tikzquanto.sty

\ProvidesPackage{tikzquanto}[2015/09/07 Tikz Quanto + ZC calculus macros]
\RequirePackage{tikzfig}  %%%% Basic tikz set up elsewhere

%% Global monochrome option
\newif\if@zxmono\@zxmonofalse
\DeclareOption{mono}{
  \@zxmonotrue
}

%% Global undirected option
\newif\if@zxundirected\@zxundirectedfalse
\DeclareOption{undirected}{
  \@zxundirectedtrue
}

\ProcessOptions\relax



%%%%%%%%%%%%%% colours -- TODO blue
\if@zxmono
     \newcommand{\gfillcolor}{gray!40!white}
     \newcommand{\gdrawcolor}{gray}
     \newcommand{\glabelcolor}{gray!30!white}
     \newcommand{\rfillcolor}{gray!65!black}
     \newcommand{\rdrawcolor}{black}
     \newcommand{\rlabelcolor}{gray}
     \newcommand{\yfillcolor}{white}
     \newcommand{\ydrawcolor}{black}
     \newcommand{\ylabelcolor}{white}
\else
     \newcommand{\gfillcolor}{green!50}
     \newcommand{\gdrawcolor}{green!30!black}
     \newcommand{\glabelcolor}{green!30}
     \newcommand{\rfillcolor}{red}
     \newcommand{\rdrawcolor}{red!40!black}
     \newcommand{\rlabelcolor}{red!15}
     \newcommand{\yfillcolor}{yellow}
     \newcommand{\ydrawcolor}{yellow!30!black}
     \newcommand{\ylabelcolor}{yellow}
\fi

%%%%%%%%%%%%%%%
%%  Now define useful tikz styles
%%%%%%%%%%%%%%%


%%%
\tikzstyle{simple}=[]

%%%% global options
\tikzstyle{every node}=[font=\small]
\tikzstyle{every picture}=[baseline=-0.25em]
\tikzstyle{dotpic}=[scale=0.5]
\tikzstyle{dot graph}=[shorten <=-0.1mm,shorten >=-0.1mm,scale=0.6]
\tikzstyle{plot point}=[circle,fill=black,minimum width=2mm,inner sep=0]
\tikzstyle{quanto}=[baseline=(current bounding
box).east,scale=0.5,node distance=5mm]

\if@zxundirected
\else
\tikzstyle{diredges}=[every to/.style={diredge}]
\fi

%%%% ZX-Calculus

\tikzstyle{vertex}=[circle,draw=black,thick,inner sep=0.4mm,minimum
size=2.5mm]

\tikzstyle{smallvertex}=[inner sep=0.4mm,minimum width=0pt,minimum
height=0pt,draw=black,shape=circle]

\tikzstyle{dotted vertex}=[vertex,densely dotted]
\tikzstyle{black vertex}=[vertex,fill=black]
\tikzstyle{white vertex}=[vertex,fill=white]
\tikzstyle{gray vertex}=[vertex,fill=gray]

\tikzstyle{dotted smallvertex}=[smallvertex,densely dotted]
\tikzstyle{black smallvertex}=[smallvertex,fill=black]
\tikzstyle{white smallvertex}=[smallvertex,fill=white]
\tikzstyle{gray smallvertex}=[smallvertex,fill=gray]


\tikzstyle{boundary vertex}=[circle,fill=black,inner sep=0.3mm]
\tikzstyle{angle}=[fill=blue!50, minimum height=5mm, right, anchor=west, rounded corners=1mm, xshift=2.5mm,font=\small]
\tikzstyle{angle left}=[angle,anchor=east,xshift=-4.5mm]
\tikzstyle{angle below}=[angle,anchor=north,xshift=-2.5mm,yshift=-2.25mm]
\tikzstyle{angle above}=[angle,anchor=south,xshift=-2.5mm,yshift=2.25mm]

%%%% compat with Bob/Aleks
\tikzstyle{dot}=[black vertex]
\tikzstyle{smalldot}=[black smallvertex]
\tikzstyle{white dot}=[white vertex]
\tikzstyle{smallwhitedot}=[white smallvertex]
\tikzstyle{alt white dot}=[white vertex]
\tikzstyle{gray dot}=[gray vertex]
\tikzstyle{smallgraydot}=[gray smallvertex]

\tikzstyle{red vertex}=[vertex,fill=\rfillcolor,draw=\rdrawcolor]
\tikzstyle{red smallvertex}=[smallvertex,fill=\rfillcolor,draw=\rdrawcolor]
\tikzstyle{red angle}=[angle,fill=\rlabelcolor]
\tikzstyle{red angle left}=[angle left,fill=\rlabelcolor]
\tikzstyle{red angle below}=[angle below,fill=\rlabelcolor]
\tikzstyle{red angle above}=[angle above,fill=\rlabelcolor]
\tikzstyle{rpp}=[red vertex,inner sep=-0.5mm,execute at end
node={${\displaystyle\color{white}\mathbf{+}}$}] 
\tikzstyle{rpi}=[red vertex,inner sep=-0.5mm,execute at end
node={\scalebox{1.1}{$\mathbf{{\displaystyle\color{white}\pi}}$}}] 
\tikzstyle{rmm}=[red vertex,inner sep=-0.5mm,execute at end
node={$\mathbf{{\displaystyle\color{white}-}}$}]  
%%%% removed from all the "pi" vertices 
%%%% vertex,fill=\rfillcolor,draw=\rdrawcolor

\tikzstyle{green vertex}=[vertex,fill=\gfillcolor,draw=\gdrawcolor]
\tikzstyle{green smallvertex}=[smallvertex,fill=\gfillcolor,draw=\gdrawcolor]
\tikzstyle{green angle}=[angle,fill=\glabelcolor]
\tikzstyle{green angle left}=[angle left,fill=\glabelcolor]
\tikzstyle{green angle above}=[angle above,fill=\glabelcolor]
\tikzstyle{green angle below}=[angle below,fill=\glabelcolor]
\tikzstyle{gpp}=[green vertex,inner
sep=-0.5mm,execute at end node={$\mathbf{{\displaystyle +}}$}] 
\tikzstyle{gpi}=[green vertex,inner
sep=-0.5mm,execute at end node={\scalebox{1.1}{$\mathbf{{\displaystyle\pi}}$}}] 
\tikzstyle{gmm}=[green vertex,inner
sep=-0.5mm,execute at end node={$\mathbf{{\displaystyle -}}$}] 

\tikzstyle{hadamard vertex}=[rectangle,fill=\yfillcolor,draw=\ydrawcolor,execute at end node={\tiny H}]
\tikzstyle{smallhadamard vertex}=[rectangle,fill=\yfillcolor,draw=\ydrawcolor,execute at end node={}]

% shorthand names
\tikzstyle{rn}=[red vertex]
\tikzstyle{gn}=[green vertex]
\tikzstyle{bn}=[boundary vertex]
\tikzstyle{hn}=[hadamard vertex]

\tikzstyle{green dot}=[green vertex]
\tikzstyle{smallgreendot}=[green smallvertex]
\tikzstyle{red dot}=[red vertex]
\tikzstyle{smallreddot}=[red smallvertex]

\tikzstyle{X}=[rn]
\tikzstyle{Z}=[gn]
\tikzstyle{wire}=[bn]
\tikzstyle{hadamard}=[hn]
\tikzstyle{directed}=[medium diredge]
%%%%%%%% General Monoidal category stuff


\tikzstyle{box}=[rectangle,fill=white,draw=black,thin]
\tikzstyle{boxa}=[box,execute at end node={$a$}]
\tikzstyle{boxb}=[box,execute at end node={$b$}]


\tikzstyle{square box}=[rectangle,fill=white,draw=black,minimum height=5mm,minimum width=5mm,font=\small]
\tikzstyle{square gray box}=[square box,fill=gray!30]
\tikzstyle{point}=[regular polygon,regular polygon sides=3,draw=black,scale=0.85,inner sep=0pt,minimum width=7mm,fill=white]
\tikzstyle{copoint}=[regular polygon,regular polygon sides=3,draw=black,scale=0.85,inner sep=0pt,minimum width=7mm,fill=white,regular polygon rotate=180]
\tikzstyle{gray point}=[point,fill=gray!40!white]
\tikzstyle{gray copoint}=[copoint,fill=gray!40!white]


\tikzstyle{wide point}=[fill=white,draw=black,shape=isosceles triangle,shape border rotate=90,isosceles triangle stretches=true,inner sep=1pt,minimum width=1.5cm,minimum height=5mm]
\tikzstyle{wide copoint}=[fill=white,draw=black,shape=isosceles triangle,shape border rotate=-90,isosceles triangle stretches=true,inner sep=1pt,minimum width=1.5cm,minimum height=4mm]
\tikzstyle{very wide copoint}=[fill=white,draw=black,shape=isosceles triangle,shape border rotate=-90,isosceles triangle stretches=true,inner sep=1pt,minimum width=2.5cm,minimum height=4mm]
\tikzstyle{very wide empty copoint}=[draw=black,shape=isosceles triangle,shape border rotate=-90,isosceles triangle stretches=true,inner sep=1pt,minimum width=2.5cm,minimum height=4mm]
\tikzstyle{symm}=[ultra thick,shorten <=-1mm,shorten >=-1mm]

% PARALLELAGRAM BOXES:
%% \makeatletter %% don't need this in a style file
\newcommand{\boxshape}[3]{%
\pgfdeclareshape{#1}{
\inheritsavedanchors[from=rectangle] % this is nearly a rectangle
\inheritanchorborder[from=rectangle]
\inheritanchor[from=rectangle]{center}
\inheritanchor[from=rectangle]{north}
\inheritanchor[from=rectangle]{south}
\inheritanchor[from=rectangle]{west}
\inheritanchor[from=rectangle]{east}
% ... and possibly more
\backgroundpath{% this is new
% store lower right in xa/ya and upper right in xb/yb
\southwest \pgf@xa=\pgf@x \pgf@ya=\pgf@y
\northeast \pgf@xb=\pgf@x \pgf@yb=\pgf@y

\@tempdima=#2
\@tempdimb=#3

\pgfpathmoveto{\pgfpoint{\pgf@xa - 1pt + \@tempdima}{\pgf@ya}}
\pgfpathlineto{\pgfpoint{\pgf@xa - 1pt - \@tempdima}{\pgf@yb}}
\pgfpathlineto{\pgfpoint{\pgf@xb + 1pt + \@tempdimb}{\pgf@yb}}
\pgfpathlineto{\pgfpoint{\pgf@xb + 1pt - \@tempdimb}{\pgf@ya}}
\pgfpathlineto{\pgfpoint{\pgf@xa - 1pt + \@tempdima}{\pgf@ya}}
\pgfpathclose
}
}}

\boxshape{NEbox}{0pt}{2pt}
\boxshape{SEbox}{0pt}{-2pt}
\boxshape{NWbox}{2pt}{0pt}
\boxshape{SWbox}{-2pt}{0pt}
%% \makeatother %% don't need this in a style file

\tikzstyle{map}=[draw,shape=NEbox,inner sep=3pt]
\tikzstyle{mapdag}=[draw,shape=SEbox,inner sep=3pt]
\tikzstyle{maptrans}=[draw,shape=SWbox,inner sep=3pt]
\tikzstyle{mapconj}=[draw,shape=NWbox,inner sep=3pt]

\tikzstyle{green map}=[map, fill=\gfillcolor,draw=\gdrawcolor]
\tikzstyle{green mapdag}=[mapdag, fill=\gfillcolor,draw=\gdrawcolor]
\tikzstyle{green maptrans}=[maptrans, fill=\gfillcolor,draw=\gdrawcolor]
\tikzstyle{green mapconj}=[mapconj, fill=\gfillcolor,draw=\gdrawcolor]
\tikzstyle{green point}=[point, fill=\gfillcolor,draw=\gdrawcolor]
\tikzstyle{green copoint}=[copoint, fill=\gfillcolor,draw=\gdrawcolor]

\tikzstyle{red map}=[map, fill=\rfillcolor,draw=\rdrawcolor]
\tikzstyle{red mapdag}=[mapdag, fill=\rfillcolor,draw=\rdrawcolor]
\tikzstyle{red maptrans}=[maptrans, fill=\rfillcolor,draw=\rdrawcolor]
\tikzstyle{red mapconj}=[mapconj, fill=\rfillcolor,draw=\rdrawcolor]
\tikzstyle{red point}=[point, fill=\rfillcolor,draw=\rdrawcolor]
\tikzstyle{red copoint}=[copoint, fill=\rfillcolor,draw=\rdrawcolor]

% temp FIXME

\pgfdeclareshape{rectangle with stripes}
{
    % This bit from \pgflibarayshapes.code.tex
    \inheritsavedanchors[from=rectangle]
    \inheritanchorborder[from=rectangle]
    \inheritanchor[from=rectangle]{north}
    \inheritanchor[from=rectangle]{north west}
    \inheritanchor[from=rectangle]{north east}
    \inheritanchor[from=rectangle]{center}
    \inheritanchor[from=rectangle]{west}
    \inheritanchor[from=rectangle]{east}
    \inheritanchor[from=rectangle]{mid}
    \inheritanchor[from=rectangle]{mid west}
    \inheritanchor[from=rectangle]{mid east}
    \inheritanchor[from=rectangle]{base}
    \inheritanchor[from=rectangle]{base west}
    \inheritanchor[from=rectangle]{base east}
    \inheritanchor[from=rectangle]{south}
    \inheritanchor[from=rectangle]{south west}
    \inheritanchor[from=rectangle]{south east}

    \inheritbackgroundpath[from=rectangle]
    \inheritbeforebackgroundpath[from=rectangle]
    \inheritbehindforegroundpath[from=rectangle]
    \inheritforegroundpath[from=rectangle]
    \inheritbeforeforegroundpath[from=rectangle]

   % Now do the background filling.
    \behindbackgroundpath{%
        % \southwest and \northeast defined by rectangle, but
        % (somewhat annoyingly) not \southeast and \northwest
        % so use this workaround.
        \pgfextractx{\pgf@xa}{\southwest}%
        \pgfextracty{\pgf@ya}{\southwest}%
        \pgfextractx{\pgf@xb}{\northeast}%
        \pgfextracty{\pgf@yb}{\northeast}%

        \pgfpathmoveto{\pgfpoint{\pgf@xa}{\pgf@ya - 0pt}}%
        \pgfpathlineto{\pgfpoint{\pgf@xa}{\pgf@ya + \pgf@stripe@width}}%
        \pgfpathlineto{\pgfpoint{\pgf@xb}{\pgf@ya + \pgf@stripe@width}}%
        \pgfpathlineto{\pgfpoint{\pgf@xb}{\pgf@ya - 0pt}}%
        \pgfpathclose
        \color{\pgf@stripe@bottom@color}%
        \pgfusepath{fill}%

        \pgfpathmoveto{\pgfpoint{\pgf@xa}{\pgf@yb + 0pt}}%
        \pgfpathlineto{\pgfpoint{\pgf@xa}{\pgf@yb - \pgf@stripe@width}}%
        \pgfpathlineto{\pgfpoint{\pgf@xb}{\pgf@yb - \pgf@stripe@width}}%
        \pgfpathlineto{\pgfpoint{\pgf@xb}{\pgf@yb + 0}}%
        \pgfpathclose
        \color{\pgf@stripe@top@color}%
        \pgfusepath{fill}%
      }
    }

\def\pgf@stripe@top@color{red}
\def\pgf@stripe@bottom@color{green}
\def\pgf@stripe@width{3pt}

% Use these with PGF
\def\pgfsetstripetopcolor#1{\def\pgf@stripe@top@color{#1}}%
\def\pgfsetstripebottomcolor#1{\def\pgf@stripe@bottom@color{#1}}%
\def\pgfsetstripewidth#1{\def\pgf@stripe@width{#1}}%


% Use these with TikZ
\tikzoption{top color}{\pgfsetstripetopcolor{#1}}
\tikzoption{bottom color}{\pgfsetstripebottomcolor{#1}}
\tikzoption{stripe width}{\pgfsetstripewidth{#1}}


%%%%%%%%% TOTAL OVERKILL TO DEFINE ANTIPODE
\pgfdeclareshape{rectangle with diagonal fill}
{
    % This bit from \pgflibarayshapes.code.tex
    \inheritsavedanchors[from=rectangle]
    \inheritanchorborder[from=rectangle]
    \inheritanchor[from=rectangle]{north}
    \inheritanchor[from=rectangle]{north west}
    \inheritanchor[from=rectangle]{north east}
    \inheritanchor[from=rectangle]{center}
    \inheritanchor[from=rectangle]{west}
    \inheritanchor[from=rectangle]{east}
    \inheritanchor[from=rectangle]{mid}
    \inheritanchor[from=rectangle]{mid west}
    \inheritanchor[from=rectangle]{mid east}
    \inheritanchor[from=rectangle]{base}
    \inheritanchor[from=rectangle]{base west}
    \inheritanchor[from=rectangle]{base east}
    \inheritanchor[from=rectangle]{south}
    \inheritanchor[from=rectangle]{south west}
    \inheritanchor[from=rectangle]{south east}

    \inheritbackgroundpath[from=rectangle]
    \inheritbeforebackgroundpath[from=rectangle]
    \inheritbehindforegroundpath[from=rectangle]
    \inheritforegroundpath[from=rectangle]
    \inheritbeforeforegroundpath[from=rectangle]

   % Now do the background filling.
    \behindbackgroundpath{%
        % \southwest and \northeast defined by rectangle, but
        % (somewhat annoyingly) not \southeast and \northwest
        % so use this workaround.
        \pgfextractx{\pgf@xa}{\southwest}%
        \pgfextracty{\pgf@ya}{\southwest}%
        \pgfextractx{\pgf@xb}{\northeast}%
        \pgfextracty{\pgf@yb}{\northeast}%
        \ifpgf@diagonal@lefttoright
            \def\pgf@diagonal@point@a{\pgfpoint{\pgf@xa}{\pgf@yb}}%
            \def\pgf@diagonal@point@b{\pgfpoint{\pgf@xb}{\pgf@ya}}%
        \else
            \def\pgf@diagonal@point@a{\southwest}%
            \def\pgf@diagonal@point@b{\northeast}%
        \fi
        \pgfpathmoveto{\pgf@diagonal@point@a}%
        \pgfpathlineto{\northeast}%
        \pgfpathlineto{\pgfpoint{\pgf@xb}{\pgf@ya}}%
        \pgfpathclose
        \ifpgf@diagonal@lefttoright
            \color{\pgf@diagonal@top@color}%
        \else
            \color{\pgf@diagonal@bottom@color}%
        \fi
        \pgfusepath{fill}%
        \pgfpathmoveto{\pgfpoint{\pgf@xa}{\pgf@yb}}%
        \pgfpathlineto{\southwest}%
        \pgfpathlineto{\pgf@diagonal@point@b}%
        \pgfpathclose
        \ifpgf@diagonal@lefttoright
            \color{\pgf@diagonal@bottom@color}%
        \else
            \color{\pgf@diagonal@top@color}%
        \fi
        \pgfusepath{fill}%
    }
}

\newif\ifpgf@diagonal@lefttoright
\def\pgf@diagonal@top@color{white}
\def\pgf@diagonal@bottom@color{gray!30}

% Use these with PGF
\def\pgfsetdiagonaltopcolor#1{\def\pgf@diagonal@top@color{#1}}%
\def\pgfsetdiagonalbottomcolor#1{\def\pgf@diagonal@bottom@color{#1}}%
\def\pgfsetdiagonallefttoright{\pgf@diagonal@lefttorighttrue}%
\def\pgfsetdiagonalrighttoleft{\pgf@diagonal@lefttorightfalse}%

% Use these with TikZ
\tikzoption{diagonal top color}{\pgfsetdiagonaltopcolor{#1}}
\tikzoption{diagonal bottom color}{\pgfsetdiagonalbottomcolor{#1}}
\tikzoption{diagonal from left to right}[]{\pgfsetdiagonallefttoright}
\tikzoption{diagonal from right to left}[]{\pgfsetdiagonalrighttoleft}

%%%%%%%%%%%%%%%%%%%%%%%%%

\tikzstyle{antipode}=[rectangle with diagonal fill, diagonal bottom
color=\gfillcolor, diagonal top color=\rfillcolor,draw]

%%%%%%%%%%%%%%%%%%%%%%%%%%

\tikzstyle{grint}=[rectangle with stripes, top color=\gfillcolor,
bottom color=\rfillcolor, minimum height=5mm,draw]
\tikzstyle{rgint}=[rectangle with stripes, top color=\rfillcolor,
bottom color=\gfillcolor, minimum height=5mm,draw]


%%%%%%% edges %%%%%%%%%%%%%%%%%%

\newcommand{\edgearrow}{{\arrow[black]{>}}}
\newcommand{\edgetick}{{\arrow[black,scale=0.7,very thick]{|}}}

\if@zxundirected
  \tikzstyle{diredge}=[->]
  \tikzstyle{rdiredge}=[<-]
  \tikzstyle{medium diredge}=[-]
  \tikzstyle{short diredge}=[->]
\else
  \tikzstyle{diredge}=[-]
  \tikzstyle{rdiredge}=[-]
  \tikzstyle{medium diredge}=[->,dashed,gray!40]
  \tikzstyle{short diredge}=[-]
\fi

\tikzstyle{halfedge}=[-)]
\tikzstyle{other halfedge}=[(-]
\tikzstyle{freeedge}=[(-)]
\tikzstyle{white edge}=[line width=5pt,white]
\tikzstyle{tick}=[postaction=decorate,decoration={markings, mark=at position 0.5 with \edgetick}]
\tikzstyle{small map edge}=[|-latex, gray!60!blue, shorten <=0.9mm, shorten >=0.5mm]
\tikzstyle{thick dashed edge}=[very thick,dashed,gray!40]
\tikzstyle{dashed edge}=[dashed,gray!40]
\tikzstyle{map edge}=[|-latex,very thick, gray!40, shorten <=1mm, shorten >=0.5mm]
\tikzstyle{tickedge}=[postaction=decorate,
  decoration={markings, mark=at position 0.5 with \edgetick}]
% \tikzstyle{dirtickedge}=[postaction=decorate,
%   decoration={markings, mark=at position 0.3 with \edgearrow},
%   decoration={markings, mark=at position 0.5 with \edgetick},
%   decoration={markings, mark=at position 0.8 with \edgearrow}]
\tikzstyle{dirtickedge}=[postaction=decorate,
  decoration={markings, mark=at position 0.5 with \edgetick},
  decoration={markings, mark=at position 0.85 with \edgearrow}]
\tikzstyle{dirdoubletickedge}=[postaction=decorate,
  decoration={markings, mark=at position 0.4 with \edgetick},
  decoration={markings, mark=at position 0.6 with \edgetick},
  decoration={markings, mark=at position 0.85 with \edgearrow}]


%%%%%%%%%

\tikzstyle{greenbox}=[rectangle,fill=\gfillcolor,draw=\gdrawcolor]
\tikzstyle{bluebox}=[rectangle,fill=blue!30,draw=blue]
\tikzstyle{whitebox}=[rectangle]

\tikzstyle{nicebg}=[execute at end picture=% 
{ 
\begin{pgfonlayer}{background}
\path (current bounding box.north west)+(-0.5,0.5) node (bg1) {};
\path (current bounding box.south east)+(0.5,-0.5) node (bg2) {};
\path[fill=gray!5!white,draw=gray,rounded corners] (bg1) rectangle (bg2);
\end{pgfonlayer}
}]

\tikzstyle{bang box}=[fill=blue!20!gray!10,draw=blue!20!black]


%%%  Misc 
\tikzstyle{ellipses}=[execute at end node={\small{...}}]
\tikzstyle{braceedge}=[decorate,decoration={brace,amplitude=2mm,raise=-1mm}]
\tikzstyle{small
  braceedge}=[decorate,decoration={brace,amplitude=1mm,raise=-1mm}]

\tikzstyle{cnot}=[fill=white,shape=circle,inner sep=-1.4pt]
\tikzstyle{wire label}=[font=\tiny, auto]


%%%%%%%%% Now define useful in-prose symbols with coloured dots.

\newcommand{\dotunit}[1]{%
\,\begin{tikzpicture}[dotpic,yshift=-1mm]
\node [#1] (a) at (0,0.25) {}; 
\draw [medium diredge] (0,-0.2)--(a);
\end{tikzpicture}\,}
\newcommand{\dotcounit}[1]{%
\,\begin{tikzpicture}[dotpic,yshift=1.5mm]
\node [#1] (a) at (0,-0.25) {}; 
\draw [medium diredge] (a)--(0,0.2);
\end{tikzpicture}\,}
\newcommand{\dotmult}[1]{%
\,\begin{tikzpicture}[dotpic,yshift=0.5mm]
  \node [#1] (a) {};
  \draw [medium diredge] (-90:0.55)--(a);
  \draw [medium diredge] (a) -- (45:0.6);
  \draw [medium diredge] (a) -- (135:0.6);
\end{tikzpicture}\,}
\newcommand{\dotcomult}[1]{%
\,\begin{tikzpicture}[dotpic]
  \node [#1] (a) {};
  \draw [medium diredge] (a) -- (90:0.55);
  \draw [medium diredge] (a) (-45:0.6) -- (a);
  \draw [medium diredge] (a) (-135:0.6) -- (a);
\end{tikzpicture}\,}

%%%%%%%%%%%%%%%%%%%%%%%%

\newcommand{\dotidualiser}[1]{%
\begin{tikzpicture}[dotpic,yshift=1.5mm]
  \node [#1] (a) {};
  \draw [medium diredge] (a) to (-90:0.35);
  \draw [medium diredge] (a) to (90:0.35);
\end{tikzpicture}}
\newcommand{\dotdualiser}[1]{%
\begin{tikzpicture}[dotpic,yshift=1.5mm]
  \node [#1] (a) {};
  \draw [medium diredge] (-90:0.35) to (a);
  \draw [medium diredge] (90:0.35) to (a);
\end{tikzpicture}}
\newcommand{\dottickunit}[1]{%
\begin{tikzpicture}[dotpic,yshift=-1mm]
\node [#1] (a) at (0,0.35) {}; 
\draw [postaction=decorate,
       decoration={markings, mark=at position 0.3 with \edgetick},
       decoration={markings, mark=at position 0.85 with \edgearrow}] (a)--(0,-0.25);
\end{tikzpicture}}
\newcommand{\dottickcounit}[1]{%
\begin{tikzpicture}[dotpic,yshift=1mm]
\node [#1] (a) at (0,-0.35) {}; 
\draw [postaction=decorate,
       decoration={markings, mark=at position 0.8 with \edgetick},
       decoration={markings, mark=at position 0.45 with \edgearrow}] (0,0.25) -- (a);
\end{tikzpicture}}
\newcommand{\dotonly}[1]{%
\,\begin{tikzpicture}[dotpic,yshift=-0.3mm]
\node [#1] (a) at (0,0) {};
\end{tikzpicture}\,}

\newcommand{\smalldotonly}[1]{%
\,\begin{tikzpicture}[dotpic,yshift=-0.15mm]
\node [#1] (a) at (0,0) {};
\end{tikzpicture}\,}

\newcommand{\dotthreestate}[1]{%
\,\begin{tikzpicture}[dotpic,yshift=2.5mm]
  \node [#1] (a) at (0,0) {};
  \draw (a) -- (0,-0.6);
  \draw [bend right] (a) to (-0.4,-0.6) (0.4,-0.6) to (a);
\end{tikzpicture}\,}
\newcommand{\dotcup}[1]{%
\,\begin{tikzpicture}[dotpic,yshift=2.5mm]
  \node [#1] (a) at (0,0) {};
  \draw [bend right,medium diredge] (a) to (-0.4,-0.6);
  \draw [bend left,medium diredge] (a) to (0.4,-0.6);
\end{tikzpicture}\,}
\newcommand{\dotcap}[1]{%
\,\begin{tikzpicture}[dotpic,yshift=4mm]
  \node [#1] (a) at (0,-0.6) {};
  \draw [bend right,medium diredge] (-0.4,0) to (a);
  \draw [bend left,medium diredge] (0.4,0) to (a);
\end{tikzpicture}\,}

% this doesn't have a colour
\newcommand{\tick}{%
\,\,\begin{tikzpicture}[dotpic]
  \node [style=none] (a) at (0,0.35) {};
  \node [style=none] (b) at (0,-0.35) {};
  \draw [dirtickedge] (a) -- (b);
\end{tikzpicture}\,\,}

% these only make sense in black
\newcommand{\lolli}{%
\,\begin{tikzpicture}[dotpic,yshift=-1mm]
  \path [use as bounding box] (-0.25,-0.25) rectangle (0.25,0.5);
  \node [style=dot] (a) at (0, 0.15) {};
  \node [style=none] (b) at (0, -0.25) {};
  \draw [medium diredge] (a) to (b.center);
  \draw [diredge, out=45, looseness=1.00, in=135, loop] (a) to ();
\end{tikzpicture}\,}

\newcommand{\cololli}{%
\,\begin{tikzpicture}[dotpic]
  \path [use as bounding box] (-0.25,-0.5) rectangle (0.25,0.5);
  \node [style=none] (a) at (0, 0.5) {};
  \node [style=dot] (b) at (0, 0) {};
  \draw [diredge, in=-45, looseness=2.00, out=-135, loop] (b) to ();
  \draw [medium diredge] (a.center) to (b);
\end{tikzpicture}\,}

% BLACK DOTS
\newcommand{\blackdot}{\dotonly{dot}\@dotnegspace}
\newcommand{\smallblackdot}{\smalldotonly{smalldot}}%NEW
\newcommand{\unit}{\dotunit{dot}}
\newcommand{\counit}{\dotcounit{dot}}
\newcommand{\mult}{\dotmult{dot}}
\newcommand{\comult}{\dotcomult{dot}}
\newcommand{\tickunit}{\dottickunit{dot}}
\newcommand{\tickcounit}{\dottickcounit{dot}}
\newcommand{\dualiser}{\dotdualiser{dot}}
\newcommand{\idualiser}{\dotidualiser{dot}}
\newcommand{\threestate}{\dotthreestate{dot}}
\newcommand{\blackcap}{\dotcap{dot}}
\newcommand{\blackcup}{\dotcup{dot}}
\newcommand{\blackobs}{\ensuremath{\mathcal O_{\!\smallblackdot}}\xspace}

% WHITE DOTS
\newcommand{\whitedot}{\dotonly{white dot}\@dotnegspace}
\newcommand{\smallwhitedot}{\smalldotonly{smallwhitedot}}%NEW
\newcommand{\whiteunit}{\dotunit{white dot}}
\newcommand{\whitecounit}{\dotcounit{white dot}}
\newcommand{\whitemult}{\dotmult{white dot}}
\newcommand{\whitecomult}{\dotcomult{white dot}}
\newcommand{\whitetickunit}{\dottickunit{white dot}}
\newcommand{\whitetickcounit}{\dottickcounit{white dot}}
\newcommand{\whitecap}{\dotcap{white dot}}
\newcommand{\whitecup}{\dotcup{white dot}}
\newcommand{\whiteobs}{\ensuremath{\mathcal O_{\!\smallwhitedot}}\xspace}


% ALTERNATE WHITE DOTS
\newcommand{\altwhitedot}{\dotonly{alt white dot}\@dotnegspace}
\newcommand{\altwhiteunit}{\dotunit{alt white dot}}
\newcommand{\altwhitecounit}{\dotcounit{alt white dot}}
\newcommand{\altwhitemult}{\dotmult{alt white dot}}
\newcommand{\altwhitecomult}{\dotcomult{alt white dot}}
\newcommand{\altwhitetickunit}{\dottickunit{alt white dot}}
\newcommand{\altwhitetickcounit}{\dottickcounit{alt white dot}}
\newcommand{\altwhitecap}{\dotcap{alt white dot}}
\newcommand{\altwhitecup}{\dotcup{alt white dot}}

% GRAY DOTS
\newcommand{\graydot}{\dotonly{gray dot}\@dotnegspace}
\newcommand{\smallgraydot}{\smalldotonly{smallgraydot}}%NEW
\newcommand{\grayunit}{\dotunit{gray dot}}
\newcommand{\graycounit}{\dotcounit{gray dot}}
\newcommand{\graymult}{\dotmult{gray dot}}
\newcommand{\graycomult}{\dotcomult{gray dot}}
\newcommand{\graytickunit}{\dottickunit{gray dot}}
\newcommand{\graytickcounit}{\dottickcounit{gray dot}}
\newcommand{\graycap}{\dotcap{gray dot}}
\newcommand{\graycup}{\dotcup{gray dot}}

\newcommand{\grayobs}{\ensuremath{\mathcal O_{\!\smallgraydot}}\xspace}


\newcommand{\blacktranspose}{\ensuremath{{\,\blackdot\!\textrm{\rm\,T}}}}
\newcommand{\graytranspose}{\ensuremath{{\,\graydot\!\textrm{\rm\,T}}}}
\newcommand{\whitetranspose}{\ensuremath{{\,\whitedot\!\textrm{\rm\,T}}}}
\newcommand{\whiteconjugate}{\circledast}

\newcommand{\circl}{\begin{tikzpicture}[dotpic]
    \node [style=none] (a) at (-0.25, 0.25) {};
    \node [style=none] (b) at (0.25, 0.25) {};
    \node [style=none] (c) at (-0.25, -0.25) {};
    \node [style=none] (d) at (0.25, -0.25) {};
    \draw [in=45, out=135] (b.center) to (a.center);
    \draw [in=135, out=225] (a.center) to (c.center);
    \draw [in=225, out=-45] (c.center) to (d.center);
    \draw [style=diredge, in=-45, out=45] (d.center) to (b.center);
\end{tikzpicture}}

%%% RED and GREEN

\newcommand{\@dotnegspace}{\hspace{-0.1em}}

\newcommand{\gdot}{\dotonly{green dot}\@dotnegspace}
\newcommand{\gsmalldot}{\smalldotonly{smallgreendot}}
\newcommand{\gunit}{\dotunit{green dot}}
\newcommand{\gcounit}{\dotcounit{green dot}}
\newcommand{\gmult}{\dotmult{green dot}}
\newcommand{\gcomult}{\dotcomult{green dot}}
\newcommand{\gtickunit}{\dottickunit{green dot}}
\newcommand{\gtickcounit}{\dottickcounit{green dot}}
\newcommand{\gcap}{\dotcap{green dot}}
\newcommand{\gcup}{\dotcup{green dot}}
\newcommand{\gtrans}{\ensuremath{^{\gsmalldot}}}
\newcommand{\gconj}{\ensuremath{_{\@dotnegspace\gsmalldot}}}

\newcommand{\rdot}{\dotonly{red dot}\@dotnegspace}
\newcommand{\rsmalldot}{\smalldotonly{smallreddot}}
\newcommand{\runit}{\dotunit{red dot}}
\newcommand{\rcounit}{\dotcounit{red dot}}
\newcommand{\rmult}{\dotmult{red dot}}
\newcommand{\rcomult}{\dotcomult{red dot}}
\newcommand{\rtickunit}{\dottickunit{red dot}}
\newcommand{\rtickcounit}{\dottickcounit{red dot}}
\newcommand{\rcap}{\dotcap{red dot}}
\newcommand{\rcup}{\dotcup{red dot}}
\newcommand{\rtrans}{\ensuremath{^{\rsmalldot}}}
\newcommand{\rconj}{\ensuremath{_{\@dotnegspace\rsmalldot}}}

\newcommand{\gdelta}{\ensuremath{\delta\gconj}\xspace}
\newcommand{\gepsilon}{\ensuremath{\epsilon\gconj}\xspace}
\newcommand{\gmu}{\ensuremath{\mu\gconj}\xspace}
\newcommand{\geta}{\ensuremath{\eta\gconj}\xspace}

\newcommand{\rdelta}{\ensuremath{\delta\rconj}\xspace}
\newcommand{\repsilon}{\ensuremath{\epsilon\rconj}\xspace}
\newcommand{\rmu}{\ensuremath{\mu\rconj}\xspace}
\newcommand{\reta}{\ensuremath{\eta\rconj}\xspace}


\newcommand{\rgtrans}{\ensuremath{^{\rsmalldot\gsmalldot}}}
\newcommand{\rgconj}{\ensuremath{_{\@dotnegspace\rsmalldot\gsmalldot}}}
\newcommand{\grtrans}{\ensuremath{^{\gsmalldot\rsmalldot}}}
\newcommand{\grconj}{\ensuremath{_{\@dotnegspace\gsmalldot\rsmalldot}}}