From 27298dc2e42f0481eaf6a0f82bfe2deaf59d1288 Mon Sep 17 00:00:00 2001 From: Jean-Luc Thiffeault Date: Tue, 9 Dec 2014 17:06:45 -0600 Subject: [PATCH 01/24] Update linecount using hg-git. --- devel/linecount.dat | 98 +++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 98 insertions(+) diff --git a/devel/linecount.dat b/devel/linecount.dat index 903e442c..9133ce3c 100644 --- a/devel/linecount.dat +++ b/devel/linecount.dat @@ -871,3 +871,101 @@ 870 1417196036 14303 871 1417197762 14302 872 1417197973 14302 +873 1417198460 14302 +874 1417200949 14302 +875 1417202456 14302 +876 1417358772 14309 +877 1417466479 14309 +878 1417794718 14307 +879 1417556218 14309 +880 1417557276 14309 +881 1417557781 14420 +882 1417553041 14309 +883 1417557797 14420 +884 1417793445 14439 +885 1417794747 14437 +886 1417798228 14434 +887 1417798533 14457 +888 1417794821 14439 +889 1417794867 14437 +890 1417798547 14457 +891 1417798924 14460 +892 1417812695 14460 +893 1417797125 14486 +894 1417797519 14525 +895 1417801790 14511 +896 1417801818 14516 +897 1417801834 14539 +898 1417812891 14539 +899 1417813181 14551 +900 1417813523 14551 +901 1417813590 14551 +902 1417813699 14551 +903 1417815837 14551 +904 1417816908 14551 +905 1417978024 14551 +906 1417978122 14551 +907 1417999073 14562 +908 1418006745 14562 +909 1418052883 14562 +910 1418055249 14562 +911 1418056923 14605 +912 1418057173 14606 +913 1418058273 14959 +914 1418059739 14972 +915 1418059770 14971 +916 1418049227 14562 +917 1418055905 14562 +918 1418059298 14562 +919 1418060458 14564 +920 1418061031 14653 +921 1418062877 14653 +922 1418064278 15062 +923 1418064585 15063 +924 1418068528 14653 +925 1418085442 14653 +926 1418092767 14654 +927 1418066561 14653 +928 1418066926 14653 +929 1418067131 14653 +930 1418072491 14667 +931 1418073753 14698 +932 1418068701 14653 +933 1418073823 14698 +934 1418074894 14736 +935 1418074976 14736 +936 1418075998 14845 +937 1418076586 14848 +938 1418077651 14848 +939 1418095023 14850 +940 1418095264 14850 +941 1418132951 14851 +942 1418135527 14861 +943 1418135989 14978 +944 1418138654 15014 +945 1418139227 15026 +946 1417995433 14551 +947 1417995525 14551 +948 1418056221 14562 +949 1418066695 14653 +950 1418076677 14848 +951 1418139424 15026 +952 1418140558 15026 +953 1418153704 15062 +954 1418154157 15435 +955 1418157544 15442 +956 1418159149 15468 +957 1418152413 14704 +958 1418153314 14724 +959 1418154816 14764 +960 1418160039 15578 +961 1418160813 15578 +962 1418161846 15578 +963 1418163301 15578 +964 1418163377 15578 +965 1418163814 15578 +966 1418141024 15026 +967 1418163447 15578 +968 1418163835 15578 +969 1418164478 15578 +970 1418164598 15578 From 53a2bf038e74cc46de49bb411cf1c340bee84ea8 Mon Sep 17 00:00:00 2001 From: Jean-Luc Thiffeault Date: Tue, 9 Dec 2014 17:09:15 -0600 Subject: [PATCH 02/24] Update commits-between-releases. --- devel/commits-between-releases | 3 ++- 1 file changed, 2 insertions(+), 1 deletion(-) diff --git a/devel/commits-between-releases b/devel/commits-between-releases index e4ae1a5f..0d643492 100755 --- a/devel/commits-between-releases +++ b/devel/commits-between-releases @@ -6,7 +6,8 @@ function howmanycom() { } export -f howmanycom -howmanycom release-2.1 HEAD +howmanycom release-3.0 HEAD +howmanycom release-2.1 release-3.0 howmanycom release-2.0 release-2.1 howmanycom release-1.0.5 release-2.0 howmanycom release-1.0.4 release-1.0.5 From 6a92d0a47909ae676d25785a3ff3a99e98445675 Mon Sep 17 00:00:00 2001 From: Jean-Luc Thiffeault Date: Tue, 9 Dec 2014 21:34:31 -0600 Subject: [PATCH 03/24] Commits prior to 1.0. --- devel/commits-between-releases | 5 ++++- 1 file changed, 4 insertions(+), 1 deletion(-) diff --git a/devel/commits-between-releases b/devel/commits-between-releases index 0d643492..6e7e3a18 100755 --- a/devel/commits-between-releases +++ b/devel/commits-between-releases @@ -2,7 +2,7 @@ function howmanycom() { VERGAP=$(git log --pretty=oneline $1..$2 | wc | cut -b -10) - printf "%-13s to %-13s: %5d commits\n" $1 $2 $VERGAP + printf "%-13s to %-13s %5d commits\n" $1 $2 $VERGAP } export -f howmanycom @@ -15,3 +15,6 @@ howmanycom release-1.0.3 release-1.0.4 howmanycom release-1.0.2 release-1.0.3 howmanycom release-1.0.1 release-1.0.2 howmanycom release-1.0 release-1.0.1 +howmanycom 6a736fe release-1.0 +# There's about 30 more changesets in +# braid-projects:Projects/braidlcs/+braidlab that weren't migrated. From 1e9a31401404099e65dd6ad04638e1148d1e4c57 Mon Sep 17 00:00:00 2001 From: Jean-Luc Thiffeault Date: Wed, 10 Dec 2014 08:36:18 -0600 Subject: [PATCH 04/24] Use anonymous links for cloning instructions in guide. --- doc/braidlab_guide.tex | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/doc/braidlab_guide.tex b/doc/braidlab_guide.tex index 33d96123..b6a592cb 100644 --- a/doc/braidlab_guide.tex +++ b/doc/braidlab_guide.tex @@ -1870,14 +1870,14 @@ \subsection{Cloning the repository} source repository with the terminal command \begin{lstlisting}[frame=single,framerule=0pt,escapechar=*,% language=bash,backgroundcolor=\color{white}] -$ git clone git@github.com:jeanluct/braidlab.git +$ git clone https://github.com/jeanluct/braidlab.git \end{lstlisting} assuming Git is installed on your system. If you prefer to use Mercurial\index{Mercurial}, make sure you have the \href{http://hg-git.github.io/}{\lstinline{hg-git}} extension enabled and type \begin{lstlisting}[frame=single,framerule=0pt,escapechar=*,% language=bash,backgroundcolor=\color{white}] -$ hg clone git+ssh://git@github.com/jeanluct/braidlab.git +$ hg clone git+https://github.com/jeanluct/braidlab.git \end{lstlisting} Either way, after the cloning finishes type \begin{lstlisting}[frame=single,framerule=0pt,escapechar=*,% From be6709bbcec8db112c6369695896c48d391cca60 Mon Sep 17 00:00:00 2001 From: Jean-Luc Thiffeault Date: Wed, 10 Dec 2014 11:26:04 -0600 Subject: [PATCH 05/24] Updated extern/cbraid to latest. --- extern/README | 2 +- extern/cbraid/CHANGELOG | 25 +- extern/cbraid/README | 9 - extern/cbraid/README.md | 5 + extern/cbraid/include/braiding.h | 268 ++++++ extern/cbraid/lib/braiding.cpp | 1043 +++++++++++++++++++++- extern/cbraid/programs/braiding_main.cpp | 198 +++- 7 files changed, 1533 insertions(+), 17 deletions(-) delete mode 100644 extern/cbraid/README create mode 100644 extern/cbraid/README.md diff --git a/extern/README b/extern/README index 6d43d41d..8f32f5cb 100644 --- a/extern/README +++ b/extern/README @@ -1,6 +1,6 @@ assignmentoptimal is obtained from http://www.mathworks.com/matlabcentral/fileexchange/6543. The compiled mex file is copied to the private folder of +braidlab. (Version 2011-07-05) -CBraid is obtained from https://github.com/jeanluct/cbraid. (rev 5c3fdc1) +CBraid is obtained from https://github.com/jeanluct/cbraid. (rev b36a3e2) trains is obtained from https://bitbucket.org/jeanluc/braid-code/raw/tip/trains. (rev 66) diff --git a/extern/cbraid/CHANGELOG b/extern/cbraid/CHANGELOG index eb7cbbdf..f20efbaf 100644 --- a/extern/cbraid/CHANGELOG +++ b/extern/cbraid/CHANGELOG @@ -1,5 +1,28 @@ -Changelog for CBraid and Braiding (lightly edited svn log): +Changelog for CBraid and Braiding +================================= +======================================================================== +After r12 the code was moved from Googlecode/SVN to GitHub/Git, so no +version numbers anymore. + +From here is the lightly edited svn log. + +------------------------------------------------------------------------ +r11 | jeanlucth@gmail.com | 2014-07-04 09:06:25 -0500 (Fri, 04 Jul 2014) | 1 line + +Removed some unused variables in new code. +------------------------------------------------------------------------ +r10 | jeanlucth@gmail.com | 2014-07-04 09:02:38 -0500 (Fri, 04 Jul 2014) | 7 lines + +New code contributed by Maria Cumplido (student of Juan +González-Meneses). Juan's description: The old code computed some +sets called Ultra Summit Sets, while the new one computes Sets of +Sliding Circuits (which are in general the same as above, but not +always). +------------------------------------------------------------------------ +r9 | jeanlucth@gmail.com | 2013-12-13 08:29:27 -0600 (Fri, 13 Dec 2013) | 1 line + +Updated CHANGELOG. ------------------------------------------------------------------------ r8 | jeanlucth@gmail.com | 2013-12-13 08:20:15 -0600 (Fri, 13 Dec 2013) | 1 line diff --git a/extern/cbraid/README b/extern/cbraid/README deleted file mode 100644 index a83f2c78..00000000 --- a/extern/cbraid/README +++ /dev/null @@ -1,9 +0,0 @@ -This is CBraid version 2001/12/07 by Jae Choon Cha. -(see http://knot.kaist.ac.kr/~jccha/cbraid/) - -and - -Braiding version v1.0 (04/10/2004) by Juan Gonzalez-Meneses -(see http://personal.us.es/meneses/index.html) - -Updated and modified by Jean-Luc Thiffeault. diff --git a/extern/cbraid/README.md b/extern/cbraid/README.md new file mode 100644 index 00000000..05d7aeed --- /dev/null +++ b/extern/cbraid/README.md @@ -0,0 +1,5 @@ +_CBraid_ is a C++ library originally written by **[Jae Choon Cha](http://gt.postech.ac.kr/~jccha/)**. It allows various computations on braid groups, such as normal forms. The code in this project is based on his final version of 2001/12/07 and distributed under the GPL. + +The library has been updated to run on modern compilers, and has been merged with _Braiding_ version v1.0 (2004/10/04) originally written by **[Juan Gonzalez-Meneses](http://personal.us.es/meneses/)** and distributed under the GPL. Maria Cumplido contributed some code for computing sets of sliding circuits. + +The code is maintained by **[Jean-Luc Thiffeault](http://www.math.wisc.edu/~jeanluc)**. diff --git a/extern/cbraid/include/braiding.h b/extern/cbraid/include/braiding.h index ba59928d..ce9f5534 100644 --- a/extern/cbraid/include/braiding.h +++ b/extern/cbraid/include/braiding.h @@ -550,4 +550,272 @@ void PrintUSS(list > & uss, list word, char * FileName(sint16 iteration, sint16 max_iteration, sint16 type, sint16 orbit, sint16 rigidity, sint16 cl); + + + +/////////////////////////////////////////////////////// +// +// Reverse(B) computes the revese of a braid B, +// that is, B written backwards. +// B must be given in left canonical form. +// +/////////////////////////////////////////////////////// + + ArtinBraid Reverse(ArtinBraid B); + + + +///////////////////////////////////////////////////////////// +// +// RightMeet(B1,B2) Given two braids B1 and B2, computes +// their right gcd. That is, the greatest braid +// B such that B1>B and B2>B. +// +///////////////////////////////////////////////////////////// + + +ArtinBraid RightMeet(ArtinBraid B1, ArtinBraid B2); + + + +///////////////////////////////////////////////////////////// +// +// LeftJoin(B1,B2) Given two braids B1 and B2, computes +// their left lcm. That is, the smallest braid +// B such that B1B1 and B>B2. +// +///////////////////////////////////////////////////////////// + +ArtinBraid RightJoin(ArtinBraid B1, ArtinBraid B2); + + +/////////////////////////////////////////////////////// +// +// InitialFactor(B) computes the initial factor of a braid B, +// given in Left Canonical Form +// +/////////////////////////////////////////////////////// + +ArtinFactor InitialFactor(ArtinBraid B); + +/////////////////////////////////////////////////////// +// +// PreferredPrefix(B) computes the preferred prefix of a braid B, +// given in Left Canonical Form +// +/////////////////////////////////////////////////////// + +ArtinFactor PreferredPrefix(ArtinBraid B); + + +/////////////////////////////////////////////////////// +// +// Sliding(B) computes the cyclic sliding of a braid B, +// given in Left Canonical Form +// +/////////////////////////////////////////////////////// + + ArtinBraid Sliding(ArtinBraid B); + +/////////////////////////////////////////////////////// +// +// PreferredSuffix(B) computes the preferred suffix of a braid B, +// given in Left Canonical Form +// +/////////////////////////////////////////////////////// + +ArtinFactor PreferredSuffix(ArtinBraid B); + + +///////////////////////////////////////////////////////////// +// +// Trajectory_Sliding(B) Computes the trajectory under cyclic sliding +// of a braid B, that is, a list containing eta^k(B), +// for k=0,1,... until the first repetition. +// +///////////////////////////////////////////////////////////// + +list Trajectory_Sliding(ArtinBraid B); + +///////////////////////////////////////////////////////////// +// +// Trajectory_Sliding(B,C,d) Computes the trajectory of a braid B for cyclic sliding, +// a braid C that conjugates B to the +// first element of a closed orbit under sliding, +// and the number d of slidings needed to reach that element +// +///////////////////////////////////////////////////////////// + +list Trajectory_Sliding(ArtinBraid B, ArtinBraid & C, sint16 & d); + +///////////////////////////////////////////////////////////// +// +// SendToSC(B) Computes a braid conjugate to B that +// belongs to its Sliding Circuits Set. +// +///////////////////////////////////////////////////////////// + +ArtinBraid SendToSC(ArtinBraid B); + + +///////////////////////////////////////////////////////////// +// +// SendToSC(B,C) Computes a braid conjugate to B that +// belongs to its Sliding Circuits Set, and a braid +// C that conjugates B to the result. +// +///////////////////////////////////////////////////////////// + + +ArtinBraid SendToSC(ArtinBraid B, ArtinBraid & C); + + +///////////////////////////////////////////////////////////// +// +// Transport_Sliding(B,F) Given a braid B (in its SC and in LCF), and a simple factor +// F such that B^F is in its SSS, computes the transport of F for sliding. +// +///////////////////////////////////////////////////////////// + +ArtinFactor Transport_Sliding(ArtinBraid B, ArtinFactor F); + + +///////////////////////////////////////////////////////////// +// +// Returns_Sliding(B,F) Given a braid B (in its SC and in LCF), and a simple factor +// F such that B^F is in its SSS, computes the iterated transports +// of F for sliding that send B to an element in the circuit of B^F. +// +///////////////////////////////////////////////////////////// + + +list Returns_Sliding(ArtinBraid B, ArtinFactor F); + + + +///////////////////////////////////////////////////////////// +// +// Pullback_Sliding(B,F) Given a braid B (in its SC and in LCF), and a +// simple factor F such that B^F is super summit, +// computes the pullback of F at s(B) for sliding. +// +///////////////////////////////////////////////////////////// + +ArtinFactor Pullback_Sliding(ArtinBraid B, ArtinFactor F); + + + +///////////////////////////////////////////////////////////// +// +// MainPullback_Sliding(B,F) Given a braid B (in its SC and in LCF), and a +// simple factor F, computes the first repeated iterated +// pullback for cyclic sliding of F. +// +///////////////////////////////////////////////////////////// + +ArtinFactor MainPullback_Sliding(ArtinBraid B, ArtinFactor F); + +// María Cumplido Cabello + + +///////////////////////////////////////////////////////////// +// +// MinSC(B,F) Given a braid B in its Set of Sliding Circuits (and in LCF), +// computes the minimal simple factor R such that +// F MinSC(ArtinBraid B); + + +///////////////////////////////////////////////////////////// +// +// SC(B) Given a braid B, computes its Set of Cyclic Slidings. +// +///////////////////////////////////////////////////////////// + + +list > SC(ArtinBraid B); + + +///////////////////////////////////////////////////////////// +// +// SC(B,mins,prev) Given a braid B, computes its Set of Sliding Circuits, +// and stores in the lists 'mins' and 'prev' the following data: +// for each i, the first braid of the orbit i is obtained by +// conjugation of the first element of the orbit prev[i] +// by the simple element mins[i]. +// +///////////////////////////////////////////////////////////// + + + + +list > SC(ArtinBraid B, list & mins, list & prev); + + +//////////////////////////////////////////////////////////////////////////////////////// +// +// PrintSC(sc,word,n,power,file,type) Prints the Set of Sliding Circuits +// of the braid (word)^power to "file". +// +//////////////////////////////////////////////////////////////////////////////////////// + +void PrintSC(list > & sc, list word, sint16 n, + sint16 power, char * file, sint16 type); + +//////////////////////////////////////////////////////////////////////////////////// +// +// AreConjugateSC(B1,B2,C) Determines if the braids B1 and B2 are +// conjugate by testing their set of sliding circuits, +// and computes a conjugating element C. +// +////////////////////////////////////////////////////////////////////////////////// + +bool AreConjugateSC(ArtinBraid B1, ArtinBraid B2, ArtinBraid & C); + + + +//////////////////////////////////////////////////////////////////////////////////// +// +// AreConjugateSC2(B1,B2,C) Determines if the braids B1 and B2 are +// conjugate by the procedure of contruct SC(B1), +// and computes a conjugating element C. +// +////////////////////////////////////////////////////////////////////////////////// + + +bool AreConjugateSC2(ArtinBraid B1, ArtinBraid B2, ArtinBraid & C); + + + + + + } // namespace Braiding diff --git a/extern/cbraid/lib/braiding.cpp b/extern/cbraid/lib/braiding.cpp index bd8d5c7b..40187d6b 100644 --- a/extern/cbraid/lib/braiding.cpp +++ b/extern/cbraid/lib/braiding.cpp @@ -31,6 +31,7 @@ using namespace CBraid; using namespace std; + namespace Braiding { // typedef ArtinPresentation P; @@ -2267,4 +2268,1044 @@ char * FileName(sint16 iteration, sint16 max_iteration, sint16 type, sint16 orbi return file; } -} // namespace Braiding +//////////////////--------------- + + + +/////////////////////////////////////////////////////// +// +// Reverse(B) computes the revese of a braid B, +// that is, B written backwards. +// B must be given in left canonical form. +// +/////////////////////////////////////////////////////// + + ArtinBraid Reverse(ArtinBraid B) +{ + sint16 i, l=CL(B); + ArtinBraid B2=ArtinBraid(B.Index()); + B2.RightDelta=B.LeftDelta; + + for(i=0;iB and B2>B. +// +///////////////////////////////////////////////////////////// + + +ArtinBraid RightMeet(ArtinBraid B1, ArtinBraid B2) +{ + return Reverse(LeftMeet(Reverse(B1),Reverse(B2))); +} + + + + + +///////////////////////////////////////////////////////////// +// +// LeftJoin(B1,B2) Given two braids B1 and B2, computes +// their left lcm. That is, the smallest braid +// B such that B10) + F2=ArtinFactor(n,1); + else if(CL(B2)==0) + F2=ArtinFactor(n,0); + else + F2=B2.FactorList.front(); + + F=Remainder(B1,F2); + + B.RightMultiply(F); + B1.RightMultiply(F); + +////////////// Multiply B1 from the left by F2^{-1}. + + B1.LeftDelta--; + B1.FactorList.push_front((~F2).Flip(B1.LeftDelta)); + B1.MakeLCF(); + +////////////// Multiply B2 from the left by F2^{-1}. + + B2.LeftDelta--; + B2.FactorList.push_front((~F2).Flip(B2.LeftDelta)); + B2.MakeLCF(); + + } + + + B.MakeLCF(); + B.LeftDelta+=shift; + return B; + + + + +} +///////////////////////////////////////////////////////////// +// +// RightJoin(B1,B2) Given two braids B1 and B2, computes +// their right lcm. That is, the smallest braid +// B such that B>B1 and B>B2. +// +///////////////////////////////////////////////////////////// + +ArtinBraid RightJoin(ArtinBraid B1, ArtinBraid B2) +{ + return Reverse(LeftJoin(Reverse(B1),Reverse(B2))); +} + +/////////////////////////////////////////////////////// +// +// InitialFactor(B) computes the initial factor of a braid B, +// given in Left Canonical Form +// +/////////////////////////////////////////////////////// + +ArtinFactor InitialFactor(ArtinBraid B) +{ + sint16 n=B.Index(); + ArtinFactor F=ArtinFactor(n,0); + + if(CL(B)>0) + F=(B.FactorList.front()).Flip(-B.LeftDelta); + + return F; +} + + +/////////////////////////////////////////////////////// +// +// PreferredPrefix(B) computes the preferred prefix of a braid B, +// given in Left Canonical Form +// +/////////////////////////////////////////////////////// + +ArtinFactor PreferredPrefix(ArtinBraid B) +{ +ArtinFactor F=ArtinFactor(B.Index(),0); + +if(CL(B)>0) + F=LeftMeet(InitialFactor(B),~B.FactorList.back()); + +return F; +} + + + + +/////////////////////////////////////////////////////// +// +// Sliding(B) computes the cyclic sliding of a braid B, +// given in Left Canonical Form +// +/////////////////////////////////////////////////////// + + ArtinBraid Sliding(ArtinBraid B) +{ + ArtinFactor F=ArtinFactor(B.Index()); + + if(CL(B)==0) + return B; + + F=PreferredPrefix(B); + B.FactorList.front()=(!(F.Flip(B.LeftDelta)))*B.FactorList.front(); + B.FactorList.push_back(F); + + return B.MakeLCF(); +} + + + +/////////////////////////////////////////////////////// +// +// PreferredSuffix(B) computes the preferred suffix of a braid B, +// given in Left Canonical Form +// +/////////////////////////////////////////////////////// + +ArtinFactor PreferredSuffix(ArtinBraid B) +{ + return !(PreferredPrefix(Reverse(B))); +} + + + + + + +///////////////////////////////////////////////////////////// +// +// Trajectory_Sliding(B) Computes the trajectory under cyclic sliding +// of a braid B, that is, a list containing eta^k(B), +// for k=0,1,... until the first repetition. +// +///////////////////////////////////////////////////////////// + +list Trajectory_Sliding(ArtinBraid B) + { + list p; + + while (find(p.begin(),p.end(),B)==p.end()) + { + p.push_back(B); + B=Sliding(B); + } + return p; + } + + + + + + + + + +///////////////////////////////////////////////////////////// +// +// Trajectory_Sliding(B,C,d) Computes the trajectory of a braid B for cyclic sliding, +// a braid C that conjugates B to the +// first element of a closed orbit under sliding, +// and the number d of slidings needed to reach that element +// +///////////////////////////////////////////////////////////// + +list Trajectory_Sliding(ArtinBraid B, ArtinBraid & C, sint16 & d) +{ + list p; + list::iterator it; + + sint16 n=B.Index(); + C=ArtinBraid(n); + d=0; + + while (find(p.begin(),p.end(),B)==p.end()) + { + p.push_back(B); + C.RightMultiply(PreferredPrefix(B)); + B=Sliding(B); + d++; + } + + ArtinBraid B2=ArtinBraid(n); + ArtinBraid C2=ArtinBraid(n); + + C2.RightMultiply(PreferredPrefix(B)); + B2=Sliding(B); + d--; + while(B2!=B) + { + C2.RightMultiply(PreferredPrefix(B2)); + B2=Sliding(B2); + d--; + } + C.RightMultiply(!C2); + C.MakeLCF(); + + return p; + } + + + + + + + + + +///////////////////////////////////////////////////////////// +// +// SendToSC(B) Computes a braid conjugate to B that +// belongs to its Sliding Circuits Set. +// +///////////////////////////////////////////////////////////// + + +ArtinBraid SendToSC(ArtinBraid B) +{ + list T=Trajectory_Sliding(B); + return Sliding(T.back()); +} + + + + + + + + + + +///////////////////////////////////////////////////////////// +// +// SendToSC(B,C) Computes a braid conjugate to B that +// belongs to its Sliding Circuits Set, and a braid +// C that conjugates B to the result. +// +///////////////////////////////////////////////////////////// + + +ArtinBraid SendToSC(ArtinBraid B, ArtinBraid & C) +{ + sint16 d; + list T=Trajectory_Sliding(B,C,d); + + return Sliding(T.back()); + +} + + + + + + + + +///////////////////////////////////////////////////////////// +// +// Transport_Sliding(B,F) Given a braid B (in its SC and in LCF), and a simple factor +// F such that B^F is in its SSS, computes the transport of F for sliding. +// +///////////////////////////////////////////////////////////// + +ArtinFactor Transport_Sliding(ArtinBraid B, ArtinFactor F) +{ +ArtinBraid B2=((!ArtinBraid(F))*B*F).MakeLCF(); +ArtinBraid B3=((!ArtinBraid(PreferredPrefix(B)))*F*(PreferredPrefix(B2))).MakeLCF(); + +ArtinFactor F2=ArtinFactor(B2.Index(),0); + +if(CL(B3)>0) + F2=B3.FactorList.front(); +else if (B3.LeftDelta==1) + F2=ArtinFactor(B2.Index(),1); + + +return F2; + +} + + + + + + + +///////////////////////////////////////////////////////////// +// +// Returns_Sliding(B,F) Given a braid B (in its SC and in LCF), and a simple factor +// F such that B^F is in its SSS, computes the iterated transports +// of F for sliding that send B to an element in the circuit of B^F. +// +///////////////////////////////////////////////////////////// + + +list Returns_Sliding(ArtinBraid B, ArtinFactor F) +{ + list ret; + list::iterator it=ret.end(); + ArtinBraid B1=B; + sint16 i, N=1; + + + B1=Sliding(B1); + while(B1!=B) + { + N++; + B1=Sliding(B1); + } + + +while(it==ret.end()) +{ + ret.push_back(F); + + B1=B; + for(i=0; i ret; +list::iterator it=ret.end(); + +ArtinBraid B2=B; + +list T=Trajectory_Sliding(B); +list::reverse_iterator itb; + +if(F.CompareWithDelta()) + return F; + + +ArtinFactor F2=F; +while (it==ret.end()) +{ + + ret.push_back(F2); + for(itb=T.rbegin(); itb!=T.rend(); itb++) + F2=Pullback_Sliding(*itb,F2); + + + it=find(ret.begin(),ret.end(),F2); +} + +return *it; +} + +// María Cumplido Cabello + + +///////////////////////////////////////////////////////////// +// +// MinSC(B,F) Given a braid B in its Set of Sliding Circuits (and in LCF), +// computes the minimal simple factor R such that +// F ret=Returns_Sliding(B,F2); + list::iterator it; + + for(it=ret.begin(); it!=ret.end(); it++) + { + if(LeftMeet(F,*it)==F) + return *it; + } + + F2=MainPullback_Sliding(B,F); + + ret=Returns_Sliding(B,F2); + + for(it=ret.begin(); it!=ret.end(); it++) + { + if(LeftMeet(F,*it)==F) + return *it; + } + +return ArtinFactor(B.Index(),1); +} + + + +///////////////////////////////////////////////////////////// +// +// MinSC(B) Given a braid B in its Set of Sliding Circuits (and in LCF), +// computes the set of minimal simple factors R that +// B^R is in the Set of Sliding Circuits. +// +///////////////////////////////////////////////////////////// + +list MinSC(ArtinBraid B) +{ + sint16 i,j,k,test; + sint16 n=B.Index(); + sint16 *table=new sint16[n]; + + list Min; + + for(i=0; iF[j+1]) + test=0; + } + for(j=i+1; jF[j+1]) + test=0; + } + if(test) + { + Min.push_back(F); + table[i-1]=1; + } + } + delete[] table; + return Min; +} + + + +///////////////////////////////////////////////////////////// +// +// SC(B) Given a braid B, computes its Set of Cyclic Slidings. +// +///////////////////////////////////////////////////////////// + + +list > SC(ArtinBraid B) +{ + list > sc; + ArtinFactor F=ArtinFactor(B.Index()); + list Min; + list::iterator itf, itf2; + list::iterator itb; + + ArtinBraid B2=SendToSC(B); + list T=Trajectory_Sliding(B2); + + sc.push_back(Trajectory_Sliding(B2)); + + B2=((!ArtinBraid(ArtinFactor(B.Index(),1)))*(B2)*ArtinFactor(B.Index(),1)).MakeLCF(); + + for(itb=(*sc.begin()).begin(); itb!=(*sc.begin()).end(); itb++) + { + if(B2==*itb) + break; + } + + + if(itb==(*sc.begin()).end()) + sc.push_back(Trajectory_Sliding(B2)); + + + list >::iterator it=sc.begin(), it2; + + while(it!=sc.end()) + { + + Min=MinSC(*(*it).begin()); + + for(itf=Min.begin(); itf!=Min.end(); itf++) + { + F=*itf; + B2=((!ArtinBraid(F))*(*(*it).begin())*F).MakeLCF(); + T=Trajectory_Sliding(B2); + for(itb=T.begin(); itb!=T.end(); itb++) + { + for(it2=sc.begin(); it2!=sc.end(); it2++) + { + if(*itb==*(*it2).begin()) + break; + } + if(it2!=sc.end()) + break; + } + + if(itb==T.end()) + { + sc.push_back(T); + B2=((!ArtinBraid(ArtinFactor(B.Index(),1)))*(*T.begin())*ArtinFactor(B.Index(),1)).MakeLCF(); + for(itb=T.begin();itb!=T.end(); itb++) + { + if(B2==*itb) + break; + } + if(itb==T.end()) + sc.push_back(Trajectory_Sliding(B2)); + } + } + it++; + } + return sc; +} + + +//////////////////////////////////////////////////////////////////////////////////////// +// +// PrintSC(sc,word,n,power,file,type) Prints the Set of Sliding Circuits +// of the braid (word)^power to "file". +// +//////////////////////////////////////////////////////////////////////////////////////// + +void PrintSC(list > & sc, list word, sint16 n, + sint16 power, char * file, sint16 type) +{ + ofstream f(file); + + sint16 orbits=0; + + list >::iterator it; + list::iterator oit, itb; + ArtinBraid B2=ArtinBraid(n); + + for(it=sc.begin(); it!=sc.end(); it++) + orbits++; + + sint16 *sizes=new sint16[orbits]; + sint16 size; + sint16 i; + + it=sc.begin(); + for(i=0; i::iterator itw; + + f << "This file contains the Set of Sliding Circuits of the braid on " << n << " strands:" << endl << endl; + if(power!=1) + f << "( "; + + for(itw=word.begin(); itw!=word.end(); itw++) + { + if(*itw==n) + f << "D "; + else if (*itw==-n) + f << "-D "; + else + f << *itw << " "; + } + + if(power!=1) + f << ")^" << power; + + sint16 total; + + if(orbits==1) + { + f << endl << endl << "It has 1 circuit, whose size is " << sizes[0] << "." << endl << endl; + total=sizes[0]; + } + else + { + f << endl << endl << "It has " << orbits << " circuits, whose sizes are: "; + + total=0; + + for(i=0; i > SC(ArtinBraid B, list & mins, list & prev) +{ + list > sc; + + ArtinBraid B2=SendToSC(B); + list T=Trajectory_Sliding(B2); + sc.push_back(Trajectory_Sliding(B2)); + + ArtinFactor F=ArtinFactor(B.Index()); + list Min; + list::iterator itf, itf2; + list::iterator itb; + + sint16 current=0; + mins.clear(); + prev.clear(); + + mins.push_back(ArtinFactor(B.Index(),0)); + prev.push_back(1); + + list >::iterator it=sc.begin(), it2; + while(it!=sc.end()) + { + current++; + + Min=MinSC(*(*it).begin()); + + for(itf=Min.begin(); itf!=Min.end(); itf++) + { + F=*itf; + B2=((!ArtinBraid(F))*(*(*it).begin())*F).MakeLCF(); + T=Trajectory_Sliding(B2); + for(itb=T.begin(); itb!=T.end(); itb++) + { + for(it2=sc.begin(); it2!=sc.end(); it2++) + { + if(*itb==*(*it2).begin()) + break; + } + if(it2!=sc.end()) + break; + } + + if(itb==T.end()) + { + sc.push_back(T); + mins.push_back(F); + prev.push_back(current); + } + } + it++; + } + + + return sc; +} + + +//////////////////////////////////////////////////////////////////////////////////// +// +// AreConjugateSC(B1,B2,C) Determines if the braids B1 and B2 are +// conjugate by testing their set of sliding circuits, +// and computes a conjugating element C. +// +////////////////////////////////////////////////////////////////////////////////// + +bool AreConjugateSC(ArtinBraid B1, ArtinBraid B2, ArtinBraid & C) +{ + sint16 n=B1.Index(); + ArtinBraid C1=ArtinBraid(n), C2=ArtinBraid(n); + + ArtinBraid BT1=SendToSC(B1,C1), BT2=SendToSC(B2,C2); + + if(CL(BT1)!=CL(BT2) || Sup(BT1)!=Sup(BT2)) + return false; + + if(CL(BT1)==0) + { + C=(C1*(!C2)).MakeLCF(); + return true; + } + + list mins; + list prev; + + list > sc=SC(BT1,mins,prev); + + list >::iterator it; + list::iterator itb; + sint16 current=0; + ArtinBraid D1=ArtinBraid(n), D2=ArtinBraid(n); + + + for(it=sc.begin(); it!=sc.end(); it++) + { + current++; + D2=ArtinBraid(n); + for(itb=(*it).begin(); itb!=(*it).end(); itb++) + { + if(*itb==BT2) + break; + D2=D2*PreferredPrefix(*itb); + } + if(itb!=(*it).end()) + break; + } + + if(it==sc.end()) + return false; + + list::iterator itprev; + list::iterator itmins; + sint16 i; + + while(current!=1) + { + itprev=prev.begin(); + itmins=mins.begin(); + for(i=1; i > sc; + sint16 n=B1.Index(); + ArtinFactor F=ArtinFactor(n); + list Min; + list::iterator itf, itf2; + list::iterator itb; + + ArtinBraid C1=ArtinBraid(n), C2=ArtinBraid(n); + ArtinBraid BT1=SendToSC(B1,C1), BT2=SendToSC(B2,C2); + + ArtinBraid D1=ArtinBraid(n), D2=ArtinBraid(n); + + list mins; + list prev; + + sint16 current=0; + sint16 current2=0; + mins.clear(); + prev.clear(); + + list::iterator itprev; + list::iterator itmins; + sint16 i; + + mins.push_back(ArtinFactor(B1.Index(),0)); + prev.push_back(1); + + list T=Trajectory_Sliding(BT1); + + sc.push_back(Trajectory_Sliding(BT1)); + + list >::iterator it=sc.begin(), it2; + + while(it!=sc.end()) + { + current++; + current2++; + D2=ArtinBraid(n); + for(itb=(*it).begin(); itb!=(*it).end(); itb++) + { + if(*itb==BT2) + { + while(current2!=1) + { + itprev=prev.begin(); + itmins=mins.begin(); + for(i=1; i sss, traj, Cent, vertices, barrows; list::iterator it, itb, itb2; - list > uss; + list > uss, sc; list >::iterator ituss, ituss2; list Min, arrows; @@ -76,11 +76,13 @@ int main() << endl << "v: Least Common Multiple ^: Greatest Common Divisor " << endl << endl - << "c: Conjugacy Test z: Centralizer " << endl + << "s: Super Summit Set z: Centralizer " << endl << endl - << "s: Super Summit Set u: Ultra Summit Set " << endl + << "e: Conjugacy Test u: Ultra Summit Set " << endl << endl - << "a: Ask for Powers (On/Off) q: Quit " << endl; + << "t: Set of Sliding Circuits a: Ask for Powers (On/Off) " << endl + << endl + << "q: Quit " << endl; while(1) { @@ -362,7 +364,7 @@ int main() ////////////////////////////////////////////////////////// - if(c=='c') + if(c=='e') { n=ReadIndex(); word=ReadWord(n); @@ -440,6 +442,163 @@ int main() ///////////////////////////////////////////////////////////// +if(c=='d') + { + n=ReadIndex(); + word=ReadWord(n); + if(p) + power=ReadPower(); + + B1=ArtinBraid(n); + B1=WordToBraid(word,n); + if(p && power!=1) + B1=RaisePower(B1,power); + + B1.MakeLCF(); + + word2=ReadWord(n); + if(p) + power2=ReadPower(); + + B2=ArtinBraid(n); + B2=WordToBraid(word2,n); + if(p && power2!=1) + B2=RaisePower(B2,power2); + + B2.MakeLCF(); + + file=ReadFileName(); + + C=ArtinBraid(n); + + conj=AreConjugateSC(B1,B2,C); + + if(conj) + { + cout << endl << "These braids are conjugate." << endl << endl + << "A conjugating braid is: "; + PrintBraidWord(C); + cout << endl; + } + else + { + cout << endl << "These braids are not conjugate." << endl; + } + + f.open(file); + + f << "The braids on " << n << " strands" << endl << endl; + f.close(); + PrintWord(word,n,power,file); + f.open(file,ios::app); + + f << endl << endl << "and" << endl << endl; + + f.close(); + PrintWord(word2,n,power2,file); + f.open(file,ios::app); + + + + f << endl << endl; + + if(conj) + { + f << "are conjugate." << endl << endl + << "A conjugating braid is" << endl << endl; + f.close(); + PrintBraidWord(C,file); + } + else + { + f << "are not conjugate."; + f.close(); + } + + word.clear(); + } + + ///////////////////////////////////////////////////////////// +if(c=='c') + { + n=ReadIndex(); + word=ReadWord(n); + if(p) + power=ReadPower(); + + B1=ArtinBraid(n); + B1=WordToBraid(word,n); + if(p && power!=1) + B1=RaisePower(B1,power); + + B1.MakeLCF(); + + word2=ReadWord(n); + if(p) + power2=ReadPower(); + + B2=ArtinBraid(n); + B2=WordToBraid(word2,n); + if(p && power2!=1) + B2=RaisePower(B2,power2); + + B2.MakeLCF(); + + file=ReadFileName(); + + C=ArtinBraid(n); + + conj=AreConjugateSC2(B1,B2,C); + + if(conj) + { + cout << endl << "These braids are conjugate." << endl << endl + << "A conjugating braid is: "; + PrintBraidWord(C); + cout << endl; + } + else + { + cout << endl << "These braids are not conjugate." << endl; + } + + f.open(file); + + f << "The braids on " << n << " strands" << endl << endl; + f.close(); + PrintWord(word,n,power,file); + f.open(file,ios::app); + + f << endl << endl << "and" << endl << endl; + + f.close(); + PrintWord(word2,n,power2,file); + f.open(file,ios::app); + + + + f << endl << endl; + + if(conj) + { + f << "are conjugate." << endl << endl + << "A conjugating braid is" << endl << endl; + f.close(); + PrintBraidWord(C,file); + } + else + { + f << "are not conjugate."; + f.close(); + } + + word.clear(); + } + + ///////////////////////////////////////////////////////////// + + + if(c=='z') { n=ReadIndex(); @@ -592,6 +751,35 @@ int main() //////////////////////////////////////////////////////////////// + if(c=='t') + { + n=ReadIndex(); + word=ReadWord(n); + if(p) + power=ReadPower(); + file=ReadFileName(); + + B=ArtinBraid(n); + B=WordToBraid(word,n); + + if(p && power!=1) + B=RaisePower(B,power); + + B.MakeLCF(); + + sc=SC(B); + + type=ThurstonType(sc); + + PrintSC(sc,word,n,power,file,type); + + word.clear(); + sc.clear(); + delete[] file; + } + + //////////////////////////////////////////////////////////////// + if(c=='a') { if(p) From 13d70f9806b66b50a946f51afdf659e018a857bb Mon Sep 17 00:00:00 2001 From: Marko Budisic Date: Wed, 10 Dec 2014 15:28:27 -0600 Subject: [PATCH 06/24] Guide: added tcsh setenv syntax in addition to bash I have answered a question from a user who couldn't get "export" command to work on her Mac OS X, and then I realized that since some time, default shell on Mac OS X is tcsh which has a different syntax. --- doc/braidlab_guide.tex | 21 +++++++++++++++------ 1 file changed, 15 insertions(+), 6 deletions(-) diff --git a/doc/braidlab_guide.tex b/doc/braidlab_guide.tex index b6a592cb..d6176dff 100644 --- a/doc/braidlab_guide.tex +++ b/doc/braidlab_guide.tex @@ -1912,11 +1912,16 @@ \subsection{Cloning the repository} use the environment variable \lstinline{CPLUS_INCLUDE_PATH} to specify path to include files. For example, if both header files reside in \lstinline{/usr/local/include} on your Linux or -Mac OS~X system, you would issue +Mac OS~X system, you would issue (in \lstinline{bash} shell): \begin{lstlisting}[frame=single,framerule=0pt,escapechar=*,% language=bash,backgroundcolor=\color{white}] $ export CPLUS_INCLUDE_PATH=/usr/local/include \end{lstlisting} +or in \lstinline{tcsh} shell (now default on Mac OS X): +\begin{lstlisting}[frame=single,framerule=0pt,escapechar=*,% + language=csh,backgroundcolor=\color{white}] +$ setenv CPLUS_INCLUDE_PATH /usr/local/include +\end{lstlisting} before issuing \lstinline{make} that builds \lstinline{braidlab}. % \index{GMP|)} @@ -2034,16 +2039,20 @@ \subsubsection{Polish \LaTeX\ gets in the way} path. Another solution is to make sure that the Matlab executable directory appears -early in bash's path variable. On Mac OS~X % -\index{OS X}% -this reads +early in bash's path variable. For Matlab R2014a on Mac OS~X % +\index{OS X}% +and under \lstinline{bash} shell this reads \begin{lstlisting}[frame=single,framerule=0pt,escapechar=*,% language=bash,backgroundcolor=\color{white}] $ export PATH=/Applications/MATLAB_R2014a.app/bin:$PATH \end{lstlisting} -for Matlab R2014a. -\index{Linux|)}% +or under \lstinline{tcsh} shell (now default in Mac OS~X) +\begin{lstlisting}[frame=single,framerule=0pt,escapechar=*,% + language=bash,backgroundcolor=\color{white}] +$ setenv PATH /Applications/MATLAB_R2014a.app/bin:$PATH +\end{lstlisting} +\index{Linux|)}% \subsubsection{\lstinline{largeArraydims} warning} From 78710b1857fdd9bcd66dc3d9ed7b8e2d8239f2b2 Mon Sep 17 00:00:00 2001 From: Jean-Luc Thiffeault Date: Fri, 12 Dec 2014 16:45:47 -0600 Subject: [PATCH 07/24] Use totaln rather than n in intersec. Resolves issue #103. --- +braidlab/@loop/intersec.m | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/+braidlab/@loop/intersec.m b/+braidlab/@loop/intersec.m index 8b2e178c..79c7bc35 100644 --- a/+braidlab/@loop/intersec.m +++ b/+braidlab/@loop/intersec.m @@ -58,8 +58,8 @@ usematlab = false; % form output vectors - mu = intcoords(1:2*obj.n-4, :).'; - nu = intcoords(2*obj.n-3:end, :).'; + mu = intcoords(1:2*obj.totaln-4, :).'; + nu = intcoords(2*obj.totaln-3:end, :).'; catch me warning(me.identifier, [ me.message ... ' Reverting to Matlab intersec'] ); From b6be866ef6c2fbbe0037e6bd371a419e8670eb9c Mon Sep 17 00:00:00 2001 From: Jean-Luc Thiffeault Date: Fri, 12 Dec 2014 18:51:04 -0600 Subject: [PATCH 08/24] Update CHANGELOG for 3.0.1. --- CHANGELOG | 7 +++++++ 1 file changed, 7 insertions(+) diff --git a/CHANGELOG b/CHANGELOG index a8f66c22..5618cdcf 100644 --- a/CHANGELOG +++ b/CHANGELOG @@ -1,3 +1,10 @@ +------------------------------------------------------------------------ +3.0.1 [201x-xx-xx] + +* Improved installation instructions in guide. + +* Fixed a big when calling C++ version of intersec. + ------------------------------------------------------------------------ 3.0 [2014-12-09] From 370b74daf702f175ef2c5b3833735a60276a38b9 Mon Sep 17 00:00:00 2001 From: Jean-Luc Thiffeault Date: Fri, 12 Dec 2014 21:41:03 -0600 Subject: [PATCH 09/24] Improve GMP troubleshotting (issue #101). --- doc/braidlab_guide.tex | 91 +++++++++++++++++++++++++++--------------- 1 file changed, 59 insertions(+), 32 deletions(-) diff --git a/doc/braidlab_guide.tex b/doc/braidlab_guide.tex index d6176dff..f5c98058 100644 --- a/doc/braidlab_guide.tex +++ b/doc/braidlab_guide.tex @@ -198,7 +198,7 @@ \subsubsection{Constructor and elementary operations} of~\citet{Bangert2002}, since finding the braid of minimum length in the standard generators is in general difficult~\citep{Paterson1991}. Hence, there is no guarantee that in general \lstinline{compact} will find the -identity braid, even though it do so here. To really test if a braid is the +identity braid, even though it does so here. To really test if a braid is the identity (trivial braid), use the method \lstinline{istrivial}: % \index{braid class@\braid\ class!istrivial@\lstinline{istrivial}} \begin{lstlisting}[frame=single,framerule=0pt] @@ -220,7 +220,7 @@ \subsubsection{Constructor and elementary operations} >> help braid \end{lstlisting} describes the class \braid. To get more information on the \braid\ -constructor, invoke % +constructor, invoke% \index{braid class@\braid\ class!constructor}% \begin{lstlisting}[frame=single,framerule=0pt] >> help braid.braid @@ -1858,8 +1858,19 @@ \subsection{Precompiled packages} Some zip and tar files of the precompiled latest released version are available at \url{http://github.com/jeanluct/braidlab/releases}. If one of those suits your system, then download and untar/unzip (it might still work -even if the system doesn't match perfectly). +even if the system doesn't match perfectly). For Mac OS~X, there is a version +compiled without \href{https://gmplib.org/}{GMP} (the GNU MultiPrecision +library) % +\index{GMP}% +since it is a bit tricky to install (see Section~\ref{sec:gmp}). +On Ubuntu or Debian Linux, you can install the GMP source and binaries with +\begin{lstlisting}[frame=single,framerule=0pt,escapechar=*,% + language=bash,backgroundcolor=\color{white}] +$ sudo apt-get install libgmp-dev +\end{lstlisting} +After you install the binaries you must set the Matlab path as described in +Section~\ref{sec:path}. \subsection{Cloning the repository} \label{sec:cloning} @@ -1890,39 +1901,16 @@ \subsection{Cloning the repository} \index{Matlab!MEX files|)} \index{GMP|(}% -If you receive error messages because GMP (the GNU MultiPrecision library) is -not installed on your system, instead of the above use +If you receive error messages because \href{https://gmplib.org/}{GMP} (the GNU +MultiPrecision library) is not installed on your system, instead of the above +use \begin{lstlisting}[frame=single,framerule=0pt,escapechar=*,% language=bash,backgroundcolor=\color{white}] $ cd braidlab; make BRAIDLAB_USE_GMP=0 \end{lstlisting} This will slow down some functions, in particular testing for equality of -large braids. +large braids. If you want to install GMP first, see Section~\ref{sec:gmp}. -If you wish to compile \braidlab\ from source using GMP, you need to make the -GMP headers \lstinline{gmp.h} and \lstinline{gmpxx.h} available to the C++ -compiler that Matlab is using. Both the % -\index{GCC compiler}% -GCC compiler (more common on Linux % -\index{Linux}% -systems) and % -\index{Clang compiler}% -Clang compiler (more common on Mac OS~X systems) % -\index{OS X}% -use the environment variable -\lstinline{CPLUS_INCLUDE_PATH} to specify path to include files. For example, -if both header files reside in \lstinline{/usr/local/include} on your Linux or -Mac OS~X system, you would issue (in \lstinline{bash} shell): -\begin{lstlisting}[frame=single,framerule=0pt,escapechar=*,% - language=bash,backgroundcolor=\color{white}] -$ export CPLUS_INCLUDE_PATH=/usr/local/include -\end{lstlisting} -or in \lstinline{tcsh} shell (now default on Mac OS X): -\begin{lstlisting}[frame=single,framerule=0pt,escapechar=*,% - language=csh,backgroundcolor=\color{white}] -$ setenv CPLUS_INCLUDE_PATH /usr/local/include -\end{lstlisting} -before issuing \lstinline{make} that builds \lstinline{braidlab}. % \index{GMP|)} @@ -1971,7 +1959,8 @@ \subsection{Troubleshooting} \label{sec:trouble} \index{installing \braidlab!troubleshooting|(} -Here are some common problems that can occur when installing braidlab. +Here are some common problems that can occur when installing or compiling +braidlab. \subsubsection{Unsupported compiler} @@ -2012,6 +2001,44 @@ \subsubsection{Unsupported compiler} \index{Linux|)}% +\subsubsection{Compiling with GMP} +\label{sec:gmp} + +\index{GMP|(}% +\href{https://gmplib.org/}{GMP} is the GNU MultiPrecision library. \braidlab\ +uses GMP to handle arbitrarily large integers, which is necessary for testing +equality of very long braids. If GMP is not available, \braidlab\ falls back +on the VPI library \citep{vpi}, which is written natively in Matlab and hence +is much slower. + +If you wish to compile \braidlab\ from source using GMP, you need to make the +GMP headers \lstinline{gmp.h} and \lstinline{gmpxx.h} available to the C++ +compiler that Matlab is using. Both the % +\index{GCC compiler}% +GCC compiler (more common on Linux % +\index{Linux}% +systems) and % +\index{Clang compiler}% +Clang compiler (more common on Mac OS~X systems) % +\index{OS X}% +use the environment variable \lstinline{CPLUS_INCLUDE_PATH} to specify path to +include files. For example, if both header files reside in +\lstinline{/usr/local/include} on your Linux or Mac OS~X system, you would +issue (in \lstinline{bash} shell): +\begin{lstlisting}[frame=single,framerule=0pt,escapechar=*,% + language=bash,backgroundcolor=\color{white}] +$ export CPLUS_INCLUDE_PATH=/usr/local/include +\end{lstlisting} +or in \lstinline{tcsh} shell (now the default on Mac OS X): +\begin{lstlisting}[frame=single,framerule=0pt,escapechar=*,% + language=csh,backgroundcolor=\color{white}] +$ setenv CPLUS_INCLUDE_PATH /usr/local/include +\end{lstlisting} +before issuing \lstinline{make} that builds \lstinline{braidlab}. + +\index{GMP|)}% + + \subsubsection{Polish \LaTeX\ gets in the way} \index{Linux|(}% @@ -2046,7 +2073,7 @@ \subsubsection{Polish \LaTeX\ gets in the way} language=bash,backgroundcolor=\color{white}] $ export PATH=/Applications/MATLAB_R2014a.app/bin:$PATH \end{lstlisting} -or under \lstinline{tcsh} shell (now default in Mac OS~X) +or under \lstinline{tcsh} shell (now the default in Mac OS~X) \begin{lstlisting}[frame=single,framerule=0pt,escapechar=*,% language=bash,backgroundcolor=\color{white}] $ setenv PATH /Applications/MATLAB_R2014a.app/bin:$PATH From 574674a16deefa7e4bfc0400eb34640ab6f4d204 Mon Sep 17 00:00:00 2001 From: Jean-Luc Thiffeault Date: Sat, 13 Dec 2014 10:05:07 -0600 Subject: [PATCH 10/24] Fix typo in help message. --- +braidlab/@databraid/databraid.m | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/+braidlab/@databraid/databraid.m b/+braidlab/@databraid/databraid.m index ddd51901..b82aa28f 100644 --- a/+braidlab/@databraid/databraid.m +++ b/+braidlab/@databraid/databraid.m @@ -121,7 +121,7 @@ function b = braid(db) %BRAID Convert a DATABRAID to a BRAID. - % C = BRAID(B) converts the databraid B to a regular braid object B + % C = BRAID(B) converts the databraid B to a regular braid object C % by dropping the crossing times. % % This is a method for the DATABRAID class. From f7662603e318e182d42ff30badde2c0d0b8a74b2 Mon Sep 17 00:00:00 2001 From: Jean-Luc Thiffeault Date: Sun, 14 Dec 2014 11:24:22 -0600 Subject: [PATCH 11/24] #106: Allow braid to act on basepoint as long as it doesn't move. --- +braidlab/@braid/braid.m | 8 ++++---- 1 file changed, 4 insertions(+), 4 deletions(-) diff --git a/+braidlab/@braid/braid.m b/+braidlab/@braid/braid.m index 3e11ef4e..78674b1f 100644 --- a/+braidlab/@braid/braid.m +++ b/+braidlab/@braid/braid.m @@ -367,6 +367,10 @@ ' Instead use matrix of loop.coords. ' ... 'Try ''help loop.loop''.']) end + if b1.n > b2.totaln + error('BRAIDLAB:braid:mtimes:badgen', ... + 'Braid has too many strings for the loop.') + end if b2.basepoint p = b1.perm; p = [p (length(p)+1):b2.totaln]; @@ -375,10 +379,6 @@ 'Braid cannot move the basepoint.') end end - if b1.n > b2.n - error('BRAIDLAB:braid:mtimes:badgen', ... - 'Braid has too many strings for the loop.') - end [varargout{1:nargout}] = loopsigma(b1.word,b2.coords); varargout{1} = braidlab.loop(varargout{1},'bp',b2.basepoint); if nargout > 1 From d066abe0a66986e861613f2bb2bca66b07c68d01 Mon Sep 17 00:00:00 2001 From: Jean-Luc Thiffeault Date: Sun, 14 Dec 2014 12:15:00 -0600 Subject: [PATCH 12/24] Update CHANGELOG. --- CHANGELOG | 5 ++++- 1 file changed, 4 insertions(+), 1 deletion(-) diff --git a/CHANGELOG b/CHANGELOG index 5618cdcf..6fe70f33 100644 --- a/CHANGELOG +++ b/CHANGELOG @@ -3,7 +3,10 @@ * Improved installation instructions in guide. -* Fixed a big when calling C++ version of intersec. +* Fixed a bug when calling C++ version of intersec. + +* Fix a bug in braid.mtimes that disallowed valid action on loop with + basepoint. ------------------------------------------------------------------------ 3.0 [2014-12-09] From 9a8d0d660fa93933c02f92354f7ecb92e68ac2dd Mon Sep 17 00:00:00 2001 From: Jean-Luc Thiffeault Date: Sun, 14 Dec 2014 16:44:33 -0600 Subject: [PATCH 13/24] #107: Delete reducing.m and related files. --- .../@braid/private/find_reducing_curves.m | 215 ------------------ +braidlab/@braid/private/snf.m | 184 --------------- +braidlab/@braid/reducing.m | 55 ----- doc/braidlab_guide.tex | 20 +- 4 files changed, 1 insertion(+), 473 deletions(-) delete mode 100644 +braidlab/@braid/private/find_reducing_curves.m delete mode 100644 +braidlab/@braid/private/snf.m delete mode 100644 +braidlab/@braid/reducing.m diff --git a/+braidlab/@braid/private/find_reducing_curves.m b/+braidlab/@braid/private/find_reducing_curves.m deleted file mode 100644 index 2c3f5a56..00000000 --- a/+braidlab/@braid/private/find_reducing_curves.m +++ /dev/null @@ -1,215 +0,0 @@ -function [linv,Q] = find_reducing_curves(b,l0) - -% -% Marko Budisic -% -% This file is part of Braidlab. -% -% Braidlab is free software: you can redistribute it and/or modify -% it under the terms of the GNU General Public License as published by -% the Free Software Foundation, either version 3 of the License, or -% (at your option) any later version. -% -% Braidlab is distributed in the hope that it will be useful, -% but WITHOUT ANY WARRANTY; without even the implied warranty of -% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -% GNU General Public License for more details. -% -% You should have received a copy of the GNU General Public License -% along with Braidlab. If not, see . -% LICENSE> - -import braidlab.* -global BRAIDLAB_debuglvl - -badbraid = false; -if nargin < 1 - % The bad reducible braid. - badbraid = true; - b = braid([-3 1 -4 2 -3 -1 -2 3 -2 4 3 4]); - lred = loop([0 -1 0 0 0 0 0 1]); -end - -n = b.n; - -if exist('BRAIDLAB_debuglvl','var') - if BRAIDLAB_debuglvl >= 1 - tn = tntype(b); - fprintf('braid is %s.\n',tn) - end -end - -% Use random initial loop if not specified. -if nargin < 2, l0 = loop(randi(5,1,2*n-2)-3); end - -[M,period] = b.cycle('iter',l0); - -Q = []; - -for i = 1:period - M{i} = full(M{i}); - - % Check the badbraid case, where we know the reducing curve. - if badbraid - lred2 = b*lred; - if ~all(lred2 == lred) - fprintf('\nbadbraid: Somethings''s wrong... not a reducing curve.\n'); - end - if any(M{i}*lred.coords' ~= lred.coords') - fprintf('M{%d}*l ~= l',i); - fprintf('\n\n') - fprintf(' l = %s\n',num2str(lred.coords)) - fprintf(' b*l = %s\n',num2str(lred2.coords)) - fprintf('M{%d}*l = %s\n\n',i,num2str((M{i}*lred.coords')')) - error('Invariant curve is not an eigenvector.') - end - end - - % Get rid of "boundary" Dynnikov coordinates, a_(n-1) and b_(n-1). - % If we don't do this there is an extra reducing curve around the - % first n punctures. - ii = [(1:n-2) (1:n-2)+n-2+1]; - M{i} = M{i}(ii,ii); - - A = M{i} - eye(size(M{i})); - [U,D,V] = snf(A); % Smith form of A. - - % Check that everything is ok. - if exist('BRAIDLAB_debuglvl','var') - if BRAIDLAB_debuglvl >= 1 - checksnf(A,U,D,V); - end - end - - D = diag(D); - - Qit{i} = round(inv(V))'; - Qit{i} = Qit{i}(:,find(D == 0)); - - if rank(Qit{i}) < size(Qit{i},2) - error('Qit{%d} doesn''t have full rank.',i) - end - - % Make sure first nonzero component is positive. - for j = 1:size(Qit{i},2) - inz = find(Qit{i}(:,j) ~= 0); - if Qit{i}(inz(1),j) < 0 - Qit{i}(:,j) = -Qit{i}(:,j); - end - end - - % Take the intersection of the coordinates, since a loop must be - % invariant for each iterate. - if isempty(Q) - Q = Qit{i}; - else - Q = intersect(Q',Qit{i}','rows')'; - end - - % If the nullspace is empty, it cannot be reducible. - if isempty(Q) - Q = []; - linv = []; - return - end -end - -% If Q has rank one, easy to check if it's an invariant loop. -if size(Q,2) == 1 - - linv = loop(Q); - if b*linv == linv - return - end - - linv = loop(-Q); - if b*linv == linv - return - end - - Q = []; - linv = []; - return -end - -% Now cycle over linear combinations of the columns of Q. - -mm = size(Q,2); - -doplot = false; -if doplot - close all - figure - for i = 1:mm - subplot(mm,1,i) - plot(loop(Q(:,i))) - end -end - -N = 3; % Go from -N to N in each component. -%nwords = (2*N+1)^mm; - -Z = -N*ones(mm,1); Z(end) = -N-1; - -linv = []; - -while 1 - incr = false; - % Do not change the first generator (leave at 1). - for w = mm:-1:1 - if Z(w) < N - incr = true; - % Increment the generator. - Z(w) = Z(w)+1; - break - else - % Otherwise reset generator at that position, and let the - % loop move on to the next position. - Z(w) = -N; - end - end - - % If nothing was changed, we're done. - if ~incr, break; end - - % Make sure the loops is actually invariant before adding to the list. - l = loop(Q*Z); - if b*l == l - % Don't add to the list if all coordinates are zero, or if its nested. - if ~all(l.coords == 0) && ~nested(l) - linv = [linv ; l]; - end - else - if exist('BRAIDLAB_debuglvl','var') - if BRAIDLAB_debuglvl >= 1 - warning('BRAIDLAB:braid:find_reducing_curves:falsepos', ... - 'False positive.') - end - end - end -end - -if exist('BRAIDLAB_debuglvl','var') - if BRAIDLAB_debuglvl >= 1 - if ~strcmp(tn,'reducible') && ~isempty(linv) - warning('BRAIDLAB:braid:find_reducing_curves:notreducible', ... - 'Braid is not reducible, yet we found a reducing curve.') - end - end -end - -if exist('BRAIDLAB_debuglvl','var') - if BRAIDLAB_debuglvl >= 1 - if strcmp(tn,'reducible') && isempty(linv) - % Example: < -3 1 -4 2 -3 -1 -2 3 -2 4 3 4 >. - % This is because of the dependence on initial loop. - warning('BRAIDLAB:braid:find_reducing_curves:isreducible', ... - 'Braid is reducible, but we didn''t find a reducing curve.') - end - end -end diff --git a/+braidlab/@braid/private/snf.m b/+braidlab/@braid/private/snf.m deleted file mode 100644 index f4c5be94..00000000 --- a/+braidlab/@braid/private/snf.m +++ /dev/null @@ -1,184 +0,0 @@ -function [U,S,V] = snf(A); -%SNF Smith normal form of an integer matrix. -% [U,S,V] = SNF(A) for an integer matrix A returns integer matrices U, S, -% and V with the properties that -% -% - A = U*S*V'; -% - S is diagonal and nonnegative; -% - S(i,i) divides S(i+1,i+1) for all i (here 0 divides 0 by convention); -% - det U = +-1, and det V = +-1. -% -% S = SNF(A) just returns diag(S). -% -% This function is in some ways analogous to SVD. - -% John Gilbert, 415-812-4487, December 1993 -% gilbert@parc.xerox.com -% Xerox Palo Alto Research Center - -% Modified by Jean-Luc Thiffeault for braidlab to work with VPI (Variable -% Precision Integers). - -if round(A) ~= A - error('BRAIDLAB:braid:snf:badarg','Requires integer input.'); -end - -% This looks much like an SVD algorithm that first bidiagonalizes -% A by Givens rotations and then chases zeros, except for -% the construction of the 2 by 2 elementary transformation. - -[m,n] = size(A); -S = A; -typ = str2func(class(A)); -U = typ(eye(m)); -V = typ(eye(n)); - -% Bidiagonalize S with elementary Hermite transforms. - -for j = 1:min(m,n) - % Zero column j below the diagonal. - for i = j+1:m - if S(i,j) ~= 0 - % Construct an elementary Hermite transformation E - % to zero S(i,j) by combining rows i and j. - E = ehermite(S(j,j),S(i,j)); - % Apply the transform to S and U. - S([j i],:) = E * S([j i],:); - U(:,[j i]) = U(:,[j i]) * inv2(E); - end - end - % Zero row j after the superdiagonal. - for i = j+2:n - if S(j,i) ~= 0 - % Construct an elementary Hermite transformation E - % to zero S(j,i) by combining columns j+1 and i. - E = ehermite(S(j,j+1),S(j,i)); - % Apply the transform to S and V. - S(:,[j+1 i]) = S(:,[j+1 i]) * E'; - V(:,[j+1 i]) = V(:,[j+1 i]) * inv2(E); - end - end -end - -% Now S is upper bidiagonal. -% Chase the superdiagonal nonzeros away. - -D = diag(S,1); -while any(D ~= 0) - b = min(find(D ~= 0)); - % Start chasing bulge at first nonzero superdiagonal element. - - % To guarantee reduction in S(b,b), first make S(b,b) positive - % and make S(b,b+1) nonnegative and less than S(b,b). - - if S(b,b) < 0 - S(b,:) = -S(b,:); - U(:,b) = -U(:,b); - end - - if S(b,b) ~= 0 - q = floor(S(b,b+1)/S(b,b)); - E = [1 0 ; -q 1]; - - S(:,[b b+1]) = S(:,[b b+1]) * E'; - V(:,[b b+1]) = V(:,[b b+1]) * inv2(E); - end - - if S(b,b+1) ~= 0 - - % Zero the first nonzero superdiagonal element - % using columns b and b+1, to start the bulge at S(b+1,b). - E = ehermite(S(b,b),S(b,b+1)); - S(:,[b b+1]) = S(:,[b b+1]) * E'; - V(:,[b b+1]) = V(:,[b b+1]) * inv2(E); - for j = 1:min(m,n) - if j+1 <= m - % Zero S(j+1,j) using rows j and j+1. - E = ehermite(S(j,j),S(j+1,j)); - S([j j+1],:) = E * S([j j+1],:); - U(:,[j j+1]) = U(:,[j j+1]) * inv2(E); - end - if j+2 <= n - % Zero S(j,j+2) using columns j+1 and j+2. - E = ehermite(S(j,j+1),S(j,j+2)); - S(:,[j+1 j+2]) = S(:,[j+1 j+2]) * E'; - V(:,[j+1 j+2]) = V(:,[j+1 j+2]) * inv2(E); - end - end - end - D = diag(S,1); -end - -% Now S is diagonal. Make it nonnegative. - -for j = 1:min(m,n) - if S(j,j) < 0 - S(j,:) = -S(j,:); - U(:,j) = -U(:,j); - end -end - -% Squeeze factors to lower right to enforce divisibility condition. - -for i = 1 : min(m,n) - for j = i+1 : min(m,n) - % Replace S(i,i), S(j,j) by their gcd and lcm respectively. - a = S(i,i); - b = S(j,j); - [g,c,d] = gcd(a,b); - if g ~= 0 - E = [ 1 d ; -b/g a*c/g]; - F = [ c 1 ; -b*d/g a/g]; - S([i j],[i j]) = E * S([i j],[i j]) * F'; - U(:,[i j]) = U(:,[i j]) * inv2(E); - V(:,[i j]) = V(:,[i j]) * inv2(F); - end - end -end - -U = round(U); -V = round(V); - -if nargout <= 1 - U = diag(S); -end - -end - -%========================================================================= -function E = ehermite(a,b); - -% Elementary Hermite tranformation. -% -% For integers a and b, E = ehermite(a,b) returns -% an integer matrix with determinant 1 such that E * [a;b] = [g;0], -% where g is the gcd of a and b. -% E = ehermite(a,b) -% -% This function is in some ways analogous to GIVENS. - -% John Gilbert, 415-812-4487, December 1993 -% gilbert@parc.xerox.com -% Xerox Palo Alto Research Center - -[g,c,d] = gcd(a,b); -if g ~= 0 - E = [c d ; -b/g a/g]; -else - E = [1 0 ; 0 1]; -end - -end - -%========================================================================= -function Ei = inv2(E) - -detE = E(1,1)*E(2,2) - E(1,2)*E(2,1); - -if abs(detE) ~= 1 - error('BRAIDLAB:braid:snf:detnotone','Determinant should be one.') -end - -Ei = detE*[E(2,2) -E(1,2); -E(2,1) E(1,1)]; - -end diff --git a/+braidlab/@braid/reducing.m b/+braidlab/@braid/reducing.m deleted file mode 100644 index 7362ecfa..00000000 --- a/+braidlab/@braid/reducing.m +++ /dev/null @@ -1,55 +0,0 @@ -function l = reducing(b,ntries) -%REDUCING Find reducing curves for a braid, if they exist. -% -% This is a method for the BRAID class. -% See also BRAID, LOOP.LOOP, BRAID.CYCLE. - -% -% Marko Budisic -% -% This file is part of Braidlab. -% -% Braidlab is free software: you can redistribute it and/or modify -% it under the terms of the GNU General Public License as published by -% the Free Software Foundation, either version 3 of the License, or -% (at your option) any later version. -% -% Braidlab is distributed in the hope that it will be useful, -% but WITHOUT ANY WARRANTY; without even the implied warranty of -% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -% GNU General Public License for more details. -% -% You should have received a copy of the GNU General Public License -% along with Braidlab. If not, see . -% LICENSE> - -% Test with the bad reducible braid: -% b = braid([-3 1 -4 2 -3 -1 -2 3 -2 4 3 4]); -% Reducing curve is -% lred = loop([0 -1 0 0 0 0 0 1]); - -warning('BRAIDLAB:braid:reducing:exp', ... - 'This function is experimental! Use with caution!') - -if nargin < 2, ntries = 5; end - -lc = []; -for i = 1:ntries - l = find_reducing_curves(b); - for j = 1:length(l) - lc = [lc ; l(j).coords]; - end -end - -lc = unique(lc,'rows'); - -if ~isempty(lc) - l = braidlab.loop(lc); -else - l = []; -end diff --git a/doc/braidlab_guide.tex b/doc/braidlab_guide.tex index f5c98058..83b76f79 100644 --- a/doc/braidlab_guide.tex +++ b/doc/braidlab_guide.tex @@ -1473,25 +1473,7 @@ \subsection{Limit cycles of the effective linear action} isotopy class. In that sense they could provide an alternative to the the Bestvina--Handel train track algorithm~\citep{Bestvina1995}, % \index{Bestvina--Handel algorithm}% -which is used to compute the isotopy class of a braid. \braidlab\ has some -experimental support for this in the form of the method -\lstinline{reducing}: % -\index{braid class@\braid\ class!reducing@\lstinline{reducing}|(}% -\begin{lstlisting}[frame=single,framerule=0pt] ->> b = braid([-3 1 -4 2 -3 -1 -2 3 -2 4 3 4]); ->> l = b.reducing -Warning: This function is experimental! Use with caution! - -ans = (( 0 -1 0 0 0 0 )) - ->> b*l % check that it is indeed a reducing curve - -ans = (( 0 -1 0 0 0 0 )) -\end{lstlisting} -\lstinline{reducing} found a reducing curve for the braid and returned it as a -set of loop coordinates. However, note that at this point -\lstinline{reducing} can return too many curves, or none even when one exists. -\index{braid class@\braid\ class!reducing@\lstinline{reducing}|)}% +which is used to compute the isotopy class of a braid. \index{cycle!of effective linear action|)}% \index{effective linear action|)}% From 9c0a5ec36cb7f6e2e3b1cbec04d026985baa8339 Mon Sep 17 00:00:00 2001 From: Jean-Luc Thiffeault Date: Sun, 14 Dec 2014 16:50:51 -0600 Subject: [PATCH 14/24] #107: Update CHANGELOG. --- CHANGELOG | 2 ++ 1 file changed, 2 insertions(+) diff --git a/CHANGELOG b/CHANGELOG index 6fe70f33..5e7d1084 100644 --- a/CHANGELOG +++ b/CHANGELOG @@ -8,6 +8,8 @@ * Fix a bug in braid.mtimes that disallowed valid action on loop with basepoint. +* Remove broken braid.reducing. + ------------------------------------------------------------------------ 3.0 [2014-12-09] From 01a09be38407b083ad2c2ac675bfc8fcfbd5abb3 Mon Sep 17 00:00:00 2001 From: Jean-Luc Thiffeault Date: Mon, 15 Dec 2014 17:29:46 -0600 Subject: [PATCH 15/24] Fix some out-of-date figs in guide (compact returns different answer). Refresh braid diagrams. Conflicts: doc/figs/fulltwist_lr.pdf --- doc/braidlab_guide.tex | 24 ++++++++++++------------ doc/figs/s1s-2_diagram.pdf | Bin 2510 -> 2960 bytes doc/figs/s1s-2s1s-2s1s2_diagram.pdf | Bin 3750 -> 5152 bytes doc/figs/s1s2s-3_4_diagram.pdf | Bin 5703 -> 8504 bytes doc/figs/s1s2s-3_diagram.pdf | Bin 3441 -> 3743 bytes doc/figs/testdata_braid.pdf | Bin 6350 -> 9570 bytes doc/figs/testdata_braidY.pdf | Bin 5014 -> 7215 bytes 7 files changed, 12 insertions(+), 12 deletions(-) diff --git a/doc/braidlab_guide.tex b/doc/braidlab_guide.tex index 83b76f79..71d312a2 100644 --- a/doc/braidlab_guide.tex +++ b/doc/braidlab_guide.tex @@ -559,10 +559,10 @@ \subsubsection{An example} \index{projection line|(}% The \braid\ constructor allows us to do this easily. -The folder \lstinline{testsuite} % +The folder \lstinline{testsuite/testcases} % \index{testsuite}% contains a dataset of trajectories, from laboratory data for granular -media~\citep{Puckett2012}. From the \lstinline{testsuite} folder, we load the +media~\citep{Puckett2012}. We load the data: \begin{lstlisting}[frame=single,framerule=0pt] >> clear; load testdata @@ -598,11 +598,11 @@ \subsubsection{An example} } \end{center} \caption{(a) A dataset of four trajectories, (b) projected along the~$X$ axis. - (c) The compacted braid~$ \sigma_1^{-1} \sigma_2^{-1} - \sigma_1^{-8}\sigma_3^2\sigma_2\sigma_1$ corresponding to the~$X$ projection - in (b). (d) The compacted - braid~$\sigma_3^{-7}\sigma_1\sigma_3^{-1}\sigma_1$ corresponding to the~$Y$ - projection, with closure enforced. % + (c) The compacted braid~$ \sigma_2^{-2} \sigma_1^{-1} \sigma_2^{-1} + \sigma_1^{-5} \sigma_3 \sigma_1^{-1}\sigma_3\sigma_2\sigma_1$ corresponding + to the~$X$ projection in (b). (d) The compacted + braid~$\sigma_3^{-4}\sigma_1\sigma_3^{-1}\sigma_1\sigma_3^{-3}$ + corresponding to the~$Y$ projection, with closure enforced. % \index{braid!closure}% The braids in (c) and (d) are conjugate.\index{braid!conjugate}} \end{figure} @@ -627,7 +627,7 @@ \subsubsection{An example} \begin{lstlisting}[frame=single,framerule=0pt] >> b = compact(b) -b = < -1 -2 -1 -1 -1 -1 -1 -1 -1 -1 3 3 2 1 > +b = < -2 -2 -1 -2 -1 -1 -1 -1 -1 3 -1 3 2 1 > >> b.length ans = 14 @@ -642,7 +642,7 @@ \subsubsection{An example} \index{braid class@\braid\ class!subbraid class@\lstinline{subbraid}}% with only those two strings: \begin{lstlisting}[frame=single,framerule=0pt] ->> subbraid(bX,[2 3]) +>> subbraid(b,[2 3]) ans = < -1 -1 -1 -1 -1 -1 -1 -1 > \end{lstlisting} @@ -663,7 +663,7 @@ \subsubsection{Changing the projection line and enforcing closure} ans = 673 >> b.compact -ans = < -3 -3 -3 -3 -3 -3 -3 1 -3 > +ans = < -3 -3 -3 -3 1 -3 -3 -3 -3 > \end{lstlisting} In general, a change of projection line only changes the braid by conjugation~\citep{Boyland1994,Thiffeault2010}. We can test for @@ -691,9 +691,9 @@ \subsubsection{Changing the projection line and enforcing closure} >> XY = closure(XY); % close braid and avoid new crossings >> bX = compact(braid(XY,0)), bY = compact(braid(XY,pi/2)) -bX = < -1 -2 -1 -1 -1 -1 -1 -1 -1 -1 3 3 2 1 > +bX = < -2 -2 -1 -2 -1 -1 -1 -1 -1 3 -1 3 2 1 > -bY = < -3 -3 -3 -3 -3 -3 -3 1 -3 1 > +bY = < -3 -3 -3 -3 1 -3 1 -3 -3 -3 > \end{lstlisting} This default closure simply draws line segments from the final points to the initial points in such a way that no new crossings are created in the~$X$ diff --git a/doc/figs/s1s-2_diagram.pdf b/doc/figs/s1s-2_diagram.pdf index 602a032a892667c0fc5da27894852bef87a091be..52e68914ed37563ba1f7f9c2a11820db912d423d 100644 GIT binary patch delta 2071 zcmaLYc{tRI8VB%X%UH7&lAmltW#%_yW)O~HOvGe~P7SFs218?*F~vlaEtO-PvR03n z(#gJztT}`Ug)B#7ExL3pxwbfzbKLH|&%Muc?sMON-tY5$KF|B_+oP0vAeE>lEq*~q z=S=)ZFXO0QFI(}<$Wm+LJv2a~A&u!Njs}n@OxgfR#D|L&xnuxypppD3Ho!l(EdX<; 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Date: Mon, 15 Dec 2014 17:45:37 -0600 Subject: [PATCH 16/24] Update CHANGELOG. --- CHANGELOG | 6 ++++-- 1 file changed, 4 insertions(+), 2 deletions(-) diff --git a/CHANGELOG b/CHANGELOG index 5e7d1084..834e69bf 100644 --- a/CHANGELOG +++ b/CHANGELOG @@ -3,10 +3,12 @@ * Improved installation instructions in guide. +* Fixed some incorrect output in guide. + * Fixed a bug when calling C++ version of intersec. -* Fix a bug in braid.mtimes that disallowed valid action on loop with - basepoint. +* Fixed a bug in braid.mtimes that disallowed valid action on loop + with basepoint. * Remove broken braid.reducing. From a8c6e262984c0442ab142ba25aa343640c302f7e Mon Sep 17 00:00:00 2001 From: Marko Budisic Date: Tue, 16 Dec 2014 10:54:08 -0600 Subject: [PATCH 17/24] (-1)^i for integer i replaced with ?: test Invoking std::pow to compute this was both unnecessary and caused confusion for some older compiler versions. Replaced by a ternary operator test ? : as there are only two possible outcomes. --- +braidlab/@loop/private/loop_helper.hpp | 7 ++----- 1 file changed, 2 insertions(+), 5 deletions(-) diff --git a/+braidlab/@loop/private/loop_helper.hpp b/+braidlab/@loop/private/loop_helper.hpp index 9979623c..24e3fc8e 100644 --- a/+braidlab/@loop/private/loop_helper.hpp +++ b/+braidlab/@loop/private/loop_helper.hpp @@ -225,11 +225,8 @@ void intersec(const int n, const T *a, const T *b, T* mu, T* nu) { // two-element loop 2k-1 and 2k for ( i = 2*k-1; i <= 2*k ; i++ ) { - mu[i] = std::pow(-1,i) * a[k] + ( - ( b[k] >= 0 ) ? - nu[k]/2 : - nu[k+1]/2 - ); + mu[i] = ( i % 2 == 0 ? a[k] : -a[k] ) + + ( b[k] >= 0 ? nu[k]/2 : nu[k+1]/2 ); } } return; From fc81f17dae42e391bcbd32ddd20a9697ec518344 Mon Sep 17 00:00:00 2001 From: Jean-Luc Thiffeault Date: Tue, 16 Dec 2014 11:28:13 -0600 Subject: [PATCH 18/24] Makefile MEX suffix for i686 (from Alex's computer). --- Makefile | 3 +++ 1 file changed, 3 insertions(+) diff --git a/Makefile b/Makefile index 03dcd168..35840dee 100644 --- a/Makefile +++ b/Makefile @@ -29,6 +29,9 @@ ifeq ($(SYS), Linux) ifeq ($(ARCH), x86_64) MEXSUFFIX = mexa64 endif + ifeq ($(ARCH), i686) + MEXSUFFIX = mexglx + endif endif ifeq ($(SYS), Darwin) ifeq ($(ARCH), x86_64) From b0d02e542918fa11332285c13ba9105cea324f0b Mon Sep 17 00:00:00 2001 From: Marko Budisic Date: Tue, 16 Dec 2014 13:14:57 -0600 Subject: [PATCH 19/24] #101: GMP installation using Homebrew on Mac OS X installed --- doc/braidlab_guide.tex | 18 +++++++++++++++--- 1 file changed, 15 insertions(+), 3 deletions(-) diff --git a/doc/braidlab_guide.tex b/doc/braidlab_guide.tex index 71d312a2..6c0859b0 100644 --- a/doc/braidlab_guide.tex +++ b/doc/braidlab_guide.tex @@ -1836,6 +1836,7 @@ \section{Installing \braidlab} compiler. \index{Matlab!MEX files|)} \subsection{Precompiled packages} +\label{sec:precompiled} Some zip and tar files of the precompiled latest released version are available at \url{http://github.com/jeanluct/braidlab/releases}. If one of @@ -1854,6 +1855,17 @@ \subsection{Precompiled packages} After you install the binaries you must set the Matlab path as described in Section~\ref{sec:path}. +Mac OS X does not have the access to \lstinline{apt} or \lstinline{aptitude}. Their functionality is in part reproduced by the \href{http://brew.sh/}{Homebrew project}. If you install Homebrew, you can easily obtain GMP by running +\begin{lstlisting}[frame=single,framerule=0pt,escapechar=*,% + language=bash,backgroundcolor=\color{white}] +$ brew install gmp +\end{lstlisting} +Since \lstinline{brew} is conservative about installing libraries and +sources into system directories, you will likely need to set +\lstinline{LD_LIBRARY_PATH}, and \lstinline{PATH} variables to include +the location of the local Homebrew library storage (see Homebrew +documentation for further instruction). + \subsection{Cloning the repository} \label{sec:cloning} @@ -1993,7 +2005,7 @@ \subsubsection{Compiling with GMP} on the VPI library \citep{vpi}, which is written natively in Matlab and hence is much slower. -If you wish to compile \braidlab\ from source using GMP, you need to make the +If you wish to compile \braidlab\ from source using GMP, you first need to install GMP (see \ref{sec:precompiled}), and then make the GMP headers \lstinline{gmp.h} and \lstinline{gmpxx.h} available to the C++ compiler that Matlab is using. Both the % \index{GCC compiler}% @@ -2009,12 +2021,12 @@ \subsubsection{Compiling with GMP} issue (in \lstinline{bash} shell): \begin{lstlisting}[frame=single,framerule=0pt,escapechar=*,% language=bash,backgroundcolor=\color{white}] -$ export CPLUS_INCLUDE_PATH=/usr/local/include +$ export CPLUS_INCLUDE_PATH=$CPLUS_INCLUDE_PATH:/usr/local/include \end{lstlisting} or in \lstinline{tcsh} shell (now the default on Mac OS X): \begin{lstlisting}[frame=single,framerule=0pt,escapechar=*,% language=csh,backgroundcolor=\color{white}] -$ setenv CPLUS_INCLUDE_PATH /usr/local/include +$ setenv CPLUS_INCLUDE_PATH $CPLUS_INCLUDE_PATH:/usr/local/include \end{lstlisting} before issuing \lstinline{make} that builds \lstinline{braidlab}. From 43188843f2f6072b78c94331e5d8e7ec27433220 Mon Sep 17 00:00:00 2001 From: Jean-Luc Thiffeault Date: Tue, 16 Dec 2014 11:34:41 -0600 Subject: [PATCH 20/24] Update CHANGELOG. --- CHANGELOG | 2 ++ 1 file changed, 2 insertions(+) diff --git a/CHANGELOG b/CHANGELOG index 834e69bf..04cd26b4 100644 --- a/CHANGELOG +++ b/CHANGELOG @@ -12,6 +12,8 @@ * Remove broken braid.reducing. +* Makefile detects Linux 32-bit architecture. + ------------------------------------------------------------------------ 3.0 [2014-12-09] From 54a9aaa6371caa4dce9167997263ac5aa629583e Mon Sep 17 00:00:00 2001 From: Jean-Luc Thiffeault Date: Tue, 16 Dec 2014 13:52:17 -0600 Subject: [PATCH 21/24] A bit of editing and indexing. --- doc/braidlab_guide.tex | 27 ++++++++++++++++++--------- 1 file changed, 18 insertions(+), 9 deletions(-) diff --git a/doc/braidlab_guide.tex b/doc/braidlab_guide.tex index 6c0859b0..e71b2af6 100644 --- a/doc/braidlab_guide.tex +++ b/doc/braidlab_guide.tex @@ -1855,7 +1855,12 @@ \subsection{Precompiled packages} After you install the binaries you must set the Matlab path as described in Section~\ref{sec:path}. -Mac OS X does not have the access to \lstinline{apt} or \lstinline{aptitude}. Their functionality is in part reproduced by the \href{http://brew.sh/}{Homebrew project}. If you install Homebrew, you can easily obtain GMP by running +\index{OS X|(}% +Mac OS~X does not have the access to \lstinline{apt} or +\lstinline{aptitude}. Their functionality is in part reproduced by the % +\index{Homebrew}% +\href{http://brew.sh/}{Homebrew project}. If you install Homebrew, you can +easily obtain GMP by running \begin{lstlisting}[frame=single,framerule=0pt,escapechar=*,% language=bash,backgroundcolor=\color{white}] $ brew install gmp @@ -1866,6 +1871,9 @@ \subsection{Precompiled packages} the location of the local Homebrew library storage (see Homebrew documentation for further instruction). +\index{OS X|)}% + + \subsection{Cloning the repository} \label{sec:cloning} @@ -2005,9 +2013,10 @@ \subsubsection{Compiling with GMP} on the VPI library \citep{vpi}, which is written natively in Matlab and hence is much slower. -If you wish to compile \braidlab\ from source using GMP, you first need to install GMP (see \ref{sec:precompiled}), and then make the -GMP headers \lstinline{gmp.h} and \lstinline{gmpxx.h} available to the C++ -compiler that Matlab is using. Both the % +If you wish to compile \braidlab\ from source using GMP, you first need to +install GMP (see \ref{sec:precompiled}), and then make the GMP headers +\lstinline{gmp.h} and \lstinline{gmpxx.h} available to the C++ compiler that +Matlab is using. Both the % \index{GCC compiler}% GCC compiler (more common on Linux % \index{Linux}% @@ -2023,12 +2032,12 @@ \subsubsection{Compiling with GMP} language=bash,backgroundcolor=\color{white}] $ export CPLUS_INCLUDE_PATH=$CPLUS_INCLUDE_PATH:/usr/local/include \end{lstlisting} -or in \lstinline{tcsh} shell (now the default on Mac OS X): +or in \lstinline{tcsh} shell (now the default on Mac OS~X): \begin{lstlisting}[frame=single,framerule=0pt,escapechar=*,% language=csh,backgroundcolor=\color{white}] $ setenv CPLUS_INCLUDE_PATH $CPLUS_INCLUDE_PATH:/usr/local/include \end{lstlisting} -before issuing \lstinline{make} that builds \lstinline{braidlab}. +before issuing the \lstinline{make} command to build \lstinline{braidlab}. \index{GMP|)}% @@ -2060,17 +2069,17 @@ \subsubsection{Polish \LaTeX\ gets in the way} path. Another solution is to make sure that the Matlab executable directory appears -early in bash's path variable. For Matlab R2014a on Mac OS~X % +early in bash's path variable. For Matlab R2014b on Mac OS~X % \index{OS X}% and under \lstinline{bash} shell this reads \begin{lstlisting}[frame=single,framerule=0pt,escapechar=*,% language=bash,backgroundcolor=\color{white}] -$ export PATH=/Applications/MATLAB_R2014a.app/bin:$PATH +$ export PATH=/Applications/MATLAB_R2014b.app/bin:$PATH \end{lstlisting} or under \lstinline{tcsh} shell (now the default in Mac OS~X) \begin{lstlisting}[frame=single,framerule=0pt,escapechar=*,% language=bash,backgroundcolor=\color{white}] -$ setenv PATH /Applications/MATLAB_R2014a.app/bin:$PATH +$ setenv PATH /Applications/MATLAB_R2014b.app/bin:$PATH \end{lstlisting} \index{Linux|)}% From 017bca37b093bd868d3b29a3706ee52ed371495f Mon Sep 17 00:00:00 2001 From: Jean-Luc Thiffeault Date: Tue, 16 Dec 2014 13:54:24 -0600 Subject: [PATCH 22/24] Update CHANGELOG. --- CHANGELOG | 8 +++++--- 1 file changed, 5 insertions(+), 3 deletions(-) diff --git a/CHANGELOG b/CHANGELOG index 04cd26b4..20953e95 100644 --- a/CHANGELOG +++ b/CHANGELOG @@ -1,9 +1,11 @@ ------------------------------------------------------------------------ -3.0.1 [201x-xx-xx] +3.0.1 [2014-12-16] -* Improved installation instructions in guide. +* Improved installation instructions in guide, in particular for GMP. -* Fixed some incorrect output in guide. +* Fixed anonymous GitHub links for cloning in guide. + +* Fixed some outdated output in guide. * Fixed a bug when calling C++ version of intersec. 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The file COPYING needs to be in -# the folder where the command is executed. - -ROOTDIR=$1 -export BPFILE=COPYING - -function checktag() { - if [ -z "$2" ]; then return 1; fi - - if !(grep --quiet "$1" $2); then - echo "Warning: file" $2 "is missing \"$1\" tag." - return 1 - fi - - return 0 -} -export -f checktag - -function ibtag() { - export OPENTAG=${1}' ' - - if !(checktag "$OPENTAG" ${2}); then exit 1; fi - if !(checktag "$CLOSETAG" ${2}); then exit 1; fi - - # Add comment character to start of boilerplate text. - sed "s,^,${1} ," ${BPFILE} >| ${BPFILE}.comment - # Insert boilerplate text. - sed -i \ - "/${OPENTAG}/,/${CLOSETAG}/ {//!d}; /${OPENTAG}/r ${BPFILE}.comment" $2 - rm -f ${BPFILE}.comment - # Remove trailing whitespace, if rtw command is available. - if hash rtw 2> /dev/null; then - rtw ${2}; rm -f ${2}.rtw - fi -} -export -f ibtag - -# Insert boilerplate for various file extensions. -find $ROOTDIR -name "*.m" -print0 | \ - xargs -0 -n 1 bash -c 'ibtag "%" "$@"' _ -find $ROOTDIR -name "*.cpp" -print0 | \ - xargs -0 -n 1 bash -c 'ibtag "\/\/" "$@"' _ -find $ROOTDIR -name "*.c" -print0 | \ - xargs -0 -n 1 bash -c 'ibtag "" "$@"' _ -find $ROOTDIR -name "*.tex" -print0 | \ - xargs -0 -n 1 bash -c 'ibtag "%" "$@"' _ -find $ROOTDIR -name "*.bib" -print0 | \ - xargs -0 -n 1 bash -c 'ibtag "%" "$@"' _ -find $ROOTDIR -name "Makefile*" -print0 | \ - xargs -0 -n 1 bash -c 'ibtag "#" "$@"' _ - -unset -f checktag -unset -f ibtag -unset BPFILE -unset OPENTAG -unset CLOSETAG diff --git a/devel/linecount b/devel/linecount deleted file mode 100755 index d964b58a..00000000 --- a/devel/linecount +++ /dev/null @@ -1,49 +0,0 @@ -#!/bin/sh - -# ** This must be run from an hg-git clone ** - -# Count lines of code in braidlab as a function of revision, for funsies. -# -# Run from the root braidlab folder as devel/linecount. -# -# Plot results in Matlab with linecount_plot.m -# -# To avoid putting the repo in a funny state, clone a fresh local copy -# first in tmp. Delete when done. - -ROOTDIR=`pwd` -DEVELDIR=$ROOTDIR/devel -LINECOUNTFILE=$DEVELDIR/linecount.dat -rm -f $LINECOUNTFILE -LASTREV=`hg id -r tip -n` -REVSTEP=1 - -cd /tmp -rm -rf braidlab-tmp -hg clone $ROOTDIR braidlab-tmp -cd braidlab-tmp - -for i in `seq 0 $REVSTEP $LASTREV`; do - hg up -c -r $i - CODEFOLDERS="+braidlab" - if [ -e 'testsuite' ]; then - CODEFOLDERS="$CODEFOLDERS testsuite" - fi - if [ -e 'doc' ]; then - CODEFOLDERS="$CODEFOLDERS doc" - fi - LINES=`find $CODEFOLDERS \ - -name '*.[cm]' -o -name '*.?pp' -o -name '*.tex' -o -name '*.bib' \ - | xargs wc -l | tail -1 | sed 's/ total$//g'` - # assignmentoptimal.c was originally included in the main tree, so - # subtract its linecount (441) if the file is present. - if [ -e '+braidlab/private/assignmentoptimal.c' ]; then - LINES=$(($LINES-441)) - fi - # The date is in UTC seconds. - DATE=`hg log -r $i --template '{date|hgdate}' | cut -d' ' -f1` - echo $i '\t' $DATE '\t' $LINES >> $LINECOUNTFILE -done - -cd /tmp -rm -rf braidlab-tmp diff --git a/devel/linecount.dat b/devel/linecount.dat deleted file mode 100644 index 9133ce3c..00000000 --- a/devel/linecount.dat +++ /dev/null @@ -1,971 +0,0 @@ -0 1316799423 1544 -1 1316800840 1469 -2 1316815267 1534 -3 1316855179 1748 -4 1316860173 1506 -5 1316973520 1504 -6 1316974969 1504 -7 1317004612 1541 -8 1317017941 1586 -9 1317158390 1600 -10 1317166961 1680 -11 1317170337 1680 -12 1317185609 1655 -13 1317279694 1658 -14 1317281208 1646 -15 1317287422 1681 -16 1317287857 1684 -17 1317704670 1684 -18 1317880666 1542 -19 1317885273 1515 -20 1317955544 1595 -21 1317959816 1573 -22 1317960151 1573 -23 1317966258 1707 -24 1317968985 1729 -25 1318043433 1767 -26 1318048008 1767 -27 1318050238 1998 -28 1318053690 2012 -29 1318290460 2011 -30 1318306483 2069 -31 1318312399 2069 -32 1318323836 2144 -33 1318366133 2175 -34 1318368226 2165 -35 1318372583 2258 -36 1318393264 2308 -37 1318633651 2267 -38 1318633762 2267 -39 1318695020 2334 -40 1318696757 2381 -41 1318741824 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file mode 100644 index 4d3f905a..00000000 --- a/devel/linecount_plot.m +++ /dev/null @@ -1,61 +0,0 @@ -function linecount_plot(ptype) - -if nargin < 1, ptype = 'rev'; end - -d = load('linecount.dat'); -ii = [1 ; find(diff(d(:,3)))+1]; - -rev = d(ii,1); -utc = d(ii,2); -lc = d(ii,3); - -% Convert Unix time to datenum. -dnum = utc/86400 + datenum(1970,1,1); - -fig = figure; - -switch lower(ptype) - case {'date','time'} - plot(dnum,lc,'.-') - datetick('x','mmm yy','keepticks') - xlabel('date (UTC)') - ylabel('# lines') - case {'rev','revision'} - plot(rev,lc,'.-') - xlabel('revision') - ylabel('# lines') - otherwise -end - -% Display clickable tooltips for each datapoint, showing Mercurial log. -dcm_obj = datacursormode(fig); -set(dcm_obj,'DisplayStyle','window','SnapToDataVertex','on',... - 'Enable','on','UpdateFcn',@hglog) - - -% ================================================================== -function txt = hglog(~,event_obj) - -pos = get(event_obj,'Position'); - -[~,shell] = system('echo $0'); -if ~isempty(findstr(shell,'bash')) - termset = 'export TERM=ansi'; -elseif ~isempty(findstr(shell,'tcsh')) - termset = 'setenv TERM ansi'; -else - error('Unknown shell.') -end - -if pos(1) > 5e5 - % pos(1) is most likely a datenum date, not a revision number. - % Convert datenum to UTC. - utc = int32(86400*(pos(1) - datenum(1970,1,1))); - hgcmd = sprintf('hg log -d "%d 0" --template ''{rev}: {desc}''',utc); -else - hgcmd = sprintf('hg log -r %d --template ''{rev}: {desc}''',pos(1)); -end - -[~,out] = system([termset ' ; ' hgcmd]); -out(end-8:end) = []; % delete rubbish at the end of the string -txt = {out}; diff --git a/devel/logo/README b/devel/logo/README deleted file mode 100644 index ea31742d..00000000 --- a/devel/logo/README +++ /dev/null @@ -1 +0,0 @@ -Original s1s-2.jpg is from ttrods/figs_unused. diff --git a/devel/logo/logo_s1s-2.jpg b/devel/logo/logo_s1s-2.jpg deleted file mode 100644 index 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http://perso.univ-rennes1.fr/bertold.wiest/logi.html - -From Bert's website: - -"Here is a maple worksheet written by Michel Bonnefont and Erwan -Hillion (using some elements of an earlier program by Juan -Gonzalez-Meneses, and with a bug fixed later by myself), which -illustrates the braid untangling procedure described in my paper with -Ivan Dynnikov. (When they wrote this program, Michel Bonnefont and -Erwan Hillion were 1st-year students in the magistère in mathematics -at the ENS in Ker Lann.)" - -Note that it must be run in a folder that doesn't contain certain -Matlab m-files, since some share the same name as Maple functions. diff --git a/devel/research/DynnikovWiest/TransmRelax.mpl b/devel/research/DynnikovWiest/TransmRelax.mpl deleted file mode 100644 index 7be11288..00000000 --- a/devel/research/DynnikovWiest/TransmRelax.mpl +++ /dev/null @@ -1,940 +0,0 @@ -### THIS PROGRAM CONTAINS AN IMPLEMENTATION OF THE -### TRANSMISSION-RELAXATION PROCEDURE OF DYNNIKOV-WIEST. IT WAS -### WRITTEN BY MICHEL BONNEFONT AND ERWAN HILLION, USING ELEMENTS OF -### AN EARLIER PROGRAM FOR DRAWING CURVE DIAGRAMS BY JUAN -### GONZALEZ-MENESES. A BUG WAS LATER FIXED BY BERT WIEST. - -# Functions defined in this file: -# -# name called by lines -# ---------------------------------------------------------------- -# crossings draw,touslesrect,transmrelax 101 -# diagram * draw 45 -# draw * transmrelax 3 -# petirond touslesrect 19 -# grorond touslesrect 38 -# touslesrect transmrelax 15 -# tracerect * transmrelax 66 -# bonsens neworder 22 -# rectordre neworder 34 -# neworder transmrelax 21 -# lexnum transmission,relaxable,arel,relaxation 11 -# numlex transmission,relaxation 15 -# transmission transmrelax 80 -# relaxable transmrelax 84 -# arel transmrelax 49 -# cross relaxation 91 -# relaxation transmrelax 118 -# transmrelax - 87 -# invers - 9 -# -# * plotting functions - -lang := `english`: - -with(plots): - -if lang = `english` then - mouvement_spirallant := `spiralling move`: - le_diagramme_de_tresse_est := `The curve diagram of the braid is:`: - les_rectangles_sont_maintenant := `The rectangles are now:`: - apres_transmission_les_rectangles_sont := `After transmission the rectangles are:`: - avant_de_pouvoir_relaxer_une_nouvelle_transmission_est_necessaire := `Before being able to relax, a new transmission is needed`: - on_peut_alors_relaxer_par_la_tresse := `We can then relax using the braid `: - de_longueur := ` with length `: - le_nouveau_diagramme_de_tresse_est_maintenant := `The new curve diagram for the braid is now:`: - la_longueur_totale_de_la_tresse_est := `The total length of the braid is:`: - la_tresse_totale_utilisee_pour_demeler_est := `The total braid used to untangle is:`: -elif lang = `francais` then - mouvement_spirallant := `mouvement spirallant`: - le_diagramme_de_tresse_est := `Le diagramme de tresse est:`: - les_rectangles_sont_maintenant := `Les rectangles sont maintenant:`: - apres_transmission_les_rectangles_sont := `Apres transmission les rectangles sont:`: - avant_de_pouvoir_relaxer_une_nouvelle_transmission_est_necessaire := `Avant de pouvoir relaxer, une nouvelle transmission est necessaire`: - on_peut_alors_relaxer_par_la_tresse := `On peut alors relaxer par la tresse `: - de_longueur := ` de longueur `: - le_nouveau_diagramme_de_tresse_est_maintenant := `Le nouveau diagramme de tresse est maintenant:`: - la_longueur_totale_de_la_tresse_est := `La longueur totale de la tresse est:`: - la_tresse_totale_utilisee_pour_demeler_est := `La tresse totale utilisee pour demeler est:`: -else - error "unknown language %1", lang -fi: - - -crossings:=proc(b,n) -local i,j,k,tot,K1,K2,K,counter,y2,l,t,circles,newcircles,y,d,u,p,x,join; - for i from 1 to nops(b) do - if b[i]<=-n or b[i]>=n then - error "the indices of the letters must be smaller than n" - fi; - if b[i]=0 then - error "the indices of the letters must be nonzero" - fi; - od; - circles:=[[],[]]; - circles[1]:=[[0,0,seq(1,i=1..n-1),0],[seq(0,j=1..n+2)],seq([1,seq(0,j=1..n+1)],i=1..n-1),[seq(0,j=1..n+2)]]; - circles[2]:=[[0,0,seq(1,i=1..n-1),0],[seq(0,j=1..n+2)],seq([1,seq(0,j=1..n+1)],i=1..n-1),[seq(0,j=1..n+2)]]; - for i from 1 to nops(b) do - if b[i]>0 then u:=1: d:=2: p:=b[i]: else u:=2: d:=1: p:=-b[i]: - fi: - newcircles:=circles: - for j from 1 to n+2 do - x:=circles[u][p+2][j]: - if j<>p+2 and j<>p+3 and x>0 then - newcircles[u][j][p+2]:=newcircles[u][j][p+2]-x: - newcircles[u][p+2][j]:=newcircles[u][p+2][j]-x: - newcircles[u][p+1][p+2]:=newcircles[u][p+1][p+2]+x: - newcircles[u][p+2][p+1]:=newcircles[u][p+2][p+1]+x: - newcircles[u][j][p+3]:=newcircles[u][j][p+3]+x: - newcircles[u][p+3][j]:=newcircles[u][p+3][j]+x: - newcircles[d][p+2][p+3]:=newcircles[d][p+2][p+3]+x: - newcircles[d][p+3][p+2]:=newcircles[d][p+3][p+2]+x: - fi; - if j=p+3 and x>0 then - newcircles[u][p+2][p+3]:=newcircles[u][p+2][p+3]-x: - newcircles[u][p+3][p+2]:=newcircles[u][p+3][p+2]-x: - newcircles[u][p+1][p+2]:=newcircles[u][p+1][p+2]+x: - newcircles[u][p+2][p+1]:=newcircles[u][p+2][p+1]+x: - fi; - y:=circles[d][p+2][j]: - if j<>p+2 and y>0 then - newcircles[d][p+2][j]:=newcircles[d][p+2][j]-y: - newcircles[d][j][p+2]:=newcircles[d][j][p+2]-y: - newcircles[d][p+1][j]:=newcircles[d][p+1][j]+y: - newcircles[d][j][p+1]:=newcircles[d][j][p+1]+y: - fi; - od; - K:=circles[u][p+2][p+3]: - counter:=0: - for j from p+1 to 1 by -1 do - y:=circles[d][p+3][j]: - if y>0 and counter0 and counter0 then - join:=[seq(0,k=1..n+2)]: - y:=0: - for j from p+3 to n+2 do - if sum(join[l],l=1..n+2)0 then - newcircles[u][j][p+1]:=newcircles[u][j][p+1]-join[j]: - newcircles[u][p+1][j]:=newcircles[u][p+1][j]-join[j]: - newcircles[u][p+1][p+2]:=newcircles[u][p+1][p+2]-join[j]: - newcircles[u][p+2][p+1]:=newcircles[u][p+2][p+1]-join[j]: - newcircles[u][j][p+2]:=newcircles[u][j][p+2]+join[j]: - newcircles[u][p+2][j]:=newcircles[u][p+2][j]+join[j]: - fi; - od; - fi; - circles:=newcircles; - od; - return circles; -end: - -diagram:=proc(c) -local i,j,k,r,x,y,n,t,left,right,counterx,countery,circup,circdown,centr,radius,total; - n:=nops(c[1])-2: - total:=0: - r:=[seq(0,i=1..n+2)]: - for i from 1 to n+2 do - r[i]:=sum(c[1][i][k],k=1..n+2)+1: - for j from 1 to n+2 do - total:=total+c[1][i][j]: - od: - od: - total:=total/2: - counterx:=0; - countery:=0; - circup:=array(1..total): - circdown:=array(1..total): - for i from 1 to n+1 do - for j from i+1 to n+2 do - x:=c[1][i][j]; - y:=c[2][i][j]; - if x>0 then - left:=sum(c[1][i][l],l=i+1..j-1): - right:=sum(c[1][j][l],l=i+1..j-1): - for k from 1 to x do - centr:=((i-1-(left+k)/r[i])+(j-2+(right+k)/r[j]))/2: - radius:=centr-(i-1-(left+k)/r[i]): - circup[counterx+k]:=plot([centr+radius*cos(t),radius*sin(t),t=0..Pi]); - od; - counterx:=counterx+x; - fi; - if y>0 then - left:=sum(c[2][i][l],l=i+1..j-1): - right:=sum(c[2][j][l],l=i+1..j-1): - for k from 1 to y do - centr:=((i-1-(left+k)/r[i])+(j-2+(right+k)/r[j]))/2: - radius:=centr-(i-1-(left+k)/r[i]): - circdown[countery+k]:=plot([centr+radius*cos(t),radius*sin(t),t=Pi..2*Pi]): - od; - countery:=countery+y; - fi; - od; - od; - print(display({seq(circup[i],i=1..counterx),seq(circdown[i],i=1..countery)},scaling=constrained)); - return: -end: - -### Type "draw([1,-2,1],3);" in order to see the curve diagram of the -### 3-strand braid sigma_1 sigma_2^{-1} sigma_1 -draw:=proc(a,b) - return diagram(crossings(a,b)); -end: - -petirond := proc(c) -local i,j,k,e,f,A,B,L,n : - n := nops(c[1][1])-2 : - L := NULL : - for i from 1 to n+2 do - k:=1+sum('c[2][i][l]','l'=1..i) ; - for j from n+2 to i+1 by -1 do - if c[2][i][j]>0 then - f:=c[2][i][j] ; e:=sum('c[2][j][l]','l'=i+1..j) ; - A:=[[i,k],[i,k+f-1]] ; B:=[[j,1+e],[j,f+e]] ; - k := k+f ; - L := L,[[A,B],-1] ; - fi ; - od; - od; - - return [L]; - -end: - -grorond := proc(L,c) -local i,j,k,m,n,recol ,g,h, V; - m := nops(L) ; - n := nops(c[1])-2 ; - recol:=[seq(0,i=1..m)] ; - for i from 1 to m-1 do - - if L[i][1][2][1][1]>1 then - - if L[i][1][2][1][2]>1 - then - if L[i][1][2][1]=L[i+1][1][2][2]+[0,1] then - recol[i]:=1 ; - fi; - else g:=round(L[i+1][1][2][2][1]); h:=eval(sum('c[1][g][j]','j=1..n+2')); - if - L[i][1][2][1]=L[i+1][1][2][2]+[1,1-h] then - recol[i]:=1 ; - fi; - fi; - - fi; - od; - - V:=NULL: - j:=1; - while j <= m do - if recol[j]=0 - then V := V,L[j] : - else k:=j : - while recol[j]=1 do - j:=j+1 od : - V:=V,[[[L[k][1][1][1],L[j][1][1][2]],[L[j][1][2][1],L[k][1][2][2]]],-1] : - fi; - j:=j+1: - od; - return V; -end: - -touslesrect := proc(b,n) -### THERE WAS A BUG IN THE ORIGINAL PROGRAM - THE SUMMARIZING OF ARCS -### INTO BANDS WENT WRONG, BUT ONLY IN THE UPPER HALF. BERT WIEST -### CORRECTED THIS BUG IN AN AWFULLY HACKY WAY, BY GLUING TOGETHER THE -### LOWER HALF OF THE TRUE BRAID WITH THE REFLECTION OF THE LOWER HALF -### OF THE BRAID WHERE ALL CROSSINGS ARE REPLACED BY THEIR NEGATIVE. -local P,c,c2,m,j : - c := crossings(b,n) ; - c2 := crossings(b*(-1),n);m := nops([grorond(petirond(c2),c2)]); - P := grorond(petirond(c2),c2),grorond(petirond(c),c); -### for j from 1 to m do THIS DOESN'T WORK, I (B.W.) DON'T UNDERSTAND WHY) -### P[j][2] := 1; -### od; - return [P],m; -end: - -tracerect := proc(c,L) -local n,m,i,j,k,q,P,Q,R,S,rect,inter,nbsegrect,pt1,pt2,pt3,pt4,ray1,ray2,T,centre1,centre2,A,B,E,C,epsilon ; - - n:=nops(c[1])-2; - m := nops(L) ; - inter := array[1..n+2] ; - for j from 1 to n+2 do - inter[j] := sum('c[1][j][l]','l'=1..n+2)+1 ; - od; - - for i from 1 to m do - rect := L[i] : - nbsegrect[i] := nops(rect[1]); - - epsilon := rect[2]; - for k from 1 to nbsegrect[i]-1 do - - if rect[1][k][1][1]pt1) and (pt2>pt4) then - R[i] := plot([t,eval(L[i][2])*0.03,t=pt1..pt3]): - S[i] := plot([t,eval(L[i][2])*(-1)^(nbsegrect[i])*0.03,t=pt4..pt2]): - else - R[i] := plot([t,eval(L[i][2])*0.03,t=pt1-0.02..pt1+0.02]): - S[i] := plot([t,eval(L[i][2])*(-1)^(nbsegrect[i])*0.03,t=pt2-0.02..pt2+0.02]): - fi; - - od: - A := NULL ; - for i from 1 to m do - for k from 1 to nbsegrect[i]-1 do - A:=A,[P[i][k],Q[i][k]]: - od: - A:=A,[R[i],S[i]] - od: - display(A,scaling=constrained); -end: - -bonsens := proc(R) -local m, epsilon,i,RR: - m := nops(R[1]): - epsilon := 1 ; - RR := R ; - if R[1][1][1][1]>R[1][m][1][1] - then epsilon := -1 - fi; - if (R[1][1][1][1]=R[1][m][1][1]) and (R[1][1][1][2]>R[1][m][1][2]) - then epsilon := -1; - fi; - - if epsilon = -1 then - for i from 1 to m do - RR[1][i] := R[1][m-i+1]; - od: - - RR[2]:=R[2]*(-1)^m ; - - fi: - return RR; -end: - -rectordre := proc(R,T) -local mr,mt,reponse : - mr:= nops(R[1]) : mt:=nops(T[1]) : - reponse := 0 : - if R[1][mr][2][1]>T[1][mt][2][1] - then reponse:=1 fi; - - if R[1][mr][2][1]=T[1][mt][2][1] - then - if R[1][mr][2][2]>T[1][mt][2][2] - then reponse := 1 fi; - - if R[1][mr][2][2]=T[1][mt][2][2] - then - if R[1][mr][1][1]0) do - k:=k+1: - od: - k:=k : - m:=nb-eval(sum('A[i]','i'=1..k-1)) : - return [k,m]; -end: - -transmission:=proc(L,c) -local H,g,h,a,b,aa,bb,k,l,m,i,j,AB,Ab,u,v,uu,vv,Segp,Segv,compteur,larg,LL,LLL: - m:=nops(L); - H:=L[m]: - g:=lexnum(H[1][eval(nops(H[1]))][1],c): - h:=lexnum(H[1][eval(nops(H[1]))][2],c): - LL:=L: - LLL:=L: - i:=m-1: - l:=0: - - if m>1 then - while (i>0) and (lexnum(L[i][1][eval(nops(L[i][1]))][1],c)>=g) do - Segp := NULL : Segv := NULL: - compteur:=0: - AB:=L[i][1][eval(nops(L[i][1]))]: - aa:=lexnum(AB[1],c): - bb:=lexnum(AB[2],c): - - Ab:=L[i][1][1]: - a:=lexnum(Ab[1],c): - b:=lexnum(Ab[2],c): - - k:=eval(nops(H[1]))-1: - while (aa>=g)and(bb<=h) do - l:=l+bb-aa+1: - for j from k to 1 by -1 do - if modp(k-j,2)=0 - then - uu:=lexnum(H[1][j][1],c)+h-bb: - vv:=lexnum(H[1][j][1],c)+h-aa: - - else - uu:=lexnum(H[1][j][2],c)-(h-aa): - vv:=lexnum(H[1][j][2],c)-(h-bb): - fi; - Segp:=Segp,[numlex(uu,c),numlex(vv,c)]: - od: - aa:=uu: - bb:=vv: - od: - - while (a>=g)and(b<=h) do - l:=l+b-a+1: - for j from k to 1 by -1 do - if modp(k-j,2)=0 - then - u:=lexnum(H[1][j][1],c)+h-b: - v:=lexnum(H[1][j][1],c)+h-a: - - else - u:=lexnum(H[1][j][2],c)-(h-a): - v:=lexnum(H[1][j][2],c)-(h-b): - fi: - Segv:=[numlex(u,c),numlex(v,c)],Segv: - od: - a:=u: - b:=v: - compteur:=compteur+1: - od: - - - LL[i]:=[[Segv,op(L[i][1]),Segp],eval(L[i][2])*(-1)^(compteur*k)]: - i:=i-1: - od: - - larg:=h-g-l: - - if larg<0 then LLL:=[seq(LL[i],i=1..m-1)] - else for j from k+1 to 1 by -1 do - if modp(k+1-j,2)=0 - then H[1][j]:=[H[1][j][1],numlex(lexnum(H[1][j][1],c)+larg,c)] - else H[1][j]:=[numlex(lexnum(H[1][j][2],c)-larg,c),H[1][j][2]] - fi: - od: - LLL:=[seq(LL[i],i=1..m-1),H] - fi: - fi; - return LLL; -end: - -relaxable := proc(L,c) -local m,i,j,k,n,mmaaxx,ind,IND ; - n := nops(L) ; - ind := NULL ; - IND:=NULL; - m := array[1..n] ; - for i from 1 to n do - m[i] := nops(L[i][1]) : - if m[i]>=4 then ind:=ind,i fi: - od: - ind := [ind]: - - for k from 1 to nops(ind) do - - for j from 2 to m[eval(ind[k])]-1 do - if lexnum(L[eval(ind[k])][1][j][2],c)+1=lexnum(L[eval(ind[k])][1][j+1][1],c) - then IND:=[ind[k],j,1,lexnum(L[eval(ind[k])][1][j][2],c)+1],IND - fi; - - if lexnum(L[eval(ind[k])][1][j+1][2],c)+1=lexnum(L[eval(ind[k])][1][j][1],c) - then IND:=[ind[k],j,-1,lexnum(L[eval(ind[k])][1][j+1][2],c)+1],IND - fi; - - od; - od;IND:=[IND]: - if nops(IND)>0 - then mmaaxx:=1; - for i from 1 to eval(nops(IND)) do - if IND[i][4]>=IND[mmaaxx][4] then mmaaxx:=i fi; - od; - return IND[mmaaxx]; - else return IND; - fi; -end: - -arel:=proc(IND,L,c,showsteps) -local i,j,LL,IN,IN1,d,g,Tr,k; - IN:=IND: - IN1:=IND[1]: - Tr:=0: - LL:=L: - for i from 1 to nops(L) do - for j from 1 to nops(L[i][1]) do - LL[i][1][j][1]:=lexnum(L[i][1][j][1],c): - LL[i][1][j][2]:=lexnum(L[i][1][j][2],c) - od; - od; - - if IN[3]=1 then g:=LL[IN[1]][1][IN[2]][1]: - d:=LL[IN[1]][1][IN[2]+1][2] - else g:=LL[IN[1]][1][IN[2]+1][1]: - d:=LL[IN[1]][1][IN[2]][2] - fi; - - k:=1: - while k=1 do - k:=0: - for i from 1 to nops(LL) do - for j from 1 to nops(LL[i][1])-1 do - if (LL[i][1][j][2]=g-1) and (LL[i][1][j+1][1]=d+1) - then if i=IN1 then if showsteps then print(mouvement_spirallant) fi; - else k:=1: - g:=LL[i][1][j][1]: - d:=LL[i][1][j+1][2]: - IN:=IN,[i,j,1]: - IN1:=i: - if (j=1) or (j=nops(LL[i][1])-1) then Tr:=1 fi; - fi; - fi; - if (LL[i][1][j+1][2]=g-1) and (LL[i][1][j][1]=d+1) - then if i=IN1 then if showsteps then print(mouvement_spirallant) fi; - else k:=1: - g:=LL[i][1][j+1][1]: - d:=LL[i][1][j][2]: - IN:=IN,[i,j,-1]: - IN1:=i: - if (j=1) or (j=nops(LL[i][1])-1) then Tr:=1 fi; - fi; - fi; - od; - od; - od; - return [IN],Tr -end: - -cross:=proc(c,b,n) -local circles,newcircles,i,j,k,l,K,join,counter,x,y,y2,cc,u,d,p; - circles:=c; - for i from 1 to nops(b) do - if b[i]>0 then u:=1: d:=2: p:=b[i]: else u:=2: d:=1: p:=-b[i]: - fi: - newcircles:=circles: - for j from 1 to n+2 do - x:=circles[u][p+2][j]: - if j<>p+2 and j<>p+3 and x>0 then - newcircles[u][j][p+2]:=newcircles[u][j][p+2]-x: - newcircles[u][p+2][j]:=newcircles[u][p+2][j]-x: - newcircles[u][p+1][p+2]:=newcircles[u][p+1][p+2]+x: - newcircles[u][p+2][p+1]:=newcircles[u][p+2][p+1]+x: - newcircles[u][j][p+3]:=newcircles[u][j][p+3]+x: - newcircles[u][p+3][j]:=newcircles[u][p+3][j]+x: - newcircles[d][p+2][p+3]:=newcircles[d][p+2][p+3]+x: - newcircles[d][p+3][p+2]:=newcircles[d][p+3][p+2]+x: - fi; - if j=p+3 and x>0 then - newcircles[u][p+2][p+3]:=newcircles[u][p+2][p+3]-x: - newcircles[u][p+3][p+2]:=newcircles[u][p+3][p+2]-x: - newcircles[u][p+1][p+2]:=newcircles[u][p+1][p+2]+x: - newcircles[u][p+2][p+1]:=newcircles[u][p+2][p+1]+x: - fi; - y:=circles[d][p+2][j]: - if j<>p+2 and y>0 then - newcircles[d][p+2][j]:=newcircles[d][p+2][j]-y: - newcircles[d][j][p+2]:=newcircles[d][j][p+2]-y: - newcircles[d][p+1][j]:=newcircles[d][p+1][j]+y: - newcircles[d][j][p+1]:=newcircles[d][j][p+1]+y: - fi; - od; - K:=circles[u][p+2][p+3]: - counter:=0: - for j from p+1 to 1 by -1 do - y:=circles[d][p+3][j]: - if y>0 and counter0 and counter0 then - join:=[seq(0,k=1..n+2)]: - y:=0: - for j from p+3 to n+2 do - if sum(join[l],l=1..n+2)0 then - newcircles[u][j][p+1]:=newcircles[u][j][p+1]-join[j]: - newcircles[u][p+1][j]:=newcircles[u][p+1][j]-join[j]: - newcircles[u][p+1][p+2]:=newcircles[u][p+1][p+2]-join[j]: - newcircles[u][p+2][p+1]:=newcircles[u][p+2][p+1]-join[j]: - newcircles[u][j][p+2]:=newcircles[u][j][p+2]+join[j]: - newcircles[u][p+2][j]:=newcircles[u][p+2][j]+join[j]: - fi; - od; - fi; - circles:=newcircles; - od; - return circles; -end: - -relaxation:=proc(L,IND,c) -local i,j,ni,k,l,m,IN,n,maxi,nbfil,NBFIL,LL,b,bb,pta,ptd,e,epsilon,circles,cc,newcircles,u,d,p,x,y,K,join,counter,y2; - IN:=IND: - LL:=L: - for i from 1 to nops(LL) do - for j from 1 to nops(LL[i][1]) do - LL[i][1][j][1]:=lexnum(LL[i][1][j][1],c): - LL[i][1][j][2]:=lexnum(LL[i][1][j][2],c) - od; - od; - bb:=NULL: - ni:=nops(IND): - epsilon:=L[IN[1][1]][2]*(-1)^(IN[1][2]): - - NBFIL:=0: - K:=0: - - if IN[ni][3]=1 then e:=1 else e:=0 fi: - ptd:=L[IN[ni][1]][1][IN[ni][2]+e][2][1]-2: - nbfil:=LL[IN[ni][1]][1][1][2]-LL[IN[ni][1]][1][1][1]+1: - NBFIL:=NBFIL+nbfil: - maxi:=LL[IN[ni][1]][1][IN[ni][2]+e][2]; - - if nbfil>1 then - for j from nbfil-1 to 1 by -1 do - - if numlex (j+LL[IN[ni][1]][1][IN[ni][2]+e][1],c)[1] - >numlex (j+LL[IN[ni][1]][1][IN[ni][2]+e][1]-1,c)[1] - then - - k:=LL[IN[ni][1]][1][IN[ni][2]-1+3*e][1]+nbfil-j: - pta:=numlex(k,c)[1]-1+K: - K:=K+1: - - if pta=0 then error "pta = 0": return 'A'; fi: - if pta= ptd (pta = %1, ptd = %2)", pta, ptd - fi; - fi; - od;fi; - - if ni>1 then - for i from ni-1 to 1 by -1 do - nbfil:=LL[IN[i][1]][1][1][2]-LL[IN[i][1]][1][1][1]+1: - NBFIL:=NBFIL+nbfil: - - if IN[i][3]=1 then e:=1 else e:=0 fi: - - for j from nbfil to 1 by -1 do - if numlex (j+LL[IN[i][1]][1][IN[i][2]+e][1],c)[1] - >numlex (j+LL[IN[i][1]][1][IN[i][2]+e][1]-1,c)[1] - then - - k:=LL[IN[i][1]][1][IN[i][2]-1+3*e][1]+nbfil-j: - pta:=numlex(k,c)[1]-1+K: - K:=K+1: - - if pta=0 then error "pta = 0": return 'A'; fi: - if pta= ptd (pta = %1, ptd = %2)", pta, ptd - fi; - fi; - od; - od;fi; - - - - for i from 1 to ni do - if IN[i][3]=1 then e:=0 else e:=1 fi: - nbfil:=LL[IN[i][1]][1][1][2]-LL[IN[i][1]][1][1][1]+1: - - for j from nbfil to 1 by -1 do - if numlex (j+LL[IN[i][1]][1][IN[i][2]+e][1],c)[1] - >numlex (j+LL[IN[i][1]][1][IN[i][2]+e][1]-1,c)[1] - then - - k:=LL[IN[i][1]][1][IN[i][2]-1+3*e][1]+nbfil-j: - pta:=numlex(k,c)[1]-1+K: - K:=K+1: - - if pta=0 then error "pta = 0": return 'A'; fi: - if pta= ptd (pta = %1, ptd = %2)", pta, ptd - fi; - fi; - od; - od; - - for m from 1 to ni do - LL[IN[m][1]][1]:=[seq(LL[IN[m][1]][1][p],p=1..eval(IN[m][2])-1), - seq(LL[IN[m][1]][1][p],p=eval(IN[m][2])+2..nops(LL[IN[m][1]][1]))] - od; - - - for i from 1 to nops(LL) do - for j from 1 to nops(LL[i][1]) do - if LL[i][1][j][1]>maxi then LL[i][1][j][1]:=LL[i][1][j][1]-2*NBFIL: - LL[i][1][j][2]:=LL[i][1][j][2]-2*NBFIL fi: - od; - od; - n:=nops(c[1])-2: - b:=[bb]: - cc:=cross(c,b,n); - - for i from 1 to nops(LL) do - for j from 1 to nops(LL[i][1]) do - LL[i][1][j][1]:=numlex(LL[i][1][j][1],cc): - LL[i][1][j][2]:=numlex(LL[i][1][j][2],cc) - od; - od; - return [LL,cc,[bb]]; -end: - -transmrelax:=proc(b,n,{showsteps := false}) -local mm,X,j,c,L,M,T,ctrivial,B,R,bb,BD,lon,Long,IND,AR,nar; - - ctrivial:=[[],[]]: - ctrivial[1]:=[[0,0,seq(1,i=1..n-1),0],[seq(0,j=1..n+2)],seq([1,seq(0,j=1..n+1)],i=1..n-1),[seq(0,j=1..n+2)]]: - ctrivial[2]:=[[0,0,seq(1,i=1..n-1),0],[seq(0,j=1..n+2)],seq([1,seq(0,j=1..n+1)],i=1..n-1),[seq(0,j=1..n+2)]]: - c := crossings(b,n): - X := touslesrect(b,n) : - L := X[1] :mm := X[2] : - for j from 1 to mm do - L[j][2] := 1; - od; - B:=b: - BD:=[]: - Long:=0; - if showsteps then - print(le_diagramme_de_tresse_est); - draw(B,n); - fi; - while c<>ctrivial do - if showsteps then - print(les_rectangles_sont_maintenant); - print(tracerect(c,L)); - fi; - M := neworder(L): - T := transmission(M,c) : - if showsteps then - print(apres_transmission_les_rectangles_sont); - print(tracerect(c,T)); - fi; - bb:=[];lon:=1; - IND:=relaxable(T,c): - if nops(IND)>=1 then AR:=[arel(IND,T,c,showsteps)] fi: - - while nops(IND)>=1 do - - while AR[2]=1 do - M := neworder(T): - T := transmission(M,c): - if showsteps then - print(avant_de_pouvoir_relaxer_une_nouvelle_transmission_est_necessaire): - print(tracerect(c,T)); - fi; - IND:=relaxable(T,c): - AR:=[arel(IND,T,c,showsteps)]: - od; - - R:=relaxation(T,AR[1],c): - if R=A then nar:=nops(AR[1]): - if nar>1 then - AR[1]:=[seq(AR[1][m],m=1..nar-1)]: - else return ERREUR? - fi: - else - T:=R[1]: - c:=R[2]: - IND:=relaxable(T,c): - B:=[op(B),op(R[3])]; - bb:=[op(bb),op(R[3])]; - BD:=[op(BD),op(R[3])]; - lon:=lon+1: - if nops(IND)>=1 then - if c<>ctrivial then - AR:=[arel(IND,T,c,showsteps)] - fi: - fi; - fi; - od; - lon:=ln(lon)/ln(2); - Long:=Long+lon; - L:=T: - - if showsteps then - if nops(bb)>=1 then - print(on_peut_alors_relaxer_par_la_tresse, bb ,de_longueur,lon); - print(le_nouveau_diagramme_de_tresse_est_maintenant); - draw(B,n); - fi; - fi; - - od; - - print(la_longueur_totale_de_la_tresse_est,Long,`ie`,evalf(Long)); - print(la_tresse_totale_utilisee_pour_demeler_est,BD); - - return BD; -end: - -invers:=proc(b) -local i,m,B; - m := nops(b); - B := b; - for i to m do - B[i] := -b[m+1-i] - end do; - return B; -end: diff --git a/devel/research/DynnikovWiest/TransmRelax_example.mw b/devel/research/DynnikovWiest/TransmRelax_example.mw deleted file mode 100644 index 256a126d..00000000 --- a/devel/research/DynnikovWiest/TransmRelax_example.mw +++ /dev/null @@ -1,115 +0,0 @@ - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -QyQqJkkickc2IiIiIkknZXN0YXJ0R0YlRiYhIiI= - - - - -QVEwVHJhbnNtUmVsYXgubXBsNiI= - - - - -QyY+SSJiRzYiNyohIiJGJyIiIyEiJEYpIiIlRigiIiQiIiI+SSJuR0YlIiImRiw= - - - - -QyQ+SSNCREc2Ii1JLHRyYW5zbXJlbGF4R0YlNiVJImJHRiVJIm5HRiUvSSpzaG93c3RlcHNHRiVJJXRydWVHJSpwcm90ZWN0ZWRHIiIi - - - - -QyY+SSJCRzYiLUknaW52ZXJzR0YlNiNJI0JER0YlIiIiLUklZHJhd0dGJTYkRiQiIiZGKg== - - - \ No newline at end of file diff --git a/devel/research/closure_tests.m b/devel/research/closure_tests.m deleted file mode 100644 index 2487e4ca..00000000 --- a/devel/research/closure_tests.m +++ /dev/null @@ -1,134 +0,0 @@ -import braidlab.* - -% Try all ways to close a braid of trajectories by drawing straight -% segments to the initial points. - -% Compute TN class and entropy. - -n = 6; -docompact = true; -dotntype = true; -permpregen = true; -paralyze = true; - -% Should try a random braid obtained from duffing or something similar, -% to have a coherent structure. -rng(0); XY = randomwalk(n,300,.1); - -poolobj = gcp('nocreate'); % If no pool, do not create new one. -if paralyze - % Open pool of workers if it isn't already allocated. - if isempty(poolobj) - parpool('local'); - end -else - % Close pool of workers. - if ~isempty(poolobj) - delete(poolobj) - end -end - -if paralyze - pctRunOnAll warning('off','BRAIDLAB:braid:colorbraiding:coincident') - pctRunOnAll warning('off','BRAIDLAB:braid:entropy:noconv') -else - warning('off','BRAIDLAB:braid:colorbraiding:coincident') - warning('off','BRAIDLAB:braid:entropy:noconv') -end - -cl = {'r' 'g' 'b' 'm' 'c' 'y' 'k'}; - -figure(1) -for k = 1:size(XY,3) - plot3(XY(:,1,k),XY(:,2,k),1:size(XY,1),cl{mod(k-1,length(cl))+1}), hold on -end -hold off - -N = factorial(n); -tn = zeros(1,N); -entr = zeros(1,N); -tntext = cell(1,N); - -P = permheap(n); % pre-generate the permutations. - -parfor i = 1:N - disp(i) - XYc = braidlab.closure(XY,P(i,:)); - b = braidlab.braid(XYc); - if docompact, b = compact(b); end - try - [tntext{i},entr(i)] = tntype(b); - catch err - entr(i) = 0; - tntext{i} = 'error'; - end - switch tntext{i} - case 'pseudo-Anosov' - tn(i) = 2; - case 'reducible' - tn(i) = 1; - if entr(i) == 0, entr(i) = entropy(b); end - case 'finite-order' - tn(i) = 0; - case 'error' - tn(i) = -1; - entr(i) = entropy(b); - otherwise - error - end -end - -fprintf('\nFinal count:\n\n') -fprintf('pseudo-Anosov %d\n',length(find(tn == 2))) -fprintf('reducible %d\n',length(find(tn == 1))) -fprintf('finite-order %d\n',length(find(tn == 0))) -fprintf('error %d\n',length(find(tn == -1))) -fprintf('-------------\n') -fprintf('total %d\n',length(tn)) -fprintf('\n') -entrnz = entr(find(entr ~= 0)); -fprintf('entropy mean: %f (%f for nonzeros)\n',mean(entr),mean(entrnz)) -fprintf('entropy std: %f (%f for nonzeros)\n',std(entr),std(entrnz)) - -% Sort according to type. -[tn,itn] = sort(tn); -entr = entr(itn); -P(:,:) = P(itn,:); - -figure(2) -clf -subplot(2,1,1) -h = bar(entr,'b'); -set(h,'EdgeColor',get(h,'FaceColor')); -axis tight -ylabel('entropy') - -subplot(2,1,2) -h = bar(double(tn == 2),'b'); -set(h,'EdgeColor',get(h,'FaceColor')); -hold on -h = bar(double(tn == 1),'r'); -set(h,'EdgeColor',get(h,'FaceColor')); -h = bar(double(tn == 0),'w'); -set(h,'EdgeColor',get(h,'FaceColor')); -hold off -axis tight -xlabel('permutation') -ylabel('TN type') -title('white - finite-order red - reducible blue - pA') - -entrmindist = entropy(braid(closure(XY,'mindist'))); -entrxproj = entropy(braid(closure(XY,'Xproj'))); -entryproj = entropy(braid(closure(XY,'Yproj'))); - -figure(3) -hist(entr,20) -hold on -aa = axis; -plot(entrmindist*[1 1],[0 aa(4)],'r-','LineWidth',2) -plot(entrxproj*[1 1],[0 aa(4)],'g--','LineWidth',2) -plot(entryproj*[1 1],[0 aa(4)],'c--','LineWidth',2) -hold off -xlabel('entropy') -ylabel('count') -legend('','mindist','Xproj','Yproj','Location','NorthWest') diff --git a/devel/research/duffing.m b/devel/research/duffing.m deleted file mode 100644 index db695ef0..00000000 --- a/devel/research/duffing.m +++ /dev/null @@ -1,23 +0,0 @@ -function yr = duffing(t,y) - -global delta gamma - -Xr = y(1,:); -Yr = y(2,:); - -Omega = 1/6; - -X = Xr.*cos(Omega.*t)+Yr.*sin(Omega.*t); -Y = -Xr.*sin(Omega.*t)+Yr.*cos(Omega.*t); - -delta = .08; gamma = .14; omega = 1; - -Xp = Y +.1*cos(omega*t); -Yp = X.*(1-X.^2)+gamma.*cos(omega*t)-delta*Y; - -Xdotr = Xp.*cos(Omega*t)-X*Omega*sin(Omega*t)-Yp.*sin(Omega*t)-Y*Omega*cos(Omega*t); -Ydotr = Xp.*sin(Omega*t)+X*Omega*cos(Omega*t)+Yp.*cos(Omega*t)-Y*Omega*sin(Omega*t); - -yr = zeros(size(y)); -yr(1,:) = Xdotr; -yr(2,:) = Ydotr; \ No newline at end of file diff --git a/devel/research/monster.m b/devel/research/monster.m deleted file mode 100644 index f7057d55..00000000 --- a/devel/research/monster.m +++ /dev/null @@ -1,14 +0,0 @@ -function sig = monster -%MONSTER The 36-string monster braid for two pairs of counter-rotating rods. - -sig = [5 13 4 -22 -28 12 -26 34 -17 -31 -19 35 16 -27 -14 17 -29 3 -25 18 ... - -26 -9 -28 -30 2 15 -23 -17 19 -29 -21 1 -27 -33 14 16 -11 -28 -34 ... - 2 8 -19 -20 -22 25 3 9 19 -35 15 7 13 -21 27 -34 6 8 -18 10 11 -33 ... - -19 22 7 -20 -1 9 19 17 5 -2 10 14 -24 8 -32 -23 -31 -25 -30 -32 ... - -33 -22 -32 6 9 -24 -26 -31 18 -21 -25 -29 -34 -32 -30 -33 -3 -23 ... - -27 -32 7 -24 23 -26 -22 -23 -31 -32 -2 8 -25 -24 -1 3 27 -20 2 25 ... - -33 1 16 -19 15 -34 2 -21 17 -11 -20 -35 3 16 -34 -9 -33 35 12 11 ... - -28 34 4 13 14 5 -13 12 -29 4 10 13 33 3 6 9 4 15 7 11 2 5 10 12 ... - -18 14 -22 -27 -30 4 6 11 3]; - -sig = braidlab.braid(sig); diff --git a/devel/research/permheap.m b/devel/research/permheap.m deleted file mode 100644 index f12a8e03..00000000 --- a/devel/research/permheap.m +++ /dev/null @@ -1,77 +0,0 @@ -function [varargout] = permheap(P,c) -%PERMHEAP Heap's algorithm for generating permutations by interchanges. -% [P,C] = PERMHEAP(P,C) returns a new permutation given a permutation P. -% C is a bookeeping vector which should be first initialized to ones(1,N), -% where N is the order of the permutation. The function uses Heap's -% algorithm, which interchanges entries of P at each call until all -% permutations have been produced. -% -% [P,C,NOTDONE] = PERMHEAP(P,C) sets NOTDONE to false after all -% permutations have been cycled over. -% -% [P,C] = PERMHEAP(N) initializes P to 1:N and C to ones(1,N). -% -% A typical use of PERMHEAP is as follows, which lists all permutations -% of N integers: -% -% [P,C] = permheap(N); notdone = true; -% while notdone -% disp(P) -% [P,C,notdone] = permheap(P,C); -% end -% -% PERMHEAP does not pre-generate the permutations, so memory is not -% wasted in storing a large number (N!) of permutations. -% -% If memory is not an issue, PP = PERMHEAP(N) returns an array PP of -% dimension N! by N giving all the permutations at once, in the same order -% that PERMHEAP would normally return them. -% -% Reference: R. Segdewick, "Permutation Generation Methods," Computing -% Surveys 9 (1977), 137-164. - -if nargin < 2 - if nargout == 2 - % Just initialize P and C. - varargout{1} = 1:P; - varargout{2} = ones(1,P); - return - else - % Return the entire list at once. - % (Use MEX file for this? Probably not worth it for the rest of the - % file, since the function call overhead probably makes this - % impractical for truly large problems.) - n = P; - N = factorial(n); - [p,c] = permheap(n); - varargout{1} = zeros(N,n); - for i = 1:N - varargout{1}(i,:) = p; - [p,c] = permheap(p,c); - end - return - end -end - -for i = 1:length(P) - if c(i) < i - if mod(i,2) == 0 - j = c(i); - else - j = 1; - end - % Swap content of P(i) and P(j). - temp = P(j); P(j) = P(i); P(i) = temp; - c(i) = c(i) + 1; - varargout{1} = P; - if nargout > 1, varargout{2} = c; end - if nargout > 2, varargout{3} = true; end - return - else - c(i) = 1; - end -end - -varargout{1} = P; -if nargout > 1, varargout{2} = c; end -if nargout > 2, varargout{3} = false; end diff --git a/devel/research/smithnf/matrixarticle.pdf b/devel/research/smithnf/matrixarticle.pdf deleted file mode 100644 index 01d0d4b81066b74abde754f0858a765de656d956..0000000000000000000000000000000000000000 GIT binary patch literal 0 HcmV?d00001 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at vertex are: 4 -4 8 -7 -% Region 3 -% -% Vertex number 3 with image vertex 3: -% Edges at vertex are: 5 -5 -8 -% Region 4 -% -% Vertex number 4 with image vertex 4: -% Edges at vertex are: -3 9 3 -% Region 2 -% -% Vertex number 5 with image vertex 2: -% Edges at vertex are: -2 -9 -6 7 2 -% Region 1 -% -% Edge number 1 from vertex 1 to vertex 1: -% Type: Peripheral about puncture number 1 -% Image is: 2 -% Path (1 -> 1): 1 -1 -% -% Edge number 2 from vertex 5 to vertex 5: -% Type: Peripheral about puncture number 2 -% Image is: 4 -% Path (1 -> 1): -2 2 -% -% Edge number 3 from vertex 4 to vertex 4: -% Type: Peripheral about puncture number 3 -% Image is: 3 -% Path (2 -> 2): -3 3 -% -% Edge number 4 from vertex 2 to vertex 2: -% Type: Peripheral about puncture number 4 -% Image is: 1 -% Path (3 -> 3): -4 4 -% -% Edge number 5 from vertex 3 to vertex 3: -% Type: Peripheral about puncture number 5 -% Image is: 5 -% Path (4 -> 4): -5 5 -% -% Edge number 6 from vertex 1 to vertex 5: -% Type: Main -% Image is: 7 4 8 5 -8 -4 8 -5 -8 -4 -7 -2 7 4 8 5 -8 -4 -7 2 -6 -1 6 -2 7 4 8 -5 -8 -4 -7 2 7 4 8 5 -8 -% Path (1 -> 1): -% -% Edge number 7 from vertex 5 to vertex 2: -% Type: Main -% Image is: 8 -5 -8 -4 -7 -2 7 4 8 5 -8 -4 -7 2 -6 -% Path (1 -> 3): -2 -3 -% -% Edge number 8 from vertex 2 to vertex 3: -% Type: Main -% Image is: 6 -2 7 4 8 -5 -8 -4 -7 2 7 4 8 5 -8 4 8 -5 -8 -4 -7 -2 7 4 8 5 -8 -4 8 -5 -8 -4 -7 -2 7 4 8 -% Path (3 -> 4): 4 -% -% Edge number 9 from vertex 4 to vertex 5: -% Type: Main -% Image is: 9 -2 7 4 8 -5 -8 -4 -7 2 7 4 8 5 -8 -% Path (2 -> 1): 2 -% -% Reducible Isotopy class -% The following main edges and their images constitute an invariant subgraph: -% 6 7 8 - -% Edge number 6 from vertex 1 to vertex 5: -% Path (1 -> 1): -% Edge number 7 from vertex 5 to vertex 2: -% Path (1 -> 3): -2 -3 -% Edge number 8 from vertex 2 to vertex 3: -% Path (3 -> 4): 4 - -b = braid([-3 1 -4 2 -3 -1 -2 3 -2 4 3 4]); -l = loop([0 -1 -1 -1 0 1 0 0]); - -gens = []; -for i = 1:length(b) - subplot(3,4,i) - plot(braid(gens,5)*l) - title(sprintf('%d (%s)',i,num2str(gens))) - gens = [gens b.word(i)]; -end diff --git a/devel/research/smithnf/smithform.mw b/devel/research/smithnf/smithform.mw deleted file mode 100644 index be88d3ae..00000000 --- a/devel/research/smithnf/smithform.mw +++ /dev/null @@ -1,165 +0,0 @@ - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 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- \ No newline at end of file diff --git a/devel/research/test_gaps.m b/devel/research/test_gaps.m deleted file mode 100644 index 5d549a15..00000000 --- a/devel/research/test_gaps.m +++ /dev/null @@ -1,28 +0,0 @@ -% Find asymptotic form of spectral gaps for psi braids. - -nmax = 300; -gaps = []; -for n = 3:nmax - r = psiroots(n); - gaps = [gaps log10(abs(r(1)/r(2)))]; -end - -n = 3:nmax; - -format long -n1 = 2000; -r = psiroots(n1); gap1 = log10(abs(r(1)/r(2))); -c = gap1 / n1^-3 - -figure(1) -loglog(n,gaps,'.') -hold on -loglog(n,c*n.^-3,'r') -hold off -xlabel('n') -ylabel('spectral gap') - -figure(2) -loglog(n,abs(gaps - c*n.^-3)./gaps,'.') -xlabel('n') -ylabel('error in spectral gap') diff --git a/devel/research/test_inc_exc.m b/devel/research/test_inc_exc.m deleted file mode 100644 index 04d0a7d1..00000000 --- a/devel/research/test_inc_exc.m +++ /dev/null @@ -1,20 +0,0 @@ -% Test inclusion/exclusion formula for addition of loops. - -n = 4; - -rng('default') - -l1 = loop(randi([-2 2],1,2*n-4)/2) -l2 = loop(randi([-2 2],1,2*n-4)) - -%l1 = loop([1 1 -1 1]) -l1 = loop([0 0 -1 1]) -l2 = loop([1 -2 -1 0]) - -subplot(2,1,1) -plot(l1,'PunctureSize',.02) -hold on -plot(l2,'LineColor','r','PunctureSize',0) -hold off -subplot(2,1,2) -plot(loop(l1.coords+l2.coords)) diff --git a/devel/research/tight.m b/devel/research/tight.m deleted file mode 100644 index 30a90c9a..00000000 --- a/devel/research/tight.m +++ /dev/null @@ -1,136 +0,0 @@ -function tight - -import braidlab.* -warning('off','BRAIDLAB:braid:entropy:noconv'); - -% Number of strands. -n = 5; -% Word length to optimise. -nw = 6; - -%istight(monster) - -N = n-1; - -% Initial braid: (1 -N-1 -N -N ...) -sig = -N*ones(1,nw); -sig(1) = 1; sig(end) = -N-1; - -nwords = (2*N)^(nw-1); - -good = 0; -bad = 0; - -goodones = []; - -while 1 - incr = false; - % Do not change the first generator (leave at 1). - for w = nw:-1:2 - if sig(w) < N - incr = true; - % Increment the generator. - sig(w) = sig(w)+1; - if sig(w) == 0, sig(w) = sig(w)+1; end - break - else - % Otherwise reset generator at that position, and let the - % loop move on to the next position. - sig(w) = -N; - end - end - - % If nothing was changed, we're done. - if ~incr, break; end - - if w == 2, disp(num2str(sig)); end - - % Check if all generators are present. - gens = unique(sort(abs(sig))); - if length(gens) ~= n-1, continue; end - - if istight(sig,n) - good = good + 1; - goodones = [goodones; sig]; - else - bad = bad + 1; - end -end - -fprintf('\ngood=%d bad=%d total=%d\n',... - good,bad,good+bad) -fprintf('\n\nThe best ones (pA candidates):\n\n') - -pAcand = []; -for i = 1:size(goodones,1) - %entr = entropy(braid(goodones(i,:)),'trains'); - entr = entropy(braid(goodones(i,:))); - if entr > 1e-4 - entrbnd = log(max(abs(eig(burau(braid(goodones(i,:)),'abs'))))); - entrbur = log(max(abs(eig(burau(braid(goodones(i,:))))))); - pAcand = [pAcand; [goodones(i,:) entr entrbnd entrbur]]; - end -end - -pAcand = sortrows(pAcand,nw+1); -colstr = sprintf(['%-' num2str(length(num2str(pAcand(1,1:nw)))) 's'],'braid'); -fprintf('%s \tentr entr(abs) entr(Burau)\n',colstr) -for i = [1 (find(diff(pAcand(:,nw+1)) > 1e-3)+1)'] - fprintf('%s \t',num2str(pAcand(i,1:nw))) - fprintf('%7.4f %7.4f %7.4f\n', ... - pAcand(i,nw+1),pAcand(i,nw+2),pAcand(i,nw+3)) -end - -% ===================================================================== -function ee = istight(sig,n) - -import braidlab.* - -if nargin < 2 - n = max(abs(sig))+1; -end - -a = braid(sig,n); - -% Compute entropy (not too accurately, to save time). -entr = a.entropy(1e-3,10); -%entr = a.entropy('trains'); -entrabs = log(max(abs(eig(burau(a,'abs'))))); - -% Return true if the entropy is equal to the monoid bound. -ee = abs(entr-entrabs) < 5e-3; - -% ===================================================================== -function ee = istightold(sig,n,nrep) - -% The old way: look at all loops between adjacent pairs. - -import braidlab.* - -% Number of repetitions of the braid to check. -if nargin < 3 - nrep = 10; -end - -ee = true; -for k = 1:n-1 - fprintf(' l%d=',k) - b = zeros(1,n-2); - if k > 1, b(k-1) = -1; end - if k < n-1, b(k) = 1; end - u = loop([zeros(1,n-2) b]); - l0 = length(u)/2; - for i = 1:nrep - for j = 1:length(sig) - u = braid(sig(j),n)*u; - l = length(u)/2; - fprintf('%3d ',l-l0) - if l-l0 < 0 - fprintf(' ...bad') - ee = false; - return - end - l0 = l; - end - end -end diff --git a/devel/research/winding.m b/devel/research/winding.m deleted file mode 100644 index fed3e659..00000000 --- a/devel/research/winding.m +++ /dev/null @@ -1,58 +0,0 @@ -N = 1000000; -T = 20000; Tkeep = 2000; -eps = .025; -r0 = .5; -% D T = a^2/4 -% r^2 = 2 D t = (a^2/2) T n = eps^2 n - -fonttype = 'Times'; -fsize = 20; fcsize = 15; lw = 2; -txtattrib = {'FontName',fonttype,'FontSize',fsize,... - 'FontWeight','normal'}; -txtattrib2 = {txtattrib{:},'Interpreter','Latex'}; - -rng(0); wind = zeros(N,floor(T/Tkeep)); -for i = 1:N - X = randomwalk([r0;0],T,eps,'disk'); - th = atan2(X(:,2),X(:,1)); - th2 = th(1:end-1); th2(find(abs(diff(th)) <= pi)) = 0; - th = th-th(1) + 2*pi*[0;cumsum(sign(th2))]; - wind(i,:) = th(Tkeep:Tkeep:end); - if ~mod(i,1000), fprintf('realization %d...\n',i); end -end - -figure(1), clf -bins = 300; -for it = 1:2:floor(T/Tkeep) - [P,w] = hist(wind(:,it),min(wind(:,it)):max(wind(:,it)),bins); - P = P./trapz(w,P); - semilogy(w,P,'b','LineWidth',lw) - hold on - t = Tkeep*it; - %a = .425/eps/sqrt(t);% N = 50000; T = 10000; Tkeep = 2000; eps = .05; - a = .39/eps/sqrt(t); % N = 100000; T = 100000; Tkeep = 20000; eps = .01; - %a = 2/log(t);%2/log(2*t*eps^2/r0^2); - Pf = .5*a*sech(.5*a*pi*w); - %Pf = 1/pi * 1/a ./ (w.^2 + a.^-2); - minP = min(P(find(P~=0))); ii = find(Pf>minP); - semilogy(w(ii),Pf(ii),'r','LineWidth',lw); -end -hold off -axis([-30 30 1e-4 .3]) -return - -a = .105; % T=100000, N=50000, eps=.05 (?) -%a = .05; % T=1000000, N=50000, eps=.01 (bad) -a = .19; % T=10000, N=50000, eps=.05 - -a = 1.9e-5 * T; -Pf = .5*a*sech(a*pi*w/2); %Pf = Pf./trapz(w,Pf); -semilogy(w,Pf,'r','LineWidth',lw); - -a = 1.9e-5 * 8000; -a = .15; -Pf = .5*a*sech(a*pi*w/2); %Pf = Pf./trapz(w,Pf); -semilogy(w,Pf,'r','LineWidth',lw); - -hold off -set(gca, txtattrib{:}) diff --git a/devel/tests/array_of_class_objects/@Aclass/Aclass.m b/devel/tests/array_of_class_objects/@Aclass/Aclass.m deleted file mode 100644 index db656010..00000000 --- a/devel/tests/array_of_class_objects/@Aclass/Aclass.m +++ /dev/null @@ -1,26 +0,0 @@ -classdef Aclass - properties - w - end - - methods - - function a = Aclass(b) - if nargin > 0 - a(size(b,1)) = Aclass; - for k = 1:size(b,1) - a(k).w = b(k,:); - end - end - end - - function value = getw(obj) - value = vertcat(obj.w); - end - - function disp(obj) - for i = 1:length(obj) - disp(['(( ' num2str(obj(i).w) ' ))']); - end - end -end diff --git a/devel/tests/array_of_class_objects/testconvert.m b/devel/tests/array_of_class_objects/testconvert.m deleted file mode 100644 index fc603e1a..00000000 --- a/devel/tests/array_of_class_objects/testconvert.m +++ /dev/null @@ -1,14 +0,0 @@ -n = 60000; k = 20; -l = zeros(n,k); - -% Convert to a cell array of Aclass objects, -tic -sz = size(l,1); -l2 = mat2cell(l,ones(1,sz),k); -l2 = reshape(cellfun(@Aclass,l2,'UniformOutput',0),[sz 1]); -toc - -% Convert to a vector of Aclass objects, -tic -l3 = Aclass(l); -toc diff --git a/devel/tests/braidconv.m b/devel/tests/braidconv.m deleted file mode 100644 index 522d341c..00000000 --- a/devel/tests/braidconv.m +++ /dev/null @@ -1,38 +0,0 @@ -% Test class: braid with user-defined convention for left-right and -% clockwise/anticlockwise. - -classdef braidconv - properties (Dependent) - word - end - properties %(Access=private) - lr = 1; % 1 for left-to-right, -1 for right-to-left. - cw = 1; % 1 for clockwise, -1 for counterclockwise. - % Maybe this should only be in 'loop'? - % Or only used in braid.mtimes? - pword - end - - methods - - function obj = braidconv(w) - obj.word = w; - end - - function obj = set.word(obj,value) - if obj.lr == 1 - obj.pword = obj.cw*value; - else - obj.pword = flip(obj.cw*value); - end - end - - function value = get.word(obj) - if obj.lr == 1 - value = obj.cw*obj.pword; - else - value = flip(obj.cw*obj.pword); - end - end - end % methods -end % classdef diff --git a/devel/tests/colorbraiding_speedtest.m b/devel/tests/colorbraiding_speedtest.m deleted file mode 100644 index 957400bd..00000000 --- a/devel/tests/colorbraiding_speedtest.m +++ /dev/null @@ -1,28 +0,0 @@ -global BRAIDLAB_colorbraiding_nomex -global BRAIDLAB_threads - -n = 100; -k = 1000; -eps = .2; -proj = .234; - -rng('default'); -XY = randomwalk(n,k,eps); - -BRAIDLAB_colorbraiding_nomex = 1; -tic -b1 = braid(XY,proj); -toc - -BRAIDLAB_colorbraiding_nomex = 0; -BRAIDLAB_threads = 1; -tic -b2 = braid(XY,proj); -toc - -BRAIDLAB_threads = 2; -tic -b2 = braid(XY,proj); -toc - -lexeq(b1,b2) diff --git a/devel/tests/entropyOverflow.m b/devel/tests/entropyOverflow.m deleted file mode 100644 index 2b5a86f2..00000000 --- a/devel/tests/entropyOverflow.m +++ /dev/null @@ -1,110 +0,0 @@ -function Ls = entropyOverflow(strands, Ntries) -%% Ls = entropyOverflow(strands, Ntries) -% Push braidlab to entropy overflow, just to test the boundaries. -% -% We generate braids of pre-specified number of strands with more -% and more generators, until the entropy computation overflows. Then -% we do a simple binary search to zero in on precisely the number of -% generators causing overflow. -% -% Generators are drawn at random using uniform distribution over -% numbers between (-Nstrands, Nstrands). Braidlab automatically -% discards sigma_0 generators, meaning that the braids sometimes end -% up being shorter than recorded, as sigma_0 should not correspond -% to any operation. We don't attempt to correct for that number. -% -% ** Inputs: ** -% -% strands - list of numbers of strands for which to test, e.g., [3, -% 10, 100] -% -% Ntries - attempts to determine at which length of braid overflow -% happens (optional) -% -% ** Outputs: ** -% -%Ls - number of generators in the braid causing overflow -% - -import braidlab.* - -% default number of attempts -if ~exist('Ntries','var') || isempty(Ntries) - Ntries=100; -end - -% output structure -Ls = nan(size(strands)); - -% loop in parallel over all numbers of strands -parfor s = 1:length(strands) - - Nstrands = strands(s); - - % boundaries of the length interval we are searching - Llower = 1; - Lupper = inf; % initial length - - - Nleft = Ntries; - while Nleft > 0 - - % the attempt is either in the middle of the interval - if Lupper < inf - L = round((Llower + Lupper)/2); - % or just go as far as you can if we haven't had overflow yet - else - L = 2*Llower; - end - - %% produce a valid set of generators - rng(1); % we need a repeatable set of generators - maxIndAllowed = Nstrands-1; - g = randi( [-maxIndAllowed, maxIndAllowed], [1, L] ); % discrete integer distribution - maxIndex = max(abs(g(:))); - assert( maxIndex <= maxIndAllowed, 'Generator index is badly set') - - %% produce a braid - B = braid(g, Nstrands); - - fprintf('S: %d, Tries left %d, L = %d in [%d, %d], max index used %d...', ... - Nstrands, Nleft, L, Llower, Lupper, maxIndex ); - overflow = false; - - %% overflow is detected using braidlab's internal error reporting - % the error code has to contain 'BRAIDLAB' and 'overflow' in it - try - % compute the entropy using - % braidlab.braid/entropy - E = entropy(B, [], 1); - catch ME - if ~isempty(strfind(ME.identifier, 'BRAIDLAB')) && ... - ~isempty(strfind(ME.identifier,'overflow')) - overflow = true; - else - rethrow ME; - end - end - - %% on overflow, set the upper boundary of the length interval - if overflow - fprintf('caught overflow error.\n'); - Lupper = L; - Ls(s) = B.length; % store braid length as output - else - fprintf('no overflow.\n'); - Llower = L; - end - - %% termination is when the boundaries surround only a single number - if abs(Llower-Lupper) <= 1 - fprintf('S: %d, Zeroed in at %d.\n', Nstrands, L); - Nleft = -1; - else - Nleft = Nleft-1; - end - - end -end - -end diff --git a/devel/tests/entropy_convergence.m b/devel/tests/entropy_convergence.m deleted file mode 100644 index 8d7b446a..00000000 --- a/devel/tests/entropy_convergence.m +++ /dev/null @@ -1,48 +0,0 @@ -% Check quality and speed of convergence of entropy for difficult braids. -% Goal is to achieve near machine precision. - -% The predicted number of iterations matches the numerics fairly well, -% showing that the power iteration is working as expected. There's not -% much room for improvement unless we somehow introduce a dynamic shift. - -global BRAIDLAB_debuglvl -BRAIDLAB_debuglvl = 1; - -n = 78; -tol = 1e-15; - -% Predict the number of iterations from the spectral gap between the -% first two roots. -r = psiroots(n); -Niter = ceil(-log10(tol) / log10(abs(r(1)/r(2)))); -ee = log(abs(r(1))); -fprintf('Predict %d iterations needed\n',Niter) - -b = braidlab.braid('psi',n); % low entropy braid - -% For train tracks, the low entropy actually helps the method. But the -% iterative method is better for high entropy. -% -% However, the train track method fails for n>77, with the message 'Growth -% not decreasing in fold and minimum tolerance of 1.00e-14 reached.' -tic -try - etr = entropy(b,'trains'); -catch err - if strcmp(err.identifier,'BRAIDLAB:braid:tntype_helper:notdecr') - warning('Growth not decreasing... giving up on train tracks.') - end - etr = 0; -end -toc - -% Now do the iteration method. Takes a while, but can achieve machine -% precision! -tic -[e,u] = entropy(b,tol,Niter); -toc -fprintf('Predicted %d iterations\n',Niter) - -fprintf('Error: iter=%e train=%e\n',abs(e-ee),abs(etr-ee)) - -clear -global BRAIDLAB_debuglvl diff --git a/devel/tests/issue82.mat b/devel/tests/issue82.mat deleted file mode 100644 index c8475d76b15458ef705c0c5356aa5dfdd05b270c..0000000000000000000000000000000000000000 GIT binary patch literal 0 HcmV?d00001 literal 260 zcmeZu4DoSvQZUssQ1EpO(M`+DN!3vZ$Vn_o%P-2cQgHY2i*PhE(NSsh5-`93qo*%FkX-}B6>}aZCnVfpJd)#Z zhHfl++{ejIjyO&_VcbA9-i+dzhx$TNc?|j#eC1I zmGa-tH=LR;9Oz?RmA1^b<#*Zss)%i~Pp{ej`?=%O+l4RMXa4`cZhgvudoRBoOZZUu U|CgWsZOb 1 - if any(n > imin), error(badbounds); end - ul = looplist_helper(n,imin); - return -end - -if any(imin > imax), error(badbounds); end - -ul = looplist_helper(imin*ones(1,n),imax*ones(1,n)); diff --git a/devel/tests/loop_speedtest/looplist_helper.c b/devel/tests/loop_speedtest/looplist_helper.c deleted file mode 100644 index 65e83c35..00000000 --- a/devel/tests/loop_speedtest/looplist_helper.c +++ /dev/null @@ -1,72 +0,0 @@ -#include -#include -#include "mex.h" - -/* */ - -#define MAX(a,b) (a > b ? a : b) - -void mexFunction(int nlhs, mxArray *plhs[], int nrhs, const mxArray *prhs[]) -{ - int m, r, n, nr, nrd; - const double *amin, *amax; - double *a; - - if (nrhs < 2) - { mexErrMsgTxt("2 input arguments required"); exit(1); } - - n = MAX(mxGetM(prhs[0]),mxGetN(prhs[0])); - if (n != MAX(mxGetM(prhs[1]),mxGetN(prhs[1]))) - { mexErrMsgTxt("Inconsistent bounds"); exit(1); } - - /* TODO: write wrapper to allow for scalar */ - amin = mxGetPr(prhs[0]); - amax = mxGetPr(prhs[1]); - - /* Compute the number of combinations */ - nr = (int) (amax[0]-amin[0]+1); - nrd = (double) nr; /* Also compute a double version to check - for overflow*/ - for (m = 1; m < n; ++m) - { - nr *= (int) (amax[m]-amin[m]+1); - nrd *= (double) (amax[m]-amin[m]+1); - if (nrd > (double)INT_MAX) - { mexErrMsgTxt("Beyond integer range..."); exit(1); } - } - - /* Create an mxArray for the output data */ - plhs[0] = mxCreateDoubleMatrix(nr, n, mxREAL); - a = mxGetPr(plhs[0]); /* a[col*nrows + row] */ - for (m = 0; m < n; ++m) { a[m*nr + 0] = amin[m]; } - - for (r = 1; r < nr; ++r) - { - /* Set coefficients to previous entry */ - for (m = 0; m < n; ++m) { a[m*nr + r] = a[m*nr + r-1]; } - - /* - Increment elements of the vector a (from the last element), - resetting each position a[m] to amin[m] if it passes amax[m]. - */ - for (m = n-1; m >= 0; --m) - { - /* The sequence that coefficients cycle through is - amin[m]...amax[m] for a[m], 0 <= m < n */ - if (a[m*nr+r] < amax[m]) - { - /* Increment the coefficient */ - a[m*nr+r] = a[m*nr+r] + 1; - break; - } - else - { - /* Otherwise reset coefficient at that position, and let - the loop move on to the next position. */ - a[m*nr+r] = amin[m]; - } - } - } - - return; -} diff --git a/devel/tests/loop_speedtest/loopsigma_helper.c b/devel/tests/loop_speedtest/loopsigma_helper.c deleted file mode 100644 index f0f7085e..00000000 --- a/devel/tests/loop_speedtest/loopsigma_helper.c +++ /dev/null @@ -1,125 +0,0 @@ -#include -#include -#include "mex.h" - -/* Helper function for loopsigma */ - -#define pos(x) (x > 0 ? x : 0) -#define neg(x) (x < 0 ? x : 0) -#define MAX(a,b) (a > b ? a : b) - -void mexFunction(int nlhs, mxArray *plhs[], int nrhs, const mxArray *prhs[]) -{ - int i, n; /* Refer to generators, so don't need to be mwIndex/mwSize. */ - mwIndex j, k, l; - mwSize N, Nr, Ngen; - const mxArray *iiA, *uA; - const int *ii; - const double *u; - double *a, *b, *ap, *bp, *uo, c, d; - - if (nrhs < 2) - { - mexErrMsgIdAndTxt("BRAIDLAB:loopsigma_helper:nargin", - "2 input arguments required."); - } - - iiA = prhs[0]; - ii = (int *)mxGetData(iiA); /* iiA contains int32's. */ - uA = prhs[1]; - u = mxGetPr(uA); - - Ngen = MAX(mxGetM(iiA),mxGetN(iiA)); - - N = mxGetN(uA); - Nr = mxGetM(uA); - if (N % 2 != 0) - { - mexErrMsgIdAndTxt("BRAIDLAB:loopsigma_helper:badarg", - "u argument should have even number of columns."); - } - n = (int)(N/2 + 2); - - /* Make 1-indexed arrays */ - a = (double *) malloc(N/2 * sizeof(double)) - 1; - b = (double *) malloc(N/2 * sizeof(double)) - 1; - ap = (double *) malloc(N/2 * sizeof(double)) - 1; - bp = (double *) malloc(N/2 * sizeof(double)) - 1; - - /* Create an mxArray for the output data */ - plhs[0] = mxCreateDoubleMatrix(Nr, N, mxREAL); - uo = mxGetPr(plhs[0]); - - for (l = 0; l < Nr; ++l) /* Loop over rows of u */ - { - /* Copy initial row data */ - for (k = 1; k <= N/2; ++k) - { - a[k] = u[(k-1 )*Nr+l]; - b[k] = u[(k-1+N/2)*Nr+l]; - ap[k] = a[k]; - bp[k] = b[k]; - } - - for (j = 0; j < Ngen; ++j) /* Loop over generators */ - { - i = abs(ii[j]); - if (ii[j] > 0) - { - if (i == 1) - { - bp[1] = a[1] + pos(b[1]); - ap[1] = -b[1] + pos(bp[1]); - } - else if (i == n-1) - { - bp[n-2] = a[n-2] + neg(b[n-2]); - ap[n-2] = -b[n-2] + neg(bp[n-2]); - } - else - { - c = a[i-1] - a[i] - pos(b[i]) + neg(b[i-1]); - ap[i-1] = a[i-1] - pos(b[i-1]) - pos(pos(b[i]) + c); - bp[i-1] = b[i] + neg(c); - ap[i] = a[i] - neg(b[i]) - neg(neg(b[i-1]) - c); - bp[i] = b[i-1] - neg(c); - } - } - else if (ii[j] < 0) - { - if (i == 1) - { - bp[1] = -a[1] + pos(b[1]); - ap[1] = b[1] - pos(bp[1]); - } - else if (i == n-1) - { - bp[n-2] = -a[n-2] + neg(b[n-2]); - ap[n-2] = b[n-2] - neg(bp[n-2]); - } - else - { - d = a[i-1] - a[i] + pos(b[i]) - neg(b[i-1]); - ap[i-1] = a[i-1] + pos(b[i-1]) + pos(pos(b[i]) - d); - bp[i-1] = b[i] - pos(d); - ap[i] = a[i] + neg(b[i]) + neg(neg(b[i-1]) + d); - bp[i] = b[i-1] + pos(d); - } - } - for (k = 1; k <= N/2; ++k) { a[k] = ap[k]; b[k] = bp[k]; } - } - for (k = 1; k <= N/2; ++k) - { - /* Copy final a and b to row of output array */ - uo[(k-1 )*Nr+l] = a[k]; - uo[(k-1+N/2)*Nr+l] = b[k]; - } - } - - free(a+1); - free(b+1); - free(ap+1); - free(bp+1); - - return; -} diff --git a/devel/tests/test_braidconv.m b/devel/tests/test_braidconv.m deleted file mode 100644 index 21168d0f..00000000 --- a/devel/tests/test_braidconv.m +++ /dev/null @@ -1,5 +0,0 @@ -b = braidconv([1 2 3]) -b.lr = -1 % change convention to right-to-left -b.cw = -1 % change convention to counterclockwise -b.word = [-4 -3 -2 -1] % now define word (read right-to-left) -b.word(2) = 2 % change the second generator, read from right-to-left diff --git a/devel/tests/test_colorbraid.m b/devel/tests/test_colorbraid.m deleted file mode 100644 index 1bca3f68..00000000 --- a/devel/tests/test_colorbraid.m +++ /dev/null @@ -1,84 +0,0 @@ -% test for colorbraid using Matlab and CPP code - -global BRAIDLAB_debuglvl -BRAIDLAB_debuglvl = 1 % or higher - -%% Set up a random physical braid in XY -rng('default'); -N = 80; -L = 20000; - -t = linspace(0,1,L); -XY = zeros( L, 2, N ); - -for k = 1:N - - XY(:,1,k) = cumsum( randn( L, 1) ); - XY(:,2,k) = cumsum( randn( L, 1) ); - -end -D = 1.1* sqrt( XY(:,1,:).^2 + XY(:,2,:).^2 ); -XY = XY ./ max(D(:)); - -% % plotting -% figure; -% hold all; -% for k = 1:5 -% plot3(XY(:,1,k), XY(:,2,k), t); -% end - -%% prepare the simulation setup by clearing all globals -clearvars -global BRAIDLAB_colorbraiding_nomex BRAIDLAB_threads - -global BRAIDLAB_colorbraiding_nomex % colorbraiding has a flag - % to select Matlab vs C++ code - -timing = {}; - -%% Compute braid using default settings (C++ and autodetect thread #) -fprintf('\n*************************************\n') -setn = 1; tic -b_cpp_p = braidlab.braid(XY); -timing{setn}.type = 'Threaded (autoset)'; -timing{setn}.time = toc; - -%% Compute braid using C++ code and fixed number of threads (3) -fprintf('\n*************************************\n') -setn = setn + 1; tic -global BRAIDLAB_threads -BRAIDLAB_threads = 3; -b_cpp_p = braidlab.braid(XY); -timing{setn}.type = sprintf('Threaded (%d threads)', BRAIDLAB_threads); -timing{setn}.time = toc; - -%% Compute braid using C++ code and a single thread -fprintf('\n*************************************\n') -setn = setn + 1; tic -BRAIDLAB_threads = 1; -b_cpp_s = braidlab.braid(XY); -timing{setn}.type = 'Unthreaded'; -timing{setn}.time = toc; - -%% Compute braid using MATLAB version of the code -fprintf('\n*************************************\n') -setn = setn + 1; tic -BRAIDLAB_colorbraiding_nomex = true; -b_matlab = braidlab.braid(XY); -timing{setn}.type = 'Matlab'; -timing{setn}.time = toc; -fprintf('\n*************************************\n') - -%% Compare Matlab and C++ single/multithreaded braids -%assert( b_matlab == b_cpp, 'Braids are not equal'); -assert( lexeq(b_matlab,b_cpp_p), ['C++ multithreaded and MATLAB ' ... - 'braids are not lexically equal'] ); -assert( lexeq(b_matlab,b_cpp_s), ['C++ singlethreaded and MATLAB ' ... - 'braids are not lexically equal'] ); -disp('BRAIDS ARE EQUAL'); - -%% Display timing info -disp('Timing information (sec)') -for k = 1:length(timing) - fprintf('Timing type: %s \n\t Time (sec): %f\n', timing{k}.type, ... - timing{k}.time) -end diff --git a/devel/tests/test_compact.m b/devel/tests/test_compact.m deleted file mode 100644 index ee33a64c..00000000 --- a/devel/tests/test_compact.m +++ /dev/null @@ -1,30 +0,0 @@ -% Test braid compaction algorithm - -% The compact method has been problematic. Use this test when in doubt. -% This is also useful for optimizing. - -% Reference values: -% -% n k avg compaction -% 3 10 50.16% -% 4 10 62.24% -% 7 10 73.62% -% 7 20 65.49% -% 10 20 70.00% -% 10 30 67.25% - -rng('default') -n = 10; % how many strings -k = 30; % how many generators -compfrac = []; -for i = 1:1000 - b = braid('random',n,k); bc = compact(b); - if b ~= bc - error('There was a problem with compact: the braids are not equal.') - end - compfrac = [compfrac bc.length/b.length]; -end - -hist(compfrac) -fprintf('Compaction: average %.2f%% (best %.2f%%, worst %.2f%%)\n', ... - 100*mean(compfrac),100*min(compfrac),100*max(compfrac)) diff --git a/devel/tests/test_cycle.m b/devel/tests/test_cycle.m deleted file mode 100644 index f13381c5..00000000 --- a/devel/tests/test_cycle.m +++ /dev/null @@ -1,66 +0,0 @@ -function test_cycle - -import braidlab.* - -rng('default') - -n = 10; -k = 10; -Nreal = 100; -maxit = 0; -maxperiod = 0; - -global BRAIDLAB_debuglvl -if exist('BRAIDLAB_debuglvl','var') - BRAIDLAB_debuglvl_save = BRAIDLAB_debuglvl; -else - BRAIDLAB_debuglvl_save = 0; -end -BRAIDLAB_debuglvl = 1; - -for r = 1:Nreal - b = braid('random',n,k); - fprintf('b = %s:\t',char(b)) - [M,period,it] = cycle(b); - maxit = max(maxit,it); - maxperiod = max(period,maxperiod); - - % Doublecheck effective linear action. - if true - try - verify_cycle(b,M,period,it,@double); - catch err - if (strcmp(err.identifier,'BRAIDLAB:test_cycle:wrong2')) - fprintf('retrying with VPI...') - verify_cycle(b,M,period,it,@vpi); - fprintf(' ok.\n') - else - BRAIDLAB_debuglvl = BRAIDLAB_debuglvl_save; - rethrow(err) - end - end - end -end - -fprintf('Max iterations: %d Max period: %d\n',maxit,maxperiod) - -BRAIDLAB_debuglvl = BRAIDLAB_debuglvl_save; - -%================================================================= -function verify_cycle(b,M,period,it,typ) - -l = braidlab.loop(b.n,typ,'bp'); - -% Make sure we've converged to the periodic cycle. -l = b^it*l; -[l1,M2] = b^period*l; - -if any(M ~= M2) - error('BRAIDLAB:test_cycle:wrong1','Something went wrong (1).') -end - -l2 = braidlab.loop(typ(M2*l.coords.'),'bp'); - -if l1 ~= l2 - error('BRAIDLAB:test_cycle:wrong2','Something went wrong (2).') -end diff --git a/devel/tests/test_entropy2.m b/devel/tests/test_entropy2.m deleted file mode 100644 index d37c254d..00000000 --- a/devel/tests/test_entropy2.m +++ /dev/null @@ -1,61 +0,0 @@ -function test_entropy(n,tol) - -% Try new method of finding entropy, directly from the linearized action matrix. - -import braidlab.* - -if nargin < 1, n = 15; end -if nargin < 2, tol = 1e-8; end - -b = compact(braid('psi',n)); - -r = psiroots(n); -eex = log(max(abs(r))); - -fprintf('Old method:\n') - -tic -tol = 1e-9; -e1 = entropy(b,tol); -toc -fprintf('diff1=%.3e\n',abs(e1-eex)) - -fprintf('New method:\n') - -tic -e2 = entropy2(b,tol); -toc - -fprintf('diff2=%.3e\n',abs(e2-eex)) - -%================================================================ -function [varargout] = entropy2(b,tol,maxit,nconvreq) -%ENTROPY Topological entropy of a braid. - -if nargin < 2, tol = 1e-6; end - -% Get defaults for maxit and nconvreq from cycle. -if nargin < 3, maxit = []; end -if nargin < 4, nconvreq = []; end - -[M,period] = cycle(b,maxit,nconvreq); - -method = 'eigs'; - -switch method - case 'charpoly' - % Use characteristic polynomial: very slow - varargout{1} = log(sort(abs(roots(charpoly(M))),'descend')); - varargout{1} = varargout{1}(1) / period; - - case 'eigs' - opts.isreal = true; - opts.tol = tol; - - varargout{1} = log(abs(eigs(M,1,'LM',opts))) / period; - - case 'eig' - varargout{1} = log(sort(abs(eig(full(M))),'descend')); - varargout{1} = varargout{1}(1) / period; - -end diff --git a/devel/tests/test_issue82.m b/devel/tests/test_issue82.m deleted file mode 100644 index 0897649f..00000000 --- a/devel/tests/test_issue82.m +++ /dev/null @@ -1,48 +0,0 @@ -load issue82 - -proj = .1; - -slice1 = XY(:,:,1); -slice2 = XY(:,:,2); -slice3 = XY(:,:,4); - -disp('first two particles are the same'); -XY = cat(3, slice1, slice1, slice2, slice3 ); - -global BRAIDLAB_braid_nomex; -try - disp('With MEX'); - BRAIDLAB_braid_nomex = 0; - braidlab.braid(XY,proj) -catch me - disp(me) -end - -try - disp('Without MEX'); - BRAIDLAB_braid_nomex = 1; - braidlab.braid(XY,proj) -catch me - disp(me) -end - -disp('first and third particles are the same') -XY = cat(3, slice1, slice2, slice1, slice3 ); - -global BRAIDLAB_braid_nomex; -try - disp('With MEX'); - BRAIDLAB_braid_nomex = 0; - braidlab.braid(XY,proj) -catch me - disp(me) -end - -try - disp('Without MEX'); - BRAIDLAB_braid_nomex = 1; - braidlab.braid(XY,proj) -catch me - disp(me) -end - diff --git a/devel/tests/test_linact.m b/devel/tests/test_linact.m deleted file mode 100644 index 566a6c1e..00000000 --- a/devel/tests/test_linact.m +++ /dev/null @@ -1,14 +0,0 @@ -Ntest = 1000; - -rng('default') - -for i = 1:Ntest - b = braid('random',5,10); - l = loop(randi(100,1,2*b.n-2)-50); - - [l2,M] = b*l; - - if any((M*l.coords.').' - l2.coords) - error('Not equal: %s',num2str((M*l.coords.').' - l2.coords)) - end -end diff --git a/devel/tests/test_loop_alloc.m b/devel/tests/test_loop_alloc.m deleted file mode 100644 index 1611c367..00000000 --- a/devel/tests/test_loop_alloc.m +++ /dev/null @@ -1,39 +0,0 @@ -% Test zeros function for pre-allocating loops. See issue #53. - -N = 2000; -n = 10; - -% Very bad: no pre-allocation. -% Completely awful running time. -if N <= 2000 - tic - l1 = []; - for i = 1:N - l1 = [l1; loop(n)]; - end - toc -end - -% Good: pre-allocation directly on the coordinates. -tic -l2 = loop(zeros(N,2*n-4)); -for i = 1:N - l2(i) = loop(n); -end -toc - -% Good: pre-allocation using default loop. -tic -l3 = loop(n,N); -for i = 1:N - l3(i) = loop(n); -end -toc - -% Good: pre-allocation with by creating the last element. -tic -l4(N) = loop(n); -for i = 1:N - l4(i) = loop(n); -end -toc diff --git a/devel/tests/test_loop_intersec.m b/devel/tests/test_loop_intersec.m deleted file mode 100644 index ab861f1c..00000000 --- a/devel/tests/test_loop_intersec.m +++ /dev/null @@ -1,33 +0,0 @@ -n = 200; % number of strands -nLoops = 200000; % number of loops -maxN = 30; - -fprintf(['Computing %d loops of %d punctures with coordinate numbers ' ... - 'between +-%d\n'], nLoops, n, round(maxN/2)); - -% generate random coordinates -C = randi(maxN, [nLoops,2*n - 4]) - round(maxN/2); - -% convert coordinates to loops -loops = braidlab.loop(C); - -global BRAIDLAB_loop_nomex - -% mex calculation -tic -BRAIDLAB_loop_nomex = 0; -intersec_cpp = loops.intersec; -mextime = toc; -fprintf('MEX computation completed in %f sec\n', mextime); -% matlab calculation -tic -BRAIDLAB_loop_nomex = 1; -intersec_mat = loops.intersec; -mattime = toc; -fprintf('MATLAB computation completed in %f sec\n', mattime); - -% assert they are the same - -assert( all(intersec_cpp(:) == intersec_mat(:)) ) -fprintf(['Results of Matlab and MEX computation of loop lengths ' ... - 'match. \nSpeedup factor: %f\n'], mattime/mextime); diff --git a/devel/tests/test_loop_length.m b/devel/tests/test_loop_length.m deleted file mode 100644 index bf5f5fc2..00000000 --- a/devel/tests/test_loop_length.m +++ /dev/null @@ -1,39 +0,0 @@ -% change to 'intaxis'/'minlength' to test it -lengthType = 'intaxis'; -n = 200; % number of strands -nLoops = 200000; % number of loops -maxN = 30; - -% n = 20; % number of strands -% nLoops = 20; % number of loops -% maxN = 6; - -fprintf(['Computing %d loops of %d punctures with coordinate numbers ' ... - 'between +-%d\n'], nLoops, n, round(maxN/2)); - -% generate random coordinates -C = randi(maxN, [nLoops,2*n - 4]) - round(maxN/2); - -% convert coordinates to loops -loops = braidlab.loop(C); - -global BRAIDLAB_loop_nomex - -% mex calculation -tic -BRAIDLAB_loop_nomex = 0; -l_cpp = loops.(lengthType).'; -mextime = toc; -fprintf('MEX computation completed in %f sec\n', mextime); -% matlab calculation -tic -BRAIDLAB_loop_nomex = 1; -l_mat = loops.(lengthType).'; -mattime = toc; -fprintf('MATLAB computation completed in %f sec\n', mattime); - -% assert they are the same - -assert( all(l_cpp == l_mat) ) -fprintf(['Results of Matlab and MEX computation of %s ' ... - 'match. \nSpeedup factor: %f\n'], lengthType, mattime/mextime); diff --git a/devel/tests/test_randomwalk.m b/devel/tests/test_randomwalk.m deleted file mode 100644 index e8847c11..00000000 --- a/devel/tests/test_randomwalk.m +++ /dev/null @@ -1,30 +0,0 @@ -n = 30; -N = 1000; -eps = .01; -domain = 'plane'; - -rng(0) - -tic -X = randomwalk(n,N,eps,domain); -toc - -figure(1) -clf, hold on -for p = 1:n - plot(X(:,1,p),X(:,2,p)) -end -switch lower(domain) - case 'square' - xx = linspace(0,1,10); - plot(0*xx,xx,'k','LineWidth',2) - plot(xx,0*xx,'k','LineWidth',2) - plot(1+0*xx,xx,'k','LineWidth',2) - plot(xx,1+0*xx,'k','LineWidth',2) - case 'disk' - th = linspace(0,2*pi,200); th = [th 0]; - plot(cos(th),sin(th),'k','LineWidth',2) -end -hold off -axis equal -axis off diff --git a/devel/tests/test_reducing.m b/devel/tests/test_reducing.m deleted file mode 100644 index 8a2b2a5d..00000000 --- a/devel/tests/test_reducing.m +++ /dev/null @@ -1,13 +0,0 @@ -warning('off','BRAIDLAB:braid:reducing:exp') - -b = braid([-3 1 -4 2 -3 -1 -2 3 -2 4 3 4]); -reducing(b) - -b = braid([1],3) -reducing(b) - -b = braid([1 2],4) -reducing(b) - -b = braid([1 2],5) -l = reducing(b) diff --git a/devel/tests/trains_vs_iter.m b/devel/tests/trains_vs_iter.m deleted file mode 100644 index 28a5a391..00000000 --- a/devel/tests/trains_vs_iter.m +++ /dev/null @@ -1,120 +0,0 @@ -% Compare computation of entropy between BH (trains) and iterative (iter). - -import braidlab.* - -rng(1) - -forcepA = false; -testred = false; -warndiscr = true; -nmax = 12;%20; -kmax = nmax+14;%+30; -nrep = 10; -tol = 1e-12; - -if forcepA - kmin = n+1; -else - kmin = 1; -end - -t_iter = zeros(nmax,kmax); -t_trains = zeros(nmax,kmax); -entr_iter = zeros(nmax,kmax); -entr_trains = zeros(nmax,kmax); -entr_diff = zeros(nmax,kmax); - -warning('off','BRAIDLAB:braid:entropy:noconv') -warning('off','BRAIDLAB:braid:entropy:reducible') - -for n = 3:nmax - disp(n) - for k = kmin:kmax - for r = 1:nrep - if forcepA - TN = 'reducible'; - while ~strcmp(TN,'pseudo-Anosov') - b = braid('random',n,k); - [TN,~] = tntype(b); - end - else - b = braid('random',n,k); - [TN,~] = tntype(b); - end - - tic - entr_iter(n,k) = entropy(b,tol); - t_iter(n,k) = t_iter(n,k) + toc; - - tic - try - entr_trains(n,k) = entropy(b,'trains'); - catch err - if strcmp(err.identifier,'BRAIDLAB:braid:tntype_helper:notdecr') - entr_trains(n,k) = NaN; - else - rethrow(err); - end - end - t_trains(n,k) = t_trains(n,k) + min(toc,1); - - if strcmp(TN,'reducible'), entr_trains(n,k) = NaN; end - - if ~isnan(entr_trains(n,k)) - discr = abs(entr_trains(n,k) - entr_iter(n,k)); - else - discr = -1; - end - entr_diff(n,k) = max(entr_diff(n,k),discr); - - if discr > 1e-3 & warndiscr - warning('Large discrepancy (%f) for braid %s.\n',... - discr,num2str(b.word)); - end - end - end -end - -% Relative time difference. -t_rdiff = .5*(t_iter - t_trains)./(t_iter + t_trains); - -figure(1) -imagesc(t_rdiff) -axis xy -colorbar -xlabel('k') -ylabel('n') -r = [1 0 0]; w = [.9 .9 .9]; b = [0 0 1]; -% colormap of size 64-by-3, ranging from red -> white -> blue -mid = round(-64*min(min(t_rdiff))/(max(max(t_rdiff)) - min(min(t_rdiff)))); -c1 = zeros(mid,3); c2 = zeros(64-mid,3); -for i = 1:3 - c1(:,i) = linspace(r(i), w(i), mid); - c2(:,i) = linspace(w(i), b(i), 64-mid); -end -c = [c1(1:end-1,:);c2]; -caxis([min(min(t_rdiff)) max(max(t_rdiff))]), colormap(c), colorbar -title('time difference: t_{iter} - t_{trains}') - -figure(2) -imagesc(log10(abs(entr_diff))) -axis xy -title('log_{10} |entr_{diff}|') -xlabel('k') -ylabel('n') -caxis([-15 max(max(log10(abs(entr_diff))))]), colorbar - -figure(3) -subplot(2,1,1) -imagesc(entr_iter) -text(1,nmax-1,'entr_{iter}') -axis xy -colorbar -ylabel('n') -subplot(2,1,2) -imagesc(entr_trains) -text(1,nmax-1,'entr_{trains}') -axis xy -colorbar -xlabel('k') -ylabel('n') diff --git a/devel/try_inviter.m b/devel/try_inviter.m deleted file mode 100644 index 1bb17d90..00000000 --- a/devel/try_inviter.m +++ /dev/null @@ -1,20 +0,0 @@ -% Try to find reducing curves using inverse iteration. - -%B = braid([1],3); -B = braid([-3 1 -4 2 -3 -1 -2 3 -2 4 3 4]); -lred = loop([0 -1 0 0 0 0]); -n = B.n; - -Niter = 10; -mu = 1; -u = loop(ones(1,2*n-4)); -%u = loop(rand(1,2*n-4)); - -for k = 1:Niter - % Get linear action. - [~,A] = B*u; A = full(A); - up = (A - mu*eye(size(A))) \ u.coords.'; - u = loop(up/norm(up)); -end - -u

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100644 devel/tests/test_loop_intersec.m delete mode 100644 devel/tests/test_loop_length.m delete mode 100644 devel/tests/test_randomwalk.m delete mode 100644 devel/tests/test_reducing.m delete mode 100644 devel/tests/trains_vs_iter.m delete mode 100644 devel/try_inviter.m diff --git a/devel/MATLAB_CLASSES_HELP b/devel/MATLAB_CLASSES_HELP deleted file mode 100644 index 280f5da0..00000000 --- a/devel/MATLAB_CLASSES_HELP +++ /dev/null @@ -1,32 +0,0 @@ -+braidlab: namespace for braidlab library - - * Adding a + to a subfolder name means that if the parent folder is - on Matlab's path, then functions inside the subfolder can be invoked - in Matlab as braidlab.. - - * To avoid having to use the braidlab. prefix, a function can import - the namespace using 'import braidlab.' 'or import - braidlab.*' to import all functions. - - * The private subfolder is only accessible to functions in the - containing folder, without needing to include the subfolder on the - path. - - * Functions in the +braidlab subfolder do *not* automatically see the - other functions in the folder. They must use the braidlab. prefix - or import functions. - - * Subfolders with a + are also allowed. For instance, the subfolder - +util contains utility functions. Functions therein are invoked - with braidlab.util.. - - * A subfolder beginning with "@" contains a class, such as @braid. - Subversion has trouble with this, so the folder must be refereed to - @braid@ within SVN. - - * Classes cannot be private, since the @ folder must be on the path. - -See -http://www.mathworks.com/help/techdoc/matlab_oop/brfynt_-1.html -http://www.mathworks.com/help/techdoc/matlab_prog/f4-70335.html -http://stackoverflow.com/questions/2748302/what-is-the-closest-thing-matlab-has-to-namespaces diff --git a/devel/MATLAB_MEX_LINUX b/devel/MATLAB_MEX_LINUX deleted file mode 100644 index 1290105f..00000000 --- a/devel/MATLAB_MEX_LINUX +++ /dev/null @@ -1,193 +0,0 @@ -Tutorial: how to get MEX files to run on Ubuntu. - -========================================================================== -MATLAB >= 2012a - -These versions support gcc-4.4, which is included in the Ubuntu 12.04 -repo (maybe also later versions?). Simply run - -sudo apt-get install gcc-4.4 g++-4.4 gfortran-4.4 - -Now that this is done, let's configure MEX/Matlab. Type (assuming the -mex command is in a folder in your PATH variable) - - mex -setup - -(*** If you get an error "mex: unrecognized option '-setup'", your mex -command in /usr/local/bin is being shadowed by the Polish latex -packages in /usr/bin. If you don't need those, run - - sudo apt-get remove texlive-lang-polish - -This removes the package. Then log out and into a new terminal window -to update the path variable. ***) - -Choose option 1, configure for gcc. Then tell it to save to to -the home folder by answering 'y'. Now the mexopts.sh file is -read-only, so type - - chmod u+w ~/.matlab//mexopts.sh - - is something like R2012a or R2012b. Next edit the -file. Search and replace instances of each of these: - - * 'gcc' and replace with 'gcc-4.4' - * 'g++' and replace with 'g++-4.4' - * 'gfortran' and replace with 'gfortran-4.4' - -And we're done! - -========================================================================== - -MATLAB < 2012 - -The problem is that Ubuntu >= 11.04 uses GCC-4.5, and Matlab MEX files -require GCC-4.3 or earlier (for Matlab R2011a and R2011b). The second -problem is that in Ubuntu 10.10 one could install GCC-4.3 alongside -the newer compiler, but this is no longer supported after 11.04. - -Hence, we have to download, compile, and install GCC-4.3 from sources! -Bummer. - -(*** But first a small fix which prevent Matlab from complaining on startup: -see http://morganbye.net/blog/2011/05/matlab-ubuntu-1104 - -For 64 bit: - - For <= 11.10 (?) - - sudo ln -s /lib64/x86_64-linux-gnu/libc-2.13.so /lib64/libc.so.6 - - or with more recent distributions (>= 12.04) - - sudo ln -s /lib/x86_64-linux-gnu/libc.so.6 /lib64/libc.so.6 - -For 32 bit: - - For <= 11.10 (?) - - sudo ln -s /lib/i386-linux-gnu/libc-2.13.so /lib/libc.so.6 - - or with more recent distributions (>= 12.04) ** check ** - - sudo ln -s /lib/i386-linux-gnu/libc.so.6 /lib/libc.so.6 -***) - -Check that the commands 'matlab' and 'mex' are on your path. -Typically, 'which mex' and 'which matlab' should tell you they're in -/usr/local/bin. - -We'll need a couple of header file libraries: - - sudo apt-get install libmpfr-dev libgmp3-dev - -For 64-bit Ubuntu, also install to cross-compiling libraries: - - sudo apt-get install libc6-dev-i386 - - # Needed? - #sudo ln -s /usr/include/x86_64-linux-gnu/asm /usr/include/asm - #sudo ln -s /usr/include/i386-linux-gnu/asm /usr/include/asm - -Let's download the sources. cd to some work directory with lots of -space. For instance, - - cd /tmp; mkdir gcc-tmp; cd gcc-tmp - -Type (all on one line): - - wget http://gcc.petsads.us/releases/gcc-4.3.6/gcc-core-4.3.6.tar.bz2 \ - http://gcc.petsads.us/releases/gcc-4.3.6/gcc-fortran-4.3.6.tar.bz2 \ - http://gcc.petsads.us/releases/gcc-4.3.6/gcc-g++-4.3.6.tar.bz2 - -This will take a little while (about 30MB is downloaded). Next, untar -the files: - - tar xvjf gcc-core-4.3.6.tar.bz2 - tar xvjf gcc-g++-4.3.6.tar.bz2 - tar xvjf gcc-fortran-4.3.6.tar.bz2 - -Now type - - mkdir gcc-build; cd gcc-build - ../gcc-4.3.6/configure --prefix=/usr/local/gcc-4.3.6 - -Make sure there are no errors. And finally, compile away! - - make - -(*** Update with Ubuntu 10.11 [2011-11-30]: - -Compilation stopped working after upgrade, with complaints that the -linker couldn't find crti.o. Kludgy solution: - -cd /usr/lib -sudo ln -s x86_64-linux-gnu/crt*.o . - -(Adjust second line for 32-bit if necessary.) Future versions of GCC -should fix this. Then type 'make' again to resume the build. - -Another solution is to specify the library path directly. If you're -using bash type - - LIBRARY_PATH=/usr/lib/x86_64-linux-gnu make - -For tcsh, [not tested] - - setenv LIBRARY_PATH /usr/lib/x86_64-linux-gnu - make - -Note that these environment variables also need to be set to compile -with GCC-4.3 later. Better to make the links above, think. -***) - -(*** With Ubuntu 12.10 32bit, I had some other problems. I had to install gcc-multilib to get things like bits/prefix.h. But I'm not sure that was really the problem, as I also had to do (on bash) - -export LIBRARY_PATH=/usr/lib/i386-linux-gnu/ -export C_INCLUDE_PATH=/usr/include/i386-linux-gnu -export CPLUS_INCLUDE_PATH=/usr/include/i386-linux-gnu - -To be confirmed... -***) - -This should take a while. After it's done, type - - sudo make install - -to install all the files to /usr/local/gcc-4.3.6. - -Now that this is done, let's configure MEX/Matlab. Type - - mex -setup - -(*** If you get an error "mex: unrecognized option '-setup'", your mex -command in /usr/local/bin is being shadowed by the Polish latex -packages in /usr/bin. If you don't need those, run - - sudo apt-get remove texlive-lang-polish - -This removes the package. Then log out and into a new terminal window -to update the path variable. ***) - -Choose option 1, configure for gcc. Then tell it to save to to -the home folder by answering 'y'. Now the mexopts.sh file is -read-only, so type - - chmod u+w ~/.matlab//mexopts.sh - - is probably R2011a or R2011b. Next edit the file. -Search and replace the *first two* instances of each of these: - - * 'gcc' and replace with '/usr/local/gcc-4.3.6/bin/gcc' - * 'g++' and replace with '/usr/local/gcc-4.3.6/bin/g++' - * 'gfortran' and replace with '/usr/local/gcc-4.3.6/bin/gfotran' - -So you should be replacing a total of 6 items. (Well, it doesn't hurt -to replace the other instances, but it's not necessary.) - -And we're done! MEX files should compile correctly now. It's now -safe to delete the /tmp/gcc-tmp folder and its contents: - - rm -rf /tmp/gcc-tmp - ------------------------------------------------------------------------- diff --git a/devel/MATLAB_MEX_OSX b/devel/MATLAB_MEX_OSX deleted file mode 100644 index b7079a60..00000000 --- a/devel/MATLAB_MEX_OSX +++ /dev/null @@ -1,29 +0,0 @@ -It can be a little tricky to get MEX files to work with Matlab. The -XCode developer SDK needs to be installed (to get GCC) and, preferrably, -Command Line Tools. (In XCode - Preferences - Downloads ) - -Then, after running 'mex -setup' (mex has to be in the search path), edit -.matlab/R201xx/mexopts.sh. Look for the line - -SDKROOT='/Developer/SDKs/MacOSX10.6.sdk' - -and change to - -SDKROOT=`xcrun --show-sdk-path` - -(these are not plain apostrophes but backticks). This command will automatically find current directory for the XCode SDK that you have selected. - -You might also update all instances of "10.7" or whichever version is specified by default your version, e.g., "10.8" (Snow Leopard), -for example in -MACOSX_DEPLOYMENT_TARGET='10.7' -but this might not be needed - -Finally, find lines (or analogous) -CC='xcrun -sdk macosx10.8 clang' -CXX='xcrun -sdk macosx10.8 clang++' - -and change to -CC=gcc -CXX=g++ - - diff --git a/devel/STYLE b/devel/STYLE deleted file mode 100644 index dfc87187..00000000 --- a/devel/STYLE +++ /dev/null @@ -1,90 +0,0 @@ -BRAIDLAB STYLE GUIDE --------------------- - -If you wish to participate in developing Braidlab, below are some -stylistic guidelines to adhere to. The easiest way to ensure -compliance, of course, is to simply start a new file by copying an -appropriate existing one. - - -GENERAL -------- - -* No tabs; always use spaces instead. -* Delete extra whitespace at the end of lines, or at the end of files. -* Every file should end with a linebreak. -* Break lines at 78 characters unless there is a compelling reason not - to (e.g., long URL). -* Indentation in blocks is two spaces. -* Please spell-check and proofread your comments and help messages! - We're not animals: we try to write well. - - -VERSION CONTROL ---------------- - -* Use a descriptive log message for commits. If you use more than one - line, the first line should be a summary. -* The log message should have proper punctuation and end with a period. -* When relevant, refer to issues on the GitHub tracker using #. - Example: "Start implementing new feature. See issue #45." -* Using "closes issue #45" or "resolves issue #45" will automatically - resolve an issue. This is a good thing to add to a log message, but - be careful not to say "does not resolve issue #45"! - - -MATLAB .m FILES ---------------- - -* Here is an example of formatting for function help: - -function [varargout] = tntype(b) -%TNTYPE Thurston-Nielsen type of a braid. -% T = TNTYPE(B) returns the Thurston-Nielsen type of a braid B. The braid -% is regarded as labeling an isotopy class on the punctured disk. The -% type T can take the values 'finite-order', 'reducible', or -% 'pseudo-Anosov', following the Thurston-Nielsen classification theorem. -% -% [T,ENTR] = TNTYPE(B) also returns the entropy ENTR of the braid. -% -% TNTYPE uses Toby Hall's implementation of the Bestvina-Handel algorithm. -% -% References: -% -% M. Bestvina and M. Handel, "Train-Tracks for surface homeomorphisms," -% Topology 34 (1995), 109-140. -% -% T. Hall, "Train: A C++ program for computing train tracks of surface -% homeomorphisms," http://www.liv.ac.uk/~tobyhall/T_Hall.html -% -% W. P. Thurston, "On the geometry and dynamics of diffeomorphisms of -% surfaces," Bull. Am. Math. Soc. 19 (1988), 417-431. -% -% This is a method for the BRAID class. -% See also BRAID, BRAID.ENTROPY. - - Note that three spaces are used between the bold function name and - the one-line summary. Three spaces are also used for indenting - thereafter. This is to be consistent with Matlab style. The - one-line summary has punctuation. - -* Optional flags should have the capitalization - 'PropertyName','value'. That is, the property itself is - capitalized, but not the value. - -* Global variables should be avoided as much as possible, but if they - are needed should be of the form BRAIDLAB_global_variable_name, with - the latter part in all lowercase. - - -C/C++ FILES ------------ - -* Braidlab-specific macros and compiler flags should have the form - BRAIDLAB_COMPILER_FLAG, all in uppercase. -* In MEX files use the Matlab macros mwSize for size of arrays and - mwIndex for indexing into them. Use mwSignedIndex for differences - between indices. See - http://www.mathworks.com/help/matlab/apiref/mwsize.html - http://www.mathworks.com/help/matlab/apiref/mwindex.html - http://www.mathworks.com/help/matlab/apiref/mwsignedindex.html diff --git a/devel/UNDOCUMENTED b/devel/UNDOCUMENTED deleted file mode 100644 index 1944a103..00000000 --- a/devel/UNDOCUMENTED +++ /dev/null @@ -1,16 +0,0 @@ -Methods and features that are not yet in the guide: - -randomwalk -braid.gencount -loop.nested -loop.components -loop.plot('Components') and other options -loop.getgraph -loop.loop('Enum') -loop.l2norm -debugmsg & BRAIDLAB_debuglvl -BRAIDLAB_threads -@cfbraid class -loop pre-allocation (see devel/test/loop_speedtest) -format loose/compact -databraid.trunc diff --git a/devel/braidlab-issues.zip b/devel/braidlab-issues.zip deleted file mode 100644 index 92fe21a18960d28b66cc00b74acea6cbf0fc31da..0000000000000000000000000000000000000000 GIT binary patch literal 0 HcmV?d00001 literal 135907 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