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authorKarl Berry <karl@freefriends.org>2024-07-06 20:29:19 +0000
committerKarl Berry <karl@freefriends.org>2024-07-06 20:29:19 +0000
commitd67153de15761383b090f2f3b8ea647ba6bb1cf8 (patch)
treeaf6fa63d042242fef51b74a8fb8fb7647817a551 /Master/texmf-dist
parent13e1241f1bbbbda982838f20c7dbec61606d3aed (diff)
dynkin-diagrams (6jul24)
git-svn-id: svn://tug.org/texlive/trunk@71723 c570f23f-e606-0410-a88d-b1316a301751
Diffstat (limited to 'Master/texmf-dist')
-rw-r--r--Master/texmf-dist/doc/latex/dynkin-diagrams/README4
-rw-r--r--Master/texmf-dist/doc/latex/dynkin-diagrams/dynkin-diagrams.bib64
-rw-r--r--Master/texmf-dist/doc/latex/dynkin-diagrams/dynkin-diagrams.pdfbin894840 -> 908783 bytes
-rw-r--r--Master/texmf-dist/doc/latex/dynkin-diagrams/dynkin-diagrams.tex93
-rw-r--r--Master/texmf-dist/tex/latex/dynkin-diagrams/dynkin-diagrams.sty219
5 files changed, 302 insertions, 78 deletions
diff --git a/Master/texmf-dist/doc/latex/dynkin-diagrams/README b/Master/texmf-dist/doc/latex/dynkin-diagrams/README
index e43f31e0b8e..5abe74143c4 100644
--- a/Master/texmf-dist/doc/latex/dynkin-diagrams/README
+++ b/Master/texmf-dist/doc/latex/dynkin-diagrams/README
@@ -1,6 +1,6 @@
Dynkin diagrams
-v3.1415926535897932384
-2 June 2023
+v3.14159265358979323846
+6 July 2024
Authors:
Ben McKay
diff --git a/Master/texmf-dist/doc/latex/dynkin-diagrams/dynkin-diagrams.bib b/Master/texmf-dist/doc/latex/dynkin-diagrams/dynkin-diagrams.bib
index 9660120699f..952e4a90bfd 100644
--- a/Master/texmf-dist/doc/latex/dynkin-diagrams/dynkin-diagrams.bib
+++ b/Master/texmf-dist/doc/latex/dynkin-diagrams/dynkin-diagrams.bib
@@ -1,6 +1,5 @@
% Encoding: ISO-8859-1
-
@Book{Adams:1996,
Title = {Lectures on exceptional {L}ie groups},
Author = {Adams, J. F.},
@@ -477,4 +476,67 @@ MRREVIEWER = {Stephen Gelbart},
url = {https://doi.org/10.1007/978-1-4612-0979-9},
}
+@Book{Knapp:2002,
+ author = {Knapp, Anthony W.},
+ publisher = {Birkh\"{a}user Boston, Inc., Boston, MA},
+ title = {Lie groups beyond an introduction},
+ year = {2002},
+ edition = {Second},
+ isbn = {0-8176-4259-5},
+ series = {Progress in Mathematics},
+ volume = {140},
+ mrclass = {22-01},
+ mrnumber = {1920389},
+ pages = {xviii+812},
+}
+
+@Article{Witt:1941,
+ author = {Witt, Ernst},
+ journal = {Abh. Math. Sem. Hansischen Univ.},
+ title = {Spiegelungsgruppen und {A}ufz\"ahlung halbeinfacher {L}iescher {R}inge},
+ year = {1941},
+ issn = {0025-5858},
+ pages = {289--322},
+ volume = {14},
+ doi = {10.1007/BF02940749},
+ fjournal = {Abhandlungen aus dem Mathematischen Seminar der Hansischen Universit\"at},
+ mrclass = {09.1X},
+ mrnumber = {5099},
+ mrreviewer = {O.\ F. G. Schilling},
+ url = {https://doi.org/10.1007/BF02940749},
+}
+
+@Article{Johnson.et.al.1999,
+ author = {Johnson, N. W. and Ratcliffe, J. G. and Kellerhals, R. and Tschantz, S. T.},
+ journal = {Transform. Groups},
+ title = {The size of a hyperbolic {C}oxeter simplex},
+ year = {1999},
+ issn = {1083-4362,1531-586X},
+ number = {4},
+ pages = {329--353},
+ volume = {4},
+ doi = {10.1007/BF01238563},
+ fjournal = {Transformation Groups},
+ mrclass = {20F55 (57M60)},
+ mrnumber = {1726696},
+ mrreviewer = {Andrei\ Yu.\ Vesnin},
+ url = {https://doi.org/10.1007/BF01238563},
+}
+
+@Book{McMullen.Schulte:2002,
+ author = {McMullen, Peter and Schulte, Egon},
+ publisher = {Cambridge University Press, Cambridge},
+ title = {Abstract regular polytopes},
+ year = {2002},
+ isbn = {0-521-81496-0},
+ series = {Encyclopedia of Mathematics and its Applications},
+ volume = {92},
+ doi = {10.1017/CBO9780511546686},
+ mrclass = {52B15 (20F55 51F15 51M20)},
+ mrnumber = {1965665},
+ mrreviewer = {Rade\ \v Zivaljevi\'c},
+ pages = {xiv+551},
+ url = {https://doi.org/10.1017/CBO9780511546686},
+}
+
@Comment{jabref-meta: databaseType:bibtex;}
diff --git a/Master/texmf-dist/doc/latex/dynkin-diagrams/dynkin-diagrams.pdf b/Master/texmf-dist/doc/latex/dynkin-diagrams/dynkin-diagrams.pdf
index 2109c1ba1ce..dceef359361 100644
--- a/Master/texmf-dist/doc/latex/dynkin-diagrams/dynkin-diagrams.pdf
+++ b/Master/texmf-dist/doc/latex/dynkin-diagrams/dynkin-diagrams.pdf
Binary files differ
diff --git a/Master/texmf-dist/doc/latex/dynkin-diagrams/dynkin-diagrams.tex b/Master/texmf-dist/doc/latex/dynkin-diagrams/dynkin-diagrams.tex
index 5f4bb33e41e..b3f0be43412 100644
--- a/Master/texmf-dist/doc/latex/dynkin-diagrams/dynkin-diagrams.tex
+++ b/Master/texmf-dist/doc/latex/dynkin-diagrams/dynkin-diagrams.tex
@@ -1,7 +1,7 @@
\documentclass{amsart}
\title[The Dynkin diagrams package]%
{The Dynkin diagrams package \\
-Version 3.141\,592\,653\,589\,793\,238\,4}
+Version 3.141\,592\,653\,589\,793\,238\,46}
%% My name:
\makeatletter
\DeclareRobustCommand{\scotsMc}{\scotsMcx{c}}
@@ -20,7 +20,8 @@ Version 3.141\,592\,653\,589\,793\,238\,4}
\author{Ben \scotsMc{}Kay}
\address{School of Mathematical Sciences, University College Cork, Cork, Ireland}
\email{b.mckay@ucc.ie}
-\date{2 June 2023}
+\date{6 July 2024}
+\thanks{Thanks to Jeffrey Adams, Paul Aspinwall, Mikhail Borovoi, Fran Burstall, Michiel Van Couwenberghe, Xu Gao, Skip Garibaldi, Enrico Gregorio, Mamuka Jibladze, Tasho Kaletha, Jordan Lambert, Sriotchilism O'Zaic, Gopal Prasad, Anthony Pulido, Andres Sambarino, Paul Schwahn, Felix Weinstein, Niels Wen and Gordon Williams.}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenx}
\usepackage{etoolbox}
@@ -168,6 +169,11 @@ before upper={\widowpenalties=3 10000 10000 150}}
\begin{document}
\maketitle
+\renewcommand\do[1]{\dyn#1}
+\renewcommand{\wdtA}{3cm}
+\begin{dynkinTable}{The Dynkin diagrams of the reduced simple root systems \cite{Bourbaki:2002} pp. 265--290, plates I--IX}{2.25cm}{2.5cm}
+\docsvlist{A{},B{},C{},D{},E6,E7,E8,F4,G2}
+\end{dynkinTable}
\begin{center}
\begin{varwidth}{\textwidth}
\tableofcontents
@@ -176,6 +182,8 @@ before upper={\widowpenalties=3 10000 10000 150}}
\setlength{\arrayrulewidth}{1.5pt}
+\newpage
+
\section{Quick introduction}
\begin{tcolorbox}[title={Load the Dynkin diagram package (see options below)}]
\begin{Verbatim}
@@ -202,7 +210,6 @@ The Dynkin diagram of \(B_3\) is
\draw[very thick,red] (root 1) to [out=-45, in=-135] (root 3);
\end{dynkinDiagram}
\end{tcblisting}
-\newpage
\section{Interaction with \TikZ}
Inside a \TikZ environment, default behaviour is to draw from the origin, so you can draw around the diagram:
\begin{tcblisting}{title={Inside a \TikZ environment}}
@@ -228,15 +235,6 @@ The Dynkin diagram of \(B_3\) is
\end{tikzpicture}
\end{tcblisting}
-\newpage
-
-\renewcommand\do[1]{\dyn#1}
-\renewcommand{\wdtA}{3cm}
-\begin{dynkinTable}{The Dynkin diagrams of the reduced simple root systems \cite{Bourbaki:2002} pp. 265--290, plates I--IX}{2.25cm}{2.5cm}
-\docsvlist{A{},B{},C{},D{},E6,E7,E8,F4,G2}
-\end{dynkinTable}
-
-
\section{Set options globally}
\begin{tcolorbox}[title={Most options set globally \dots}]
@@ -251,6 +249,7 @@ The Dynkin diagram of \(B_3\) is
densely dashed}}
\end{Verbatim}
\end{tcolorbox}
+
You can also pass options to the package in \verb!\usepackage!.
\emph{Danger:} spaces in option names are replaced with hyphens: \texttt{edge length=1cm} is \texttt{edge-length=1cm} as a global option; moreover you should drop the extension \verb!/.style! on any option with spaces in its name (but not otherwise). For example,
\begin{tcolorbox}[title={\dots or pass global options to the package}]
@@ -275,6 +274,9 @@ The Dynkin diagram of \(B_3 \times A_2\) is \dynkins{B3|A2}.
The Dynkin diagram of \(B_3 \times A_2\) is
\begin{DynkinDiagrams}{B3|A2}\end{DynkinDiagrams}
\end{tcblisting}
+
+\newpage
+
Each factor can have its own options.
\begin{tcblisting}{title={Environment}}
The Dynkin diagram of \(B_3 \times A_2\) is
@@ -297,11 +299,11 @@ They are spaced out by the length of one edge between successive diagrams; chang
\endfoot
\endlastfoot
A_1\times A_1&\dynkins{A1|A1}&\texttt{\detokenize{\dynkins}\{A1|A1\}}\\
-A_2&\dynkins{A2}&\texttt{\detokenize{\dynkins}\{A2\}}\\
-B_2&\dynkins{B2}&\texttt{\detokenize{\dynkins}\{B2\}}\\
-C_2&\dynkins{C2}&\texttt{\detokenize{\dynkins}\{C2\}}\\
-D_2&\dynkins{D2}&\texttt{\detokenize{\dynkins}\{D2\}}\\
-G_2&\dynkins{G2}&\texttt{\detokenize{\dynkins}\{G2\}}\\
+A_2&\dynkin A2&\texttt{\detokenize{\dynkin} A2}\\
+B_2&\dynkin B2&\texttt{\detokenize{\dynkin} B2}\\
+C_2&\dynkin C2&\texttt{\detokenize{\dynkin} C2}\\
+D_2&\dynkin D2&\texttt{\detokenize{\dynkin} D2}\\
+G_2&\dynkin G2&\texttt{\detokenize{\dynkin} G2}\\
\end{longtable}
\section{Coxeter diagrams}
@@ -333,6 +335,35 @@ G_2&\dynkins{G2}&\texttt{\detokenize{\dynkins}\{G2\}}\\
[Coxeter,gonality=n]I{}}
\end{dynkinTable}
+\newpage
+
+Some people prefer Coxeter diagrams to have these labels appear on the bottom of the diagram, so say \verb!Coxeter above=false!, most likely as a global option.
+
+\pgfkeys{/Dynkin diagram,
+Coxeter above=false}
+
+\renewcommand\do[1]{\dyn#1}
+\begin{dynkinTable}{The Coxeter diagrams of the simple reflection groups}{2.25cm}{6cm}
+\forDynkinSemicolonsvlist{\do}{
+[Coxeter]A{};
+[Coxeter]B{};
+[Coxeter]C{};
+[Coxeter]D{};
+[Coxeter]E6;
+[Coxeter]E7;
+[Coxeter]E8;
+[Coxeter]F4;
+[Coxeter,gonality=n]G2;
+[Coxeter]H2;
+[Coxeter]H3;
+[Coxeter]H4;
+[Coxeter,gonality=n]I{}}
+\end{dynkinTable}
+
+\pgfkeys{/Dynkin diagram,
+Coxeter above=true}
+
+
\section{Satake diagrams}\label{section:Satake}
\begin{tcblisting}{title={Satake diagrams use the standard name instead of a rank}}
\(A_{IIIb}=\dynkin A{IIIb}\)
@@ -340,6 +371,8 @@ G_2&\dynkins{G2}&\texttt{\detokenize{\dynkins}\{G2\}}\\
We use a solid gray bar to denote the folding of a Dynkin diagram, rather than the usual double arrow, since the diagrams turn out simpler and easier to read.
+\newpage
+
\renewcommand\do[1]{\dyn#1}
\begin{dynkinTable}{The Satake diagrams of the real simple Lie algebras \cite{Helgason:2001} p. 532--534}{2.75cm}{3cm}
\docsvlist{A{I},A{II},A{IIIa},A{IIIb},A{IV},B{I},B{II},C{I},C{IIa},C{IIb},
@@ -968,7 +1001,7 @@ D_4 &
\dynkin[label,ordering=Kac]E6
\end{tcblisting}
Default is Bourbaki.
-Sources are Adams \cite{Adams:1996} p. 56--57, Bourbaki \cite{Bourbaki:2002} p. pp. 265--290 plates I-IX, Carter \cite{Carter:2005} p. 540--609, Dynkin \cite{Dynkin:1952}, Kac \cite{Kac:1990} p. 43.
+Sources are Adams \cite{Adams:1996} p. 56--57, Bourbaki \cite{Bourbaki:2002} p. 265--290 plates I-IX, Carter \cite{Carter:2005} p. 540--609, Dynkin \cite{Dynkin:1952} (reprinted, translated into English, in Dynkin \cite{Dynkin:2000} p. 180), Kac \cite{Kac:1990} p. 43.
\NewDocumentCommand\tablerow{mm}%
{%
@@ -1108,9 +1141,31 @@ D[3]4,E[2]6}
\renewcommand{\do}[1]{\dyn[extended,Coxeter]#1}
\begin{dynkinTable}{The extended (affine) Coxeter diagrams}{3cm}{6cm}
-\docsvlist{A{},B{},C{},D{},E6,E7,E8,F4,G2,H3,H4,I1}
+\docsvlist{A{},B{},C{},D{},E6,E7,E8,F4,G2,H2,H3,H4,I1}
\end{dynkinTable}
+
+\section{Witt symbols}
+
+The \emph{Witt symbol} \cite{Johnson.et.al.1999,McMullen.Schulte:2002,Witt:1941} is a different notation for the various series:
+\[
+\begin{array}{rll}
+\text{Witt symbol}&\text{Cartan symbol}\\
+P_{n+1}&A_n\\
+S_{n+1}&B_n\\
+R_{n+1}&C_n\\
+Q_{n+1}&D_n\\
+T_{n+1}&E_n&n=6,7,8\\
+U_5&F_4\\
+V_3&G_2\\
+W_2&I_1
+\end{array}
+\]
+\begin{tcblisting}{title={Witt symbols}}
+\dynkin[extended]P7, \dynkin[extended]Q7, \dynkin[extended]T7
+\end{tcblisting}
+
+
\newpage
\section{Kac style}
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 e45f21ee182..7a92e22048e 100644
--- a/Master/texmf-dist/tex/latex/dynkin-diagrams/dynkin-diagrams.sty
+++ b/Master/texmf-dist/tex/latex/dynkin-diagrams/dynkin-diagrams.sty
@@ -1,6 +1,6 @@
% The Dynkin Diagrams package.
%
-% Version 3.141 592 653 589 793 238 4
+% Version 3.141 592 653 589 793 238 46
%
% This package draws Dynkin diagrams in LaTeX
% documents, using the TikZ package.
@@ -13,7 +13,7 @@
% Released under the LaTeX Project Public License v1.3c or later, see
% http://www.latex-project.org/lppl.txt
\NeedsTeXFormat{LaTeX2e}[1994/06/01]
-\ProvidesPackage{dynkin-diagrams}[2023/06/02 Dynkin diagrams]
+\ProvidesPackage{dynkin-diagrams}[2024/07/05 Dynkin diagrams]
\RequirePackage{tikz}
\RequirePackage{xstring}
\RequirePackage{etoolbox}
@@ -1873,6 +1873,7 @@
}%
+
%% \dynkinQuadrupleEdge{<p>}{<q>}
%% \dynkinQuadrupleEdge*{<p>}{<q>}
%% Draws an oriented edge of valence 4 from root <p> to root <q> on the current Dynkin diagram.
@@ -2041,6 +2042,8 @@
% Is the right side of the Dynkin diagram folded?
\newif\ifdynkin@Coxeter
% Should we draw Coxeter diagrams?
+\newif\ifdynkin@Coxeter@above
+% Should we draw Coxeter diagram extra labels above or below?
\newif\ifdynkin@Kac@arrows
% Should we draw arrows following Kac?
\newif\ifdynkin@odd
@@ -2097,6 +2100,8 @@
},
Coxeter/.is if = dynkin@Coxeter,
Coxeter=false,
+ Coxeter above/.is if = dynkin@Coxeter@above,
+ Coxeter above=true,
double edges/.style = {
fold style/.style = {
draw=black,
@@ -2598,6 +2603,10 @@
{%
\global\dynkin@rank=\dynkin@string\relax%
\global\dynkin@nodes=\dynkin@string\relax%
+ \ifWitt@symbol%
+ \global\advance\dynkin@rank by -1\relax%
+ \global\advance\dynkin@nodes by -1\relax%
+ \fi
\ifdynkin@is@twisted%
\IfStrEqCase{\dynkin@series}%
{%
@@ -2800,7 +2809,6 @@
% 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,
@@ -2881,20 +2889,41 @@
\global\dynkin@rank@minus@three\the\dynkin@rank@minus@two\relax%
\global\advance\dynkin@rank@minus@three by -1\relax%
}%
+
+\newif\ifWitt@symbol
\newcount\dynkin@lenny%
%% \dynkin@grok@series
%% Interprets the dynkin@series, to see if it is extended, twisted, and what twisted series it is.
\NewDocumentCommand\dynkin@grok@series{}%
{%
- \StrLen{\dynkin@series}[\dynkin@lenny]
+ \StrLen{\dynkin@series}[\dynkin@lenny]\relax%
\ifnum\dynkin@lenny>1\relax%
\dynkin@error@series%
\fi%
+% We need to check if the series is a Witt symbol.
+ \IfSubStr{PSRQTUVW}{\dynkin@series}%
+ {%
+ \global\Witt@symboltrue%
+ \IfStrEqCase{\dynkin@series}%
+ {%
+ {P}{\global\xdef\dynkin@series{A}}%
+ {S}{\global\xdef\dynkin@series{B}}%
+ {R}{\global\xdef\dynkin@series{C}}%
+ {Q}{\global\xdef\dynkin@series{D}}%
+ {T}{\global\xdef\dynkin@series{E}}%
+ {U}{\global\xdef\dynkin@series{F}}%
+ {V}{\global\xdef\dynkin@series{G}}%
+ {W}{\global\xdef\dynkin@series{I}}%
+ }%
+ }%
+ {%
+ \global\Witt@symbolfalse%
+ }%
\edef\series{\dynkin@series}%
\IfStrEqCase{\dynkin@twisted@series}%
{%
{0}{}%
- {1}{ \global\dynkin@is@extendedtrue}%
+ {1}{\global\dynkin@is@extendedtrue}%
{2}{%
\IfSubStr{ADE}{\dynkin@series}%
{%
@@ -3459,19 +3488,6 @@
}%
[\global#5=#4\relax]%
}%
- {G}%
- {%
- \IfStrEqCase{#3}%
- {%
- {Carter}{\global#5=%
- \stringCharacterInPosition{21}{#4}%
- \relax}%
- {Dynkin}{\global#5=%
- \stringCharacterInPosition{21}{#4}%
- \relax}%
- }%
- [\global#5=#4\relax]%
- }%
}%
[\global#5=#4\relax]%
}%
@@ -3640,25 +3656,6 @@
}%
[\global#5=#3\relax]%
}%
- {G}%
- {%
- \IfStrEqCase{#4}%
- {%
- {Carter}%
- {%
- \global#5=%
- \stringCharacterInPosition{21}{#3}%
- \relax%
- }%
- {Dynkin}%
- {%
- \global#5=%
- \stringCharacterInPosition{21}{#3}%
- \relax%
- }%
- }%
- [\global#5=#3\relax]%
- }%
}%
[\global#5=#3\relax]%
}%
@@ -3777,12 +3774,14 @@
}%
{G}%
{%
- \IfStrEqCase{\dynkin@ordering}%
- {%
- {Carter}{\global\dynkin@Root@Number=\stringCharacterInPosition{21}{#1}\relax}%
- {Dynkin}{\global\dynkin@Root@Number=\stringCharacterInPosition{21}{#1}\relax}%
- }%
- [\global\dynkin@Root@Number=#1\relax]%
+ \global\dynkin@Root@Number=#1\relax%
+% \IfStrEqCase{\dynkin@ordering}%
+% {%
+% {Carter}{\global\dynkin@Root@Number=\stringCharacterInPosition{21}{#1}\relax}%
+% {Dynkin}{\global\dynkin@Root@Number=\stringCharacterInPosition{21}{#1}\relax}%
+% {Kac}{\global\dynkin@Root@Number=\stringCharacterInPosition{21}{#1}\relax}%
+% }%
+% [\global\dynkin@Root@Number=#1\relax]%
}%
}%
[\global\dynkin@Root@Number=#1\relax]%
@@ -4338,9 +4337,15 @@
\else%
\ifdynkin@Coxeter%
\Adynkin%
- \dynkinEdgeLabel%
- {\the\dynkin@rank@minus@one}%
- {\the\dynkin@rank}{4}%
+ \ifdynkin@Coxeter@above%
+ \dynkinEdgeLabel%
+ {\the\dynkin@rank@minus@one}%
+ {\the\dynkin@rank}{4}%
+ \else%
+ \dynkinEdgeLabel*%
+ {\the\dynkin@rank@minus@one}%
+ {\the\dynkin@rank}{4}%
+ \fi%
\else
% Create the roots.
\ifnum\dynkin@ply>1\relax%
@@ -4994,7 +4999,11 @@
\dynkinEdge*{SingleEdge}{1}{2}%
\dynkinEdge*{SingleEdge}{2}{3}%
\dynkinEdge*{SingleEdge}{3}{4}%
- \dynkinEdgeLabel{2}{3}{4}%
+ \ifdynkin@Coxeter@above%
+ \dynkinEdgeLabel{2}{3}{4}%
+ \else%
+ \dynkinEdgeLabel*{2}{3}{4}%
+ \fi%
\else%
\dynkinEdge*{SingleEdge}{1}{2}%
\dynkinEdge*{SingleEdge}{3}{4}%
@@ -5002,6 +5011,9 @@
\fi%
\fi%
}%
+
+\newif\ifGtwo@old@dynkin@reverse@arrows
+
%% \Gdynkin
%% Draws a G series Dynkin diagram.
\NewDocumentCommand\Gdynkin{}%
@@ -5013,14 +5025,72 @@
\dynkin@jump{1}%
\dynkinPlaceRootHere*{1}{left}{above}%
\dynkinPlaceRootRelativeTo*{2}{1}{southfold}{left}{below}%
+ \ifdynkin@reverse@arrows%
+ \global\Gtwo@old@dynkin@reverse@arrowstrue\relax%
+ \else%
+ \global\Gtwo@old@dynkin@reverse@arrowsfalse\relax%
+ \fi%
+ \IfStrEqCase{\dynkin@ordering}%
+ {%
+ {Adams}{%
+ \ifdynkin@reverse@arrows%
+ \global\dynkin@reverse@arrowsfalse\relax%
+ \else%
+ \global\dynkin@reverse@arrowstrue\relax%
+ \fi\relax}%
+ {Bourbaki}{%
+ \ifdynkin@reverse@arrows%
+ \global\dynkin@reverse@arrowsfalse\relax%
+ \else%
+ \global\dynkin@reverse@arrowstrue\relax%
+ \fi\relax}%
+ {Carter}{\relax}%
+ {Dynkin}{\relax}%
+ {Kac}{\relax}%
+ }%
+ [\relax]%
\dynkinEdge*{TripleDownRightSemiCircle}{1}{2}%
+ \ifGtwo@old@dynkin@reverse@arrows%
+ \global\dynkin@reverse@arrowstrue\relax%
+ \else%
+ \global\dynkin@reverse@arrowsfalse\relax%
+ \fi%
\ifdynkin@arrows%
\dynkinLeftFold*{1}{2}%
\fi%
\else%
\dynkinPlaceRootHere*{1}{below}{above}%
\dynkinPlaceRootRelativeTo*{2}{1}{east}{below}{above}%
- \dynkinTripleEdge*{1}{2}%
+ \ifdynkin@reverse@arrows%
+ \global\Gtwo@old@dynkin@reverse@arrowstrue\relax%
+ \else%
+ \global\Gtwo@old@dynkin@reverse@arrowsfalse\relax%
+ \fi%
+ \IfStrEqCase{\dynkin@ordering}%
+ {%
+ {Adams}{%
+ \ifdynkin@reverse@arrows%
+ \global\dynkin@reverse@arrowsfalse\relax%
+ \else%
+ \global\dynkin@reverse@arrowstrue\relax%
+ \fi\relax}%
+ {Bourbaki}{%
+ \ifdynkin@reverse@arrows%
+ \global\dynkin@reverse@arrowsfalse\relax%
+ \else%
+ \global\dynkin@reverse@arrowstrue\relax%
+ \fi\relax}%
+ {Carter}{\relax}%
+ {Dynkin}{\relax}%
+ {Kac}{\relax}%
+ }%
+ [\relax]%
+ \dynkinTripleEdge*{1}{2}\relax%
+ \ifGtwo@old@dynkin@reverse@arrows%
+ \global\dynkin@reverse@arrowstrue\relax%
+ \else%
+ \global\dynkin@reverse@arrowsfalse\relax%
+ \fi%
\fi%
\fi%
}%
@@ -5030,7 +5100,11 @@
\newcommand*{\Hdynkin}%
{%
\Adynkin%
- \dynkinEdgeLabel{1}{2}{5}%
+ \ifdynkin@Coxeter@above%
+ \dynkinEdgeLabel{1}{2}{5}%
+ \else%
+ \dynkinEdgeLabel*{1}{2}{5}%
+ \fi%
}%
%% \Idynkin
%% Draws an I series Coxeter diagram.
@@ -5038,7 +5112,11 @@
{%
\dynkin@rank=2\relax%
\Adynkin%
- \dynkinEdgeLabel{1}{2}{\dynkin@gonality}%
+ \ifdynkin@Coxeter@above%
+ \dynkinEdgeLabel{1}{2}{\dynkin@gonality}%
+ \else%
+ \dynkinEdgeLabel*{1}{2}{\dynkin@gonality}%
+ \fi%
}%
%% \extendedAdynkin
@@ -5183,9 +5261,15 @@
\dynkinEdge*{SingleEdge}%
{\the\dynkin@rank@minus@one}%
{\the\dynkin@rank}%
- \dynkinEdgeLabel%
- {\the\dynkin@rank@minus@one}%
- {\the\dynkin@rank}{4}%
+ \ifdynkin@Coxeter@above%
+ \dynkinEdgeLabel%
+ {\the\dynkin@rank@minus@one}%
+ {\the\dynkin@rank}{4}%
+ \else%
+ \dynkinEdgeLabel*%
+ {\the\dynkin@rank@minus@one}%
+ {\the\dynkin@rank}{4}%
+ \fi%
\else%
\ifnum\dynkin@ply<3\relax%
\dynkinEdge*{DoubleEdge}%
@@ -5211,7 +5295,11 @@
\Cdynkin{}%
\ifdynkin@Coxeter%
\dynkinEdge*{SingleEdge}{0}{1}%
- \dynkinEdgeLabel{0}{1}{4}%
+ \ifdynkin@Coxeter@above%
+ \dynkinEdgeLabel{0}{1}{4}%
+ \else%
+ \dynkinEdgeLabel*{0}{1}{4}%
+ \fi%
\else%
\dynkinEdge*{DoubleEdge}{0}{1}%
\fi%
@@ -5391,8 +5479,11 @@
\xdef\dynkin@gonality{6}%
\dynkinPlaceRootHere*{0}{below}{above}%
\dynkinEast%
+ \let\extended@G@old@order\dynkin@ordering%
+ \xdef\dynkin@ordering{Carter}%
\Gdynkin%
\dynkinEdge*{SingleEdge}{0}{1}%
+ \xdef\dynkin@ordering{\extended@G@old@order}%
}%
%% \extendedHdynkin
@@ -5423,7 +5514,11 @@
\dynkin@rank=1\relax%
\Adynkin%
\dynkinEdge*{SingleEdge}{0}{1}%
- \dynkinEdgeLabel{0}{1}{\infty}%
+ \ifdynkin@Coxeter@above%
+ \dynkinEdgeLabel{0}{1}{\infty}%
+ \else%
+ \dynkinEdgeLabel*{0}{1}{\infty}%
+ \fi%
}%
\newcount\dynkin@height@minus@one%
%% \twistedAdynkin
@@ -5531,6 +5626,8 @@
\fi%
\fi%
}%
+
+\newif\iftwisted@D@old@dynkin@reverse@arrows
%% \twistedDdynkin
%% Draws a twisted D series affine Dynkin diagram.
\NewDocumentCommand\twistedDdynkin{}%
@@ -5546,7 +5643,17 @@
\dynkinPlaceRootRelativeTo*{1}{0}{east}{below}{above}%
\dynkinPlaceRootRelativeTo*{2}{1}{east}{below}{above}%
\dynkinEdge*{SingleEdge}{0}{1}%
- \dynkinTripleEdge*{2}{1}%
+ \ifdynkin@reverse@arrows%
+ \global\dynkin@reverse@arrowsfalse\relax%
+ \else%
+ \global\dynkin@reverse@arrowstrue\relax%
+ \fi%
+ \dynkinTripleEdge*{1}{2}%
+ \ifdynkin@reverse@arrows%
+ \global\dynkin@reverse@arrowsfalse\relax%
+ \else%
+ \global\dynkin@reverse@arrowstrue\relax%
+ \fi%
\else%
\ClassError%
{Dynkin diagrams}%