From 4f8d8a303ae1f3c7a2a6b1eb4624a4c6a3b31d07 Mon Sep 17 00:00:00 2001 From: Karl Berry Date: Sun, 11 Feb 2018 22:49:52 +0000 Subject: dynkin-diagrams (11feb18) git-svn-id: svn://tug.org/texlive/trunk@46600 c570f23f-e606-0410-a88d-b1316a301751 --- .../tex/latex/dynkin-diagrams/dynkin-diagrams.sty | 4511 +++++++++++++++----- 1 file changed, 3357 insertions(+), 1154 deletions(-) (limited to 'Master/texmf-dist/tex/latex/dynkin-diagrams') diff --git a/Master/texmf-dist/tex/latex/dynkin-diagrams/dynkin-diagrams.sty b/Master/texmf-dist/tex/latex/dynkin-diagrams/dynkin-diagrams.sty index 8ed53464f8f..aec4b70689c 100644 --- a/Master/texmf-dist/tex/latex/dynkin-diagrams/dynkin-diagrams.sty +++ b/Master/texmf-dist/tex/latex/dynkin-diagrams/dynkin-diagrams.sty @@ -2,7 +2,7 @@ % % The Dynkin Diagrams package. % -% Version 2 +% Version 3.1 % % % This package draws Dynkin diagrams in LaTeX documents, using the TikZ package. @@ -18,7 +18,7 @@ % % \NeedsTeXFormat{LaTeX2e}[1994/06/01] -\ProvidesPackage{dynkin-diagrams}[2017/11/14 Dynkin diagrams] +\ProvidesPackage{dynkin-diagrams}[2018/02/11 Dynkin diagrams] \RequirePackage{tikz} \RequirePackage{xstring} \RequirePackage{xparse} @@ -29,122 +29,240 @@ \usetikzlibrary{decorations.markings} \usetikzlibrary{arrows,arrows.meta} \usetikzlibrary{calc} +\usetikzlibrary{fit} %% %% Application programming interface: %% See dynkin-diagrams.tex file for examples of use. %% -\NewDocumentCommand\dynkin{O{}mm}% +\NewDocumentCommand\dynkin{O{}mO{0}m}% {% \ifdefined\filldraw% - \@dynkin[#1]{#2}{#3}% + \@dynkin[#1]{#2}[#3]{#4}% \else% - \tikz[baseline=-\the\dimexpr\fontdimen22\textfont2\relax ]{\@dynkin[#1]{#2}{#3}}% + \tikz[baseline=-0.5ex]{\@dynkin[#1]{#2}[#3]{#4}}% \fi% }% -%% \convertRootNumber{} -%% -> -%% Converts from Bourbaki ordering to the current ordering, storing the result in a count called \RootNumber. -\NewDocumentCommand\convertRootNumber{m}% +\NewDocumentCommand\dynkinRefreshRoots{}% +{% + \dynkin@draw@all@roots{}% + \ifdynkin@label@the@roots\dynkinPrintLabels{}\fi% +}% + + +%% \dynkinLabelRoot{}{} or \dynkinLabelRoot*{}{} +%% Prints the label string on the Dynkin diagram at root number , in the current ordering convention. +%% Starred form uses the opposite label location. +\NewDocumentCommand\dynkinLabelRoot{smm}% {% - \IfStrEq{#1}{0} - { - \global\RootNumber=0 - } - { - \IfStrEqCase{\dynkinseries}% + \ifnum\dynkin@nodes<#2% + \ClassError{Dynkin diagrams}{Unrecognized root: ``#2'' found when labelling Dynkin diagram \dynkin@user@series{\dynkin@user@string}. Allowed values are up to \the\dynkin@nodes}{}% + \fi% + \newcount\rpo% + \rpo=#2% + \advance\rpo by 1% + \StrMid{\dynkin@label@directions}{\the\rpo}{\the\rpo}[\temp]% + \IfBooleanTF{#1}% {% - {E}% - {% - \ifnum\dynkinrank=6% - \IfStrEqCase{\dynkinordering}% - {% - {Adams}{\RootNumber=\stringcharacterinposition{152436}{#1}}% - {Carter}{\RootNumber=\stringcharacterinposition{142356}{#1}}% - {Dynkin}{\RootNumber=\stringcharacterinposition{162345}{#1}}% - {Kac}{\RootNumber=\stringcharacterinposition{162345}{#1}}% + \IfStrEqCase{\temp}{% + {l}{% + \node[inner sep=\dynkin@root@radius,% + label={% + [/Dynkin diagram,/Dynkin diagram/text]% + right:% + \(\pgfkeys{/Dynkin diagram/labelMacro=#3}\)% }% - [\RootNumber=#1]% - \else% - \ifnum\dynkinrank=7% - \IfStrEqCase{\dynkinordering}% - {% - {Adams}{\RootNumber=\stringcharacterinposition{6354217}{#1}}% - {Carter}{\RootNumber=\stringcharacterinposition{7564321}{#1}}% - {Dynkin}{\RootNumber=\stringcharacterinposition{1723456}{#1}}% - {Kac}{\RootNumber=\stringcharacterinposition{1723456}{#1}}% + ]% + at (\dynkin@root@name #2){};% + }% + {r}{% + \node[inner sep=\dynkin@root@radius,% + label={% + [/Dynkin diagram,/Dynkin diagram/text]% + left:% + \(\pgfkeys{/Dynkin diagram/labelMacro=#3}\)% }% - [\RootNumber=#1]% - \else% - \ifnum\dynkinrank=8% - \IfStrEqCase{\dynkinordering}% - {% - {Adams}{\RootNumber=\stringcharacterinposition{13245678}{#1}}% - {Carter}{\RootNumber=\stringcharacterinposition{86754321}{#1}}% - {Dynkin}{\RootNumber=\stringcharacterinposition{18234567}{#1}}% - {Kac}{\RootNumber=\stringcharacterinposition{78654321}{#1}}% - }% - [\RootNumber=#1]% - \else% - \fi% - \fi% - \fi% - }% - {F}% - {% - \IfStrEqCase{\dynkinordering}% - {% - {Adams}{\RootNumber=\stringcharacterinposition{4321}{#1}}% + ]% + at (\dynkin@root@name #2){};% + }% + {a}{% + \node[inner sep=\dynkin@root@radius,% + label={% + [/Dynkin diagram,/Dynkin diagram/text]% + below:% + \(\pgfkeys{/Dynkin diagram/labelMacro=#3}\)% + }% + ]% + at (\dynkin@root@name #2){};% + }% + {b}{% + \node[inner sep=\dynkin@root@radius,% + label={% + [/Dynkin diagram,/Dynkin diagram/text]% + above:% + \(\pgfkeys{/Dynkin diagram/labelMacro=#3}\)% + }% + ]% + at (\dynkin@root@name #2){};% + }% + {d}{% + \node[inner sep=\dynkin@root@radius,% + label={% + [/Dynkin diagram,/Dynkin diagram/text]% + above right:% + \(\pgfkeys{/Dynkin diagram/labelMacro=#3}\)% + }% + ]% + at (\dynkin@root@name #2){};% }% - [\RootNumber=#1]% }% - {G}% - {% - \IfStrEqCase{\dynkinordering}% - {% - {Carter}{\RootNumber=\stringcharacterinposition{21}{#1}}% - {Dynkin}{\RootNumber=\stringcharacterinposition{21}{#1}}% - {Kac}{\RootNumber=\stringcharacterinposition{21}{#1}}% + [\ClassError% + {Dynkin diagrams}% + {Unrecognized root label direction: + ``\temp'' in Dynkin diagram \dynkin@user@series{\dynkin@user@string} for root #2}% + {}] + }% + {% + \IfStrEqCase{\temp}{% + {l}{% + \node[inner sep=\dynkin@root@radius,% + label={% + [/Dynkin diagram,/Dynkin diagram/text]% + left:% + \(\pgfkeys{/Dynkin diagram/labelMacro=#3}\)% + }% + ]% + at (\dynkin@root@name #2){};% + }% + {r}{% + \node[inner sep=\dynkin@root@radius,% + label={% + [/Dynkin diagram,/Dynkin diagram/text]% + right:% + \(\pgfkeys{/Dynkin diagram/labelMacro=#3}\)% + }% + ]% + at (\dynkin@root@name #2){};% + }% + {a}{% + \node[inner sep=\dynkin@root@radius,% + label={% + [/Dynkin diagram,/Dynkin diagram/text]% + above:% + \(\pgfkeys{/Dynkin diagram/labelMacro=#3}\)% + }% + ]% + at (\dynkin@root@name #2){};% + }% + {b}{ % + \node[inner sep=\dynkin@root@radius,% + label={% + [/Dynkin diagram,/Dynkin diagram/text]% + below:% + \(\pgfkeys{/Dynkin diagram/labelMacro=#3}\)% + }% + ]% + at (\dynkin@root@name #2){};% + }% + {d}{% + \node[inner sep=\dynkin@root@radius,% + label={% + [/Dynkin diagram,/Dynkin diagram/text]% + below right:% + \(\pgfkeys{/Dynkin diagram/labelMacro=#3}\)% + }% + ]% + at (\dynkin@root@name #2){};% }% - [\RootNumber=#1]% }% + [\ClassError% + {Dynkin diagrams}% + {Unrecognized root label direction: + ``\temp'' in Dynkin diagram \dynkin@user@series{\dynkin@user@string} for root #2}% + {}] }% - [\RootNumber=#1]% - } }% -\NewDocumentCommand\dynkinprint{m}% +%% \dynkinPrintLabels +%% Prints the default labels on the Dynkin diagram, in the given ordering. +\newcommand{\dynkinPrintLabels}% {% - \scalebox{\dynkintextscale}{\(#1\)}% + \foreach \i in {1,...,\the\dynkin@nodes}{\dynkinLabelRoot{\i}{\i}}% + \ifdynkin@is@extended% + \dynkinLabelRoot{0}{0}% + \else% + \ifdynkin@is@twisted% + \dynkinLabelRoot{0}{0}% + \fi% + \fi% }% -%% \rootlabel{}{} or \rootlabel*{}{} -%% -> -%% Prints the label string on the Dynkin diagram at root number , in the current ordering convention. -\NewDocumentCommand\rootlabel{smm}% +%% \dynkinCrossRootMark{} +%% Prints a cross at root on the current Dynkin diagram. +%% The starred form accepts in the Bourbaki ordering. +\NewDocumentCommand\dynkinCrossRootMark{sO{}m}% {% \IfBooleanTF{#1}% - {\node at (root label swap #2) {\dynkinprint{#3}};}% - {\node at (root label #2) {\dynkinprint{#3}};}% + {% + \convertRootNumber{#3}% + }% + {% + \RootNumber=#3% + }% + \draw[/Dynkin diagram,/Dynkin diagram/x,#2]% + ($(\dynkin@root@name \the\RootNumber)+(\dynkin@root@radius,\dynkin@root@radius)$)% + --% + ($(\dynkin@root@name \the\RootNumber)-(\dynkin@root@radius,\dynkin@root@radius)$);% + \draw[/Dynkin diagram,/Dynkin diagram/x,#2]% + ($(\dynkin@root@name \the\RootNumber)+(-\dynkin@root@radius,\dynkin@root@radius)$)% + --% + ($(\dynkin@root@name \the\RootNumber)+(\dynkin@root@radius,-\dynkin@root@radius)$);% }% -%% \dynkinprintlabels -%% -> -%% Prints the default labels on the Dynkin diagram, in the given ordering. -\newcommand{\dynkinprintlabels}% +%% \dynkinHeavyCrossRootMark{} +%% Prints a heavy cross at root on the current Dynkin diagram. +%% The starred form accepts in the Bourbaki ordering. +\NewDocumentCommand\dynkinHeavyCrossRootMark{sO{}m}% +{% + \IfBooleanTF{#1}% + {% + \convertRootNumber{#3}% + }% + {% + \RootNumber=#3% + }% + \draw[/Dynkin diagram,/Dynkin diagram/X,#2]% + ($(\dynkin@root@name \the\RootNumber)+(\dynkin@root@radius,\dynkin@root@radius)$)% + --% + ($(\dynkin@root@name \the\RootNumber)-(\dynkin@root@radius,\dynkin@root@radius)$);% + \draw[/Dynkin diagram,/Dynkin diagram/X,#2]% + ($(\dynkin@root@name \the\RootNumber)+(-\dynkin@root@radius,\dynkin@root@radius)$)% + --% + ($(\dynkin@root@name \the\RootNumber)+(\dynkin@root@radius,-\dynkin@root@radius)$);% +}% + + +%% \dynkinHollowRootMark{} +%% Prints an hollow dot at root on the current Dynkin diagram. +%% The starred form accepts in the Bourbaki ordering. +\NewDocumentCommand\dynkinHollowRootMark{sO{}m}% {% - \foreach \i in {1,...,\the\dynkinrank}% - {\rootlabel{\i}{\i}}% - \ifisaffine\rootlabel{0}{0}\fi% + \IfBooleanTF{#1}% + {% + \convertRootNumber{#3}% + }% + {% + \RootNumber=#3% + }% + \fill[/Dynkin diagram,/Dynkin diagram/o,#2] (\dynkin@root@name \the\RootNumber) circle (\dynkin@root@radius);% }% -%% \dynkincross{} -%% -> -%% Prints a cross at root on the current Dynkin diagram. +%% \dynkinDoubleHollowRootMark{} +%% Prints a double hollow dot at root on the current Dynkin diagram. %% The starred form accepts in the Bourbaki ordering. -\NewDocumentCommand\dynkincross{sO{}m}% +\NewDocumentCommand\dynkinDoubleHollowRootMark{sO{}m}% {% \IfBooleanTF{#1}% {% @@ -153,21 +271,14 @@ {% \RootNumber=#3% }% - \draw[\dynkincrossstyle,\dynkincolor,#2]% - ($(root \the\RootNumber)+(\dynkinradius,\dynkinradius)$)% - --% - ($(root \the\RootNumber)-(\dynkinradius,\dynkinradius)$);% - \draw[\dynkincrossstyle,\dynkincolor]% - ($(root \the\RootNumber)+(-\dynkinradius,\dynkinradius)$)% - --% - ($(root \the\RootNumber)+(\dynkinradius,-\dynkinradius)$);% + \fill[/Dynkin diagram,/Dynkin diagram/o,#2] (\dynkin@root@name \the\RootNumber) circle (2*\dynkin@root@radius);% + \fill[/Dynkin diagram,/Dynkin diagram/o,#2] (\dynkin@root@name \the\RootNumber) circle (\dynkin@root@radius);% }% -%% \dynkinopendot{} -%% -> -%% Prints an open dot at root on the current Dynkin diagram. +%% \dynkinSolidRootMark{} +%% Prints a solid dot at root on the current Dynkin diagram. %% The starred form accepts in the Bourbaki ordering. -\NewDocumentCommand\dynkinopendot{sO{}m}% +\NewDocumentCommand\dynkinSolidRootMark{sO{}m}% {% \IfBooleanTF{#1}% {% @@ -176,14 +287,13 @@ {% \RootNumber=#3% }% - \fill[\dynkinbackcolor,draw=\dynkincolor,#2] (root \the\RootNumber) circle (\dynkinradius);% + \fill[/Dynkin diagram,/Dynkin diagram/*,#2] (\dynkin@root@name \the\RootNumber) circle (\dynkin@root@radius);% }% -%% \dynkincloseddot{} -%% -> -%% Prints a closed dot at root on the current Dynkin diagram. +%% \dynkinTensorRootMark{} +%% Prints a tensor product symbol at root on the current Dynkin diagram. %% The starred form accepts in the Bourbaki ordering. -\NewDocumentCommand\dynkincloseddot{sO{}m}% +\NewDocumentCommand\dynkinTensorRootMark{sO{}m}% {% \IfBooleanTF{#1}% {% @@ -192,53 +302,60 @@ {% \RootNumber=#3% }% - \fill[\dynkincolor,draw=\dynkincolor,#2] (root \the\RootNumber) circle (\dynkinradius);% + \fill[/Dynkin diagram,/Dynkin diagram/o,#2] (\dynkin@root@name \the\RootNumber) circle ({\dynkin@root@radius});% + \draw[/Dynkin diagram,/Dynkin diagram/x,#2]% + ($(\dynkin@root@name \the\RootNumber)+({\dynkin@root@radius/sqrt(2)},{\dynkin@root@radius/sqrt(2)})$)% + --% + ($(\dynkin@root@name \the\RootNumber)-({\dynkin@root@radius/sqrt(2)},{\dynkin@root@radius/sqrt(2)})$);% + \draw[/Dynkin diagram,/Dynkin diagram/x,#2]% + ($(\dynkin@root@name \the\RootNumber)+({-\dynkin@root@radius/sqrt(2)},{\dynkin@root@radius/sqrt(2)})$)% + --% + ($(\dynkin@root@name \the\RootNumber)+({\dynkin@root@radius/sqrt(2)},{-\dynkin@root@radius/sqrt(2)})$);% }% -%% \dynkindot{} -%% -> -%% Prints a dot at root on the current Dynkin diagram in the default style. +%% \dynkinRootMark{}{} +%% Prints a dot at root on the current Dynkin diagram using mark style . +%% Use empty to get the default mark style. %% The starred form accepts in the Bourbaki ordering. -\NewDocumentCommand\dynkindot{sO{}m}% +\NewDocumentCommand\dynkinRootMark{smm}% {% \IfBooleanTF{#1}% {% - \ifnum#3=0% - \ifdynkinopendots% - \dynkincloseddot*[#2]{0}% - \else% - \dynkinopendot*[#2]{0}% - \fi% - \else% - \ifdynkinopendots% - \dynkinopendot*[#2]{#3}% - \else% - \dynkincloseddot*[#2]{#3}% - \fi% - \fi% + \IfStrEqCase{#2}% + {% + {}{\dynkinRootMark*{\dynkin@root@mark}{#3}}% + {*}{\dynkinSolidRootMark*{#3}}% + {O}{\dynkinDoubleHollowRootMark*{#3}}% + {X}{\dynkinHeavyCrossRootMark*{#3}}% + {o}{\dynkinHollowRootMark*{#3}}% + {t}{\dynkinTensorRootMark*{#3}}% + {x}{\dynkinCrossRootMark*{#3}}% + }% + [\ClassError% + {Dynkin diagrams}% + {Unrecognized root mark: ``#2'' in Dynkin diagram% + \dynkin@user@series{\dynkin@user@string}}% + {}] }% {% - \ifnum#3=0% - \ifdynkinopendots% - \dynkincloseddot[#2]{0}% - \else% - \dynkinopendot[#2]{0}% - \fi% - \else% - \ifdynkinopendots% - \dynkinopendot[#2]{#3}% - \else% - \dynkincloseddot[#2]{#3}% - \fi% - \fi% + \IfStrEqCase{#2}% + {% + {}{\dynkinRootMark{\dynkin@root@mark}{#3}}% + {*}{\dynkinSolidRootMark{#3}}% + {O}{\dynkinDoubleHollowRootMark{#3}}% + {X}{\dynkinHeavyCrossRootMark{#3}}% + {o}{\dynkinHollowRootMark{#3}}% + {t}{\dynkinTensorRootMark{#3}}% + {x}{\dynkinCrossRootMark{#3}}% + }% + [\ClassError{Dynkin diagrams}{Unrecognized root mark: ``#2'' in Dynkin diagram \dynkin@user@series{\dynkin@user@string}}{}] }% }% -%% \dynkinline{

}{} -%% -> +%% \dynkinDefiniteSingleEdge{

}{} %% Draws a single line from root

to root on the current Dynkin diagram in the current label ordering. %% The starred form accepts

and in the Bourbaki ordering. -\NewDocumentCommand\dynkinline{sO{}mm}% +\NewDocumentCommand\dynkinDefiniteSingleEdge{sO{}mm}% {% \IfBooleanTF{#1}% {% @@ -248,14 +365,19 @@ \@fromRoot=#3% \@toRoot=#4% }% - \draw[\dynkincolor,\dynkinedgestyle,#2] ($(root \the\@fromRoot)$) -- ($(root \the\@toRoot)$);% + \begin{scope}[on background layer]% + \draw[/Dynkin diagram,edge,#2] + ($(\dynkin@root@name \the\@fromRoot)$) + -- + ($(\dynkin@root@name \the\@toRoot)$);% + \end{scope}% }% -%% \dynkinfoldarrow{

}{} -%% -> -%% Draws an arrow to represent folding from root

to root on the current Dynkin diagram in the current label ordering. +%% \dynkinIndefiniteSingleEdge{

}{} +%% Draws a single line from root

to root on the current Dynkin diagram in the current label ordering, +%% drawn as dashed to indicate an edge containing an indefinite number of roots. %% The starred form accepts

and in the Bourbaki ordering. -\NewDocumentCommand\dynkinfoldarrow{sO{}mm}% +\NewDocumentCommand\dynkinIndefiniteSingleEdge{sO{}mm}% {% \IfBooleanTF{#1}% {% @@ -265,14 +387,54 @@ \@fromRoot=#3% \@toRoot=#4% }% - \draw[\dynkinfoldarrowstyle,\dynkinfoldarrowcolor,#2] (root \the\@fromRoot) -- (root \the\@toRoot);% + \begin{scope}[on background layer]% + \draw[/Dynkin diagram,edge,#2] + ($(\dynkin@root@name \the\@fromRoot)$) + -- + (${(2/3)}*(\dynkin@root@name \the\@fromRoot)+{(1/3)}*(\dynkin@root@name \the\@toRoot)$); + \draw[/Dynkin diagram,/Dynkin diagram/indefiniteEdge,#2] + (${(2/3)}*(\dynkin@root@name \the\@fromRoot)+{(1/3)}*(\dynkin@root@name \the\@toRoot)$) + -- + (${(1/3)}*(\dynkin@root@name \the\@fromRoot)+{(2/3)}*(\dynkin@root@name \the\@toRoot)$); + \draw[/Dynkin diagram,/Dynkin diagram/edge,#2] + (${(1/3)}*(\dynkin@root@name \the\@fromRoot)+{(2/3)}*(\dynkin@root@name \the\@toRoot)$) + -- + ($(\dynkin@root@name \the\@toRoot)$); + \end{scope}% +}% + +%%% \dynkinRightFold{

}{} +%%% Draws an arrow to represent folding from root

to root on the current Dynkin diagram in the current label ordering, curving to the right. +%%% The starred form accepts

and in the Bourbaki ordering. +\NewDocumentCommand\dynkinRightFold{sO{}mm}% +{% + \IfBooleanTF{#1}% + {% + \dynkinFold*[/Dynkin diagram/rightFold,#2]{#3}{#4}% + }% + {% + \dynkinFold[/Dynkin diagram/rightFold,#2]{#3}{#4}% + }% }% -%% \dynkindownarc{

}{} -%% -> -%% Draws a quarter circle from root

to root on the current Dynkin diagram in the current label ordering. +%%% \dynkinLeftFold{

}{} +%%% Draws an arrow to represent folding from root

to root on the current Dynkin diagram in the current label ordering, curving to the left. +%%% The starred form accepts

and in the Bourbaki ordering. +\NewDocumentCommand\dynkinLeftFold{sO{}mm}% +{% + \IfBooleanTF{#1}% + {% + \dynkinFold*[/Dynkin diagram/leftFold,#2]{#3}{#4}% + }% + {% + \dynkinFold[/Dynkin diagram/leftFold,#2]{#3}{#4}% + }% +}% + +%% \dynkinFold{

}{} +%% Draws some colouring to indicate which roots are being folded together, including roots

and . %% The starred form accepts

and in the Bourbaki ordering. -\NewDocumentCommand\dynkindownarc{sO{}mm}% +\NewDocumentCommand\dynkinFold{sO{}mm}% {% \IfBooleanTF{#1}% {% @@ -282,14 +444,21 @@ \@fromRoot=#3% \@toRoot=#4% }% - \draw[\dynkincolor,\dynkinedgestyle,#2] ($(root \the\@fromRoot)$) arc (90:0:\dynkinedgelength);% + \convertRootPair{\@fromRoot}{\@toRoot}% + \begin{scope}[on background layer] + \draw + [/Dynkin diagram/foldStyle,#2] + ($(\dynkin@root@name \the\@fromRoot)$) + to + ($(\dynkin@root@name \the\@toRoot)$); + \end{scope}% }% -%% \dynkinuparc{

}{} -%% -> + +%% \dynkinDefiniteRightDownArc{

}{} %% Draws a quarter circle from root

to root on the current Dynkin diagram in the current label ordering. %% The starred form accepts

and in the Bourbaki ordering. -\NewDocumentCommand\dynkinuparc{sO{}mm}% +\NewDocumentCommand\dynkinDefiniteRightDownArc{sO{}mm}% {% \IfBooleanTF{#1}% {% @@ -299,14 +468,17 @@ \@fromRoot=#3% \@toRoot=#4% }% - \draw[\dynkincolor,\dynkinedgestyle,#2] ($(root \the\@fromRoot)$) arc (0:-90:\dynkinedgelength);% + \begin{scope}[on background layer]% + \draw[/Dynkin diagram,/Dynkin diagram/edge,fill=none,#2]% + ($(\dynkin@root@name \the\@fromRoot)$)% + arc (90:0:\dynkin@fold@radius) -- ($(\dynkin@root@name \the\@toRoot)$);% + \end{scope}% }% -%% \dynkinsemicircle{

}{} -%% -> -%% Draws a half circle from root

to root on the current Dynkin diagram in the current label ordering. +%% \dynkinIndefiniteRightDownArc{

}{} +%% Draws a quarter circle from root

to root on the current Dynkin diagram in the current label ordering. %% The starred form accepts

and in the Bourbaki ordering. -\NewDocumentCommand\dynkinsemicircle{sO{}mm}% +\NewDocumentCommand\dynkinIndefiniteRightDownArc{sO{}mm}% {% \IfBooleanTF{#1}% {% @@ -316,14 +488,27 @@ \@fromRoot=#3% \@toRoot=#4% }% - \draw[\dynkincolor,\dynkinedgestyle,#2] ($(root \the\@fromRoot)$) arc (90:-90:\dynkinedgelength);% + \node (center) at ($(\dynkin@root@name \the\@fromRoot)-(0,\dynkin@fold@radius)$) {};% + \begin{scope}[on background layer]% + \draw[/Dynkin diagram,/Dynkin diagram/edge,fill=none,#2] + (center) + ++(90:\dynkin@fold@radius) + arc [start angle=90, end angle=60, radius=\dynkin@fold@radius];% + \draw[/Dynkin diagram,/Dynkin diagram/indefiniteEdge,fill=none,#2] + (center) + ++(60:\dynkin@fold@radius) + arc [start angle=60, end angle=30, radius=\dynkin@fold@radius];% + \draw[/Dynkin diagram,/Dynkin diagram/edge,fill=none,#2] + (center) + ++(30:\dynkin@fold@radius) + arc [start angle=30, end angle=0, radius=\dynkin@fold@radius];% + \end{scope}% }% -%% \dynkindots{

}{s} -%% -> -%% Draws a dotted line from root

to root on the current Dynkin diagram. +%% \dynkinDefiniteRightUpArc{

}{} +%% Draws a quarter circle from root

to root on the current Dynkin diagram in the current label ordering. %% The starred form accepts

and in the Bourbaki ordering. -\NewDocumentCommand\dynkindots{sO{}mm}% +\NewDocumentCommand\dynkinDefiniteRightUpArc{sO{}mm}% {% \IfBooleanTF{#1}% {% @@ -333,14 +518,17 @@ \@fromRoot=#3% \@toRoot=#4% }% - \draw[densely dotted,\dynkincolor,#2] ($(root \the\@fromRoot)$) -- ($(root \the\@toRoot)$);% + \begin{scope}[on background layer]% + \draw[/Dynkin diagram,/Dynkin diagram/edge,fill=none,#2] + ($(\dynkin@root@name \the\@fromRoot)$) + arc (-90:0:\dynkin@fold@radius) -- ($(\dynkin@root@name \the\@toRoot)$);% + \end{scope}% }% -%% \dynkindoubleline{

}{} -%% -> -%% Draws an oriented double line from root

to root on the current Dynkin diagram. +%% \dynkinIndefiniteRightUpArc{

}{} +%% Draws a quarter circle from root

to root on the current Dynkin diagram in the current label ordering. %% The starred form accepts

and in the Bourbaki ordering. -\NewDocumentCommand\dynkindoubleline{sO{}mm}% +\NewDocumentCommand\dynkinIndefiniteRightUpArc{sO{}mm}% {% \IfBooleanTF{#1}% {% @@ -350,20 +538,28 @@ \@fromRoot=#3% \@toRoot=#4% }% - \ifdynkinarrows% - \draw[double,postaction={decorate},\dynkincolor,\dynkinedgestyle,#2]% - ($(root \the\@fromRoot)$) -- ($(root \the\@toRoot)$);% - \else% - \draw[double,\dynkincolor,\dynkinedgestyle,#2]% - ($(root \the\@fromRoot)$) -- ($(root \the\@toRoot)$);% - \fi% + \node (center) at ($(\dynkin@root@name \the\@fromRoot)+(0,\dynkin@fold@radius)$) {};% + \begin{scope}[on background layer]% + \draw[/Dynkin diagram,/Dynkin diagram/edge,fill=none,#2] + (center) + ++(-90:\dynkin@fold@radius) + arc [start angle=-90, end angle=-60, radius=\dynkin@fold@radius];% + \draw[/Dynkin diagram,/Dynkin diagram/indefiniteEdge,fill=none,#2] + (center) + ++(-60:\dynkin@fold@radius) + arc [start angle=-60, end angle=-30, radius=\dynkin@fold@radius];% + \draw[/Dynkin diagram,/Dynkin diagram/edge,fill=none,#2] + (center) + ++(-30:\dynkin@fold@radius) + arc [start angle=-30, end angle=0, radius=\dynkin@fold@radius] -- ($(\dynkin@root@name \the\@toRoot)$);% + \end{scope}% }% -%% \dynkintripleline{

} -%% -> -%% Draws an oriented triple line from root

to root on the current Dynkin diagram. + +%% \dynkinDefiniteLeftDownArc{

}{} +%% Draws a quarter circle from root

to root on the current Dynkin diagram in the current label ordering. %% The starred form accepts

and in the Bourbaki ordering. -\NewDocumentCommand\dynkintripleline{sO{}mm}% +\NewDocumentCommand\dynkinDefiniteLeftDownArc{sO{}mm}% {% \IfBooleanTF{#1}% {% @@ -373,1113 +569,3120 @@ \@fromRoot=#3% \@toRoot=#4% }% - \pgfmathparse{mod(div(\dynkinparabolic,2),2)}% - \let\onesbit\pgfmathresult% - \pgfmathparse{mod(div(\dynkinparabolic,4),2)}% - \let\twosbit\pgfmathresult% - \draw[\dynkincolor,fill=\dynkinbackcolor,\dynkinedgestyle,#2] % - ($(root \the\@fromRoot)$)% - --% - +(\onesbit*\dynkinradius,\dynkinradius)% - --% - ($(root \the\@toRoot)+(-\twosbit*\dynkinradius,\dynkinradius)$)% - --% - ($(root \the\@toRoot)$)% - --% - ($(root \the\@toRoot)-(\twosbit*\dynkinradius,\dynkinradius)$)% - --% - ($(root \the\@fromRoot)+(\onesbit*\dynkinradius,-\dynkinradius)$)% - --% - cycle;% - \ifdynkinarrows% - \draw[% - \dynkincolor,% - \dynkinedgestyle,% - -{Classical TikZ Rightarrow[length={3*\dynkinradius}]},% - #2% - ]% - ($(root \the\@toRoot)$) --% - ($.65*(root \the\@fromRoot)+.35*(root \the\@toRoot)$);% - \fi% - \draw[\dynkincolor,#2] ($(root \the\@fromRoot)$) -- ($(root \the\@toRoot)$);% + \begin{scope}[on background layer]% + \draw[/Dynkin diagram,/Dynkin diagram/edge,fill=none,#2]% + ($(\dynkin@root@name \the\@fromRoot)$)% + arc (90:180:\dynkin@fold@radius) -- ($(\dynkin@root@name \the\@toRoot)$);% + \end{scope}% }% - -%%% -%%% Implementation: -%%% - -\def\dynkinseries{A} % Which series of root system: A,B,C,D,E,F,G -\newcount\dynkinrank % Which rank of root system: 1,2,... -\newif\ifisaffine % Is this an affine extended root system? -\newif\iflabeltheroots % Should we label the roots by the current root ordering convention? -\newif\ifdynkinopendots % Should we draw the roots using open circles or closed dots? -\newif\ifdynkinarrows % Should we draw arrows on Dynkin diagrams? -\newif\ifdynkincoxeter % Should we draw Coxeter diagrams? -\newif\ifdynkinfolded % Should we fold our Dynkin diagrams? - -\pgfkeys{% - /dynkin/.is family,% - /tikz/decoration={markings,mark=at position 0.7 with {\arrow{>}}},% - /dynkin,% - open/.is if = dynkinopendots,% - open=false,% - Coxeter/.is if = dynkincoxeter,% - Coxeter=false,% - arrows/.is if = dynkinarrows,% - arrows=true,% - dotradius/.estore in = \dynkinradius,% - dotradius=.05cm,% - color/.store in =\dynkincolor,% - backgroundcolor/.store in =\dynkinbackcolor,% - color = black,% - backgroundcolor = white,% - edge/.store in = \dynkinedgestyle,% - edge = thin,% - cross/.store in = \dynkincrossstyle,% - cross = thick,% - edgelength/.estore in = \dynkinedgelength,% - edgelength = .35cm,% - ordering/.store in = \dynkinordering,% - ordering = Bourbaki,% - textscale/.estore in = \dynkintextscale,% - textscale = 0.7,% - foldarrowstyle/.estore in = \dynkinfoldarrowstyle,% - foldarrowstyle = stealth-stealth,% - foldarrowcolor/.estore in = \dynkinfoldarrowcolor,% - foldarrowcolor = black!50,% - default/.style = {% - label/.is if = labeltheroots,% - label = false,% - parabolic = 0,% - affine/.is if = isaffine,% - affine = false,% - folded/.is if = dynkinfolded,% - folded=false,% - },% - parabolic/.estore in = \dynkinparabolic,% - .search also={/tikz},% -}% - -\ProcessPgfPackageOptions{/dynkin}\relax - -% *=not a Satake diagram -% Anything else is the Roman numeral of the diagram, i.e. EVIII diagrams have numeral VIII. -\gdef\dynkinSatake{*} - -\NewDocumentCommand\@dynkin{O{}mm}{% - \pgfkeys{/dynkin, default, #1}% - \xdef\dynkinseries{#2}% - \IfSubStr{ABCDEFGHI}{#2}{}{\errorSeries}% - \global\dynkinrank=0% - \xdef\dynkinSatake{#3}% - \newif\ifwerefolded - \ifdynkinfolded - \global\werefoldedtrue - \else - \global\werefoldedfalse - \fi - \IfInteger{#3}% +%% \dynkinIndefiniteLeftDownArc{

}{} +%% Draws a quarter circle from root

to root on the current Dynkin diagram in the current label ordering. +%% The starred form accepts

and in the Bourbaki ordering. +\NewDocumentCommand\dynkinIndefiniteLeftDownArc{sO{}mm}% +{% + \IfBooleanTF{#1}% {% - \global\dynkinrank=#3% - \gdef\dynkinSatake{*}% + \convertRootPair{#3}{#4}% }% {% - \IfStrEqCase{#2}% - {% - {A}% - {% - \IfStrEqCase{#3}% - {% - {*}{ }% - {I}{ }% - {II}{}% - {III}{}% - {IV} {}% - }% - [\errorRank]% - }% - {B}% - {% - \IfStrEqCase{#3}% - {% - {*}{ }% - {I}{}% - {II} {}% - }% - [\errorRank]% - }% - {C}% - {% - \IfStrEqCase{#3}% - {% - {*}{ }% - {I}{}% - {II} {}% - }% - [\errorRank]% - }% - {D}% - {% - \IfStrEqCase{#3}% - {% - {*}{ }% - {I}{ }% - {II} {}% - {III}{}% - }% - [\errorRank]% - }% - {E}% - {% - \IfStrEqCase{#3}% - {% - {I}{ \global\dynkinrank=6}% - {II}% - {% - \global\dynkinfoldedtrue% - \global\dynkinrank=6% - }% - {III}% - {% - \global\dynkinfoldedtrue% - \global\dynkinrank=6% - }% - {IV}% - {% - \global\dynkinrank=6% - }% - {V}% - {% - \global\dynkinrank=7% - }% - {VI}% - {% - \global\dynkinrank=7% - }% - {VII}% - {% - \global\dynkinrank=7% - }% - {VIII}% - {% - \global\dynkinrank=8% - }% - {XI}% - {% - \global\dynkinrank=8% - }% - }% - [\errorRank]% - }% - {F}% - {% - \global\dynkinrank=4% - \IfStrEqCase{#3}% - {% - {I}{ }% - {II} {}% - }% - [\errorRank]% - }% - {G}% - {% - \global\dynkinrank=2% - \IfStrEqCase{#3}% - {% - {I}{ }% - }% - [\errorRank]% - }% - {H}% - {% - \IfStrEqCase{#3}% - {% - {*}% - {% - }% - }% - [\errorRank]% - }% - {I}% - {% - \IfStrEqCase{#3}% - {% - {*}% - {% - }% - }% - [\errorRank]% - }% - }% - [\errorSeries]% + \@fromRoot=#3% + \@toRoot=#4% }% - \checkDynkinDiagram% - \ifisaffine% - \csname affine#2dynkin\endcsname% - \else% - \csname#2dynkin\endcsname% - \fi% - \iflabeltheroots\dynkinprintlabels\fi% - \ifwerefolded - \global\dynkinfoldedtrue - \else - \global\dynkinfoldedfalse - \fi + \node (center) at ($(\dynkin@root@name \the\@fromRoot)-(0,\dynkin@fold@radius)$) {};% + \begin{scope}[on background layer]% + \draw[/Dynkin diagram,/Dynkin diagram/edge,fill=none,#2] + (center) + ++(90:\dynkin@fold@radius) + arc [start angle=90, end angle=120, radius=\dynkin@fold@radius];% + \draw[/Dynkin diagram,/Dynkin diagram/indefiniteEdge,fill=none,#2] + (center) + ++(120:\dynkin@fold@radius) + arc [start angle=120, end angle=150, radius=\dynkin@fold@radius];% + \draw[/Dynkin diagram,/Dynkin diagram/edge,fill=none,#2] + (center) + ++(150:\dynkin@fold@radius) + arc [start angle=150, end angle=180, radius=\dynkin@fold@radius] -- ($(\dynkin@root@name \the\@toRoot)$);% + \end{scope}% }% -%% \stringcharacterinposition{}{} -%% -> the element of string in position . -\ExplSyntaxOn -\cs_new:Npn \stringcharacterinposition #1 #2 -{ -\str_item:fn { #1 } { #2 } -} -\cs_generate_variant:Nn \str_item:nn {f} -\ExplSyntaxOff - -\NewDocumentCommand\errorRootOrdering{} +%% \dynkinDefiniteLeftUpArc{

}{} +%% Draws a quarter circle from root

to root on the current Dynkin diagram in the current label ordering. +%% The starred form accepts

and in the Bourbaki ordering. +\NewDocumentCommand\dynkinDefiniteLeftUpArc{sO{}mm}% {% - \ClassWarning{Unrecognized root ordering: ``\dynkinordering'' in Dynkin diagram}% + \IfBooleanTF{#1}% + {% + \convertRootPair{#3}{#4}% + }% + {% + \@fromRoot=#3% + \@toRoot=#4% + }% + \begin{scope}[on background layer]% + \draw[/Dynkin diagram,/Dynkin diagram/edge,fill=none,#2] + ($(\dynkin@root@name \the\@fromRoot)$) + arc (-90:-180:\dynkin@fold@radius) -- ($(\dynkin@root@name \the\@toRoot)$);% + \end{scope}% }% -\NewDocumentCommand\errorRank{}% +%% \dynkinIndefiniteLeftUpArc{

}{} +%% Draws a quarter circle from root

to root on the current Dynkin diagram in the current label ordering. +%% The starred form accepts

and in the Bourbaki ordering. +\NewDocumentCommand\dynkinIndefiniteLeftUpArc{sO{}mm}% {% - \ClassWarning{Unrecognized \dynkinseries{} series rank: ``\the\dynkinrank'' in Dynkin diagram}% + \IfBooleanTF{#1}% + {% + \convertRootPair{#3}{#4}% + }% + {% + \@fromRoot=#3% + \@toRoot=#4% + }% + \node (center) at ($(\dynkin@root@name \the\@fromRoot)+(0,\dynkin@fold@radius)$) {};% + \begin{scope}[on background layer]% + \draw[/Dynkin diagram,/Dynkin diagram/edge,fill=none,#2] + (center) + ++(-90:\dynkin@fold@radius) + arc [start angle=-90, end angle=-120, radius=\dynkin@fold@radius];% + \draw[/Dynkin diagram,/Dynkin diagram/indefiniteEdge,fill=none,#2] + (center) + ++(-120:\dynkin@fold@radius) + arc [start angle=-120, end angle=-150, radius=\dynkin@fold@radius];% + \draw[/Dynkin diagram,/Dynkin diagram/edge,fill=none,#2] + (center) + ++(-150:\dynkin@fold@radius) + arc [start angle=-150, end angle=-180, radius=\dynkin@fold@radius] -- ($(\dynkin@root@name \the\@toRoot)$);% + \end{scope}% }% -\NewDocumentCommand\errorSeries{}% -{% - \ClassWarning{Unrecognized series ``\dynkinseries{}'' in Dynkin diagram}% -}% -%% \checkDynkinDiagram -%% -> -%% Raises error messages for erroneous inputs. -\NewDocumentCommand\checkDynkinDiagram{}% +%% \dynkinDefiniteSemiCircle{

}{} +%% Draws a half circle from root

to root on the current Dynkin diagram in the current label ordering. +%% The starred form accepts

and in the Bourbaki ordering. +\NewDocumentCommand\dynkinDefiniteSemiCircle{sO{}mm}% {% - \IfStrEqCase{\dynkinordering}% + \IfBooleanTF{#1}% {% - {Adams}{}% - {Bourbaki}{}% - {Carter}{}% - {Dynkin}{}% - {Kac}{}% + \convertRootPair{#3}{#4}% }% - [\ClassWarning{Unrecognized label ordering: ``\dynkinordering'' in Dynkin diagram}]% - \IfStrEqCase{\dynkinseries}% {% - {A}{}% - {B}{}% - {C}{}% - {D}{}% - {E}% - {% - \ifnum\dynkinrank=6% - \else% - \ifnum\dynkinrank=7% - \else% - \ifnum\dynkinrank=8% - \else% - \errorRank% - \fi% - \fi% - \fi% - }% - {F}% - {% - \ifnum\dynkinrank=4% - \else% - \errorRank% - \fi% - }% - {G}% - {% - \ifnum\dynkinrank=2% - \else% - \errorRank% - \fi% - }% - {H}{}% - {I}{}% + \@fromRoot=#3% + \@toRoot=#4% }% - [\errorSeries]% + \begin{scope}[on background layer]% + \draw[/Dynkin diagram,/Dynkin diagram/edge,fill=none,#2] + ($(\dynkin@root@name \the\@fromRoot)$) + arc (90:-90:\dynkin@fold@radius) + -- ($(\dynkin@root@name \the\@toRoot)$);% + \end{scope}% }% -% We store the number of a root, converted to the current root ordering convention, here. -\newcount\RootNumber +%% \dynkinIndefiniteSemiCircle{

}{} +%% Draws a half circle from root

to root on the current Dynkin diagram in the current label ordering. +%% The starred form accepts

and in the Bourbaki ordering. +\NewDocumentCommand\dynkinIndefiniteSemiCircle{sO{}mm}% +{% + \IfBooleanTF{#1}% + {% + \convertRootPair{#3}{#4}% + }% + {% + \@fromRoot=#3% + \@toRoot=#4% + }% + \node (center) at ($(\dynkin@root@name \the\@fromRoot)-(0,\dynkin@fold@radius)$) {};% + \begin{scope}[on background layer]% + \draw[/Dynkin diagram,/Dynkin diagram/edge,fill=none,#2] + (center) + ++(90:\dynkin@fold@radius) + arc [start angle=90, end angle=30, radius=\dynkin@fold@radius];% + \draw[/Dynkin diagram,/Dynkin diagram/indefiniteEdge,fill=none,#2] + (center) + ++(30:\dynkin@fold@radius) + arc [start angle=30, end angle=-30, radius=\dynkin@fold@radius];% + \draw[/Dynkin diagram,/Dynkin diagram/edge,fill=none,#2] + (center) + ++(-30:\dynkin@fold@radius) + arc [start angle=-30, end angle=-90, radius=\dynkin@fold@radius] -- ($(\dynkin@root@name \the\@toRoot)$);% + \end{scope}% +}% -% A slight headache: all of the routines that draw Dynkin diagrams are written -% in Bourbaki ordering. We store the roots in the current ordering. -% So when we draw edges, we need to convert from the Bourbaki ordering each time. -% We store the conversions here. -\newcount\@fromRoot -\newcount\@toRoot +%% \dynkinDefiniteDoubleRightDownArc{

}{} +%% Draws a quarter circle from root

to root on the current Dynkin diagram in the current label ordering +%% as a double path. +%% The starred form accepts

and in the Bourbaki ordering. +\NewDocumentCommand\dynkinDefiniteDoubleRightDownArc{sO{}mm}% +{% + \IfBooleanTF{#1}% + {% + \convertRootPair{#3}{#4}% + }% + {% + \@fromRoot=#3% + \@toRoot=#4% + }% + \begin{scope}[on background layer]% + \draw[/Dynkin diagram,/Dynkin diagram/edge,double,fill=none,#2]% + ($(\dynkin@root@name \the\@fromRoot)$)% + arc (90:0:{\dynkin@fold@radius}) -- ($(\dynkin@root@name \the\@toRoot)$);% + \ifdynkin@arrows% + \ifdynkin@reverse@arrows% + \path[-<,tips] + ($(\dynkin@root@name \the\@fromRoot)$)% + arc (90:45:{\dynkin@fold@radius});% + \else% + \path[->,tips] + ($(\dynkin@root@name \the\@fromRoot)$)% + arc (90:45:{\dynkin@fold@radius});% + \fi% + \fi% + \end{scope}% +}% -%% \convertRootPair{

}{} -%% -> -%% Stores conversions in \@fromRoot and \@toRoot. -\NewDocumentCommand\convertRootPair{mm} + +%% \dynkinDefiniteDoubleUpRightArc{

}{} +%% Draws a quarter circle from root

to root on the current Dynkin diagram in the current label ordering +%% as a double path. +%% The starred form accepts

and in the Bourbaki ordering. +\NewDocumentCommand\dynkinDefiniteDoubleUpRightArc{sO{}mm}% {% - \convertRootNumber{#1}% - \@fromRoot=\RootNumber% - \convertRootNumber{#2}% - \@toRoot=\RootNumber% + \IfBooleanTF{#1}% + {% + \convertRootPair{#3}{#4}% + }% + {% + \@fromRoot=#3% + \@toRoot=#4% + }% + \begin{scope}[on background layer]% + \draw[/Dynkin diagram,/Dynkin diagram/edge,double,fill=none,#2]% + ($(\dynkin@root@name \the\@fromRoot)$)% + arc (180:90:{\dynkin@fold@radius}) -- ($(\dynkin@root@name \the\@toRoot)$);% + \ifdynkin@arrows% + \ifdynkin@reverse@arrows% + \path[-<,tips] + ($(\dynkin@root@name \the\@fromRoot)$)% + arc (180:135:{\dynkin@fold@radius});% + \else% + \path[->,tips] + ($(\dynkin@root@name \the\@fromRoot)$)% + arc (180:135:{\dynkin@fold@radius});% + \fi% + \fi% + \end{scope}% }% -%% \testbit{}{}{}{} -%% If bit number of is 1 then expand else expand . -\newcommand*{\testbit}[4]% + +%% \dynkinDefiniteDoubleUpLeftArc{

}{} +%% Draws a quarter circle from root

to root on the current Dynkin diagram in the current label ordering +%% as a double path. +%% The starred form accepts

and in the Bourbaki ordering. +\NewDocumentCommand\dynkinDefiniteDoubleUpLeftArc{sO{}mm}% {% - \pgfmathparse{int(mod(div(#1,2^(#2)),2))}% - \let\tf\pgfmathresult% - \IfStrEq{\tf}{1}{#3}{#4}% + \IfBooleanTF{#1}% + {% + \convertRootPair{#3}{#4}% + }% + {% + \@fromRoot=#3% + \@toRoot=#4% + }% + \begin{scope}[on background layer]% + \draw[/Dynkin diagram,/Dynkin diagram/edge,double,fill=none,#2]% + ($(\dynkin@root@name \the\@fromRoot)$)% + arc (-90:0:{\dynkin@fold@radius}) -- ($(\dynkin@root@name \the\@toRoot)$);% + \ifdynkin@arrows% + \ifdynkin@reverse@arrows% + \path[-<,tips] + ($(\dynkin@root@name \the\@fromRoot)$)% + arc (-90:-45:{\dynkin@fold@radius});% + \else% + \path[->,tips] + ($(\dynkin@root@name \the\@fromRoot)$)% + arc (-90:-45:{\dynkin@fold@radius});% + \fi% + \fi% + \end{scope}% }% -%% \placeRoot{}{}{} -%% -> -%% Tell TikZ where to place node (in Bourbaki ordering) for a root of a Dynkin diagram. Draws nothing. -%% Starred form swaps label positions. -\NewDocumentCommand\placeRoot{smmm}% + + + +%% \dynkinDefiniteDoubleDownRightArc{

}{} +%% Draws a quarter circle from root

to root on the current Dynkin diagram in the current label ordering +%% as a double path. +%% The starred form accepts

and in the Bourbaki ordering. +\NewDocumentCommand\dynkinDefiniteDoubleDownRightArc{sO{}mm}% {% - \convertRootNumber{#2}% - \node (root \the\RootNumber) at ({(#3)*\dynkinedgelength},{(#4)*\dynkinedgelength}) {};% \IfBooleanTF{#1}% {% - \node[above] (root label \the\RootNumber)% - at ({(#3)*\dynkinedgelength},{((#4)*\dynkinedgelength)+2*\dynkinradius}) {};% - \node[below] (root label swap \the\RootNumber)% - at ({(#3)*\dynkinedgelength},{((#4)*\dynkinedgelength)-2*\dynkinradius}) {};% + \convertRootPair{#3}{#4}% }% {% - \node[above] (root label swap \the\RootNumber)% - at ({(#3)*\dynkinedgelength},{((#4)*\dynkinedgelength)+2*\dynkinradius}) {};% - \node[below] (root label \the\RootNumber)% - at ({(#3)*\dynkinedgelength},{((#4)*\dynkinedgelength)-2*\dynkinradius}) {};% + \@fromRoot=#3% + \@toRoot=#4% }% + \begin{scope}[on background layer]% + \draw[/Dynkin diagram,/Dynkin diagram/edge,double,fill=none,#2]% + ($(\dynkin@root@name \the\@fromRoot)$)% + -- + ($(\dynkin@root@name \the\@toRoot)+(-\dynkin@fold@radius,\dynkin@fold@radius)$)% + arc (-180:-90:{\dynkin@fold@radius}) -- ($(\dynkin@root@name \the\@toRoot)$);% + \ifdynkin@arrows% + \ifdynkin@reverse@arrows% + \path[-<,tips] + ($(\dynkin@root@name \the\@toRoot)+(-\dynkin@fold@radius,\dynkin@fold@radius)$)% + arc (-180:-135:{\dynkin@fold@radius});% + \else% + \path[->,tips] + ($(\dynkin@root@name \the\@toRoot)+(-\dynkin@fold@radius,\dynkin@fold@radius)$)% + arc (-180:-135:{\dynkin@fold@radius});% + \fi% + \fi% + \end{scope}% }% -%% \placeRootHorizontalLabels{}{}{} -%% -> -%% Tell TikZ where to place node (in Bourbaki ordering) for a root of a Dynkin diagram. Draws nothing. -%% Places labels to the left or right of the root. -%% Starred form swaps label positions. -\NewDocumentCommand\placeRootHorizontalLabels{smmm}% + +%% \dynkinDefiniteDoubleRightUpArc{

}{} +%% Draws a quarter circle from root

to root on the current Dynkin diagram in the current label ordering +%% as a double path. +%% The starred form accepts

and in the Bourbaki ordering. +\NewDocumentCommand\dynkinDefiniteDoubleRightUpArc{sO{}mm}% {% - \convertRootNumber{#2}% - \node (root \the\RootNumber) at ({(#3)*\dynkinedgelength},{(#4)*\dynkinedgelength}) {};% \IfBooleanTF{#1}% {% - \node[left] (root label \the\RootNumber)% - at ({((#3)*\dynkinedgelength)-\dynkinradius},{(#4)*\dynkinedgelength}) {};% - \node[right] (root label swap \the\RootNumber)% - at ({((#3)*\dynkinedgelength)+\dynkinradius},{(#4)*\dynkinedgelength}) {};% + \convertRootPair{#3}{#4}% }% {% - \node[left] (root label swap \the\RootNumber)% - at ({((#3)*\dynkinedgelength)-\dynkinradius},{(#4)*\dynkinedgelength}) {};% - \node[right] (root label \the\RootNumber)% - at ({((#3)*\dynkinedgelength)+\dynkinradius},{(#4)*\dynkinedgelength}) {};% + \@fromRoot=#3% + \@toRoot=#4% }% + \begin{scope}[on background layer]% + \draw[/Dynkin diagram,/Dynkin diagram/edge,double,fill=none,#2]% + ($(\dynkin@root@name \the\@fromRoot)$)% + arc (270:360:{\dynkin@fold@radius}) -- ($(\dynkin@root@name \the\@toRoot)$);% + \ifdynkin@arrows% + \path[->,tips] + ($(\dynkin@root@name \the\@fromRoot)$)% + arc (270:315:\dynkin@fold@radius);% + \fi% + \end{scope}% }% -%% \Adynkinnodes -%% -> -%% Tell TikZ where to place the nodes for an A series Dynkin diagram. Draws nothing. -\newcommand*{\Adynkinnodes}% +%% \dynkinDefiniteDoubleLeftDownArc{

}{} +%% Draws a quarter circle from root

to root on the current Dynkin diagram in the current label ordering +%% as a double path. +%% The starred form accepts

and in the Bourbaki ordering. +\NewDocumentCommand\dynkinDefiniteDoubleLeftDownArc{sO{}mm}% {% - \ifdynkinfolded% - \newcount\halfrank% - \halfrank=\dynkinrank% - \divide\halfrank by 2% - \newcount\countdown% - \countdown=\dynkinrank% - \ifodd\dynkinrank% - \foreach \b in {1,...,\the\halfrank}% - {% - \placeRoot*{\b}{\b}{1}% - \placeRoot{\the\countdown}{\b}{-1}% - \ifdynkinarrows% - \ifnum\dynkinrank>1% - \dynkinfoldarrow*{\b}{\the\countdown}% - \fi% - \fi% - \global\advance\countdown by -1% - }% - \advance\halfrank by 1% - \placeRootHorizontalLabels{\the\halfrank}{\the\halfrank}{0}% + \IfBooleanTF{#1}% + {% + \convertRootPair{#3}{#4}% + }% + {% + \@fromRoot=#3% + \@toRoot=#4% + }% + \begin{scope}[on background layer]% + \draw[/Dynkin diagram,/Dynkin diagram/edge,double,fill=none,#2]% + ($(\dynkin@root@name \the\@fromRoot)$)% + arc (90:180:{\dynkin@fold@radius}) -- ($(\dynkin@root@name \the\@toRoot)$);% + \ifdynkin@arrows% + \ifdynkin@reverse@arrows% + \path[-<,tips] + ($(\dynkin@root@name \the\@fromRoot)$)% + arc (90:135:{\dynkin@fold@radius});% \else% - \foreach \b in {1,...,\the\halfrank}% - {% - \placeRoot*{\b}{\b}{1}% - \placeRoot{\the\countdown}{\b}{-1}% - \ifdynkinarrows% - \dynkinfoldarrow*{\b}{\the\countdown} % - \fi% - \global\advance\countdown by -1% - }% + \path[->,tips] + ($(\dynkin@root@name \the\@fromRoot)$)% + arc (90:135:{\dynkin@fold@radius});% \fi% - \else% - \foreach \b in {1,...,\the\dynkinrank}% - {% - \placeRoot{\b}{\b}{0}% - }% \fi% + \end{scope}% }% -%% \Adynkin -%% -> -%% Draws an A series Dynkin diagram. -\newcommand*{\Adynkin} -{ - \newif\ifwasfolded - \ifdynkinfolded - \global\wasfoldedtrue - \else - \global\wasfoldedfalse - \fi - \ifnum\dynkinrank=0% - \global\dynkinrank=7% - % Create the nodes. - \Adynkinnodes% - % Draw the edges. - \dynkinline*{1}{2}% - \dynkindots*{2}{3}% - \ifdynkinfolded% - \dynkindownarc*{3}{4}% - \dynkinuparc*{4}{5}% + +%% \dynkinDefiniteDoubleDownLeftArc{

}{} +%% Draws a quarter circle from root

to root on the current Dynkin diagram in the current label ordering +%% as a double path. +%% The starred form accepts

and in the Bourbaki ordering. +\NewDocumentCommand\dynkinDefiniteDoubleDownLeftArc{sO{}mm}% +{% + \IfBooleanTF{#1}% + {% + \convertRootPair{#3}{#4}% + }% + {% + \@fromRoot=#3% + \@toRoot=#4% + }% + \begin{scope}[on background layer]% + \draw[/Dynkin diagram,/Dynkin diagram/edge,double,fill=none,#2]% + ($(\dynkin@root@name \the\@fromRoot)$)% + arc (360:270:{\dynkin@fold@radius}) -- ($(\dynkin@root@name \the\@toRoot)$);% + \ifdynkin@arrows% + \ifdynkin@reverse@arrows% + \path[-<,tips] + ($(\dynkin@root@name \the\@fromRoot)$)% + arc (360:315:{\dynkin@fold@radius});% \else% - \dynkinline*{3}{4}% - \dynkinline*{4}{5}% + \path[->,tips] + ($(\dynkin@root@name \the\@fromRoot)$)% + arc (360:315:{\dynkin@fold@radius});% \fi% - \dynkindots*{5}{6}% - \dynkinline*{6}{7}% - \else% - \ifnum\dynkinrank=1% - \global\dynkinfoldedfalse% + \fi% + \end{scope}% +}% + + + +%% \dynkinDefiniteDoubleLeftUpArc{

}{} +%% Draws a quarter circle from root

to root on the current Dynkin diagram in the current label ordering +%% as a double path. +%% The starred form accepts

and in the Bourbaki ordering. +\NewDocumentCommand\dynkinDefiniteDoubleLeftUpArc{sO{}mm}% +{% + \IfBooleanTF{#1}% + {% + \convertRootPair{#3}{#4}% + }% + {% + \@fromRoot=#3% + \@toRoot=#4% + }% + \begin{scope}[on background layer]% + \draw[/Dynkin diagram,/Dynkin diagram/edge,double,fill=none,#2]% + ($(\dynkin@root@name \the\@fromRoot)$)% + arc (-90:-180:{\dynkin@fold@radius}) -- ($(\dynkin@root@name \the\@toRoot)$);% + \ifdynkin@arrows% + \ifdynkin@reverse@arrows% + \path[-<,tips] + ($(\dynkin@root@name \the\@fromRoot)$)% + arc (-90:-135:\dynkin@fold@radius);% + \else% + \path[->,tips] + ($(\dynkin@root@name \the\@fromRoot)$)% + arc (-90:-135:\dynkin@fold@radius);% + \fi% \fi% - % Create the nodes. - \Adynkinnodes% - % Draw the edges. - \ifnum\dynkinrank>1% - \ifnum\dynkinrank=2% - \ifdynkinfolded% - \dynkinsemicircle*{1}{2}% - \else% - \dynkinline*{1}{2}% - \fi% + \end{scope}% +}% + + +%% \dynkinDefiniteDoubleDownRightSemiCircle{

}{} +%% Draws a semi circle from root

to root on the current Dynkin diagram in the current label ordering +%% as a double path. +%% The starred form accepts

and in the Bourbaki ordering. +\NewDocumentCommand\dynkinDefiniteDoubleDownRightSemiCircle{sO{}mm}% +{% + \IfBooleanTF{#1}% + {% + \convertRootPair{#3}{#4}% + }% + {% + \@fromRoot=#3% + \@toRoot=#4% + }% + \begin{scope}[on background layer]% + \draw[/Dynkin diagram,/Dynkin diagram/edge,double,fill=none,#2]% + ($(\dynkin@root@name \the\@fromRoot)$)% + arc (90:-90:{\dynkin@fold@radius}) -- ($(\dynkin@root@name \the\@toRoot)$);% + \ifdynkin@arrows% + \ifdynkin@reverse@arrows% + \path[-<,tips] + ($(\dynkin@root@name \the\@fromRoot)$)% + arc (90:0:\dynkin@fold@radius);% \else% - \newcount\bpo% - \bpo=2% - \newcount\drmo% - \drmo=\dynkinrank% - \advance \drmo by -1% - \ifdynkinfolded% - \newcount\halfrank% - \halfrank=\dynkinrank% - \divide\halfrank by 2% - \newcount\hrmo% - \hrmo=\halfrank% - \advance\hrmo by -1% - \ifnum\halfrank>1% - \foreach \b in {1,...,\the\hrmo}% - {% - \dynkinline*{\b}{\bpo}% - \global\advance\bpo by 1% - }% - \fi% - \newcount\hrpo% - \hrpo=\halfrank% - \advance\hrpo by 1% - \ifodd\dynkinrank% - \newcount\hrpt% - \hrpt=\hrpo% - \advance\hrpt by 1% - \dynkindownarc*{\the\halfrank}{\the\hrpo}% - \dynkinuparc*{\the\hrpo}{\the\hrpt}% - \ifdynkinarrows% - \dynkinfoldarrow*{\the\halfrank}{\the\hrpt}% - \fi% - \global\advance\bpo by 2% - \ifnum\hrpt<\dynkinrank% - \foreach \b in {\the\hrpt,...,\the\drmo}% - {% - \dynkinline*{\b}{\bpo}% - \global\advance\bpo by 1% - }% - \fi% - \else% - \dynkinsemicircle*{\the\halfrank}{\the\hrpo}% - \global\advance\bpo by 1% - \ifnum\halfrank<\drmo% - \foreach \b in {\the\hrpo,...,\the\drmo}% - {% - \dynkinline*{\b}{\bpo}% - \global\advance\bpo by 1% - }% - \fi% - \fi% - \else% - \foreach \b in {1,...,\the\drmo}% - {% - \dynkinline*{\b}{\bpo}% - \global\advance\bpo by 1% - }% - \fi% + \path[->,tips] + ($(\dynkin@root@name \the\@fromRoot)$)% + arc (90:0:\dynkin@fold@radius);% \fi% \fi% - \fi% - \ifisaffine% - \dynkinline*{0}{1}% - \dynkinline*{0}{\the\dynkinrank}% - \dynkindot*{0}% - \fi% - % Draw the nodes. - \IfStrEqCase{\dynkinSatake}% + \end{scope}% +}% + + + +%% \dynkinDefiniteDoubleUpRightSemiCircle{

}{} +%% Draws a semi circle from root

to root on the current Dynkin diagram in the current label ordering +%% as a double path. +%% The starred form accepts

and in the Bourbaki ordering. +\NewDocumentCommand\dynkinDefiniteDoubleUpRightSemiCircle{sO{}mm}% +{% + \IfBooleanTF{#1}% {% - {*}% - {% - \foreach \b in {1,...,\the\dynkinrank}% - {% - \testbit{\dynkinparabolic}{\b}{\dynkincross{\b}}{\dynkindot{\b}}% - }% - }% - {I}% - {% - \ifisaffine% - \dynkinline*{0}{1}% - \dynkinline*{0}{\the\dynkinrank}% - \dynkindot*{0}% + \convertRootPair{#3}{#4}% + }% + {% + \@fromRoot=#3% + \@toRoot=#4% + }% + \begin{scope}[on background layer]% + \draw[/Dynkin diagram,/Dynkin diagram/edge,double,fill=none,#2]% + ($(\dynkin@root@name \the\@fromRoot)$)% + arc (-90:90:{\dynkin@fold@radius}) -- ($(\dynkin@root@name \the\@toRoot)$);% + \ifdynkin@arrows% + \ifdynkin@reverse@arrows% + \path[-<,tips] + ($(\dynkin@root@name \the\@fromRoot)$)% + arc (-90:0:\dynkin@fold@radius);% + \else% + \path[->,tips] + ($(\dynkin@root@name \the\@fromRoot)$)% + arc (-90:0:\dynkin@fold@radius);% \fi% - \foreach \b in {1,...,\the\dynkinrank}% - {% - \testbit{\dynkinparabolic}{\b}{\dynkincross{\b}}{\dynkinopendot{\b}}% - }% + \fi% + \end{scope}% +}% + + +%% \dynkinEdge[]{}{

}{} +%% Applies \dynkinDefinite[]{

}{} if the edge

is definite, +%% otherwise applies \dynkinIndefinite[]{

}{} +%% The starred form accepts

and in the Bourbaki ordering. +\NewDocumentCommand\dynkinEdge{sO{}mmm}% +{% + \IfBooleanTF{#1}% + {% + \convertRootPair{#4}{#5}% + \dynkin@is@edge@indefinite{\@fromRoot}{\@toRoot}% + \ifdynkin@is@indefinite@edge% + \csname dynkinIndefinite#3\endcsname[#2]{\@fromRoot}{\@toRoot}% + \else% + \csname dynkinDefinite#3\endcsname[#2]{\@fromRoot}{\@toRoot}% + \fi% + }% + {% + \dynkin@is@edge@indefinite{#4}{#5}% + \ifdynkin@is@indefinite@edge% + \csname dynkinIndefinite#3\endcsname[#2]{#4}{#5}% + \else% + \csname dynkinDefinite#3\endcsname[#2]{#4}{#5}% + \fi% + }% +}% + +%% \dynkinEdgeArrow{

}{} +%% Draws an arrow head on the edge from root

to root . +%% The starred form accepts

and in the Bourbaki ordering. +\NewDocumentCommand\dynkinEdgeArrow{sO{}mm}% +{% + \ifdynkin@arrows% + \IfBooleanTF{#1}% + {% + \convertRootPair{#3}{#4}% }% - {II}% {% - \newcount\bb% - \bb=1% - \foreach \b in {1,...,\the\dynkinrank}% - {% - \ifodd\bb% - \testbit{\dynkinparabolic}{\b}{\dynkincross{\b}}{\dynkincloseddot{\b}}% - \else% - \testbit{\dynkinparabolic}{\b}{\dynkincross{\b}}{\dynkinopendot{\b}}% - \fi% - \global\advance \bb by 1% - }% + \@fromRoot=#3% + \@toRoot=#4% }% - }% - \ifwasfolded - \global\dynkinfoldedtrue - \else - \global\dynkinfoldedfalse - \fi -} - -%% \Bdynkin -%% -> + \begin{scope}[on background layer]% + \ifdynkin@reverse@arrows% + \path[-<,tips] + ($(\dynkin@root@name \the\@fromRoot)$) + -- + ($.3*(\dynkin@root@name \the\@fromRoot)+.7*(\dynkin@root@name \the\@toRoot)$);% + \else% + \path[->,tips] + ($(\dynkin@root@name \the\@fromRoot)$) + -- + ($.3*(\dynkin@root@name \the\@fromRoot)+.7*(\dynkin@root@name \the\@toRoot)$);% + \fi% + \end{scope}% + \fi% +}% + +%% \dynkinDefiniteDoubleEdge{

}{} +%% Draws an oriented double line from root

to root on the current Dynkin diagram. +%% The starred form accepts

and in the Bourbaki ordering. +\NewDocumentCommand\dynkinDefiniteDoubleEdge{sO{}mm}% +{% + \IfBooleanTF{#1}% + {% + \convertRootPair{#3}{#4}% + }% + {% + \@fromRoot=#3% + \@toRoot=#4% + }% + \newcount\onesbit% + \newcount\twosbit% + \StrChar{\dynkin@roots}{\the\@fromRoot}[\my@root@marker]% + \IfStrEq{\my@root@marker}{x}% + {% + \global\onesbit=1% + }% + {% + \global\onesbit=0% + }% + \StrChar{\dynkin@roots}{\the\@toRoot}[\my@root@marker]% + \IfStrEq{\my@root@marker}{x}% + {% + \global\twosbit=1% + }% + {% + \global\twosbit=0% + }% + \def\LL{.5*\dynkin@root@radius} + \begin{scope}[on background layer]% + \draw[/Dynkin diagram,/Dynkin diagram/edge,#2]% + ($(\dynkin@root@name \the\@fromRoot)$)% + --% + +({\the\onesbit*\LL},{\LL})% + --% + ($(\dynkin@root@name \the\@toRoot)+(-\the\twosbit*\LL,\LL)$)% + --% + ($(\dynkin@root@name \the\@toRoot)$)% + --% + ($(\dynkin@root@name \the\@toRoot)-(\the\twosbit*\LL,\LL)$)% + --% + ($(\dynkin@root@name \the\@fromRoot)+(\the\onesbit*\LL,-\LL)$)% + --% + cycle;% + \end{scope}% + \ifdynkin@arrows% + \dynkinEdgeArrow[#2]{\the\@fromRoot}{\the\@toRoot}% + \fi% +}% + +%% \dynkinTripleEdge{

} +%% Draws an oriented triple line from root

to root on the current Dynkin diagram. +%% The starred form accepts

and in the Bourbaki ordering. +\NewDocumentCommand\dynkinTripleEdge{sO{}mm}% +{% + \IfBooleanTF{#1}% + {% + \convertRootPair{#3}{#4}% + }% + {% + \@fromRoot=#3% + \@toRoot=#4% + }% + \newcount\onesbit + \newcount\twosbit + \StrChar{\dynkin@roots}{\the\@fromRoot}[\my@root@marker]% + \IfStrEq{\my@root@marker}{x}% + {% + \global\onesbit=1% + }% + {% + \global\onesbit=0% + }% + \StrChar{\dynkin@roots}{\the\@toRoot}[\my@root@marker]% + \IfStrEq{\my@root@marker}{x}% + {% + \global\twosbit=1% + }% + {% + \global\twosbit=0% + }% + \begin{scope}[on background layer]% + \draw[/Dynkin diagram,/Dynkin diagram/edge,#2]% + ($(\dynkin@root@name \the\@fromRoot)$)% + --% + +({\the\onesbit*\dynkin@root@radius},{\dynkin@root@radius})% + --% + ($(\dynkin@root@name \the\@toRoot)+(-\twosbit*\dynkin@root@radius,\dynkin@root@radius)$)% + --% + ($(\dynkin@root@name \the\@toRoot)$)% + --% + ($(\dynkin@root@name \the\@toRoot)-(\twosbit*\dynkin@root@radius,\dynkin@root@radius)$)% + --% + ($(\dynkin@root@name \the\@fromRoot)+(\onesbit*\dynkin@root@radius,-\dynkin@root@radius)$)% + --% + cycle;% + \draw[/Dynkin diagram,/Dynkin diagram/edge,#2] + ($(\dynkin@root@name \the\@fromRoot)$) + -- + ($(\dynkin@root@name \the\@toRoot)$);% + \end{scope}% + \ifdynkin@arrows% + \dynkinEdgeArrow[#2]{\the\@fromRoot}{\the\@toRoot}% + \fi% +}% + + +%% \dynkinQuadrupleEdge{

}{} +%% \dynkinQuadrupleEdge*{

}{} +%% Draws an oriented edge of valence 4 from root

to root on the current Dynkin diagram. +%% The starred form accepts

and in the Bourbaki ordering. +\NewDocumentCommand\dynkinQuadrupleEdge{sO{}mm}% +{% + \IfBooleanTF{#1}% + {% + \convertRootPair{#3}{#4}% + }% + {% + \@fromRoot=#3% + \@toRoot=#4% + }% + \begin{scope}[on background layer]% + \draw[% + /Dynkin diagram, + /Dynkin diagram/edge, + #2, + ]% + ($(\dynkin@root@name \the\@fromRoot)+(0,\dynkin@root@radius)$)--% + ($(\dynkin@root@name \the\@toRoot)+(0,\dynkin@root@radius)$)--% + ($(\dynkin@root@name \the\@toRoot)+(0,-\dynkin@root@radius)$)--% + ($(\dynkin@root@name \the\@fromRoot)+(0,-\dynkin@root@radius)$)--% + cycle; + \draw[% + /Dynkin diagram,/Dynkin diagram/edge, + #2, + ]% + ($(\dynkin@root@name \the\@fromRoot)+(0,\dynkin@root@radius/3)$)--% + ($(\dynkin@root@name \the\@toRoot)+(0,\dynkin@root@radius/3)$)--% + ($(\dynkin@root@name \the\@toRoot)+(0,-\dynkin@root@radius/3)$)--% + ($(\dynkin@root@name \the\@fromRoot)+(0,-\dynkin@root@radius/3)$)--% + cycle; + \end{scope}% + \ifdynkin@arrows% + \dynkinEdgeArrow[#2]{\the\@fromRoot}{\the\@toRoot}% + \fi% +}% + + +%% \repeatCharacter{}{} +%% Outputs copies of the string +\ExplSyntaxOn +\DeclareExpandableDocumentCommand{\repeatCharacter}{O{}mm} + { + \int_compare:nT { #2 > 0 } + { + #3 \prg_replicate:nn { #2 - 1 } { #1#3 } + } + } +\ExplSyntaxOff + +%% \stringCharacterInPosition{}{} +%% Outputs the element of string in position . +\ExplSyntaxOn +\cs_new:Npn \stringCharacterInPosition #1 #2 +{ +\str_item:fn { #1 } { #2 } +} +\cs_generate_variant:Nn \str_item:nn {f} +\ExplSyntaxOff + + + + +%%% +%%% Implementation: +%%% + +\def\dynkin@diagram@name{anonymous} +% Default diagram name + +\def\dynkin@root@mark{*} +% Default mark + +\def\dynkin@affine@root@mark{o} +% Default affine root mark + +\def\dynkin@roots{} +% List of marks for each root. + +\def\dynkin@user@series{} +% Series string passed from user. +% For example: +% \dynkin{A}{3} passes the string A, +% \dynkin{A2}{*o*} passes the string A2, +% \dynkin{E2}{} passes the string E2. + +\def\dynkin@user@string{} +% Control string passed from user. +% For example: +% \dynkin{A}{3} passes the string 3, +% \dynkin{A}{*o*} passes the string *o*, +% \dynkin{A}{III} passes the string III. + +\def\dynkin@string{} +% \dynkin@user@string{} with some modifications to it to expand it out. + +\def\dynkin@series{A} +% Which series of root system: A,B,C,D,E,F,G + +\newcount\dynkin@rank +% Which rank of root system: 1,2,... + +\newcount\dynkin@nodes +% How many nodes (besides the zero node for affine diagrams) are there? + +\newif\ifdynkin@is@extended +% Is this an extended extended root system? + +\newif\ifdynkin@is@twisted +% Is this a twisted extended root system? + +\def\dynkin@twisted@series{0} +% Which Kac series? 0=finite, 1,2,3->infinite + +\newif\ifdynkin@label@the@roots +% Should we label the roots by the current root ordering convention? + +\newif\ifdynkin@reverse@arrows +% Should we reverse the directions of all arrows? + +\newif\ifdynkin@arrows +% Should we draw arrows on Dynkin diagrams? + +\newif\ifdynkin@left@fold +% Is the left side of the Dynkin diagram folded? + +\newif\ifdynkin@right@fold +% Is the right side of the Dynkin diagram folded? + +\newif\ifdynkin@Coxeter +% Should we draw Coxeter diagrams? + +\newif\ifdynkin@odd +% For twisted A series diagrams, is the rank odd? + +\newcount\dynkin@ply +% Maximum number of nodes arranged vertically in the folding of the Dynkin diagram + +\def\dynkin@ply@value{1} +% Default maximum number of nodes arranged vertically in the folding of the Dynkin diagram + +\def\dynkin@label@directions{} +% List of directions in which to draw the labels attached to the roots: a=above, b=below, l=left, r=right. + +\def\dynkin@current@location{(0,0)} + +\NewDocumentCommand\regurgitate{m}{#1} + +\pgfkeys{ + /Dynkin diagram/.is family, + /Dynkin diagram, + name/.estore in = \dynkin@diagram@name, + name = anonymous, + mark/.estore in = \dynkin@root@mark, + mark = *, + affineMark/.estore in = \dynkin@affine@root@mark, + affineMark = o, + edgeLength/.estore in = \dynkin@edge@length, + edgeLength = .35cm, + edge/.style={draw=black,fill=white,thin}, + makeIndefiniteEdge/.code={\dynkin@set@edge@indefinite@pair{#1}}, + indefiniteEdgeRatio/.estore in = \dynkin@indefinite@edge@ratio, + indefiniteEdgeRatio = 1.6, + indefiniteEdge/.style={draw=black,fill=white,thin,densely dotted}, + arrows/.is if = dynkin@arrows, + arrows = true, + reverseArrows/.is if = dynkin@reverse@arrows, + reverseArrows = false, + foldStyle/.style = {draw=black!40,fill=none,line width=\dynkin@root@radius}, + leftFold/.style = {}, + rightFold/.style = {}, + doubleEdges/.style = { + foldStyle/.style = { + draw=black, + double=white, + fill=none, + double distance=\dynkin@root@radius, + line width=\defaultpgflinewidth} + }, + doubleFold/.style = { + foldStyle/.style = { + draw=black, + double=black!40, + fill=none, + double distance=\dynkin@root@radius, + line width=\defaultpgflinewidth} + }, + doubleLeft/.style = { + leftFold/.style = { + draw=black, + double=white, + fill=none, + double distance=\dynkin@root@radius, + line width=\defaultpgflinewidth} + }, + doubleFoldLeft/.style = { + leftFold/.style = { + draw=black, + double=black!40, + fill=none, + double distance=\dynkin@root@radius, + line width=\defaultpgflinewidth} + }, + doubleRight/.style = { + rightFold/.style = { + draw=black, + double=white, + fill=none, + double distance=\dynkin@root@radius, + line width=\defaultpgflinewidth} + }, + doubleFoldRight/.style = { + rightFold/.style = { + draw=black, + double=black!40, + fill=none, + double distance=\dynkin@root@radius, + line width=\defaultpgflinewidth} + }, + radius/.estore in = \dynkin@root@radius, + radius=.05cm, + foldradius/.estore in = \dynkin@fold@radius, + foldradius=.3cm, + */.style = { + draw=black, + fill=black, + }, + O/.style = { + draw=black, + fill=white, + }, + X/.style = { + draw=black, + thick + }, + o/.style = { + draw=black, + fill=white, + }, + t/.style = { + draw=black, + fill=white, + }, + x/.style = { + draw=black, + }, + Coxeter/.is if = dynkin@Coxeter, + Coxeter=false, + ordering/.store in = \dynkin@ordering, + ordering = Bourbaki, + text/.style={scale=.7}, + labelMacro/.code = {\regurgitate{#1}}, + odd/.is if = dynkin@odd, + odd=false, + Kac/.style={ + ordering=Kac, + radius=.05cm, + edgeLength=.66cm, + indefiniteEdgeRatio = 3, + o/.style = + { + draw=black, + fill=white, + preaction={ + draw=white, + line width=.9mm + } + }, + mark=o, + indefiniteEdge/.style={draw=black,fill=white,thin,loosely dotted}, + }, + default/.style = { + label/.is if = dynkin@label@the@roots, + label = false, + at/.estore in = \dynkin@current@location, + at = {(0,0)}, + parabolic/.estore in = \dynkin@parabolic, + parabolic = 0, + gonality/.estore in = \dynkin@gonality, + gonality = 0, + extended/.is if = dynkin@is@extended, + extended = false, + twisted/.is if = dynkin@is@twisted, + twisted = false, + twistedSeries/.estore in = \dynkin@twisted@series, + twistedSeries = 0, + ply/.estore in = \dynkin@ply@value, + ply = 1, + fold/.style = {ply=2}, + foldleft/.is if = dynkin@left@fold, + foldleft = false, + foldright/.is if = dynkin@right@fold, + foldright = false, + }, + .search also={/tikz}, +} + +\ProcessPgfPackageOptions{/Dynkin diagram}\relax + +%% \dynkin@put@direction{}{} +%% Assigns to \dynkin@label@directions the direction that the label of root (in default ordering) should sit from the root node location, =left, right, above, below or diagonal. +\NewDocumentCommand\dynkin@put@direction{mm}% +{% + \newcount\drpo% + \drpo=\the\dynkin@nodes% + \advance\drpo by 1% + \newcount\dynkin@where% + \dynkin@where=#1% + \StrMid{\dynkin@label@directions}{1}{\the\dynkin@where}[\dynkin@start]% + \advance\dynkin@where by 2 + \StrMid{\dynkin@label@directions}{\the\dynkin@where}{\the\drpo}[\dynkin@end]% + \IfStrEqCase{#2}{% + {left}{\xdef\dynkin@label@directions{\dynkin@start l\dynkin@end}}% + {right}{\xdef\dynkin@label@directions{\dynkin@start r\dynkin@end}}% + {above}{\xdef\dynkin@label@directions{\dynkin@start a\dynkin@end}}% + {below}{\xdef\dynkin@label@directions{\dynkin@start b\dynkin@end}}% + {diagonal}{\xdef\dynkin@label@directions{\dynkin@start d\dynkin@end}}% + }% + [\ClassError{Dynkin diagrams}{Unrecognized direction: ``#2'' in Dynkin diagram \dynkin@user@series{\dynkin@user@string}}{}]% +}% + + +\xdef\replace@DR{} + +% \expand@Dynkin@Roots@By@Char{}, +% for example if is the letter x, expands out any expression like +% x7 in \dynkin@string into 7 copies of the letter x. +\NewDocumentCommand\expand@Dynkin@Roots@By@Char{m}% +{% + \xdef\replace@DR{} + \foreach \i in {0,...,9}% + {% + \StrSubstitute[0]{\dynkin@string}{#1\i}{\replace@DR}[\temp@DR]% + \xdef\dynkin@string{\temp@DR}% + \xdef\replace@DR{\replace@DR #1}% + }% +}% + +% \expand@Dynkin@Roots@Digits{} expands out any expression like x7 in \dynkin@roots into 7 copies of the letter x, and so on for any letter which is not a digit. +\NewDocumentCommand\expand@Dynkin@Roots@Digits{}% +{% + \edef\current@string{\dynkin@string} + \StrLen{\current@string}[\string@len] + \foreach \j in {1,...,\string@len}% + {% + \StrChar{\current@string}{\j}[\cccc]% + \IfInteger{\cccc}% + {}% + {% + \expand@Dynkin@Roots@By@Char{\cccc}% + }% + }% +}% + +% \dynkin@integer@rank{} expands a \dynkin@string 3 into ***, i.e. +% writes the given number of copies of the default root mark into the string \dynkin@string. +\NewDocumentCommand\dynkin@integer@rank{}% +{% + \global\dynkin@rank=\dynkin@string% + \global\dynkin@nodes=\dynkin@string% + \ifdynkin@is@twisted% + \IfStrEqCase{\dynkin@series}% + {% + {A}% + {% + \divide\dynkin@nodes by 2% + \ifodd\dynkin@rank% + \global\dynkin@oddtrue% + \advance\dynkin@nodes by 1% + \else% + \global\dynkin@oddfalse% + \fi% + }% + {D}% + {% + \IfStrEqCase{\dynkin@twisted@series}% + {% + {2}% + {% + \global\advance\dynkin@nodes by -1% + }% + {3}% + {% + \IfStrEq{\dynkin@string}{4}% + {% + \global\dynkin@nodes=2% + }% + {% + \dynkin@error@series% + }% + }% + }% + [\dynkin@error@series]% + }% + {E}% + {% + \IfStrEq{\dynkin@twisted@series}{2}% + {% + \IfStrEq{\dynkin@string}{6}% + {% + \global\dynkin@nodes=4% + }% + {% + \dynkin@error@series% + }% + }% + {% + \dynkin@error@series% + }% + }% + }% + \fi% + \xdef\dynkin@string{\repeatCharacter{\the\dynkin@nodes}{\dynkin@root@mark}}% +}% + +\NewDocumentCommand\dynkin@clear@indefinite@edge@list{}% +{% + \xdef\dynkin@indefinite@edge@list{}% +}% + +\NewDocumentCommand\dynkin@set@edge@indefinite{mm}% +{% + \newcount\first% + \first=#1\relax% + \newcount\second% + \second=#2\relax% + \ifnum\the\first<\the\second% + \listxadd\dynkin@indefinite@edge@list{\the\first,\the\second}% + \else% + \listxadd\dynkin@indefinite@edge@list{\the\second,\the\first}% + \fi% +}% + +\NewDocumentCommand\dynkin@set@edge@indefinite@pair{>{\SplitArgument{1}{-}}m}% +{% +\dynkin@set@edge@indefinite#1 +}% + +\newif\ifdynkin@is@indefinite@edge + +\NewDocumentCommand\dynkin@typeout@indefinite@edge@list{}% +{% + \renewcommand*{\do}[1]{\typeout{##1}}% + \typeout{Indefinite edges: [}\dolistloop{\dynkin@indefinite@edge@list}\typeout{]}% +}% + + +%% \dynkin@is@edge@indefinite{

}{} sets the global if \ifdynkin@is@indefinite@edge to true or false +%% depending on whether there is an indefinite edge between roots

and . +%% The starred form uses Bourbaki ordering. +\NewDocumentCommand\dynkin@is@edge@indefinite{smm}% +{% + \IfBooleanTF{#1}% + {% + \convertRootPair{#2}{#3}% + }% + {% + \@fromRoot=#2% + \@toRoot=#3% + }% + % Next we sort the order, since edges are stored as undirected edges. + \newcount\first% + \global\first=\@fromRoot\relax% + \newcount\second% + \global\second=\@toRoot\relax% + \ifnum\the\second<\the\first% + \global\first=\@toRoot\relax% + \global\second=\@fromRoot\relax% + \fi% + \global\dynkin@is@indefinite@edgefalse\relax% + \renewcommand*{\do}[1]{% + \IfStrEq{##1}{\the\first,\the\second}% + {\global\dynkin@is@indefinite@edgetrue\listbreak}% + {}}% + \dolistloop{\dynkin@indefinite@edge@list}% +}% + +% \dynkin@grok@indefinite@edges{} reads the input string found when you write \dynkin{}{}, and +% interprets it to say which edges are indefinite edges. +\NewDocumentCommand\dynkin@grok@indefinite@edges{}% +{% + \newcount\rootnum + \rootnum=1 + \newcount\dynkin@string@length + \StrLen{\dynkin@string}[\temp]% + \dynkin@string@length=\temp + \foreach \i in {2,...,\the\dynkin@string@length}% + {% + \StrChar{\dynkin@string}{\i}[\c]% + \IfStrEq{\c}{.}% + {% + \newcount\rootnumpo% + \rootnumpo=\rootnum% + \advance\rootnumpo by 1\relax% + \ifnum\the\rootnum<\the\dynkin@nodes% + \dynkin@set@edge@indefinite{\rootnum}{\rootnumpo}% + \fi% + }% + {% + \global\advance\rootnum by 1% + }% + }% +}% + +\xdef\spacy{ } + +\xdef\questionMarks{} + +\NewDocumentCommand\dynkin@clear@label@directions{}% +{% + \xdef\dynkin@label@directions{}% +}% + + +\NewDocumentCommand\dynkin@set@default@label@directions{}% +{% + \newcount\drpo% + \drpo=\the\dynkin@nodes% + \advance\drpo by 1\relax% + \xdef\dynkin@label@directions{\repeatCharacter{\the\drpo}{?}}% +}% + +\newlength{\defaultpgflinewidth}% + + +% \@dynkin[]{}[]{} +% Draws a complete Dynkin diagram of +% series and +% subseries , +% described by the string +% with TikZ options specified by . +\NewDocumentCommand\@dynkin{O{}mO{0}m}% +{% + \setlength{\defaultpgflinewidth}{\pgflinewidth}% + \global\defaultpgflinewidth=\defaultpgflinewidth\relax% + \dynkin@clear@indefinite@edge@list% + \xdef\dynkin@parabolic{0}% + \pgfkeys{/Dynkin diagram, default, #1}% + \xdef\dynkin@user@series{#2}% + \xdef\dynkin@twisted@series{#3}% + \xdef\dynkin@user@string{#4}% + \global\dynkin@ply=\dynkin@ply@value\relax% + \xdef\dynkin@indefinite@edge@length{(\dynkin@edge@length*\dynkin@indefinite@edge@ratio)}\relax% + \xdef\dynkin@series{#2}% + \IfStrEq{\dynkin@diagram@name}{anonymous}% + {% + \xdef\dynkin@root@name{root\spacy}% + }% + {% + \xdef\dynkin@root@name{\dynkin@diagram@name\spacy root\spacy}% + }% + \dynkin@grok@series% + \IfSubStr{ABCDEFGHI}{\dynkin@series}{}{\dynkin@error@series}% + \xdef\dynkin@string{#4} + \IfInteger{\dynkin@string}% + {% + \dynkin@integer@rank% + }% + {% + % Turn Satake codes into Dynkin diagram expressions in \dynkin@string. + \dynkin@grok@Satake@codes% + }% + % Expand out any digits in \dynkin@string into multiples of the various root marks. + \expand@Dynkin@Roots@Digits% + % Assign to \dynkin@roots the input string \dynkin@string with all . symbols removed, + % so we only get the symbols representing the marks for the various roots. + \StrDel{\dynkin@string}{.}[\temp]% + \xdef\dynkin@roots{\temp}% + \StrLen{\dynkin@roots}[\temp]% + \global\dynkin@nodes=\temp\relax% + \dynkin@grok@indefinite@edges% + \dynkin@find@rank{}% + \dynkin@cross@out@parabolics{}% + \dynkin@set@default@label@directions{}% + \check@Dynkin@diagram{}% + \node (Dynkin current) at \dynkin@current@location{};% + \ifdynkin@is@twisted% + \csname twisted\dynkin@series dynkin\endcsname% + \else% + \ifdynkin@is@extended% + \csname extended\dynkin@series dynkin\endcsname% + \else% + \csname\dynkin@series dynkin\endcsname% + \fi% + \fi% + \dynkinRefreshRoots% +}% + +%% We know the number of nodes; lets find the rank. +\NewDocumentCommand\dynkin@find@rank{}% +{% + \global\dynkin@rank=\the\dynkin@nodes% + \ifdynkin@is@twisted% + \IfStrEqCase{\dynkin@series}% + {% + {A}% + {% + \multiply\dynkin@rank by 2% + \ifdynkin@odd% + \advance\dynkin@rank by -1% + \fi% + }% + {D}% + {% + \IfStrEqCase{\dynkin@twisted@series}% + {% + {2} + {% + \advance\dynkin@rank by 1% + }% + {3} + {% + \advance\dynkin@rank by 2% + }% + }% + }% + {E}% + {% + \advance\dynkin@rank by 2% + }% + }% + \fi% +}% + +%% \dynkin@grok@series +%% Interprets the dynkin@series, to see if it is extended, twisted, and what twisted series it is. +\NewDocumentCommand\dynkin@grok@series{}% +{% + \newcount\lenny + \StrLen{\dynkin@series}[\lenny] + \ifnum\lenny>1% + \dynkin@error@series% + \fi + \edef\series{\dynkin@series} + \IfStrEqCase{\dynkin@twisted@series}% + {% + {0}{}% + {1}{ \global\dynkin@is@extendedtrue}% + {2}{% + \IfSubStr{ADE}{\dynkin@series}% + {% + \global\dynkin@is@twistedtrue% + }% + {% + \dynkin@error@series% + }% + }% + {3}{% + \IfStrEq{\dynkin@series}{D}% + {% + \global\dynkin@is@twistedtrue% + }% + {% + \dynkin@error@series% + }% + }% + }% + [\dynkin@error@series]% +}% + + +\newif\ifdynkin@Satake@diagram + +\NewDocumentCommand\dynkin@grok@Satake@codes{}% +{% + \ifdynkin@is@extended% + \else% + \ifdynkin@is@twisted% + \else% + \global\dynkin@Satake@diagramtrue% + \fi% + \fi% + \IfStrEqCase{\dynkin@series}% + {% + {A}% + {% + \IfStrEqCase{\dynkin@string}% + {% + {even}{\gdef\dynkin@string{***.***}\global\dynkin@oddfalse\global\dynkin@Satake@diagramfalse}% + {odd}{\gdef\dynkin@string{****.***}\global\dynkin@oddtrue\global\dynkin@Satake@diagramfalse}% + {}{\gdef\dynkin@string{**.**}\global\dynkin@Satake@diagramfalse}% + {I}{ \gdef\dynkin@string{oo.oo}}% + {II}{\gdef\dynkin@string{*o*.o*}}% + {IIIa}{\global\dynkin@ply=2\gdef\dynkin@string{oo.o**.**o.oo}}% + {IIIb}{\global\dynkin@ply=2\gdef\dynkin@string{oo.ooo.oo}}% + {IV} {\global\dynkin@ply=2\gdef\dynkin@string{o*.*o}}% + }% + [\global\dynkin@Satake@diagramfalse]% + }% + {B}% + {% + \IfStrEqCase{\dynkin@string}% + {% + {}{% + \global\dynkin@Satake@diagramfalse% + \ifdynkin@Coxeter% + \gdef\dynkin@string{***.***}% + \else% + \ifdynkin@is@extended% + \gdef\dynkin@string{***.***}% + \else% + \gdef\dynkin@string{**.***}% + \fi% + \fi% + }% + {I}{\gdef\dynkin@string{oo.o*.**}}% + {II}{\gdef\dynkin@string{o*.**}}% + }% + [\global\dynkin@Satake@diagramfalse]% + }% + {C}% + {% + \IfStrEqCase{\dynkin@string}% + {% + {}{% + \global\dynkin@Satake@diagramfalse% + \ifdynkin@Coxeter% + \gdef\dynkin@string{***.***}% + \else% + \gdef\dynkin@string{**.***}% + \fi% + }% + {I}{\gdef\dynkin@string{oo.oo}}% + {IIa}{\gdef\dynkin@string{*o*.o*.**}}% + {IIb}{\gdef\dynkin@string{*o*.o*o}}% + }% + [\global\dynkin@Satake@diagramfalse]% + }% + {D}% + {% + \IfStrEqCase{\dynkin@string}% + {% + {}{% + \global\dynkin@Satake@diagramfalse% + \ifdynkin@is@extended% + \ifnum\dynkin@ply=4% + \gdef\dynkin@string{****.*.*****} + \else% + \gdef\dynkin@string{***.****}% + \fi% + \else% + \ifdynkin@is@twisted% + \IfStrEqCase{\dynkin@twisted@series}% + {% + {2}{ \gdef\dynkin@string{**.***}}% + {3}{\gdef\dynkin@string{***}}% + }% + [\dynkin@error@series]% + \else% + \gdef\dynkin@string{**.****}% + \fi% + \fi% + }% + {Ia}{\gdef\dynkin@string{oo.o*.***}}% + {Ib}{\global\dynkin@ply=2\gdef\dynkin@string{o.ooo}}% + {Ic}{\gdef\dynkin@string{o.ooo}}% + {II} {\gdef\dynkin@string{o*.***}}% + {IIIa}{\gdef\dynkin@string{*o*.o*o}}% + {IIIb}{\global\dynkin@ply=2\gdef\dynkin@string{*o*.o*oo}}% + }% + [\global\dynkin@Satake@diagramfalse]% + }% + {E}% + {% + \IfStrEqCase{\dynkin@string}% + {% + {}% + {% + \global\dynkin@Satake@diagramfalse% + \IfStrEq{\dynkin@twisted@series}{2}% + {% + \gdef\dynkin@string{*****}% + }% + {% + \dynkin@error@series% + }% + }% + {I}{ \global\dynkin@rank=6\gdef\dynkin@string{oooooo}}% + {II} {\global\dynkin@ply=2\gdef\dynkin@string{oooooo}}% + {III}{\global\dynkin@ply=2\gdef\dynkin@string{oo***o}}% + {IV} {\gdef\dynkin@string{oo***o}}% + {V}{ \gdef\dynkin@string{ooooooo}}% + {VI} {\gdef\dynkin@string{o*oo*o*} }% + {VII}{\gdef\dynkin@string{o****oo}}% + {VIII}{\gdef\dynkin@string{oooooooo}}% + {IX} {\gdef\dynkin@string{o****ooo}}% + }% + [\global\dynkin@Satake@diagramfalse]% + }% + {F}% + {% + \global\dynkin@rank=4% + \IfStrEqCase{\dynkin@string}% + {% + {I}{ \gdef\dynkin@string{oooo}}% + {II} {\gdef\dynkin@string{***o}}% + }% + [\global\dynkin@Satake@diagramfalse]% + }% + {G}% + {% + \IfStrEqCase{\dynkin@string}% + {% + {I}{\gdef\dynkin@string{oo}}% + }% + [\global\dynkin@Satake@diagramfalse]% + }% + {H}% + {% + \IfStrEqCase{\dynkin@string}% + {% + {}{\gdef\dynkin@string{**}}% + }% + [\global\dynkin@Satake@diagramfalse]% + }% + {I}% + {% + \IfStrEqCase{\dynkin@string}% + {% + {}{\gdef\dynkin@string{**}}% + {% + }% + }% + [\global\dynkin@Satake@diagramfalse]% + }% + }% + [\dynkin@error@series]% + \ifdynkin@Satake@diagram% + \else% + \StrSubstitute{\dynkin@string}{*}{\dynkin@root@mark}[\temp]% + \xdef\dynkin@string{\temp}% + \fi% +}% + +\NewDocumentCommand\dynkin@error@root@ordering{} +{% + \ClassError% + {Dynkin diagrams}% + {Unrecognized root ordering: ``\dynkin@ordering'' + in Dynkin diagram \dynkin@user@series{\dynkin@user@string}}% + {}% +}% + +\NewDocumentCommand\dynkin@error@rank{}% +{% + \ClassError% + {Dynkin diagrams}% + {Unrecognized \dynkin@user@series\spacy series rank: + ``\the\dynkin@rank'' in Dynkin diagram \dynkin@user@series{\dynkin@user@string}}% + {}% +}% + +\NewDocumentCommand\dynkin@error@series{}% +{% + \ClassError% + {Dynkin diagrams}% + {Unrecognized series ``\dynkin@user@series'' + in Dynkin diagram \dynkin@user@series{\dynkin@user@string}}% + {}% +}% + + +\NewDocumentCommand\dynkin@error@ply{} +{% + \ClassError% + {Dynkin diagrams}% + {Unrecognized ply: ``\the\dynkin@ply'' + in Dynkin diagram \dynkin@user@series{\dynkin@user@string}}% + {}% +}% + + +%% \check@Dynkin@Roots +%% Raises error messages for erroneous input in the list of Dynkin roots. +\NewDocumentCommand\check@Dynkin@Roots{}% +{% + \foreach \i in {1,...,\the\dynkin@nodes}% + {% + \StrChar{\dynkin@roots}{\i}[\cccc]% + \IfSubStr{*OXotx}{\cccc}% + {% + }% + {%else + \ClassError% + {Dynkin diagrams}% + {Unrecognized Dynkin diagram root mark: + ``\cccc'' in Dynkin diagram \dynkin@user@series{\dynkin@user@string}}% + {}% + }% + }% +}% + +%% \check@Dynkin@diagram +%% Raises error messages for erroneous inputs. +\NewDocumentCommand\check@Dynkin@diagram{}% +{% + \IfSubStr{1234}{\the\dynkin@ply}{}{\dynkin@error@ply}% + \check@Dynkin@Roots% + \IfStrEqCase{\dynkin@ordering}% + {% + {Adams}{}% + {Bourbaki}{}% + {Carter}{}% + {Dynkin}{}% + {Kac}{}% + {TestOrder}{}% + }% + [\ClassError% + {Dynkin diagrams}% + {Unrecognized label ordering: ``\dynkin@ordering'' + in Dynkin diagram \dynkin@user@series{\dynkin@user@string}}% + {}]% + \IfStrEqCase{\dynkin@series}% + {% + {A}{}% + {B}{}% + {C}{}% + {D}{}% + {E}% + {% + \ifnum\dynkin@nodes=5% + \ifnum\dynkin@rank=6% + \IfStrEq{\dynkin@twisted@series}{2}% + {% + }% + {% + \dynkin@error@rank% + }% + \else% + \dynkin@error@rank% + \fi% + \else + \ifnum\dynkin@rank=6% + \else% + \ifnum\dynkin@rank=7% + \else% + \ifnum\dynkin@rank=8% + \else% + \dynkin@error@rank% + \fi% + \fi% + \fi% + \fi% + }% + {F}% + {% + \ifnum\dynkin@rank=4% + \else% + \dynkin@error@rank% + \fi% + }% + {G}% + {% + \ifnum\dynkin@rank=2% + \else% + \dynkin@error@rank% + \fi% + }% + {H}{}% + {I}{}% + }% + [\dynkin@error@series]% +}% + + +% A slight headache: all of the routines that draw Dynkin diagrams are written +% in Bourbaki ordering. We store the roots in the current ordering. +% So when we draw edges, we need to convert from the Bourbaki ordering each time. +% We store the conversions here. +\newcount\RootNumber +\newcount\@fromRoot +\newcount\@toRoot + +%% \swapRootIfInLastTwoRoots{} +%% If the input root is one of the last two roots, then put the other in \RootNumber, otherwise +%% let \RootNumber be . +\NewDocumentCommand\swapRootIfInLastTwoRoots{m}% +{% + \ifnum\dynkin@rank>1% + \newcount\drmo\relax% + \drmo=\dynkin@rank\relax% + \advance\drmo by -1\relax% + \ifnum\dynkin@rank=#1% + \global\RootNumber=\the\drmo\relax% + \else% + \ifnum\drmo=#1% + \global\RootNumber=\the\dynkin@rank\relax% + \else% + \global\RootNumber=#1\relax% + \fi% + \fi% + \else% + \global\RootNumber=#1\relax% + \fi% +}% + +%% \convertRootNumber{} +%% Converts from Bourbaki ordering to the current ordering, storing the result in a count called \RootNumber. +\NewDocumentCommand\convertRootNumber{m}% +{% + \IfStrEq{#1}{0}% + {% + \global\RootNumber=0% + }% + {% + \IfStrEqCase{\dynkin@series}% + {% + {A}% + {% + \IfStrEqCase{\dynkin@ordering}% + {% + {TestOrder}% + {% + \RootNumber=#1 + \advance\RootNumber by 1 + \ifnum\RootNumber>\the\dynkin@rank% + \RootNumber=1% + \fi% + }% + }% + [\global\RootNumber=#1]% + }% + {D}% + {% + \IfStrEqCase{\dynkin@ordering}% + {% + {Adams}{\swapRootIfInLastTwoRoots{#1}}% + {Dynkin}{\swapRootIfInLastTwoRoots{#1}}% + {Kac}{\swapRootIfInLastTwoRoots{#1}}% + }% + [\global\RootNumber=#1]% + }% + {E}% + {% + \ifdynkin@is@twisted% + \global\RootNumber=#1% + \else% + \ifnum\dynkin@rank=6% + \IfStrEqCase{\dynkin@ordering}% + {% + {Adams}{\global\RootNumber=\stringCharacterInPosition{152436}{#1}}% + {Carter}{\global\RootNumber=\stringCharacterInPosition{142356}{#1}}% + {Dynkin}{\global\RootNumber=\stringCharacterInPosition{162345}{#1}}% + {Kac}{\global\RootNumber=\stringCharacterInPosition{162345}{#1}}% + }% + [\global\RootNumber=#1]% + \else% + \ifnum\dynkin@rank=7% + \IfStrEqCase{\dynkin@ordering}% + {% + {Adams}{\global\RootNumber=\stringCharacterInPosition{6354217}{#1}}% + {Carter}{\global\RootNumber=\stringCharacterInPosition{7564321}{#1}}% + {Dynkin}{\global\RootNumber=\stringCharacterInPosition{1723456}{#1}}% + {Kac}{\global\RootNumber=\stringCharacterInPosition{1723456}{#1}}% + }% + [\global\RootNumber=#1]% + \else% + \ifnum\dynkin@rank=8% + \IfStrEqCase{\dynkin@ordering}% + {% + {Adams}{\global\RootNumber=\stringCharacterInPosition{13245678}{#1}}% + {Carter}{\global\RootNumber=\stringCharacterInPosition{86754321}{#1}}% + {Dynkin}{\global\RootNumber=\stringCharacterInPosition{18234567}{#1}}% + {Kac}{\global\RootNumber=\stringCharacterInPosition{78654321}{#1}}% + }% + [\global\RootNumber=#1]% + \else% + \fi% + \fi% + \fi% + \fi% + }% + {F}% + {% + \IfStrEqCase{\dynkin@ordering}% + {% + {Adams}{\global\RootNumber=\stringCharacterInPosition{4321}{#1}}% + }% + [\global\RootNumber=#1]% + }% + {G}% + {% + \IfStrEqCase{\dynkin@ordering}% + {% + {Carter}{\global\RootNumber=\stringCharacterInPosition{21}{#1}}% + {Dynkin}{\global\RootNumber=\stringCharacterInPosition{21}{#1}}% + }% + [\global\RootNumber=#1]% + }% + }% + [\global\RootNumber=#1]% + }% +}% + +%% \convertRootPair{

}{} +%% Stores conversions in \@fromRoot and \@toRoot. +\NewDocumentCommand\convertRootPair{mm} +{% + \convertRootNumber{#1}% + \@fromRoot=\RootNumber% + \convertRootNumber{#2}% + \@toRoot=\RootNumber% +}% + +\ExplSyntaxOn +\NewDocumentCommand\moduloInt{mm}{\int_mod:nn{#1}{#2}} +\ExplSyntaxOff + +%% \testbit{}{}{}{} +%% If bit number of is 1 then expand else expand . +\NewDocumentCommand\testbit{mmmm}% +{% + \newcount\x\relax% + \x=#1\relax% + \newcount\whichbit\relax% + \whichbit=#2\relax% + \ifnum\whichbit>0% + \foreach \i in {1,...,#2}% + {% + \global\divide \x by 2% + }% + \fi% + \xdef\temp{\moduloInt{\the\x}{2}}% + \x=\temp\relax% + \ifnum\the\x=1 #3\else #4\fi% +}% + +\NewDocumentCommand\dynkin@put@cross{m}% +{% + \newcount\dynkin@where% + \dynkin@where=#1% + \StrMid{\dynkin@roots}{1}{#1}[\dynkin@start]% + \advance\dynkin@where by 1% + \StrMid{\dynkin@roots}{\the\dynkin@where}{\the\dynkin@nodes}[\dynkin@end]% + \xdef\dynkin@roots{\dynkin@start x\dynkin@end}% +}% + +\NewDocumentCommand\dynkin@cross@out@parabolics{}% +{% + \IfInteger{\dynkin@parabolic}% + {% + \IfStrEq{\dynkin@parabolic}{0}% + {% + }% + {% + \newcount\drmo\relax% + \drmo=\the\dynkin@nodes\relax% + \advance\drmo by -1\relax% + \foreach \b in {0,...,\the\drmo}% + {% + \testbit{\dynkin@parabolic}{\b}{\dynkin@put@cross{\b}}{}% + }% + }% + }% +}% + +\NewDocumentCommand\dynkinMoveToRoot{sm}% +{% + \IfBooleanTF{#1}% + {% + \convertRootNumber{#2}% + }% + {% + \global\RootNumber=#2 + }% + \node (Dynkin current) at (\dynkin@root@name \the\RootNumber){};% +}% + +%% \dynkinPlaceRootHere{}{} +%% \dynkinPlaceRootHere*{}{} +%% Tell TikZ to place node for a root of a Dynkin diagram at the current +%% cursor location. Draws nothing. +%% =label positioning: above, below, left, right +%% Starred form converts from Bourbaki ordering to default ordering. +\NewDocumentCommand\dynkinPlaceRootHere{smm}% +{% + \IfBooleanTF{#1}% + {% + \convertRootNumber{#2}% + }% + {% + \global\RootNumber=#2 + }% + \node (\dynkin@root@name \the\RootNumber) at (Dynkin current) {};% + \dynkin@put@direction{\the\RootNumber}{#3}% +}% + +%% \dynkinPlaceRootRelativeTo{

}{}{}{} +%% \dynkinPlaceRootRelativeTo*{

}{}{}{} +%% Tell TikZ to place node

for a root of a Dynkin diagram at a location +%% in direction from root . Draws nothing. +%% is the label position: above, below, left, right. +%% is the direction from : +%% west,east,south,north, +%% northeast,northwest,southeast,southwest, +%% southfold,northfold, +%% southeastfold,southwestfold,northeastfold,northwestfold. +%% Starred form is in Bourbaki root ordering; otherwise default ordering. +\NewDocumentCommand\dynkinPlaceRootRelativeTo{smmmm}% +{% + \IfBooleanTF{#1}% + {% + \convertRootPair{#3}{#2}% + }% + {% + \global\@fromRoot=#3% + \global\@toRoot=#2% + }% + \dynkin@is@edge@indefinite{\@fromRoot}{\@toRoot}% + \ifdynkin@is@indefinite@edge% + \xdef\dynkin@distance{\dynkin@indefinite@edge@length} + \else + \xdef\dynkin@distance{\dynkin@edge@length} + \fi + \IfStrEqCase{#4}% + {% + {west}{\xdef\x{-\dynkin@distance}\xdef\y{0}}% + {east}{\xdef\x{\dynkin@distance}\xdef\y{0}}% + {south}{\xdef\x{0}\xdef\y{-\dynkin@distance}}% + {north}{\xdef\x{0}\xdef\y{\dynkin@distance}}% + {southeast}{\xdef\x{cos(-60)*\dynkin@distance}\xdef\y{sin(-60)*\dynkin@distance}}% + {southwest}{\xdef\x{cos(240)*\dynkin@distance}\xdef\y{sin(240)*\dynkin@distance}}% + {northeast}{\xdef\x{cos(60)*\dynkin@distance}\xdef\y{sin(60)*\dynkin@distance}}% + {northwest}{\xdef\x{cos(120)*\dynkin@distance}\xdef\y{sin(120)*\dynkin@distance}}% + {southeastfold}{\xdef\x{\dynkin@fold@radius}\xdef\y{-\dynkin@fold@radius}}% + {southwestfold}{\xdef\x{-\dynkin@fold@radius}\xdef\y{-\dynkin@fold@radius}}% + {northeastfold}{\xdef\x{\dynkin@fold@radius}\xdef\y{\dynkin@fold@radius}}% + {northwestfold}{\xdef\x{-\dynkin@fold@radius}\xdef\y{\dynkin@fold@radius}}% + {northfold}{\xdef\x{0}\xdef\y{2*\dynkin@fold@radius}}% + {southfold}{\xdef\x{0}\xdef\y{-2*\dynkin@fold@radius}}% + }% + \node (Dynkin current) at ($(\dynkin@root@name \the\@fromRoot)+({\x},{\y})$){}; + \dynkinPlaceRootHere{\@toRoot}{#5}% +}% + +%% \dynkinEast +%% Moves the TikZ cursor one edge to the right. +%% Starred form for an indefinite edge. +\NewDocumentCommand\dynkinEast{s}% +{% + \xdef\distance{\IfBooleanTF{#1}{\dynkin@indefinite@edge@length}{\dynkin@edge@length}} + \node (Dynkin current) at ($(Dynkin current)+({\distance},0)$) {};% +}% + + + +%% \dynkinWest +%% Moves the TikZ cursor one edge to the left. +%% Starred form for an indefinite edge. +\NewDocumentCommand\dynkinWest{s}% +{% + \xdef\distance{\IfBooleanTF{#1}{\dynkin@indefinite@edge@length}{\dynkin@edge@length}} + \node (Dynkin current) at ($(Dynkin current)+({-\distance},0)$) {};% +}% + +%% \dynkinNorth +%% Moves the TikZ cursor one edge up. +%% Starred form for an indefinite edge. +\NewDocumentCommand\dynkinNorth{s}% +{% + \xdef\distance{\IfBooleanTF{#1}{\dynkin@indefinite@edge@length}{\dynkin@edge@length}} + \node (Dynkin current) at ($(Dynkin current)+(0,{\distance})$) {};% +}% + +%% \dynkinSouth +%% Moves the TikZ cursor one edge to the left. +%% Starred form for an indefinite edge. +\NewDocumentCommand\dynkinSouth{s}% +{% + \xdef\distance{\IfBooleanTF{#1}{\dynkin@indefinite@edge@length}{\dynkin@edge@length}} + \node (Dynkin current) at ($(Dynkin current)+(0,{-\distance})$) {};% +}% + +%% \dynkinNorthEast +%% Moves the TikZ cursor one edge to the north east. +%% Starred form for an indefinite edge. +\NewDocumentCommand\dynkinNorthEast{s}% +{% + \xdef\distance{\IfBooleanTF{#1}{\dynkin@indefinite@edge@length}{\dynkin@edge@length}} + \node (Dynkin current) at + ($(Dynkin current)+ + ({cos(60)*\distance},{sin(60)*\distance})$) {};% +}% + +%% \dynkinSouthEast +%% Moves the TikZ cursor one edge to the south east. +%% Starred form for an indefinite edge. +\NewDocumentCommand\dynkinSouthEast{s}% +{% + \xdef\distance{\IfBooleanTF{#1}{\dynkin@indefinite@edge@length}{\dynkin@edge@length}} + \node (Dynkin current) at + ($(Dynkin current)+ + ({cos(-60)*\distance},{sin(-60)*\distance})$) {};% +}% + +%% \dynkinNorthWest +%% Moves the TikZ cursor one edge to the north west. +%% Starred form for an indefinite edge. +\NewDocumentCommand\dynkinNorthWest{s}% +{% + \xdef\distance{\IfBooleanTF{#1}{\dynkin@indefinite@edge@length}{\dynkin@edge@length}} + \node (Dynkin current) at + ($(Dynkin current)+ + ({cos(120)*\distance},{sin(120)*\distance})$) {};% +}% + +%% \dynkinSouthWest +%% Moves the TikZ cursor one edge to the south west. +%% Starred form for an indefinite edge. +\NewDocumentCommand\dynkinSouthWest{s}% +{% + \xdef\distance{\IfBooleanTF{#1}{\dynkin@indefinite@edge@length}{\dynkin@edge@length}} + \node (Dynkin current) at + ($(Dynkin current)+ + ({cos(240)*\distance},{sin(240)*\distance})$) {};% +}% + + +%% \dynkinSouthEastFold +%% Moves the TikZ cursor one edge to the south east in the middle of a fold. +\NewDocumentCommand\dynkinSouthEastFold{}% +{% + \node (Dynkin current) at ($(Dynkin current)+({\dynkin@fold@radius},{-\dynkin@fold@radius})$) {};% +}% + +%% \dynkinSouthWestFold +%% Moves the TikZ cursor one edge to the south west in the middle of a fold. +\NewDocumentCommand\dynkinSouthWestFold{}% +{% + \node (Dynkin current) at ($(Dynkin current)+({-\dynkin@fold@radius},{-\dynkin@fold@radius})$) {};% +}% + +%% \dynkinSouthFold +%% Moves the TikZ cursor one edge to the south in the middle of a fold. +\NewDocumentCommand\dynkinSouthFold{}% +{% + \node (Dynkin current) at ($(Dynkin current)+(0,{-2*\dynkin@fold@radius})$) {};% +}% + +\NewDocumentCommand\find@mark@of@root{m}% +{% + \StrChar{\dynkin@roots}{#1}[\my@root@marker]% + \my@root@marker +}% + +\NewDocumentCommand\dynkin@draw@all@roots{}% +{% + \foreach \b in {1,...,\the\dynkin@nodes}% + {% + \StrChar{\dynkin@roots}{\b}[\c]% + \dynkinRootMark*{\c}{\b}% + }% + \ifdynkin@is@extended% + \dynkinRootMark*{\dynkin@affine@root@mark}{0}% + \else% + \ifdynkin@is@twisted% + \dynkinRootMark*{\dynkin@affine@root@mark}{0}% + \fi% + \fi% +}% + + +%% \dynkin@fold@arrow@if@oo{

}{} +%% Inputs are roots (in Bourbaki ordering). +%% If we are working on a Satake diagram, and both roots are +%% marked with hollow circles o, then draws a fold arrow between them. +\NewDocumentCommand\dynkin@fold@arrow@if@oo{mm}% +{% + \convertRootPair{#1}{#2}% + \ifdynkin@Satake@diagram% + \StrChar{\dynkin@roots}{\the\@fromRoot}[\my@root@marker]% + \IfStrEq{\my@root@marker}{o}% + {% + \StrChar{\dynkin@roots}{\the\@toRoot}[\my@other@root@marker]% + \IfStrEq{\my@other@root@marker}{o}% + {% + \dynkinFold{\the\@fromRoot}{\the\@toRoot}% + }% + {}% + }{}% + \else% + \dynkinFold{\the\@fromRoot}{\the\@toRoot}% + \fi% +}% + +%% \dynkin@pipe{}{}{}{} +%% Layout the roots (as TikZ nodes) , +1, \dots, in the Bourbaki ordering, in a straight line, +%% starting at the current position (Dynkin current), moving in the direction =east, west, north, south, with labels placed according to =left,right,above,below. +%% Assumes that the root is already created as a node in TikZ, but the others are not. +\NewDocumentCommand\dynkin@pipe{mmmm}% +{% + \newcount\start@root + \start@root=#1 + \ifnum\start@root<#2% + \newcount\bmo + \bmo=#1 + \newcount\fpo + \fpo=#1 + \advance\fpo by 1 + \foreach \b in {\the\fpo,...,#2}% + {% + \dynkinPlaceRootRelativeTo*{\b}{\the\bmo}{#3}{#4}% + \dynkinEdge*{SingleEdge}{\b}{\the\bmo}% + \global\advance\bmo by 1% + }% + \fi% +}% + +%% \dynkin@fold{}{} +%% Layout the roots (as TikZ nodes) , +1, \dots, in the Bourbaki ordering, in a folded arrangement, +%% moving first east, then down, then west, starting at the current position (Dynkin current). +%% Assumes that the root is already created as a node in TikZ, but the others are not. +\NewDocumentCommand\dynkin@fold{mm}% +{% + \newcount\h% + \h=#1% + \advance\h by #2% + \advance\h by -1% + \divide\h by 2% + \dynkin@pipe{#1}{\the\h}{east}{above} + \newcount\hpo + \hpo=\the\h + \advance\hpo by 1 + \newcount\afterfold + \global\afterfold=\the\hpo + \newcount\nrts + \nrts=#2 + \advance\nrts by 1 + \advance\nrts by -#1 + \ifodd\nrts% + \global\advance\afterfold by 1 + \dynkinPlaceRootRelativeTo*{\the\hpo}{\the\h}{southeastfold}{right} + \dynkinEdge*{RightDownArc}{\the\h}{\the\hpo}% + \dynkinPlaceRootRelativeTo*{\the\afterfold}{\the\hpo}{southwestfold}{below} + \dynkinEdge*{RightUpArc}{\the\afterfold}{\the\hpo}% + \else + \dynkinPlaceRootRelativeTo*{\the\afterfold}{\the\h}{southfold}{below} + \dynkinEdge*{SemiCircle}{\the\h}{\the\afterfold}% + \fi + \dynkin@pipe{\the\afterfold}{#2}{west}{below} + \ifdynkin@arrows% + \newcount\countdown% + \countdown=#2% + \foreach \b in {#1,...,\the\h}% + {% + \dynkin@fold@arrow@if@oo{\b}{\the\countdown}% + \global\advance\countdown by -1% + }% + \fi% +}% + +%% \Adynkin +%% Draws an A series Dynkin diagram. +\NewDocumentCommand\Adynkin{}% +{% + \ifnum\dynkin@rank=1% + \global\dynkin@ply=1\relax% + \fi% +% % Create the roots. + \ifnum\dynkin@ply>1% + \dynkinPlaceRootHere*{1}{above}% + \dynkin@fold{1}{\the\dynkin@rank}% + \else% + \dynkinPlaceRootHere*{1}{below}% + \ifnum\dynkin@rank>1% + \dynkin@pipe{1}{\the\dynkin@rank}{east}{below}% + \fi% + \fi% +}% + +%% \Bdynkin %% Draw a B series Dynkin diagram. \newcommand*{\Bdynkin} { - \ifdynkincoxeter + \ifnum\dynkin@rank<2 \Adynkin - \convertRootPair{1}{2} - \node[above] at ($.5*(root \the\@fromRoot)+.5*(root \the\@toRoot)$) {\dynkinprint{4}}; \else - \ifnum\dynkinrank=0 - \dynkinrank=5 - % Create the nodes. - \Adynkinnodes - % Draw the edges. - \dynkinline*{1}{2} - \dynkindots*{2}{3} - \dynkinline*{3}{4} - \dynkindoubleline*{4}{5} + \newcount\drmo + \drmo=\the\dynkin@rank + \advance\drmo by -1 + \ifdynkin@Coxeter + \Adynkin + \convertRootPair{\the\drmo}{\the\dynkin@rank} + \node[/Dynkin diagram/text,above] + at ($.5*(\dynkin@root@name \the\@fromRoot)+.5*(\dynkin@root@name \the\@toRoot)$) + {\(4\)}; \else - % Create the nodes. - \Adynkinnodes - % Draw the edges. - \dynkinline*{1}{\the\dynkinrank}% - \newcount\rmo - \rmo=\dynkinrank - \advance \rmo by -1 - \dynkindoubleline*{\the\rmo}{\the\dynkinrank} - \fi - % Draw the nodes. - \ifisaffine - \dynkinline*{0}{2} - \dynkindot*{0} - \fi - \foreach \b in {1,...,\the\dynkinrank} - { - \testbit{\dynkinparabolic}{\b}{\dynkincross{\b}}{\dynkindot{\b}} - } - \fi + % Create the roots. + \ifnum\dynkin@ply>1% + \ifnum\dynkin@rank>3% + \dynkinPlaceRootHere*{1}{above}% + \dynkinPlaceRootRelativeTo*{2}{1}{east}{above}% + \dynkin@fold{2}{\the\drmo}% + \dynkinPlaceRootRelativeTo*{\the\dynkin@rank}{\the\drmo}{west}{below}% + \dynkinEdge*{DoubleEdge}{\the\drmo}{\the\dynkin@rank}% + \dynkinEdge*{SingleEdge}{1}{2}% + \else% + \ifnum\dynkin@rank=2% + \dynkinPlaceRootHere*{1}{left}% + \dynkinPlaceRootRelativeTo*{2}{1}{southfold}{left}% + \dynkinEdge*{DoubleDownRightSemiCircle}{1}{2}% + \else% + \dynkinPlaceRootHere*{1}{left}% + \dynkinPlaceRootRelativeTo*{2}{1}{southeastfold}{right}% + \dynkinPlaceRootRelativeTo*{3}{2}{southwestfold}{left}% + \dynkinEdge*{RightDownArc}{1}{2}% + \dynkinEdge*{DoubleDownLeftArc}{2}{3}% + \fi% + \fi% + \else% + \dynkinPlaceRootHere*{1}{below} + \dynkin@pipe{1}{\the\drmo}{east}{below} + \dynkinPlaceRootRelativeTo*{\the\dynkin@rank}{\the\drmo}{east}{below} + \dynkinEdge*{DoubleEdge}{\the\drmo}{\the\dynkin@rank}% + \fi% + \ifdynkin@arrows% + \ifnum\dynkin@ply>1% + \dynkinLeftFold*{1}{\the\dynkin@rank}% + \fi% + \fi% + \fi% + \fi% } %% \Cdynkin -%% -> %% Draws a C series Dynkin diagram. \newcommand*{\Cdynkin} { - \ifdynkincoxeter - \Bdynkin - \else - \ifnum\dynkinrank=0 - \dynkinrank=5 - % Create the nodes. - \Adynkinnodes - % Draw the edges. - \dynkinline*{1}{2} - \dynkindots*{2}{3} - \dynkinline*{3}{4} - \dynkindoubleline*{5}{4} - \else - % Create the nodes. - \Adynkinnodes - % Draw the edges. - \newcount\rmo - \rmo=\dynkinrank - \advance\rmo by -1 - \dynkinline*{1}{\the\rmo}% - \dynkindoubleline*{\the\dynkinrank}{\the\rmo} - \fi - % Draw the nodes. - \ifisaffine - \dynkindoubleline*{0}{1} - \dynkindot*{0} - \fi - \foreach \b in {1,...,\the\dynkinrank} - { - \testbit{\dynkinparabolic}{\b}{\dynkincross{\b}}{\dynkindot{\b}} - } - \fi + \ifdynkin@reverse@arrows% + \global\dynkin@reverse@arrowsfalse% + \else% + \global\dynkin@reverse@arrowstrue% + \fi% + \Bdynkin% + \ifdynkin@reverse@arrows% + \global\dynkin@reverse@arrowsfalse% + \else% + \global\dynkin@reverse@arrowstrue% + \fi% } -%% \Ddynkinnodes -%% -> -%% Tell TikZ where to place the nodes for a D series Dynkin diagram. Draws nothing. -\newcommand*{\Ddynkinnodes} +%% \Ddynkin@roots +%% Tell TikZ where to place the @roots for a D series Dynkin diagram. Draws nothing. +\newcommand*{\Ddynkin@roots} { + % Create the roots. + \ifdynkin@is@extended% + \ifnum\dynkin@ply>1% + \ifnum\dynkin@rank=4% + \dynkinPlaceRootRelativeTo*{2}{0}{southeastfold}{right}% + \else% + \dynkinPlaceRootRelativeTo*{2}{0}{southeastfold}{below}% + \fi% + \dynkinPlaceRootRelativeTo*{1}{2}{southwestfold}{left}% + \else% + \ifdynkin@left@fold% + \dynkinPlaceRootRelativeTo*{2}{0}{southeastfold}{below}% + \dynkinPlaceRootRelativeTo*{1}{2}{southwestfold}{left}% + \else% + \dynkinPlaceRootRelativeTo*{2}{0}{southeast}{left}% + \dynkinPlaceRootRelativeTo*{1}{2}{southwest}{left}% + \fi% + \fi% + \dynkinMoveToRoot*{2}% + \else + \dynkinPlaceRootHere*{1}{below} + \ifnum\dynkin@rank=4% + \ifdynkin@right@fold% + \dynkinPlaceRootRelativeTo*{2}{1}{east}{below}% + \else% + \ifnum\dynkin@ply>1% + \dynkinPlaceRootRelativeTo*{2}{1}{east}{below}% + \else% + \dynkinPlaceRootRelativeTo*{2}{1}{east}{right}% + \fi% + \fi% + \else% + \dynkinPlaceRootRelativeTo*{2}{1}{east}{below}% + \fi% + \fi \newcount\rmo - \rmo=\dynkinrank + \rmo=\dynkin@rank \advance \rmo by -1 \newcount\rmt \rmt=\rmo \advance\rmt by -1 - % Create the nodes. - \foreach \b in {1,...,\the\rmt} - { - \placeRoot{\b}{\b}{0} - } - \pgfmathparse{subtract(\the\rmo,.5)} - \let\rmh\pgfmathresult - \ifdynkinfolded - \placeRoot{\the\rmo}{\rmh}{-.9} - \placeRoot*{\the\dynkinrank}{\rmh}{.9} - \else - \placeRootHorizontalLabels{\the\rmo}{\rmh}{-.9} - \placeRootHorizontalLabels{\the\dynkinrank}{\rmh}{.9} - \fi -} + \newcount\rmth + \rmth=\rmt + \advance\rmth by -1 + \ifnum\dynkin@rank>2 + \ifnum\dynkin@rank>5% + \dynkinPlaceRootRelativeTo*{3}{2}{east}{below}% + \else% + \ifnum\dynkin@ply>1% + \dynkinPlaceRootRelativeTo*{3}{2}{east}{below}% + \else% +% \ifdynkin@left@fold% +% \dynkinPlaceRootRelativeTo*{3}{2}{east}{below}% +% \else% + \ifnum\dynkin@rank=5% + \ifdynkin@right@fold% + \dynkinPlaceRootRelativeTo*{3}{2}{east}{below}% + \else% + \dynkinPlaceRootRelativeTo*{3}{2}{east}{right}% + \fi% + \else% + \dynkinPlaceRootRelativeTo*{3}{2}{east}{right}% + \fi% +% \fi% + \fi% + \fi% + \ifnum\rmth>3% + \dynkin@pipe{3}{\the\rmth}{east}{below}% + \fi% + \ifnum\rmt>3% + \ifnum\dynkin@ply>1% + \dynkinPlaceRootRelativeTo*{\rmt}{\rmth}{east}{below}% + \else% + \ifdynkin@right@fold% + \dynkinPlaceRootRelativeTo*{\rmt}{\rmth}{east}{below}% + \else% + \dynkinPlaceRootRelativeTo*{\rmt}{\rmth}{east}{right}% + \fi% + \fi% + \dynkinEdge*{SingleEdge}{\rmt}{\rmth}% + \fi% + \ifnum\dynkin@ply=1% + \ifdynkin@right@fold% + \dynkinPlaceRootRelativeTo*{\the\rmo}{\the\rmt}{northeastfold}{right}% + \dynkinPlaceRootRelativeTo*{\the\dynkin@rank}{\the\rmt}{southeastfold}{right}% + \else% + \dynkinPlaceRootRelativeTo*{\the\rmo}{\the\rmt}{northeast}{right}% + \dynkinPlaceRootRelativeTo*{\the\dynkin@rank}{\the\rmt}{southeast}{right}% + \fi% + \else% + \dynkinPlaceRootRelativeTo*{\the\rmo}{\the\rmt}{northeastfold}{right}% + \dynkinPlaceRootRelativeTo*{\the\dynkin@rank}{\the\rmt}{southeastfold}{right}% + \fi% + \fi% +}% + +%% \Ddynkin@edges +%% Draws edges on a D series Dynkin diagram. +\NewDocumentCommand\Ddynkin@edges{}% +{% + % Draw the edges. + \newcount\rmo + \rmo=\dynkin@rank + \advance \rmo by -1 + \newcount\rmt + \rmt=\rmo + \advance\rmt by -1 + \newcount\rmtr + \rmtr=\rmt + \advance\rmtr by -1 + \ifnum\dynkin@ply>1% + \ifdynkin@is@extended% + \dynkinEdge*{RightUpArc}{1}{2}% + \else% + \dynkinEdge*{SingleEdge}{1}{2}% + \fi% + \ifnum\dynkin@rank>4% + \dynkinEdge*{SingleEdge}{2}{3}% + \fi% + \dynkinEdge*{LeftDownArc}{\the\rmo}{\the\rmt}% + \dynkinEdge*{LeftUpArc}{\the\dynkin@rank}{\the\rmt}% + \ifdynkin@arrows% + \dynkinRightFold*{\the\rmo}{\the\dynkin@rank}% + \ifdynkin@is@extended% + \dynkinLeftFold*{0}{1}% + \fi% + \fi% + \else% + \ifnum\dynkin@rank=4% + \else% + \dynkinEdge*{SingleEdge}{2}{3}% + \fi% + \ifdynkin@is@extended% + \ifdynkin@left@fold% + \dynkinEdge*{RightUpArc}{1}{2}% + \ifdynkin@arrows% + \ifdynkin@is@extended% + \dynkinLeftFold*{0}{1}% + \fi% + \fi% + \else% + \dynkinEdge*{SingleEdge}{1}{2}% + \fi% + \else% + \dynkinEdge*{SingleEdge}{1}{2}% + \fi% + \ifdynkin@right@fold% + \dynkinEdge*{LeftDownArc}{\the\rmo}{\the\rmt}% + \dynkinEdge*{LeftUpArc}{\the\dynkin@rank}{\the\rmt}% + \dynkinRightFold*{\the\rmo}{\the\dynkin@rank}% + \else% + \dynkinEdge*{SingleEdge}{\the\rmt}{\the\rmo}% + \dynkinEdge*{SingleEdge}{\the\rmt}{\the\dynkin@rank}% + \fi% + \fi% +}% + +%% \DthreePly +%% Draws a D series Dynkin diagram of rank 4, folded over a G2. +\NewDocumentCommand\DthreePly{}% +{% + \dynkinPlaceRootHere*{2}{right}% + \xdef\old@edge@length{\dynkin@edge@length}% + \pgfmathparse{1.5*\dynkin@edge@length}% + \xdef\dynkin@edge@length{\pgfmathresult pt}% + \dynkinPlaceRootRelativeTo*{3}{2}{south}{right}% + \dynkinPlaceRootRelativeTo*{4}{3}{south}{right}% + \xdef\dynkin@edge@length{\old@edge@length}% + \dynkinPlaceRootRelativeTo*{1}{3}{west}{left}% + \edef\old@fold@radius{\dynkin@fold@radius}% + \xdef\dynkin@fold@radius{\dynkin@edge@length}% + \dynkinEdge*{SingleEdge}{1}{3}% + \dynkinEdge*{LeftDownArc}{2}{1}% + \dynkinEdge*{LeftUpArc}{4}{1}% + \xdef\dynkin@fold@radius{\old@fold@radius}% + \ifdynkin@arrows% + \dynkin@fold@arrow@if@oo{2}{3}% + \dynkin@fold@arrow@if@oo{3}{4}% + \fi% +}% %% \Ddynkin -%% -> %% Draws a D series Dynkin diagram. -\newcommand*{\Ddynkin}% -{ - \ifnum\dynkinrank=1 - \gdef\dynkinseries{A} - \Adynkin - \else - \ifnum\dynkinrank=0 - \dynkinrank=6 - \Ddynkinnodes - % Draw the edges. - \dynkinline*{1}{2} - \dynkindots*{2}{3} - \dynkinline*{3}{4} - \dynkinline*{4}{5} - \dynkinline*{4}{6} - \else - \Ddynkinnodes - % Draw the edges. - \dynkinline*{1}{\the\rmt} - \dynkinline*{\the\rmt}{\the\rmo} - \dynkinline*{\the\rmt}{\the\dynkinrank} - \fi - \ifdynkinfolded - \ifdynkinarrows - \draw[\dynkinfoldarrowstyle,\dynkinfoldarrowcolor] - (root \the\rmo.east) - to [out=45, in=-45] - (root \the\dynkinrank.east); - \fi - \fi - % Draw the nodes. - \ifisaffine - \dynkinline*{0}{2} - \dynkindot*{0} - \fi - \foreach \b in {1,...,\the\dynkinrank} - { - \testbit{\dynkinparabolic}{\b}{\dynkincross{\b}}{\dynkindot{\b}} - } - \fi -} +\NewDocumentCommand\Ddynkin{}% +{% + \ifnum\dynkin@rank>3% + \ifnum\dynkin@rank=4% + \ifnum\dynkin@ply=3% + \DthreePly% + \else% + \Ddynkin@roots% + \Ddynkin@edges% + \fi% + \else% + \Ddynkin@roots% + \Ddynkin@edges% + \fi% + \else% + \gdef\dynkin@series{A}% + \Adynkin% + \ifnum\dynkin@ply>1% + \ifdynkin@arrows% + \ifnum\dynkin@rank=1% + \else% + \dynkinLeftFold*{1}{\the\dynkin@rank}% + \fi% + \fi% + \fi% + \fi% +}% -%% \Edynkinunfolded -%% -> +%% \Edynkin@unfolded %% Draws an E series Dynkin diagram not folded. -\newcommand*{\Edynkinunfolded}% +\newcommand*{\Edynkin@unfolded}% { - % Create the nodes. - \placeRoot{1}{1}{0} - \ifisaffine - \ifnum\dynkinrank=6 - \placeRootHorizontalLabels{2}{3}{1} + % Create the @roots. + \dynkinPlaceRootHere*{1}{below}% + \dynkinPlaceRootRelativeTo*{3}{1}{east}{below}% + \dynkinPlaceRootRelativeTo*{4}{3}{east}{below}% + \ifdynkin@is@extended + \ifnum\dynkin@rank=6 + \dynkinPlaceRootRelativeTo*{2}{4}{north}{right}% \else - \placeRoot*{2}{3}{1} + \dynkinPlaceRootRelativeTo*{2}{4}{north}{above}% \fi \else - \placeRoot*{2}{3}{1} + \dynkinPlaceRootRelativeTo*{2}{4}{north}{above}% \fi - \foreach \b in {3,...,\dynkinrank} - { - \newcount\bmo - \bmo=\b - \advance\bmo by -1 - \placeRoot{\b}{\the\bmo}{0} - } -% % Draw the edges. - \dynkinline*{1}{\the\dynkinrank} - \dynkinline*{2}{4} -} + \newcount\bmo\relax% + \bmo=4\relax% + \foreach \b in {5,...,\dynkin@rank}% + {% + \dynkinPlaceRootRelativeTo*{\b}{\the\bmo}{east}{below}% + \dynkinEdge*{SingleEdge}{\the\bmo}{\b}% + \global\advance\bmo by 1% + }% +% % Draw the remaining edges. + \dynkinEdge*{SingleEdge}{1}{3} + \dynkinEdge*{SingleEdge}{3}{4} + \dynkinEdge*{SingleEdge}{4}{2} + \ifdynkin@is@extended% + \ifnum\dynkin@rank=6% + \dynkinPlaceRootRelativeTo*{0}{2}{north}{above}% + \dynkinEdge*{SingleEdge}{0}{2}% + \else% + \ifnum\dynkin@rank=7% + \dynkinPlaceRootRelativeTo*{0}{1}{west}{below}% + \dynkinEdge*{SingleEdge}{0}{1}% + \else% + \dynkinPlaceRootRelativeTo*{0}{8}{east}{below}% + \dynkinEdge*{SingleEdge}{0}{8}% + \fi% + \fi% + \fi% +}% + + +%% \Edynkin@folded +%% Draws a folded E6, affine E6 or affine E7 Dynkin diagram. +\NewDocumentCommand\Edynkin@folded{}% +{% + \ifnum\dynkin@rank=6% + \ifnum\dynkin@ply=2\ESixTwoPly\else\ESixThreePly\fi% + \else% + \extendedESevenFolded% + \fi% +}% + +\NewDocumentCommand\ESixTwoPly{}% +{% + \dynkinPlaceRootHere*{1}{above}% + \dynkinPlaceRootRelativeTo*{3}{1}{east}{above}% + \dynkinPlaceRootRelativeTo*{4}{3}{southeastfold}{below}% + \dynkinPlaceRootRelativeTo*{5}{4}{southwestfold}{below}% + \dynkinPlaceRootRelativeTo*{6}{5}{west}{below}% + \ifdynkin@is@extended% + \dynkinPlaceRootRelativeTo*{2}{4}{east}{below}% + \dynkinPlaceRootRelativeTo*{0}{2}{east}{right}% + \dynkinEdge*{SingleEdge}{0}{2}% + \else% + \dynkinPlaceRootRelativeTo*{2}{4}{east}{right}% + \fi% + \dynkinEdge*{SingleEdge}{1}{3}% + \dynkinEdge*{SingleEdge}{2}{4}% + \dynkinEdge*{SingleEdge}{5}{6}% + \dynkinEdge*{RightDownArc}{3}{4}% + \dynkinEdge*{RightUpArc}{5}{4}% + \ifdynkin@arrows% + \dynkin@fold@arrow@if@oo{1}{6}% + \dynkin@fold@arrow@if@oo{3}{5}% + \fi% +}% + +\NewDocumentCommand\ESixThreePly{}% +{% + \dynkinPlaceRootHere*{3}{above}% + \edef\old@edge@length{\dynkin@edge@length}% + \pgfmathparse{1.5*\dynkin@edge@length}% + \xdef\dynkin@edge@length{\pgfmathresult pt}% + \dynkinPlaceRootRelativeTo*{2}{3}{south}{diagonal}% + \dynkinPlaceRootRelativeTo*{5}{2}{south}{below}% + \xdef\dynkin@edge@length{\old@edge@length}% + \dynkinPlaceRootRelativeTo*{1}{3}{west}{left}% + \dynkinPlaceRootRelativeTo*{0}{2}{west}{left}% + \dynkinPlaceRootRelativeTo*{6}{5}{west}{left}% + \edef\old@fold@radius{\dynkin@fold@radius}% + \xdef\dynkin@fold@radius{\dynkin@edge@length}% + \dynkinPlaceRootRelativeTo*{4}{2}{east}{right}% + \dynkinEdge*{SingleEdge}{4}{2}% + \dynkinEdge*{SingleEdge}{3}{1}% + \dynkinEdge*{SingleEdge}{2}{0}% + \dynkinEdge*{SingleEdge}{5}{6}% + \dynkinEdge*{RightDownArc}{3}{4}% + \dynkinEdge*{RightUpArc}{5}{4}% + \xdef\dynkin@fold@radius{\old@fold@radius}% + \ifdynkin@arrows% + \dynkin@fold@arrow@if@oo{1}{0}% + \dynkin@fold@arrow@if@oo{6}{0}% + \dynkin@fold@arrow@if@oo{3}{2}% + \dynkin@fold@arrow@if@oo{2}{5}% + \fi% +}% + +\NewDocumentCommand\extendedESevenFolded{}% +{% + \dynkinPlaceRootHere*{0}{above}% + \dynkinPlaceRootRelativeTo*{1}{0}{east}{above}% + \dynkinPlaceRootRelativeTo*{3}{1}{east}{above}% + \dynkinPlaceRootRelativeTo*{4}{3}{southeastfold}{left}% + \dynkinPlaceRootRelativeTo*{5}{4}{southwestfold}{below}% + \dynkinPlaceRootRelativeTo*{6}{5}{west}{below}% + \dynkinPlaceRootRelativeTo*{7}{6}{west}{below}% + \dynkinPlaceRootRelativeTo*{2}{4}{east}{below}% + \dynkinEdge*{SingleEdge}{0}{1}% + \dynkinEdge*{SingleEdge}{1}{3}% + \dynkinEdge*{SingleEdge}{2}{4}% + \dynkinEdge*{SingleEdge}{5}{6}% + \dynkinEdge*{SingleEdge}{6}{7}% + \dynkinEdge*{RightDownArc}{3}{4}% + \dynkinEdge*{RightUpArc}{5}{4}% + \ifdynkin@arrows% + \dynkin@fold@arrow@if@oo{0}{7}% + \dynkin@fold@arrow@if@oo{1}{6}% + \dynkin@fold@arrow@if@oo{3}{5}% + \fi% +}% -%% \Edynkinfolded -%% -> -%% Draws a folded E6 Dynkin diagram. -\newcommand*{\Edynkinfolded}% -{ - \placeRoot*{1}{0}{1} - \placeRoot*{3}{1}{1} - \placeRootHorizontalLabels*{4}{2}{0} - \placeRootHorizontalLabels{2}{3}{0} - \placeRoot{5}{1}{-1} - \placeRoot{6}{0}{-1} - \dynkinline*{1}{3} - \dynkinline*{2}{4} - \dynkinline*{5}{6} - \dynkindownarc*{3}{4} - \dynkinuparc*{4}{5} -} %% \Edynkin -%% -> %% Draws an E6 Dynkin diagram. -\newcommand*{\Edynkin}% -{ - \ifdynkinfolded - \ifnum\dynkinrank=6 - \Edynkinfolded - \else - \ClassWarning{Can not fold a diagram of type \dynkinseries\the\dynkinrank.} - \fi - \else - \Edynkinunfolded - \fi - % Draw the nodes. - \ifisaffine - \ifnum\dynkinrank=6 - \dynkinline*{0}{2} - \else - \dynkinline*{0}{1} - \fi - \dynkindot{0} - \fi - \IfStrEqCase{\dynkinSatake}% - {% - {*}% - {% - \foreach \b in {1,...,\the\dynkinrank}% - {% - \testbit{\dynkinparabolic}{\b}{\dynkincross{\b}}{\dynkindot{\b}}% - }% - \ifdynkinfolded - \ifdynkinarrows - \dynkinfoldarrow*{1}{6} - \dynkinfoldarrow*{3}{5} - \fi - \fi - }% - {I}% - {% - \foreach \b in {1,...,6}% - {% - \testbit{\dynkinparabolic}{\b}{\dynkincross{\b}}{\dynkinopendot{\b}}% - }% - }% - {II}% - {% - \ifdynkinarrows - \dynkinfoldarrow*{1}{6}% - \dynkinfoldarrow*{3}{5}% - \fi - \foreach \b in {1,...,6}% - {% - \testbit{\dynkinparabolic}{\b}{\dynkincross{\b}}{\dynkinopendot{\b}}% - }% - }% - {III}% - {% - \dynkinfoldarrow*{1}{6}% - \foreach \b in {1,2,6}% - {% - \dynkinopendot*{\b}% - }% - \foreach \b in {3,4,5}% - {% - \dynkincloseddot*{\b}% - }% - }% - {IV}% - {% - \foreach \b in {1,6}% - {% - \dynkinopendot*{\b}% - }% - \foreach \b in {2,3,4,5}% - {% - \dynkincloseddot*{\b}% - }% - }% - {V}% - {% - \foreach \b in {1,...,7}% - {% - \testbit{\dynkinparabolic}{\b}{\dynkincross{\b}}{\dynkinopendot{\b}}% - }% - }% - {VI}% - {% - \foreach \b in {1,3,4,6}% - {% - \dynkinopendot*{\b}% - }% - \foreach \b in {2,5,7}% - {% - \dynkincloseddot*{\b}% - }% - }% - {VII}% - {% - \foreach \b in {1,6,7}% - {% - \dynkinopendot*{\b}% - }% - \foreach \b in {2,3,4,5}% - {% - \dynkincloseddot*{\b}% - }% - }% - {VIII}% - {% - \foreach \b in {1,...,8}% - {% - \testbit{\dynkinparabolic}{\b}{\dynkincross{\b}}{\dynkinopendot{\b}}% - }% - }% - {XI}% - {% - \foreach \b in {1,6,7,8}% - {% - \dynkinopendot*{\b}% - }% - \foreach \b in {2,3,4,5}% - {% - \dynkincloseddot*{\b}% - }% - }% - }% -} +\NewDocumentCommand\Edynkin{}% +{% + \ifnum\dynkin@ply>1% + \ifnum\dynkin@rank=6% + \Edynkin@folded% + \else% + \ifnum\dynkin@rank=7% + \ifdynkin@is@extended% + \Edynkin@folded% + \else% + \ClassError{Dynkin diagrams}% + {Can not fold a diagram of type \dynkin@user@series{} \the\dynkin@rank.}{}% + \fi% + \fi% + \fi% + \else% + \Edynkin@unfolded% + \fi% +}% %% \Fdynkin -%% -> %% Draws an F series Dynkin diagram. \newcommand*{\Fdynkin}% { - \Adynkinnodes - \ifdynkincoxeter - \dynkinline*{1}{4} + \dynkinPlaceRootHere*{1}{below} + \dynkinPlaceRootRelativeTo*{2}{1}{east}{below}% + \dynkinPlaceRootRelativeTo*{3}{2}{east}{below}% + \dynkinPlaceRootRelativeTo*{4}{3}{east}{below}% + \ifdynkin@Coxeter + \dynkinEdge*{SingleEdge}{1}{2} + \dynkinEdge*{SingleEdge}{2}{3} + \dynkinEdge*{SingleEdge}{3}{4} \convertRootPair{2}{3} - \node[above] at ($.5*(root \the\@fromRoot)+.5*(root \the\@toRoot)$) {\dynkinprint{4}}; - \foreach \b in {1,...,4}% - {% - \testbit{\dynkinparabolic}{\b}{\dynkincross{\b}}{\dynkindot{\b}}% - }% + \node[/Dynkin diagram/text,above] + at ($.5*(\dynkin@root@name \the\@fromRoot)+.5*(\dynkin@root@name \the\@toRoot)$) + {\(4\)}; \else - \dynkinline*{1}{2} - \dynkinline*{3}{4} - \dynkindoubleline*{2}{3} - \ifisaffine - \dynkinline*{0}{1} - \dynkindot{0} - \fi - \IfStrEqCase{\dynkinSatake} - {% - {*}% - {% - \foreach \b in {1,...,4}% - {% - \testbit{\dynkinparabolic}{\b}{\dynkincross{\b}}{\dynkindot{\b}}% - }% - }% - {I}% - {% - \foreach \b in {1,...,4}% - {% - \testbit{\dynkinparabolic}{\b}{\dynkincross{\b}}{\dynkinopendot{\b}}% - }% - }% - {II}% - {% - \dynkincloseddot*{1}% - \dynkincloseddot*{2}% - \dynkincloseddot*{3}% - \dynkinopendot*{4}% - }% - }% + \dynkinEdge*{SingleEdge}{1}{2} + \dynkinEdge*{SingleEdge}{3}{4} + \dynkinEdge*{DoubleEdge}{2}{3} \fi } %% \Gdynkin -%% -> %% Draws a G series Dynkin diagram. -\newcommand*{\Gdynkin}% -{ - \newif\ifwasopen - \ifdynkinopendots - \global\wasopentrue - \else - \global\wasopenfalse - \fi - \Adynkinnodes - \ifisaffine - \dynkinline*{0}{2} - \fi - \ifdynkincoxeter - \convertRootPair{1}{2} - \node[above] at ($.5*(root \the\@fromRoot)+.5*(root \the\@toRoot)$) {\dynkinprint{6}}; - \dynkinline*{1}{2} - \else - \dynkintripleline*{1}{2} - \IfStrEq{\dynkinSatake}{I}{\global\dynkinopendotstrue}{} - \ifisaffine - \dynkindot{0} - \fi - \fi - \foreach \b in {1,...,2} - { - \testbit{\dynkinparabolic}{\b}{\dynkincross{\b}}{\dynkindot{\b}} - } - \ifwasopen - \global\dynkinopendotstrue - \else - \global\dynkinopendotsfalse - \fi -} +\NewDocumentCommand\Gdynkin{}% +{% + \ifdynkin@Coxeter% + \Idynkin% + \else% + \dynkinPlaceRootHere*{1}{below}% + \dynkinPlaceRootRelativeTo*{2}{1}{east}{below}% + \dynkinTripleEdge*{1}{2}% + \fi% +}% %% \Hdynkin -%% -> %% Draws an H series Coxeter diagram. \newcommand*{\Hdynkin}% -{ - \newcount\Hn - \Hn=\dynkinrank - \dynkinrank=2 - \Adynkin - \convertRootPair{1}{2} - \node[above] at ($.5*(root \the\@fromRoot)+.5*(root \the\@toRoot)$) {\dynkinprint{\the\Hn}}; -} +{% + \Adynkin% + \convertRootPair{1}{2}% + \node[/Dynkin diagram/text,above] at ($.5*(\dynkin@root@name \the\@fromRoot)+.5*(\dynkin@root@name \the\@toRoot)$) {\(5\)};% +}% %% \Idynkin -%% -> %% Draws an I series Coxeter diagram. \newcommand*{\Idynkin}% -{ - \Adynkin - \convertRootPair{1}{2} - \node[above] at ($.5*(root \the\@fromRoot)+.5*(root \the\@toRoot)$) {\dynkinprint{5}}; -} +{% + \newcount\In% + \In=\dynkin@rank% + \dynkin@rank=2% + \Adynkin% + \convertRootPair{1}{2}% + \node[/Dynkin diagram/text,above] at ($.5*(\dynkin@root@name \the\@fromRoot)+.5*(\dynkin@root@name \the\@toRoot)$) {\(\dynkin@gonality\)};% +}% -\newcommand*{\affineAdynkin}% -{ -\ifnum\dynkinrank=0 - \placeRoot*{0}{4}{1} - \Adynkin -\else - \ifnum\dynkinrank=1 - \placeRoot{0}{0}{0} - \placeRoot{1}{2}{0} - \convertRootNumber{1} - \draw[ - double, - \dynkincolor, - {Classical TikZ Rightarrow[length={3*\dynkinradius}]}-{Classical TikZ Rightarrow[length={3*\dynkinradius}]} - ] - ($(root 0)+(\dynkinradius,0)$) -- ($(root \the\RootNumber)-(\dynkinradius,0)$); - \else - \pgfmathparse{(.5+.5*\the\dynkinrank)}% - \let\halfway\pgfmathresult% - \placeRoot*{0}{\halfway}{1} - \Adynkin - \fi -\fi -} +%% \extendedAdynkin +%% Draws an A series affine Dynkin/Coxeter diagram. +\NewDocumentCommand\extendedAdynkin{}% +{% + \ifnum\dynkin@rank=1% + \dynkinPlaceRootHere{0}{below}% + \dynkinPlaceRootRelativeTo*{1}{0}{east}{below}% + \convertRootNumber{1}% + \begin{scope}{on background layer}% + \draw[% + /Dynkin diagram/edge, + double, + {Classical TikZ Rightarrow[length={2*\dynkin@root@radius}]}% + -{Classical TikZ Rightarrow[length={2*\dynkin@root@radius}]}% + ]% + ($(\dynkin@root@name 0)+(\dynkin@root@radius,0)$) + -- + ($(\dynkin@root@name \the\RootNumber)-(\dynkin@root@radius,0)$);% + \end{scope}% + \else% + \ifnum\dynkin@ply=4% + \dynkinPlaceRootHere*{0}{left}% + \dynkinPlaceRootRelativeTo*{1}{0}{east}{right}% + \dynkinPlaceRootRelativeTo*{2}{0}{south}{left}% + \dynkinPlaceRootRelativeTo*{3}{1}{south}{right}% + \dynkinEdge*{SingleEdge}{0}{1}% + \dynkinEdge*{SingleEdge}{1}{2}% + \dynkinEdge*{SingleEdge}{2}{3}% + \dynkinEdge*{SingleEdge}{3}{0}% + \dynkinFold*{0}{2}% + \dynkinFold*{1}{3}% + \else% + \Adynkin{}% + \ifnum\dynkin@ply>1% + \dynkinPlaceRootRelativeTo*{0}{1}{southwestfold}{right}% + \dynkinEdge*{LeftDownArc}{1}{0}% + \dynkinEdge*{LeftUpArc}{\the\dynkin@rank}{0}% + \else% + \node (Dynkin current) at ($.5*(\dynkin@root@name 1)+.5*(\dynkin@root@name \the\dynkin@rank)$){};% + \dynkinNorth% + \dynkinPlaceRootHere*{0}{above}% + \dynkinEdge*{SingleEdge}{0}{1}% + \dynkinEdge*{SingleEdge}{0}{\the\dynkin@rank}% + \fi% + \dynkinRootMark*{}{0}% + \fi% + \fi% +}% -\newcommand*{\affineBdynkin}% -{ - \placeRoot*{0}{2}{1} - \Bdynkin -} +\NewDocumentCommand\extendedBthreePly{}% +{% + \dynkinPlaceRootHere*{0}{right}% + \edef\old@edge@length{\dynkin@edge@length}% + \pgfmathparse{1.5*\dynkin@edge@length}% + \xdef\dynkin@edge@length{\pgfmathresult pt}% + \dynkinPlaceRootRelativeTo*{1}{0}{south}{right}% + \dynkinPlaceRootRelativeTo*{3}{1}{south}{right}% + \xdef\dynkin@edge@length{\old@edge@length}% + \edef\old@fold@radius{\dynkin@fold@radius}% + \xdef\dynkin@fold@radius{\dynkin@edge@length}% + \dynkinPlaceRootRelativeTo*{2}{1}{west}{left}% + \dynkinEdge*{LeftDownArc}{0}{2}% + \dynkinFold*{0}{1}% + \dynkinFold*{1}{3}% + \dynkinEdge*{SingleEdge}{1}{2}% + \dynkinEdge*{DoubleDownRightArc}{2}{3}% + \xdef\dynkin@fold@radius{\old@fold@radius}% +}% + +%% \extendedBdynkin +%% Draws a B series affine Dynkin/Coxeter diagram. +\newcommand*{\extendedBdynkin}% +{% + \ifnum\the\dynkin@rank=1 + \extendedAdynkin% + \else% + \ifnum\the\dynkin@rank=2 + \dynkinPlaceRootHere*{0}{left}% + \dynkinPlaceRootRelativeTo*{1}{0}{east}{below}% + \dynkinPlaceRootRelativeTo*{2}{1}{east}{left}% + \dynkinEdge*{SingleEdge}{0}{1}% + \dynkinEdge*{DoubleEdge}{1}{2}% + \else% + \ifnum\dynkin@ply=3% + \extendedBthreePly% + \else% + \ifnum\dynkin@ply=2% + \dynkinPlaceRootHere*{0}{left}% + \dynkinPlaceRootRelativeTo*{2}{0}{southeastfold}{below}% + \dynkinPlaceRootRelativeTo*{1}{2}{southwestfold}{left}% + \dynkinLeftFold*{0}{1}% + \dynkinEdge*{RightDownArc}{0}{2}% + \dynkinEdge*{RightUpArc}{1}{2}% + \else% + \dynkinPlaceRootHere*{0}{left}% + \dynkinPlaceRootRelativeTo*{2}{0}{southeast}{left}% + \dynkinPlaceRootRelativeTo*{1}{2}{southwest}{left}% + \dynkinEdge*{SingleEdge}{0}{2}% + \dynkinEdge*{SingleEdge}{1}{2}% + \fi% + \newcount\drmo% + \drmo=\the\dynkin@rank\relax% + \advance\drmo by -1\relax% + \newcount\bmo% + \bmo=2% + \ifnum\dynkin@rank>3% + \foreach \b in {3,...,\the\drmo}% + {% + \dynkinPlaceRootRelativeTo*{\b}{\the\bmo}{east}{below}% + \dynkinEdge*{SingleEdge}{\b}{\the\bmo}% + \global\advance\bmo by 1\relax% + }% + \fi% + \ifnum\dynkin@ply<3% + \dynkinPlaceRootRelativeTo*{\the\dynkin@rank}{\the\drmo}{east}{below}% + \fi% + \ifdynkin@Coxeter% + \dynkinEdge*{SingleEdge}{\the\drmo}{\the\dynkin@rank}% + \convertRootPair{\the\drmo}{\the\dynkin@rank} + \node[/Dynkin diagram/text,above] at + ($.5*(\dynkin@root@name \the\@fromRoot)+.5*(\dynkin@root@name \the\@toRoot)$) {\(4\)}; + \else% + \ifnum\dynkin@ply<3% + \dynkinEdge*{DoubleEdge}{\the\drmo}{\the\dynkin@rank}% + \else% + \dynkinEdge*{DoubleDownRightArc}{\the\drmo}{\the\dynkin@rank}% + \fi% + \fi% + \fi% + \fi% + \fi% +}% + +%% \extendedCdynkin +%% Draws an C series affine Dynkin/Coxeter diagram. +\newcommand*{\extendedCdynkin}% +{% + \dynkinPlaceRootHere*{0}{below}% + \dynkinEast% + \Cdynkin{}% + \ifdynkin@Coxeter% + \dynkinEdge*{SingleEdge}{0}{1}% + \convertRootPair{0}{1} + \node[/Dynkin diagram/text,above] at + ($.5*(\dynkin@root@name \the\@fromRoot)+.5*(\dynkin@root@name \the\@toRoot)$) {\(4\)}; + \else% + \dynkinEdge*{DoubleEdge}{0}{1}% + \fi% +}% + +%% \DOneFourFourPly +%% Draws a D^1_4 series affine Dynkin diagram folded about an A^2_2. +\NewDocumentCommand\DOneFourFourPly{}% +{% + \dynkinPlaceRootHere*{0}{right}% + \edef\old@edge@length{\dynkin@edge@length}% + \pgfmathparse{1.5*\dynkin@edge@length}% + \xdef\dynkin@edge@length{\pgfmathresult pt}% + \dynkinPlaceRootRelativeTo*{1}{0}{south}{right}% + \dynkinPlaceRootRelativeTo*{3}{1}{south}{right}% + \dynkinPlaceRootRelativeTo*{4}{3}{south}{right}% + \xdef\dynkin@edge@length{\old@edge@length}% + \convertRootPair{0}{4}% + \node + (Dynkin current) + at + ($.5*(\dynkin@root@name \the\@fromRoot)+.5*(\dynkin@root@name \the\@toRoot)$){};% + \dynkinWest% + \dynkinPlaceRootHere*{2}{left}% + \dynkinEdge*{SingleEdge}{0}{2}% + \dynkinEdge*{SingleEdge}{1}{2}% + \dynkinEdge*{SingleEdge}{3}{2}% + \dynkinEdge*{SingleEdge}{4}{2}% + \dynkinFold*{0}{1}% + \dynkinFold*{1}{3}% + \dynkinFold*{3}{4}% +}% + + +%% \DfourPly +%% Draws a D series affine Dynkin diagram folded about its middle. +\NewDocumentCommand\DfourPly{}% +{% + \dynkinPlaceRootHere*{0}{left}% + \dynkinPlaceRootRelativeTo*{2}{0}{southeastfold}{above}% + \dynkinPlaceRootRelativeTo*{1}{2}{southwestfold}{left}% + \dynkinMoveToRoot*{2}% + \newcount\drmo% + \drmo=\the\dynkin@rank% + \advance\drmo by -1% + \newcount\drmt% + \drmt=\the\drmo% + \advance\drmt by -1% + \xdef\old@fold{\dynkin@fold@radius}% + \pgfmathparse{\dynkin@fold@radius+2*cos(60)*\dynkin@edge@length}% + \xdef\dynkin@fold@radius{\pgfmathresult pt}% + \dynkin@fold{2}{\the\drmt}% + \xdef\dynkin@fold@radius{\old@fold}% + \dynkinPlaceRootRelativeTo*{\the\drmo}{\the\drmt}{northwestfold}{left}% + \dynkinPlaceRootRelativeTo*{\the\dynkin@rank}{\the\drmt}{southwestfold}{left}% +% \ifdynkin@arrows% +% \dynkinLeftFold*{0}{1}% +% \dynkinLeftFold*{\the\drmo}{\the\dynkin@rank}% +% \fi% + \dynkinEdge*{RightDownArc}{0}{2}% + \dynkinEdge*{RightUpArc}{1}{2}% + \dynkinEdge*{RightDownArc}{\the\drmo}{\the\drmt}% + \dynkinEdge*{RightUpArc}{\the\dynkin@rank}{\the\drmt}% +}% + +%% \extendedDthreePly +%% Draws a D^1_4 series Dynkin diagram, folded over a B^1_3. +\NewDocumentCommand\extendedDthreePly{}% +{% + \dynkinPlaceRootHere*{2}{right}% + \edef\old@edge@length{\dynkin@edge@length}% + \pgfmathparse{1.5*\dynkin@edge@length}% + \xdef\dynkin@edge@length{\pgfmathresult pt}% + \dynkinPlaceRootRelativeTo*{3}{2}{south}{right}% + \dynkinPlaceRootRelativeTo*{4}{3}{south}{right}% + \xdef\dynkin@edge@length{\old@edge@length}% + \dynkinPlaceRootRelativeTo*{1}{3}{west}{diagonal}% + \dynkinPlaceRootRelativeTo*{0}{1}{west}{left}% + \dynkinEdge*{SingleEdge}{1}{3}% + \edef\old@fold@radius{\dynkin@fold@radius}% + \xdef\dynkin@fold@radius{\dynkin@edge@length}% + \dynkinEdge*{LeftDownArc}{2}{1}% + \dynkinEdge*{LeftUpArc}{4}{1}% + \xdef\dynkin@fold@radius{\old@fold@radius}% + \ifdynkin@arrows% + \dynkin@fold@arrow@if@oo{2}{3}% + \dynkin@fold@arrow@if@oo{3}{4}% + \fi% + \dynkinEdge*{SingleEdge}{0}{1}% +}% + + +%% \extendedDdynkin +%% Draws an D series affine Dynkin/Coxeter diagram. +\NewDocumentCommand\extendedDdynkin{}% +{% + \ifnum\dynkin@ply=4% + \ifnum\dynkin@rank=4% + \DOneFourFourPly% + \else% + \DfourPly% + \fi% + \else% + \ifnum\dynkin@ply=3% + \extendedDthreePly% + \else% + \ifnum\the\dynkin@rank=1% + \extendedAdynkin% + \else + \dynkinPlaceRootHere*{0}{left}% + \Ddynkin% + \ifnum\dynkin@ply=2% + \dynkinEdge*{RightDownArc}{0}{2}% + \else% + \ifdynkin@left@fold% + \dynkinEdge*{RightDownArc}{0}{2}% + \else% + \dynkinEdge*{SingleEdge}{0}{2}% + \fi% + \fi% + \fi% + \fi% + \fi% +}% + +%% \extendedEdynkin +%% Draws an E series affine Dynkin/Coxeter diagram. +\newcommand*{\extendedEdynkin}% +{% + \Edynkin% +}% + +%% \extendedFdynkin +%% Draws an F series affine Dynkin/Coxeter diagram. +\newcommand*{\extendedFdynkin}% +{% + \ifnum\dynkin@ply=1% + \dynkinPlaceRootHere*{0}{below}% + \dynkinEast% + \Fdynkin% + \dynkinEdge*{SingleEdge}{0}{1}% + \else% + \dynkinPlaceRootHere*{0}{above}% + \dynkinPlaceRootRelativeTo*{1}{0}{east}{above}% + \dynkinEdge*{SingleEdge}{0}{1}% + \dynkinPlaceRootRelativeTo*{2}{1}{southeastfold}{right}% + \dynkinDefiniteRightDownArc*{1}{2}% + \dynkinPlaceRootRelativeTo*{3}{2}{southwestfold}{below}% + \dynkinDefiniteDoubleDownLeftArc*{2}{3}% + \dynkinPlaceRootRelativeTo*{4}{3}{west}{below}% + \dynkinEdge*{SingleEdge}{3}{4}% + \ifdynkin@arrows% + \dynkinFold*{0}{4}% + \dynkinFold*{1}{3}% + \fi% + \fi% +}% + +%% \extendedGdynkin +%% Draws an G series affine Dynkin/Coxeter diagram. +\newcommand*{\extendedGdynkin}% +{% + \xdef\dynkin@gonality{6}% + \dynkinPlaceRootHere*{0}{below}% + \dynkinEast% + \Gdynkin% + \dynkinEdge*{SingleEdge}{0}{1}% +}% + +%% \extendedHdynkin +%% Draws an H series affine Coxeter diagram. +\newcommand*{\extendedHdynkin}% +{% + \dynkinPlaceRootHere*{0}{below}% + \dynkinEast% + \Adynkin% + \dynkinEdge*{SingleEdge}{0}{1}% + \ifnum\dynkin@rank=3% + \convertRootPair{1}{2}% + \else% + \convertRootPair{0}{1}% + \fi% + \node[/Dynkin diagram/text,above] + at + ($.5*(\dynkin@root@name \the\@fromRoot)+.5*(\dynkin@root@name \the\@toRoot)$) + {\(5\)};% +}% -\newcommand*{\affineCdynkin} -{ - \placeRoot{0}{0}{0} - \Cdynkin -} -\newcommand*{\affineDdynkin} +%% \extendedIdynkin +%% Draws an I series affine Coxeter diagram. +\newcommand*{\extendedIdynkin}% { - \placeRoot*{0}{2}{1} - \Ddynkin + \dynkinPlaceRootHere*{0}{below}% + \dynkinEast% + \dynkin@rank=1% + \Adynkin% + \dynkinEdge*{SingleEdge}{0}{1}% + \convertRootPair{0}{1}% + \node[/Dynkin diagram/text,above] + at + ($.5*(\dynkin@root@name \the\@fromRoot)+.5*(\dynkin@root@name \the\@toRoot)$) + {\(\infty\)};% } -\newcommand*{\affineEdynkin} -{ - \ifnum\dynkinrank=6 - \placeRoot*{0}{3}{2} - \Edynkin - \else - \placeRoot{0}{0}{0} - \Edynkin + +%% \twistedAdynkin +%% Draws a twisted A series affine Dynkin diagram. +\NewDocumentCommand\twistedAdynkin{}% +{% + \ifnum\dynkin@rank=3 + \ClassError{Dynkin diagrams}{A2 series twisted diagrams cannot have rank \the\dynkin@rank}{}% \fi -} + \ifnum\dynkin@rank=2% + \dynkinPlaceRootHere*{0}{below}% + \dynkinPlaceRootRelativeTo*{1}{0}{east}{below}% + \dynkinQuadrupleEdge*{1}{0}% + \else% + \newcount\hmo% + \hmo=\the\dynkin@nodes% + \advance\hmo by -1% + \ifodd\dynkin@rank% + \ifnum\dynkin@ply>1% + \dynkinPlaceRootHere*{0}{above}% + \dynkinPlaceRootRelativeTo*{2}{0}{southeastfold}{below}% + \dynkinPlaceRootRelativeTo*{1}{2}{southwestfold}{below}% + \dynkinEdge*{RightDownArc}{0}{2}% + \dynkinEdge*{RightUpArc}{1}{2}% + \else% + \dynkinPlaceRootHere*{0}{left}% + \dynkinPlaceRootRelativeTo*{2}{0}{southeast}{left}% + \dynkinPlaceRootRelativeTo*{1}{2}{southwest}{left}% + \dynkinEdge*{SingleEdge}{0}{2}% + \dynkinEdge*{SingleEdge}{1}{2}% + \fi% + \dynkinMoveToRoot*{2}% + \dynkin@pipe{2}{\the\hmo}{east}{below}% + \dynkinPlaceRootRelativeTo*{\the\dynkin@nodes}{\the\hmo}{east}{below}% + \dynkinEdge*{DoubleEdge}{\the\dynkin@nodes}{\the\hmo}% + \ifnum\dynkin@ply>1% + \dynkinLeftFold*{0}{1}% + \fi% + \else% + \dynkinPlaceRootHere*{0}{below}% + \dynkinPlaceRootRelativeTo*{1}{0}{east}{below}% + \dynkinEdge*{DoubleEdge}{1}{0}% + \ifnum\dynkin@nodes>1% + \ifnum\dynkin@ply>1% + \ifnum\hmo>1% + \dynkin@fold{1}{\the\hmo}% + \fi% + \dynkinPlaceRootRelativeTo*{\the\dynkin@nodes}{\the\hmo}{west}{below}% + \else% + \ifnum\hmo>1% + \dynkin@pipe{1}{\the\hmo}{east}{below}% + \fi% + \dynkinPlaceRootRelativeTo*{\the\dynkin@nodes}{\the\hmo}{east}{below}% + \fi% + \dynkinEdge*{DoubleEdge}{\the\dynkin@nodes}{\the\hmo}% + \fi% + \fi% + \fi% +}% -\newcommand*{\affineFdynkin} -{ - \placeRoot{0}{0}{0} - \Fdynkin -} +%% \twistedDdynkin +%% Draws a twisted D series affine Dynkin diagram. +\NewDocumentCommand\twistedDdynkin{}% +{% + \IfStrEqCase{\dynkin@twisted@series}% + {% + {1}{\extendedDdynkin}% + {2}{\twistedDTwo}% + {3}% + {% + \ifnum\dynkin@rank=4% + \dynkinPlaceRootHere*{0}{below}% + \dynkinPlaceRootRelativeTo*{1}{0}{east}{below}% + \dynkinPlaceRootRelativeTo*{2}{1}{east}{below}% + \dynkinEdge*{SingleEdge}{0}{1}% + \dynkinTripleEdge*{2}{1}% + \else% + \ClassError% + {Dynkin diagrams}% + {D3 series twisted diagrams must have rank 2 and cannot have rank \the\dynkin@rank}% + {}% + \fi% + }% + }% +}% -\newcommand*{\affineGdynkin} -{ - \placeRoot{0}{3}{0} - \Gdynkin -} +\NewDocumentCommand\twistedDTwo{}% +{% + \ifnum\dynkin@rank<3% + \ClassError{Dynkin diagrams}{D2 series twisted diagrams cannot have rank \the\dynkin@rank}{}% + \fi% + \newcount\drmo% + \drmo=\the\dynkin@nodes% + \advance\drmo by -1% + \ifnum\dynkin@ply=1% + \dynkinPlaceRootHere*{0}{below}% + \dynkinPlaceRootRelativeTo*{1}{0}{east}{below}% + \else% + \ifnum\dynkin@rank=3% + \dynkinPlaceRootHere*{0}{right}% + \dynkinPlaceRootRelativeTo*{1}{0}{southwestfold}{left}% + \dynkinPlaceRootRelativeTo*{2}{1}{southeastfold}{right}% + \else% + \dynkinPlaceRootHere*{0}{above}% + \dynkinPlaceRootRelativeTo*{1}{0}{east}{above}% + \fi% + \fi% + \ifnum\dynkin@ply=2% + \dynkinEdge*{DoubleUpRightArc}{1}{0}% + \else + \dynkinEdge*{DoubleEdge}{1}{0}% + \fi% + \ifnum\dynkin@ply>1% + \ifnum\dynkin@rank>3% + \dynkin@fold{1}{\the\drmo}% + \dynkinPlaceRootRelativeTo*{\the\dynkin@nodes}{\the\drmo}{west}{below}% + \dynkinFold*{0}{\the\dynkin@nodes}% + \else% + \dynkinFold*{0}{2}% + \fi% + \else% + \ifnum\dynkin@rank>2% + \dynkin@pipe{1}{\the\drmo}{east}{below}% + \fi% + \dynkinPlaceRootRelativeTo*{\the\dynkin@nodes}{\the\drmo}{east}{below}% + \fi% + \ifnum\dynkin@ply=2% + \dynkinEdge*{DoubleDownRightArc}{\the\drmo}{\the\dynkin@nodes}% + \else + \dynkinEdge*{DoubleEdge}{\the\drmo}{\the\dynkin@nodes}% + \fi% +}% + + +%% \twistedEdynkin +%% Draws a twisted E series affine Dynkin diagram. +\NewDocumentCommand\twistedEdynkin{}% +{% + \IfStrEqCase{\dynkin@twisted@series}% + {% + {0}{\Edynkin}% + {1}{\extendedEdynkin}% + {2}% + {% + \dynkinPlaceRootHere*{0}{below}% + \dynkin@pipe{0}{2}{east}{below}% + \dynkinPlaceRootRelativeTo*{3}{2}{east}{below}% + \dynkinPlaceRootRelativeTo*{4}{3}{east}{below}% + \dynkinEdge*{SingleEdge}{3}{4}% + \dynkinEdge*{DoubleEdge}{3}{2}% + }% + }% + [\dynkin@error@series]% +}% + \endinput -- cgit v1.2.3