strands (5jul21)

git-svn-id: svn://tug.org/texlive/trunk@59838 c570f23f-e606-0410-a88d-b1316a301751

1 files changed, 1443 insertions, 0 deletions

diff --git a/Master/texmf-dist/tex/latex/strands/strands.sty b/Master/texmf-dist/tex/latex/strands/strands.sty
new file mode 100644
index 00000000000..b82941397ee
--- /dev/null
+++ b/Master/texmf-dist/tex/latex/strands/strands.sty
@@ -0,0 +1,1443 @@
+%%
+%% This is file `strands.sty',
+%% generated with the docstrip utility.
+%%
+%% The original source files were:
+%%
+%% strands.dtx  (with options: `package')
+%% 
+%% This is a generated file.
+%% 
+%% Copyright (C) 2021 by Diego Arcis <arcisd@gmail.com>
+%% --------------------------------------------------------------------------
+%% This work may be distributed and/or modified under the
+%% conditions of the LaTeX Project Public License, either version 1.3
+%% of this license or (at your option) any later version.
+%% The latest version of this license is in
+%%   http://www.latex-project.org/lppl.txt
+%% and version 1.3 or later is part of all distributions of LaTeX
+%% version 2005/12/01 or later.
+%% 
+\NeedsTeXFormat{LaTeX2e}[1999/12/01]
+\ProvidesPackage{strands}
+    [<+date+> <+version+> <+description+>]
+
+\NeedsTeXFormat{LaTeX2e}
+\ProvidesPackage{strands}[Diego Arcis 2021/07/05 Strands v1.0]
+\RequirePackage{forarray}
+\RequirePackage{ifthen}
+\RequirePackage{tikz}
+\RequirePackage{xfp}
+\RequirePackage{xstring}
+\RequirePackage{xkeyval}
+\usetikzlibrary{snakes}
+\newcommand{\getelem}[3]{ % \getelem{list}{index}{\name}
+\StrBetween[#2,\fpeval{#2+1}]{,#1,}{,}{,}[#3]
+}
+\makeatletter
+\define@cmdkey[str]{strands}{backcolor}{}
+\define@cmdkey[str]{strands}{bend}{}
+\define@cmdkey[str]{strands}{bendbraid}{}
+\define@cmdkey[str]{strands}{bendtangle}{}
+\define@cmdkey[str]{strands}{bulletsize}{}
+\define@cmdkey[str]{strands}{braidcross}{}
+\define@cmdkey[str]{strands}{braidsingcross}{}
+\define@cmdkey[str]{strands}{braidvirtcross}{}
+\define@cmdkey[str]{strands}{coverunion}{}
+\define@cmdkey[str]{strands}{direction}{}
+\define@cmdkey[str]{strands}{externalize}{}
+\define@cmdkey[str]{strands}{font}{}
+\define@cmdkey[str]{strands}{gencharposbraid}{}
+\define@cmdkey[str]{strands}{gencharnegbraid}{}
+\define@cmdkey[str]{strands}{gencharvirtual}{}
+\define@cmdkey[str]{strands}{gencharsingular}{}
+\define@cmdkey[str]{strands}{genchartangle}{}
+\define@cmdkey[str]{strands}{genchartie}{}
+\define@cmdkey[str]{strands}{genchartiedtangle}{}
+\define@cmdkey[str]{strands}{genchartrivial}{}
+\define@cmdkey[str]{strands}{height}{}
+\define@cmdkey[str]{strands}{labelver}{}
+\define@cmdkey[str]{strands}{labelhor}{}
+\define@cmdkey[str]{strands}{norma}{}
+\define@cmdkey[str]{strands}{normb}{}
+\define@cmdkey[str]{strands}{normcolor}{}
+\define@cmdkey[str]{strands}{normsymbol}{}
+\define@cmdkey[str]{strands}{nstr}{}
+\define@cmdkey[str]{strands}{num}{}
+\define@cmdkey[str]{strands}{rotate}{}
+\define@cmdkey[str]{strands}{scale}{}
+\define@cmdkey[str]{strands}{strwidth}{}
+\define@cmdkey[str]{strands}{tiebend}{}
+\define@cmdkey[str]{strands}{tiebull}{}
+\define@cmdkey[str]{strands}{tiebullsize}{}
+\define@cmdkey[str]{strands}{tiecolor}{}
+\define@cmdkey[str]{strands}{tieheight}{}
+\define@cmdkey[str]{strands}{tiesnake}{}
+\define@cmdkey[str]{strands}{tiesnakeamp}{}
+\define@cmdkey[str]{strands}{tiesnakends}{}
+\define@cmdkey[str]{strands}{tiesnakelen}{}
+\define@cmdkey[str]{strands}{tiestyle}{}
+\define@cmdkey[str]{strands}{tiewidth}{}
+\define@cmdkey[str]{strands}{timeswidth}{}
+\define@cmdkey[str]{strands}{tkzpic}{}
+\define@cmdkey[str]{strands}{width}{}
+\presetkeys[str]{strands}{
+backcolor=white, % color of the paper.
+bend=45, % bend of partitions.
+bendbraid=30, % bend for braid crossings.
+bendtangle=45, % bend for tangles.
+braidcross=3, % size of the braid crossing.
+braidsingcross=1.6, % size of the singular braid crossing.
+braidvirtcross=8, % size of the virtual braid crossing.
+bulletsize=0.04,
+coverunion=0.001, % extra length to cover the union of strands.
+direction=1,
+externalize=0, % use 1 to transform images to PDF.
+font=0.7, % size of the fonts for labels.
+gencharposbraid=p,
+gencharnegbraid=n,
+gencharvirtual=v,
+gencharsingular=s,
+genchartangle=t,
+genchartie=e,
+genchartiedtangle=f,
+genchartrivial=i,
+height=1, % to set the height of strands.
+labelver=0.2,
+labelhor=0.03,
+norma=0, % to normalize the height above.
+normb=0, % to normalize the height below.
+normcolor=transparent,
+normsymbol=-,
+nstr=0, % number of strands.
+num=0, % number of dots for arc partitions.
+rotate=0, % to rotate all pictures.
+scale=1, % to scale all pictures.
+strwidth=0.7, % to set the width of the strands.
+tiebend=0, % to set bend of ties.
+tiebull=0, % bullets for ties.
+tiebullsize=0.04,
+tiecolor=red, % to set color of the ties.
+tieheight=0.5, % height of ties respect to the global height.
+tiesnake=false,
+tiesnakeamp=1,
+tiesnakends=0,
+tiesnakelen=3,
+tiestyle=dashed, % to set the type of the tie lines.
+tiewidth=0.5, % to set the width of tie lines.
+timeswidth=3,
+tkzpic=1,
+width=0.6, % to set the width between strands.
+}{}
+\setkeys[str]{strands}{}
+\DeclareOptionX{backcolor}{\renewcommand{\cmdstr@strands@backcolor}{#1}}
+\DeclareOptionX{bend}{\renewcommand{\cmdstr@strands@bend}{#1}}
+\DeclareOptionX{bendbraid}{\renewcommand{\cmdstr@strands@bendbraid}{#1}}
+\DeclareOptionX{bendtangle}{\renewcommand{\cmdstr@strands@bendtangle}{#1}}
+\DeclareOptionX{braidcross}{\renewcommand{\cmdstr@strands@braidcross}{#1}}
+\DeclareOptionX{braidsingcross}{\renewcommand{\cmdstr@strands@braidsingcross}{#1}}
+\DeclareOptionX{braidvirtcross}{\renewcommand{\cmdstr@strands@braidvirtcross}{#1}}
+\DeclareOptionX{bulletsize}{\renewcommand{\cmdstr@strands@bulletsize}{#1}}
+\DeclareOptionX{coverunion}{\renewcommand{\cmdstr@strands@coverunion}{#1}}
+\DeclareOptionX{direction}{\renewcommand{\cmdstr@strands@direction}{#1}}
+\DeclareOptionX{externalize}{\renewcommand{\cmdstr@strands@externalize}{#1}}
+\DeclareOptionX{font}{\renewcommand{\cmdstr@strands@font}{#1}}
+\DeclareOptionX{gencharposbraid}{\renewcommand{\cmdstr@strands@gencharposbraid}{#1}}
+\DeclareOptionX{gencharnegbraid}{\renewcommand{\cmdstr@strands@gencharnegbraid}{#1}}
+\DeclareOptionX{gencharvirtual}{\renewcommand{\cmdstr@strands@gencharvirtual}{#1}}
+\DeclareOptionX{gencharsingular}{\renewcommand{\cmdstr@strands@gencharsingular}{#1}}
+\DeclareOptionX{genchartangle}{\renewcommand{\cmdstr@strands@genchartangle}{#1}}
+\DeclareOptionX{genchartie}{\renewcommand{\cmdstr@strands@genchartie}{#1}}
+\DeclareOptionX{genchartiedtangle}{\renewcommand{\cmdstr@strands@genchartiedtangle}{#1}}
+\DeclareOptionX{height}{\renewcommand{\cmdstr@strands@height}{#1}}
+\DeclareOptionX{labelver}{\renewcommand{\cmdstr@strands@labelver}{#1}}
+\DeclareOptionX{labelhor}{\renewcommand{\cmdstr@strands@labelhor}{#1}}
+\DeclareOptionX{norma}{\renewcommand{\cmdstr@strands@norma}{#1}}
+\DeclareOptionX{normb}{\renewcommand{\cmdstr@strands@normb}{#1}}
+\DeclareOptionX{normcolor}{\renewcommand{\cmdstr@strands@normcolor}{#1}}
+\DeclareOptionX{nstr}{\renewcommand{\cmdstr@strands@nstr}{#1}}
+\DeclareOptionX{num}{\renewcommand{\cmdstr@strands@num}{#1}}
+\DeclareOptionX{rotate}{\renewcommand{\cmdstr@strands@rotate}{#1}}
+\DeclareOptionX{scale}{\renewcommand{\cmdstr@strands@scale}{#1}}
+\DeclareOptionX{strwidth}{\renewcommand{\cmdstr@strands@strwidth}{#1}}
+\DeclareOptionX{tiebend}{\renewcommand{\cmdstr@strands@tiebend}{#1}}
+\DeclareOptionX{tiebull}{\renewcommand{\cmdstr@strands@tiebull}{#1}}
+\DeclareOptionX{tiebullsize}{\renewcommand{\cmdstr@strands@tiebullsize}{#1}}
+\DeclareOptionX{tiecolor}{\renewcommand{\cmdstr@strands@tiecolor}{#1}}
+\DeclareOptionX{tiesnake}{\renewcommand{\cmdstr@strands@tiesnake}{#1}}
+\DeclareOptionX{tiestyle}{\renewcommand{\cmdstr@strands@tiestyle}{#1}}
+\DeclareOptionX{tiewidth}{\renewcommand{\cmdstr@strands@tiewidth}{#1}}
+\DeclareOptionX{timeswidth}{\renewcommand{\cmdstr@strands@timeswidth}{#1}}
+\DeclareOptionX{tkzpic}{\renewcommand{\cmdstr@strands@tkzpic}{#1}}
+\DeclareOptionX{width}{\renewcommand{\cmdstr@strands@width}{#1}}
+\DeclareOptionX*{\PackageWarning{strands}{`\CurrentOption' ignored}} % ignore unknown options.
+\ProcessOptionsX\relax
+\ifnum\cmdstr@strands@externalize=1
+\usetikzlibrary{external}
+\tikzexternalize[optimize=false,prefix=strpack]
+\fi
+\makeatletter
+\define@cmdkey[str]{decor}{bulla}{}
+\define@cmdkey[str]{decor}{bullb}{}
+\define@cmdkey[str]{decor}{bulletends}{}
+\define@cmdkey[str]{decor}{floor}{}
+\define@cmdkey[str]{decor}{font}{}
+\define@cmdkey[str]{decor}{height}{}
+\define@cmdkey[str]{decor}{labelver}{}
+\define@cmdkey[str]{decor}{labelhor}{}
+\define@cmdkey[str]{decor}{nstr}{}
+\define@cmdkey[str]{decor}{type}{}
+\define@cmdkey[str]{decor}{width}{}
+\presetkeys[str]{decor}{
+bulla=1,
+bullb=1,
+bulletends=\cmdstr@strands@bulletsize,
+floor=0,
+font=\cmdstr@strands@font,
+height=\cmdstr@strands@height,
+labelver=\cmdstr@strands@labelver,
+labelhor=\cmdstr@strands@labelhor,
+nstr=\cmdstr@strands@nstr,
+type=3,
+width=\cmdstr@strands@width
+}{}
+\newcommand{\decoratestrands}[1][]{
+\setkeys[str]{decor}{#1} % set variables.
+\foreach\ind in{0,...,\fpeval{\cmdstr@decor@nstr-1}}{
+\ifnum \cmdstr@decor@bulla=1 % bullets above.
+\filldraw(\fpeval{\ind*\cmdstr@decor@width},
+\fpeval{(\cmdstr@decor@floor+1)*\cmdstr@decor@height})circle(\cmdstr@decor@bulletends);
+\fi
+\ifnum \cmdstr@decor@bullb=1 % bullets below.
+\filldraw(\fpeval{\ind*\cmdstr@decor@width},
+\fpeval{\cmdstr@decor@floor*\cmdstr@decor@height})circle(\cmdstr@decor@bulletends);
+\fi
+\ifnum \cmdstr@decor@type<5;
+\ifnum \cmdstr@decor@type>0 % labels above from 1 to n.
+\node[scale=\cmdstr@decor@font]at
+(\fpeval{\ind*\cmdstr@decor@width},
+\fpeval{(\cmdstr@decor@floor+1)*\cmdstr@decor@height+\cmdstr@decor@labelver})
+{$\fpeval{\ind+1}$};
+\fi
+\node[scale=\cmdstr@decor@font]at
+(\fpeval{\ind*\cmdstr@decor@width},
+\fpeval{\cmdstr@decor@floor*\cmdstr@decor@height-\cmdstr@decor@labelver})
+{$\ifnum\fpeval{(\cmdstr@decor@type+1)*(\cmdstr@decor@type-2)}=0{
+\fpeval{\ind+1}
+}\else{\ifnum\fpeval{abs(\cmdstr@decor@type)}=3{
+\fpeval{\ind+\cmdstr@decor@nstr+1}
+}\else{\ifnum\fpeval{abs(\cmdstr@decor@type)}=4{
+\fpeval{\ind+1}'
+}\fi}\fi}\fi$};
+\fi
+\ifnum \cmdstr@decor@type=5
+\ifnum\ind<\fpeval{\cmdstr@decor@nstr/2} % labels from -2n to 2n.
+\node[scale=\cmdstr@decor@font]at
+(\fpeval{(\ind+\cmdstr@decor@nstr/2)*\cmdstr@decor@width},
+\fpeval{(\cmdstr@decor@floor+1)*\cmdstr@decor@height+\cmdstr@decor@labelver})
+{$\fpeval{\ind+1}$};
+\node[scale=\cmdstr@decor@font]at
+(\fpeval{\ind*\cmdstr@decor@width-\cmdstr@decor@labelhor},
+\fpeval{(\cmdstr@decor@floor+1)*\cmdstr@decor@height+\cmdstr@decor@labelver})
+{-$\fpeval{\cmdstr@decor@nstr/2-\ind}$};
+\node[scale=\cmdstr@decor@font]at
+(\fpeval{(\ind+\cmdstr@decor@nstr/2)*\cmdstr@decor@width},
+\fpeval{\cmdstr@decor@floor*\cmdstr@decor@height-\cmdstr@decor@labelver})
+{$\fpeval{\ind+\cmdstr@decor@nstr/2+1}$};
+\node[scale=\cmdstr@decor@font]at
+(\fpeval{\ind*\cmdstr@decor@width-\cmdstr@decor@labelhor},
+\fpeval{\cmdstr@decor@floor*\cmdstr@decor@height-\cmdstr@decor@labelver})
+{-$\fpeval{\cmdstr@decor@nstr-\ind}$};
+\fi
+\fi
+}
+}
+\makeatletter
+\define@cmdkey[str]{vvpart}{bend}{}
+\define@cmdkey[str]{vvpart}{bulla}{}
+\define@cmdkey[str]{vvpart}{bullb}{}
+\define@cmdkey[str]{vvpart}{bulletends}{}
+\define@cmdkey[str]{vvpart}{floor}{}
+\define@cmdkey[str]{vvpart}{font}{}
+\define@cmdkey[str]{vvpart}{height}{}
+\define@cmdkey[str]{vvpart}{labelver}{}
+\define@cmdkey[str]{vvpart}{labelhor}{}
+\define@cmdkey[str]{vvpart}{norma}{}
+\define@cmdkey[str]{vvpart}{normb}{}
+\define@cmdkey[str]{vvpart}{nstr}{}
+\define@cmdkey[str]{vvpart}{permut}{}
+\define@cmdkey[str]{vvpart}{reflect}{}
+\define@cmdkey[str]{vvpart}{strwidth}{}
+\define@cmdkey[str]{vvpart}{type}{}
+\define@cmdkey[str]{vvpart}{width}{}
+\presetkeys[str]{vvpart}{
+bend=\cmdstr@strands@bend,
+bulla=1,
+bullb=1,
+bulletends=\cmdstr@strands@bulletsize,
+floor=0,
+font=\cmdstr@strands@font,
+height=\cmdstr@strands@height,
+labelver=\cmdstr@strands@labelver,
+labelhor=\cmdstr@strands@labelhor,
+norma=\cmdstr@strands@norma,
+normb=\cmdstr@strands@normb,
+nstr=\cmdstr@strands@nstr,
+permut=0, % use 1 to draw permutations (to use with \permutation).
+reflect=0,
+strwidth=\cmdstr@strands@strwidth,
+type=3,
+width=\cmdstr@strands@width
+}{}
+\newcommand{\vvpartition}[2][]{
+\setkeys[str]{vvpart}{#1} % set variables.
+\node[\cmdstr@strands@normcolor]at(0,\cmdstr@vvpart@norma){\cmdstr@strands@normsymbol};
+\node[\cmdstr@strands@normcolor]at(0,\cmdstr@vvpart@normb){\cmdstr@strands@normsymbol};
+\StrRemoveBraces{#2}[\nobracespart]
+\let\oldnumstrands\cmdstr@vvpart@nstr
+\renewcommand{\cmdstr@vvpart@nstr}
+{\fpeval{max(abs(min(\nobracespart)),abs(max(\nobracespart)),\fpeval{abs(\oldnumstrands)})}}
+\decoratestrands[
+bulla=\cmdstr@vvpart@bulla,
+bullb=\cmdstr@vvpart@bullb,
+bulletends=\cmdstr@vvpart@bulletends,
+floor=\cmdstr@vvpart@floor,
+font=\cmdstr@vvpart@font,
+height=\cmdstr@vvpart@height,
+labelver=\cmdstr@vvpart@labelver,
+labelhor=\cmdstr@vvpart@labelhor,
+nstr=\cmdstr@vvpart@nstr,
+type=\cmdstr@vvpart@type,
+width=\cmdstr@vvpart@width
+]
+\foreach\ind in{0,...,\fpeval{\cmdstr@vvpart@nstr-1}}{
+\ifnum\cmdstr@vvpart@permut=1
+\getelem{#2}{\fpeval{\ind+1}}{\index}
+\draw[line width=\cmdstr@vvpart@strwidth](\fpeval{\ind*\cmdstr@vvpart@width},
+\fpeval{\cmdstr@vvpart@height+\cmdstr@vvpart@floor*\cmdstr@vvpart@height})to
+(\fpeval{(\ifnum\fpeval{\index+0}>0 \index\else\fpeval{\ind+1}\fi-1)*
+\cmdstr@vvpart@width},\cmdstr@vvpart@floor*\cmdstr@vvpart@height);
+\fi
+}
+\ifnum\cmdstr@vvpart@permut=0 \foreach\block in{#2}{
+\StrCount{\block}{,}[\numcom]
+\ifnum\numcom>0\foreach\ind in {2,...,\fpeval{\numcom+1}}{
+\getelem{\block}{\fpeval{\ind-1}}{\firbul}
+\getelem{\block}{\ind}{\secbul}
+\ifnum \cmdstr@vvpart@reflect=1 % reflect connections vertically.
+\let\oldfirbul\firbul
+\renewcommand{\firbul}{-\oldfirbul}
+\let\oldsecbul\secbul
+\renewcommand{\secbul}{-\oldsecbul}
+\fi
+\draw[line width=\cmdstr@vvpart@strwidth]
+(\fpeval{(abs(\firbul)-1)*\cmdstr@vvpart@width},
+\ifnum\firbul>0
+\fpeval{(\cmdstr@vvpart@floor+1)*\cmdstr@vvpart@height}
+\else
+\fpeval{\cmdstr@vvpart@floor*\cmdstr@vvpart@height}
+\fi
+)
+to[bend right=\ifnum \fpeval{\firbul*\secbul}>0
+\fpeval{(\firbul/abs(\firbul))*((abs(\secbul)-abs(\firbul))/
+abs(abs(\secbul)-abs(\firbul)))*\cmdstr@vvpart@bend}
+\else
+0
+\fi]
+(\fpeval{(abs(\secbul)-1)*\cmdstr@vvpart@width},
+\ifnum\secbul>0
+\fpeval{(\cmdstr@vvpart@floor+1)*\cmdstr@vvpart@height}
+\else
+\fpeval{\cmdstr@vvpart@floor*\cmdstr@vvpart@height}
+\fi
+);
+}\fi
+}\fi
+}
+\makeatletter
+\define@cmdkey[str]{vpart}{bend}{}
+\define@cmdkey[str]{vpart}{bulla}{}
+\define@cmdkey[str]{vpart}{bullb}{}
+\define@cmdkey[str]{vpart}{bulletends}{}
+\define@cmdkey[str]{vpart}{floor}{}
+\define@cmdkey[str]{vpart}{font}{}
+\define@cmdkey[str]{vpart}{height}{}
+\define@cmdkey[str]{vpart}{labelver}{}
+\define@cmdkey[str]{vpart}{labelhor}{}
+\define@cmdkey[str]{vpart}{norma}{}
+\define@cmdkey[str]{vpart}{normb}{}
+\define@cmdkey[str]{vpart}{nstr}{}
+\define@cmdkey[str]{vpart}{permut}{}
+\define@cmdkey[str]{vpart}{reflect}{}
+\define@cmdkey[str]{vpart}{rotate}{}
+\define@cmdkey[str]{vpart}{scale}{}
+\define@cmdkey[str]{vpart}{strwidth}{}
+\define@cmdkey[str]{vpart}{tkzpic}{}
+\define@cmdkey[str]{vpart}{type}{}
+\define@cmdkey[str]{vpart}{width}{}
+\presetkeys[str]{vpart}{
+bend=\cmdstr@strands@bend,
+bulla=1,
+bullb=1,
+bulletends=\cmdstr@strands@bulletsize,
+floor=0,
+font=\cmdstr@strands@font,
+height=\cmdstr@strands@height,
+labelver=\cmdstr@strands@labelver,
+labelhor=\cmdstr@strands@labelhor,
+norma=\cmdstr@strands@norma,
+normb=\cmdstr@strands@normb,
+nstr=\cmdstr@strands@nstr,
+permut=0, % use 1 to draw permutations (to use with \permutation).
+reflect=0,
+rotate=\cmdstr@strands@rotate,
+scale=\cmdstr@strands@scale,
+strwidth=\cmdstr@strands@strwidth,
+tkzpic=\cmdstr@strands@tkzpic,
+type=3,
+width=\cmdstr@strands@width
+}{}
+\newcommand{\vpartition}[2][]{
+\setkeys[str]{vpart}{#1} % set variables.
+\ifthenelse{\equal{\cmdstr@vpart@tkzpic}{1}}{
+\begin{tikzpicture}[rotate=\cmdstr@vpart@rotate,scale=\cmdstr@vpart@scale]
+\vvpartition[
+bend=\cmdstr@vpart@bend,
+bulla=\cmdstr@vpart@bulla,
+bullb=\cmdstr@vpart@bullb,
+bulletends=\cmdstr@vpart@bulletends,
+floor=\cmdstr@vpart@floor,
+font=\cmdstr@vpart@font,
+height=\cmdstr@vpart@height,
+labelver=\cmdstr@vpart@labelver,
+labelhor=\cmdstr@vpart@labelhor,
+norma=\cmdstr@vpart@norma,
+normb=\cmdstr@vpart@normb,
+nstr=\cmdstr@vpart@nstr,
+permut=\cmdstr@vpart@permut,
+reflect=\cmdstr@vpart@reflect,
+strwidth=\cmdstr@vpart@strwidth,
+type=\cmdstr@vpart@type,
+width=\cmdstr@vpart@width
+]{#2}
+\end{tikzpicture}
+}{
+\vvpartition[
+bend=\cmdstr@vpart@bend,
+bulla=\cmdstr@vpart@bulla,
+bullb=\cmdstr@vpart@bullb,
+bulletends=\cmdstr@vpart@bulletends,
+floor=\cmdstr@vpart@floor,
+font=\cmdstr@vpart@font,
+height=\cmdstr@vpart@height,
+labelver=\cmdstr@vpart@labelver,
+labelhor=\cmdstr@vpart@labelhor,
+norma=\cmdstr@vpart@norma,
+normb=\cmdstr@vpart@normb,
+nstr=\cmdstr@vpart@nstr,
+permut=\cmdstr@vpart@permut,
+reflect=\cmdstr@vpart@reflect,
+strwidth=\cmdstr@vpart@strwidth,
+type=\cmdstr@vpart@type,
+width=\cmdstr@vpart@width
+]{#2}
+}
+}
+\makeatletter
+\define@cmdkey[str]{apart}{bend}{}
+\define@cmdkey[str]{apart}{bull}{}
+\define@cmdkey[str]{apart}{bulletsize}{}
+\define@cmdkey[str]{apart}{floor}{}
+\define@cmdkey[str]{apart}{font}{}
+\define@cmdkey[str]{apart}{labelver}{}
+\define@cmdkey[str]{apart}{labelhor}{}
+\define@cmdkey[str]{apart}{norma}{}
+\define@cmdkey[str]{apart}{normb}{}
+\define@cmdkey[str]{apart}{num}{}
+\define@cmdkey[str]{apart}{rotate}{}
+\define@cmdkey[str]{apart}{scale}{}
+\define@cmdkey[str]{apart}{strwidth}{}
+\define@cmdkey[str]{apart}{tkzpic}{}
+\define@cmdkey[str]{apart}{type}{}
+\define@cmdkey[str]{apart}{width}{}
+\presetkeys[str]{apart}{
+bend=\cmdstr@strands@bend,
+bull=1,
+bulletsize=\cmdstr@strands@bulletsize,
+floor=0,
+font=\cmdstr@strands@font,
+labelver=\cmdstr@strands@labelver,
+labelhor=\cmdstr@strands@labelhor,
+norma=\cmdstr@strands@norma,
+normb=\cmdstr@strands@normb,
+num=\cmdstr@strands@num,
+rotate=\cmdstr@strands@rotate,
+scale=\cmdstr@strands@scale,
+strwidth=\cmdstr@strands@strwidth,
+tkzpic=\cmdstr@strands@tkzpic,
+type=1,
+width=\cmdstr@strands@width
+}{}
+\newcommand{\arcpartition}[2][]{
+\setkeys[str]{apart}{#1}
+\vpartition[
+bend=\cmdstr@apart@bend,
+bulla=0, % no bullets above.
+bullb=\cmdstr@apart@bull,
+bulletends=\cmdstr@apart@bulletsize,
+floor=\cmdstr@apart@floor,
+font=\cmdstr@apart@font,
+labelver=\cmdstr@apart@labelver,
+labelhor=\cmdstr@apart@labelhor,
+norma=\cmdstr@apart@norma,
+normb=\cmdstr@apart@normb,
+nstr=\cmdstr@apart@num,
+reflect=1, % put connections below.
+rotate=\cmdstr@apart@rotate,
+scale=\cmdstr@apart@scale,
+strwidth=\cmdstr@apart@strwidth,
+tkzpic=\cmdstr@apart@tkzpic,
+type=-\cmdstr@apart@type,
+width=\cmdstr@apart@width
+]{#2}
+}
+\makeatletter
+\define@cmdkey[str]{perm}{bulla}{}
+\define@cmdkey[str]{perm}{bullb}{}
+\define@cmdkey[str]{perm}{bulletends}{}
+\define@cmdkey[str]{perm}{floor}{}
+\define@cmdkey[str]{perm}{font}{}
+\define@cmdkey[str]{perm}{height}{}
+\define@cmdkey[str]{perm}{labelver}{}
+\define@cmdkey[str]{perm}{labelhor}{}
+\define@cmdkey[str]{perm}{norma}{}
+\define@cmdkey[str]{perm}{normb}{}
+\define@cmdkey[str]{perm}{nstr}{}
+\define@cmdkey[str]{perm}{rotate}{}
+\define@cmdkey[str]{perm}{scale}{}
+\define@cmdkey[str]{perm}{strwidth}{}
+\define@cmdkey[str]{perm}{tkzpic}{}
+\define@cmdkey[str]{perm}{type}{}
+\define@cmdkey[str]{perm}{width}{}
+\presetkeys[str]{perm}{
+bulla=1,
+bullb=1,
+bulletends=\cmdstr@strands@bulletsize,
+floor=0,
+font=\cmdstr@strands@font,
+height=\cmdstr@strands@height,
+labelver=\cmdstr@strands@labelver,
+labelhor=\cmdstr@strands@labelhor,
+norma=\cmdstr@strands@norma,
+normb=\cmdstr@strands@normb,
+nstr=\cmdstr@strands@nstr,
+rotate=\cmdstr@strands@rotate,
+scale=\cmdstr@strands@scale,
+strwidth=\cmdstr@strands@strwidth,
+tkzpic=\cmdstr@strands@tkzpic,
+type=2,
+width=\cmdstr@strands@width
+}{}
+\newcommand{\permutation}[2][]{
+\setkeys[str]{perm}{#1}
+\vpartition[
+bulla=\cmdstr@perm@bulla,
+bullb=\cmdstr@perm@bullb,
+bulletends=\cmdstr@perm@bulletends,
+floor=\cmdstr@perm@floor,
+font=\cmdstr@perm@font,
+height=\cmdstr@perm@height,
+labelver=\cmdstr@perm@labelver,
+labelhor=\cmdstr@perm@labelhor,
+norma=\cmdstr@perm@norma,
+normb=\cmdstr@perm@normb,
+nstr=\cmdstr@perm@nstr,
+permut=1, % permutation.
+rotate=\cmdstr@perm@rotate,
+scale=\cmdstr@perm@scale,
+strwidth=\cmdstr@perm@strwidth,
+tkzpic=\cmdstr@perm@tkzpic,
+type=\cmdstr@perm@type,
+width=\cmdstr@perm@width
+]{#2}
+}
+\makeatletter
+\define@cmdkey[str]{tpair}{above}{}
+\define@cmdkey[str]{tpair}{bend}{}
+\define@cmdkey[str]{tpair}{bulla}{}
+\define@cmdkey[str]{tpair}{bullb}{}
+\define@cmdkey[str]{tpair}{bulletends}{}
+\define@cmdkey[str]{tpair}{floor}{}
+\define@cmdkey[str]{tpair}{font}{}
+\define@cmdkey[str]{tpair}{height}{}
+\define@cmdkey[str]{tpair}{labelver}{}
+\define@cmdkey[str]{tpair}{labelhor}{}
+\define@cmdkey[str]{tpair}{norma}{}
+\define@cmdkey[str]{tpair}{normb}{}
+\define@cmdkey[str]{tpair}{nstr}{}
+\define@cmdkey[str]{tpair}{rotate}{}
+\define@cmdkey[str]{tpair}{scale}{}
+\define@cmdkey[str]{tpair}{strwidth}{}
+\define@cmdkey[str]{tpair}{tkzpic}{}
+\define@cmdkey[str]{tpair}{type}{}
+\define@cmdkey[str]{tpair}{width}{}
+\presetkeys[str]{tpair}{
+above=1,
+bend=\cmdstr@strands@bend,
+bulla=1,
+bullb=1,
+bulletends=\cmdstr@strands@bulletsize,
+floor=0,
+font=\cmdstr@strands@font,
+height=\cmdstr@strands@height,
+labelver=\cmdstr@strands@labelver,
+labelhor=\cmdstr@strands@labelhor,
+norma=\cmdstr@strands@norma,
+normb=\cmdstr@strands@normb,
+nstr=\cmdstr@strands@nstr,
+rotate=\cmdstr@strands@rotate,
+scale=\cmdstr@strands@scale,
+strwidth=\cmdstr@strands@strwidth,
+tkzpic=\cmdstr@strands@tkzpic,
+type=-1,
+width=\cmdstr@strands@width
+}{}
+\newcommand{\tiedpair}[3][]{
+\setkeys[str]{tpair}{#1}
+\ifthenelse{\equal{\cmdstr@tpair@tkzpic}{1}}{
+\begin{tikzpicture}[rotate=\cmdstr@tpair@rotate,scale=\cmdstr@tpair@scale]
+\permutation[
+bulla=\cmdstr@tpair@bulla,
+bullb=\cmdstr@tpair@bullb,
+bulletends=\cmdstr@tpair@bulletends,
+floor=\cmdstr@tpair@floor,
+font=\cmdstr@tpair@font,
+height=\cmdstr@tpair@height,
+labelver=\cmdstr@tpair@labelver,
+labelhor=\cmdstr@tpair@labelhor,
+norma=\cmdstr@tpair@norma,
+normb=\cmdstr@tpair@normb,
+nstr=\cmdstr@tpair@nstr,
+strwidth=\cmdstr@tpair@strwidth,
+tkzpic=0,
+type=\cmdstr@tpair@type,
+width=\cmdstr@tpair@width
+]{#2}
+\arcpartition[
+bend=\cmdstr@tpair@bend,
+bull=0, % no bullets.
+bulletsize=\cmdstr@tpair@bulletsize,
+floor=\fpeval{\cmdstr@tpair@floor+\cmdstr@tpair@above*\cmdstr@tpair@height},
+tkzpic=0,
+type=0, % no labels.
+strwidth=\cmdstr@tpair@strwidth,
+width=\cmdstr@tpair@width
+]{#3}
+\end{tikzpicture}
+}{
+\permutation[
+bulla=\cmdstr@tpair@bulla,
+bullb=\cmdstr@tpair@bullb,
+bulletends=\cmdstr@tpair@bulletends,
+floor=\cmdstr@tpair@floor,
+font=\cmdstr@tpair@font,
+height=\cmdstr@tpair@height,
+labelver=\cmdstr@tpair@labelver,
+labelhor=\cmdstr@tpair@labelhor,
+norma=\cmdstr@tpair@norma,
+normb=\cmdstr@tpair@normb,
+nstr=\cmdstr@tpair@nstr,
+strwidth=\cmdstr@tpair@strwidth,
+tkzpic=0,
+type=\cmdstr@tpair@type,
+width=\cmdstr@tpair@width
+]{#2}
+\arcpartition[
+bend=\cmdstr@tpair@bend,
+bull=0, % no bullets.
+floor=\fpeval{\cmdstr@tpair@floor+\cmdstr@tpair@above*\cmdstr@tpair@height},
+tkzpic=0,
+type=0, % no labels.
+strwidth=\cmdstr@tpair@strwidth,
+width=\cmdstr@tpair@width
+]{#3}
+}
+}
+\makeatletter
+\define@cmdkey[str]{tie}{bend}{}
+\define@cmdkey[str]{tie}{bull}{}
+\define@cmdkey[str]{tie}{bulletie}{}
+\define@cmdkey[str]{tie}{floor}{}
+\define@cmdkey[str]{tie}{height}{}
+\define@cmdkey[str]{tie}{color}{}
+\define@cmdkey[str]{tie}{snake}{}
+\define@cmdkey[str]{tie}{snakeamp}{}
+\define@cmdkey[str]{tie}{snakends}{}
+\define@cmdkey[str]{tie}{snakelen}{}
+\define@cmdkey[str]{tie}{style}{}
+\define@cmdkey[str]{tie}{tieheight}{}
+\define@cmdkey[str]{tie}{tiewidth}{}
+\define@cmdkey[str]{tie}{width}{}
+\presetkeys[str]{tie}{
+bend=\cmdstr@strands@tiebend, % bend of the ties.
+bull=1, % use 1 to use bullets, 0 otherwise.
+bulletie=\cmdstr@strands@bulletsize,
+color=\cmdstr@strands@tiecolor, % color of the ties.
+floor=0, % the picture starts at floor*height.
+height=\cmdstr@strands@height, % height of the strands.
+snake=\cmdstr@strands@tiesnake, % true or false to snake the tie line.
+snakeamp=\cmdstr@strands@tiesnakeamp, % snake amplitude.
+snakends=\cmdstr@strands@tiesnakends, % snake lengths of ends.
+snakelen=\cmdstr@strands@tiesnakelen, % snake lengths.
+style=\cmdstr@strands@tiestyle, % type of the tie (solid, dashed, dotted, etc).
+tieheight=\cmdstr@strands@tieheight, % height of the tie respect to the global height.
+tiewidth=\cmdstr@strands@tiewidth, % width of the tie line.
+width=\cmdstr@strands@width % width between strands.
+}{}
+\newcommand{\tie}[2][]{
+\setkeys[str]{tie}{#1}
+\foreach\elem[count=\ind]in{#2}{
+\StrRemoveBraces{\elem}[\nobrace]
+\getelem{\nobrace}{1}{\elemwidth} % get width of elem.
+\getelem{\nobrace}{2}{\elemheight} % get height of elem.
+\StrCount{\nobrace}{,}[\elemcoms]
+\ifnum\elemcoms=0 \renewcommand{\elemheight}{\cmdstr@tie@tieheight}\fi % update height of elem.
+\ifnum \cmdstr@tie@bull=1
+\filldraw[\cmdstr@tie@color](\fpeval{(\elemwidth-1)*\cmdstr@tie@width},
+\fpeval{\elemheight*\cmdstr@tie@height+\cmdstr@tie@floor*\cmdstr@tie@height})
+circle(\cmdstr@tie@bulletie);
+\fi
+\ifnum\ind>1
+\getelem{#2}{\fpeval{\ind-1}}{\prevelem}
+\StrRemoveBraces{\prevelem}[\prevnobrace]
+\getelem{\prevnobrace}{1}{\prevelemwidth}
+\getelem{\prevnobrace}{2}{\prevelemheight}
+\StrCount{\prevnobrace}{,}[\prevelemcoms]
+\ifnum\prevelemcoms=0 \renewcommand{\prevelemheight}{\cmdstr@tie@tieheight}\fi
+\draw[
+bend right=\cmdstr@tie@bend,
+color=\cmdstr@tie@color,
+line width=\cmdstr@tie@tiewidth,
+decorate=\cmdstr@tie@snake,
+decoration={
+snake,
+amplitude=\cmdstr@tie@snakeamp,
+post length=\cmdstr@tie@snakends,
+pre length=\cmdstr@tie@snakends,
+segment length=\cmdstr@tie@snakelen
+},
+style=\cmdstr@tie@style
+]
+(\fpeval{(\elemwidth-1)*\cmdstr@tie@width},
+\fpeval{\elemheight*\cmdstr@tie@height+\cmdstr@tie@floor*\cmdstr@tie@height})to
+(\fpeval{(\prevelemwidth-1)*\cmdstr@tie@width},
+\fpeval{\prevelemheight*\cmdstr@tie@height+\cmdstr@tie@floor*\cmdstr@tie@height});
+\fi
+}
+}
+\makeatletter
+\define@cmdkey[str]{bbackstr}{cdnx}{}
+\define@cmdkey[str]{bbackstr}{cdny}{}
+\define@cmdkey[str]{bbackstr}{color}{}
+\define@cmdkey[str]{bbackstr}{height}{}
+\define@cmdkey[str]{bbackstr}{strwidth}{}
+\define@cmdkey[str]{bbackstr}{timeswidth}{}
+\define@cmdkey[str]{bbackstr}{width}{}
+\presetkeys[str]{bbackstr}{
+cdnx=nothing,
+cdny=nothing,
+height=\cmdstr@strands@height,
+strwidth=\cmdstr@strands@strwidth,
+timeswidth=\cmdstr@strands@timeswidth, % times the width of the back line is bigger.
+width=\cmdstr@strands@width
+}{}
+\newcommand{\bbackstrands}[1][]{ %
+\setkeys[str]{bbackstr}{#1}
+\draw[
+color=\cmdstr@strands@backcolor,
+line width=\fpeval{\cmdstr@bbackstr@timeswidth*\cmdstr@bbackstr@strwidth}pt
+](\cmdstr@bbackstr@cdnx,\cmdstr@bbackstr@cdny)
+to(\cmdstr@bbackstr@cdnx,\fpeval{\cmdstr@bbackstr@cdny-\cmdstr@bbackstr@height});
+\draw[
+color=\cmdstr@strands@backcolor,
+line width=\fpeval{\cmdstr@bbackstr@timeswidth*\cmdstr@bbackstr@strwidth}pt
+](\fpeval{\cmdstr@bbackstr@cdnx+\cmdstr@bbackstr@width},\cmdstr@bbackstr@cdny)
+to(\fpeval{\cmdstr@bbackstr@cdnx+\cmdstr@bbackstr@width},
+\fpeval{\cmdstr@bbackstr@cdny-\cmdstr@bbackstr@height});
+}
+\makeatletter
+\define@cmdkey[str]{lleftstr}{bend}{}
+\define@cmdkey[str]{lleftstr}{cdnx}{}
+\define@cmdkey[str]{lleftstr}{cdny}{}
+\define@cmdkey[str]{lleftstr}{color}{}
+\define@cmdkey[str]{lleftstr}{height}{}
+\define@cmdkey[str]{lleftstr}{strwidth}{}
+\define@cmdkey[str]{lleftstr}{width}{}
+\presetkeys[str]{lleftstr}{
+bend=\cmdstr@strands@bendbraid,
+cdnx=nothing,
+cdny=nothing,
+color=black,
+height=\cmdstr@strands@height,
+strwidth=\cmdstr@strands@strwidth,
+width=\cmdstr@strands@width
+}{}
+\newcommand{\lleftstrand}[1][]{
+\setkeys[str]{lleftstr}{#1}
+\draw[
+color=\cmdstr@lleftstr@color,
+line width=\cmdstr@lleftstr@strwidth pt
+](\cmdstr@lleftstr@cdnx,\fpeval{\cmdstr@lleftstr@cdny+\cmdstr@strands@coverunion})
+to[bend right=\cmdstr@lleftstr@bend]
+(\fpeval{\cmdstr@lleftstr@cdnx+\cmdstr@lleftstr@width/2},
+\fpeval{\cmdstr@lleftstr@cdny-\cmdstr@lleftstr@height/2})
+to[bend left=\cmdstr@lleftstr@bend]
+(\fpeval{\cmdstr@lleftstr@cdnx+\cmdstr@lleftstr@width},
+\fpeval{\cmdstr@lleftstr@cdny-\cmdstr@lleftstr@height-\cmdstr@strands@coverunion});
+}
+\makeatletter
+\define@cmdkey[str]{rrightstr}{bend}{}
+\define@cmdkey[str]{rrightstr}{cdnx}{}
+\define@cmdkey[str]{rrightstr}{cdny}{}
+\define@cmdkey[str]{rrightstr}{color}{}
+\define@cmdkey[str]{rrightstr}{floor}{}
+\define@cmdkey[str]{rrightstr}{height}{}
+\define@cmdkey[str]{rrightstr}{strwidth}{}
+\define@cmdkey[str]{rrightstr}{width}{}
+\presetkeys[str]{rrightstr}{
+bend=\cmdstr@strands@bendbraid,
+cdnx=nothing,
+cdny=nothing,
+color=black,
+floor=0,
+height=\cmdstr@strands@height,
+strwidth=\cmdstr@strands@strwidth,
+width=\cmdstr@strands@width
+}{}
+\newcommand{\rrightstrand}[1][]{ % color / init-x-coordinate / init-y-coordinate.
+\setkeys[str]{rrightstr}{#1}
+\draw[
+color=\cmdstr@rrightstr@color,
+line width=\cmdstr@rrightstr@strwidth pt
+](\fpeval{\cmdstr@rrightstr@cdnx+\cmdstr@rrightstr@width},
+\fpeval{\cmdstr@rrightstr@cdny+\cmdstr@strands@coverunion})
+to[bend left=\cmdstr@rrightstr@bend]
+(\fpeval{\cmdstr@rrightstr@cdnx+\cmdstr@rrightstr@width/2},
+\fpeval{\cmdstr@rrightstr@cdny-\cmdstr@rrightstr@height/2})
+to[bend right=\cmdstr@rrightstr@bend]
+(\cmdstr@rrightstr@cdnx,
+\fpeval{\cmdstr@rrightstr@cdny-\cmdstr@rrightstr@height-\cmdstr@strands@coverunion});
+}
+\makeatletter
+\define@cmdkey[str]{ccrossback}{cdnx}{}
+\define@cmdkey[str]{ccrossback}{cdny}{}
+\define@cmdkey[str]{ccrossback}{height}{}
+\define@cmdkey[str]{ccrossback}{width}{}
+\presetkeys[str]{ccrossback}{
+cdnx=nothing,
+cdny=nothing,
+height=\cmdstr@strands@height,
+width=\cmdstr@strands@width
+}{}
+\newcommand{\ccrossback}[1][]{
+\setkeys[str]{ccrossback}{#1}
+\filldraw[\cmdstr@strands@backcolor]
+(\fpeval{\cmdstr@ccrossback@cdnx+\cmdstr@ccrossback@width/2},
+\fpeval{\cmdstr@ccrossback@cdny-\cmdstr@ccrossback@height/2})
+circle(\cmdstr@strands@braidcross pt);
+}
+\makeatletter
+\define@cmdkey[str]{bbraidgen}{bend}{}
+\define@cmdkey[str]{bbraidgen}{cdnx}{}
+\define@cmdkey[str]{bbraidgen}{cdny}{}
+\define@cmdkey[str]{bbraidgen}{colorleft}{}
+\define@cmdkey[str]{bbraidgen}{coloright}{}
+\define@cmdkey[str]{bbraidgen}{colorsingular}{}
+\define@cmdkey[str]{bbraidgen}{colorvirtual}{}
+\define@cmdkey[str]{bbraidgen}{height}{}
+\define@cmdkey[str]{bbraidgen}{strwidth}{}
+\define@cmdkey[str]{bbraidgen}{type}{}
+\define@cmdkey[str]{bbraidgen}{width}{}
+\presetkeys[str]{bbraidgen}{
+bend=\cmdstr@strands@bendbraid,
+cdnx=0,
+cdny=0,
+colorleft=black,
+coloright=black,
+colorsingular=black,
+colorvirtual=black,
+height=\cmdstr@strands@height,
+strwidth=\cmdstr@strands@strwidth,
+type=1, % negative-braid=-1 | positive-braid=1 | virtual-braid=2 | singular-braid=3
+width=\cmdstr@strands@width
+}{}
+\tikzset{
+cross/.style={ % node style to draw x--crosses inside nodes.
+path picture={
+   \draw[black]
+(path picture bounding box.south east)--
+(path picture bounding box.north west)
+(path picture bounding box.south west)--
+(path picture bounding box.north east);
+}
+}
+}
+\newcommand{\bbraidgen}[1][]{
+\setkeys[str]{bbraidgen}{#1}
+\bbackstrands[ % trivial two-strands-braid.
+cdnx=\cmdstr@bbraidgen@cdnx,
+cdny=\cmdstr@bbraidgen@cdny,
+height=\cmdstr@bbraidgen@height,
+strwidth=\cmdstr@bbraidgen@strwidth,
+width=\cmdstr@bbraidgen@width
+]
+\ifnum\cmdstr@bbraidgen@type<1 % negative generator.
+\rrightstrand[
+bend=\cmdstr@bbraidgen@bend,
+cdnx=\cmdstr@bbraidgen@cdnx,
+cdny=\cmdstr@bbraidgen@cdny,
+color=\cmdstr@bbraidgen@coloright,
+height=\cmdstr@bbraidgen@height,
+strwidth=\cmdstr@bbraidgen@strwidth,
+width=\cmdstr@bbraidgen@width
+]
+\ifnum\cmdstr@bbraidgen@type<2
+\ccrossback[
+cdnx=\cmdstr@bbraidgen@cdnx,
+cdny=\cmdstr@bbraidgen@cdny,
+height=\cmdstr@bbraidgen@height,
+width=\cmdstr@bbraidgen@width
+]
+\fi
+\lleftstrand[
+bend=\cmdstr@bbraidgen@bend,
+cdnx=\cmdstr@bbraidgen@cdnx,
+cdny=\cmdstr@bbraidgen@cdny,
+color=\cmdstr@bbraidgen@colorleft,
+height=\cmdstr@bbraidgen@height,
+strwidth=\cmdstr@bbraidgen@strwidth,
+width=\cmdstr@bbraidgen@width
+]
+\else % positive generator.
+\lleftstrand[
+bend=\cmdstr@bbraidgen@bend,
+cdnx=\cmdstr@bbraidgen@cdnx,
+cdny=\cmdstr@bbraidgen@cdny,
+color=\cmdstr@bbraidgen@colorleft,
+height=\cmdstr@bbraidgen@height,
+strwidth=\cmdstr@bbraidgen@strwidth,
+width=\cmdstr@bbraidgen@width
+]
+\ifnum\cmdstr@bbraidgen@type<2 % over-under circle only if type is one.
+\ccrossback[
+cdnx=\cmdstr@bbraidgen@cdnx,
+cdny=\cmdstr@bbraidgen@cdny,
+height=\cmdstr@bbraidgen@height,
+width=\cmdstr@bbraidgen@width
+]
+\fi
+\rrightstrand[
+bend=\cmdstr@bbraidgen@bend,
+cdnx=\cmdstr@bbraidgen@cdnx,
+cdny=\cmdstr@bbraidgen@cdny,
+color=\cmdstr@bbraidgen@coloright,
+height=\cmdstr@bbraidgen@height,
+strwidth=\cmdstr@bbraidgen@strwidth,
+width=\cmdstr@bbraidgen@width
+]
+\ifnum\cmdstr@bbraidgen@type=2 % virtual crossing.
+\node[
+circle,
+cross,
+draw=\cmdstr@bbraidgen@colorvirtual,
+fill=\cmdstr@strands@backcolor,
+inner sep=0,
+line width=\cmdstr@bbraidgen@strwidth,
+minimum width=\cmdstr@strands@braidvirtcross
+]
+at(\fpeval{\cmdstr@bbraidgen@cdnx+\cmdstr@bbraidgen@width/2},
+\fpeval{\cmdstr@bbraidgen@cdny-\cmdstr@bbraidgen@height/2}){};
+\fi
+\ifnum\cmdstr@bbraidgen@type=3 % singular crossing.
+\filldraw[\cmdstr@bbraidgen@colorsingular]
+(\fpeval{\cmdstr@bbraidgen@cdnx+\cmdstr@bbraidgen@width/2},
+\fpeval{\cmdstr@bbraidgen@cdny-\cmdstr@bbraidgen@height/2})
+circle(\cmdstr@strands@braidsingcross pt);
+\fi
+\fi
+}
+\makeatletter
+\define@cmdkey[str]{ttanglegen}{bend}{}
+\define@cmdkey[str]{ttanglegen}{cdnx}{}
+\define@cmdkey[str]{ttanglegen}{cdny}{}
+\define@cmdkey[str]{ttanglegen}{color}{}
+\define@cmdkey[str]{ttanglegen}{height}{}
+\define@cmdkey[str]{ttanglegen}{strwidth}{}
+\define@cmdkey[str]{ttanglegen}{tiecolor}{}
+\define@cmdkey[str]{ttanglegen}{tied}{}
+\define@cmdkey[str]{ttanglegen}{tiesnake}{}
+\define@cmdkey[str]{ttanglegen}{tiesnakeamp}{}
+\define@cmdkey[str]{ttanglegen}{tiesnakelen}{}
+\define@cmdkey[str]{ttanglegen}{tiesnakends}{}
+\define@cmdkey[str]{ttanglegen}{tiestyle}{}
+\define@cmdkey[str]{ttanglegen}{tiewidth}{}
+\define@cmdkey[str]{ttanglegen}{width}{}
+\presetkeys[str]{ttanglegen}{
+bend=\cmdstr@strands@bendtangle,
+cdnx=0,
+cdny=0,
+color=black,
+height=\cmdstr@strands@height,
+strwidth=\cmdstr@strands@strwidth,
+tiecolor=\cmdstr@strands@tiecolor,
+tied=0,
+tiesnake=\cmdstr@strands@tiesnake,
+tiesnakeamp=\cmdstr@strands@tiesnakeamp,
+tiesnakelen=\cmdstr@strands@tiesnakelen,
+tiesnakends=\cmdstr@strands@tiesnakends,
+tiestyle=\cmdstr@strands@tiestyle,
+tiewidth=\cmdstr@strands@tiewidth,
+width=\cmdstr@strands@width 
+}{}
+\newcommand{\ttanglegen}[1][]{
+\setkeys[str]{ttanglegen}{#1}
+\bbackstrands[ % trivial two-strands-braid.
+cdnx=\cmdstr@ttanglegen@cdnx,
+cdny=\cmdstr@ttanglegen@cdny,
+height=\cmdstr@ttanglegen@height,
+strwidth=\cmdstr@ttanglegen@strwidth,
+width=\cmdstr@ttanglegen@width
+]
+\draw[
+bend right=\cmdstr@strands@bendtangle,
+color=\cmdstr@ttanglegen@color,
+line width=\cmdstr@strands@strwidth
+](\cmdstr@ttanglegen@cdnx,\fpeval{\cmdstr@ttanglegen@cdny+\cmdstr@strands@coverunion})
+to(\fpeval{\cmdstr@ttanglegen@cdnx+\cmdstr@ttanglegen@width/2},
+\fpeval{\cmdstr@ttanglegen@cdny-\cmdstr@ttanglegen@height/3+0.03})
+to(\fpeval{\cmdstr@ttanglegen@cdnx+\cmdstr@ttanglegen@width},
+\fpeval{\cmdstr@ttanglegen@cdny+\cmdstr@strands@coverunion});
+\draw[
+bend left=\cmdstr@strands@bendtangle,
+color=\cmdstr@ttanglegen@color,
+line width=\cmdstr@strands@strwidth
+](\cmdstr@ttanglegen@cdnx,
+\fpeval{\cmdstr@ttanglegen@cdny-\cmdstr@ttanglegen@height-\cmdstr@strands@coverunion})
+to(\fpeval{\cmdstr@ttanglegen@cdnx+\cmdstr@ttanglegen@width/2},
+\fpeval{\cmdstr@ttanglegen@cdny-(2*\cmdstr@ttanglegen@height)/3-0.03})
+to(\fpeval{\cmdstr@ttanglegen@cdnx+\cmdstr@ttanglegen@width},
+\fpeval{\cmdstr@ttanglegen@cdny-\cmdstr@ttanglegen@height-\cmdstr@strands@coverunion});
+\ifnum\cmdstr@ttanglegen@tied=1 % tied version.
+\draw[
+color=\cmdstr@ttanglegen@tiecolor,
+line width=\cmdstr@ttanglegen@tiewidth,
+decorate=\cmdstr@ttanglegen@tiesnake,
+decoration={
+snake,
+amplitude=\cmdstr@ttanglegen@tiesnakeamp,
+post length=\cmdstr@ttanglegen@tiesnakends,
+pre length=\cmdstr@ttanglegen@tiesnakends,
+segment length=\cmdstr@ttanglegen@tiesnakelen
+},
+style=\cmdstr@ttanglegen@tiestyle
+](\fpeval{\cmdstr@ttanglegen@cdnx+\cmdstr@ttanglegen@width/2},
+\fpeval{\cmdstr@ttanglegen@cdny-\cmdstr@ttanglegen@height/3+0.03})
+to(\fpeval{\cmdstr@ttanglegen@cdnx+\cmdstr@ttanglegen@width/2},
+\fpeval{\cmdstr@ttanglegen@cdny-(2*\cmdstr@ttanglegen@height)/3-0.03});
+\fi
+}
+\makeatletter
+\define@cmdkey[str]{aaddgen}{bendbraid}{}
+\define@cmdkey[str]{aaddgen}{bendtangle}{}
+\define@cmdkey[str]{aaddgen}{direction}{}
+\define@cmdkey[str]{aaddgen}{floor}{}
+\define@cmdkey[str]{aaddgen}{generator}{}
+\define@cmdkey[str]{aaddgen}{height}{}
+\define@cmdkey[str]{aaddgen}{level}{}
+\define@cmdkey[str]{aaddgen}{numlevs}{}
+\define@cmdkey[str]{aaddgen}{posx}{}
+\define@cmdkey[str]{aaddgen}{posy}{}
+\define@cmdkey[str]{aaddgen}{strwidth}{}
+\define@cmdkey[str]{aaddgen}{tiebull}{}
+\define@cmdkey[str]{aaddgen}{tiebullsize}{}
+\define@cmdkey[str]{aaddgen}{tiecolor}{}
+\define@cmdkey[str]{aaddgen}{tieheight}{}
+\define@cmdkey[str]{aaddgen}{tiesnake}{}
+\define@cmdkey[str]{aaddgen}{tiesnakeamp}{}
+\define@cmdkey[str]{aaddgen}{tiesnakends}{}
+\define@cmdkey[str]{aaddgen}{tiesnakelen}{}
+\define@cmdkey[str]{aaddgen}{tiestyle}{}
+\define@cmdkey[str]{aaddgen}{tiewidth}{}
+\define@cmdkey[str]{aaddgen}{width}{}
+\presetkeys[str]{aaddgen}{
+bendbraid=\cmdstr@strands@bendbraid,
+bendtangle=\cmdstr@strands@bendtangle,
+direction=\cmdstr@strands@direction,
+floor=0,
+generator=s1,
+height=\cmdstr@strands@height,
+level=0,
+numlevs=0,
+posx=nothing, % internal.
+posy=nothing, % internal.
+strwidth=\cmdstr@strands@strwidth,
+tiebull=\cmdstr@strands@tiebull,
+tiebullsize=\cmdstr@strands@tiebullsize,
+tiecolor=\cmdstr@strands@tiecolor,
+tieheight=\cmdstr@strands@tieheight, 
+tiesnake=\cmdstr@strands@tiesnake,
+tiesnakeamp=\cmdstr@strands@tiesnakeamp,
+tiesnakends=\cmdstr@strands@tiesnakends,
+tiesnakelen=\cmdstr@strands@tiesnakelen,
+tiestyle=\cmdstr@strands@tiestyle,
+tiewidth=\cmdstr@strands@tiewidth,
+width=\cmdstr@strands@width
+}{}
+\newcommand{\aaddgen}[1][]{
+\setkeys[str]{aaddgen}{#1}
+\StrChar{\cmdstr@aaddgen@generator}{1}[\firstchar]
+\StrBehind{\cmdstr@aaddgen@generator}{\firstchar}[\numstrand]
+\renewcommand{\cmdstr@aaddgen@posx}{\fpeval{(\numstrand-1)*\cmdstr@aaddgen@width}}
+\ifnum\cmdstr@aaddgen@direction=1
+\renewcommand{\cmdstr@aaddgen@posy}{\fpeval{(\cmdstr@aaddgen@numlevs+2+\cmdstr@aaddgen@floor-\cmdstr@aaddgen@level)*\cmdstr@aaddgen@height}}
+\fi 
+\ifnum\cmdstr@aaddgen@direction=0
+\renewcommand{\cmdstr@aaddgen@posy}{\fpeval{\cmdstr@aaddgen@level*\cmdstr@aaddgen@height}}
+\fi
+\ifthenelse{\equal{\firstchar}{\cmdstr@strands@gencharnegbraid}}{
+\bbraidgen[
+bend=\cmdstr@aaddgen@bendbraid,
+cdnx=\cmdstr@aaddgen@posx,
+cdny=\cmdstr@aaddgen@posy,
+height=\cmdstr@aaddgen@height,
+strwidth=\cmdstr@aaddgen@strwidth,
+type=-1,
+width=\cmdstr@aaddgen@width
+]
+}{\ifthenelse{\equal{\firstchar}{\cmdstr@strands@gencharposbraid}}{
+\bbraidgen[
+bend=\cmdstr@aaddgen@bendbraid,
+cdnx=\cmdstr@aaddgen@posx,
+cdny=\cmdstr@aaddgen@posy,
+height=\cmdstr@aaddgen@height,
+strwidth=\cmdstr@aaddgen@strwidth,
+type=1,
+width=\cmdstr@aaddgen@width
+]
+}{\ifthenelse{\equal{\firstchar}{\cmdstr@strands@gencharvirtual}}{
+\bbraidgen[
+bend=\cmdstr@aaddgen@bendbraid,
+cdnx=\cmdstr@aaddgen@posx,
+cdny=\cmdstr@aaddgen@posy,
+height=\cmdstr@aaddgen@height,
+strwidth=\cmdstr@aaddgen@strwidth,
+type=2,
+width=\cmdstr@aaddgen@width
+]
+}{\ifthenelse{\equal{\firstchar}{\cmdstr@strands@gencharsingular}}{
+\bbraidgen[
+bend=\cmdstr@aaddgen@bendbraid,
+cdnx=\cmdstr@aaddgen@posx,
+cdny=\cmdstr@aaddgen@posy,
+height=\cmdstr@aaddgen@height,
+strwidth=\cmdstr@aaddgen@strwidth,
+type=3,
+width=\cmdstr@aaddgen@width
+]
+}{\ifthenelse{\equal{\firstchar}{\cmdstr@strands@genchartangle}}{
+\ttanglegen[
+bend=\cmdstr@aaddgen@bendtangle,
+cdnx=\cmdstr@aaddgen@posx,
+cdny=\cmdstr@aaddgen@posy,
+height=\cmdstr@aaddgen@height,
+strwidth=\cmdstr@aaddgen@strwidth,
+tied=0,
+width=\cmdstr@aaddgen@width
+]
+}{\ifthenelse{\equal{\firstchar}{\cmdstr@strands@genchartie}}{
+\tie[
+bull=\cmdstr@aaddgen@tiebull,
+bulletie=\cmdstr@aaddgen@tiebullsize, %%%%%%%%%%%%%%%%%%%%%
+color=\cmdstr@aaddgen@tiecolor,
+height=\cmdstr@aaddgen@height,
+floor=\fpeval{\cmdstr@aaddgen@posy-1},
+snake=\cmdstr@aaddgen@tiesnake,
+snakeamp=\cmdstr@aaddgen@tiesnakeamp,
+snakelen=\cmdstr@aaddgen@tiesnakelen,
+snakends=\cmdstr@aaddgen@tiesnakends,
+style=\cmdstr@aaddgen@tiestyle,
+tieheight=\cmdstr@aaddgen@tieheight,
+tiewidth=\cmdstr@aaddgen@tiewidth,
+width=\cmdstr@aaddgen@width
+]{\numstrand,\fpeval{\numstrand+1}}
+}{\ifthenelse{\equal{\firstchar}{\cmdstr@strands@genchartiedtangle}}{
+\ttanglegen[
+bend=\cmdstr@aaddgen@bendtangle,
+cdnx=\cmdstr@aaddgen@posx,
+cdny=\cmdstr@aaddgen@posy,
+height=\cmdstr@aaddgen@height,
+strwidth=\cmdstr@aaddgen@strwidth,
+tiecolor=\cmdstr@aaddgen@tiecolor,
+tied=1,
+tiesnake=\cmdstr@aaddgen@tiesnake,
+tiesnakeamp=\cmdstr@aaddgen@tiesnakeamp,
+tiesnakelen=\cmdstr@aaddgen@tiesnakelen,
+tiesnakends=\cmdstr@aaddgen@tiesnakends,
+tiestyle=\cmdstr@aaddgen@tiestyle,
+tiewidth=\cmdstr@aaddgen@tiewidth,
+width=\cmdstr@aaddgen@width
+]
+}{DO NOTHING!}}}}}}} % \ifthenelse always use "else", so it will do nothing if other letter.
+}
+\makeatletter
+\define@cmdkey[str]{ggens}{bendbraid}{}
+\define@cmdkey[str]{ggens}{bendtangle}{}
+\define@cmdkey[str]{ggens}{bulla}{}
+\define@cmdkey[str]{ggens}{bullb}{}
+\define@cmdkey[str]{ggens}{bulletends}{}
+\define@cmdkey[str]{ggens}{direction}{}
+\define@cmdkey[str]{ggens}{floor}{}
+\define@cmdkey[str]{ggens}{font}{}
+\define@cmdkey[str]{ggens}{height}{}
+\define@cmdkey[str]{ggens}{labelver}{}
+\define@cmdkey[str]{ggens}{labelhor}{}
+\define@cmdkey[str]{ggens}{nstr}{}
+\define@cmdkey[str]{ggens}{nstrsave}{}
+\define@cmdkey[str]{ggens}{strwidth}{}
+\define@cmdkey[str]{ggens}{tiebull}{}
+\define@cmdkey[str]{ggens}{tiebullsize}{}
+\define@cmdkey[str]{ggens}{tiecolor}{}
+\define@cmdkey[str]{ggens}{tieheight}{}
+\define@cmdkey[str]{ggens}{tiesnake}{}
+\define@cmdkey[str]{ggens}{tiesnakeamp}{}
+\define@cmdkey[str]{ggens}{tiesnakends}{}
+\define@cmdkey[str]{ggens}{tiesnakelen}{}
+\define@cmdkey[str]{ggens}{tiestyle}{}
+\define@cmdkey[str]{ggens}{tiewidth}{}
+\define@cmdkey[str]{ggens}{type}{}
+\define@cmdkey[str]{ggens}{width}{}
+\presetkeys[str]{ggens}{
+bendbraid=\cmdstr@strands@bendbraid,
+bendtangle=\cmdstr@strands@bendtangle,
+bulla=1,
+bullb=1,
+bulletends=\cmdstr@strands@bulletsize,
+direction=\cmdstr@strands@direction,
+floor=0,
+font=\cmdstr@strands@font,
+height=\cmdstr@strands@height,
+labelver=\cmdstr@strands@labelver,
+labelhor=\cmdstr@strands@labelhor,
+nstr=0,
+nstrsave=0,
+strwidth=\cmdstr@strands@strwidth,
+tiebull=\cmdstr@strands@tiebull,
+tiebullsize=\cmdstr@strands@tiebullsize,
+tiecolor=\cmdstr@strands@tiecolor,
+tieheight=\cmdstr@strands@tieheight, 
+tiesnake=\cmdstr@strands@tiesnake,
+tiesnakeamp=\cmdstr@strands@tiesnakeamp,
+tiesnakends=\cmdstr@strands@tiesnakends,
+tiesnakelen=\cmdstr@strands@tiesnakelen,
+tiestyle=\cmdstr@strands@tiestyle,
+tiewidth=\cmdstr@strands@tiewidth,
+type=3,
+width=\cmdstr@strands@width
+}{}
+\newcounter{levelscounter} % count levels.
+\newcommand{\sstrands}[2][]{
+\setkeys[str]{ggens}{#1}
+\StrSubstitute{#2}{ }{}[\cmdstr@ggens@nstrsave] % remove whitespaces.
+\StrSubstitute{\cmdstr@ggens@nstrsave}{\cmdstr@strands@gencharposbraid}{}[\cmdstr@ggens@nstrsave]
+\StrSubstitute{\cmdstr@ggens@nstrsave}{\cmdstr@strands@gencharnegbraid}{}[\cmdstr@ggens@nstrsave]
+\StrSubstitute{\cmdstr@ggens@nstrsave}{\cmdstr@strands@gencharvirtual}{}[\cmdstr@ggens@nstrsave]
+\StrSubstitute{\cmdstr@ggens@nstrsave}{\cmdstr@strands@gencharsingular}{}[\cmdstr@ggens@nstrsave]
+\StrSubstitute{\cmdstr@ggens@nstrsave}{\cmdstr@strands@genchartangle}{}[\cmdstr@ggens@nstrsave]
+\StrSubstitute{\cmdstr@ggens@nstrsave}{\cmdstr@strands@genchartie}{}[\cmdstr@ggens@nstrsave]
+\StrSubstitute{\cmdstr@ggens@nstrsave}{\cmdstr@strands@genchartiedtangle}{}[\cmdstr@ggens@nstrsave]
+\StrSubstitute{\cmdstr@ggens@nstrsave}{\cmdstr@strands@genchartrivial}{}[\cmdstr@ggens@nstrsave]
+\StrSubstitute{\cmdstr@ggens@nstrsave}{*}{,}[\cmdstr@ggens@nstrsave]
+\StrSubstitute{\cmdstr@ggens@nstrsave}{-}{,}[\cmdstr@ggens@nstrsave]
+\let\oldnstr\cmdstr@ggens@nstr
+\renewcommand{\cmdstr@ggens@nstr}{\fpeval{max(max(\cmdstr@ggens@nstrsave)+1,\oldnstr)}}
+\StrCount{#2}{*}[\numlevs]
+\permutation[ % backstrands.
+bulla=0,
+bullb=0,
+floor=\fpeval{\cmdstr@ggens@floor/((\numlevs+1)*\cmdstr@ggens@height)}, % ??????????????
+height=\fpeval{(\numlevs+1)*\cmdstr@ggens@height},
+nstr=\cmdstr@ggens@nstr,
+tkzpic=0,
+type=0
+]{1}
+\setcounter{levelscounter}{0}
+\ForEach{*}{ % for each level.
+\stepcounter{levelscounter}
+\ForEachSublevel{-}{ % for each generator in level.
+\aaddgen[ % add the generator.
+bendbraid=\cmdstr@ggens@bendbraid,
+bendtangle=\cmdstr@ggens@bendtangle,
+direction=\cmdstr@ggens@direction,
+floor=\cmdstr@ggens@floor,
+generator=\thislevelitem,
+height=\cmdstr@ggens@height,
+level=\thelevelscounter,
+numlevs=\numlevs,
+strwidth=\cmdstr@ggens@strwidth,
+tiebull=\cmdstr@ggens@tiebull,
+tiebullsize=\cmdstr@ggens@tiebullsize,
+tiecolor=\cmdstr@ggens@tiecolor,
+tieheight=\cmdstr@ggens@tieheight, 
+tiesnake=\cmdstr@ggens@tiesnake,
+tiesnakeamp=\cmdstr@ggens@tiesnakeamp,
+tiesnakends=\cmdstr@ggens@tiesnakends,
+tiesnakelen=\cmdstr@ggens@tiesnakelen,
+tiestyle=\cmdstr@ggens@tiestyle,
+tiewidth=\cmdstr@ggens@tiewidth,
+width=\cmdstr@ggens@width
+]
+}
+}{#2}
+\decoratestrands[
+bulla=\cmdstr@ggens@bulla,
+bullb=\cmdstr@ggens@bullb,
+bulletends=\cmdstr@ggens@bulletends,
+floor=\fpeval{\cmdstr@ggens@floor/((\numlevs+1)*\cmdstr@ggens@height)},
+font=\cmdstr@ggens@font,
+height=\fpeval{(\numlevs+1)*\cmdstr@ggens@height},
+labelver=\cmdstr@ggens@labelver,
+labelhor=\cmdstr@ggens@labelhor,
+nstr=\cmdstr@ggens@nstr,
+type=\cmdstr@ggens@type,
+width=\cmdstr@ggens@width
+]
+}
+\makeatletter
+\define@cmdkey[str]{gens}{bendbraid}{}
+\define@cmdkey[str]{gens}{bendtangle}{}
+\define@cmdkey[str]{gens}{bulla}{}
+\define@cmdkey[str]{gens}{bullb}{}
+\define@cmdkey[str]{gens}{bulletends}{}
+\define@cmdkey[str]{gens}{direction}{}
+\define@cmdkey[str]{gens}{floor}{}
+\define@cmdkey[str]{gens}{font}{}
+\define@cmdkey[str]{gens}{height}{}
+\define@cmdkey[str]{gens}{labelver}{}
+\define@cmdkey[str]{gens}{labelhor}{}
+\define@cmdkey[str]{gens}{nstr}{}
+\define@cmdkey[str]{gens}{nstrsave}{}
+\define@cmdkey[str]{gens}{rotate}{}
+\define@cmdkey[str]{gens}{scale}{}
+\define@cmdkey[str]{gens}{strwidth}{}
+\define@cmdkey[str]{gens}{tiebull}{}
+\define@cmdkey[str]{gens}{tiebullsize}{}
+\define@cmdkey[str]{gens}{tiecolor}{}
+\define@cmdkey[str]{gens}{tieheight}{}
+\define@cmdkey[str]{gens}{tiesnake}{}
+\define@cmdkey[str]{gens}{tiesnakeamp}{}
+\define@cmdkey[str]{gens}{tiesnakends}{}
+\define@cmdkey[str]{gens}{tiesnakelen}{}
+\define@cmdkey[str]{gens}{tiestyle}{}
+\define@cmdkey[str]{gens}{tiewidth}{}
+\define@cmdkey[str]{gens}{tkzpic}{}
+\define@cmdkey[str]{gens}{type}{}
+\define@cmdkey[str]{gens}{width}{}
+\presetkeys[str]{gens}{
+bendbraid=\cmdstr@strands@bendbraid,
+bendtangle=\cmdstr@strands@bendtangle,
+bulla=1,
+bullb=1,
+bulletends=\cmdstr@strands@bulletsize,
+direction=\cmdstr@strands@direction,
+floor=0,
+font=\cmdstr@strands@font,
+height=\cmdstr@strands@height,
+labelver=\cmdstr@strands@labelver,
+labelhor=\cmdstr@strands@labelhor,
+nstr=0,
+nstrsave=0,
+rotate=\cmdstr@strands@rotate,
+scale=\cmdstr@strands@scale,
+strwidth=\cmdstr@strands@strwidth,
+tiebull=\cmdstr@strands@tiebull,
+tiebullsize=\cmdstr@strands@tiebullsize,
+tiecolor=\cmdstr@strands@tiecolor,
+tieheight=\cmdstr@strands@tieheight, 
+tiesnake=\cmdstr@strands@tiesnake,
+tiesnakeamp=\cmdstr@strands@tiesnakeamp,
+tiesnakends=\cmdstr@strands@tiesnakends,
+tiesnakelen=\cmdstr@strands@tiesnakelen,
+tiestyle=\cmdstr@strands@tiestyle,
+tiewidth=\cmdstr@strands@tiewidth,
+tkzpic=\cmdstr@strands@tkzpic,
+type=3,
+width=\cmdstr@strands@width
+}{}
+\newcommand{\strands}[2][]{
+\setkeys[str]{gens}{#1}
+\ifthenelse{\equal{\cmdstr@gens@tkzpic}{1}}{
+\begin{tikzpicture}[rotate=\cmdstr@gens@rotate,scale=\cmdstr@gens@scale]
+\sstrands[
+bendbraid=\cmdstr@gens@bendbraid,
+bendtangle=\cmdstr@gens@bendtangle,
+bulla=\cmdstr@gens@bulla,
+bullb=\cmdstr@gens@bullb,
+bulletends=\cmdstr@gens@bulletends,
+direction=\cmdstr@gens@direction,
+floor=\cmdstr@gens@floor,
+font=\cmdstr@gens@font,
+height=\cmdstr@gens@height,
+labelver=\cmdstr@gens@labelver,
+labelhor=\cmdstr@gens@labelhor,
+nstr=\cmdstr@gens@nstr,
+nstrsave=\cmdstr@gens@nstrsave,
+strwidth=\cmdstr@gens@strwidth,
+tiebull=\cmdstr@gens@tiebull,
+tiebullsize=\cmdstr@gens@tiebullsize,
+tiecolor=\cmdstr@gens@tiecolor,
+tieheight=\cmdstr@gens@tieheight,
+tiesnake=\cmdstr@gens@tiesnake,
+tiesnakeamp=\cmdstr@gens@tiesnakeamp,
+tiesnakends=\cmdstr@gens@tiesnakends,
+tiesnakelen=\cmdstr@gens@tiesnakelen,
+tiestyle=\cmdstr@gens@tiestyle,
+tiewidth=\cmdstr@gens@tiewidth,
+type=\cmdstr@gens@type,
+width=\cmdstr@gens@width
+]{#2}
+\end{tikzpicture}
+}{
+\sstrands[
+bendbraid=\cmdstr@gens@bendbraid,
+bendtangle=\cmdstr@gens@bendtangle,
+bulla=\cmdstr@gens@bulla,
+bullb=\cmdstr@gens@bullb,
+bulletends=\cmdstr@gens@bulletends,
+direction=\cmdstr@gens@direction,
+floor=\cmdstr@gens@floor,
+font=\cmdstr@gens@font,
+height=\cmdstr@gens@height,
+labelver=\cmdstr@gens@labelver,
+labelhor=\cmdstr@gens@labelhor,
+nstr=\cmdstr@gens@nstr,
+nstrsave=\cmdstr@gens@nstrsave,
+strwidth=\cmdstr@gens@strwidth,
+tiebull=\cmdstr@gens@tiebull,
+tiebullsize=\cmdstr@gens@tiebullsize,
+tiecolor=\cmdstr@gens@tiecolor,
+tieheight=\cmdstr@gens@tieheight,
+tiesnake=\cmdstr@gens@tiesnake,
+tiesnakeamp=\cmdstr@gens@tiesnakeamp,
+tiesnakends=\cmdstr@gens@tiesnakends,
+tiesnakelen=\cmdstr@gens@tiesnakelen,
+tiestyle=\cmdstr@gens@tiestyle,
+tiewidth=\cmdstr@gens@tiewidth,
+type=\cmdstr@gens@type,
+width=\cmdstr@gens@width
+]{#2}
+}
+}%    \end{macrocode}
+
+\endinput
+%%
+%% End of file `strands.sty'.