% a manual is available from CTAN and http://www.math.ksu.edu/~lub/ % \usepackage[emtex]{t-angles} % for emtex drivers, dviwin, dvips, yap or % \usepackage{t-angles} = \usepackage[TPIC]{t-angles} % % for TPIC drivers such as dviwin, xdvi, dvips, yap, dvipdfm % \usepackage[kluwer]{t-angles} or \usepackage[emtex,kluwer]{t-angles} % % to use with kluwer.cls %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % % This is file t-angles.sty ( version 14.08.2006 ) % % % % Diagram macros for tangles and braided Hopf algebras % % % % (Yu. Bespalov, V. Lyubashenko) % % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Copyright (C) 2006 Yu. Bespalov, V. Lyubashenko % This program is free software; you can redistribute it and/or modify % it under the terms of the GNU General Public License as published by % the Free Software Foundation. \RequirePackage{ifpdf} \newcount{\hstretch} \hstretch 100 \newcount{\vstretch} \vstretch 100 \newlength{\unitlens} \unitlens 10pt \def\FillCircDiam{3} \DeclareOption{pdflatex}{% %% Hans Hagen's CONTEXT Support Macros from supp-emp.tex \def\EMmoveto% {\EMgetposition\EMlastmovex\EMlastmovey} \def\EMlinewd{.4} \def\EMlineto% {\bgroup \EMgetposition\EMlastlinex\EMlastliney \count0=\EMlastmovex \advance\count0 by -\EMlastlinex \count2=\EMlastmovey \advance\count2 by -\EMlastliney \ifnum\count0>0 %this \ifnum is added by VL \advance\count0 32768 \else \advance\count0 -32768 \fi \ifnum\count2>0 %this \ifnum is added by VL \advance\count2 32768 \else \advance\count2 -32768 \fi \divide\count0 by 65536 \divide\count2 by 65536 \pdfliteral{\EMlinewd\space w 0 0 m \the\count0 \space\the\count2 \space l S}% \global\let\EMlastmovex\EMlastlinex \global\let\EMlastmovey\EMlastliney \egroup} \def\resetEMspecials% {\gdef\EMlastmovex{0}\gdef\EMlastmovey{0}} \def\EMgetposition#1#2% {\bgroup \pdfsavepos \global\advance\EMcounter by 1 \expandafter\write\expandafter\EMfile\expandafter {\expandafter\noexpand\expandafter\EMsetpos\number\EMcounter \space\number\pdflastxpos\space\number\pdflastypos}% \EMsetcounters \xdef#1{\the\count0}% \xdef#2{\the\count2}% \egroup} \newcount\EMcounter \newwrite\EMfile \def\EMfilename{\jobname.emp} \def\startEMspecials% {\resetEMspecials \openin\scratchread=\EMfilename \relax \ifeof\scratchread\else \input \EMfilename \relax \fi \closein\scratchread \immediate\openout\EMfile=\EMfilename\relax} \def\stopEMspecials% {\closeout\EMfile} \ifx\undefined\scratchread \newread\scratchread \fi \def\EMsetpos#1 #2 #3 % number x y {\expandafter\xdef\csname EM:#1\endcsname{\count0=#2 \count2=#3}} \def\EMsetcounters% {\count0=0 \count2=0 \csname EM:\the\EMcounter\endcsname} %% end of macros "EMTEX specials to PDF conversion" \gdef\thinlines{\let\@linefnt\tenln \let\@circlefnt\tencirc \@wholewidth\fontdimen8\tenln \@halfwidth .5\@wholewidth \def\EMlinewd{0.4}} %\@wholewidth=0.4pt \gdef\thicklines{\let\@linefnt\tenlnw \let\@circlefnt\tencircw \@wholewidth\fontdimen8\tenlnw \@halfwidth .5\@wholewidth \def\EMlinewd{0.8}} %\@wholewidth=0.8pt \def\emline#1#2#3#4#5#6{% \put(#1,#2){\EMmoveto}% \put(#4,#5){\EMlineto}}% \def\drawpath#1#2#3#4{\emline{#1}{#2}1{#3}{#4}2} % graphics for *.lp } % \DeclareOption{emtex}{% \ifpdf \ExecuteOptions{pdflatex} \else \gdef\thinlines{\let\@linefnt\tenln \let\@circlefnt\tencirc \@wholewidth\fontdimen8\tenln \@halfwidth .5\@wholewidth \special{em:linewidth \the\@wholewidth}} %\@wholewidth=0.4pt \gdef\thicklines{\let\@linefnt\tenlnw \let\@circlefnt\tencircw \@wholewidth\fontdimen8\tenlnw \@halfwidth .5\@wholewidth \special{em:linewidth \the\@wholewidth}} %\@wholewidth=0.8pt \def\emline#1#2#3#4#5#6{% \put(#1,#2){\special{em:moveto}}% \put(#4,#5){\special{em:lineto}}}% \def\drawpath#1#2#3#4{\emline{#1}{#2}1{#3}{#4}2} % graphics for *.lp \fi} % \newcount\@gphlinewidth % \DeclareOption{TPIC}{% \ifpdf \ExecuteOptions{pdflatex} \else \@gphlinewidth\@wholewidth \divide\@gphlinewidth 4736 \advance\@gphlinewidth\@ne %\@gphlinewidth=6 \gdef\thinlines{\let\@linefnt\tenln \let\@circlefnt\tencirc \@wholewidth\fontdimen8\tenln \@halfwidth .5\@wholewidth \@gphlinewidth\@wholewidth \divide\@gphlinewidth 4736 \advance\@gphlinewidth\@ne} %\@gphlinewidth=6 \gdef\thicklines{\let\@linefnt\tenlnw \let\@circlefnt\tencircw \@wholewidth\fontdimen8\tenlnw \@halfwidth .5\@wholewidth \@gphlinewidth\@wholewidth \divide\@gphlinewidth 4736} %\@gphlinewidth=11 \def\@paspecial#1#2{% \special{pa #1 #2}} \def\path(#1,#2){% \special{pn \the\@gphlinewidth}% \@path(#1,#2)} \def\@path(#1,#2){% \@tempdima #1\unitlength \@tempdimb #2\unitlength \@tempcnta \@tempdima \advance\@tempcnta 2368 \divide\@tempcnta 4736 \@tempcntb -\@tempdimb \advance\@tempcntb -2368 \divide\@tempcntb 4736 \@paspecial{\the\@tempcnta}{\the\@tempcntb}% \@ifnextchar ({\@path}{\special{fp}}} \providecommand{\drawpath}[4]{\path(#1,#2)(#3,#4)} % TPIC graphics for *.lp \providecommand{\emline}[6]{\path(#1,#2)(#4,#5)} % TPIC graphics for *.pic \fi} % \DeclareOption{kluwer}{% \def\tangle{\begingroup\let\hline\savehline\t@ngle\array{l}} \def\tanglec{\begingroup\let\hline\savehline\t@ngle\array{c}} \def\tangler{\begingroup\let\hline\savehline\t@ngle\array{r}} \def\tangles{\begingroup\let\hline\savehline\t@ngle\array} } % \ExecuteOptions{TPIC} \newcount{\h@r} \newcount{\v@r} \newcount{\h@z} \newcount{\v@t} \newlength{\unith} \newlength{\unitv} \newlength{\textwd} % \let\kilglu\@killglue % \def\@step[#1]{\unith\unitlens \divide\unith 1000 \multiply\unith 10 \multiply\unith\hstretch \@killglue\kern #1\unith} \def\step{\@ifnextchar[{\@step}{\@step[1]}} \def\hhstep{\step[-.5]} \def\hstep{\step[.5]} \def\Step{\step[2]} % \def\object#1{\settowidth{\textwd}{${#1}$} \hbox{\put(0,0){\kern -.5\textwd${#1}$}\hss}} % \def\t@ngl@{% \gdef\hm@dehalf{1}\gdef\hm@de{2}\gdef\hm@defives{10}\gdef\hm@detens{20} \gdef\hm@dethree{7}\gdef\hm@deseven{13}\gdef\hm@defiveteen{15}} % \def\t@ngle{\t@ngl@ \gdef\above@bjectskip{0pt}\gdef\below@bjectskip{4pt} % \def\object##1{{\settowidth{\textwd}{${##1}$} \@killglue\setbox0=\hbox{\kern -.5\textwd${##1}$}% \unith\ht0\unitv\dp0% \advance\unith\above@bjectskip\advance\unitv\below@bjectskip% \ht0=\unith\dp0=\unitv\wd0=0pt\box0}} % \unitlength\unitlens\divide\unitlength 1000 \unith\unitlength \multiply\unith10 \multiply\unith\hstretch \unitv\unitlength \multiply\unitv10 \multiply\unitv\vstretch \def\@step[##1]{\@killglue\kern ##1\unith} % \def\hbx(##1,##2)##3{% \@killglue\setbox0=\hbox{##3}\ht0=##2\unitv\dp0=0pt\wd0=##1\unith\box0} \def\hln##1{\hbx(##1,0){\hbox to ##1\unith{\hrulefill}}} % \def\hstr##1{\unith\unitlength \multiply\unith10 \hstretch ##1 \multiply\unith\hstretch} \def\vstr##1{\unitv\unitlength \multiply\unitv10 \vstretch ##1 \multiply\unitv\vstretch} % \def\c@@rds(##1,##2,##3,##4){% \h@r\hstretch\v@r\vstretch\h@z\hstretch\v@t\vstretch% \multiply\h@r ##1 \multiply\v@r ##2 \multiply\h@z ##3 \multiply\v@t ##4% \put(\h@r,\v@r)} \def\EMl@ne(##1,##2,##3,##4){% \h@r\hstretch\v@r\vstretch\h@z\hstretch\v@t\vstretch% \multiply\h@r ##1 \multiply\v@r ##2 \multiply\h@z ##3 \multiply\v@t ##4% \emline{\h@r}{\v@r}1{\h@z}{\v@t}2} % % N O D E S A N D L I N E S \def\id{\hbx(0,\hm@de){\c@@rds(0,0,0,\hm@detens){\line(0,1){\v@t}}}} \def\idash{\hbx(0,2){\c@@rds(0,0,0,3){\line(0,1){\v@t}}% \c@@rds(0,5,0,2){\line(0,1){\v@t}}\c@@rds(0,9,0,2){\line(0,1){\v@t}}% \c@@rds(0,13,0,2){\line(0,1){\v@t}}\c@@rds(0,17,0,3){\line(0,1){\v@t}}}} \def\node{\hbx(0,0){\c@@rds(0,0,\FillCircDiam,0){\circle*{\h@z}}}} \def\n{\hbx(0,\hm@de){\c@@rds(0,0,0,\hm@detens){\line(0,1){\v@t}}% \c@@rds(0,0,\FillCircDiam,0){\circle*{\h@z}}}} \def\s{\hbx(0,\hm@de){\c@@rds(0,0,0,\hm@detens){\line(0,1){\v@t}}% \c@@rds(0,\hm@detens,\FillCircDiam,0){\circle*{\h@z}}}} \def\unit{\hbx(0,\hm@de){\c@@rds(0,0,0,10){\line(0,1){\v@t}}% \c@@rds(0,12,4,0){\circle{\h@z}}}} \def\counit{\hbx(0,\hm@de){\c@@rds(0,10,0,10){\line(0,1){\v@t}}% \c@@rds(0,8,4,0){\circle{\h@z}}}} % %%%% ARGUMENT OF \ne,\nw,\se,\sw,\ned,\nwd,\sed,\swd IS 0,1,2,3 OR 4; %%%% 0 PRODUCES EMPTY BOX AND %%%% OTHER PRODUCE LINES WITH HORIZONTAL PROJECTIONS =##1 \def\@nsew##1##2##3##4##5{\hbx(1,\hm@de){\ifcase##1 \or\EMl@ne(##2)\or\EMl@ne(##3)\or\EMl@ne(##4)\or\EMl@ne(##5)\fi}} \def\ne##1{\@nsew{##1}{0,0,10,\hm@detens}{-10,0,10,\hm@detens}% {-20,0,10,\hm@detens}{-30,0,10,\hm@detens}} \def\nw##1{\@nsew{##1}{0,\hm@detens,10,0}{0,\hm@detens,20,0}% {0,\hm@detens,30,0}{0,\hm@detens,40,0}} \def\se##1{\@nsew{##1}{10,0,0,\hm@detens}{10,0,-10,\hm@detens}% {10,0,-20,\hm@detens}{10,0,-30,\hm@detens}} \def\sw##1{\@nsew{##1}{0,0,10,\hm@detens}{0,0,20,\hm@detens}% {0,0,30,\hm@detens}{0,0,40,\hm@detens}} % \def\nd{\hbx(0,2){\c@@rds(0,0,0,3){\line(0,1){\v@t}}% \c@@rds(0,5,0,2){\line(0,1){\v@t}}\c@@rds(0,9,0,2){\line(0,1){\v@t}}% \c@@rds(0,13,0,2){\line(0,1){\v@t}}\c@@rds(0,17,0,3){\line(0,1){\v@t}}% \c@@rds(0,0,\FillCircDiam,0){\circle*{\h@z}}}} \def\ned##1{\hbx(1,2){\ifcase##1\or% \EMl@ne(0,0,1,2)\EMl@ne(2,4,4,8)\EMl@ne(5,10,7,14)\EMl@ne(8,16,10,20)\or% \EMl@ne(-10,0,-7,3)\EMl@ne(-5,5,-3,7)\EMl@ne(-1,9,1,11)% \EMl@ne(3,13,5,15)\EMl@ne(7,17,10,20)\or% \EMl@ne(-20,0,-14,4)\EMl@ne(-11,6,-8,8)\EMl@ne(-5,10,-2,12) \EMl@ne(1,14,4,16)\EMl@ne(7,18,10,20)\or% \EMl@ne(-30,0,-26,2)\EMl@ne(-24,3,-20,5)\EMl@ne(-18,6,-14,8)% \EMl@ne(-12,9,-8,11)\EMl@ne(-6,12,-2,14)\EMl@ne(0,15,4,17)% \EMl@ne(6,18,10,20)\fi}} \def\nwd##1{\hbx(1,2){\ifcase##1\or% \EMl@ne(0,20,2,16)\EMl@ne(3,14,5,10)\EMl@ne(6,8,8,4)\EMl@ne(9,2,10,0)\or% \EMl@ne(0,20,3,17)\EMl@ne(5,15,7,13)\EMl@ne(9,11,11,9)% \EMl@ne(13,7,15,5)\EMl@ne(17,3,20,0)\or% \EMl@ne(0,20,3,18)\EMl@ne(6,16,9,14)\EMl@ne(12,12,15,10)% \EMl@ne(18,8,21,6)\EMl@ne(24,4,30,0)\or% \EMl@ne(0,20,4,18)\EMl@ne(6,17,10,15)\EMl@ne(12,14,16,12)\EMl@ne(18,11,22,9)% \EMl@ne(24,8,28,6)\EMl@ne(30,5,34,3)\EMl@ne(36,2,40,0)\fi}} \def\sd{\hbx(0,2){\c@@rds(0,0,0,3){\line(0,1){\v@t}}% \c@@rds(0,5,0,2){\line(0,1){\v@t}}\c@@rds(0,9,0,2){\line(0,1){\v@t}}% \c@@rds(0,13,0,2){\line(0,1){\v@t}}\c@@rds(0,17,0,3){\line(0,1){\v@t}}% \c@@rds(0,20,\FillCircDiam,0){\circle*{\h@z}}}} \def\sed##1{\hbx(1,2){\ifcase##1\or% \EMl@ne(10,0,8,4)\EMl@ne(7,6,5,10)\EMl@ne(4,12,2,16)\EMl@ne(1,18,0,20)\or% \EMl@ne(10,0,7,3)\EMl@ne(5,5,3,7)\EMl@ne(1,9,-1,11)% \EMl@ne(-3,13,-5,15)\EMl@ne(-7,17,-10,20)\or% \EMl@ne(10,0,7,2)\EMl@ne(4,4,1,6)\EMl@ne(-2,8,-5,10)% \EMl@ne(-8,12,-11,14)\EMl@ne(-14,16,-20,20)\or% \EMl@ne(10,0,6,2)\EMl@ne(4,3,0,5)\EMl@ne(-2,6,-6,8)\EMl@ne(-8,9,-12,11)% \EMl@ne(-14,12,-18,14)\EMl@ne(-20,15,-24,17)\EMl@ne(-26,18,-30,20)\fi}} \def\swd##1{\hbx(1,2){\ifcase##1\or% \EMl@ne(0,0,2,4)\EMl@ne(3,6,5,10)\EMl@ne(6,12,8,16)\EMl@ne(9,18,10,20)\or% \EMl@ne(0,0,3,3)\EMl@ne(5,5,7,7)\EMl@ne(9,9,11,11)% \EMl@ne(13,13,15,15)\EMl@ne(17,17,20,20)\or% \EMl@ne(0,0,3,2)\EMl@ne(6,4,9,6)\EMl@ne(12,8,15,10)% \EMl@ne(18,12,21,14)\EMl@ne(24,16,30,20)\or% \EMl@ne(0,0,4,2)\EMl@ne(6,3,10,5)\EMl@ne(12,6,16,8)\EMl@ne(18,9,22,11)% \EMl@ne(24,12,28,14)\EMl@ne(30,15,34,17)\EMl@ne(36,18,40,20)\fi}} % % D A S H E D C R O S S E S \def\xd{\hbx(2,2){\EMl@ne(0,0,4,4)\EMl@ne(6,6,8,8)\EMl@ne(12,12,14,14)% \EMl@ne(16,16,20,20)\EMl@ne(0,20,4,16)\EMl@ne(6,14,14,6)\EMl@ne(16,4,20,0)}} \def\xxd{\hbx(2,2){\EMl@ne(0,0,4,4)\EMl@ne(6,6,14,14)\EMl@ne(16,16,20,20)% \EMl@ne(0,20,4,16)\EMl@ne(6,14,8,12)\EMl@ne(12,8,14,6)\EMl@ne(16,4,20,0)}} \def\hxd{\hbx(1,2){\EMl@ne(0,0,2,4)\EMl@ne(3,6,4,8)\EMl@ne(6,12,7,14)% \EMl@ne(8,16,10,20)\EMl@ne(0,20,2,16)\EMl@ne(3,14,7,6)\EMl@ne(8,4,10,0)}} \def\hxxd{\hbx(1,2){\EMl@ne(0,0,2,4)\EMl@ne(3,6,7,14)\EMl@ne(8,16,10,20)% \EMl@ne(0,20,2,16)\EMl@ne(3,14,4,12)\EMl@ne(6,8,7,6)\EMl@ne(8,4,10,0)}} % % O T H E R L I N E S \def\@d##1##2{\hbx(\hm@dehalf,\hm@de){% \EMl@ne(##1\hm@defives,##2\hm@detens)}} \def\d{\@d{}{0,0,}} \def\dd{\@d{0,0,}{}} \def\@hd##1##2##3{\hbx(.5,\hm@de){\EMl@ne(##1,\hm@defives,##2)% \c@@rds(##1,\hm@defives,0,\hm@defives){\line(0,##31){\v@t}}}} \def\hd{\@hd{5}{0,\hm@detens}{-}} \def\dh{\@hd{0}{5,0}{}} \def\hdd{\@hd{0}{5,\hm@detens}{-}} \def\ddh{\@hd{5}{0,0}{}} % % P U T S O M E T H I N G A N Y W H E R E \def\n@de##1##2##3{\hbx(0,0){% \c@@rds(##1,0,0){\makebox(0,0)[##2]{$\scriptstyle ##3$}}}} \def\nodeu##1{\hbx(0,0){\n@de{0,3}{cb}{##1}}} \def\noded##1{\hbx(0,0){\n@de{0,-3}{ct}{##1}}} \def\nodel##1{\hbx(0,0){\n@de{-2,0}{rc}{##1}}} \def\noder##1{\hbx(0,0){\n@de{2,0}{lc}{##1}}} \def\noderu##1{\hbx(0,0){\n@de{5,2}{lb}{##1}}} \def\noderd##1{\hbx(0,0){\n@de{5,-2}{lt}{##1}}} \def\nodelu##1{\hbx(0,0){\n@de{-5,2}{rb}{##1}}} \def\nodeld##1{\hbx(0,0){\n@de{-5,-2}{rt}{##1}}} \def\Put(##1,##2)[##3]##4{% \h@r\hstretch \multiply\h@r ##1 \v@r\vstretch \multiply\v@r ##2 \put(\h@r,\v@r){\makebox(\h@z,\v@t)[##3]{\scriptsize$##4$}}} % \def\negobj##1{\raise -0.2\unitv\hbox{\put(0,0){$##1$}}} % \def\obj##1{\raise .2\unitv\hbox{\put(0,0){$##1$}}} % \def\Obj##1{\settowidth{\textwd}{$##1$}% % \raise 1.1\unitv\hbox{\kern -1\textwd $##1$}} % % B O X E S \def\dbox##1##2{\hbx(##1,\hm@de){\multiply\hstretch ##1% \c@@rds(0,0,10,\hm@detens){\dashbox{100}(\h@z,\v@t){\scriptsize$##2$}}}} \def\ffbox##1##2{\hbx(##1,\hm@de){\multiply\hstretch ##1% \c@@rds(0,0,10,\hm@detens){\framebox(\h@z,\v@t){\scriptsize$##2$}}}} \def\obox##1##2{\hbx(##1,\hm@de){\multiply\hstretch ##1% \c@@rds(5,\hm@defives,10,\hm@detens){\oval(\h@z,\v@t)}% \c@@rds(0,0,10,\hm@detens){\makebox(\h@z,\v@t)[cc]{\scriptsize$##2$}}}} \def\tbox##1##2{\hbx(##1,\hm@de){\multiply\hstretch ##1% \c@@rds(0,0,10,\hm@detens){\makebox(\h@z,\v@t)[cc]{\scriptsize$##2$}}}} % % ( C O ) P A I R I N G S \def\@ev##1##2##3##4{\hbx(##1){\c@@rds(##2,##3,##3){\oval(\h@z,\v@t)[##4]}}} \def\ev{\@ev{\hm@de,\hm@de}{\hm@defives,\hm@detens}\hm@detens b} \def\coev{\@ev{\hm@de,\hm@de}{\hm@defives,0}\hm@detens t} \def\hcoev{\@ev{1,\hm@de}{5,0}{10}t} \def\hev{\@ev{1,\hm@de}{5,\hm@detens}{10}b} \def\Coev{\@ev{1,\hm@de}{15,0}{30}t} \def\Ev{\@ev{1,\hm@de}{15,\hm@detens}{30}b} \def\COEV{\@ev{2,2}{30,0}{60}t} \def\EV{\@ev{2,2}{30,20}{60}b} % % ( O V E R / U N D E R ) C R O S S I N G S \def\X{\hbx(1,\hm@de){\EMl@ne(0,\hm@detens,10,0)\EMl@ne(0,0,10,\hm@detens)}} \def\XX{\hbx(\hm@de,\hm@de){\EMl@ne(0,\hm@detens,\hm@detens,0)% \EMl@ne(0,0,\hm@detens,\hm@detens)}} \def\x{\hbx(\hm@de,\hm@de){\EMl@ne(0,\hm@detens,\hm@detens,0)% \EMl@ne(0,0,\hm@dethree,\hm@dethree)% \EMl@ne(\hm@detens,\hm@detens,\hm@deseven,\hm@deseven)}} \def\xx{\hbx(\hm@de,\hm@de){\EMl@ne(0,\hm@detens,\hm@dethree,\hm@deseven)% \EMl@ne(0,0,\hm@detens,\hm@detens)% \EMl@ne(\hm@detens,0,\hm@deseven,\hm@dethree)}} \def\hx{\hbx(1,2){\EMl@ne(0,20,10,0)\EMl@ne(0,0,3,6)\EMl@ne(10,20,7,14)}} \def\hxx{\hbx(1,2){\EMl@ne(0,20,3,14)\EMl@ne(0,0,10,20)\EMl@ne(10,0,7,6)}} % % ( C O ) P R O D U C T S \def\pr@d##1##2##3{% \c@@rds(##1){\oval(\h@z,\v@t)[c##2]}\c@@rds(##3){\line(0,1){\v@t}}}% \def\pr@dd##1##2##3##4{\c@@rds(5,##1,10,10){\oval(\h@z,\v@t)[c##2]}% \EMl@ne(5,10,##3)\c@@rds(5,##4,0,5){\line(0,1){\v@t}}} \def\c@cyc##1{\c@@rds(##1,\FillCircDiam,0){\circle*{\h@z}}} \def\cu{\@ifnextchar*% {\hbx(\hm@de,\hm@de){\pr@d{\hm@defives,\hm@detens,\hm@detens,\hm@detens}% {b}{\hm@defives,0,0,\hm@defives}% \c@cyc{\hm@defives,\hm@defives}}\@gobble}% {\hbx(\hm@de,\hm@de){\pr@d{\hm@defives,\hm@detens,\hm@detens,\hm@detens}% {b}{\hm@defives,0,0,\hm@defives}}}} \def\cd{\@ifnextchar*% {\hbx(\hm@de,\hm@de){\pr@d{\hm@defives,0,\hm@detens,\hm@detens}% {t}{\hm@defives,\hm@defives,0,\hm@defives}% \c@cyc{\hm@defives,\hm@defives}}\@gobble}% {\hbx(\hm@de,\hm@de){\pr@d{\hm@defives,0,\hm@detens,\hm@detens}% {t}{\hm@defives,\hm@defives,0,\hm@defives}}}} \def\hcu{\@ifnextchar*% {\hbx(1,\hm@de){\pr@d{5,\hm@detens,10,10}{b}{5,0,0,\hm@defiveteen}% \c@cyc{5,\hm@defiveteen}}\@gobble}% {\hbx(1,\hm@de){\pr@d{5,\hm@detens,10,10}{b}{5,0,0,\hm@defiveteen}}}} \def\hcd{\@ifnextchar*% {\hbx(1,\hm@de){\pr@d{5,0,10,10}{t}{5,5,0,\hm@defiveteen}% \c@cyc{5,5}}\@gobble}% {\hbx(1,\hm@de){\pr@d{5,0,10,10}{t}{5,5,0,\hm@defiveteen}}}} \def\Cu{\@ifnextchar*% {\hbx(4,2){\pr@d{20,20,40,20}{b}{20,0,0,10}\c@cyc{20,10}}\@gobble}% {\hbx(4,2){\pr@d{20,20,40,20}{b}{20,0,0,10}}}} \def\Cd{\@ifnextchar*% {\hbx(4,2){\pr@d{20,0,40,20}{t}{20,10,0,10}\c@cyc{20,10}}\@gobble}% {\hbx(4,2){\pr@d{20,0,40,20}{t}{20,10,0,10}}}} \def\hd@cd##1{\@ifnextchar*% {\hbx(1,2){\pr@dd{0}{t}{##1,20}{5}\c@cyc{5,5}}\@gobble}% {\hbx(1,2){\pr@dd{0}{t}{##1,20}{5}}}} \def\hd@cu##1{\@ifnextchar*% {\hbx(1,2){\pr@dd{20}{b}{##1,0}{10}\c@cyc{5,15}}\@gobble}% {\hbx(1,2){\pr@dd{20}{b}{##1,0}{10}}}} \def\hdcd{\hd@cd 0} \def\hddcd{\hd@cd{10}} \def\hdcu{\hd@cu{10}} \def\hddcu{\hd@cu 0} % % A C T I O N S \def\@ct##1##2##3##4##5{\hbx(##1,\hm@de){% \c@@rds(##2,##3,##4,##4){\oval(\h@z,\v@t)[##5]}% \c@@rds(##2,0,0,\hm@detens){\line(0,1){\v@t}}}} \def\@lu[##1]{{\multiply\hstretch##1\@ct{##1}{10}{\hm@detens}{20}{lb}}} \def\@ru[##1]{{\multiply\hstretch##1\@ct{##1}{0} {\hm@detens}{20}{rb}}} \def\@ld[##1]{{\multiply\hstretch##1\@ct{##1}{10}{0}{20}{lt}}} \def\@rd[##1]{{\multiply\hstretch##1\@ct{##1}{0}{0}{20}{rt}}} \def\lu{\@ifnextchar[{\@lu}{\@lu[1]}} \def\ru{\@ifnextchar[{\@ru}{\@ru[1]}} \def\ld{\@ifnextchar[{\@ld}{\@ld[1]}} \def\rd{\@ifnextchar[{\@rd}{\@rd[1]}} \def\Lu{\lu[2]}\def\Ru{\ru[2]}\def\Ld{\ld[2]}\def\Rd{\rd[2]} \def\@hlu[##1]{{\divide\unith2\multiply\hstretch##1% \@ct{##1}{5}{\hm@detens}{10}{lb}}} \def\@hru[##1]{{\divide\unith2\multiply\hstretch##1% \@ct{##1}{0}{\hm@detens}{10}{rb}}} \def\@hld[##1]{{\divide\unith2\multiply\hstretch##1% \@ct{##1}{5}{0}{10}{lt}}} \def\@hrd[##1]{{\divide\unith2\multiply\hstretch##1% \@ct{##1}{0}{0}{10}{rt}}} \def\hlu{\@ifnextchar[{\@hlu}{\@hlu[1]}} \def\hru{\@ifnextchar[{\@hru}{\@hru[1]}} \def\hld{\@ifnextchar[{\@hld}{\@hld[1]}} \def\hrd{\@ifnextchar[{\@hrd}{\@hrd[1]}} % \def\hlu{\@ct{.5}{5}{\hm@detens}{10}{lb}} % \def\hru{\@ct{.5}{0}{\hm@detens}{10}{rb}} % \def\hld{\@ct{.5}{5}{0}{10}{lt}} % \def\hrd{\@ct{.5}{0}{0}{10}{rt}} % % C O M P O S I T I O N S \def\c@mp##1##2##3##4##5##6{\hbx(##1,2){% \c@@rds(##2,0,##3){\oval(\h@z,\v@t)[##4t]}% \c@@rds(##2,20,##3){\oval(\h@z,\v@t)[##4b]}% \c@@rds(##2,##5,0,##6){\line(0,1){\v@t}}}} \def\cucd{\c@mp{1}{5}{10,10}{}{5}{10}} \def\k{\c@mp{1}{0}{20,10}{r}{0}{20}} \def\kk{\c@mp{1}{10}{20,10}{l}{0}{20}} \def\rurd{\c@mp{.5}{0}{10,10}{r}{0}{20}} \def\luld{\c@mp{.5}{5}{10,10}{l}{0}{20}} % % M O R P H I S M S I N A C I R C L E \def\c@rcled##1##2{\c@@rds(##1,12,12){\oval(\h@z,\v@t)}% \c@@rds(##1,0,0){\makebox(\h@z,\v@t)[cc]{\scriptsize$##2$}}} % ( 1, 0 ) -, ( 0, 1 ) - T E N S O R S \def\@Q##1##2{\hbx(0,\hm@de){% \c@@rds(0,##1,0,4){\line(0,1){\v@t}}\c@rcled{0,10}{##2}}} \def\Q##1{\@Q{0}{##1}} \def\QQ##1{\@Q{16}{##1}} % ( 1, 1 ) - T E N S O R S \def\O##1{\hbx(0,\hm@de){\c@@rds(0,0,0,4){\line(0,1){\v@t}}% \c@@rds(0,16,0,4){\line(0,1){\v@t}}\c@rcled{0,10}{##1}}} \def\S{\O{S}} \def\SS{\O{S^{-1}}} %\def\circ##1{\hbx(2,2){\c@rcled{10,4}{##1}}} \def\morph##1{\hbx(2,2){\c@@rds(10,10,10,10){\oval(\h@z,\v@t)}% \c@@rds(5,5,10,10){\makebox(\h@z,\v@t)[cc]{\scriptsize$##1$}}% \c@@rds(10,0,0,5){\line(0,1){\v@t}}% \c@@rds(10,15,0,5){\line(0,1){\v@t}}}} % ( 2, 0 ) -, ( 0, 2 ) - T E N S O R S \def\r@##1##2##3##4##5{\hbx(2,\hm@de){% \c@@rds(0,##1,0,4){\line(0,##41){\v@t}}% \c@@rds(20,##1,0,4){\line(0,##41){\v@t}}% \c@@rds(4,##1,8,8){\oval(\h@z,\v@t)[l##2]}% \c@@rds(16,##1,8,8){\oval(\h@z,\v@t)[r##2]}\c@rcled{##3}{##5}}} \def\ro##1{\r@{4}{t}{10,8}{-}{##1}} \def\coro##1{\r@{16}{b}{10,12}{}{##1}} % \def\R@##1##2##3{\hbx(4,\hm@de){% \c@@rds(14,##1,28,20){\oval(\h@z,\v@t)[l##2]}% \c@@rds(26,##1,28,20){\oval(\h@z,\v@t)[r##2]}\c@rcled{20,10}{##3}}} \def\Ro##1{\R@{0}{t}{##1}} \def\coRo##1{\R@{20}{b}{##1}} % ( 2, 1 ) -, ( 1, 2 ) - T E N S O R S \def\t@##1##2##3##4##5##6{\hbx(2,2){% \c@@rds(4,##1,8,8){\oval(\h@z,\v@t)[l##2]}% \c@@rds(16,##1,8,8){\oval(\h@z,\v@t)[r##2]}% \c@@rds(0,##1,0,5){\line(0,##31){\v@t}}% \c@@rds(20,##1,0,5){\line(0,##31){\v@t}}% \c@@rds(10,##4,0,5){\line(0,##31){\v@t}}% \c@rcled{10,##5}{##6}}} \def\tu##1{\t@{15}b{}{0}{11}{##1}} \def\td##1{\t@{5}t{-}{20}{9}{##1}} % ( 2, 2 ) - T E N S O R S \def\ox##1{\hbx(2,2){\c@@rds(10,10,14,14){\oval(\h@z,\v@t)}% \c@@rds(10,10,0,0){\makebox(\h@z,\v@t)[cc]{\scriptsize$##1$}} \EMl@ne(0,0,5,5)\EMl@ne(0,20,5,15)\EMl@ne(20,20,15,15)\EMl@ne(20,0,15,5)}} % % HALF HEIGHT ROW IS PRODUCED BY \hh or \HH AT THE BEGINNING OF THE ROW % \HH is global for a row, \hh is local \def\HH{\gdef\hm@dehalf{.5}\gdef\hm@de{1} \gdef\hm@dethree{3}\gdef\hm@defives{5}\gdef\hm@deseven{7} \gdef\hm@detens{10}\gdef\hm@defiveteen{5}} \def\hh{\def\hm@dehalf{.5}\def\hm@de{1} \def\hm@dethree{3}\def\hm@defives{5}\def\hm@deseven{7} \def\hm@detens{10}\def\hm@defiveteen{5}} % \def\array{\let\@acol\@arrayacol \let\@classz\@arrayclassz \let\@classiv\@arrayclassiv \def\arraystretch{0}\arraycolsep0pt \def\\{\gdef\above@bjectskip{4pt}\gdef\below@bjectskip{0pt}\t@ngl@\@arraycr} \let\@halignto\@empty\@tabarray} } % E N D \def\t@ngle % \def\tangle{\t@ngle\array{l}} \def\endtangle{\endarray\t@ngl@} \def\tanglec{\t@ngle\array{c}} \let\endtanglec\endtangle \def\tangler{\t@ngle\array{r}} \let\endtangler\endtangle \def\tangles{\t@ngle\array} \let\endtangles\endtangle % \ProcessOptions \ifpdf \startEMspecials \let\EMenddocument\enddocument \def\enddocument{\stopEMspecials\EMenddocument} \fi \endinput