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diagram.tex
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diagram.tex
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% This should appear in a file named diagram.tex
% Copyright 1988,1989 Michael Barr
% Department of Mathematics and Statistics
% McGill University
% 805 Sherbrooke St., W
% Montreal, Quebec, Canada
% H3P 1S4
%
% barr@triples.math.mcgill.ca
%
% All commercial rights reserved. May be freely distributed
% and used with the following exceptions:
% 1. No commercial use without explicit permission.
% 2. It may not be used by any employee of a telephone
% company.
% 3. It may not be distributed without this notice.
%
% Last revised 91-05-04
% Ascii character test:
% 32: 33: ! 34: " 35: # 36: $ 37: % 38: & 39: '
% 40: ( 41: ) 42: * 43: + 44: , 45: - 46: . 47: /
% 48: 0 49: 1 50: 2 51: 3 52: 4 53: 5 54: 6 55: 7
% 56: 8 57: 9 58: : 59: ; 60: < 61: = 62: > 63: ?
% 64: @ 65: A 66: B 67: C 68: D 69: E 70: F 71: G
% 72: H 73: I 74: J 75: K 76: L 77: M 78: N 79: O
% 80: P 81: Q 82: R 83: S 84: T 85: U 86: V 87: W
% 88: X 89: Y 90: Z 91: [ 92: \ 93: ] 94: ^ 95: _
% 96: ` 97: a 98: b 99: c 100: d 101: e 102: f 103: g
% 104: h 105: i 106: j 107: k 108: l 109: m 110: n 111: o
% 112: p 113: q 114: r 115: s 116: t 117: u 118: v 119: w
% 120: x 121: y 122: z 123: { 124: | 125: } 126: ~
\makeatletter
\def\diagram{\m@th\leftwidth=\z@ \rightwidth=\z@ \topheight=\z@
\botheight=\z@ \setbox\@picbox\hbox\bgroup}
\def\enddiagram{\egroup\wd\@picbox\rightwidth\unitlength
\ht\@picbox\topheight\unitlength \dp\@picbox\botheight\unitlength
\hskip\leftwidth\unitlength\box\@picbox}
\def\bfig{\begin{diagram}}
\def\efig{\end{diagram}}
\newcount\wideness \newcount\leftwidth \newcount\rightwidth
\newcount\highness \newcount\topheight \newcount\botheight
\def\ratchet#1#2{\ifnum#1<#2 \global #1=#2 \fi}
\def\putbox(#1,#2)#3{%
\horsize{\wideness}{#3} \divide\wideness by 2
{\advance\wideness by #1 \ratchet{\rightwidth}{\wideness}}
{\advance\wideness by -#1 \ratchet{\leftwidth}{\wideness}}
\vertsize{\highness}{#3} \divide\highness by 2
{\advance\highness by #2 \ratchet{\topheight}{\highness}}
{\advance\highness by -#2 \ratchet{\botheight}{\highness}}
\put(#1,#2){\makebox(0,0){$#3$}}}
\def\putlbox(#1,#2)#3{%
\horsize{\wideness}{#3}
{\advance\wideness by #1 \ratchet{\rightwidth}{\wideness}}
{\ratchet{\leftwidth}{-#1}}
\vertsize{\highness}{#3} \divide\highness by 2
{\advance\highness by #2 \ratchet{\topheight}{\highness}}
{\advance\highness by -#2 \ratchet{\botheight}{\highness}}
\put(#1,#2){\makebox(0,0)[l]{$#3$}}}
\def\putrbox(#1,#2)#3{%
\horsize{\wideness}{#3}
{\ratchet{\rightwidth}{#1}}
{\advance\wideness by -#1 \ratchet{\leftwidth}{\wideness}}
\vertsize{\highness}{#3} \divide\highness by 2
{\advance\highness by #2 \ratchet{\topheight}{\highness}}
{\advance\highness by -#2 \ratchet{\botheight}{\highness}}
\put(#1,#2){\makebox(0,0)[r]{$#3$}}}
\def\adjust[#1]{} % For compatibility
\newcount \coefa
\newcount \coefb
\newcount \coefc
\newcount\tempcounta
\newcount\tempcountb
\newcount\tempcountc
\newcount\tempcountd
\newcount\xext
\newcount\yext
\newcount\xoff
\newcount\yoff
\newcount\gap%
\newcount\arrowtypea
\newcount\arrowtypeb
\newcount\arrowtypec
\newcount\arrowtyped
\newcount\arrowtypee
\newcount\height
\newcount\width
\newcount\xpos
\newcount\ypos
\newcount\run
\newcount\rise
\newcount\arrowlength
\newcount\halflength
\newcount\arrowtype
\newdimen\tempdimen
\newdimen\xlen
\newdimen\ylen
\newsavebox{\tempboxa}%
\newsavebox{\tempboxb}%
\newsavebox{\tempboxc}%
\newdimen\w@dth
\def\setw@dth#1#2{\setbox\z@\hbox{\m@th$#1$}\w@dth=\wd\z@
\setbox\@ne\hbox{\m@th$#2$}\ifnum\w@dth<\wd\@ne \w@dth=\wd\@ne \fi
\advance\w@dth by 1.2em}
%The definitions below look more elaborate than they need to be.
%The reason is that an empty asscript will still cause extra vertical
%spacing and the only way to avoid ugly extra space seems to be using
%some such method as this.
\def\t@^#1_#2{\allowbreak\def\n@one{#1}\def\n@two{#2}\mathrel
{\setw@dth{#1}{#2}
\mathop{\hbox to \w@dth{\rightarrowfill}}\limits
\ifx\n@one\empty\else ^{\box\z@}\fi
\ifx\n@two\empty\else _{\box\@ne}\fi}}
%\def\t@^#1_#2{\mathrel{\mathop{\hbox{\rightarrowfill}}\limits
%^{\mkern12mu#1\mkern12mu}_{\mkern12mu#2\mkern12mu}}}
\def\t@@^#1{\@ifnextchar_{\t@^{#1}}{\t@^{#1}_{}}}
\def\to{\@ifnextchar^{\t@@}{\t@@^{}}}
\def\t@left^#1_#2{\def\n@one{#1}\def\n@two{#2}\mathrel{\setw@dth{#1}{#2}
\mathop{\hbox to \w@dth{\leftarrowfill}}\limits
\ifx\n@one\empty\else ^{\box\z@}\fi
\ifx\n@two\empty\else _{\box\@ne}\fi}}
%\def\t@left^#1_#2{\mathrel{\mathop{\hbox{\leftarrowfill}}\limits
%^{\mkern12mu#1\mkern12mu}_{\mkern12mu#2\mkern12mu}}}
\def\t@@left^#1{\@ifnextchar_{\t@left^{#1}}{\t@left^{#1}_{}}}
\def\toleft{\@ifnextchar^{\t@@left}{\t@@left^{}}}
\def\two@^#1_#2{\allowbreak
\def\n@one{#1}\def\n@two{#2}\mathrel{\setw@dth{#1}{#2}
\mathop{\vcenter{\lineskip\z@\baselineskip\z@
\hbox to \w@dth{\rightarrowfill}%
\hbox to \w@dth{\rightarrowfill}}%
}\limits
\ifx\n@one\empty\else ^{\box\z@}\fi
\ifx\n@two\empty\else _{\box\@ne}\fi}}
\def\tw@@^#1{\@ifnextchar _{\two@^{#1}}{\two@^{#1}_{}}}
\def\two{\@ifnextchar ^{\tw@@}{\tw@@^{}}}
\def\tofr@^#1_#2{\def\n@one{#1}\def\n@two{#2}\mathrel{\setw@dth{#1}{#2}
\mathop{\vcenter{\hbox to \w@dth{\rightarrowfill}\kern-1.7ex
\hbox to \w@dth{\leftarrowfill}}%
}\limits
\ifx\n@one\empty\else ^{\box\z@}\fi
\ifx\n@two\empty\else _{\box\@ne}\fi}}
\def\t@fr@^#1{\@ifnextchar_ {\tofr@^{#1}}{\tofr@^{#1}_{}}}
\def\tofro{\@ifnextchar^ {\t@fr@}{\t@fr@^{}}}
\def\epi{\mathop{\mathchar"221\mkern -12mu\mathchar"221}\limits}
\def\leftepi{\mathop{\mathchar"220\mkern -12mu\mathchar"220}\limits}
\def\mon{\mathop{\m@th\hbox to
14.6\P@{\lasyb\char'51\hskip-2.1\P@$\arrext$\hss
$\mathord\rightarrow$}}\limits} % width of \epi
\def\leftmono{\mathrel{\m@th\hbox to
14.6\P@{$\mathord\leftarrow$\hss$\arrext$\hskip-2.1\P@\lasyb\char'50%
}}\limits} % width of \epi
\mathchardef\arrext="0200 % amr minus for arrow extension (see \into)
\setlength{\unitlength}{.01em}%
\def\settypes(#1,#2,#3){\arrowtypea#1 \arrowtypeb#2 \arrowtypec#3}
\def\settoheight#1#2{\setbox\@tempboxa\hbox{#2}#1\ht\@tempboxa\relax}%
\def\settodepth#1#2{\setbox\@tempboxa\hbox{#2}#1\dp\@tempboxa\relax}%
\def\settokens`#1`#2`#3`#4`{%
\def\tokena{#1}\def\tokenb{#2}\def\tokenc{#3}\def\tokend{#4}}
\def\setsqparms[#1`#2`#3`#4;#5`#6]{%
\arrowtypea #1
\arrowtypeb #2
\arrowtypec #3
\arrowtyped #4
\width #5
\height #6
}
\def\setpos(#1,#2){\xpos=#1 \ypos#2}
\def\settriparms[#1`#2`#3;#4]{\settripairparms[#1`#2`#3`1`1;#4]}%
\def\settripairparms[#1`#2`#3`#4`#5;#6]{%
\arrowtypea #1
\arrowtypeb #2
\arrowtypec #3
\arrowtyped #4
\arrowtypee #5
\width #6
\height #6
}
\def\resetparms{\settripairparms[1`1`1`1`1;500]\width 500}%default values%
\resetparms
\def\mvector(#1,#2)#3{%%
\put(0,0){\vector(#1,#2){#3}}%
\put(0,0){\vector(#1,#2){26}}%
}
\def\evector(#1,#2)#3{{%%
\arrowlength #3
\put(0,0){\vector(#1,#2){\arrowlength}}%
\advance \arrowlength by-30
\put(0,0){\vector(#1,#2){\arrowlength}}%
}}
\def\horsize#1#2{%
\settowidth{\tempdimen}{$#2$}%
#1=\tempdimen
\divide #1 by\unitlength
}
\def\vertsize#1#2{%
\settoheight{\tempdimen}{$#2$}%
#1=\tempdimen
\settodepth{\tempdimen}{$#2$}%
\advance #1 by\tempdimen
\divide #1 by\unitlength
}
\def\putvector(#1,#2)(#3,#4)#5#6{{%
\ifnum3<\arrowtype
\putdashvector(#1,#2)(#3,#4)#5\arrowtype
\else
\ifnum\arrowtype<-3
\putdashvector(#1,#2)(#3,#4)#5\arrowtype
\else
\xpos=#1
\ypos=#2
\run=#3
\rise=#4
\arrowlength=#5
\ifnum \arrowtype<0
\ifnum \run=0
\advance \ypos by-\arrowlength
\else
\tempcounta \arrowlength
\multiply \tempcounta by\rise
\divide \tempcounta by\run
\ifnum\run>0
\advance \xpos by\arrowlength
\advance \ypos by\tempcounta
\else
\advance \xpos by-\arrowlength
\advance \ypos by-\tempcounta
\fi
\fi
\multiply \arrowtype by-1
\multiply \rise by-1
\multiply \run by-1
\fi
\ifcase \arrowtype
\or \put(\xpos,\ypos){\vector(\run,\rise){\arrowlength}}%
\or \put(\xpos,\ypos){\mvector(\run,\rise)\arrowlength}%
\or \put(\xpos,\ypos){\evector(\run,\rise){\arrowlength}}%
\fi\fi\fi
}}
\def\putsplitvector(#1,#2)#3#4{%%
\xpos #1
\ypos #2
\arrowtype #4
\halflength #3
\arrowlength #3
\gap 140
\advance \halflength by-\gap
\divide \halflength by2
\ifnum\arrowtype>0
\ifcase \arrowtype
\or \put(\xpos,\ypos){\line(0,-1){\halflength}}%
\advance\ypos by-\halflength
\advance\ypos by-\gap
\put(\xpos,\ypos){\vector(0,-1){\halflength}}%
\or \put(\xpos,\ypos){\line(0,-1)\halflength}%
\put(\xpos,\ypos){\vector(0,-1)3}%
\advance\ypos by-\halflength
\advance\ypos by-\gap
\put(\xpos,\ypos){\vector(0,-1){\halflength}}%
\or \put(\xpos,\ypos){\line(0,-1)\halflength}%
\advance\ypos by-\halflength
\advance\ypos by-\gap
\put(\xpos,\ypos){\evector(0,-1){\halflength}}%
\fi
\else \arrowtype=-\arrowtype
\ifcase\arrowtype
\or \advance \ypos by-\arrowlength
\put(\xpos,\ypos){\line(0,1){\halflength}}%
\advance\ypos by\halflength
\advance\ypos by\gap
\put(\xpos,\ypos){\vector(0,1){\halflength}}%
\or \advance \ypos by-\arrowlength
\put(\xpos,\ypos){\line(0,1)\halflength}%
\put(\xpos,\ypos){\vector(0,1)3}%
\advance\ypos by\halflength
\advance\ypos by\gap
\put(\xpos,\ypos){\vector(0,1){\halflength}}%
\or \advance \ypos by-\arrowlength
\put(\xpos,\ypos){\line(0,1)\halflength}%
\advance\ypos by\halflength
\advance\ypos by\gap
\put(\xpos,\ypos){\evector(0,1){\halflength}}%
\fi
\fi
}
\def\putmorphism(#1)(#2,#3)[#4`#5`#6]#7#8#9{{%
\run #2
\rise #3
\ifnum\rise=0
\puthmorphism(#1)[#4`#5`#6]{#7}{#8}#9%
\else\ifnum\run=0
\putvmorphism(#1)[#4`#5`#6]{#7}{#8}#9%
\else
\setpos(#1)%
\arrowlength #7
\arrowtype #8
\ifnum\run=0
\else\ifnum\rise=0
\else
\ifnum\run>0
\coefa=1
\else
\coefa=-1
\fi
\ifnum\arrowtype>0
\coefb=0
\coefc=-1
\else
\coefb=\coefa
\coefc=1
\arrowtype=-\arrowtype
\fi
\width=2
\multiply \width by\run
\divide \width by\rise
\ifnum \width<0 \width=-\width\fi
\advance\width by60
\if l#9 \width=-\width\fi
\putbox(\xpos,\ypos){#4}% %node 1
{\multiply \coefa by\arrowlength% %node 2
\advance\xpos by\coefa
\multiply \coefa by\rise
\divide \coefa by\run
\advance \ypos by\coefa
\putbox(\xpos,\ypos){#5} }%
{\multiply \coefa by\arrowlength% %label
\divide \coefa by2
\advance \xpos by\coefa
\advance \xpos by\width
\multiply \coefa by\rise
\divide \coefa by\run
\advance \ypos by\coefa
\if l#9%
\putrbox(\xpos,\ypos){#6}%
\else\if r#9%
\putlbox(\xpos,\ypos){#6}%
\fi\fi }%
{\multiply \rise by-\coefc% %arrow
\multiply \run by-\coefc
\multiply \coefb by\arrowlength
\advance \xpos by\coefb
\multiply \coefb by\rise
\divide \coefb by\run
\advance \ypos by\coefb
\multiply \coefc by70
\advance \ypos by\coefc
\multiply \coefc by\run
\divide \coefc by\rise
\advance \xpos by\coefc
\multiply \coefa by140
\multiply \coefa by\run
\divide \coefa by\rise
\advance \arrowlength by\coefa
\ifcase\arrowtype
\or \put(\xpos,\ypos){\vector(\run,\rise){\arrowlength}}%
\or \put(\xpos,\ypos){\mvector(\run,\rise){\arrowlength}}%
\or \put(\xpos,\ypos){\evector(\run,\rise){\arrowlength}}%
\fi}\fi\fi\fi\fi}}
\newcount\numbdashes \newcount\lengthdash \newcount\increment
\def\howmanydashes{% Actually returns both number and length
\numbdashes=\arrowlength \lengthdash=40
\divide\numbdashes by \lengthdash
\lengthdash=\arrowlength
\divide\lengthdash by \numbdashes
%This futzing around is to minimize round-off error.
\increment=\lengthdash
\multiply\lengthdash by 3
\divide\lengthdash by 5
}
\def\putdashvector(#1)(#2,#3)#4#5{%
\ifnum#3=0 \putdashhvector(#1){#4}#5
\else
\ifnum#2=0
\putdashvvector(#1){#4}#5\fi\fi}
\def\putdashhvector(#1,#2)#3#4{{%
\arrowlength=#3 \howmanydashes
\multiput(#1,#2)(\increment,0){\numbdashes}%
{\vrule height .4pt width \lengthdash\unitlength}
\arrowtype=#4 \xpos=#1
\ifnum\arrowtype<0 \advance\arrowtype by 7 \fi
\ifcase\arrowtype
\or \advance\xpos by 10
\put(\xpos,#2){\vector(-1,0){\lengthdash}}
\advance\xpos by 40
\put(\xpos,#2){\vector(-1,0){\lengthdash}}
\or \advance \xpos by 10
\put(\xpos,#2){\vector(-1,0){\lengthdash}}
\advance\xpos by \arrowlength
\advance\xpos by -50
\put(\xpos,#2){\vector(-1,0){\lengthdash}}
\or \advance\xpos by 10
\put(\xpos,#2){\vector(-1,0){\lengthdash}}
\or \advance\xpos by \arrowlength
\advance\xpos by -\lengthdash
\put(\xpos,#2){\vector(1,0){\lengthdash}}
\or {\advance\xpos by 10
\put(\xpos,#2){\vector(1,0){\lengthdash}}}
\advance\xpos by \arrowlength
\advance\xpos by -\lengthdash
\put(\xpos,#2){\vector(1,0){\lengthdash}}
\or \advance\xpos by \arrowlength
\advance\xpos by -\lengthdash
\put(\xpos,#2){\vector(1,0){\lengthdash}}
\advance\xpos by -40
\put(\xpos,#2){\vector(1,0){\lengthdash}}
\fi
}}
\def\putdashvvector(#1,#2)#3#4{{%
\arrowlength=#3 \howmanydashes
\ypos=#2 \advance\ypos by -\arrowlength
\multiput(#1,#2)(0,\increment){\numbdashes}%
{\vrule width .4pt height \lengthdash\unitlength}
\arrowtype=#4 \ypos=#2
\ifnum\arrowtype<0 \advance\arrowtype by 7 \fi
\ifcase\arrowtype
\or \advance\ypos by \arrowlength \advance\ypos by -40
\put(#1,\ypos){\vector(0,1){\lengthdash}}
\advance\ypos by -40
\put(#1,\ypos){\vector(0,1){\lengthdash}}
\or \advance\ypos by 10
\put(#1,\ypos){\vector(0,1){\lengthdash}}
\advance\ypos by \arrowlength \advance\ypos by -40
\put(#1,\ypos){\vector(0,1){\lengthdash}}
\or \advance\ypos by \arrowlength \advance\ypos by -40
\put(#1,\ypos){\vector(0,1){\lengthdash}}
\or \advance\ypos by 10
\put(#1,\ypos){\vector(0,-1){\lengthdash}}
\or \advance\ypos by 10
\put(#1,\ypos){\vector(0,-1){\lengthdash}}
\advance\ypos by \arrowlength \advance\ypos by -40
\put(#1,\ypos){\vector(0,-1){\lengthdash}}
\or \advance\ypos by 10
\put(#1,\ypos){\vector(0,-1){\lengthdash}}
\advance\ypos by 40
\put(#1,\ypos){\vector(0,-1){\lengthdash}}
\fi
}}
\def\puthmorphism(#1,#2)[#3`#4`#5]#6#7#8{{%
\xpos #1
\ypos #2
\width #6
\arrowlength #6
\arrowtype=#7
\putbox(\xpos,\ypos){#3\vphantom{#4}}%
{\advance \xpos by\arrowlength
\putbox(\xpos,\ypos){\vphantom{#3}#4}}%
\horsize{\tempcounta}{#3}%
\horsize{\tempcountb}{#4}%
\divide \tempcounta by2
\divide \tempcountb by2
\advance \tempcounta by30
\advance \tempcountb by30
\advance \xpos by\tempcounta
\advance \arrowlength by-\tempcounta
\advance \arrowlength by-\tempcountb
\putvector(\xpos,\ypos)(1,0)\arrowlength\arrowtype
\divide \arrowlength by2
\advance \xpos by\arrowlength
\vertsize{\tempcounta}{#5}%
\divide\tempcounta by2
\advance \tempcounta by20
\if a#8 %
\advance \ypos by\tempcounta
\putbox(\xpos,\ypos){#5}%
\else
\advance \ypos by-\tempcounta
\putbox(\xpos,\ypos){#5}%
\fi}}
\def\putvmorphism(#1,#2)[#3`#4`#5]#6#7#8{{%
\xpos #1
\ypos #2
\arrowlength #6
\arrowtype #7
\settowidth{\xlen}{$#5$}%
\putbox(\xpos,\ypos){#3}%
{\advance \ypos by-\arrowlength
\putbox(\xpos,\ypos){#4}}%
{\advance\arrowlength by-140
\advance \ypos by-70
\ifdim\xlen>0pt
\if m#8%
\putsplitvector(\xpos,\ypos)\arrowlength\arrowtype
\else
\putvector(\xpos,\ypos)(0,-1)\arrowlength\arrowtype
\fi
\else
\putvector(\xpos,\ypos)(0,-1)\arrowlength\arrowtype
\fi}%
\ifdim\xlen>0pt
\divide \arrowlength by2
\advance\ypos by-\arrowlength
\if l#8%
\advance \xpos by-40
\putrbox(\xpos,\ypos){#5}%
\else\if r#8%
\advance \xpos by40
\putlbox(\xpos,\ypos){#5}%
\else
\putbox(\xpos,\ypos){#5}%
\fi\fi
\fi
}}
\def\putsquarep<#1>(#2)[#3;#4`#5`#6`#7]{{%
\setsqparms[#1]%
\setpos(#2)%
\settokens`#3`%
\puthmorphism(\xpos,\ypos)[\tokenc`\tokend`{#7}]{\width}{\arrowtyped}b%
\advance\ypos by \height
\puthmorphism(\xpos,\ypos)[\tokena`\tokenb`{#4}]{\width}{\arrowtypea}a%
\putvmorphism(\xpos,\ypos)[``{#5}]{\height}{\arrowtypeb}l%
\advance\xpos by \width
\putvmorphism(\xpos,\ypos)[``{#6}]{\height}{\arrowtypec}r%
}}
\def\putsquare{\@ifnextchar <{\putsquarep}{\putsquarep%
<\arrowtypea`\arrowtypeb`\arrowtypec`\arrowtyped;\width`\height>}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Next definition was corrected by DMVN Corporation
% to make this package compatible with AMS-TEX.
% Reason:
% \square command already defined in AMS, so \square
% command changed to \dsquare <-- the only modification
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\def\dsquare{\@ifnextchar< {\squarep}{\squarep
<\arrowtypea`\arrowtypeb`\arrowtypec`\arrowtyped;\width`\height>}}
% #6
\def\squarep<#1>[#2`#3`#4`#5;#6`#7`#8`#9]{{% % #2------>#3
\setsqparms[#1]% % | |
\diagram% % | |
\putsquarep<\arrowtypea`\arrowtypeb`\arrowtypec`% % #7| |#8
\arrowtyped;\width`\height>% % | |
(0,0)[#2`#3`#4`{#5};#6`#7`#8`{#9}]% % | |
\enddiagram% % v v
}} % #4------>#5
% #9
\def\putptrianglep<#1>(#2,#3)[#4`#5`#6;#7`#8`#9]{{%
\settriparms[#1]%
\xpos=#2 \ypos=#3
\advance\ypos by \height
\puthmorphism(\xpos,\ypos)[#4`#5`{#7}]{\height}{\arrowtypea}a%
\putvmorphism(\xpos,\ypos)[`#6`{#8}]{\height}{\arrowtypeb}l%
\advance\xpos by\height
\putmorphism(\xpos,\ypos)(-1,-1)[``{#9}]{\height}{\arrowtypec}r%
}}
\def\putptriangle{\@ifnextchar <{\putptrianglep}{\putptrianglep
<\arrowtypea`\arrowtypeb`\arrowtypec;\height>}}
\def\ptriangle{\@ifnextchar <{\ptrianglep}{\ptrianglep
<\arrowtypea`\arrowtypeb`\arrowtypec;\height>}}
% #5
\def\ptrianglep<#1>[#2`#3`#4;#5`#6`#7]{{%% % #2----->#3
\settriparms[#1]% % | /
\diagram% % | /
\putptrianglep<\arrowtypea`\arrowtypeb`% % #6| /#7
\arrowtypec;\height>% % | /
(0,0)[#2`#3`#4;#5`#6`{#7}]% % | /
\enddiagram%% % v v
}} % #4
\def\putqtrianglep<#1>(#2,#3)[#4`#5`#6;#7`#8`#9]{{%
\settriparms[#1]%
\xpos=#2 \ypos=#3
\advance\ypos by\height
\puthmorphism(\xpos,\ypos)[#4`#5`{#7}]{\height}{\arrowtypea}a%
\putmorphism(\xpos,\ypos)(1,-1)[``{#8}]{\height}{\arrowtypeb}l%
\advance\xpos by\height
\putvmorphism(\xpos,\ypos)[`#6`{#9}]{\height}{\arrowtypec}r%
}}
\def\putqtriangle{\@ifnextchar <{\putqtrianglep}{\putqtrianglep
<\arrowtypea`\arrowtypeb`\arrowtypec;\height>}}
\def\qtriangle{\@ifnextchar <{\qtrianglep}{\qtrianglep
<\arrowtypea`\arrowtypeb`\arrowtypec;\height>}}
% #5
\def\qtrianglep<#1>[#2`#3`#4;#5`#6`#7]{{%% % #2----->#3
\settriparms[#1]% % \ |
\width=\height % \ |
\diagram% % #6\ |#7
\putqtrianglep<\arrowtypea`\arrowtypeb`% % \ |
\arrowtypec;\height>% % \ |
(0,0)[#2`#3`#4;#5`#6`{#7}]% % v v
\enddiagram%% % #4
}}
\def\putdtrianglep<#1>(#2,#3)[#4`#5`#6;#7`#8`#9]{{%
\settriparms[#1]%
\xpos=#2 \ypos=#3
\puthmorphism(\xpos,\ypos)[#5`#6`{#9}]{\height}{\arrowtypec}b%
\advance\xpos by \height \advance\ypos by\height
\putmorphism(\xpos,\ypos)(-1,-1)[``{#7}]{\height}{\arrowtypea}l%
\putvmorphism(\xpos,\ypos)[#4``{#8}]{\height}{\arrowtypeb}r%
}}
\def\putdtriangle{\@ifnextchar <{\putdtrianglep}{\putdtrianglep
<\arrowtypea`\arrowtypeb`\arrowtypec;\height>}}
\def\dtriangle{\@ifnextchar <{\dtrianglep}{\dtrianglep
<\arrowtypea`\arrowtypeb`\arrowtypec;\height>}}
% #2
\def\dtrianglep<#1>[#2`#3`#4;#5`#6`#7]{{%% % / |
\settriparms[#1]% % / |
\width=\height % #5/ |#6
\diagram% % / |
\putdtrianglep<\arrowtypea`\arrowtypeb`% % / |
\arrowtypec;\height>% % v v
(0,0)[#2`#3`#4;#5`#6`{#7}]% % #3----->#4
\enddiagram%% % #7
}}
\def\putbtrianglep<#1>(#2,#3)[#4`#5`#6;#7`#8`#9]{{%
\settriparms[#1]%
\xpos=#2 \ypos=#3
\puthmorphism(\xpos,\ypos)[#5`#6`{#9}]{\height}{\arrowtypec}b%
\advance\ypos by\height
\putmorphism(\xpos,\ypos)(1,-1)[``{#8}]{\height}{\arrowtypeb}r%
\putvmorphism(\xpos,\ypos)[#4``{#7}]{\height}{\arrowtypea}l%
}}
\def\putbtriangle{\@ifnextchar <{\putbtrianglep}{\putbtrianglep
<\arrowtypea`\arrowtypeb`\arrowtypec;\height>}}
\def\btriangle{\@ifnextchar <{\btrianglep}{\btrianglep
<\arrowtypea`\arrowtypeb`\arrowtypec;\height>}}
% #2
\def\btrianglep<#1>[#2`#3`#4;#5`#6`#7]{{%% % | \
\settriparms[#1]% % | \
\width=\height % #5| \#6
\diagram% % | \
\putbtrianglep<\arrowtypea`\arrowtypeb`% % | \
\arrowtypec;\height>% % v v
(0,0)[#2`#3`#4;#5`#6`{#7}]% % #3----->#4
\enddiagram%% % #7
}}
\def\putAtrianglep<#1>(#2,#3)[#4`#5`#6;#7`#8`#9]{{%
\settriparms[#1]%
\xpos=#2 \ypos=#3
{\multiply \height by2
\puthmorphism(\xpos,\ypos)[#5`#6`{#9}]{\height}{\arrowtypec}b}%
\advance\xpos by\height \advance\ypos by\height
\putmorphism(\xpos,\ypos)(-1,-1)[#4``{#7}]{\height}{\arrowtypea}l%
\putmorphism(\xpos,\ypos)(1,-1)[``{#8}]{\height}{\arrowtypeb}r%
}}
\def\putAtriangle{\@ifnextchar <{\putAtrianglep}{\putAtrianglep
<\arrowtypea`\arrowtypeb`\arrowtypec;\height>}}
\def\Atriangle{\@ifnextchar <{\Atrianglep}{\Atrianglep
<\arrowtypea`\arrowtypeb`\arrowtypec;\height>}}
% #2
\def\Atrianglep<#1>[#2`#3`#4;#5`#6`#7]{{%% % / \
\settriparms[#1]% % / \
\width=\height % #5/ \#6
\diagram% % / \
\putAtrianglep<\arrowtypea`\arrowtypeb`% % / \
\arrowtypec;\height>% % v v
(0,0)[#2`#3`#4;#5`#6`{#7}]% % #3------------>#4
\enddiagram%% % #7
}}
\def\putAtrianglepairp<#1>(#2)[#3;#4`#5`#6`#7`#8]{{%
\settripairparms[#1]%
\setpos(#2)%
\settokens`#3`%
\puthmorphism(\xpos,\ypos)[\tokenb`\tokenc`{#7}]{\height}{\arrowtyped}b%
\advance\xpos by\height
\puthmorphism(\xpos,\ypos)[\phantom{\tokenc}`\tokend`{#8}]%
{\height}{\arrowtypee}b%
\advance\ypos by\height
\putmorphism(\xpos,\ypos)(-1,-1)[\tokena``{#4}]{\height}{\arrowtypea}l%
\putvmorphism(\xpos,\ypos)[``{#5}]{\height}{\arrowtypeb}m%
\putmorphism(\xpos,\ypos)(1,-1)[``{#6}]{\height}{\arrowtypec}r%
}}
\def\putAtrianglepair{\@ifnextchar <{\putAtrianglepairp}{\putAtrianglepairp%
<\arrowtypea`\arrowtypeb`\arrowtypec`\arrowtyped`\arrowtypee;\height>}}
\def\Atrianglepair{\@ifnextchar <{\Atrianglepairp}{\Atrianglepairp%
<\arrowtypea`\arrowtypeb`\arrowtypec`\arrowtyped`\arrowtypee;\height>}}
\def\Atrianglepairp<#1>[#2;#3`#4`#5`#6`#7]{{% % #2a
\settripairparms[#1]% % / | \
\settokens`#2`% % / | \
\width=\height % #3/ #4 \#5
\diagram% % / | \
\putAtrianglepairp % / | \
<\arrowtypea`\arrowtypeb`\arrowtypec`% % v v v
\arrowtyped`\arrowtypee;\height>% % #2b---->#2c---->#2d
(0,0)[{#2};#3`#4`#5`#6`{#7}]% % #6 #7
\enddiagram%%
}}
\def\putVtrianglep<#1>(#2,#3)[#4`#5`#6;#7`#8`#9]{{%
\settriparms[#1]%
\xpos=#2 \ypos=#3
\advance\ypos by\height
{\multiply\height by2
\puthmorphism(\xpos,\ypos)[#4`#5`{#7}]{\height}{\arrowtypea}a}%
\putmorphism(\xpos,\ypos)(1,-1)[`#6`{#8}]{\height}{\arrowtypeb}l%
\advance\xpos by\height
\advance\xpos by\height
\putmorphism(\xpos,\ypos)(-1,-1)[``{#9}]{\height}{\arrowtypec}r%
}}
\def\putVtriangle{\@ifnextchar <{\putVtrianglep}{\putVtrianglep
<\arrowtypea`\arrowtypeb`\arrowtypec;\height>}}
\def\Vtriangle{\@ifnextchar <{\Vtrianglep}{\Vtrianglep
<\arrowtypea`\arrowtypeb`\arrowtypec;\height>}}
% #5
\def\Vtrianglep<#1>[#2`#3`#4;#5`#6`#7]{{%% % #2------------->#3
\settriparms[#1]% % \ /
\width=\height % \ /
\diagram% % #6\ /#7
\putVtrianglep<\arrowtypea`\arrowtypeb`% % \ /
\arrowtypec;\height>% % \ /
(0,0)[#2`#3`#4;#5`#6`{#7}]% % v v
\enddiagram%% % #4
}}
\def\putVtrianglepairp<#1>(#2)[#3;#4`#5`#6`#7`#8]{{
\settripairparms[#1]%
\setpos(#2)%
\settokens`#3`%
\advance\ypos by\height
\putmorphism(\xpos,\ypos)(1,-1)[`\tokend`{#6}]{\height}{\arrowtypec}l%
\puthmorphism(\xpos,\ypos)[\tokena`\tokenb`{#4}]{\height}{\arrowtypea}a%
\advance\xpos by\height
\puthmorphism(\xpos,\ypos)[\phantom{\tokenb}`\tokenc`{#5}]%
{\height}{\arrowtypeb}a%
\putvmorphism(\xpos,\ypos)[``{#7}]{\height}{\arrowtyped}m%
\advance\xpos by\height
\putmorphism(\xpos,\ypos)(-1,-1)[``{#8}]{\height}{\arrowtypee}r%
}}
\def\putVtrianglepair{\@ifnextchar <{\putVtrianglepairp}{\putVtrianglepairp%
<\arrowtypea`\arrowtypeb`\arrowtypec`\arrowtyped`\arrowtypee;\height>}}
\def\Vtrianglepair{\@ifnextchar <{\Vtrianglepairp}{\Vtrianglepairp%
<\arrowtypea`\arrowtypeb`\arrowtypec`\arrowtyped`\arrowtypee;\height>}}
% #3 #4
\def\Vtrianglepairp<#1>[#2;#3`#4`#5`#6`#7]{{% % #2a---->#2b---->#2c
\settripairparms[#1]% % \ | /
\settokens`#2`% % \ | /
\diagram% % #5\ #6 /#7
\putVtrianglepairp % \ | /
<\arrowtypea`\arrowtypeb`\arrowtypec`% % \ | /
\arrowtyped`\arrowtypee;\height>% % v v v
(0,0)[{#2};#3`#4`#5`#6`{#7}]% % #2d
\enddiagram%%
}}
\def\putCtrianglep<#1>(#2,#3)[#4`#5`#6;#7`#8`#9]{{%
\settriparms[#1]%
\xpos=#2 \ypos=#3
\advance\ypos by\height
\putmorphism(\xpos,\ypos)(1,-1)[``{#9}]{\height}{\arrowtypec}l%
\advance\xpos by\height
\advance\ypos by\height
\putmorphism(\xpos,\ypos)(-1,-1)[#4`#5`{#7}]{\height}{\arrowtypea}l%
{\multiply\height by 2
\putvmorphism(\xpos,\ypos)[`#6`{#8}]{\height}{\arrowtypeb}r}%
}}
\def\putCtriangle{\@ifnextchar <{\putCtrianglep}{\putCtrianglep
<\arrowtypea`\arrowtypeb`\arrowtypec;\height>}}
\def\Ctriangle{\@ifnextchar <{\Ctrianglep}{\Ctrianglep
<\arrowtypea`\arrowtypeb`\arrowtypec;\height>}}
% #2
\def\Ctrianglep<#1>[#2`#3`#4;#5`#6`#7]{{%% % / |
\settriparms[#1]% % #5/ |
\width=\height % / |
\diagram% % v |
\putCtrianglep<\arrowtypea`\arrowtypeb`% % #3 |#6
\arrowtypec;\height>% % \ |
(0,0)[#2`#3`#4;#5`#6`{#7}]% % #7\ |
\enddiagram%% % \ |
}} % v v
% #4
\def\putDtrianglep<#1>(#2,#3)[#4`#5`#6;#7`#8`#9]{{%
\settriparms[#1]%
\xpos=#2 \ypos=#3
\advance\xpos by\height \advance\ypos by\height
\putmorphism(\xpos,\ypos)(-1,-1)[``{#9}]{\height}{\arrowtypec}r%
\advance\xpos by-\height \advance\ypos by\height
\putmorphism(\xpos,\ypos)(1,-1)[`#5`{#8}]{\height}{\arrowtypeb}r%
{\multiply\height by 2
\putvmorphism(\xpos,\ypos)[#4`#6`{#7}]{\height}{\arrowtypea}l}%
}}
\def\putDtriangle{\@ifnextchar <{\putDtrianglep}{\putDtrianglep
<\arrowtypea`\arrowtypeb`\arrowtypec;\height>}}
\def\Dtriangle{\@ifnextchar <{\Dtrianglep}{\Dtrianglep
<\arrowtypea`\arrowtypeb`\arrowtypec;\height>}}
% #2
\def\Dtrianglep<#1>[#2`#3`#4;#5`#6`#7]{{%% % | \
\settriparms[#1]% % | \#6
\width=\height % | \
\diagram% % | v
\putDtrianglep<\arrowtypea`\arrowtypeb`% % #5| #3
\arrowtypec;\height>% % | /
(0,0)[#2`#3`#4;#5`#6`{#7}]% % | /#7
\enddiagram%% % | /
}} % v v
% #4
\def\setrecparms[#1`#2]{\width=#1 \height=#2}%
% #4
% #3b<-------#3a x #3b
% ^ | |
% / | |
% #5/ | |
% / | |
% / | |
% / | |
% #3c |#6 |#3a x #5
% \ | |
% \ | |
% #8\ | |
% \ | |
% \ | |
% v v v
% #3d<-------#3a x #3d
% #8
\def\recursep<#1`#2>[#3;#4`#5`#6`#7`#8]{{\m@th
\width=#1 \height=#2
\settokens`#3`
\settowidth{\tempdimen}{$\tokena$}
\ifdim\tempdimen=0pt
\savebox{\tempboxa}{\hbox{$\tokenb$}}%
\savebox{\tempboxb}{\hbox{$\tokend$}}%
\savebox{\tempboxc}{\hbox{$#6$}}%
\else
\savebox{\tempboxa}{\hbox{$\hbox{$\tokena$}\times\hbox{$\tokenb$}$}}%
\savebox{\tempboxb}{\hbox{$\hbox{$\tokena$}\times\hbox{$\tokend$}$}}%
\savebox{\tempboxc}{\hbox{$\hbox{$\tokena$}\times\hbox{$#6$}$}}%
\fi
\ypos=\height
\divide\ypos by 2
\xpos=\ypos
\advance\xpos by \width
\bfig
\putCtrianglep<-1`1`1;\ypos>(0,0)[`\tokenc`;#5`#6`{#7}]%
\puthmorphism(\ypos,0)[\tokend`\usebox{\tempboxb}`{#8}]{\width}{-1}b%
\puthmorphism(\ypos,\height)[\tokenb`\usebox{\tempboxa}`{#4}]{\width}{-1}a%
\advance\ypos by \width
\putvmorphism(\ypos,\height)[``\usebox{\tempboxc}]{\height}1r%
\efig
}}
\def\recurse{\@ifnextchar <{\recursep}{\recursep<\width`\height>}}
\def\puttwohmorphisms(#1,#2)[#3`#4;#5`#6]#7#8#9{{%
% 1 and 2 are position, 3 and 4 are the nodes, 5 and 6 the labels,
% 7 the distance between node centers and 8 & 9 are the arrow types.
% #5
% #3 ===========> #4
% #6
%
\puthmorphism(#1,#2)[#3`#4`]{#7}0a
\ypos=#2
\advance\ypos by 20
\puthmorphism(#1,\ypos)[\phantom{#3}`\phantom{#4}`#5]{#7}{#8}a
\advance\ypos by -40
\puthmorphism(#1,\ypos)[\phantom{#3}`\phantom{#4}`#6]{#7}{#9}b
}}
\def\puttwovmorphisms(#1,#2)[#3`#4;#5`#6]#7#8#9{{%
% 1 and 2 are position, 3 and 4 are the nodes, 5 and 6 the labels,
% 7 the distance between node centers and 8 & 9 are the arrow types.
%
% #3
% ||
% ||
% #5 || #6
% ||
% ||
% vv
% #4
%
\putvmorphism(#1,#2)[#3`#4`]{#7}0a
\xpos=#1
\advance\xpos by -20
\putvmorphism(\xpos,#2)[\phantom{#3}`\phantom{#4}`#5]{#7}{#8}l
\advance\xpos by 40
\putvmorphism(\xpos,#2)[\phantom{#3}`\phantom{#4}`#6]{#7}{#9}r
}}
\def\puthcoequalizer(#1)[#2`#3`#4;#5`#6`#7]#8#9{{%
% #1 is (\xpos,\ypos), the next 6 are the nodes and arrow labels
% #8 is the distance between each pair of nodes and #9 is the pos of #7
% either a (above) or b (below)
% #5 #7
% #2 ===========> #3 --------> #4
% #6
%
\setpos(#1)%
\puttwohmorphisms(\xpos,\ypos)[#2`#3;#5`#6]{#8}11%
\advance\xpos by #8
\puthmorphism(\xpos,\ypos)[\phantom{#3}`#4`#7]{#8}1{#9}
}}
\def\putvcoequalizer(#1)[#2`#3`#4;#5`#6`#7]#8#9{{%
% #1 is (\xpos,\ypos), the next 6 are the nodes and arrow labels
% #8 is the distance between each pair of nodes and #9 is the pos of #7
% either l (left) or r (right)
%
% #2
% | |
% | |
% #5 | | #6
% | |
% | |
% v v
% #3
% |
% |
% #7 |
% |
% v
% #4
%
\setpos(#1)%
\puttwovmorphisms(\xpos,\ypos)[#2`#3;#5`#6]{#8}11%
\advance\ypos by -#8
\putvmorphism(\xpos,\ypos)[\phantom{#3}`#4`#7]{#8}1{#9}
}}
\def\putthreehmorphisms(#1)[#2`#3;#4`#5`#6]#7(#8)#9{{%
% Use: \putthreehmorphisms(xpos,ypos)[lnode`rnode;toplabel`midlabel%
% botlabel]{distance}(toparrowtype,midarrowtype,botarrowtype){position}
\setpos(#1) \settypes(#8)
\if a#9 %
\vertsize{\tempcounta}{#5}%
\vertsize{\tempcountb}{#6}%
\ifnum \tempcounta<\tempcountb \tempcounta=\tempcountb \fi
\else
\vertsize{\tempcounta}{#4}%
\vertsize{\tempcountb}{#5}%
\ifnum \tempcounta<\tempcountb \tempcounta=\tempcountb \fi
\fi
\advance \tempcounta by 60
\puthmorphism(\xpos,\ypos)[#2`#3`#5]{#7}{\arrowtypeb}{#9}
\advance\ypos by \tempcounta
\puthmorphism(\xpos,\ypos)[\phantom{#2}`\phantom{#3}`#4]{#7}{\arrowtypea}{#9}
\advance\ypos by -\tempcounta \advance\ypos by -\tempcounta
\puthmorphism(\xpos,\ypos)[\phantom{#2}`\phantom{#3}`#6]{#7}{\arrowtypec}{#9}
}}
\def\setarrowtoks[#1`#2`#3`#4`#5`#6]{%
\def\toka{#1}
\def\tokb{#2}
\def\tokc{#3}
\def\tokd{#4}
\def\toke{#5}
\def\tokf{#6}
}
\def\hex{\@ifnextchar <{\hexp}{\hexp<1000`400>}}
\def\hexp<#1`#2>[#3`#4`#5`#6`#7`#8;#9]{%
\setarrowtoks[#9]
\yext=#2 \advance \yext by #2
\xext=#1 \advance\xext by \yext
\bfig