%%
%% This is file `tqft.sty',
%% generated with the docstrip utility.
%%
%% The original source files were:
%%
%% tqft_code.dtx  (with options: `package')
%% ----------------------------------------------------------------
%% tqft --- a TikZ library for drawing TQFT diagrams
%% E-mail: loopspace@mathforge.org
%% Released under the LaTeX Project Public License v1.3c or later
%% See http://www.latex-project.org/lppl.txt
%% ----------------------------------------------------------------
%% 
\NeedsTeXFormat{LaTeX2e}
\ProvidesPackage{tqft}[2017/06/01 v2.1 Tikz/PGF commands for drawing TQFT diagrams]
\RequirePackage{pgfkeys}
\RequirePackage{pgf}
\def\pgf@tqft@minus{-}
\let\pgf@tqft@upper\@empty
\let\pgf@tqft@lower\pgf@tqft@minus
\def\tqftset#1{\pgfkeys{/pgf/tqft/.cd,#1}}
\def\tqft@process#1#2{%
  \edef\tqft@px{#1}
  \edef\tqft@py{#2}
  \pgf@process{
    \pgftransformreset
    \let\tikz@transform=\pgfutil@empty
    \expandafter\tikzset\expandafter{\tqft@transformation}
    \tikz@transform
    \pgfpointtransformed{\pgfqpoint{\tqft@px}{\tqft@py}}
  }
}
\newdimen\tqft@xa
\newdimen\tqft@xb
\newdimen\tqft@c
\newdimen\tqft@ch
\newdimen\tqft@h
\newdimen\tqft@s
\newdimen\tqft@w
\newif\iftqft@within@node
\pgfkeys{
  /tikz/tqft/use nodes/.is choice,
  /tikz/tqft/use nodes/true/.code={%
    \tikzset{
      tqft/.style={%
        /tikz/shape=tqft cobordism,
        /pgf/tqft,
        /tikz/every tqft/.try
      },
      tqft/.unknown/.code={%
        \let\tqft@searchname=\pgfkeyscurrentname%
        \pgfkeys{%
          /pgf/tqft/\tqft@searchname={##1}
        }
      },
    }%
  },
  /tikz/tqft/use nodes/false/.code={%
    \tikzset{
      tqft/.style={%
        pic type=cobordism,
        tqft/.cd,
        every tqft/.try,
      },
      tqft/.unknown/.code={%
        \let\tqft@searchname=\pgfkeyscurrentname%
        \pgfkeys{%
          /tikz/\tqft@searchname={##1}
        }
      },
    }%
  },
  /tikz/tqft/use nodes=true,
  /pgf/tqft/.unknown/.code={%
    \let\tqft@searchname=\pgfkeyscurrentname%
    \pgfkeysalso{%
      /tikz/\tqft@searchname={#1}
    }
  },
  /pgf/tqft/.is family,
  /pgf/tqft,
  boundary circle/.style={
    /tikz/shape=tqft boundary circle
  },
  incoming boundary components/.initial=5,
  outgoing boundary components/.initial=4,
  offset/.initial=0,
  cobordism height/.initial=2cm,
  boundary separation/.initial=2cm,
  circle width/.initial=10pt,
  circle depth/.initial=5pt,
  outer xsep/.initial=0pt,
  outer ysep/.initial=0pt,
  outer sep/.style={
    outer xsep=#1,
    outer ysep=#1
  },
  flow/.code={%
    \pgfkeys{/pgf/tqft/flow transformation/.expand twice/.expand once=\pgfkeysvalueof{/pgf/tqft/flow transformation #1}}
  },
  flow transformation south/.initial={},
  flow transformation north/.initial={%
    xscale=-1,rotate=180
  },
  flow transformation east/.initial={%
    rotate=90,xscale=-1
  },
  flow transformation west/.initial={%
    rotate=270
  },
  flow transformation/.initial={},
  view from/.is choice,
  view from/incoming/.code={%
    \let\pgf@tqft@upper\pgf@tqft@minus
    \let\pgf@tqft@lower\@empty
  },
  view from/outgoing/.code={%
  \let\pgf@tqft@lower\pgf@tqft@minus
    \let\pgf@tqft@upper\@empty
  },
  boundary lower style contents/.initial={},
  boundary lower style/.code={%
    \pgfkeys{/pgf/tqft/boundary lower style contents/.style={%
        /tikz/.cd,#1
      }
    }
  },
  boundary style contents/.initial={},
  boundary style/.code={%
    \pgfkeys{/pgf/tqft/boundary style contents/.style={%
        /tikz/.cd,#1
      }
    }
  },
  boundary upper style contents/.initial={},
  boundary upper style/.code={%
    \pgfkeys{/pgf/tqft/boundary upper style contents/.style={%
        /tikz/.cd,#1
      }
    }
  },
  cobordism style contents/.initial={},
  cobordism style/.code={%
    \pgfkeys{/pgf/tqft/cobordism style contents/.style={%
        /tikz/.cd,#1%
      }
    }
  },
  pair of pants/.style={
    /tikz/tqft,
    incoming boundary components=1,
    outgoing boundary components=2,
    offset=-.5
  },
  /tikz/tqft pair of pants/.style={
    /pgf/tqft/pair of pants,
  },
  reverse pair of pants/.style={
    /tikz/tqft,
    incoming boundary components=2,
    outgoing boundary components=1,
    offset=.5
  },
  /tikz/tqft reverse pair of pants/.style={
    /pgf/tqft/reverse pair of pants,
  },
  cylinder to prior/.style={
    /tikz/tqft,
    incoming boundary components=1,
    outgoing boundary components=1,
    offset=-.5
  },
  /tikz/tqft cylinder to prior/.style={
    /pgf/tqft/cylinder to prior,
  },
  cylinder to next/.style={
    /tikz/tqft,
    incoming boundary components=1,
    outgoing boundary components=1,
    offset=.5
  },
  /tikz/tqft cylinder to next/.style={
    /pgf/tqft/cylinder to next,
  },
  cylinder/.style={
    /tikz/tqft,
    incoming boundary components=1,
    outgoing boundary components=1
  },
  /tikz/tqft cylinder/.style={
    /pgf/tqft/cylinder,
  },
  cup/.style={
    /tikz/tqft,
    incoming boundary components=1,
    outgoing boundary components=0
  },
  /tikz/tqft cup/.style={
    /pgf/tqft/cup,
  },
  cap/.style={
    /tikz/tqft,
    incoming boundary components=0,
    outgoing boundary components=1
  },
  /tikz/tqft cap/.style={
    /pgf/tqft/cap,
  },
}
\pgfdeclareshape{tqft cobordism}{
  \savedmacro{\tqft@incoming}{\edef\tqft@incoming{\pgfkeysvalueof{/pgf/tqft/incoming boundary components}}}
  \savedmacro{\tqft@outgoing}{\edef\tqft@outgoing{\pgfkeysvalueof{/pgf/tqft/outgoing boundary components}}}
  \savedmacro{\tqft@offset}{\edef\tqft@offset{\pgfkeysvalueof{/pgf/tqft/offset}}}
  \saveddimen{\tqft@height}{\pgf@x=\pgfkeysvalueof{/pgf/tqft/cobordism height}}
  \saveddimen{\tqft@separation}{\pgf@x=\pgfkeysvalueof{/pgf/tqft/boundary separation}}
  \saveddimen{\tqft@width}{\pgf@x=\pgfkeysvalueof{/pgf/tqft/circle width}}
  \saveddimen{\tqft@depth}{\pgf@x=\pgfkeysvalueof{/pgf/tqft/circle depth}}
  \saveddimen{\tqft@outerxsep}{\pgf@x=\pgfkeysvalueof{/pgf/tqft/outer xsep}}
  \saveddimen{\tqft@outerysep}{\pgf@x=\pgfkeysvalueof{/pgf/tqft/outer ysep}}
  \saveddimen{\tqft@control}{
  \pgfkeysgetvalue{/pgf/tqft/cobordism height}{\tqft@tempa}
  \pgfkeysgetvalue{/pgf/tqft/circle depth}{\tqft@tempb}
  \pgfmathsetlength{\pgf@x}{.5 * \tqft@tempa - 4 * \tqft@tempb}
}
   \savedmacro{\tqft@transformation}{%
  \pgfkeysgetvalue{/pgf/tqft/flow transformation}{\tqft@transformation}
}
   \savedanchor{\tqft@start@incoming}{%
    \pgfmathsetlength{\pgf@x}{-(max(\pgfkeysvalueof{/pgf/tqft/incoming boundary components} - 1,\pgfkeysvalueof{/pgf/tqft/outgoing boundary components} - 1 + \pgfkeysvalueof{/pgf/tqft/offset}) + min(0,\pgfkeysvalueof{/pgf/tqft/offset}) )*\pgfkeysvalueof{/pgf/tqft/boundary separation}/2}
    \pgfmathsetlength{\pgf@y}{.5 * \pgfkeysvalueof{/pgf/tqft/cobordism height}}
}
   \savedanchor{\tqft@start@outgoing}{%
    \pgfmathsetlength{\pgf@x}{-(max(\pgfkeysvalueof{/pgf/tqft/incoming boundary components} - 1,\pgfkeysvalueof{/pgf/tqft/outgoing boundary components} - 1 + \pgfkeysvalueof{/pgf/tqft/offset}) + min(0,\pgfkeysvalueof{/pgf/tqft/offset})- 2*\pgfkeysvalueof{/pgf/tqft/offset})*\pgfkeysvalueof{/pgf/tqft/boundary separation}/2}
    \pgfmathsetlength{\pgf@y}{-.5 * \pgfkeysvalueof{/pgf/tqft/cobordism height}}
}
\savedanchor{\tqft@textsize}{%
  \pgf@y=-.5\ht\pgfnodeparttextbox%
  \pgf@x=-.5\wd\pgfnodeparttextbox%
}
  \anchor{centre}{\pgfpointorigin}
  \anchor{center}{\pgfpointorigin}
\anchor{text}{
  \tqft@textsize
}
\anchor{north}{%
  \pgf@ya=\tqft@height\relax
  \pgf@yb=.5\pgf@ya
  \advance\pgf@yb by \tqft@outerysep\relax
  \tqft@process{0pt}{\the\pgf@yb}
}
\anchor{south}{%
  \pgf@yb=\tqft@height\relax
  \pgf@ya=.5\pgf@yb
  \advance\pgf@ya by \tqft@outerysep\relax
  \pgf@yb=-\pgf@ya
  \tqft@process{0pt}{\the\pgf@yb}
}
\anchor{west}{%
  \tqft@start@incoming
  \pgf@xa=\pgf@x
  \advance\pgf@xa by -\tqft@width
  \pgf@ya=\pgf@y
  \tqft@start@outgoing
  \pgf@xb=\pgf@x
  \advance\pgf@xb by -\tqft@width
  \pgf@yb=\pgf@y
  \pgf@xc=.5\pgf@xa
  \advance\pgf@xc by .5\pgf@xb
  \pgf@yc=.5\pgf@ya
  \advance\pgf@yc by .5\pgf@yb
  \advance\pgf@xc by -\tqft@outerxsep\relax
  \tqft@process{\the\pgf@xc}{\the\pgf@yc}
}
\anchor{east}{%
  \tqft@start@incoming
  \pgf@xa=\pgf@x
  \pgfmathsetlength{\pgf@xa}{\pgf@xa + (\tqft@incoming - 1) * \tqft@separation}
  \advance\pgf@xa by \tqft@width\relax
  \pgf@ya=\pgf@y
  \tqft@start@outgoing
  \pgf@xb=\pgf@x
  \pgfmathsetlength{\pgf@xb}{\pgf@xb + (\tqft@outgoing - 1) * \tqft@separation}
  \advance\pgf@xb by \tqft@width\relax
  \pgf@yb=\pgf@y
  \pgf@xc=.5\pgf@xa
  \advance\pgf@xc by .5\pgf@xb
  \pgf@yc=.5\pgf@ya
  \advance\pgf@yc by .5\pgf@yb
  \advance\pgf@xc by \tqft@outerxsep\relax
  \tqft@process{\the\pgf@xc}{\the\pgf@yc}
}
\anchor{north west}{
  \tqft@start@incoming
  \pgf@xc=\pgf@x
  \pgf@yc=\pgf@y
  \advance\pgf@xc by -\tqft@width\relax
  \advance\pgf@yc by \tqft@outerysep\relax
  \advance\pgf@xc by -\tqft@outerxsep\relax
  \tqft@process{\the\pgf@xc}{\the\pgf@yc}
}
\anchor{south west}{
  \tqft@start@outgoing
  \pgf@xc=\pgf@x
  \pgf@yc=\pgf@y
  \advance\pgf@xc by -\tqft@width\relax
  \advance\pgf@yc by -\tqft@outerysep\relax
  \advance\pgf@xc by -\tqft@outerxsep\relax
  \tqft@process{\the\pgf@xc}{\the\pgf@yc}
}
\anchor{north east}{
  \tqft@start@incoming
  \pgf@xc=\pgf@x
  \pgfmathsetlength{\pgf@xc}{\pgf@xc + (\tqft@incoming - 1)*\tqft@separation}
  \pgf@yc=\pgf@y
  \advance\pgf@xc by \tqft@width\relax
  \advance\pgf@yc by \tqft@outerysep\relax
  \advance\pgf@xc by \tqft@outerxsep\relax
  \tqft@process{\the\pgf@xc}{\the\pgf@yc}
}
\anchor{south east}{
  \tqft@start@outgoing
  \pgf@xc=\pgf@x
  \pgfmathsetlength{\pgf@xc}{\pgf@xc + (\tqft@outgoing - 1)*\tqft@separation}
  \pgf@yc=\pgf@y
  \advance\pgf@xc by \tqft@width\relax
  \advance\pgf@yc by -\tqft@outerysep\relax
  \advance\pgf@xc by \tqft@outerxsep\relax
  \tqft@process{\the\pgf@xc}{\the\pgf@yc}
}
\expandafter\pgfutil@g@addto@macro\csname pgf@sh@s@tqft cobordism\endcsname{%
  \c@pgf@counta\tqft@incoming\relax%
  \pgfmathloop%
  \ifnum\c@pgf@counta>0\relax%
  \pgfutil@ifundefined{pgf@anchor@tqft cobordism@incoming boundary\space\the\c@pgf@counta}{%
    \expandafter\xdef\csname pgf@anchor@tqft cobordism@incoming boundary\space\the\c@pgf@counta\endcsname{%
  \noexpand\tqft@start@incoming
  \noexpand\pgfmathsetlength{\noexpand\pgf@y}{\noexpand\pgf@y + \noexpand\tqft@outerysep}
  \noexpand\pgfmathsetlength{\noexpand\pgf@x}{\noexpand\pgf@x + (\the\c@pgf@counta - 1) * \noexpand\tqft@separation}
  \noexpand\tqft@process{\noexpand\the\noexpand\pgf@x}{\noexpand\the\noexpand\pgf@y}
  }
  }{\c@pgf@counta0\relax}%
  \advance\c@pgf@counta-1\relax%
  \repeatpgfmathloop%
}
\expandafter\pgfutil@g@addto@macro\csname pgf@sh@s@tqft cobordism\endcsname{%
  \c@pgf@counta\tqft@outgoing\relax%
  \pgfmathloop%
  \ifnum\c@pgf@counta>0\relax%
  \pgfutil@ifundefined{pgf@anchor@tqft cobordism@outgoing boundary\space\the\c@pgf@counta}{%
    \expandafter\xdef\csname pgf@anchor@tqft cobordism@outgoing boundary\space\the\c@pgf@counta\endcsname{%
  \noexpand\tqft@start@outgoing
  \noexpand\pgfmathsetlength{\noexpand\pgf@y}{\noexpand\pgf@y - \noexpand\tqft@outerysep}
  \noexpand\pgfmathsetlength{\noexpand\pgf@x}{\noexpand\pgf@x + (\the\c@pgf@counta - 1) * \noexpand\tqft@separation}
  \noexpand\tqft@process{\noexpand\the\noexpand\pgf@x}{\noexpand\the\noexpand\pgf@y}
  }
  }{\c@pgf@counta0\relax}%
  \advance\c@pgf@counta-1\relax%
  \repeatpgfmathloop%
}
\expandafter\pgfutil@g@addto@macro\csname pgf@sh@s@tqft cobordism\endcsname{%
  \c@pgf@counta\tqft@incoming\relax%
  \advance\c@pgf@counta-1\relax
  \pgfmathloop%
  \ifnum\c@pgf@counta>0\relax%
  \pgfutil@ifundefined{pgf@anchor@tqft cobordism@after incoming boundary\space\the\c@pgf@counta}{%
    \expandafter\xdef\csname pgf@anchor@tqft cobordism@after incoming boundary\space\the\c@pgf@counta\endcsname{%
  \noexpand\tqft@start@incoming
  \noexpand\pgfmathsetlength{\noexpand\pgf@y}{.25 * \noexpand\pgf@y +.75 * \noexpand\tqft@control + \noexpand\tqft@outerysep}
  \noexpand\pgfmathsetlength{\noexpand\pgf@x}{\noexpand\pgf@x + (\the\c@pgf@counta - .5) * \noexpand\tqft@separation}
  \noexpand\tqft@process{\noexpand\the\noexpand\pgf@x}{\noexpand\the\noexpand\pgf@y}
  }
  }{\c@pgf@counta0\relax}%
  \advance\c@pgf@counta-1\relax%
  \repeatpgfmathloop%
}
\expandafter\pgfutil@g@addto@macro\csname pgf@sh@s@tqft cobordism\endcsname{%
  \c@pgf@counta\tqft@outgoing\relax%
  \advance\c@pgf@counta-1\relax
  \pgfmathloop%
  \ifnum\c@pgf@counta>0\relax%
  \pgfutil@ifundefined{pgf@anchor@tqft cobordism@after outgoing boundary\space\the\c@pgf@counta}{%
    \expandafter\xdef\csname pgf@anchor@tqft cobordism@after outgoing boundary\space\the\c@pgf@counta\endcsname{%
  \noexpand\tqft@start@outgoing
  \noexpand\pgfmathsetlength{\noexpand\pgf@y}{.25 * \noexpand\pgf@y -.75 * \noexpand\tqft@control - \noexpand\tqft@outerysep}
  \noexpand\pgfmathsetlength{\noexpand\pgf@x}{\noexpand\pgf@x + (\the\c@pgf@counta - .5) * \noexpand\tqft@separation}
  \noexpand\tqft@process{\noexpand\the\noexpand\pgf@x}{\noexpand\the\noexpand\pgf@y}
  }
  }{\c@pgf@counta0\relax}%
  \advance\c@pgf@counta-1\relax%
  \repeatpgfmathloop%
}
  \backgroundpath{
    \let\tikz@transform=\pgfutil@empty
    \expandafter\tikzset\expandafter{\tqft@transformation}
    \tikz@transform
    \pgfmathsetlength{\tqft@s}{\tqft@separation}
    \pgfmathsetlength{\tqft@w}{2*\tqft@width}
\tqft@start@incoming
\tqft@xa=\pgf@x
    \advance\tqft@xa by -.5\tqft@w\relax
\tqft@h=\pgf@y
    \tqft@xb=\tqft@xa
    \advance\tqft@xb by \tqft@w\relax
\tqft@c=\tqft@control\relax
    \ifnum\tqft@incoming>0
    \pgfpathmoveto{\pgfqpoint{\tqft@xa}{\tqft@h}}
     \pgfpatharc{\pgf@tqft@upper180}{0}{\tqft@width and \tqft@depth}
   \ifnum\tqft@incoming>1
    \foreach \tqft@k in {2,...,\tqft@incoming} {
     \advance\tqft@xa by \tqft@k\tqft@s
     \advance\tqft@xb by \tqft@k\tqft@s
     \advance\tqft@xb by -2\tqft@s
     \advance\tqft@xa by -\tqft@s
     \pgfpathcurveto{\pgfqpoint{\tqft@xb}{\tqft@c}}{\pgfqpoint{\tqft@xa}{\tqft@c}}{\pgfqpoint{\tqft@xa}{\tqft@h}}
     \pgfpatharc{\pgf@tqft@upper180}{0}{\tqft@width and \tqft@depth}
    }
    \fi
    \ifnum\tqft@outgoing=0
     \advance\tqft@xb by \tqft@incoming\tqft@s
     \advance\tqft@xb by -\tqft@s
     \pgfmathsetlength{\tqft@ch}{min(0,max(-\tqft@h,\tqft@h - (\tqft@h - \tqft@c) * ((abs(\tqft@xb - \tqft@xa) - \tqft@w)/\tqft@s + 1)))}
     \pgfpathcurveto{\pgfqpoint{\tqft@xb}{\tqft@ch}}{\pgfqpoint{\tqft@xa}{\tqft@ch}}{\pgfqpoint{\tqft@xa}{\tqft@h}}
    \fi
    \fi
    \ifnum\tqft@outgoing>0
     \advance\tqft@xb by \tqft@incoming\tqft@s
     \advance\tqft@xb by -\tqft@s
     \pgfmathsetlength{\tqft@xa}{\tqft@xa + (\tqft@outgoing - 1 + \tqft@offset) * \tqft@separation + 2*\tqft@width}
    \ifnum\tqft@incoming>0
     \pgfmathsetlength{\tqft@ch}{min(0,max(-\tqft@h,\tqft@h - (\tqft@h - \tqft@c) * ((abs(\tqft@xb - \tqft@xa) - \tqft@w)/\tqft@s + 1)))}
     \pgfpathcurveto{\pgfqpoint{\tqft@xb}{\tqft@ch}}{\pgfqpoint{\tqft@xa}{-\tqft@ch}}{\pgfqpoint{\tqft@xa}{-\tqft@h}}
    \else
     \pgfpathmoveto{\pgfqpoint{\tqft@xa}{-\tqft@h}}
    \fi
     \tqft@xb=\tqft@xa
     \advance\tqft@xb by -\tqft@w
     \pgfpatharc{0}{\pgf@tqft@upper180}{\tqft@width and \tqft@depth}
    \ifnum\tqft@outgoing>1
    \foreach \tqft@k in {2,...,\tqft@outgoing} {
     \advance\tqft@xa by -\tqft@k\tqft@s
     \advance\tqft@xb by -\tqft@k\tqft@s
     \advance\tqft@xb by 2\tqft@s
     \advance\tqft@xa by \tqft@s
     \pgfpathcurveto{\pgfqpoint{\tqft@xb}{-\tqft@c}}{\pgfqpoint{\tqft@xa}{-\tqft@c}}{\pgfqpoint{\tqft@xa}{-\tqft@h}}
     \pgfpatharc{0}{\pgf@tqft@upper180}{\tqft@width and \tqft@depth}
    }
    \fi
     \advance\tqft@xb by -\tqft@outgoing\tqft@s
     \advance\tqft@xb by \tqft@s
    \ifnum\tqft@incoming>0
     \pgfmathsetlength{\tqft@xa}{\tqft@xa - (\tqft@outgoing -1 + \tqft@offset) * \tqft@separation - 2*\tqft@width}
     \pgfmathsetlength{\tqft@ch}{min(0,max(-\tqft@h,\tqft@h - (\tqft@h - \tqft@c) * ((abs(\tqft@xb - \tqft@xa) - \tqft@w)/\tqft@s + 1)))}
     \pgfpathcurveto{\pgfqpoint{\tqft@xb}{-\tqft@ch}}{\pgfqpoint{\tqft@xa}{\tqft@ch}}{\pgfqpoint{\tqft@xa}{\tqft@h}}
    \else
     \pgfmathsetlength{\tqft@ch}{min(0,max(-\tqft@h,\tqft@h - (\tqft@h - \tqft@c) * ((abs(\tqft@xb - \tqft@xa) - \tqft@w)/\tqft@s + 1)))}
     \pgfpathcurveto{\pgfqpoint{\tqft@xb}{-\tqft@ch}}{\pgfqpoint{\tqft@xa}{-\tqft@ch}}{\pgfqpoint{\tqft@xa}{-\tqft@h}}
    \fi
    \fi
     \pgfpathclose
  }
  \behindbackgroundpath{
    \let\tikz@transform=\pgfutil@empty
    \expandafter\tikzset\expandafter{\tqft@transformation}
    \tikz@transform
    \pgfmathsetlength{\tqft@s}{\tqft@separation}
    \pgfmathsetlength{\tqft@w}{2*\tqft@width}
    \pgfmathsetlength{\tqft@xa}{-(max(\tqft@incoming - 1,\tqft@outgoing - 1 + \tqft@offset) + min(0,\tqft@offset) + 2)*\tqft@separation/2}
    \pgfmathsetlength{\tqft@h}{.5 * \tqft@height}
    {
      \tikz@mode@fillfalse%
      \tikz@mode@drawfalse%
      \let\tikz@mode=\pgfutil@empty
      \let\tikz@options=\pgfutil@empty
      \tqftset{boundary style contents}
      \tikz@mode
      \tikz@options
    \ifnum\tqft@incoming>0
    \foreach \tqft@k in {1,...,\tqft@incoming} {
     \advance\tqft@xa by \tqft@k\tqft@s
     \pgfpathellipse{\pgfqpoint{\tqft@xa}{\tqft@h}}{\pgfqpoint{\tqft@width}{0pt}}{\pgfqpoint{0pt}{\tqft@depth}}
    }
    \fi
    \ifnum\tqft@outgoing>0
     \pgfmathsetlength{\tqft@xa}{\tqft@xa + (\tqft@outgoing + \tqft@offset + 1) * \tqft@separation}
    \foreach \tqft@k in {1,...,\tqft@outgoing} {
     \advance\tqft@xa by -\tqft@k\tqft@s
     \pgfpathellipse{\pgfqpoint{\tqft@xa}{-\tqft@h}}{\pgfqpoint{\tqft@width}{0pt}}{\pgfqpoint{0pt}{\tqft@depth}}
    }
    \fi
      \edef\tikz@temp{\noexpand\pgfusepath{%
          \iftikz@mode@fill fill,\fi%
          \iftikz@mode@draw draw\fi%
      }}%
      \tikz@temp
    }
    {
      \tikz@mode@fillfalse%
      \tikz@mode@drawfalse%
      \let\tikz@mode=\pgfutil@empty
      \let\tikz@options=\pgfutil@empty
      \tqftset{boundary lower style contents}
      \tikz@mode
      \tikz@options
      \advance\tqft@xa by .5\tqft@w
    \ifnum\tqft@incoming>0
    \foreach \tqft@k in {1,...,\tqft@incoming} {
     \advance\tqft@xa by \tqft@k\tqft@s
     \pgfpathmoveto{\pgfqpoint{\tqft@xa}{\tqft@h}}
     \pgfpatharc{0}{\pgf@tqft@lower180}{\tqft@width and \tqft@depth}
    }
    \fi
    \ifnum\tqft@outgoing>0
     \pgfmathsetlength{\tqft@xa}{\tqft@xa + (\tqft@outgoing + \tqft@offset + 1) * \tqft@separation}
    \foreach \tqft@k in {1,...,\tqft@outgoing} {
     \advance\tqft@xa by -\tqft@k\tqft@s
     \pgfpathmoveto{\pgfqpoint{\tqft@xa}{-\tqft@h}}
     \pgfpatharc{0}{\pgf@tqft@lower180}{\tqft@width and \tqft@depth}
    }
    \fi
      \edef\tikz@temp{\noexpand\pgfusepath{%
          \iftikz@mode@fill fill,\fi%
          \iftikz@mode@draw draw\fi%
      }}%
      \tikz@temp
    }
  }
  \beforebackgroundpath{
    \pgfmathsetlength{\tqft@s}{\tqft@separation}
    \pgfmathsetlength{\tqft@w}{2*\tqft@width}
    \pgfmathsetlength{\tqft@xa}{-(max(\tqft@incoming - 1,\tqft@outgoing - 1 + \tqft@offset) + min(0,\tqft@offset))*\tqft@s/2 - \tqft@width}
    \tqft@xb=\tqft@xa
    \advance\tqft@xb by \tqft@w
\tqft@c=\tqft@control\relax
    \pgfmathsetlength{\tqft@h}{.5 * \tqft@height}
   {
      \tikz@mode@fillfalse%
      \tikz@mode@drawfalse%
      \let\tikz@mode=\pgfutil@empty
      \let\tikz@options=\pgfutil@empty
      \tqftset{cobordism style contents}
      \tikz@mode
      \tikz@options
    \ifnum\tqft@incoming>0
   \ifnum\tqft@incoming>1
    \foreach \tqft@k in {2,...,\tqft@incoming} {
     \advance\tqft@xa by \tqft@k\tqft@s
     \advance\tqft@xb by \tqft@k\tqft@s
     \advance\tqft@xb by -2\tqft@s
     \advance\tqft@xa by -\tqft@s
    \pgfpathmoveto{\pgfqpoint{\tqft@xb}{\tqft@h}}
     \pgfpathcurveto{\pgfqpoint{\tqft@xb}{\tqft@c}}{\pgfqpoint{\tqft@xa}{\tqft@c}}{\pgfqpoint{\tqft@xa}{\tqft@h}}
    }
    \fi
    \ifnum\tqft@outgoing=0
     \advance\tqft@xb by \tqft@incoming\tqft@s
     \advance\tqft@xb by -\tqft@s
     \pgfmathsetlength{\tqft@ch}{min(0,max(-\tqft@h,\tqft@h - (\tqft@h - \tqft@c) * ((abs(\tqft@xb - \tqft@xa) - \tqft@w)/\tqft@s + 1)))}
    \pgfpathmoveto{\pgfqpoint{\tqft@xb}{\tqft@h}}
     \pgfpathcurveto{\pgfqpoint{\tqft@xb}{\tqft@ch}}{\pgfqpoint{\tqft@xa}{\tqft@ch}}{\pgfqpoint{\tqft@xa}{\tqft@h}}
    \fi
    \fi
    \ifnum\tqft@outgoing>0
     \advance\tqft@xb by \tqft@incoming\tqft@s
     \advance\tqft@xb by -\tqft@s
     \pgfmathsetlength{\tqft@xa}{\tqft@xa + (\tqft@outgoing - 1 + \tqft@offset) * \tqft@separation + 2*\tqft@width}
    \ifnum\tqft@incoming>0
     \pgfmathsetlength{\tqft@ch}{min(0,max(-\tqft@h,\tqft@h - (\tqft@h - \tqft@c) * ((abs(\tqft@xb - \tqft@xa) - \tqft@w)/\tqft@s + 1)))}
     \pgfpathmoveto{\pgfqpoint{\tqft@xb}{\tqft@h}}
     \pgfpathcurveto{\pgfqpoint{\tqft@xb}{\tqft@ch}}{\pgfqpoint{\tqft@xa}{-\tqft@ch}}{\pgfqpoint{\tqft@xa}{-\tqft@h}}
    \else
     \pgfpathmoveto{\pgfqpoint{\tqft@xa}{-\tqft@h}}
    \fi
     \tqft@xb=\tqft@xa
     \advance\tqft@xb by -\tqft@w
     \pgfpathmoveto{\pgfqpoint{\tqft@xb}{-\tqft@h}}
    \ifnum\tqft@outgoing>1
    \foreach \tqft@k in {2,...,\tqft@outgoing} {
     \advance\tqft@xa by -\tqft@k\tqft@s
     \advance\tqft@xb by -\tqft@k\tqft@s
     \advance\tqft@xb by 2\tqft@s
     \advance\tqft@xa by \tqft@s
     \pgfpathcurveto{\pgfqpoint{\tqft@xb}{-\tqft@c}}{\pgfqpoint{\tqft@xa}{-\tqft@c}}{\pgfqpoint{\tqft@xa}{-\tqft@h}}
     \advance\tqft@xa by -\tqft@w
     \pgfpathmoveto{\pgfqpoint{\tqft@xa}{-\tqft@h}}
    }
    \fi
     \advance\tqft@xb by -\tqft@outgoing\tqft@s
     \advance\tqft@xb by \tqft@s
    \ifnum\tqft@incoming>0
     \pgfmathsetlength{\tqft@xa}{\tqft@xa - (\tqft@outgoing -1 + \tqft@offset) * \tqft@separation - 2*\tqft@width}
     \pgfmathsetlength{\tqft@ch}{min(0,max(-\tqft@h,\tqft@h - (\tqft@h - \tqft@c) * ((abs(\tqft@xb - \tqft@xa) - \tqft@w)/\tqft@s + 1)))}
     \pgfpathcurveto{\pgfqpoint{\tqft@xb}{-\tqft@ch}}{\pgfqpoint{\tqft@xa}{\tqft@ch}}{\pgfqpoint{\tqft@xa}{\tqft@h}}
    \else
     \pgfmathsetlength{\tqft@ch}{min(0,max(-\tqft@h,\tqft@h - (\tqft@h - \tqft@c) * ((abs(\tqft@xb - \tqft@xa) - \tqft@w)/\tqft@s + 1)))}
     \pgfpathcurveto{\pgfqpoint{\tqft@xb}{-\tqft@ch}}{\pgfqpoint{\tqft@xa}{-\tqft@ch}}{\pgfqpoint{\tqft@xa}{-\tqft@h}}
    \fi
    \fi
      \edef\tikz@temp{\noexpand\pgfusepath{%
          \iftikz@mode@fill fill,\fi%
          \iftikz@mode@draw draw\fi%
      }}%
      \tikz@temp
}
    {
\let\tqft@bdry@path=\pgfutil@empty
\let\tqft@bdry@node@path=\pgfutil@empty
\pgfsyssoftpath@setcurrentpath{\tqft@bdry@path}
      \tikz@mode@fillfalse%
      \tikz@mode@drawfalse%
      \let\tikz@mode=\pgfutil@empty
      \let\tikz@options=\pgfutil@empty
      \tqftset{boundary upper style contents}
      \tikz@mode
      \tikz@options
      \advance\tqft@xa by -\tqft@s
      \advance\tqft@xa by \tqft@w
    \ifnum\tqft@incoming>0
    \foreach \tqft@k in {1,...,\tqft@incoming} {
     \advance\tqft@xa by \tqft@k\tqft@s
     \pgfpathmoveto{\pgfqpoint{\tqft@xa}{\tqft@h}}
     \pgfpatharc{0}{\pgf@tqft@upper180}{\tqft@width and \tqft@depth}
  \ifx\tikz@fig@name\pgfutil@empty
  \else
  {
    \advance\tqft@xa by -\tqft@width
    \pgftransformshift{\pgfqpoint{\tqft@xa}{\tqft@h}}
    \tqft@within@nodetrue
    \pgfsyssoftpath@getcurrentpath{\tqft@bdry@path}
    \pgfsyssoftpath@setcurrentpath{\tqft@bdry@node@path}
    \pgfnode{tqft boundary circle}{centre}{}{\tikz@fig@name\space incoming \tqft@k}{}
    \pgfsyssoftpath@getcurrentpath{\tqft@bdry@node@path}
    \pgfsyssoftpath@setcurrentpath{\tqft@bdry@path}
  }
  \fi
    }
    \fi
    \ifnum\tqft@outgoing>0
     \pgfmathsetlength{\tqft@xa}{\tqft@xa + (\tqft@outgoing + \tqft@offset + 1) * \tqft@separation}
    \foreach \tqft@k in {1,...,\tqft@outgoing} {
     \advance\tqft@xa by -\tqft@k\tqft@s
     \pgfpathmoveto{\pgfqpoint{\tqft@xa}{-\tqft@h}}
     \pgfpatharc{0}{\pgf@tqft@upper180}{\tqft@width and \tqft@depth}
  \ifx\tikz@fig@name\pgfutil@empty
  \else
  {
    \pgfmathtruncatemacro{\tqft@l}{\tqft@outgoing + 1 - \tqft@k}
    \advance\tqft@xa by -\tqft@width
    \pgftransformshift{\pgfqpoint{\tqft@xa}{-\tqft@h}}
    \tqft@within@nodetrue
    \pgfsyssoftpath@getcurrentpath{\tqft@bdry@path}
    \pgfsyssoftpath@setcurrentpath{\tqft@bdry@node@path}
    \pgfnode{tqft boundary circle}{centre}{}{\tikz@fig@name\space outgoing \tqft@l}{}
    \pgfsyssoftpath@getcurrentpath{\tqft@bdry@node@path}
    \pgfsyssoftpath@setcurrentpath{\tqft@bdry@path}
  }
  \fi
    }
    \fi
      \edef\tikz@temp{\noexpand\pgfusepath{%
          \iftikz@mode@fill fill,\fi%
          \iftikz@mode@draw draw\fi%
      }}%
      \tikz@temp
    }
  }
}
\pgfdeclareshape{tqft boundary circle}{
  \saveddimen{\tqft@height}{\pgf@x=\pgfkeysvalueof{/pgf/tqft/cobordism height}}
  \saveddimen{\tqft@separation}{\pgf@x=\pgfkeysvalueof{/pgf/tqft/boundary separation}}
  \saveddimen{\tqft@width}{\pgf@x=\pgfkeysvalueof{/pgf/tqft/circle width}}
  \saveddimen{\tqft@depth}{\pgf@x=\pgfkeysvalueof{/pgf/tqft/circle depth}}
   \savedmacro{\tqft@transformation}{%
  \iftqft@within@node
  \let\tqft@transformation=\pgfutil@empty
  \else
  \pgfkeysgetvalue{/pgf/tqft/flow transformation}{\tqft@transformation}
  \fi
}
   \savedanchor{\tqft@centre}{%
  \pgfpointorigin}
\savedanchor{\tqft@textsize}{%
  \pgf@y=-.5\ht\pgfnodeparttextbox%
  \pgf@x=-.5\wd\pgfnodeparttextbox%
}
  \anchor{centre}{\tqft@centre}
  \anchor{center}{\tqft@centre}
\anchor{text}{
  \tqft@textsize
}
  \anchor{next}{%
  \tqft@process{\tqft@separation}{0pt}}%
  \anchor{prior}{%
  \tqft@process{-\tqft@separation}{0pt}}%
  \anchor{above}{%
  \tqft@process{0pt}{\tqft@height}}%
  \anchor{below}{%
  \tqft@process{0pt}{-\tqft@height}}%
  \anchorborder{
  \tqft@process{\the\pgf@x}{\the\pgf@y}
  \edef\tqft@marshal{%
    \noexpand\pgfpointborderellipse
    {\noexpand\pgfqpoint{\the\pgf@x}{\the\pgf@y}}
    {\noexpand\pgfqpoint{\tqft@width}{\tqft@depth}}
  }%
  \tqft@marshal
  \tqft@process{\the\pgf@x}{\the\pgf@y}
}
  \backgroundpath{
    \let\tikz@transform=\pgfutil@empty
    \expandafter\tikzset\expandafter{\tqft@transformation}
    \tikz@transform
  \pgfpathellipse{\pgfqpoint{0pt}{0pt}}{\pgfqpoint{\tqft@width}{0pt}}{\pgfqpoint{0pt}{\tqft@depth}}
  }
  \beforebackgroundpath{
  \iftqft@within@node
  \else
    \tikz@mode@fillfalse%
    \tikz@mode@drawfalse%
    \let\tikz@mode=\pgfutil@empty
    \let\tikz@options=\pgfutil@empty
    {
    \pgfsys@beginscope
      \tqftset{boundary lower style contents}
      \tikz@mode
      \tikz@options
      \pgfpathmoveto{\pgfqpoint{\tqft@width}{0pt}}
      \pgfpatharc{0}{\pgf@tqft@lower180}{\tqft@width and \tqft@depth}
      \edef\tikz@temp{\noexpand\pgfusepath{%
          \iftikz@mode@fill fill,\fi%
          \iftikz@mode@draw draw\fi%
      }}%
      \tikz@temp
      \pgfsys@endscope
    }
    {
      \pgfsys@beginscope
      \tqftset{boundary upper style contents}
      \tikz@mode
      \tikz@options
      \pgfpathmoveto{\pgfqpoint{\tqft@width}{0pt}}
      \pgfpatharc{0}{\pgf@tqft@upper180}{\tqft@width and \tqft@depth}
      \edef\tikz@temp{\noexpand\pgfusepath{%
          \iftikz@mode@fill fill,\fi%
          \iftikz@mode@draw draw\fi%
      }}%
      \tikz@temp
      \pgfsys@endscope
    }
    \fi
  }
  }

%% 
%% Copyright (C) 2011-2024 by Andrew Stacey <loopspace@mathforge.org>
%% 
%% This work may be distributed and/or modified under the
%% conditions of the LaTeX Project Public License (LPPL), either
%% version 1.3c of this license or (at your option) any later
%% version.  The latest version of this license is in the file:
%% 
%% http://www.latex-project.org/lppl.txt
%% 
%% This work is "maintained" (as per LPPL maintenance status) by
%% Andrew Stacey.
%% 
%% This work consists of the files  tqft_code.dtx,
%%                                  tqft.tex,
%% and the derived files            tqft_code.ins,
%%                                  tqft_code.pdf,
%%                                  tqft.pdf,
%%                                  tqft.sty, and
%%                                  tikzlibrarytqft.code.tex.
%% 
%%
%% End of file `tqft.sty'.