\newcommand{\nhorder}{ {\stackrel{0}{\prec}} } 

\newcommand{\cent}[1]{ \makebox(0,0){#1} }

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

\newcommand{\ATA}{%
  \put(-.5,0  ){\line(-1,0){1.3}}
  \qbezier[100](-.5,0)(0,0.25)(.5,0.5)
  \put(.5,-.5){\line(0,1){1}}
  \qbezier[100](-.5,0)(0,-.25)(.5,-.5)
  \put(0.5,0  ){\line( 1,0){1.3}}
}
\newcommand{\ATB}{%
  \put(-.5,0  ){\line(-1,0){1.3}}
  \qbezier[100](-.5,0)(0,0.25)(.5,0.5)
  \put(.5,-.5){\line(0,1){1}}
  \qbezier[100](-.5,0)(0,-.25)(.5,-.5)
  \put(0.5,0.1){\line( 1,0){1.3}}
  \put(0.5,-.1){\line( 1,0){1.3}}
}
\newcommand{\BTA}{%
  \put(-.3,0.1){\line(-1,0){1.5}}
  \put(-.3,-.1){\line(-1,0){1.5}}
  \qbezier[100](-.5,0)(0,0.25)(.5,0.5)
  \put(.5,-.5){\line(0,1){1}}
  \qbezier[100](-.5,0)(0,-.25)(.5,-.5)
  \put(0.5,0  ){\line( 1,0){1.3}}
}
\newcommand{\BTB}{%
  \put(-.3,0.1){\line(-1,0){1.5}}
  \put(-.3,-.1){\line(-1,0){1.5}}
  \qbezier[100](-.5,0)(0,0.25)(.5,0.5)
  \put(.5,-.5){\line(0,1){1}}
  \qbezier[100](-.5,0)(0,-.25)(.5,-.5)
  \put(0.5,0.1){\line( 1,0){1.3}}
  \put(0.5,-.1){\line( 1,0){1.3}}
}

\renewcommand{\OO}{%
  \qbezier[10](-2,0)(-1.2,0)(-.4,0)
  \put(0,0){\circle{.8}}
  \qbezier[10]( 2,0)( 1.2,0)( .4,0)
}
\renewcommand{\AA}{%
  \put(-2,0){\line(1, 0){4}}
}
\newcommand{\BB}{%
  \put(-2,0.1){\line(1, 0){4}}
  \put(-2,-.1){\line(1, 0){4}}
}

\newcommand{\Rel}[1]{%
  \setlength{\unitlength}{2mm}
  \begin{picture}(4,1)(-2,-.5)
  #1
  \end{picture}
}

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



\newcommand{\tlbar}  {
  \begin{picture}(3,1)
  \put(0,.5){\line(1, 0){1}}
  \qbezier[100](1,0.5)(1.5,0.75)(2,1)
  \put(2,0 ){\line(0, 1){1}}
  \qbezier[100](1,0.5)(1.5,0.25)(2,0)
  \put(2,.5){\line(1, 0){1}}
  \end{picture}
}
\newcommand{\tlbarw} {
  \begin{picture}(3,1)
  \put(0,.5){\line(1, 0){1}}
  \qbezier[100](1,0.5)(1.5,0.75)(2,1)
  \put(2,0 ){\line(0, 1){1}}
  \qbezier[100](1,0.5)(1.5,0.25)(2,0)
  \put(2,.6){\line(1, 0){1}}
  \put(2,.4){\line(1, 0){1}}
  \end{picture}
}
\newcommand{\wtlbar} {
  \begin{picture}(3,1)
  \put(0,.6){\line(1, 0){1.2}}
  \put(0,.4){\line(1, 0){1.2}}
  \qbezier[100](1,0.5)(1.5,0.75)(2,1)
  \put(2,0 ){\line(0, 1){1}}
  \qbezier[100](1,0.5)(1.5,0.25)(2,0)
  \put(2,.5){\line(1, 0){1}}
  \end{picture}
}
\newcommand{\wtlbarw}{
  \begin{picture}(3,1)
  \put(0,.6){\line(1, 0){1.2}}
  \put(0,.4){\line(1, 0){1.2}}
  \qbezier[100](1,0.5)(1.5,0.75)(2,1)
  \put(2,0 ){\line(0, 1){1}}
  \qbezier[100](1,0.5)(1.5,0.25)(2,0)
  \put(2,.6){\line(1, 0){1}}
  \put(2,.4){\line(1, 0){1}}
  \end{picture}
}

\newcommand{\relo}{
  \begin{picture}(3,1)
  \qbezier[6](0,.5)(0.5,.5)(1,.5)
%  \put(0,.5){\line(1, 0){1}}
  \put(1.5,.5){\circle{1}}
%  \put(2,.5){\line(1, 0){1}}
  \qbezier[6](2,.5)(2.5,.5)(3,.5)
  \end{picture}
}
\newcommand{\relw}{
  \begin{picture}(3,1)
  \put(0,.5){\line(1, 0){3}}
  \end{picture}
}
\newcommand{\relww}{
  \begin{picture}(3,1)
  \put(0,.4){\line(1, 0){3}}
  \put(0,.6){\line(1, 0){3}}
  \end{picture}
}

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

%\newcommand{\tlbar}  { {-\hspace{-.40em}\tl\hspace{-.35em}-} }
%\newcommand{\tlbarw} { {-\hspace{-.15em}\tl\hspace{-.37em}=} }
%\newcommand{\wtlbarw}{ {=\hspace{-.60em}\tl\hspace{-.37em}=} }
%\newcommand{\wtlbar} { {=\hspace{-.60em}\tl\hspace{-.13em}-} }

\newcommand{\tgbar}  { {-\hspace{-.35em}\tg\hspace{-.40em}-} }
\newcommand{\tgbarw} { {-\hspace{-.13em}\tg\hspace{-.60em}=} }
\newcommand{\wtgbarw}{ {=\hspace{-.40em}\tg\hspace{-.60em}=} }
\newcommand{\wtgbar} { {=\hspace{-.40em}\tg\hspace{-.14em}-} }

%\newcommand{\wtlbar} { {\vdash\hspace{-.42em}\tl\hspace{-.13em}-} }
%\newcommand{\tlbarw} { {-\hspace{-.15em}\tl\hspace{-.37em}\dashv} }
%\newcommand{\wtlbarw}{ {\vdash\hspace{-.42em}\tl\hspace{-.37em}\dashv} }
%\newcommand{\wtgbar} { {\vdash\hspace{-.40em}\tg\hspace{-.14em}-} }
%\newcommand{\tgbarw} { {-\hspace{-.13em}\tg\hspace{-.42em}\dashv} }
%\newcommand{\wtgbarw}{ {\vdash\hspace{-.40em}\tg\hspace{-.42em}\dashv} }

%\newcommand{\ttlbar}{ {-\hspace{-.40em}\tl\hspace{-.315em}\tl\hspace{-.12em}-} }
%\newcommand{\ttgbar}{ {-\hspace{-.35em}\tg\hspace{-.315em}\tg\hspace{-.17em}-} }


\newcommand{\Int}{ \mathrm{Int} }


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

\setlength{\unitlength}{2mm}



\newcommand{\BOX}[1]{%
\put(-2,-2){\makebox(4,4){}}
%\put(-2,-2){\framebox(4,4){}}
%\put(-4,-.5){\framebox(8,1){}}
%\put(-10,-.5){\framebox(20,1){}}
#1
%\put(-2, 2){\circle*{0.3}} \put(2, 2){\circle{0.3}}
%\put(-2,-2){\circle{0.3}}  \put(2,-2){\circle*{0.3}}
}

\newcommand{\SLIDEo}[1]{%
\put(0,0){#1}
}
\newcommand{\SLIDEa}[1]{%
\put(-1.41421356,0){#1}
}
\newcommand{\SLIDEb}[1]{%
\put(-2,0){#1}
}

\newcommand{\SLIDE}[1]{
  \put(-.375,0){#1}
}



\newcommand{\PicA}{ \beta }
\newcommand{\PicB}{ \gamma_1 }
\newcommand{\PicC}{ \gamma_2 }
\newcommand{\PicD}{ \delta }

\newcommand{\VARIABLE}[4]{
  \renewcommand{\PicA}{ #1 }
  \renewcommand{\PicB}{ #2 }
  \renewcommand{\PicC}{ #3 }
  \renewcommand{\PicD}{ #4 }
}

\newcommand{\PicAA}{
  \begin{picture}(8,8)
  \put(2,6){\SLIDEa{\rotatebox{45}{\BOX{\ATA}}}}  \put(4,8){\cent{\( \PicC^\vee \)}} \put(6,6){\SLIDEa{\rotatebox{135}{\BOX{\ATA}}}}
  \put(0,4){\cent{\( \PicD^\vee \)}}                                                 \put(8,4){\cent{\( \PicA^\vee \)}}
  \put(2,2){\SLIDEa{\rotatebox{135}{\BOX{\ATA}}}} \put(4,0){\cent{\( \PicB^\vee \)}} \put(6,2){\SLIDEa{\rotatebox{45}{\BOX{\ATA}}}}
  \put(4,4){\SLIDEb{\rotatebox{90}{\BOX{\OO}}}}
  \put(4,4){\SLIDEo{\rotatebox{0}{\BOX{\OO}}}}
  \end{picture}
}
\newcommand{\PicBA}{
  \begin{picture}(8,8)
  \put(2,6){\SLIDEa{\rotatebox{45}{\BOX{\BTA}}}}  \put(4,8){\cent{\( \PicC^\vee \)}} \put(6,6){\SLIDEa{\rotatebox{135}{\BOX{\BTA}}}}
  \put(0,4){\cent{\( \PicD^\vee \)}}                                                 \put(8,4){\cent{\( \PicA^\vee \)}}
  \put(2,2){\SLIDEa{\rotatebox{135}{\BOX{\ATA}}}} \put(4,0){\cent{\( \PicB^\vee \)}} \put(6,2){\SLIDEa{\rotatebox{45}{\BOX{\ATA}}}}
  \put(4,4){\SLIDEb{\rotatebox{90}{\BOX{\OO}}}}
  \put(4,4){\SLIDEo{\rotatebox{0}{\BOX{\AA}}}}
  \end{picture}
}
\newcommand{\PicAB}{
  \begin{picture}(8,8)
  \put(2,6){\SLIDEa{\rotatebox{45}{\BOX{\ATA}}}}  \put(4,8){\cent{\( \PicC^\vee \)}} \put(6,6){\SLIDEa{\rotatebox{135}{\BOX{\ATA}}}}
  \put(0,4){\cent{\( \PicD^\vee \)}}                                                 \put(8,4){\cent{\( \PicA^\vee \)}}
  \put(2,2){\SLIDEa{\rotatebox{135}{\BOX{\ATB}}}} \put(4,0){\cent{\( \PicB^\vee \)}} \put(6,2){\SLIDEa{\rotatebox{45}{\BOX{\ATB}}}}
  \put(4,4){\SLIDEb{\rotatebox{90}{\BOX{\OO}}}}
  \put(4,4){\SLIDEo{\rotatebox{0}{\BOX{\AA}}}}
  \end{picture}
}
\newcommand{\PicBB}{
  \begin{picture}(8,8)
  \put(2,6){\SLIDEa{\rotatebox{45}{\BOX{\BTA}}}}  \put(4,8){\cent{\( \PicC^\vee \)}} \put(6,6){\SLIDEa{\rotatebox{135}{\BOX{\BTA}}}}
  \put(0,4){\cent{\( \PicD^\vee \)}}                                                 \put(8,4){\cent{\( \PicA^\vee \)}}
  \put(2,2){\SLIDEa{\rotatebox{135}{\BOX{\ATB}}}} \put(4,0){\cent{\( \PicB^\vee \)}} \put(6,2){\SLIDEa{\rotatebox{45}{\BOX{\ATB}}}}
  \put(4,4){\SLIDEb{\rotatebox{90}{\BOX{\OO}}}}
  \put(4,4){\SLIDEo{\rotatebox{0}{\BOX{\BB}}}}
 \end{picture}
}


\newcommand{\PIcAA}{
  \begin{picture}(8,8)
  \put(2,6){\SLIDEa{\rotatebox{45}{\BOX{\ATA}}}}  \put(4,8){\cent{\( \PicD^\vee \)}} \put(6,6){\SLIDEa{\rotatebox{135}{\BOX{\ATA}}}}
  \put(0,4){\cent{\( \PicB^\vee \)}}                                                 \put(8,4){\cent{\( \PicC^\vee \)}}
  \put(2,2){\SLIDEa{\rotatebox{135}{\BOX{\ATA}}}} \put(4,0){\cent{\( \PicA^\vee \)}} \put(6,2){\SLIDEa{\rotatebox{45}{\BOX{\ATA}}}}
  \put(4,4){\SLIDEb{\rotatebox{90}{\BOX{\OO}}}}
  \put(4,4){\SLIDEo{\rotatebox{0}{\BOX{\OO}}}}
  \end{picture}
}
\newcommand{\PIcBA}{
  \begin{picture}(8,8)
  \put(2,6){\SLIDEa{\rotatebox{45}{\BOX{\ATB}}}}  \put(4,8){\cent{\( \PicD^\vee \)}} \put(6,6){\SLIDEa{\rotatebox{135}{\BOX{\ATA}}}}
  \put(0,4){\cent{\( \PicB^\vee \)}}                                                 \put(8,4){\cent{\( \PicC^\vee \)}}
  \put(2,2){\SLIDEa{\rotatebox{135}{\BOX{\BTA}}}} \put(4,0){\cent{\( \PicA^\vee \)}} \put(6,2){\SLIDEa{\rotatebox{45}{\BOX{\ATA}}}}
  \put(4,4){\SLIDEb{\rotatebox{90}{\BOX{\AA}}}}
  \put(4,4){\SLIDEo{\rotatebox{0}{\BOX{\OO}}}}
  \end{picture}
}
\newcommand{\PIcAB}{
  \begin{picture}(8,8)
  \put(2,6){\SLIDEa{\rotatebox{45}{\BOX{\ATA}}}}  \put(4,8){\cent{\( \PicD^\vee \)}} \put(6,6){\SLIDEa{\rotatebox{135}{\BOX{\ATB}}}}
  \put(0,4){\cent{\( \PicB^\vee \)}}                                                 \put(8,4){\cent{\( \PicC^\vee \)}}
  \put(2,2){\SLIDEa{\rotatebox{135}{\BOX{\ATA}}}} \put(4,0){\cent{\( \PicA^\vee \)}} \put(6,2){\SLIDEa{\rotatebox{45}{\BOX{\BTA}}}}
  \put(4,4){\SLIDEb{\rotatebox{90}{\BOX{\AA}}}}
  \put(4,4){\SLIDEo{\rotatebox{0}{\BOX{\OO}}}}
  \end{picture}
}
\newcommand{\PIcBB}{
  \begin{picture}(8,8)
  \put(2,6){\SLIDEa{\rotatebox{45}{\BOX{\ATB}}}}  \put(4,8){\cent{\( \PicD^\vee \)}} \put(6,6){\SLIDEa{\rotatebox{135}{\BOX{\ATB}}}}
  \put(0,4){\cent{\( \PicB^\vee \)}}                                                 \put(8,4){\cent{\( \PicC^\vee \)}}
  \put(2,2){\SLIDEa{\rotatebox{135}{\BOX{\BTA}}}} \put(4,0){\cent{\( \PicA^\vee \)}} \put(6,2){\SLIDEa{\rotatebox{45}{\BOX{\BTA}}}}
  \put(4,4){\SLIDEb{\rotatebox{90}{\BOX{\BB}}}}
  \put(4,4){\SLIDEo{\rotatebox{0}{\BOX{\OO}}}}
 \end{picture}
}

