advertise for libgap in src/doc

src/doc/de/tutorial/interactive_shell.rst

@@ -356,9 +356,9 @@ dem man nachgehen sollte.
     sage: time g = maple('1938^99484')
     CPU times: user 0.00 s, sys: 0.00 s, total: 0.00 s
     Wall time: 0.11
-    sage: gap(0)
+    sage: libgap(0)
     0
-    sage: time g = gap.eval('1938^99484;;')
+    sage: time g = libgap.eval('1938^99484;')
     CPU times: user 0.00 s, sys: 0.00 s, total: 0.00 s
     Wall time: 1.02
 
@@ -742,7 +742,7 @@ nicht erlaubt.
 
 ::
 
-    sage: a = gap(2)
+    sage: a = libgap(2)
     sage: a.save('a')
     sage: load('a')
     Traceback (most recent call last):

src/doc/en/constructions/groups.rst

@@ -124,31 +124,25 @@ You can compute conjugacy classes of a finite group using "natively"::
 
 You can use the Sage-GAP interface::
 
-    sage: gap.eval("G := Group((1,2)(3,4),(1,2,3))")
-    'Group([ (1,2)(3,4), (1,2,3) ])'
-    sage: gap.eval("CG := ConjugacyClasses(G)")
-    '[ ()^G, (2,3,4)^G, (2,4,3)^G, (1,2)(3,4)^G ]'
-    sage: gap.eval("gamma := CG[3]")
-    '(2,4,3)^G'
-    sage: gap.eval("g := Representative(gamma)")
-    '(2,4,3)'
+    sage: libgap.eval("G := Group((1,2)(3,4),(1,2,3))")
+    Group([ (1,2)(3,4), (1,2,3) ])
+    sage: libgap.eval("CG := ConjugacyClasses(G)")
+    [ ()^G, (2,3,4)^G, (2,4,3)^G, (1,2)(3,4)^G ]
+    sage: libgap.eval("gamma := CG[3]")
+    (2,4,3)^G
+    sage: libgap.eval("g := Representative(gamma)")
+    (2,4,3)
 
 Or, here's another (more "pythonic") way to do this type of computation::
 
-    sage: G = gap.Group('[(1,2,3), (1,2)(3,4), (1,7)]')
+    sage: G = libgap.eval("Group([(1,2,3), (1,2)(3,4), (1,7)])")
     sage: CG = G.ConjugacyClasses()
     sage: gamma = CG[2]
     sage: g = gamma.Representative()
     sage: CG; gamma; g
-    [ ConjugacyClass( SymmetricGroup( [ 1, 2, 3, 4, 7 ] ), () ),
-      ConjugacyClass( SymmetricGroup( [ 1, 2, 3, 4, 7 ] ), (4,7) ),
-      ConjugacyClass( SymmetricGroup( [ 1, 2, 3, 4, 7 ] ), (3,4,7) ),
-      ConjugacyClass( SymmetricGroup( [ 1, 2, 3, 4, 7 ] ), (2,3)(4,7) ),
-      ConjugacyClass( SymmetricGroup( [ 1, 2, 3, 4, 7 ] ), (2,3,4,7) ),
-      ConjugacyClass( SymmetricGroup( [ 1, 2, 3, 4, 7 ] ), (1,2)(3,4,7) ),
-      ConjugacyClass( SymmetricGroup( [ 1, 2, 3, 4, 7 ] ), (1,2,3,4,7) ) ]
-    ConjugacyClass( SymmetricGroup( [ 1, 2, 3, 4, 7 ] ), (4,7) )
-    (4,7)
+    [ ()^G, (4,7)^G, (3,4,7)^G, (2,3)(4,7)^G, (2,3,4,7)^G, (1,2)(3,4,7)^G, (1,2,3,4,7)^G ]
+    (3,4,7)^G
+    (3,4,7)
 
 .. index::
    pair: group; normal subgroups
@@ -162,29 +156,29 @@ If you want to find all the normal subgroups of a permutation group
 :math:`G` (up to conjugacy), you can use Sage's interface to GAP::
 
     sage: G = AlternatingGroup( 5 )
-    sage: gap(G).NormalSubgroups()
-    [ AlternatingGroup( [ 1 .. 5 ] ), Group( () ) ]
+    sage: libgap(G).NormalSubgroups()
+    [ Alt( [ 1 .. 5 ] ), Group(()) ]
 
 or
 
 ::
 
-    sage: G = gap("AlternatingGroup( 5 )")
+    sage: G = libgap.AlternatingGroup( 5 )
     sage: G.NormalSubgroups()
-    [ AlternatingGroup( [ 1 .. 5 ] ), Group( () ) ]
+    [ Alt( [ 1 .. 5 ] ), Group(()) ]
 
 Here's another way, working more directly with GAP::
 
-    sage: print(gap.eval("G := AlternatingGroup( 5 )"))
+    sage: libgap.eval("G := AlternatingGroup( 5 )")
     Alt( [ 1 .. 5 ] )
-    sage: print(gap.eval("normal := NormalSubgroups( G )"))
+    sage: libgap.eval("normal := NormalSubgroups( G )")
     [ Alt( [ 1 .. 5 ] ), Group(()) ]
-    sage: G = gap.new("DihedralGroup( 10 )")
+    sage: G = libgap.eval("DihedralGroup( 10 )")
     sage: G.NormalSubgroups().SortedList()
-    [ Group( <identity> of ... ), Group( [ f2 ] ), Group( [ f1, f2 ] ) ]
-    sage: print(gap.eval("G := SymmetricGroup( 4 )"))
+    [ Group([  ]), Group([ f2 ]), <pc group of size 10 with 2 generators> ]
+    sage: libgap.eval("G := SymmetricGroup( 4 )")
     Sym( [ 1 .. 4 ] )
-    sage: print(gap.eval("normal := NormalSubgroups( G );"))
+    sage: libgap.eval("normal := NormalSubgroups( G );")
     [ Sym( [ 1 .. 4 ] ), Alt( [ 1 .. 4 ] ), Group([ (1,4)(2,3),  ... ]),
           Group(()) ]
 
@@ -201,7 +195,7 @@ How do you compute the center of a group in Sage?
 Although Sage calls GAP to do the computation of the group center,
 ``center`` is "wrapped" (i.e., Sage has a class PermutationGroup with
 associated class method "center"), so the user does not need to use
-the ``gap`` command. Here's an example::
+the ``libgap`` command. Here's an example::
 
     sage: G = PermutationGroup(['(1,2,3)(4,5)', '(3,4)'])
     sage: G.center()

src/doc/en/constructions/interface_issues.rst

@@ -92,7 +92,7 @@ Sage and other computer algebra systems
 
 If ``foo`` is a Pari, GAP ( without ending semicolon), Singular,
 Maxima command, resp., enter ``gp("foo")`` for Pari,
-``gap.eval("foo")}`` ``singular.eval("foo")``, ``maxima("foo")``, resp..
+``libgap.eval("foo")}`` ``singular.eval("foo")``, ``maxima("foo")``, resp..
 These programs merely send the command string to the external
 program, execute it, and read the result back into Sage. Therefore,
 these will not work if the external program is not installed and in

src/doc/en/constructions/linear_algebra.rst

@@ -306,11 +306,11 @@ Finally, you can use Sage's GAP interface as well to compute
 
 ::
 
-    sage: print(gap.eval("A := [[1,2,3],[4,5,6],[7,8,9]]"))
+    sage: A = libgap([[1,2,3],[4,5,6],[7,8,9]]); A
     [ [ 1, 2, 3 ], [ 4, 5, 6 ], [ 7, 8, 9 ] ]
-    sage: print(gap.eval("v := Eigenvectors( Rationals,A)"))
+    sage: libgap(QQ).Eigenvectors(A)
     [ [ 1, -2, 1 ] ]
-    sage: print(gap.eval("lambda := Eigenvalues( Rationals,A)"))
+    sage: libgap(QQ).Eigenvalues(A)
     [ 0 ]
 
 .. _section-rref:

src/doc/en/constructions/polynomials.rst

@@ -42,23 +42,24 @@ Another approach to this:
     sage: a = S.gen()
     sage: a^20062006
     80*a
-    sage: print(gap.eval("R:= PolynomialRing( GF(97))"))
+    sage: libgap.eval("R:= PolynomialRing( GF(97))")
     GF(97)[x_1]
-    sage: print(gap.eval("i:= IndeterminatesOfPolynomialRing(R)"))
+    sage: libgap.eval("i:= IndeterminatesOfPolynomialRing(R)")
     [ x_1 ]
-    sage: gap.eval("x:= i[1];; f:= x;;")
-    ''
-    sage: print(gap.eval("PowerMod( R, x, 20062006, x^3+7 );"))
+    sage: libgap.eval("x:= i[1]"); libgap.eval("f:= x;")
+    x_1
+    x_1
+    sage: libgap.eval("PowerMod( R, x, 20062006, x^3+7 );")
     Z(97)^41*x_1
-    sage: print(gap.eval("PowerMod( R, x, 20062006, x^3+7 );"))
+    sage: libgap.eval("PowerMod( R, x, 20062006, x^3+7 );")
     Z(97)^41*x_1
-    sage: print(gap.eval("PowerMod( R, x, 2006200620062006, x^3+7 );"))
+    sage: libgap.eval("PowerMod( R, x, 2006200620062006, x^3+7 );")
     Z(97)^4*x_1^2
     sage: a^2006200620062006
     43*a^2
-    sage: print(gap.eval("PowerMod( R, x, 2006200620062006, x^3+7 );"))
+    sage: libgap.eval("PowerMod( R, x, 2006200620062006, x^3+7 );")
     Z(97)^4*x_1^2
-    sage: print(gap.eval("Int(Z(97)^4)"))
+    sage: libgap.eval("Int(Z(97)^4)")
     43
 
 .. index::
@@ -136,11 +137,11 @@ interface.
 
 ::
 
-    sage: R = gap.PolynomialRing(gap.GF(2)); R
-    PolynomialRing( GF(2), ["x_1"] )
+    sage: R = libgap.PolynomialRing(GF(2)); R
+    GF(2)[x_1]
     sage: i = R.IndeterminatesOfPolynomialRing(); i
     [ x_1 ]
-    sage: x_1 = i[1]
+    sage: x_1 = i[0]
     sage: f = (x_1^3 - x_1 + 1)*(x_1 + x_1^2); f
     x_1^5+x_1^4+x_1^3+x_1
     sage: g = (x_1^3 - x_1 + 1)*(x_1 + 1); g

src/doc/en/constructions/rep_theory.rst

@@ -16,7 +16,7 @@ Sage-GAP interface can be used to compute character tables.
 You can construct the table of character values of a permutation
 group :math:`G` as a Sage matrix, using the method
 ``character_table`` of the PermutationGroup class, or via the
-pexpect interface to the GAP command ``CharacterTable``.
+interface to the GAP command ``CharacterTable``.
 
 ::
 
@@ -29,8 +29,8 @@ pexpect interface to the GAP command ``CharacterTable``.
     [ 1 -1  1 -1  1]
     [ 1  1 -1 -1  1]
     [ 2  0  0  0 -2]
-    sage: CT = gap(G).CharacterTable()
-    sage: print(gap.eval("Display(%s)"%CT.name()))
+    sage: CT = libgap(G).CharacterTable()
+    sage: CT.Display()
     CT1
     <BLANKLINE>
      2  3  2  2  2  3
@@ -55,11 +55,10 @@ Here is another example:
     [         1 -zeta3 - 1      zeta3          1]
     [         1      zeta3 -zeta3 - 1          1]
     [         3          0          0         -1]
-    sage: gap.eval("G := Group((1,2)(3,4),(1,2,3))")
-    'Group([ (1,2)(3,4), (1,2,3) ])'
-    sage: gap.eval("T := CharacterTable(G)")
-    'CharacterTable( Alt( [ 1 .. 4 ] ) )'
-    sage: print(gap.eval("Display(T)"))
+    sage: G = libgap.eval("Group((1,2)(3,4),(1,2,3))"); G
+    Group([ (1,2)(3,4), (1,2,3) ])
+    sage: T = G.CharacterTable()
+    sage: T.Display()
     CT2
     <BLANKLINE>
          2  2  .  .  2
@@ -82,28 +81,30 @@ denotes a square root of :math:`-3`, say :math:`i\sqrt{3}`, and
 :math:`b3 = \frac{1}{2}(-1+i \sqrt{3})`. Note the added ``print``
 Python command. This makes the output look much nicer.
 
+.. link
+
 ::
 
-    sage: print(gap.eval("irr := Irr(G)"))
+    sage: irr = G.Irr(); irr
     [ Character( CharacterTable( Alt( [ 1 .. 4 ] ) ), [ 1, 1, 1, 1 ] ), 
       Character( CharacterTable( Alt( [ 1 .. 4 ] ) ), [ 1, E(3)^2, E(3), 1 ] ), 
       Character( CharacterTable( Alt( [ 1 .. 4 ] ) ), [ 1, E(3), E(3)^2, 1 ] ), 
       Character( CharacterTable( Alt( [ 1 .. 4 ] ) ), [ 3, 0, 0, -1 ] ) ]
-    sage: print(gap.eval("Display(irr)"))
+    sage: irr.Display()
     [ [       1,       1,       1,       1 ],
       [       1,  E(3)^2,    E(3),       1 ],
       [       1,    E(3),  E(3)^2,       1 ],
       [       3,       0,       0,      -1 ] ]
-    sage: gap.eval("CG := ConjugacyClasses(G)")
-    '[ ()^G, (2,3,4)^G, (2,4,3)^G, (1,2)(3,4)^G ]'
-    sage: gap.eval("gamma := CG[3]")
-    '(2,4,3)^G'
-    sage: gap.eval("g := Representative(gamma)")
-    '(2,4,3)'
-    sage: gap.eval("chi := irr[2]")
-    'Character( CharacterTable( Alt( [ 1 .. 4 ] ) ), [ 1, E(3)^2, E(3), 1 ] )'
-    sage: gap.eval("g^chi")
-    'E(3)'
+    sage: CG = G.ConjugacyClasses(); CG
+    [ ()^G, (2,3,4)^G, (2,4,3)^G, (1,2)(3,4)^G ]
+    sage: gamma = CG[2]; gamma
+    (2,4,3)^G
+    sage: g = gamma.Representative(); g
+    (2,4,3)
+    sage: chi = irr[1]; chi
+    Character( CharacterTable( Alt( [ 1 .. 4 ] ) ), [ 1, E(3)^2, E(3), 1 ] )
+    sage: g^chi
+    E(3)
 
 This last quantity is the value of the character ``chi`` at the group
 element ``g``.
@@ -117,11 +118,11 @@ table prints nicely.
 
     sage: %Pprint
     Pretty printing has been turned OFF
-    sage: gap.eval("G := Group((1,2)(3,4),(1,2,3))")
-    'Group([ (1,2)(3,4), (1,2,3) ])'
-    sage: gap.eval("T := CharacterTable(G)")
-    'CharacterTable( Alt( [ 1 .. 4 ] ) )'
-    sage: gap.eval("Display(T)")
+    sage: G = libgap.eval("Group((1,2)(3,4),(1,2,3))"); G
+    Group([ (1,2)(3,4), (1,2,3) ])
+    sage: T = G.CharacterTable(); T
+    CharacterTable( Alt( [ 1 .. 4 ] ) )
+    sage: T.Display()
     CT3
     <BLANKLINE>
          2  2  2  .  .
@@ -138,12 +139,12 @@ table prints nicely.
     <BLANKLINE>
     A = E(3)^2
       = (-1-Sqrt(-3))/2 = -1-b3
-    sage: gap.eval("irr := Irr(G)")
+    sage: irr = G.Irr(); irr
     [ Character( CharacterTable( Alt( [ 1 .. 4 ] ) ), [ 1, 1, 1, 1 ] ),
       Character( CharacterTable( Alt( [ 1 .. 4 ] ) ), [ 1, 1, E(3)^2, E(3) ] ),
       Character( CharacterTable( Alt( [ 1 .. 4 ] ) ), [ 1, 1, E(3), E(3)^2 ] ),
       Character( CharacterTable( Alt( [ 1 .. 4 ] ) ), [ 3, -1, 0, 0 ] ) ]
-    sage: gap.eval("Display(irr)")
+    sage: irr.Display()
     [ [       1,       1,       1,       1 ],
       [       1,       1,  E(3)^2,    E(3) ],
       [       1,       1,    E(3),  E(3)^2 ],
@@ -162,15 +163,15 @@ Brauer characters
 
 The Brauer character tables in GAP do not yet have a "native"
 interface. To access them you can directly interface with GAP using
-pexpect and the ``gap.eval`` command.
+the ``libgap.eval`` command.
 
 The example below using the GAP interface illustrates the syntax.
 
 ::
 
-    sage: print(gap.eval("G := Group((1,2)(3,4),(1,2,3))"))
+    sage: G = libgap.eval("Group((1,2)(3,4),(1,2,3))"); G
     Group([ (1,2)(3,4), (1,2,3) ])
-    sage: print(gap.eval("irr := IrreducibleRepresentations(G,GF(7))"))   # random arch. dependent output
+    sage: irr = G.IrreducibleRepresentations(GF(7)); irr   # random arch. dependent output
     [ [ (1,2)(3,4), (1,2,3) ] -> [ [ [ Z(7)^0 ] ], [ [ Z(7)^4 ] ] ],
       [ (1,2)(3,4), (1,2,3) ] -> [ [ [ Z(7)^0 ] ], [ [ Z(7)^2 ] ] ],
       [ (1,2)(3,4), (1,2,3) ] -> [ [ [ Z(7)^0 ] ], [ [ Z(7)^0 ] ] ],
@@ -179,16 +180,15 @@ The example below using the GAP interface illustrates the syntax.
             [ Z(7), Z(7)^5, Z(7)^2 ] ],
           [ [ 0*Z(7), Z(7)^0, 0*Z(7) ], [ 0*Z(7), 0*Z(7), Z(7)^0 ],
             [ Z(7)^0, 0*Z(7), 0*Z(7) ] ] ] ]
-    sage: gap.eval("brvals := List(irr,chi->List(ConjugacyClasses(G),c->BrauerCharacterValue(Image(chi,Representative(c)))))")
-    ''
-    sage: print(gap.eval("Display(brvals)"))              # random architecture dependent output
+    sage: brvals = [[chi.Image(c.Representative()).BrauerCharacterValue()
+    ....:            for c in G.ConjugacyClasses()] for chi in irr]
+    sage: brvals         # random architecture dependent output
     [ [       1,       1,  E(3)^2,    E(3) ],
       [       1,       1,    E(3),  E(3)^2 ],
       [       1,       1,       1,       1 ],
       [       3,      -1,       0,       0 ] ]
-    sage: print(gap.eval("T := CharacterTable(G)"))
-    CharacterTable( Alt( [ 1 .. 4 ] ) )
-    sage: print(gap.eval("Display(T)"))
+    sage: T = G.CharacterTable()
+    sage: T.Display()
     CT3
     <BLANKLINE>
          2  2  .  .  2

src/doc/en/constructions/rings.rst

@@ -72,16 +72,13 @@ Here is another approach using GAP:
 
 ::
 
-    sage: R = gap.new("PolynomialRing(GF(97), 4)"); R
-    PolynomialRing( GF(97), ["x_1", "x_2", "x_3", "x_4"] )
+    sage: R = libgap.PolynomialRing(GF(97), 4); R
+    GF(97)[x_1,x_2,x_3,x_4]
     sage: I = R.IndeterminatesOfPolynomialRing(); I
     [ x_1, x_2, x_3, x_4 ]
-    sage: vars = (I.name(), I.name(), I.name(), I.name())
-    sage: _ = gap.eval(
-    ....:     "x_0 := %s[1];; x_1 := %s[2];; x_2 := %s[3];;x_3 := %s[4];;"
-    ....:     % vars)
-    sage: f = gap.new("x_1*x_2+x_3"); f
-    x_2*x_3+x_4
+    sage: x1, x2, x3, x4 = I
+    sage: f = x1*x2 + x3; f
+    x_1*x_2+x_3
     sage: f.Value(I,[1,1,1,1])
     Z(97)^34