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| -rw-r--r-- | Master/texmf-dist/doc/latex/strands/README.md | 15 | ||||
| -rw-r--r-- | Master/texmf-dist/doc/latex/strands/strands.pdf | bin | 0 -> 156024 bytes | |||
| -rw-r--r-- | Master/texmf-dist/source/latex/strands/strands.dtx | 1835 | ||||
| -rw-r--r-- | Master/texmf-dist/source/latex/strands/strands.ins | 57 | ||||
| -rw-r--r-- | Master/texmf-dist/tex/latex/strands/strands.sty | 1443 | ||||
| -rwxr-xr-x | Master/tlpkg/bin/tlpkg-ctan-check | 2 | ||||
| -rw-r--r-- | Master/tlpkg/tlpsrc/collection-pictures.tlpsrc | 1 | ||||
| -rw-r--r-- | Master/tlpkg/tlpsrc/strands.tlpsrc | 0 |
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diff --git a/Master/texmf-dist/doc/latex/strands/README.md b/Master/texmf-dist/doc/latex/strands/README.md new file mode 100644 index 00000000000..88b84d5b4cc --- /dev/null +++ b/Master/texmf-dist/doc/latex/strands/README.md @@ -0,0 +1,15 @@ +% +% 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. +% +% This work has the LPPL maintenance status `maintained'. +% +% The Current Maintainer of this work is Diego Arcis. +%
\ No newline at end of file diff --git a/Master/texmf-dist/doc/latex/strands/strands.pdf b/Master/texmf-dist/doc/latex/strands/strands.pdf Binary files differnew file mode 100644 index 00000000000..b09fa4ed880 --- /dev/null +++ b/Master/texmf-dist/doc/latex/strands/strands.pdf diff --git a/Master/texmf-dist/source/latex/strands/strands.dtx b/Master/texmf-dist/source/latex/strands/strands.dtx new file mode 100644 index 00000000000..a1ac4f1b4b0 --- /dev/null +++ b/Master/texmf-dist/source/latex/strands/strands.dtx @@ -0,0 +1,1835 @@ +% \iffalse meta-comment +% +% 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. +% +% This work has the LPPL maintenance status `maintained'. +% +% The Current Maintainer of this work is Diego Arcis. +% +% This work consists of the files strands.dtx and strands.ins +% and the derived filebase strands.sty. +% +% \fi +% +% \iffalse +%<*driver> +\ProvidesFile{strands.dtx} +%</driver> +%<package>\NeedsTeXFormat{LaTeX2e}[1999/12/01] +%<package>\ProvidesPackage{strands} +%<*package> + [<+date+> <+version+> <+description+>] +%</package> +% +%<*driver> +\documentclass{ltxdoc} +\usepackage{strands}[<+date+>] +\EnableCrossrefs +\CodelineIndex +\RecordChanges +\begin{document} + \DocInput{strands.dtx} + \PrintChanges + \PrintIndex +\end{document} +%</driver> +% \fi +% +% \CheckSum{1713} +% +% \CharacterTable +% {Upper-case \A\B\C\D\E\F\G\H\I\J\K\L\M\N\O\P\Q\R\S\T\U\V\W\X\Y\Z +% Lower-case \a\b\c\d\e\f\g\h\i\j\k\l\m\n\o\p\q\r\s\t\u\v\w\x\y\z +% Digits \0\1\2\3\4\5\6\7\8\9 +% Exclamation \! Double quote \" Hash (number) \# +% Dollar \$ Percent \% Ampersand \& +% Acute accent \' Left paren \( Right paren \) +% Asterisk \* Plus \+ Comma \, +% Minus \- Point \. Solidus \/ +% Colon \: Semicolon \; Less than \< +% Equals \= Greater than \> Question mark \? +% Commercial at \@ Left bracket \[ Backslash \\ +% Right bracket \] Circumflex \^ Underscore \_ +% Grave accent \` Left brace \{ Vertical bar \| +% Right brace \} Tilde \~} +% +% +% \changes{<+version+>}{<+date+>}{Converted to DTX file} +% +% \DoNotIndex{\newcommand,\newenvironment} +% +% \providecommand*{\url}{\texttt} +% \GetFileInfo{strands.dtx} +% \title{The \textsf{strands} package} +% \author{Diego Arcis \\ \url{arcisd@gmail.com}} +% \date{\fileversion~from \filedate} +% +% \maketitle +% +% \section{Introduction} +% +% Put text here. +% +% \section{Usage} +% +% Put text here. +% +% +% \DescribeMacro{\getelem} +% +% +% \DescribeMacro{\decoratestrands} +% +% +% \DescribeMacro{\vvpartition} +% +% +% \DescribeMacro{\vpartition} +% +% +% \DescribeMacro{\arcpartition} +% +% +% \DescribeMacro{\permutation} +% +% +% \DescribeMacro{\tiedpair} +% +% +% \DescribeMacro{\tie} +% +% +% \DescribeMacro{\bbackstrands} +% +% +% \DescribeMacro{\lleftstrand} +% +% +% \DescribeMacro{\rrightstrand} +% +% +% \DescribeMacro{\ccrossback} +% +% +% \DescribeMacro{\bbraidgen} +% +% +% \DescribeMacro{\ttanglegen} +% +% +% \DescribeMacro{\aaddgen} +% +% +% \DescribeMacro{\sstrands} +% +% +% \DescribeMacro{\strands} +% + +% +% \StopEventually{} +% +% \section{Implementation} +% +% \iffalse +%<*package> +% \fi +% +% \begin{macrocode} +\NeedsTeXFormat{LaTeX2e} +\ProvidesPackage{strands}[Diego Arcis 2021/07/05 Strands v1.0] +% \end{macrocode} +% packages: +% \begin{macrocode} +\RequirePackage{forarray} +\RequirePackage{ifthen} +\RequirePackage{tikz} +\RequirePackage{xfp} +\RequirePackage{xstring} +\RequirePackage{xkeyval} +\usetikzlibrary{snakes} +% \end{macrocode} +% +% \begin{macro}{\getelem} +% \begin{macrocode} +\newcommand{\getelem}[3]{ % \getelem{list}{index}{\name} + \StrBetween[#2,\fpeval{#2+1}]{,#1,}{,}{,}[#3] +} +% \end{macrocode} +% \end{macro} +% +% global variables: +% \begin{macrocode} +\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}{} +% \end{macrocode} +% default options: +% \begin{macrocode} +\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}{} +% \end{macrocode} +% declare custom options: +% \begin{macrocode} +\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 +% \end{macrocode} +% \decoratestrands - macro to add bullets and labels to picture. +% +% \begin{macrocode} +\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 +}{} +% \end{macrocode} +% +% \begin{macro}{\decoratestrands} +% \begin{macrocode} +\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 +% \end{macrocode} +% classic labels. +% \begin{macrocode} + \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 +% \end{macrocode} +% signed labels (n must be even). +% \begin{macrocode} + \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 + } +} +% \end{macrocode} +% \end{macro} +% +% \vpartition - macro to draw set partitions in the partition monoid. +% +% Example: the set partition {1,2}{3,-4}{4,-3} of [2*4] is drawn as follows: +% +% \vpartition[<options>]{{1,2},{3,-4},{4,-3}} +% +% 1 2 3 4 +% | | | | +% ----- - - +% - +% - - +% | | +% 5 6 7 8 +% +% \begin{macrocode} +\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 +}{} +% \end{macrocode} +% +% \begin{macro}{\vvpartition} +% \begin{macrocode} +\newcommand{\vvpartition}[2][]{ + \setkeys[str]{vvpart}{#1} % set variables. +% \end{macrocode} +% normalize vertical size. +% \begin{macrocode} + \node[\cmdstr@strands@normcolor]at(0,\cmdstr@vvpart@norma){\cmdstr@strands@normsymbol}; + \node[\cmdstr@strands@normcolor]at(0,\cmdstr@vvpart@normb){\cmdstr@strands@normsymbol}; +% \end{macrocode} +% number of strands. +% \begin{macrocode} + \StrRemoveBraces{#2}[\nobracespart] + \let\oldnumstrands\cmdstr@vvpart@nstr + \renewcommand{\cmdstr@vvpart@nstr} + {\fpeval{max(abs(min(\nobracespart)),abs(max(\nobracespart)),\fpeval{abs(\oldnumstrands)})}} +% \end{macrocode} +% bullets and labels. +% \begin{macrocode} + \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 + ] +% \end{macrocode} +% connections: permutation case. +% \begin{macrocode} + \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 + } +% \end{macrocode} +% connections: general case. +% \begin{macrocode} + \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] +% \end{macrocode} +% from. +% \begin{macrocode} + (\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 + ) +% \end{macrocode} +% bending. +% \begin{macrocode} + 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] +% \end{macrocode} +% to. +% \begin{macrocode} + (\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 +} +% \end{macrocode} +% \end{macro} +% +% \begin{macrocode} +\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 +}{} +% \end{macrocode} +% +% \begin{macro}{\vpartition} +% \begin{macrocode} +\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} + } +} +% \end{macrocode} +% \end{macro} +% +% \arcpartition - macro to draw set partitions via arcs. +% +% Example: the set partition {1,4}{2,3,7} of [7] is drawn as follows: +% +% \arcpartition[<options>]{{1,4},{2,3,7}} +% +% ----------------- +% | | +% ------------- | +% | | | | +% | ----- | | +% | | | | | +% 1 2 3 4 5 6 7 +% +% \begin{macrocode} +\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 +}{} +% \end{macrocode} +% +% \begin{macro}{\arcpartition} +% \begin{macrocode} +\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} +} +% \end{macrocode} +% \end{macro} +% +% \permutation - macro to draw permutations by lines. +% +% Example: the permutation 2134 of [4] is drawn as follows: +% +% \permutation[<options>]{2,1,3,4} +% +% 1 2 3 4 +% | | | | +% - - | | +% - | | +% - - | | +% | | | | +% 1 2 3 4 +% +% \begin{macrocode} +\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 +}{} +% \end{macrocode} +% +% \begin{macro}{\permutation} +% \begin{macrocode} +\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} +} +% \end{macrocode} +% \end{macro} +% +% \tiedpair - macro to draw a tied permutation as a pair. +% +% Example: the permutation ({2,4},2134) of [4] is drawn as follows: +% +% \tiedpair[<options>]{{2,4}}{2,1,3,4} +% +% 2 4 +% --------- +% 1 | 3 | +% | | | | +% - - | | +% - | | +% - - | | +% | | | | +% 1 2 3 4 +% +% \begin{macrocode} +\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 +}{} +% \end{macrocode} +% +% \begin{macro}{\tiedpair} +% \begin{macrocode} +\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} + } +} +% \end{macrocode} +% \end{macro} +% +% \tie - macro to draw a tie. +% +% \begin{tikzpicture} \tie[height=1.5]{{1,0.8},{3,0.7},{4,0.8}} \end{tikzpicture} +% \begin{tikzpicture} \tie[height=1.5]{1,2,5} \end{tikzpicture} +% +% \begin{macrocode} +\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. +}{} +% \end{macrocode} +% +% \begin{macro}{\tie} +% \begin{macrocode} +\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 + } +} +% \end{macrocode} +% \end{macro} +% +% \bbackstrands - macro to draws a trivial two-strands-braid of double strand width. +% +% \begin{macrocode} +\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 +}{} +% \end{macrocode} +% +% \begin{macro}{\bbackstrands} +% \begin{macrocode} +\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}); +} +% \end{macrocode} +% \end{macro} +% +% \lleftstrand - macro to draws a strand starting from the left. +% +% \begin{macrocode} +\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 +}{} +% \end{macrocode} +% +% \begin{macro}{\lleftstrand} +% \begin{macrocode} +\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}); +} +% \end{macrocode} +% \end{macro} +% +% \rrightstrand - macro to draw a strand starting from the right. +% +% \begin{macrocode} +\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 +}{} +% \end{macrocode} +% +% \begin{macro}{\rrightstrand} +% \begin{macrocode} +\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}); +} +% \end{macrocode} +% \end{macro} +% +% \ccrossback - macro to draw a \backcolor filled circle to create an over-under / under-over crossing. +% +% \begin{macrocode} +\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 +}{} +% \end{macrocode} +% +% \begin{macro}{\ccrossback} +% \begin{macrocode} +\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); +} +% \end{macrocode} +% \end{macro} +% +% \bbraidgen - macro to draw a braid crossing (classic, virtual or singular). +% +% \begin{macrocode} +\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); + } + } +} +% \end{macrocode} +% +% \begin{macro}{\bbraidgen} +% \begin{macrocode} +\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 +} +% \end{macrocode} +% \end{macro} +% +% \ttanglegen - macro to draw a tangle generator. +% +% \begin{macrocode} +\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 +}{} +% \end{macrocode} +% +% \begin{macro}{\ttanglegen} +% \begin{macrocode} +\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 +} +% \end{macrocode} +% \end{macro} +% +% \aaddgen - macro to add a generator on a strand level. +% +% \begin{macrocode} +\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 +}{} +% \end{macrocode} +% +% \begin{macro}{\aaddgen} +% \begin{macrocode} +\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. +} +% \end{macrocode} +% \end{macro} +% +% \strands - macro to draw braid-like element via generators (with tikz environment). +% +% \begin{macrocode} +\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. +% \end{macrocode} +% +% \begin{macro}{\sstrands} +% \begin{macrocode} +\newcommand{\sstrands}[2][]{ + \setkeys[str]{ggens}{#1} +% \end{macrocode} +% number of strands. +% \begin{macrocode} + \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)}} +% \end{macrocode} +% backstrands. +% \begin{macrocode} + \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} +% \end{macrocode} +% generators. +% \begin{macrocode} + \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 + ] +} +% \end{macrocode} +% \end{macro} +% +% \begin{macrocode} +\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 +}{} +% \end{macrocode} +% +% \begin{macro}{\strands} +% \begin{macrocode} +\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} +% \end{macro} +% + +% +% \iffalse +%</package> +% \fi +% +% \Finale +\endinput diff --git a/Master/texmf-dist/source/latex/strands/strands.ins b/Master/texmf-dist/source/latex/strands/strands.ins new file mode 100644 index 00000000000..5f38a838aeb --- /dev/null +++ b/Master/texmf-dist/source/latex/strands/strands.ins @@ -0,0 +1,57 @@ +%% 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. +%% +%% This work has the LPPL maintenance status `maintained'. +%% +%% The Current Maintainer of this work is Diego Arcis. +%% +%% This work consists of the files strands.dtx and strands.ins +%% and the derived filebase strands.sty. +%% + +\input docstrip.tex +\keepsilent + +\usedir{tex/latex/strands} + +\preamble + +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. + +\endpreamble + +\generate{\file{strands.sty}{\from{strands.dtx}{package}}} + +\obeyspaces +\Msg{*************************************************************} +\Msg{* *} +\Msg{* To finish the installation you have to move the following *} +\Msg{* file into a directory searched by TeX: *} +\Msg{* *} +\Msg{* strands.sty *} +\Msg{* *} +\Msg{* To produce the documentation run the file strands.dtx *} +\Msg{* through LaTeX. *} +\Msg{* *} +\Msg{* Happy TeXing! *} +\Msg{* *} +\Msg{*************************************************************} + +\endbatchfile 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'. diff --git a/Master/tlpkg/bin/tlpkg-ctan-check b/Master/tlpkg/bin/tlpkg-ctan-check index 4760da1c76b..add9cbf3b61 100755 --- a/Master/tlpkg/bin/tlpkg-ctan-check +++ b/Master/tlpkg/bin/tlpkg-ctan-check @@ -718,7 +718,7 @@ my @TLP_working = qw( stdclsdv stdpage stealcaps steinmetz stellenbosch step stepgreek stex stickstoo stix stix2-otf stix2-type1 stmaryrd storebox storecmd - stricttex stringenc stringstrings structmech struktex + strands stricttex stringenc stringstrings structmech struktex sttools stubs studenthandouts sty2dtx suanpan subdocs subdepth subeqn subeqnarray subfig subfigmat subfigure subfiles subfloat substances diff --git a/Master/tlpkg/tlpsrc/collection-pictures.tlpsrc b/Master/tlpkg/tlpsrc/collection-pictures.tlpsrc index 89d5a655c70..31037806659 100644 --- a/Master/tlpkg/tlpsrc/collection-pictures.tlpsrc +++ b/Master/tlpkg/tlpsrc/collection-pictures.tlpsrc @@ -147,6 +147,7 @@ depend simpleoptics depend smartdiagram depend spath3 depend spectralsequences +depend strands depend swimgraf depend syntaxdi depend table-fct diff --git a/Master/tlpkg/tlpsrc/strands.tlpsrc b/Master/tlpkg/tlpsrc/strands.tlpsrc new file mode 100644 index 00000000000..e69de29bb2d --- /dev/null +++ b/Master/tlpkg/tlpsrc/strands.tlpsrc |