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-rw-r--r--Master/texmf-dist/doc/latex/dynkin-diagrams/dynkin-diagrams.tex68
1 files changed, 47 insertions, 21 deletions
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 5557830a45c..806a2960d67 100644
--- a/Master/texmf-dist/doc/latex/dynkin-diagrams/dynkin-diagrams.tex
+++ b/Master/texmf-dist/doc/latex/dynkin-diagrams/dynkin-diagrams.tex
@@ -1,8 +1,8 @@
\documentclass{amsart}
-\title{The Dynkin diagrams package \\ Version 3.12}
+\title{The Dynkin diagrams package \\ Version 3.13}
\author{Ben McKay}
-\date{30 April 2018}
+\date{18 July 2018}
\usepackage{etex}
\usepackage[T1]{fontenc}
@@ -101,8 +101,7 @@
}%
-
-\definecolor{example-color}{gray}{1}
+\definecolor{example-color}{gray}{.85}
\definecolor{example-border-color}{gray}{.7}
\tcbset{coltitle=black,colback=example-color,colframe=example-border-color,enhanced,breakable,pad at break*=1mm,
@@ -128,12 +127,6 @@ before upper={\widowpenalties=3 10000 10000 150}}
\makeatother
\begin{document}
-
-
-
-
-
-
\maketitle
\begin{center}
\begin{varwidth}{\textwidth}
@@ -313,7 +306,10 @@ We use a solid gray bar to denote the folding of a Dynkin diagram, rather than t
\section{Style}
\begin{tcblisting}{title={Colours}}
-\dynkin[edge/.style={blue!50,thick},*/.style=blue!50!red]{F}{4}
+\dynkin[
+ edge/.style={blue!50,thick},
+ */.style=blue!50!red,
+ arrowColor=red]{F}{4}
\end{tcblisting}
\begin{tcblisting}{title={Edge lengths}}
\dynkin[edgeLength=1.2,parabolic=3]{A}{3}
@@ -397,9 +393,15 @@ The mark list \verb!oo**ttxx! has one mark for each root: \verb!o!, \verb!o!, \d
Roots are listed in the current default ordering.
(Careful: in an affine root system, a mark list will \emph{not} contain a mark for root zero.)
-\NewDocumentCommand\ClassicalLieSuperalgebras{m}%
+
+\NewDocumentCommand\ClassicalLieSuperalgebras{om}%
{%
-\begin{dynkinTable}{Classical Lie superalgebras \cite{Frappat/Sciarrino/Sorba:1989}. #1}{3.5cm}{6.5cm}
+\IfValueT{#1}{\tikzset{/Dynkin diagram,radius=#1}}
+\RenewDocumentCommand\wdtE{}{10cm}
+\begin{dynkinTable}{Classical Lie superalgebras \cite{Frappat/Sciarrino/Sorba:1989}. #2}{3.5cm}{6.5cm}
+\IfValueT{#1}{
+& & \texttt{\textbackslash{}tikzset\{/Dynkin diagram,radius=#1\}} \\
+}
A_{mn} & \dynk{A}{ooo.oto.oo}
B_{mn} & \dynk{B}{ooo.oto.oo}
B_{0n} & \dynk{B}{ooo.ooo.o*}
@@ -407,18 +409,18 @@ C_{n} & \dynk{C}{too.oto.oo}
D_{mn} & \dynk{D}{ooo.oto.oooo}
D_{21\alpha} & \dynk{A}{oto}
F_4 & \dynk{F}{ooot}
-G_3 & \dynk[extended,affineMark=t]{G}{2}
+G_3 & \dynk[extended,affineMark=t,
+reverseArrows]{G}{2}
\end{dynkinTable}
+\IfValueT{#1}{\tikzset{/Dynkin diagram,radius=.05cm}}
}%
-\begingroup
-\tikzset{/Dynkin diagram,radius=.07cm}
-\ClassicalLieSuperalgebras{We need a slightly larger radius parameter to distinguish the tensor product symbols from the solid dots.}
-\endgroup
+\ClassicalLieSuperalgebras[.07cm]{We need a slightly larger radius parameter to distinguish the tensor product symbols from the solid dots.}
\ClassicalLieSuperalgebras{Here we see the problem with using the default radius parameter, which is too small for tensor product symbols.}
+
\section{Indefinite edges}
An \emph{indefinite edge} is a dashed edge between two roots, \dynkin{A}{*.*} indicating that an indefinite number of roots have been omitted from the Dynkin diagram.
@@ -765,6 +767,7 @@ Most diagrams can only allow a 2-ply folding, so \verb!fold! is a synonym for \v
\begin{tcblisting}{title={3-ply}}
\dynkin[ply=3]{D}{4}
+\dynkin[ply=3,foldright]{D}{4}
\dynkin[ply=3]{D}[1]{4}
\end{tcblisting}
@@ -853,7 +856,7 @@ We have to be careful about the 4-ply foldings of \(D^{(1)}_{2\ell}\), for which
\pgfkeys{/Dynkin diagram,foldradius=.35cm}
\begin{longtable}{@{}p{15cm}@{}}
-\caption{Some foldings of Dynkin diagrams}\\
+\caption{Some foldings of Dynkin diagrams. For these diagrams, we want to compare a folding diagram with the diagram that results when we fold it, so it looks best to set \texttt{foldradius} and \texttt{edgeLength} to equal lengths.}\\
\endfirsthead
\caption{\dots continued}\\
\endhead
@@ -864,7 +867,7 @@ We have to be careful about the 4-ply foldings of \(D^{(1)}_{2\ell}\), for which
\foldingTable{A}{0}{2\ell-1}{\dynk[fold]{A}{**.*****.**}}%
{C}{0}{\ell}{\dynk{C}{}}
\fold*{B}{0}{3}{G}{0}{2}
-\foldingTable{D}{0}{4}{\dynk[ply=3]{D}{4}}%
+\foldingTable{D}{0}{4}{\dynk[ply=3,foldright]{D}{4}}%
{G}{0}{2}{\dynk{G}{2}}
\foldingTable{D}{0}{\ell+1}{\dynk[fold]{D}{}}%
{B}{0}{\ell}{\dynk{B}{}}
@@ -914,6 +917,27 @@ We have to be careful about the 4-ply foldings of \(D^{(1)}_{2\ell}\), for which
\endgroup
+\begingroup
+\RenewDocumentCommand\wdtA{}{.8cm}
+\begin{dynkinTable}{Frobenius fixed point subgroups of finite simple groups of Lie type \cite{Carter:1995} p. 15}{3cm}{6cm}
+A_{\ell\ge 1} & \dynk{A}{}
+{}^2\!A_{\ell\ge 2} & \dynk[fold]{A}{}
+B_{\ell\ge 2} & \dynk{B}{}
+{}^2\!B_2 & \dynk[fold]{B}{2}
+C_{\ell\ge3} & \dynk{C}{}
+D_{\ell\ge4} & \dynk{D}{}
+{}^2\!D_{\ell\ge4} & \dynk[fold]{D}{}
+{}^3\!D_4 & \dynk[ply=3]{D}{4}
+E_6 & \dynk{E}{6}
+{}^2\!E_6 & \dynk[fold]{E}{6}
+E_7 & \dynk{E}{7}
+E_8 & \dynk{E}{8}
+F_4 & \dynk{F}{4}
+{}^2\!F_4 & \dynk[fold]{F}{4}
+G_2 & \dynk{G}{2}
+{}^2G_2 & \dynk[fold]{G}{2}
+\end{dynkinTable}
+\endgroup
\section{Root ordering}\label{section:order}
@@ -1008,7 +1032,7 @@ The following diagrams arise in the Satake diagrams of the pseudo-Riemannian sym
\end{tcblisting}
\begin{tcblisting}{}
-\pgfkeys{/Dynkin diagram/edgeLength=.75cm,/Dynkin diagram/edge/.style={draw=white,double=black,very thick},
+\pgfkeys{/Dynkin diagram/edgeLength=.75cm,/Dynkin diagram/edge/.style={draw=example-color,double=black,very thick},
}
\begin{tikzpicture}
\foreach \d in {1,...,4}
@@ -1489,6 +1513,8 @@ are indicated with double edges (like those of an \(F_4\) Dynkin diagram without
\optionLabel{doubleFoldRight}{\typ{}}{not set}
& set to override the \texttt{fold} style when folding roots together at the right side of a Dynkin diagram, so that the foldings are indicated with double edges (like those of an \(F_4\) Dynkin diagram without arrows), but filled in solidly.
\\
+\optionLabel{arrowColor}{\typ{}}{black}
+& set to override the default color for the arrows in nonsimply laced Dynkin diagrams. \\
\optionLabel{Coxeter}{\typ{true or false}}{false}
& whether to draw a Coxeter diagram, rather than a Dynkin diagram. \\
\optionLabel{ordering}{\typ{Adams, Bourbaki, Carter, Dynkin, Kac}}{Bourbaki}