, 9h 55m 49s.
-
-
-Computing boundary-matrix in dimension 2.
-Rank of the source-module : 2.
-
-
-;; Clock -> 2011-07-14, 9h 55m 49s.
-Computing the boundary of the generator 1/2 (dimension 2) :
-"g11" 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 55m 49s.
-Computing the boundary of the generator 2/2 (dimension 2) :
-"g12" 
-End of computing.
-
-
-Computing boundary-matrix in dimension 3.
-Rank of the source-module : 3.
-
-
-;; Clock -> 2011-07-14, 9h 55m 49s.
-Computing the boundary of the generator 1/3 (dimension 3) :
-"g21" 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 55m 49s.
-Computing the boundary of the generator 2/3 (dimension 3) :
-"g22" 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 55m 49s.
-Computing the boundary of the generator 3/3 (dimension 3) :
-"g23" 
-End of computing.
-
-
-
-;; Clock -> 2011-07-14, 9h 55m 49s.
-
-
-Computing boundary-matrix in dimension 2.
-Rank of the source-module : 2.
-
-
-;; Clock -> 2011-07-14, 9h 55m 49s.
-Computing the boundary of the generator 1/2 (dimension 2) :
-"g11" 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 55m 49s.
-Computing the boundary of the generator 2/2 (dimension 2) :
-"g12" 
-End of computing.
-
-
-Computing boundary-matrix in dimension 3.
-Rank of the source-module : 3.
-
-
-;; Clock -> 2011-07-14, 9h 55m 49s.
-Computing the boundary of the generator 1/3 (dimension 3) :
-"g21" 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 55m 49s.
-Computing the boundary of the generator 2/3 (dimension 3) :
-"g22" 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 55m 49s.
-Computing the boundary of the generator 3/3 (dimension 3) :
-"g23" 
-End of computing.
-
-
-
-;; Clock -> 2011-07-14, 9h 55m 49s.
-
-
-Computing boundary-matrix in dimension 3.
-Rank of the source-module : 6.
-
-
-;; Clock -> 2011-07-14, 9h 55m 50s.
-Computing the boundary of the generator 1/6 (dimension 3) :
-<TnPr S-BSGN 3> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 55m 50s.
-Computing the boundary of the generator 2/6 (dimension 3) :
-<TnPr g11 1> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 55m 50s.
-Computing the boundary of the generator 3/6 (dimension 3) :
-<TnPr g12 1> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 55m 50s.
-Computing the boundary of the generator 4/6 (dimension 3) :
-<TnPr g21 0> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 55m 50s.
-Computing the boundary of the generator 5/6 (dimension 3) :
-<TnPr g22 0> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 55m 50s.
-Computing the boundary of the generator 6/6 (dimension 3) :
-<TnPr g23 0> 
-End of computing.
-
-
-Computing boundary-matrix in dimension 4.
-Rank of the source-module : 10.
-
-
-;; Clock -> 2011-07-14, 9h 55m 50s.
-Computing the boundary of the generator 1/10 (dimension 4) :
-<TnPr S-BSGN 4> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 55m 50s.
-Computing the boundary of the generator 2/10 (dimension 4) :
-<TnPr g11 2> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 55m 50s.
-Computing the boundary of the generator 3/10 (dimension 4) :
-<TnPr g12 2> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 55m 50s.
-Computing the boundary of the generator 4/10 (dimension 4) :
-<TnPr g21 1> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 55m 50s.
-Computing the boundary of the generator 5/10 (dimension 4) :
-<TnPr g22 1> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 55m 50s.
-Computing the boundary of the generator 6/10 (dimension 4) :
-<TnPr g23 1> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 55m 50s.
-Computing the boundary of the generator 7/10 (dimension 4) :
-<TnPr g31 0> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 55m 50s.
-Computing the boundary of the generator 8/10 (dimension 4) :
-<TnPr g32 0> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 55m 50s.
-Computing the boundary of the generator 9/10 (dimension 4) :
-<TnPr g33 0> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 55m 50s.
-Computing the boundary of the generator 10/10 (dimension 4) :
-<TnPr g34 0> 
-End of computing.
-
-
-
-;; Clock -> 2011-07-14, 9h 55m 50s.
-
-
-Computing boundary-matrix in dimension 4.
-Rank of the source-module : 16.
-
-
-;; Clock -> 2011-07-14, 9h 55m 50s.
-Computing the boundary of the generator 1/16 (dimension 4) :
-<TnPr <TnPr S-BSGN 0> <<Abar[4 3]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 55m 50s.
-Computing the boundary of the generator 2/16 (dimension 4) :
-<TnPr <TnPr S-BSGN 0> <<Abar[2 1][2 1]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 55m 51s.
-Computing the boundary of the generator 3/16 (dimension 4) :
-<TnPr <TnPr S-BSGN 1> <<Abar[3 2]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 55m 51s.
-Computing the boundary of the generator 4/16 (dimension 4) :
-<TnPr <TnPr S-BSGN 2> <<Abar[2 1]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 55m 51s.
-Computing the boundary of the generator 5/16 (dimension 4) :
-<TnPr <TnPr g11 0> <<Abar[2 1]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 55m 51s.
-Computing the boundary of the generator 6/16 (dimension 4) :
-<TnPr <TnPr g12 0> <<Abar[2 1]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 55m 51s.
-Computing the boundary of the generator 7/16 (dimension 4) :
-<TnPr <TnPr S-BSGN 4> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 55m 51s.
-Computing the boundary of the generator 8/16 (dimension 4) :
-<TnPr <TnPr g11 2> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 55m 51s.
-Computing the boundary of the generator 9/16 (dimension 4) :
-<TnPr <TnPr g12 2> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 55m 51s.
-Computing the boundary of the generator 10/16 (dimension 4) :
-<TnPr <TnPr g21 1> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 55m 51s.
-Computing the boundary of the generator 11/16 (dimension 4) :
-<TnPr <TnPr g22 1> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 55m 51s.
-Computing the boundary of the generator 12/16 (dimension 4) :
-<TnPr <TnPr g23 1> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 55m 51s.
-Computing the boundary of the generator 13/16 (dimension 4) :
-<TnPr <TnPr g31 0> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 55m 51s.
-Computing the boundary of the generator 14/16 (dimension 4) :
-<TnPr <TnPr g32 0> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 55m 51s.
-Computing the boundary of the generator 15/16 (dimension 4) :
-<TnPr <TnPr g33 0> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 55m 51s.
-Computing the boundary of the generator 16/16 (dimension 4) :
-<TnPr <TnPr g34 0> <<Abar>>> 
-End of computing.
-
-
-Computing boundary-matrix in dimension 5.
-Rank of the source-module : 29.
-
-
-;; Clock -> 2011-07-14, 9h 55m 51s.
-Computing the boundary of the generator 1/29 (dimension 5) :
-<TnPr <TnPr S-BSGN 0> <<Abar[5 4]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 55m 51s.
-Computing the boundary of the generator 2/29 (dimension 5) :
-<TnPr <TnPr S-BSGN 0> <<Abar[2 1][3 2]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 55m 51s.
-Computing the boundary of the generator 3/29 (dimension 5) :
-<TnPr <TnPr S-BSGN 0> <<Abar[3 2][2 1]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 55m 51s.
-Computing the boundary of the generator 4/29 (dimension 5) :
-<TnPr <TnPr S-BSGN 1> <<Abar[4 3]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 55m 51s.
-Computing the boundary of the generator 5/29 (dimension 5) :
-<TnPr <TnPr S-BSGN 1> <<Abar[2 1][2 1]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 55m 51s.
-Computing the boundary of the generator 6/29 (dimension 5) :
-<TnPr <TnPr S-BSGN 2> <<Abar[3 2]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 55m 51s.
-Computing the boundary of the generator 7/29 (dimension 5) :
-<TnPr <TnPr g11 0> <<Abar[3 2]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 55m 52s.
-Computing the boundary of the generator 8/29 (dimension 5) :
-<TnPr <TnPr g12 0> <<Abar[3 2]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 55m 52s.
-Computing the boundary of the generator 9/29 (dimension 5) :
-<TnPr <TnPr S-BSGN 3> <<Abar[2 1]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 55m 52s.
-Computing the boundary of the generator 10/29 (dimension 5) :
-<TnPr <TnPr g11 1> <<Abar[2 1]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 55m 52s.
-Computing the boundary of the generator 11/29 (dimension 5) :
-<TnPr <TnPr g12 1> <<Abar[2 1]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 55m 52s.
-Computing the boundary of the generator 12/29 (dimension 5) :
-<TnPr <TnPr g21 0> <<Abar[2 1]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 55m 52s.
-Computing the boundary of the generator 13/29 (dimension 5) :
-<TnPr <TnPr g22 0> <<Abar[2 1]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 55m 52s.
-Computing the boundary of the generator 14/29 (dimension 5) :
-<TnPr <TnPr g23 0> <<Abar[2 1]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 55m 52s.
-Computing the boundary of the generator 15/29 (dimension 5) :
-<TnPr <TnPr S-BSGN 5> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 55m 52s.
-Computing the boundary of the generator 16/29 (dimension 5) :
-<TnPr <TnPr g11 3> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 55m 52s.
-Computing the boundary of the generator 17/29 (dimension 5) :
-<TnPr <TnPr g12 3> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 55m 52s.
-Computing the boundary of the generator 18/29 (dimension 5) :
-<TnPr <TnPr g21 2> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 55m 52s.
-Computing the boundary of the generator 19/29 (dimension 5) :
-<TnPr <TnPr g22 2> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 55m 52s.
-Computing the boundary of the generator 20/29 (dimension 5) :
-<TnPr <TnPr g23 2> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 55m 53s.
-Computing the boundary of the generator 21/29 (dimension 5) :
-<TnPr <TnPr g31 1> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 55m 53s.
-Computing the boundary of the generator 22/29 (dimension 5) :
-<TnPr <TnPr g32 1> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 55m 53s.
-Computing the boundary of the generator 23/29 (dimension 5) :
-<TnPr <TnPr g33 1> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 55m 53s.
-Computing the boundary of the generator 24/29 (dimension 5) :
-<TnPr <TnPr g34 1> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 55m 53s.
-Computing the boundary of the generator 25/29 (dimension 5) :
-<TnPr <TnPr g41 0> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 55m 53s.
-Computing the boundary of the generator 26/29 (dimension 5) :
-<TnPr <TnPr g42 0> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 55m 53s.
-Computing the boundary of the generator 27/29 (dimension 5) :
-<TnPr <TnPr g43 0> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 55m 53s.
-Computing the boundary of the generator 28/29 (dimension 5) :
-<TnPr <TnPr g44 0> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 55m 53s.
-Computing the boundary of the generator 29/29 (dimension 5) :
-<TnPr <TnPr g45 0> <<Abar>>> 
-End of computing.
-
-
-
-;; Clock -> 2011-07-14, 9h 55m 53s.
-
-
-Computing boundary-matrix in dimension 4.
-Rank of the source-module : 16.
-
-
-;; Clock -> 2011-07-14, 9h 55m 53s.
-Computing the boundary of the generator 1/16 (dimension 4) :
-<TnPr <TnPr S-BSGN 0> <<Abar[4 3]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 55m 53s.
-Computing the boundary of the generator 2/16 (dimension 4) :
-<TnPr <TnPr S-BSGN 0> <<Abar[2 1][2 1]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 55m 53s.
-Computing the boundary of the generator 3/16 (dimension 4) :
-<TnPr <TnPr S-BSGN 1> <<Abar[3 2]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 55m 53s.
-Computing the boundary of the generator 4/16 (dimension 4) :
-<TnPr <TnPr S-BSGN 2> <<Abar[2 1]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 55m 53s.
-Computing the boundary of the generator 5/16 (dimension 4) :
-<TnPr <TnPr g11 0> <<Abar[2 1]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 55m 53s.
-Computing the boundary of the generator 6/16 (dimension 4) :
-<TnPr <TnPr g12 0> <<Abar[2 1]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 55m 53s.
-Computing the boundary of the generator 7/16 (dimension 4) :
-<TnPr <TnPr S-BSGN 4> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 55m 53s.
-Computing the boundary of the generator 8/16 (dimension 4) :
-<TnPr <TnPr g11 2> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 55m 53s.
-Computing the boundary of the generator 9/16 (dimension 4) :
-<TnPr <TnPr g12 2> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 55m 53s.
-Computing the boundary of the generator 10/16 (dimension 4) :
-<TnPr <TnPr g21 1> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 55m 53s.
-Computing the boundary of the generator 11/16 (dimension 4) :
-<TnPr <TnPr g22 1> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 55m 53s.
-Computing the boundary of the generator 12/16 (dimension 4) :
-<TnPr <TnPr g23 1> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 55m 53s.
-Computing the boundary of the generator 13/16 (dimension 4) :
-<TnPr <TnPr g31 0> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 55m 53s.
-Computing the boundary of the generator 14/16 (dimension 4) :
-<TnPr <TnPr g32 0> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 55m 53s.
-Computing the boundary of the generator 15/16 (dimension 4) :
-<TnPr <TnPr g33 0> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 55m 53s.
-Computing the boundary of the generator 16/16 (dimension 4) :
-<TnPr <TnPr g34 0> <<Abar>>> 
-End of computing.
-
-
-Computing boundary-matrix in dimension 5.
-Rank of the source-module : 29.
-
-
-;; Clock -> 2011-07-14, 9h 55m 53s.
-Computing the boundary of the generator 1/29 (dimension 5) :
-<TnPr <TnPr S-BSGN 0> <<Abar[5 4]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 55m 53s.
-Computing the boundary of the generator 2/29 (dimension 5) :
-<TnPr <TnPr S-BSGN 0> <<Abar[2 1][3 2]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 55m 53s.
-Computing the boundary of the generator 3/29 (dimension 5) :
-<TnPr <TnPr S-BSGN 0> <<Abar[3 2][2 1]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 55m 53s.
-Computing the boundary of the generator 4/29 (dimension 5) :
-<TnPr <TnPr S-BSGN 1> <<Abar[4 3]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 55m 53s.
-Computing the boundary of the generator 5/29 (dimension 5) :
-<TnPr <TnPr S-BSGN 1> <<Abar[2 1][2 1]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 55m 53s.
-Computing the boundary of the generator 6/29 (dimension 5) :
-<TnPr <TnPr S-BSGN 2> <<Abar[3 2]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 55m 53s.
-Computing the boundary of the generator 7/29 (dimension 5) :
-<TnPr <TnPr g11 0> <<Abar[3 2]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 55m 53s.
-Computing the boundary of the generator 8/29 (dimension 5) :
-<TnPr <TnPr g12 0> <<Abar[3 2]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 55m 53s.
-Computing the boundary of the generator 9/29 (dimension 5) :
-<TnPr <TnPr S-BSGN 3> <<Abar[2 1]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 55m 54s.
-Computing the boundary of the generator 10/29 (dimension 5) :
-<TnPr <TnPr g11 1> <<Abar[2 1]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 55m 54s.
-Computing the boundary of the generator 11/29 (dimension 5) :
-<TnPr <TnPr g12 1> <<Abar[2 1]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 55m 54s.
-Computing the boundary of the generator 12/29 (dimension 5) :
-<TnPr <TnPr g21 0> <<Abar[2 1]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 55m 54s.
-Computing the boundary of the generator 13/29 (dimension 5) :
-<TnPr <TnPr g22 0> <<Abar[2 1]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 55m 54s.
-Computing the boundary of the generator 14/29 (dimension 5) :
-<TnPr <TnPr g23 0> <<Abar[2 1]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 55m 54s.
-Computing the boundary of the generator 15/29 (dimension 5) :
-<TnPr <TnPr S-BSGN 5> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 55m 54s.
-Computing the boundary of the generator 16/29 (dimension 5) :
-<TnPr <TnPr g11 3> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 55m 54s.
-Computing the boundary of the generator 17/29 (dimension 5) :
-<TnPr <TnPr g12 3> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 55m 54s.
-Computing the boundary of the generator 18/29 (dimension 5) :
-<TnPr <TnPr g21 2> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 55m 54s.
-Computing the boundary of the generator 19/29 (dimension 5) :
-<TnPr <TnPr g22 2> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 55m 54s.
-Computing the boundary of the generator 20/29 (dimension 5) :
-<TnPr <TnPr g23 2> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 55m 54s.
-Computing the boundary of the generator 21/29 (dimension 5) :
-<TnPr <TnPr g31 1> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 55m 54s.
-Computing the boundary of the generator 22/29 (dimension 5) :
-<TnPr <TnPr g32 1> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 55m 54s.
-Computing the boundary of the generator 23/29 (dimension 5) :
-<TnPr <TnPr g33 1> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 55m 54s.
-Computing the boundary of the generator 24/29 (dimension 5) :
-<TnPr <TnPr g34 1> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 55m 54s.
-Computing the boundary of the generator 25/29 (dimension 5) :
-<TnPr <TnPr g41 0> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 55m 54s.
-Computing the boundary of the generator 26/29 (dimension 5) :
-<TnPr <TnPr g42 0> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 55m 54s.
-Computing the boundary of the generator 27/29 (dimension 5) :
-<TnPr <TnPr g43 0> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 55m 54s.
-Computing the boundary of the generator 28/29 (dimension 5) :
-<TnPr <TnPr g44 0> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 55m 54s.
-Computing the boundary of the generator 29/29 (dimension 5) :
-<TnPr <TnPr g45 0> <<Abar>>> 
-End of computing.
-
-
-
-;; Clock -> 2011-07-14, 9h 55m 54s.
-
-
-
-
-Homotopy in dimension 4 :
-
-
-Component Z/12Z
-
-NIL
-CL-USER(35): (homotopy s-k-s3-1 5)
-
-Computing boundary-matrix in dimension 1.
-Rank of the source-module : 0.
-
-
-Computing boundary-matrix in dimension 2.
-Rank of the source-module : 2.
-
-
-;; Clock -> 2011-07-14, 9h 56m 7s.
-Computing the boundary of the generator 1/2 (dimension 2) :
-"g11" 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 7s.
-Computing the boundary of the generator 2/2 (dimension 2) :
-"g12" 
-End of computing.
-
-
-
-;; Clock -> 2011-07-14, 9h 56m 7s.
-
-
-Computing boundary-matrix in dimension 2.
-Rank of the source-module : 2.
-
-
-;; Clock -> 2011-07-14, 9h 56m 7s.
-Computing the boundary of the generator 1/2 (dimension 2) :
-"g11" 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 7s.
-Computing the boundary of the generator 2/2 (dimension 2) :
-"g12" 
-End of computing.
-
-
-Computing boundary-matrix in dimension 3.
-Rank of the source-module : 3.
-
-
-;; Clock -> 2011-07-14, 9h 56m 7s.
-Computing the boundary of the generator 1/3 (dimension 3) :
-"g21" 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 7s.
-Computing the boundary of the generator 2/3 (dimension 3) :
-"g22" 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 7s.
-Computing the boundary of the generator 3/3 (dimension 3) :
-"g23" 
-End of computing.
-
-
-
-;; Clock -> 2011-07-14, 9h 56m 7s.
-
-
-Computing boundary-matrix in dimension 2.
-Rank of the source-module : 2.
-
-
-;; Clock -> 2011-07-14, 9h 56m 7s.
-Computing the boundary of the generator 1/2 (dimension 2) :
-"g11" 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 7s.
-Computing the boundary of the generator 2/2 (dimension 2) :
-"g12" 
-End of computing.
-
-
-Computing boundary-matrix in dimension 3.
-Rank of the source-module : 3.
-
-
-;; Clock -> 2011-07-14, 9h 56m 7s.
-Computing the boundary of the generator 1/3 (dimension 3) :
-"g21" 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 7s.
-Computing the boundary of the generator 2/3 (dimension 3) :
-"g22" 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 7s.
-Computing the boundary of the generator 3/3 (dimension 3) :
-"g23" 
-End of computing.
-
-
-
-;; Clock -> 2011-07-14, 9h 56m 7s.
-
-
-Computing boundary-matrix in dimension 3.
-Rank of the source-module : 6.
-
-
-;; Clock -> 2011-07-14, 9h 56m 7s.
-Computing the boundary of the generator 1/6 (dimension 3) :
-<TnPr S-BSGN 3> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 7s.
-Computing the boundary of the generator 2/6 (dimension 3) :
-<TnPr g11 1> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 7s.
-Computing the boundary of the generator 3/6 (dimension 3) :
-<TnPr g12 1> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 7s.
-Computing the boundary of the generator 4/6 (dimension 3) :
-<TnPr g21 0> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 7s.
-Computing the boundary of the generator 5/6 (dimension 3) :
-<TnPr g22 0> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 7s.
-Computing the boundary of the generator 6/6 (dimension 3) :
-<TnPr g23 0> 
-End of computing.
-
-
-Computing boundary-matrix in dimension 4.
-Rank of the source-module : 10.
-
-
-;; Clock -> 2011-07-14, 9h 56m 7s.
-Computing the boundary of the generator 1/10 (dimension 4) :
-<TnPr S-BSGN 4> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 7s.
-Computing the boundary of the generator 2/10 (dimension 4) :
-<TnPr g11 2> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 7s.
-Computing the boundary of the generator 3/10 (dimension 4) :
-<TnPr g12 2> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 7s.
-Computing the boundary of the generator 4/10 (dimension 4) :
-<TnPr g21 1> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 8s.
-Computing the boundary of the generator 5/10 (dimension 4) :
-<TnPr g22 1> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 8s.
-Computing the boundary of the generator 6/10 (dimension 4) :
-<TnPr g23 1> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 8s.
-Computing the boundary of the generator 7/10 (dimension 4) :
-<TnPr g31 0> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 8s.
-Computing the boundary of the generator 8/10 (dimension 4) :
-<TnPr g32 0> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 8s.
-Computing the boundary of the generator 9/10 (dimension 4) :
-<TnPr g33 0> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 8s.
-Computing the boundary of the generator 10/10 (dimension 4) :
-<TnPr g34 0> 
-End of computing.
-
-
-
-;; Clock -> 2011-07-14, 9h 56m 8s.
-
-
-Computing boundary-matrix in dimension 4.
-Rank of the source-module : 16.
-
-
-;; Clock -> 2011-07-14, 9h 56m 8s.
-Computing the boundary of the generator 1/16 (dimension 4) :
-<TnPr <TnPr S-BSGN 0> <<Abar[4 3]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 8s.
-Computing the boundary of the generator 2/16 (dimension 4) :
-<TnPr <TnPr S-BSGN 0> <<Abar[2 1][2 1]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 8s.
-Computing the boundary of the generator 3/16 (dimension 4) :
-<TnPr <TnPr S-BSGN 1> <<Abar[3 2]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 8s.
-Computing the boundary of the generator 4/16 (dimension 4) :
-<TnPr <TnPr S-BSGN 2> <<Abar[2 1]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 8s.
-Computing the boundary of the generator 5/16 (dimension 4) :
-<TnPr <TnPr g11 0> <<Abar[2 1]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 8s.
-Computing the boundary of the generator 6/16 (dimension 4) :
-<TnPr <TnPr g12 0> <<Abar[2 1]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 8s.
-Computing the boundary of the generator 7/16 (dimension 4) :
-<TnPr <TnPr S-BSGN 4> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 8s.
-Computing the boundary of the generator 8/16 (dimension 4) :
-<TnPr <TnPr g11 2> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 8s.
-Computing the boundary of the generator 9/16 (dimension 4) :
-<TnPr <TnPr g12 2> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 8s.
-Computing the boundary of the generator 10/16 (dimension 4) :
-<TnPr <TnPr g21 1> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 8s.
-Computing the boundary of the generator 11/16 (dimension 4) :
-<TnPr <TnPr g22 1> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 8s.
-Computing the boundary of the generator 12/16 (dimension 4) :
-<TnPr <TnPr g23 1> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 8s.
-Computing the boundary of the generator 13/16 (dimension 4) :
-<TnPr <TnPr g31 0> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 8s.
-Computing the boundary of the generator 14/16 (dimension 4) :
-<TnPr <TnPr g32 0> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 8s.
-Computing the boundary of the generator 15/16 (dimension 4) :
-<TnPr <TnPr g33 0> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 8s.
-Computing the boundary of the generator 16/16 (dimension 4) :
-<TnPr <TnPr g34 0> <<Abar>>> 
-End of computing.
-
-
-Computing boundary-matrix in dimension 5.
-Rank of the source-module : 29.
-
-
-;; Clock -> 2011-07-14, 9h 56m 8s.
-Computing the boundary of the generator 1/29 (dimension 5) :
-<TnPr <TnPr S-BSGN 0> <<Abar[5 4]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 8s.
-Computing the boundary of the generator 2/29 (dimension 5) :
-<TnPr <TnPr S-BSGN 0> <<Abar[2 1][3 2]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 8s.
-Computing the boundary of the generator 3/29 (dimension 5) :
-<TnPr <TnPr S-BSGN 0> <<Abar[3 2][2 1]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 9s.
-Computing the boundary of the generator 4/29 (dimension 5) :
-<TnPr <TnPr S-BSGN 1> <<Abar[4 3]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 9s.
-Computing the boundary of the generator 5/29 (dimension 5) :
-<TnPr <TnPr S-BSGN 1> <<Abar[2 1][2 1]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 9s.
-Computing the boundary of the generator 6/29 (dimension 5) :
-<TnPr <TnPr S-BSGN 2> <<Abar[3 2]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 9s.
-Computing the boundary of the generator 7/29 (dimension 5) :
-<TnPr <TnPr g11 0> <<Abar[3 2]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 9s.
-Computing the boundary of the generator 8/29 (dimension 5) :
-<TnPr <TnPr g12 0> <<Abar[3 2]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 9s.
-Computing the boundary of the generator 9/29 (dimension 5) :
-<TnPr <TnPr S-BSGN 3> <<Abar[2 1]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 9s.
-Computing the boundary of the generator 10/29 (dimension 5) :
-<TnPr <TnPr g11 1> <<Abar[2 1]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 9s.
-Computing the boundary of the generator 11/29 (dimension 5) :
-<TnPr <TnPr g12 1> <<Abar[2 1]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 9s.
-Computing the boundary of the generator 12/29 (dimension 5) :
-<TnPr <TnPr g21 0> <<Abar[2 1]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 9s.
-Computing the boundary of the generator 13/29 (dimension 5) :
-<TnPr <TnPr g22 0> <<Abar[2 1]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 9s.
-Computing the boundary of the generator 14/29 (dimension 5) :
-<TnPr <TnPr g23 0> <<Abar[2 1]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 9s.
-Computing the boundary of the generator 15/29 (dimension 5) :
-<TnPr <TnPr S-BSGN 5> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 9s.
-Computing the boundary of the generator 16/29 (dimension 5) :
-<TnPr <TnPr g11 3> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 9s.
-Computing the boundary of the generator 17/29 (dimension 5) :
-<TnPr <TnPr g12 3> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 9s.
-Computing the boundary of the generator 18/29 (dimension 5) :
-<TnPr <TnPr g21 2> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 9s.
-Computing the boundary of the generator 19/29 (dimension 5) :
-<TnPr <TnPr g22 2> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 9s.
-Computing the boundary of the generator 20/29 (dimension 5) :
-<TnPr <TnPr g23 2> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 9s.
-Computing the boundary of the generator 21/29 (dimension 5) :
-<TnPr <TnPr g31 1> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 9s.
-Computing the boundary of the generator 22/29 (dimension 5) :
-<TnPr <TnPr g32 1> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 9s.
-Computing the boundary of the generator 23/29 (dimension 5) :
-<TnPr <TnPr g33 1> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 9s.
-Computing the boundary of the generator 24/29 (dimension 5) :
-<TnPr <TnPr g34 1> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 9s.
-Computing the boundary of the generator 25/29 (dimension 5) :
-<TnPr <TnPr g41 0> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 9s.
-Computing the boundary of the generator 26/29 (dimension 5) :
-<TnPr <TnPr g42 0> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 9s.
-Computing the boundary of the generator 27/29 (dimension 5) :
-<TnPr <TnPr g43 0> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 9s.
-Computing the boundary of the generator 28/29 (dimension 5) :
-<TnPr <TnPr g44 0> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 9s.
-Computing the boundary of the generator 29/29 (dimension 5) :
-<TnPr <TnPr g45 0> <<Abar>>> 
-End of computing.
-
-
-
-;; Clock -> 2011-07-14, 9h 56m 9s.
-
-
-Computing boundary-matrix in dimension 5.
-Rank of the source-module : 36.
-
-
-;; Clock -> 2011-07-14, 9h 56m 9s.
-Computing the boundary of the generator 1/36 (dimension 5) :
-<TnPr <TnPr <TnPr S-BSGN 0> <<Abar>>> <<Abar[5 <<Abar[4 3]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 9s.
-Computing the boundary of the generator 2/36 (dimension 5) :
-<TnPr <TnPr <TnPr S-BSGN 0> <<Abar>>> <<Abar[5 <<Abar[2 1][2 1]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 9s.
-Computing the boundary of the generator 3/36 (dimension 5) :
-<TnPr <TnPr <TnPr S-BSGN 1> <<Abar>>> <<Abar[4 <<Abar[3 2]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 9s.
-Computing the boundary of the generator 4/36 (dimension 5) :
-<TnPr <TnPr <TnPr S-BSGN 0> <<Abar[2 1]>>> <<Abar[3 <<Abar[2 1]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 9s.
-Computing the boundary of the generator 5/36 (dimension 5) :
-<TnPr <TnPr <TnPr S-BSGN 2> <<Abar>>> <<Abar[3 <<Abar[2 1]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 9s.
-Computing the boundary of the generator 6/36 (dimension 5) :
-<TnPr <TnPr <TnPr g11 0> <<Abar>>> <<Abar[3 <<Abar[2 1]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 9s.
-Computing the boundary of the generator 7/36 (dimension 5) :
-<TnPr <TnPr <TnPr g12 0> <<Abar>>> <<Abar[3 <<Abar[2 1]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 9s.
-Computing the boundary of the generator 8/36 (dimension 5) :
-<TnPr <TnPr <TnPr S-BSGN 0> <<Abar[5 4]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 9s.
-Computing the boundary of the generator 9/36 (dimension 5) :
-<TnPr <TnPr <TnPr S-BSGN 0> <<Abar[2 1][3 2]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 9s.
-Computing the boundary of the generator 10/36 (dimension 5) :
-<TnPr <TnPr <TnPr S-BSGN 0> <<Abar[3 2][2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 9s.
-Computing the boundary of the generator 11/36 (dimension 5) :
-<TnPr <TnPr <TnPr S-BSGN 1> <<Abar[4 3]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 9s.
-Computing the boundary of the generator 12/36 (dimension 5) :
-<TnPr <TnPr <TnPr S-BSGN 1> <<Abar[2 1][2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 9s.
-Computing the boundary of the generator 13/36 (dimension 5) :
-<TnPr <TnPr <TnPr S-BSGN 2> <<Abar[3 2]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 9s.
-Computing the boundary of the generator 14/36 (dimension 5) :
-<TnPr <TnPr <TnPr g11 0> <<Abar[3 2]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 9s.
-Computing the boundary of the generator 15/36 (dimension 5) :
-<TnPr <TnPr <TnPr g12 0> <<Abar[3 2]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 9s.
-Computing the boundary of the generator 16/36 (dimension 5) :
-<TnPr <TnPr <TnPr S-BSGN 3> <<Abar[2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 9s.
-Computing the boundary of the generator 17/36 (dimension 5) :
-<TnPr <TnPr <TnPr g11 1> <<Abar[2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 10s.
-Computing the boundary of the generator 18/36 (dimension 5) :
-<TnPr <TnPr <TnPr g12 1> <<Abar[2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 10s.
-Computing the boundary of the generator 19/36 (dimension 5) :
-<TnPr <TnPr <TnPr g21 0> <<Abar[2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 10s.
-Computing the boundary of the generator 20/36 (dimension 5) :
-<TnPr <TnPr <TnPr g22 0> <<Abar[2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 10s.
-Computing the boundary of the generator 21/36 (dimension 5) :
-<TnPr <TnPr <TnPr g23 0> <<Abar[2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 10s.
-Computing the boundary of the generator 22/36 (dimension 5) :
-<TnPr <TnPr <TnPr S-BSGN 5> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 10s.
-Computing the boundary of the generator 23/36 (dimension 5) :
-<TnPr <TnPr <TnPr g11 3> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 10s.
-Computing the boundary of the generator 24/36 (dimension 5) :
-<TnPr <TnPr <TnPr g12 3> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 10s.
-Computing the boundary of the generator 25/36 (dimension 5) :
-<TnPr <TnPr <TnPr g21 2> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 10s.
-Computing the boundary of the generator 26/36 (dimension 5) :
-<TnPr <TnPr <TnPr g22 2> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 10s.
-Computing the boundary of the generator 27/36 (dimension 5) :
-<TnPr <TnPr <TnPr g23 2> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 11s.
-Computing the boundary of the generator 28/36 (dimension 5) :
-<TnPr <TnPr <TnPr g31 1> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 11s.
-Computing the boundary of the generator 29/36 (dimension 5) :
-<TnPr <TnPr <TnPr g32 1> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 11s.
-Computing the boundary of the generator 30/36 (dimension 5) :
-<TnPr <TnPr <TnPr g33 1> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 11s.
-Computing the boundary of the generator 31/36 (dimension 5) :
-<TnPr <TnPr <TnPr g34 1> <<Abar>>> <<Abar>>> 
-*CR* -- Cut = 0.026471086 -- N = 10197
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 11s.
-Computing the boundary of the generator 32/36 (dimension 5) :
-<TnPr <TnPr <TnPr g41 0> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 12s.
-Computing the boundary of the generator 33/36 (dimension 5) :
-<TnPr <TnPr <TnPr g42 0> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 12s.
-Computing the boundary of the generator 34/36 (dimension 5) :
-<TnPr <TnPr <TnPr g43 0> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 12s.
-Computing the boundary of the generator 35/36 (dimension 5) :
-<TnPr <TnPr <TnPr g44 0> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 12s.
-Computing the boundary of the generator 36/36 (dimension 5) :
-<TnPr <TnPr <TnPr g45 0> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-Computing boundary-matrix in dimension 6.
-Rank of the source-module : 69.
-
-
-;; Clock -> 2011-07-14, 9h 56m 13s.
-Computing the boundary of the generator 1/69 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN 0> <<Abar>>> <<Abar[6 <<Abar[5 4]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 13s.
-Computing the boundary of the generator 2/69 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN 0> <<Abar>>> <<Abar[6 <<Abar[2 1][3 2]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 13s.
-Computing the boundary of the generator 3/69 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN 0> <<Abar>>> <<Abar[6 <<Abar[3 2][2 1]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 13s.
-Computing the boundary of the generator 4/69 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN 0> <<Abar>>> <<Abar[3 <<Abar[2 1]>>][3 <<Abar[2 1]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 13s.
-Computing the boundary of the generator 5/69 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN 1> <<Abar>>> <<Abar[5 <<Abar[4 3]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 13s.
-Computing the boundary of the generator 6/69 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN 1> <<Abar>>> <<Abar[5 <<Abar[2 1][2 1]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 13s.
-Computing the boundary of the generator 7/69 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN 0> <<Abar[2 1]>>> <<Abar[4 <<Abar[3 2]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 13s.
-Computing the boundary of the generator 8/69 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN 2> <<Abar>>> <<Abar[4 <<Abar[3 2]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 13s.
-Computing the boundary of the generator 9/69 (dimension 6) :
-<TnPr <TnPr <TnPr g11 0> <<Abar>>> <<Abar[4 <<Abar[3 2]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 13s.
-Computing the boundary of the generator 10/69 (dimension 6) :
-<TnPr <TnPr <TnPr g12 0> <<Abar>>> <<Abar[4 <<Abar[3 2]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 14s.
-Computing the boundary of the generator 11/69 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN 0> <<Abar[3 2]>>> <<Abar[3 <<Abar[2 1]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 14s.
-Computing the boundary of the generator 12/69 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN 1> <<Abar[2 1]>>> <<Abar[3 <<Abar[2 1]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 14s.
-Computing the boundary of the generator 13/69 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN 3> <<Abar>>> <<Abar[3 <<Abar[2 1]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 14s.
-Computing the boundary of the generator 14/69 (dimension 6) :
-<TnPr <TnPr <TnPr g11 1> <<Abar>>> <<Abar[3 <<Abar[2 1]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 14s.
-Computing the boundary of the generator 15/69 (dimension 6) :
-<TnPr <TnPr <TnPr g12 1> <<Abar>>> <<Abar[3 <<Abar[2 1]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 14s.
-Computing the boundary of the generator 16/69 (dimension 6) :
-<TnPr <TnPr <TnPr g21 0> <<Abar>>> <<Abar[3 <<Abar[2 1]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 14s.
-Computing the boundary of the generator 17/69 (dimension 6) :
-<TnPr <TnPr <TnPr g22 0> <<Abar>>> <<Abar[3 <<Abar[2 1]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 14s.
-Computing the boundary of the generator 18/69 (dimension 6) :
-<TnPr <TnPr <TnPr g23 0> <<Abar>>> <<Abar[3 <<Abar[2 1]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 14s.
-Computing the boundary of the generator 19/69 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN 0> <<Abar[6 5]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 14s.
-Computing the boundary of the generator 20/69 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN 0> <<Abar[2 1][4 3]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 14s.
-Computing the boundary of the generator 21/69 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN 0> <<Abar[3 2][3 2]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 14s.
-Computing the boundary of the generator 22/69 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN 0> <<Abar[4 3][2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 14s.
-Computing the boundary of the generator 23/69 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN 0> <<Abar[2 1][2 1][2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 14s.
-Computing the boundary of the generator 24/69 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN 1> <<Abar[5 4]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 15s.
-Computing the boundary of the generator 25/69 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN 1> <<Abar[2 1][3 2]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 15s.
-Computing the boundary of the generator 26/69 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN 1> <<Abar[3 2][2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 15s.
-Computing the boundary of the generator 27/69 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN 2> <<Abar[4 3]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 15s.
-Computing the boundary of the generator 28/69 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN 2> <<Abar[2 1][2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 15s.
-Computing the boundary of the generator 29/69 (dimension 6) :
-<TnPr <TnPr <TnPr g11 0> <<Abar[4 3]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 15s.
-Computing the boundary of the generator 30/69 (dimension 6) :
-<TnPr <TnPr <TnPr g11 0> <<Abar[2 1][2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 15s.
-Computing the boundary of the generator 31/69 (dimension 6) :
-<TnPr <TnPr <TnPr g12 0> <<Abar[4 3]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 15s.
-Computing the boundary of the generator 32/69 (dimension 6) :
-<TnPr <TnPr <TnPr g12 0> <<Abar[2 1][2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 15s.
-Computing the boundary of the generator 33/69 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN 3> <<Abar[3 2]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 15s.
-Computing the boundary of the generator 34/69 (dimension 6) :
-<TnPr <TnPr <TnPr g11 1> <<Abar[3 2]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 16s.
-Computing the boundary of the generator 35/69 (dimension 6) :
-<TnPr <TnPr <TnPr g12 1> <<Abar[3 2]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 16s.
-Computing the boundary of the generator 36/69 (dimension 6) :
-<TnPr <TnPr <TnPr g21 0> <<Abar[3 2]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 16s.
-Computing the boundary of the generator 37/69 (dimension 6) :
-<TnPr <TnPr <TnPr g22 0> <<Abar[3 2]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 16s.
-Computing the boundary of the generator 38/69 (dimension 6) :
-<TnPr <TnPr <TnPr g23 0> <<Abar[3 2]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 16s.
-Computing the boundary of the generator 39/69 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN 4> <<Abar[2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 16s.
-Computing the boundary of the generator 40/69 (dimension 6) :
-<TnPr <TnPr <TnPr g11 2> <<Abar[2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 18s.
-Computing the boundary of the generator 41/69 (dimension 6) :
-<TnPr <TnPr <TnPr g12 2> <<Abar[2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 18s.
-Computing the boundary of the generator 42/69 (dimension 6) :
-<TnPr <TnPr <TnPr g21 1> <<Abar[2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 19s.
-Computing the boundary of the generator 43/69 (dimension 6) :
-<TnPr <TnPr <TnPr g22 1> <<Abar[2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 20s.
-Computing the boundary of the generator 44/69 (dimension 6) :
-<TnPr <TnPr <TnPr g23 1> <<Abar[2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 21s.
-Computing the boundary of the generator 45/69 (dimension 6) :
-<TnPr <TnPr <TnPr g31 0> <<Abar[2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 22s.
-Computing the boundary of the generator 46/69 (dimension 6) :
-<TnPr <TnPr <TnPr g32 0> <<Abar[2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 22s.
-Computing the boundary of the generator 47/69 (dimension 6) :
-<TnPr <TnPr <TnPr g33 0> <<Abar[2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 22s.
-Computing the boundary of the generator 48/69 (dimension 6) :
-<TnPr <TnPr <TnPr g34 0> <<Abar[2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 22s.
-Computing the boundary of the generator 49/69 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN 6> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 23s.
-Computing the boundary of the generator 50/69 (dimension 6) :
-<TnPr <TnPr <TnPr g11 4> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 25s.
-Computing the boundary of the generator 51/69 (dimension 6) :
-<TnPr <TnPr <TnPr g12 4> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 25s.
-Computing the boundary of the generator 52/69 (dimension 6) :
-<TnPr <TnPr <TnPr g21 3> <<Abar>>> <<Abar>>> 
-*CR* -- Cut = 0.026193824 -- N = 10254
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 30s.
-Computing the boundary of the generator 53/69 (dimension 6) :
-<TnPr <TnPr <TnPr g22 3> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 33s.
-Computing the boundary of the generator 54/69 (dimension 6) :
-<TnPr <TnPr <TnPr g23 3> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 36s.
-Computing the boundary of the generator 55/69 (dimension 6) :
-<TnPr <TnPr <TnPr g31 2> <<Abar>>> <<Abar>>> 
-*CR* -- Cut = 0.026362488 -- N = 10311
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 43s.
-Computing the boundary of the generator 56/69 (dimension 6) :
-<TnPr <TnPr <TnPr g32 2> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 46s.
-Computing the boundary of the generator 57/69 (dimension 6) :
-<TnPr <TnPr <TnPr g33 2> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 56m 51s.
-Computing the boundary of the generator 58/69 (dimension 6) :
-<TnPr <TnPr <TnPr g34 2> <<Abar>>> <<Abar>>> 
-*CR* -- Cut = 0.026545823 -- N = 10368
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 57m 2s.
-Computing the boundary of the generator 59/69 (dimension 6) :
-<TnPr <TnPr <TnPr g41 1> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 57m 3s.
-Computing the boundary of the generator 60/69 (dimension 6) :
-<TnPr <TnPr <TnPr g42 1> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 57m 7s.
-Computing the boundary of the generator 61/69 (dimension 6) :
-<TnPr <TnPr <TnPr g43 1> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 57m 11s.
-Computing the boundary of the generator 62/69 (dimension 6) :
-<TnPr <TnPr <TnPr g44 1> <<Abar>>> <<Abar>>> 
-*CR* -- Cut = 0.02681824 -- N = 10420
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 57m 18s.
-Computing the boundary of the generator 63/69 (dimension 6) :
-<TnPr <TnPr <TnPr g45 1> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 57m 25s.
-Computing the boundary of the generator 64/69 (dimension 6) :
-<TnPr <TnPr <TnPr g51 0> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 57m 25s.
-Computing the boundary of the generator 65/69 (dimension 6) :
-<TnPr <TnPr <TnPr g52 0> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 57m 26s.
-Computing the boundary of the generator 66/69 (dimension 6) :
-<TnPr <TnPr <TnPr g53 0> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 57m 28s.
-Computing the boundary of the generator 67/69 (dimension 6) :
-<TnPr <TnPr <TnPr g54 0> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 57m 28s.
-Computing the boundary of the generator 68/69 (dimension 6) :
-<TnPr <TnPr <TnPr g55 0> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 57m 30s.
-Computing the boundary of the generator 69/69 (dimension 6) :
-<TnPr <TnPr <TnPr g56 0> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-
-;; Clock -> 2011-07-14, 9h 57m 32s.
-
-
-Computing boundary-matrix in dimension 5.
-Rank of the source-module : 36.
-
-
-;; Clock -> 2011-07-14, 9h 57m 32s.
-Computing the boundary of the generator 1/36 (dimension 5) :
-<TnPr <TnPr <TnPr S-BSGN 0> <<Abar>>> <<Abar[5 <<Abar[4 3]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 57m 32s.
-Computing the boundary of the generator 2/36 (dimension 5) :
-<TnPr <TnPr <TnPr S-BSGN 0> <<Abar>>> <<Abar[5 <<Abar[2 1][2 1]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 57m 32s.
-Computing the boundary of the generator 3/36 (dimension 5) :
-<TnPr <TnPr <TnPr S-BSGN 1> <<Abar>>> <<Abar[4 <<Abar[3 2]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 57m 32s.
-Computing the boundary of the generator 4/36 (dimension 5) :
-<TnPr <TnPr <TnPr S-BSGN 0> <<Abar[2 1]>>> <<Abar[3 <<Abar[2 1]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 57m 32s.
-Computing the boundary of the generator 5/36 (dimension 5) :
-<TnPr <TnPr <TnPr S-BSGN 2> <<Abar>>> <<Abar[3 <<Abar[2 1]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 57m 32s.
-Computing the boundary of the generator 6/36 (dimension 5) :
-<TnPr <TnPr <TnPr g11 0> <<Abar>>> <<Abar[3 <<Abar[2 1]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 57m 32s.
-Computing the boundary of the generator 7/36 (dimension 5) :
-<TnPr <TnPr <TnPr g12 0> <<Abar>>> <<Abar[3 <<Abar[2 1]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 57m 32s.
-Computing the boundary of the generator 8/36 (dimension 5) :
-<TnPr <TnPr <TnPr S-BSGN 0> <<Abar[5 4]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 57m 32s.
-Computing the boundary of the generator 9/36 (dimension 5) :
-<TnPr <TnPr <TnPr S-BSGN 0> <<Abar[2 1][3 2]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 57m 32s.
-Computing the boundary of the generator 10/36 (dimension 5) :
-<TnPr <TnPr <TnPr S-BSGN 0> <<Abar[3 2][2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 57m 32s.
-Computing the boundary of the generator 11/36 (dimension 5) :
-<TnPr <TnPr <TnPr S-BSGN 1> <<Abar[4 3]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 57m 32s.
-Computing the boundary of the generator 12/36 (dimension 5) :
-<TnPr <TnPr <TnPr S-BSGN 1> <<Abar[2 1][2 1]>>> <<Abar>>> 
-*CR* -- Cut = 0.027058253 -- N = 10497
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 57m 32s.
-Computing the boundary of the generator 13/36 (dimension 5) :
-<TnPr <TnPr <TnPr S-BSGN 2> <<Abar[3 2]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 57m 32s.
-Computing the boundary of the generator 14/36 (dimension 5) :
-<TnPr <TnPr <TnPr g11 0> <<Abar[3 2]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 57m 32s.
-Computing the boundary of the generator 15/36 (dimension 5) :
-<TnPr <TnPr <TnPr g12 0> <<Abar[3 2]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 57m 32s.
-Computing the boundary of the generator 16/36 (dimension 5) :
-<TnPr <TnPr <TnPr S-BSGN 3> <<Abar[2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 57m 32s.
-Computing the boundary of the generator 17/36 (dimension 5) :
-<TnPr <TnPr <TnPr g11 1> <<Abar[2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 57m 32s.
-Computing the boundary of the generator 18/36 (dimension 5) :
-<TnPr <TnPr <TnPr g12 1> <<Abar[2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 57m 32s.
-Computing the boundary of the generator 19/36 (dimension 5) :
-<TnPr <TnPr <TnPr g21 0> <<Abar[2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 57m 32s.
-Computing the boundary of the generator 20/36 (dimension 5) :
-<TnPr <TnPr <TnPr g22 0> <<Abar[2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 57m 32s.
-Computing the boundary of the generator 21/36 (dimension 5) :
-<TnPr <TnPr <TnPr g23 0> <<Abar[2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 57m 32s.
-Computing the boundary of the generator 22/36 (dimension 5) :
-<TnPr <TnPr <TnPr S-BSGN 5> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 57m 32s.
-Computing the boundary of the generator 23/36 (dimension 5) :
-<TnPr <TnPr <TnPr g11 3> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 57m 33s.
-Computing the boundary of the generator 24/36 (dimension 5) :
-<TnPr <TnPr <TnPr g12 3> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 57m 33s.
-Computing the boundary of the generator 25/36 (dimension 5) :
-<TnPr <TnPr <TnPr g21 2> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 57m 33s.
-Computing the boundary of the generator 26/36 (dimension 5) :
-<TnPr <TnPr <TnPr g22 2> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 57m 33s.
-Computing the boundary of the generator 27/36 (dimension 5) :
-<TnPr <TnPr <TnPr g23 2> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 57m 33s.
-Computing the boundary of the generator 28/36 (dimension 5) :
-<TnPr <TnPr <TnPr g31 1> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 57m 34s.
-Computing the boundary of the generator 29/36 (dimension 5) :
-<TnPr <TnPr <TnPr g32 1> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 57m 34s.
-Computing the boundary of the generator 30/36 (dimension 5) :
-<TnPr <TnPr <TnPr g33 1> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 57m 34s.
-Computing the boundary of the generator 31/36 (dimension 5) :
-<TnPr <TnPr <TnPr g34 1> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 57m 34s.
-Computing the boundary of the generator 32/36 (dimension 5) :
-<TnPr <TnPr <TnPr g41 0> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 57m 34s.
-Computing the boundary of the generator 33/36 (dimension 5) :
-<TnPr <TnPr <TnPr g42 0> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 57m 34s.
-Computing the boundary of the generator 34/36 (dimension 5) :
-<TnPr <TnPr <TnPr g43 0> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 57m 35s.
-Computing the boundary of the generator 35/36 (dimension 5) :
-<TnPr <TnPr <TnPr g44 0> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 57m 35s.
-Computing the boundary of the generator 36/36 (dimension 5) :
-<TnPr <TnPr <TnPr g45 0> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-Computing boundary-matrix in dimension 6.
-Rank of the source-module : 69.
-
-
-;; Clock -> 2011-07-14, 9h 57m 35s.
-Computing the boundary of the generator 1/69 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN 0> <<Abar>>> <<Abar[6 <<Abar[5 4]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 57m 37s.
-Computing the boundary of the generator 2/69 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN 0> <<Abar>>> <<Abar[6 <<Abar[2 1][3 2]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 57m 37s.
-Computing the boundary of the generator 3/69 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN 0> <<Abar>>> <<Abar[6 <<Abar[3 2][2 1]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 57m 37s.
-Computing the boundary of the generator 4/69 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN 0> <<Abar>>> <<Abar[3 <<Abar[2 1]>>][3 <<Abar[2 1]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 57m 37s.
-Computing the boundary of the generator 5/69 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN 1> <<Abar>>> <<Abar[5 <<Abar[4 3]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 57m 37s.
-Computing the boundary of the generator 6/69 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN 1> <<Abar>>> <<Abar[5 <<Abar[2 1][2 1]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 57m 37s.
-Computing the boundary of the generator 7/69 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN 0> <<Abar[2 1]>>> <<Abar[4 <<Abar[3 2]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 57m 37s.
-Computing the boundary of the generator 8/69 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN 2> <<Abar>>> <<Abar[4 <<Abar[3 2]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 57m 37s.
-Computing the boundary of the generator 9/69 (dimension 6) :
-<TnPr <TnPr <TnPr g11 0> <<Abar>>> <<Abar[4 <<Abar[3 2]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 57m 37s.
-Computing the boundary of the generator 10/69 (dimension 6) :
-<TnPr <TnPr <TnPr g12 0> <<Abar>>> <<Abar[4 <<Abar[3 2]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 57m 37s.
-Computing the boundary of the generator 11/69 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN 0> <<Abar[3 2]>>> <<Abar[3 <<Abar[2 1]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 57m 37s.
-Computing the boundary of the generator 12/69 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN 1> <<Abar[2 1]>>> <<Abar[3 <<Abar[2 1]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 57m 37s.
-Computing the boundary of the generator 13/69 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN 3> <<Abar>>> <<Abar[3 <<Abar[2 1]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 57m 37s.
-Computing the boundary of the generator 14/69 (dimension 6) :
-<TnPr <TnPr <TnPr g11 1> <<Abar>>> <<Abar[3 <<Abar[2 1]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 57m 37s.
-Computing the boundary of the generator 15/69 (dimension 6) :
-<TnPr <TnPr <TnPr g12 1> <<Abar>>> <<Abar[3 <<Abar[2 1]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 57m 37s.
-Computing the boundary of the generator 16/69 (dimension 6) :
-<TnPr <TnPr <TnPr g21 0> <<Abar>>> <<Abar[3 <<Abar[2 1]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 57m 37s.
-Computing the boundary of the generator 17/69 (dimension 6) :
-<TnPr <TnPr <TnPr g22 0> <<Abar>>> <<Abar[3 <<Abar[2 1]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 57m 38s.
-Computing the boundary of the generator 18/69 (dimension 6) :
-<TnPr <TnPr <TnPr g23 0> <<Abar>>> <<Abar[3 <<Abar[2 1]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 57m 38s.
-Computing the boundary of the generator 19/69 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN 0> <<Abar[6 5]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 57m 38s.
-Computing the boundary of the generator 20/69 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN 0> <<Abar[2 1][4 3]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 57m 38s.
-Computing the boundary of the generator 21/69 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN 0> <<Abar[3 2][3 2]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 57m 38s.
-Computing the boundary of the generator 22/69 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN 0> <<Abar[4 3][2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 57m 38s.
-Computing the boundary of the generator 23/69 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN 0> <<Abar[2 1][2 1][2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 57m 38s.
-Computing the boundary of the generator 24/69 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN 1> <<Abar[5 4]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 57m 38s.
-Computing the boundary of the generator 25/69 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN 1> <<Abar[2 1][3 2]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 57m 38s.
-Computing the boundary of the generator 26/69 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN 1> <<Abar[3 2][2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 57m 38s.
-Computing the boundary of the generator 27/69 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN 2> <<Abar[4 3]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 57m 38s.
-Computing the boundary of the generator 28/69 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN 2> <<Abar[2 1][2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 57m 38s.
-Computing the boundary of the generator 29/69 (dimension 6) :
-<TnPr <TnPr <TnPr g11 0> <<Abar[4 3]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 57m 39s.
-Computing the boundary of the generator 30/69 (dimension 6) :
-<TnPr <TnPr <TnPr g11 0> <<Abar[2 1][2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 57m 39s.
-Computing the boundary of the generator 31/69 (dimension 6) :
-<TnPr <TnPr <TnPr g12 0> <<Abar[4 3]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 57m 39s.
-Computing the boundary of the generator 32/69 (dimension 6) :
-<TnPr <TnPr <TnPr g12 0> <<Abar[2 1][2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 57m 39s.
-Computing the boundary of the generator 33/69 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN 3> <<Abar[3 2]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 57m 39s.
-Computing the boundary of the generator 34/69 (dimension 6) :
-<TnPr <TnPr <TnPr g11 1> <<Abar[3 2]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 57m 39s.
-Computing the boundary of the generator 35/69 (dimension 6) :
-<TnPr <TnPr <TnPr g12 1> <<Abar[3 2]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 57m 40s.
-Computing the boundary of the generator 36/69 (dimension 6) :
-<TnPr <TnPr <TnPr g21 0> <<Abar[3 2]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 57m 40s.
-Computing the boundary of the generator 37/69 (dimension 6) :
-<TnPr <TnPr <TnPr g22 0> <<Abar[3 2]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 57m 40s.
-Computing the boundary of the generator 38/69 (dimension 6) :
-<TnPr <TnPr <TnPr g23 0> <<Abar[3 2]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 57m 40s.
-Computing the boundary of the generator 39/69 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN 4> <<Abar[2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 57m 40s.
-Computing the boundary of the generator 40/69 (dimension 6) :
-<TnPr <TnPr <TnPr g11 2> <<Abar[2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 57m 41s.
-Computing the boundary of the generator 41/69 (dimension 6) :
-<TnPr <TnPr <TnPr g12 2> <<Abar[2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 57m 41s.
-Computing the boundary of the generator 42/69 (dimension 6) :
-<TnPr <TnPr <TnPr g21 1> <<Abar[2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 57m 42s.
-Computing the boundary of the generator 43/69 (dimension 6) :
-<TnPr <TnPr <TnPr g22 1> <<Abar[2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 57m 42s.
-Computing the boundary of the generator 44/69 (dimension 6) :
-<TnPr <TnPr <TnPr g23 1> <<Abar[2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 57m 44s.
-Computing the boundary of the generator 45/69 (dimension 6) :
-<TnPr <TnPr <TnPr g31 0> <<Abar[2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 57m 44s.
-Computing the boundary of the generator 46/69 (dimension 6) :
-<TnPr <TnPr <TnPr g32 0> <<Abar[2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 57m 44s.
-Computing the boundary of the generator 47/69 (dimension 6) :
-<TnPr <TnPr <TnPr g33 0> <<Abar[2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 57m 44s.
-Computing the boundary of the generator 48/69 (dimension 6) :
-<TnPr <TnPr <TnPr g34 0> <<Abar[2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 57m 45s.
-Computing the boundary of the generator 49/69 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN 6> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 57m 45s.
-Computing the boundary of the generator 50/69 (dimension 6) :
-<TnPr <TnPr <TnPr g11 4> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 57m 46s.
-Computing the boundary of the generator 51/69 (dimension 6) :
-<TnPr <TnPr <TnPr g12 4> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 57m 46s.
-Computing the boundary of the generator 52/69 (dimension 6) :
-<TnPr <TnPr <TnPr g21 3> <<Abar>>> <<Abar>>> 
-*CR* -- Cut = 0.027114734 -- N = 10505
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 57m 50s.
-Computing the boundary of the generator 53/69 (dimension 6) :
-<TnPr <TnPr <TnPr g22 3> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 57m 52s.
-Computing the boundary of the generator 54/69 (dimension 6) :
-<TnPr <TnPr <TnPr g23 3> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 57m 54s.
-Computing the boundary of the generator 55/69 (dimension 6) :
-<TnPr <TnPr <TnPr g31 2> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 57m 56s.
-Computing the boundary of the generator 56/69 (dimension 6) :
-<TnPr <TnPr <TnPr g32 2> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 57m 57s.
-Computing the boundary of the generator 57/69 (dimension 6) :
-<TnPr <TnPr <TnPr g33 2> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 0s.
-Computing the boundary of the generator 58/69 (dimension 6) :
-<TnPr <TnPr <TnPr g34 2> <<Abar>>> <<Abar>>> 
-*CR* -- Cut = 0.027164893 -- N = 10514
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 6s.
-Computing the boundary of the generator 59/69 (dimension 6) :
-<TnPr <TnPr <TnPr g41 1> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 7s.
-Computing the boundary of the generator 60/69 (dimension 6) :
-<TnPr <TnPr <TnPr g42 1> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 9s.
-Computing the boundary of the generator 61/69 (dimension 6) :
-<TnPr <TnPr <TnPr g43 1> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 11s.
-Computing the boundary of the generator 62/69 (dimension 6) :
-<TnPr <TnPr <TnPr g44 1> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 15s.
-Computing the boundary of the generator 63/69 (dimension 6) :
-<TnPr <TnPr <TnPr g45 1> <<Abar>>> <<Abar>>> 
-*CR* -- Cut = 0.027187303 -- N = 10525
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 18s.
-Computing the boundary of the generator 64/69 (dimension 6) :
-<TnPr <TnPr <TnPr g51 0> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 18s.
-Computing the boundary of the generator 65/69 (dimension 6) :
-<TnPr <TnPr <TnPr g52 0> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 18s.
-Computing the boundary of the generator 66/69 (dimension 6) :
-<TnPr <TnPr <TnPr g53 0> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 20s.
-Computing the boundary of the generator 67/69 (dimension 6) :
-<TnPr <TnPr <TnPr g54 0> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 20s.
-Computing the boundary of the generator 68/69 (dimension 6) :
-<TnPr <TnPr <TnPr g55 0> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 21s.
-Computing the boundary of the generator 69/69 (dimension 6) :
-<TnPr <TnPr <TnPr g56 0> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-
-;; Clock -> 2011-07-14, 9h 58m 23s.
-
-
-
-
-Homotopy in dimension 5 :
-
-
-Component Z/2Z
-
-Component Z/2Z
-
-NIL
-CL-USER(36): (homotopy s-k-s3-1 6)
-
-Computing boundary-matrix in dimension 1.
-Rank of the source-module : 0.
-
-
-Computing boundary-matrix in dimension 2.
-Rank of the source-module : 2.
-
-
-;; Clock -> 2011-07-14, 9h 58m 48s.
-Computing the boundary of the generator 1/2 (dimension 2) :
-"g11" 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 48s.
-Computing the boundary of the generator 2/2 (dimension 2) :
-"g12" 
-End of computing.
-
-
-
-;; Clock -> 2011-07-14, 9h 58m 48s.
-
-
-Computing boundary-matrix in dimension 2.
-Rank of the source-module : 2.
-
-
-;; Clock -> 2011-07-14, 9h 58m 48s.
-Computing the boundary of the generator 1/2 (dimension 2) :
-"g11" 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 48s.
-Computing the boundary of the generator 2/2 (dimension 2) :
-"g12" 
-End of computing.
-
-
-Computing boundary-matrix in dimension 3.
-Rank of the source-module : 3.
-
-
-;; Clock -> 2011-07-14, 9h 58m 48s.
-Computing the boundary of the generator 1/3 (dimension 3) :
-"g21" 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 48s.
-Computing the boundary of the generator 2/3 (dimension 3) :
-"g22" 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 48s.
-Computing the boundary of the generator 3/3 (dimension 3) :
-"g23" 
-End of computing.
-
-
-
-;; Clock -> 2011-07-14, 9h 58m 48s.
-
-
-Computing boundary-matrix in dimension 2.
-Rank of the source-module : 2.
-
-
-;; Clock -> 2011-07-14, 9h 58m 48s.
-Computing the boundary of the generator 1/2 (dimension 2) :
-"g11" 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 48s.
-Computing the boundary of the generator 2/2 (dimension 2) :
-"g12" 
-End of computing.
-
-
-Computing boundary-matrix in dimension 3.
-Rank of the source-module : 3.
-
-
-;; Clock -> 2011-07-14, 9h 58m 48s.
-Computing the boundary of the generator 1/3 (dimension 3) :
-"g21" 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 48s.
-Computing the boundary of the generator 2/3 (dimension 3) :
-"g22" 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 48s.
-Computing the boundary of the generator 3/3 (dimension 3) :
-"g23" 
-End of computing.
-
-
-
-;; Clock -> 2011-07-14, 9h 58m 48s.
-
-
-Computing boundary-matrix in dimension 3.
-Rank of the source-module : 6.
-
-
-;; Clock -> 2011-07-14, 9h 58m 48s.
-Computing the boundary of the generator 1/6 (dimension 3) :
-<TnPr S-BSGN 3> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 48s.
-Computing the boundary of the generator 2/6 (dimension 3) :
-<TnPr g11 1> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 48s.
-Computing the boundary of the generator 3/6 (dimension 3) :
-<TnPr g12 1> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 48s.
-Computing the boundary of the generator 4/6 (dimension 3) :
-<TnPr g21 0> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 48s.
-Computing the boundary of the generator 5/6 (dimension 3) :
-<TnPr g22 0> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 48s.
-Computing the boundary of the generator 6/6 (dimension 3) :
-<TnPr g23 0> 
-End of computing.
-
-
-Computing boundary-matrix in dimension 4.
-Rank of the source-module : 10.
-
-
-;; Clock -> 2011-07-14, 9h 58m 48s.
-Computing the boundary of the generator 1/10 (dimension 4) :
-<TnPr S-BSGN 4> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 48s.
-Computing the boundary of the generator 2/10 (dimension 4) :
-<TnPr g11 2> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 48s.
-Computing the boundary of the generator 3/10 (dimension 4) :
-<TnPr g12 2> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 48s.
-Computing the boundary of the generator 4/10 (dimension 4) :
-<TnPr g21 1> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 48s.
-Computing the boundary of the generator 5/10 (dimension 4) :
-<TnPr g22 1> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 48s.
-Computing the boundary of the generator 6/10 (dimension 4) :
-<TnPr g23 1> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 48s.
-Computing the boundary of the generator 7/10 (dimension 4) :
-<TnPr g31 0> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 48s.
-Computing the boundary of the generator 8/10 (dimension 4) :
-<TnPr g32 0> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 48s.
-Computing the boundary of the generator 9/10 (dimension 4) :
-<TnPr g33 0> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 48s.
-Computing the boundary of the generator 10/10 (dimension 4) :
-<TnPr g34 0> 
-End of computing.
-
-
-
-;; Clock -> 2011-07-14, 9h 58m 48s.
-
-
-Computing boundary-matrix in dimension 4.
-Rank of the source-module : 16.
-
-
-;; Clock -> 2011-07-14, 9h 58m 48s.
-Computing the boundary of the generator 1/16 (dimension 4) :
-<TnPr <TnPr S-BSGN 0> <<Abar[4 3]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 48s.
-Computing the boundary of the generator 2/16 (dimension 4) :
-<TnPr <TnPr S-BSGN 0> <<Abar[2 1][2 1]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 48s.
-Computing the boundary of the generator 3/16 (dimension 4) :
-<TnPr <TnPr S-BSGN 1> <<Abar[3 2]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 48s.
-Computing the boundary of the generator 4/16 (dimension 4) :
-<TnPr <TnPr S-BSGN 2> <<Abar[2 1]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 48s.
-Computing the boundary of the generator 5/16 (dimension 4) :
-<TnPr <TnPr g11 0> <<Abar[2 1]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 48s.
-Computing the boundary of the generator 6/16 (dimension 4) :
-<TnPr <TnPr g12 0> <<Abar[2 1]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 48s.
-Computing the boundary of the generator 7/16 (dimension 4) :
-<TnPr <TnPr S-BSGN 4> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 48s.
-Computing the boundary of the generator 8/16 (dimension 4) :
-<TnPr <TnPr g11 2> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 48s.
-Computing the boundary of the generator 9/16 (dimension 4) :
-<TnPr <TnPr g12 2> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 48s.
-Computing the boundary of the generator 10/16 (dimension 4) :
-<TnPr <TnPr g21 1> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 48s.
-Computing the boundary of the generator 11/16 (dimension 4) :
-<TnPr <TnPr g22 1> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 48s.
-Computing the boundary of the generator 12/16 (dimension 4) :
-<TnPr <TnPr g23 1> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 48s.
-Computing the boundary of the generator 13/16 (dimension 4) :
-<TnPr <TnPr g31 0> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 48s.
-Computing the boundary of the generator 14/16 (dimension 4) :
-<TnPr <TnPr g32 0> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 48s.
-Computing the boundary of the generator 15/16 (dimension 4) :
-<TnPr <TnPr g33 0> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 48s.
-Computing the boundary of the generator 16/16 (dimension 4) :
-<TnPr <TnPr g34 0> <<Abar>>> 
-End of computing.
-
-
-Computing boundary-matrix in dimension 5.
-Rank of the source-module : 29.
-
-
-;; Clock -> 2011-07-14, 9h 58m 48s.
-Computing the boundary of the generator 1/29 (dimension 5) :
-<TnPr <TnPr S-BSGN 0> <<Abar[5 4]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 48s.
-Computing the boundary of the generator 2/29 (dimension 5) :
-<TnPr <TnPr S-BSGN 0> <<Abar[2 1][3 2]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 48s.
-Computing the boundary of the generator 3/29 (dimension 5) :
-<TnPr <TnPr S-BSGN 0> <<Abar[3 2][2 1]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 48s.
-Computing the boundary of the generator 4/29 (dimension 5) :
-<TnPr <TnPr S-BSGN 1> <<Abar[4 3]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 48s.
-Computing the boundary of the generator 5/29 (dimension 5) :
-<TnPr <TnPr S-BSGN 1> <<Abar[2 1][2 1]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 48s.
-Computing the boundary of the generator 6/29 (dimension 5) :
-<TnPr <TnPr S-BSGN 2> <<Abar[3 2]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 48s.
-Computing the boundary of the generator 7/29 (dimension 5) :
-<TnPr <TnPr g11 0> <<Abar[3 2]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 48s.
-Computing the boundary of the generator 8/29 (dimension 5) :
-<TnPr <TnPr g12 0> <<Abar[3 2]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 48s.
-Computing the boundary of the generator 9/29 (dimension 5) :
-<TnPr <TnPr S-BSGN 3> <<Abar[2 1]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 48s.
-Computing the boundary of the generator 10/29 (dimension 5) :
-<TnPr <TnPr g11 1> <<Abar[2 1]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 48s.
-Computing the boundary of the generator 11/29 (dimension 5) :
-<TnPr <TnPr g12 1> <<Abar[2 1]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 48s.
-Computing the boundary of the generator 12/29 (dimension 5) :
-<TnPr <TnPr g21 0> <<Abar[2 1]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 48s.
-Computing the boundary of the generator 13/29 (dimension 5) :
-<TnPr <TnPr g22 0> <<Abar[2 1]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 48s.
-Computing the boundary of the generator 14/29 (dimension 5) :
-<TnPr <TnPr g23 0> <<Abar[2 1]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 48s.
-Computing the boundary of the generator 15/29 (dimension 5) :
-<TnPr <TnPr S-BSGN 5> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 48s.
-Computing the boundary of the generator 16/29 (dimension 5) :
-<TnPr <TnPr g11 3> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 49s.
-Computing the boundary of the generator 17/29 (dimension 5) :
-<TnPr <TnPr g12 3> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 49s.
-Computing the boundary of the generator 18/29 (dimension 5) :
-<TnPr <TnPr g21 2> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 49s.
-Computing the boundary of the generator 19/29 (dimension 5) :
-<TnPr <TnPr g22 2> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 49s.
-Computing the boundary of the generator 20/29 (dimension 5) :
-<TnPr <TnPr g23 2> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 49s.
-Computing the boundary of the generator 21/29 (dimension 5) :
-<TnPr <TnPr g31 1> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 49s.
-Computing the boundary of the generator 22/29 (dimension 5) :
-<TnPr <TnPr g32 1> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 49s.
-Computing the boundary of the generator 23/29 (dimension 5) :
-<TnPr <TnPr g33 1> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 49s.
-Computing the boundary of the generator 24/29 (dimension 5) :
-<TnPr <TnPr g34 1> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 49s.
-Computing the boundary of the generator 25/29 (dimension 5) :
-<TnPr <TnPr g41 0> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 49s.
-Computing the boundary of the generator 26/29 (dimension 5) :
-<TnPr <TnPr g42 0> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 49s.
-Computing the boundary of the generator 27/29 (dimension 5) :
-<TnPr <TnPr g43 0> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 49s.
-Computing the boundary of the generator 28/29 (dimension 5) :
-<TnPr <TnPr g44 0> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 49s.
-Computing the boundary of the generator 29/29 (dimension 5) :
-<TnPr <TnPr g45 0> <<Abar>>> 
-End of computing.
-
-
-
-;; Clock -> 2011-07-14, 9h 58m 49s.
-
-
-Computing boundary-matrix in dimension 5.
-Rank of the source-module : 36.
-
-
-;; Clock -> 2011-07-14, 9h 58m 49s.
-Computing the boundary of the generator 1/36 (dimension 5) :
-<TnPr <TnPr <TnPr S-BSGN 0> <<Abar>>> <<Abar[5 <<Abar[4 3]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 49s.
-Computing the boundary of the generator 2/36 (dimension 5) :
-<TnPr <TnPr <TnPr S-BSGN 0> <<Abar>>> <<Abar[5 <<Abar[2 1][2 1]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 49s.
-Computing the boundary of the generator 3/36 (dimension 5) :
-<TnPr <TnPr <TnPr S-BSGN 1> <<Abar>>> <<Abar[4 <<Abar[3 2]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 49s.
-Computing the boundary of the generator 4/36 (dimension 5) :
-<TnPr <TnPr <TnPr S-BSGN 0> <<Abar[2 1]>>> <<Abar[3 <<Abar[2 1]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 49s.
-Computing the boundary of the generator 5/36 (dimension 5) :
-<TnPr <TnPr <TnPr S-BSGN 2> <<Abar>>> <<Abar[3 <<Abar[2 1]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 49s.
-Computing the boundary of the generator 6/36 (dimension 5) :
-<TnPr <TnPr <TnPr g11 0> <<Abar>>> <<Abar[3 <<Abar[2 1]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 49s.
-Computing the boundary of the generator 7/36 (dimension 5) :
-<TnPr <TnPr <TnPr g12 0> <<Abar>>> <<Abar[3 <<Abar[2 1]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 49s.
-Computing the boundary of the generator 8/36 (dimension 5) :
-<TnPr <TnPr <TnPr S-BSGN 0> <<Abar[5 4]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 49s.
-Computing the boundary of the generator 9/36 (dimension 5) :
-<TnPr <TnPr <TnPr S-BSGN 0> <<Abar[2 1][3 2]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 49s.
-Computing the boundary of the generator 10/36 (dimension 5) :
-<TnPr <TnPr <TnPr S-BSGN 0> <<Abar[3 2][2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 49s.
-Computing the boundary of the generator 11/36 (dimension 5) :
-<TnPr <TnPr <TnPr S-BSGN 1> <<Abar[4 3]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 49s.
-Computing the boundary of the generator 12/36 (dimension 5) :
-<TnPr <TnPr <TnPr S-BSGN 1> <<Abar[2 1][2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 49s.
-Computing the boundary of the generator 13/36 (dimension 5) :
-<TnPr <TnPr <TnPr S-BSGN 2> <<Abar[3 2]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 49s.
-Computing the boundary of the generator 14/36 (dimension 5) :
-<TnPr <TnPr <TnPr g11 0> <<Abar[3 2]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 49s.
-Computing the boundary of the generator 15/36 (dimension 5) :
-<TnPr <TnPr <TnPr g12 0> <<Abar[3 2]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 49s.
-Computing the boundary of the generator 16/36 (dimension 5) :
-<TnPr <TnPr <TnPr S-BSGN 3> <<Abar[2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 49s.
-Computing the boundary of the generator 17/36 (dimension 5) :
-<TnPr <TnPr <TnPr g11 1> <<Abar[2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 49s.
-Computing the boundary of the generator 18/36 (dimension 5) :
-<TnPr <TnPr <TnPr g12 1> <<Abar[2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 50s.
-Computing the boundary of the generator 19/36 (dimension 5) :
-<TnPr <TnPr <TnPr g21 0> <<Abar[2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 50s.
-Computing the boundary of the generator 20/36 (dimension 5) :
-<TnPr <TnPr <TnPr g22 0> <<Abar[2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 50s.
-Computing the boundary of the generator 21/36 (dimension 5) :
-<TnPr <TnPr <TnPr g23 0> <<Abar[2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 50s.
-Computing the boundary of the generator 22/36 (dimension 5) :
-<TnPr <TnPr <TnPr S-BSGN 5> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 50s.
-Computing the boundary of the generator 23/36 (dimension 5) :
-<TnPr <TnPr <TnPr g11 3> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 50s.
-Computing the boundary of the generator 24/36 (dimension 5) :
-<TnPr <TnPr <TnPr g12 3> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 50s.
-Computing the boundary of the generator 25/36 (dimension 5) :
-<TnPr <TnPr <TnPr g21 2> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 50s.
-Computing the boundary of the generator 26/36 (dimension 5) :
-<TnPr <TnPr <TnPr g22 2> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 50s.
-Computing the boundary of the generator 27/36 (dimension 5) :
-<TnPr <TnPr <TnPr g23 2> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 50s.
-Computing the boundary of the generator 28/36 (dimension 5) :
-<TnPr <TnPr <TnPr g31 1> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 51s.
-Computing the boundary of the generator 29/36 (dimension 5) :
-<TnPr <TnPr <TnPr g32 1> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 51s.
-Computing the boundary of the generator 30/36 (dimension 5) :
-<TnPr <TnPr <TnPr g33 1> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 51s.
-Computing the boundary of the generator 31/36 (dimension 5) :
-<TnPr <TnPr <TnPr g34 1> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 51s.
-Computing the boundary of the generator 32/36 (dimension 5) :
-<TnPr <TnPr <TnPr g41 0> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 51s.
-Computing the boundary of the generator 33/36 (dimension 5) :
-<TnPr <TnPr <TnPr g42 0> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 51s.
-Computing the boundary of the generator 34/36 (dimension 5) :
-<TnPr <TnPr <TnPr g43 0> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 51s.
-Computing the boundary of the generator 35/36 (dimension 5) :
-<TnPr <TnPr <TnPr g44 0> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 51s.
-Computing the boundary of the generator 36/36 (dimension 5) :
-<TnPr <TnPr <TnPr g45 0> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-Computing boundary-matrix in dimension 6.
-Rank of the source-module : 69.
-
-
-;; Clock -> 2011-07-14, 9h 58m 51s.
-Computing the boundary of the generator 1/69 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN 0> <<Abar>>> <<Abar[6 <<Abar[5 4]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 52s.
-Computing the boundary of the generator 2/69 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN 0> <<Abar>>> <<Abar[6 <<Abar[2 1][3 2]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 52s.
-Computing the boundary of the generator 3/69 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN 0> <<Abar>>> <<Abar[6 <<Abar[3 2][2 1]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 52s.
-Computing the boundary of the generator 4/69 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN 0> <<Abar>>> <<Abar[3 <<Abar[2 1]>>][3 <<Abar[2 1]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 52s.
-Computing the boundary of the generator 5/69 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN 1> <<Abar>>> <<Abar[5 <<Abar[4 3]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 52s.
-Computing the boundary of the generator 6/69 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN 1> <<Abar>>> <<Abar[5 <<Abar[2 1][2 1]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 52s.
-Computing the boundary of the generator 7/69 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN 0> <<Abar[2 1]>>> <<Abar[4 <<Abar[3 2]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 52s.
-Computing the boundary of the generator 8/69 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN 2> <<Abar>>> <<Abar[4 <<Abar[3 2]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 52s.
-Computing the boundary of the generator 9/69 (dimension 6) :
-<TnPr <TnPr <TnPr g11 0> <<Abar>>> <<Abar[4 <<Abar[3 2]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 52s.
-Computing the boundary of the generator 10/69 (dimension 6) :
-<TnPr <TnPr <TnPr g12 0> <<Abar>>> <<Abar[4 <<Abar[3 2]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 52s.
-Computing the boundary of the generator 11/69 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN 0> <<Abar[3 2]>>> <<Abar[3 <<Abar[2 1]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 52s.
-Computing the boundary of the generator 12/69 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN 1> <<Abar[2 1]>>> <<Abar[3 <<Abar[2 1]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 52s.
-Computing the boundary of the generator 13/69 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN 3> <<Abar>>> <<Abar[3 <<Abar[2 1]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 52s.
-Computing the boundary of the generator 14/69 (dimension 6) :
-<TnPr <TnPr <TnPr g11 1> <<Abar>>> <<Abar[3 <<Abar[2 1]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 52s.
-Computing the boundary of the generator 15/69 (dimension 6) :
-<TnPr <TnPr <TnPr g12 1> <<Abar>>> <<Abar[3 <<Abar[2 1]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 52s.
-Computing the boundary of the generator 16/69 (dimension 6) :
-<TnPr <TnPr <TnPr g21 0> <<Abar>>> <<Abar[3 <<Abar[2 1]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 53s.
-Computing the boundary of the generator 17/69 (dimension 6) :
-<TnPr <TnPr <TnPr g22 0> <<Abar>>> <<Abar[3 <<Abar[2 1]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 53s.
-Computing the boundary of the generator 18/69 (dimension 6) :
-<TnPr <TnPr <TnPr g23 0> <<Abar>>> <<Abar[3 <<Abar[2 1]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 53s.
-Computing the boundary of the generator 19/69 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN 0> <<Abar[6 5]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 53s.
-Computing the boundary of the generator 20/69 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN 0> <<Abar[2 1][4 3]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 53s.
-Computing the boundary of the generator 21/69 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN 0> <<Abar[3 2][3 2]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 53s.
-Computing the boundary of the generator 22/69 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN 0> <<Abar[4 3][2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 53s.
-Computing the boundary of the generator 23/69 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN 0> <<Abar[2 1][2 1][2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 53s.
-Computing the boundary of the generator 24/69 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN 1> <<Abar[5 4]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 53s.
-Computing the boundary of the generator 25/69 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN 1> <<Abar[2 1][3 2]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 53s.
-Computing the boundary of the generator 26/69 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN 1> <<Abar[3 2][2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 54s.
-Computing the boundary of the generator 27/69 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN 2> <<Abar[4 3]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 54s.
-Computing the boundary of the generator 28/69 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN 2> <<Abar[2 1][2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 54s.
-Computing the boundary of the generator 29/69 (dimension 6) :
-<TnPr <TnPr <TnPr g11 0> <<Abar[4 3]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 54s.
-Computing the boundary of the generator 30/69 (dimension 6) :
-<TnPr <TnPr <TnPr g11 0> <<Abar[2 1][2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 54s.
-Computing the boundary of the generator 31/69 (dimension 6) :
-<TnPr <TnPr <TnPr g12 0> <<Abar[4 3]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 54s.
-Computing the boundary of the generator 32/69 (dimension 6) :
-<TnPr <TnPr <TnPr g12 0> <<Abar[2 1][2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 54s.
-Computing the boundary of the generator 33/69 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN 3> <<Abar[3 2]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 54s.
-Computing the boundary of the generator 34/69 (dimension 6) :
-<TnPr <TnPr <TnPr g11 1> <<Abar[3 2]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 55s.
-Computing the boundary of the generator 35/69 (dimension 6) :
-<TnPr <TnPr <TnPr g12 1> <<Abar[3 2]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 55s.
-Computing the boundary of the generator 36/69 (dimension 6) :
-<TnPr <TnPr <TnPr g21 0> <<Abar[3 2]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 55s.
-Computing the boundary of the generator 37/69 (dimension 6) :
-<TnPr <TnPr <TnPr g22 0> <<Abar[3 2]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 55s.
-Computing the boundary of the generator 38/69 (dimension 6) :
-<TnPr <TnPr <TnPr g23 0> <<Abar[3 2]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 55s.
-Computing the boundary of the generator 39/69 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN 4> <<Abar[2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 55s.
-Computing the boundary of the generator 40/69 (dimension 6) :
-<TnPr <TnPr <TnPr g11 2> <<Abar[2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 56s.
-Computing the boundary of the generator 41/69 (dimension 6) :
-<TnPr <TnPr <TnPr g12 2> <<Abar[2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 57s.
-Computing the boundary of the generator 42/69 (dimension 6) :
-<TnPr <TnPr <TnPr g21 1> <<Abar[2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 57s.
-Computing the boundary of the generator 43/69 (dimension 6) :
-<TnPr <TnPr <TnPr g22 1> <<Abar[2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 58s.
-Computing the boundary of the generator 44/69 (dimension 6) :
-<TnPr <TnPr <TnPr g23 1> <<Abar[2 1]>>> <<Abar>>> 
-*CR* -- Cut = 0.02723752 -- N = 10538
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 58m 59s.
-Computing the boundary of the generator 45/69 (dimension 6) :
-<TnPr <TnPr <TnPr g31 0> <<Abar[2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 59m 0s.
-Computing the boundary of the generator 46/69 (dimension 6) :
-<TnPr <TnPr <TnPr g32 0> <<Abar[2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 59m 0s.
-Computing the boundary of the generator 47/69 (dimension 6) :
-<TnPr <TnPr <TnPr g33 0> <<Abar[2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 59m 0s.
-Computing the boundary of the generator 48/69 (dimension 6) :
-<TnPr <TnPr <TnPr g34 0> <<Abar[2 1]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 59m 0s.
-Computing the boundary of the generator 49/69 (dimension 6) :
-<TnPr <TnPr <TnPr S-BSGN 6> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 59m 1s.
-Computing the boundary of the generator 50/69 (dimension 6) :
-<TnPr <TnPr <TnPr g11 4> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 59m 1s.
-Computing the boundary of the generator 51/69 (dimension 6) :
-<TnPr <TnPr <TnPr g12 4> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 59m 2s.
-Computing the boundary of the generator 52/69 (dimension 6) :
-<TnPr <TnPr <TnPr g21 3> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 59m 4s.
-Computing the boundary of the generator 53/69 (dimension 6) :
-<TnPr <TnPr <TnPr g22 3> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 59m 6s.
-Computing the boundary of the generator 54/69 (dimension 6) :
-<TnPr <TnPr <TnPr g23 3> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 59m 8s.
-Computing the boundary of the generator 55/69 (dimension 6) :
-<TnPr <TnPr <TnPr g31 2> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 59m 10s.
-Computing the boundary of the generator 56/69 (dimension 6) :
-<TnPr <TnPr <TnPr g32 2> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 59m 12s.
-Computing the boundary of the generator 57/69 (dimension 6) :
-<TnPr <TnPr <TnPr g33 2> <<Abar>>> <<Abar>>> 
-*CR* -- Cut = 0.02728105 -- N = 10552
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 59m 15s.
-Computing the boundary of the generator 58/69 (dimension 6) :
-<TnPr <TnPr <TnPr g34 2> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 59m 19s.
-Computing the boundary of the generator 59/69 (dimension 6) :
-<TnPr <TnPr <TnPr g41 1> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 59m 20s.
-Computing the boundary of the generator 60/69 (dimension 6) :
-<TnPr <TnPr <TnPr g42 1> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 59m 22s.
-Computing the boundary of the generator 61/69 (dimension 6) :
-<TnPr <TnPr <TnPr g43 1> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 59m 24s.
-Computing the boundary of the generator 62/69 (dimension 6) :
-<TnPr <TnPr <TnPr g44 1> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 59m 26s.
-Computing the boundary of the generator 63/69 (dimension 6) :
-<TnPr <TnPr <TnPr g45 1> <<Abar>>> <<Abar>>> 
-*CR* -- Cut = 0.027316269 -- N = 10565
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 59m 30s.
-Computing the boundary of the generator 64/69 (dimension 6) :
-<TnPr <TnPr <TnPr g51 0> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 59m 30s.
-Computing the boundary of the generator 65/69 (dimension 6) :
-<TnPr <TnPr <TnPr g52 0> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 59m 31s.
-Computing the boundary of the generator 66/69 (dimension 6) :
-<TnPr <TnPr <TnPr g53 0> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 59m 32s.
-Computing the boundary of the generator 67/69 (dimension 6) :
-<TnPr <TnPr <TnPr g54 0> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 59m 32s.
-Computing the boundary of the generator 68/69 (dimension 6) :
-<TnPr <TnPr <TnPr g55 0> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 9h 59m 33s.
-Computing the boundary of the generator 69/69 (dimension 6) :
-<TnPr <TnPr <TnPr g56 0> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-
-;; Clock -> 2011-07-14, 9h 59m 33s.
-
-
-*CR* -- Cut = 0.027431589 -- N = 10574
-*CR* -- Cut = 0.027409986 -- N = 10581
-*CR* -- Cut = 0.027447063 -- N = 10601
-*CR* -- Cut = 0.027479827 -- N = 10657
-*CR* -- Cut = 0.02755706 -- N = 10710
-*CR* -- Cut = 0.027726682 -- N = 10786
-*CR* -- Cut = 0.027987706 -- N = 10898
-*CR* -- Cut = 0.028594453 -- N = 11093
-*CR* -- Cut = 0.028853327 -- N = 11175
-*CR* -- Cut = 0.029098665 -- N = 11284
-*CR* -- Cut = 0.02917352 -- N = 11327
-*CR* -- Cut = 0.02930427 -- N = 11396
-*CR* -- Cut = 0.030319087 -- N = 11615
-*CR* -- Cut = 0.030405309 -- N = 11708
-*CR* -- Cut = 0.030384291 -- N = 11746
-*CR* -- Cut = 0.030515656 -- N = 11774
-*CR* -- Cut = 0.031394616 -- N = 8479
-*CR* -- Cut = 0.028224792 -- N = 8561
-*CR* -- Cut = 0.028261755 -- N = 8604
-*CR* -- Cut = 0.028326884 -- N = 8629
-*CR* -- Cut = 0.028889015 -- N = 8819
-*CR* -- Cut = 0.028893422 -- N = 8847
-*CR* -- Cut = 0.029014897 -- N = 8881
-*CR* -- Cut = 0.029757868 -- N = 9103
-*CR* -- Cut = 0.029971622 -- N = 9210
-*CR* -- Cut = 0.029928245 -- N = 9238
-*CR* -- Cut = 0.030070832 -- N = 9262
-*CR* -- Cut = 0.03054888 -- N = 9378
-*CR* -- Cut = 0.030755755 -- N = 9475
-*CR* -- Cut = 0.03078257 -- N = 9500
-*CR* -- Cut = 0.030935898 -- N = 9529
-*CR* -- Cut = 0.031507302 -- N = 9483
-*CR* -- Cut = 0.03135413 -- N = 9549
-*CR* -- Cut = 0.031555425 -- N = 9583
-*CR* -- Cut = 0.031551644 -- N = 9600
-*CR* -- Cut = 0.031776916 -- N = 9652
-*CR* -- Cut = 0.032632053 -- N = 8387
-*CR* -- Cut = 0.03133738 -- N = 8454
-*CR* -- Cut = 0.031436592 -- N = 8525
-*CR* -- Cut = 0.03143434 -- N = 8539
-*CR* -- Cut = 0.031562917 -- N = 8575
-*CR* -- Cut = 0.031557184 -- N = 8594
-*CR* -- Cut = 0.031637106 -- N = 8596
-*CR* -- Cut = 0.03194841 -- N = 8740
-*CR* -- Cut = 0.032019418 -- N = 8688
-*CR* -- Cut = 0.032713216 -- N = 8806
-*CR* -- Cut = 0.033036035 -- N = 8895
-*CR* -- Cut = 0.032949958 -- N = 8901
-*CR* -- Cut = 0.033048354 -- N = 8908
-*CR* -- Cut = 0.03341168 -- N = 8989
-*CR* -- Cut = 0.033435553 -- N = 9025
-*CR* -- Cut = 0.033545233 -- N = 9039
-*CR* -- Cut = 0.034353748 -- N = 9204
-*CR* -- Cut = 0.034458824 -- N = 9268
-*CR* -- Cut = 0.034690924 -- N = 9348
-*CR* -- Cut = 0.034693472 -- N = 9355
-*CR* -- Cut = 0.03482469 -- N = 9367
-*CR* -- Cut = 0.03489123 -- N = 9387
-*CR* -- Cut = 0.03490389 -- N = 9415
-*CR* -- Cut = 0.03562493 -- N = 9585
-*CR* -- Cut = 0.035654992 -- N = 9635
-*CR* -- Cut = 0.035713308 -- N = 9652
-*CR* -- Cut = 0.035746217 -- N = 9667
-*CR* -- Cut = 0.035940286 -- N = 9706
-*CR* -- Cut = 0.036304988 -- N = 9849
-*CR* -- Cut = 0.036636807 -- N = 9935
-*CR* -- Cut = 0.037287433 -- N = 10126
-Computing boundary-matrix in dimension 6.
-Rank of the source-module : 83.
-
-
-;; Clock -> 2011-07-14, 10h 18m 15s.
-Computing the boundary of the generator 1/83 (dimension 6) :
-<TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar[6 <<Abar[5 <<Abar[4 3]>>]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 10h 18m 15s.
-Computing the boundary of the generator 2/83 (dimension 6) :
-<TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar[6 <<Abar[5 <<Abar[2 1][2 1]>>]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 10h 18m 15s.
-Computing the boundary of the generator 3/83 (dimension 6) :
-<TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 1> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar[5 <<Abar[4 <<Abar[3 2]>>]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 10h 18m 15s.
-Computing the boundary of the generator 4/83 (dimension 6) :
-<TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> <<Abar[2 1]>>> <<Abar>>> <<Abar>>> <<Abar[4 <<Abar[3 <<Abar[2 1]>>]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 10h 18m 15s.
-Computing the boundary of the generator 5/83 (dimension 6) :
-<TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 2> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar[4 <<Abar[3 <<Abar[2 1]>>]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 10h 18m 15s.
-Computing the boundary of the generator 6/83 (dimension 6) :
-<TnPr <TnPr <TnPr <TnPr <TnPr g11 0> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar[4 <<Abar[3 <<Abar[2 1]>>]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 10h 18m 15s.
-Computing the boundary of the generator 7/83 (dimension 6) :
-<TnPr <TnPr <TnPr <TnPr <TnPr g12 0> <<Abar>>> <<Abar>>> <<Abar>>> <<Abar[4 <<Abar[3 <<Abar[2 1]>>]>>]>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 10h 18m 15s.
-Computing the boundary of the generator 8/83 (dimension 6) :
-<TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> <<Abar>>> <<Abar>>> <<Abar[6 <<Abar[5 <<Abar[4 3]>>]>>]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 10h 18m 15s.
-Computing the boundary of the generator 9/83 (dimension 6) :
-<TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> <<Abar>>> <<Abar>>> <<Abar[6 <<Abar[5 <<Abar[2 1][2 1]>>]>>]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 10h 18m 15s.
-Computing the boundary of the generator 10/83 (dimension 6) :
-<TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 1> <<Abar>>> <<Abar>>> <<Abar[5 <<Abar[4 <<Abar[3 2]>>]>>]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 10h 18m 16s.
-Computing the boundary of the generator 11/83 (dimension 6) :
-<TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> <<Abar[2 1]>>> <<Abar>>> <<Abar[4 <<Abar[3 <<Abar[2 1]>>]>>]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 10h 18m 16s.
-Computing the boundary of the generator 12/83 (dimension 6) :
-<TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 2> <<Abar>>> <<Abar>>> <<Abar[4 <<Abar[3 <<Abar[2 1]>>]>>]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 10h 18m 16s.
-Computing the boundary of the generator 13/83 (dimension 6) :
-<TnPr <TnPr <TnPr <TnPr <TnPr g11 0> <<Abar>>> <<Abar>>> <<Abar[4 <<Abar[3 <<Abar[2 1]>>]>>]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 10h 18m 16s.
-Computing the boundary of the generator 14/83 (dimension 6) :
-<TnPr <TnPr <TnPr <TnPr <TnPr g12 0> <<Abar>>> <<Abar>>> <<Abar[4 <<Abar[3 <<Abar[2 1]>>]>>]>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 10h 18m 16s.
-Computing the boundary of the generator 15/83 (dimension 6) :
-<TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> <<Abar>>> <<Abar[6 <<Abar[5 4]>>]>>> <<Abar>>> <<Abar>>> 
-*CR* -- Cut = 0.037479904 -- N = 10189
-*CR* -- Cut = 0.037520714 -- N = 10227
-*CR* -- Cut = 0.037702538 -- N = 10266
-*CR* -- Cut = 0.03763576 -- N = 10288
-End of computing.
-
-
-;; Clock -> 2011-07-14, 10h 18m 50s.
-Computing the boundary of the generator 16/83 (dimension 6) :
-<TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> <<Abar>>> <<Abar[6 <<Abar[2 1][3 2]>>]>>> <<Abar>>> <<Abar>>> 
-*CR* -- Cut = 0.03776791 -- N = 10319
-End of computing.
-
-
-;; Clock -> 2011-07-14, 10h 19m 0s.
-Computing the boundary of the generator 17/83 (dimension 6) :
-<TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> <<Abar>>> <<Abar[6 <<Abar[3 2][2 1]>>]>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 10h 19m 4s.
-Computing the boundary of the generator 18/83 (dimension 6) :
-<TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 0> <<Abar>>> <<Abar[3 <<Abar[2 1]>>][3 <<Abar[2 1]>>]>>> <<Abar>>> <<Abar>>> 
-End of computing.
-
-
-;; Clock -> 2011-07-14, 10h 19m 4s.
-Computing the boundary of the generator 19/83 (dimension 6) :
-<TnPr <TnPr <TnPr <TnPr <TnPr S-BSGN 1> <<Abar>>> <<Abar[5 <<Abar[4 3]>>]>>> <<Abar>>> <<Abar>>> 
-Error: `#<Closure (:INTERNAL (FLET BAR-CMPR RSLT) 0) @ #x2d0c02c2>' is not of the expected type `NUMBER'
-[condition type: TYPE-ERROR]
-CL-USER(37): 
\ No newline at end of file
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-{
- "cells": [
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "# Common Lisp, Typing, and Mathematics\n",
-    "\n",
-    "By [*Francis Sergeraert*](https://www-fourier.ujf-grenoble.fr/~sergerar/Papers/Ezcaray.pdf), August 2001\n",
-    "(Adapted for [`cl-jupyter`](https://github.com/fredokun/cl-jupyter) by Gerd Heber, February 2017)\n",
-    "\n",
-    "## Introduction.\n",
-    "\n",
-    "Common Lisp is seldom used by mathematicians and this is an anomaly. The high level of quality of Common Lisp comes from a simple reason: Common Lisp is a *mathematical* object, certainly one of the most beautiful and *potentially* productive existing at this time. Common Lisp is a descendant of the fantastic $\\lambda$-calculus, designed by Church to produce one of the deepest *mathematical* results of the last century, namely the negative answer to Hilbert's Entscheidungsproblem (\"decision problem\"): no algorithm can determine whether an arbitrary mathematical statement is true, false or undecidable.\n",
-    "\n",
-    "Then, by a quite indirect route, $\\lambda$-calculus became a fascinating programming language, Lisp. Lisp's birth is old, at the end of the fifties, and forty years later it is clear it remains the most advanced \"common\" programming language, \"common\" meaning *with an ANSI norm*, in this case the $\\ldots$ Common Lisp norm. The Common Lisp language is so advanced that it is not so easy to use it for serious applications: a reasonable lucidity about its complex and far-reaching structure is required; so that the initiation stage in the learning process of this language is a little hard. The present paper is a tutorial to introduce *mathematicians* to the main components of Object Oriented Programming in Common Lisp. The extraordinary work of Guy Steele and his X3J13 committee during the years 1980-1994 led to a powerful language, on one hand, but on the other hand taking seriously account of standard *practical constraints* in *actual* programming work. Common Lisp is now widely used for complex industrial applications, mainly because of the powerful *dynamic* tools that are available; but it is not used very much for scientific applications, in particular for mathematical applications, and this must be corrected.\n",
-    "\n",
-    "No *concrete* language can be completely formalized, but the mathematical precision of the definition of Common Lisp gives its user much security, the precision which is required for sophisticated mathematical applications, in particular when complicated data-sharing arrangements are necessary. Another aspect of Common Lisp is without any equivalent with the other languages: the user may *freely* design his application at the best programming level, sometimes at a very high level, directly handling rich and complex mathematical structures; for example it is explained in [Section 5.2](#Kenzo-classes.) that three simple lines of Lisp code are sufficient to explain to the machine that a simplicial group is simultaneously a Kan space and a Hopf algebra, sharing a common graded differential coalgebra structure, but with some added data, namely two simplicial morphisms describing the simplicial group structure. Other times, in the *same* program, you may on the contrary work at a very low level, in an assembler-like style. The language is carefully *stratified* to help the developer to remain lucid and at ease about these questions. The Common Lisp *macro generator*, without any equivalent in other common languages, allows also the programmer to easily use his low level code when he is on the contrary working at a high level.\n",
-    "\n",
-    "Which is a good element for appreciation is the ability of a language to be quickly adapted to new *mandatory* evolutions; at this time, Object Oriented Programming (OOP) must be integrated in a language claimed *common*, and Common Lisp succeeded in doing it so nicely that it can even be used to *describe* what OOP exactly is. The CLOS (Common Lisp Object\n",
-    "System) chapter of [[STEL2]](#STEL2) is one of the most amazing parts of Computer Science. The general *dynamic* feature of Common Lisp has in particular been kept: the user may dynamically change the class of his objects; he may also redefine dynamically the classes without loosing the objects of this class; and the user may freely decide exactly what happens for these objects. If this is not yet flexible enough, the Metaobject Protocol (MOP), not yet ormalized, but already widely used, allows our user to freely define his own OP system; CLOS is in fact only a particular application of MOP, see [[KCRB]](#KCRB).\n",
-    "\n",
-    "This paper is devoted to a few didactical examples to help mathematicians to understand how Common Lisp and more precisely CLOS can be used for mathematical applications. It is organized as follows. Firstly, a small set of artificial examples is used to explain the general structure of CLOS. The main work in OOP, and certainly the most difficult one, is at the initialization stage of the instances (objects). Even if a user does not intend to use the current Common-Lisp, studying how the initialization process is designed in this environment will explain to him the good points of view in this domain.\n",
-    "\n",
-    "Then a more significant example is described to show the actual workstyle when CLOS is used in a non-beginner job. Because the OOP subject is strongly related to *typing*, a possible description of what typing *could be* is used as a theme of an exercise showing how CLOS allows to implement the consequences of this description. This example is very simple and should be a good tutorial to simultaneously understand the initial points of OOP under Common Lisp and what typing is, at least from the point of view of the *actual* programmer.\n",
-    "\n",
-    "The next section is more mathematically oriented: it is explained how the basic mathematical *categories*, sets, magmas and monoids, can be directly implemented in CLOS, without meeting any kind of difficulty. The possibility for the Lisp user to arbitrarily mix OOP and high level functional programming (lexical closures) gives at once the required tools. The specialized programming environments such as Axiom, Gap, Magma $\\ldots$ so can be skipped and the mathematician may freely work at an arbitrary level *in the programming language itself*, keeping a perfect control of the environment, without being bothered by a restrictive environment, seldom well-adjusted to an arbitrary new *research* work.\n",
-    "\n",
-    "It was the case of the author and his colleagues when the central problems of Algebraic Topology were considered from a computational point of view [[SRGR3]](#SRGR3)[[RBSR6]](#RBSR6). The resulting Lisp program Kenzo [[DRSS]](#DRSS) shows a concrete example of use of CLOS for a relatively large implementation work[<sup>1</sup>](#footnote_1). The Kenzo program is not at all didactic, it is an actual program able to produce mathematical results that are unreachable otherwise. Some points of the experience acquired by Kenzo's authors are discussed in the last section and in this way the reader will see a few more concrete points of CLOS.\n",
-    "\n",
-    "<a id='footnote_1'><sup>1</sup></a> 16000 Common Lisp lines and a 340pp documentation.\n",
-    "\n",
-    "## CLOS (= Common Lisp Object System).\n",
-    "\n",
-    "Strictly speaking, the notion of *Common Lisp Object System*, CLOS in short, does not make sense anymore. The first definition of Common Lisp, known as Common-Lisp-1984 [[STEL1]](#STEL1), did not have any \"object system\". Typing was already strong in CL-1984, at least if wished by the user; standard types were defined and the initial type system was freely extendable by the user, but the now classical notions of *classes*, *instances*, *generic functions* and *methods* were not yet available. The pre-ANSI version of Common Lisp, namely Common-Lisp-1990, contained a *proposal* for an OOP system, called Common Lisp Object System [Ch. 28, pp 770-864 [STEL2]](#STEL2); the pre-versions of this object system were already widely used at this time by the Lisp programmers. Finally, the ANSI specification [[ANSI]](#ANSI) of Common Lisp (1994) completely integrated the so-called Common Lisp Object System in the very definition of the language. The standard Lisp programmer is now assumed working according to the spirit of OOP, constantly using classes, instances of classes, methods and so on, like in C++ or Java[<sup>2</sup>](#footnote_2). But the perfect integration of the general ideas of OOP with the so powerful Common Lisp gives its user many capabilities which are at this time outside of scope with other languages, mainly when *functional programming* is involved. However we continue to call CLOS the part of the ANSI Common Lisp language devoted to OOP.\n",
-    "\n",
-    "This object system in Common Lisp coexists with the old typing system and also the old *structure* system, which allowed the user to define, construct and use the classical *record* objects, with several fields, typed or not. From a hierarchical point of view, the typing system and the structure system are *subsystems* of the object system: special predefined classes correspond to the main classical data types, and the same for the structured objects. But normaly the current Lisp programmer mainly works with the object system, organizing his workspace in classes, subclasses, methods and so on.\n",
-    "\n",
-    "The Common Lisp object system is elegant and powerful. As usual in Common Lisp, it is organized so that the user keeps a very large freedom. A *standard style* is carefully designed, but the user may go far from this standard style if special situations are encountered.\n",
-    "\n",
-    "<a id='footnote_2'><sup>2</sup></a> With a slightly different terminology.\n",
-    "\n",
-    "### A quick comparison with C++ and Java.\n",
-    "\n",
-    "A few indications are given in this section about the main OOP features of Java, C++ and CLOS. In Java, the classes are \"above\" the methods (member functions): the specific functions for a class are defined *inside this class* so that the class and member function hierarchies are more or less *parallel*. This leads sometimes to artificial classes, typically the `System` class and the `Math` class, when this *rule* becomes non-sense in particular situations. The *member functions* are available under C++ too.\n",
-    "\n",
-    "In C++ you may also *overload* the functions, in particular the member functions. There are no member functions in CLOS[<sup>3</sup>](#footnote_3), there is only an overloading feature. But three other features are provided by CLOS which make particularly convenient and elegant the developer work:\n",
-    "\n",
-    "- The initialization process of the objects is essential in OOP; the general CLOS organisation of this work is really wonderful, in particular conceptually very simple, leading the programmer towards the good points of view, see [Section 2.3](#Initializing-instances.) for a small introduction to this point.\n",
-    "- The *method qualifiers* give much flexibility to organize the work of all the *applicable* methods; numerous simple examples in this paper.\n",
-    "- The functional basis of Common Lisp allows the user to easily install *functional slots* (members) of any sort, in particular *compiled closure slots*, dramatically extending the programming scope; [Section 4](#CLOS-and-Mathematical-Structures.) gives striking applications of this feature; in particular the instances may be themselves *funcallable*, in other words the instances become also functional objects, see [Section 3](#What-typing-is.) for a typical illustration.\n",
-    "\n",
-    "In CLOS, the *basic ingredients* are clearly distinguished:\n",
-    "\n",
-    "- The *class system*, mainly used through the `defclass` statement, allows the user to define the structure of his *instances* (objects), in particular through the notion of *subclass* (derived class).\n",
-    "- The *function type* is *primitive*; a function is an object which can be *funcalled* (called) for some work about some *arguments*.\n",
-    "- The *packaging system* allows the developer to precisely define what parts of his source code are normally directly known and/or reachable by a user of his program, obtaining in particular the equivalent of the `private` C++ code.\n",
-    "\n",
-    "Then, if the *class system* and the *functional* organization of Common Lisp are to be simultaneously considered, the particular notions of *generic functions* and *methods* must be used.\n",
-    "\n",
-    "- A *generic function* is a functional object the exact work of which will depend on the class of its arguments.\n",
-    "- The code for *some* specific work of a generic function corresponding to *some* particular class distribution of its arguments and *some qualifier* is a *method* object; each method is defined by a `defmethod` statement.\n",
-    "- In general *several* methods are involved when a *generic function* is invoked, they are called the *applicable* methods. CLOS gives its user a large freedom to organize these methods with respect to each other, to cover any possible situation, in particular when a sophisticated chronology of their work is required. This feature has no equivalent in C++ or Java, this is obtained by the *method qualifiers*.\n",
-    "\n",
-    "In this way, the CLOS *methods* can be thought of arranged in a *three*-dimensional array where each entry is associated to a generic function, the first index, the class distribution of the parameters, the second index, and the method qualifier, the third index.\n",
-    "\n",
-    "The CLOS method qualifiers have no equivalent in C++ or Java; a predefined qualifier organization is provided, already rather rich, sufficient for most of the ordinary cases[<sup>4</sup>](#footnote_4). If still more sophisticated combinations of methods are required, the `define-method-combination` function allows the developer to freely extend this organization.\n",
-    "\n",
-    "For example, and this will be detailed in [Section 4](#CLOS-and-Mathematical-Structures.), a mathematician who installs under CLOS the traditional mathematical categories must organize his work as follows:\n",
-    "\n",
-    "- The `defclass` statements will be used to define what a *set* object is, what a *group* object is, what a *chain complex* object is, and so on.\n",
-    "- The `defgeneric` statements will be used to define functions working on these objects, but these \"functions\" are traditionnally called in this case *functors* in mathematics; therefore one `defgeneric` statement for the *sum* functor, another *defgeneric* for the *product* functor, another `defgeneric` for the *classifying space* functor, and so on.\n",
-    "- Finally each generic function will have various methods to adapt the generic function to specific cases; for example the product of two objects of some category is also an object of this category with the corresponding structure to be defined. Therefore one product method for the *sets*, another product method for the *magmas*, another product method for the *monoids*, and so on. The `call-next-method` and `change-class` functions will allow these methods to *possibly* refer to the *less specific* ones.\n",
-    "\n",
-    "<a id='footnote_3'><sup>3</sup></a> A C++ or Java member function is nothing but a CLOS generic function where the first argument is given *before* the function reference, with an implicit `with-slots` for this particular argument; such a feature can be easily added to the environment with the Metaobject Protocol; in general CLOS prefers to keep the maximal symmetry between the critical arguments.\n",
-    "\n",
-    "<a id='footnote_4'><sup>4</sup></a> For example quite sufficient for the Kenzo program.\n",
-    "\n",
-    "### Very simple CLOS examples.\n",
-    "\n",
-    "Classes can be defined with the traditional hierarchy and methods may be defined which will be called, or not, according to the argument classes. The general `call-next-method` function allows the user to invoke shadowed methods.\n",
-    "\n",
-    "Let us define[<sup>5</sup>](#footnote_5) a simple class `C1` and a subclass `C2`.\n",
-    "\n",
-    "<a id='footnote_5'><sup>5</sup></a> In the original paper, the small Lisp examples showed for illustration have really been run under Allegro Common Lisp and may be repeated under any ANSI Common Lisp; the Lisp prompt is here '`>`'; the maltese cross $\\maltese$ corresponds to the `<Return>` key asking for the evaluation of the typed-in statement; usually the symbols are keyed in lower case, and Lisp displays the answers with upper case."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 1,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "#<STANDARD-CLASS CL-JUPYTER-USER::C1>"
-      ]
-     },
-     "execution_count": 1,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(DEFCLASS C1 ()\n",
-    "          ((sl1 :initarg :sl1 :reader sl1)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 2,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "#<STANDARD-CLASS CL-JUPYTER-USER::C2>"
-      ]
-     },
-     "execution_count": 2,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(DEFCLASS C2 (C1)\n",
-    "          ((sl2 :initarg :sl2 :reader sl2)))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "The `C2` class is a *subclass* of the `C1` class. A `C1`-object, in Lisp you must say a `C1`-*instance*, has only\n",
-    "one component, you must say in Lisp one *slot*, labelled `sl1`, and a `C2`-instance has one further slot labelled `sl2`. Because of the `:initarg` slot-options, these slots may be initialized through the keyword arguments `:sl1` and `:sl2`. We create a `C1`-instance and a `C2`-instance."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 3,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "I1"
-      ]
-     },
-     "execution_count": 3,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(defvar i1 (make-instance 'c1 :sl1 1))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 4,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "I2"
-      ]
-     },
-     "execution_count": 4,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(defvar i2 (make-instance 'c2 :sl1 11 :sl2 22))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "You see, and this is the *default display*, only the class of the instance and its machine address are displayed. We would like to display our simple instances with their slots[<sup>6</sup>](#footnote_6). In general every object is displayed through the generic function `print-object`, and the user is advised to write specific *methods* for this generic function to obtain the desired display. Just to illustrate the general organisation of methods in CLOS, we\n",
-    "will define three `print-object` methods to \"print\" a `C1`- or `C2`-instance, to show the `sl1` and possibly the `sl2` slot(s). The `C2`-method calls the `C1`-method through `call-next-method`, and the `:after` method allows to print the '`>`' terminal.\n",
-    "\n",
-    "<a id='footnote_6'><sup>6</sup></a> This is not standard: frequently the slots are numerous and complicated, and it is not sensible to display the instances with all their slots."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 5,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "#<STANDARD-METHOD COMMON-LISP:PRINT-OBJECT (C1 T) {10049393A3}>"
-      ]
-     },
-     "execution_count": 5,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(DEFMETHOD PRINT-OBJECT ((c1 c1) stream)\n",
-    "           (declare (type stream stream))\n",
-    "           (format stream \"#<~S sl1=~S\" (class-name (class-of c1)) (sl1 c1))\n",
-    "           c1)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 6,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "#<STANDARD-METHOD COMMON-LISP:PRINT-OBJECT :AFTER (C1 T) {1004A27303}>"
-      ]
-     },
-     "execution_count": 6,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(DEFMETHOD PRINT-OBJECT :after ((c1 c1) stream)\n",
-    "           (declare (type stream stream))\n",
-    "           (format stream \">\"))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 7,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "#<STANDARD-METHOD COMMON-LISP:PRINT-OBJECT (C2 T) {1004CA0CF3}>"
-      ]
-     },
-     "execution_count": 7,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(DEFMETHOD PRINT-OBJECT ((c2 c2) stream)\n",
-    "           (declare (type stream stream))\n",
-    "           (call-next-method)\n",
-    "           (format stream \" sl2=~S\" (sl2 c2))\n",
-    "           c2)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "The `format` statement is analogous to the traditional `printf` of C. Frequently[<sup>7</sup>](#footnote_7), Lisp objects are displayed as strings which begin with '`#<`'. Now we redisplay our existing `C1`- and `C2`-instances.\n",
-    "\n",
-    "<a id='footnote_7'><sup>7</sup></a> In principle a *non-readable* display must begin with '`#<`', but in this case, because of the complete display, in fact it could be read ..."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 8,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(#<C1 sl1=1> #<C2 sl1=11 sl2=22>)"
-      ]
-     },
-     "execution_count": 8,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(list i1 i2)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "We can play to change the class of these instances."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 9,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "#<C2 sl1=1 sl2=2>"
-      ]
-     },
-     "execution_count": 9,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(change-class i1 'c2 :sl2 2)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 10,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "#<C1 sl1=11>"
-      ]
-     },
-     "execution_count": 10,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(change-class i2 'c1)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "You see CLOS has taken the most natural decisions, but we will explain later how the process can be freely customized by the programmer.\n",
-    "\n",
-    "There is also the possibility of `:around` methods, encapsulating the so-called *primary* ones:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 11,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "#<STANDARD-METHOD COMMON-LISP:PRINT-OBJECT :AROUND (C1 T) {100512B8A3}>"
-      ]
-     },
-     "execution_count": 11,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(DEFMETHOD PRINT-OBJECT :around ((c1 c1) stream)\n",
-    "           (declare (type stream stream))\n",
-    "           (format stream \"*\")\n",
-    "           (call-next-method)\n",
-    "           (format stream \"*\")\n",
-    "           c1)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 12,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "#<STANDARD-METHOD COMMON-LISP:PRINT-OBJECT :AROUND (C2 T) {100539FE43}>"
-      ]
-     },
-     "execution_count": 12,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(DEFMETHOD PRINT-OBJECT :around ((c2 c2) stream)\n",
-    "           (declare (type stream stream))\n",
-    "           (format stream \"+\")\n",
-    "           (call-next-method)\n",
-    "           (format stream \"+\")\n",
-    "           c2)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "And we see the role of these methods:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 13,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(+*#<C2 sl1=1 sl2=2>*+ *#<C1 sl1=11>*)"
-      ]
-     },
-     "execution_count": 13,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(list i1 i2)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Again it is interesting to deduce from this example the chronology of the calls of the five user-defined `print-object` methods. The standard organization allows the user to define *primary* and *auxiliary* methods, the last ones being *qualified* by the keyword `:before`, `:after` or `:around`; the methods are *specialized* by giving arbitrary combination of classes of the arguments; here, only the first argument was specialized, but we will see later natural situations where\n",
-    "several arguments are specialized. Simple but mathematically coherent rules, in particular based on topological sorting, explain what methods work in a particular case and in what order. Furthermore these possibilities may be freely modified or extended by the user through the `define-method-combination` function.\n",
-    "\n",
-    "###  Initializing instances.\n",
-    "\n",
-    "It is well known the main part and the main difficulties of the OOP job are in the initialization work for the instances. Let us examine the general organization of the CLOS initialization process.\n",
-    "\n",
-    "The essential components of the initialization process in CLOS are the following generic functions:\n",
-    "\n",
-    "- The *standard* `make-instance` allocates the memory space for the instance to be created and calls `initialize-instance` to initialize it;\n",
-    "- The *standard* `initialize-instance` in fact calls `shared-initialize` to do the initialization work.\n",
-    "\n",
-    "The role of `shared-initialize` is the following. Frequently the initialization work to be done is essentially the same when an instance is created, or *re*initialized, or when its class is changed, or finally when the underlying class is itself redefined. If possible, the user is advised to define this common work in `shared-initialize` methods. If on the contrary there are significant differences between these cases, the user may write particular methods for the following generic functions:\n",
-    "\n",
-    "![](the-main-initialization-generic-functions.png)\n",
-    "\n",
-    "- `initialize-instance`: called by `make-instance` to initialize a just created instance; the user can extend and/or modify the standard initialization by writing specific methods for some classes.\n",
-    "- `reinitialize-instance`: called by the user when he wants to \"refresh\" some instance; sometimes it is the same as initializing from scratch, sometimes not; in the first case it is better to write an appropriate `shared-initialize` method; in the second case, the user must write specific methods for `reinitialize-instance`.\n",
-    "- `change-class`: called by the user when the class of an instance is *changed*; this function asks for a kind of conversion. Normally this function calls the generic function `update-instance-for-different-class` and the user may write methods for the latter. A simple example follows.\n",
-    "- `defclass`: if a `defclass` is in fact a *redefinition* of the class, each time an instance of the old version is considered,  the generic function `update-` `instance-for-redefined-class` is applied, allowing in principle to coherently continue the work.\n",
-    "- `make-instance`: the user can also entirely redefine the creation and initialization process.\n",
-    "\n",
-    "Writing appropriate methods for these generic functions, the user can freely define the initialization work, clearly distinguishing the various levels from each other; if sufficient, the programmer may partially or totally use the *standard style* without any further work. You understand that combining these methods with the user-defined class hierarchy, combining also with the various possibilities of *auxiliary methods* (`:before`, `:after`, `:around`), the user has a fantastically large workspace. However, once this structure is reasonably understood, it is not difficult to be used, and quickly very powerful.\n",
-    "\n",
-    "### The example of `change-class`.\n",
-    "\n",
-    "The various situations that are met in the artificial simple example of this section around the `change-class` generic function allow to easily understand the general CLOS organisation of the initialization work."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 14,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "#<STANDARD-CLASS CL-JUPYTER-USER::E12>"
-      ]
-     },
-     "execution_count": 14,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(DEFCLASS E12 ()\n",
-    "          ((sl1 :initarg :sl1 :reader sl1)\n",
-    "           (sl2 :initarg :sl2 :reader sl2)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 15,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "#<STANDARD-CLASS CL-JUPYTER-USER::E13>"
-      ]
-     },
-     "execution_count": 15,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(DEFCLASS E13 ()\n",
-    "          ((sl1 :initarg :sl1 :reader sl1)\n",
-    "           (sl3 :initarg :sl3 :reader sl3)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 16,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "INS"
-      ]
-     },
-     "execution_count": 16,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(defvar ins (make-instance 'e12 :sl1 1 :sl2 2))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 17,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "#<E13 {10055847F3}>"
-      ]
-     },
-     "execution_count": 17,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(change-class ins 'e13)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 18,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "#<E13 {10055847F3}>"
-      ]
-     },
-     "execution_count": 18,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "ins"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 19,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "1"
-      ]
-     },
-     "execution_count": 19,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(sl1 ins)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 20,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "UNBOUND-SLOT: \n",
-      "  #<UNBOUND-SLOT SL3 {10056EACC3}>\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 20,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(sl3 ins)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Ther is no relation at all between both classes `E12` and `E13`; there is a common slot *name*, namely `sl1`, but this does not imply any relation between both classes. With an exception, if ever the class of an instance is changed from `E12` to `E13`, this common slot name will be considered by the standard `change-class` which in fact calls the standard `update-instance-for-different-class`: this method transmits the slots with the same *names* in both classes, gives up the other slots in the source instance, and lets unbound the other slots of the target instance. Here, the `sl1` slot has been kept, the `sl2` slot has been given up, and the `sl3` slot in the result is let unbound, which implies the error when this slot is read by the `:reader` method `sl3`. Note also the pseudo-new instance is at the same machine address, but the small\n",
-    "invisible steps of the garbage-collector continually modify the actual addresses, which is made obvious by the value of the symbol `ins` locating our *unique* but *variable* instance.\n",
-    "\n",
-    "Let us convert again our instance, but with an additional keyword argument."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 21,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "#<E12 {10055847F3}>"
-      ]
-     },
-     "execution_count": 21,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(change-class ins 'e12 :sl2 22)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 22,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "22"
-      ]
-     },
-     "execution_count": 22,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(sl2 ins)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "The default methods are sufficient to pass initial arguments to `change-class` to obtain partial initializations of the new *version* of the *same* instance. Let us consider now the situation where for some strange \"theoretical\" reason, when the class is changed from `E12` to `E13`, the value of the `sl3` slot must be computed as the product of the `sl2` slot of the source instance multiplied by some number included in the `change-class` data. This is obtained as follows."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 23,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "#<STANDARD-METHOD COMMON-LISP:UPDATE-INSTANCE-FOR-DIFFERENT-CLASS :AFTER (E12 E13) {10059CC1A3}>"
-      ]
-     },
-     "execution_count": 23,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(DEFMETHOD UPDATE-INSTANCE-FOR-DIFFERENT-CLASS :after\n",
-    "           ((source e12) (target e13) &key (multiplier 1))\n",
-    "           (declare (type number multiplier))\n",
-    "           (setf (slot-value target 'sl3)\n",
-    "                 (* (sl2 source) multiplier)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 24,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "#<E13 {10055847F3}>"
-      ]
-     },
-     "execution_count": 24,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(change-class ins 'e13 :multiplier 4)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 25,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(1 88)"
-      ]
-     },
-     "execution_count": 25,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(list (sl1 ins) (sl3 ins))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Because we have used an `:after` method, the standard *primary* method is firstly called, solving the `sl1` transfer. And after this is done, our auxiliary method works. Note in particular the elegant handling of the extra multiplier argument; because this keyword argument is used in our method, it becomes available for the user when a `change-class` `E12` $\\rightarrow$ `E13` happens.\n",
-    "\n",
-    "We want finally to consider the situation where a conversion `E13` $\\rightarrow$ `E12` must be installed, where the new version of the instance must have both slots redefined to zero. In this case the old version of the instance is useless, so that we can directly obtain this conversion by a `change-class` method."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 26,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "#<STANDARD-METHOD COMMON-LISP:CHANGE-CLASS :AFTER (E13 (EQL E12)) {1005E41C23}>"
-      ]
-     },
-     "execution_count": 26,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(DEFMETHOD CHANGE-CLASS :after ((ins e13) (class (eql 'e12)) &rest rest)\n",
-    "           (declare (ignore rest))\n",
-    "           (setf (slot-value ins 'sl1) 0\n",
-    "                 (slot-value ins 'sl2) 0))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 27,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "#<E12 {10055847F3}>"
-      ]
-     },
-     "execution_count": 27,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(change-class ins 'e12)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 28,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(0 0)"
-      ]
-     },
-     "execution_count": 28,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(list (sl1 ins) (sl2 ins))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "## What typing is.\n",
-    "\n",
-    "The small examples of the previous section were artificial, and we want to consider now a *plausible* situation. We want to use CLOS to implement a simple coherent *typing system*, allowing the user to simultaneously use arbitrary types and high levels of *functional programming*, both subjects being furthermore strongly dependent on each other.\n",
-    "\n",
-    "What is typing? If a *mathematical* definition of typing is wished, many definitions are possible, and one of them is to be illustrated by a small CLOS program. Note this *new* typing system will be installed while the standard one remains active in our environment.\n",
-    "\n",
-    "Typing consists in giving the programmer the ability of *partial* descriptions of his algorithms. Let us call $\\mathcal{A}$ the *universe* of all the machine objects, $\\mathcal{A}$ for <u>a</u>nything. Any algorithm can be viewed as a map $\\mathcal{A}\\rightarrow\\mathcal{A}$ *not everywhere defined*. Typically the Euclid algorithm is defined on the set $\\mathbb{N}_* \\times \\mathbb{N}_*$ of pairs of positive integers, and returns such an integer. The set $\\mathbb{N}_*$ is a subset of $\\mathcal{A}$, and the latter contains also the set $\\mathcal{L}$ of lists of any length; among these lists, some of them are made of two positive integers; let us call $\\mathcal{L}(\\mathbb{N}_* , \\mathbb{N}_*)$ the corresponding subtype. The type specification (signature) for the Euclid algorithm $E$ is then $E: \\mathcal{L}(\\mathbb{N}_* , \\mathbb{N}_*) \\rightarrow \\mathbb{N}_*$.\n",
-    "\n",
-    "Speaking so, we have used a few subsets of $\\mathcal{A}$. Such a simple example could create some wrong ideas. On one hand, one could think two different types should be disjoint, but it is not the case for $\\mathcal{L}$ and $\\mathcal{L}(\\mathbb{N}_* , \\mathbb{N}_*)$. If not disjoint, one could then require one of the considered types is included in the\n",
-    "other one; for example $\\mathcal{L}(\\mathbb{N}_* , \\mathbb{N}_*) \\subset \\mathcal{L}$ and it seems sensible to organize the types as a large *oriented graph* describing more and more finely the various sets of objects the user works with. Simple typing systems usually are of this sort.\n",
-    "\n",
-    "Another idea has a much larger scope; it consists in deciding a type is nothing but some subset of $\\mathcal{A}$, where the *membership property* may be verified by an algorithm. In other words we start only with two predefined types, $\\mathcal{A}$ and $\\mathcal{B}$; the second one, the *Boolean* type, has only two objects, $\\top$ and $\\bot$, implemented in Lisp as the symbols `T` and `NIL`. It is then interesting to define a type as an algorithm $\\mathcal{A}\\rightarrow\\mathcal{B}$ *everywhere* defined; in other words, the algorithm defining a type has the special signature $\\mathcal{A}\\rightarrow\\mathcal{B}$.\n",
-    "\n",
-    "This is sufficient in simple programming, but fails as soon as functional programming must be considered. In fact we meet the Russell paradox or if you prefer the G&#246;del theorem. Let us call $\\mathcal{T}$ the type of ... types, that is the set of functional objects $\\alpha:\\mathcal{A}\\rightarrow\\mathcal{B}$. Then no algorithm can verify the membership of $\\mathcal{T}$! Let us assume $\\tau$ is such an algorithm; therefore $\\tau:\\mathcal{A}\\rightarrow\\mathcal{B}$ is everywhere defined and $\\tau(\\alpha) = \\top$ if and only if $\\alpha$ defines a type, that is, $\\alpha:\\mathcal{A}\\rightarrow\\mathcal{B}$ is also everywhere defined. Then one could design the subtype $\\mathcal{T}'$ made of the algorithms $\\alpha \\in \\mathcal{T}$ such that $\\alpha(\\alpha) = \\bot$, in other words the type of \"typing algorithms\" $\\alpha$ that are *not* \"element\" of the type associated with $\\alpha$. It would be easy to write down the algorithm $\\tau'$ corresponding to the new type $\\mathcal{T}'$:\n",
-    "\n",
-    "$$\n",
-    "\\begin{array}{rcll}\n",
-    " \\tau'(\\alpha) &=& \\mathtt{if}\\ \\tau(\\alpha) &\\mathtt{then}\\\n",
-    " \\mathtt{not}\\ \\alpha(\\alpha)\\\\\n",
-    "               & & &  \\mathtt{else}\\ \\bot\n",
-    "\\end{array}\n",
-    "$$\n",
-    "\n",
-    "The algorithm $\\tau'$ firstly examines whether its argument $\\alpha$ is an algorithm $\\mathcal{A}\\rightarrow\\mathcal{B}$; if yes, the algorithm $\\alpha$ may work on any object, in particular on itself, and $\\tau'$ returns the opposite of $\\alpha(\\alpha)$; otherwise the answer is negative. Once the algorithm $\\tau:\\mathcal{A}\\rightarrow\\mathcal{B}$ is available, then the object $\\tau':\\mathcal{A}\\rightarrow\\mathcal{B}$ is available too, but Cantor and Russell remarked there is no possible answer for $\\tau'(\\tau')$: the answer of $\\tau(\\tau')$ should certainly be $\\top$, so that we obtain the contradictory relation $\\tau'(\\tau') = \\mathtt{not}\\ \\tau'(\\tau')$. Therefore the algorithm $\\tau$ may not exist.\n",
-    "\n",
-    "The traditional (pseudo-) solution for this difficult problem consists in *delaying* the examination of the type of functional objects. If an object $\\alpha$ is claimed to be an algorithm $\\mathcal{T}_1\\rightarrow\\mathcal{T}_2$, this\n",
-    "cannot be verified by a *general* algorithm; instead, we must *wait* for an actual run of the algorithm $\\alpha$: if the computation of $\\alpha(\\omega)$ is asked for, some process can *then* verify the argument $\\omega$ is really in the type $\\mathcal{T}_1$; if yes the computation of $\\alpha(\\omega)$ is started and the result $\\omega'$ is examined in turn, verifying the relation $\\omega' \\in\\mathcal{T}_2$. In other words it is not possible to verify the type of a functional object *in general*; the only possible verification consists, each time the algorithm works, in verifying that the argument and the result have the correct type; this \"verification\" is not at all complete, it can be applied only to a finite number of calls of the algorithm $\\alpha$.\n",
-    "\n",
-    "This organization must be recursive: the source and/or target types could in turn be functional, so that the verifications $\\omega \\in \\mathcal{T}_1$ and $\\omega' \\in \\mathcal{T}_2$ maybe must also be \"delayed\" with the meaning just explained. In particular if $\\omega$ and $\\omega'$ are both functional, then the functional object $\\omega$ *will* probably *be* used when the object $\\omega'$ will work. It is only at this time the correctness of the claimed types for $\\omega$, at least for this particular use, may be verified. Examples of this sort are showed in this paper.\n",
-    "\n",
-    "In this way, when a whole program is executed, all the *particular uses* of the functional objects imply that the type of arguments and result are verified, so that when the program is finished, for all the invocations of functional objects, types of input and output are confirmed. Thinking a little about this situation finally leads to the following conclusion: as far as they have been used, the type rules about functional objects have been satisfied *for this specific run*. A quite satisfactory conclusion.\n",
-    "\n",
-    "To illustrate the Common Lisp object system, we take as exercise subject the implementation of such an organization in Common Lisp, using the main components of CLOS.\n",
-    "\n",
-    "### Classes as structured types.\n",
-    "\n",
-    "A *class* is firstly a structured type. Each *instance* (element) of a *standard* class has several *slots* (components, fields, members), and each slot has various properties described in the definition of the class. The *builtin* classes, corresponding to old classical types (integers, symbols, ...), are not standard.\n",
-    "\n",
-    "The classes are organized in a hierarchical way: a class may be or not a *subclass* of another one, and this defines an *order* between the defined classes. This order must be coherent but in general it is not *total*, that is, for two classes $\\mathcal{C}_1$ and $\\mathcal{C}_2$, they may or may not be compared. But any class is a subclass of the maximal type~$\\mathcal{A}$, which contains any object, in particular the corresponding class object itself; to prove this point, we assign this class object to the symbol `universe` and verify the object so located is of the type so described; this maximal class $\\mathcal{A}$ corresponds to the set (type) $\\mathcal{A}$ of the previous section."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 29,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "UNIVERSE"
-      ]
-     },
-     "execution_count": 29,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(defvar universe (find-class 't))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 30,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "T"
-      ]
-     },
-     "execution_count": 30,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(typep universe universe)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "The *types* of the proposed organization for typing in this paper are pointed out by the letters `TP` only. This is necessary because we have to simultaneously work with three typing systems:\n",
-    "\n",
-    "1. The old one of Common Lisp, still present in our workspace; we call it the *type-system*;\n",
-    "2. The *class-system* which is the main constituent of CLOS;\n",
-    "3. The theoretical proposal of our exercise; it is called the `TP`*-system* in this text.\n",
-    "\n",
-    "> In the following, we use a metaobject protocol for CLOS which is not part of the ANSI Common Lisp standard. The SBCL compiler implements this protocol in the `sb-mop` package."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 31,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "T"
-      ]
-     },
-     "execution_count": 31,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(use-package :sb-mop)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "### The `TP`-class.\n",
-    "\n",
-    "Each `TP`-type is described by an instance of the `TP` class now to be defined. We define this class as follows:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 32,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "#<FUNCALLABLE-STANDARD-CLASS CL-JUPYTER-USER::TP>"
-      ]
-     },
-     "execution_count": 32,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(DEFCLASS TP ()\n",
-    "          ((name :type symbol :initarg :name :initform (gensym) :reader name))\n",
-    "          (:metaclass funcallable-standard-class))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "At this time, only one slot called `name` is defined for an instance of `TP`. Four *slot-options* have been used with the following meanings:\n",
-    "\n",
-    "- The `:type` option explains the `name` slot must contain a `symbol`;\n",
-    "- The `:initarg` option says the `name` slot may be initialized through the keyword `:name`;\n",
-    "- The `:initform` option says that if the `name` slot is not otherwise initialized, it must be automatically initialized by the `gensym` function, a predefined Lisp function which creates from scratch a certainly *new* symbol;\n",
-    "- Finally the `:reader` option asks CLOS to construct a *method* named `name` allowing the user to call this method to obtain the value of the slot.\n",
-    "\n",
-    "The `:metaclass` class option is explained later.\n",
-    "\n",
-    "A *type descriptor* of the `TP` system is always an instance of the `TP`-class. The corresponding type is functional or not; if <u>f</u>unctional the type descriptor is in fact an instance of the `FTP` class, a subclass of the `TP` class, else the type descriptor is an instance of the `DTP` class (<u>d</u>iscriminant type), another subclass of the `TP` class. The situation is here particularly simple: a type descriptor is *always* a `TP` instance, and in fact always an instance of only one subclass, either `FTP`, or `DTP`. Much more complicated situations between classes and subclasses can be designed under CLOS, but this simple situation allows us to show the main points of the nature of CLOS. In other words, the class diagram is this one.\n",
-    "\n",
-    "![](class-diagram.png)\n",
-    "\n",
-    "The type descriptor is firstly some `TP` instance, but it is convenient in this situation to locate the descriptor through a symbol and this is the reason of the `name` slot: this slot contains the symbol which in principle locates the `TP`-type descriptor. So that we have two (almost) \"symmetric\" pointers: the symbol points to the descriptor and the `name` slot of this descriptor points to this symbol; this is nothing but an *explicit* C++-`this` method. If ever the user is not really interested in the symbol, the `gensym` will automatically generate a symbol for completeness.\n",
-    "\n",
-    "![](tp-instance.png)\n",
-    "\n",
-    "The method `name` may now be applied to a `TP`-descriptor to obtain the associate symbol.\n",
-    "\n",
-    "We have explained in the previous section the role of the `print-object` generic function. Here, our strategy consists in simply locating `TP`-types through symbols to be considered as *labels*, so that it is natural to display such a type by the associate symbol."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 33,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "#<STANDARD-METHOD COMMON-LISP:PRINT-OBJECT (TP T) {10064E6213}>"
-      ]
-     },
-     "execution_count": 33,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(DEFMETHOD PRINT-OBJECT ((tp tp) stream)\n",
-    "           (format stream\n",
-    "                   \"#<~S ~S>\"\n",
-    "                   (class-name (class-of tp)) (name tp)))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "What is finally displayed through the (implicit) call of this method could be for example `#<DTP INTEGER>`; it is a tradition in Lisp to begin the display of a *non-readable* object by '`#<`'; this notion is carefully defined in ANSI Common-Lisp, but it is not the subject of this text. The value of `(name tp)` is the associate *name* of the\n",
-    "type-descriptor; the value of `(class-of tp)` is the `class` of `tp`, therefore the *class-object* `DTP` or `FTP`, and\n",
-    "the `class-name` is the symbol naming this class. We do not want to explain here the technical details of the `format` Lisp function, which is similar to the traditional `printf` C function, but fantastically more flexible.\n",
-    "\n",
-    "A little earlier the symmetry property between a `TP`-type descriptor and the symbol locating it was explained. It is a little painful for the user to manage the necessary pointers, but an appropriate method can be used to automate the process during the initialization stage."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 34,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "#<STANDARD-METHOD COMMON-LISP:INITIALIZE-INSTANCE :AFTER (TP) {10065A4C73}>"
-      ]
-     },
-     "execution_count": 34,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(DEFMETHOD INITIALIZE-INSTANCE :after ((tp tp) &rest rest)\n",
-    "           (declare (ignore rest))\n",
-    "           (set (name tp) tp))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "The `:after` *qualified* method shown above means that *after* the standard initialization process, something must be done: the symbol in the `name` slot must be bound to the `TP`-instance itself.\n",
-    "\n",
-    "### The `DTP`-class.\n",
-    "\n",
-    "We define now the subclass `DTP` (discriminant type) of the class `TP`."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 35,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "#<FUNCALLABLE-STANDARD-CLASS CL-JUPYTER-USER::DTP>"
-      ]
-     },
-     "execution_count": 35,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(DEFCLASS DTP (TP)\n",
-    "          ((sub :type list :accessor sub)\n",
-    "           (sup :type list :accessor sup))\n",
-    "          (:metaclass funcallable-standard-class))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "In the first line, the pseudo-argument `TP` indicates the new class is a subclass of the class `TP`. Two new slots are defined, so that a `DTP`-instance will have three slots because of the `name` slot already defined for a `TP`-instance:\n",
-    "\n",
-    "- The `sub` slot (sub-types) is a list of the types that are known equal or smaller than the one which is described by the `DTP`-instance.\n",
-    "- The `sup` slot (super-types) is a list of the types that are known equal or larger than the one which is described by the `DTP`-instance.\n",
-    "\n",
-    "Note that `:accessor` methods (`sub` and `sup`) have been required for the corresponding slots; this means these methods will allow to *read* the corresponding slot but they can also be used to *write* it or *update* it. In fact, these slots must in general be modified after the creation, to maintain the coherence of the `TP`-system.\n",
-    "\n",
-    "We create now the minimal and  the maximal type objects of the `TP`-system, namely the `tp-void` and `tp-any` types. A special initialization work is done here because the general initialization process will assume these types are *already* defined in the environment."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 36,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "TP-VOID"
-      ]
-     },
-     "execution_count": 36,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(DEFVAR tp-void (MAKE-INSTANCE 'DTP :name 'tp-void))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 37,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(TP-VOID TP-ANY)"
-      ]
-     },
-     "execution_count": 37,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(SETF (sub tp-void) '(tp-void)\n",
-    "      (sup tp-void) '(tp-void tp-any))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 38,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "#<FUNCTION (LAMBDA (OBJ) :IN \"/home/jovyan/cl-jupyter-master/cl-jupyter.lisp\") {100680518B}>"
-      ]
-     },
-     "execution_count": 38,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(SET-FUNCALLABLE-INSTANCE-FUNCTION tp-void\n",
-    "                                   #'(lambda (obj)\n",
-    "                                             (declare (type t obj) (ignore obj))\n",
-    "                                             (the boolean nil)))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Firstly the `DTP`-instance to be assigned to the `tp-void` symbol is created by the call of the generic function `make-instance`, then the `sub` and `sup` slots are defined, and finally, because of the `:metaclass` class option, it is possible to associate a functional object to this instance, namely the function which always returns `nil`; this is nothing but the characteristic function of the void type in our environment. Example of use of this function:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 39,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 39,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(funcall tp-void 'anything)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Because of the `funcall`, the functional object associate to the object pointed by the symbol `tp-void` is called with the symbol `anything` as argument. Whatever is the argument, the answer is `nil`. We can verify the pointer symmetry between the `name` slot and the corresponding symbol:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 40,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "#<DTP TP-VOID>"
-      ]
-     },
-     "execution_count": 40,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "tp-void"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 41,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "TP-VOID"
-      ]
-     },
-     "execution_count": 41,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(name tp-void)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "We do exactly the same work for the `tp-any` type, perfectly symmetric of the `tp-void` work."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 42,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "TP-ANY"
-      ]
-     },
-     "execution_count": 42,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(DEFVAR tp-any (MAKE-INSTANCE 'DTP :name 'tp-any))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 43,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(TP-ANY)"
-      ]
-     },
-     "execution_count": 43,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(SETF (sub tp-any) '(tp-void tp-any)\n",
-    "      (sup tp-any) '(tp-any))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 44,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "#<FUNCTION (LAMBDA (OBJ) :IN \"/home/jovyan/cl-jupyter-master/cl-jupyter.lisp\") {100265E9EB}>"
-      ]
-     },
-     "execution_count": 44,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(SET-FUNCALLABLE-INSTANCE-FUNCTION tp-any\n",
-    "                                   #'(lambda (obj)\n",
-    "                                             (declare (type t obj) (ignore obj))\n",
-    "                                             (the boolean t)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 45,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "T"
-      ]
-     },
-     "execution_count": 45,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(funcall tp-any 'anything)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "The general process of initialization of a `DTP`-instance can now be defined. Firstly we need an `add-relation` function, allowing us to *add* a new order relation to the environment, something like \"`integer` < `number`\", *and all the consequent relations*. This function *updates* the `sub` and `sup` slots of the involved `DTP`-instances with the `union` Lisp function."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 46,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "#<STANDARD-GENERIC-FUNCTION CL-JUPYTER-USER::ADD-RELATION (0)>"
-      ]
-     },
-     "execution_count": 46,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(DEFGENERIC ADD-RELATION (dtp1 dtp2))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 47,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "#<STANDARD-METHOD CL-JUPYTER-USER::ADD-RELATION (SYMBOL SYMBOL) {1003AE0103}>"
-      ]
-     },
-     "execution_count": 47,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(DEFMETHOD ADD-RELATION ((dtp1 symbol) (dtp2 symbol))\n",
-    "           (the list\n",
-    "                (with-slots (sub) (eval dtp1)\n",
-    "                    (declare (type list sub))\n",
-    "                    (with-slots (sup) (eval dtp2)\n",
-    "                        (declare (type list sup))\n",
-    "                        (dolist (item sub)\n",
-    "                            (declare (type symbol item))\n",
-    "                            (setf (sup (eval item))\n",
-    "                                  (union (sup (eval item)) sup)))\n",
-    "                        (dolist (item sup)\n",
-    "                            (declare (type symbol item))\n",
-    "                            (setf (sub (eval item))\n",
-    "                                  (union (sub (eval item)) sub)))\n",
-    "                        (list dtp1 dtp2)))))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "A new `:after` method can then be defined this time for the `DTP`-type. Again because this is an `:after` method, the defined process is *added* to the standard initialization process, in particular giving the allocation of the instance, the initialization of arguments through initargs and initforms."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 48,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "#<STANDARD-METHOD COMMON-LISP:INITIALIZE-INSTANCE :AFTER (DTP) {1003EF0A23}>"
-      ]
-     },
-     "execution_count": 48,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(DEFMETHOD INITIALIZE-INSTANCE :after ((dtp dtp)\n",
-    "                                       &key prdc\n",
-    "                                       (dsub '(tp-void))\n",
-    "                                       (dsup '(tp-any)))\n",
-    "           (declare\n",
-    "            (type (function (t) boolean) prdc)\n",
-    "            (type list dsub dsup))\n",
-    "           (with-slots (name sub sup) dtp\n",
-    "               (declare\n",
-    "                (type symbol name)\n",
-    "                (type list sub sup))\n",
-    "               (setf\n",
-    "                sub (union dsub (list name))\n",
-    "                sup (union dsup (list name)))\n",
-    "               (dolist (item dsub)\n",
-    "                   (declare (type symbol item))\n",
-    "                   (add-relation item name))\n",
-    "               (dolist (item dsup)\n",
-    "                   (declare (type symbol item))\n",
-    "                   (add-relation name item)))\n",
-    "           (set-funcallable-instance-function dtp prdc))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "This method for the generic function `initialize-instance` uses not only the `dtp`-instance to be initialized, but also the keyword optional arguments `:prdc` (predicate), `dsub` (direct subtypes) and `dsup` (direct supertypes). This mechanism works as follows: if an `initialize-instance` method uses a keyword argument, this argument is available to the user when it creates an instance of the corresponding class; usually this argument is used for a small work to be done during the initialization stage. Artificial example:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 49,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "#<STANDARD-CLASS CL-JUPYTER-USER::CC>"
-      ]
-     },
-     "execution_count": 49,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(defclass cc () ((slot :initarg :slot :reader slot)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 50,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "#<STANDARD-METHOD COMMON-LISP:INITIALIZE-INSTANCE :AFTER (CC) {10040B1ED3}>"
-      ]
-     },
-     "execution_count": 50,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(defmethod initialize-instance :after ((cc cc) &key incslot)\n",
-    "    (incf (slot-value cc 'slot) (* 2 incslot)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 51,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "CC-INSTANCE"
-      ]
-     },
-     "execution_count": 51,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(defvar cc-instance (make-instance 'cc :slot 3 :incslot 5))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 52,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "13"
-      ]
-     },
-     "execution_count": 52,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(slot cc-instance)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "The `:slot` argument, because it is an `:initarg`, is used to ordinarily initialize the unique slot named `slot` of a\n",
-    "`c`-instance; but the `:after` `initialize-instance` method, then adds twice the other keyword argument `:incslot`.\n",
-    "\n",
-    "For the initialization of a `dtp`-instance, the `:prdc` argument is used to define the predicate function defining the type, which is associated to the the `dtp`-instance and used when the `dtp`-instance is *funcalled*; the `:dsub` and `:dsup` arguments allow the user to give the list of *direct* sub- and super-types; the method then computes, with the help of `add-relation`, all the sub- and super-types. If not used, these arguments default to an obvious value.\n",
-    "\n",
-    "Let us define the `TP`-version of the boolean type."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 53,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "TP-BOOLEAN"
-      ]
-     },
-     "execution_count": 53,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(DEFVAR TP-BOOLEAN\n",
-    "        (MAKE-INSTANCE 'DTP\n",
-    "                       :name 'TP-BOOLEAN\n",
-    "                       :prdc #'(lambda (obj)\n",
-    "                                       (declare (type t obj))\n",
-    "                                       (the boolean\n",
-    "                                            (if (member obj '(nil t))\n",
-    "                                                t nil)))))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 54,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "T"
-      ]
-     },
-     "execution_count": 54,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(funcall tp-boolean 't)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 55,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 55,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(funcall tp-boolean 'true)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {
-    "collapsed": true
-   },
-   "source": [
-    "We use now the standard number types `tp-number`, `tp-integer` and `tp-fixnum` to give examples of use of the `:dsub` and `:dsup` arguments."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 56,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "TP-NUMBER"
-      ]
-     },
-     "execution_count": 56,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(defvar tp-number (make-instance 'dtp :name 'tp-number :prdc #'numberp))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 57,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "TP-FIXNUM"
-      ]
-     },
-     "execution_count": 57,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(defvar tp-fixnum\n",
-    "    (make-instance 'dtp :name 'tp-fixnum\n",
-    "                   :prdc #'(lambda (obj)\n",
-    "                                   (declare (type t obj))\n",
-    "                                   (the boolean\n",
-    "                                        (typep obj 'fixnum)))\n",
-    "                   :dsup '(tp-number)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 58,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "TP-INTEGER"
-      ]
-     },
-     "execution_count": 58,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(defvar tp-integer\n",
-    "    (make-instance 'dtp :name 'tp-integer :prdc #'integerp\n",
-    "                   :dsub '(tp-fixnum) :dsup '(tp-number)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 59,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(TP-INTEGER TP-FIXNUM TP-NUMBER TP-ANY)"
-      ]
-     },
-     "execution_count": 59,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(sup tp-fixnum)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 60,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "T"
-      ]
-     },
-     "execution_count": 60,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(funcall tp-fixnum 3)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 61,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 61,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(funcall tp-fixnum 3.3)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 62,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "T"
-      ]
-     },
-     "execution_count": 62,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(funcall tp-number 3.3)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "In particular the relations \"`tp-fixnum` < `integer`\" and \"`tp-integer` < `tp-number`\" have implied \"`tp-fixnum` < `tp-number`\". Note in these examples, the `prdc` slots for `tp-number` and `tp-integer` have been defined through symbols, for example `#'numberp` points to the functional value of the symbol `numberp`, in this case a predefined Lisp function examining whether its argument is a number. On the contrary, the `prdc` slot of the `tp-fixnum` `TP`-instance is a function constructed in the call of `make-instance`.\n",
-    "\n",
-    "The user may also construct several new types, and *after* the fact, explicitly using the `add-relation`, define the order relations between them."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 63,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "T1"
-      ]
-     },
-     "execution_count": 63,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(defvar t1\n",
-    "    (make-instance 'dtp\n",
-    "                   :name 't1\n",
-    "                   :prdc #'(lambda (obj)\n",
-    "                                   (declare (type t obj))\n",
-    "                                   (the boolean (eql obj 1)))))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 64,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "T12"
-      ]
-     },
-     "execution_count": 64,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(defvar t12\n",
-    "    (make-instance 'dtp\n",
-    "                   :name 't12\n",
-    "                   :prdc #'(lambda (obj)\n",
-    "                                   (declare (type t obj))\n",
-    "                                   (the boolean\n",
-    "                                        (if (member obj '(1 2))\n",
-    "                                            t nil)))))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 65,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "T123"
-      ]
-     },
-     "execution_count": 65,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(defvar t123\n",
-    "    (make-instance 'dtp\n",
-    "                   :name 't123\n",
-    "                   :prdc #'(lambda (obj)\n",
-    "                                   (declare (type t obj))\n",
-    "                                   (the boolean\n",
-    "                                        (if (member obj '(1 2 3))\n",
-    "                                            t nil)))))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 66,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "T1234"
-      ]
-     },
-     "execution_count": 66,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(defvar t1234\n",
-    "    (make-instance 'dtp\n",
-    "                   :name 't1234\n",
-    "                   :prdc #'(lambda (obj)\n",
-    "                                   (declare (type t obj))\n",
-    "                                   (the boolean\n",
-    "                                        (if (member obj '(1 2 3 4))\n",
-    "                                            t nil)))))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "We have constructed the types without using the `:dsub` and `:dsup` arguments. Then the user can maintain the structure of his type set; the `mapcar` shows the list of the `sup` slots of the just defined types."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 67,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "((T1 TP-ANY) (T12 TP-ANY) (T123 TP-ANY) (T1234 TP-ANY))"
-      ]
-     },
-     "execution_count": 67,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(mapcar #'sup (list t1 t12 t123 t1234))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 68,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(T1 T12)"
-      ]
-     },
-     "execution_count": 68,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(add-relation 't1 't12)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 69,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "((T1 T12 TP-ANY) (T12 TP-ANY) (T123 TP-ANY) (T1234 TP-ANY))"
-      ]
-     },
-     "execution_count": 69,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(mapcar #'sup (list t1 t12 t123 t1234))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 70,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(T123 T1234)"
-      ]
-     },
-     "execution_count": 70,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(add-relation 't123 't1234)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 71,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "((T1 T12 TP-ANY) (T12 TP-ANY) (T123 T1234 TP-ANY) (T1234 TP-ANY))"
-      ]
-     },
-     "execution_count": 71,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(mapcar #'sup (list t1 t12 t123 t1234))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 72,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(T12 T123)"
-      ]
-     },
-     "execution_count": 72,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(add-relation 't12 't123)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 73,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "((T12 T1 T123 T1234 TP-ANY) (T1234 T123 T12 TP-ANY) (T123 T1234 TP-ANY) (T1234 TP-ANY))"
-      ]
-     },
-     "execution_count": 73,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(mapcar #'sup (list t1 t12 t123 t1234))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "What is striking in such a process is the fact that the order relations must be explained to the machine by the user, again a case of a necessary *intuitionistic* work! Of course it would be easy to design a simple generator of enumerative types which would itself determine the order relations that are satisfied, but, because of Cantor, Russell and G&#246;del, this is definitively impossible for general types.\n",
-    "\n",
-    "### The `FTP` and `SF` classes.\n",
-    "\n",
-    "Now we process the `FTP`-class, devoted to the `functional` types. To simplify the presentation, we consider only the functions $\\mathcal{T}_1\\rightarrow\\mathcal{T}_2$, in other words the functions with exactly *one* argument. It is easy to prove this is theoretically sufficient, but practically it is not. The standard trick consists in considering a function with two arguments as a function defined for a list of two elements. The further technicalities for the case of an arbitrary number of arguments are far from the subject of this paper, so that we do not want to consider them[<sup>8</sup>](#footnote_8).\n",
-    "\n",
-    "<a id='footnote_8'><sup>8</sup></a> Common Lisp is also there fantastically more advanced than the other current languages: the numerous types of argument transfer that are available give the user a great flexibility to manage the various cases; they are allowed only because of the great *mathematical* precision of the definition of the language structure.\n",
-    "\n",
-    "The `FTP`-class is defined as follows:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 74,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "#<FUNCALLABLE-STANDARD-CLASS CL-JUPYTER-USER::FTP>"
-      ]
-     },
-     "execution_count": 74,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(DEFCLASS FTP (TP)\n",
-    "          ((sorc :type symbol :initarg :sorc :reader sorc)\n",
-    "           (trgt :type symbol :initarg :trgt :reader trgt))\n",
-    "          (:metaclass funcallable-standard-class))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "This time, two slots, `sorc` (source) and `trgt` (target), are added to the `name` slot of the underlying `TP`-structure; these slots must be two `TP`-types, in fact two symbols locating them, according to our organization. Note these source and target types can be discriminant or functional.\n",
-    "\n",
-    "A functional object will be an instance of the class `SF`, for <u>s</u>*afe*-<u>f</u>*unction*, safe because the types of argument and result are systematically verified when the function is called:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 75,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "#<FUNCALLABLE-STANDARD-CLASS CL-JUPYTER-USER::SF>"
-      ]
-     },
-     "execution_count": 75,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(DEFCLASS SF ()\n",
-    "          ((sorc :type symbol :initarg :sorc :reader sorc)\n",
-    "           (trgt :type symbol :initarg :trgt :reader trgt))\n",
-    "          (:metaclass funcallable-standard-class))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "The definition of `FTP` and `SF` are almost the same! In the case of an `FTP`-instance, the associated function will examine whether some object is in this type. In the case of an `SF`-instance, the associated function will be the functional object itself; the slots `sorc` and `trgt` are then additional information about the correct types of argument and result.\n",
-    "\n",
-    "To explain the main part of the work to be done now, let us consider a functional type $\\mathcal{T}_1\\rightarrow\\mathcal{T}_2$ and a particular function $f$ declared to be $f:\\mathcal{T}'_1\\rightarrow\\mathcal{T}'_2$; under what circumstances, is this particular $f$ of the functional type $\\mathcal{T}_1\\rightarrow\\mathcal{T}_2$? There is only one solution: we must have the order relations: $\\mathcal{T}_1\\leq\\mathcal{T}'_1$  and $\\mathcal{T}_2\\leq\\mathcal{T}'_2$, and the reader understands now why we took care of these order relations. We therefore need a `subtypep` Lisp function to compare types. If both arguments are discriminant types, the answer is read in a `sup` slot; if both arguments are functional, the appropriate comparisons must be applied to the respective sources and targets; if the types are not of the same nature, one being discriminant and the other one being functional, the answer is certainly negative[<sup>9</sup>](#footnote_9).\n",
-    "\n",
-    "<a id='footnote_9'><sup>9</sup></a> It would be easy to work only with (pseudo-) \"discriminant\" types, even for functional objects, but the organization chosen here makes more obvious the deep difference of nature between both kinds of types; in particular in this way, a `DTP`-type and an `FTP`-type can never be compared.\n",
-    "\n",
-    "The Lisp translation:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 76,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "SUBTYPE-P"
-      ]
-     },
-     "execution_count": 76,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(DEFUN SUBTYPE-P (tp1 tp2)\n",
-    "       (declare (type symbol tp1 tp2))\n",
-    "       (the boolean\n",
-    "            (etypecase (eval tp1)\n",
-    "                (dtp\n",
-    "                 (etypecase (eval tp2)\n",
-    "                     (dtp (if (member tp2 (sup (eval tp1)))\n",
-    "                              t nil))\n",
-    "                     (ftp nil)))\n",
-    "                (ftp\n",
-    "                 (etypecase (eval tp2)\n",
-    "                     (dtp nil)\n",
-    "                     (ftp (and (subtype-p (sorc (eval tp2)) (sorc (eval tp1)))\n",
-    "                               (subtype-p (trgt (eval tp1)) (trgt (eval tp2))))))))))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "We cannot try the `subtype-p` function until the initialization work for `FTP`-instances has been completed. Remember in general a `TP`-instance must also be *funcallable* to verify the type of any object. The standard initialization work is therefore completed as follows."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 77,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "#<STANDARD-METHOD COMMON-LISP:INITIALIZE-INSTANCE :AFTER (FTP) {1004F65DC3}>"
-      ]
-     },
-     "execution_count": 77,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(DEFMETHOD INITIALIZE-INSTANCE :after ((ftp ftp) &rest rest)\n",
-    "           (declare (ignore rest))\n",
-    "           (set-funcallable-instance-function ftp\n",
-    "                                              #'(lambda (obj)\n",
-    "                                                        (declare (type t obj))\n",
-    "                                                        (the boolean\n",
-    "                                                             (and (typep obj 'sf)\n",
-    "                                                                  (subtype-p (sorc ftp) (sorc obj))\n",
-    "                                                                  (subtype-p (trgt obj) (trgt ftp)))))))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "This time the associated function is entirely deduced from the `sorc` and `trgt` slots, available *after* the standard initialization work. You see the *only* objects of type some `FTP`-descriptor are `SF`-instances, and the appropriate order relations must be verified between source, target and the considered functional type. Now we can create a\n",
-    "few `FTP`-instances and do the obvious tests for `subtype-p`."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 78,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "T"
-      ]
-     },
-     "execution_count": 78,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(subtype-p 'tp-fixnum 'tp-integer)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 79,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "T"
-      ]
-     },
-     "execution_count": 79,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(subtype-p 'tp-fixnum 'tp-fixnum)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 80,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 80,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(subtype-p 'tp-integer 'tp-fixnum)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 81,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "FII"
-      ]
-     },
-     "execution_count": 81,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(defvar fii (make-instance 'ftp\n",
-    "                           :name 'fii\n",
-    "                           :sorc 'tp-integer\n",
-    "                           :trgt 'tp-integer))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 82,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "FNF"
-      ]
-     },
-     "execution_count": 82,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(defvar fnf (make-instance 'ftp\n",
-    "                           :name 'fnf\n",
-    "                           :sorc 'tp-number\n",
-    "                           :trgt 'tp-fixnum))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 83,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 83,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(subtype-p 'fii 'tp-fixnum)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 84,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 84,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(subtype-p 'fii 'fnf)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 85,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "T"
-      ]
-     },
-     "execution_count": 85,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(subtype-p 'fnf 'fii)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "In order to make them work, the initialization of the `SF`-instances remains to be defined. An `SF`-instance is funcallable and the associate function will be the ordinary function the user intends to define, with the type verifications automatically added. The Lisp translation:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 86,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "#<STANDARD-METHOD COMMON-LISP:INITIALIZE-INSTANCE :AFTER (SF) {10053D2373}>"
-      ]
-     },
-     "execution_count": 86,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(DEFMETHOD INITIALIZE-INSTANCE :after ((sf sf) &key f)\n",
-    "           (declare (type (function (t) t) f))\n",
-    "           (set-funcallable-instance-function\n",
-    "            sf\n",
-    "            (with-slots (sorc trgt) sf\n",
-    "                #'(lambda (arg)\n",
-    "                          (declare (type t arg))\n",
-    "                          (unless (funcall (eval sorc) arg)\n",
-    "                              (error \"The argument ~S should be of type ~S.\"\n",
-    "                                     arg sorc))\n",
-    "                          (the t\n",
-    "                               (let ((rslt (funcall f arg)))\n",
-    "                                    (unless (funcall (eval trgt) rslt)\n",
-    "                                        (error \"The result ~S should be of type ~S.\"\n",
-    "                                               rslt trgt))\n",
-    "                                    rslt))))))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Note the extra `:f`initialization argument. An obvious test:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 87,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "2+"
-      ]
-     },
-     "execution_count": 87,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(defvar 2+ (make-instance 'sf\n",
-    "                          :sorc 'tp-integer\n",
-    "                          :trgt 'tp-integer\n",
-    "                          :f #'(lambda (n) (+ n 2))))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 88,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "7"
-      ]
-     },
-     "execution_count": 88,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(funcall 2+ 5)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 89,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "SIMPLE-ERROR: \n",
-      "The argument 5.5 should be of type TP-INTEGER.\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 89,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(funcall 2+ 5.5)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "### Improvements.\n",
-    "\n",
-    "It is a little painful to use the `make-instance` method with its keywords. Let's use another aspect of the Common Lisp environment, the *macro generator* to automate the appropriate call to `make-instance`. Here we detail the work for the creation of `SF`-instances."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 90,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "MAKE-SF"
-      ]
-     },
-     "execution_count": 90,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(DEFMACRO MAKE-SF (sorc trgt f)\n",
-    "          `(make-instance 'sf\n",
-    "                          :sorc ,sorc :trgt ,trgt :f ,f))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 91,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(MAKE-INSTANCE (QUOTE SF) :SORC (QUOTE NUMBER) :TRGT (QUOTE TP-INTEGER) :F (FUNCTION (LAMBDA (N) (+ N 5))))"
-      ]
-     },
-     "execution_count": 91,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(macroexpand\n",
-    " '(make-sf 'number 'tp-integer #'(lambda (n) (+ n 5)))))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 92,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "5+"
-      ]
-     },
-     "execution_count": 92,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(defvar 5+ (make-sf 'tp-number 'tp-integer\n",
-    "                    #'(lambda (n) (+ n 5))))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 93,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "11"
-      ]
-     },
-     "execution_count": 93,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(funcall 5+ 6)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 94,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "SIMPLE-ERROR: \n",
-      "The result 11.5 should be of type TP-INTEGER.\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 94,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(funcall 5+ 6.5)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "The `defmacro` must be considered as defining a *source text translator* converting a call to `make-sf` into some\n",
-    "`make-instance`. The translation mechanism is *tested* by using the `macroexpand` Lisp function. Then the `5+` function is really created and then used. This time the error is in the result type.\n",
-    "\n",
-    "Constructing the `DTP` and `FTP` instances can be processed in the same way."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 95,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "MAKE-DTP"
-      ]
-     },
-     "execution_count": 95,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(DEFMACRO MAKE-DTP (name prdc)\n",
-    "          `(make-instance 'dtp\n",
-    "                          :name ,name :prdc ,prdc))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "To explain the coherence of this type system, we add another stage of verification: a discriminant type is essentially a function $\\mathcal{A}\\rightarrow\\mathcal{B}$, so that the functional type of this function should be also verified. Let us solve this challenge. We slightly modify the `DTP`-initializer."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 96,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "REDEFINITION-WITH-DEFMETHOD: \n",
-      "  redefining INITIALIZE-INSTANCE :AFTER (#<FUNCALLABLE-STANDARD-CLASS CL-JUPYTER-USER::DTP>) in DEFMETHOD\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "#<STANDARD-METHOD COMMON-LISP:INITIALIZE-INSTANCE :AFTER (DTP) {1005C5B453}>"
-      ]
-     },
-     "execution_count": 96,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(DEFMETHOD INITIALIZE-INSTANCE :after ((dtp dtp)\n",
-    "                                       &key prdc\n",
-    "                                       (dsub '(tp-void))\n",
-    "                                       (dsup '(tp-any)))\n",
-    "           (declare\n",
-    "            (type (function (t) boolean) prdc)\n",
-    "            (type list dsub dsup))\n",
-    "           (with-slots (name sub sup) dtp\n",
-    "               (declare\n",
-    "                (type symbol name)\n",
-    "                (type list sub sup))\n",
-    "               (setf\n",
-    "                sub (union dsub (list name))\n",
-    "                sup (union dsup (list name)))\n",
-    "               (dolist (item dsub)\n",
-    "                   (declare (type symbol item))\n",
-    "                   (add-relation item name))\n",
-    "               (dolist (item dsup)\n",
-    "                   (declare (type symbol item))\n",
-    "                   (add-relation name item)))\n",
-    "           (set-funcallable-instance-function dtp\n",
-    "                                              (make-sf 'tp-any 'tp-boolean prdc)))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "As an example, let us consider the frequent case of a user who forgets the positive answer of the `member` function is not the boolean `T`:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 97,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(3 4 5)"
-      ]
-     },
-     "execution_count": 97,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(member 3 '(1 2 3 4 5))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Such a user could erroneously define an enumerative type as follows:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 98,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "COLORS"
-      ]
-     },
-     "execution_count": 98,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(defvar colors (make-dtp 'colors\n",
-    "                         #'(lambda (obj)\n",
-    "                                   (member obj '(red orange yellow green blue indigo violet)))))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 99,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 99,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(funcall colors 'black)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 100,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "SIMPLE-ERROR: \n",
-      "The result (BLUE INDIGO VIOLET) should be of type TP-BOOLEAN.\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 100,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(funcall colors 'blue)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "and you see the type error ... during the type verification is detected and a clear message is displayed. This cannot be applied to the `boolean` type itself, because an infinite loop would be generated. You see also in such a case the functional object associated with an instance (`DTP`) is not purely functional but another (`SF`)-instance which in turn has an associated functional object.\n",
-    "\n",
-    "### The function `compose`.\n",
-    "\n",
-    "It is customary in discussions between Lisp and C++ or Java programmers to use the example of the `compose` function to illustrate how weak C++ is when *functional programming* is involved; have a look at [[CMPS]](#CMPS) for the \"official\" solution in C++ and see how technically difficult it is. Here we give a simple Lisp solution, which furthermore is at once valid for arbitrary data types.\n",
-    "\n",
-    "Firstly we construct the `pair` and `any-sf` types[<sup>10</sup>](#footnote_10):\n",
-    "\n",
-    "<a id='footnote_10'><sup>10</sup></a> Exercise: a previous version of this paper had the claimed \"subtle\" definition of the `any-sf` type: `(make-ftp 'any-sf 'tp-void 'tp-any)`; this really defines a type, but the `compose` `SF`-instance would not have the `any-sf` type, why? Analyzing precisely the difference between both definitions for `any-sf` is quite interesting and shows that any *strict* typing system cannot be entirely satisfactory, some *freedom* must necessarily be given to the programmer; it is exactly the point of view of the Common Lisp designers."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 101,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "PAIR"
-      ]
-     },
-     "execution_count": 101,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(defvar pair (make-dtp 'pair\n",
-    "                       #'(lambda (obj)\n",
-    "                                 (and (consp obj)\n",
-    "                                      (consp (cdr obj))\n",
-    "                                      (null (cddr obj))))))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 102,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "ANY-SF"
-      ]
-     },
-     "execution_count": 102,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(defvar any-sf (make-dtp 'any-sf\n",
-    "                         #'(lambda (obj)\n",
-    "                                   (typep obj 'sf))))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Then the `2-sf-that-may-be-composed` type may be defined[<sup>11</sup>](#footnote_11).\n",
-    "\n",
-    "<a id='footnote_11'><sup>11</sup></a> Exercise: Design a `make-subdtp` constructor to automate the generation of the `:dsup` argument which uses the predicate associated to the initial type."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 103,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "2-SF-THAT-MAY-BE-COMPOSED"
-      ]
-     },
-     "execution_count": 103,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(defvar 2-sf-that-may-be-composed \n",
-    "    (make-dtp '2-sf-that-may-be-composed\n",
-    "              #'(lambda (obj)\n",
-    "                        (and (funcall pair obj)\n",
-    "                             (funcall any-sf (first obj))\n",
-    "                             (funcall any-sf (second obj))\n",
-    "                             (subtype-p (trgt (second obj)) (sorc (first obj)))))))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "> GH: Fix the `make-dtp` macro to accomodate the `:dsup` parameter!"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 104,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(PAIR)"
-      ]
-     },
-     "execution_count": 104,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(setf (sup 2-sf-that-may-be-composed) '(pair))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 105,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "COMPOSE"
-      ]
-     },
-     "execution_count": 105,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(defvar compose\n",
-    "    (make-sf '2-sf-that-may-be-composed 'any-sf\n",
-    "             #'(lambda (arg)\n",
-    "                       (let ((sf2 (first arg))\n",
-    "                             (sf1 (second arg)))\n",
-    "                            (make-sf (sorc sf1) (trgt sf2)\n",
-    "                                     #'(lambda (arg)\n",
-    "                                               (funcall sf2 (funcall sf1 arg))))))))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 106,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "4+"
-      ]
-     },
-     "execution_count": 106,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(defvar 4+ (funcall compose (list 2+ 2+)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 107,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "9"
-      ]
-     },
-     "execution_count": 107,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(funcall 4+ 5)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 108,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "SIMPLE-ERROR: \n",
-      "The argument 5.5 should be of type TP-INTEGER.\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 108,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(funcall 4+ 5.5)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "A more subtle example: the composed function is in the right type with respect the argument, but a *used* function is not."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 109,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "3/2+"
-      ]
-     },
-     "execution_count": 109,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(defvar 3/2+ (make-sf 'tp-integer 'tp-integer\n",
-    "                      #'(lambda (x) (+ x 3/2))))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 110,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "3+"
-      ]
-     },
-     "execution_count": 110,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(defvar 3+ (funcall compose (list 3/2+ 3/2+)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 111,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "SIMPLE-ERROR: \n",
-      "The result 15/2 should be of type TP-INTEGER.\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 111,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(funcall 3+ 6)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "The last type-error example; this time, the `compose` function itself observes its argument does not have the required type."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 112,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "SIMPLE-ERROR: \n",
-      "The argument (#<SF {10061D8A3B}> #<SF {10061D8A3B}>) should be of type 2-SF-THAT-MAY-BE-COMPOSED.\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 112,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(funcall compose (list compose compose))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "# CLOS and Mathematical Structures.\n",
-    "\n",
-    "We give a small example to explain how CLOS can easily be used to implement the classical *mathematical structures*. Most often, an object of some *type* in mathematics is a structure with several components, frequently of *functional* nature. In this small presentation, we consider the case of a user who wants to handle *sets*, *magmas*, *associative* magmas and *monoids*; these simple particular cases are sufficient to understand how CLOS gives the right tools to process mathematical structures. In the following section, we will describe how these simple methods have been used in [[DRSS]](#DRSS) to implement the main structures of *Algebraic Topology* such as *chain complexes*, *simplicial sets*,\n",
-    "*simplicial groups*, *Hopf algebras*, and also the various *morphisms* between these objects.\n",
-    "\n",
-    "## Sets.\n",
-    "\n",
-    "We define a `/SET/` class whose instances correspond to the *sets* of the classical *set theory*."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 113,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "#<STANDARD-CLASS CL-JUPYTER-USER::/SET/>"
-      ]
-     },
-     "execution_count": 113,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(DEFCLASS /SET/ ()\n",
-    "          ((name :type symbol :initarg :name :initform (gensym) :reader name)\n",
-    "           (prdcf :type function :initarg :prdcf :reader prdcf)\n",
-    "           (cmprf :type function :initarg :cmprf :reader cmprf)))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "In this organization, a set is made of three slots. The `name` slot has the same role as for the types of the previous section: it is only an auxiliary tool to locate easily the sets; the slot contains the symbol that locates the set, and we automate this organization:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 114,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "#<STANDARD-METHOD COMMON-LISP:SHARED-INITIALIZE :AFTER (/SET/ T) {10066AA863}>"
-      ]
-     },
-     "execution_count": 114,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(DEFMETHOD SHARED-INITIALIZE :after ((set /set/) slot-names &rest rest)\n",
-    "           (declare (ignore slot-names rest))\n",
-    "           (set (name set) set))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "The appropriate `print-object` method; when a *set* or an object of a subclass will be displayed, the output will show the corresponding class and the `name`:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 115,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "#<STANDARD-METHOD COMMON-LISP:PRINT-OBJECT (/SET/ T) {10067EC5B3}>"
-      ]
-     },
-     "execution_count": 115,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(DEFMETHOD PRINT-OBJECT ((set /set/) stream)\n",
-    "           (declare (type stream stream))\n",
-    "           (format stream \"#<~S ~S>\" (class-name (class-of set)) (name set))\n",
-    "           (the /set/ set))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "The second slot of a set, namely the `prdcf` slot (predicate-function), contains a function which can be called to examine whether some *arbitrary* object is an element of the set. In order to use this slot easily, we define two functions, `owns` and `in`; the first one may answer yes or no, that is, `t` or `nil`; and the second one generates an *error* if the membership relation is not satisfied[<sup>12</sup>](#footnote_12).\n",
-    "\n",
-    "<a id='footnote_12'><sup>12</sup></a> The sections bout our two main didactical examples, typing and mathematical categories, are entirely *independent*; but the lucid reader will observe the root class of the second application, namely the `/set/` class, can after all be also considered as a typing system in a mathematical context!"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 116,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "OWNS"
-      ]
-     },
-     "execution_count": 116,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(DEFUN OWNS (set obj)\n",
-    "       (declare\n",
-    "        (type /set/ set)\n",
-    "        (type t obj))\n",
-    "       (the boolean\n",
-    "            (funcall (prdcf set) obj)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 117,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "IN"
-      ]
-     },
-     "execution_count": 117,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(DEFUN IN (set obj)\n",
-    "       (declare\n",
-    "        (type /set/ set)\n",
-    "        (type t obj))\n",
-    "       (if (funcall (prdcf set) obj)\n",
-    "           obj\n",
-    "           (error \"The object ~S is not in ~S.\"\n",
-    "                  obj set)))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "The explanation of the third slot `cmpr` is given a little later; we construct the set `N` of non-negative integers."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 118,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "N"
-      ]
-     },
-     "execution_count": 118,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(defvar N\n",
-    "    (MAKE-INSTANCE '/set/\n",
-    "                   :name 'N\n",
-    "                   :prdcf #'(lambda (obj)\n",
-    "                                    (declare (type t obj))\n",
-    "                                    (the boolean\n",
-    "                                         (and (integerp obj)\n",
-    "                                              (>= obj 0))))\n",
-    "                   :cmprf #'=))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "The symbol `N` locates the constructed set"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 119,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "#</SET/ N>"
-      ]
-     },
-     "execution_count": 119,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "N"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "and the function `owns` allows the user to examine the membership relation:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 120,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "T"
-      ]
-     },
-     "execution_count": 120,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(owns N +1)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 121,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 121,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(owns N -1)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "The `cmprf` slot is essential in this context. There are frequently strong differences between an element of a set *as thought by the mathematician* and its possible machine representation<u>s</u>, the *s* being important. The notion of *equality* in mathematics is \"primitive\" and rarely *logically* considered by mathematicians. On the contrary, this notion is crucial in Computer Science, and Common Lisp is by far the most precise language from this point of view[<sup>13</sup>](#footnote_13). Here, we want to let the user freely decide how equality is defined between the elements of his sets, and this is the role of the `cmprf` slot (comparison function). For example, the comparison between elements in the set `N` is done by the Lisp predefined function `#'=`, in particular appropriate to compare integers. Again we define a function `cmpr` to easily use the `cmprf` slot of a set.\n",
-    "\n",
-    "<a id='footnote_13'><sup>13</sup></a> In particular all the standard predefined Lisp functions allow the user to *freely* define the equality relation to be used for every particular call."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 122,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "ELT-CMPR"
-      ]
-     },
-     "execution_count": 122,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(DEFUN ELT-CMPR (set elmn1 elmn2)\n",
-    "       (declare\n",
-    "        (type /set/ set)\n",
-    "        (type t elmn1 elmn2))\n",
-    "       (the boolean\n",
-    "            (funcall (cmprf set)\n",
-    "                     (in set elmn1) (in set elmn2))))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Note the use of the `in` function to verify that the compared elements are really in the considered set. Now we can compare two elements of `N`."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 123,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 123,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(elt-cmpr N 4 9)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 124,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "SIMPLE-ERROR: \n",
-      "The object -9 is not in #</SET/ N>.\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 124,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(elt-cmpr N 4 -9)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Let us construct now the set `Z/5`, that is the set of *integers modulo 5*. In our context, the most elegant method to implement this set consists in admitting a representation of an element of `Z/5` by an *arbitrary* integer, possibly negative or `> 4`, and to define the comparison with the help of the `mod` function, a predefined Lisp function."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 125,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "Z/5"
-      ]
-     },
-     "execution_count": 125,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(defvar Z/5\n",
-    "    (MAKE-INSTANCE '/SET/\n",
-    "                   :name 'Z/5\n",
-    "                   :prdcf #'integerp\n",
-    "                   :cmprf #'(lambda (elmn1 elmn2)\n",
-    "                                    (= 0 (mod (- elmn1 elmn2) 5)))))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 126,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "T"
-      ]
-     },
-     "execution_count": 126,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(elt-cmpr Z/5 4 9)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "This time the comparison between 4 and 9 is positive: these machine integers are *different* representations of the *same* mathematical object. You will understand that it is easy in this framework to define *quotient* sets.\n",
-    "\n",
-    "### Magmas.\n",
-    "\n",
-    "A magma is a set provided with a law of composition without any particular required property. It is a set with an additional ingredient, a function able to work on two elements of the magma and returning another element, their composition according the composition law. It is natural in this context to define the `magma` *subclass* of the `/set/` class; any `magma` instance is a set with a further slot, the `lawf` slot."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 127,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "#<STANDARD-CLASS CL-JUPYTER-USER::MAGMA>"
-      ]
-     },
-     "execution_count": 127,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(DEFCLASS MAGMA (/set/)\n",
-    "          ((lawf :type function :initarg :lawf :reader lawf)))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Again a function is added to the environment allowing the user to easily refer the `lawf` slot of a magma."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 128,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "#<STANDARD-GENERIC-FUNCTION CL-JUPYTER-USER::LAW (0)>"
-      ]
-     },
-     "execution_count": 128,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(DEFGENERIC LAW (magma &rest rest))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 129,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "#<STANDARD-METHOD CL-JUPYTER-USER::LAW (MAGMA) {1003C2ADC3}>"
-      ]
-     },
-     "execution_count": 129,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(DEFMETHOD LAW ((magma magma) &rest rest)\n",
-    "           (case (length rest)\n",
-    "               (1 (in magma (first rest)))\n",
-    "               (2 (in magma\n",
-    "                      (funcall (lawf magma)\n",
-    "                               (in magma (first rest))\n",
-    "                               (in magma (second rest)))))\n",
-    "               (otherwise\n",
-    "                (error \"Non-correct arguments in:~@\n",
-    "                       (LAW ~S~{ ~S~}).\" magma rest))))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "We intend in general to allow the user to refer the *law* defining a magma with an *arbitrary* number of elements, at least if this makes sense. In such a case, CLOS allows the user to define a generic function, here the `law` generic function, with one mandatory argument, called here `magma` and any number of other arguments put together in a list reachable through the symbol `rest`[<sup>14</sup>](#footnote_14). The ingredient `(magma magma)` in the parameter list has two meanings: the first `magma` names the first parameter, and the second `magma` explains the corresponding argument must be of *class* `magma`, otherwise the method is not applicable.\n",
-    "\n",
-    "<a id='footnote_14'><sup>14</sup></a> More precisely, the symbol `&rest` *marks* in the parameter list a new zone, in this case with a symbol locating the \"other\" arguments; the Lisp programmer almost always chooses the symbol `rest` to locate this list.\n",
-    "\n",
-    "For a magma without any further claimed property, it is sensible to allow one argument, and then this argument is returned, or two arguments and then the *product* of these arguments according to the composition law is returned.\n",
-    "Otherwise an error message is displayed. Note how the `in` function is used to verify the correct type of the arguments.\n",
-    "\n",
-    "We have defined the *set* `N` and it is possible to transform it now into a *magma*. Note how the standard initialization process of an instance allows the user to obtain such a conversion without any further work."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 130,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "#<MAGMA N>"
-      ]
-     },
-     "execution_count": 130,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(change-class N 'magma\n",
-    "              :lawf #'(lambda (n1 n2)\n",
-    "                              (* n1 (- n2 3))))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "The *law* which is defined is $(n_1,n_2) \\mapsto n_1(n_2-3)$. The obvious trials:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 131,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "8"
-      ]
-     },
-     "execution_count": 131,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(law N 4 5)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 132,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "SIMPLE-ERROR: \n",
-      "The object -5 is not in #<MAGMA N>.\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 132,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(law N 4 -5)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 133,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "SIMPLE-ERROR: \n",
-      "The object -3 is not in #<MAGMA N>.\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 133,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(law N 1 0)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 134,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "4"
-      ]
-     },
-     "execution_count": 134,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(law N 4)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 135,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "SIMPLE-ERROR: \n",
-      "Non-correct arguments in:\n",
-      "(LAW #<MAGMA N> 4 5 6).\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 135,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(law N 4 5 6)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "The constructed magma in fact is not correct; let us construct a classical correct one:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 136,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "Q"
-      ]
-     },
-     "execution_count": 136,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(defvar Q \n",
-    "    (make-instance 'magma\n",
-    "                   :name 'Q\n",
-    "                   :prdcf #'rationalp\n",
-    "                   :cmprf #'=\n",
-    "                   :lawf #'+))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 137,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "13/6"
-      ]
-     },
-     "execution_count": 137,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(law Q 3/2 2/3)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 138,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "SIMPLE-ERROR: \n",
-      "Non-correct arguments in:\n",
-      "(LAW #<MAGMA Q> 3/2 2/3 4/5).\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 138,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(law Q 3/2 2/3 4/5)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "This is simply the set `Q` of rationals equipped with the standard addition law. The last result is not satisfactory: the law is *associative* and it should be possible to make operate this law on an arbitrary number of arguments. The solution consists in defining a new class `A-MAGMA` (associative magma). There is no new slot in this class: membership of the new class only means the object, some magma, has an associative law."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 139,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "#<STANDARD-CLASS CL-JUPYTER-USER::A-MAGMA>"
-      ]
-     },
-     "execution_count": 139,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(DEFCLASS A-MAGMA (magma) ())"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "But this new class may be used to define a new method for the generic function `law`; in this new case, an arbitrary *positive* number of arguments can be used. A simple recursive process defines the new method from the old one: if the argument number is three or more, the computation is decomposed, otherwise the *next* method is called; the law is associative and this definition is coherent."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 140,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "#<STANDARD-METHOD CL-JUPYTER-USER::LAW (A-MAGMA) {100432C8D3}>"
-      ]
-     },
-     "execution_count": 140,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(DEFMETHOD LAW ((a-magma a-magma) &rest rest)\n",
-    "           (if (> (length rest) 2)\n",
-    "               (law a-magma\n",
-    "                    (in a-magma (first rest))\n",
-    "                    (apply #'law a-magma (rest rest)))\n",
-    "               (call-next-method)))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "You see in particular how the very basic Lisp function `apply` allows to recall the same method with one argument removed. We inform now the environment that our magma `Q` is associative:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 141,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "#<A-MAGMA Q>"
-      ]
-     },
-     "execution_count": 141,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(change-class Q 'a-magma)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "which allows us to compute the composition in `Q` of an arbitrary number of elements. Because the `magma` method will eventually be called, a possible type fault is intercepted."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 142,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "163/60"
-      ]
-     },
-     "execution_count": 142,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(law Q 1/2 2/3 3/4 4/5)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 143,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "SIMPLE-ERROR: \n",
-      "The object 0.75 is not in #<A-MAGMA Q>.\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 143,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(law Q 1/2 2/3 0.75 4/5)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "### Monoids.\n",
-    "\n",
-    "And the process can be continued for ever and ever, allowing the user to enrich as far as necessary the considered mathematical structures. Here, the following step consists in considering the structure of *monoids*. A monoid is an\n",
-    "associative magma with a unit. Only a `unit` slot is to be added to the `a-magma` structure. It is impossible in general to verify the claimed *unit* $e$ satisfies the required property, but however the property $e\\ast e = e$ can be tested; doing this test through a `shared-initialize` method allows it to be used in a `make-instance`, or in a `change-class`, or in a `reinitialize-instance` as well. The membership of the monoid may be also tested."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 144,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "#<STANDARD-CLASS CL-JUPYTER-USER::MONOID>"
-      ]
-     },
-     "execution_count": 144,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(DEFCLASS MONOID (a-magma)\n",
-    "          ((unit :initarg :unit :reader unit)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 145,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "#<STANDARD-METHOD COMMON-LISP:SHARED-INITIALIZE :AFTER (MONOID T) {10045E20C3}>"
-      ]
-     },
-     "execution_count": 145,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(DEFMETHOD SHARED-INITIALIZE :after ((monoid monoid) slot-names &rest rest)\n",
-    "           (declare (ignore rest))\n",
-    "           (let ((unit (unit monoid)))\n",
-    "                (unless (owns monoid unit)\n",
-    "                    (error \"Sorry, the claimed unit ~S is not in ~S.\"\n",
-    "                           unit monoid))\n",
-    "                (unless (elt-cmpr monoid unit (law monoid unit unit))\n",
-    "                    (error \"Sorry, ~S does not look like a unit in ~S.\"\n",
-    "                           unit monoid))))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 146,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "SIMPLE-ERROR: \n",
-      "Sorry, 1 does not look like a unit in #<MONOID Q>.\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 146,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(change-class Q 'monoid :unit 1)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 147,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "#<MONOID Q>"
-      ]
-     },
-     "execution_count": 147,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(reinitialize-instance Q :unit 0)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Note the error about the unit is intercepted *after* the standard initialization process, so that our `Q` is then become a `monoid`, as observed in the error message, but a wrong monoid; it is natural in this situation to use `reinitialize-instance` to redefine the object. A little more sophisticated use of `:around` methods would allow us to verify the coherence `before` changing class, and to refuse it if detected non-coherent.\n",
-    "\n",
-    "It is interesting to convert `Z/5`, currently a set, into a monoid with the unit `10`. Why not?"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 148,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "#<MONOID Z/5>"
-      ]
-     },
-     "execution_count": 148,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(change-class Z/5 'monoid\n",
-    "              :lawf #'+\n",
-    "              :unit 10)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 149,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "T"
-      ]
-     },
-     "execution_count": 149,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(elt-cmpr Z/5 10 (law Z/5 10 10))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "In a monoid, the composition law may logically be called for *zero* argument; in this case, the *unit* is the result. A new method for the generic function `law` is therefore stacked."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 150,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "#<STANDARD-METHOD CL-JUPYTER-USER::LAW (MONOID) {10049FA4B3}>"
-      ]
-     },
-     "execution_count": 150,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(DEFMETHOD LAW ((monoid monoid) &rest rest)\n",
-    "           (if (= 0 (length rest))\n",
-    "               (unit monoid)\n",
-    "               (call-next-method)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 151,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(0 10)"
-      ]
-     },
-     "execution_count": 151,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(list (law Q) (law Z/5))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "This looks a little artificial because `(law Q)` and `(unit Q)` are in fact synonymous, but think of the frequent case where you have to process a statement like `(apply #'law Q some-list)` where the last argument is a *computed* list, which could be sometimes empty; with our new `monoid` method for the `law` generic function, even if the value of `some-list` is the empty list, the correct process is applied.\n",
-    "\n",
-    "### What about the morphisms?\n",
-    "\n",
-    "So far we have only worked with the *objects* of the mathematical categories of sets, magmas, associative magmas, monoids. What about the *morphisms*? The solution is easy, but needs a little lucidity about the usual *compatibility* properties with ambient structures. We only sketch a possible solution, the expansion of which being obvious.\n",
-    "\n",
-    "The root of our classes of morphisms is the class of morphisms between sets.\n",
-    "\n",
-    "```lisp\n",
-    "(DEFCLASS SET-MRPH ()\n",
-    "          ((sorc :type set :initarg :sorc :reader sorc)\n",
-    "           (trgt :type set :initarg :trgt :reader trgt)\n",
-    "           (f :type function :initarg :f :reader f)))\n",
-    "```\n",
-    "\n",
-    "A `set-mrph` instance is essentially a *source*, some set, a *target*, some set, and a function mapping any object of the source to an object of the target. Again the standard *functional* properties of Common Lisp give the developper the right environment. We could also hide the `f` slot into the special hidden functional slot of a *funcallable* instance, as we did for the `TP`-instances in [Section 3](#What-typing-is.); it is only a question of taste.\n",
-    "\n",
-    "We need something to be able to \"funcall\" a `set-mrph`:\n",
-    "\n",
-    "```lisp\n",
-    "(DEFUN ? (mrph elmn)\n",
-    "    (...\n",
-    "         code which:\n",
-    "             1) verifies elmn is in the source of mrph;\n",
-    "             2) applies the f slot of mrph to elmn to compute the image;\n",
-    "             3) verifies this image is in the target of mrph;\n",
-    "             4) returns the image.\n",
-    "    ))\n",
-    "\n",
-    "(? some-set-mrph some-source-element)\n",
-    "```\n",
-    "\n",
-    "Now a magma-morphism is nothing but a set-morphism satisfying the standard compatibility properties with the magma structures of source and target. So that:\n",
-    "\n",
-    "```lisp\n",
-    "(DEFCLASS MAGMA-MRPH (set-mrph) ())\n",
-    "```\n",
-    "\n",
-    "and the same for `a-magma-mrph`, `monoid-mrph` and so on. Note this organization allows the user to clearly distinguish a\n",
-    "*set*-morphism between magmas from a *magma*-morphism between the same magmas; in the first case the compatibility properties are not satisfied or optional; in the second case the compatibility properties are assumed satisfied. Such morphisms are intensively used in the Kenzo program and considered in the following section.\n",
-    "\n",
-    "### What about functors?\n",
-    "\n",
-    "Working with categories, the mathematician inevitably will have to work with functors. In this organisation a tower of compatible functors is nothing but *one* generic function with various methods corresponding to the different cases. For example the *cartesian product* functor is defined for sets, magmas, associative magmas, monoids, and many other categories. It is sufficient to implement *all these functors* in *one* generic function, as follows."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 152,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "#<STANDARD-GENERIC-FUNCTION CL-JUPYTER-USER::PRODUCT (0)>"
-      ]
-     },
-     "execution_count": 152,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(DEFGENERIC PRODUCT (set1 set2))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 153,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "#<STANDARD-METHOD CL-JUPYTER-USER::PRODUCT (/SET/ /SET/) {1004C8F443}>"
-      ]
-     },
-     "execution_count": 153,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(DEFMETHOD PRODUCT ((set1 /set/) (set2 /set/))\n",
-    "           (make-instance '/set/\n",
-    "                          :name (intern (format nil \"~S-PRDC-~S\" (name set1) (name set2)))\n",
-    "                          :prdcf #'(lambda (obj)\n",
-    "                                           (declare (type t obj))\n",
-    "                                           (the boolean\n",
-    "                                                (and (listp obj)\n",
-    "                                                     (= 2 (length obj))\n",
-    "                                                     (owns set1 (first obj))\n",
-    "                                                     (owns set2 (second obj)))))\n",
-    "                          :cmprf #'(lambda (pair1 pair2)\n",
-    "                                           (declare (type list pair1 pair2))\n",
-    "                                           (the boolean\n",
-    "                                                (and (elt-cmpr set1 (first pair1) (first pair2))\n",
-    "                                                     (elt-cmpr set2 (second pair1) (second pair2)))))))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 154,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "#</SET/ N-PRDC-Z/5>"
-      ]
-     },
-     "execution_count": 154,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(product N Z/5)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 155,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 155,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(elt-cmpr N-prdc-Z/5 '(4 5) '(9 5))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 156,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "T"
-      ]
-     },
-     "execution_count": 156,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(elt-cmpr N-prdc-Z/5 '(4 5) '(4 10))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 157,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "SIMPLE-ERROR: \n",
-      "The object (-4 10) is not in #</SET/ N-PRDC-Z/5>.\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 157,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(elt-cmpr N-prdc-Z/5 '(4 5) '(-4 10))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "You see how clear and natural is the code of the `product` method. It is only a question of constructing the appropriate `prdcf` and `cmprf` slots, some functions, from the corresponding slots of the arguments `set1` and `set2`; the process is always the same, so that the Lisp *closures*, a subtle notion not available in C++ or Java[<sup>15</sup>](#footnote_15), give the user the natural tool, even he does not know exactly what a closure is!\n",
-    "\n",
-    "<a id='footnote_15'><sup>15</sup></a> available in Maple since the Release 5, but no OOP in Maple...\n",
-    "\n",
-    "For the richer structures of `magma`, `a-magma` and `monoid`, it is sufficient to write down new specific methods for the *same* generic function, defining the additional work to be done, using the previous work thanks to `call-next-method`."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 158,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "#<STANDARD-METHOD CL-JUPYTER-USER::PRODUCT (MAGMA MAGMA) {100515B453}>"
-      ]
-     },
-     "execution_count": 158,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(DEFMETHOD PRODUCT ((magma1 magma) (magma2 magma))\n",
-    "           (change-class (call-next-method) 'magma\n",
-    "                         :lawf #'(lambda (pair1 pair2)\n",
-    "                                         (list\n",
-    "                                          (law magma1 (first pair1) (first pair2))\n",
-    "                                          (law magma2 (second pair1) (second pair2))))))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 159,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "#<STANDARD-METHOD CL-JUPYTER-USER::PRODUCT (A-MAGMA A-MAGMA) {1005372D83}>"
-      ]
-     },
-     "execution_count": 159,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(DEFMETHOD PRODUCT ((magma1 a-magma) (magma2 a-magma))\n",
-    "           (change-class (call-next-method) 'a-magma))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 160,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "#<STANDARD-METHOD CL-JUPYTER-USER::PRODUCT (MONOID MONOID) {1005594E23}>"
-      ]
-     },
-     "execution_count": 160,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(DEFMETHOD PRODUCT ((monoid1 monoid) (monoid2 monoid))\n",
-    "           (change-class (call-next-method) 'monoid\n",
-    "                         :unit (list (unit monoid1) (unit monoid2))))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 161,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "Q2"
-      ]
-     },
-     "execution_count": 161,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(DEFVAR Q2 (product Q Q))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 162,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "Q4"
-      ]
-     },
-     "execution_count": 162,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(DEFVAR Q4 (product Q2 Q2))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 163,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "((4/3 32/21) (13/8 76/45))"
-      ]
-     },
-     "execution_count": 163,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(law Q4 '((1/2 2/3) (3/4 4/5))\n",
-    "     '((5/6 6/7) (7/8 8/9)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 164,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "((0 0) (0 0))"
-      ]
-     },
-     "execution_count": 164,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(unit Q4)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Note also the applicability rule for methods of a generic function implies the product of a monoid by a magma, for example, will fortunately be a magma."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 165,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "#<MAGMA Q-PRDC-N>"
-      ]
-     },
-     "execution_count": 165,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(product Q N)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "# CLOS and the Kenzo program.\n",
-    "\n",
-    "> Some of the comments in this section apply to an [older Kenzo version](https://github.com/gheber/kenzo/tree/master/archive/Kenzo-2). They are called out whenever there's a difference in implementation and behavior with the [newer version](https://github.com/gheber/kenzo).\n",
-    "\n",
-    "The Kenzo program is the first significant *machine program* about classical Algebraic Topology. It is not only a program implementing various *known* algorithms; *new* methods have been developped to *transform* the main \"tools\" of Algebraic Topology, mainly the spectral sequences, not at all *algorithmic* in the traditionnal organisation, into actual *computing* methods.\n",
-    "\n",
-    "## An example of Kenzo work.\n",
-    "\n",
-    "Let us show a simple example to illustrate which is possible with this program. The homology group $H_5 \\Omega^3 \\mathrm{Moore}(\\mathbb{Z}_2,4)$[<sup>16</sup>](#footnote_16) is \"in principle\" reachable thanks to old methods, see [[CRML]](#CRML), but experience\n",
-    "shows even the most skilful topologists meet some difficulties to determine it, see [[RBSR6]](#RBSR6)[[SRGR5]](#SRGR5). With the Kenzo program, you construct the Moore space.\n",
-    "\n",
-    "<a id='footnote_16'><sup>16</sup></a> The space $\\mathrm{Moore}(\\mathbb{Z}_2,4)$ is a \"canonical\" space having only non-trivial homology in dimension~4, namely $\\mathbb{Z}_2$, and $\\Omega^3\\mathrm{Moore}(\\mathbb{Z}_2,4)$, its third loop space, is the space of continuous maps from the 3-sphere~$S^3$ to this Moore space; the challenge is to determine the fifth homology group of this functional space."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 166,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "---done---"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 166,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(cat-init)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 167,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K1 Simplicial-Set]"
-      ]
-     },
-     "execution_count": 167,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def m4 (moore 2 4))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "The program returns the Kenzo-object `#1`, a simplicial set, that is, a combinatorial version of the Moore space which is asked for, and this object is assigned to the symbol `m4`. Then you construct the third loop-space of this Moore space."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 168,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K30 Simplicial-Group]"
-      ]
-     },
-     "execution_count": 168,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def o3m4 (loop-space m4 3))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "The combinatorial version of the loop space is *highly* infinite: it is a combinatorial version of the space of *continuous* maps $S^3 \\rightarrow \\mathrm{Moore}(\\mathbb{Z}_2,4)$ but functionnally coded as a small set of functions\n",
-    "in a `simplicial-group` object, that is, a simplicial set with an added group structure compatible with the simplicial structure. Finally the fifth homology-group is asked for."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 169,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "Computing boundary-matrix in dimension 5.\n",
-      "Rank of the source-module : 23.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-02-26, 2h 19m 16s.\n",
-      "Computing the boundary of the generator 1/23 (dimension 5) :\n",
-      "<<AlLp[5 <<AlLp[6 <<AlLp[3 M4][4 N5]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-02-26, 2h 19m 16s.\n",
-      "Computing the boundary of the generator 2/23 (dimension 5) :\n",
-      "<<AlLp[5 <<AlLp[6 <<AlLp[4 N5][3 M4]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-02-26, 2h 19m 16s.\n",
-      "Computing the boundary of the generator 3/23 (dimension 5) :\n",
-      "<<AlLp[5 <<AlLp[3 <<AlLp[4 N5]>>][3 <<AlLp[4 N5]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-02-26, 2h 19m 16s.\n",
-      "Computing the boundary of the generator 4/23 (dimension 5) :\n",
-      "<<AlLp[5 <<AlLp[2 <<AlLp[3 M4]>>][2 <<AlLp[3 M4]>>][2 <<AlLp[3 M4]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-02-26, 2h 19m 16s.\n",
-      "Computing the boundary of the generator 5/23 (dimension 5) :\n",
-      "<<AlLp[1 <<AlLp[2 <<AlLp[3 M4]>>]>>][4 <<AlLp[5 <<AlLp[3 M4][3 M4]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-02-26, 2h 19m 16s.\n",
-      "Computing the boundary of the generator 6/23 (dimension 5) :\n",
-      "<<AlLp[1 <<AlLp[2 <<AlLp[3 M4]>>]>>][4 <<AlLp[2 <<AlLp[3 M4]>>][3 <<AlLp[4 N5]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-02-26, 2h 19m 16s.\n",
-      "Computing the boundary of the generator 7/23 (dimension 5) :\n",
-      "<<AlLp[1 <<AlLp[2 <<AlLp[3 M4]>>]>>][4 <<AlLp[3 <<AlLp[4 N5]>>][2 <<AlLp[3 M4]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-02-26, 2h 19m 16s.\n",
-      "Computing the boundary of the generator 8/23 (dimension 5) :\n",
-      "<<AlLp[2 <<AlLp[3 <<AlLp[4 N5]>>]>>][3 <<AlLp[2 <<AlLp[3 M4]>>][2 <<AlLp[3 M4]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-02-26, 2h 19m 16s.\n",
-      "Computing the boundary of the generator 9/23 (dimension 5) :\n",
-      "<<AlLp[3 <<AlLp[2 <<AlLp[3 M4]>>][2 <<AlLp[3 M4]>>]>>][2 <<AlLp[3 <<AlLp[4 N5]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-02-26, 2h 19m 16s.\n",
-      "Computing the boundary of the generator 10/23 (dimension 5) :\n",
-      "<<AlLp[4 <<AlLp[5 <<AlLp[3 M4][3 M4]>>]>>][1 <<AlLp[2 <<AlLp[3 M4]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-02-26, 2h 19m 16s.\n",
-      "Computing the boundary of the generator 11/23 (dimension 5) :\n",
-      "<<AlLp[4 <<AlLp[2 <<AlLp[3 M4]>>][3 <<AlLp[4 N5]>>]>>][1 <<AlLp[2 <<AlLp[3 M4]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-02-26, 2h 19m 16s.\n",
-      "Computing the boundary of the generator 12/23 (dimension 5) :\n",
-      "<<AlLp[4 <<AlLp[3 <<AlLp[4 N5]>>][2 <<AlLp[3 M4]>>]>>][1 <<AlLp[2 <<AlLp[3 M4]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-02-26, 2h 19m 16s.\n",
-      "Computing the boundary of the generator 13/23 (dimension 5) :\n",
-      "<<AlLp[1 <<AlLp[2 <<AlLp[3 M4]>>]>>][1 <<AlLp[2 <<AlLp[3 M4]>>]>>][3 <<AlLp[2 <<AlLp[3 M4]>>][2 <<AlLp[3 M4]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-02-26, 2h 19m 16s.\n",
-      "Computing the boundary of the generator 14/23 (dimension 5) :\n",
-      "<<AlLp[1 <<AlLp[2 <<AlLp[3 M4]>>]>>][2 <<AlLp[3 <<AlLp[4 N5]>>]>>][2 <<AlLp[3 <<AlLp[4 N5]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-02-26, 2h 19m 16s.\n",
-      "Computing the boundary of the generator 15/23 (dimension 5) :\n",
-      "<<AlLp[1 <<AlLp[2 <<AlLp[3 M4]>>]>>][3 <<AlLp[2 <<AlLp[3 M4]>>][2 <<AlLp[3 M4]>>]>>][1 <<AlLp[2 <<AlLp[3 M4]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-02-26, 2h 19m 16s.\n",
-      "Computing the boundary of the generator 16/23 (dimension 5) :\n",
-      "<<AlLp[2 <<AlLp[3 <<AlLp[4 N5]>>]>>][1 <<AlLp[2 <<AlLp[3 M4]>>]>>][2 <<AlLp[3 <<AlLp[4 N5]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-02-26, 2h 19m 16s.\n",
-      "Computing the boundary of the generator 17/23 (dimension 5) :\n",
-      "<<AlLp[2 <<AlLp[3 <<AlLp[4 N5]>>]>>][2 <<AlLp[3 <<AlLp[4 N5]>>]>>][1 <<AlLp[2 <<AlLp[3 M4]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-02-26, 2h 19m 16s.\n",
-      "Computing the boundary of the generator 18/23 (dimension 5) :\n",
-      "<<AlLp[3 <<AlLp[2 <<AlLp[3 M4]>>][2 <<AlLp[3 M4]>>]>>][1 <<AlLp[2 <<AlLp[3 M4]>>]>>][1 <<AlLp[2 <<AlLp[3 M4]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-02-26, 2h 19m 16s.\n",
-      "Computing the boundary of the generator 19/23 (dimension 5) :\n",
-      "<<AlLp[1 <<AlLp[2 <<AlLp[3 M4]>>]>>][1 <<AlLp[2 <<AlLp[3 M4]>>]>>][1 <<AlLp[2 <<AlLp[3 M4]>>]>>][2 <<AlLp[3 <<AlLp[4 N5]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-02-26, 2h 19m 16s.\n",
-      "Computing the boundary of the generator 20/23 (dimension 5) :\n",
-      "<<AlLp[1 <<AlLp[2 <<AlLp[3 M4]>>]>>][1 <<AlLp[2 <<AlLp[3 M4]>>]>>][2 <<AlLp[3 <<AlLp[4 N5]>>]>>][1 <<AlLp[2 <<AlLp[3 M4]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-02-26, 2h 19m 16s.\n",
-      "Computing the boundary of the generator 21/23 (dimension 5) :\n",
-      "<<AlLp[1 <<AlLp[2 <<AlLp[3 M4]>>]>>][2 <<AlLp[3 <<AlLp[4 N5]>>]>>][1 <<AlLp[2 <<AlLp[3 M4]>>]>>][1 <<AlLp[2 <<AlLp[3 M4]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-02-26, 2h 19m 16s.\n",
-      "Computing the boundary of the generator 22/23 (dimension 5) :\n",
-      "<<AlLp[2 <<AlLp[3 <<AlLp[4 N5]>>]>>][1 <<AlLp[2 <<AlLp[3 M4]>>]>>][1 <<AlLp[2 <<AlLp[3 M4]>>]>>][1 <<AlLp[2 <<AlLp[3 M4]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-02-26, 2h 19m 16s.\n",
-      "Computing the boundary of the generator 23/23 (dimension 5) :\n",
-      "<<AlLp[1 <<AlLp[2 <<AlLp[3 M4]>>]>>][1 <<AlLp[2 <<AlLp[3 M4]>>]>>][1 <<AlLp[2 <<AlLp[3 M4]>>]>>][1 <<AlLp[2 <<AlLp[3 M4]>>]>>][1 <<AlLp[2 <<AlLp[3 M4]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 6.\n",
-      "Rank of the source-module : 53.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-02-26, 2h 19m 16s.\n",
-      "Computing the boundary of the generator 1/53 (dimension 6) :\n",
-      "<<AlLp[6 <<AlLp[7 <<AlLp[4 N5][4 N5]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-02-26, 2h 19m 16s.\n",
-      "Computing the boundary of the generator 2/53 (dimension 6) :\n",
-      "<<AlLp[6 <<AlLp[2 <<AlLp[3 M4]>>][5 <<AlLp[3 M4][3 M4]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-02-26, 2h 19m 16s.\n",
-      "Computing the boundary of the generator 3/53 (dimension 6) :\n",
-      "<<AlLp[6 <<AlLp[5 <<AlLp[3 M4][3 M4]>>][2 <<AlLp[3 M4]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-02-26, 2h 19m 17s.\n",
-      "Computing the boundary of the generator 4/53 (dimension 6) :\n",
-      "<<AlLp[6 <<AlLp[2 <<AlLp[3 M4]>>][2 <<AlLp[3 M4]>>][3 <<AlLp[4 N5]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-02-26, 2h 19m 17s.\n",
-      "Computing the boundary of the generator 5/53 (dimension 6) :\n",
-      "<<AlLp[6 <<AlLp[2 <<AlLp[3 M4]>>][3 <<AlLp[4 N5]>>][2 <<AlLp[3 M4]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-02-26, 2h 19m 17s.\n",
-      "Computing the boundary of the generator 6/53 (dimension 6) :\n",
-      "<<AlLp[6 <<AlLp[3 <<AlLp[4 N5]>>][2 <<AlLp[3 M4]>>][2 <<AlLp[3 M4]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-02-26, 2h 19m 17s.\n",
-      "Computing the boundary of the generator 7/53 (dimension 6) :\n",
-      "<<AlLp[1 <<AlLp[2 <<AlLp[3 M4]>>]>>][5 <<AlLp[6 <<AlLp[3 M4][4 N5]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-02-26, 2h 19m 17s.\n",
-      "Computing the boundary of the generator 8/53 (dimension 6) :\n",
-      "<<AlLp[1 <<AlLp[2 <<AlLp[3 M4]>>]>>][5 <<AlLp[6 <<AlLp[4 N5][3 M4]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-02-26, 2h 19m 17s.\n",
-      "Computing the boundary of the generator 9/53 (dimension 6) :\n",
-      "<<AlLp[1 <<AlLp[2 <<AlLp[3 M4]>>]>>][5 <<AlLp[3 <<AlLp[4 N5]>>][3 <<AlLp[4 N5]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-02-26, 2h 19m 17s.\n",
-      "Computing the boundary of the generator 10/53 (dimension 6) :\n",
-      "<<AlLp[1 <<AlLp[2 <<AlLp[3 M4]>>]>>][5 <<AlLp[2 <<AlLp[3 M4]>>][2 <<AlLp[3 M4]>>][2 <<AlLp[3 M4]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-02-26, 2h 19m 17s.\n",
-      "Computing the boundary of the generator 11/53 (dimension 6) :\n",
-      "<<AlLp[2 <<AlLp[3 <<AlLp[4 N5]>>]>>][4 <<AlLp[5 <<AlLp[3 M4][3 M4]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-02-26, 2h 19m 17s.\n",
-      "Computing the boundary of the generator 12/53 (dimension 6) :\n",
-      "<<AlLp[2 <<AlLp[3 <<AlLp[4 N5]>>]>>][4 <<AlLp[2 <<AlLp[3 M4]>>][3 <<AlLp[4 N5]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-02-26, 2h 19m 17s.\n",
-      "Computing the boundary of the generator 13/53 (dimension 6) :\n",
-      "<<AlLp[2 <<AlLp[3 <<AlLp[4 N5]>>]>>][4 <<AlLp[3 <<AlLp[4 N5]>>][2 <<AlLp[3 M4]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-02-26, 2h 19m 17s.\n",
-      "Computing the boundary of the generator 14/53 (dimension 6) :\n",
-      "<<AlLp[3 <<AlLp[2 <<AlLp[3 M4]>>][2 <<AlLp[3 M4]>>]>>][3 <<AlLp[2 <<AlLp[3 M4]>>][2 <<AlLp[3 M4]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-02-26, 2h 19m 17s.\n",
-      "Computing the boundary of the generator 15/53 (dimension 6) :\n",
-      "<<AlLp[4 <<AlLp[5 <<AlLp[3 M4][3 M4]>>]>>][2 <<AlLp[3 <<AlLp[4 N5]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-02-26, 2h 19m 17s.\n",
-      "Computing the boundary of the generator 16/53 (dimension 6) :\n",
-      "<<AlLp[4 <<AlLp[2 <<AlLp[3 M4]>>][3 <<AlLp[4 N5]>>]>>][2 <<AlLp[3 <<AlLp[4 N5]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-02-26, 2h 19m 17s.\n",
-      "Computing the boundary of the generator 17/53 (dimension 6) :\n",
-      "<<AlLp[4 <<AlLp[3 <<AlLp[4 N5]>>][2 <<AlLp[3 M4]>>]>>][2 <<AlLp[3 <<AlLp[4 N5]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-02-26, 2h 19m 17s.\n",
-      "Computing the boundary of the generator 18/53 (dimension 6) :\n",
-      "<<AlLp[5 <<AlLp[6 <<AlLp[3 M4][4 N5]>>]>>][1 <<AlLp[2 <<AlLp[3 M4]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-02-26, 2h 19m 17s.\n",
-      "Computing the boundary of the generator 19/53 (dimension 6) :\n",
-      "<<AlLp[5 <<AlLp[6 <<AlLp[4 N5][3 M4]>>]>>][1 <<AlLp[2 <<AlLp[3 M4]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-02-26, 2h 19m 17s.\n",
-      "Computing the boundary of the generator 20/53 (dimension 6) :\n",
-      "<<AlLp[5 <<AlLp[3 <<AlLp[4 N5]>>][3 <<AlLp[4 N5]>>]>>][1 <<AlLp[2 <<AlLp[3 M4]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-02-26, 2h 19m 17s.\n",
-      "Computing the boundary of the generator 21/53 (dimension 6) :\n",
-      "<<AlLp[5 <<AlLp[2 <<AlLp[3 M4]>>][2 <<AlLp[3 M4]>>][2 <<AlLp[3 M4]>>]>>][1 <<AlLp[2 <<AlLp[3 M4]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-02-26, 2h 19m 17s.\n",
-      "Computing the boundary of the generator 22/53 (dimension 6) :\n",
-      "<<AlLp[1 <<AlLp[2 <<AlLp[3 M4]>>]>>][1 <<AlLp[2 <<AlLp[3 M4]>>]>>][4 <<AlLp[5 <<AlLp[3 M4][3 M4]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-02-26, 2h 19m 17s.\n",
-      "Computing the boundary of the generator 23/53 (dimension 6) :\n",
-      "<<AlLp[1 <<AlLp[2 <<AlLp[3 M4]>>]>>][1 <<AlLp[2 <<AlLp[3 M4]>>]>>][4 <<AlLp[2 <<AlLp[3 M4]>>][3 <<AlLp[4 N5]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-02-26, 2h 19m 17s.\n",
-      "Computing the boundary of the generator 24/53 (dimension 6) :\n",
-      "<<AlLp[1 <<AlLp[2 <<AlLp[3 M4]>>]>>][1 <<AlLp[2 <<AlLp[3 M4]>>]>>][4 <<AlLp[3 <<AlLp[4 N5]>>][2 <<AlLp[3 M4]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-02-26, 2h 19m 17s.\n",
-      "Computing the boundary of the generator 25/53 (dimension 6) :\n",
-      "<<AlLp[1 <<AlLp[2 <<AlLp[3 M4]>>]>>][2 <<AlLp[3 <<AlLp[4 N5]>>]>>][3 <<AlLp[2 <<AlLp[3 M4]>>][2 <<AlLp[3 M4]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-02-26, 2h 19m 17s.\n",
-      "Computing the boundary of the generator 26/53 (dimension 6) :\n",
-      "<<AlLp[1 <<AlLp[2 <<AlLp[3 M4]>>]>>][3 <<AlLp[2 <<AlLp[3 M4]>>][2 <<AlLp[3 M4]>>]>>][2 <<AlLp[3 <<AlLp[4 N5]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-02-26, 2h 19m 17s.\n",
-      "Computing the boundary of the generator 27/53 (dimension 6) :\n",
-      "<<AlLp[1 <<AlLp[2 <<AlLp[3 M4]>>]>>][4 <<AlLp[5 <<AlLp[3 M4][3 M4]>>]>>][1 <<AlLp[2 <<AlLp[3 M4]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-02-26, 2h 19m 17s.\n",
-      "Computing the boundary of the generator 28/53 (dimension 6) :\n",
-      "<<AlLp[1 <<AlLp[2 <<AlLp[3 M4]>>]>>][4 <<AlLp[2 <<AlLp[3 M4]>>][3 <<AlLp[4 N5]>>]>>][1 <<AlLp[2 <<AlLp[3 M4]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-02-26, 2h 19m 17s.\n",
-      "Computing the boundary of the generator 29/53 (dimension 6) :\n",
-      "<<AlLp[1 <<AlLp[2 <<AlLp[3 M4]>>]>>][4 <<AlLp[3 <<AlLp[4 N5]>>][2 <<AlLp[3 M4]>>]>>][1 <<AlLp[2 <<AlLp[3 M4]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-02-26, 2h 19m 17s.\n",
-      "Computing the boundary of the generator 30/53 (dimension 6) :\n",
-      "<<AlLp[2 <<AlLp[3 <<AlLp[4 N5]>>]>>][1 <<AlLp[2 <<AlLp[3 M4]>>]>>][3 <<AlLp[2 <<AlLp[3 M4]>>][2 <<AlLp[3 M4]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-02-26, 2h 19m 17s.\n",
-      "Computing the boundary of the generator 31/53 (dimension 6) :\n",
-      "<<AlLp[2 <<AlLp[3 <<AlLp[4 N5]>>]>>][2 <<AlLp[3 <<AlLp[4 N5]>>]>>][2 <<AlLp[3 <<AlLp[4 N5]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-02-26, 2h 19m 17s.\n",
-      "Computing the boundary of the generator 32/53 (dimension 6) :\n",
-      "<<AlLp[2 <<AlLp[3 <<AlLp[4 N5]>>]>>][3 <<AlLp[2 <<AlLp[3 M4]>>][2 <<AlLp[3 M4]>>]>>][1 <<AlLp[2 <<AlLp[3 M4]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-02-26, 2h 19m 17s.\n",
-      "Computing the boundary of the generator 33/53 (dimension 6) :\n",
-      "<<AlLp[3 <<AlLp[2 <<AlLp[3 M4]>>][2 <<AlLp[3 M4]>>]>>][1 <<AlLp[2 <<AlLp[3 M4]>>]>>][2 <<AlLp[3 <<AlLp[4 N5]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-02-26, 2h 19m 17s.\n",
-      "Computing the boundary of the generator 34/53 (dimension 6) :\n",
-      "<<AlLp[3 <<AlLp[2 <<AlLp[3 M4]>>][2 <<AlLp[3 M4]>>]>>][2 <<AlLp[3 <<AlLp[4 N5]>>]>>][1 <<AlLp[2 <<AlLp[3 M4]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-02-26, 2h 19m 18s.\n",
-      "Computing the boundary of the generator 35/53 (dimension 6) :\n",
-      "<<AlLp[4 <<AlLp[5 <<AlLp[3 M4][3 M4]>>]>>][1 <<AlLp[2 <<AlLp[3 M4]>>]>>][1 <<AlLp[2 <<AlLp[3 M4]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-02-26, 2h 19m 18s.\n",
-      "Computing the boundary of the generator 36/53 (dimension 6) :\n",
-      "<<AlLp[4 <<AlLp[2 <<AlLp[3 M4]>>][3 <<AlLp[4 N5]>>]>>][1 <<AlLp[2 <<AlLp[3 M4]>>]>>][1 <<AlLp[2 <<AlLp[3 M4]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-02-26, 2h 19m 18s.\n",
-      "Computing the boundary of the generator 37/53 (dimension 6) :\n",
-      "<<AlLp[4 <<AlLp[3 <<AlLp[4 N5]>>][2 <<AlLp[3 M4]>>]>>][1 <<AlLp[2 <<AlLp[3 M4]>>]>>][1 <<AlLp[2 <<AlLp[3 M4]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-02-26, 2h 19m 18s.\n",
-      "Computing the boundary of the generator 38/53 (dimension 6) :\n",
-      "<<AlLp[1 <<AlLp[2 <<AlLp[3 M4]>>]>>][1 <<AlLp[2 <<AlLp[3 M4]>>]>>][1 <<AlLp[2 <<AlLp[3 M4]>>]>>][3 <<AlLp[2 <<AlLp[3 M4]>>][2 <<AlLp[3 M4]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-02-26, 2h 19m 18s.\n",
-      "Computing the boundary of the generator 39/53 (dimension 6) :\n",
-      "<<AlLp[1 <<AlLp[2 <<AlLp[3 M4]>>]>>][1 <<AlLp[2 <<AlLp[3 M4]>>]>>][2 <<AlLp[3 <<AlLp[4 N5]>>]>>][2 <<AlLp[3 <<AlLp[4 N5]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-02-26, 2h 19m 18s.\n",
-      "Computing the boundary of the generator 40/53 (dimension 6) :\n",
-      "<<AlLp[1 <<AlLp[2 <<AlLp[3 M4]>>]>>][1 <<AlLp[2 <<AlLp[3 M4]>>]>>][3 <<AlLp[2 <<AlLp[3 M4]>>][2 <<AlLp[3 M4]>>]>>][1 <<AlLp[2 <<AlLp[3 M4]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-02-26, 2h 19m 18s.\n",
-      "Computing the boundary of the generator 41/53 (dimension 6) :\n",
-      "<<AlLp[1 <<AlLp[2 <<AlLp[3 M4]>>]>>][2 <<AlLp[3 <<AlLp[4 N5]>>]>>][1 <<AlLp[2 <<AlLp[3 M4]>>]>>][2 <<AlLp[3 <<AlLp[4 N5]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-02-26, 2h 19m 18s.\n",
-      "Computing the boundary of the generator 42/53 (dimension 6) :\n",
-      "<<AlLp[1 <<AlLp[2 <<AlLp[3 M4]>>]>>][2 <<AlLp[3 <<AlLp[4 N5]>>]>>][2 <<AlLp[3 <<AlLp[4 N5]>>]>>][1 <<AlLp[2 <<AlLp[3 M4]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-02-26, 2h 19m 18s.\n",
-      "Computing the boundary of the generator 43/53 (dimension 6) :\n",
-      "<<AlLp[1 <<AlLp[2 <<AlLp[3 M4]>>]>>][3 <<AlLp[2 <<AlLp[3 M4]>>][2 <<AlLp[3 M4]>>]>>][1 <<AlLp[2 <<AlLp[3 M4]>>]>>][1 <<AlLp[2 <<AlLp[3 M4]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-02-26, 2h 19m 18s.\n",
-      "Computing the boundary of the generator 44/53 (dimension 6) :\n",
-      "<<AlLp[2 <<AlLp[3 <<AlLp[4 N5]>>]>>][1 <<AlLp[2 <<AlLp[3 M4]>>]>>][1 <<AlLp[2 <<AlLp[3 M4]>>]>>][2 <<AlLp[3 <<AlLp[4 N5]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-02-26, 2h 19m 18s.\n",
-      "Computing the boundary of the generator 45/53 (dimension 6) :\n",
-      "<<AlLp[2 <<AlLp[3 <<AlLp[4 N5]>>]>>][1 <<AlLp[2 <<AlLp[3 M4]>>]>>][2 <<AlLp[3 <<AlLp[4 N5]>>]>>][1 <<AlLp[2 <<AlLp[3 M4]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-02-26, 2h 19m 18s.\n",
-      "Computing the boundary of the generator 46/53 (dimension 6) :\n",
-      "<<AlLp[2 <<AlLp[3 <<AlLp[4 N5]>>]>>][2 <<AlLp[3 <<AlLp[4 N5]>>]>>][1 <<AlLp[2 <<AlLp[3 M4]>>]>>][1 <<AlLp[2 <<AlLp[3 M4]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-02-26, 2h 19m 18s.\n",
-      "Computing the boundary of the generator 47/53 (dimension 6) :\n",
-      "<<AlLp[3 <<AlLp[2 <<AlLp[3 M4]>>][2 <<AlLp[3 M4]>>]>>][1 <<AlLp[2 <<AlLp[3 M4]>>]>>][1 <<AlLp[2 <<AlLp[3 M4]>>]>>][1 <<AlLp[2 <<AlLp[3 M4]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-02-26, 2h 19m 18s.\n",
-      "Computing the boundary of the generator 48/53 (dimension 6) :\n",
-      "<<AlLp[1 <<AlLp[2 <<AlLp[3 M4]>>]>>][1 <<AlLp[2 <<AlLp[3 M4]>>]>>][1 <<AlLp[2 <<AlLp[3 M4]>>]>>][1 <<AlLp[2 <<AlLp[3 M4]>>]>>][2 <<AlLp[3 <<AlLp[4 N5]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-02-26, 2h 19m 18s.\n",
-      "Computing the boundary of the generator 49/53 (dimension 6) :\n",
-      "<<AlLp[1 <<AlLp[2 <<AlLp[3 M4]>>]>>][1 <<AlLp[2 <<AlLp[3 M4]>>]>>][1 <<AlLp[2 <<AlLp[3 M4]>>]>>][2 <<AlLp[3 <<AlLp[4 N5]>>]>>][1 <<AlLp[2 <<AlLp[3 M4]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-02-26, 2h 19m 18s.\n",
-      "Computing the boundary of the generator 50/53 (dimension 6) :\n",
-      "<<AlLp[1 <<AlLp[2 <<AlLp[3 M4]>>]>>][1 <<AlLp[2 <<AlLp[3 M4]>>]>>][2 <<AlLp[3 <<AlLp[4 N5]>>]>>][1 <<AlLp[2 <<AlLp[3 M4]>>]>>][1 <<AlLp[2 <<AlLp[3 M4]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-02-26, 2h 19m 18s.\n",
-      "Computing the boundary of the generator 51/53 (dimension 6) :\n",
-      "<<AlLp[1 <<AlLp[2 <<AlLp[3 M4]>>]>>][2 <<AlLp[3 <<AlLp[4 N5]>>]>>][1 <<AlLp[2 <<AlLp[3 M4]>>]>>][1 <<AlLp[2 <<AlLp[3 M4]>>]>>][1 <<AlLp[2 <<AlLp[3 M4]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-02-26, 2h 19m 18s.\n",
-      "Computing the boundary of the generator 52/53 (dimension 6) :\n",
-      "<<AlLp[2 <<AlLp[3 <<AlLp[4 N5]>>]>>][1 <<AlLp[2 <<AlLp[3 M4]>>]>>][1 <<AlLp[2 <<AlLp[3 M4]>>]>>][1 <<AlLp[2 <<AlLp[3 M4]>>]>>][1 <<AlLp[2 <<AlLp[3 M4]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-02-26, 2h 19m 18s.\n",
-      "Computing the boundary of the generator 53/53 (dimension 6) :\n",
-      "<<AlLp[1 <<AlLp[2 <<AlLp[3 M4]>>]>>][1 <<AlLp[2 <<AlLp[3 M4]>>]>>][1 <<AlLp[2 <<AlLp[3 M4]>>]>>][1 <<AlLp[2 <<AlLp[3 M4]>>]>>][1 <<AlLp[2 <<AlLp[3 M4]>>]>>][1 <<AlLp[2 <<AlLp[3 M4]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 5 :\n",
-      "\n",
-      "\n",
-      "Component Z/2Z\n",
-      "\n",
-      "Component Z/2Z\n",
-      "\n",
-      "Component Z/2Z\n",
-      "\n",
-      "Component Z/2Z\n",
-      "\n",
-      "Component Z/2Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-02-26, 2h 19m 19s.\n",
-      "\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 169,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(homology o3m4 5)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "and the result $H_5 \\Omega^3 \\mathrm{Moore}(\\mathbb{Z}_2,4) = \\mathbb{Z}_2^5$ is obtained in 1m30s with a PC 400MHZ. In natural situations a little more complicated, the Kenzo program has already computed new homology groups unreachable so far with \"classical\" Algebraic Topology, even from a theoretical point of view.\n",
-    "\n",
-    "## Kenzo classes.\n",
-    "\n",
-    "> This class hierarchy applies to the [older version of Kenzo](https://github.com/gheber/kenzo/tree/master/archive/Kenzo-2).\n",
-    "\n",
-    "![](kenzo-class-diagram.png)\n",
-    "\n",
-    "In the figure, the class diagram of Kenzo objects is shown. The situation is to be compared with which was explained in [Section 4](#CLOS-and-Mathematical-Structures.) about the most elementary mathematical structures. The lefthand part of the class diagram is made of the main mathematical categories that are used in combinatorial Algebraic Topology. A *chain complex* is a graded differential module; an *algebra* is a chain complex with a compatible multiplicative structure, the same for a *coalgebra* but with a comultiplicative[<sup>17</sup>](#footnote_17) structure. If a multiplicative and a comultiplicative structures are added and if they are compatible with each other in a natural sense, then it is a *Hopf algebra*, and so on.\n",
-    "\n",
-    "<a id='footnote_17'><sup>17</sup></a> That is, some *co*operator $A \\rightarrow A \\otimes A$.\n",
-    "\n",
-    "The `hopf-algebra` and `simplicial-group` classes are typical cases where a *multiple inheritance* situation is met; we show the `actual` Kenzo definitions of these classes.\n",
-    "\n",
-    "```lisp\n",
-    "(DEFCLASS HOPF-ALGEBRA (coalgebra algebra)\n",
-    "          ())\n",
-    "    \n",
-    "(DEFCLASS SIMPLICIAL-GROUP (kan hopf-algebra)\n",
-    "          ((grml :type simplicial-mrph :reader grml1)\n",
-    "           (grin :type simplicial-mrph :reader grin1)))\n",
-    "```\n",
-    "\n",
-    "You see the definition of the *hopf-algebra* class is particularly striking; it explains that a Hopf-algebra is nothing but an algebra *and* a coalgebra; the compatibility conditions between both structures *cannot* be verified by a program and they necessarily depend on the programmer's \"lucidity\". In the same way, a *simplicial group* is a *kan* object and a `hopf-algebra` object sharing some common data, namely a coalgebra structure, with two further slots, `grml` (group\n",
-    "multiplication) and `grin` (group inversion), those slots being some simplicial morphisms.\n",
-    "\n",
-    "In such a multiple inheritance situation, it is important the `call-next-method` function works as hoped-for. Look at this artificial situation just to show the process; The `C` class has two subclasses `CD` and `CE`, which have in common the subclass `CDE`; the artificial `initialize-instance` methods let you verify that `call-next-method` *remembers its story* when deciding what really the *next method* must be. Here, when processing the `CD`-level, `call-next-method` \"remembers\" the process was initiated from the `CDE`-level, so that the `CE`-level stage is not forgotten.\n",
-    "\n",
-    "![](cde.png)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 170,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "#<STANDARD-CLASS CL-JUPYTER-USER::C>"
-      ]
-     },
-     "execution_count": 170,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(defclass C () ())"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 171,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "#<STANDARD-CLASS CL-JUPYTER-USER::CD>"
-      ]
-     },
-     "execution_count": 171,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(defclass CD (C) ())"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 172,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "#<STANDARD-CLASS CL-JUPYTER-USER::CE>"
-      ]
-     },
-     "execution_count": 172,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(defclass CE (C) ())"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 173,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "#<STANDARD-CLASS CL-JUPYTER-USER::CDE>"
-      ]
-     },
-     "execution_count": 173,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(defclass CDE (CD CE) ())"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 174,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "#<STANDARD-METHOD COMMON-LISP:INITIALIZE-INSTANCE (C) {10055B7993}>"
-      ]
-     },
-     "execution_count": 174,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(defmethod initialize-instance ((c c) &rest rest)\n",
-    "    (declare (ignore rest))\n",
-    "    (print \"C-initialization\"))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 175,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "#<STANDARD-METHOD COMMON-LISP:INITIALIZE-INSTANCE (CD) {100580EFD3}>"
-      ]
-     },
-     "execution_count": 175,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(defmethod initialize-instance ((cd cd) &rest rest)\n",
-    "    (declare (ignore rest))\n",
-    "    (print \"beginning CD-initialization\")\n",
-    "    (call-next-method)\n",
-    "    (print \"finishing CD-initialization\"))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 176,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "#<STANDARD-METHOD COMMON-LISP:INITIALIZE-INSTANCE (CE) {1005A66013}>"
-      ]
-     },
-     "execution_count": 176,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(defmethod initialize-instance ((ce ce) &rest rest)\n",
-    "    (declare (ignore rest))\n",
-    "    (print \"beginning CE-initialization\")\n",
-    "    (call-next-method)\n",
-    "    (print \"finishing CE-initialization\"))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 177,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "#<STANDARD-METHOD COMMON-LISP:INITIALIZE-INSTANCE (CDE) {1005CDDA23}>"
-      ]
-     },
-     "execution_count": 177,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(defmethod initialize-instance ((cde cde) &rest rest)\n",
-    "    (declare (ignore rest))\n",
-    "    (print \"beginning CDE-initialization\")\n",
-    "    (call-next-method)\n",
-    "    (print \"finishing CDE-initialization\"))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 178,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "\"C-initialization\" "
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "#<C {1005D3FE63}>"
-      ]
-     },
-     "execution_count": 178,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(make-instance 'C)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 179,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "\"beginning CD-initialization\" \n",
-      "\"C-initialization\" \n",
-      "\"finishing CD-initialization\" "
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "#<CD {1005DA9813}>"
-      ]
-     },
-     "execution_count": 179,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(make-instance 'CD)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 180,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "\"beginning CE-initialization\" \n",
-      "\"C-initialization\" \n",
-      "\"finishing CE-initialization\" "
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "#<CE {1005E2BF93}>"
-      ]
-     },
-     "execution_count": 180,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(make-instance 'CE)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 181,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "\"beginning CDE-initialization\" \n",
-      "\"beginning CD-initialization\" \n",
-      "\"beginning CE-initialization\" \n",
-      "\"C-initialization\" \n",
-      "\"finishing CE-initialization\" \n",
-      "\"finishing CD-initialization\" \n",
-      "\"finishing CDE-initialization\" "
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "#<CDE {1005E970C3}>"
-      ]
-     },
-     "execution_count": 181,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(make-instance 'CDE)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "And you may also play with the *auxiliary* `:before`, `:after` and `:around` methods to order as you like the various initialization steps. As a typical example, when the essential part of the initialization work of any `kenzo-object` is done, then the object is *finally* pushed in a list which is used later as explained in the next section. This is obtained as follows.\n",
-    "\n",
-    "```lisp\n",
-    "(DEFMETHOD INITIALIZE-INSTANCE :after ((k kenzo-object) &rest rest)\n",
-    "           (push k *k-list*))\n",
-    "```\n",
-    "\n",
-    "In this way this is done if and only if the initialization work is successfully finished, even for the more specialized structures: if for example the specialized initialization work for a simplicial set fails and stops on error, then the pushing statement concerning the weakest structure is not run.\n",
-    "\n",
-    "## Optimizing computations.\n",
-    "\n",
-    "The Kenzo program is certainly one of the most *functional* programs ever written down. It is frequent that several thousands of functions are present in memory, each one being *dynamically* defined from other ones, which in turn are defined from other ones, and so on. In this quite original situation, the same calculations are frequently *asked again*. To avoid repeating these calculations, it is better to store the results and to systematically examine for each calculation whether the result is already available.\n",
-    "\n",
-    "Because of this situation, it is very important not to have *several copies* of the same function; otherwise it is impossible for one copy to guess some calculation has already been done by another copy. This is a very important question in this program, so that the following strategy has been used. Each Kenzo object has a rigorous *definition*, stored as a list in the `dfnt` slot of the object. This is the main reason of the top class `kenzo-object`: making easier this process. The actual definition of the `kenzo-object` class:\n",
-    "\n",
-    "```lisp\n",
-    "(DEFCLASS KENZO-OBJECT ()\n",
-    "          ((idnm :type fixnum :reader idnm)\n",
-    "           (dfnt :type list :reader dfnt)\n",
-    "           (prpr :type list :reader prpr)\n",
-    "           (cmmn :type list :reader cmmn)))\n",
-    "```\n",
-    "\n",
-    "> This class exists only in the [older version of Kenzo](https://github.com/gheber/kenzo/tree/master/archive/Kenzo-2).\n",
-    "\n",
-    "Then, when any `kenzo-object` is to be considered, its *definition* is constructed and the program firstly looks in `*k-list*` whether some object corresponding to this definition already exists; if yes, no `kenzo-object` is constructed, the already existing one is simply returned. Look at this small example where we construct the second loop space of $S^3$, then the first loop space, and then again the second loop space. In fact the initial construction of the second loop space required the first loop space, and examining the identification number `K??` of these objects shows that when the first loop space is later asked for, Kenzo is able to return the already existing one."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 182,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K405 Simplicial-Set]"
-      ]
-     },
-     "execution_count": 182,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def s3 (sphere 3))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 183,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K422 Simplicial-Group]"
-      ]
-     },
-     "execution_count": 183,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def o2s3 (loop-space s3 2))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 184,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K410 Simplicial-Group]"
-      ]
-     },
-     "execution_count": 184,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def os3 (loop-space s3 1))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 185,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K422 Simplicial-Group]"
-      ]
-     },
-     "execution_count": 185,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def o2s3-2 (loop-space s3 2))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 186,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "T"
-      ]
-     },
-     "execution_count": 186,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(eq o2s3 o2s3-2)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "The last statement shows the symbols `o2s3` and `o2s3-2` points to the same machine address. In this way we are sure any kenzo-object has no duplicate, so that the memory process for the values of numerous functions cannot miss an already computed result. Let us look some `dfnt` slots:\n",
-    "\n",
-    "> In the newer version of Kenzo, the slot name is `orgn` for *origin*."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 187,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(LOOP-SPACE [K410 Simplicial-Group])"
-      ]
-     },
-     "execution_count": 187,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(orgn o2s3)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 188,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(LOOP-SPACE [K405 Simplicial-Set])"
-      ]
-     },
-     "execution_count": 188,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(orgn (k 410))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 189,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(SPHERE 3)"
-      ]
-     },
-     "execution_count": 189,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(orgn (k 405))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "You see in this way the history of the construction process can be freely examined by the user, which is important in the development stage.\n",
-    "\n",
-    "## Delaying initializations.\n",
-    "\n",
-    "The complete structure of a Kenzo object is extremely complicated, and many components are often useless. Another CLOS feature is therefore used to avoid the maybe non-necessary initialization works. The following artificial example explains how this is possible; it is a kind of \\emph{autoloading} mechanism, elegant, easy to be used, and useful to avoid initializing needless slots. We assume a `C` class, where each `C` object has two slots, `sl1` and `sl2`; the first one is necessary, but the second one would be the result of a *complex* process here simulated as being 1000 times the value of the first one."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 190,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "#<STANDARD-CLASS CAT:F>"
-      ]
-     },
-     "execution_count": 190,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(DEFCLASS F ()\n",
-    "          ((sl1 :type integer :initarg :sl1 :reader sl1)\n",
-    "           (sl2 :type integer :reader sl2)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 191,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "#<STANDARD-METHOD COMMON-LISP:SLOT-UNBOUND (T F (EQL SL2)) {10063DB733}>"
-      ]
-     },
-     "execution_count": 191,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(DEFMETHOD SLOT-UNBOUND (class (fi f) (slot-name (eql 'sl2)))\n",
-    "           (declare (ignore class))\n",
-    "           (setf (slot-value fi 'sl2) (* 1000 (sl1 fi)))\n",
-    "           (sl2 fi))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 192,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "FI"
-      ]
-     },
-     "execution_count": 192,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(DEFVAR FI (make-instance 'f :sl1 23))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 193,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 193,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(SLOT-BOUNDP fi 'sl2)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 194,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "23000"
-      ]
-     },
-     "execution_count": 194,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(sl2 fi)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 195,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "T"
-      ]
-     },
-     "execution_count": 195,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(SLOT-BOUNDP fi 'sl2)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "You see the generic function `slot-unbound` is available which is called by the error manager when a non-initialized slot is asked for. The standard process finally does generate an error. But the user can write specialized methods for this generic function, allowing him instead to initialize the missing slot by some process using the available information. You see the initialization process lets uninitialized the `sl2` slot of the `F`-instance located by `fi`, but when this slot is asked for, the \"right\" value is in fact returned! A new examination by `slot-boundp` shows the slot is now bound.\n",
-    "\n",
-    "This process is extremely convenient to organize the data as a living object where each time some missing component is questionned, an automatic \"repairing process\" is started, computing the missing information. The process may be recursive, so that if, in the repairing process, some other datum is again missing, another repairing process is recursively started, and so on.\n",
-    "\n",
-    "> The following discussion (counters) applies to the [older version of Kenzo](https://github.com/gheber/kenzo/tree/master/archive/Kenzo-2).\n",
-    "\n",
-    "This possibility is intensively used in the Kenzo program. Look at this small example. Firstly we reinitialize the environment by `cat-init`. When the fourth loop space $\\Omega^4 S^5$ is constructed, you see only 26 Kenzo objects are present in the environment. Then the homology group $H_2 \\Omega^4 S^5$ is asked for. The answer, $\\mathbb{Z}_2$ is quickly obtained, but the number of present Kenzo objects is now 504; an enormous set of `slot-unbound` calls has generated the construction of 478 new Kenzo objects, necessary to do the calculation. Furthermore a `:before` method had been added just to count the number of `slot-unbound` calls, a convenient debugging trick; you see the homology calculation has recursively generated 240 `slot-unbound` calls."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 196,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "---done---"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 196,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(cat-init)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 197,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K1 Simplicial-Set]"
-      ]
-     },
-     "execution_count": 197,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def s5 (sphere 5))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 198,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[K42 Simplicial-Group]"
-      ]
-     },
-     "execution_count": 198,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(def o4s5 (loop-space s5 4))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 199,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "     4 SMGRs\n",
-      "     0 KANs\n",
-      "     8 SMMRs\n",
-      "     9 SMSTs\n",
-      "     0 HOPFs\n",
-      "     0 ALGBs\n",
-      "     9 CLGBs\n",
-      "     0 HMEQs\n",
-      "     0 RDCTs\n",
-      "    35 MRPHs\n",
-      "    18 CHCMs\n",
-      "---done---"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 199,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(how-many-objects)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 200,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "COUNTER"
-      ]
-     },
-     "execution_count": 200,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(defparameter counter 0)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 201,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "#<STANDARD-METHOD COMMON-LISP:SLOT-UNBOUND :BEFORE (T T T) {1006853193}>"
-      ]
-     },
-     "execution_count": 201,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(defmethod slot-unbound :before (class instance slot)\n",
-    "    (declare (ignore class instance slot))\n",
-    "    (incf counter))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 202,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "Computing boundary-matrix in dimension 2.\n",
-      "Rank of the source-module : 1.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-02-26, 2h 19m 19s.\n",
-      "Computing the boundary of the generator 1/1 (dimension 2) :\n",
-      "<<AlLp[1 <<AlLp[2 <<AlLp[3 <<AlLp[4 S5]>>]>>]>>][1 <<AlLp[2 <<AlLp[3 <<AlLp[4 S5]>>]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "Computing boundary-matrix in dimension 3.\n",
-      "Rank of the source-module : 2.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-02-26, 2h 19m 19s.\n",
-      "Computing the boundary of the generator 1/2 (dimension 3) :\n",
-      "<<AlLp[3 <<AlLp[2 <<AlLp[3 <<AlLp[4 S5]>>]>>][2 <<AlLp[3 <<AlLp[4 S5]>>]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      ";; Clock -> 2017-02-26, 2h 19m 19s.\n",
-      "Computing the boundary of the generator 2/2 (dimension 3) :\n",
-      "<<AlLp[1 <<AlLp[2 <<AlLp[3 <<AlLp[4 S5]>>]>>]>>][1 <<AlLp[2 <<AlLp[3 <<AlLp[4 S5]>>]>>]>>][1 <<AlLp[2 <<AlLp[3 <<AlLp[4 S5]>>]>>]>>]>> \n",
-      "End of computing.\n",
-      "\n",
-      "\n",
-      "\n",
-      "\n",
-      "Homology in dimension 2 :\n",
-      "\n",
-      "\n",
-      "Component Z/2Z\n",
-      "\n",
-      "\n",
-      "---done---\n",
-      "\n",
-      ";; Clock -> 2017-02-26, 2h 19m 19s.\n",
-      "\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 202,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(homology o4s5 2)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 203,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "     4 SMGRs\n",
-      "     0 KANs\n",
-      "     8 SMMRs\n",
-      "    17 SMSTs\n",
-      "     0 HOPFs\n",
-      "     0 ALGBs\n",
-      "    17 CLGBs\n",
-      "    16 HMEQs\n",
-      "    46 RDCTs\n",
-      "   395 MRPHs\n",
-      "    90 CHCMs\n",
-      "---done---"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 203,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(how-many-objects)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 204,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "5"
-      ]
-     },
-     "execution_count": 204,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "counter"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "## Mixing low level and high level programming.\n",
-    "\n",
-    "Computing time is crucial for the applications of the Kenzo program. The complexity of the implemented algorithms is highly exponential, so that the developer must carefully consider how he can improve the computing time of the written down Lisp code. In particular, if the heart of the program may be written close to the machine language, large amounts of computing time can be saved. But conversely this must not penalize the *readability* and the *modularity* of the program.\n",
-    "\n",
-    "Which is striking with the current version of Common Lisp is the possibility of easily mixing *low level* and *high level* programming. The features about OOP previously described in this paper show how Common Lisp is powerful in high level programming, allowing the user to directly handle the sophisticated objects of Algebraic Topology such as chain complexes, products and coproducts, Hopf algebras, simplicial sets and simplicial groups.\n",
-    "\n",
-    "iut on the other hand, the Kenzo program intensively uses the low level part of the Common Lisp language, that is, the quasi-assembler language which is the very root of the language, such as the popular (?) `car`, `cdr`, and `cons`. This is possible thanks to the Common Lisp *macrogenerator*, already mentioned [Section 3.5](#Improvements.). Let us consider the case of the type `absm`, that is, *abstract simplex*. These objects are really the most elementary consituents of the Kenzo geometric  objects, and they are so intensively used, billions of times for every sgnificant Kenzo run, that you *must not* use CLOS for these kernel structures. Kenzo defines the `absm` type as follows:\n",
-    "\n",
-    "```lisp\n",
-    "(DEFUN ABSM-P (object)\n",
-    "       (declare (type any object))\n",
-    "       (the boolean\n",
-    "            (and (consp object)\n",
-    "                 (eq :absm (car object))\n",
-    "                 (typep (cdr object) 'iabsm))))\n",
-    "\n",
-    "(DEFTYPE ABSM () '(satisfies absm-p))\n",
-    "```\n",
-    "\n",
-    "The `absm-p` function explains an `absm` is a `cons` (pair) where the lefthand component is the keyword `:absm` and the righthand one is an `iabsm`, that is, an *internal* `absm`; in the same way, elsewhere in the program, it is explained an `iabsm` is again a `cons` where the righthand component is anything and the lefthand component is a fixnum coding a *degeneracy operator*. Most of computations in Algebraic Topology are in fact low level computations about degeneracy\n",
-    "operators where such an operator is a decreasing list of small integers, like `(5 2 0)`; because this list is *strictly* decreasing, it can be represented by the fixnum 37 because $37 = 2^5 + 2^2 + 2^0$, so that all the standard calculations about degeneracy operators become fine calculations *at the bit level* on binary fixnums. But Common Lisp has all the\n",
-    "predefined functions to do such a job, so that the programmer can efficiently work according to this strategy. A considerable memory space is saved so and furthermore the calculations are much faster.\n",
-    "\n",
-    "If a degeneracy operator is to be extracted from an `absm`, the `dgop` macro is used:\n",
-    "\n",
-    "```lisp\n",
-    "(DEFMACRO DGOP (absm)\n",
-    "          `(the dgop (cadr (the cadr ,absm)))\n",
-    "```\n",
-    "\n",
-    "which explains that in fact the call of `dgop` is synonymous with a call of the assembler-like `cadr`, but the types of argument and result are verified:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 205,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "37"
-      ]
-     },
-     "execution_count": 205,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(dgop (absm 37 'something))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 206,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "TYPE-ERROR: \n",
-      "  #<TYPE-ERROR expected-type: \"ABSM\"datum: NOT-AN-ABSM>\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 206,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(dgop 'not-an-absm)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "When the program is compiled, the compiler firstly translates the source code when a macro call is found, so that it is an assembler-like statement which is compiled; furthermore an appropriate compiler option allows the compiled code to ignore or not the type verifications through the `(the ...)` statements. When the program is finalized for production work, of course these type verifications are discarded to save computing time. You see in this way the Lisp code is *readable*, this code being firstly translated in low level Lisp statements, therefore very efficiently compiled, without loosing if\n",
-    "necessary the type verifications.\n",
-    "\n",
-    "# References\n",
-    "\n",
-    "<a id='ANSI'><b>[ANSI]</b></a> [ANSI Common-Lisp.](http://www.lispworks.com/documentation/HyperSpec/Front/index.htm)\n",
-    "\n",
-    "<a id='CRML'><b>[CRML]</b></a> Gunnar Carlsson and R. James Milgram. *Stable homotopy and iterated loop spaces*. in [[JAMS]](#JAMS), pp 505-583.\n",
-    "\n",
-    "<a id='CMPS'><b>[CMPS]</b></a> [Chapter 1. Boost.Bind](http://www.boost.org/doc/libs/1_63_0/libs/bind/doc/html/bind.html#nested_binds)\n",
-    "\n",
-    "<a id='DRSS'><b>[DRSS]</b></a> Xavier Dousson, Julio Rubio, Francis Sergeraert and Yvon Siret.*The Kenzo program*. [Source](http://www-fourier.ujf-grenoble.fr/~sergerar/Kenzo/)\n",
-    "\n",
-    "<a id='JAMS'><b>[JAMS]</b></a>  *Handbook of Algebraic Topology* (Edited by I.M. James). North-Holland (1995).\n",
-    "\n",
-    "<a id='KCRB'><b>[KCRB]</b></a> Gregor Kiczales, Jim des Rivi&#232;res and Daniel G. Bobrow. *The Art of the Metaobject Protocol*. MIT Press, 1991.\n",
-    "\n",
-    "<a id='RBSR6'><b>[RBSR6]</b></a> Julio Rubio, Francis Sergeraert.*Constructive Algebraic Topology*. Talk at the EACA Conference of Tenerife, 1999. To appear in *Bulletin des Sciences Math&#233;matiques*.\n",
-    "\n",
-    "<a id='SRGR3'><b>[SRGR3]</b></a> Francis Sergeraert.*The computability problem in algebraic topology*. Advances in Mathematics, 1994, vol. 104, pp 1-29.\n",
-    "\n",
-    "<a id='SRGR5'><b>[SRGR5]</b></a> Francis Sergeraert. $\\maltese_k$, *objet du 3*<sup>e</sup> *type*. Gazette des Math&#233;maticiens, 2000, vol. 86, pp 29-45.\n",
-    "\n",
-    "<a id='STEL1'><b>[STEL1]</b></a> Guy L. Steele Jr. *Common Lisp*. Digital Press, 1984.\n",
-    "\n",
-    "<a id='STEL2'><b>[STEL2]</b></a> Guy L. Steele Jr. *Common Lisp, second edition*. Digital Press, 1990."
-   ]
-  }
- ],
- "metadata": {
-  "kernelspec": {
-   "display_name": "SBCL Lisp",
-   "language": "lisp",
-   "name": "lisp"
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-   "mimetype": "text/x-common-lisp",
-   "name": "common-lisp",
-   "pygments_lexer": "common-lisp",
-   "version": "X3J13"
-  }
- },
- "nbformat": 4,
- "nbformat_minor": 1
-}
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-{
- "cells": [
-  {
-   "cell_type": "markdown",
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-   "source": [
-    "<big><big><big><big>Functional Programming is Free</big></big></big></big>\n",
-    "\n",
-    "\n",
-    "By [*Francis Sergeraert*](https://arxiv.org/pdf/1504.00527.pdf), January 2015 \n",
-    "(Adapted for [`cl-jupyter`](https://github.com/fredokun/cl-jupyter) by Gerd Heber, March 2017)\n",
-    "\n",
-    "\n",
-    "**Abstract.** A paper [[5]](#ckmvw) has recently been published. This paper is faulty: 1) The standard requirements about the definition of an algorithm are not respected, 2) The main point in the complexity study, namely the *functional programming* component, is absent. The Editorial Board of the SIAM JC had been warned a confirmed publication would be openly commented, it is the role of this text[<sup>1</sup>](#footnote_1).\n",
-    "\n",
-    "<a id='footnote_1'><sup>1</sup></a> Kent Pitman informed me that the esoteric form `#'(lambda ...)` is no longer necessary in ANSI Common Lisp; the text is updated to the simpler form `(lambda ...)`.\n",
-    "\n",
-    "# History of the subject\n",
-    "\n",
-    "I started the subject of *Effective Homology* in 1984, trying first to implement the Edgar Brown's \"algorithm\" [[4]](#browne1) computing the homotopy groups of the finite simply connected simplicial sets. This idea was quickly understood as ridiculous; thirty years later, there remains difficult to hope for an actual implementation of this algorithm, much too complex.\n",
-    "\n",
-    "Other methods were soon imagined to overcome the essential difficulty, consisting in using the strange power of the *functional programming*. Julio Rubio's contribution was essential to make the project succeed: he understood in 1989 that the best theoretical tool to organize the work is the so-called *Basic Perturbation Lemma* [[9]](#shih), [[3]](#brownr), more and more often called now the *Homological Perturbation Theorem*, you may question `Google(Galway perturbation)` to see numerous examples.\n",
-    "\n",
-    "Using Julio's idea, a program called EAT (Effective Algebraic Topology) was soon obtained in 1990, mainly devoted to the computation of the homology groups of iterated loop spaces, already allowing us to produce homology groups so far unreachable by the \"standard\" methods.\n",
-    "\n",
-    "In the years 1995-8, Xavier Dousson's thesis was devoted to the calculation of homotopy groups; the same tools, *functional programming* combined with the *homological perturbation theorem*, were successfully applied to the so-called Whitehead and Postnikov towers, the most \"elementary\" methods to compute the homotopy groups. Leading to the Kenzo program [[6]](#dsrbss). In particular, Ana Romero extended the scope of the program to the classifying spaces of non-commutative groups, detecting an error [[8]](#romrun) in a published paper, for a homotopy group of a relatively contorted simplicial set.\n",
-    "\n",
-    "These programs, once the basics of algebraic topology are understood, are elementary and certainly not the best possible: it is well known the Adams spectral sequence and all its derivatives are central in the subject and efficient methods *must* use them. Nevertheless, the experience of the Kenzo program, where everything is so elementary, made tempting a\n",
-    "non-negligible theoretical result: If a dimension $n$ is fixed, our algorithm computing the homotopy group $\\pi_n X$ of a simply connected simplicial set $X$ has a polynomial complexity *with respect to* $X$; of course not with respect to $n$, as it is well known since David Anick's paper [[1]](#anick), unless $P = NP$.\n",
-    "\n",
-    "This polynomiality result is so natural when you know the details of the Kenzo program, and of course the authors of the corresponding 16000 lines of Lisp code know these details, that I often stated this result without any other justification. The authors of [[5]](#ckmvw), after a few years of interesting common work with myself on problems of constructive algebraic topology, suggested to write down a common paper on this polynomiality result. Why not.\n",
-    "\n",
-    "First Jiri Matousek identified a real difficulty that I had not seen: the program rests on the effective homology of the Eilenberg-MacLane spaces, itself based on the effective homology of $K(\\mathbb{Z},1)$, quite simple, but the standard\n",
-    "effective homology of this monstrous version of the circle $S^1$ has *exponential* complexity! Jiri solved the problem for $K(\\mathbb{N},1)$, using a lovely discrete vector field, and I gave the complement to obtain the same result for $K(\\mathbb{Z},1)$, essentially an elementary process of normalization. This is explained in [[7]](#krmtsr).\n",
-    "\n",
-    "No other obstacle against polynomiality was later found in the Kenzo algorithm where everything is elementary. The paper [[5]](#ckmvw) is a rereading of the Kenzo source, or rather of the Kenzo documentation [[10]](#siret), with some mathematical complements most often not included in the documentation. As it often happens in journalistic reports, the very nature of the Kenzo program is unfortunately in [[5]](#ckmvw) misunderstood. The authors have an excuse: it is hard to understand the core of such a program if you never worked with its source code, or if you never did some similar concrete programming work.\n",
-    "\n",
-    "Everything is elementary in Kenzo, except the functional programming component, to my knowledge so far never so essentially and intensively used in a computer program processing a *specific* mathematical problem. All the *general* programs \"doing mathematics\", mainly computational algebra, such as Maple, Mathematica, Axiom, Macsyma, Gap, Sage, ... also intensively use functional programming, it is inevitable, but the corresponding complexity problems are *outside* the scope of functional programming. To my knowledge, in our case, it is the first time an essential component of\n",
-    "functional programming is used in a program doing a work as specific as computing a homotopy group.\n",
-    "\n",
-    "It so happened the authors of [[5]](#ckmvw) in 2012 started preparing pages and pages about our problem of complexity. I soon warned them: sorry, your draft totally forgets the component *functional programming*; without the minimal indications about this matter, the paper is not correct. For example, a Coq proof of this polynomiality result could not avoid studying the cost of this functional programming. It was proposed I cosign the paper [[5]](#ckmvw), I answered it is not possible to cosign a paper you would reject as referee.\n",
-    "\n",
-    "Every mathematican knows how it is difficult in conversations with non-mathematicians to explain what mathematical research is, and also why it is useful~(!). Sometimes the same when a computer scientist tries to explain to \"pure\" mathematicians the exact nature of a computer program; and in particular where the difficulties are hidden. Modern programming, in particular functional programming with the so-called *functional programming languages*, seems so natural for a pure mathematician, so close to his habits that he cannot believe some difficulty in complexity is hidden there. Finally, it is not so hard to overcome this difficulty, but a few prerequisites cannot be avoided. It is the role of this text to clarify this point.\n",
-    "\n",
-    "# Functional Programming.\n",
-    "\n",
-    "It is common in Mathematics to study functions taking as arguments one or several functions, the value of which being also a function. For example, an elementary exercise of topology could be: Let $\\mathcal{F} := \\mathcal{C}([0,1], [0,1])$ be the space of the continuous functions $f: [0,1]\\rightarrow [0,1]$ with the usual metric topology; prove the function $F: \\mathcal{F} \\rightarrow \\mathcal{F} : f \\mapsto (f \\circ f)$ is continuous. The argument is $f$, a function, the value is $f \\circ f$ a function, and the problem concerns $F$, a function: function $\\mapsto$ function.\n",
-    "\n",
-    "We want to study in this text the analogous situation in computer science. It is not difficult in most programming languages to write some code for functions having as value a function; in programming, we say such a function *returns* a function, to emphasize the dynamic character of the process: before been invoked, the \"value\" does not yet exist; when the dominating function is *invoked*, one says also it is *called*, its work starts and when the work is finished, a new object is born in the environment, a *functional object*, the object which is *returned*. This functional object may later in turn be invoked with appropriate arguments, returning arbitrary objects, maybe again other functional objects, why not.\n",
-    "\n",
-    "A programmer using such programming tools uses *Functional Programming*[<sup>2</sup>](#footnote_2). Functional programming is more or less easy, depending on the programming language the programmer is using; some languages have been specifically organized in particular to make easy this style of programming, such a language then deserves the qualifier *functional*. The main functional languages are those of the Lisp family, those of the ML family and Haskell.\n",
-    "\n",
-    "Algebraic Topology is often considered as a difficult subject, and our experience allows us to point out the main reason causing this difficulty. With only pen and paper, you cannot reasonably practice functional programming, it is much too complex. A complexity which *begins* to be illustrated by the few diagrams of this text, used to explain the most elementary techniques which are necessary when implementing functional programming. So that an algebraic topologist wishing to work only with pen and paper must design quite sophisticated methods to overcome this essential difficulty or more precisely to use different strategies which avoid this obstacle: the exact and spectral sequences are *not* constructive; they become constructive only if you add an essential dose of functional programming in the recipes. Most often, our topologists must invent new high level exact sequences, spectral sequences, spectra, operads, ..., made of higher homology or homotopy operators, also of exotic spaces, with a *constructive* scope always limited, a scope\n",
-    "which of course does not lower at all the interest of all these objects. While our methods using functional programming have a unique constructive limitation, the available material resources (computing time and memory space).\n",
-    "\n",
-    "<a id='footnote_2'><sup>2</sup></a> This expression \"Functional Programming\" is also used for a strict style of programming where *every* (*!*) object is a function, the simplest example being the $\\lambda$-calculus, the wonderful\n",
-    "theoretical machine invented by Alonzo Church to disprove Hilbert's hope for a general algorithm solving any mathematical problem. More reasonably, most often, only the dynamic process defining how the program works then has a functional nature.\n",
-    "\n",
-    "# Mathematics and Computer Science.\n",
-    "\n",
-    "It is not exceptional to observe mathematicians having a knowledge of computer science which is a little superficial. This is true for any domain of mathematics as well, but a mathematician often is not conscious of his exact status with respect to computer science, the source of many problems.\n",
-    "\n",
-    "Two extreme behaviours: some of them think a computer can only make essentially trivial computations, which \"of course\" cannot do any relevant work for \"theoretical\" Mathematics. I remember a high level topologist who, sincerely and honestly, declared he could not imagine a computer can determine whether a natural number is prime or not. This happened frequently in the last decades of the 20th century; many impressive results have been produced since then with the help of computers and it becomes difficult to find extreme examples of this sort.\n",
-    "\n",
-    "The opposite extreme, now more frequent, is the following. Some mathematicians think a computer is of course trivially able to implement any mathematical idea, and some of them are surprised when their idea, a little naive, in fact do not correspond to anything concretely feasible on a machine. Or is feasible but using non-trivial implementations, the study of which then needing significant and interesting work, in particular to justify *theoretical* mathematical results, for example in *complexity*.\n",
-    "\n",
-    "In a discussion with an excellent topologist, he explained a theoretical algorithm for computing homotopy groups is known for a long time: it is enough to use the *combinatorial* definition of the homotopy groups by Kan and Moore. He \"only\" forgot a finitely generated subgroup of a non-commutative free group of finite type is free, but not necessarily of finite type and the claimed \"algorithm\" is not valid.\n",
-    "\n",
-    "Many topologists for example are persuaded the *exact* and *spectral sequences* of Algebraic Topology can be trivially transformed into algorithms computing some homology or homotopy groups. A referee recently claimed that deducing an algorithm from the Adams spectral sequence is \"folklore\", sic. I naively thought the mathematicians are the scientists the most careful for the precise *definition* of the objects they work with; it happens an *algorithm* is a non-trivial mathematical object with a deterministic definition, due to the best representatives of our profession in the last century: G&#246;del, Church and Turing, and such a definition cannot be reduced to some intuitive \"folklore\". As long as the referee reports will be *anonymous*, such accidents will be frequent: Juridically, an expert cannot be anonymous, why this exception for the alleged \"experts\" judging our articles?\n",
-    "\n",
-    "This text is devoted to clarifying the particular case of *functional programming*. On the one hand, coding functions returning functions is *now* as easy in programming as in mathematics, mainly if you use a so-called *functional* programming language. On the other hand, the cost in complexity is essentially *null*, which is summarized by the title:\n",
-    "Functional Programming is *free*; good news, but why? Because of the subtle notion of *closure*; of course the notion of closure in programming, unknown by most mathematicians and even by a large proportion of computer scientists.\n",
-    "\n",
-    "Some complex programs intensively use functional programming, and studying their complexity needs a lucid knowledge of this wonderful tool, the art of producing *closures*. Working in this way, you obtain efficient programs, the structure of which is limpid; furthermore without any cost in complexity. It is the subject of this article to explain this notion of closure, not so complicated, but not trivial at all.\n",
-    "\n",
-    "# Defining an algorithm.\n",
-    "\n",
-    "The paper [[5]](#ckmvw) in principle proves some algorithm $\\pi_n: X \\mapsto \\pi_n X$ is polynomial. Before proving this property, the algorithm $\\pi_n$ must be available.\n",
-    "\n",
-    "The proof of a *theorem* is decomposed in simpler statements, often called *propositions*, maybe in turn decomposed in still simpler statements, often called *lemmas*, and these lemmas should have simple proofs directly understandable. A similar scheme is to be applied for the definition of an *algorithm*.\n",
-    "\n",
-    "The execution of a program finally is sequential, instruction by instruction, so that the description of an algorithm consists in dividing the long sequence of instructions into partial segments, divided in turn in shorter segments, and so on, up to sufficiently elementary segments the implementation of which is a routine task. Often, smaller segments consist in fact in a call of a functional object done with respect to some prepared inputs, the caller waiting for the corresponding output returned by the functional object. This is the standard top-down view of algorithms, dual of the bottom-up understanding, the latter easier to handle when writing source code.\n",
-    "\n",
-    "The article [[5]](#ckmvw) uses the Postnikov tower. The Whitehead tower is a little simpler, produces also the homotopy groups, but not the *Postnikov classes*[<sup>3</sup>](#footnote_3). The difficulty with respect to functional programming is the same for the Whitehead tower and this framework is enough for our explanations.\n",
-    "\n",
-    "<a id='footnote_3'><sup>3</sup></a>Often erroneously called Postnikov *invariants*.\n",
-    "\n",
-    "The process computing $\\pi_n X$ thanks to the Whitehead tower consists in iteratively constructing the stages of the tower, so that the first level decomposition of the desired algorithm $X \\mapsto \\pi_n X$ is necessarily:\n",
-    "\n",
-    "$$\n",
-    "X = X_2 \\stackrel{w_3}{\\longmapsto} X_3 \\cdots X_{n-1}\n",
-    "\\stackrel{w_n}{\\longmapsto} X_n \\stackrel{H_n}{\\longmapsto} \\pi_n X\n",
-    "$$\n",
-    "\n",
-    "The stage $X_i$ of the tower is the inital space $X$ where the first homotopy groups $\\pi_j X$ have been \"killed\" for $j < i$, its homotopy starts at the index $i$. The Hurewicz theorem therefore allows the program to compute $H_i X_i = \\pi_i X_i = \\pi_i X$, and an appropriate fibration using this group then produces the next stage $X_{i+1}$. The last step $H_n: X_n \\mapsto H_n X_n = \\pi_n X_n = \\pi_n X$ is again an application of the Hurewicz theorem. The program starts with $X = X_2$ simply connected, without any homotopy in dimensions 0 and 1.\n",
-    "\n",
-    "An algorithm is a functional object \"*input* $\\mapsto$ *output*\" and the computer scientists know for a long time the appropriate *types* of the input and the output are to be carefully defined. I invite a reader sufficiently patient to reach this part of this text to analyse the article [[5]](#ckmvw) with the Adobe searcher for the word \"type\": the reader will see this matter of the (computer) *types* of the used objects is never considered. The reader must probably understand the definition of these types is a minor subject: the slave who some day maybe will implement the described algorithm should be able to find out these details.\n",
-    "\n",
-    "This matter of *type* is yet become central in the very *foundations* of mathematics, see the Wikipedia page \"Homotopy Type Theory\". A point which does not seem really understood by our authors. If they had taken a little care of this question of *types*, they would have realized some functional programming is inevitable in such a programming.\n",
-    "\n",
-    "In the first level decomposition of the Kenzo algorithm above, the main step is the partial algorithm $w_i: X_{i-1} \\mapsto X_i$. The input and the output are a simplicial set *with effective homology*. We must therefore consider the (computer) *type* of the simplicial sets with effective homology.\n",
-    "\n",
-    "It is not the right place to define all the details of this quite complex computer type, a large collection of functional objects defining a simplicial set in general not of finite type, combined with a set of other functional objects sufficiently rich to contain the *homotopy type* of this simplicial set: this is nothing but the key point of *Effective Homology*. To illustrate our subject we just consider the simplest component of such an object, the face operator $\\partial_{X}$ of a simplicial set $X$.\n",
-    "\n",
-    "Such a face operator is a functional object, and you must first define ... the type of its input and output. The type of the simplices of $X$ can be chosen as a dependent type $S := \\mathbb{N} \\widetilde{\\times} S_n$ where, for every integer $n \\in \\mathbb{N}$, the type $S_n$ is the type of the $n$-simplices of $X$. For example for the standard presentation of $K(\\mathbb{Z},1)$, a simplicial set *not* of finite type even if we limit the dimension, $S_n$ is the type of the lists of length $n$ made of integers. The face operator $\\partial$ is then a functional object:\n",
-    "\n",
-    "$$\n",
-    "\\partial:  [\\mathbb{N} \\widetilde{\\times} S_n] \\widetilde{\\times} \\mathbb{N}_\\ast \\rightarrow\n",
-    "[\\mathbb{N} \\widetilde{\\times} S_n] : ((n,\\sigma),i) \\mapsto \\partial_i(\\sigma)\n",
-    "$$\n",
-    "\n",
-    "where $\\sigma$ is an $n$-simplex of $X$ and $i$ an index $0 \\leq i\\leq n$. For example for $X = K(\\mathbb{Z},1)$, a possible 4-simplex is $\\sigma =(-19, -14, 8, 4)$ and:\n",
-    "\n",
-    "$$\n",
-    "\\partial_{K(\\mathbb{Z},1)}((4, (-19, -14, 8, 4)), 2) = (3, (-19, -6, 4))\n",
-    "$$\n",
-    "\n",
-    "Let $X_{i-1}$ be a possible $(i-1)$-th stage of a Whitehead tower, necessarily implemented as a *simplicial set with effective homology*. This object contains a large collection of functional objects and in particular the face operator $\\partial_{X_{i-1}}$. The step $w_i$ of the program must then construct $X_i := w_i(X_{i-1})$, the output $X_i$ being again a simplicial set with effective homology, this object containing in particular a similar collection of functional objects, in particular the face operator $\\partial_{X_i}$; the construction of $\\partial_{X_i}$ depends of course on the object $\\partial_{X_{i-1}}$, but also of all the other components of $X_i$, in particular on the other functional components, according to a process computationnally not simple: a collection of various Eilenberg-MacLane spaces must in particular be constructed also as simplicial sets with effective homology, each Eilenberg-MacLane space being again the output of a functional subprogram.\n",
-    "\n",
-    "The paper [[5]](#ckmvw) does not consider at all the cost of the generation of all these functional objects. It is a pity:\n",
-    "\n",
-    "- On the one hand, this *functional programming* is the heart of the Kenzo algorithm: if such a programming tool was not necessary, the topologists would have used such an algorithm for a long time.\n",
-    "- On the other hand, the complexity cost of the dynamic generation of the functional objects is in this particular case essentially null. The rest of this text is devoted to this point.\n",
-    "\n",
-    "# A toy example.\n",
-    "\n",
-    "It could be interesting in a program, given two functional objects $f_1, f_2: \\mathbb{N} \\rightarrow \\mathbb{N}$, to be able to dynamically construct the composition $f_2 \\circ f_1: \\mathbb{N} \\rightarrow \\mathbb{N}$, to be used later for some reason.\n",
-    "\n",
-    "The Common Lisp style is convenient to illustrate such a situation. Let us consider this short Lisp session.\n",
-    "\n",
-    "> The original paper uses `SETQ` to define and initialize new variables. Unfortunately, the SBCL compiler used here creates a ``\"SIMPLE WARNING: undefined variable: ...\"`` which looks rather intimidating. In order to keep the distraction at a minimum, we will use the more portable ``DEFVAR`` instead of ``SETQ`` as long as there are no unintended side-effects. In places where the use of ``DEFVAR`` is not appropriate, we will use ``SETQ`` and ignore the warning."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 1,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "F1"
-      ]
-     },
-     "execution_count": 1,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(defvar f1 (lambda (n) (* n 3)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 2,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "#<FUNCTION (LAMBDA (N) :IN \"/home/jovyan/cl-jupyter-master/cl-jupyter.lisp\") {100468D17B}>"
-      ]
-     },
-     "execution_count": 2,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "f1"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 3,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "F2"
-      ]
-     },
-     "execution_count": 3,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(defvar f2 (lambda (n) (+ n 8)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 4,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(15 13)"
-      ]
-     },
-     "execution_count": 4,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(list (funcall f1 5) (funcall f2 5))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "The first statement defines a function labeled \"`f1`\" mathematically defined as $f_1: n \\mapsto 3n$; read: assign to the symbol `f1` the function defined by the $\\lambda$-expression $\\lambda n\\,(n\\,*\\,3)$; the same for $f_2: n \\mapsto n+8$. The last statement constructs a list, its first element is $f_1(5)$, the second one is $f_2(5)$. Notice the Lisp notation `(funcall f1 5)` (read: call the function located by the symbol `f1` for the input `5`) for the usual mathematical notation $f_1(5)$.`; \n",
-    "\n",
-    "The second statement looks for the *value* of the symbol `f1`, just defined; this value is a *function*, the external display being rather poor, mainly the machine hexa-address where the object is stored. The internal object is too technical, a collection of machine statements, too technical to be usefully displayed there.\n",
-    "\n",
-    "If we want now to work with $f_3 := f_2 \\circ f_1$, we can use the Lisp statement:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 5,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "F3"
-      ]
-     },
-     "execution_count": 5,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(defvar f3\n",
-    "    (lambda (n)\n",
-    "            (funcall f2 (funcall f1 n))))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 6,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "23"
-      ]
-     },
-     "execution_count": 6,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(funcall f3 5)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "But this is essentially *static*, the process constructing $f_3$ should be repeated if another composition is desired. If a program must construct a large number of compositions, it would be painful to rewrite the same sort of statement for each composition. It is better to write a general composition function:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 7,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "COMPOSE"
-      ]
-     },
-     "execution_count": 7,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(defvar compose\n",
-    "    (lambda (af2 af1)\n",
-    "            (lambda (n)\n",
-    "                    (funcall af2 (funcall af1 n)))))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 8,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "F4"
-      ]
-     },
-     "execution_count": 8,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(defvar f4 (funcall compose f2 f1))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 9,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "23"
-      ]
-     },
-     "execution_count": 9,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(funcall f4 5)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 10,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "F5"
-      ]
-     },
-     "execution_count": 10,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(defvar f5 (funcall compose f1 f2)) "
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 11,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "39"
-      ]
-     },
-     "execution_count": 11,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(funcall f5 5)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "You can read: the function `compose` is the function which, given the functions `af2` and `af1`, returns the function which, given the integer `n`, returns `af2`(`af1`(`n`)).\n",
-    "\n",
-    "We have for example chosen the symbol `af1` as vaguely meaning \"abstract function &#x23;1\" to improve the readability, but any arbitrary symbol could have been chosen here, even the symbol `f1`. The qualifier \"abstract\" means that no concrete function is to be defined when the value of `compose` is *constructed*; only later, when the functional object is *used*, then the abstract function will be replaced by some \"concrete\" function, as you observe in the next statements.\n",
-    "\n",
-    "But the most important point in this short Lisp session is the following: the values of the constructed compositions `f4` and `f5` are *closures*, not functions. What does this mean? It is the role of this text to clarify the exact nature of such an object, to illustrate the amazing power of these objects, on the one hand in flexibility, on the other hand their *cost in complexity* is essentially *null*.\n",
-    "\n",
-    "# Functional objects.\n",
-    "\n",
-    "Except if you work with exotic machines, in particular machines allowing to use multiprocessing, a program is finally a sequence of *machine instructions*, sequentially executed, except when some specific instruction, a *jump* instruction, says the next instruction to be executed is to be taken at some machine address; the execution then again continues sequentially from this address up to the next jump, and so on.\n",
-    "\n",
-    "A program can also *invoke* a functional object, this functional object is then called a *callee*, while the program at the origin of this call is the *caller*. The callee must then execute some task, and when this task is finished, the *control* is given back to the caller. The scheme below illustrates such an organization; each rectangle contains some machine instruction, and the arrows show the path followed by the *control*. Such a call consists in two jumps, one starting the callee, the other one leaving it.\n",
-    "\n",
-    "<img src=Figure1.png>\n",
-    "\n",
-    "In fact the caller, before invoking the callee, pushes onto the *stack* the *return address*; in this way, when the callee has finished its task, it can read this return address to give back the control to the caller, at the next point where the caller must continue its work; the functional object can so be called from anywhere in the program, avoiding to repeat its code in the memory if this functional object is called several times, quite frequent.\n",
-    "\n",
-    "A part of the computer memory is called the *stack*; it is a continuous area of the memory, where objects are *piled*, the system being allowed to add a new object onto it, or on the contrary to remove the last one having been added; a special system register always keeps the address of the last object. In particular, each time a functional object is launched for execution by a caller, the caller adds (pushes) the return address onto the stack, so that when the work of this functional object is finished, this address on the stack is used by the callee to return to the caller at the right place, and this return address is erased (popped); we will see this stack will be used also for another specific usage of the closures, quite essential.\n",
-    "\n",
-    "A *closure* is also a functional object, but with a sophisticated structure opening interesting new possibilities, in particular making easy functional programming. A closure is *abstractly* made of three components:\n",
-    "\n",
-    "- the *body* of the closure, containing mainly:\n",
-    "  - a pointer to its *code*;\n",
-    "  - a collection of pointers defining its *own* environment.\n",
-    "- the *code* of this closure;\n",
-    "- the *environment* of this closure.\n",
-    "\n",
-    "The *apparent* redundancies in this description are voluntary. In a sense, the wonderful power of our computers is due to the intensive and remarkable use of the *pointers*; a pointer is a machine object giving \"only\" the machine address of another machine object; and it is not so rare the last machine object is again a pointer, this is *indirect addressing*, the key point to implement the notion of closure (and many others).\n",
-    "\n",
-    "When the functional object *closure* will be invoked, its code will be executed, but a part of this code may use the specific environment of *this* closure, the pointers available in the body itself allowing the code to reach the relevant part of the current environment.\n",
-    "\n",
-    "There remains to detail how this game of pointers is really organized, and why this organization justifies the title of this text.\n",
-    "\n",
-    "# The standard toy example.\n",
-    "\n",
-    "The standard mini-example which is used to explain the nature of the closures, quite artificial but instructive, is the following. Let us imagine a programmer wants to construct several arbitrary *multipliers*, a multiplier $\\mu_m$ being a functional object ready to multiply an arbitrary input $n$ by some fixed number $m$. In standard programming, you could write:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 12,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "MUL3"
-      ]
-     },
-     "execution_count": 12,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(defvar mul3 (lambda (n) (* n 3)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 13,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "15"
-      ]
-     },
-     "execution_count": 13,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(funcall mul3 5)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "But our programmer intends to be able to *dynamically*, that is, during *runtime*, *generate* multipliers $\\mu_m$ with various and arbitrary $m$'s, all these multipliers remaining simultaneously \"alive\", and in particular such that they could be repeatedly called in arbitrary orders. We assign a *generator* of multipliers to the symbol `genmul`, and immediately use it:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 14,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "GENMUL"
-      ]
-     },
-     "execution_count": 14,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(defvar genmul\n",
-    "    (lambda (m)\n",
-    "            (lambda (n) (* m n))))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 15,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "MUL5"
-      ]
-     },
-     "execution_count": 15,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(defvar mul5 (funcall genmul 5))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 16,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "#<CLOSURE (LAMBDA (N) :IN \"/home/jovyan/cl-jupyter-master/cl-jupyter.lisp\") {1004C3BCDB}>"
-      ]
-     },
-     "execution_count": 16,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "mul5"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 17,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "MUL7"
-      ]
-     },
-     "execution_count": 17,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(defvar mul7 (funcall genmul 7))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 18,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "#<CLOSURE (LAMBDA (N) :IN \"/home/jovyan/cl-jupyter-master/cl-jupyter.lisp\") {1004CE8A8B}>"
-      ]
-     },
-     "execution_count": 18,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "mul7"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 19,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "45"
-      ]
-     },
-     "execution_count": 19,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(funcall mul5 9)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 20,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "63"
-      ]
-     },
-     "execution_count": 20,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(funcall mul7 9)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "The reader is invited to \"think\" like Lisp when these statements are processed. This goes as follows.\n",
-    "\n",
-    "- `(setq genmul ...)`: Lisp understands the user wants to use the symbol `genmul` and in particular assigns to it the object defined by the continuation of the text.\n",
-    "- `(lambda (m) ...)`: This object is an \"ordinary\" functional object, the input *will* be some object denoted by `m` in the source code and returning some output, some object defined by the subsequent text. Important: at this time this functional object *does not* work, it is then just *generated* and installed somewhere in the memory space; it will be called only *later*. We will also detail *later*, *when* this functional object is called, how it works.\n",
-    "- It happens the next statement `(setq mul5 ...)` now *calls* `genmul`, more precisely the functional object assigned to it, the input being 5. At this time, the binding \"`m` $\\mapsto$ 5\" defined by the parameter `m` and the input 5 is installed in the environment, more precisely in the *local* environment of the functional object just starting its work.\n",
-    "- The *body* `(lambda (n) ...)` of our functional object is then executed, which body asks again for the *generation* of a functional object, not its execution.\n",
-    "- Lisp then \"knows\" this generation happens in a *local* environment, a local environment having in this case only the binding \"`m` $\\mapsto$ 5\". Then Lisp generates the next functional object `(lambda (n) ...)`, *saving* also the current local environment, that is, in this case the binding \"`m` $\\mapsto$ 5\", this environment being made visible *only* from the just created functional object. This *pair* made of a functional object *and* an environment valid only for this object is a *closure*, notion detailed later. This closure is the *output* of `genmul` for this invocation, which closure is assigned to `mul5`.\n",
-    "- Same story for `(defvar mul7 ...)`: *another* functional object is generated, assigned to `mul7`, and this object, *another* closure, sees an environment where, this time the only binding is \"`m` $\\mapsto$ 7\". This closure is assigned to `mul7`.\n",
-    "- The value of `mul5` is *called* with the argument 9, in other words, the binding \"`n` $\\mapsto$ 9\" is installed. The value of `mul5` is a closure which *still sees* the binding \"`m` $\\mapsto$ 5\", so that the *code* of our closure, the Lisp statement `(* m n)` returns 45.\n",
-    "- The value of `mul7` is *called* with the same argument 9, in other words, the binding \"`n` $\\mapsto$ 9\" is again installed. This value is a closure, not the same as the previous one, which *sees* the *different* binding \"`m` $\\mapsto$ 7\", so that the *body* of this closure, the Lisp statement `(* m n)` this time returns 63.\n",
-    "\n",
-    "These details are a little lengthy but necessary to avoid deep misunderstandings. Usually the following \"magic\" explanation is given: a closure *keeps* the local environment which *was* present at *generation time*. A little more precisely: a closure *encloses* the local environment existing at generation time, explaining the terminology. Partially true, but in general not sufficient, and the actual process is more powerful.\n",
-    "\n",
-    "# Detailing the structure of the closure `mul5`.\n",
-    "\n",
-    "When `genmul` is *called* to *generate* the closure which will be assigned to `mul5`, Lisp does the following work. The local environment of *this* invocation of `genmul` has only the binding \"`m` $\\mapsto$ 5\". Having to generate the functional object `(lambda (n) (* m n)`, Lisp *generates* in fact only a *small* structure, the body of the closure to be generated, containing only three components:\n",
-    "\n",
-    "- A specific label indicating the object so entitled is a *closure*;\n",
-    "- The address of the code `(lambda (n) (* m n)`;\n",
-    "- The address of the machine word containing the value 5 for the symbol `m`, value valid only for *this* closure.\n",
-    "\n",
-    "You understand that, when `genmul` will be later called to generate a second closure assigned to `mul7`, *another* structure of the same sort is again generated, \"disjoint\" of the first one, with the same label, with, very important, the *same* address of the (same!) code, but the third component will be this time the address of the value 7 valid for this closure.\n",
-    "\n",
-    "You must carefully distinguish in this story the functional object which, *when* it is called, generates a closure:\n",
-    "```cl\n",
-    "(lambda (m)\n",
-    "    (lambda (n) (* m n)))\n",
-    "```\n",
-    "from the *code*  `(lambda (n) (* m n)` of the generated closure. When the interpreter or the compiler processes the functional object assigned to `genmul`, it \"sees\" this (ordinary) functional object will have to generate a closure. The compiler then generates somewhere the (interpreted or compiled) code of the closure, and this *unique* copy of this code\n",
-    "*will* be used by *every* closure generated by `genmul`.\n",
-    "\n",
-    "However, this code, this unique code, according to the closure for which it is working, has to use *different* values for `m`, values defined beforehand, when the closure *was* generated; how this is possible?\n",
-    "\n",
-    "The solution is another use of the *stack*, already mentionned to keep the *return* address from a functional object. When Lisp executes `(funcall mul5 9)`, Lisp works as follows:\n",
-    "\n",
-    "- `(funcall ...)` means the *value* of the first argument `mul5` of `funcall` is a functional object.\n",
-    "- Examining the nature of this functional object, in this case a *closure*, Lisp pushes on the stack *three* addresses:\n",
-    "  - The return address, which will be used as for an ordinary functional object;\n",
-    "  - The address of the closure.\n",
-    "  - The adress of the second argument `9`.\n",
-    "- This done, Lisp reads the address of the relevant code of *this* closure and gives the *control* to this code.\n",
-    "  ![](Figure2.png)\n",
-    "- In other words this code is now executed.\n",
-    "- And when this code must use the *value* of `m` valid for *this* closure, the code has been prepared by the compiler to reach this value as follows:\n",
-    "  - Read the address of the closure from the stack;\n",
-    "  - Read the third component of the closure, which contains the *address* of the value of `m` valid for *this* closure.\n",
-    "  - Finally read the value of `m` valid for *this* closure. Typical use of *indirect addressing*.\n",
-    "- Via the stack, the code of our closure can also reach when necessary the second argument `9` of `funcall`, that is, in this case, the unique argument `n` of the invoked closure. \n",
-    "- When the execution of the code is finished, the code erases from the top of the stack the address of the argument `9` and the address of the closure, no longer necessary, reads the return address on the stack, erases also this return address, and is now able to *return* to the caller at the right place.\n",
-    "- Most often, a functional object must also return an *output*, here `45`; the address of the output which has just been computed by the closure is then put onto the stack, in this way the caller is able to reach this output.\n",
-    "\n",
-    "Such a process:\n",
-    "\n",
-    "- Preparing some input for a callee;\n",
-    "- Giving control to this callee;\n",
-    "- The callee does its work;\n",
-    "- When the work is finished, the callee prepares the appropriate output;\n",
-    "- The callee gives back the control to the caller;\n",
-    "- All these steps using the stack to make the involved objects communicate between each other;\n",
-    "\n",
-    "is so essential in any *programming* language that the *machine* language has always specific instructions to conveniently and efficiently handle the top of the stack as roughly described above. Examine for example the entry \"Stack instructions\" in the Wikipedia page \"x86 assembly language\". The particular case of the call of a closure is nothing but a variant of this process where the address of the closure is also put onto the stack, to allow the called code to reach the environment specific to this closure.\n",
-    "\n",
-    "# A local environment is alive.\n",
-    "\n",
-    "An acute reader maybe wondered why the closures above had their third component containing the *address* of the value of `m` and not this value itself, so needing an indirection.\n",
-    "\n",
-    "But consider the next standard toy example:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 21,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "MAKE_PACKAGE"
-      ]
-     },
-     "execution_count": 21,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(defvar make_package\n",
-    "    (lambda (m)\n",
-    "            (values\n",
-    "             (lambda (n) (* m n))\n",
-    "             (lambda () (setq m (1+ m))))))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 22,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "#<FUNCTION (LAMBDA (M) :IN \"/home/jovyan/cl-jupyter-master/cl-jupyter.lisp\") {1004E8745B}>"
-      ]
-     },
-     "execution_count": 22,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "make_package"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "The object assigned to the symbol `make_package` is an ordinary functional object using one argument `m`. When this object is called, it returns *two* values, namely two closures. The first one is a multiplier $\\mu_m$ as before. The second value is another closure which increases the value of `m` by 1. For example, we can call `make_package` with the argument \"`m` $\\mapsto$ `5`\"; the returned values are respectively assigned to the symbols `mul_1` and `inc_1` as follows:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 23,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "#<CLOSURE (LAMBDA (N) :IN \"/home/jovyan/cl-jupyter-master/cl-jupyter.lisp\") {1004F5EC5B}>"
-      ]
-     },
-     "execution_count": 23,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(defvar mul_1)\n",
-    "(defvar inc_1)\n",
-    "(multiple-value-setq (mul_1 inc_1)\n",
-    "                     (funcall make_package 5))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Only the first closure assigned to `mul_1` is displayed. The same for two other closures where now \"`m` $\\mapsto$ `18`\", and the symbols `mul_2` and `inc_2` are used instead:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 24,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "#<CLOSURE (LAMBDA (N) :IN \"/home/jovyan/cl-jupyter-master/cl-jupyter.lisp\") {1004FDFA1B}>"
-      ]
-     },
-     "execution_count": 24,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(defvar mul_2)\n",
-    "(defvar inc_2)\n",
-    "(multiple-value-setq (mul_2 inc_2)\n",
-    "                     (funcall make_package 18))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "The reader probably guesses the continuation of the story:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 25,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "-25"
-      ]
-     },
-     "execution_count": 25,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(funcall mul_1 -5)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 26,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "6"
-      ]
-     },
-     "execution_count": 26,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(funcall inc_1)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 27,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "-30"
-      ]
-     },
-     "execution_count": 27,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(funcall mul_1 -5)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 28,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "-90"
-      ]
-     },
-     "execution_count": 28,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(funcall mul_2 -5)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 29,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "19"
-      ]
-     },
-     "execution_count": 29,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(funcall inc_2)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 30,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "-95"
-      ]
-     },
-     "execution_count": 30,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(funcall mul_2 -5)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 31,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "7"
-      ]
-     },
-     "execution_count": 31,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(funcall inc_1)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 32,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "-35"
-      ]
-     },
-     "execution_count": 32,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(funcall mul_1 -5)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "The new point is that both closures assigned to `mul_1` and `inc_1` *share* the *same* \"local\" variable `m`, for the environment containing the initial binding was the *same* for both closures. So that once `inc_1` has increased the value of `m` from 5 to 6, the call of `mul_1` of course then uses the *updated* value of `m`. The same for the closures assigned to the symbols `mul_2` and `inc_2` with respect to their *own* local environment, *another* binding \"`m` $\\mapsto$ `18`\", updated to 19.\n",
-    "\n",
-    "These complications do not prevent for example `mul_1` and `mul_2` to share the same code. The appropriate scheme is the following one.\n",
-    "\n",
-    "![](Figure3.png)\n",
-    "\n",
-    "The central components are the four closures, each one located by a symbol; in this way, the programmer can call them easily. These closures share some codes and share also some environments, but in this case not in parallel: if two closures share a code, they do not share an environment, and conversely. This, once the source code is interpreted or compiled, is *static*.\n",
-    "\n",
-    "In the diagram above, the state of the memory is also sketched when, a *dynamic* event, the closure located by `mul_1` is called with the argument `9`. Then the control is given to the code of \"`(lambda (n) (* m n))`\", reached via the closure, which code can reach the binding \"`m` $\\mapsto$ `5`\" of the *relevant* environment via the stack and its *fn-obj* component; the code can reach the binding \"`n` $\\mapsto$ `9`\" also via the stack.\n",
-    "\n",
-    "We hope this diagram could make clear the role of the closures: they are very small boxes containing the address of the corresponding code and also the addresses of the variables of the corresponding environment. *When* a closure is called, the control is given to the corresponding code, which reaches the appropriate arguments via the stack and the closure, in particular the variables of the closure itself.\n",
-    "\n",
-    "This is nothing but a *toy example*. In more general situations, it is quickly impossible to draw a planar diagram as above! Taking account of the descriptive power of the addressing mechanism - $n$ bits can denote $2^n$ different addresses! -, this is not at all a problem for the interpreter or the compiler. This is why, as it is detailed in the next section, functional programming is essentially *free*.\n",
-    "\n",
-    "# When is a closure generated?\n",
-    "\n",
-    "We hope the reader is now sufficiently advanced in this matter of closures to understand another point. Our reader could have been puzzled by the quoted adjective \"ordinary\" often attributed to a functional object. How the interpreter or the compiler can decide whether such an object must be \"ordinary\" or not, that is, in the negative case, a closure?\n",
-    "\n",
-    "Some *global* environment is always defined, that is, a collection of bindings everywhere visible in the program, except when such a binding is \"hidden\" by a local one; on the contrary a *local* environment is visible only from a small (local) part of the code, *and also* from the closures which *were* generated when this local environment was active.\n",
-    "\n",
-    "When a functional object is to be generated, Lisp examines the state of the environment where this generation is to be done. If only the global environment is visible, an  ordinary functional object is generated; on the contrary, if the generation happens inside some local environment, then a closure is generated.\n",
-    "\n",
-    "However, some \"clever\" Lisp systems are able to prove the *local* nature of some variable does not matter, for it can be proved this variable cannot be modified, so being in fact nothing but a constant, which does not need the sophisticated structure of a closure. The Sbcl environment underlying the present CL-Jupyter notebook is of this sort. See the example later.\n",
-    "\n",
-    "The simplest way in Lisp to generate a local environment uses a `let` instruction."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 33,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "A1"
-      ]
-     },
-     "execution_count": 33,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(defvar a1 25)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 34,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "25"
-      ]
-     },
-     "execution_count": 34,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "a1"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 35,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "510"
-      ]
-     },
-     "execution_count": 35,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(let ((a1 255))\n",
-    "     (+ a1 a1))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 36,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "50"
-      ]
-     },
-     "execution_count": 36,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(+ a1 a1)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "In this short session above, two uses of the variable `a1` coexist. The global environment defines a binding \"`a1` $\\mapsto$ `25`\", while, when the `(let ...)` instruction is run, a local environment with the binding \"`a1` $\\mapsto$ `255`\" is defined. In this local environment, adding `a1` and `a1` produces 510, but this done, this local environment is definitively dead, so that in the next statement, the same code `(+ a1 a1)` returns this time 50: the global environment was let unchanged and is reused as such."
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "In the next statement, the functional object to be created uses only the argument `b`, redefined at each call, and the global variable `a`. No closure is necessary, a simple function is returned."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 37,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "A2"
-      ]
-     },
-     "execution_count": 37,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(defvar a2 222)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 38,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "ADDA2"
-      ]
-     },
-     "execution_count": 38,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(defvar adda2 (lambda (b)\n",
-    "                      (+ a2 b)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 39,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "#<FUNCTION (LAMBDA (B) :IN \"/home/jovyan/cl-jupyter-master/cl-jupyter.lisp\") {10054CE12B}>"
-      ]
-     },
-     "execution_count": 39,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "adda2"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 40,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "232"
-      ]
-     },
-     "execution_count": 40,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(funcall adda2 10)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "In the next exemple, the *local* variable `a3` is used, but (this) Lisp (and you?) can prove the value of this variable cannot be modified. This pseudo-variable is therefore processed (by this Lisp) as a constant. No closure is necessary."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 41,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "ADDA3"
-      ]
-     },
-     "execution_count": 41,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(defvar adda3\n",
-    "    (let ((a3 333))\n",
-    "         (lambda (b)\n",
-    "                 (+ a3 b))))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 42,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "#<FUNCTION (LAMBDA (B) :IN \"/home/jovyan/cl-jupyter-master/cl-jupyter.lisp\") {10055FB85B}>"
-      ]
-     },
-     "execution_count": 42,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "adda3"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 43,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "343"
-      ]
-     },
-     "execution_count": 43,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(funcall adda3 10)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "In the next example, a little more sophisticated, we assign to the variable  `adda4` a *list* of two functional objects. The first one adds the value of the *local* variable `a4` to the argument, the second one, without any argument, adds 1 to this variable. Then the value of `adda4` is made of two closures, and the next statements are the obvious tests. An example already presented in a slightly different way."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 44,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "ADDA4"
-      ]
-     },
-     "execution_count": 44,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(defvar adda4\n",
-    "    (let ((a4 444))\n",
-    "         (list (lambda (n) (+ a4 n))\n",
-    "               (lambda () (setf a4 (+ a4 1))))))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 45,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(#<CLOSURE (LAMBDA (N) :IN \"/home/jovyan/cl-jupyter-master/cl-jupyter.lisp\") {100574813B}> #<CLOSURE (LAMBDA NIL :IN \"/home/jovyan/cl-jupyter-master/cl-jupyter.lisp\") {100574815B}>)"
-      ]
-     },
-     "execution_count": 45,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "adda4"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 46,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "454"
-      ]
-     },
-     "execution_count": 46,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(funcall (first adda4) 10)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 47,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "445"
-      ]
-     },
-     "execution_count": 47,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(funcall (second adda4))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 48,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "455"
-      ]
-     },
-     "execution_count": 48,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(funcall (first adda4) 10)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Notice the (internal) value of `a4` is now unreachable. Except in this very particular case, by the dirty trick:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 49,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "445"
-      ]
-     },
-     "execution_count": 49,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(funcall (first adda4) 0)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "The fact the *value* of the local variable `a4` can be modified by the second functional object definitively requires both functional objects must be implemented as *closures*."
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "The Kenzo program generates during runtime thousands of closures, implementing components of the sophisticated objects of Algebraic Topology: simplicial sets, chain complexes, algebra and coalgebra structures, cohomology classes, ... So that a lucid study of the corresponding complexity problems cannot avoid a reasonable knowledge of the structure of these closures."
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "The author of this note does not forget his serious difficulties when he tried in the 70's to understand the very notion of the *funarg problem* in Maclisp, see:\n",
-    "\n",
-    "[http://www.maclisp.info/pitmanual/eval.html](http://www.maclisp.info/pitmanual/eval.html)\n",
-    "\n",
-    "when the birth of the notion of closure was just under way: the programmer had to manage himself the problem of identifier scope through the *association lists*. The discussion described in this web page is instructive to follow the hesitations of the best implementers of this time.\n",
-    "\n",
-    "See also:\n",
-    "\n",
-    "[https://en.wikipedia.org/wiki/Funarg_problem](https://en.wikipedia.org/wiki/Funarg_problem)\n",
-    "\n",
-    "There remains to see why the use of these closures is *free*, we mean in complexity studies, and also why this organization is exactly the right one to implement high level mathematics, we mean when notions coming from the\n",
-    "*Category Theory*, typically the *functors*, have to be implemented.\n",
-    "\n",
-    "# Functional Programming is Free.\n",
-    "\n",
-    "We mean that, in a complexity study, the cost of the *production* of a new closure during the execution of a program is \"null\", more exactly is *constant*. In most complexity studies, the input $\\alpha$ of a program $\\pi$ is assumed to have a *size* $\\sigma(\\alpha)$, the program is run to produce some output $\\omega = \\pi(\\alpha)$, and we would like to bound the\n",
-    "computing time $\\tau(\\pi, \\alpha)$ in function of $\\sigma(\\alpha)$. For example, the program $\\pi$ is said to be *polynomial* if an exponent $e$ and a coefficient $c$ can be determined, such that for any meaningful input $\\alpha$, the estimate $\\tau(\\pi, \\alpha) \\leq c(1 + \\sigma(\\alpha))^e$ is satisfied.\n",
-    "\n",
-    "Let us assume we would like to prove the program $\\pi$ is polynomial. If the number of closures to be produced is bounded *independently* of $\\alpha$, the fact that the cost of the production of a closure is constant implies the production time of these closures can be omitted: it is enough to increase the coefficient $c$ to take account of the production of closures. Otherwise, when the number of closures depends on $\\alpha$, such a hasty claim could fail, but anyway using the fact the production cost of *one* copy of the closure is constant can be used conveniently.\n",
-    "\n",
-    "Producing a closure of a certain type is only allocating a memory segment of fixed length, a segment containing the label *closure*, the address of the corresponding code, always the same, and the addresses of a *fixed* number of local values.\n",
-    "\n",
-    "Of course you must distinguish the computing time necessary to *generate* the closure from the computing time of the closure itself when it is *called* later by the program; this computing time can on the contrary strongly depend on the inputs given by the caller to the closure. For example the closure could be an Ackermann function depending on some parameters; the production of the closure is then constant, but the computing time of such a closure when it is *called* of course is not constant at all, depending on the input *and also* possibly on the specific parameters of *this* Ackermann function.\n",
-    "\n",
-    "The investigator in complexity must also be lucid about another factor. The *production* itself of a closure needs a constant time, but *preparing* the local environment valid for this closure can on the contrary be costly, depending on the parameters of this closure. Let us consider for example the case of a function depending on a natural number $n$, this function having to produce a closure which must use the $n$-th prime number. It is then better to compute this prime number before generating the closure, and to insert the result in the environment known by the closure. In Common Lisp the structure of the function generating the closure could be:\n",
-    "\n",
-    "```cl\n",
-    "(setq closure_gen\n",
-    "    (lambda (n ...)\n",
-    "        (let ((nth_p (funcall nth_prime n)))\n",
-    "            ...\n",
-    "            (lambda (...) ... nth_p ...))))\n",
-    "```\n",
-    "\n",
-    "In other words, three steps when a closure is used:\n",
-    "\n",
-    "- Preparing the appropriate local environment, the cost depends on the specific necessary work;\n",
-    "- Generating the closure itself, constant cost.\n",
-    "- Using the closure when it is called, cost depending on the code of the closure, on the arguments given by the caller, and also possibly of the nature of the environment used by the closure.\n",
-    "\n",
-    "# Implementing functors thanks to appropriate closures.\n",
-    "\n",
-    "To explain why the notion of closure is the right tool to implement *functors*, we use the following elementary example. Let us assume a programmer has to work with (the category of) monoids, and in particular, he must implement the product *bifunctor*.\n",
-    "\n",
-    "He decides a monoid is a pair, the first element being the *identity* of the monoid, the second one being the *operation* of the monoid. Such an operation is a process, a function, which, given two elements of the monoid computes their product. For example the additive monoid of the natural numbers could be implemented as:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 50,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "N+"
-      ]
-     },
-     "execution_count": 50,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(defvar N+ (list 0 #'+))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "The cryptic text `#'+` means in Lisp the functional object associated to the standard addition operator '`+`'. Test:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 51,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "9"
-      ]
-     },
-     "execution_count": 51,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(funcall #'+ 4 5)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 52,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "#<FUNCTION +>"
-      ]
-     },
-     "execution_count": 52,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "#'+"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "The *value* of the expression `#'+` is `#<Function +>`, an external simple representation of the functional object, too complicated  to be exactly displayed, it is some machine code, readable only by experts.\n",
-    "\n",
-    "Our programmer uses also the multiplicative monoid of the integers."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 53,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "N*"
-      ]
-     },
-     "execution_count": 53,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(defvar N* (list 1 #'*))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 54,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "20"
-      ]
-     },
-     "execution_count": 54,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(funcall #'* 4 5)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "An *identity* function is defined to legibly extract the identity of a monoid."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 55,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "MONOID-IDENTITY"
-      ]
-     },
-     "execution_count": 55,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(defvar monoid-identity\n",
-    "    (lambda (monoid)\n",
-    "            (first monoid)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 56,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "0"
-      ]
-     },
-     "execution_count": 56,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(funcall monoid-identity N+)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "And an *operation* function is also defined to conveniently compute *inside* some monoid; the second statement below constructs a list made of the respective \"products\" of `4` and `5` in the monoids `N+` and `N*`."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 57,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "OPERATION"
-      ]
-     },
-     "execution_count": 57,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(defvar operation\n",
-    "    (lambda (monoid item1 item2)\n",
-    "            (funcall (second monoid) item1 item2)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 58,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(9 20)"
-      ]
-     },
-     "execution_count": 58,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(list (funcall operation N+ 4 5)\n",
-    "      (funcall operation N* 4 5))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Now we implement the product *bifunctor*. If $M_1$ and $M_2$ are two monoids, an element of $M_1 \\times M_2$ is represented as a pair. So that the identity of $M_1 \\times M_2$ is the pair of the respective identities. The function which, given the monoids $M_1$ and $M_2$, constructs the identity of $M_1 \\times M_2$ therefore is:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 59,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "MONOID-PRODUCT-IDENTITY"
-      ]
-     },
-     "execution_count": 59,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(defvar monoid-product-identity\n",
-    "    (lambda (monoid1 monoid2)\n",
-    "            (list (funcall monoid-identity monoid1)\n",
-    "                  (funcall monoid-identity monoid2))))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 60,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(0 1)"
-      ]
-     },
-     "execution_count": 60,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(funcall monoid-product-identity N+ N*)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "We did not yet have seen any closure. In the same way, we must be able to construct, given two *arbitrary* monoids $M_1$ and $M_2$, the operation of the product monoid $M_1 \\times M_2$."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 61,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "MONOID-PRODUCT-OPERATION"
-      ]
-     },
-     "execution_count": 61,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(defvar monoid-product-operation\n",
-    "    (lambda (monoid1 monoid2)\n",
-    "            (lambda (item1 item2)\n",
-    "                    (list (funcall operation monoid1\n",
-    "                                   (first item1) (first item2))\n",
-    "                          (funcall operation monoid2\n",
-    "                                   (second item1) (second item2))))))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 62,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "#<CLOSURE (LAMBDA (ITEM1 ITEM2) :IN \"/home/jovyan/cl-jupyter-master/cl-jupyter.lisp\") {1005E5630B}>"
-      ]
-     },
-     "execution_count": 62,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(funcall monoid-product-operation N+ N*)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "The operation to be constructed uses the operation of the first monoid and makes it work on the first components of the \"items\", the same for the second components with respect to the second monoid, and finally makes a pair, a list, with both results.\n",
-    "\n",
-    "Using this constructor with respect to our monoids `N+` and `N*` this time produces a *closure*. The point is that the internal `(lambda (item1 ...) ...)` uses `monoid1` and `monoid2` constituting the *local* environment where the functional object is generated, so that this environment must be *saved*, it is the role of the closure technology.\n",
-    "\n",
-    "We have now in our toolbox the necessary ingredients allowing us to implement the product bifunctor."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 63,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "MONOID-PRODUCT"
-      ]
-     },
-     "execution_count": 63,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(defvar monoid-product\n",
-    "    (lambda (monoid1 monoid2)\n",
-    "            (list (funcall monoid-product-identity monoid1 monoid2)\n",
-    "                  (funcall monoid-product-operation monoid1 monoid2))))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 64,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "N+_X_N*"
-      ]
-     },
-     "execution_count": 64,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(defvar N+_x_N* (funcall monoid-product N+ N*))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 65,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(9 20)"
-      ]
-     },
-     "execution_count": 65,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(funcall operation N+_x_N*\n",
-    "         (list 4 4) (list 5 5))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "In other words, in the monoid $\\mathtt{N+} \\times \\mathtt{N*}$, the product of $(4,4)$ and $(5,5)$ is $(9,20)$. Now these constructors can be used for arbitrary monoids. For example the monoid `CS` of the character strings and their concatenation is constructed in Lisp as follows. Using the generic function `concatenate` of Lisp, a specific function\n",
-    "`string-conc` is constructed, giving the second component of our monoid; the identity is the empty string."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 66,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "STRING-CONC"
-      ]
-     },
-     "execution_count": 66,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(defvar string-conc\n",
-    "      (lambda (string1 string2)\n",
-    "              (concatenate 'string string1 string2)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 67,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\"qwertyuiop\""
-      ]
-     },
-     "execution_count": 67,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(funcall string-conc \"qwert\" \"yuiop\")"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 68,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "CS"
-      ]
-     },
-     "execution_count": 68,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(defvar CS (list \"\" string-conc))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 69,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\"qwertyuiop\""
-      ]
-     },
-     "execution_count": 69,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(funcall operation CS \"qwert\" \"yuiop\")"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "The product $\\mathtt{CS} \\times \\mathtt{N+}$ is then constructed and tested:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 70,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "CS_X_N+"
-      ]
-     },
-     "execution_count": 70,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(defvar CS_x_N+ (funcall monoid-product CS N+))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 71,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(\"qwertyuiop\" 9)"
-      ]
-     },
-     "execution_count": 71,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(funcall operation CS_x_N+\n",
-    "         (list \"qwert\" 4) (list \"yuiop\" 5))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "The product $\\mathtt{CS} \\times (\\mathtt{N+} \\times \\mathtt{N*})$ is constructed in the same way."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 72,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "CS_X_[N+_X_N*]"
-      ]
-     },
-     "execution_count": 72,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(defvar CS_x_[N+_x_N*] (funcall monoid-product CS N+_x_N*))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 73,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(\"qwertyuiop\" (8 25))"
-      ]
-     },
-     "execution_count": 73,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(funcall operation CS_x_[N+_x_N*]\n",
-    "         (list \"qwert\" (list 4 5))\n",
-    "         (list \"yuiop\" (list 4 5)))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "The product bifunctor is present in our environment and can be used as in category theory. Its main component is a functional object constructing a new functional object from two other functional objects, the closure notion allowing the user to naturally construct this higher functional object, for the constructed closure \"keeps\" the environment where it has been generated. In this way, arbitrary complex uses of the product bifunctor can be done whithout any confusion: every closure will see the right references. *And* the complexity cost in this case is constant, only the addresses of `monoid1` and `monoid2` are used; the code constituting the heart of the function `monoid-product-operation` being once for all installed in the environment, which code can be used by *any* product of monoids, thanks to the indirect addressing mechanism.\n",
-    "\n",
-    "# When computing homotopy groups.\n",
-    "\n",
-    "Computing the homotopy groups of a finite simply connected simplicial set, or more generally a simply connected simplicial set *with effective homology*, using its Whitehead or Postnikov tower, is just the application of a long sequence of applications of functors similar to the one used as example in the previous section. For example the construction of $\\partial_{X_i}$ from $X_{i-1}$ discussed in [Section 4](#Defining-an-algorithm.) is obtained by such a long process, and the same for the other components of $X_i$.\n",
-    "\n",
-    "When the functional components of the initial objects are polynomial, all the used functors are so simple that of course the resulting objects obviously again have polynomial functional components.\n",
-    "\n",
-    "But this is not enough: the \"measure of polynomiality\" of the output functional objects must in turn polynomially depend on the measure of polynomiality of the inputs.\n",
-    "\n",
-    "The final scaffolding of functors is certainly a little impressive, but once you master the notion of closure, the proof of polynomiality is a simple recursive process.\n",
-    "\n",
-    "We just give here a minimal significant example of the method to be applied. Let $A, B, C, D$ be four \"ordinary\" types of objects for which a size is defined, such as integers, lists of such objects, matrices of such objects, etc. Let $[A \\rightarrow B]$ (resp. $[C \\rightarrow D]$) be the functional types of the functional objects which, when an input is an element of $A$ (resp. $C$), return an element of $B$ (resp. $D$). Let finally $\\alpha \\in [[A \\rightarrow B] \\rightarrow [C \\rightarrow D]]$ be a sort of \"functor\" between these functional types. Question, how to define the polynomiality of $\\alpha$?\n",
-    "\n",
-    "We would like to express that *any* polynomiality of $f: A \\rightarrow B$ implies *some* polynomiality of $\\alpha(f): C \\rightarrow D$, but in a \"polynomial\" way. After a little work, you quickly find the appropriate definitions are the following ones.\n",
-    "\n",
-    "**Definition.**  A functional object $f: A \\rightarrow B$ is an element of $P^d_c(A,B)$ if for any element $a \\in A$, the estimate $\\tau(f, a) \\leq c(1+\\sigma(a))^d$ holds, where $\\sigma(a)$ is the size of the input $a$ and $\\tau(f, a)$ is the computing time of the output $f(a)$.\n",
-    "\n",
-    "**Definition.** The functional object $\\alpha : [A \\rightarrow B] \\rightarrow [C \\rightarrow D]$ is polynomial if for every degree $d \\in \\mathbb{N}$, there exists a degree $d' \\in \\mathbb{N}$ and a polynomial $\\chi_d \\in \\mathbb{N}[c]$ satisfying the following requirement: if $f \\in P^d_c(A,B)$, then $\\alpha(f) \\in P^{d'}_{\\chi_\\alpha(c)}$.\n",
-    "\n",
-    "In particular, no type of relation between $d'$ and $d$ is required, but a *unique* $d'$ must be associated to a fixed $d$; on the contrary the \"measure of $d'$-polynomiality\" of $\\alpha(f)$ must polynomially depend on the \"measure of $d$-polynomiality\" of $f$.\n",
-    "\n",
-    "It is then obvious the composition of polynomial maps $f_i: [A_{i-1} \\rightarrow B_{i-1}] \\rightarrow [A_i \\rightarrow B_i]$ is again polynomial.\n",
-    "\n",
-    "The reader must be lucid: the definitions above concern the relations between the respective complexities of $\\alpha: A \\rightarrow B$ and $f(\\alpha): C\\rightarrow D$, and not the complexity of $f$ itself. In the case of the Kenzo program, this complexity is uniformly bounded by a constant and can finally be omitted. This is the point never studied in [[5]](#ckmvw). In more complex situations, the complexity of $f$ could have a non-negligible role.\n",
-    "\n",
-    "Also, you must handle more complicated cases where inputs and outputs are mixtures of \"ordinary\" objects with an \"ordinary\" size and functional objects of arbitrary level. There is an essentially unique way to extend the simple case explained above to the general situation; it is not useful to detail this point here.\n",
-    "\n",
-    "In this way, the Kenzo algorithm can be mathematically described exactly as it was programmed many years ago, directly following Postnikov; and the desired polynomiality proof is then quite simple; and correct.\n",
-    "\n",
-    "# Functional vs Ordinary programming.\n",
-    "\n",
-    "To be complete, it is probably useful to detail the exact status of *functional* programming with respect to \"ordinary\" programming.\n",
-    "\n",
-    "The standard definitions of theoretical programming carefully distinguish the *primitive* recursive programs from the *general* recursive programs; necessarily illustrated by the example of the Ackermann function, which can be programmed as a general recursive program, not as a primitive recursive program. A reader of this text could wonder whether there exists such a theoretical difference between functional programming and ordinary programming.\n",
-    "\n",
-    "In a sense, this text proves there is no difference. The closure technology is nothing but a process translating a functional program into an ordinary program, so that you cannot program *more* algorithms with functional programming. But if you do not want to use functional programming, you will have to manage by yourself the serious related problem of identifier scope. The closure technology has precisely been invented to free the user of these low level programming problems, without any cost in complexity, thanks to a skilful use of indirect addressing[<sup>4</sup>](#footnote_4).\n",
-    "\n",
-    "The reader could usefully consult again the Wikipedia page \"Closure (computer programming)\"; it is there explained the so-called functional languages all have integrated the notion of closure, in a so essential way that the keyword *closure* is even not present in these languages: their users employ closures as Monsieur Jourdain wrote in prose.\n",
-    "\n",
-    "In the same Wikipedia page, it is explained how in the other languages it is possible to explicitly implement closures if necessary; the *object oriented programming* tool is then often used to solve the problem of identifier scope, while in fact this tool is not at all devoted to this matter. Once these techniques are understood, you should be able to translate the Lisp Kenzo program into any other language, with a source code, for the non-functional languages, certainly much less convenient; ask for example `Google(compose1 c++)` to see the problems met by the `C++`-writers of the *toy* example of [Section 5](#A-toy-example.) and imagine them translating the 16000 lines of Kenzo in `C++`.\n",
-    "\n",
-    "But using these (pseudo-)alternatives does not change anything to the problem: anyway, functional objects have to be dynamically generated during the execution of the program and you must control the cost of these generations. If you can prove the cost of the generation of *one* functional object is uniformly bounded - be careful: independently of the *size of the initial object* - you have finished. Otherwise, you have to study this dependency, good luck! You understand now how the closure technology is powerful: in the case of the Kenzo program, it is easy to prove the cost of the generation of a closure is uniformly bounded, independently of the initial object.\n",
-    "\n",
-    "Other techniques can be used. For example it can be proved the functional style used in Kenzo can be replaced by a strong recursive style; in fact closer ($!$) to the *strict* theoretical functional style. More precisely, the bottom-up programming style of Kenzo may be replaced by a top-down programming style, producing a program where it *seems* no functional object is dynamically constructed. It is not at all convenient, would you like to start the building of a house by the roof and finish by the foundations?  And this would not change anything in the problem: this time you have to study the cost of the handling of the recursiveness, not easy in this situation with a terrible graph of crossed multi-recursiveness. And the \"upside-down\" understanding of the algorithm probably makes the complexity study rather painful. Anyway it would be a *different* algorithm.\n",
-    "\n",
-    "In fact, the paper [[5]](#ckmvw) does not give the smallest indication about the solution of the authors for this problem. Following the Kenzo program, the authors vaguely explain that for any simplicial set with effective homology $X$, an algorithm $\\pi^X_n$ can be written down computing $\\pi_n(X)$ which is claimed uniformly polynomial with respect to $X$, but the study of the algorithm $X \\mapsto \\pi^X_n$ is missing. No indication at all about which is written before and after ($!$) launching the execution, for example about the Eilenberg-MacLane spaces to be *generated*, with all their *functional* components, during the execution of $w_i$, see [Section 4](#Defining-an-algorithm.).\n",
-    "\n",
-    "Also, trivially using functional programming, the Kenzo program is independent of the $n$ of $\\pi_n(X)$; nothing is said about this point in [[5]](#ckmvw). It would be funny, for a process so simply iterative, to see a program depending on the number of steps.\n",
-    "\n",
-    "In summary, the cost of the generation of the countless functional objects is not considered in the paper, while it is the heart of the program. Nothing is explained either about a possible method to avoid functional programming. Observe in particular the footnote 11 of [[5]](#ckmvw), which explains \"functional programming\" could be an \"alternative\" framework to process our complexity problem ; the confusion is total: the program as it is described in [[5]](#ckmvw) must inevitably use functional programming; and \"functional programming\" cannot be a *tool* to study the complexity of an algorithm.\n",
-    "\n",
-    "The article [[5]](#ckmvw) reasonably updated could be a useful introduction to the subject, but the claimed proof of polynomiality is incomplete. It is true it is difficult to master this subject if you do not have any serious concrete experience of programming. The same authors, along the same lines, have proved an impressive collection of computability and undecidability results, results which, as far as I know, are correct; opening, in the positive case, a wonderful field for concrete programming. It is a pity to spoil the excellent appreciation due to all these results by the paper [[5]](#ckmvw).\n",
-    "\n",
-    "<a id='footnote_4'><sup>4</sup></a>An amusing illustration of which happens without closures is the funny \"solution\" used by Bourbaki [[2]](#bourbk) to solve this problem by the *graphic* connections between Hilbert's $\\tau$'s and the white boxes $\\Box$.\n",
-    "\n",
-    "## References\n",
-    "\n",
-    "<a id='anick'><b>[1]</b></a> D. J. Anick. The computation of rational homotopy groups is #p-hard. In M. Tangora, editor, *Computers in geometry and topology*. Decker, 1989. Lecture Notes in Pure and Applied Mathematics, vol. 114.\n",
-    "\n",
-    "<a id='bourbk'><b>[2]</b></a> N. Bourbaki. Th&#233;orie des Ensembles, Chapitre I. Hermann, 1960.\n",
-    "\n",
-    "<a id='brownr'><b>[3]</b></a> R. Brown. The twisted Eilenberg-Zilber theorem. In *Celebrazioni Arch. Secolo XX, Simp. Top.*, pages 34–37, 1967.\n",
-    "\n",
-    "<a id='browne1'><b>[4]</b></a> E. Brown Jr. Finite computability of Postnikov complexes. *Annals of Mathematics*, 65:1–20, 1957.\n",
-    "\n",
-    "<a id='ckmvw'><b>[5]</b></a> M. Cadek, M. Krcal, J. Matousek, L. Vokrinek, and U. Wagner. Polynomial-time computation of homotopy groups and Postnikov systems in fixed dimension. *Siam Journal on Computing*, 43:1728–1780, 2014.\n",
-    "\n",
-    "<a id='dsrbss'><b>[6]</b></a> Xavier Dousson, Julio Rubio, Francis Sergeraert and Yvon Siret. The Kenzo program. [http://www-fourier.ujf-grenoble.fr/~sergerar/Kenzo/](http://www-fourier.ujf-grenoble.fr/~sergerar/Kenzo/)\n",
-    "\n",
-    "<a id='krmtsr'><b>[7]</b></a>  M. Krcal, J. Matousek, and F. Sergeraert. Polynomial-time homology for simplicial EilenbergMacLane spaces. *J. Found. Comput. Math.*, 13:935–963, 2013.\n",
-    "\n",
-    "<a id='romrub'><b>[8]</b></a>  A. Romero and J. Rubio. Homotopy groups of suspended classifying spaces: an experimental approach. *Mathematics of Computation*., 82:2237–2244, 2013.\n",
-    "\n",
-    "<a id='shih'><b>[9]</b></a>  W. Shih. Homologie des espaces fibr&#233;s. *Publications Math&#233;matiques de l’IHES*, 13, 1962.\n",
-    "\n",
-    "<a id='siret'><b>[10]</b></a> Yvon Siret. The Kenzo documentation. [http://www-fourier.ujf-grenoble.fr/~sergerar/Kenzo/Kenzo-doc.pdf](http://www-fourier.ujf-grenoble.fr/~sergerar/Kenzo/Kenzo-doc.pdf)"
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-{
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-  {
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-   "metadata": {},
-   "source": [
-    "---\n",
-    "<big><big><big><big><b>Infinity and Effectiveness from a Functional Point of View</b></big></big></big></big>\n",
-    "\n",
-    "\n",
-    "By [*Francis Sergeraert*](https://www-fourier.ujf-grenoble.fr/~sergerar/Papers/Images.pdf), Published in the French journal *Images des Mathématiques*, 1990, vol.76, pp. 71 - 81.\n",
-    "\n",
-    "(Translation by Gerd Heber and [Google Translate](https://translate.google.com/), 16 April 2017.)\n",
-    "\n",
-    "---\n",
-    "\n",
-    "# Introduction\n",
-    "\n",
-    "*Infinity* and *effectiveness* are two concepts which seem to belong to two very distinct worlds. Is it possible to think of *infinity* in terms of *effectiveness*? The infinite is an *abstract* notion and thus appears beyond the reach of any *effective* approach, by which we mean one that can be translated into a concrete reality. Against this superficial impression, in this article, we will argue that effectiveness does not have to be sacrificed at the outset of an undertaking in which the infinite plays an essential role. This pursuit leads to many questions - and answers (!) - and is very exciting indeed.\n",
-    "\n",
-    "Mathematicians' ability to deal effectively with problems in which the infinite plays, in one form or another, an essential role, intimidates some and has earned them an air of sorcery. It can't be denied that this prowess has its place among the finest human achievements. The fame of several mathematicians can be attached directly to how they advanced our understanding of the infinite: Leibniz and Newton (infinitesimal calculus), Cantor (infinite sets), Cauchy (infinitesimal analysis), Hilbert (spaces of infinite dimension), Gödel (incompleteness), Robinson (non-standard analysis).\n",
-    "\n",
-    "Compared to the world of his mathematician colleague, superficial reflection might suggest that the computer scientist lives in a world more peaceful and less esoteric. The computer scientist works with machines (concrete or theoretical) that are in essence *finite*. Such machines can only work with programs, represented as *finite* texts, over necessarily *finite* data, for a *finite* time. But this view is not correct, and it is so for a variety of reasons. Perhaps the simplest reason is to point out that infinity is not studied by mathematicians for pleasure alone, but also because, very often, it is a powerful modeling tool. An example that immediately comes to mind is a numerical calculation: note that without an error estimation it is generally of little interest. However, most of the time such an estimation can only be done conveniently by means of differential calculus or the use of the *infinitely small*. On the (opposite) side, the infinitely large, we can point, for example, to the studies of algorithmic complexity, whose practical interest goes without saying and that are often based on asymptotic methods.\n",
-    "\n",
-    "In this article, we want to study a link between infinity and programming of an entirely different nature, the *functional* link. It is a rather subtle link, the description of which, however, is of extraordinary simplicity. It is so extraordinary that there is no reason to beat around the bush; let us describe it at once.\n",
-    "\n",
-    "A program is a finite object. In a specific instance, it will be represented by a piece of text, which is nothing but a finite sequence of characters, drawn from a finite alphabet, possibly the set of ASCII characters. Such a program may work on some given data (input) and retrun a result (output). Take for example a program $P$ that computes the square of a positive integer. It is capable of working on *every* integer $n\\in\\mathbb{N}$, and we immediately have our link: $P$ is finite while the set $\\mathbb{N}$ of the integers on which $P$ can work is not. In general, if $P$ is a program, let $I(P)$ ($I$ for *input*) denote the set of data on which it can work. The program $P$ is inherently finite whereas $I(P)$ can very well be infinite.\n",
-    "\n",
-    "Thus, by this sleight of hand, we've brought together the finite universe of ordinary objects with the mathematicians' realm, a people used to \"infinite monsters.\" It may seem that this is a mere philosophical consideration and without real interest. The purpose of this article is to convince you otherwise.\n",
-    "\n",
-    "It is organized as follows. We begin with the elementary example of a good program for calculating the chromatic number of a graph, which is well known to graph theorists and uses the functional point of view. It will be carefully described in order to isolate and highlight the problems of programming and *effectiveness* that are encountered in this kind of situation. It is hoped that the nature of the method and the difficulties to be anticipated will be well understood. It will then be time to examine the state of computer science in this matter. We will see that it is quite excellent: today's computer scientists have just what we need (lambda-calculus, functional languages) so that we can work on these issues in the best conditions. The machine construction of the *loop-space* functor, which is very easy to describe, will give a good example of the available programming capabilities. Once the right viewpoint is adopted and the right tools are available, rather simple programs, which require no more than student-level skills, can be used to build highly infinite spaces, in a blink of an eye, *on a machine*. These spaces are convenient to impress the galleries, but they do not serve only that: although infinite, Jean-Pierre Serre invented them around 1950 to solve problems of a *finite* nature (homotopy groups of spheres). We have similar intentions. In the last section, we will give the reader an idea of the substantial theoretical results already obtained in algebraic topology and a description of the beautiful field of work now open to programming to all who want to apply these methods concretely on a machine.\n",
-    "\n",
-    "Section 2 gives readers not accustomed to computer science a more precise description of the possibly infinite nature of the set $I(P)$.\n",
-    "\n",
-    "The basic approach to infinity using the functional method has often been used: Cauchy's approach to infinitesimal analysis is of this kind and is the subject of section 3.\n",
-    "\n",
-    "# Concerning the non-finiteness of the input set.\n",
-    "\n",
-    "In the introduction, we have considered the program $P$ which assigns to an integer $n$ its square $n^2$. Thus, if the program $P$ were presented with the integer 97, it should return 9409. To write such a program is straightforward in any language, for example on a calculator programmable in Basic.\n",
-    "\n",
-    "We denote by $I(P)$ the set of data that the program $P$ accepts as inputs. In the example of the square calculation, the set $I(P)$ is the set $\\mathbb{N}$ of the integers, which is known to be infinite.\n",
-    "\n",
-    "This statement might raise the suspicion of a reader who is used to doing practical work on a computer. The assertion that the set $I(P)$ is infinite may indeed suggest that its author is unaware of the real constraints in the use of such machines. On a Basic calculator, for example, an *integer* can only be used if it is smaller than a certain integer defined by the engineer who conceived this calculator. Often it is something like $2^{31}$ or $10^{10}$, so that the number of integers on which our example program is *actually* capable of working is really finite, and our critic is in the right. And this kind of constraint is present in most programming languages.\n",
-    "\n",
-    "This difficulty, however, can be circumvented by programs known to work in *multiprecision*. These programs use the following technique: Suppose that our machine only accepts integers smaller than $10^{10}$. Let us call an integer smaller than $b = 10^5$ ($b$ for base) a *small integer*. If $n$ is an arbitrary integer, we can always write it, and moreover in only one way, in the form $n = a_pb^p + a_{p-1}b^{p-1} + \\ldots + a_0$, where the $a_i$ are small integers. This amounts to cutting the decimal notation of $n$ into five-digit slices. It is also the base $b = 10^5$ notation of $n$. It is then easy to see that the analogous notation of the square $n^2$ of $n$ can be determined by means of a succession of operations on small integers alone, and hence on our calculator. Technically, we will represent $n$ as an *array* of small integers and the result $n^2$ will come out in a similar form. The rest is technique of index manipulations, elementary operations on small integers and carried numbers.\n",
-    "\n",
-    "It is thus possible, even on a modest calculator, to calculate the square of quite substantial integers, including ones with hundreds of digits. What has just been described was invented long ago by our ancestors, when they understood the surprising possibilities of writing numbers in any base, 10 for example. They realized that the same method, or shall we say *program*, can be used to multiply two integers admitting *any* number of digits! It is strictly the same phenomenon that has just been described, except that the base is $10^5$ instead of $10$, but this does not change the case. And it is thanks to this that the usual multiplication table does not need to go beyond $9\\times 9 = 81$. Multiprecision computing software is now becoming more widespread. It is even integrated in some languages (Lisp) and can be found in most formal computational systems.\n",
-    "\n",
-    "But our astute critic might try another argument. Of course, we are now able to multiply arbitrarily large integers, but there remains a limitation, that of the amount of available memory in the machine. The critic is right. If, for example, each small integer occupies a memory cell, then the largest integer that can be *stored* in the machine in an array of small integers will be $N = 10^{5M}-1$, where $M$ is the number of available memory cells. If an integer is greater than $N$, it is impossible to enter it in the machine and a fortiori to calculate the square.\n",
-    "\n",
-    "However, this limitation can be overcome by *expandable memory* machines, which can carry out the following operations. In a first step, a program is written, for example, a program that works on multiprecision integers. Then the program is called upon to perform a certain task. It is then possible to determine the amount of memory needed *for this particular use*. If need be, the memory can be extended before the computation gets underway. We see that, *in this sense*, our program can work on any integer.\n",
-    "\n",
-    "The critic may shrug his shoulders one last time: If the number of memory cells required for a calculation is greater than the number of atoms of our galaxy, it is going to be a long wait for the necessary memory extensions, which would be already difficult for much smaller extensions. Be that as it may, the theoretician is satisfied with this fact: *potentially* his program is able to work on an integer of any size.\n",
-    "\n",
-    "The term *theorist*, which has just been used, is sometimes a little pejorative: the appellation of theorist often designates a person especially incapable of practical realizations! In this article, we will convince the reader that these theoretical considerations of programs with potential infinities are, on the contrary, capable of quite concrete applications! Since we speak here of theory, we cannot fail to recall that this type of an extensible memory machine was perfectly modeled by the English mathematician Turing, well before the very existence of the word *computer*. Turing had invented his model to respond negatively to Hilbert's conjecture of a universal algorithm for solving mathematical problems. Knowing that Turing's work played an essential role in the genesis of modern computing, we have a good argument to use against those who still have doubts about the interest of fundamental research. For more on these questions, we highly recommoned *\"Allen Turing, the enigma\"* by Andrew Hodges (Simon & Schuster, 1983). A French translation was published in 1987 under the title *\"Alan Turing ou l'énigme de l'intelligence\"* at the Bibliothèque Scientifique Payot.\n",
-    "\n",
-    "# The Cauchy solution for infinitesimal analysis.\n",
-    "\n",
-    "The *functional trick*, an application which is the topic of this article, has been known for a long time. It is, for example, the essential tool of the modern formalization of the infinitesimal analysis, usually attributed to Cauchy. According to Bourbaki, *Elements of the History of Mathematics* (Masson, 1984), he was the first who succeeded in giving infinitesimal analysis a sufficiently precise form so that it could be turned into a usable textbook, which is an excellent criterion. Of course, the reality is more complex and the work of Cauchy is culmination of a long and difficult gestation to which many predecessors contributed in an essential way. See Bourbaki (op. Cit.). In any case, Cauchy explained how to articulate the demonstrations of infinitesimal analysis using quantities very traditionally denoted $\\epsilon$ and $\\eta$ (or $\\delta$) since Weierstrass, which can assume more or less arbitrary values, but whose interdependence is essential. Usually, $\\epsilon$ is arbitrary and, *given such* an $\\epsilon$, one must *be able* to demonstrate the existence of an $\\eta$ verifying such and such a property. For example, a function $f:\\mathbb{R}\\rightarrow\\mathbb{R}$ is continuous at $x_0\\in\\mathbb{R}$ if for all $\\epsilon > 0$ one can prove the existence of an $\\eta > 0$ such that if $\\lvert x-x_0 \\rvert<\\eta$, then $\\lvert f(x)-f(x_0)\\rvert<\\epsilon$.\n",
-    "\n",
-    "The words \"given\" and \"able\" were emphasized deliberately to point out that this is exactly as in the situation of a program specification. To press once more and drive home the point, one could say that the demonstration of the continuity of the function $f$ at $x_0$ is nothing but a program admitting as input a real strictly positive $\\epsilon$ and returning as output another real strictly positive $\\eta$ that satisfies the indicated property. The continuity of $f$ at $x_0$ is thus equivalent to the existence of a *function* $\\mu:\\mathbb{R}_+ \\rightarrow \\mathbb{R}_+$ ($\\mathbb{R}_+$ denotes the set of strictly positive real numbers) such that if $\\lvert x- x_0\\rvert < \\mu(\\epsilon)$ then $\\lvert f(x) - f(x_0)\\rvert <\\epsilon$. A function $\\mu$ which has this property is called a *continuity module* for $f$ at $x_0$. Logicians say that if, moreover, $\\mu$ is *recursive*, then $f$ is *effectively continuous*.\n",
-    "\n",
-    "It has been rather time consuming to relate in two ways essentially the same thing, in order to emphasize different viewpoints, each having its own interest. We can see that there is a fairly canonical correspondence between the *logical* point of view of using quantifiers ($\\forall\\epsilon\\; ,\\exists\\eta\\ldots$) and the *functional* point of view which affirms the existence of *one* function such that any argument of that function and its value satisfy a certain property.\n",
-    "\n",
-    "It will be noted that in all that precedes neither the word *infinite* nor any of its derivatives is pronounced! A question might be raised as to \"what happens\" *infinitely close* to $x_0$. The fact that $x$ is very close to $x_0$ is only of secondary interest. What is essential is that the examination of a *finite number* of $x$ close to $x_0$ will never be sufficient to reach a conclusion regarding the continuity of $f$ at $x_0$. Such an assertion must be proven for an infinity of values of $x$. Cauchy resolved this formidable and essential difficulty through a *functional* turn: he replaced the examination of an infinity of $x$ and their properties with an assertion about a *single function*, the function $\\mu$. Yet Cauchy preferred to use a logical formulation (for all $\\epsilon$ there exists an $\\eta$ such that ...), which is equivalent, but which precisely serves us well because this formulation underlines a crucial aspect of the case. The adjective \"able\" was highlighted above to draw attention to the fact that the infinite is reached by means of an affirmation on the *potential* aspect of work: *if* you give me a strictly positive $\\epsilon$, *then* I would be *able* to produce an $\\eta$ such that a certain property is verified.\n",
-    "\n",
-    "This is a situation similar to a famous sketch on clairvoyance with [Pierre Dac and Francis Blanche](https://www.youtube.com/results?search_query=pierre+dac+francis+blanche): the mathematician is content to say \"If you give me an $\\epsilon$, then I will find an $\\eta$ such that ... yes, I could do that!\" Of course, unlike Pierre Dac, the mathematician argues and demonstrates *why* he could do it, but never actually does it!\n",
-    "\n",
-    "Everyone knows how difficult it is for beginners to understand and learn $\\epsilon-\\eta$ methods. For comparison, let us look at the difficulty of a proof using the functional method. To demonstrate the continuity of $f$ at $x_0$, we must construct a module of continuity, a function with real arguments and values. Let us study the proof of the continuity of $f^2$ where $f$ is assumed to be continuous. As far as a continuity modulus is concerned, if $\\mu:\\mathbb{R}_+ \\rightarrow \\mathbb{R}_+$ is a continuity modulus of $f$ at $x_0$, the function $\\mu'(\\epsilon)=\\min\\Big(\\mu(1),\\mu\\big(\\epsilon/(2\\lvert f(x_0)\\rvert + 1)\\big)\\Big)$ is a continuity modulus for $f^2$ at $x_0$ and it follows that the continuity of $f$ at $x_0$ implies the continuity of $f^2$ at the same point. Here, a new difficulty emerges, which stems precisely from the fact that the proof is about constructing a function whose argument ($\\mu$) and the value ($\\mu'$) are themselves functions. Pedagogically, can the distinction between argument and value of a function (argument and/or value being in turn functions) be more convenient than the distinction between universal quantifier and existential quantifier? It will be noted that the tree-like structure of the various arguments and values can be followed easily in the functional formalism while the logical formalism requires a relatively sophisticated conversion algorithm. We should also remember the distance still to be traveled to arrive at effective calculations on a machine. Here the functional method is obviously superior. The question of functions whose arguments and/or values are functions themselves plays a crucial role in this article, which is the reason why this complement to our explanations of infinitesimal analysis has been deemed useful.\n",
-    "\n",
-    "# The chromatic number of a graph.\n",
-    "\n",
-    "A graph is a pair $(S, A)$ where $S$ is a finite set, the set of the vertices of the graph, and where $A$ is a subset of $S\\times S$, the set of pairs of vertices connected by an *edge*. Given a set of *colors* $c_1, c_2, \\ldots, c_p$, we are looking to obtain a *good coloring* of the graph, that is to say, to assign one color to each vertex, so that any two vertices connected by an edge are of distinct colors. We denote $s_1, s_2, \\ldots, s_n$ the vertices of the graph and $d_1, d_2, \\ldots, d_n$ the colors that are attributed to them. The condition of good coloring can then be expresses as follows: if a pair $(s_i, s_j)$ is an element of $A$, then $d_i \\neq d_j$. This condition is rather restrictive, and if we don't have enough colors, in other words if $p$ is too small, we cannot find a good coloring. The smallest integer $p$ for which a good coloring of the graph $G$ with $p$ colors can be obtained is called the *chromatic number* of $G$. This number has raised and always continues to raise a lot of interest. The famous *four-color problem* is whether four colors are sufficient for any planar graph.\n",
-    "\n",
-    "An interesting programming challenge might be to ask for a program whose input is a graph and whose output is its chromatic number. The simplest if not most simplistic method is the following: A coloring (perhaps erroneous) with $p$ colors of the graph $G$ is a sequence $d_1, \\ldots, d_n$ of colors chosen from $c_1,\\ldots, c_p$. There are exactly $p^n$ such colorings. All these colorings can be tested, one after another, until either one finds a suitable coloring with $p$ colors or all combinations are exhausted without finding a single good coloring. In the first case, the chromatic number is $\\leq p$, in the second it must be $> p$. We start with $p = 1$, then $p = 2$, and so on. The first satisfactory integer $p$ we find is the chromatic number sought.\n",
-    "\n",
-    "This naive program demonstrates the *computability* of the chromatic number, but it would be so ruinous in computing time that certainly nobody would ever actually use this idea. However, it can be improved as follows: Let us take a subgraph $G'$ of $G$ containing a certain number of vertices of $G$ and all corresponding edges, and suppose we have found a good coloring with $p$ colors of $G'$. Add to $G'$ a vertex of $G$ which was missing from $G'$ and all corresponding edges: We obtain a graph $G''$ that we can attempt to color using the coloring already found for $G'$, and by giving the new vertex one of the colors considered so that the condition on the vertices of $G''$ is satisfied. There are usually several ways to do this. If an attempt succeeds we continue likewise by adding a vertex and edges to obtain the graph $G'''$... If it fails, we try another possibility for the last vertex of $G''$ and so on. If none of these tests is successful, the coloring of $G'$ cannot be *extended* and we have to find another good coloring of $G'$ by changing the color of its *lastest* vertex, the one that finished defining $G'$, and retry the recurrence with this new coloring... If a good coloring of $G$ with $p$ colors exists, it can be obtained by this process. Here again we start with $p = 1$, then $p = 2$, etc., until a sufficient integer $p$ is found, which is the chromatic number sought. This method, which is more cunning than the naive method, is well known to computer scientists as *backtracking* or the method of *trial and error*. It requires a little skill to be programmed. See in this regard chapter 3 of the excellent work of Niklaus Wirth, *Algorithms + data structures = programs* (Prentice Hall, 1976).\n",
-    "\n",
-    "This method, although better than the naive method, is still far too slow for practical use with more complex graphs.\n",
-    "It turns out that graph theorists discovered another method of an entirely different nature. Already in the preceding methods we tried a *recurrence* to determine if the number $p$ is sufficient. In this context, the following question is natural: Given a a graph $G$, let's remove a vertex and the corresponding edges to obtain a somewhat simpler graph $G'$, and let us suppose that we know the chromatic number of $G'$. Is it possible to deduce the chromatic number of $G$, given this information? Unfortunately, the answer is negative: the examination of some simple graphs shows that there can be no direct relation between the chromatic numbers of the graphs $G'$ and $G$, and a simple recursion based on the number of vertices of a graph cannot be obtained in this way.\n",
-    "\n",
-    "... Unless the \"chromatic number\" information is replaced by other, *considerably richer*, information. This is a phenomenon which seems a little paradoxical but is quite frequent in mathematics, where one succeeds by first finding the solution to a problem which appears more difficult, before solving the \"simpler\" problem. Let us associate with a graph $G$ the function $\\chi_G: \\mathbb{N}\\rightarrow\\mathbb{N}$ which assigns to an integer $p$ the number of good colorings of $G$ with $p$ colors. This function contains chromatic number as a *by-product*: the chromatic number of $G$ is the smallest integer $p$ such that $\\chi_G(p)\\neq 0$. Once the function $\\chi_G$ is known, it is easy to find this integer because this function is necessarily a polynomial that will be called the *chromatic polynomial* of $G$.\n",
-    "\n",
-    "We thus seek to deduce the chromatic polynomial of $G$ from chromatic polynomials of graphs *immediately simpler* than $G$. If the graph $G$ has no edges (in which case it is only a set of n unconnected vertices), then any coloring is a good coloring of $G$, so that $\\chi_G (p) = p^n$, and $\\chi_G$ is therefore already a polynomial. Otherwise the graph has at least one edge, for example, between the vertices $s_1$ and $s_2$. From graph $G$ two other graphs, $G_1$ and $G_2$, can be derived: The first, $G_1$, is obtained simply by deleting the edge between $s_1$ and $s_2$. The second, $G_2$, is obtained by *contracting* that same edge and convert its two ends into a single vertex of the graph $G_2$. We note that if $s_1$ and $s_2$ both were connected by edges to the vertex $s_k$, then the *two* old edges would be replaced by only *one* edge in the new graph.\n",
-    "\n",
-    "![](Figure1.png)\n",
-    "\n",
-    "Consider a good coloring of $G_1$. If the two vertices $s_1$ and $s_2$ have the same color, a good coloring of $G_2$ is derived by \"collapsing\", however, the corresponding coloring of $G$ is not good. Conversely, if $s_1$ and $s_2$ have different color, a good coloring of $G$ can be derived, but it is no longer possible to derive a coloring of $G_2$ therefrom. It is easy to see that any good coloring of $G$ and $G_2$ could be obtained in this way. If $p$ is the number of colors, it follows immediately that $\\chi_G (p) = \\chi_{G_1} (p) - \\chi_{G_2} (p)$ or, if this is true for any integer $p$, $\\chi_G = \\chi_{G_1} - \\chi_{G_2}$, which is a relationship between polynomials, and the desired recurrence relation is maintained. We already deduce, by induction, that the chromatic polynomial... is indeed a polynomial! Once this is understood, it is a child's play to derive a recursive program for calculating $\\chi_G$ given $G$. The chromatic number of $G$ can then be obtained as a by-product. This last program, which is based on a simple recurrence, is considerably better than the one described previously.\n",
-    "\n",
-    "But it may be time to return to our subject, *infinity and effectiveness*. What is the relationship with our graph problem? It has been emphasized that the *chromatic polynomial* information is much richer than the *chromatic number* information: in a certain way it contains an *infinity* of information since this polynomial is defined *for any* number of colors $p$. Of course, this *infinity* of information cannot be described as such. The *functional trick* is used. Rather than considering the *set* of all pairs $(p,\\chi_G(p))$, we prefer to consider the *function* $\\chi_G$. For a bourbakist mathematician there is no difference since he defines a function as a set of argument-value pairs! But for a computer scientist it is quite different, because she can code this *infinity* of couples as a *polynomial* and thus in the form of a finite sequence of coefficients and exponents, which *can be stored in a machine*! This polynomial can be considered as a *program*, a finite text, *capable*, if asked, of giving a response, a value, whatever integer (here a number of colors) is communicated to it. This general scheme only works well because one is able to write and use programs that admit polynomials (programs) as input and provide as output another polynomial (program). This is necessary when using the recurrence formula. This kind of work is easy for polynomials but a little more difficult for algorithms of a a more general nature which will be examined later.\n",
-    "\n",
-    "If this phenomenon and its solution have been described so carefully, it is because they are closely related to what will be described in the last section of this paper about a very active but more esoteric field of research, that of *algebraic topology*: The two problems (and their solutions) are indeed of identical natures.\n",
-    "\n",
-    "# The lambda calculus.\n",
-    "\n",
-    "In the world of lambda-calculus there are only functions, as opposed to ordinary programming, where, in particular in courses for beginners (think of the perforated cards of yesteryear), the *program* (some text) is carefully distinguished from the *data* (another text, on which the program must work). In lambda-calculus there exist only functions which can serve interchangeably as programs or data. One mechanism, the *reduction* (described briefly in the article by M. Parigot), defines by what process the coupling of two functions, the first considered as a program, the second as data, sets in motion a theoretical machine which eventually produces a result (again a function) to be considered as the result of the program function working on the data function. It can also happen that the machine turns indefinitely in which case the result is indefinite.\n",
-    "\n",
-    "A lambda-calculus function is a text written in an entirely ordinary alphabet which consists of letters and some ad hoc signs, and obeys a few simple rules (a grammar). One can, if you like, consider such a text as a program written in the lambda-calculus language. This uniformity of nature, any object is a function, requires some acrobatics when dealing with ordinary data such as an integer. The lambda-calculus trick consists in coding an integer $n$ as the function that assigns to any function $f$ the function\n",
-    "\n",
-    "$$\n",
-    "\\underbrace{f\\circ f \\circ f\\circ\\ldots\\circ f}_{n}\n",
-    "$$\n",
-    "\n",
-    "It may seem overly complicated to encode an object as simple as an integer. Still, it is perfectly possible to program any recursive function in lambda-calculus. In section 2 of the article by M. Parigot, the realization of the addition of 2 and 2 in lambda-calculus is explained in great detail!\n",
-    "\n",
-    "The interest in lambda-calculus stems from the fact that, as a programming language, *programs capable of working on programs as input while producing programs as output* can be written in it.\n",
-    "\n",
-    "The story of lambda-calculus is rather curious. It was conceived and developed by the logicians of the 1930s to formalize the algorithmic aspect of mathematics in a sufficiently simple manner, and thus allowing to formulate a negative answer to Hilbert's conjecture regarding the existence of a universal algorithm capable of solving all mathematical problems. The proof is inspired by Gödel's incompleteness theorem and requires the admission of statements that can work on themselves. In terms of algorithms, it is necessary to consider programs capable of working on themselves. But this is obviously impossible if, in the programming environment, one carefully separates programs and data!\n",
-    "\n",
-    "Church's solution was to create an ingenious algorithmic model with only programs: this is the lambda-calculus.\n",
-    "Church thus contradicted Hilbert's conjecture. Turing reached the same conclusion by constructing instead an algorithmic model (Turing machine) where a program is nothing but data! Thus Turing discovered the very notion and the theoretical realization of a universal machine, which is the foundation of modern computer science. It can also be shown that Church's and Turing's solutions are equivalent.\n",
-    "\n",
-    "\n",
-    "# The manipulation of functional objects in a machine.\n",
-    "\n",
-    "The preceding sections can be summarized as follows: an apparently infinite object can sometimes be coded in the form of a finite text which represents a certain *function*. The example of the chromatic polynomial shows, however, that this *trick* is truly productive only if means are available to *calculate* other functional codings. Let us clarify this point!\n",
-    "\n",
-    "In the example of the chromatic polynomial we looked at functions whose domain and range are the set $\\mathbb{N}$ of the (non-negative) integers. As it turns out, these functions are in fact polynomials. This allows us to write - it would be better to say *encode*  - them in the form of a finite text which consists of signs, coefficients, and of an insignificant letter (for example, $x$), and of exponents. By very simple conventions it is possible to represent such a polynomial, for example, as an ASCII string. The *chromatic polynomial* program must then be able to determine the *difference* polynomial of two given polynomials, in order to exploit the recurrence formula described earlier. More precisely, one must be able to write in the programming language used a two-argument function (the two *representations* of polynomials), which returns a representation of the difference polynomial. This is a simple exercise regardless of the programming language.\n",
-    "\n",
-    "It is easy because our functions are very special: they are polynomial functions. This exercise becomes much more difficult if one wants to handle functions of *any* kind. The first question is one of *coding*: How can one *encode*, in the form of a *finite* string, any function whose domain and range is the set $\\mathbb{N}$ of integers? The alphabet is finite, the set of these strings is enumerable, whereas, on the contrary, the set of functions $\\mathbb{N}\\rightarrow\\mathbb{N}$ has the cardinality of the continuum! Whatever the ingenuity of the writing system, it will only be possible to code a subset of all of these functions.\n",
-    "\n",
-    "Which functions should be selected? How should they be written? How can one write a program which relates, for example, the texts of two such functions to the text of the *difference* function? It turns that logicians, well before computer scientists and computer science, had given much thought to these questions. A good set of functions to select is the set of recursive functions, which, by a certain measure, is a very small subset of the set of all functions. But, in a certain sense, they are the only ones that are interesting! Various methods have been devised to represent them. They have all been demonstrated to be equivalent in terms of their capabilities.\n",
-    "\n",
-    "One of the most interesting representations is *lambda-calculus*. Luckily, the previous issue of Images de Mathématiques contained an excellent article by Michel Parigot entitled \"Proofs and programs: mathematics as\n",
-    "programming language,\" where he explained, among other things, lambda-calculus. See in particular the section *lambda-calculus as a machine language* and section 2 *normalization and lambda-calculus*. Readers who don't have time and energy to refer to Parigot's article might be satisfied with the indications given in section 4 of the present article.\n",
-    "\n",
-    "Unlike the Turing machine which ritually appears at the beginning of every theoretical computer course, the lambda-calculus was almost forgotten at the beginning of this half-century. It first reappeared in the research of the American computer scientist McCarthy who created the *Lisp* language at the end of the fifties of the last century. This programming language, which began out of simple curiosity and without the possibility of concrete applications worthy of the name, is in effect directly inspired by lambda-calculus. Like any formal mathematics, lambda-calculus rapidly produces *terms* whose length is such that it rules out any practical use: very quickly, this length exceeds for example the number of atoms of our galaxy! McCarthy reflected on methods (essentially the use of symbols as abbreviations) which would make it possible to overcome this difficulty. It was a long and difficult task. Sixty years later it is clear that in its current version, *Common Lisp*, it is one of the most powerful programming languages available! For example, the best formal computing systems such as Macsyma, Reduce, Scratchpad, etc, software of a very high complexity, are all based on Lisp.\n",
-    "\n",
-    "Since Lisp is directly inspired by lambda-calculus, it can easily, *during the execution of a program*, create programs which in turn are able to work on other programs to create others... This opens possibilities that are quite inaccessible to ordinary programming Pascal-style languages (Fortran, Ada, C, etc.). And these are precisely the capabilities that one needs to solve the problems of processing *functional code* objects that are considered here. \n",
-    "\n",
-    "For example, the Lisp function which, given two functions on $\\mathbb{Z}$ with values in $\\mathbb{Z}$, returns the difference function, is written quite simply:\n",
-    "```\n",
-    "(setf sub-functions\n",
-    "  #'(lambda (f g)\n",
-    "      #'(lambda (n) (- (funcall f n) (funcall g n)))))\n",
-    "```\n",
-    "The program text can be that reads as follows: The function `sub-functions` requires two arguments `f` and `g` (two functions) and maps them to the function which, given an integer `n`, assigns to it the difference of the two integers obtained by applying `f` and `g` to `n`. Here, we shall not attempt to explain the presence of the \"cabalistic\" signs `#` and `'`. They allow for certain optimizations and scope of identifiers, and are not available in ordinary languages, but we won't discuss them here.\n",
-    "\n",
-    "In the follwoing sequence of Lisp expressions\n",
-    "```\n",
-    "(setf f1 #'(lambda (x) (* x 3)))\n",
-    "(setf f2 #'(lambda (x) (* x x)))\n",
-    "(setf f3\n",
-    "  (funcall sub-functions f1 f2))\n",
-    "```\n",
-    "the function $f_1 (x) = 3x$ and the function $f_2 (x) = x^2$ are defined, and then, *from the codes of these functions*, Lisp constructs the code of the difference function $f_3 = f_1 - f_2$.\n",
-    "\n",
-    "One can continue indefinitely in the same spirit and write, for example, a function whose argument is a binary operator on the integers. This function will return the function which is capable of working on pairs of functions $\\mathbb{N}\\rightarrow\\mathbb{N}$ according to the operator in question:\n",
-    "```\n",
-    "(setf create-op-function\n",
-    "  #'(lambda (operator)\n",
-    "      #'(lambda (f g)\n",
-    "          #'(lambda (n)\n",
-    "              (funcall operator (funcall f n) (funcall g n))))))\n",
-    "```\n",
-    "which one can read as: \"will provide the function which, with two functions $f$ and $g$, will associate the function which, to $n$, ...\". And instead of defining our function `sub-functions` as above, we could simply obtain the same result by:\n",
-    "```\n",
-    "(setf sub-functions (funcall create-op-function #'-))\n",
-    "```\n",
-    "\n",
-    "# Simplical complexes.\n",
-    "\n",
-    "It is hoped that the preceding section will have reassured the reader as to the possibilities of processing functional objects in a machine, even *during* program execution. In this section, we explain how it is possible to use the functional trick to encode *geometric* objects that can be quite monstrous. Playing with monsters in a machine is not, however, a goal in itself, and the few monsters exhibited in this section actually have no real interest. In the next section, we will explain how the same methods allow us to work on machines with highly infinite and *really useful* spaces (at least for mathematicians!). The example of loop spaces, which is easy to understand, is ideal to illustrate our purpose.\n",
-    "\n",
-    "Let us first explain what a *simplicial complex* is. The definition is *combinatorial*, but there is a *geometrical* object associated with any simplicial complex, the one we want to model by the combinatorial definition: a *simplicial complex* $K$ is a pair $K = (V, S)$ where $V$ is any set, the set of vertices of $K$, and $S$ is a set of *finite* subsets of $V$, the set of *simplices* of $K$. These data must satisfy the following conditions:\n",
-    "\n",
-    "1. If $v$ is a vertex of $K$, in other words, if $v\\in V$, then $\\{v\\}\\in S$;\n",
-    "2. If $s$ is a simplex of $K$, in other words, if $s\\in S$, and if $s'\\subset s$, then $s'\\in S$: any sub-simplex of $K$ is still a simplex of $K$.\n",
-    "\n",
-    "Let's say for example $K_1=(V_1,S_1)$, where\n",
-    "$$\n",
-    "\\begin{aligned}\n",
-    "V_1=\\big\\{ & 0,1,2,3,4,5 \\big\\}, \\mathrm{and}\\\\\n",
-    "S_1 = \\big\\{ & \\{\\}, \\\\\n",
-    "             & \\{0\\},\\{1\\},\\{2\\},\\{3\\},\\{4\\},\\{5\\},\\\\\n",
-    "             & \\{0,1\\},\\{0,2\\},\\{1,2\\},\\{2,3\\},\\{3,4\\},\\{3,5\\},\\{4,5\\},\\\\\n",
-    "             & \\{0,1,2\\}\\big\\}.\n",
-    "\\end{aligned}\n",
-    "$$\n",
-    "The complex $K_1$ has six vertices and fifteen simplices. The associated the geometric object can represented as shown in the following figure:\n",
-    "\n",
-    "![](Figure2.png)\n",
-    "\n",
-    "The triangle 012 is *filled* while the triangle 345 is *hollow*. The method of correspondence between lists of vertices and simplices on the one hand and geometric objects on the other hand is clear: the figure associated with a simplicial complex has as many \"marked points\" as there are vertices in the complex. Two marked points are connected by a segment if the set of these two vertices is included in the list of simplices. Three vertices underlie a full triangle, if all of all three vertices appear in the list of simplices, etc. It can be shown that, by chosing a Euclidian space of a sufficiently high dimension, one can always associate with a simplicial complex, sometimes called an *abstract* simplicial complex, a geometrical object of this nature, which is then called a *geometric* simplicial complex.\n",
-    "\n",
-    "Here's another example. With the abstract simplicial complex:\n",
-    "\n",
-    "$K_2=(V_2,S_2)$, where\n",
-    "$$\n",
-    "\\begin{aligned}\n",
-    "V_2=\\big\\{ & 0,1,2,3\\big\\}, \\mathrm{and} \\\\\n",
-    "S_2 = \\big\\{ & \\{\\}, \\\\\n",
-    "             & \\{0\\},\\{1\\},\\{2\\},\\{3\\},\\\\\n",
-    "             & \\{0,1\\},\\{0,2\\},\\{0,3\\},\\{1,2\\},\\{1,3\\},\\{2,3\\},\\\\\n",
-    "             & \\{0,1,2\\}, \\{0,1,3\\}, \\{0,2,3\\}, \\{1,2,3\\}\\big\\}.\n",
-    "\\end{aligned}\n",
-    "$$\n",
-    "we can associate the hollow tetrahedron:\n",
-    "\n",
-    "![](Figure3.png)\n",
-    "\n",
-    "It is hollow because in the list of its simplices the simplex $\\{0,1,2,3\\}$ *does not appear*. Otherwise the associated geometrical object would have been a *solid* tetrahedron.\n",
-    "\n",
-    "A *finite* simplicial complex can easily be machine-coded as a list of simplices. In fact, one could be content with the maximal simplices, the others being deducible. Thus our first example of a simplicial complex could be coded:\n",
-    "```\n",
-    "((0 1 2) (2 3) (3 4) (3 5) (4 5))\n",
-    "```\n",
-    "While the hollow tetrahedron would be written:\n",
-    "```\n",
-    "((0 1 2) (0 1 3) (0 2 3) (1 2 3))\n",
-    "```\n",
-    "And the solid tetrahedron:\n",
-    "```\n",
-    "((0 1 2 3))\n",
-    "```\n",
-    "\n",
-    "Nothing prevents us from considering *infinite* simplicial complexes. Consider, for example, the complex $K_3 = (V_3, S_3)$ where $V_3$ is the set of natural numbers and $S_3$ the set of all finite subsets of $\\mathbb{N}$.\n",
-    "\n",
-    "$K_3=(V_3,S_3)$, where\n",
-    "$$\n",
-    "\\begin{aligned}\n",
-    "V_3=\\big\\{ & 0,1,2,3,4,5,6,7,8,\\ldots\\big\\}, \\mathrm{and}\\\\\n",
-    "S_3 = \\big\\{ & \\{\\}, \\\\\n",
-    "             & \\{0\\},\\{1\\},\\{2\\},\\{3\\},\\{4\\},\\{5\\},\\{6\\},\\{7\\},\\ldots\\\\\n",
-    "             & \\{0,1\\},\\{0,2\\},\\{0,3\\},\\{0,4\\},\\{0,5\\},\\{0,6\\},\\ldots\\\\\n",
-    "             & \\{1,2\\},\\{1,3\\},\\{1,4\\},\\{1,5\\},\\{1,6\\},\\ldots\\\\\n",
-    "             & \\{2,3\\},\\{2,4\\},\\{2,5\\},\\{2,6\\},\\ldots\\\\\n",
-    "             & \\ldots\\\\\n",
-    "             & \\{0,1,2\\}, \\{0,1,3\\}, \\{0,1,4\\}, \\{0,1,5\\},\\ldots\\\\\n",
-    "             & \\{0,2,3\\}, \\ldots\\\\\n",
-    "             & \\ldots \\\\\n",
-    "             & \\{0,1,2,3\\},\\ldots\\\\\n",
-    "             & \\ldots\\\\\n",
-    "             & \\ldots\\big\\}.\n",
-    "\\end{aligned}\n",
-    "$$\n",
-    "\n",
-    "The associated geometric object contains a segment for any pair of different integers, a solid triangle for any triplet of pairwise different integers, a solid tetrahedron for any quadruplet of pairwise different integers, and so on. Obviously, such an object cannot be represented in $\\mathbb{R}^3$, but it is not difficult to define rigorously a geometrical object in $\\mathbb{R}^\\infty$ corresponding to the simplicial complex $K_3$. Here's another example, which is somewhat of a *sub-example* of the preceding one: Take $K_4 = (V_4, S_4)$ where $V_4$ is still the set $\\mathbb{N}$ of natural numbers, and $S_4$ is the set of subsets of $\\mathbb{N}$ which contain *at most* two elements:\n",
-    "\n",
-    "$K_4=(V_4,S_4)$, where\n",
-    "$$\n",
-    "\\begin{aligned}\n",
-    "V_4=\\big\\{ & 0,1,2,3,4,5,6,7,8,\\ldots\\big\\}, \\mathrm{and}\\\\\n",
-    "S_4 = \\big\\{ & \\{\\}, \\\\\n",
-    "             & \\{0\\},\\{1\\},\\{2\\},\\{3\\},\\{4\\},\\{5\\},\\{6\\},\\{7\\},\\ldots\\\\\n",
-    "             & \\{0,1\\},\\{0,2\\},\\{0,3\\},\\{0,4\\},\\{0,5\\},\\{0,6\\},\\ldots\\\\\n",
-    "             & \\{1,2\\},\\{1,3\\},\\{1,4\\},\\{1,5\\},\\{1,6\\},\\ldots\\\\\n",
-    "             & \\{2,3\\},\\{2,4\\},\\{2,5\\},\\{2,6\\},\\ldots\\\\\n",
-    "             & \\ldots\\\\\n",
-    "             & \\ldots\\big\\}.\n",
-    "\\end{aligned}\n",
-    "$$\n",
-    "\n",
-    "This time the associated geometrical object will contain an infinity of segments, but on the other hand no triangle, no tetrahedron, ...\n",
-    "\n",
-    "Of course, it is absolutely impossible to represent such simplicial complexes using lists of simplices. Only lists of finite length can be represented in a machine, and the lists which would be needed for the complexes $K_3$ and $K_4$ are infinite. Given the preparations of the previous sections, the reader will probably guess that we will use the *functional trick* to overcome this difficulty. How should we proceed?\n",
-    "\n",
-    "We may decide the functional coding for a simplicial complex is a function $f$ which can be applied to any list of machine objects and which returns **true** or **false**. In addition, this function must satisfy the following condition: if $f(l) = \\mathbf{true}$ and $l'\\subset l$, then $f(l')=\\mathbf{true}$. It is easy to associate a simplicial complex with such a function $f$: let $V_f$ be the set of objects $v$ such that $f\\big(\\{v\\}\\big) = \\mathbf{true}$, and $S_f$ the set of all lists for which $f$ answers $\\mathrm{true}$. Then $K_f = (V_f, S_f)$ is a simplicial complex called the simplicial complex associated with $f$. By this very simple process, the simplicial complexes are *functionally* coded. Since the function $f$ can *potentially* work on an infinite number of objects (see section 2), nothing prevents us from coding infinite simplicial complexes.\n",
-    "\n",
-    "The various examples of complexes which have been given previously can be coded in Lisp as follows:\n",
-    "\n",
-    "```\n",
-    "(setf K1\n",
-    "  #'(lambda (list)\n",
-    "      (or (subsetp list '(0 1 2))\n",
-    "          (subsetp list '(2 3))\n",
-    "          (subsetp list '(3 4))\n",
-    "          (subsetp list '(4 5))\n",
-    "          (subsetp list '(3 5)))))\n",
-    "```\n",
-    "\n",
-    "If we interrogate `K1` for the list `(0 2)`, it will answer **true**, whereas it will answer **false** for example for the list `(0 3)`. The hollow tetrahedron might be coded like this:\n",
-    "\n",
-    "```\n",
-    "(setf K2\n",
-    "  #'(lambda (list)\n",
-    "      (and      (subsetp list      '(0 1 2 3))\n",
-    "           (not (subsetp '(0 1 2 3) list)))))\n",
-    "```\n",
-    "\n",
-    "This requires that all elements of the argument list can be extracted from the list `(0 1 2 3)`, but all elements of the latter list must not appear at the same time. If this last condition were removed, one would have the functional code of the full tetrahedron. The functional code of the infinite complex $K_3$ is not much longer. It is even shorter:\n",
-    "\n",
-    "```\n",
-    "(setf K3\n",
-    "  #'(lambda (list)\n",
-    "       (every #'integerp list)))\n",
-    "```\n",
-    "\n",
-    "It is enough to check that every element of the list argument is an integer, which, as we see, can easily be written. \n",
-    "\n",
-    "Let $K_4$ be the complex $K_3$ with all the simplices of dimension $> 1$ removed. Topologists call $K_4$ the 1-skeleton of $K_3$, and it can be functionally coded as follows:\n",
-    "```\n",
-    "(setf K4\n",
-    "  #'(lambda (list)\n",
-    "      (and (every #'integerp list)\n",
-    "           (< (length (remove-duplicates list))\n",
-    "              3))))\n",
-    "```\n",
-    "\n",
-    "Indeed, this time it is necessary to verify additionally that the number of *different* vertices in the list is less than 2.\n",
-    "\n",
-    "This description of $K_4$ as the 1-skeleton of $K_3$ is a good opportunity to illustrate some of the functional possibilities of Lisp: we would like to have a function to which we pass two arguments, where the first argument is the functional code of a simplicial complex $K$, and the second argument is a dimension $d$. We want this function to *produce* a functional code of the $d$-skeleton of $K$, which is the new simplicial complex obtained from $K$ by *removing* all the simplices of dimension $>d$. This is very easy:\n",
-    "\n",
-    "```\n",
-    "(setf skeleton\n",
-    "  #'(lambda (complex dimension)\n",
-    "      #'(lambda (list)\n",
-    "          (and (funcall complex list)\n",
-    "               (< (length (remove-duplicates list))\n",
-    "                  (+ 2 dimension)))))\n",
-    "```\n",
-    "\n",
-    "So that instead of getting tired from writing a functional code of $K_4$, one could have asked the Lisp machine to do it:\n",
-    "\n",
-    "```\n",
-    "(setf K4 (funcall skeleton K3 1))\n",
-    "```\n",
-    "\n",
-    "\n",
-    "# Constructing a loop space in a machine.\n",
-    "\n",
-    "Let $K = (V,S)$ be a simplicial complex and $s_0$ one of its vertices, which will play a particular role and which is called the *base point* of $K$. We assume that $K$ is *connected*, in other words, starting from the base point, any other vertex is *accessible* by traveling along the edges of $K$. The loop space of $(K, s_0)$, which we denote by $\\Omega(K,s_0)$, is another simplicial complex defined from $K$ and $s_0$, which is always infinite (except when $V = \\{s_0\\}$). This loop space plays a particularly important role in algebraic topology: it was invented by Jean-Pierre Serre in the early fifties and in a certain sense acts as the *inverse space* of $K$. This is not the place to define in what sense, but it is the type of construction that allowed Jean-Pierre Serre to advance the \"state of the art\" in Algebraic Topology (the homotopy groups of the spheres), a contribution which earned him the Fields Medal.\n",
-    "\n",
-    "It is not difficult to define the loop space and it gives a striking example of the possibilities offered by *functional coding* methods. Since $K = (V, S)$ is given, as well as a vertex $s_0$ of $V$, the *complex* $\\Omega(K, s_0)$, *the loop space of* $(K, s_0)$ is, like every complex, defined by its set of Vertices $V'$ and its set of simplices $S': \\Omega(K, s_0) = (V',S')$.\n",
-    "\n",
-    "Let us first describe the set of vertices $V'$. A vertex of $\\Omega(K, s_0)$ is a loop of $K$ based on $s_0$, by which we mean an infinite sequence of vertices $(a_0, a_1, a_2,\\ldots, a_{k-1}, a_k,\\ldots)$ satisfying the following conditions:\n",
-    "\n",
-    "a) The first vertex of this sequence must be the base point $s_0$ of $K$: $a_0 = s_0$;\n",
-    "\n",
-    "b) There must be an integer $n$ such that, if $k \\geq n$, then $a_k = s_0$;\n",
-    "\n",
-    "c) For every integer $k > 0$, $\\{a_{k-1},a_k\\}$ is a simplex of $K$: $\\{a_{k-1},a_k\\}\\in S$ (repetition is permitted, in which case this simplex has only one element).\n",
-    "\n",
-    "![](Figure4.png)\n",
-    "\n",
-    "This sequence must be understood as a *path* on $K$, more precisely along the edges of $K$. At time 0, we start from the base point: $a_0 = s_0$; at time 1, one reaches the vertex $a_1$ of $K$, which, to be legitimate, requires that $\\{a_0,a_1\\}$ be a simplex of $K$. Intuitively, between times 0 and 1, the loop runs *along* the edge of $K$ between $a_0$ and $a_1$. Similarly, between the instants $k-1$ and $k$, the loop runs along the edge of $K$ between $a_{k-1}$ and $a_k$, which requires that $\\{a_{k-1},a_k\\}$ belongs to $S$. We also require that this journey be essentially finite, which is the role of condition b): after a certain time $n$, the loop remains fixed at the base point $s_0$ of $K$. For example, if $K$ is the example complex $K_1$ of the preceding section with the base $s_0 = 2$, the following sequence $\\lambda = (2, 3, 4, 5, 3, 4, 5, 3, 2, 2, 2,\\ldots)$ is an example of a *vertex* of $\\Omega(K_1, 2)$.\n",
-    "\n",
-    "Thus the data of a *single* vertex of $\\Omega(K, s_0)$ requires several vertices and edges of $K$. Let us now define the simplices of $\\Omega(K, s_0)$. For example, let $\\lambda=(a_0,a_1,\\ldots)$ and $\\lambda'=(a'_0,a'_1,\\ldots$ be two vertices of $\\Omega(K, s_0)$. Under what circumstances is the pair $\\{\\lambda,\\lambda'\\}$ a simplex of $\\Omega(K, s_0)$? The condition that must be satisfied is the following:\n",
-    "\n",
-    "> For each integer $k > 0$, the set $\\{a_{k-1},a_k,a'_{k-1},a'_k\\}$ (repetitions are allowed) must be a simplex of $K$: $\\{a_{k-1},a_k,a'_{k-1},a'_k\\}\\in S$.\n",
-    "\n",
-    "The interpretation of this condition is not difficult. It requires that one be able to define an *intermediate* path between the paths $\\lambda=(a_0,a_1,\\ldots)$ and $\\lambda'=(a'_0,a'_1,\\ldots)$. At the instant $k \\in \\mathbb{N}$, this intermediate path should pass through the middle of the segment $[a_k,a'_k]$, which requires to be defined that $\\{a_k,a'_k\\}$ belongs to $S$.\n",
-    "\n",
-    "Better, at instant $k-\\frac{1}{2}$, the intermediate path must pass through the middle of the segment $\\big[\\lambda(k-\\frac{1}{2}),\\lambda'(k-\\frac{1}{2})\\big]$, which is also the barycenter of the four points $\\lambda(k-1), \\lambda(k),\\lambda'(k-1)$ and $\\lambda(k)$, in other words, $a_{k-1},a_k,a'_{k-1}$ and $a'_k$. Therefore, for this barycentre to be defined, we ask that these four points define a simplex of the complex $K$ (repetitions are permitted). For example, for the example complex $K_1$ of the previous section, if we take $\\lambda=(2,3,4,5,3,2,2,2,\\ldots)$ and $\\lambda'=(2,3,3,4,5,3,2,2,...)$, this condition is not satisfied at time 3 since $\\{3,4,5\\}$ does not belong to $S$, and so $\\{\\lambda,\\lambda'\\}$ *is not* a simplex of $\\Omega(K_1,2)$. On the other hand, if we take $\\mu=(2,0,1,2,2,2,\\ldots)$ and $\\mu'=(2,2,0,1,2,2,\\ldots)$, the condition is always satisfied, essentially because $\\{0,1,2\\}$ belongs to $S$, and therefore $\\{\\mu,\\mu'\\}$ is an element of $S'$: $\\{\\mu,\\mu'\\}$ *is* a simplex of $\\Omega(K_1,2)$.\n",
-    "\n",
-    "More generally and in the same spirit, let $\\lambda^i=(a_0^i,a_1^i,a_2^i,\\ldots), 1\\leq i\\leq m$, be a family of loops of $\\Omega(K, s_0)$. This family will constitute a simplex of $\\Omega(K, s_0)$ if and only if, for every integer $k > 1$, the family $\\{a_{k-1}^1,a_k^1,a_{k-1}^2,a_k^2,\\ldots,a_{k-1}^m,a_k^m\\}$ belongs to $S$, which, intuitively, makes it possible to define a *barycentre* path of the paths $\\lambda^1,\\ldots,\\lambda^m$.\n",
-    "\n",
-    "Let us now examine the possibility of constructing a function with two arguments where the first argument is the functional code of a simplicial complex and the second argument is one of its vertices (the base point), and which returns the functional code of its loop space. This last code must be able to work on lists and must answer 'yes' or 'no' to the question: *is this list a simplex of the loop space complex*? Each list element must be a vertex, which poses a bit of a problem, because a vertex of the loop space has been defined as an *infinite* sequence. But this problem is easy to overcome since condition b) ensures that, starting from a certain rank, which might vary from one sequence to another, all the terms of this sequence are equal to the base point. It is therefore sufficient that such a sequence is represented in the form of a *finite* list, where all the missing terms are equal to the base point. The test of the conditions to be satisfied in order for a list of lists to represent (modulo this convention) a simplex of our loop space is then a small program using inter alia the *functional code of the original complex*. The program transformation of the functional code of a complex to the functional code of its loop space can itself be implemented, for example, by the following program which is shown only to satisfy the possible curiosity of the reader:\n",
-    "```\n",
-    "(setf loop-space\n",
-    "  #'(lambda (K s0)\n",
-    "      #'(lambda (ll)\n",
-    "          (and (maplistp ll)\n",
-    "               (let ((ll (transpose (complete ll s0))))\n",
-    "                 (essential-test K ll)))))\n",
-    "```\n",
-    "The `loop-space` function uses various auxiliary list-processing functions (`maplistp`, `transpose`, `complete`, `essential-test`) whose implementation is a routine programming exercise. As a result, a very modest microcomputer *calculates* in less than one hundredth of a second the functional code of a loop space, a space yet highly infinite!\n",
-    "\n",
-    "\n",
-    "# Applications to algebraic topology.\n",
-    "\n",
-    "In this last section, we describe very briefly the results that can be obtained from this method of functional coding when applied to algebraic topology. The situation is very similar to that which has been explained for the chromatic polynomial and the parallelism is summarized in Table 1.\n",
-    "\n",
-    "The object of the algebraic topology is to associate with (topological) spaces algebraic objects capable of essentially measuring some of their properties. The *homology groups* are a very important example of such an association, however, their precise definition is too esoteric to be explained here. In a way, these groups measure how *perforated* a space is. For example, topologists explain that the first homology group of the Euclidean plane $\\mathbb{R}^2$, denoted by $H_1(\\mathbb{R}^2)$, is zero, whereas if $D$ is the unit disk of this plane, $H_1(\\mathbb{R}^2-D)$ is not zero, which expresses the fact that $\\mathbb{R}^2-D$ is *punctured*. In the present case, this can be seen on the group $H_1$ since the hole in question can be enclosed in a circle, an object of dimension 1. If we did the same for the Euclidean space $\\mathbb{R}^3$ and its unit ball $B$, it would be this time the group $H_2$ which would be non-zero, because the corresponding hole can be enclosed in a sphere, a two-dimensional object. Algebraic topologists can define very precisely these notions which produce, for a space $K$, the homology groups $H_n(K)$, for every positive integer $n$.\n",
-    "\n",
-    "The calculation of the homology groups of many spaces of interest to topologists is a difficult sport and remains a very active research topic today. It is this type of calculation where functional coding methods have recently made significant progress, very much as the chromatic polynomial method makes it possible to simplify the calculation of the chromatic number. The parallel between the two situations is fairly well summarized in this table:\n",
-    "\n",
-    "| Graphs | Algebraic Topology |\n",
-    "|--------|--------------------|\n",
-    "| Graph $G$ | Simplicial set $K$ |\n",
-    "| Chromatic number | Ordinary homology |\n",
-    "| Known chromatic number $N_G$ <br/> Simple construction of $G'$ from $G$ <br/> $N_{G'}=???$ | Known ordinary homology $H_*(K)$ <br/> Simple construction of $K'$ from $K$ <br/> $H_*(K')=???$ |\n",
-    "| Chromatic polynomial $\\chi_G$ | Effective homology $EH_*(K)$ |\n",
-    "| The chromatic polynomial contains an infinity of information | The effective homology contains an infinity of information |\n",
-    "| *Functionally* coded information; on a machine, this information appears as a *finite* string of bits | *Functionally* coded information; on a machine, this information appears as a *finite* string of bits |\n",
-    "| The chromatic polynomial contains the chromatic number as a *by-product* | The effective homology contains the ordinary homology as a *by-product* |\n",
-    "| Construction of $G$ from $G_1, G_2$ <br/> Algorithm for $N$ from $N_1,N_2$ |  Construction of $K$ from $K_1, K_2$ <br/> Algorithm for $EH$ from $EH_1,EH_2$\n",
-    "\n",
-    "There is, however, a slight difference in the case of algebraic topology: many methods (exact sequences and spectral sequences in particular) had already been developed by topologists, so that when we construct a space $K$ from spaces $K_1$ and $K_2$ whose homologies are known, we can glean at least some information about the homology of $K$. Often we can even deduce the homology of $K$, but often these methods prove insufficient.\n",
-    "\n",
-    "The methods of *effective homology*, developed by the author in collaboration with other researchers (see references at the end of the article), make it possible to overcome the difficulties presented by the other methods. The constraints of this article do not allow much more explanation. Let us say only that the objects with *effective homology* contain, like a chromatic polynomial, an infinity of information, but the *functional trick* nevertheless allows to manipulate them without any particular difficulty on theoretical and concrete machines. The classical methods of algebraic topology are thus transformed into true *algorithms* that are capable of computing the coveted groups.\n",
-    "\n",
-    "Numerous computability results have already been obtained in this way, in particular for the homology groups of iterated loop spaces. By implementing these methods on concrete machines, it would be most interesting of course to calculate the homology and homotopy groups that have hitherto resisted such attempts. A lot of work is going on in this direction, specifically for the homology of iterated loop spaces.\n",
-    "\n",
-    "The wide field of research, which ranges from the purest mathematics (homological algebra and algebraic topology) to the very concrete problems of the realization of algorithms on machines, is exciting. It also opens unexpected horizons for researchers in complexity (what can we say about the complexity of algorithms based on functional programming?) and parallel computation.\n",
-    "\n",
-    "\n",
-    "**To learn more:**\n",
-    "\n",
-    "- Francis SERGERAERT. *Homologie effective*, I et II. C. R. Acad Sc. Paris, Série I, 1987, vol. 304, pp 279-282 et 319-321.\n",
-    "- Julio RUBIO, Francis SERGERAERT. *Homologie effective et suites spectrales d'Eilenberg-Moore*. C. R. Acad. Sc. Paris, Série I, 1988, vol. 306, pp 723-726.\n",
-    "- Francis SERGERAERT. *The computability problem in algebraic topology*. Prépublication de l'Institut Fourier, n o 119, 1988.\n",
-    "- Julio RUBIO. *Homologie effective des espaces de lacets itérés*. Prépublication de l'Institut Fourier, no. 138, 1989"
-   ]
-  }
- ],
- "metadata": {
-  "kernelspec": {
-   "display_name": "SBCL Lisp",
-   "language": "lisp",
-   "name": "lisp"
-  },
-  "language_info": {
-   "codemirror_mode": "text/x-common-lisp",
-   "mimetype": "text/x-common-lisp",
-   "name": "common-lisp",
-   "pygments_lexer": "common-lisp",
-   "version": "X3J13"
-  }
- },
- "nbformat": 4,
- "nbformat_minor": 2
-}
diff --git a/examples/ie/Infinity and Effectiveness from a Functional Point of View.pdf b/examples/ie/Infinity and Effectiveness from a Functional Point of View.pdf
deleted file mode 100644
index e0d7c62..0000000
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diff --git a/examples/moebiuss.png b/examples/moebiuss.png
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diff --git a/examples/overview.lisp b/examples/overview.lisp
deleted file mode 100644
index 5681a33..0000000
--- a/examples/overview.lisp
+++ /dev/null
@@ -1,141 +0,0 @@
-
-(require 'asdf)
-
-(asdf:operate 'asdf:load-op 'kenzo)
-
-(format t "~%Initializing Kenzo...")
-(cat:cat-init)
-(cat:kenzo-version)
-
-(setf cat:*results-verbose* nil)
-
-(format t "~%Creating simplicial set Moore(Z/2Z,3):")
-(cat:def m23 (cat:moore 2 3))
-
-(format t "~%~%Calculating the homology groups of dimensions 0 to 4:~%")
-(cat:homology m23 0 5)
-
-(format t "~%~%Creating the cartesian product Moore(Z/2Z,3)xMoore(Z/2Z,3):~%")
-(cat:def m23xm23 (cat:crts-prdc m23 m23))
-
-(let ((b (cat:basis m23xm23 6)))
-  (format t "~%~%Basis in dimension 6:~%")
-  (print b)
-  (format t "~%~%Length: ~A~%" (length b)))
-
-(format t "~%~%Creating the tensor product Moore(Z/2Z,3)#Moore(Z/2Z,3):~%")
-(cat:def t2m23 (cat:tnsr-prdc m23 m23))
-
-(format t "Basis in dimension 6: ~%")
-(print (cat:basis t2m23 6))
-
-(format t "~%~%Calculating the homology groups of dimensions 0 to 8:~%")
-(cat:homology t2m23 0 8)
-
-(format t "~%Creating the abelian simplicial group K(Z,1):")
-(cat:def kz1 (cat:k-z 1))
-
-(format t "~%~%Calculating coproduct:")
-(print (cat:cprd kz1 4 '(2 3 4 5)))
-
-(format t "~%~%Calculating product:")
-(print (cat:aprd kz1 6 (cat:tnpr 2 '(1 2) 4 '(3 4 5 6))))
-
-(format t "~%Creating the abelian simplicial group K(Z/2Z,2):")
-(cat:def k-z2-2 (cat:k-z2 2))
-
-(format t "~%~%Calculating the homology group of dimension 4:~%")
-(cat:homology k-z2-2 4)
-
-(format t "~%Creating sphere S^3:")
-(cat:def s3 (cat:sphere 3))
-(print s3)
-
-(format t "~%Creating loop space Omega^2S^3:")
-(cat:def o2s3 (cat:loop-space s3 2))
-
-(format t "~%~%Calculating the homology groups of dimensions 4 to 6:~%")
-(cat:homology o2s3 4 6)
-
-(format t "~%Creating loop space Omega^1S^3:")
-(cat:def os3 (cat:loop-space s3))
-
-(format t "~%~%Creating the canonical generator of pi_2(Omega^1S^3):")
-(cat:def L1 (cat:loop3 0 's3 1))
-
-(cat:def null-simp (cat:absm 3 cat:+null-loop+))
-
-(format t "~%~%Pasting a 3-simplex named D3 to Omega^1S^3:")
-(cat:def dos3 (cat:disk-pasting os3 3 '<D3>
-			       (list L1 null-simp L1 null-simp)))
-
-(format t "~%~%Calculating the homology groups of dimensions 2 to 4:~%")
-(cat:homology dos3 2 4)
-
-(format t "~%~%Creating loop space of disk pasting space:")
-(cat:def odos3 (cat:loop-space dos3))
-
-(format t "~%~%Calculating the homology group of dimensions 5:~%")
-(cat:homology odos3 5)
-
-(format t "~%~%Is S^3 of type Kan? ~A~%" (typep s3 'cat:kan))
-
-(format t "~%~%Is Omega^1S^3 a simplicial group? ~A~%"
-	(typep os3 'cat:simplicial-group))
-
-(format t "~%~%Is Omega^1S^3 an abelian simplicial group? ~A~%"
-	(typep os3 'cat:simplicial-group))
-
-(format t "~%~%Creating L2 = (S3)^2 in Omega^1S^3):")
-(cat:def L2 (cat:loop3 0 's3 2))
-
-(format t "~%~%Applying the product of the underlying algebra to L2#L2:")
-(cat:def square (cat:aprd os3 4 (cat:tnpr 2 L2 2 L2)))
-
-(format t "~%~%Select the generator part of the second element:")
-(cat:def L4 (cat:gnrt (second (cat:cmbn-list square))))
-
-(format t "~%~%Create the \"Kan hat\", the list of the faces 1, 2, 3, 4 of L4:")
-(cat:def hat (mapcar #'(lambda (i) (cat:face os3 i 4 L4)) '(1 2 3 4)))
-
-(format t "~%~%Try to find a filling of this \"Kan hat\":")
-(cat:def kan-simplex (cat:kfll os3 0 4 hat))
-
-(format t "~%~%Face two of the previous simplex is the same as face 2 of L4:")
-(print (cat:face os3 2 4 kan-simplex))
-(print (second hat))
-
-(format t "~%~%Creating the classifying space of Omega^1S^3):")
-(cat:def cls-os3 (cat:classifying-space os3))
-
-(format t "~%~%Is it a simplicial group? ~A~%"
-	(typep cls-os3 'cat:simplicial-group))
-
-(format t "~%~%Verifying that its 4th homology is null:~%")
-(cat:homology cls-os3 4)
-
-(format t "~%~%Constructing the fundamental cohomology class of Moore(Z/2Z,3):")
-(cat:def ch3 (cat:chml-clss m23 3))
-
-(format t "~%~%Build a fibration over Moore(Z/Z2,3) associated w/ this class:")
-(cat:def f3 (cat:z2-whitehead m23 ch3))
-
-(format t "~%~%Build the fibration's total space:")
-(cat:def x4 (cat:fibration-total f3))
-
-(format t "~%~%The H_4 of this total space is the pi_4 of Moore(Z/2Z):~%")
-(cat:homology x4 3 5)
-
-(format t "~%~%We iterate the process to compute pi_5 of Moore(Z/2Z):~%")
-(cat:def ch4 (cat:chml-clss x4 4))
-
-(cat:def f4 (cat:z2-whitehead x4 ch4))
-
-(cat:def x5 (cat:fibration-total f4))
-
-(cat:homology x5 4 6)
-
-(format t "~%~%Hence, pi_5(Moore(Z/2Z)) is Z/4Z. QED~%")
-
-#+(or ccl ecl) (quit)
-#+sbcl (sb-ext:exit)
diff --git a/examples/pcl/Packages in Common Lisp.ipynb b/examples/pcl/Packages in Common Lisp.ipynb
deleted file mode 100644
index 129453c..0000000
--- a/examples/pcl/Packages in Common Lisp.ipynb	
+++ /dev/null
@@ -1,5655 +0,0 @@
-{
- "cells": [
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "# Packages in Common Lisp, a tutorial\n",
-    "\n",
-    "By [*Francis Sergeraert*](https://www-fourier.ujf-grenoble.fr/~sergerar/Papers/Packaging.pdf), January 2014\n",
-    "(Adapted for [`cl-jupyter`](https://github.com/fredokun/cl-jupyter) by Gerd Heber, December 2016)\n",
-    "\n",
-    "> In `cl-jupyter`, the current package is called `\"CL-JUPYTER-USER\"`. On the other hand, the paper was written with `\"COMMON-LISP-USER\"` as the current package. Let's begin at the beginning!"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 1,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "#<PACKAGE \"COMMON-LISP-USER\">"
-      ]
-     },
-     "execution_count": 1,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(in-package \"COMMON-LISP-USER\")"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {
-    "latex_metadata": {
-     "author": "Francis Sergeraert",
-     "date": "January 2014",
-     "title": "Packages in Common Lisp, a tutorial"
-    }
-   },
-   "source": [
-    "## Introduction.\n",
-    "\n",
-    "It is not possible to write a serious piece of code without the use of some kind of *identifiers* or names. Such identifiers are convenient means for the programmer to reference, process and modify data using more or less descriptive names, which represent the data and depend in some way on the context. The standard *modularization* technology encourages the divison of large programs in *modules*. Such modules can be relatively independent of each other, but conversely, they must be able to *communicate*. Most programming languages offer methods for such an organization. For example, the set of identifiers of a module could be divided into two parts, the *private* identifiers, known only inside this module, and the *public* identifiers, known everywhere.\n",
-    "\n",
-    "In this domain as in many others, Common Lisp is by far the most powerful and flexible programming language. At the expense of considerable complexity, Common Lisp's modular technology requires a good grasp of the corresponding *definitions* in the language standard. If the ANSI definition of the language is the only available documentation, these definitions are not easy to understand. An identifier in Lisp is a *symbol* which has a rich internal structure and which has lifetime and visibility during a Lisp session. The modular structure of a Lisp program is defined through the *packaging* system, which allows a programmer to divide a large program into several files, where each file is aware of all the symbols of a certain package, among them the current *default* package, and only the *external* (public) symbols of some other packages. A symbol which is not external in a package is *internal* (private). Also, a package may *import* (that is, \"see\") an arbitrary collection of symbols, internal or external to other packages. In the general spirit of Lisp, the whole structure of such an organization, if necessary, can be modified dynamically, even though this is not usually the best course of action.\n",
-    "\n",
-    "In this tutorial, a *mathematical* definition of this system is provided. This should elucidate the process for many a Lisp programmer and enable her to use it more effectively. A basic but *inexact* description of the packaging system is the following:\n",
-    "\n",
-    "- A *package* is a Lisp object in the same way that numbers, lists, and character strings are Lisp objects. In particular, the *type* of a package object is the system class [`package`](http://clhs.lisp.se/Body/t_pkg.htm). In Common Lisp, packages are first class citizens, which means they can be the value of a symbol, can be passed as an argument to a function, can be returned by a function, etc.\n",
-    "- A *symbol* is a Lisp object whose *type* is the system class [`symbol`](http://clhs.lisp.se/Body/t_symbol.htm). The comments made about packages apply for symbols. In particular, a symbol can be the value of another symbol, or even of itself.\n",
-    "- Symbols are divided into packages.\n",
-    "- At any time during a Lisp session, some package is the *default package* and, as a first approximation, only the symbols of this package are *accessible*. The default package can be modified at any time by the user or a program.\n",
-    "- If necessary, there are several methods to access the symbols of packages other than the default package. Conversely, a package may make its symbols more or less easily accessible from the other packages.\n",
-    "\n",
-    "This first approximation of the packaging system conveys a general idea of its organization, but general ideas can be deceiving. For example, the idea that the symbols are divided into packages is essentially *false*. More precisely, this divison can be made to appear essential (!), via the so-called home package of a symbol, but it plays only a *minor* role and can be ignored by the programmer risk-free. This notion of a home package is terribly misleading for beginners when they have to design non-trivial packaging structures. In a Lisp environment, one has to deal with two realms, the space of symbols and the space of packages. It is only *inside* of packages that something can be read, which, as an organization, looks a *little* like a division of symbols into packages, but the symbols themselves essentially *ignore* this division. Our subject is to clarify and explain this organization.\n",
-    "\n",
-    "The ANSI definition of the packaging system is a *complete* description of this organization, and, in a sense, nothing is missing. However, experience shows that it is easily misunderstood, especially, in non-trivial situations, where it can lead to erroneous programming choices and mysterious bugs. The ANSI definition of packaging is complete and it is the perfect *Reference Manual*. However, for a topic of this complexity a reference guide is not sufficient and a *User Guide* might be useful. And for that matter, an elementary *mathematical* description of the Common Lisp packaging system might help programmers to understand it, and then to use it with greater ease and also to greater effect. In every domain, when precise mathematical language can be employed and is understood, the state-of-affairs improves.\n",
-    "\n",
-    "We begin with a review of the ANSI definition of the packaging system while adding in parallel a mathematical description of the main concepts. Finally, we give a complete mathematical definition of this system as a set of mathematical formulas.\n",
-    "\n",
-    "## Main sets of objects.\n",
-    "\n",
-    "The first part of the packaging system is made of three disjoint sets:\n",
-    "\n",
-    "- The set $St$ of *strings*.\n",
-    "- The set $P$ of *packages*.\n",
-    "- The set $Sm$ of *symbols*.\n",
-    "\n",
-    "In our description of the packaging system, the statuses of these sets are different. Think of the (infinite) set $St$ of *strings* as made of *all* the character strings that *can* be used by a user or a program at any time. Any string can be used at any time, whatever the history of the Lisp session in which we are working may be. In the packaging system, most often, a particular string is used only for a short time, mainly during the read-eval-print loop, when the Lisp reader works. A string is just an intermediary connecting the user and the Lisp session, more precisely the current environment. In contrast, in a given environment, at any time during a Lisp session, some finite set $P$ of *specific* packages is installed in this environment, and also a finite set $Sm$ of *specific* symbols is available. Those packages and symbols can *then* be used, and they are the historical consequence of the current Lisp session. Various Lisp functions allow the user to modify the sets $P$ and $Sm$, and the way they are combined and releated to each other. In other words, consider the set of strings $St$ as constant, vast and independent of the environment, while, on the contrary, the sets $P$ and $Sm$ are restricted, they change during a Lisp session, and they are an essential component of the *current* environment.\n",
-    "\n",
-    "## Packages.\n",
-    "\n",
-    "There is a simple, almost bijective (one-to-one), correspondence between strings and packages, and a convenient place to start our subject. First, at any time during a Lisp session, a *default package* is defined and it can be discovered via the global symbol [`*package*`](http://clhs.lisp.se/Body/v_pkg.htm):"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 2,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "#<PACKAGE \"COMMON-LISP-USER\">"
-      ]
-     },
-     "execution_count": 2,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "*package*"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "This is to be read as: the *value* of the *symbol* `*package*` is the package whose *name* is the string `\"COMMON-LISP-USER\"`. The types `symbol` and `package` are system-defined, disjoint sets of machine objects. A symbol is frequently used as a convenient intermediate object, which allows the user to reach some object of arbitrary nature, its *value*. Here, `*package*` is a symbol, the value of which is the package named `\"COMMON-LISP-USER\"`. Technically, a symbol contains a pointer to its (possible) value, here a package which happens to be the package used ordinarily in a simple Lisp session. There are no facilities to refer to a package object *directly*. However, one can use its *name* and the function [`find-package`](http://clhs.lisp.se/Body/f_find_p.htm) to obtain a reference:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 3,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "#<PACKAGE \"COMMON-LISP-USER\">"
-      ]
-     },
-     "execution_count": 3,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(find-package \"COMMON-LISP-USER\")"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Conversely, given a package, the function [`package-name`](http://clhs.lisp.se/Body/f_pkg_na.htm) returns its name:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 4,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\"COMMON-LISP-USER\""
-      ]
-     },
-     "execution_count": 4,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(package-name (find-package \"COMMON-LISP-USER\"))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "The example was given to illustrate that the functions `find-package` and `package-name` are the inverse of each other, defining a 1-1 correspondence between the packages *currently* defined in the environment and their respective names, some character strings. Because of rules not of interest here, it is common and convenient to use only uppercase character strings to name packages. If a name does not correspond to any current package, the `find-package` function returns the symbol `nil`, usually displayed uppercase:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 5,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 5,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(find-package \"COMMON-LISP-user\")"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "which illustrates that a package name is case-sensitive. Frequently, only a few packages are in use, and because of their importance, descriptive names are used. These descriptive names can be a little long, and it is possible to define and use various *nicknames* for these names. For example, the `\"COMMON-LISP-USER\"` package usually has the nicknames `\"CL-USER\"` and `\"USER\"`. The function [`package-nicknames`](http://clhs.lisp.se/Body/f_pkg_ni.htm) can be used to retrieve the list of nicknames (strings) for a package, which doesn't include the name of the package."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 6,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "#<PACKAGE \"COMMON-LISP-USER\">"
-      ]
-     },
-     "execution_count": 6,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(find-package \"COMMON-LISP-USER\")"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 7,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(\"CL-USER\")"
-      ]
-     },
-     "execution_count": 7,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(package-nicknames (find-package \"COMMON-LISP-USER\"))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "If a package is to be unambiguously identified by its name or one of its nicknames, two different packages must have disjoint sets of *name + nicknames*.\n",
-    "\n",
-    "## Tracking a symbol.\n",
-    "\n",
-    "The Lisp symbols are very particular when compared to the identifiers of other programming languages. They persist throughout the runtime of an environment and are an important component of the power of Lisp. A package is referenced via its name; the same goes for a symbol, but the process is much more complex. The first and most common method to create or \"to *allocate* a symbol\" consists in just writing it down and passing it to the Lisp reader using the standard Lisp conventions. In a Lisp environment, there is a set of \"pre-defined\" symbols ready to be used. To caution the reader about the complexity of the subject, we begin with a seemingly strange example:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 8,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(NIL NIL)"
-      ]
-     },
-     "execution_count": 8,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(multiple-value-list (find-symbol \"X\" \"COMMON-LISP-USER\"))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 9,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "UNBOUND-VARIABLE: \n",
-      "  #<UNBOUND-VARIABLE X {1004980253}>\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 9,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "x"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 10,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(X :INTERNAL)"
-      ]
-     },
-     "execution_count": 10,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(multiple-value-list (find-symbol \"X\" \"COMMON-LISP-USER\"))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "The function [`find-symbol`](http://clhs.lisp.se/Body/f_find_s.htm) is analogous to the function `find-package`: given some *name*, a character string, it looks for a symbol with this name. Remember the correspondence between packages and names? A similar correspondence exists between symbols and names, but it's more involved. In particular, a name is *never sufficient* to determine a symbol, a *package* is also necessary. This is why the `find-symbol` function requires *two* arguments, the name of the symbol and the package with respect to which the search is to be done.\n",
-    "\n",
-    "At the beginning of our story, no symbol with the name `\"X\"` existed in the default package `\"COMMON-LISP-USER\"`, and the return value of `find-symbol` is negative, `nil`. (We will explain the second `nil` value in a moment.) Then we pass the Lisp reader the one character expression '`x`'. Lisp evaluates it according to its *read-eval-print* cycle. First, Lisp *reads* the expression and notices that the symbol `x` is used. It examines the current package `\"COMMON-LISP-USER\"`, and does *not* find such a symbol. Before doing anything else, Lisp *allocates* (creates) this symbol, the right terminology being: \"Lisp *interns* a symbol `x` of name `\"X\"` in the package `\"COMMON-LISP-USER\"`.\" To refer to this symbol, the pair made of *its* name `\"X\"` and the (not *its*!!) package `\"COMMON-LISP-USER\"` are necessary, but it would be cumbersome to have to write the expression `(find-symbol \"X\" \"COMMON-LISP-USER\")` every time this symbol is used. To simplify the process of referring to a symbol the designers of Lisp have organized the workspace as follows: if a symbol is read, its character string is capitalized, giving its *name*, and the default package is assumed. In other words, the text `'x'` is roughly  equivalent to the text `(find-symbol \"X\" \"COMMON-LISP-USER\")`. How convenient! ('Roughly', because '`x`' may trigger the allocation of a symbol. In contrast, `find-symbol` never allocates a symbol; but see the function `intern` later.) In the second expression of our example, once Lisp has \"understood\" that the user intends to use the symbol `x`, and observing that such a symbol is not present in the package `\"COMMON-LISP-USER\"`, it allocates a symbol of name `\"X\"` and *interns* it in the package `\"COMMON-LISP-USER\"`. More specifically, a pointer referring to the just allocated symbol is added to the list $InS(p)$ of the internal symbols of the package $p$.\n",
-    "\n",
-    "Note also that it is common in Lisp to input the symbols in lowercase letters, and Lisp prints them in uppercase. This might be convenient for distinguishing input from output in an interactive session, but requires some clarification. In particular, there is no difference between the symbols `nil` and `NIL`, whereas the strings `\"nil\"` and `\"NIL\"` are different."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 11,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(NIL NIL)"
-      ]
-     },
-     "execution_count": 11,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(multiple-value-list (find-symbol \"nil\" \"COMMON-LISP-USER\"))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 12,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(NIL :INHERITED)"
-      ]
-     },
-     "execution_count": 12,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(multiple-value-list (find-symbol \"NIL\" \"COMMON-LISP-USER\"))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "The fruitless search for a *symbol* with the lower-case name `\"nil\"` (a *string*) returns a double negative answer, but it is the second `NIL` that is meaningful! Compare that with the second expression which has the same first return value, but a different second one. The symbol `NIL` also plays in Lisp the role of the boolean *false*, which creates an ambiguity: if the answer is the symbol `NIL` is that a negative answer or is it a positive answer made of the symbol `NIL`? The ambiguity is resolved by the *second* return value. In the first case, the second `NIL` *confirms* that the first `NIL` is to be interpreted as the boolean *false*. In the second expression, the second return value `:INHERITED`, not a negative, indicates that the symbol `NIL` has been found, and that its *accessibility* via the package `\"COMMON-LISP-USER\"` is *inherited*, a point to be explained later. In other words, the function `find-symbol` returns a genuine symbol *and* its accessibility via the package argument, or a pair of `nil`'s if no symbol is found. The logician can deduce that an accessibility cannot be the symbol `nil`!\n",
-    "\n",
-    "Let us return to the one character expression '`x`'. The read part of the read-eval-print loop cycle reads the symbol `x` and interns it in the package `\"COMMON-LISP-USER\"`. The expression is *read* and must now be *evaluated*. The evaluation of a symbol consists in looking for a *value* of this symbol. To this end a value pointer in the symbol's internal representation is examined. In this case it is found that, at this time, there is no value for the freshly allocated symbol `x`. Therefore the *eval* step of the *read-eval-print* cycle generates an error, terminating the cycle with an informative error message. In any case, a symbol of name `\"X\"` is now present in the package `\"COMMON-LISP-USER\"`, as confirmed by the value of the last expression. The symbol's accessibility via the `\"COMMON-LISP-USER\"` package is *internal*, which is to be explained later.\n",
-    "\n",
-    "## Examining a symbol.\n",
-    "\n",
-    "A symbol is a Lisp object with a rich internal structure and there are several functions for exploring symbols and their properties. Let us examine in detail the symbol `x` allocated in the previous section."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 13,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\"X\""
-      ]
-     },
-     "execution_count": 13,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(symbol-name 'x)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "The [`symbol-name`](http://clhs.lisp.se/Body/f_symb_2.htm) function returns the *name* of a symbol; it is analogous to the `package-name` function for a package. The Lisp function `symbol-name` is crucial for our subject, and we denote it as a mathemaical function $sn: Sm \\longrightarrow St$, a function which in general is not injective: several symbols may have the same name, this is our main subject.\n",
-    "\n",
-    "Note that in the previous expression the symbol `x` has been quoted `'x` to prevent its evaluation. More precisely, `'x` is an abbreviation for the expression `(quote x)`, where [`quote`](http://clhs.lisp.se/Body/s_quote.htm) is a *special* function which *does not* evaluate its argument, and it returns this argument as is. Hence, the previous expression is equivalent to:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 14,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\"X\""
-      ]
-     },
-     "execution_count": 14,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(symbol-name (quote x))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Here, the non-quoted `x` does not generate an error. If instead you do not quote the symbol `x` (implicitly via `'`, or explicitly via `quote`) it will be evaluated before being used and generate an error:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 15,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "UNBOUND-VARIABLE: \n",
-      "  #<UNBOUND-VARIABLE X {1004BFF623}>\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 15,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(symbol-name x)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "The package which *owns* a symbol, its *home package*, can be determined with the function [`symbol-package`](http://clhs.lisp.se/Body/f_symb_3.htm)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 16,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "#<PACKAGE \"COMMON-LISP-USER\">"
-      ]
-     },
-     "execution_count": 16,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(symbol-package 'x)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 17,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(X :INTERNAL)"
-      ]
-     },
-     "execution_count": 17,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(multiple-value-list (find-symbol \"X\" \"COMMON-LISP-USER\"))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "As we have just seen, a symbol produces a name and a package (with the help of `symbol-name` and `symbol-package`). Conversely, given a name and a package, `find-symbol` produces the symbol with this name *via* this package. The reader might think that there is a correspondence between symbols and pairs of strings and packages:\n",
-    "$$Sm \\longleftrightarrow St\\times P$$\n",
-    "However, the situation is more involved: for the beginner, this might be a convenient point of view, but in fact such a point of view is wrong. If you intend to fully understand the complex relationship between strings, packages and symbols, please forget this tempting but terribly misleading correspondence. The goal of the next sections is to establish the correct point of view. For completeness we finish this section with a brief glance at the other data possibly stored in a symbol. A symbol can have a value. You may remember that in our Lisp session the symbol `x` does not (yet) have a value. This can be established by the predicate [`boundp`](http://clhs.lisp.se/Body/f_boundp.htm):"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 18,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 18,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(boundp 'x)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "The main method to give a symbol a value is the [`setf`](http://clhs.lisp.se/Body/m_setf_.htm) function (a macro). In most Common Lisp implementations, the `setf` macro may be used directly, in which case the default status of the argument symbol is *variable*. In strict ANSI implementations such as SBCL here, a `defvar` statement is required to explicitly define this status. Other possible statuses are *constant* (via `defconstant`) and *parameter* (via `defparameter`)."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 19,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "X"
-      ]
-     },
-     "execution_count": 19,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(defvar x)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 20,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(4 5 6)"
-      ]
-     },
-     "execution_count": 20,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(setf x '(4 5 6))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 21,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "T"
-      ]
-     },
-     "execution_count": 21,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(boundp 'x)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Note that the first argument of `setf`, the symbol `x`, is not evaluated. Otherwise an error would be generated, since the symbol `x` does not yet have a value. After the `(setf ...)` expression has been evaluated, the symbol `x` does have a value, in this case, the list `(4 5 6)`. This value would now be the result of the evaluation of the expression `x`. It can also be obtained with the function [`symbol-value`](http://clhs.lisp.se/Body/f_symb_5.htm). (In this tutorial, we do not study the possible difference between, on the one hand, the simple *evaluation* of the symbol `x` asked for by the expression `'x'` and the *evaluation* of `(symbol-value 'x)` on the other. In our elementary examples there is no difference between the two. Possible differences might come from different variable scopes, such as *lexical* or *dynamic*, but this subject is not studied here.) "
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 22,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(4 5 6)"
-      ]
-     },
-     "execution_count": 22,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "x"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 23,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(4 5 6)"
-      ]
-     },
-     "execution_count": 23,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(symbol-value 'x)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Don't forget to quote the symbol! See the following error:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 24,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "TYPE-ERROR: \n",
-      "  #<TYPE-ERROR expected-type: \"SYMBOL\"datum: (4 5 6)>\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 24,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(symbol-value x)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "A symbol can also have a *functional value*. This does not mean that the value we just discussed could be a function (which it could be!). It means that *besides* the previous value, a symbol can also have an *additional* value, a function, which can be used independently of the \"ordinary\" value of this symbol. For example the function $n \\mapsto 10−n$ could be recorded as the *functional* value of the same symbol, and this function could then be used as shown below."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 25,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "X"
-      ]
-     },
-     "execution_count": 25,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(defun x (n) (- 10 n))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 26,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "7"
-      ]
-     },
-     "execution_count": 26,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(x 3)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Both values coexist in the symbol without any interference:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 27,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(4 5 6)"
-      ]
-     },
-     "execution_count": 27,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(symbol-value 'x)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 28,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "#<FUNCTION X>"
-      ]
-     },
-     "execution_count": 28,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(symbol-function 'x)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "and can be used jointly and independently:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 29,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "6"
-      ]
-     },
-     "execution_count": 29,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(x (first x))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "You might already suspect that the position of `x` just after a left parenthesis `(x ...)` makes Lisp extract the *functional* value and not the \"ordinary\" value. This is correct, but not the subject of this tutorial. Finally, we mention only in passing the following:\n",
-    "\n",
-    "1. A symbol can have a functional value while not having an ordinary value.\n",
-    "2. An ordinary value can be a functional object, usually then called via `funcall` or `apply`.\n",
-    "3. A symbol also contains a property list or `plist`, with many possible uses, but not at all studied here.\n",
-    "\n",
-    "The internal structure of the [symbol](http://clhs.lisp.se/Body/t_symbol.htm#symbol) `x` might be visualized thus:\n",
-    "\n",
-    "```\n",
-    "+-----------------+\n",
-    "| Name          o-|-----> \"x\"\n",
-    "+-----------------+\n",
-    "| Value         o-|-----> (4 5 6)\n",
-    "+-----------------+\n",
-    "| Function      o-|-----> (lambda (n) (- 10 n))\n",
-    "+-----------------+\n",
-    "| Package       o-|-----> #<PACKAGE \"COMMON-LISP-USER\">\n",
-    "+ ----------------+\n",
-    "| Property list o-|-----> NIL\n",
-    "+-----------------+\n",
-    "```\n",
-    "\n",
-    "## But what the hell is a package?\n",
-    "\n",
-    "Now we attack the heart of our subject.\n",
-    "\n",
-    "> **Fact 1:** A package $p\\in P$ maintains four fundamental lists:\n",
-    "- A list $InS(p)$ of its internal symbols.\n",
-    "- A list $ExS(p)$ of its external symbols.\n",
-    "- A list $ShgS(p)$ of its shadowing symbols.\n",
-    "- A list $U(p)$ of its used packages.\n",
-    "\n",
-    "The first important fact toward understanding the subject is this: the first three lists are lists of *symbols* or, more precisely, lists of pointers (machine addresses) aimed at the symbols. Every symbol has a *unique* \"existence\": a symbol is a unique machine object in the environment, but *several* packages may *see* the same symbol, that is, include the machine address of this symbol. In particular these lists are not lists of symbol names (strings). There is another mechanism that allows Lisp to reach a symbol given its name. Every symbol can be accessed directly via a suitable package, and several packages can in general play this role for the same symbol at a given moment in a Lisp session. For example, all the [standard Lisp symbols](http://clhs.lisp.se/Front/X_Symbol.htm) in the `\"COMMON-LISP\"` package typically are accessible via any package.\n",
-    "\n",
-    "No duplicate symbol (more precisely, no duplicate pointer) is to be found in each of these lists. Also the relations $InS(p)\\cap ExS(p)=\\emptyset$ and $ShgS(p)\\subset InS(p)\\cup ExS(p)$ must be satisfied, for reasons to be studied later.\n",
-    "\n",
-    "> **Fact 2:** Given the current set of packages, assumed *coherent*, and given the current state of all the fundamental lists of these packages, the function `find-symbol` can unambiguously determine *whether* a symbol of a given name (some string) is *accessible* via some package; if so, this symbol is unique.\n",
-    "\n",
-    "The importance of the package argument of `find-symbol` could make the reader believe the function `symbol-package` will be useful for various tests. This is not the case: All this function returns is the \"birth place\" of the symbol, technically called its *home package*, which says almost nothing about the current status of this symbol with respect to any package. All it says is that at least it is *interned* in this package. In particular, a symbol can be accessible via several packages, possibly different from its home package. Here is a simple illustration:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 30,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "#<PACKAGE \"COMMON-LISP\">"
-      ]
-     },
-     "execution_count": 30,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(symbol-package 'nil)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 31,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(NIL :EXTERNAL)"
-      ]
-     },
-     "execution_count": 31,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(multiple-value-list (find-symbol \"NIL\" \"COMMON-LISP\"))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 32,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(NIL :INHERITED)"
-      ]
-     },
-     "execution_count": 32,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(multiple-value-list (find-symbol \"NIL\" \"COMMON-LISP-USER\"))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 33,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "T"
-      ]
-     },
-     "execution_count": 33,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(eq (find-symbol \"NIL\" \"COMMON-LISP\")\n",
-    "    (find-symbol \"NIL\" \"COMMON-LISP-USER\"))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "The *home package* of `nil` is `\"COMMON-LISP\"`, and this symbol of name `\"NIL\"` is accessible via `\"COMMON-LISP\"`, but also via `\"COMMON-LISP-USER\"`, though not with the same status. It is *external* in the first case and *inherited* in the second case, points to be examined later. The value (`T`) of the last expression *proves* that both symbols, determined by `find-symbol` via different packages, in fact are the same. Fact 2 can be made a little more precise: At any given time during a Lisp session, a set $P$ of packages and a set $Sm$ of symbols are defined. The various lists of symbols $InS(p)$, $ExS(p)$ and $ShgS(p)$, and the list $U(p)$ of packages used by a package $p\\in P$ together define without any ambiguity which symbols are accessible via the package $p$. In other words, there is a well defined function $\\rho$:\n",
-    "\n",
-    "$$\n",
-    "\\rho: P \\longrightarrow [St \\longrightarrow Sm \\cup \\{\\mathtt{nil}\\}]\n",
-    "$$\n",
-    "\n",
-    "\n",
-    "We chose the letter $\\rho$ for reader, because this function is mainly used by the reader. Our \"mathematical\" function $\\rho$ is nothing but an avatar of the Lisp function `find-symbol`. Let $p\\in P$ be a package and $st\\in St$ be a string. Then:\n",
-    "\n",
-    "$$\n",
-    "\\rho(p)(st) = (\\mathtt{find-symbol}\\; st\\; p)\n",
-    "$$\n",
-    "\n",
-    "The left-hand side uses the standard mathematical functional notation, and the right-hand one uses the Lisp notation. If no symbol is found for a pair $(st, p)$, the symbol (!) `nil` is returned and the second value of `find-symbol`, the symbol `nil` again, tells the user that the symbol search did not return anything. A package $p$ is nothing but a way of defining the function $\\rho(p):St\\longrightarrow Sm\\cup\\{\\mathtt{nil}\\}$. In other words, the four fundamental lists of a package determine what character strings appear as the names of the symbols accessible via this package. This approach is described in detail now.\n",
-    "\n",
-    "## Internal symbols.\n",
-    "\n",
-    "The first fundamental list of a package is the list of its *internal symbols*. It is a pity that no standard Lisp function can produce this list, but here is a simple solution to the problem:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 34,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "PACKAGE-INTERNAL-SYMBOLS"
-      ]
-     },
-     "execution_count": 34,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(defun package-internal-symbols (package)\n",
-    "    (let ((rslt))\n",
-    "         (do-symbols (s package)\n",
-    "             (when (eq (second\n",
-    "                        (multiple-value-list\n",
-    "                         (find-symbol (symbol-name s) package)))\n",
-    "                       :internal)\n",
-    "                 (push s rslt)))\n",
-    "         rslt))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "We can list now all the internal symbols of a package:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 35,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(X QUICKLISP-INIT DEF-DIR CMD-ARGS N PACKAGE-INTERNAL-SYMBOLS S RSLT)"
-      ]
-     },
-     "execution_count": 35,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(package-internal-symbols \"COMMON-LISP-USER\")"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "In fact, only the first ten internal symbols are displayed. We see in particular the symbols `package-internal-symbols`, `s` and `rslt` used in the definition of our function. Some are rather esoteric, strictly speaking illegal: at the beginning of a Lisp session, the `\"COMMON-LISP-USER\"` package should in principle be void of symbols. To make our experiments more understandable it is better to allocate and use toy packages. The [`defpackage`](http://clhs.lisp.se/Body/m_defpkg.htm) function (a macro) allocates a package of a given name."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 36,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "#<PACKAGE \"P1\">"
-      ]
-     },
-     "execution_count": 36,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(defpackage \"P1\" (:use \"CL\"))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "A package `\"P1\"` is now present in our environment, without any internal symbols."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 37,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 37,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(package-internal-symbols \"P1\")"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "(The symbol `nil` also represents the empty list.) Let's allocate a few symbols and make them internal in the package `\"P1\"`! The current default package is `\"COMMON-LISP-USER\"` and we switch it to `\"P1\"` like this:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 38,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "#<PACKAGE \"P1\">"
-      ]
-     },
-     "execution_count": 38,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(in-package \"P1\")"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 39,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "#<PACKAGE \"P1\">"
-      ]
-     },
-     "execution_count": 39,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "*package*"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "From now on, the default package is `\"P1\"`. If we write down a symbol then it will be understood by the Lisp reader as accessed via the package `\"P1\"`, that is, unless we use a special syntax. Let us create a list of three symbols and assign it to the symbol `list`, and then examine the internal symbols of the package `\"P1\"`:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 40,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(SYMB1 SYMB2 SYMB3)"
-      ]
-     },
-     "execution_count": 40,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(setf (symbol-value 'list) '(symb1 symb2 symb3))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "The reader probably would prefer `(defvar list)` followed by `(setf list ...)`, which is rejected by some Lisp implementations, in particular SBCL, because in principle the symbol `list`, owned by the package `\"COMMON-LISP\"`, is \"locked\". It is possible to unlock such a symbol, which is a little technical, but using `(symbol-value 'list)` as above gets the job done."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 41,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "SIMPLE-STYLE-WARNING: \n",
-      "  undefined function: PACKAGE-INTERNAL-SYMBOLS\n",
-      "\n",
-      "UNDEFINED-FUNCTION: \n",
-      "  #<UNDEFINED-FUNCTION PACKAGE-INTERNAL-SYMBOLS {10056B8623}>\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 41,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(package-internal-symbols \"P1\")"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Oops! What happened? We've successfully used the function `package-internal-symbols` earlier and suddenly it seems to have disappeared from the environment. The point is that it was *defined when* `\"COMMON-LISP-USER\"` was the default package. Let us examine the situation!"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 42,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(COMMON-LISP-USER::PACKAGE-INTERNAL-SYMBOLS :INTERNAL)"
-      ]
-     },
-     "execution_count": 42,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(multiple-value-list (find-symbol \"PACKAGE-INTERNAL-SYMBOLS\" \"COMMON-LISP-USER\"))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 43,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(PACKAGE-INTERNAL-SYMBOLS :INTERNAL)"
-      ]
-     },
-     "execution_count": 43,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(multiple-value-list (find-symbol \"PACKAGE-INTERNAL-SYMBOLS\" \"P1\"))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "A symbol with the given name is found in both packages. Before encountering the undefined functional value error, Lisp ( more precisely, the Lisp reader) had interned a *new* symbol with the name `\"PACKAGE-INTERNAL-SYMBOLS\"` in the current default package, `\"P1\"`, for the sole reason that it was present in the source text. Let us verify that both symbols are different!"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 44,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 44,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(eq (find-symbol \"PACKAGE-INTERNAL-SYMBOLS\" \"COMMON-LISP-USER\")\n",
-    "    (find-symbol \"PACKAGE-INTERNAL-SYMBOLS\" \"P1\"))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "The symbols are different. Compare that with the status of `nil`, where the same symbol `nil` was accessible via `\"COMMON-LISP\"` and via `\"COMMON-LISP-USER\"`. In our present situation both symbols are *different*, and so are their respective properties. For example, the first symbol does have a functional value and the second does not, which can be tested with the function [`fboundp`](http://clhs.lisp.se/Body/f_fbound.htm):"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 45,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "T"
-      ]
-     },
-     "execution_count": 45,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(fboundp (find-symbol \"PACKAGE-INTERNAL-SYMBOLS\" \"COMMON-LISP-USER\"))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 46,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 46,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(fboundp (find-symbol \"PACKAGE-INTERNAL-SYMBOLS\" \"P1\"))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "This is the first time we have seen the double-colon `‘::’` notation: When the symbol `package-internal-symbols` was searched via `\"COMMON-LISP-USER\"`, the answer was positive but the returned symbol was a little lengthy: `COMMON-LISP-USER::PACKAGE-INTERNAL-SYMBOLS`. The current default package is `\"P1\"`, via which *this* symbol is not accessible. However, we may access it using the double-colon notation:\n",
-    "\n",
-    "> `package-name::symbol-name`\n",
-    "\n",
-    "This is one of the methods which allows the user or Lisp to refer to a symbol not accessible via the default package. The Lisp reader is told: \"We mean the symbol `symbol-name` via the package `package-name`.\" In contrast, for the symbol with the same name but interned in the different `\"P1\"` package, because `\"P1\"` is the current default package, the double colon notation is not necessary. The longer notation lets us access a symbol interned in the `\"COMMON-LISP-USER\"` package and its functional value as follows:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 47,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(PACKAGE-INTERNAL-SYMBOLS SYMB2 SYMB1 SYMB3)"
-      ]
-     },
-     "execution_count": 47,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(cl-user::package-internal-symbols \"P1\")"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "The `cl-user::` prefix tells Lisp to look for the symbol via the `\"CL-USER\"` package (Remember that `\"CL-USER\"` is a nickname for `\"COMMON-LISP-USER\"`?) and, because of its position just after a left parenthesis, to use its functional value. Currently, there are four internal symbols in the package `\"P1\"` and they are returned in an arbitrary order. By the way, what about the symbol `list`, to which we assigned a list (!) of symbols?"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 48,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(LIST :INHERITED)"
-      ]
-     },
-     "execution_count": 48,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(multiple-value-list (find-symbol \"LIST\" \"P1\"))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "The symbol is accessible via the package `\"P1\"` but with a different status, the status *inherited*. We will examine this situation later. In fact, the symbol `list`, one of the most important symbols in Lisp, is already present in the package `\"COMMON-LISP\"` at the beginning of a session, and by default accessible from any package.\n",
-    "\n",
-    "We must mention also that our function $\\rho$, or the function `find-symbol` if you prefer, is (almost) injective *with respect to* $st$. Let $p_1$ and $p_2$ be two packages, $st_1$ and $st_2$ two strings. Then if $\\rho(p_1, st_1) = \\rho(p_2, st_2)\\neq\\mathtt{nil}$, then $st_1 = st_2$. Pay attention to the fact that the equality is an equality between *symbols*. This is a consequence of $\\mathtt{symbol-name}(\\rho(p, st)) = st$; in other words, there is no possibility of nicknames for a symbol name. In particular, there is a 1-1 correspondence between the internal symbols of a package and their respective names.\n",
-    "\n",
-    "## Importing a symbol.\n",
-    "\n",
-    "Instead of using the lengthy notation `cl-user::xxx` to make an internal symbol in `\"CL-USER\"` accessible from `\"P1\"`, we may opt to *import* this symbol in the package `\"P1\"`. However, in doing so there is another problem due to a name conflict, a point which will be examined in detail later:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 49,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "NAME-CONFLICT: \n",
-      "  #<SB-EXT:NAME-CONFLICT {10059F26B3}>\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 49,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(import 'cl-user::package-internal-symbols \"P1\")"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "The problem is a \"collision\" between two *different* symbols, which cannot coexist as internal symbols in the *same* package `\"P1\"` with the *same* name. Importing the symbol internal in `\"CL-USER\"` into the package `\"P1\"` is not compatible with the current presence of *another* symbol in `\"P1\"` with the same `symbol-name`. We must first [`unintern`](http://clhs.lisp.se/Body/f_uninte.htm) the accidental, pre-existing symbol in `\"P1\"` to \"make room\" for the symbol from `\"CL-USER\"`."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 50,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "T"
-      ]
-     },
-     "execution_count": 50,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(unintern 'package-internal-symbols \"P1\")"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 51,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "T"
-      ]
-     },
-     "execution_count": 51,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(import 'cl-user::package-internal-symbols \"P1\")"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 52,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(PACKAGE-INTERNAL-SYMBOLS SYMB2 SYMB1 SYMB3)"
-      ]
-     },
-     "execution_count": 52,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(package-internal-symbols \"P1\")"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "The Lisp terminology is rather misleading: in fact, it is not at all the symbol which is imported, but the connection *string* $\\mapsto$ *symbol*. More precisely, let $p_1$ and $p_2$ be two packages, $st$ a string and $sm$ a symbol. If $\\rho(p_1)(st) = sm$ holds before the importation, then, after the importation, both relations $\\rho(p_1)(st) = sm$ *and* $\\rho(p_2)(st) = sm$ are satisfied. In particular, the first relation remains valid. It is not really an importation; it is a *copy* in the package $p_2$ of the connection $st \\mapsto sm$, available in the package $p_1$.\n",
-    "\n",
-    "Furthermore, nothing is modified about the symbol itself, except *possibly*, but rarely, its home package, as will be examined later. It is tempting for a beginner to think the home-package of the symbol is being modified. Not at all! Another erroneous interpretation would be to think a *copy* of the symbol to be imported is made \"inside\" the target package, with all the corresponding ingredients of the symbol, value, functional value, and so on. Wrong again! A copy is made, but only of a *pointer* toward our symbol found in $InS(p_1)$ and copied in $InS(p_2)$.\n",
-    "\n",
-    "The [`import`](http://clhs.lisp.se/Body/f_import.htm) function has two arguments, the *symbol* to be imported and the *target package*. The symbol must be well defined, that is, taking account of the current state of the environment. Here, before the import, the symbol is accessible only via `\"CL-USER\"`, and it is mandatory to use the notation `cl-user::...` (and the symbol must also be quoted to preclude its evaluation). After the import, as can be seen in the example, the symbol can be used functionally from the package `\"P1\"` without the prefix notation. Although the imported symbol is in the list of the internal symbols of the package `\"P1\"`, it is not quite the same as before. The next mandatory exercise consists in comparing the original symbol and the imported one."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 53,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "T"
-      ]
-     },
-     "execution_count": 53,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(eq 'cl-user::package-internal-symbols\n",
-    "    'package-internal-symbols)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "The function `eq` proves that both notations name the same symbol. Here's another proof:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 54,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "T"
-      ]
-     },
-     "execution_count": 54,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(eq (find-symbol \"PACKAGE-INTERNAL-SYMBOLS\" \"CL-USER\")\n",
-    "    (find-symbol \"PACKAGE-INTERNAL-SYMBOLS\" \"P1\"))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "If you remember the `symbol-package` function, the next test is revealing:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 55,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "#<PACKAGE \"COMMON-LISP-USER\">"
-      ]
-     },
-     "execution_count": 55,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(symbol-package (find-symbol \"PACKAGE-INTERNAL-SYMBOLS\" \"CL-USER\"))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 56,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "#<PACKAGE \"COMMON-LISP-USER\">"
-      ]
-     },
-     "execution_count": 56,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(symbol-package (find-symbol \"PACKAGE-INTERNAL-SYMBOLS\" \"P1\"))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "The *unique* symbol accessed by two different paths has of course a unique home package, namely its *birth place*, the `\"CL-USER\"` package. Please, do not pay too much attention to this symbol package; it is just an artifact of the session's history and does not have any real interest. You must focus on the chain $\\mathit{package}\\rightarrow[\\mathit{string}\\rightarrow \\mathit{symbol}]$ and not much else. There is no real reason to be concerned about the map `symbol-package`: $\\mathit{symbol}\\rightarrow\\mathit{package}$.\n",
-    "\n",
-    "## Name conflicts.\n",
-    "\n",
-    "If poorly understood, the introduction of Lisp packages to a Lisp project will sooner or later lead to *name conflicts*. There is nothing mysterious about them and there are standard \"home remedies\" for dealing with them.\n",
-    "\n",
-    "**Warning.** A name conflict can only be generated if two *different* symbols $sm$, $sm' \\in Sm$ end up with the same name: $sn(sm) = sn(sm')$. A name conflict occurs if these symbols $sm$ and $sm'$ become accessible via the same package $p$, which is a forbidden situation, since it would introduce ambiguity to the `find-symbol` function. On the other hand, the fact that some symbol (singular) is accessible via *different* packages never generates a name conflict by itself.\n",
-    "\n",
-    "Lisp constantly is on the lookout for possible name conflicts and stops with an error if the evaluation of an expression causes a name conflict. Some errors are *continuable*, which means that Lisp is able to propose a conflict resolution via `unintern` or `shadowing-import`. Remember the use of `unintern` in the previous section?\n",
-    "\n",
-    "What happens if an imported symbol has the same *name* as a symbol already accessible in the target package? In mathematical language, let $p_1$ and $p_2$ be two different packages, $st$ some string, and $sm_1$ and $sm_2$ two different symbols, internal in the respective packages $p_1$ and $p_2$, with the same name $st$. In other words,  assume $\\rho(p_1)(st) = sm_1$ and $\\rho(p_2)(st) = sm_2$, $sm_1 \\in InS(p_1)$ and $sm_2 \\in InS(p_2)$, and $sm_1\\neq sm_2$. A situation of this sort could be the following (Remember the current default package is `\"P1\"`!):"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 57,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "COMMON-LISP-USER::SYMB4"
-      ]
-     },
-     "execution_count": 57,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(defvar cl-user::symb4)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 58,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "111"
-      ]
-     },
-     "execution_count": 58,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(setf cl-user::symb4 111)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 59,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "SYMB4"
-      ]
-     },
-     "execution_count": 59,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(defvar symb4)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 60,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "111"
-      ]
-     },
-     "execution_count": 60,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(setf symb4 111)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 61,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 61,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(eq 'cl-user::symb4 'symb4)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "The evaluation of the first expression interns a symbol of name `\"SYMB4\"` in the package `\"CL-USER\"` and gives it the value 111, while the second expression interns a *different* symbol, again of name `\"SYMB4\"`, in the package `\"P1\"`, the current default package, and also gives it the value 111. As a result two symbols have been allocated, installed somewhere in the environment, with the same value of 111. Also the connections $\\rho(\\mathtt{\"CL-USER\"}): \\mathtt{\"SYMB4\"}\\mapsto \\mathtt{cl-user::symb4}$ and $\\rho(\\mathtt{\"P1\"}): \\mathtt{\"SYMB4\"}\\mapsto\\mathtt{p1::symb4}$ have been installed, that is, the addresses of both symbols have been pushed to the *respective* lists of *internal* symbols of the packages `\"CL-USER\"` and `\"P1\"`. The `eq` comparison confirms that the symbols just allocated are different. Two symbols with the same name `\"SYMB4\"` are now present in our environment. This is possible because these symbols are interned in different packages. Each one is accessible via the appropriate package. Both symbols are live and can be freely used:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 62,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "222"
-      ]
-     },
-     "execution_count": 62,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(setf cl-user::symb4 (+ symb4 cl-user::symb4))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "What happens if we import `cl-user::symb4` into the package `\"P1\"`? Let's try!"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 63,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "NAME-CONFLICT: \n",
-      "  #<SB-EXT:NAME-CONFLICT {1005ED3203}>\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 63,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(import 'cl-user::symb4 \"P1\") "
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "The importation is rejected, for it would not be possible anymore to coherently define $\\rho(\\mathtt{\"P1\"})(\\mathtt{\"SYMB4\"})$. We will see later that another process called *shadowing* allows the user to suppress the symbol `symb4` already present in `\"P1\"` and to authorize the importation of the symbol present in `\"CL-USER\"`.\n",
-    "\n",
-    "## The function `intern`.\n",
-    "\n",
-    "**Fact 3:** Let $p$ be a package and $(sm_1,...,sm_n)$ the list of its internal symbols. If $p$ is the default package, any of these symbols can be directly used without the double colon notation `'::'`. If $p$ is not the default package, these symbols can be used thanks to the notation $p::sm_i$. All these internal symbols have different names. Nothing prevents several packages from having the same symbols in their lists of internal symbols. This is possible thanks to the `import` function which can work only if no name conflict is generated.\n",
-    "\n",
-    "To be complete on this matter, we now to consider the Lisp function [`intern`](http://clhs.lisp.se/Body/f_intern.htm). It is used almost exactly as the function `find-symbol` with just a difference: if no symbol is found, then a symbol is allocated and interned in the package referred to in its second argument. Compare the follwing:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 64,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(NIL NIL)"
-      ]
-     },
-     "execution_count": 64,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(multiple-value-list (find-symbol \"SYMB5\" \"P1\"))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 65,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(SYMB5 NIL)"
-      ]
-     },
-     "execution_count": 65,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(multiple-value-list (intern \"SYMB5\" \"P1\"))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 66,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(SYMB5 :INTERNAL)"
-      ]
-     },
-     "execution_count": 66,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(multiple-value-list (intern \"SYMB5\" \"P1\"))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "We start without any `symb5` symbol in `\"P1\"`, which is confirmed by the double negative answer of `find-symbol`. If instead we use the function `intern`, Lisp notices that such a symbol is absent from `\"P1\"` and therefore allocates a symbol of name `\"SYMB5\"` and *interns* it in the package `\"P1\"` as an internal symbol. The second value `nil` is an indicator of the allocation just made. If we repeat the same expression, which is not an error, then Lisp signals that such a symbol is already present and returns its status, which also informs us of its previous presence. A little weird! This definition of the function `intern` guarantees the coherence of the set of internal symbols of packages. A symbol can be allocated only through this function `intern`. It requires two arguments, a string $st$ and a package $p$. In a sense, the function `intern` first calls `(find-symbol st p)` with the same arguments. If a symbol is found it is returned without modification and no allocation of a new symbol takes place, which otherwise would create a name conflict. On the other hand, if a corresponding symbol is not found, it is allocated and interned in the package explicitly or implicitly quoted, and this new symbol certainly does not generate a name conflict. In this way, the uniqueness of the names of internal symbols of a package is enforced. This does not prevent two different symbols of the environment from having the same name, but the packaging system is organized such that they cannot be accessed via the same package."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 67,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(PACKAGE-INTERNAL-SYMBOLS SYMB2 SYMB1 SYMB4 SYMB5 SYMB3)"
-      ]
-     },
-     "execution_count": 67,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(package-internal-symbols \"P1\")"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "In practice, the Lisp reader constantly uses the `intern` function, for example when reading an expression. If it detects the presence of a symbol, the colon notation allows it to decide if a package is explicitly given, otherwise it must use the default package. The name of the symbol, alone or package-qualified using the colon notation, then unambiguously determines the symbol. If present, it is used, otherwise it is allocated and then used. This is exactly the role of the `intern` function.\n",
-    "\n",
-    "## Moving a symbol between two packages.\n",
-    "\n",
-    "Up until now, we have seen no means of modifying the home package of a symbol. In fact, it is possible but may seem a little contorted. It is almost without any practical interest except as an opportunity to use this as a vehicle to discover other facts. First, it is possible to *unintern* a symbol. For example, we can unintern the symbol `\"SYMB1\"` from the package `\"P1\"`. What happens is precisely that this symbol is removed from the list of the internal symbols of `\"P1\"`."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 68,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "T"
-      ]
-     },
-     "execution_count": 68,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(unintern 'symb1 \"P1\")"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 69,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(PACKAGE-INTERNAL-SYMBOLS SYMB2 SYMB4 SYMB5 SYMB3)"
-      ]
-     },
-     "execution_count": 69,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(package-internal-symbols \"P1\")"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "What is modified is the *list* of internal symbols in the package `\"P1\"`. The symbol `symb1` itself has not been modified at all, except possibly its home package. In particular the symbol is not deallocated or destroyed, and therefore always present somewhere in the environment.\n",
-    "\n",
-    "But it's become inaccessible as such, for a symbol most often is accessible only via a package, the default one or some other explicitly given. The symbol `symb1` was interned only in the package `\"P1\"`, so that it appears now to be unreachable! If a symbol is truly unreachable, the Lisp garbage collector, always silently working in the background, will establish that fact and free the corresponding part of memory for reuse. Except that our symbol remains reachable, for it was the first element of the list assigned to the symbol `list`. Let's have a look at its value!"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 70,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(#:SYMB1 SYMB2 SYMB3)"
-      ]
-     },
-     "execution_count": 70,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "list"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Our symbol is still present in the list but in a little different form. To be sure, it is still a symbol:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 71,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "SYMBOL"
-      ]
-     },
-     "execution_count": 71,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(type-of (first list))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "But what about its home package?"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 72,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 72,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(symbol-package (first list))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "No home package, i.e., our symbol is \"homeless\"! The prefix `'#:'` indicates that this symbol is homeless. The `unintern` function had this effect because the package argument of `unintern` was the package which *owned* the symbol. Otherwise the home package would not be modified. Although our symbol has become homeless, it continues to be an ordinary symbol, for example, we can assign it a value:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 73,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "444"
-      ]
-     },
-     "execution_count": 73,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(set (first list) 444)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 74,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "444"
-      ]
-     },
-     "execution_count": 74,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(symbol-value (first list))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 75,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "444"
-      ]
-     },
-     "execution_count": 75,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(eval (first list))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Unlike `setf` (macro), the `set` function evaluates its arguments, so that before the assignment, the expression `(first list)` is evaluated, which returns our mysterious symbol `#:symb1`. Once that's done, the `set` function assigns (the value of) the second argument to it, as is confirmed by the other expressions. It is even possible to *import* a homeless symbol in a package, but then the target package becomes the home package of the imported symbol. The importing package can be different from the original home package. As a result our symbol is \"moved\" into another package. This explains the new form of the value of `list`."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 76,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "T"
-      ]
-     },
-     "execution_count": 76,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(import (first list) \"CL-USER\")"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 77,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "#<PACKAGE \"COMMON-LISP-USER\">"
-      ]
-     },
-     "execution_count": 77,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(symbol-package 'cl-user::symb1)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 78,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(COMMON-LISP-USER::SYMB1 SYMB2 SYMB3)"
-      ]
-     },
-     "execution_count": 78,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "list"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Our symbol could also have been imported in other packages before being uninterned from its home package. The status of our symbol with respect to other packages would not have been modified."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 79,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "T"
-      ]
-     },
-     "execution_count": 79,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(import 'symb3 \"CL-USER\")"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 80,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "T"
-      ]
-     },
-     "execution_count": 80,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(eq 'cl-user::symb3 'symb3)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 81,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "T"
-      ]
-     },
-     "execution_count": 81,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(unintern 'symb3 \"P1\")"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 82,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "T"
-      ]
-     },
-     "execution_count": 82,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(eq 'cl-user::symb3 (third list))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 83,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 83,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(symbol-package 'cl-user::symb3)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 84,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "T"
-      ]
-     },
-     "execution_count": 84,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(import 'cl-user::symb3 \"CL-USER\")"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 85,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "#<PACKAGE \"COMMON-LISP-USER\">"
-      ]
-     },
-     "execution_count": 85,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(symbol-package 'cl-user::symb3)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Here we import `symb3` in the package `\"CL-USER\"` before uninterning it from the package `\"P1\"`. The symbol is then accessible via the package `\"CL-USER\"` or via the list `list`. The evaluation of the expression `(eq ...)` proves that both paths lead to the same address. When the first `(import ...)` expression is evaluated, the symbol does have a home package and that it is not changed. When it is uninterned from the package `\"P1\"`, it becomes homeless. Lisp does not take account of the fact it is internal in other packages. In theory, this would allow it to select one of these packages as an \"emergency home\" package, but the choice would be quite arbitrary? Furthermore this would force Lisp to examine the list of all other packages and all their accessible symbols, which would be very expensive! Here, despite the symbol being internal and therefore interned in the package `\"CL-USER\"`, it becomes homeless after evaluating the `(unintern ...)` expression. Finally we import it in the package `\"CL-USER\"`, where, in fact, it is already present. According to the ANSI standard (see the following note), in such a situation, its status remains unchanged. In particular its home package remains `nil`. A little esoteric, huh? Don’t worry: the home package does not have any real role for the Lisp user.\n",
-    "\n",
-    "---\n",
-    "\n",
-    " **Note:** The [passage](http://clhs.lisp.se/Body/f_import.htm#import) in the [Common Lisp HyperSpec](http://clhs.lisp.se/Front/index.htm) reads like this: *\"If the symbol is already present in the importing package, import has no effect.\"* It appears that the behavior of SBCL and some other compilers is different: `Out[85]` is `#<PACKAGE \"COMMON-LISP-USER\">` not `NIL`.\n",
-    "\n",
-    "---\n",
-    "\n",
-    "We will prove later that if a symbol $sm$ has a home package $p$, then $sm$ is certainly present in $p$, that is, internal or external in this package. The \"converse\" is false: a symbol may be present in several packages $p_1,\\ldots , p_k$ while not having a home package. This might sound a little weird, but you shouldn't lose much sleep over it: except for the internal efficiency of the Lisp interpeter or compiler, the notion of a home-package is almost useless for the programmer.\n",
-    "\n",
-    "## External symbols and used packages.\n",
-    "\n",
-    "The analysis of this notion of an internal symbol was a little lengthy, but, in this way, the general structure of the packaging system is now very clear, and it will be a lot easier to understand the other concepts. Two fundamental lists maintained in the packages play a \"dual\" role in the packaging system, the list of *external* symbols and the list of *used* packages. The following function gives the list of the external symbols of a package."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 86,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "#<PACKAGE \"P1\">"
-      ]
-     },
-     "execution_count": 86,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "*package*"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 87,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "PACKAGE-EXTERNAL-SYMBOLS"
-      ]
-     },
-     "execution_count": 87,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(defun package-external-symbols (package)\n",
-    "    (let ((rslt nil))\n",
-    "         (do-external-symbols (s package)\n",
-    "             (push s rslt))\n",
-    "         rslt))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "The evaluation of the first expression is just to confirm that the default package remains `\"P1\"`. Let us see what the lists of external symbols of the packages `\"P1\"`, `\"CL-USER\"` and `\"COMMON-LISP\"` are:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 88,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 88,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(package-external-symbols \"P1\")"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 89,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 89,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(package-external-symbols \"CL-USER\")"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 90,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(SIMPLE-ERROR DEBUG BOOLE-EQV MULTIPLE-VALUES-LIMIT ALPHA-CHAR-P WRITE-TO-STRING DEFSETF SHORT-FLOAT NOTINLINE CLASS-NAME ...)"
-      ]
-     },
-     "execution_count": 90,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(package-external-symbols \"COMMON-LISP\")"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 91,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "978"
-      ]
-     },
-     "execution_count": 91,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(length *)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "There are no external symbols in `\"P1\"` and `\"CL-USER\"`, but 978 such symbols in the package `\"COMMON-LISP\"`. (Only the first ten are being displayed.) A point of concern might be the following: these symbols are accessible via the package `\"COMMON-LISP\"` and yet the double-colon notation  `common-lisp::simple-error` was not used. The explanation has two \"dual\" parts:\n",
-    "1. The symbol `simple-error` is external in the package `\"COMMON-LISP\"`.\n",
-    "2. The package `\"COMMON-LISP\"` is in the `package-use-list` of the package `\"P1\"`:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 92,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(SIMPLE-ERROR :EXTERNAL)"
-      ]
-     },
-     "execution_count": 92,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(multiple-value-list (find-symbol \"SIMPLE-ERROR\" \"COMMON-LISP\"))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 93,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(#<PACKAGE \"COMMON-LISP\">)"
-      ]
-     },
-     "execution_count": 93,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(package-use-list \"P1\")"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 94,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(\"CL\")"
-      ]
-     },
-     "execution_count": 94,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(package-nicknames (find-package \"COMMON-LISP\"))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "`\"CL\"` is the nickname of the package whose official name is `\"COMMON-LISP\"`, and which is not to be confused with `\"COMMON-LISP-USER\"`."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 95,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "T"
-      ]
-     },
-     "execution_count": 95,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(eq (find-package \"CL\")\n",
-    "    (find-package \"COMMON-LISP\")) "
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 96,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "#<PACKAGE \"COMMON-LISP\"> \n",
-      "#<PACKAGE \"COMMON-LISP-USER\"> "
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 96,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(eq (print (find-package \"CL\"))\n",
-    "    (print (find-package \"CL-USER\")))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Applied to a package $p$, the Lisp function [`package-use-list`](http://clhs.lisp.se/Body/f_pkg_us.htm) returns the list of all the packages used by $p$. If $p_1$ uses $p_2$, then it is said that $p_2$ is used by $p_1$. Whether this relation is reflexive can be doubted (What does \"$p$ uses $p$\" mean?), and it is neither symmetric (\"$p_1$ uses $p_2$\" does not imply \"$p_2$ uses $p_1$\") nor transitive (\"$p_1$ uses $p_2$\" and \"$p_2$ uses $p_3$” does not imply \"$p_1$ uses $p_3$\"). The oriented graph of the *use* relation is totally arbitrary.\n",
-    "\n",
-    "## First toy examples.\n",
-    "\n",
-    "Let's start over with two \"fresh\" packages `\"P1\"` and `\"P2\"`."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 97,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "#<PACKAGE \"COMMON-LISP-USER\">"
-      ]
-     },
-     "execution_count": 97,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(in-package \"CL-USER\")"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 98,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "T"
-      ]
-     },
-     "execution_count": 98,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(delete-package (find-package \"P1\"))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 99,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "#<PACKAGE \"P1\">"
-      ]
-     },
-     "execution_count": 99,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(defpackage \"P1\" (:use \"CL\"))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 100,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "#<PACKAGE \"P2\">"
-      ]
-     },
-     "execution_count": 100,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(defpackage \"P2\" (:use \"CL\"))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "We switch the default package to `\"P1\"`:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 101,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "#<PACKAGE \"P1\">"
-      ]
-     },
-     "execution_count": 101,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(in-package \"P1\")"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "and we assume that, *in this environment*, we define the functions `package-internal-symbols` and `package-external-symbols` as explained before."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 102,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "PACKAGE-INTERNAL-SYMBOLS"
-      ]
-     },
-     "execution_count": 102,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(defun package-internal-symbols (package)\n",
-    "    (let ((rslt))\n",
-    "         (do-symbols (s package)\n",
-    "             (when (eq (second\n",
-    "                        (multiple-value-list\n",
-    "                         (find-symbol (symbol-name s) package)))\n",
-    "                       :internal)\n",
-    "                 (push s rslt)))\n",
-    "         rslt))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 103,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "PACKAGE-EXTERNAL-SYMBOLS"
-      ]
-     },
-     "execution_count": 103,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(defun package-external-symbols (package)\n",
-    "    (let ((rslt))\n",
-    "         (do-external-symbols (s package)\n",
-    "             (push s rslt))\n",
-    "         rslt))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "What about the internal symbols of `\"P1\"`?"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 104,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(PACKAGE-EXTERNAL-SYMBOLS PACKAGE-INTERNAL-SYMBOLS S RSLT)"
-      ]
-     },
-     "execution_count": 104,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(package-internal-symbols \"P1\")"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "We see the symbols naming our functions and also the symbols `rslt` and `s` used to define them. All the other symbols used in their definitions are in fact external in `\"COMMON-LISP\"` and absent here. We move now to the package `\"P2\"` from where we cannot access the symbol `package-internal-symbols` directly."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 105,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "#<PACKAGE \"P2\">"
-      ]
-     },
-     "execution_count": 105,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(in-package \"P2\")"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 106,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(NIL NIL)"
-      ]
-     },
-     "execution_count": 106,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(multiple-value-list (find-symbol \"PACKAGE-INTERNAL-SYMBOLS\" \"P2\"))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "We have already seen the use of the `'::'` notation to make reference to the symbol at once. We can also *import* the symbol, in which case it becomes directly accessible from `\"P2\"` permanently:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 107,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "T"
-      ]
-     },
-     "execution_count": 107,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(import 'p1::package-internal-symbols \"P2\")"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 108,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(PACKAGE-INTERNAL-SYMBOLS)"
-      ]
-     },
-     "execution_count": 108,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(package-internal-symbols \"P2\")"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Another solution requires *two* steps:\n",
-    "\n",
-    "1. Make the symbol `external` in some package, which is the role of the Lisp function [`export`](http://clhs.lisp.se/Body/f_export.htm).\n",
-    "2. Declare that the current package *uses* the package where the symbol is external.\n",
-    "\n",
-    "Let us use this method to make the symbol `package-external-symbols` directly visible from `\"P2\"`."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 109,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "T"
-      ]
-     },
-     "execution_count": 109,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(export 'p1::package-external-symbols \"P1\")"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 110,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "T"
-      ]
-     },
-     "execution_count": 110,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(use-package \"P1\" \"P2\")"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 111,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 111,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(package-external-symbols \"P2\")"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 112,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(PACKAGE-EXTERNAL-SYMBOLS)"
-      ]
-     },
-     "execution_count": 112,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(package-external-symbols \"P1\")"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "An `export` expression has the same form as an `import` one: `(export` $sm$ $st$ `)`, where $sm$ is a symbol and $st$ is a string naming a package. The symbol $sm$ must be readable from the current default package, for us `\"P2\"`, which explains the (required) prefix `'p1::'`. The argument $st$ is a string naming the package where the symbol $sm$ is to become external. Again, the terminology is somewhat misleading: the function `export` does not export anything. All it does is to make some connection $st \\rightarrow sm$ \"exportable\" to other packages via `use-package` expressions. The 978 external symbols of `\"COMMON-LISP\"` contain all the standard Lisp constants, variables and functions. Because an allocated package is always initialized with the package `\"COMMON-LISP\"` in its `package-use-list`, these basic Lisp objects will be accessible from any package. If we remove `\"COMMON-LISP\"` from the `use-package-list` of the current default package, via `unuse-package`, the situation becomes a little tricky.\n",
-    "\n",
-    "---\n",
-    "\n",
-    "**Note:** *We can't let go of* `progn`. *Otherwise* `cl-jupyter` *will stop functioning.*"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 113,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "T"
-      ]
-     },
-     "execution_count": 113,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(common-lisp::import 'common-lisp::progn \"P2\")"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "---"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 114,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "COMMON-LISP:T"
-      ]
-     },
-     "execution_count": 114,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(unuse-package \"COMMON-LISP\" \"P2\")"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 115,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "SIMPLE-STYLE-WARNING: \n",
-      "  undefined function: +\n",
-      "\n",
-      "UNDEFINED-FUNCTION: \n",
-      "  #<COMMON-LISP:UNDEFINED-FUNCTION + {1004076333}>\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "COMMON-LISP:NIL"
-      ]
-     },
-     "execution_count": 115,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(+ 2 2)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "The notation for the external symbol `t` in the package `\"COMMON-LISP\"` has become `common-lisp:t`, for `\"COMMON-LISP\"` is no longer used by `\"P2\"`. Since the symbol `t` is external in `\"COMMON-LISP\"`, the simple colon notation is sufficient. However, the most elementary operations are not easily accessible anymore, for example, the addition function `'+'`. This is not a good position to be in. Let us go back to the previous environment!"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 116,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "SIMPLE-STYLE-WARNING: \n",
-      "  undefined function: USE-PACKAGE\n",
-      "\n",
-      "UNDEFINED-FUNCTION: \n",
-      "  #<COMMON-LISP:UNDEFINED-FUNCTION USE-PACKAGE {1004100DA3}>\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "COMMON-LISP:NIL"
-      ]
-     },
-     "execution_count": 116,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(use-package \"COMMON-LISP\" \"P2\")"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "This does not work since the symbol `use-package` can't be reached easily either, and we *must* use the prefix notation."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 117,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "NAME-CONFLICT: \n",
-      "  #<SB-EXT:NAME-CONFLICT {1004172963}>\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "COMMON-LISP:NIL"
-      ]
-     },
-     "execution_count": 117,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(common-lisp:use-package \"COMMON-LISP\" \"P2\")"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "But here is a new problem: earlier, when when we tried to use the symbol `'+'` from `\"P2\"`, Lisp detected that this symbol is not accessible from `\"P2\"` and therefore interned a fresh symbol of name `\"+\"` in `\"P2\"`. This was legitimate then, but it is now incompatible with `\"COMMON-LISP\"` having a different symbol with the same name `\"+\"`, if `\"P2\"` were to use `\"COMMON-LISP\"`. The same goes for `use-package`. We must unintern these symbols from `\"P2\"` to resolve the conflict. Let's not forget to use the colon notation for `unintern`, which is otherwise unreachable!"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 118,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "COMMON-LISP:T"
-      ]
-     },
-     "execution_count": 118,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(common-lisp:unintern '+ \"P2\")"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 119,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "COMMON-LISP:T"
-      ]
-     },
-     "execution_count": 119,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(common-lisp:unintern 'use-package \"P2\")"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 120,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "T"
-      ]
-     },
-     "execution_count": 120,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(common-lisp:use-package \"COMMON-LISP\" \"P2\")"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Phew, we are back in a state where Lisp is usable!\n",
-    "\n",
-    "## Importing an external symbol.\n",
-    "\n",
-    "Recall that a symbol $sm$ is *accessible* from a package $p$ if $\\rho(p)(st) = sm$ for $st = \\mathtt{symbol-name}(sm)$. In that case, the possible return values from `find-symbol` are as follows:\n",
-    "\n",
-    "1. If $sm$ is one of the internal symbols of $p$ the second value returned by `find-symbol` is `:internal`.\n",
-    "2. If $sm$ is one of the external symbols of $p$ the second value returned by `find-symbol` is `:external`.\n",
-    "3. If $sm$ is an external symbol of a package $p'$ used by the package $p$ the second value returned by `find-symbol` is `:inherited`.\n",
-    "\n",
-    "We have seen how to import a symbol from a package $p'$ into a package $p$. The example given used a symbol $sm$ internal in the package $p'$, which then became also an internal symbol of the package $p$ . This also works if $sm$ is external in the package $p'$, regardless of $p$ using or not using $p'$. (... assuming that no name conflict is generated.)\n",
-    "\n",
-    "Let's continue our journey in `\"P1\"`!"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 121,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "#<PACKAGE \"P1\">"
-      ]
-     },
-     "execution_count": 121,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(in-package \"P1\")"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 122,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "T"
-      ]
-     },
-     "execution_count": 122,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(export (intern \"SYMB1\" \"P2\") \"P2\")"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 123,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(P2:SYMB1 :EXTERNAL)"
-      ]
-     },
-     "execution_count": 123,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(multiple-value-list (find-symbol \"SYMB1\" \"P2\"))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 124,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(NIL NIL)"
-      ]
-     },
-     "execution_count": 124,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(multiple-value-list (find-symbol \"SYMB1\" \"P1\"))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "We intern a symbol `p2::symb1` in `\"P2\"` and make it external immediately. As it stands this symbol is not accessible via `\"P1\"`. The fact that it is external in `\"P2\"` does not prevent us from importing it in `\"P1\"`."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 125,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "T"
-      ]
-     },
-     "execution_count": 125,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(import 'p2:symb1 \"P1\")"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 126,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(SYMB1 :INTERNAL)"
-      ]
-     },
-     "execution_count": 126,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(multiple-value-list (find-symbol \"SYMB1\" \"P1\") )"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 127,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(SYMB1 :EXTERNAL)"
-      ]
-     },
-     "execution_count": 127,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(multiple-value-list (find-symbol \"SYMB1\" \"P2\"))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Once the importation is done, the symbol is accessible via `\"P1\"` with the status *internal*. The *external* status with respect to `\"P2\"` is unchanged, which underlines that the status of a symbol does not depend on anything in the symbol itself. It is the *package* which must be examined to determine the status of a symbol *with respect to this package*.\n",
-    "\n",
-    "Curiously, the last `find-symbol` returns the symbol `symb1`, without the prefix `'p2:'`. Lisp prints a symbol according to the following rule:\n",
-    "\n",
-    "> First, Lisp determines whether a symbol is accessible via the current default package, in which case it is printed without using the colon notation. Otherwise, Lisp examines the home package, where the symbol is certainly internal or external, and it is printed with the double or simple colon notation. The only exception to this rule appears to be a *keyword*, that is, a symbol of the package `\"KEYWORD\"`. (Though the ANSI definition is somewhat incomplete for the `\"KEYWORD\"` package, we can assume that it is forbidden to change anything about the scope of keywords.) Keywords are printed simply as `':xxx'`, without any prefix. Finally, if the symbol is homeless, it is printed as `#:xxx`.\n",
-    "\n",
-    "The take-home message here is that an importation does not change anything for the relevant symbol; it is just a matter of updating a list of internal symbols in some package, that is, a list of respective pointers toward these symbols. Installing a new signpost in San Francisco that reads \"New York\" does not change anything in New York. Once more:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 128,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "T"
-      ]
-     },
-     "execution_count": 128,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(eq (find-symbol \"SYMB1\" \"P1\") (find-symbol \"SYMB1\" \"P2\"))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "A novice could believe that adding `\"P2\"` to the `package-use-list` of `\"P1\"` could generate a name conflict, because the symbols `p1::symb1` and `p2::symb1` would become both accessible via `\"P1\"`. This is not the case: both notations represent one and the same symbol, and there is no ambiguity."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 129,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "T"
-      ]
-     },
-     "execution_count": 129,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(use-package \"P2\" \"P1\")"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 130,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(SYMB1 :INTERNAL)"
-      ]
-     },
-     "execution_count": 130,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(multiple-value-list (find-symbol \"SYMB1\" \"P1\"))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 131,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(SYMB1 :EXTERNAL)"
-      ]
-     },
-     "execution_count": 131,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(multiple-value-list (find-symbol \"SYMB1\" \"P2\"))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Note that because our symbol is internal in `\"P1\"`, the function `find-symbol` reports its status as `:internal`. This is in a sense preferred to the status `:inherited`, which after all would be possible. A name conflict occurs only if two *different* symbols with the same name could be accessible via the same package, possibly via another package used by the first one. Two symmetrical illustrations:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 132,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "T"
-      ]
-     },
-     "execution_count": 132,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(export (intern \"SYMB2\" \"P2\") \"P2\")"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 133,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(SYMB2 :INHERITED)"
-      ]
-     },
-     "execution_count": 133,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(multiple-value-list (intern \"SYMB2\" \"P1\") )"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "This is not an error: The second `intern` *does not* allocate a new symbol, a symbol of name `\"SYMB2\"` being already accessible via `\"P1\"`, which uses `\"P2\"`. In particular the second `intern` does not import the pre-existing symbol.\n",
-    "\n",
-    "We have to come up with something else to really allocate a new symbol."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 134,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "#:SYMB2"
-      ]
-     },
-     "execution_count": 134,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(make-symbol \"SYMB2\")"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 135,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "NAME-CONFLICT: \n",
-      "  #<SB-EXT:NAME-CONFLICT {10048CD493}>\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 135,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(import * \"P1\")"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "(The `'*'` denotes a symbol which is always bound to the value of the last evaluation, here, our homeless symbol.)\n",
-    "\n",
-    "The function [`make-symbol`](http://clhs.lisp.se/Body/f_mk_sym.htm) allocates a *homeless* symbol of a given name, that's its definition. A homeless symbol cannot cause a name conflict, because it is *not* accessible via any package. Nothing prevents us from trying to `import` this symbol in `\"P1\"`, but this generates a name conflict between two different symbols: the freshly allocated `#:symb2` and the symbol external in `\"P2\"` accessible via `\"P1\"` which uses `\"P2\"`.\n",
-    "\n",
-    "Here's another way to cause a name conflict:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 136,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(SYMB3 NIL)"
-      ]
-     },
-     "execution_count": 136,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(multiple-value-list (intern \"SYMB3\" \"P1\"))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 137,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(P2::SYMB3 NIL)"
-      ]
-     },
-     "execution_count": 137,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(multiple-value-list (intern \"SYMB3\" \"P2\"))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 138,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "NAME-CONFLICT: \n",
-      "  #<SB-EXT:NAME-CONFLICT {1004A24353}>\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 138,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(export * \"P2\")"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "The package `\"P1\"` uses the package `\"P2\"`, but this does not prevent them from having two different internal symbols with the same name `\"SYMB3\"`, for `\"P1\"` does not see the symbol internal in `\"P2\"`. If we try to make this symbol external in `\"P2\"`, a name conflict arises. \n",
-    "\n",
-    "Another sort of name conflict can occur between two used packages:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 139,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "T"
-      ]
-     },
-     "execution_count": 139,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(export (intern \"SYMB4\" \"P2\") \"P2\")"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 140,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "T"
-      ]
-     },
-     "execution_count": 140,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(export (intern \"SYMB4\" (defpackage :p3)) \"P3\")"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 141,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "NAME-CONFLICT: \n",
-      "  #<SB-EXT:NAME-CONFLICT {1004B3B5B3}>\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 141,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(use-package \"P3\" \"P1\")"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Compare that with:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 142,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "T"
-      ]
-     },
-     "execution_count": 142,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(export (intern \"SYMB5\" \"P2\") \"P2\")"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 143,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "T"
-      ]
-     },
-     "execution_count": 143,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(export (import 'p2:symb5 \"P3\"))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 144,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "T"
-      ]
-     },
-     "execution_count": 144,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(unexport 'p3:symb4 \"P3\")"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 145,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "T"
-      ]
-     },
-     "execution_count": 145,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(use-package \"P3\" \"P1\")"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Two symbols of name `\"SYMB5\"` are external in `\"P2\"` and `\"P3\"`, but the second one is in fact the same as the first one: it has been imported and immediately made external in `\"P3\"`.\n",
-    "\n",
-    "This time the `use-package`, which makes the external symbols of `\"P2\"` *and* `\"P3\"` visible from `\"P1\"`, does not generate a name conflict, since we are dealing with two different paths which lead to the same *symbol*. This works as long as we do not forget to first `unexport` the symbol `\"SYMB4\"` of `\"P3\"`, i.e., to downgrade its status from *external* to *internal*.\n",
-    "\n",
-    "## A symbol can shadow another symbol.\n",
-    "\n",
-    "In the matter of name conflicts, the Lisp creators could have adopted another strategy and decided that the symbols *present* in a package, that is, *internal* or *external* in this package, have precedence over *inherited*, possibly different, symbols. However, they reasoned that this could easily generate true programming errors because of possible perverse collisions of identifiers, and turn into a source of obscure bugs. Nevertheless, in line with the general spirit of Lisp, if a programmer really wants to use such a strategy, she can do it on a case-by-case basis and explicitly describe the intended exemptions. This is the role of the [`package-shadowing-symbols`](http://clhs.lisp.se/Body/f_pkg_sh.htm) list, which is maintained in every package $p$ and denoted by $ShgS(p)$. This list is empty initially. $ShgS(p)$ can contain symbols present in the concerned package, internal or external. These symbols will automatically *shadow* any other competing symbol, such as symbols exported in other used packages and with the same `symbol-name`.\n",
-    "\n",
-    "The function [`shadow`](http://clhs.lisp.se/Body/f_shadow.htm) takes a symbol name (or a list of symbol names) and a package name, allocates a symbol with this name if it is not *present* in this package, and records it in the shadowing list of the package."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 146,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "T"
-      ]
-     },
-     "execution_count": 146,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(shadow \"SYMB6\" \"P1\")"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 147,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(SYMB6)"
-      ]
-     },
-     "execution_count": 147,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(package-shadowing-symbols \"P1\")"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 148,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "T"
-      ]
-     },
-     "execution_count": 148,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(export (intern \"SYMB6\" \"P2\") \"P2\")"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 149,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 149,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(eq 'symb6 'p2:symb6)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Once the symbol `p1::symb6` is on the shadowing-list of `\"P1\"` the existence of a different external symbol with the same name in the used package `\"P2\"` does not generate a name conflict. The last `eq`-test proves both symbols are really different. Along the same lines, the function [`shadowing-import`](http://clhs.lisp.se/Body/f_shdw_i.htm), as clearly indicated in its name, imports a symbol and immediately adds it to the shadowing list, which could resolve a possible name conflict. For example the *different* symbols `p2:symb4` (external in `\"P2\"`) and `p3::symb4` (internal in `\"P3\"`) are in our environment; the package `\"P1\"` uses both packages `\"P2\"` and `\"P3\"`, but `p3::symb4` is internal in `\"P3\"` and therefore not in conflict with `p2::symb4`. Remember also the current default package is `\"P1\"`. A simple importation of `p3::symb4` in `\"P1\"` generates a conflict, while a `shadowing-import` adds the imported symbol to the shadowing list, shadowing the symbol `p2:symb4` and resolving the name conflict."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 150,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(SYMB4 :EXTERNAL)"
-      ]
-     },
-     "execution_count": 150,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(multiple-value-list (find-symbol \"SYMB4\" \"P2\"))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 151,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(P3::SYMB4 :INTERNAL)"
-      ]
-     },
-     "execution_count": 151,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(multiple-value-list (find-symbol \"SYMB4\" \"P3\"))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 152,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "NAME-CONFLICT: \n",
-      "  #<SB-EXT:NAME-CONFLICT {1004F4B583}>\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 152,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(import 'p3::symb4 \"P1\")"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 153,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "T"
-      ]
-     },
-     "execution_count": 153,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(shadowing-import 'p3::symb4 \"P1\")"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 154,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(SYMB4 SYMB6)"
-      ]
-     },
-     "execution_count": 154,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(package-shadowing-symbols \"P1\")"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "If necessary, `p2:symb4`, shadowed by the internal `symb4` in `\"P1\"`, remains accessible via the colon notation.\n",
-    "The evaluations of the following expressions assign the same symbol value to both symbols as is confirmed by the subsequent '=' form.  Evaluating the next `eq` expression proves that both *symbols* are different. In contrast, because `p1::symb4` was imported from `\"P3\"`, the last `eq`-test is affirmative."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 155,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "SYMB4"
-      ]
-     },
-     "execution_count": 155,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(defvar symb4)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 156,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "P2:SYMB4"
-      ]
-     },
-     "execution_count": 156,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(defvar p2:symb4)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 157,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "111"
-      ]
-     },
-     "execution_count": 157,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(setf symb4 (setf p2:symb4 111))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 158,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "T"
-      ]
-     },
-     "execution_count": 158,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(= symb4 p2:symb4)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 159,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 159,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(eq 'symb4 'p2:symb4)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 160,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "T"
-      ]
-     },
-     "execution_count": 160,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(eq 'symb4 'p3::symb4)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "It is even possible to add an *inherited* symbol to the shadowing list, maybe to declare a precedence with respect to another future competing symbol in another package intended to be used later. This experiment assumes three different packages, where one of them is not yet used. We first \"detach\" for example the package `\"P3\"` from `\"P1\"`, leaving `\"P2\"` used by `\"P1\"`. (Remember `\"P1\"` is the current default package.)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 161,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "T"
-      ]
-     },
-     "execution_count": 161,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(unuse-package \"P3\" \"P1\")"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "We then install two new external symbols with the same name in `\"P2\"` and `\"P3\"`:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 162,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "T"
-      ]
-     },
-     "execution_count": 162,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(export (intern \"SYMB7\" \"P2\") \"P2\")"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 163,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "T"
-      ]
-     },
-     "execution_count": 163,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(export (intern \"SYMB7\" \"P3\") \"P3\")"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "As we have seen already with essentially the same example, if `\"P1\"` now decides to use `\"P3\"`, the two `\"SYMB7\"` symbols collide:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 164,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "NAME-CONFLICT: \n",
-      "  #<SB-EXT:NAME-CONFLICT {1005371073}>\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 164,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(use-package \"P3\" \"P1\")"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "In some context, it could happen that `\"P1\"` has no reason to use `p3:symb7` directly, and instead would like to give precedence to `p2:symb7`. This can be achieved with a shadowing import."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 165,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(SYMB7 :INHERITED)"
-      ]
-     },
-     "execution_count": 165,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(multiple-value-list (find-symbol \"SYMB7\" \"P1\") )"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 166,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "T"
-      ]
-     },
-     "execution_count": 166,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(shadowing-import 'symb7 \"P1\")"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 167,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "T"
-      ]
-     },
-     "execution_count": 167,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(use-package \"P3\" \"P1\")"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "The `shadowing-import` refers to `p2:symb7` implicitly, which is external in a package used by `\"P1\"` and therefore inherited by `\"P1\"`. We see how the use of `shadowing-import` solves the name conflict, which otherwise would be raised by `use-package`. Let us review our symbols as seen now from our three packages:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 168,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(SYMB7 :INTERNAL)"
-      ]
-     },
-     "execution_count": 168,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(multiple-value-list (find-symbol \"SYMB7\" \"P1\"))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 169,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(SYMB7 :EXTERNAL)"
-      ]
-     },
-     "execution_count": 169,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(multiple-value-list (find-symbol \"SYMB7\" \"P2\"))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 170,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "T"
-      ]
-     },
-     "execution_count": 170,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(eq 'symb7 'p2:symb7)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 171,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(P3:SYMB7 :EXTERNAL)"
-      ]
-     },
-     "execution_count": 171,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(multiple-value-list (find-symbol \"SYMB7\" \"P3\"))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 172,
-   "metadata": {
-    "collapsed": false,
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(#<PACKAGE \"P3\"> #<PACKAGE \"P2\"> #<PACKAGE \"COMMON-LISP\">)"
-      ]
-     },
-     "execution_count": 172,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(package-use-list \"P1\")"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "The statuses of `symb7` have not changed in `\"P2\"` and `\"P3\"`, but seen from `\"P1\"`, the symbol is now *internal*. This is to satisfy the rule that any shadowing symbol in a package must be internal or external in this package, and also a consequence of the implied importation.\n",
-    "\n",
-    "## A mathematical definition of the packaging system.\n",
-    "\n",
-    "We recall that there are three general sets we must study:\n",
-    "\n",
-    "- The set $St$ of *strings*\n",
-    "- The set $P$ of *packages*\n",
-    "- The set $Sm$ of *symbols*\n",
-    "\n",
-    "There is one important difference: the set $St$ is the *infinite* set of all the possible strings, while $P$ and $Sm$ are *finite* sets made of the packages and symbols previously *allocated* in the current Lisp session.\n",
-    "\n",
-    "We use the notations $pn$ to denote the function `package-name` $pn: P \\rightarrow St$ and $sn$ to denote the function `symbol-name` $sn: Sm\\rightarrow St$.\n",
-    "\n",
-    "The map $pn$ is *injective* for the packages; the function $pn: P \\rightarrow pn(P)$ defines a 1-1 correspondence between the packages and their respective names. Here, we ignore the potential nicknames of a package, which is not essential for our discussion.\n",
-    "\n",
-    "Every package $P$ contains four *fundamental* lists:\n",
-    "\n",
-    "- The list $InS(P)$ of its internal symbols\n",
-    "- The list $ExS(P)$ of its external symbols\n",
-    "- The list $ShgS(P)$ of its shadowing symbols\n",
-    "- The list $U(P)$ of its used packages\n",
-    "\n",
-    "More precisely, these lists are lists of *pointers* to the mentioned objects, or, if you prefer, of the machine addresses of these objects. It is important to understand these lists are made of (pointers to) *symbols*, not of their names. Each of these lists is *without any duplicates*.\n",
-    "\n",
-    "The fundamental lists defined in a package are the source of a relatively extensive terminology, which is detailed now. The set of symbols *present* in a package $p$, denoted by $PrS(p)$, is defined as the union $PrS(p) := InS(p) \\cup ExS(p)$: a symbol is present in a package if it is internal or external in this package. This union is *disjoint*, the intersection $InS(p) \\cap ExS(p)$ must be empty. Also the relation $ShgS(P) \\subset Pr(P)$ is required. A shadowing symbol of the package $p$ must be internal or external in this package, i.e., a shadowing symbol is present.\n",
-    "\n",
-    "Let $q$ be a package used by the package $p$. The symbols of $q$ *shadowed* by a symbol of $p$ are:\n",
-    "$$\n",
-    "ShdS(q, p) = \\{sm \\in ExS(q)\\;\\mathbf{\\underline{st}}\\;\\exists sm' \\in ShgS(p)\\;\\mathbf{\\underline{st}}\\; sn(sm) = sn(sm')\\}\n",
-    "$$\n",
-    "\n",
-    "In other words, a *precedence* relation is defined by the list $ShgS(p)$: if ever a symbol $sm' \\in ShgS(p)$ and a symbol $sm\\in ExS(q)$ have the same name, then, with respect to the package $p$, $sm'$ takes precedence over $sm$, which means $sm$ is *shadowed*. If $sm'$ is present in $p$ but not shadowing, with $sm'\\neq sm$ and $sn(sm') = sn(sm)$, then a name conflict would be raised, which is forbidden.\n",
-    "\n",
-    "The inherited symbols of a package $p$, denoted by $InhS(p)$, are defined as:\n",
-    "$$\n",
-    "InhS(p) := \\Big\\{ \\bigcup_{q\\in U(P)}(ExS(q) − ShdS(q,p)) \\Big\\} − PrS(P)\n",
-    "$$\n",
-    "\n",
-    "A symbol is inherited in a package $p$ if it is external in a *used* package $q$, not shadowed by a shadowing symbol of $p$, and not present in $p$. The union in the preceding formula is not necessarily disjoint: a symbol can be external in several packages simultaneously, and without causing a name conflict. A symbol could be simultaneously present in $p$ and external in a package $q$ used by $p$. That is why the the last term, $−PrS(P)$, is necessary to define unambiguously what an inherited symbol is.\n",
-    "\n",
-    "Finally the accessible symbols $AccS(p) := PrS(p) \\cup InhS(p)$ are the symbols which are present or inherited. The very definition of $InhS(p)$ implies that this union is disjoint. In this way, the *status* of a symbol with respect to a package $p$ via which it is accessible is unambiguously defined as a keyword `:internal`, `:external` or `:inherited`. For a package $q\\neq p$ there is no relation whatsoever between the status of some symbol $sm$ with respect to $p$ and its status with respect to $q$. **Exercise:** Show that the sixteen pairs of possible status combinations can be realized!\n",
-    "\n",
-    "It is important to be clear about possible intersections (overlaps) between the lists defined above. Let $p$ be some package and $q$ another package used by $p.$ If $sm\\in ExS(q)$ is an external symbol of $q$, the symbol $sm$ *may* also be present in $p$, in which case its status is internal or external, but not inherited. In particular, this does not generate a name conflict, because it is the same symbol which is visible in two different packages via the same name, and a symbol has only *one* name! Nevertheless its status *with respect to* $p$ is not inherited. The status of a symbol is so defined deterministically, even if it is present in two interacting packages by one using the other. Of course the same symbol has status external in $q$.\n",
-    "\n",
-    "Following the same logic, if $q,q'\\in U(p)$, the intersection $ExS(q)\\cap ExS(q')$ is not necessarily empty.\n",
-    "\n",
-    "The Lisp system maintains the *coherence* of these lists, which is defined as follows:\n",
-    "\n",
-    "**Definition.** A set of packages is *coherent* if, for every package $p$, the function `symbol-name` defines a 1-1 correspondence $sn: AccS(p) \\rightarrow sn(AccS(p))$.\n",
-    "\n",
-    "This map is by definition surjective; it is injective if two different symbols accessible via $p$ have different names. In this way the function `find-symbol` is free of ambiguity. It searches first in the present symbols, and finally in the external symbols of the used packages. It is not necessary to compute the list of shadowed symbols since a shadow*ing* symbol, which is also a present symbol, is found first. The main purpose of the coherence rule is to prevent users from designing too contorted situations in name scopes, wich are frequently the source of subtle and difficult to find bugs.\n",
-    "\n",
-    "Several symbols with the same name may coexist in an environment. The most common way to access a symbol consists in using its *name*, but *different* symbols may have the *same* name. In fact, its symbol name is not sufficient to access a symbol, a package must also be specified. This can be the default package, in which case the direct notation without any colons is possible, or the package name can be explicitly used to prefix the symbol name using the one- or two-colon notation. Of course, the symbol so accessed must be defined in a *deterministic* manner. The definition just given says that a *unique* symbol of some name is accessible from some package.\n",
-    "\n",
-    "The main function in the packaging organization is a map:\n",
-    "$$\n",
-    "\\rho:P \\rightarrow [St \\rightarrow ((Sm\\cup\\mathtt{nil})\\times Stt)]\n",
-    "$$\n",
-    "where $Stt$ is a constant set of four symbols, the Lisp symbol `nil`, and three keywords, the possible statuses of an accessible symbol:\n",
-    "$$\n",
-    "Stt = \\{\\mathtt{nil}, \\mathtt{:internal}, \\mathtt{:external}, \\mathtt{:inherited}\\}\n",
-    "$$\n",
-    "Because of the assumed coherence of the package configuration, the function $\\rho$, an avatar of the function `find-symbol` of a package $p$ and a string $st$, determines a *unique* symbol named $st$ and accessible via $p$, and also its status. It is possible that the search fails, in which case the function returns the pair `(nil,nil)`. (More precisely `(values nil nil)`.) The second `nil` is a kind of a null status: \"There is nothing accessible via $p$ under the name $st$.\" The relation $\\rho(p)(s) = \\mathtt{(find-symbol}\\;p\\;st\\mathtt{)}$ is always satisfied.\n",
-    "\n",
-    "It is now relatively simple to understand the various Lisp functions for handling packages and symbols, in particular what name conflicts might be generated.\n",
-    "\n",
-    "### (intern $st\\;p$)\n",
-    "\n",
-    "This function first evaluates `(find-symbol` $st\\; p$`)`. If a symbol is found, *both* values of `(find-symbol ...)` are returned.\n",
-    "\n",
-    "If no symbol is found, then Lisp *allocates* (creates in memory) a new symbol without any value or function value. The `symbol-package` is initialized to $p$ and this symbol is added to $InS(p)$. In this case, `(values` $sm$ `nil)` is returned, the second value `nil` being a code for saying a new symbol has just been allocated.\n",
-    "\n",
-    "No name conflict can be created this way.\n",
-    "\n",
-    "This function is used implicitly by the Lisp reader when it encounters a symbol in an expression. If the colon syntax is not used, the default package is used for $p.$ Otherwise the (capitalized) package name of $p$ preceding the colon(s) is read, followed by the (capitalized) `symbol-name` $st$ after the colon(s). Finally, `(intern` $st\\; p$`)` is evaluated, which yields the symbol so *read* by the Lisp reader. In this way, the symbol can be either a pre-existing one or one freshly allocated as a consequence of this reading.\n",
-    "\n",
-    "\n",
-    "### (unintern $sm\\;p$)\n",
-    "\n",
-    "A symbol $sm$ is *interned* in a package $p$ if it is present in this package. It is *present* in package $p$  if $sm\\in PrS(p) = InS(p) \\cup ExS(p).$ Uninterning a symbol asks for this membership to be \"revoked.\"\n",
-    "\n",
-    "If $sm\\notin PrS(p)$, nothing is changed and `nil` is returned. Otherwise $sm$ is removed from $InS(p)$ or $ExS(p)$, and also from $Shg(p)$ if $sm$ was shadowing with respect to $p$; in this case, `unintern` returns `t`. In the last case, when uninterning a shadowing symbol, a name conflict can be generated: it is possible for symbols $sm'\\in ExS(q)$ and $sm''\\in ExS(q')$ to have the same name while being *different* symbols in the respective packages $q$ and $q'$ used by $p$, and that this collision was resolved by the symbol $sm$ shadowing both. If this happens, the `unintern` request is rejected.\n",
-    "\n",
-    "Also, if a symbol $sm$ is uninterned from a package $p$ and $p$ is the home package of $sm$, then the home package of $sm$ is modified and becomes `nil`, that is, the symbol becomes homeless. This is the only case where the symbol itself is modified by `unintern`. The same symbol could be external in another package used by $p$, in which case the symbol *remains* accessible via $p$. Otherwise, if the home package was `nil` or another package, it is not modified.\n",
-    "\n",
-    "### (import $sm\\; p$)\n",
-    "\n",
-    "This is a request for the symbol $sm$ to be added to $InS(p)$. Lisp first looks for a possible name conflict. This happens only if a *different* symbol $sm'\\neq sm$ with the same name ($sn(sm) = sn(sm')$) is already accessible via $p$. If so, the importation is rejected.\n",
-    "\n",
-    "If no name conflict is detected, Lisp proceeds as follows: If the symbol is already *present*, it is left *unchanged* in $InS(p)$ or $ExS(p)$. Else, if the symbol is *inherited* because of a package $q$ used by $p$, $ExS(q)$ is left unchanged and $sm$ is added to $InS(p)$ (not $ExS(p)$!). If $sm$ is not accessible via $p$, it is simply added to $InS(p)$.\n",
-    "\n",
-    "In the specific case of an imported homeless symbol, the `symbol-package` of the symbol is updated to $p$. This is the only case where a symbol object is modified by an importation. If the imported symbol is already owned by a package, whatever its home package, it is not modified.\n",
-    "\n",
-    "If the importation succeeds, the symbol will always be *present* in the target package, even if it was previously accessible only via a used package.\n",
-    "\n",
-    "### (export $sm\\; p$)\n",
-    "\n",
-    "The terminology \"export\" is not really appropriate, \"externalize\" would be more precise. The user of an `export` expression asks Lisp to record the symbol $sm$ in $ExS(p).$ This is allowed only if $sm$ is accessible from $p.$ In other words, the `export` function cannot *add* an accessible symbol to $p.$ In view of the rule $InS(p)\\cap ExS(p) = \\emptyset$, if present in $InS(p)$, the symbol $sm$ is also erased from that list. If $sm$ is external in a package $q$ used by $p$, its status in $q$ remains unchanged, but $sm$ is nevertheless added to $ExS(p)$.\n",
-    "\n",
-    "Remember that the `use-package` relation is not transitive. The fact that $sm\\in ExS(q)$ makes $sm$ accessible via $p$ using $q$ but not via $p'$ using $p$. If it is desired that $sm$ be accessible via $p'$, it is possible to make it external in $p$ by an `export` expression. Another solution would be to import $sm$ in $p'$, an operation which doesn't involve $p$.\n",
-    "\n",
-    "After exporting it, the symbol $sm$ becomes accessible from any package $q$ using $p$, that is, if $p\\in U(q)$. This can generate a name conflict with a possible *different* symbol $sm'$ of the same name, which is present in $q$ or accessible via $q$ in another package $p'\\in U(p)$, that is, if $sm'\\in ExS(p')$. If this happens, the *export* request is rejected.\n",
-    "\n",
-    "### (unexport $sm\\; p$)\n",
-    "\n",
-    "The symbol $sm$ must be accesible via the package $p.$ If the status of $sm$ is *external*, it is downgraded to *internal*. Otherwise it remains unchanged, even if it is *inherited*.\n",
-    "\n",
-    "### (shadow {$sm$ or $st$} $p$)\n",
-    "\n",
-    "It is intended to *import* the symbol $sm$ in $p$, to record it in the shadowing list $Shg(p)$ of the package $p$, and also to *resolve* any name conflict possibly raised by the importation.\n",
-    "\n",
-    "This time the first argument must be a *symbol*, a pre-existing one or a symbol just allocated because of its presence in the source statement. The symbol is imported (See the function `import`.) and added to the shadowing list $Shg(p)$ of $p$ if not yet present in this list. This addition to the shadowing list solves the possible name conflicts with symbols inherited from packages used by $p.$  It is possible that a *different* symbol *sm'* with the same name was *present* in $p$ beforehand. If so, such a symbol is *uninterned* from $p$, that is, erased from the lists $InS(p)$, $ExS(p)$ and $Shg(p)$.\n",
-    "\n",
-    "The difference between `shadow` and `shadowing-import` is clarified by the following toy example. We start a new Lisp session, allocate a package `\"P\"` and experiment with symbols named `\"A\"` and `\"B\"` in the packages `\"CL-USER\"` and `\"P\"`."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 173,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "#<PACKAGE \"COMMON-LISP-USER\">"
-      ]
-     },
-     "execution_count": 173,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(in-package \"CL-USER\")"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 174,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "#<PACKAGE \"P\">"
-      ]
-     },
-     "execution_count": 174,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(defpackage \"P\" (:use :cl))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 175,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(A B P::A P::B)"
-      ]
-     },
-     "execution_count": 175,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(setf (symbol-value 'list) '(a b p::a p::b))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 176,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "T"
-      ]
-     },
-     "execution_count": 176,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(shadow 'p::a \"CL-USER\")"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 177,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "T"
-      ]
-     },
-     "execution_count": 177,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(shadowing-import 'p::b \"CL-USER\")"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 178,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(B A)"
-      ]
-     },
-     "execution_count": 178,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(package-shadowing-symbols \"CL-USER\")"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 179,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 179,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(eq 'a 'p::a)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 180,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "T"
-      ]
-     },
-     "execution_count": 180,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(eq 'b 'p::b)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 181,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(A #:B P::A B)"
-      ]
-     },
-     "execution_count": 181,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "list"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "If we `shadow` the symbol `p::a` in `\"CL-USER\"`, the symbol `a` remains different from the symbol `p::a`. In contrast, if we `shadowing-import` the symbol `p::b` in `\"CL-USER\"`, then the symbols `b` and `p::b` are equal. In a sense, the expression `(shadow ’p::a \"CL-USER\")` is cheating because the presence of `'p::'` has no role whatsoever, for only the name of the symbol `p::a` is used and this name is the same as the name `\"A\"` of `a`, that is, because of the default package, `cl-user::a`. The symbol defined by `\"A\"` via the package `\"CL-USER\"` remains unchanged, in particular, it remains different from the symbol `p::a`.\n",
-    "\n",
-    "In contrast, if `shadowing-import` is used, an `import` operation is induced, so that the symbol `p::b` becomes directly accessible via `\"CL-USER\"`. The previous symbol $\\rho:($`\"CL-USER\"`$)($`\"B\"`$)$ has therefore been *uninterned* and is now unreachable by `find-symbol`. However, it is still visible in the list named `list` as the homeless symbol `#:B`.\n",
-    "\n",
-    "The conclusion of our test is this:\n",
-    "\n",
-    "* The symbol `cl-user::a` is unchanged but added to $ShgS($ `\"USER\"` $)$.\n",
-    "* The symbol `cl-user::b` is almost unchanged, but no longer accessible via `\"CL-USER\"`. The only change is its `symbol-package` becomes `nil`, because the symbol has been uninterned from its home-package.\n",
-    "* The symbol `p::a` remains unchanged; only its name has been used for something which does not really concern it.\n",
-    "* The symbol `p::b` remains unchanged, except that it is now directly accessible via `\"CL-USER\"` and now printed as `B` in the value of `list`.\n",
-    "\n",
-    "\n",
-    "### (use-package $q$ $p$)\n",
-    "\n",
-    "Unless $q$ is already in $U(p)$, the package $q$ is added to the `package-use-list` of $p.$\n",
-    "\n",
-    "Lisp checks beforehand for possible name conflicts. A symbol $sm \\in PrS(p)$ could collide with a *different* symbol $sm'\\in ExS(q)$ if they have the same name $sn(sm) =sn(sm')$. If $sm = sm'$, no name conflict is generated. One cannot resolve such a name conflict by adding $sm'$ to $ShgS(q)$, hoping to give the precedence to the new inherited symbol: shadowing operates in a uni-directional manner, from a using package toward a used package. If one does so by a `shadowing-import` of $sm'$ into $p$, the symbol $sm$ would be coherently uninterned, erased from $PrS(p)$, and in a sense replaced by $sm'$. One can prepare the precedence of $sm$ over $sm'$ before the `use-package` by previously `shadow`ing $sm$ in $p.$ Also Lisp on its own can propose to *unintern* the symbol $sm$ in a *continuable* error in order to resolve such an observed name conflict.\n",
-    "\n",
-    "Another type of name conflict could be raised if another package $q'$ is already used by $p.$ It is then possible that two *different* symbols $sm \\neq sm'$ with the same name $st$ are external, respectively in $q$ and $q'$, in which case $\\rho(p)(st)$ is ambiguous. If so, evaluating the `use-package` expression would generate an error. On the other hand, the intersection $ExS(q) \\cap ExS(q')$ may be non-empty: a symbol external in both packages does not generate any ambiguity via $p$. As usual, it is always important to remember the lists such as $ExS(q)$ and $ExS(q')$ are lists of *symbols*, not strings. A name conflict can be generated only by *different* symbols having the same `symbol-name`.\n",
-    "\n",
-    "If no name conflict is detected, the package $q$ is added to $U(p)$ so that the new set of accessible symbols via $p$ is:\n",
-    "\n",
-    "$$\n",
-    "\\mathrm{new-}AccS(p) = \\mathrm{old-}AccS(p) \\cup (ExS(q) − ShdS(q, p))\n",
-    "$$\n",
-    "\n",
-    "### (unuse-package $q$ $p$)\n",
-    "\n",
-    "If the package $q$ is in $U(p)$, it is removed from this list.\n",
-    "\n",
-    "### A bug in package-internal-symbols?\n",
-    "\n",
-    "While preparing these notes, the author thought for a moment to have encountered a mysterious bug. The minimal model for this bug goes as follows:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 182,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "T"
-      ]
-     },
-     "execution_count": 182,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(unuse-package \"P2\" \"P1\")"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 183,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "T"
-      ]
-     },
-     "execution_count": 183,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(unuse-package \"P1\" \"P2\")"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 184,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "T"
-      ]
-     },
-     "execution_count": 184,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(delete-package \"P1\")"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 185,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "T"
-      ]
-     },
-     "execution_count": 185,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(delete-package \"P2\")"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 186,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "#<PACKAGE \"P1\">"
-      ]
-     },
-     "execution_count": 186,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(defpackage \"P1\" (:use :cl))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 187,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "#<PACKAGE \"P2\">"
-      ]
-     },
-     "execution_count": 187,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(defpackage \"P2\" (:use :cl))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 188,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "T"
-      ]
-     },
-     "execution_count": 188,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(use-package \"P2\" \"P1\")"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 189,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "T"
-      ]
-     },
-     "execution_count": 189,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(export 'p2::a \"P2\")"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 190,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "T"
-      ]
-     },
-     "execution_count": 190,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(import 'p2::a \"P1\")"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 191,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(P2:A P2:A)"
-      ]
-     },
-     "execution_count": 191,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(package-internal-symbols \"P1\")"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "The point is that the standard Lisp function `do-symbols` runs through all the symbols *accessible* via `\"P1\"`, but it does not check for possible duplicates. Really? It seems possible that a symbol can appear more than once in $AccS($`\"P1\"`$)$!? This does not seem compatible with the exclusion of duplicates in general in $InS(p)$ and $ExS(p)$, and also the rule $InS(p) \\cap ExS(p) = \\emptyset$. Yes, but a – one !– symbol can be simultaneously in $InS(p)$ and $ExS(q)$ for a package $q$ used by $p$, which is the case here for our symbol `p1::a` = `p2:a`.\n",
-    "\n",
-    "The evaluation of `(do-symbols (s p) ...)` makes `s` run through all the internal symbols of $p$, then through all the external symbols of $p$, and finally through all the external symbols of $q$ for every package $q$ used by $p$. It happens that our symbol is in $InS($`\"P1\"`$)$ because it was imported there, and also in $ExS($`\"P2\"`$)$ where it was initially defined. Didn't the programmer of `package-internal-symbols` check the status of the symbol, so that the (fake) second symbol should have been rejected? No, not really, and it is interesting to see the path followed by Lisp: only the symbol-name and the examined package are used, so that when Lisp computes `(find-symbol (symbol-name s) package)`, it obtains *the* symbol, in fact the only one in this story, together with its status with respect to the `package` argument. In our case that is the package `\"P1\"` and the symbol's status (with respect to `\"P1\"`) is `:internal`, even if at the same time $s \\in ExS($ `\"P2\"` $)$.\n",
-    "\n",
-    "This illustrates some of the hidden traps and pitfalls that one might encounter as a result of different packages seeing the same symbol in various ways. Remember: no name conflict can be caused by one symbol alone. A name conflict happens only if *two* different symbols with the same name are \"visible\" by the same package. Nothing of this sort happened here, where *one* symbol is visible by several packages.\n",
-    "\n",
-    "To overcome this weakness in the implementation of `package-internal-symbols`, using the Lisp function `delete-duplicates` is sufficient."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 192,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "PACKAGE-INTERNAL-SYMBOLS-DEDUP"
-      ]
-     },
-     "execution_count": 192,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(defun package-internal-symbols-dedup (package)\n",
-    "    (let ((rslt))\n",
-    "         (do-symbols (s package)\n",
-    "             (when (eq (second\n",
-    "                        (multiple-value-list\n",
-    "                         (find-symbol (symbol-name s) package)))\n",
-    "                       :internal)\n",
-    "                 (push s rslt)))\n",
-    "         (delete-duplicates rslt)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 193,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(P2:A)"
-      ]
-     },
-     "execution_count": 193,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(package-internal-symbols-dedup \"P1\")"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "### Symbol-package revisited.\n",
-    "\n",
-    "Throughout this tutorial, we kept insisting that this function is not really interesting. To be complete, we prove that a symbol $sm \\in PrS($ `(symbol-package ` $sm$ `)` $).$ In other words, if the symbol-package of the symbol $sm$ is $p$, then $sm$ is present in $p$, either internal or external. When a symbol is allocated (necessarily via `intern`), it is in particular interned in the package which is the second argument of `intern` so that it becomes a member of $InS(p)$. It may be exported in this package, which would make it a member of $ExS(p)$, but it remains present. The symbol can be added to $InS(q)$ for other packages $q$ via `import` or `shadowing-import`. It can also then be \"upgraded\" to $ExS(q)$ in those packages, but the membership in the initial package $PrS(p)$ remains unaffected.\n",
-    "\n",
-    "The only way to change this situation is using `unintern` with the package argument being $p.$ Then the symbol becomes homeless.\n",
-    "In turn, this can be changed with `import` and `shadowing-import`, in which case the symbol is interned in a possibly new package, and the story continues along similar lines. Finally, unless a symbol is homeless, it is always present in its home-package.\n",
-    "\n",
-    "This also shows that, as was mentioned in the introduction, the `symbol-package` qualifier of a symbol does divide the set of *interned* symbols into packages. It is impossible to have two different interned symbols with the same symbol-name and also the same symbol-package, for they would be interned in the same package, with the same name, and then the set of packages would not be *coherent*.\n",
-    "\n",
-    "An interned symbol is internal or external in its symbol-package, and certainly visible via this package. However, it may be visible from many other packages, and this information is not stored in the internal representation of the symbol. If it is external, it is accessible via the packages which use its package. The list of these packages can be determined by the standard Lisp function `package-used-by-list`. But a symbol can also be imported by other packages, which in turn may decide to make (the pointer to) this symbol external, and so visible from other packages.\n",
-    "\n",
-    "**Exercise:** Try to define a function `symbol-accessible-from` with one argument, a symbol, that returns the list of all packages where this symbol is accessible. Do not forget the contorted particular case of `common-lisp:nil`! Hint: Have a look at the standard Lisp function [`list-all-packages`](http://clhs.lisp.se/Body/f_list_a.htm#list-all-packages).\n",
-    "\n",
-    "An arbitrary number of homeless symbols may have the same name, as illustrated by:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 194,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "#:Z \n",
-      "#:Z "
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "NIL"
-      ]
-     },
-     "execution_count": 194,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(eq (print (make-symbol \"Z\")) (print (make-symbol \"Z\")))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "When `make-symbol` is called, Lisp allocates a *new* homeless symbol with the prescribed name, even if another one with the same name has been already allocated. You see *both* homeless symbols allocated above are printed in the same way, yet they are *different*.\n",
-    "\n",
-    "###  Practical uses of the packaging system.\n",
-    "\n",
-    "Many of the somewhat esoteric technichalities detailed in this tutorial have no direct use in concrete programming. On the other hand, they can help to understand and demystify the behaviour of your Lisp system.\n",
-    "\n",
-    "A particularly irritating fact exhibited by some systems is the following: When you merely install, not load, a source file in the editor of your Lisp IDE, these systems immediately scan for symbols appearing in these files and intern them in a separate package. Sometimes this is the package indicated in an inital `(in-package \"XXX\")` of the file, or still more inappropriately, the standard `\"CL-USER\"` package, or also the current default package, even if the initial `in-package` references another package. Often this later leads to symbol collisions which are sometimes hard to identify. A developer who meets this kind of mysterious symbol collisions is advised to search first in this direction. In this case, you should make independent micro-experiments to study the actual behavior of your IDE when you install a file in your development environment. Probably in the early days of Lisp, this was done to improve the efficiency, but on modern systems, it is difficult to see compelling reasons to justify such a strategy.\n",
-    "\n",
-    "Most symbols of a Lisp file in fact are symbols with lexical scope, a scope limited to a small part of the code, typically *inside* a function, a `let` form, a `do` form and so on. These references are converted by the compiler into raw machine addresses, and these symbols have no real life at runtime.\n",
-    "\n",
-    "The most important symbols that have a real life at runtime are those that name functions, those defined through a `defun` form and the like. If a large program is divided in several files, then some decisions must be taken about the status of such a symbol.\n",
-    "\n",
-    "Usually, a correspondance \"file $\\leftrightarrow$ package\" is maintained. Several Lisp systems require that a file begins with an appropriate `(in-package ...)` expression, declaring that all the symbols used in this file are to be understood as present in this package, except when something else is a consequence of decisions taken outside this file or even in this file.\n",
-    "\n",
-    "In the ANSI definition of [`in-package`](http://clhs.lisp.se/Body/m_in_pkg.htm), the referenced package must already exist in the environment. Beginning a file by:\n",
-    "```cl\n",
-    "(defpackage \"MY-PACKAGE\")\n",
-    "(in-package \"MY-PACKAGE\")\n",
-    "```\n",
-    "is tempting but does not obey the requirement about the first instruction of a file being the appropriate `(in-package ...)`.\n",
-    "\n",
-    "The solution is to have a separate file in the project which is called aptly `packages.lisp` and which contains all the necessary `(defpackage ...)` expressions for the project. The `defpackage` form is flexible and can contain also all the main information about a package, in particular the list of its external symbols and its used packages. (See the ANSI definition of [`defpackage`](http://clhs.lisp.se/Body/m_defpkg.htm#defpackage).) This file is a good foundation for structuring the \"public\" documentation, explaining the role of these packages and their external symbols.\n",
-    "\n",
-    "Along the same lines, it might be worthwhile to have an `\"EXTERNAL\"` package which contains all the external symbols of the application. In this way, the other packages may use this package systematically, giving to this package a status similar to the status of the `\"COMMON-LISP\"` package. This does not prevent another package to import some symbols of other packages, symbols whose role is too specific to justify to make them \"globally\" external.\n",
-    "\n",
-    "### Shortcuts.\n",
-    "\n",
-    "There are several ways for the developer to shorten the Lisp expressions dealing with the packaging system.\n",
-    "\n",
-    "To be rigorous in our explanations and close to the deep structure of Lisp, in this turorial, we used a string identifier everywhere for a package. A symbol could be used instead, its name then being used as the intended string. For example, `(defpackage :my-package)` is equivalent to `(defpackage \"MY-PACKAGE\")`, for the name of the keyword `:my-package` is used, and because of the capitalization rule of the symbols applied by the Lisp reader. The name of `:my-package` is `\"MY-PACKAGE\"`, which through the `defpackage` expression becomes a package-name by following the standard rule which asks for an uppercase name.\n",
-    "\n",
-    "Also, each time a package argument is needed, frequently the second one, it can be omitted if this package is the current default package, which justifies this terminology. When using these shortcuts, do not forget about maintaining maximum readability of the source code!"
-   ]
-  }
- ],
- "metadata": {
-  "kernelspec": {
-   "display_name": "SBCL Lisp",
-   "language": "lisp",
-   "name": "lisp"
-  },
-  "language_info": {
-   "codemirror_mode": "text/x-common-lisp",
-   "mimetype": "text/x-common-lisp",
-   "name": "common-lisp",
-   "pygments_lexer": "common-lisp",
-   "version": "X3J13"
-  }
- },
- "nbformat": 4,
- "nbformat_minor": 0
-}
diff --git a/examples/pcl/Packages_in_Common_Lisp.org b/examples/pcl/Packages_in_Common_Lisp.org
deleted file mode 100644
index ef176ce..0000000
--- a/examples/pcl/Packages_in_Common_Lisp.org
+++ /dev/null
@@ -1,2391 +0,0 @@
-#+TITLE: Packages in Common Lisp, a tutorial
-#+AUTHOR: Francis Sergeraert
-#+DATE: January 2014
-#+OPTIONS: toc:nil
-
-* Introduction.
-
-  It is not possible to write a serious piece of code without the use of some
-  kind of /identifiers/ or names. Such identifiers are convenient means for the
-  programmer to reference, process and modify data using more or less
-  descriptive names, which represent the data and depend in some way on the
-  context. The standard /modularization/ technology encourages the division of
-  large programs in /modules/. Such modules can be relatively independent of
-  each other, but conversely, they must be able to /communicate/. Most
-  programming languages offer methods for such an organization. For example,
-  the set of identifiers of a module could be divided into two parts, the
-  /private/ identifiers, known only inside this module, and the /public/
-  identifiers, known everywhere.
-
-  In this domain as in many others, Common Lisp is by far the most powerful and
-  flexible programming language. At the expense of considerable complexity,
-  Common Lisp's modular technology requires a good grasp of the corresponding
-  /definitions/ in the language standard. If the ANSI definition of the
-  language is the only available documentation, these definitions are not easy
-  to understand. An identifier in Lisp is a /symbol/ which has a rich internal
-  structure and which has lifetime and visibility during a Lisp session. The
-  modular structure of a Lisp program is defined through the /packaging/
-  system, which allows a programmer to divide a large program into several
-  files, where each file is aware of all the symbols of a certain package,
-  among them the current /default/ package, and only the /external/ (public)
-  symbols of some other packages. A symbol which is not external in a package
-  is /internal/ (private). Also, a package may /import/ (that is, "see") an
-  arbitrary collection of symbols, internal or external to other packages. In
-  the general spirit of Lisp, the whole structure of such an organization, if
-  necessary, can be modified dynamically, even though this is not usually the
-  best course of action.
-
-  In this tutorial, a /mathematical/ definition of this system is provided.
-  This should elucidate the process for many a Lisp programmer and enable her
-  to use it more effectively. A basic but /inexact/ description of the
-  packaging system is the following:
-
-  - A /package/ is a Lisp object in the same way that numbers, lists, and
-    character strings are Lisp objects. In particular, the /type/ of a package
-    object is the system class [[http://clhs.lisp.se/Body/t_pkg.htm][=package=]]. In Common Lisp, packages are first
-    class citizens, which means they can be the value of a symbol, can be
-    passed as an argument to a function, can be returned by a function, etc.
-  - A /symbol/ is a Lisp object whose /type/ is the system class [[http://clhs.lisp.se/Body/t_symbol.htm][=symbol=]]. The
-    comments made about packages apply for symbols. In particular, a symbol can
-    be the value of another symbol, or even of itself.
-  - Symbols are divided into packages.
-  - At any time during a Lisp session, some package is the /default package/
-    and, as a first approximation, only the symbols of this package are
-    /accessible/. The default package can be modified at any time by the user
-    or a program.
-  - If necessary, there are several methods to access the symbols of packages
-    other than the default package. Conversely, a package may make its symbols
-    more or less easily accessible from the other packages.
-
-  This first approximation of the packaging system conveys a general idea of
-  its organization, but general ideas can be deceiving. For example, the idea
-  that the symbols are divided into packages is essentially /false/. More
-  precisely, this division can be made to appear essential (!), via the
-  so-called home package of a symbol, but it plays only a /minor/ role and can
-  be ignored by the programmer risk-free. This notion of a home package is
-  terribly misleading for beginners when they have to design non-trivial
-  packaging structures. In a Lisp environment, one has to deal with two realms,
-  the space of symbols and the space of packages. It is only /inside/ of
-  packages that something can be read, which, as an organization, looks a
-  /little/ like a division of symbols into packages, but the symbols themselves
-  essentially /ignore/ this division. Our subject is to clarify and explain
-  this organization.
-
-  The ANSI definition of the packaging system is a /complete/ description of
-  this organization, and, in a sense, nothing is missing. However, experience
-  shows that it is easily misunderstood, especially, in non-trivial situations,
-  where it can lead to erroneous programming choices and mysterious bugs. The
-  ANSI definition of packaging is complete and it is the perfect /Reference
-  Manual/. However, for a topic of this complexity a reference guide is not
-  sufficient and a /User Guide/ might be useful. And for that matter, an
-  elementary /mathematical/ description of the Common Lisp packaging system
-  might help programmers to understand it, and then to use it with greater ease
-  and also to greater effect. In every domain, when precise mathematical
-  language can be employed and is understood, the state-of-affairs improves.
-
-  We begin with a review of the ANSI definition of the packaging system while
-  adding in parallel a mathematical description of the main concepts. Finally,
-  we give a complete mathematical definition of this system as a set of
-  mathematical formulas.
-
-* Main sets of objects.
-
-  The first part of the packaging system is made of three disjoint sets:
-
-  - The set $St$ of *strings*.
-  - The set $P$ of *packages*.
-  - The set $Sm$ of *symbols*.
-
-  In our description of the packaging system, the statuses of these sets are
-  different. Think of the (infinite) set $St$ of /strings/ as made of /all/
-  the character strings that /can/ be used by a user or a program at any time.
-  Any string can be used at any time, whatever the history of the Lisp session
-  in which we are working may be. In the packaging system, most often, a
-  particular string is used only for a short time, mainly during the
-  read-eval-print loop, when the Lisp reader works. A string is just an
-  intermediary connecting the user and the Lisp session, more precisely the
-  current environment. In contrast, in a given environment, at any time during
-  a Lisp session, some finite set $P$ of /specific/ packages is installed in
-  this environment, and also a finite set $Sm$ of /specific/ symbols is
-  available. Those packages and symbols can /then/ be used, and they are the
-  historical consequence of the current Lisp session. Various Lisp functions
-  allow the user to modify the sets $P$ and $Sm$, and the way they are
-  combined and related to each other. In other words, consider the set of
-  strings $St$ as constant, vast and independent of the environment, while, on
-  the contrary, the sets $P$ and $Sm$ are restricted, they change during a
-  Lisp session, and they are an essential component of the /current/
-  environment.
-
-* Packages
-
-  There is a simple, almost bijective (one-to-one), correspondence between
-  strings and packages, and a convenient place to start our subject. First, at
-  any time during a Lisp session, a /default package/ is defined and it can be
-  discovered via the global symbol [[http://clhs.lisp.se/Body/v_pkg.htm][=*package*=]]:
-
-  #+BEGIN_SRC lisp :session pcl :exports both
-  *package*
-  #+END_SRC
-
-  This is to be read as: the /value/ of the /symbol/ =*package*= is the
-  package whose /name/ is the string ="COMMON-LISP-USER"=. The types =symbol=
-  and =package= are system-defined, disjoint sets of machine objects. A symbol
-  is frequently used as a convenient intermediate object, which allows the
-  user to reach some object of arbitrary nature, its /value/. Here,
-  =*package*= is a symbol, the value of which is the package named
-  ="COMMON-LISP-USER"=. Technically, a symbol contains a pointer to its
-  (possible) value, here a package which happens to be the package used
-  ordinarily in a simple Lisp session. There are no facilities to refer to a
-  package object /directly/. However, one can use its /name/ and the function
-  [[http://clhs.lisp.se/Body/f_find_p.htm][=find-package=]] to obtain a reference:
-
-  #+BEGIN_SRC lisp :session pcl :exports both
-  (find-package "COMMON-LISP-USER")
-  #+END_SRC
-
-  Conversely, given a package, the function [[http://clhs.lisp.se/Body/f_pkg_na.htm][=package-name=]] returns its name:
-
-  #+BEGIN_SRC lisp :session pcl :exports both
-  (package-name (find-package "COMMON-LISP-USER"))
-  #+END_SRC
-
-  The example was given to illustrate that the functions =find-package= and
-  =package-name= are the inverse of each other, defining a 1-1 correspondence
-  between the packages /currently/ defined in the environment and their
-  respective names, some character strings. Because of rules not of interest
-  here, it is common and convenient to use only uppercase character strings to
-  name packages. If a name does not correspond to any current package, the
-  =find-package= function returns the symbol =nil=, usually displayed
-  uppercase:
-
-  #+BEGIN_SRC lisp :session pcl :exports both
-  (find-package "COMMON-LISP-user")
-  #+END_SRC
-
-  which illustrates that a package name is case-sensitive. Frequently, only a
-  few packages are in use, and because of their importance, descriptive names
-  are used. These descriptive names can be a little long, and it is possible
-  to define and use various /nicknames/ for these names. For example, the
-  ="COMMON-LISP-USER"= package usually has the nicknames ="CL-USER"= and
-  ="USER"=. The function [[http://clhs.lisp.se/Body/f_pkg_ni.htm][=package-nicknames=]] can be used to retrieve the list
-  of nicknames (strings) for a package, which doesn't include the name of the
-  package.
-
-  #+BEGIN_SRC lisp :session pcl :exports both
-  (find-package "COMMON-LISP-USER")
-  #+END_SRC
-
-  #+BEGIN_SRC lisp :session pcl :exports both :results value verbatim
-  (package-nicknames (find-package "COMMON-LISP-USER"))
-  #+END_SRC
-
-  If a package is to be unambiguously identified by its name or one of its
-  nicknames, two different packages must have disjoint sets of
-  /name + nicknames/.
-
-* Tracking a symbol.
-
-  The Lisp symbols are very particular when compared to the identifiers of
-  other programming languages. They persist throughout the runtime of an
-  environment and are an important component of the power of Lisp. A package
-  is referenced via its name; the same goes for a symbol, but the process is
-  much more complex. The first and most common method to create or "to
-  /allocate/ a symbol" consists in just writing it down and passing it to the
-  Lisp reader using the standard Lisp conventions. In a Lisp environment,
-  there is a set of "pre-defined" symbols ready to be used. To caution the
-  reader about the complexity of the subject, we begin with a seemingly
-  strange example:
-
-  #+BEGIN_SRC lisp :session pcl :exports both :results value verbatim
-  (multiple-value-list (find-symbol "X" "COMMON-LISP-USER"))
-  #+END_SRC
-
-  #+BEGIN_SRC lisp :session pcl :exports both :results value verbatim
-  (multiple-value-list (ignore-errors x))
-  #+END_SRC
-
-  #+BEGIN_SRC lisp :session pcl :exports both :results value verbatim
-  (multiple-value-list (find-symbol "X" "COMMON-LISP-USER"))
-  #+END_SRC
-
-  The function [[http://clhs.lisp.se/Body/f_find_s.htm][=find-symbol=]] is analogous to the function =find-package=:
-  given some /name/, a character string, it looks for a symbol with this name.
-  Remember the correspondence between packages and names? A similar
-  correspondence exists between symbols and names, but it's more involved. In
-  particular, a name is /never sufficient/ to determine a symbol, a
-  /package/ is also necessary. This is why the =find-symbol= function requires
-  /two/ arguments, the name of the symbol and the package with respect to
-  which the search is to be done.
-
-  At the beginning of our story, no symbol with the name ="X"= existed in the
-  default package ="COMMON-LISP-USER"=, and the return value of =find-symbol=
-  is negative, =nil=. (We will explain the second =nil= value in a moment.)
-  Then we pass the Lisp reader the one character expression '=x='. Lisp
-  evaluates it according to its /read-eval-print/ cycle. First, Lisp
-  /reads/ the expression and notices that the symbol =x= is used. It examines
-  the current package ="COMMON-LISP-USER"=, and does /not/ find such a symbol.
-  Before doing anything else, Lisp /allocates/ (creates) this symbol, the
-  right terminology being: "Lisp /interns/ a symbol =x= of name ="X"= in the
-  package ="COMMON-LISP-USER"=." To refer to this symbol, the pair made of
-  /its/ name ="X"= and the (not /its/!!) package ="COMMON-LISP-USER"= are
-  necessary, but it would be cumbersome to have to write the expression
-  =(find-symbol "X" "COMMON-LISP-USER")= every time this symbol is used. To
-  simplify the process of referring to a symbol the designers of Lisp have
-  organized the workspace as follows: if a symbol is read, its character
-  string is capitalized, giving its /name/, and the default package is
-  assumed. In other words, the text ='x'= is roughly  equivalent to the text
-  =(find-symbol "X" "COMMON-LISP-USER")=. How convenient! ('Roughly', because
-  '=x=' may trigger the allocation of a symbol. In contrast, =find-symbol=
-  never allocates a symbol; but see the function =intern= later.) In the
-  second expression of our example, once Lisp has "understood" that the user
-  intends to use the symbol =x=, and observing that such a symbol is not
-  present in the package ="COMMON-LISP-USER"=, it allocates a symbol of name
-  ="X"= and /interns/ it in the package ="COMMON-LISP-USER"=. More
-  specifically, a pointer referring to the just allocated symbol is added to
-  the list $InS(p)$ of the internal symbols of the package $p$.
-
-  Note also that it is common in Lisp to input the symbols in lowercase
-  letters, and Lisp prints them in uppercase. This might be convenient for
-  distinguishing input from output in an interactive session, but requires
-  some clarification. In particular, there is no difference between the
-  symbols =nil= and =NIL=, whereas the strings ="nil"= and ="NIL"= are
-  different.
-
-  #+BEGIN_SRC lisp :session pcl :exports both :results value verbatim
-  (multiple-value-list (find-symbol "nil" "COMMON-LISP-USER"))
-  #+END_SRC
-
-  #+BEGIN_SRC lisp :session pcl :exports both :results value verbatim
-  (multiple-value-list (find-symbol "NIL" "COMMON-LISP-USER"))
-  #+END_SRC
-
-  The fruitless search for a /symbol/ with the lower-case name ="nil"= (a
-  /string/) returns a double negative answer, but it is the second =NIL= that
-  is meaningful! Compare that with the second expression which has the same
-  first return value, but a different second one. The symbol =NIL= also plays
-  in Lisp the role of the boolean /false/, which creates an ambiguity: if the
-  answer is the symbol =NIL= is that a negative answer or is it a positive
-  answer made of the symbol =NIL=? The ambiguity is resolved by the /second/
-  return value. In the first case, the second =NIL= /confirms/ that the first
-  =NIL= is to be interpreted as the boolean /false/. In the second expression,
-  the second return value =:INHERITED=, not a negative, indicates that the
-  symbol =NIL= has been found, and that its /accessibility/ via the package
-  ="COMMON-LISP-USER"= is /inherited/, a point to be explained later. In other
-  words, the function =find-symbol= returns a genuine symbol /and/ its
-  accessibility via the package argument, or a pair of =nil='s if no symbol is
-  found. The logician can deduce that an accessibility cannot be the symbol
-  =nil=!
-
-  Let us return to the one character expression '=x='. The read part of the
-  read-eval-print loop cycle reads the symbol =x= and interns it in the
-  package ="COMMON-LISP-USER"=. The expression is /read/ and must now be
-  /evaluated/. The evaluation of a symbol consists in looking for a /value/
-  of this symbol. To this end a value pointer in the symbol's internal
-  representation is examined. In this case it is found that, at this time,
-  there is no value for the freshly allocated symbol =x=. Therefore the /eval/
-  step of the /read-eval-print/ cycle generates an error, terminating the
-  cycle with an informative error message. In any case, a symbol of name
-  ="X"= is now present in the package ="COMMON-LISP-USER"=, as confirmed by
-  the value of the last expression. The symbol's accessibility via the
-  ="COMMON-LISP-USER"= package is /internal/, which is to be explained later.
-
-* Examining a symbol.
-
-  A symbol is a Lisp object with a rich internal structure and there are
-  several functions for exploring symbols and their properties. Let us
-  examine in detail the symbol =x= allocated in the previous section.
-
-  #+BEGIN_SRC lisp :session pcl :exports both
-  (symbol-name 'x)
-  #+END_SRC
-   
-  The [[http://clhs.lisp.se/Body/f_symb_2.htm][=symbol-name=]] function returns the /name/ of a symbol; it is analogous
-  to the =package-name= function for a package. The Lisp function
-  =symbol-name= is crucial for our subject, and we denote it as a mathematical
-  function $sn: Sm \longrightarrow St$, a function which in general is not
-  injective: several symbols may have the same name, this is our main subject.
-
-  Note that in the previous expression the symbol =x= has been quoted ='x= to
-  prevent its evaluation. More precisely, ='x= is an abbreviation for the
-  expression =(quote x)=, where [[http://clhs.lisp.se/Body/s_quote.htm][=quote=]] is a /special/ function which /does
-  not/ evaluate its argument, and it returns this argument as is. Hence, the
-  previous expression is equivalent to:
-
-  #+BEGIN_SRC lisp :session pcl :exports both
-  (symbol-name (quote x))
-  #+END_SRC
-
-  Here, the non-quoted =x= does not generate an error. If instead you do not
-  quote the symbol =x= (implicitly via ='=, or explicitly via =quote=) it will
-  be evaluated before being used and generate an error:
-
-  #+BEGIN_SRC lisp :session pcl :exports both :results value verbatim
-  (multiple-value-list
-   (ignore-errors
-     (symbol-name x)))
-  #+END_SRC
-
-  The package which /owns/ a symbol, its /home package/, can be determined
-  with the function [[http://clhs.lisp.se/Body/f_symb_3.htm][=symbol-package=]].
-
-  #+BEGIN_SRC lisp :session pcl :exports both
-  (symbol-package 'x)
-  #+END_SRC
-
-  #+BEGIN_SRC lisp :session pcl :exports both :results value verbatim
-  (multiple-value-list (find-symbol "X" "COMMON-LISP-USER"))
-  #+END_SRC
-
-  As we have just seen, a symbol produces a name and a package (with the help
-  of =symbol-name= and =symbol-package=). Conversely, given a name and a
-  package, =find-symbol= produces the symbol with this name /via/ this
-  package. The reader might think that there is a correspondence between
-  symbols and pairs of strings and packages:
-  $$Sm \longleftrightarrow St\times P$$
-  However, the situation is more involved: for the beginner, this might be a
-  convenient point of view, but in fact such a point of view is wrong. If you
-  intend to fully understand the complex relationship between strings,
-  packages and symbols, please forget this tempting but terribly misleading
-  correspondence. The goal of the next sections is to establish the correct
-  point of view. For completeness we finish this section with a brief glance
-  at the other data possibly stored in a symbol. A symbol can have a value.
-  You may remember that in our Lisp session the symbol =x= does not (yet) have
-  a value. This can be established by the predicate [[http://clhs.lisp.se/Body/f_boundp.htm][=boundp=]]:
-
-  #+BEGIN_SRC lisp :session pcl :exports both
-  (boundp 'x)
-  #+END_SRC
-
-  The main method to give a symbol a value is the [[http://clhs.lisp.se/Body/m_setf_.htm][=setf=]] function (a macro).
-  In most Common Lisp implementations, the =setf= macro may be used directly,
-  in which case the default status of the argument symbol is /variable/. In
-  strict ANSI implementations such as SBCL here, a =defvar= statement is
-  required to explicitly define this status. Other possible statuses are
-  /constant/ (via =defconstant=) and /parameter/ (via =defparameter=).
-
-  #+BEGIN_SRC lisp :session pcl :exports both
-  (defvar x)
-  #+END_SRC
-   
-  #+BEGIN_SRC lisp :session pcl :exports both :results value verbatim
-  (setf x '(4 5 6))
-  #+END_SRC
-
-  #+BEGIN_SRC lisp :session pcl :exports both
-  (boundp 'x)
-  #+END_SRC
-
-  Note that the first argument of =setf=, the symbol =x=, is not evaluated.
-  Otherwise an error would be generated, since the symbol =x= does not yet
-  have a value. After the =(setf ...)= expression has been evaluated, the
-  symbol =x= does have a value, in this case, the list =(4 5 6)=. This value
-  would now be the result of the evaluation of the expression =x=. It can also
-  be obtained with the function [[http://clhs.lisp.se/Body/f_symb_5.htm][=symbol-value=]]. (In this tutorial, we do not
-  study the possible difference between, on the one hand, the simple
-  /evaluation/ of the symbol =x= asked for by the expression ='x'= and the
-  /evaluation/ of =(symbol-value 'x)= on the other. In our elementary examples
-  there is no difference between the two. Possible differences might come from
-  different variable scopes, such as /lexical/ or /dynamic/, but this subject
-  is not studied here.)
-   
-  #+BEGIN_SRC lisp :session pcl :exports both :results value verbatim
-  x
-  #+END_SRC
-
-  #+BEGIN_SRC lisp :session pcl :exports both :results value verbatim
-  (symbol-value 'x)
-  #+END_SRC
-
-  Don't forget to quote the symbol! See the following error:
-
-  #+BEGIN_SRC lisp :session pcl :exports both :results value verbatim
-  (multiple-value-list
-   (ignore-errors
-     (symbol-value x)))
-  #+END_SRC
-
-  A symbol can also have a /functional value/. This does not mean that the
-  value we just discussed could be a function (which it could be!). It means
-  that /besides/ the previous value, a symbol can also have an /additional/
-  value, a function, which can be used independently of the "ordinary" value
-  of this symbol. For example the function $n \mapsto 10 - n$ could be recorded
-  as the /functional/ value of the same symbol, and this function could then
-  be used as shown below.
-
-  #+BEGIN_SRC lisp :session pcl :exports both
-  (defun x (n) (- 10 n))
-  #+END_SRC
-
-  #+BEGIN_SRC lisp :session pcl :exports both
-  (x 3)
-  #+END_SRC
-
-  Both values coexist in the symbol without any interference:
-
-  #+BEGIN_SRC lisp :session pcl :exports both :results value verbatim
-  (symbol-value 'x)
-  #+END_SRC
-
-  #+BEGIN_SRC lisp :session pcl :exports both :results value verbatim
-  (symbol-function 'x)
-  #+END_SRC
-
-  and can be used jointly and independently:
-
-  #+BEGIN_SRC lisp :session pcl :exports both
-  (x (first x))
-  #+END_SRC
-   
-  You might already suspect that the position of =x= just after a left
-  parenthesis =(x ...)= makes Lisp extract the /functional/ value and not the
-  "ordinary" value. This is correct, but not the subject of this tutorial.
-  Finally, we mention only in passing the following:
-
-  1. A symbol can have a functional value while not having an ordinary value.
-  2. An ordinary value can be a functional object, usually then called via
-     =funcall= or =apply=.
-  3. A symbol also contains a property list or =plist=, with many possible
-     uses, but not at all studied here.
-
-     The internal structure of the [[http://clhs.lisp.se/Body/t_symbol.htm#symbol][symbol]] =x= might be visualized thus:
-   
-     #+BEGIN_EXAMPLE
-     +-----------------+
-     | Name          o-|-----> "x"
-     +-----------------+
-     | Value         o-|-----> (4 5 6)
-     +-----------------+
-     | Function      o-|-----> (lambda (n) (- 10 n))
-     +-----------------+
-     | Package       o-|-----> #<PACKAGE "COMMON-LISP-USER">
-     + ----------------+
-     | Property list o-|-----> NIL
-     +-----------------+
-     #+END_EXAMPLE
-
-* But what the hell is a package?
-
-  Now we attack the heart of our subject.\\
-
-  **Fact 1:** A package $p\in P$ maintains four fundamental lists:
-
-  - A list $InS(p)$ of its internal symbols.
-  - A list $ExS(p)$ of its external symbols.
-  - A list $ShgS(p)$ of its shadowing symbols.
-  - A list $U(p)$ of its used packages.\\
-
-  The first important fact toward understanding the subject is this: the first
-  three lists are lists of /symbols/ or, more precisely, lists of pointers
-  (machine addresses) aimed at the symbols. Every symbol has a /unique/
-  "existence": a symbol is a unique machine object in the environment, but
-  /several/ packages may /see/ the same symbol, that is, include the machine
-  address of this symbol. In particular these lists are not lists of symbol
-  names (strings). There is another mechanism that allows Lisp to reach a
-  symbol given its name. Every symbol can be accessed directly via a suitable
-  package, and several packages can in general play this role for the same
-  symbol at a given moment in a Lisp session. For example, all the
-  [[http://clhs.lisp.se/Front/X_Symbol.htm][standard Lisp symbols]] in the ="COMMON-LISP"= package typically are
-  accessible via any package.
-
-  No duplicate symbol (more precisely, no duplicate pointer) is to be found in
-  each of these lists. Also the relations $InS(p)\cap ExS(p)=\emptyset$ and
-  $ShgS(p)\subset InS(p)\cup ExS(p)$ must be satisfied, for reasons to be
-  studied later.\\
-
-  **Fact 2:** Given the current set of packages, assumed /coherent/, and given
-  the current state of all the fundamental lists of these packages, the
-  function =find-symbol= can unambiguously determine /whether/ a symbol of a
-  given name (some string) is /accessible/ via some package; if so, this
-  symbol is unique.\\
-
-  The importance of the package argument of =find-symbol= could make the
-  reader believe the function =symbol-package= will be useful for various
-  tests. This is not the case: All this function returns is the "birth place"
-  of the symbol, technically called its /home package/, which says almost
-  nothing about the current status of this symbol with respect to any package.
-  All it says is that at least it is /interned/ in this package. In
-  particular, a symbol can be accessible via several packages, possibly
-  different from its home package. Here is a simple illustration:
-
-  #+BEGIN_SRC lisp :session pcl :exports both
-  (symbol-package 'nil)
-  #+END_SRC
-
-  #+BEGIN_SRC lisp :session pcl :exports both :results value verbatim
-  (multiple-value-list (find-symbol "NIL" "COMMON-LISP"))
-  #+END_SRC
-   
-  #+BEGIN_SRC lisp :session pcl :exports both :results value verbatim
-  (multiple-value-list (find-symbol "NIL" "COMMON-LISP-USER"))
-  #+END_SRC
-
-  #+BEGIN_SRC lisp :session pcl :exports both :results value verbatim
-  (eq (find-symbol "NIL" "COMMON-LISP")
-      (find-symbol "NIL" "COMMON-LISP-USER"))
-  #+END_SRC
-
-  The /home package/ of =nil= is ="COMMON-LISP"=, and this symbol of name
-  ="NIL"= is accessible via ="COMMON-LISP"=, but also via
-  ="COMMON-LISP-USER"=, though not with the same status. It is /external/ in
-  the first case and /inherited/ in the second case, points to be examined
-  later. The value (=T=) of the last expression /proves/ that both symbols,
-  determined by =find-symbol= via different packages, in fact are the same.
-  Fact 2 can be made a little more precise: At any given time during a Lisp
-  session, a set $P$ of packages and a set $Sm$ of symbols are defined. The
-  various lists of symbols $InS(p)$, $ExS(p)$ and $ShgS(p)$, and the list
-  $U(p)$ of packages used by a package $p\in P$ together define without any
-  ambiguity which symbols are accessible via the package $p$. In other words,
-  there is a well defined function $\rho$:
-  $$
-  \rho: P \longrightarrow [St \longrightarrow Sm \cup \{\mathtt{nil}\}]
-  $$
-  We chose the letter $\rho$ for reader, because this function is mainly used
-  by the reader. Our "mathematical" function $\rho$ is nothing but an avatar
-  of the Lisp function =find-symbol=. Let $p\in P$ be a package and
-  $st\in St$ be a string. Then:
-  $$
-  \rho(p)(st) = (\mathtt{find-symbol}\; st\; p)
-  $$
-  The left-hand side uses the standard mathematical functional notation, and
-  the right-hand one uses the Lisp notation. If no symbol is found for a pair
-  $(st, p)$, the symbol (!) =nil= is returned and the second value of
-  =find-symbol=, the symbol =nil= again, tells the user that the symbol search
-  did not return anything. A package $p$ is nothing but a way of defining the
-  function $\rho(p):St\longrightarrow Sm\cup\{\mathtt{nil}\}$. In other words,
-  the four fundamental lists of a package determine what character strings
-  appear as the names of the symbols accessible via this package.
-  This approach is described in detail now.
-
-* Internal symbols.
-
-  The first fundamental list of a package is the list of its /internal
-  symbols/. It is a pity that no standard Lisp function can produce this list,
-  but here is a simple solution to the problem:
-
-  #+BEGIN_SRC lisp :session pcl :exports both :results value verbatim
-  (defun package-internal-symbols (package)
-    (let ((rslt))
-      (do-symbols (s package)
-        (when (eq (second
-                   (multiple-value-list
-                    (find-symbol (symbol-name s) package)))
-                  :internal)
-          (push s rslt)))
-      rslt))
-  #+END_SRC
-
-  We can list now all the internal symbols of a package:
-
-  #+BEGIN_SRC lisp :session pcl :exports both :results value verbatim
-  (package-internal-symbols "COMMON-LISP-USER")
-  #+END_SRC
-
-  In fact, only the first ten internal symbols are displayed. We see in
-  particular the symbols =package-internal-symbols=, =s= and =rslt= used in
-  the definition of our function. Some are rather esoteric, strictly speaking
-  illegal: at the beginning of a Lisp session, the ="COMMON-LISP-USER"=
-  package should in principle be void of symbols. To make our experiments more
-  understandable it is better to allocate and use toy packages. The
-  [[http://clhs.lisp.se/Body/m_defpkg.htm][=defpackage=]] function (a macro) allocates a package of a given name.
-
-  #+BEGIN_SRC lisp :session pcl :exports both :results value verbatim
-  (defpackage "P1" (:use "CL"))
-  #+END_SRC
-
-  A package ="P1"= is now present in our environment, without any internal
-  symbols.
-
-  #+BEGIN_SRC lisp :session pcl :exports both :results value verbatim
-  (package-internal-symbols "P1")
-  #+END_SRC
-
-  (The symbol =nil= also represents the empty list.) Let's allocate a few
-  symbols and make them internal in the package ="P1"=! The current default
-  package is ="COMMON-LISP-USER"= and we switch it to ="P1"= like this:
-
-  #+BEGIN_SRC lisp :session pcl :exports both :results value verbatim
-  (in-package "P1")
-  #+END_SRC
-
-  #+BEGIN_SRC lisp :session pcl :exports both :package "P1"
-  *package*
-  #+END_SRC
-
-  From now on, the default package is ="P1"=. If we write down a symbol then it
-  will be understood by the Lisp reader as accessed via the package ="P1"=,
-  that is, unless we use a special syntax. Let us create a list of three
-  symbols and assign it to the symbol =my-list=, and then examine the internal
-  symbols of the package ="P1"=:
-
-  #+BEGIN_SRC lisp :session pcl :exports both :package "P1" :results value verbatim
-  (setf (symbol-value 'my-list) '(symb1 symb2 symb3))
-  #+END_SRC
-
-  The reader probably would prefer =(defvar list)= followed by
-  =(setf list ...)=, which is rejected by some Lisp implementations, in
-  particular SBCL, because in principle the symbol =list=, owned by the package
-  ="COMMON-LISP"=, is "locked". We use the symbol =my-list= instead.
-
-  #+BEGIN_SRC lisp :session pcl :exports both :package "P1" :results value verbatim
-  (multiple-value-list
-   (ignore-errors
-     (package-internal-symbols "P1")))
-  #+END_SRC
-
-  Oops! What happened? We've successfully used the function
-  =package-internal-symbols= earlier and suddenly it seems to have disappeared
-  from the environment. The point is that it was /defined when/
-  ="COMMON-LISP-USER"= was the default package. Let us examine the situation!
-
-  #+BEGIN_SRC lisp :session pcl :exports both :package "P1" :results value verbatim
-  (multiple-value-list (find-symbol "PACKAGE-INTERNAL-SYMBOLS" "COMMON-LISP-USER"))
-  #+END_SRC
-
-  #+BEGIN_SRC lisp :session pcl :exports both :package "P1" :results value verbatim
-  (multiple-value-list (find-symbol "PACKAGE-INTERNAL-SYMBOLS" "P1"))
-  #+END_SRC
-  
-  A symbol with the given name is found in both packages. Before encountering
-  the undefined functional value error, Lisp ( more precisely, the Lisp reader)
-  had interned a /new/ symbol with the name ="PACKAGE-INTERNAL-SYMBOLS"= in the
-  current default package, ="P1"=, for the sole reason that it was present in
-  the source text. Let us verify that both symbols are different!
-
-  #+BEGIN_SRC lisp :session pcl :exports both :package "P1"
-  (eq (find-symbol "PACKAGE-INTERNAL-SYMBOLS" "COMMON-LISP-USER")
-      (find-symbol "PACKAGE-INTERNAL-SYMBOLS" "P1"))
-  #+END_SRC
-  
-  The symbols are different. Compare that with the status of =nil=, where the
-  same symbol =nil= was accessible via ="COMMON-LISP"= and via
-  ="COMMON-LISP-USER"=. In our present situation both symbols are /different/,
-  and so are their respective properties. For example, the first symbol does
-  have a functional value and the second does not, which can be tested with the
-  function [[http://clhs.lisp.se/Body/f_fbound.htm][=fboundp=]]x:
-
-  #+BEGIN_SRC lisp :session pcl :exports both :package "P1"
-  (fboundp (find-symbol "PACKAGE-INTERNAL-SYMBOLS" "COMMON-LISP-USER"))
-  #+END_SRC
-
-  #+BEGIN_SRC lisp :session pcl :exports both :package "P1"
-  (fboundp (find-symbol "PACKAGE-INTERNAL-SYMBOLS" "P1"))
-  #+END_SRC
-
-  This is the first time we have seen the double-colon =‘::’= notation: When
-  the symbol =package-internal-symbols= was searched via ="COMMON-LISP-USER"=,
-  the answer was positive but the returned symbol was a little lengthy:
-  =COMMON-LISP-USER::PACKAGE-INTERNAL-SYMBOLS=. The current default package is
-  ="P1"=, via which /this/ symbol is not accessible. However, we may access it
-  using the double-colon notation:
-
-  #+BEGIN_CENTER
-  =package-name::symbol-name=
-  #+END_CENTER
-  
-  This is one of the methods which allows the user or Lisp to refer to a symbol
-  not accessible via the default package. The Lisp reader is told: "We mean the
-  symbol =symbol-name= via the package =package-name=." In contrast, for the
-  symbol with the same name but interned in the different ="P1"= package,
-  because ="P1"= is the current default package, the double colon notation is
-  not necessary. The longer notation lets us access a symbol interned in the
-  ="COMMON-LISP-USER"= package and its functional value as follows:
-
-  #+BEGIN_SRC lisp :session pcl :exports both :package "P1" :results value verbatim
-  (cl-user::package-internal-symbols "P1")
-  #+END_SRC
-
-  The =cl-user::= prefix tells Lisp to look for the symbol via the ="CL-USER"=
-  package (Remember that ="CL-USER"= is a nickname for ="COMMON-LISP-USER"=?)
-  and, because of its position just after a left parenthesis, to use its
-  functional value. Currently, there are four internal symbols in the package
-  ="P1"= and they are returned in an arbitrary order. By the way, what about
-  the symbol =list=, to which we assigned a list (!) of symbols?
-
-  #+BEGIN_SRC lisp :session pcl :exports both :package "P1" :results value verbatim
-  (multiple-value-list (find-symbol "LIST" "P1"))
-  #+END_SRC
-
-  The symbol is accessible via the package ="P1"= but with a different status,
-  the status /inherited/. We will examine this situation later. In fact, the
-  symbol =list=, one of the most important symbols in Lisp, is already present
-  in the package ="COMMON-LISP"= at the beginning of a session, and by default
-  accessible from any package.
-
-  We must mention also that our function $\rho$, or the function =find-symbol=
-  if you prefer, is (almost) injective /with respect to/ $st$. Let $p_1$ and
-  $p_2$ be two packages, $st_1$ and $st_2$ two strings. Then if
-  $\rho(p_1, st_1) = \rho(p_2, st_2)\neq\mathtt{nil}$, then $st_1 = st_2$. Pay
-  attention to the fact that the equality is an equality between /symbols/.
-  This is a consequence of $\mathtt{symbol-name}(\rho(p, st)) = st$; in other
-  words, there is no possibility of nicknames for a symbol name. In particular,
-  there is a 1-1 correspondence between the internal symbols of a package and
-  their respective names.
-
-* Importing a symbol.
-
-  Instead of using the lengthy notation =cl-user::xxx= to make an internal
-  symbol in ="CL-USER"= accessible from ="P1"=, we may opt to /import/ this
-  symbol in the package ="P1"=. However, in doing so there is another problem
-  due to a name conflict, a point which will be examined in detail later:
-
-  #+BEGIN_SRC lisp :session pcl :exports both :package "P1" :results value verbatim
-  (multiple-value-list
-   (ignore-errors
-     (import 'cl-user::package-internal-symbols "P1")))
-  #+END_SRC
-
-  The problem is a "collision" between two /different/ symbols, which cannot
-  coexist as internal symbols in the /same/ package ="P1"= with the /same/
-  name. Importing the symbol internal in ="CL-USER"= into the package ="P1"= is
-  not compatible with the current presence of /another/ symbol in ="P1"= with
-  the same =symbol-name=. We must first [[http://clhs.lisp.se/Body/f_uninte.htm][=unintern=]] the accidental, pre-existing
-  symbol in ="P1"= to "make room" for the symbol from ="CL-USER"=.
-
-  #+BEGIN_SRC lisp :session pcl :exports both :package "P1" :results value verbatim
-  (unintern 'package-internal-symbols "P1")
-  #+END_SRC
-
-  #+BEGIN_SRC lisp :session pcl :exports both :package "P1" :results value verbatim
-  (import 'cl-user::package-internal-symbols "P1")
-  #+END_SRC
-
-  #+BEGIN_SRC lisp :session pcl :exports both :package "P1" :results value verbatim
-  (package-internal-symbols "P1")
-  #+END_SRC
-
-  The Lisp terminology is rather misleading: in fact, it is not at all the
-  symbol which is imported, but the connection /string/ $\mapsto$ /symbol/.
-  More precisely, let $p_1$ and $p_2$ be two packages, $st$ a string and $sm$
-  a symbol. If $\rho(p_1)(st) = sm$ holds before the importation, then, after
-  the importation, both relations
-  $\rho(p_1)(st) = sm$ /and/ $\rho(p_2)(st) = sm$ are satisfied. In particular,
-  the first relation remains valid. It is not really an importation; it is a
-  /copy/ in the package $p_2$ of the connection $st \mapsto sm$, available in
-  the package $p_1$.
-
-  Furthermore, nothing is modified about the symbol itself, except /possibly/,
-  but rarely, its home package, as will be examined later. It is tempting for a
-  beginner to think the home-package of the symbol is being modified. Not at
-  all! Another erroneous interpretation would be to think a /copy/ of the
-  symbol to be imported is made "inside" the target package, with all the
-  corresponding ingredients of the symbol, value, functional value, and so on.
-  Wrong again! A copy is made, but only of a /pointer/ toward our symbol found
-  in $InS(p_1)$ and copied in $InS(p_2)$.
-
-  The [[http://clhs.lisp.se/Body/f_import.htm][=import=]] function has two arguments, the /symbol/ to be imported and the
-  /target package/. The symbol must be well defined, that is, taking account of
-  the current state of the environment. Here, before the import, the symbol is
-  accessible only via ="CL-USER"=, and it is mandatory to use the notation
-  =cl-user::...= (and the symbol must also be quoted to preclude its
-  evaluation). After the import, as can be seen in the example, the symbol can
-  be used functionally from the package ="P1"= without the prefix notation.
-  Although the imported symbol is in the list of the internal symbols of the
-  package ="P1"=, it is not quite the same as before. The next mandatory
-  exercise consists in comparing the original symbol and the imported one.
-
-  #+BEGIN_SRC lisp :session pcl :exports both :package "P1" :results value verbatim
-  (eq 'cl-user::package-internal-symbols
-      'package-internal-symbols)
-  #+END_SRC
-
-  The function =eq= proves that both notations name the same symbol. Here's
-  another proof:
-
-  #+BEGIN_SRC lisp :session pcl :exports both :package "P1" :results value verbatim
-  (eq (find-symbol "PACKAGE-INTERNAL-SYMBOLS" "CL-USER")
-      (find-symbol "PACKAGE-INTERNAL-SYMBOLS" "P1"))
-  #+END_SRC
-
-  If you remember the =symbol-package= function, the next test is revealing:
-
-  #+BEGIN_SRC lisp :session pcl :exports both :package "P1" :results value verbatim
-  (symbol-package (find-symbol "PACKAGE-INTERNAL-SYMBOLS" "CL-USER"))
-  #+END_SRC
-
-  #+BEGIN_SRC lisp :session pcl :exports both :package "P1" :results value verbatim
-  (symbol-package (find-symbol "PACKAGE-INTERNAL-SYMBOLS" "P1"))
-  #+END_SRC
-  
-  The /unique/ symbol accessed by two different paths has of course a unique
-  home package, namely its /birth place/, the ="CL-USER"= package. Please, do
-  not pay too much attention to this symbol package; it is just an artifact of
-  the session's history and does not have any real interest. You must focus on
-  the chain
-  $\mathit{package}\rightarrow[\mathit{string}\rightarrow \mathit{symbol}]$ and
-  not much else. There is no real reason to be concerned about the map
-  =symbol-package=: $\mathit{symbol}\rightarrow\mathit{package}$.
-
-* Name conflicts.
-
-  If poorly understood, the introduction of Lisp packages to a Lisp project
-  will sooner or later lead to /name conflicts/. There is nothing mysterious
-  about them and there are standard "home remedies" for dealing with them.\\
-
-  *Warning.* A name conflict can only be generated if two /different/ symbols
-  $sm$, $sm' \in Sm$ end up with the same name: $sn(sm) = sn(sm')$. A name
-  conflict occurs if these symbols $sm$ and $sm'$ become accessible via the
-  same package $p$, which is a forbidden situation, since it would introduce
-  ambiguity to the =find-symbol= function. On the other hand, the fact that
-  some symbol (singular) is accessible via /different/ packages never generates
-  a name conflict by itself.
-
-  Lisp constantly is on the lookout for possible name conflicts and stops with
-  an error if the evaluation of an expression causes a name conflict. Some
-  errors are /continuable/, which means that Lisp is able to propose a conflict
-  resolution via =unintern= or =shadowing-import=. Remember the use of
-  =unintern= in the previous section?
-
-  What happens if an imported symbol has the same /name/ as a symbol already
-  accessible in the target package? In mathematical language, let $p_1$ and
-  $p_2$ be two different packages, $st$ some string, and $sm_1$ and $sm_2$ two
-  different symbols, internal in the respective packages $p_1$ and $p_2$, with
-  same name $st$. In other words,  assume $\rho(p_1)(st) = sm_1$ and
-  $\rho(p_2)(st) = sm_2$, $sm_1 \in InS(p_1)$ and $sm_2 \in InS(p_2)$, and
-  $sm_1\neq sm_2$. A situation of this sort could be the following (Remember
-  the current default package is ="P1"=!):
-
-  #+BEGIN_SRC lisp :session pcl :exports both :package "P1" :results value verbatim
-  (defvar cl-user::symb4)
-  #+END_SRC
-
-  #+BEGIN_SRC lisp :session pcl :exports both :package "P1" :results value verbatim
-  (setf cl-user::symb4 111)
-  #+END_SRC
-
-  #+BEGIN_SRC lisp :session pcl :exports both :package "P1" :results value verbatim
-  (defvar symb4)
-  #+END_SRC
-
-  #+BEGIN_SRC lisp :session pcl :exports both :package "P1" :results value verbatim
-  (setf symb4 111)
-  #+END_SRC
-
-  #+BEGIN_SRC lisp :session pcl :exports both :package "P1" :results value verbatim
-  (eq 'cl-user::symb4 'symb4)
-  #+END_SRC
-
-  The evaluation of the first expression interns a symbol of name ="SYMB4"= in
-  the package ="CL-USER"= and gives it the value 111, while the second
-  expression interns a /different/ symbol, again of name ="SYMB4"=, in the
-  package ="P1"=, the current default package, and also gives it the value 111.
-  As a result two symbols have been allocated, installed somewhere in the
-  environment, with the same value of 111. Also the connections
-  $\rho(\mathtt{"CL-USER"}): \mathtt{"SYMB4"}\mapsto \mathtt{cl-user::symb4}$
-  and $\rho(\mathtt{"P1"}): \mathtt{"SYMB4"}\mapsto\mathtt{p1::symb4}$ have
-  been installed, that is, the addresses of both symbols have been pushed to
-  the /respective/ lists of /internal/ symbols of the packages ="CL-USER"= and
-  ="P1"=. The =eq= comparison confirms that the symbols just allocated are
-  different. Two symbols with the same name ="SYMB4"= are now present in our
-  environment. This is possible because these symbols are interned in different
-  packages. Each one is accessible via the appropriate package. Both symbols
-  are live and can be freely used:
-
-  #+BEGIN_SRC lisp :session pcl :exports both :package "P1" :results value verbatim
-  (setf cl-user::symb4 (+ symb4 cl-user::symb4))
-  #+END_SRC
-
-  What happens if we import =cl-user::symb4= into the package ="P1"=? Let's
-  try!
-
-  #+BEGIN_SRC lisp :session pcl :exports both :package "P1" :results value verbatim
-  (multiple-value-list
-   (ignore-errors
-     (import 'cl-user::symb4 "P1")))
-  #+END_SRC
-
-  The importation is rejected, for it would not be possible anymore to
-  coherently define $\rho(\mathtt{"P1"})(\mathtt{"SYMB4"})$. We will see later
-  that another process called /shadowing/ allows the user to suppress the
-  symbol =symb4= already present in ="P1"= and to authorize the importation of
-  the symbol present in ="CL-USER"=.
-
-* The function =intern=.
-
-  **Fact 3:** Let $p$ be a package and $(sm_1,...,sm_n)$ the list of its
-  internal symbols. If $p$ is the default package, any of these symbols can be
-  directly used without the double colon notation ='::'=. If $p$ is not the
-  default package, these symbols can be used thanks to the notation $p::sm_i$.
-  All these internal symbols have different names. Nothing prevents several
-  packages from having the same symbols in their lists of internal symbols.
-  This is possible thanks to the =import= function which can work only if no
-  name conflict is generated.\\
-
-  To be complete on this matter, we now to consider the Lisp function
-  [[http://clhs.lisp.se/Body/f_intern.htm][=intern=]]. It is used almost exactly as the function =find-symbol= with just a
-  difference: if no symbol is found, then a symbol is allocated and interned in
-  the package referred to in its second argument. Compare the following:
-
-  #+BEGIN_SRC lisp :session pcl :exports both :package "P1" :results value verbatim
-  (multiple-value-list (find-symbol "SYMB5" "P1"))
-  #+END_SRC
-
-  #+BEGIN_SRC lisp :session pcl :exports both :package "P1" :results value verbatim
-  (multiple-value-list (intern "SYMB5" "P1"))
-  #+END_SRC
-
-  #+BEGIN_SRC lisp :session pcl :exports both :package "P1" :results value verbatim
-  (multiple-value-list (intern "SYMB5" "P1"))
-  #+END_SRC
-
-  We start without any =symb5= symbol in ="P1"=, which is confirmed by the
-  double negative answer of =find-symbol=. If instead we use the function
-  =intern=, Lisp notices that such a symbol is absent from ="P1"= and therefore
-  allocates a symbol of name ="SYMB5"= and /interns/ it in the package ="P1"=
-  as an internal symbol. The second value =nil= is an indicator of the
-  allocation just made. If we repeat the same expression, which is not an
-  error, then Lisp signals that such a symbol is already present and returns
-  its status, which also informs us of its previous presence. A little weird!
-  This definition of the function =intern= guarantees the coherence of the set
-  of internal symbols of packages. A symbol can be allocated only through this
-  function =intern=. It requires two arguments, a string $st$ and a package
-  $p$. In a sense, the function =intern= first calls =(find-symbol st p)= with
-  the same arguments. If a symbol is found it is returned without modification
-  and no allocation of a new symbol takes place, which otherwise would create
-  a name conflict. On the other hand, if a corresponding symbol is not found,
-  it is allocated and interned in the package explicitly or implicitly quoted,
-  and this new symbol certainly does not generate a name conflict. In this way,
-  the uniqueness of the names of internal symbols of a package is enforced.
-  This does not prevent two different symbols of the environment from having
-  the same name, but the packaging system is organized such that they cannot be
-  accessed via the same package.
-
-  #+BEGIN_SRC lisp :session pcl :exports both :package "P1" :results value verbatim
-  (package-internal-symbols "P1")
-  #+END_SRC
-
-  In practice, the Lisp reader constantly uses the =intern= function, for
-  example when reading an expression. If it detects the presence of a symbol,
-  the colon notation allows it to decide if a package is explicitly given,
-  otherwise it must use the default package. The name of the symbol, alone or
-  package-qualified using the colon notation, then unambiguously determines the
-  symbol. If present, it is used, otherwise it is allocated and then used. This
-  is exactly the role of the =intern= function.
-
-* Moving a symbol between two packages.
-
-  Up until now, we have seen no means of modifying the home package of a
-  symbol. In fact, it is possible but may seem a little contorted. It is almost
-  without any practical interest except as an opportunity to use this as a
-  vehicle to discover other facts. First, it is possible to /unintern/ a
-  symbol. For example, we can unintern the symbol ="SYMB1"= from the package
-  ="P1"=. What happens is precisely that this symbol is removed from the list
-  of the internal symbols of ="P1"=.
-
-  #+BEGIN_SRC lisp :session pcl :exports both :package "P1" :results value verbatim
-  (unintern 'symb1 "P1")
-  #+END_SRC
-
-  #+BEGIN_SRC lisp :session pcl :exports both :package "P1" :results value verbatim
-  (package-internal-symbols "P1")
-  #+END_SRC
-
-  What is modified is the /list/ of internal symbols in the package ="P1"=. The
-  symbol =symb1= itself has not been modified at all, except possibly its home
-  package. In particular the symbol is not deallocated or destroyed, and
-  therefore always present somewhere in the environment.
-
-  But it's become inaccessible as such, for a symbol most often is accessible
-  only via a package, the default one or some other explicitly given. The
-  symbol =symb1= was interned only in the package ="P1"=, so that it appears
-  now to be unreachable! If a symbol is truly unreachable, the Lisp garbage
-  collector, always silently working in the background, will establish that
-  fact and free the corresponding part of memory for reuse. Except that our
-  symbol remains reachable, for it was the first element of the list assigned
-  to the symbol =my-list=. Let's have a look at its value!
-
-  #+BEGIN_SRC lisp :session pcl :exports both :package "P1" :results value verbatim
-  my-list
-  #+END_SRC
-
-  Our symbol is still present in the list but in a little different form.
-  To be sure, it is still a symbol:
-
-  #+BEGIN_SRC lisp :session pcl :exports both :package "P1" :results value verbatim
-  (type-of (first my-list))
-  #+END_SRC
-
-  #+BEGIN_SRC lisp :session pcl :exports both :package "P1" :results value verbatim
-  (symbol-package (first my-list))
-  #+END_SRC
-
-  No home package, i.e., our symbol is "homeless"! The prefix ='#:'= indicates
-  that this symbol is homeless. The =unintern= function had this effect because
-  the package argument of =unintern= was the package which /owned/ the symbol.
-  Otherwise the home package would not be modified. Although our symbol has
-  become homeless, it continues to be an ordinary symbol, for example, we can
-  assign it a value:
-
-  #+BEGIN_SRC lisp :session pcl :exports both :package "P1" :results value verbatim
-  (set (first my-list) 444)
-  #+END_SRC
-  
-  #+BEGIN_SRC lisp :session pcl :exports both :package "P1" :results value verbatim
-  (symbol-value (first my-list))
-  #+END_SRC
-
-  #+BEGIN_SRC lisp :session pcl :exports both :package "P1" :results value verbatim
-  (eval (first my-list))
-  #+END_SRC
-  
-  Unlike =setf= (macro), the =set= function evaluates its arguments, so that
-  before the assignment, the expression =(first my-list)= is evaluated, which
-  returns our mysterious symbol =#:symb1=. Once that's done, the =set= function
-  assigns (the value of) the second argument to it, as is confirmed by the
-  other expressions. It is even possible to /import/ a homeless symbol in a
-  package, but then the target package becomes the home package of the imported
-  symbol. The importing package can be different from the original home
-  package. As a result our symbol is "moved" into another package. This
-  explains the new form of the value of =my-list=.
-
-  #+BEGIN_SRC lisp :session pcl :exports both :package "P1" :results value verbatim
-  (import (first my-list) "CL-USER")
-  #+END_SRC
-
-  #+BEGIN_SRC lisp :session pcl :exports both :package "P1" :results value verbatim
-  (symbol-package 'cl-user::symb1)
-  #+END_SRC
-
-  #+BEGIN_SRC lisp :session pcl :exports both :package "P1" :results value verbatim
-  my-list
-  #+END_SRC
-
-  Our symbol could also have been imported in other packages before being
-  uninterned from its home package. The status of our symbol with respect to
-  other packages would not have been modified.
-
-  #+BEGIN_SRC lisp :session pcl :exports both :package "P1" :results value verbatim
-  (import 'symb3 "CL-USER")
-  #+END_SRC
-
-  #+BEGIN_SRC lisp :session pcl :exports both :package "P1" :results value verbatim
-  (eq 'cl-user::symb3 'symb3)
-  #+END_SRC
-
-  #+BEGIN_SRC lisp :session pcl :exports both :package "P1" :results value verbatim
-  (unintern 'symb3 "P1")
-  #+END_SRC
-
-  #+BEGIN_SRC lisp :session pcl :exports both :package "P1" :results value verbatim
-  (eq 'cl-user::symb3 (third my-list))
-  #+END_SRC
-
-  #+BEGIN_SRC lisp :session pcl :exports both :package "P1" :results value verbatim
-  (import 'cl-user::symb3 "CL-USER")
-  #+END_SRC
-
-  #+BEGIN_SRC lisp :session pcl :exports both :package "P1" :results value verbatim
-  (symbol-package 'cl-user::symb3)
-  #+END_SRC
-
-  Here we import =symb3= in the package ="CL-USER"= before uninterning it from
-  the package ="P1"=. The symbol is then accessible via the package ="CL-USER"=
-  or via the list =my-list=. The evaluation of the expression =(eq ...)= proves
-  that both paths lead to the same address. When the first =(import ...)=
-  expression is evaluated, the symbol does have a home package and that it is
-  not changed. When it is uninterned from the package ="P1"=, it becomes
-  homeless. Lisp does not take account of the fact it is internal in other
-  packages. In theory, this would allow it to select one of these packages as
-  an "emergency home" package, but the choice would be quite arbitrary?
-  Furthermore this would force Lisp to examine the list of all other packages
-  and all their accessible symbols, which would be very expensive! Here,
-  despite the symbol being internal and therefore interned in the package
-  ="CL-USER"=, it becomes homeless after evaluating the =(unintern ...)=
-  expression. Finally we import it in the package ="CL-USER"=, where, in fact,
-  it is already present. According to the ANSI standard (see the following
-  note), in such a situation, its status remains unchanged. In particular its
-  home package remains =nil=. A little esoteric, huh? Don’t worry: the home
-  package does not have any real role for the Lisp user.
-
-  -----
-
-  *Note:* The [[http://clhs.lisp.se/Body/f_import.htm#import][passage]] in the [[http://clhs.lisp.se/Front/index.htm][Common Lisp HyperSpec]] reads like this: /"If the
-  symbol is already present in the importing package, import has no effect."/
-  It appears that the behavior of SBCL and some other compilers is different:
-  The output is =#<PACKAGE "COMMON-LISP-USER">= not =NIL=.
-
-  -----
-
-  We will prove later that if a symbol $sm$ has a home package $p$, then $sm$
-  is certainly present in $p$, that is, internal or external in this package.
-  The "converse" is false: a symbol may be present in several packages
-  $p_1,\ldots , p_k$ while not having a home package. This might sound a little
-  weird, but you shouldn't lose much sleep over it: except for the internal
-  efficiency of the Lisp interpeter or compiler, the notion of a home-package
-  is almost useless for the programmer.
-
-* External symbols and used packages.
-
-  The analysis of this notion of an internal symbol was a little lengthy, but,
-  in this way, the general structure of the packaging system is now very clear,
-  and it will be a lot easier to understand the other concepts. Two fundamental
-  lists maintained in the packages play a "dual" role in the packaging system,
-  the list of /external/ symbols and the list of /used/ packages. The following
-  function gives the list of the external symbols of a package.
-
-  #+BEGIN_SRC lisp :session pcl :exports both :package "P1" :results value verbatim
-  *package*
-  #+END_SRC
-
-  #+BEGIN_SRC lisp :session pcl :exports both :package "P1" :results value verbatim
-  (defun package-external-symbols (package)
-      (let ((rslt nil))
-           (do-external-symbols (s package)
-               (push s rslt))
-           rslt))
-  #+END_SRC
-
-  The evaluation of the first expression is just to confirm that the default
-  package remains ="P1"=. Let us see what the lists of external symbols of the
-  packages ="P1"=, ="CL-USER"= and ="COMMON-LISP"= are:
-
-  #+BEGIN_SRC lisp :session pcl :exports both :package "P1" :results value verbatim
-  (package-external-symbols "P1")
-  #+END_SRC
-
-  #+BEGIN_SRC lisp :session pcl :exports both :package "P1" :results value verbatim
-  (package-external-symbols "CL-USER")
-  #+END_SRC
-
-  #+BEGIN_SRC lisp :session pcl :exports both :package "P1" :results value verbatim
-  (subseq (package-external-symbols "COMMON-LISP") 0 10)
-  #+END_SRC
-
-  #+BEGIN_SRC lisp :session pcl :exports both :package "P1" :results value verbatim
-  (length (package-external-symbols "COMMON-LISP"))
-  #+END_SRC
-
-  There are no external symbols in ="P1"= and ="CL-USER"=, but 978 such symbols
-  in the package ="COMMON-LISP"=. (Only the first ten are being displayed.) A
-  point of concern might be the following: these symbols are accessible via the
-  package ="COMMON-LISP"= and yet the double-colon notation
-  =common-lisp::simple-error= was not used. The explanation has two "dual"
-  parts:
-
-  1. The symbol =simple-error= is external in the package ="COMMON-LISP"=.
-  2. The package ="COMMON-LISP"= is in the =package-use-list= of the package
-     ="P1"=:
-
-  #+BEGIN_SRC lisp :session pcl :exports both :package "P1" :results value verbatim
-  (multiple-value-list (find-symbol "SIMPLE-ERROR" "COMMON-LISP"))
-  #+END_SRC
-
-  #+BEGIN_SRC lisp :session pcl :exports both :package "P1" :results value verbatim
-  (package-use-list "P1")
-  #+END_SRC
-
-  #+BEGIN_SRC lisp :session pcl :exports both :package "P1" :results value verbatim
-  (package-nicknames (find-package "COMMON-LISP"))
-  #+END_SRC
-
-  ="CL"= is the nickname of the package whose official name is ="COMMON-LISP"=,
-  and which is not to be confused with ="COMMON-LISP-USER"=.
-
-  #+BEGIN_SRC lisp :session pcl :exports both :package "P1" :results value verbatim
-  (eq (find-package "CL")
-      (find-package "COMMON-LISP"))
-  #+END_SRC
-
-  #+BEGIN_SRC lisp :session pcl :exports both :package "P1" :results value verbatim
-  (eq (print (find-package "CL"))
-      (print (find-package "CL-USER")))
-  #+END_SRC
-
-  Applied to a package $p$, the Lisp function [[http://clhs.lisp.se/Body/f_pkg_us.htm][=package-use-list=]] returns the
-  list of all the packages used by $p$. If $p_1$ uses $p_2$, then it is said
-  that $p_2$ is used by $p_1$. Whether this relation is reflexive can be
-  doubted (What does "$p$ uses $p$" mean?), and it is neither symmetric
-  ("$p_1$ uses $p_2$" does not imply "$p_2$ uses $p_1$") nor transitive
-  ("$p_1$ uses $p_2$" and "$p_2$ uses $p_3$” does not imply
-  "$p_1$ uses $p_3$"). The oriented graph of the /use/ relation is totally
-  arbitrary.
-
-* First toy examples.
-
-  Let's start over with two "fresh" packages ="P1"= and ="P2"=.
-
-  #+BEGIN_SRC lisp :session pcl :exports both :package "P1" :results value verbatim
-  (in-package "CL-USER")
-  #+END_SRC
-
-  #+BEGIN_SRC lisp :session pcl :exports both :results value verbatim
-  (delete-package (find-package "P1"))
-  #+END_SRC
-
-  #+BEGIN_SRC lisp :session pcl :exports both :results value verbatim
-  (defpackage "P1" (:use "CL"))
-  #+END_SRC
-
-  #+BEGIN_SRC lisp :session pcl :exports both :results value verbatim
-  (defpackage "P2" (:use "CL"))
-  #+END_SRC
-
-  We switch the default package to ="P1"=:
-
-  #+BEGIN_SRC lisp :session pcl :exports both :results value verbatim
-  (in-package "P1")
-  #+END_SRC
-
-  and we assume that, /in this environment/, we define the functions
-  =package-internal-symbols= and =package-external-symbols= as explained
-  before.
-
-  #+BEGIN_SRC lisp :session pcl :package "P1" :exports both :results value verbatim
-  (defun package-internal-symbols (package)
-      (let ((rslt))
-           (do-symbols (s package)
-               (when (eq (second
-                          (multiple-value-list
-                           (find-symbol (symbol-name s) package)))
-                         :internal)
-                   (push s rslt)))
-           rslt))
-  #+END_SRC
-
-
-  #+BEGIN_SRC lisp :session pcl :package "P1" :exports both :results value verbatim
-  (defun package-external-symbols (package)
-      (let ((rslt))
-           (do-external-symbols (s package)
-               (push s rslt))
-           rslt))
-  #+END_SRC
-
-  What about the internal symbols of ="P1"=?
-
-  #+BEGIN_SRC lisp :session pcl :package "P1" :exports both :results value verbatim
-  (package-internal-symbols "P1")
-  #+END_SRC
-  
-  We see the symbols naming our functions and also the symbols =rslt= and =s=
-  used to define them. All the other symbols used in their definitions are in
-  fact external in ="COMMON-LISP"= and absent here. We move now to the package
-  ="P2"= from where we cannot access the symbol =package-internal-symbols=
-  directly.
-
-  #+BEGIN_SRC lisp :session pcl :package "P1" :exports both :results value verbatim
-  (in-package "P2")
-  #+END_SRC
-
-  #+BEGIN_SRC lisp :session pcl :package "P2" :exports both :results value verbatim
-  (multiple-value-list (find-symbol "PACKAGE-INTERNAL-SYMBOLS" "P2"))
-  #+END_SRC
-
-  We have already seen the use of the ='::'= notation to make reference to the
-  symbol at once. We can also /import/ the symbol, in which case it becomes
-  directly accessible from ="P2"= permanently:
-
-  #+BEGIN_SRC lisp :session pcl :package "P2" :exports both :results value verbatim
-  (import 'p1::package-internal-symbols "P2")
-  #+END_SRC
-
-  #+BEGIN_SRC lisp :session pcl :package "P2" :exports both :results value verbatim
-  (package-internal-symbols "P2")
-  #+END_SRC
-
-  Another solution requires /two/ steps:
-
-  1. Make the symbol =external= in some package, which is the role of the Lisp
-     function [[http://clhs.lisp.se/Body/f_export.htm][=export=]].
-  2. Declare that the current package /uses/ the package where the symbol is
-     external.
-
-  Let us use this method to make the symbol =package-external-symbols= directly
-  visible from ="P2"=.
-
-  #+BEGIN_SRC lisp :session pcl :package "P2" :exports both :results value verbatim
-  (export 'p1::package-external-symbols "P1")
-  #+END_SRC
-
-  #+BEGIN_SRC lisp :session pcl :package "P2" :exports both :results value verbatim
-  (use-package "P1" "P2")
-  #+END_SRC
-
-  #+BEGIN_SRC lisp :session pcl :package "P2" :exports both :results value verbatim
-  (package-external-symbols "P2")
-  #+END_SRC
-
-  #+BEGIN_SRC lisp :session pcl :package "P2" :exports both :results value verbatim
-  (package-external-symbols "P1")
-  #+END_SRC
-  
-  An =export= expression has the same form as an =import= one:
-  =(export= $sm$ $st$ =)=, where $sm$ is a symbol and $st$ is a string naming a
-  package. The symbol $sm$ must be readable from the current default package,
-  for us ="P2"=, which explains the (required) prefix ='p1::'=. The argument
-  $st$ is a string naming the package where the symbol $sm$ is to become
-  external. Again, the terminology is somewhat misleading: the function
-  =export= does not export anything. All it does is to make some connection
-  $st \rightarrow sm$ "exportable" to other packages via =use-package=
-  expressions. The 978 external symbols of ="COMMON-LISP"= contain all the
-  standard Lisp constants, variables and functions. Because an allocated
-  package is always initialized with the package ="COMMON-LISP"= in its
-  =package-use-list=, these basic Lisp objects will be accessible from any
-  package. If we remove ="COMMON-LISP"= from the =use-package-list= of the
-  current default package, via =unuse-package=, the situation becomes a little
-  tricky.
-
-  -----
-
-  *Note:* Before setting the saw to the branch on which we are sitting,
-  we have to take one precaution: We can't let go of =LET=. Otherwise the
-  interaction between Emacs and SLIME will cease to function.
-
-  #+BEGIN_SRC lisp :session pcl :package "P2" :exports both :results value verbatim
-  (cl::import 'cl::let "P2")
-  #+END_SRC
-
-  -----
-
-  #+BEGIN_SRC lisp :session pcl :package "P2" :exports both :results value verbatim
-  (unuse-package "COMMON-LISP" "P2")
-  #+END_SRC
-
-  #+BEGIN_SRC lisp :session pcl :package "P2" :exports both :results value verbatim
-  (cl::multiple-value-list
-   (cl::ignore-errors
-     (+ 2 2)))
-  #+END_SRC
-
-  The notation for the external symbol =t= in the package ="COMMON-LISP"= has
-  become =COMMON-LISP:T=, for ="COMMON-LISP"= is no longer used by ="P2"=.
-  Since the symbol =T= is external in ="COMMON-LISP"=, the simple colon
-  notation is sufficient. However, the most elementary operations are not
-  easily accessible anymore, for example, the addition function ='+'=. This is
-  not a good position to be in. Let us go back to the previous environment!
-
-  #+BEGIN_SRC lisp :session pcl :package "P2" :exports both :results value verbatim
-  (cl::multiple-value-list
-   (cl::ignore-errors
-     (use-package "COMMON-LISP" "P2")))
-  #+END_SRC
-
-  This does not work since the symbol =use-package= can't be reached easily
-  either, and we /must/ use the prefix notation.
-
-  #+BEGIN_SRC lisp :session pcl :package "P2" :exports both :results value verbatim
-  (cl::multiple-value-list
-   (cl::ignore-errors
-     (cl::use-package "COMMON-LISP" "P2")))
-  #+END_SRC
-
-  But here is a new problem: earlier, when when we tried to use the symbol
-  ='+'= from ="P2"=, Lisp detected that this symbol is not accessible from
-  ="P2"= and therefore interned a fresh symbol of name ="+"= in ="P2"=. This
-  was legitimate then, but it is now incompatible with ="COMMON-LISP"= having a
-  different symbol with the same name ="+"=, if ="P2"= were to use
-  ="COMMON-LISP"=. The same goes for =use-package=. We must unintern these
-  symbols from ="P2"= to resolve the conflict. Let's not forget to use the
-  colon notation for =unintern=, which is otherwise unreachable!
-
-  #+BEGIN_SRC lisp :session pcl :package "P2" :exports both :results value verbatim
-  (cl::unintern '+ "P2")
-  #+END_SRC
-
-  #+BEGIN_SRC lisp :session pcl :package "P2" :exports both :results value verbatim
-  (cl::unintern 'use-package "P2")
-  #+END_SRC
-
-  -----
-
-  *Note:* The following is necessary to keep the interaction between Emacs
-  and SLIME going. Otherwise, this would be another conflicting symbol.
-  
-  #+BEGIN_SRC lisp :session pcl :package "P2" :exports both :results value verbatim
-  (cl::unintern '*default-pathname-defaults* "P2")
-  #+END_SRC
-
-  -----
-
-  #+BEGIN_SRC lisp :session pcl :exports both :results value verbatim
-  (cl::use-package "COMMON-LISP" "P2")
-  #+END_SRC
-
-  Phew, we are back in a state where Lisp is usable!
-
-* Importing an external symbol.
-
-  Recall that a symbol $sm$ is /accessible/ from a package $p$ if
-  $\rho(p)(st) = sm$ for $st = \mathtt{symbol-name}(sm)$. In that case, the
-  possible return values from =find-symbol= are as follows:
-
-  1. If $sm$ is one of the internal symbols of $p$ the second value returned by
-     =find-symbol= is =:internal=.
-  2. If $sm$ is one of the external symbols of $p$ the second value returned by
-     =find-symbol= is =:external=.
-  3. If $sm$ is an external symbol of a package $p'$ used by the package $p$
-     the second value returned by =find-symbol= is =:inherited=.
-
-  We have seen how to import a symbol from a package $p'$ into a package $p$.
-  The example given used a symbol $sm$ internal in the package $p'$, which then
-  became also an internal symbol of the package $p$ . This also works if $sm$
-  is external in the package $p'$, regardless of $p$ using or not using $p'$.
-  (... assuming that no name conflict is generated.)
-
-  Let's continue our journey in ="P1"=!
-
-  #+BEGIN_SRC lisp :session pcl :package "P2" :exports both :results value verbatim
-  (in-package "P1")
-  #+END_SRC
-
-  #+BEGIN_SRC lisp :session pcl :package "P1" :exports both :results value verbatim
-  (export (intern "SYMB1" "P2") "P2")
-  #+END_SRC
-
-  #+BEGIN_SRC lisp :session pcl :package "P1" :exports both :results value verbatim
-  (multiple-value-list (find-symbol "SYMB1" "P2"))
-  #+END_SRC
-
-  #+BEGIN_SRC lisp :session pcl :package "P1" :exports both :results value verbatim
-  (multiple-value-list (find-symbol "SYMB1" "P1"))
-  #+END_SRC
-
-  We intern a symbol =p2::symb1= in ="P2"= and make it external immediately. As
-  it stands this symbol is not accessible via ="P1"=. The fact that it is
-  external in ="P2"= does not prevent us from importing it in ="P1"=.
-
-  #+BEGIN_SRC lisp :session pcl :package "P1" :exports both :results value verbatim
-  (import 'p2:symb1 "P1")
-  #+END_SRC
-
-  #+BEGIN_SRC lisp :session pcl :package "P1" :exports both :results value verbatim
-  (multiple-value-list (find-symbol "SYMB1" "P1"))
-  #+END_SRC
-
-  #+BEGIN_SRC lisp :session pcl :package "P1" :exports both :results value verbatim
-  (multiple-value-list (find-symbol "SYMB1" "P2"))
-  #+END_SRC
-
-  Once the importation is done, the symbol is accessible via ="P1"= with the
-  status /internal/. The /external/ status with respect to ="P2"= is unchanged,
-  which underlines that the status of a symbol does not depend on anything in
-  the symbol itself. It is the /package/ which must be examined to determine
-  the status of a symbol /with respect to this package/.
-
-  Curiously, the last =find-symbol= returns the symbol =symb1=, without the
-  prefix ='p2:'=. Lisp prints a symbol according to the following rule:
-
-  #+BEGIN_QUOTE
-  First, Lisp determines whether a symbol is accessible via the current default
-  package, in which case it is printed without using the colon notation.
-  Otherwise, Lisp examines the home package, where the symbol is certainly
-  internal or external, and it is printed with the double or simple colon
-  notation. The only exception to this rule appears to be a /keyword/, that is,
-  a symbol of the package ="KEYWORD"=. (Though the ANSI definition is somewhat
-  incomplete for the ="KEYWORD"= package, we can assume that it is forbidden to
-  change anything about the scope of keywords.) Keywords are printed simply as
-  =':xxx'=, without any prefix. Finally, if the symbol is homeless, it is
-  printed as =#:xxx=.
-  #+END_QUOTE
-  
-  The take-home message here is that an importation does not change anything
-  for the relevant symbol; it is just a matter of updating a list of internal
-  symbols in some package, that is, a list of respective pointers toward these
-  symbols. Installing a new signpost in San Francisco that reads "New York"
-  does not change anything in New York. Once more:
-
-  #+BEGIN_SRC lisp :session pcl :package "P1" :exports both :results value verbatim
-   (eq (find-symbol "SYMB1" "P1")
-       (find-symbol "SYMB1" "P2"))
-  #+END_SRC
-
-  A novice could believe that adding ="P2"= to the =package-use-list= of ="P1"=
-  could generate a name conflict, because the symbols =p1::symb1= and
-  =p2::symb1= would become both accessible via ="P1"=. This is not the case:
-  both notations represent one and the same symbol, and there is no ambiguity.
-
-  #+BEGIN_SRC lisp :session pcl :package "P1" :exports both :results value verbatim
-  (use-package "P2" "P1")
-  #+END_SRC
-
-  #+BEGIN_SRC lisp :session pcl :package "P1" :exports both :results value verbatim
-  (multiple-value-list (find-symbol "SYMB1" "P1"))
-  #+END_SRC
-
-  #+BEGIN_SRC lisp :session pcl :package "P1" :exports both :results value verbatim
-  (multiple-value-list (find-symbol "SYMB1" "P2"))
-  #+END_SRC
-
-  Note that because our symbol is internal in ="P1"=, the function
-  =find-symbol= reports its status as =:internal=. This is in a sense preferred
-  to the status =:inherited=, which after all would be possible. A name
-  conflict occurs only if two /different/ symbols with the same name could be
-  accessible via the same package, possibly via another package used by the
-  first one. Two symmetrical illustrations:
-
-  #+BEGIN_SRC lisp :session pcl :package "P1" :exports both :results value verbatim
-  (export (intern "SYMB2" "P2") "P2")
-  #+END_SRC
-
-  #+BEGIN_SRC lisp :session pcl :package "P1" :exports both :results value verbatim
-  (multiple-value-list (intern "SYMB2" "P1") )
-  #+END_SRC
-
-  This is not an error: The second =intern= /does not/ allocate a new symbol, a
-  symbol of name ="SYMB2"= being already accessible via ="P1"=, which uses
-  ="P2"=. In particular the second =intern= does not import the pre-existing
-  symbol.
-
-  We have to come up with something else to really allocate a new symbol.
-
-  #+BEGIN_SRC lisp :session pcl :package "P1" :exports both :results value verbatim
-  (multiple-value-list
-   (ignore-errors
-     (import (make-symbol "SYMB2") "P1")))
-  #+END_SRC
-
-  The function [[http://clhs.lisp.se/Body/f_mk_sym.htm][=make-symbol=]] allocates a /homeless/ symbol of a given name,
-  that's its definition. A homeless symbol cannot cause a name conflict,
-  because it is /not/ accessible via any package. Nothing prevents us from
-  trying to =import= this symbol in ="P1"=, but this generates a name conflict
-  between two different symbols: the freshly allocated =#:symb2= and the symbol
-  external in ="P2"= accessible via ="P1"= which uses ="P2"=.
-
-  Here's another way to cause a name conflict:
-
-  #+BEGIN_SRC lisp :session pcl :package "P1" :exports both :results value verbatim
-  (multiple-value-list (intern "SYMB3" "P1"))
-  #+END_SRC
-
-  #+BEGIN_SRC lisp :session pcl :package "P1" :exports both :results value verbatim
-  (multiple-value-list (intern "SYMB3" "P2"))
-  #+END_SRC
-
-  #+BEGIN_SRC lisp :session pcl :package "P1" :exports both :results value verbatim
-  (multiple-value-list
-   (ignore-errors
-     (export 'p2::symb3 "P2")))
-  #+END_SRC
-
-  The package ="P1"= uses the package ="P2"=, but this does not prevent them
-  from having two different internal symbols with the same name ="SYMB3"=, for
-  ="P1"= does not see the symbol internal in ="P2"=. If we try to make this
-  symbol external in ="P2"=, a name conflict arises. 
-
-  Another sort of name conflict can occur between two used packages:
-
-  #+BEGIN_SRC lisp :session pcl :package "P1" :exports both :results value verbatim
-  (export (intern "SYMB4" "P2") "P2")
-  #+END_SRC
-
-  #+BEGIN_SRC lisp :session pcl :package "P1" :exports both :results value verbatim
-  (export (intern "SYMB4" (defpackage :p3)) "P3")
-  #+END_SRC
-
-  #+BEGIN_SRC lisp :session pcl :package "P1" :exports both :results value verbatim
-  (multiple-value-list
-   (ignore-errors
-     (use-package "P3" "P1")))
-  #+END_SRC
-
-  Compare that with:
-
-  #+BEGIN_SRC lisp :session pcl :package "P1" :exports both :results value verbatim
-  (export (intern "SYMB5" "P2") "P2")
-  #+END_SRC
-
-  #+BEGIN_SRC lisp :session pcl :package "P1" :exports both :results value verbatim
-  (export (import 'p2:symb5 "P3"))
-  #+END_SRC
-
-  #+BEGIN_SRC lisp :session pcl :package "P1" :exports both :results value verbatim
-  (unexport 'p3:symb4 "P3")
-  #+END_SRC
-
-  #+BEGIN_SRC lisp :session pcl :package "P1" :exports both :results value verbatim
-  (use-package "P3" "P1")
-  #+END_SRC
-  
-  Two symbols of name ="SYMB5"= are external in ="P2"= and ="P3"=, but the
-  second one is in fact the same as the first one: it has been imported and
-  immediately made external in ="P3"=.
-
-  This time the =use-package=, which makes the external symbols of ="P2"= /and/
-  ="P3"= visible from ="P1"=, does not generate a name conflict, since we are
-  dealing with two different paths which lead to the same /symbol/. This works
-  as long as we do not forget to first =unexport= the symbol ="SYMB4"= of
-  ="P3"=, i.e., to downgrade its status from /external/ to /internal/.
-
-* A symbol can shadow another symbol.
-
-  In the matter of name conflicts, the Lisp creators could have adopted another
-  strategy and decided that the symbols /present/ in a package, that is,
-  /internal/ or /external/ in this package, have precedence over /inherited/,
-  possibly different, symbols. However, they reasoned that this could easily
-  generate true programming errors because of possible perverse collisions of
-  identifiers, and turn into a source of obscure bugs. Nevertheless, in line
-  with the general spirit of Lisp, if a programmer really wants to use such a
-  strategy, she can do it on a case-by-case basis and explicitly describe the
-  intended exemptions. This is the role of the [[http://clhs.lisp.se/Body/f_pkg_sh.htm][=package-shadowing-symbols=]]
-  list, which is maintained in every package $p$ and denoted by $ShgS(p)$.
-  This list is empty initially. $ShgS(p)$ can contain symbols present in the
-  concerned package, internal or external. These symbols will automatically
-  /shadow/ any other competing symbol, such as symbols exported in other used
-  packages and with the same =symbol-name=.
-
-  The function [[http://clhs.lisp.se/Body/f_shadow.htm][=shadow=]] takes a symbol name (or a list of symbol names) and a
-  package name, allocates a symbol with this name if it is not /present/ in
-  this package, and records it in the shadowing list of the package.
-  
-  #+BEGIN_SRC lisp :session pcl :package "P1" :exports both :results value verbatim
-  (shadow "SYMB6" "P1")
-  #+END_SRC
-
-  #+BEGIN_SRC lisp :session pcl :package "P1" :exports both :results value verbatim
-  (package-shadowing-symbols "P1")
-  #+END_SRC
-
-  #+BEGIN_SRC lisp :session pcl :package "P1" :exports both :results value verbatim
-  (export (intern "SYMB6" "P2") "P2")
-  #+END_SRC
-
-  #+BEGIN_SRC lisp :session pcl :package "P1" :exports both :results value verbatim
-  (eq 'symb6 'p2:symb6)
-  #+END_SRC
-
-  Once the symbol =p1::symb6= is on the shadowing-list of ="P1"= the existence
-  of a different external symbol with the same name in the used package ="P2"=
-  does not generate a name conflict. The last =eq=-test proves both symbols are
-  really different. Along the same lines, the function [[http://clhs.lisp.se/Body/f_shdw_i.htm][=shadowing-import=]], as
-  clearly indicated in its name, imports a symbol and immediately adds it to
-  the shadowing list, which could resolve a possible name conflict. For example
-  the *different* symbols =p2:symb4= (external in ="P2"=) and =p3::symb4=
-  (internal in ="P3"=) are in our environment; the package ="P1"= uses both
-  packages ="P2"= and ="P3"=, but =p3::symb4= is internal in ="P3"= and
-  therefore not in conflict with =p2::symb4=. Remember also the current default
-  package is ="P1"=. A simple importation of =p3::symb4= in ="P1"= generates a
-  conflict, while a =shadowing-import= adds the imported symbol to the
-  shadowing list, shadowing the symbol =p2:symb4= and resolving the name
-  conflict.
-
-  #+BEGIN_SRC lisp :session pcl :package "P1" :exports both :results value verbatim
-  (multiple-value-list (find-symbol "SYMB4" "P2"))
-  #+END_SRC
-
-  #+BEGIN_SRC lisp :session pcl :package "P1" :exports both :results value verbatim
-  (multiple-value-list (find-symbol "SYMB4" "P3"))
-  #+END_SRC
-
-  #+BEGIN_SRC lisp :session pcl :package "P1" :exports both :results value verbatim
-  (multiple-value-list
-   (ignore-errors
-    (import 'p3::symb4 "P1")))
-  #+END_SRC
-
-  #+BEGIN_SRC lisp :session pcl :package "P1" :exports both :results value verbatim
-  (shadowing-import 'p3::symb4 "P1")
-  #+END_SRC
-
-  #+BEGIN_SRC lisp :session pcl :package "P1" :exports both :results value verbatim
-  (package-shadowing-symbols "P1")
-  #+END_SRC
-
-  If necessary, =p2:symb4=, shadowed by the internal =symb4= in ="P1"=, remains
-  accessible via the colon notation. The evaluations of the following
-  expressions assign the same symbol value to both symbols as is confirmed by
-  the subsequent '=' form.  Evaluating the next =eq= expression proves that
-  both /symbols/ are different. In contrast, because =p1::symb4= was imported
-  from ="P3"=, the last =eq=-test is affirmative.
-
-  #+BEGIN_SRC lisp :session pcl :package "P1" :exports both :results value verbatim
-  (defvar symb4)
-  #+END_SRC
-
-  #+BEGIN_SRC lisp :session pcl :package "P1" :exports both :results value verbatim
-  (defvar p2:symb4)
-  #+END_SRC
-
-  #+BEGIN_SRC lisp :session pcl :package "P1" :exports both :results value verbatim
-  (setf symb4 (setf p2:symb4 111))
-  #+END_SRC
-
-  #+BEGIN_SRC lisp :session pcl :package "P1" :exports both :results value verbatim
-  (= symb4 p2:symb4)
-  #+END_SRC
-
-  #+BEGIN_SRC lisp :session pcl :package "P1" :exports both :results value verbatim
-  (eq 'symb4 'p2:symb4)
-  #+END_SRC
-
-  #+BEGIN_SRC lisp :session pcl :package "P1" :exports both :results value verbatim
-  (eq 'symb4 'p3::symb4)
-  #+END_SRC
-
-  It is even possible to add an /inherited/ symbol to the shadowing list, maybe
-  to declare a precedence with respect to another future competing symbol in
-  another package intended to be used later. This experiment assumes three
-  different packages, where one of them is not yet used. We first "detach" for
-  example the package ="P3"= from ="P1"=, leaving ="P2"= used by ="P1"=.
-  (Remember ="P1"= is the current default package.)
-
-  #+BEGIN_SRC lisp :session pcl :package "P1" :exports both :results value verbatim
-  (unuse-package "P3" "P1")
-  #+END_SRC
-
-  We then install two new external symbols with the same name in ="P2"= and
-  ="P3"=:
-
-  #+BEGIN_SRC lisp :session pcl :package "P1" :exports both :results value verbatim
-  (export (intern "SYMB7" "P2") "P2")
-  #+END_SRC
-
-  #+BEGIN_SRC lisp :session pcl :package "P1" :exports both :results value verbatim
-  (export (intern "SYMB7" "P3") "P3")
-  #+END_SRC
-
-  As we have seen already with essentially the same example, if ="P1"= now
-  decides to use ="P3"=, the two ="SYMB7"= symbols collide:
-
-  #+BEGIN_SRC lisp :session pcl :package "P1" :exports both :results value verbatim
-  (multiple-value-list
-   (ignore-errors
-     (use-package "P3" "P1")))
-  #+END_SRC
-
-  In some context, it could happen that ="P1"= has no reason to use =p3:symb7=
-  directly, and instead would like to give precedence to =p2:symb7=. This can
-  be achieved with a shadowing import.
-
-  #+BEGIN_SRC lisp :session pcl :package "P1" :exports both :results value verbatim
-  (multiple-value-list (find-symbol "SYMB7" "P1") )
-  #+END_SRC
-
-  #+BEGIN_SRC lisp :session pcl :package "P1" :exports both :results value verbatim
-  (shadowing-import 'symb7 "P1")
-  #+END_SRC
-
-  #+BEGIN_SRC lisp :session pcl :package "P1" :exports both :results value verbatim
-  (use-package "P3" "P1")
-  #+END_SRC
-
-  The =shadowing-import= refers to =p2:symb7= implicitly, which is external in
-  a package used by ="P1"= and therefore inherited by ="P1"=. We see how the
-  use of =shadowing-import= solves the name conflict, which otherwise would be
-  raised by =use-package=. Let us review our symbols as seen now from our three
-  packages:
-
-  #+BEGIN_SRC lisp :session pcl :package "P1" :exports both :results value verbatim
-  (multiple-value-list (find-symbol "SYMB7" "P1"))
-  #+END_SRC
-
-  #+BEGIN_SRC lisp :session pcl :package "P1" :exports both :results value verbatim
-  (multiple-value-list (find-symbol "SYMB7" "P2"))
-  #+END_SRC
-
-  #+BEGIN_SRC lisp :session pcl :package "P1" :exports both :results value verbatim
-  (eq 'symb7 'p2:symb7)
-  #+END_SRC
-
-  #+BEGIN_SRC lisp :session pcl :package "P1" :exports both :results value verbatim
-  (multiple-value-list (find-symbol "SYMB7" "P3"))
-  #+END_SRC
-
-  #+BEGIN_SRC lisp :session pcl :package "P1" :exports both :results value verbatim
-  (package-use-list "P1")
-  #+END_SRC
-
-  The statuses of =symb7= have not changed in ="P2"= and ="P3"=, but seen from
-  ="P1"=, the symbol is now /internal/. This is to satisfy the rule that any
-  shadowing symbol in a package must be internal or external in this package,
-  and also a consequence of the implied importation.
-
-* A mathematical definition of the packaging system.
-
-  We recall that there are three general sets we must study:
-
-  - The set $St$ of /strings/
-  - The set $P$ of /packages/
-  - The set $Sm$ of /symbols/
-
-  There is one important difference: the set $St$ is the /infinite/ set of all
-  the possible strings, while $P$ and $Sm$ are /finite/ sets made of the
-  packages and symbols previously /allocated/ in the current Lisp session.
-
-  We use the notations $pn$ to denote the function =package-name=
-  $pn: P \rightarrow St$ and $sn$ to denote the function =symbol-name=
-  $sn: Sm\rightarrow St$.
-
-  The map $pn$ is /injective/ for the packages; the function
-  $pn: P \rightarrow pn(P)$ defines a 1-1 correspondence between the packages and their respective names. Here, we ignore the potential nicknames of a package, which is not essential for our discussion.
-
-  Every package $P$ contains four /fundamental/ lists:
-
-  - The list $InS(P)$ of its internal symbols
-  - The list $ExS(P)$ of its external symbols
-  - The list $ShgS(P)$ of its shadowing symbols
-  - The list $U(P)$ of its used packages
-
-  More precisely, these lists are lists of /pointers/ to the mentioned objects,
-  or, if you prefer, of the machine addresses of these objects. It is important
-  to understand these lists are made of (pointers to) /symbols/, not of their
-  names. Each of these lists is /without any duplicates/.
-
-  The fundamental lists defined in a package are the source of a relatively
-  extensive terminology, which is detailed now. The set of symbols /present/ in
-  a package $p$, denoted by $PrS(p)$, is defined as the union
-  $PrS(p) := InS(p) \cup ExS(p)$: a symbol is present in a package if it is
-  internal or external in this package. This union is /disjoint/, the
-  intersection $InS(p) \cap ExS(p)$ must be empty. Also the relation
-  $ShgS(P) \subset Pr(P)$ is required. A shadowing symbol of the package $p$
-  must be internal or external in this package, i.e., a shadowing symbol is
-  present.
-
-  Let $q$ be a package used by the package $p$. The symbols of $q$ /shadowed/
-  by a symbol of $p$ are:
-  $$
-  ShdS(q, p) = \{sm \in ExS(q)\;\mathbf{\underline{st}}\;\exists sm' \in ShgS(p)\;\mathbf{\underline{st}}\; sn(sm) = sn(sm')\}
-  $$
-
-  In other words, a /precedence/ relation is defined by the list $ShgS(p)$: if
-  ever a symbol $sm' \in ShgS(p)$ and a symbol $sm\in ExS(q)$ have the same
-  name, then, with respect to the package $p$, $sm'$ takes precedence over
-  $sm$, which means $sm$ is /shadowed/. If $sm'$ is present in $p$ but not
-  shadowing, with $sm'\neq sm$ and $sn(sm') = sn(sm)$, then a name conflict
-  would be raised, which is forbidden.
-
-  The inherited symbols of a package $p$, denoted by $InhS(p)$, are defined as:
-  $$
-  InhS(p) := \Big\{ \bigcup_{q\in U(P)}(ExS(q) - ShdS(q,p)) \Big\} - PrS(P)
-  $$
-
-  A symbol is inherited in a package $p$ if it is external in a /used/ package
-  $q$, not shadowed by a shadowing symbol of $p$, and not present in $p$. The
-  union in the preceding formula is not necessarily disjoint: a symbol can be
-  external in several packages simultaneously, and without causing a name
-  conflict. A symbol could be simultaneously present in $p$ and external in a
-  package $q$ used by $p$. That is why the the last term, $-PrS(P)$, is
-  necessary to define unambiguously what an inherited symbol is.
-
-  Finally the accessible symbols $AccS(p) := PrS(p) \cup InhS(p)$ are the
-  symbols which are present or inherited. The very definition of $InhS(p)$
-  implies that this union is disjoint. In this way, the /status/ of a symbol
-  with respect to a package $p$ via which it is accessible is unambiguously
-  defined as a keyword =:internal=, =:external= or =:inherited=. For a package
-  $q\neq p$ there is no relation whatsoever between the status of some symbol
-  $sm$ with respect to $p$ and its status with respect to $q$.
-  *Exercise:* Show that the sixteen pairs of possible status combinations can
-  be realized!
-
-  It is important to be clear about possible intersections (overlaps) between
-  the lists defined above. Let $p$ be some package and $q$ another package used
-  by $p.$ If $sm\in ExS(q)$ is an external symbol of $q$, the symbol $sm$ /may/
-  also be present in $p$, in which case its status is internal or external, but
-  not inherited. In particular, this does not generate a name conflict, because
-  it is the same symbol which is visible in two different packages via the same
-  name, and a symbol has only /one/ name! Nevertheless its status /with respect
-  to/ $p$ is not inherited. The status of a symbol is so defined
-  deterministically, even if it is present in two interacting packages by one
-  using the other. Of course the same symbol has status external in $q$.
-
-  Following the same logic, if $q,q'\in U(p)$, the intersection
-  $ExS(q)\cap ExS(q')$ is not necessarily empty.
-
-  The Lisp system maintains the /coherence/ of these lists, which is defined as
-  follows:
-
-  *Definition.* A set of packages is /coherent/ if, for every package $p$, the
-  function =symbol-name= defines a 1-1 correspondence
-  $sn: AccS(p) \rightarrow sn(AccS(p))$.
-
-  This map is by definition surjective; it is injective if two different
-  symbols accessible via $p$ have different names. In this way the function
-  =find-symbol= is free of ambiguity. It searches first in the present symbols,
-  and finally in the external symbols of the used packages. It is not necessary
-  to compute the list of shadowed symbols since a shadow/ing/ symbol, which is
-  also a present symbol, is found first. The main purpose of the coherence rule
-  is to prevent users from designing too contorted situations in name scopes,
-  wich are frequently the source of subtle and difficult to find bugs.
-
-  Several symbols with the same name may coexist in an environment. The most
-  common way to access a symbol consists in using its /name/, but /different/
-  symbols may have the /same/ name. In fact, its symbol name is not sufficient
-  to access a symbol, a package must also be specified. This can be the default
-  package, in which case the direct notation without any colons is possible, or
-  the package name can be explicitly used to prefix the symbol name using the
-  one- or two-colon notation. Of course, the symbol so accessed must be defined
-  in a /deterministic/ manner. The definition just given says that a /unique/
-  symbol of some name is accessible from some package.
-
-  The main function in the packaging organization is a map:
-  $$
-  \rho:P \rightarrow [St \rightarrow ((Sm\cup\mathtt{nil})\times Stt)]
-  $$
-  where $Stt$ is a constant set of four symbols, the Lisp symbol =nil=, and
-  three keywords, the possible statuses of an accessible symbol:
-  $$
-  Stt = \{\mathtt{nil}, \mathtt{:internal}, \mathtt{:external}, \mathtt{:inherited}\}
-  $$
-  Because of the assumed coherence of the package configuration, the function
-  $\rho$, an avatar of the function =find-symbol= of a package $p$ and a string
-  $st$, determines a /unique/ symbol named $st$ and accessible via $p$, and
-  also its status. It is possible that the search fails, in which case the
-  function returns the pair =(nil,nil)=. (More precisely =(values nil nil)=.)
-  The second =nil= is a kind of a null status: "There is nothing accessible via
-  $p$ under the name $st$." The relation
-  $\rho(p)(s) = \mathtt{(find-symbol}\;p\;st\mathtt{)}$ is always satisfied.
-
-  It is now relatively simple to understand the various Lisp functions for
-  handling packages and symbols, in particular what name conflicts might be
-  generated.
-
-** (intern $st\;p$)
-
-   This function first evaluates =(find-symbol= $st\; p$=)=. If a symbol is
-   found, /both/ values of =(find-symbol ...)= are returned.
-
-   If no symbol is found, then Lisp /allocates/ (creates in memory) a new
-   symbol without any value or function value. The =symbol-package= is
-   initialized to $p$ and this symbol is added to $InS(p)$. In this case,
-   =(values= $sm$ =nil)= is returned, the second value =nil= being a code for
-   saying a new symbol has just been allocated.
-
-   No name conflict can be created this way.
-
-   This function is used implicitly by the Lisp reader when it encounters a
-   symbol in an expression. If the colon syntax is not used, the default
-   package is used for $p.$ Otherwise the (capitalized) package name of $p$
-   preceding the colon(s) is read, followed by the (capitalized) =symbol-name=
-   $st$ after the colon(s). Finally, =(intern= $st\; p$=)= is evaluated, which
-   yields the symbol so /read/ by the Lisp reader. In this way, the symbol can
-   be either a pre-existing one or one freshly allocated as a consequence of
-   this reading.
-
-
-** (unintern $sm\;p$)
-
-   A symbol $sm$ is /interned/ in a package $p$ if it is present in this
-   package. It is /present/ in package $p$ if
-   $sm\in PrS(p) = InS(p) \cup ExS(p).$ Uninterning a symbol asks for this
-   membership to be "revoked."
-
-   If $sm\notin PrS(p)$, nothing is changed and =nil= is returned. Otherwise
-   $sm$ is removed from $InS(p)$ or $ExS(p)$, and also from $Shg(p)$ if $sm$
-   was shadowing with respect to $p$; in this case, =unintern= returns =t=. In
-   the last case, when uninterning a shadowing symbol, a name conflict can be
-   generated: it is possible for symbols $sm'\in ExS(q)$ and $sm''\in ExS(q')$
-   to have the same name while being /different/ symbols in the respective
-   packages $q$ and $q'$ used by $p$, and that this collision was resolved by
-   the symbol $sm$ shadowing both. If this happens, the =unintern= request is
-   rejected.
-
-   Also, if a symbol $sm$ is uninterned from a package $p$ and $p$ is the home
-   package of $sm$, then the home package of $sm$ is modified and becomes
-   =nil=, that is, the symbol becomes homeless. This is the only case where the
-   symbol itself is modified by =unintern=. The same symbol could be external
-   in another package used by $p$, in which case the symbol /remains/
-   accessible via $p$. Otherwise, if the home package was =nil= or another
-   package, it is not modified.
-
-** (import $sm\; p$)
-
-   This is a request for the symbol $sm$ to be added to $InS(p)$. Lisp first
-   looks for a possible name conflict. This happens only if a /different/
-   symbol $sm'\neq sm$ with the same name ($sn(sm) = sn(sm')$) is already
-   accessible via $p$. If so, the importation is rejected.
-
-   If no name conflict is detected, Lisp proceeds as follows: If the symbol is
-   already /present/, it is left /unchanged/ in $InS(p)$ or $ExS(p)$. Else, if
-   the symbol is /inherited/ because of a package $q$ used by $p$, $ExS(q)$ is
-   left unchanged and $sm$ is added to $InS(p)$ (not $ExS(p)$!). If $sm$ is not
-   accessible via $p$, it is simply added to $InS(p)$.
-
-   In the specific case of an imported homeless symbol, the =symbol-package= of
-   the symbol is updated to $p$. This is the only case where a symbol object is
-   modified by an importation. If the imported symbol is already owned by a
-   package, whatever its home package, it is not modified.
-
-   If the importation succeeds, the symbol will always be /present/ in the
-   target package, even if it was previously accessible only via a used
-   package.
-
-** (export $sm\; p$)
-
-   The terminology "export" is not really appropriate, "externalize" would be
-   more precise. The user of an =export= expression asks Lisp to record the
-   symbol $sm$ in $ExS(p).$ This is allowed only if $sm$ is accessible from
-   $p.$ In other words, the =export= function cannot /add/ an accessible symbol
-   to $p.$ In view of the rule $InS(p)\cap ExS(p) = \emptyset$, if present in
-   $InS(p)$, the symbol $sm$ is also erased from that list. If $sm$ is external
-   in a package $q$ used by $p$, its status in $q$ remains unchanged, but $sm$
-   is nevertheless added to $ExS(p)$.
-
-   Remember that the =use-package= relation is not transitive. The fact that
-   $sm\in ExS(q)$ makes $sm$ accessible via $p$ using $q$ but not via $p'$
-   using $p$. If it is desired that $sm$ be accessible via $p'$, it is possible
-   to make it external in $p$ by an =export= expression. Another solution would
-   be to import $sm$ in $p'$, an operation which doesn't involve $p$.
-
-   After exporting it, the symbol $sm$ becomes accessible from any package $q$
-   using $p$, that is, if $p\in U(q)$. This can generate a name conflict with
-   a possible /different/ symbol $sm'$ of the same name, which is present in
-   $q$ or accessible via $q$ in another package $p'\in U(p)$, that is, if
-   $sm'\in ExS(p')$. If this happens, the /export/ request is rejected.
-
-** (unexport $sm\; p$)
-
-   The symbol $sm$ must be accesible via the package $p.$ If the status of
-   $sm$ is /external/, it is downgraded to /internal/. Otherwise it remains
-   unchanged, even if it is /inherited/.
-
-** (shadow {$sm$ or $st$} $p$)
-
-   It is intended to /import/ the symbol $sm$ in $p$, to record it in the
-   shadowing list $Shg(p)$ of the package $p$, and also to /resolve/ any name
-   conflict possibly raised by the importation.
-
-   This time the first argument must be a /symbol/, a pre-existing one or a
-   symbol just allocated because of its presence in the source statement. The
-   symbol is imported (See the function =import=.) and added to the shadowing
-   list $Shg(p)$ of $p$ if not yet present in this list. This addition to the
-   shadowing list solves the possible name conflicts with symbols inherited
-   from packages used by $p.$  It is possible that a /different/ symbol /sm'/
-   with the same name was /present/ in $p$ beforehand. If so, such a symbol is
-   /uninterned/ from $p$, that is, erased from the lists $InS(p)$, $ExS(p)$ and
-   $Shg(p)$.
-
-   The difference between =shadow= and =shadowing-import= is clarified by the
-   following toy example. We start a new Lisp session, allocate a package
-   ="P"= and experiment with symbols named ="A"= and ="B"= in the packages
-   ="CL-USER"= and ="P"=.
-
-  #+BEGIN_SRC lisp :session pcl :package "P1" :exports both :results value verbatim
-  (in-package "CL-USER")
-  #+END_SRC
-
-  #+BEGIN_SRC lisp :session pcl :exports both :results value verbatim
-  (defpackage "P" (:use :cl))
-  #+END_SRC
-
-  #+BEGIN_SRC lisp :session pcl :exports both :results value verbatim
-  (setf my-list '(a b p::a p::b))
-  #+END_SRC
-
-  #+BEGIN_SRC lisp :session pcl :exports both :results value verbatim
-  (shadow 'p::a "CL-USER")
-  #+END_SRC
-
-  #+BEGIN_SRC lisp :session pcl :exports both :results value verbatim
-  (shadowing-import 'p::b "CL-USER")
-  #+END_SRC
-
-  #+BEGIN_SRC lisp :session pcl :exports both :results value verbatim
-  (package-shadowing-symbols "CL-USER")
-  #+END_SRC
-
-  #+BEGIN_SRC lisp :session pcl :exports both :results value verbatim
-  (eq 'a 'p::a)
-  #+END_SRC
-
-  #+BEGIN_SRC lisp :session pcl :exports both :results value verbatim
-  (eq 'b 'p::b)
-  #+END_SRC
-
-  #+BEGIN_SRC lisp :session pcl :exports both :results value verbatim
-  my-list
-  #+END_SRC
-
-  If we =shadow= the symbol =p::a= in ="CL-USER"=, the symbol =a= remains
-  different from the symbol =p::a=. In contrast, if we =shadowing-import= the
-  symbol =p::b= in ="CL-USER"=, then the symbols =b= and =p::b= are equal. In
-  a sense, the expression =(shadow ’p::a "CL-USER")= is cheating because the
-  presence of ='p::'= has no role whatsoever, for only the name of the symbol
-  =p::a= is used and this name is the same as the name ="A"= of =a=, that is,
-  because of the default package, =cl-user::a=. The symbol defined by ="A"= via
-  the package ="CL-USER"= remains unchanged, in particular, it remains
-  different from the symbol =p::a=.
-
-  In contrast, if =shadowing-import= is used, an =import= operation is induced,
-  so that the symbol =p::b= becomes directly accessible via ="CL-USER"=. The
-  previous symbol $\rho:($="CL-USER"=$)($="B"=$)$ has therefore been
-  /uninterned/ and is now unreachable by =find-symbol=. However, it is still
-  visible in the list named =list= as the homeless symbol =#:B=.
-
-  The conclusion of our test is this:
-
-  - The symbol =cl-user::a= is unchanged but added to $ShgS($ ="USER"= $)$.
-  - The symbol =cl-user::b= is almost unchanged, but no longer accessible via
-    ="CL-USER"=. The only change is its =symbol-package= becomes =nil=, because
-    the symbol has been uninterned from its home-package.
-  - The symbol =p::a= remains unchanged; only its name has been used for
-    something which does not really concern it.
-  - The symbol =p::b= remains unchanged, except that it is now directly
-    accessible via ="CL-USER"= and now printed as =B= in the value of =list=.
-
-** (use-package $q$ $p$)
-
-   Unless $q$ is already in $U(p)$, the package $q$ is added to the
-   =package-use-list= of $p.$
-
-   Lisp checks beforehand for possible name conflicts. A symbol
-   $sm \in PrS(p)$ could collide with a /different/ symbol $sm'\in ExS(q)$ if
-   they have the same name $sn(sm) =sn(sm')$. If $sm = sm'$, no name conflict
-   is generated. One cannot resolve such a name conflict by adding $sm'$ to
-   $ShgS(q)$, hoping to give the precedence to the new inherited symbol:
-   shadowing operates in a uni-directional manner, from a using package toward
-   a used package. If one does so by a =shadowing-import= of $sm'$ into $p$,
-   the symbol $sm$ would be coherently uninterned, erased from $PrS(p)$, and
-   in a sense replaced by $sm'$. One can prepare the precedence of $sm$ over
-   $sm'$ before the =use-package= by previously =shadow=ing $sm$ in $p.$ Also
-   Lisp on its own can propose to /unintern/ the symbol $sm$ in a /continuable/
-   error in order to resolve such an observed name conflict.
-
-   Another type of name conflict could be raised if another package $q'$ is
-   already used by $p.$ It is then possible that two /different/ symbols
-   $sm \neq sm'$ with the same name $st$ are external, respectively in $q$ and
-   $q'$, in which case $\rho(p)(st)$ is ambiguous. If so, evaluating the
-   =use-package= expression would generate an error. On the other hand, the
-   intersection $ExS(q) \cap ExS(q')$ may be non-empty: a symbol external in
-   both packages does not generate any ambiguity via $p$. As usual, it is
-   always important to remember the lists such as $ExS(q)$ and $ExS(q')$ are
-   lists of /symbols/, not strings. A name conflict can be generated only by
-   /different/ symbols having the same =symbol-name=.
-
-   If no name conflict is detected, the package $q$ is added to $U(p)$ so that
-   the new set of accessible symbols via $p$ is:
-
-   $$
-   \mathrm{new-}AccS(p) = \mathrm{old-}AccS(p) \cup (ExS(q) - ShdS(q, p))
-   $$
-
-** (unuse-package $q$ $p$)
-
-   If the package $q$ is in $U(p)$, it is removed from this list.
-
-** A bug in package-internal-symbols?
-
-   While preparing these notes, the author thought for a moment to have
-   encountered a mysterious bug. The minimal model for this bug goes as
-   follows:
-
-  #+BEGIN_SRC lisp :session pcl :exports both :results value verbatim
-  (unuse-package "P2" "P1")
-  #+END_SRC
-
-  #+BEGIN_SRC lisp :session pcl :exports both :results value verbatim
-  (unuse-package "P1" "P2")
-  #+END_SRC
-
-  #+BEGIN_SRC lisp :session pcl :exports both :results value verbatim
-  (delete-package "P1")
-  #+END_SRC
-
-  #+BEGIN_SRC lisp :session pcl :exports both :results value verbatim
-  (delete-package "P2")
-  #+END_SRC
-
-  #+BEGIN_SRC lisp :session pcl :exports both :results value verbatim
-  (defpackage "P1" (:use :cl))
-  #+END_SRC
-
-  #+BEGIN_SRC lisp :session pcl :exports both :results value verbatim
-  (defpackage "P2" (:use :cl))
-  #+END_SRC
-
-  #+BEGIN_SRC lisp :session pcl :exports both :results value verbatim
-  (use-package "P2" "P1")
-  #+END_SRC
-
-  #+BEGIN_SRC lisp :session pcl :exports both :results value verbatim
-  (export 'p2::a "P2")
-  #+END_SRC
-
-  #+BEGIN_SRC lisp :session pcl :exports both :results value verbatim
-  (import 'p2::a "P1")
-  #+END_SRC
-
-  #+BEGIN_SRC lisp :session pcl :exports both :results value verbatim
-  (package-internal-symbols "P1")
-  #+END_SRC
-  
-  The point is that the standard Lisp function =do-symbols= runs through all
-  the symbols /accessible/ via ="P1"=, but it does not check for possible
-  duplicates. Really? It seems possible that a symbol can appear more than once
-  in $AccS($="P1"=$)$!? This does not seem compatible with the exclusion of
-  duplicates in general in $InS(p)$ and $ExS(p)$, and also the rule
-  $InS(p) \cap ExS(p) = \emptyset$. Yes, but a – one !– symbol can be
-  simultaneously in $InS(p)$ and $ExS(q)$ for a package $q$ used by $p$, which
-  is the case here for our symbol =p1::a= = =p2:a=.
-
-  The evaluation of =(do-symbols (s p) ...)= makes =s= run through all the
-  internal symbols of $p$, then through all the external symbols of $p$, and
-  finally through all the external symbols of $q$ for every package $q$ used
-  by $p$. It happens that our symbol is in $InS($="P1"=$)$ because it was
-  imported there, and also in $ExS($="P2"=$)$ where it was initially defined.
-  Didn't the programmer of =package-internal-symbols= check the status of the
-  symbol, so that the (fake) second symbol should have been rejected? No, not
-  really, and it is interesting to see the path followed by Lisp: only the
-  symbol-name and the examined package are used, so that when Lisp computes
-  =(find-symbol (symbol-name s) package)=, it obtains /the/ symbol, in fact
-  the only one in this story, together with its status with respect to the
-  =package= argument. In our case that is the package ="P1"= and the symbol's
-  status (with respect to ="P1"=) is =:internal=, even if at the same time
-  $s \in ExS($ ="P2"= $)$.
-
-  This illustrates some of the hidden traps and pitfalls that one might
-  encounter as a result of different packages seeing the same symbol in various
-  ways. Remember: no name conflict can be caused by one symbol alone. A name
-  conflict happens only if /two/ different symbols with the same name are
-  "visible" by the same package. Nothing of this sort happened here, where
-  /one/ symbol is visible by several packages.
-
-  To overcome this weakness in the implementation of
-  =package-internal-symbols=, using the Lisp function =delete-duplicates= is
-  sufficient.
-
-  #+BEGIN_SRC lisp :session pcl :exports both :results value verbatim
-  (defun package-internal-symbols-dedup (package)
-      (let ((rslt))
-           (do-symbols (s package)
-               (when (eq (second
-                          (multiple-value-list
-                           (find-symbol (symbol-name s) package)))
-                         :internal)
-                   (push s rslt)))
-           (delete-duplicates rslt)))
-  #+END_SRC
-
-  #+BEGIN_SRC lisp :session pcl :exports both :results value verbatim
-  (package-internal-symbols-dedup "P1")
-  #+END_SRC
-
-** Symbol-package revisited.
-
-   Throughout this tutorial, we kept insisting that this function is not really
-   interesting. To be complete, we prove that a symbol
-   $sm \in PrS($ =(symbol-package = $sm$ =)= $).$ In other words, if the symbol
-   -package of the symbol $sm$ is $p$, then $sm$ is present in $p$, either
-   internal or external. When a symbol is allocated (necessarily via =intern=),
-   it is in particular interned in the package which is the second argument of
-   =intern= so that it becomes a member of $InS(p)$. It may be exported in this
-   package, which would make it a member of $ExS(p)$, but it remains present.
-   The symbol can be added to $InS(q)$ for other packages $q$ via =import= or
-   =shadowing-import=. It can also then be "upgraded" to $ExS(q)$ in those
-   packages, but the membership in the initial package $PrS(p)$ remains
-   unaffected.
-
-   The only way to change this situation is using =unintern= with the package
-   argument being $p.$ Then the symbol becomes homeless.
-   In turn, this can be changed with =import= and =shadowing-import=, in which
-   case the symbol is interned in a possibly new package, and the story
-   continues along similar lines. Finally, unless a symbol is homeless, it is
-   always present in its home-package.
-
-   This also shows that, as was mentioned in the introduction, the
-   =symbol-package= qualifier of a symbol does divide the set of /interned/
-   symbols into packages. It is impossible to have two different interned
-   symbols with the same symbol-name and also the same symbol-package, for they
-   would be interned in the same package, with the same name, and then the set
-   of packages would not be /coherent/.
-
-   An interned symbol is internal or external in its symbol-package, and
-   certainly visible via this package. However, it may be visible from many
-   other packages, and this information is not stored in the internal
-   representation of the symbol. If it is external, it is accessible via the
-   packages which use its package. The list of these packages can be determined
-   by the standard Lisp function =package-used-by-list=. But a symbol can also
-   be imported by other packages, which in turn may decide to make (the pointer
-   to) this symbol external, and so visible from other packages.
-
-   *Exercise:* Try to define a function =symbol-accessible-from= with one
-   argument, a symbol, that returns the list of all packages where this symbol
-   is accessible. Do not forget the contorted particular case of
-   =common-lisp:nil=! Hint: Have a look at the standard Lisp function
-   [[http://clhs.lisp.se/Body/f_list_a.htm#list-all-packages][=list-all-packages=]].
-
-   An arbitrary number of homeless symbols may have the same name, as
-   illustrated by:
-
-  #+BEGIN_SRC lisp :session pcl :exports both :results output
-   (eq (print (make-symbol "Z"))
-       (print (make-symbol "Z")))
-  #+END_SRC
-
-  When =make-symbol= is called, Lisp allocates a /new/ homeless symbol with the
-  prescribed name, even if another one with the same name has been already
-  allocated. You see /both/ homeless symbols allocated above are printed in the
-  same way, yet they are /different/.
-
-* Practical uses of the packaging system.
-
-   Many of the somewhat esoteric technicalities detailed in this tutorial have
-   no direct use in concrete programming. On the other hand, they can help to
-   understand and demystify the behaviour of your Lisp system.
-
-   A particularly irritating fact exhibited by some systems is the following:
-   When you merely install, not load, a source file in the editor of your Lisp
-   IDE, these systems immediately scan for symbols appearing in these files and
-   intern them in a separate package. Sometimes this is the package indicated
-   in an inital =(in-package "XXX")= of the file, or still more
-   inappropriately, the standard ="CL-USER"= package, or also the current
-   default package, even if the initial =in-package= references another
-   package. Often this later leads to symbol collisions which are sometimes
-   hard to identify. A developer who meets this kind of mysterious symbol
-   collisions is advised to search first in this direction. In this case, you
-   should make independent micro-experiments to study the actual behavior of
-   your IDE when you install a file in your development environment. Probably
-   in the early days of Lisp, this was done to improve the efficiency, but on
-   modern systems, it is difficult to see compelling reasons to justify such a
-   strategy.
-
-   Most symbols of a Lisp file in fact are symbols with lexical scope, a scope
-   limited to a small part of the code, typically /inside/ a function, a =let=
-   form, a =do= form and so on. These references are converted by the compiler
-   into raw machine addresses, and these symbols have no real life at runtime.
-
-   The most important symbols that have a real life at runtime are those that
-   name functions, those defined through a =defun= form and the like. If a
-   large program is divided in several files, then some decisions must be taken
-   about the status of such a symbol.
-
-   Usually, a correspondence "file $\leftrightarrow$ package" is maintained.
-   Several Lisp systems require that a file begins with an appropriate
-   =(in-package ...)= expression, declaring that all the symbols used in this
-   file are to be understood as present in this package, except when something
-   else is a consequence of decisions taken outside this file or even in this
-   file.
-
-   In the ANSI definition of [[http://clhs.lisp.se/Body/m_in_pkg.htm][=in-package=]], the referenced package must already
-   exist in the environment. Beginning a file by:
-
-   #+BEGIN_EXAMPLE
-   (defpackage "MY-PACKAGE")
-   (in-package "MY-PACKAGE")
-   #+END_EXAMPLE
-
-   is tempting but does not obey the requirement about the first instruction of
-   a file being the appropriate =(in-package ...)=.
-
-   The solution is to have a separate file in the project which is called aptly
-   =packages.lisp= and which contains all the necessary =(defpackage ...)=
-   expressions for the project. The =defpackage= form is flexible and can
-   contain also all the main information about a package, in particular the
-   list of its external symbols and its used packages. (See the ANSI definition
-   of [[http://clhs.lisp.se/Body/m_defpkg.htm#defpackage][=defpackage=]].) This file is a good foundation for structuring the
-   "public" documentation, explaining the role of these packages and their
-   external symbols.
-
-   Along the same lines, it might be worthwhile to have an ="EXTERNAL"= package
-   which contains all the external symbols of the application. In this way, the
-   other packages may use this package systematically, giving to this package a
-   status similar to the status of the ="COMMON-LISP"= package. This does not
-   prevent another package to import some symbols of other packages, symbols
-   whose role is too specific to justify to make them "globally" external.
-
-* Shortcuts.
-
-   There are several ways for the developer to shorten the Lisp expressions
-   dealing with the packaging system.
-
-   To be rigorous in our explanations and close to the deep structure of Lisp,
-   in this tutorial, we used a string identifier everywhere for a package. A
-   symbol could be used instead, its name then being used as the intended
-   string. For example, =(defpackage :my-package)= is equivalent to
-   =(defpackage "MY-PACKAGE")=, for the name of the keyword =:my-package= is
-   used, and because of the capitalization rule of the symbols applied by the
-   Lisp reader. The name of =:my-package= is ="MY-PACKAGE"=, which through the
-   =defpackage= expression becomes a package-name by following the standard
-   rule which asks for an uppercase name.
-
-   Also, each time a package argument is needed, frequently the second one, it
-   can be omitted if this package is the current default package, which
-   justifies this terminology. When using these shortcuts, do not forget about
-   maintaining maximum readability of the source code!
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