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Diffstat (limited to 'Master/texmf-dist/doc/latex/t-angles')
-rw-r--r-- | Master/texmf-dist/doc/latex/t-angles/readme | 16 | ||||
-rw-r--r-- | Master/texmf-dist/doc/latex/t-angles/t-manual.tex | 1122 |
2 files changed, 1138 insertions, 0 deletions
diff --git a/Master/texmf-dist/doc/latex/t-angles/readme b/Master/texmf-dist/doc/latex/t-angles/readme new file mode 100644 index 00000000000..4a646e75498 --- /dev/null +++ b/Master/texmf-dist/doc/latex/t-angles/readme @@ -0,0 +1,16 @@ + t-angles.sty +is a LaTeX2e style for drawing tangles, trees, +Hopf algebra operations and other pictures. + +It is based on emTeX or TPIC \special's. +Therefore, it can be used with the most popular drivers: + emTeX drivers, dviwin, yap, xdvi and dvips. + +The manual t-manual.tex contains the style file (10.09.2000) +t-angles.sty as well, so you may download only the manual. + +You can contact the authors: + Yu. Bespalov, V. Lyubashenko +via e-mail: +lub@imath.kiev.ua + diff --git a/Master/texmf-dist/doc/latex/t-angles/t-manual.tex b/Master/texmf-dist/doc/latex/t-angles/t-manual.tex new file mode 100644 index 00000000000..35e08fe1743 --- /dev/null +++ b/Master/texmf-dist/doc/latex/t-angles/t-manual.tex @@ -0,0 +1,1122 @@ + + %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + % % + % This is file t-manual.tex ( version 10.09.00 ) % + % % + % Diagrammatic macros for tangles and braided Hopf algebras % + % % + % (Yu. Bespalov, V. Lyubashenko) % + % % + % available from http://www.math.ksu.edu/~lub/ % + % % + %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\begin{filecontents*}{t-angles.sty} +% a manual is available from http://www.math.ksu.edu/~lub/ +% \usepackage[emtex]{t-angles} % for emtex drivers, dviwin and dvips or +% \usepackage{t-angles} = \usepackage[TPIC]{t-angles} +% % for TPIC drivers such as dviwin, xdvi, dvips +% \usepackage[kluwer]{t-angles} or \usepackage[emtex,kluwer]{t-angles} +% % to use with kluwer.cls + + %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + % % + % This is file t-angles.sty ( version 10.09.00 ) % + % % + % Diagrammatic macros for tangles and braided Hopf algebras % + % % + % (Yu. Bespalov, V. Lyubashenko) % + % % + %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\newcount{\hstretch} \hstretch 100 +\newcount{\vstretch} \vstretch 100 +\newlength{\unitlens} \unitlens 10pt +\def\FillCircDiam{3} + +\DeclareOption{emtex}{% +\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 +} +% +\newcount\@gphlinewidth +% +\DeclareOption{TPIC}{% +\@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 +} +\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 +\endinput +\end{filecontents*} +\begin{filecontents}{t-manual.bbl} +\providecommand{\bysame}{\leavevmode\hbox to3em{\hrulefill}\thinspace} +\begin{thebibliography}{1} + +\bibitem{Bes:cross} +Yu.~N. Bespalov, \emph{Crossed modules and quantum groups in braided + categories}, Applied Categorical Structures \textbf{5} (1997), no.~2, + 155--204, http://xxx.lanl.gov/abs/q-alg/9510013. + +\bibitem{Bes:FRT} +\bysame, \emph{On the braided {FRT}-construction}, J. Nonlinear Math. Phys. + \textbf{4} (1997), no.~1-2, 195--205, http://xxx.lanl.gov/abs/q-alg/9510012. + +\bibitem{BKLT:int} +Yu.~N. Bespalov, T.~Kerler, V.~V. Lyubashenko, and V.~G. Turaev, + \emph{Integrals for braided {H}opf algebras}, J. Pure and Appl. Algebra + \textbf{148} (2000), no.~2, 113--164, Available as + http://xxx.lanl.gov/abs/q-alg/9709020. + +\end{thebibliography} +\end{filecontents} + +\documentclass[11pt]{article} + +\usepackage{amsmath} +\usepackage{t-angles} +%\usepackage[emtex]{t-angles} +%\usepackage{t-erratr} + +\setlength{\textwidth}{16 true cm} +\setlength{\textheight}{22.5 true cm} +\setlength{\topmargin}{-1.4 true cm} +\setlength{\oddsidemargin}{0mm} + +\title{{\Huge\tt t-angles.sty } +\footnote{t-angles.sty is available from {\tt +http://www.math.ksu.edu/$\sim$lub/} or from CTAN} +\\ +\mbox{\Large\bf (Diagrammatic macros for tangles and braided Hopf algebras)} +} +\author{Yu. Bespalov \and V. Lyubashenko} +\date{Version 10.09.00} + +\def\subsec#1{\subsection*{#1}\addcontentsline{toc}{subsection}{#1}} + +\def\hhmode{{{\tt hh}-mode }} +\def\Command#1{\hbox{\tt\string#1}} +\def\command#1{\ \hbox{\tt\string#1} \ } +\def\SHOW#1#2{\begin{array}{c} + \begin{tangle}#1\end{tangle}\\ + \hbox{\tt\string#2} + \end{array}} +\def\Show#1{\SHOW#1#1} +\def\Showh#1{\SHOW{\hh#1}#1} + + +\bibliographystyle{amsplain} + +\begin{document} + +\maketitle +\tableofcontents + +\section{Introduction} + +\subsection*{Usage:} +\addcontentsline{toc}{subsection}{Usage} +$$ +\vcenter{\hbox{\command{\usepackage[emtex]\{t-angles\}}} + \hbox{(for \command{emtex} drivers, {\tt dviwin, dvips, yap} )}} +\qquad \hbox{or} \qquad +\vcenter{\hbox{\command{\usepackage\{t-angles\}} $\equiv$} + \hbox{\command{\usepackage[TPIC]\{t-angles\}}} + \hbox{(for TPIC drivers such as} + \hbox{ {\tt dviwin, xdvi, dvips, yap} )}} +$$ +To use with \command{kluwer.cls} add the option \command{kluwer}:\\ +\command{\usepackage[emtex,kluwer]\{t-angles\}} or +\command{\usepackage[kluwer]\{t-angles\}} + +\subsection*{Main features:} +\addcontentsline{toc}{subsection}{Main features} +\begin{itemize} +\item +The environments +$$ +\vcenter{\hbox{\tt \{tangle\}} + \hbox{\tt \{tanglec\}} + \hbox{\tt \{tangler\}} + \hbox{\tt \{tangles\}}} +\qquad +\vcenter{\hbox{are arrays with} + \hbox{one or more} + \hbox{column style:}} +\qquad +\vcenter{\hbox{\tt \{array\}\{l\}} + \hbox{\tt \{array\}\{c\}} + \hbox{\tt \{array\}\{r\}} + \hbox{\tt \{array\}} } +\quad +\vcenter{\hbox{(left)} + \hbox{(centered)} + \hbox{(right)} + \hbox{(any)}} +$$ +respectively. Likewise {\tt \{array\}}, the {\tt \{tangles\}} +environment allows an optional argument {\tt t} or {\tt b} to align +the upper base line or the bottom of the tangle with the exterior +base line: \verb+\begin{tangles}[b]{l*3cr}+. +\item + \command\unitlens is the global length parameter. + Default value is \command{10 pt} . +\item + \command\hstretch and \command\vstretch are relative length + parameters, horizontal and vertical stretch: +\begin{equation*} +\begin{split} +\command\unith = \command\hstretch \%\;\; \text{of}\; \command\unitlens \,, +\\ +\command\unitv = \command\vstretch \%\;\; \text{of}\; \command\unitlens \,, +\end{split} +\end{equation*} + set to an integer number of percents before the beginning of a tangle. +\newline + Default settings are +\command{\hstretch}{\tt 100} and \command{\vstretch}{\tt 100}. + The commands \command\hstretch and \command\vstretch should be used only + outside of tangle environments (with an exception of embedded tangle + environments). +\item +The commands \command{\hstr \{<number>\}} , +\command{\vstr \{<number>\}} can be used inside tangle environments +instead of \command{\hstretch <number>} , \command{\vstretch <number>}. +They will act within their \LaTeX{} scope. +\item +The height of every row is \ {\tt 2}\command\unitv +or \command\unitv if the command \command\hh (see below) is used; +\newline +the widths of standard fragments are \ {\tt 0, .5, 1, 2, 3} or {\tt 4} +\command\unith +\item +The command \command\hh obeys to \LaTeX{} scope rules. The command +\command\HH acts in the same way as \command\hh but put at the +beginning of a row works for the whole row in the \ {\tt \{tangles\}} +environment. +\item +The style understands the commands +\command\thinlines and \command\thicklines . +\item +The command \command{\step[<number>]} is used to produce horizontal space +\command\kern{\tt <number>}\command\unith and works in any mode +(inside and outside of the \command{tangle} environment). +\begin{eqnarray*} +&\command\step = \command{\step[1]} +\qquad +&\command\Step = \command{\step[2]} +\\ +&\command\hstep = \command{\step[.5]} +\quad +&\command\hhstep = \command{\step[-.5]} +\end{eqnarray*} +\item +Vertical spacing before the next row is produced by +\ $\backslash\backslash[\langle\hbox{\tt vertical\_space}\rangle]$ \ +with optional argument (like in standard \ {\tt \{array\}} \ +environment). +\item +The command \command{\object\#1} is used to put the object \command{#1} +directly over or under the end of the string (inside and outside of the +\ {\tt \{tangle\}} \ environment). It adds a vertical space below or +above as required. More space can be added as above. +\newline +The command +\command{\Put(x\_coord,y\_coord)[binding\_point]<object>} puts +{\tt <object>} into the intended position and works in +\ {\tt \{tangle[cs]\}} \ environment like a combination of \command\put +and \command\makebox. Coordinates are integers, measured in +{\tt .1}\command\unith, {\tt .1}\command\unitv units; +\command{binding\_point} is a combination of two letters \ {\tt lcr} \ +and \ {\tt tcb} \ according to the usual \LaTeX{} rules. +\newline +The commands +\command{\nodeu\#1,} \command{\noded\#1,} +\command{\nodel\#1,} \command{\noder\#1,} +\command{\noderu\#1,} \command{\noderd\#1,} +\command{\nodelu\#1,} \command{\nodeld\#1} +produce zero boxes and put \ {\tt \#1} \ into the corresponding +position. +\newline +\begin{minipage}{0.4\textwidth} +The picture +\begin{equation*} +\vstretch 200 \hstretch 200 +\begin{tangle} +\nodeu.\noded.\nodel.\noder.\noderu.\noderd.\nodelu.\nodeld. +\end{tangle} +\end{equation*} +is described by the lines: +\end{minipage} +\begin{minipage}{0.5\textwidth} +\begin{verbatim} +\vstretch 200 \hstretch 200 +\begin{tangle} +\nodeu.\noded.\nodel.\noder. +\noderu.\noderd.\nodelu.\nodeld. +\end{tangle} +\end{verbatim} +\end{minipage} +\end{itemize} + +\section{Macros in pictures} + +\subsec{Straight lines and nodes} + +\begin{itemize} +\item +The commands \command\id, \command\n, \command\s,\command\node, +\command\unit, \command\counit work in \hhmode. +$$ +\Show\id \quad +\Show\idash \quad +\Show\n \quad +\Show\s \quad +\Show\nd \quad +\Show\sd \quad +\Show\node \quad +\Show\unit \quad +\Show\counit +$$ +The command \command\FillCircDiam denotes the filled circle diameter. +It is set to an integer between 1 and 9 (here the measure unit is +0.1 \command\unith). Default value is 4. +\item +The command \command\hln{\tt <number>} \ produces horizontal line on +\ {\tt <number>}\command\unith. +\item +Argument of \command\ne,\command\nw,\command\se,\command\sw, +\command\ned,\command\nwd,\command\sed,\command\swd +is \ {\tt 0,1,2,3} or {\tt 4}; {\tt 0} produces empty box and +other produce (dash) lines with horizontal projections equal +\ {\tt <argument>}\command{\unith} cribbed into {\tt 1$\times$2} box. +The commands \command\ne,\command\nw,\command\se,\command\sw +produce {\tt 1$\times$1} box in \hhmode. +$$ +\SHOW{\nw1}{\nw{1}}\quad +\SHOW{\nwd1}{\nwd{1}}\quad +\SHOW{\sw0}{\sw{0}}\quad +\SHOW{\se3}{\se{3}}\quad +\SHOW{\sed3}{\sed{3}}\quad +\SHOW{\nw3\nw2\nw1\n\ne1\ne2\ne3}{\nw{3}\string\nw{2}% +\string\nw{1}\string\n\string\ne{1}\string\ne{2}\string\ne{3}} +$$ +\item +All the following commands work in \hhmode and produce +the similar diagrams in {\tt .5$\times$1} boxes. +$$ +\Show\d \quad +\Show\dd \quad +\Show\hd \quad +\Show\hdd \quad +\Show\dh \quad +\Show\ddh +$$ +\end{itemize} + + +\subsec{(Under/over)crossings. Braiding and symmetry} +The following crossings and dashed crossings are shown in normal mode. +$$ +\Show\x \quad +\Show\xx \quad +\Show\hx \quad +\Show\hxx \quad +\Show\X \quad +\Show\XX \quad +\Show\xd \quad +\Show\xxd \quad +\Show\hxd \quad +\Show\hxxd +$$ +The commands \command\X, \command\XX, \command\x, \command\xx work in +\hhmode and produce similar diagrams of half width and height +({\tt 1$\times$1} boxes). + +\subsec{(Co)pairings.} +The commands \command\ev, \command\coev work in \hhmode and produce +the similar diagrams of half width and height ({\tt .5$\times$1} boxes). +For convenience in \hhmode \command\hev $\equiv$ \command\ev and +\command\hev $\equiv$ \command\ev. +\begin{align*} +\Show\hev \quad +&\Show\ev \quad +&\Show\Ev \quad +&\Show\EV +&\\ +\Show\hcoev \quad +&\Show\coev \quad +&\Show\Coev \quad +&\Show\COEV +&\end{align*} + + +\subsec{Morphisms. Frame and dash boxes} +\begin{itemize} +\item +$$ +\SHOW{\Q f}{\Q \ f} \quad +\SHOW{\QQ f}{\QQ \ f} \quad +\SHOW{\O f}{\O \ f} \quad +%\SHOW{\circ f}{\circ \ f} \quad +\SHOW{\morph f}{\morph \ f} \quad +\SHOW{\tu f}{\tu \ f} \quad +\SHOW{\td f}{\td \ f} \quad +\Show\S \quad +\Show\SS +$$ +\item +$$ +\SHOW{\ox f}{\ox \ f} \qquad\qquad +\SHOW{\ro p}{\ro \ p} \quad +\SHOW{\coro q}{\coro \ q} \quad +\SHOW{\Ro p}{\Ro \ p} \quad +\SHOW{\coRo q}{\coRo \ q} +$$ +\item +The commands \command{\dbox\#1\#2,}\command{\ffbox\#1\#2,} +\command{\obox\#1\#2,}\command{\tbox\#1\#2} put {\tt \$\#2\$} in the middle +of \ {\tt \#1}$\times${\tt 2} (or {\tt \#1}$\times${\tt 1} \ in +\hhmode ) box with dash, rectangle, oval frame or without frame. +\par +For example, the text +\newline +\begin{minipage}{.4\textwidth} +\begin{verbatim} +\begin{tangles}{rcl} +\HH\obox 10&&\obox 10\\ +\HH\d&&\dd\\ +&\hhstep\obox 3V\hhstep& +\end{tangles} +\end{verbatim} +\end{minipage} +produces +\begin{minipage}{.4\textwidth} +\begin{equation*} +\begin{tangles}{rcl} +\HH\obox 10&&\obox 10\\ +\HH\d&&\dd\\ +&\hhstep\obox 3V\hhstep& +\end{tangles} +\end{equation*} +\end{minipage} +\end{itemize} + +\subsec{(Co)multiplications and cocycles} +The commands \command\cu, {\tt \string\cu *}, +\command\cd, {\tt \string\cd *} work in \hhmode and produce the similar +diagrams of half width and height ({\tt .5$\times$1} boxes). +For convenience in \hhmode \command\hcu $\equiv$ \command\cu and +\command\hcd $\equiv$ \command\cd . +\begin{equation*} +\begin{split} +\Show\Cu \quad +\Show\cu \quad +\Show\hcu \quad +\Show\hdcu \quad +\Show\hddcu +\\ +\SHOW{\Cu *}{\Cu *} \quad +\SHOW{\cu *}{\cu *} \quad +\SHOW{\hcu *}{\hcu *} \quad +\SHOW{\hdcu *}{\hdcu *} \quad +\SHOW{\hddcu *}{\hddcu *} +\\ +\SHOW{\Cd *}{\Cd *} \quad +\SHOW{\cd *}{\cd *} \quad +\SHOW{\hcd *}{\hcd *} \quad +\SHOW{\hdcd *}{\hdcd *} \quad +\SHOW{\hddcd *}{\hddcd *} +\\ +\Show\Cd \quad +\Show\cd \quad +\Show\hcd \quad +\Show\hdcd \quad +\Show\hddcd +\end{split} +\end{equation*} + +\subsec{(Co)actions} +Commands \command\lu, \command\ld, \command\ru, \command\rd +have optional parameter \ {\tt [\#1]} which equals to width of the box: +\begin{align*} +&\command\hh +& \SHOW{\hh\Lu}{\Lu$\equiv\!\!\!\!$\command\lu$\!\!\!\!\!\!$[2]} \quad + \SHOW{\hh\lu} {\lu$\equiv\!\!\!\!$\command\lu$\!\!\!\!\!\!$[1]} \quad + \Showh\hlu \quad + \Showh\hru \quad + \SHOW{\hh\ru} {\ru$\equiv\!\!\!\!$\command\ru$\!\!\!\!\!\!$[1]} \quad + \SHOW{\hh\Ru} {\Ru$\equiv\!\!\!\!$\command\ru$\!\!\!\!\!\!$[2]} +&\\ +&&\SHOW\Lu{\Lu$\equiv\!\!\!\!$\command\lu$\!\!\!\!\!\!$[2]} \quad + \SHOW\lu{\lu$\equiv\!\!\!\!$\command\lu$\!\!\!\!\!\!$[1]} \quad + \Show\hlu \quad + \Show\hru \quad + \SHOW\ru{\ru$\equiv\!\!\!\!$\command\ru$\!\!\!\!\!\!$[1]} \quad + \SHOW\Ru{\Ru$\equiv\!\!\!\!$\command\ru$\!\!\!\!\!\!$[2]} +&\\ +&&\SHOW\Ld{\Ld$\equiv\!\!\!\!$\command\ld$\!\!\!\!\!\!$[2]} \quad + \SHOW\ld{\ld$\equiv\!\!\!\!$\command\ld$\!\!\!\!\!\!$[1]} \quad + \Show\hld \quad + \Show\hrd \quad + \SHOW\rd{\rd$\equiv\!\!\!\!$\command\rd$\!\!\!\!\!\!$[1]} \quad + \SHOW\Rd{\Rd$\equiv\!\!\!\!$\command\rd$\!\!\!\!\!\!$[2]} +&\\ +&\command\hh +& \SHOW{\hh\Ld}{\Ld$\equiv\!\!\!\!$\command\ld$\!\!\!\!\!\!$[2]} \quad + \SHOW{\hh\ld}{\ld$\equiv\!\!\!\!$\command\ld$\!\!\!\!\!\!$[1]} \quad + \Showh\hld \quad + \Showh\hrd \quad + \SHOW{\hh\rd}{\rd$\equiv\!\!\!\!$\command\rd$\!\!\!\!\!\!$[1]} \quad + \SHOW{\hh\Rd}{\Rd$\equiv\!\!\!\!$\command\rd$\!\!\!\!\!\!$[2]} +&\end{align*} + +\subsec{Compositions} +$$ +\Show\kk \quad +\Show\luld \quad +\Show\cucd \quad +\Show\rurd \quad +\Show\k +$$ + +\section{Examples} + +\begin{minipage}{.3\textwidth} +\[ +\begin{tangle} +\object{B}\step\object{B}\\ +\cucd\\ +\object{B}\step\object{B} +\end{tangle} +\;=\enspace +\begin{tangles}{lcr} +\HH \cd && \cd \\ +\HH \id & \x & \id \\ +\HH \cu && \cu +\end{tangles} +\] +\begin{equation*} +\hstretch 90 \vstretch 60 +\begin{tangle} +\step\hcoev\step\coev\\ +\dd\step\hxx\step\dd\\ +\id\Step\id\step\hx\\ +\d\step\hxx\step\d\\ +\step\hev\step\ev +\end{tangle} +\end{equation*} +\end{minipage} +\begin{minipage}{.2\textwidth} +The first picture is produced by: +\end{minipage} +\quad +\begin{minipage}{.4\textwidth} +\begin{verbatim} +\[ +\begin{tangle} +\object{B}\step\object{B}\\ +\cucd\\ +\object{B}\step\object{B} +\end{tangle} +\;=\enspace +\begin{tangles}{lcr} +\HH \cd && \cd \\ +\HH \id & \x & \id \\ +\HH \cu && \cu +\end{tangles} +\] +\end{verbatim} +\end{minipage} + +\begin{minipage}{0.23\textwidth} +Nested environments: +\[ +\begin{tanglec} + \begin{tangles}[b]{c} + \vstr{200} \xx \\ \vstr{200} \xx + \end{tangles} +\step[4] + \begin{tangles}[b]{*3c} + & \object{F} & \\ & \xx & \\ \id && \O{u_1^2} \\ + & \xx & \\ \id && \O{u_1^2} + \end{tangles} +\\ +\id \Step \coRo\omega \Step \id \\ +\hstr{200} \coRo\omega +\end{tanglec} +\] +The level of nesting depends on the save size of your \TeX. +\end{minipage} +\ \ +\begin{minipage}{0.7\textwidth} +\begin{verbatim} +\[ +\begin{tanglec} + \begin{tangles}[b]{c} + \vstr{200} \xx \\ \vstr{200} \xx + \end{tangles} +\step[4] + \begin{tangles}[b]{*3c} + & \object{F} & \\ & \xx & \\ \id && \O{u_1^2} \\ + & \xx & \\ \id && \O{u_1^2} + \end{tangles} +\\ +\id \Step \coRo\omega \Step \id \\ +\hstr{200} \coRo\omega +\end{tanglec} +\] +\end{verbatim} +\end{minipage} +\smallskip + +Note the use of optional argument \verb+[b]+ to align the subtangles +at the bottom. + +\section{Development} + +\subsec{History and versions} + +The style is produced by the first author in 1994 and used in +\cite{Bes:cross,Bes:FRT}. +It was completely modified and essentially improved by the second author +for applications in \cite{BKLT:int}. + +{%beginenumerate +\setlength{\leftmargini}{34mm} +\begin{enumerate} +\item[04.04.99$\to$20.04.00] +The output of commands \command{\tu\#1,}\command{\td\#1,} +\command{\ro\#1,}\command{\coro\#1,}\command{\Ro\#1,}\command{\coRo\#1} +slightly differs. Now they fit their boxes. + +\item[20.04.00$\to$10.09.00] +Dashed crossings are represented by the commands +\command{\xd,}\command{\xxd,}\command{\hxd,}\command{\hxxd.} + +\end{enumerate} +}%endenumerate + + +%\subsec{Bugs} +%\begin{itemize} +%\item +%\end{itemize} + +\subsec{Directions for modification +%\protect\footnote{What can you suggest?} +} + +\begin{itemize} +\item +In the future some problems can be solved by introducing global +(logical) parameters that switch configuration and behavior of certain +families of commands in questionable situations. +\item +To adopt commands like in {\tt \{picture\}} environment to +produce special fragments of one time use. +\item +To make the second argument of the command \command{\Put(\#1)[\#2]\#3} +optional. +\item +To produce command index for this manual. +\item +To add possibility to change size of circle in circled morphisms +(in particular, to turn \command\morph into a special case of \command\O). +\end{itemize} + + +\subsec{Acknowledgments} +Optional parameter for (co)actions is proposed by Bernhard Drabant. + \command{t-angles.sty} contains parts of \command{emlines2.sty} by + Georg Horn and Eberhard Mattes and parts of \command{eepic.sty} by + Conrad Kwok. +\medskip +\begin{center} +\fbox{Suggestions are welcomed.} +\end{center} + +\bibliography{yuri} + +\appendix +\section{Exercises} +How to produce the following ? +\begin{equation*} +\vstretch 300 +\begin{tanglec} +\hh\dd\d\step[1.5]\dd\d \\ +\obox 6{\hstretch 85 \vstretch 80 + \begin{tangles}{rcl} + \HH\obox 10&&\obox 10\\ + \HH\d&&\dd\\ + &\hhstep\obox 3V\hhstep& + \end{tangles} } +\end{tanglec} +\end{equation*} + +\end{document} + + +\section{\tt t-erratr.sty} + +Macros from the old versions of \ {\tt tangles.sty} \ are stored in +this file for compatibility. +\begin{itemize} +\item +The following commands are special cases of +\command{\ffbox\#1\#2,}\command{\dbox\#1\#2}: +\begin{align*} +&\SHOW{\dash f}{\dash \ f} \enspace +&\SHOW{\Dash f}{\Dash \ f} \enspace +&\SHOW{\DDash f}{\DDash \ f} \quad +&\SHOW{\Frabox f}{\Frabox \ f} \enspace +&\SHOW{\doubleFrabox f}{\doubleFrabox \ f} +\\ +\command\hh +&\SHOW{\hh\dash f}{\dash \ f} \enspace +&\SHOW{\hh\Dash f}{\Dash \ f} \enspace +&\SHOW{\hh\DDash f}{\DDash \ f} \quad +&\SHOW{\hh\Frabox f}{\Frabox \ f} \enspace +&\SHOW{\hh\doubleFrabox f}{\doubleFrabox \ f} +\end{align*} +and \command{\frabox} is equivalent to \command{\Frabox}. +\item +The following morphisms are special cases of +\command{\ro\#1,} \command{\coro\#1,} \command{\Ro\#1,} \command{\coro\#1}: +\vstretch 150 \hstretch 150 +\begin{align*} +&\hstep\Show\r +&\hstep\Show\rh +&\hstep\Show\ra +&\hstep\Show\rb +\\ +&\hstep\Show\rr +&\hstep\Show\rrr +&\hstep\Show\rra +&\hstep\Show\rrb +\\ +&\Show\R +&\Show\Rh +&\Show\Ra +&\Show\Rb +\\ +&\Show\RR +&&\Show\RRa +&\Show\RRb +\end{align*} +\item +The following commands are special cases of \command{\O\#1}: +$$ +\vstretch 150 \hstretch 150 +\Show\tS \quad +\Show\tSS \quad +\SHOW{\Ointl H}{\Ointl \ H} \; +\SHOW{\Ointr H}{\Ointr \ H} \; +\SHOW{\Ocointl H}{\Ocointl \ H} \; +\SHOW{\Ocointr H}{\Ocointr \ H} +$$ +\item +$$ +\SHOW{\pairing p}{\pairing \ p} \quad +\SHOW{\Pairing P}{\Pairing \ P} \quad +$$ +\item +Functions of the old unsightly commands +\command{\obj\#1,} \command{\Obj\#1,} \command{\negobj\#1} +are shouldered by the command \command{\Put(\#1)[\#2]\#3}. +\end{itemize} + +Commands \command{\harc}, \command{\inarc}, \command{\outarc} have two +arguments -- horizontal and vertical diameters of an ellipse +\vspace*{5mm} +\[ +\SHOW{\inarc{15}{20}}{\inarc \{15\}\{20\}} \qquad +\SHOW{\harc{20}{15}}{\harc \{20\}\{15\}} \qquad +\SHOW{\outarc{30}{25}}{\outarc \{30\}\{25\}} +\] + +\end{document} |