braids.sty

\NeedsTeXFormat{LaTeX2e}[1994/12/01]
\ProvidesPackage{braids}
\RequirePackage{tikz}
\usetikzlibrary{shapes.geometric}

\def\braids@debug#1{}
%\let\braids@debug = \wlog

\def\braids@over{draw=white,double=black,very thick}
\newcount\braids@i
\newcount\braids@x\newcount\braids@xa\newcount\braids@xb
\newcount\braids@y\newcount\braids@iy\newcount\braids@ny

\newtoks\braids@name
\newtoks\braids@strand
\newtoks\braids@prevstrand
\def\braids@unshift{%
	\ifx\names\@empty
	\else
		\edef\doit{\noexpand\braids@unshift@name\the\braids@name\relax}%
		\doit
	\fi
}
\def\braids@unshift@name{\@ifnextchar=\braids@eq@unshift@name\braids@noeq@unshift@name}
\def\braids@eq@unshift@name={%
	\tikzstyle{every path} = [draw=black,double=white,thick]%
	\braids@pushstrand=\braids@unsh@ft@name}
\def\braids@noeq@unshift@name{%
	\tikzstyle{every path} = [draw=white,double=black,ultra thick]%
	\braids@pushstrand-\braids@unsh@ft@name}
\def\braids@unsh@ft@name#1,#2\relax{\global\braids@name={#2}\gdef\braids@thelabel{#1}}
\def\braids@pushstrand#1{\edef\doit{\noexpand\braids@push@strand#1\the\braids@strand\relax}\doit}
\def\braids@push@strand#1#2\relax{\braids@debug{pushing #1 after #2}\global\braids@strand={#2#1}}

\def\braids@rotstrand{%
	\@ifnextchar[\braids@rotstrand@brack\braids@rotstrand@nobr}
\def\braids@rotstrand@nobr{%
	\braids@debug{before rotation: \the\braids@prevstrand|\the\braids@strand}%
	\edef\doit{\noexpand\braids@rot@strand\the\braids@strand\relax\the\braids@prevstrand\relax}%
	\doit
	\braids@debug{after rotation: \the\braids@prevstrand|\the\braids@strand}%
}
\def\braids@rotstrand@brack[#1]{%
	\braids@debug{before rotation[#1]: \the\braids@prevstrand|\the\braids@strand}%
	\edef\doit{\noexpand\braids@rot@strand@brack[#1]\the\braids@strand\relax\the\braids@prevstrand\relax}%
	\doit\braids@debug{after rotation: \the\braids@prevstrand|\the\braids@strand}}
\def\braids@rot@strand#1#2\relax#3\relax{%
	\ifx=#1
		\tikzstyle{every path} = [draw=black,double=white,thick]%
	\else
		\tikzstyle{every path} = [draw=white,double=black,ultra thick]%
	\fi
	\global\braids@strand={#2}%
	\global\braids@prevstrand={#3#1}%
}
\def\braids@rot@strand@brack[#1]#2#3\relax#4\relax{%
	\ifx=#1
		\tikzstyle{every path} = [draw=black,double=white,thick]%
	\else
		\tikzstyle{every path} = [draw=white,double=black,ultra thick]%
	\fi
	\ifx=#2
		\tikzstyle{incoming strand} = [draw=black,double=white,thick]%
	\else
		\tikzstyle{incoming strand} = [draw=white,double=black,ultra thick]%
	\fi
	\global\braids@strand={#3}%
	\global\braids@prevstrand={#4#1}%
}


\setcounter{errorcontextlines}{20}


\newtoks\braids@savednames
\def\braids@savenames#1{%
	\braids@i=0\loop\ifnum\braids@i<#1
		\advance\braids@i by 1
		\ifx\names\@empty
			\braids@savestrand
		\else
			\braids@savename
		\fi
	\repeat
	\ignorespaces
}
\def\braids@savename{%
	\ifx\names\@empty\else
		\edef\doit{\noexpand\braids@dosave\the\braids@savednames\relax\the\braids@name\relax}%
		\doit
		\braids@debug{after savename: (\the\braids@savednames)\the\braids@name}%
	\fi
}
\def\braids@dosave#1\relax#2,#3\relax{%
	\global\braids@savednames = {#1#2,}%
	\global\braids@name  = {#3}%
}

\def\braids@restorenames{%
	\edef\doit{%
		\noexpand\global\noexpand\braids@name={\the\braids@savednames\the\braids@name}%
	}%
	\doit
	\global\braids@savednames={}%
	\braids@doswap@neg
	\ignorespaces
}

\newtoks\braids@savedstrands
\def\braids@savestrand{%
	\braids@debug{before savestrand: \the\braids@prevstrand|\the\braids@strand}%
	\edef\doit{%
		\noexpand\braids@save@strand\the\braids@strand\relax\the\braids@savedstrands\relax}%
	\doit
	\braids@debug{after savestrand: \the\braids@prevstrand|\the\braids@strand}}
\def\braids@save@strand#1#2\relax#3\relax{%
	\ifx=#1
		\tikzstyle{every path} = [draw=black,double=white,thick]%
	\else
		\tikzstyle{every path} = [draw=white,double=black,ultra thick]%
	\fi
	\global\braids@strand={#2}%
	\global\braids@savedstrands={#3#1}%
}
\def\braids@doswap@pos{%
	\edef\doit{\noexpand\global\noexpand\braids@do@swap@pos\the\braids@prevstrand\the\braids@savedstrands\relax}%
	\doit
	\global\braids@savedstrands={}%
	\braids@debug{after doswap(pos): \the\braids@prevstrand|\the\braids@strand}}
\def\braids@do@swap@pos#1\relax{%
	\global\braids@prevstrand={#1}}

\def\braids@doswap@neg{%
	\edef\doit{\noexpand\global\noexpand\braids@do@swap@neg\the\braids@savedstrands\the\braids@strand\relax}%
	\doit
	\global\braids@savedstrands={}%
	\braids@debug{after doswap(neg): \the\braids@prevstrand|\the\braids@strand}}
\def\braids@do@swap@neg#1\relax{%
	\global\braids@strand={#1}}


\newcount\braids@result
\def\braids@componentcount#1#2{%
	\braids@result = 0
	\braids@component@count{#1}{#2#1}}
\def\braids@component@count#1#2{%
	\edef\componentlist{#2}%
	\ifx\componentlist\@empty\else
		\def\takeit##1#1##2\relax{\advance\braids@result by 1%
			\braids@component@count{#1}{##2}}%
		\edef\doit{\noexpand\takeit#2\relax}%
		\doit
	\fi}


% next must be called before calling label, name(s)toend, drawstrand
\def\braids@next{\edef\names{\the\braids@name}\braids@unshift\braids@rotstrand}
\def\braids@toswap{\edef\names{\the\braids@name}\braids@unshift\braids@savestrand}
\def\braids@label{\ifx\names\@empty\else
	node[fill=white, anchor=mid east] {$\braids@thelabel$}\fi}

\def\braids@drawstrand{
	\draw
		(\braids@xa,\braids@y)
		[draw=white, ultra thick]
		..
		controls (\braids@xa,\braids@iy)
		and (\braids@xb,\braids@iy)
		..
		(\braids@xb,\braids@ny) ;
	%
	\draw
		(\braids@xa,\braids@y) \braids@label
		node [above right] {$\scriptstyle \braids@superlabel$}
		..
		controls (\braids@xa,\braids@iy)
		and (\braids@xb,\braids@iy)
		..
		(\braids@xb,\braids@ny) ;
	\advance\braids@xa by 1
	\advance\braids@xb by 1
}
\tikzstyle{braidtriangle}=[regular polygon,regular polygon sides=3,regular polygon rotate=30,draw=black,fill=white,thick,inner sep=2pt,thin]
\def\braids@triangle(#1,#2)#3;{%
	\node[style=braidtriangle] at (#1,#2) {$\vphantom{\mathop{f}}\!\!\mathop{#3}$} ;
}

\def\braids@s{%
	\def\braids@superlabels{}%
	\def\braids@superlabel{}%
	\@ifnextchar'\braids@neg@s\braids@pos@s}
\def\braids@pos@s{\@ifnextchar<\braids@pos@labelled@s\braids@pos@choose@s}
\def\braids@neg@s'{\@ifnextchar<\braids@pos@labelled@s\braids@neg@choose@s}
\def\braids@pos@choose@s{\@ifnextchar(\braids@pos@plain@s\braids@pos@default@s} 
\def\braids@pos@default@s{\braids@pos@plain@s(1,1)} 
\def\braids@pos@plain@s(#1,#2){ 
	\braids@xa = \braids@x
	\braids@xb = \braids@x
	\advance\braids@xb by #2
	\braids@i=0\loop\ifnum\braids@i<#1
		\braids@toswap
		\advance\braids@i by 1
		\braids@drawstrand
	\repeat
	%
	\braids@xa = \braids@x
	\braids@xb = \braids@x
	\advance\braids@xa by #1
	\braids@i=0\loop\ifnum\braids@i<#2
		\braids@next
		\advance\braids@i by 1
		\braids@drawstrand
	\repeat
	%
	\advance\braids@x by #1
	\advance\braids@x by #2
	\braids@doswap@pos
}
\def\braids@neg@choose@s{\@ifnextchar(\braids@neg@plain@s\braids@neg@default@s} 
\def\braids@neg@default@s{\braids@neg@plain@s(1,1)} 
\def\braids@neg@plain@s(#1,#2){ 
	\braids@savenames{#1}
	\braids@xa = \braids@x
	\braids@xb = \braids@x
	\advance\braids@xa by #1
	\braids@i=0\loop\ifnum\braids@i<#2
		\braids@next
		\advance\braids@i by 1
		\braids@drawstrand
	\repeat
	%
	\braids@restorenames
	\braids@debug{names restored}%
	\braids@xa = \braids@x
	\braids@xb = \braids@x
	\advance\braids@xb by #2
	\braids@i=0\loop\ifnum\braids@i<#1
		\braids@next
		\advance\braids@i by 1
		\braids@drawstrand
	\repeat
	%
	\advance\braids@x by #1
	\advance\braids@x by #2
}
\def\braids@superlabels{}
\def\braids@superlabel{}
\def\braids@nextsuperlabel{%
	\ifx\braids@superlabels\@empty
		\def\braids@superlabel{}
	\else
		\edef\doit{\noexpand\braids@super@labels\braids@superlabels\relax}\doit
	\fi}
\def\braids@super@labels#1/#2\relax{%
	\global\def\braids@superlabels{#2}\global\def\braids@superlabel{#1}}
\def\braids@pos@labelled@s<#1,#2>{
	\braids@xa = \braids@x
	\braids@xb = \braids@x
	\global\edef\braids@superlabels{#1/}
	\braids@componentcount/{#2}
	\advance\braids@xb by \braids@result
	\braids@i=0\loop
		\braids@nextsuperlabel
		\ifx\braids@superlabel\@empty\else
		\braids@toswap
		\advance\braids@i by 1
		\braids@drawstrand
	\repeat
	%
	\braids@xa = \braids@x
	\braids@xb = \braids@x
	\global\edef\braids@superlabels{#2/}
	\braids@componentcount/{#1}
	\advance\braids@xa by \braids@result
	\braids@i=0\loop
		\braids@nextsuperlabel
		\ifx\braids@superlabel\@empty\else
		\braids@next
		\advance\braids@i by 1
		\braids@drawstrand
	\repeat
	%
	\braids@componentcount/{#1/#2}
	\advance\braids@x by \braids@result
	\braids@doswap@pos
}
\def\braids@neg@labelled@s<#1,#2>{
	% !!! TODO !!!
}
\newcount\braids@c@count
\newif\ifbraids@narrow\braids@narrowfalse
\newcommand \braids@c[1][1]{%
	\braids@c@count=#1\@ifnextchar^\braids@labelled@c\braids@plain@c}
\def\braids@plain@c{%
	\braids@i=0\loop\ifnum\braids@i<\braids@c@count
		\braids@next
		\advance\braids@i by 1
		\ifbraids@narrow
			\draw (\braids@x,\braids@y) \braids@label
				-- (\braids@x,\braids@iy) ;
		\else
			\draw (\braids@x,\braids@y) \braids@label
				-- (\braids@x,\braids@ny) ;
		\fi
		\advance \braids@x by 1
	\repeat
}
\def\braids@labelled@c^#1{%
	\braids@i=0\loop\ifnum\braids@i<\braids@c@count
		\braids@next
		\advance\braids@i by 1
		\ifbraids@narrow
			\draw (\braids@x,\braids@y) \braids@label
				node[above right] {$\scriptstyle #1$}
				-- (\braids@x,\braids@iy) ;
		\else
			\draw (\braids@x,\braids@y) \braids@label
				node[above right] {$\scriptstyle #1$}
				-- (\braids@x,\braids@ny) ;
		\fi
		\advance \braids@x by 1
	\repeat
}
\newcommand \braids@C[1][1]{%
	\braids@c@count=#1\@ifnextchar^\braids@labelled@C\braids@plain@C}
\def\braids@plain@C{%
	\braids@i=0\loop\ifnum\braids@i<\braids@c@count
		\braids@next
		\advance\braids@i by 2
		\ifbraids@narrow
			\draw (0.5+\braids@x,\braids@y) \braids@label
				-- (0.5+\braids@x,\braids@iy) ;
		\else
			\draw (0.5+\braids@x,\braids@y) \braids@label
				-- (0.5+\braids@x,\braids@ny) ;
		\fi
		\advance \braids@x by 2
	\repeat
}
\def\braids@labelled@C^#1{%
	\braids@i=0\loop\ifnum\braids@i<\braids@c@count
		\braids@next
		\advance\braids@i by 2
		\ifbraids@narrow
			\draw (0.5+\braids@x,\braids@y) \braids@label
				node[above right] {$\scriptstyle #1$}
				-- (0.5+\braids@x,\braids@iy) ;
		\else
			\draw (0.5+\braids@x,\braids@y) \braids@label
				node[above right] {$\scriptstyle #1$}
				-- (0.5+\braids@x,\braids@ny) ;
		\fi
		\advance \braids@x by 2
	\repeat
}
\newcommand\braids@f[1][]{%
	\braids@next
	\draw (\braids@x,\braids@y) \braids@label
		-- node[circle,draw=black,fill=white,thick] {$#1$}
	(\braids@x,\braids@ny) ;
	\advance \braids@x by 1
}
\newcommand\braids@t[1][]{%
	\edef\braids@t@label{#1}%
	\@ifnextchar^\braids@labelled@t\braids@plain@t}
\def\braids@plain@t{%
	\braids@next[-]
	\draw (\braids@x,\braids@y) \braids@label
		[style=incoming strand] -- (\braids@x,\braids@iy) ;
	\draw (\braids@x,\braids@iy)
		-- (\braids@x,\braids@ny) ;
	\braids@triangle(\braids@x,\braids@iy) {\braids@t@label} ;
	\advance \braids@x by 1
}
\def\braids@labelled@t^#1{%
	\braids@next[-]
	\draw (\braids@x,\braids@y) \braids@label
		node[above right] {$\scriptstyle #1$}
		[style=incoming strand] -- (\braids@x,\braids@iy) ;
	\draw (\braids@x,\braids@iy)
		-- (\braids@x,\braids@ny) ;
	\braids@triangle(\braids@x,\braids@iy) {\braids@t@label} ;
	\advance \braids@x by 1
}
\newcommand\braids@T[1][]{%
	\edef\braids@t@label{#1}%
	\@ifnextchar^\braids@labelled@T\braids@plain@T}
\def\braids@plain@T{%
	\braids@next[-]
	\draw (\braids@x,\braids@y) \braids@label
		[style=incoming strand] -- (\braids@x,\braids@iy) ;
	\braids@next[-]
	\draw (1+\braids@x,\braids@y) \braids@label
		[style=incoming strand] -- (1+\braids@x,\braids@iy) ;
	\draw (0.5+\braids@x,\braids@iy)
		-- (0.5+\braids@x,\braids@ny) ;
	\braids@triangle(0.5+\braids@x,\braids@iy) {\braids@t@label} ;
	\advance \braids@x by 2
}
\def\braids@labelled@T^#1/#2{%
	\braids@next[-]
	\draw (\braids@x,\braids@y) \braids@label
		node[above right] {$\scriptstyle #1$}
		[style=incoming strand] -- (\braids@x,\braids@iy) ;
	\braids@next[-]
	\draw (1+\braids@x,\braids@y) \braids@label
		node[above right] {$\scriptstyle #2$}
		[style=incoming strand] -- (1+\braids@x,\braids@iy) ;
	\draw (0.5+\braids@x,\braids@iy)
		-- (0.5+\braids@x,\braids@ny) ;
	\braids@triangle(0.5+\braids@x,\braids@iy) {\braids@t@label} ;
	\advance \braids@x by 2
}
\def\braids@newline{
	\braids@debug{new line}%
	\edef\names{\the\braids@name}\ifx\names\@empty\else
		\@latex@error{Too many strand names specified}
	\fi
	\global\braids@name = {}
	\global\braids@strand = \braids@prevstrand
	\global\braids@prevstrand = {}
	\ifbraids@narrow
		\advance\braids@y  by 1
		\advance\braids@iy by 1
		\advance\braids@ny by 1
	\else
		\advance\braids@y  by 2
		\advance\braids@iy by 2
		\advance\braids@ny by 2
	\fi
	\braids@narrowfalse
	\braids@x = 0
}

\tikzstyle{braidextras}=[]
\newcommand\braidstyle[1]{\tikzstyle{braidextras}=[#1]}
\newenvironment{braid}[2][]
	{%
	\global\braids@name = {#2,}
	\global\braids@savednames={}
	\global\braids@strand={}
	\global\braids@prevstrand={}
	%
	\begin{tikzpicture}[baseline=(current bounding box.east),cm={0,-0.6,.75,0,(0,0)},style=braidextras,#1]
		\braids@x  = 0
		\braids@y  = 0
		\braids@iy = 1
		\braids@ny = 2
		%
		\let\c\braids@c
		\let\C\braids@C
		\let\s\braids@s
		\let\f\braids@f
		\let\t\braids@t
		\let\T\braids@T
		\let\\\braids@newline
		\let\narrow\braids@narrowtrue
	}
	{\end{tikzpicture}\ignorespacesafterend}