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Diffstat (limited to 'Master/texmf-dist/tex/latex')
| -rw-r--r-- | Master/texmf-dist/tex/latex/dynkin-diagrams/dynkin-diagrams.sty | 347 |
1 files changed, 347 insertions, 0 deletions
diff --git a/Master/texmf-dist/tex/latex/dynkin-diagrams/dynkin-diagrams.sty b/Master/texmf-dist/tex/latex/dynkin-diagrams/dynkin-diagrams.sty new file mode 100644 index 00000000000..5626893c931 --- /dev/null +++ b/Master/texmf-dist/tex/latex/dynkin-diagrams/dynkin-diagrams.sty @@ -0,0 +1,347 @@ +\NeedsTeXFormat{LaTeX2e}[1994/06/01] +\ProvidesPackage{dynkin-diagrams}[2016/06/28 Dynkin diagrams] + +\RequirePackage{tikz} +\RequirePackage{xstring} +\RequirePackage{etoolbox} +\RequirePackage{pgfkeys} +\usetikzlibrary{decorations.markings} + +\ProcessOptions\relax + + +%% +%% Application programming interface: +%% + +\newcommand*{\dynk}[3][]{%% +\tikz[baseline=-\the\dimexpr\fontdimen22\textfont2\relax ] \dynkin[#1]{#2}{#3};% +}%% + +% See test1.tex file for examples of use. + +\newcommand*{\dynkin}[3][]{ +\pgfkeys{/dynkin, default, #1}% +\IfStrEq{#3}{*}{}{\dynkinrank=#3} +\IfStrEq{#2}{A}{\Adynkin[\dynkinparabolic]{#3}}{} +\IfStrEq{#2}{B}{\Bdynkin[\dynkinparabolic]{#3}}{} +\IfStrEq{#2}{C}{\Cdynkin[\dynkinparabolic]{#3}}{} +\IfStrEq{#2}{D}{\Ddynkin[\dynkinparabolic]{#3}}{} +\IfStrEq{#2}{E}{\Edynkin[\dynkinparabolic]{#3}}{} +\IfStrEq{#2}{F}{\Ffourdynkin[\dynkinparabolic]{#3}}{} +\IfStrEq{#2}{G}{\Gtwodynkin[\dynkinparabolic]}{} +\IfStrEq{\dynkinlabeltheroots}{true}{\dynkinprintlabels}{} +} + + + +%%% +%%% Implementation: +%%% + +\newcount\dynkinrank + +\pgfkeys{ + /dynkin/.is family, + /tikz/decoration={markings,mark=at position 0.7 with {\arrow{>}}}, + /dynkin, + default/.style = { + label = false, + parabolic = 0, + color = black, + background color = white, + dotradius=.04cm, + edgelength=.35cm, + crosssize=.07cm + }, + label/.estore in = \dynkinlabeltheroots, + parabolic/.estore in = \dynkinparabolic, + color/.store in =\dynkincolor, + background color/.store in =\dynkinbackcolor, + dotradius/.estore in = \dynkinradius, + edgelength/.estore in = \dykinedgelength, + crosssize/.estore in = \dynkinXsize, + .search also={/tikz}, +} + + +\newcommand{\dynkinprintlabels} +{ +\newcount\rmo +\rmo=\dynkinrank +\advance\rmo by -1 +\foreach \i in {0,...,\the\rmo} +{ +\node at (root label \i) {\scalebox{0.5}{\(\i\)}}; +} +} + + +\newcommand{\dynkincross}[2]{ +\dynkindot{#1}{#2} +\draw[thick,\dynkincolor] ({#1*\dykinedgelength},{#2*\dykinedgelength}) -- ++ ({(1/sqrt(2))*\dynkinXsize},{(1/sqrt(2))*\dynkinXsize}); +\draw[thick,\dynkincolor] ({#1*\dykinedgelength},{#2*\dykinedgelength}) -- ++ ({-(1/sqrt(2))*\dynkinXsize},{(1/sqrt(2))*\dynkinXsize}); +\draw[thick,\dynkincolor] ({#1*\dykinedgelength},{#2*\dykinedgelength}) -- ++ ({(1/sqrt(2))*\dynkinXsize},{-(1/sqrt(2))*\dynkinXsize}); +\draw[thick,\dynkincolor] ({#1*\dykinedgelength},{#2*\dykinedgelength}) -- ++ ({-(1/sqrt(2))*\dynkinXsize},{-(1/sqrt(2))*\dynkinXsize}); +} + +\newcommand{\dynkindot}[2]{% +\fill[\dynkincolor] (\dykinedgelength*#1,\dykinedgelength*#2) circle (\dynkinradius);% +} + +% Line between nodes. +\newcommand{\dynkinline}[4]{\draw[thin,\dynkincolor] (\dykinedgelength*#1,\dykinedgelength*#2) -- (\dykinedgelength*#3,\dykinedgelength*#4);} + +% Dotted line between nodes. +\newcommand{\dynkindots}[4]{\draw[densely dotted,\dynkincolor] (\dykinedgelength*#1,\dykinedgelength*#2) -- (\dykinedgelength*#3,\dykinedgelength*#4);} + +% Double line between nodes. +\newcommand{\dynkindoubleline}[4]{\draw[double,postaction={decorate},\dynkincolor] (\dykinedgelength*#1,\dykinedgelength*#2) -- (\dykinedgelength*#3,\dykinedgelength*#4);} + +% Triple line between nodes. +\newcommand{\dynkintripleline}[4]{ +\draw[triple={[line width=.1mm,\dynkincolor] in + [line width=.6mm,\dynkinbackcolor] in + [line width=.8mm,\dynkincolor]}] (\dykinedgelength*#3,\dykinedgelength*#4) -- (\dykinedgelength*#1,\dykinedgelength*#2); +\draw[postaction={decorate},double,\dynkincolor] ({0.401*\dykinedgelength*#3+0.599*\dykinedgelength*#1},\dykinedgelength*#4) -- ({0.399*\dykinedgelength*#3+0.601*\dykinedgelength*#1},\dykinedgelength*#2); +} +\tikzset{ + triple/.style args={[#1] in [#2] in [#3]}{ + #1,preaction={preaction={draw,#3},draw,#2} + } +} + +\newcommand*{\testbit}[4]% +% if bit number #2 of #1 is 1 then expand #3 else expand #4. +{% +\pgfmathparse{mod(div(#1,2^(#2)),2)}% +\let\tf\pgfmathresult% +\IfStrEq{\tf}{1.0}{#3}{#4}% +}%% + + +\newcommand*{\Adynkin}[2][0]% +%\Adynkin[p]{n} gives the Dynkin diagram of An with parabolic subgroup p. +%\Adynkin[p]{*} allows for an indefinite choice of n, but then the possible parabolics are only from 0 to 2^7. +{%% +\IfStrEq{#2}{*}% +{%% + \dynkinrank=7 + \dynkinline{0}{0}{1}{0}; + \dynkindots{1}{0}{2}{0}; + \dynkinline{2}{0}{4}{0}; + \dynkindots{4}{0}{5}{0}; + \dynkinline{5}{0}{6}{0}; + \foreach \b in {0,...,6}%%% + {%%% + \testbit{#1}{\b}{\dynkincross{\b}{0}}{\dynkindot{\b}{0}} + \node (root \b) at ({\b*\dykinedgelength},0) {}; + \node[below] (root label \b) at ({\b*\dykinedgelength},0) {}; + \node[above] (root label swap \b) at ({\b*\dykinedgelength},0) {}; + }%%% +}%% +{%% +% \draw[\dykinbackcolor] (0,{-\dykinedgelength}) rectangle ({#2*\dykinedgelength},{\dykinedgelength}); + \newcount\rmo + \rmo=#2 + \advance\rmo by -1 + \dynkinline{0}{0}{\the\rmo}{0};% + \foreach \b in {0,...,\the\rmo}%%% + {%%% + \testbit{#1}{\b}{\dynkincross{\b}{0}}{\dynkindot{\b}{0}} + \node (root \b) at ({\b*\dykinedgelength},0) {}; + \node[below] (root label \b) at ({\b*\dykinedgelength},0) {}; + \node[above] (root label swap \b) at ({\b*\dykinedgelength},0) {}; + }%%% +} +}%% + + +\newcommand*{\Bdynkin}[2][0]% +%\Bdynkin[p]{n} gives the Dynkin diagram of Bn with parabolic subgroup p. +%\Bdynkin[p]{*} allows for an indefinite choice of n, but then the possible parabolics are only from 0 to 2^5. +{% +\IfStrEq{#2}{*}% +{%% + \dynkinrank=5 + \dynkinline{0}{0}{1}{0}; + \dynkindots{1}{0}{2}{0}; + \dynkinline{2}{0}{3}{0}; + \dynkindoubleline{3}{0}{4}{0}; + \foreach \b in {0,...,4}%%% + {%%% + \testbit{#1}{\b}{\dynkincross{\b}{0}}{\dynkindot{\b}{0}} + \node (root \b) at ({\b*\dykinedgelength},0) {}; + \node[below] (root label \b) at ({\b*\dykinedgelength},0) {}; + \node[above] (root label swap \b) at ({\b*\dykinedgelength},0) {}; + }%%% +}%% +{%% +\pgfmathparse{subtract(#2,1)}% +\let\rmo\pgfmathresult% +\pgfmathparse{subtract(\rmo,1)}% +\let\rmt\pgfmathresult% +\dynkinline{0}{0}{\rmo}{0};% +\dynkindoubleline{\rmt}{0}{\rmo}{0}; +\foreach \b in {0,...,\rmo}%%% +{%%% +\testbit{#1}{\b}{\dynkincross{\b}{0}}{\dynkindot{\b}{0}} +\node (root \b) at ({\b*\dykinedgelength},0) {}; +\node[below] (root label \b) at ({\b*\dykinedgelength},0) {}; +\node[above] (root label swap \b) at ({\b*\dykinedgelength},0) {}; +}%%% +}%% +}% + +\newcommand*{\Cdynkin}[2][0]% +%\Cdynkin[p]{n} gives the Dynkin diagram of Cn with parabolic subgroup p. +%\Cdynkin[p]{*} allows for an indefinite choice of n, but then the possible parabolics are only from 0 to 2^5. +{%% +\IfStrEq{#2}{*}% +{%% + \dynkinrank=5 + \dynkinline{0}{0}{1}{0}; + \dynkindots{1}{0}{2}{0}; + \dynkinline{2}{0}{3}{0}; + \dynkindoubleline{4}{0}{3}{0}; + \foreach \b in {0,...,4}%%% + {%%% + \testbit{#1}{\b}{\dynkincross{\b}{0}}{\dynkindot{\b}{0}} + \node (root \b) at ({\b*\dykinedgelength},0) {}; + \node[below] (root label \b) at ({\b*\dykinedgelength},0) {}; + \node[above] (root label swap \b) at ({\b*\dykinedgelength},0) {}; + }%%% +}%% +{%% +\pgfmathparse{subtract(#2,1)}% +\let\rmo\pgfmathresult% +\pgfmathparse{subtract(\rmo,1)}% +\let\rmt\pgfmathresult% +\dynkinline{0}{0}{\rmo}{0};% +\dynkindoubleline{\rmo}{0}{\rmt}{0}; +\foreach \b in {0,...,\rmo}%%% +{%%% +\testbit{#1}{\b}{\dynkincross{\b}{0}}{\dynkindot{\b}{0}} +\node (root \b) at ({\b*\dykinedgelength},0) {}; +\node[below] (root label \b) at ({\b*\dykinedgelength},0) {}; +\node[above] (root label swap \b) at ({\b*\dykinedgelength},0) {}; +}%%% +}%% +}% + + +\newcommand*{\Ddynkin}[2][0]% +%\Ddynkin[p]{n} gives the Dynkin diagram of Dn with parabolic subgroup p. +%\Ddynkin[p]{*} allows for an indefinite choice of n, but then the possible parabolics are only from 0 to 2^6. +{%% +\IfStrEq{#2}{*}% +{%% + \dynkinrank=6 + \foreach \x in {0,...,3} + { + \dynkindot{\x}{0} + } + \dynkinline{0}{0}{1}{0} + \dynkindots{1}{0}{2}{0} + \dynkinline{2}{0}{3}{0} + \dynkinline{3}{0}{3.5}{.9} + \dynkinline{3}{0}{3.5}{-.9} +\foreach \b in {0,...,3}%%% +{%%% +\testbit{#1}{\b}{\dynkincross{\b}{0}}{\dynkindot{\b}{0}} +\node (root \b) at ({\b*\dykinedgelength},0) {}; +\node[below] (root label \b) at ({\b*\dykinedgelength},0) {}; +}%%% +\testbit{#1}{4}{\dynkincross{3.5}{-.9}}{\dynkindot{3.5}{-.9}} +\node (root 4) at ({3.5*\dykinedgelength},{-.9*\dykinedgelength}) {}; +\node[below] (root label 4) at ({3.5*\dykinedgelength},{-.9*\dykinedgelength}) {}; +\testbit{#1}{5}{\dynkincross{3.5}{.9}}{\dynkindot{3.5}{.9}} +\node (root 5) at ({3.5*\dykinedgelength},{.9*\dykinedgelength}) {}; +\node[above] (root label 5) at ({3.5*\dykinedgelength},{.9*\dykinedgelength}) {}; +}%% +{%% +\newcount\rmo +\rmo=#2 +\advance\rmo by -1 +\newcount\rmt +\rmt=\rmo +\advance\rmt by -1 +\newcount\rmtt +\rmtt=\rmt +\advance\rmtt by -1 +\dynkinline{0}{0}{\the\rmtt}{0};% +\pgfmathparse{subtract(\the\rmt,.5)} +\let\rmh\pgfmathresult% +\dynkinline{\the\rmtt}{0}{\rmh}{.9} +\dynkinline{\the\rmtt}{0}{\rmh}{-.9} +\foreach \b in {0,...,\the\rmtt}%%% +{%%% +\testbit{#1}{\b}{\dynkincross{\b}{0}}{\dynkindot{\b}{0}} +\node (root \b) at ({\b*\dykinedgelength},0) {}; +\node[below] (root label \b) at ({\b*\dykinedgelength},0) {}; +}%%% +\testbit{#1}{\the\rmt}{\dynkincross{\rmh}{-.9}}{\dynkindot{\rmh}{-.9}} +\node (root \the\rmt) at ({\rmh*\dykinedgelength},{-.9*\dykinedgelength}) {}; +\node[below] (root label \the\rmt) at ({\rmh*\dykinedgelength},{-.9*\dykinedgelength}) {}; +\testbit{#1}{\the\rmo}{\dynkincross{\rmh}{.9}}{\dynkindot{\rmh}{.9}} +\node (root \the\rmo) at ({\rmh*\dykinedgelength},{.9*\dykinedgelength}) {}; +\node[above] (root label \the\rmo) at ({\rmh*\dykinedgelength},{.9*\dykinedgelength}) {}; +}%% +}% + +\newcommand*{\Edynkin}[2][0]% +%\Edynkin[p]{n} gives the Dynkin diagram of En, n=6,7,8, with parabolic subgroup p. +{ +\pgfmathparse{subtract(#2,1)}% +\let\rmo\pgfmathresult% +\pgfmathparse{subtract(\rmo,1)}% +\let\rmt\pgfmathresult% +\dynkinline{0}{0}{\rmt}{0};% +\dynkinline{2}{0}{2}{1} +\testbit{#1}{0}{\dynkincross{0}{0}}{\dynkindot{0}{0}} +\node (root 0) at (0,0) {}; +\node[below] (root label 0) at (0,0) {}; +\testbit{#1}{1}{\dynkincross{2}{1}}{\dynkindot{2}{1}} +\node (root 1) at ({2*\dykinedgelength},{1*\dykinedgelength}) {}; +\node[above] (root label 1) at ({2*\dykinedgelength},{1*\dykinedgelength}) {}; +\foreach \b in {2,...,\rmo}%%% +{%%% +\pgfmathparse{subtract(\b,1)}% +\let\bmo\pgfmathresult% +\testbit{#1}{\b}{\dynkincross{\bmo}{0}}{\dynkindot{\bmo}{0}} +\node (root \b) at ({\bmo*\dykinedgelength},0) {}; +\node[below] (root label \b) at ({\bmo*\dykinedgelength},0) {}; +}%%% +} + + +\newcommand*{\Ffourdynkin}[1][0]% +%\Fdynkin[p]{n} gives the Dynkin diagram of F4 with parabolic subgroup p. +{ +\dynkinline{0}{0}{3}{0};% +\dynkindoubleline{1}{0}{2}{0} +\foreach \b in {0,...,3}%%% +{%%% +\testbit{#1}{\b}{\dynkincross{\b}{0}}{\dynkindot{\b}{0}} +\node (root \b) at ({\b*\dykinedgelength},0) {}; +\node[below] (root label \b) at ({\b*\dykinedgelength},0) {}; +\node[above] (root label swap \b) at ({\b*\dykinedgelength},0) {}; +}%%% +} + +\newcommand*{\Gtwodynkin}[1][0]% +%\Gtwodynkin[p] gives the Dynkin diagram of G2 with parabolic subgroup p. +{%% +\dynkintripleline{0}{0}{1}{0};% +\foreach \b in {0,...,1}%%% +{%%% +\testbit{#1}{\b}{\dynkincross{\b}{0}}{\dynkindot{\b}{0}} +\node (root \b) at ({\b*\dykinedgelength},0) {}; +\node[below] (root label \b) at ({\b*\dykinedgelength},0) {}; +\node[above] (root label swap \b) at ({\b*\dykinedgelength},0) {}; +}%%% +}%% + + + +\endinput |