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Diffstat (limited to 'Master/texmf-dist/tex/latex/barr/diagxy.tex')
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diff --git a/Master/texmf-dist/tex/latex/barr/diagxy.tex b/Master/texmf-dist/tex/latex/barr/diagxy.tex new file mode 100644 index 00000000000..5fc36e7cf54 --- /dev/null +++ b/Master/texmf-dist/tex/latex/barr/diagxy.tex @@ -0,0 +1,952 @@ + \def\dated#1{\def\thedate{#1}} + \dated{2001-10-14} + % This is a package of commutative diagram macros built on top of Xy-pic + % by Michael Barr (email: barr@barrs.org). Its use is unrestricted. It + % may be freely distributed, unchanged, for non-commercial or commercial + % use. If changed, it must be renamed. Inclusion in a commercial + % software package is also permitted, but I would appreciate receiving a + % free copy for my personal examination and use. There are no guarantees + % that this package is good for anything. I have tested it with LaTeX 2e, + % LaTeX 2.09 and Plain TeX. Although I know of no reason it will not work + % with AMSTeX, I have not tested it. + +\input xy +\xyoption{arrow} + +\newdir{ >}{{ }*!/-9pt/@{>}} +\newdir{ (}{{ }*!/-5pt/@{(}} +\newdir^{ (}{{ }*!/-5pt/@^{(}} +\newdir{< }{!/9pt/@{<}*{ }} + +\newbox\Label% +\newdimen\high% +\newdimen\deep% +\newdimen\ul% +\newcount\deltax% +\newcount\deltay% +\newcount\deltaX% +\newcount\deltaY% + +\newdimen\wdth +\newcount\xend% +\newcount\yend% +\newcount\Xend +\newcount\Yend +\newcount\xpos% +\newcount\ypos% +\newcount\default \default=500% +\newcount\defaultmargin \defaultmargin=150 +\newcount\topw% +\newcount\botw% +\newcount\Xpos% +\newcount\Ypos% +\def\ratchet#1#2{\ifnum#1<#2\global #1=#2\fi}% + +\newcount\atcode \atcode=\catcode`\@% +\catcode`\@=11 +\expandafter\ifx\csname @ifnextchar\endcsname\relax +\def\ifnextchar#1#2#3{\let\@tempe +#1\def\@tempa{#2}\def\@tempb{#3}\futurelet + \@tempc\@ifnch}% +\def\@ifnch{\ifx \@tempc \@sptoken \let\@tempd\@xifnch + \else \ifx \@tempc \@tempe\let\@tempd\@tempa\else\let\@tempd\@tempb\fi + \fi \@tempd}% +\def\:{\let\@sptoken= } \: % this makes \@sptoken a space token +\def\:{\@xifnch} \expandafter\def\: {\futurelet\@tempc\@ifnch}% +\else +\let\ifnextchar\@ifnextchar +\fi +\ul=.01em% +\X@xbase =.01em% +\Y@ybase =.01em% +\def\scalefactor#1{\ul=#1\ul \X@xbase=#1\X@xbase \Y@ybase=#1\Y@ybase}% +\catcode`\@=12% + +\def\fontscale#1{% +\if#1h\relax +\font\xydashfont=xydash10 scaled \magstephalf +\font\xyatipfont=xyatip10 scaled \magstephalf +\font\xybtipfont=xybtip10 scaled \magstephalf +\font\xybsqlfont=xybsql10 scaled \magstephalf +\font\xycircfont=xycirc10 scaled \magstephalf +\else +\font\xydashfont=xydash10 scaled \magstep#1% +\font\xyatipfont=xyatip10 scaled \magstep#1% +\font\xybtipfont=xybtip10 scaled \magstep#1% +\font\xybsqlfont=xybsql10 scaled \magstep#1% +\font\xycircfont=xycirc10 scaled \magstep#1% +\fi} + +\let\bfig\xy% +\let\efig\endxy% + +\def\car#1#2\nil{#1}% + +\def\morphism{\ifnextchar({\morphismp}{\morphismp(0,0)}}% +\def\morphismp(#1){\ifnextchar|{\morphismpp(#1)}{\morphismpp(#1)|a|}}% +\def\morphismpp(#1)|#2|{\ifnextchar/{\morphismppp(#1)|#2|}% + {\morphismppp(#1)|#2|/>/}}% +\def\morphismppp(#1)|#2|/#3/{% + \ifnextchar<{\morphismpppp(#1)|#2|/#3/}% + {\morphismpppp(#1)|#2|/#3/<\default,0>}}% + +\def\morphismpppp(#1,#2)|#3|/#4/<#5,#6>[#7`#8;#9]{% +\xend#1\advance \xend by #5% +\yend#2\advance \yend by #6% +\domorphism(#1,#2)|#3|/#4/<#5,#6>[#7`#8;#9]} + +\def\domorphism(#1,#2)|#3|/#4/<#5,#6>[#7`#8;#9]{% +\edef\next{#4}% +\ifx\next\empty\relax + \POS(#1,#2)*+!!<0ex,.75ex>{#7}\ar@{} (\xend,\yend)*+!!<0ex,.75ex>{#8}% +\else \def\next{\car#4\nil}\fi +\if@\next\relax + \if#3l% + \ifnum #6>0% + \POS(#1,#2)*+!!<0ex,.75ex>{#7}\ar#4^-{#9} (\xend,\yend)*+!!<0ex,.75ex>{#8}% + \else% + \POS(#1,#2)*+!!<0ex,.75ex>{#7}\ar#4_-{#9} (\xend,\yend)*+!!<0ex,.75ex>{#8}% + \fi% + \else \if#3m% + \setbox0\hbox{$#9$}% + \ifdim \wd0=0pt + \POS(#1,#2)*+!!<0ex,.75ex>{#7}\ar#4 (\xend,\yend)*+!!<0ex,.75ex>{#8}% + \else + \setbox\Label=\hbox{\kern .5pt $\labelstyle #9$\kern .5pt}% + \high=\ht\Label \advance\high by 2pt \ht\Label=\high% + \deep=\dp\Label \advance\deep by 2pt \dp\Label=\deep% + \POS(#1,#2)*+!!<0ex,.75ex>{#7}\ar#4|-{\box\Label} (\xend,\yend)*+!!<0ex,.75ex>{#8}% + \fi + \else \if#3r% + \ifnum #6<0% + \POS(#1,#2)*+!!<0ex,.75ex>{#7}\ar#4^-{#9} (\xend,\yend)*+!!<0ex,.75ex>{#8}% + \else% + \POS(#1,#2)*+!!<0ex,.75ex>{#7}\ar#4_-{#9} (\xend,\yend)*+!!<0ex,.75ex>{#8}% + \fi% + \else \if#3a% + \ifnum #5>0% + \POS(#1,#2)*+!!<0ex,.75ex>{#7}\ar#4^-{#9} (\xend,\yend)*+!!<0ex,.75ex>{#8}% + \else% + \POS(#1,#2)*+!!<0ex,.75ex>{#7}\ar#4_-{#9} (\xend,\yend)*+!!<0ex,.75ex>{#8}% + \fi% + \else \if#3b% + \ifnum #5<0% + \POS(#1,#2)*+!!<0ex,.75ex>{#7}\ar#4^-{#9} (\xend,\yend)*+!!<0ex,.75ex>{#8}% + \else% + \POS(#1,#2)*+!!<0ex,.75ex>{#7}\ar#4_-{#9} (\xend,\yend)*+!!<0ex,.75ex>{#8}% + \fi% + \else + \POS(#1,#2)*+!!<0ex,.75ex>{#7}\ar#4 (\xend,\yend)*+!!<0ex,.75ex>{#8}% + \fi\fi\fi\fi\fi% +\else% +\edef\next{#4}% + \ifx\next\empty\relax + \POS(#1,#2)*+!!<0ex,.75ex>{#7}; (\xend,\yend)*+!!<0ex,.75ex>{#8}% + \else \edef\next{#4}% + \ifx\next\empty\relax + \POS(#1,#2)*+!!<0ex,.75ex>{#7}\ar (\xend,\yend)*+!!<0ex,.75ex>{#8}% + \else \if#3l% + \ifnum #6>0% + \POS(#1,#2)*+!!<0ex,.75ex>{#7}\ar@{#4}^-{#9} (\xend,\yend)*+!!<0ex,.75ex>{#8}% + \else% + \POS(#1,#2)*+!!<0ex,.75ex>{#7}\ar@{#4}_-{#9} (\xend,\yend)*+!!<0ex,.75ex>{#8}% + \fi% + \else \if#3m% + \setbox0\hbox{$#9$}% + \ifdim \wd0=0pt + \POS(#1,#2)*+!!<0ex,.75ex>{#7}\ar@{#4} (\xend,\yend)*+!!<0ex,.75ex>{#8}% + \else + \setbox\Label=\hbox{\kern .5pt $\labelstyle #9$\kern .5pt}% + \high=\ht\Label \advance\high by 2pt \ht\Label=\high% + \deep=\dp\Label \advance\deep by 2pt \dp\Label=\deep% + \POS(#1,#2)*+!!<0ex,.75ex>{#7}\ar@{#4}|-{\box\Label} (\xend,\yend)*+!!<0ex,.75ex>{#8}% + \fi + \else \if#3r% + \ifnum #6<0% + \POS(#1,#2)*+!!<0ex,.75ex>{#7}\ar@{#4}^-{#9} (\xend,\yend)*+!!<0ex,.75ex>{#8}% + \else% + \POS(#1,#2)*+!!<0ex,.75ex>{#7}\ar@{#4}_-{#9} (\xend,\yend)*+!!<0ex,.75ex>{#8}% + \fi% + \else \if#3a% + \ifnum #5>0% + \POS(#1,#2)*+!!<0ex,.75ex>{#7}\ar@{#4}^-{#9} (\xend,\yend)*+!!<0ex,.75ex>{#8}% + \else% + \POS(#1,#2)*+!!<0ex,.75ex>{#7}\ar@{#4}_-{#9} (\xend,\yend)*+!!<0ex,.75ex>{#8}% + \fi% + \else \if#3b% + \ifnum #5<0% + \POS(#1,#2)*+!!<0ex,.75ex>{#7}\ar@{#4}^-{#9} (\xend,\yend)*+!!<0ex,.75ex>{#8}% + \else% + \POS(#1,#2)*+!!<0ex,.75ex>{#7}\ar@{#4}_-{#9} (\xend,\yend)*+!!<0ex,.75ex>{#8}% + \fi% + \else + \POS(#1,#2)*+!!<0ex,.75ex>{#7}\ar@{#4} (\xend,\yend)*+!!<0ex,.75ex>{#8}% + \fi\fi\fi\fi\fi\fi\fi% +\fi\ignorespaces}% + +\def\squarepppp(#1,#2)|#3|/#4`#5`#6`#7/<#8>[#9]{% +\xpos#1\ypos#2% +\def\next|##1##2##3##4|{% + \def\xa{##1}\def\xb{##2}\def\xc{##3}\def\xd{##4}\ignorespaces}% +\next|#3|% +\def\next<##1,##2>{\deltax=##1\deltay=##2\ignorespaces}% +\next<#8>% +\def\next[##1`##2`##3`##4;##5`##6`##7`##8]{% + \def\nodea{##1}\def\nodeb{##2}\def\nodec{##3}\def\noded{##4}% + \def\labela{##5}\def\labelb{##6}\def\labelc{##7}\def\labeld{##8}\ignorespaces}% +\next[#9]% +\morphism(\xpos,\ypos)|\xd|/{#7}/<\deltax,0>[\nodec`\noded;\labeld]% +\advance \ypos by \deltay% +\morphism(\xpos,\ypos)|\xb|/{#5}/<0,-\deltay>[\nodea`\nodec;\labelb]% +\morphism(\xpos,\ypos)|\xa|/{#4}/<\deltax,0>[\nodea`\nodeb;\labela]% + \advance \xpos by \deltax% +\morphism(\xpos,\ypos)|\xc|/{#6}/<0,-\deltay>[\nodeb`\noded;\labelc]% +\ignorespaces}% + +\def\square{\ifnextchar({\squarep}{\squarep(0,0)}}% +\def\squarep(#1){\ifnextchar|{\squarepp(#1)}{\squarepp(#1)|alrb|}}% +\def\squarepp(#1)|#2|{\ifnextchar/{\squareppp(#1)|#2|}% + {\squareppp(#1)|#2|/>`>`>`>/}}% +\def\squareppp(#1)|#2|/#3`#4`#5`#6/{% + \ifnextchar<{\squarepppp(#1)|#2|/#3`#4`#5`#6/}% + {\squarepppp(#1)|#2|/#3`#4`#5`#6/<\default,\default>}}% + +\def\ptrianglepppp(#1,#2)|#3|/#4`#5`#6/<#7>[#8]{% +\xpos#1\ypos#2% +\def\next|##1##2##3|{\def\xa{##1}\def\xb{##2}\def\xc{##3}}% +\next|#3|% +\def\next<##1,##2>{\deltax=##1\deltay=##2\ignorespaces}% +\next<#7>% +\def\next[##1`##2`##3;##4`##5`##6]{% + \def\nodea{##1}\def\nodeb{##2}\def\nodec{##3}% + \def\labela{##4}\def\labelb{##5}\def\labelc{##6}}% +\next[#8]% +\advance\ypos by \deltay% +\morphism(\xpos,\ypos)|\xa|/{#4}/<\deltax,0>[\nodea`\nodeb;\labela]% +\morphism(\xpos,\ypos)|\xb|/{#5}/<0,-\deltay>[\nodea`\nodec;\labelb]% +\advance\xpos by \deltax% +\morphism(\xpos,\ypos)|\xc|/{#6}/<-\deltax,-\deltay>[\nodeb`\nodec;\labelc]% +\ignorespaces}% + +\def\qtrianglepppp(#1,#2)|#3|/#4`#5`#6/<#7>[#8]{% +\xpos#1\ypos#2% +\def\next|##1##2##3|{\def\xa{##1}\def\xb{##2}\def\xc{##3}}% +\next|#3|% +\def\next<##1,##2>{\deltax=##1\deltay=##2\ignorespaces}% +\next<#7>% +\def\next[##1`##2`##3;##4`##5`##6]{% + \def\nodea{##1}\def\nodeb{##2}\def\nodec{##3}% + \def\labela{##4}\def\labelb{##5}\def\labelc{##6}}% +\next[#8]% +\advance\ypos by \deltay% +\morphism(\xpos,\ypos)|\xa|/{#4}/<\deltax,0>[\nodea`\nodeb;\labela]% +\morphism(\xpos,\ypos)|\xb|/{#5}/<\deltax,-\deltay>[\nodea`\nodec;\labelb]% +\advance\xpos by \deltax% +\morphism(\xpos,\ypos)|\xc|/{#6}/<0,-\deltay>[\nodeb`\nodec;\labelc]% +\ignorespaces}% + +\def\dtrianglepppp(#1,#2)|#3|/#4`#5`#6/<#7>[#8]{% +\xpos#1\ypos#2% +\def\next|##1##2##3|{\def\xa{##1}\def\xb{##2}\def\xc{##3}}% +\next|#3|% +\def\next<##1,##2>{\deltax=##1\deltay=##2\ignorespaces}% +\next<#7>% +\def\next[##1`##2`##3;##4`##5`##6]{% + \def\nodea{##1}\def\nodeb{##2}\def\nodec{##3}% + \def\labela{##4}\def\labelb{##5}\def\labelc{##6}}% +\next[#8]% +\morphism(\xpos,\ypos)|\xc|/{#6}/<\deltax,0>[\nodeb`\nodec;\labelc]% +\advance\ypos by \deltay\advance \xpos by \deltax% +\morphism(\xpos,\ypos)|\xa|/{#4}/<-\deltax,-\deltay>[\nodea`\nodeb;\labela]% +\morphism(\xpos,\ypos)|\xb|/{#5}/<0,-\deltay>[\nodea`\nodec;\labelb]% +\ignorespaces}% + +\def\btrianglepppp(#1,#2)|#3|/#4`#5`#6/<#7>[#8]{% +\xpos#1\ypos#2% +\def\next|##1##2##3|{\def\xa{##1}\def\xb{##2}\def\xc{##3}}% +\next|#3|% +\def\next<##1,##2>{\deltax=##1\deltay=##2\ignorespaces}% +\next<#7>% +\def\next[##1`##2`##3;##4`##5`##6]{% + \def\nodea{##1}\def\nodeb{##2}\def\nodec{##3}% + \def\labela{##4}\def\labelb{##5}\def\labelc{##6}}% +\next[#8]% +\morphism(\xpos,\ypos)|\xc|/{#6}/<\deltax,0>[\nodeb`\nodec;\labelc]% +\advance\ypos by \deltay% +\morphism(\xpos,\ypos)|\xa|/{#4}/<0,-\deltay>[\nodea`\nodeb;\labela]% +\morphism(\xpos,\ypos)|\xb|/{#5}/<\deltax,-\deltay>[\nodea`\nodec;\labelb]% +\ignorespaces}% + +\def\Atrianglepppp(#1,#2)|#3|/#4`#5`#6/<#7>[#8]{% +\xpos#1\ypos#2% +\def\next|##1##2##3|{\def\xa{##1}\def\xb{##2}\def\xc{##3}}% +\next|#3|% +\def\next<##1,##2>{\deltax=##1\deltay=##2\ignorespaces}% +\next<#7>% +\def\next[##1`##2`##3;##4`##5`##6]{% + \def\nodea{##1}\def\nodeb{##2}\def\nodec{##3}% + \def\labela{##4}\def\labelb{##5}\def\labelc{##6}}% +\next[#8]% +\multiply\deltax by 2% +\morphism(\xpos,\ypos)|\xc|/{#6}/<\deltax,0>[\nodeb`\nodec;\labelc]% +\divide\deltax by 2 +\advance\ypos by \deltay\advance\xpos by \deltax% +\morphism(\xpos,\ypos)|\xa|/{#4}/<-\deltax,-\deltay>[\nodea`\nodeb;\labela]% +\morphism(\xpos,\ypos)|\xb|/{#5}/<\deltax,-\deltay>[\nodea`\nodec;\labelb]% +\ignorespaces}% + +\def\Vtrianglepppp(#1,#2)|#3|/#4`#5`#6/<#7>[#8]{% +\xpos#1\ypos#2% +\def\next|##1##2##3|{\def\xa{##1}\def\xb{##2}\def\xc{##3}}% +\next|#3|% +\def\next<##1,##2>{\deltax=##1\deltay=##2\ignorespaces}% +\next<#7>% +\def\next[##1`##2`##3;##4`##5`##6]{% + \def\nodea{##1}\def\nodeb{##2}\def\nodec{##3}% + \def\labela{##4}\def\labelb{##5}\def\labelc{##6}}% +\next[#8]% +\advance\ypos by \deltay% +\morphism(\xpos,\ypos)|\xb|/{#5}/<\deltax,-\deltay>[\nodea`\nodec;\labelb]% +\multiply\deltax by 2% +\morphism(\xpos,\ypos)|\xa|/{#4}/<\deltax,0>[\nodea`\nodeb;\labela]% +\advance\xpos by \deltax \divide \deltax by 2 +\morphism(\xpos,\ypos)|\xc|/{#6}/<-\deltax,-\deltay>[\nodeb`\nodec;\labelc]% +\ignorespaces}% + +\def\Ctrianglepppp(#1,#2)|#3|/#4`#5`#6/<#7>[#8]{% +\xpos#1\ypos#2% +\def\next|##1##2##3|{\def\xa{##1}\def\xb{##2}\def\xc{##3}}% +\next|#3|% +\def\next<##1,##2>{\deltax=##1\deltay=##2\ignorespaces}% +\next<#7>% +\def\next[##1`##2`##3;##4`##5`##6]{% + \def\nodea{##1}\def\nodeb{##2}\def\nodec{##3}% + \def\labela{##4}\def\labelb{##5}\def\labelc{##6}}% +\next[#8]% +\advance \ypos by \deltay% +\morphism(\xpos,\ypos)|\xc|/{#6}/<\deltax,-\deltay>[\nodeb`\nodec;\labelc]% +\advance\ypos by \deltay \advance \xpos by \deltax% +\morphism(\xpos,\ypos)|\xa|/{#4}/<-\deltax,-\deltay>[\nodea`\nodeb;\labela]% +\multiply\deltay by 2% +\morphism(\xpos,\ypos)|\xb|/{#5}/<0,-\deltay>[\nodea`\nodec;\labelb]% +\ignorespaces}% + +\def\Dtrianglepppp(#1,#2)|#3|/#4`#5`#6/<#7>[#8]{% +\xpos#1\ypos#2% +\def\next|##1##2##3|{\def\xa{##1}\def\xb{##2}\def\xc{##3}}% +\next|#3|% +\def\next<##1,##2>{\deltax=##1\deltay=##2\ignorespaces}% +\next<#7>% +\def\next[##1`##2`##3;##4`##5`##6]{% + \def\nodea{##1}\def\nodeb{##2}\def\nodec{##3}% + \def\labela{##4}\def\labelb{##5}\def\labelc{##6}}% +\next[#8]% +\advance\xpos by \deltax \advance\ypos by \deltay% +\morphism(\xpos,\ypos)|\xc|/{#6}/<-\deltax,-\deltay>[\nodeb`\nodec;\labelc]% +\advance\xpos by -\deltax \advance\ypos by \deltay% +\morphism(\xpos,\ypos)|\xb|/{#5}/<\deltax,-\deltay>[\nodea`\nodeb;\labelb]% +\multiply \deltay by 2% +\morphism(\xpos,\ypos)|\xa|/{#4}/<0,-\deltay>[\nodea`\nodec;\labela]% +\ignorespaces}% + +\def\ptriangle{\ifnextchar({\ptrianglep}{\ptrianglep(0,0)}}% +\def\ptrianglep(#1){\ifnextchar|{\ptrianglepp(#1)}{\ptrianglepp(#1)|alr|}}% +\def\ptrianglepp(#1)|#2|{\ifnextchar/{\ptriangleppp(#1)|#2|}% + {\ptriangleppp(#1)|#2|/>`>`>/}}% +\def\ptriangleppp(#1)|#2|/#3`#4`#5/{% + \ifnextchar<{\ptrianglepppp(#1)|#2|/#3`#4`#5/}% + {\ptrianglepppp(#1)|#2|/#3`#4`#5/<\default,\default>}}% + +\def\qtriangle{\ifnextchar({\qtrianglep}{\qtrianglep(0,0)}}% +\def\qtrianglep(#1){\ifnextchar|{\qtrianglepp(#1)}{\qtrianglepp(#1)|alr|}}% +\def\qtrianglepp(#1)|#2|{\ifnextchar/{\qtriangleppp(#1)|#2|}% + {\qtriangleppp(#1)|#2|/>`>`>/}}% +\def\qtriangleppp(#1)|#2|/#3`#4`#5/{% + \ifnextchar<{\qtrianglepppp(#1)|#2|/#3`#4`#5/}% + {\qtrianglepppp(#1)|#2|/#3`#4`#5/<\default,\default>}}% + +\def\dtriangle{\ifnextchar({\dtrianglep}{\dtrianglep(0,0)}}% +\def\dtrianglep(#1){\ifnextchar|{\dtrianglepp(#1)}{\dtrianglepp(#1)|lrb|}}% +\def\dtrianglepp(#1)|#2|{\ifnextchar/{\dtriangleppp(#1)|#2|}% + {\dtriangleppp(#1)|#2|/>`>`>/}}% +\def\dtriangleppp(#1)|#2|/#3`#4`#5/{% + \ifnextchar<{\dtrianglepppp(#1)|#2|/#3`#4`#5/}% + {\dtrianglepppp(#1)|#2|/#3`#4`#5/<\default,\default>}}% + +\def\btriangle{\ifnextchar({\btrianglep}{\btrianglep(0,0)}}% +\def\btrianglep(#1){\ifnextchar|{\btrianglepp(#1)}{\btrianglepp(#1)|lrb|}}% +\def\btrianglepp(#1)|#2|{\ifnextchar/{\btriangleppp(#1)|#2|}% + {\btriangleppp(#1)|#2|/>`>`>/}}% +\def\btriangleppp(#1)|#2|/#3`#4`#5/{% + \ifnextchar<{\btrianglepppp(#1)|#2|/#3`#4`#5/}% + {\btrianglepppp(#1)|#2|/#3`#4`#5/<\default,\default>}}% + +\def\Atriangle{\ifnextchar({\Atrianglep}{\Atrianglep(0,0)}}% +\def\Atrianglep(#1){\ifnextchar|{\Atrianglepp(#1)}{\Atrianglepp(#1)|lrb|}}% +\def\Atrianglepp(#1)|#2|{\ifnextchar/{\Atriangleppp(#1)|#2|}% + {\Atriangleppp(#1)|#2|/>`>`>/}}% +\def\Atriangleppp(#1)|#2|/#3`#4`#5/{% + \ifnextchar<{\Atrianglepppp(#1)|#2|/#3`#4`#5/}% + {\Atrianglepppp(#1)|#2|/#3`#4`#5/<\default,\default>}}% + +\def\Vtriangle{\ifnextchar({\Vtrianglep}{\Vtrianglep(0,0)}}% +\def\Vtrianglep(#1){\ifnextchar|{\Vtrianglepp(#1)}{\Vtrianglepp(#1)|alb|}}% +\def\Vtrianglepp(#1)|#2|{\ifnextchar/{\Vtriangleppp(#1)|#2|}% + {\Vtriangleppp(#1)|#2|/>`>`>/}}% +\def\Vtriangleppp(#1)|#2|/#3`#4`#5/{% + \ifnextchar<{\Vtrianglepppp(#1)|#2|/#3`#4`#5/}% + {\Vtrianglepppp(#1)|#2|/#3`#4`#5/<\default,\default>}}% + +\def\Ctriangle{\ifnextchar({\Ctrianglep}{\Ctrianglep(0,0)}}% +\def\Ctrianglep(#1){\ifnextchar|{\Ctrianglepp(#1)}{\Ctrianglepp(#1)|arb|}}% +\def\Ctrianglepp(#1)|#2|{\ifnextchar/{\Ctriangleppp(#1)|#2|}% + {\Ctriangleppp(#1)|#2|/>`>`>/}}% +\def\Ctriangleppp(#1)|#2|/#3`#4`#5/{% + \ifnextchar<{\Ctrianglepppp(#1)|#2|/#3`#4`#5/}% + {\Ctrianglepppp(#1)|#2|/#3`#4`#5/<\default,\default>}}% + +\def\Dtriangle{\ifnextchar({\Dtrianglep}{\Dtrianglep(0,0)}}% +\def\Dtrianglep(#1){\ifnextchar|{\Dtrianglepp(#1)}{\Dtrianglepp(#1)|alb|}}% +\def\Dtrianglepp(#1)|#2|{\ifnextchar/{\Dtriangleppp(#1)|#2|}% + {\Dtriangleppp(#1)|#2|/>`>`>/}}% +\def\Dtriangleppp(#1)|#2|/#3`#4`#5/{% + \ifnextchar<{\Dtrianglepppp(#1)|#2|/#3`#4`#5/}% + {\Dtrianglepppp(#1)|#2|/#3`#4`#5/<\default,\default>}}% + + +\def\Atrianglepairpppp(#1)|#2|/#3`#4`#5`#6`#7/<#8>[#9]{% +\def\next(##1,##2){\xpos##1\ypos##2}% +\next(#1)% +\def\next|##1##2##3##4##5|{\def\xa{##1}\def\xb{##2}% +\def\xc{##3}\def\xd{##4}\def\xe{##5}}% +\next|#2|% +\def\next<##1,##2>{\deltax=##1\deltay=##2\ignorespaces}% +\next<#8>% +\def\next[##1`##2`##3`##4;##5`##6`##7`##8`##9]{% + \def\nodea{##1}\def\nodeb{##2}\def\nodec{##3}\def\noded{##4}% + \def\labela{##5}\def\labelb{##6}\def\labelc{##7}\def\labeld{##8}\def\labele{##9}}% +\next[#9]% +\morphism(\xpos,\ypos)|\xd|/{#6}/<\deltax,0>[\nodeb`\nodec;\labeld]% +\advance\xpos by \deltax% +\morphism(\xpos,\ypos)|\xe|/{#7}/<\deltax,0>[\nodec`\noded;\labele]% +\advance\ypos by \deltay% +\morphism(\xpos,\ypos)|\xa|/{#3}/<-\deltax,-\deltay>[\nodea`\nodeb;\labela]% +\morphism(\xpos,\ypos)|\xb|/{#4}/<0,-\deltay>[\nodea`\nodec;\labelb]% +\morphism(\xpos,\ypos)|\xc|/{#5}/<\deltax,-\deltay>[\nodea`\noded;\labelc]% +\ignorespaces}% + +\def\Vtrianglepairpppp(#1)|#2|/#3`#4`#5`#6`#7/<#8>[#9]{% +\def\next(##1,##2){\xpos##1\ypos##2}% +\next(#1)% +\def\next|##1##2##3##4##5|{\def\xa{##1}\def\xb{##2}% +\def\xc{##3}\def\xd{##4}\def\xe{##5}}% +\next|#2|% +\def\next<##1,##2>{\deltax=##1\deltay=##2\ignorespaces}% +\next<#8>% +\def\next[##1`##2`##3`##4;##5`##6`##7`##8`##9]{% + \def\nodea{##1}\def\nodeb{##2}\def\nodec{##3}\def\noded{##4}% + \def\labela{##5}\def\labelb{##6}\def\labelc{##7}\def\labeld{##8}\def\labele{##9}}% +\next[#9]% +\advance\ypos by \deltay% +\morphism(\xpos,\ypos)|\xa|/{#3}/<\deltax,0>[\nodea`\nodeb;\labela]% +\morphism(\xpos,\ypos)|\xc|/{#5}/<\deltax,-\deltay>[\nodea`\noded;\labelc]% +\advance\xpos by \deltax% +\morphism(\xpos,\ypos)|\xb|/{#4}/<\deltax,0>[\nodeb`\nodec;\labelb]% +\morphism(\xpos,\ypos)|\xd|/{#6}/<0,-\deltay>[\nodeb`\noded;\labeld]% +\advance\xpos by \deltax% +\morphism(\xpos,\ypos)|\xe|/{#7}/<-\deltax,-\deltay>[\nodec`\noded;\labele]% +\ignorespaces}% + +\def\Ctrianglepairpppp(#1)|#2|/#3`#4`#5`#6`#7/<#8>[#9]{% +\def\next(##1,##2){\xpos##1\ypos##2}% +\next(#1)% +\def\next|##1##2##3##4##5|{\def\xa{##1}\def\xb{##2}% +\def\xc{##3}\def\xd{##4}\def\xe{##5}}% +\next|#2|% +\def\next<##1,##2>{\deltax=##1\deltay=##2\ignorespaces}% +\next<#8>% +\def\next[##1`##2`##3`##4;##5`##6`##7`##8`##9]{% + \def\nodea{##1}\def\nodeb{##2}\def\nodec{##3}\def\noded{##4}% + \def\labela{##5}\def\labelb{##6}\def\labelc{##7}\def\labeld{##8}\def\labele{##9}}% +\next[#9]% +\advance\ypos by \deltay% +\morphism(\xpos,\ypos)|\xe|/{#7}/<0,-\deltay>[\nodec`\noded;\labele]% +\advance\xpos by -\deltax% +\morphism(\xpos,\ypos)|\xc|/{#5}/<\deltax,0>[\nodeb`\nodec;\labelc]% +\morphism(\xpos,\ypos)|\xd|/{#6}/<\deltax,-\deltay>[\nodeb`\noded;\labeld]% +\advance\ypos by \deltay% +\advance\xpos by \deltax% +\morphism(\xpos,\ypos)|\xa|/{#3}/<-\deltax,-\deltay>[\nodea`\nodeb;\labela]% +\morphism(\xpos,\ypos)|\xb|/{#4}/<0,-\deltay>[\nodea`\nodec;\labelb]% +\ignorespaces}% + +\def\Dtrianglepairpppp(#1)|#2|/#3`#4`#5`#6`#7/<#8>[#9]{% +\def\next(##1,##2){\xpos##1\ypos##2}% +\next(#1)% +\def\next|##1##2##3##4##5|{\def\xa{##1}\def\xb{##2}% +\def\xc{##3}\def\xd{##4}\def\xe{##5}}% +\next|#2|% +\def\next<##1,##2>{\deltax=##1\deltay=##2\ignorespaces}% +\next<#8>% +\def\next[##1`##2`##3`##4;##5`##6`##7`##8`##9]{% + \def\nodea{##1}\def\nodeb{##2}\def\nodec{##3}\def\noded{##4}% + \def\labela{##5}\def\labelb{##6}\def\labelc{##7}\def\labeld{##8}\def\labele{##9}}% +\next[#9]% +\advance\ypos by \deltay% +\morphism(\xpos,\ypos)|\xc|/{#5}/<\deltax,0>[\nodeb`\nodec;\labelc]% +\morphism(\xpos,\ypos)|\xd|/{#6}/<0,-\deltay>[\nodeb`\noded;\labeld]% +\advance\ypos by \deltay% +\morphism(\xpos,\ypos)|\xa|/{#3}/<0,-\deltay>[\nodea`\nodeb;\labela]% +\morphism(\xpos,\ypos)|\xb|/{#4}/<\deltax,-\deltay>[\nodea`\nodec;\labelb]% +\advance\ypos by -\deltay% +\advance\xpos by \deltax% +\morphism(\xpos,\ypos)|\xe|/{#7}/<-\deltax,-\deltay>[\nodec`\noded;\labele]% +\ignorespaces}% + +\def\Atrianglepair{\ifnextchar({\Atrianglepairp}{\Atrianglepairp(0,0)}}% +\def\Atrianglepairp(#1){\ifnextchar|{\Atrianglepairpp(#1)}% +{\Atrianglepairpp(#1)|lmrbb|}}% +\def\Atrianglepairpp(#1)|#2|{\ifnextchar/{\Atrianglepairppp(#1)|#2|}% + {\Atrianglepairppp(#1)|#2|/>`>`>`>`>/}}% +\def\Atrianglepairppp(#1)|#2|/#3`#4`#5`#6`#7/{% + \ifnextchar<{\Atrianglepairpppp(#1)|#2|/#3`#4`#5`#6`#7/}% + {\Atrianglepairpppp(#1)|#2|/#3`#4`#5`#6`#7/<\default,\default>}}% + +\def\Vtrianglepair{\ifnextchar({\Vtrianglepairp}{\Vtrianglepairp(0,0)}}% +\def\Vtrianglepairp(#1){\ifnextchar|{\Vtrianglepairpp(#1)}% +{\Vtrianglepairpp(#1)|aalmr|}}% +\def\Vtrianglepairpp(#1)|#2|{\ifnextchar/{\Vtrianglepairppp(#1)|#2|}% + {\Vtrianglepairppp(#1)|#2|/>`>`>`>`>/}}% +\def\Vtrianglepairppp(#1)|#2|/#3`#4`#5`#6`#7/{% + \ifnextchar<{\Vtrianglepairpppp(#1)|#2|/#3`#4`#5`#6`#7/}% + {\Vtrianglepairpppp(#1)|#2|/#3`#4`#5`#6`#7/<\default,\default>}}% + +\def\Ctrianglepair{\ifnextchar({\Ctrianglepairp}{\Ctrianglepairp(0,0)}}% +\def\Ctrianglepairp(#1){\ifnextchar|{\Ctrianglepairpp(#1)}% +{\Ctrianglepairpp(#1)|lrmlr|}}% +\def\Ctrianglepairpp(#1)|#2|{\ifnextchar/{\Ctrianglepairppp(#1)|#2|}% + {\Ctrianglepairppp(#1)|#2|/>`>`>`>`>/}}% +\def\Ctrianglepairppp(#1)|#2|/#3`#4`#5`#6`#7/{% + \ifnextchar<{\Ctrianglepairpppp(#1)|#2|/#3`#4`#5`#6`#7/}% + {\Ctrianglepairpppp(#1)|#2|/#3`#4`#5`#6`#7/<\default,\default>}}% + +\def\Dtrianglepair{\ifnextchar({\Dtrianglepairp}{\Dtrianglepairp(0,0)}}% +\def\Dtrianglepairp(#1){\ifnextchar|{\Dtrianglepairpp(#1)}% +{\Dtrianglepairpp(#1)|lrmlr|}}% +\def\Dtrianglepairpp(#1)|#2|{\ifnextchar/{\Dtrianglepairppp(#1)|#2|}% + {\Dtrianglepairppp(#1)|#2|/>`>`>`>`>/}}% +\def\Dtrianglepairppp(#1)|#2|/#3`#4`#5`#6`#7/{% + \ifnextchar<{\Dtrianglepairpppp(#1)|#2|/#3`#4`#5`#6`#7/}% + {\Dtrianglepairpppp(#1)|#2|/#3`#4`#5`#6`#7/<\default,\default>}}% + +\def\place(#1,#2)[#3]{\POS(#1,#2)*+!!<0ex,.75ex>{#3}\ignorespaces}% + +\def\pullback#1]#2]{\square#1]\trident#2]\ignorespaces}% + +\def\tridentppp|#1#2#3|/#4`#5`#6/<#7,#8>[#9]{% +\def\next[##1;##2`##3`##4]{\def\nodee{##1}\def\labele{##2}% + \def\labelf{##3}\def\labelg{##4}}% +\next[#9]% +\advance \xpos by -\deltax% +\advance \xpos by -#7\advance \ypos by #8% +\advance\deltax by #7% +\morphism(\xpos,\ypos)|#1|/{#4}/<\deltax,-#8>[\nodee`\nodeb;\labele]% +\advance\deltax by -#7% +\morphism(\xpos,\ypos)|#2|/{#5}/<#7,-#8>[\nodee`\nodea;\labelf]% +\advance\deltay by #8% +\morphism(\xpos,\ypos)|#3|/{#6}/<#7,-\deltay>[\nodee`\nodec;\labelg]% +\ignorespaces}% + +\def\trident{\ifnextchar|{\tridentp}{\tridentp|amb|}}% +\def\tridentp|#1|{\ifnextchar/{\tridentpp|#1|}{\tridentpp|#1|/{>}`{>}`{>}/}}% +\def\tridentpp|#1|/#2/{\ifnextchar<{\tridentppp|#1|/#2/}% + {\tridentppp|#1|/#2/<500,500>}}% + +\def\setmorphismwidth#1#2#3#4{% + \setbox0=\hbox{$#1{\labelstyle#3#3}#2$}#4=\wd0% + \divide #4 by 2 \divide #4 by \ul% + \advance #4 by 350 \ratchet{#4}{500}}% + +\def\setSquarewidth[#1`#2`#3`#4;#5`#6`#7`#8]{% + \setmorphismwidth{#1}{#2}{#5}{\topw}% + \setmorphismwidth{#3}{#4}{#8}{\botw}% +\ratchet{\topw}{\botw}}% + +\def\Squarepppp(#1)|#2|/#3/<#4>[#5]{% + \setSquarewidth[#5]% + \squarepppp(#1)|#2|/#3/<\topw,#4>[#5]% +\ignorespaces}% + +\def\Square{\ifnextchar({\Squarep}{\Squarep(0,0)}}% +\def\Squarep(#1){\ifnextchar|{\Squarepp(#1)}{\Squarepp(#1)|alrb|}}% +\def\Squarepp(#1)|#2|{\ifnextchar/{\Squareppp(#1)|#2|}% + {\Squareppp(#1)|#2|/>`>`>`>/}}% +\def\Squareppp(#1)|#2|/#3`#4`#5`#6/{% + \ifnextchar<{\Squarepppp(#1)|#2|/#3`#4`#5`#6/}% + {\Squarepppp(#1)|#2|/#3`#4`#5`#6/<\default>}}% + +\def\hSquarespppp(#1,#2)|#3|/#4/<#5>[#6;#7]{% +\Xpos=#1\Ypos=#2% +\def\next|##1##2##3##4##5##6##7|{% + \def\Xa{##1}\def\Xb{##2}\def\Xc{##3}\def\Xd{##4}% + \def\Xe{##5}\def\Xf{##6}\def\Xg{##7}}% +\next|#3|% +\deltaY=#5% +\def\next[##1`##2`##3`##4`##5`##6]{% + \def\Nodea{##1}\def\Nodeb{##2}\def\Nodec{##3}% + \def\Noded{##4}\def\Nodee{##5}\def\Nodef{##6}}% +\next[#6]% +\def\next[##1`##2`##3`##4`##5`##6`##7]{% + \def\Labela{##1}\def\Labelb{##2}\def\Labelc{##3}\def\Labeld{##4}% + \def\Labele{##5}\def\Labelf{##6}\def\Labelg{##7}}% +\next[#7]% +\dohSquares/#4/}% + +\def\dohSquares/#1`#2`#3`#4`#5`#6`#7/{% +\Squarepppp(\Xpos,\Ypos)|\Xa\Xc\Xd\Xf|/#1`#3`#4`#6/<\deltaY>% + [\Nodea`\Nodeb`\Noded`\Nodee;\Labela`\Labelc`\Labeld`\Labelf]% + \advance \Xpos by \topw +\Squarepppp(\Xpos,\Ypos)|\Xb\Xd\Xe\Xg|/#2``#5`#7/<\deltaY>% +[\Nodeb`\Nodec`\Nodee`\Nodef;\Labelb``\Labele`\Labelg]% +\ignorespaces}% + +\def\hSquares{\ifnextchar({\hSquaresp}{\hSquaresp(0,0)}}% +\def\hSquaresp(#1){\ifnextchar|{\hSquarespp(#1)}{\hSquarespp% +(#1)|aalmrbb|}}% +\def\hSquarespp(#1)|#2|{\ifnextchar/{\hSquaresppp(#1)|#2|}% + {\hSquaresppp(#1)|#2|/>`>`>`>`>`>`>/}}% +\def\hSquaresppp(#1)|#2|/#3/{% + \ifnextchar<{\hSquarespppp(#1)|#2|/#3/}% + {\hSquarespppp(#1)|#2|/#3/<\default>}}% + +\def\vSquarespppp(#1,#2)|#3|/#4/<#5,#6>[#7;#8]{% +\Xpos=#1\Ypos=#2% +\def\next|##1##2##3##4##5##6##7|{% + \def\Xa{##1}\def\Xb{##2}\def\Xc{##3}\def\Xd{##4}% + \def\Xe{##5}\def\Xf{##6}\def\Xg{##7}}% +\next|#3|% +\deltaX=#5% +\deltaY=#6% +\def\next[##1`##2`##3`##4`##5`##6]{% + \def\Nodea{##1}\def\Nodeb{##2}\def\Nodec{##3}% + \def\Noded{##4}\def\Nodee{##5}\def\Nodef{##6}}% +\next[#7]% +\def\next[##1`##2`##3`##4`##5`##6`##7]{% + \def\Labela{##1}\def\Labelb{##2}\def\Labelc{##3}\def\Labeld{##4}% + \def\Labele{##5}\def\Labelf{##6}\def\Labelg{##7}}% +\next[#8]% +\dovSquares/#4/\ignorespaces}% + +\def\dovSquares/#1`#2`#3`#4`#5`#6`#7/{% +\setmorphismwidth{\Nodea}{\Nodeb}{\Labela}{\topw}% +\setmorphismwidth{\Nodec}{\Noded}{\Labeld}{\botw}% +\ratchet{\topw}{\botw}% +\setmorphismwidth{\Nodee}{\Nodef}{\Labelg}{\botw}% +\ratchet{\topw}{\botw}% +\square(\Xpos,\Ypos)|\Xd\Xe\Xf\Xg|/`#5`#6`#7/<\topw,\deltaX>% + [\Nodec`\Noded`\Nodee`\Nodef;`\Labele`\Labelf`\Labelg]% +\advance \Ypos by \deltaX% +\square(\Xpos,\Ypos)|\Xa\Xb\Xc\Xd|/#1`#2`#3`#4/<\topw,\deltaY>% + [\Nodea`\Nodeb`\Nodec`\Noded;\Labela`\Labelb`\Labelc`\Labeld]% +}% + +\def\vSquares{\ifnextchar({\vSquaresp}{\vSquaresp(0,0)}}% +\def\vSquaresp(#1){\ifnextchar|{\vSquarespp(#1)}{\vSquarespp% +(#1)|alrmlrb|}}% +\def\vSquarespp(#1)|#2|{\ifnextchar/{\vSquaresppp(#1)|#2|}% + {\vSquaresppp(#1)|#2|/>`>`>`>`>`>`>/}}% +\def\vSquaresppp(#1)|#2|/#3/{% + \ifnextchar<{\vSquarespppp(#1)|#2|/#3/}% + {\vSquarespppp(#1)|#2|/#3/<\default,\default>}}% + +\def\osquarepppp(#1)|#2|/#3`#4`#5`#6/<#7>[#8]{\squarepppp% + (#1)|#2|/#3`#4`#5`#6/<#7>[#8]% + \let\Nodea\nodea\let\Nodeb\nodeb% +\let\Nodec\nodec\let\Noded\noded\Xpos=\xpos\Ypos=\ypos% +\deltaX=\deltax \deltaY=\deltay \isquare} + +\def\cube{\ifnextchar({\osquarep}{\osquarep(0,0)}}% +\def\osquarep(#1){\ifnextchar|{\osquarepp(#1)}{\osquarepp(#1)|alrb|}}% +\def\osquarepp(#1)|#2|{\ifnextchar/{\osquareppp(#1)|#2|}% + {\osquareppp(#1)|#2|/>`>`>`>/}}% +\def\osquareppp(#1)|#2|/#3`#4`#5`#6/{% + \ifnextchar<{\osquarepppp(#1)|#2|/#3`#4`#5`#6/}% + {\osquarepppp(#1)|#2|/#3`#4`#5`#6/<1500,1500>}}% + +\def\isquarepppp(#1)|#2|/#3`#4`#5`#6/<#7>[#8]{% + \squarepppp(#1)|#2|/#3`#4`#5`#6/<#7>[#8]% +\ifnextchar|{\cubep}{\cubep|mmmm|}}% +\def\cubep|#1|{\ifnextchar/{\cubepp|#1|}{\cubepp|#1|/>`>`>`>/}}% + +\def\isquare{\ifnextchar({\isquarep}{\isquarep(\default,\default)}}% +\def\isquarep(#1){\ifnextchar|{\isquarepp(#1)}{\isquarepp(#1)|alrb|}} +\def\isquarepp(#1)|#2|{\ifnextchar/{\isquareppp(#1)|#2|}% + {\isquareppp(#1)|#2|/>`>`>`>/}}% +\def\isquareppp(#1)|#2|/#3`#4`#5`#6/{% + \ifnextchar<{\isquarepppp(#1)|#2|/#3`#4`#5`#6/}% + {\isquarepppp(#1)|#2|/#3`#4`#5`#6/<500,500>}}% + +\def\cubepp|#1#2#3#4|/#5`#6`#7`#8/[#9]{% +\def\next[##1`##2`##3`##4]{\gdef\Labela{##1}% +\gdef\Labelb{##2}\gdef\Labelc{##3}\gdef\Labeld{##4}}\next[#9]% +\xend\xpos \yend\ypos +\Xend\xend\advance\Xend by -\Xpos +\Yend\yend\advance\Yend by -\Ypos +\domorphism(\Xpos,\Ypos)|#2|/#6/<\Xend,\Yend>[\Nodeb`\nodeb;\Labelb]% +\advance\Xpos by-\deltaX +\advance\xend by-\deltax +\Xend\xend\advance\Xend by -\Xpos +\domorphism(\Xpos,\Ypos)|#1|/#5/<\Xend,\Yend>[\Nodea`\nodea;\Labela]% +\advance\Ypos by-\deltaY +\advance\yend by-\deltay +\Yend\yend\advance\Yend by -\Ypos +\domorphism(\Xpos,\Ypos)|#3|/#7/<\Xend,\Yend>[\Nodec`\nodec;\Labelc]% +\advance\Xpos by\deltaX +\advance\xend by\deltax +\Xend\xend\advance\Xend by -\Xpos +\domorphism(\Xpos,\Ypos)|#4|/#8/<\Xend,\Yend>[\Noded`\noded;\Labeld]% +\ignorespaces} + +\def\setwdth#1#2{\setbox0\hbox{$\labelstyle#1$}\wdth=\wd0 +\setbox0\hbox{$\labelstyle#2$}\ifnum\wdth<\wd0 \wdth=\wd0 \fi} + +\def\topppp/#1/<#2>^#3_#4{\allowbreak\mathrel{% +\ifnum#2=0 + \setwdth{#3}{#4}\deltax=\wdth \divide \deltax by \ul + \advance \deltax by \defaultmargin \ratchet{\deltax}{200}% +\else \deltax #2 +\fi +\xy\ar@{#1}^{#3}_{#4}(\deltax,0) \endxy +\ignorespaces}} + +\def\toppp/#1/<#2>^#3{\ifnextchar_{\topppp/#1/<#2>^{#3}}{\topppp/#1/<#2>^{#3}_{}}} +\def\topp/#1/<#2>{\ifnextchar^{\toppp/#1/<#2>}{\toppp/#1/<#2>^{}}} +\def\top/#1/{\ifnextchar<{\topp/#1/}{\topp/#1/<0>}} +\def\to{\ifnextchar/{\top}{\top/>/}} + +\def\mon{\to/ >->/} +\def\epi{\to/->>/} +\def\toleft{\to/<-/} +\def\monleft{\to/<-< /} +\def\epileft{\to/<<-/} + + +\def\twopppp/#1`#2/<#3>^#4_#5{\allowbreak\mathrel{% +\ifnum0=#3 + \setwdth{#4}{#5}\deltax=\wdth \divide \deltax by \ul \advance \deltax + by \defaultmargin \ratchet{\deltax}{200}% +\else \deltax#3 \fi +\xy\ar@{#1}@<2.5pt>^{#4}(\deltax,0)% +\ar@{#2}@<-2.5pt>_{#5}(\deltax,0)\endxy\ignorespaces}} + +\def\twoppp/#1`#2/<#3>^#4{\ifnextchar_{\twopppp/#1`#2/<#3>^{#4}}% + {\twopppp/#1`#2/<#3>^{#4}_{}}} +\def\twopp/#1`#2/<#3>{\ifnextchar^{\twoppp/#1`#2/<#3>}{\twoppp/#1`#2/<#3>^{}}} +\def\twop/#1`#2/{\ifnextchar<{\twopp/#1`#2/}{\twopp/#1`#2/<0>}} +\def\two{\ifnextchar/{\twop}{\twop/>`>/}} + +\def\twoleft{\two/<-`<-/} + +\def\threeppppp/#1`#2`#3/<#4>^#5|#6_#7{\allowbreak\mathrel{% +\ifnum0=#4 +\setbox0\hbox{$\labelstyle#5$}\wdth=\wd0 +\setbox0\hbox{$\labelstyle#6$}\ifnum\wdth<\wd0 \wdth=\wd0 \fi +\setbox0\hbox{$\labelstyle#7$}\ifnum\wdth<\wd0 \wdth=\wd0 \fi +\deltax=\wdth \divide \deltax by \ul \advance \deltax by +\defaultmargin \ratchet{\deltax}{300}% +\else\deltax#4 \fi + \xy \ifnum\wd0=0 \ar@{#2}(\deltax,0) + \else \ar@{#2}|{#6}(\deltax,0)\fi +\ar@{#1}@<4.5pt>^{#5}(\deltax,0) +\ar@{#3}@<-4.5pt>_{#7}(\deltax,0)\endxy\ignorespaces}} + +\def\threepppp/#1`#2`#3/<#4>^#5|#6{\ifnextchar_{\threeppppp + /#1`#2`#3/<#4>^{#5}|{#6}}{\threeppppp/#1`#2`#3/<#4>^{#5}|{#6}_{}}} +\def\threeppp/#1`#2`#3/<#4>^#5{\ifnextchar|{\threepppp + /#1`#2`#3/<#4>^{#5}}{\threepppp/#1`#2`#3/<#4>^{#5}|{}}} +\def\threepp/#1`#2`#3/<#4>{\ifnextchar^{\threeppp/#1`#2`#3/<#4>}% + {\threeppp/#1`#2`#3/<#4>^{}}} +\def\threep/#1`#2`#3/{\ifnextchar<{\threepp/#1`#2`#3/}% + {\threepp/#1`#2`#3/<0>}} +\def\three{\ifnextchar/{\threep}{\threep/>`>`>/}} + + +\def\twoar(#1,#2){{% + \scalefactor{0.1} + \deltax#1\deltay#2% + \deltaX=\ifnum\deltax<0-\fi\deltax + \deltaY=\ifnum\deltay<0-\fi\deltay + \Xend\deltax \multiply \Xend by \deltax + \Yend\deltay \multiply \Yend by \deltay + \advance\Xend by \Yend \multiply \Xend by 3 + \ifnum \deltaX > \deltaY + \multiply \deltaX by 3 \advance \deltaX by \deltaY + \else + \multiply \deltaY by 3 \advance \deltaX by \deltaY + \fi + \multiply\deltax by 500 + \multiply\deltay by 500 + \xpos\deltax \multiply \xpos by 3 \divide\xpos by \deltaX + \Xpos\deltax \multiply \Xpos by \deltaX \divide \Xpos by \Xend + \advance \xpos by \Xpos + \ypos\deltay \multiply \ypos by 3 \divide\ypos by \deltaX + \Ypos\deltay \multiply \Ypos by \deltaX \divide \Ypos by \Xend + \advance \ypos by \Ypos + \xy \ar@{=>}(\xpos,\ypos) \endxy +}\ignorespaces} + +\def\iiixiiipppppp(#1,#2)|#3|/#4/<#5>#6<#7>[#8;#9]{% + \xpos#1\ypos#2\relax + \def\next|##1##2##3##4##5##6##7|{\def\xa{##1}\def\xb{##2}% + \def\xc{##3}\def\xd{##4}\def\xe{##5}\def\xf{##6}\nextt|##7|}% + \def\nextt|##1##2##3##4##5##6|{\def\xg{##1}\def\xh{##2}% + \def\xi{##3}\def\xj{##4}\def\xk{##5}\def\xl{##6}}% + \next|#3|% + \def\next<##1,##2>{\deltax##1\deltay##2}% + \next<#5>% + \def\next<##1,##2>{\deltaX##1\deltaY##2}% + \next<#7>% + \def\next##1{\topw##1\relax + \ifodd\topw \def\zl{}\else\def\zl{\relax}\fi \divide\topw by 2 + \ifodd\topw \def\zk{}\else\def\zk{\relax}\fi \divide\topw by 2 + \ifodd\topw \def\zj{}\else\def\zj{\relax}\fi \divide\topw by 2 + \ifodd\topw \def\zi{}\else\def\zi{\relax}\fi \divide\topw by 2 + \ifodd\topw \def\zh{}\else\def\zh{\relax}\fi \divide\topw by 2 + \ifodd\topw \def\zg{}\else\def\zg{\relax}\fi \divide\topw by 2 + \ifodd\topw \def\zf{}\else\def\zf{\relax}\fi \divide\topw by 2 + \ifodd\topw \def\ze{}\else\def\ze{\relax}\fi \divide\topw by 2 + \ifodd\topw \def\zd{}\else\def\zd{\relax}\fi \divide\topw by 2 + \ifodd\topw \def\zc{}\else\def\zc{\relax}\fi \divide\topw by 2 + \ifodd\topw \def\zb{}\else\def\zb{\relax}\fi \divide\topw by 2 + \ifodd\topw \def\za{}\else\def\za{\relax}\fi}% + \next{#6}% + \def\next[##1`##2`##3`##4`##5`##6`##7`##8`##9]{% + \def\nodea{##1}\def\nodeb{##2}\def\nodec{##3}% + \def\noded{##4}\def\nodee{##5}\def\nodef{##6}% + \def\nodeg{##7}\def\nodeh{##8}\def\nodei{##9}}% + \next[#8]% + \def\next[##1`##2`##3`##4`##5`##6`##7]{% + \def\labela{##1}\def\labelb{##2}\def\labelc{##3}% + \def\labeld{##4}\def\labele{##5}\def\labelf{##6}\nextt[##7]}% + \def\nextt[##1`##2`##3`##4`##5`##6]{% + \def\labelg{##1}\def\labelh{##2}\def\labeli{##3}% + \def\labelj{##4}\def\labelk{##5}\def\labell{##6}}% + \next[#9]% + \def\next/##1`##2`##3`##4`##5`##6`##7/{% +\morphism(\xpos,\ypos)|\xe|/{##5}/<\deltax,0>[\nodeg`\nodeh;\labele]% + \ifx\zi\empty\relax \morphism(\xpos,\ypos)||/<-/<-\deltaX,0>[\nodeg`0;]\fi + \ifx\zd\empty\relax \morphism(\xpos,\ypos)||<0,-\deltaY>[\nodeg`0;]\fi + \advance\xpos by \deltax + \morphism(\xpos,\ypos)|\xf|/{##6}/<\deltax,0>[\nodeh`\nodei;\labelf]% + \ifx\ze\empty\relax \morphism(\xpos,\ypos)||<0,-\deltaY>[\nodeh`0;]\fi + \advance\xpos by \deltax + \ifx\zf\empty\relax \morphism(\xpos,\ypos)||<0,-\deltaY>[\nodei`0;]\fi + \ifx\zl\empty\relax \morphism(\xpos,\ypos)||<\deltaX,0>[\nodei`0;]\fi + \advance\ypos by \deltay + \ifx\zk\empty\relax \morphism(\xpos,\ypos)||<\deltaX,0>[\nodef`0;]\fi + \advance\xpos by -\deltax + \morphism(\xpos,\ypos)|\xd|/{##4}/<\deltax,0>[\nodee`\nodef;\labeld]% + \advance\xpos by -\deltax + \morphism(\xpos,\ypos)|\xc|/{##3}/<\deltax,0>[\noded`\nodee;\labelc]% + \ifx\zh\empty\relax \morphism(\xpos,\ypos)||/<-/<-\deltaX,0>[\noded`0;]\fi + \advance\ypos by \deltay + \morphism(\xpos,\ypos)|\xa|/{##1}/<\deltax,0>[\nodea`\nodeb;\labela]% + \ifx\zg\empty\relax \morphism(\xpos,\ypos)||/<-/<-\deltaX,0>[\nodea`0;]\fi + \ifx\za\empty\relax \morphism(\xpos,\ypos)||/<-/<0,\deltaY>[\nodea`0;]\fi + \advance\xpos by \deltax + \morphism(\xpos,\ypos)|\xb|/{##2}/<\deltax,0>[\nodeb`\nodec;\labelb]% + \ifx\zb\empty\relax \morphism(\xpos,\ypos)||/<-/<0,\deltaY>[\nodeb`0;]\fi + \advance\xpos by \deltax + \ifx\zc\empty\relax \morphism(\xpos,\ypos)||/<-/<0,\deltaY>[\nodec`0;]\fi + \ifx\zj\empty\relax \morphism(\xpos,\ypos)||<\deltaX,0>[\nodec`0;]\fi + \nextt/##7/}% + \def\nextt/##1`##2`##3`##4`##5`##6/{% + \morphism(\xpos,\ypos)|\xi|/{##3}/<0,-\deltay>[\nodec`\nodef;\labeli]% + \advance\xpos by -\deltax + \morphism(\xpos,\ypos)|\xh|/{##2}/<0,-\deltay>[\nodeb`\nodee;\labelh]% + \advance\xpos by -\deltax + \morphism(\xpos,\ypos)|\xg|/{##1}/<0,-\deltay>[\nodea`\noded;\labelg]% + \advance\ypos by -\deltay + \morphism(\xpos,\ypos)|\xj|/{##4}/<0,-\deltay>[\noded`\nodeg;\labelj]% + \advance\xpos by \deltax + \morphism(\xpos,\ypos)|\xk|/{##5}/<0,-\deltay>[\nodee`\nodeh;\labelk]% + \advance\xpos by \deltax + \morphism(\xpos,\ypos)|\xl|/{##6}/<0,-\deltay>[\nodef`\nodei;\labell]}% + \next/#4/\ignorespaces} + +\def\iiixiii{\ifnextchar({\iiixiiip}{\iiixiiip(0,0)}}% +\def\iiixiiip(#1){\ifnextchar|{\iiixiiipp(#1)}% + {\iiixiiipp(#1)|aammbblmrlmr|}}% +\def\iiixiiipp(#1)|#2|{\ifnextchar/{\iiixiiippp(#1)|#2|}% + {\iiixiiippp(#1)|#2|/>`>`>`>`>`>`>`>`>`>`>`>/}}% +\def\iiixiiippp(#1)|#2|/#3/{% + \ifnextchar<{\iiixiiipppp(#1)|#2|/#3/}% + {\iiixiiipppp(#1)|#2|/#3/<\default,\default>}}% +\def\iiixiiipppp(#1)|#2|/#3/<#4>{\ifnextchar[{\iiixiiippppp(#1)|#2|/#3/% + <#4>0<0,0>}{\iiixiiippppp(#1)|#2|/#3/<#4>}}% +\def\iiixiiippppp(#1)|#2|/#3/<#4>#5{\ifnextchar<% + {\iiixiiipppppp(#1)|#2|/#3/<#4>{#5}}% + {\iiixiiipppppp(#1)|#2|/#3/<#4>{#5}<400,400>}}% + +\def\iiixiipppppp(#1,#2)|#3|/#4/<#5>#6<#7>[#8;#9]{% + \xpos#1\ypos#2\relax + \def\next|##1##2##3##4##5##6##7|{\def\xa{##1}\def\xb{##2}% + \def\xc{##3}\def\xd{##4}\def\xe{##5}\def\xf{##6}\def\xg{##7}}% + \next|#3|% + \def\next<##1,##2>{\deltax##1\deltay##2}% + \next<#5>% + \deltaX#7 + \topw#6 + \def\next{% + \ifodd\topw \def\zd{}\else\def\zd{\relax}\fi \divide\topw by 2 + \ifodd\topw \def\zc{}\else\def\zc{\relax}\fi \divide\topw by 2 + \ifodd\topw \def\zb{}\else\def\zb{\relax}\fi \divide\topw by 2 + \ifodd\topw \def\za{}\else\def\za{\relax}\fi}% + \next + \def\next[##1`##2`##3`##4`##5`##6]{% + \def\nodea{##1}\def\nodeb{##2}\def\nodec{##3}% + \def\noded{##4}\def\nodee{##5}\def\nodef{##6}}% + \next[#8]% + \def\next[##1`##2`##3`##4`##5`##6`##7]{% + \def\labela{##1}\def\labelb{##2}\def\labelc{##3}% + \def\labeld{##4}\def\labele{##5}\def\labelf{##6}\def\labelg{##7}}% + \next[#9]% + \def\next/##1`##2`##3`##4`##5`##6`##7/{% + \ifx\zc\empty\relax\morphism(\xpos,\ypos)<\deltaX,0>[0`\noded;]\fi + \advance\xpos by\deltaX + \morphism(\xpos,\ypos)|\xc|/##3/<\deltax,0>[\noded`\nodee;\labelc]% + \advance\xpos by \deltax + \morphism(\xpos,\ypos)|\xd|/##4/<\deltax,0>[\nodee`\nodef;\labeld]% + \advance\xpos by \deltax + \ifx\zd\empty\relax \morphism(\xpos,\ypos)<\deltaX,0>[\nodef`0;]\fi + \advance\xpos by -\deltaX \advance\xpos by -\deltax + \advance\xpos by -\deltax \advance\ypos by \deltay + \ifx\za\empty\relax\morphism(\xpos,\ypos)<\deltaX,0>[0`\nodea;]\fi + \advance\xpos by\deltaX + \morphism(\xpos,\ypos)|\xa|/##1/<\deltax,0>[\nodea`\nodeb;\labela]% + \morphism(\xpos,\ypos)|\xe|/##5/<0,-\deltay>[\nodea`\noded;\labele]% + \advance\xpos by \deltax + \morphism(\xpos,\ypos)|\xb|/##2/<\deltax,0>[\nodeb`\nodec;\labelb]% + \morphism(\xpos,\ypos)|\xf|/##6/<0,-\deltay>[\nodeb`\nodee;\labelf]% + \advance\xpos by \deltax + \morphism(\xpos,\ypos)|\xg|/##7/<0,-\deltay>[\nodec`\nodef;\labelg]% + \ifx\zb\empty\relax \morphism(\xpos,\ypos)<\deltaX,0>[\nodec`0;]\fi}% + \next/#4/\ignorespaces} + + +\def\iiixii{\ifnextchar({\iiixiip}{\iiixiip(0,0)}}% +\def\iiixiip(#1){\ifnextchar|{\iiixiipp(#1)}% + {\iiixiipp(#1)|aabblmr|}}% +\def\iiixiipp(#1)|#2|{\ifnextchar/{\iiixiippp(#1)|#2|}% + {\iiixiippp(#1)|#2|/>`>`>`>`>`>`>/}}% +\def\iiixiippp(#1)|#2|/#3/{% + \ifnextchar<{\iiixiipppp(#1)|#2|/#3/}% + {\iiixiipppp(#1)|#2|/#3/<\default,\default>}}% +\def\iiixiipppp(#1)|#2|/#3/<#4>{\ifnextchar[{\iiixiippppp(#1)|#2|/#3/% + <#4>{0}<0>}{\iiixiippppp(#1)|#2|/#3/<#4>}}% +\def\iiixiippppp(#1)|#2|/#3/<#4>#5{\ifnextchar<% + {\iiixiipppppp(#1)|#2|/#3/<#4>{#5}}% + {\iiixiipppppp(#1)|#2|/#3/<#4>{#5}<0>}}% + +\catcode`\@=\atcode% +\endinput |