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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 5685bbe4a50..49693610825 100644 --- a/Master/texmf-dist/doc/latex/dynkin-diagrams/dynkin-diagrams.tex +++ b/Master/texmf-dist/doc/latex/dynkin-diagrams/dynkin-diagrams.tex @@ -1,6 +1,6 @@ \documentclass{amsart} -\title{The Dynkin diagrams package \\ Version 3.14159265} +\title{The Dynkin diagrams package \\ Version 3.141592653} \makeatletter \DeclareRobustCommand{\scotsMc}{\scotsMcx{c}} @@ -20,7 +20,7 @@ \author{Ben \scotsMc{}Kay} \address{School of Mathematical Sciences, University College Cork, Cork, Ireland} \email{b.mckay@ucc.ie} -\date{26 November 2019} +\date{4 December 2019} \usepackage{etex} \usepackage[T1]{fontenc} @@ -261,8 +261,6 @@ You can also pass options to the package in \verb!\usepackage!. \dyn[Coxeter,gonality=n]{I}{} \end{dynkinTable} - -\newpage \section{Satake diagrams}\label{section:Satake} \begin{tcblisting}{title={Satake diagrams use the standard name instead of a rank}} @@ -310,9 +308,6 @@ We use a solid gray bar to denote the folding of a Dynkin diagram, rather than t \invol{1}{6}\invol{3}{5} \end{dynkinDiagram} \end{tcblisting} - -\newpage - \begin{tcblisting}{title={The double arrows for \(A_{IIIa}\) are big}} \newcommand{\invol}[2]{\draw[latex-latex] (root #1) to [out=-60,in=-120] node[midway,below]{$\sigma$} (root #2);} @@ -332,8 +327,6 @@ shorten <=1mm,shorten >=1mm,}} \end{dynkinDiagram} \end{tcblisting} -\newpage - \begin{tcblisting}{title={\dots but you could try springs pulling roots together}} \tikzset{/Dynkin diagram/fold style/.style= {decorate,decoration={name=coil,aspect=0.5, @@ -350,10 +343,10 @@ segment length=1mm,amplitude=.6mm}}} \section{Labels for the roots} \begin{tcblisting}{title={Make a macro to assign labels to roots}} -\dynkin[label,label macro/.code={\alpha_{\mathrlap{#1}}},edge length=.75cm]{D}{5} +\dynkin[label,label macro/.code={\alpha_{\drlap{#1}}},edge length=.75cm]{D}{5} \end{tcblisting} \begin{tcblisting}{title={Labelling several roots}} -\dynkin[labels={,2,...,5,,7},label macro/.code={\alpha_{\mathrlap#1}}]{A}{7} +\dynkin[labels={,2,...,5,,7},label macro/.code={\alpha_{\drlap#1}}]{A}{7} \end{tcblisting} \begin{tcblisting}{title={The \texttt{foreach} notation I}} \dynkin[labels={1,3,...,7},]{A}{9} @@ -362,22 +355,21 @@ segment length=1mm,amplitude=.6mm}}} \dynkin[labels={,\alpha_2,\alpha_...,\alpha_7},]{A}{7} \end{tcblisting} \begin{tcblisting}{title={The \texttt{foreach} notation III}} -\dynkin[label macro/.code={\beta_{\mathrlap{#1}}},labels={,2,...,7},]{A}{7} +\dynkin[label macro/.code={\beta_{\drlap{#1}}},labels={,2,...,7},]{A}{7} \end{tcblisting} \begin{tcblisting}{title={Label the roots individually by root number}} \dynkin[label]{B}{3} \end{tcblisting} \begin{tcblisting}{title={Label a single root}} \begin{dynkinDiagram}{B}{3} -\dynkinLabelRoot{2}{\alpha_2} +\dynkinLabelRoot{2}{\alpha_{\drlap{2}}} \end{dynkinDiagram} \end{tcblisting} \begin{tcblisting}{title={Access root labels via TikZ}} \begin{dynkinDiagram}{B}{3} -\node[below] at (root 2) {\(\alpha_{\mathrlap{2}}\)}; +\node[below] at (root 2) {\(\alpha_{\drlap{2}}\)}; \end{dynkinDiagram} \end{tcblisting} -\newpage \begin{tcblisting}{title={Commands to label several roots}} \begin{dynkinDiagram}{A}{7} \dynkinLabelRoots{,\alpha_2,\alpha_3,\alpha_4,\alpha_5,,\alpha_7} @@ -391,12 +383,11 @@ segment length=1mm,amplitude=.6mm}}} \end{tcblisting} \begin{tcblisting}{title={Labelling several roots and alternates}} \dynkin[% -label macro/.code={\alpha_{\mathrlap{#1}}}, -label macro*/.code={\gamma_{\mathrlap{#1}}}, +label macro/.code={\alpha_{\drlap{#1}}}, +label macro*/.code={\gamma_{\drlap{#1}}}, labels={,2,...,5,,7}, labels*={1,3,4,5,6}]{A}{7} \end{tcblisting} -\newpage \begin{tcblisting}{title={Commands to label several roots}} \begin{dynkinDiagram}{A}{7} \dynkinLabelRoots{,\alpha_2,\alpha_3,\alpha_4,\alpha_5,,\alpha_7} @@ -405,11 +396,29 @@ labels*={1,3,4,5,6}]{A}{7} \end{tcblisting} \section{Label subscripts} -Note the slight improvement that \verb!\mathrlap! makes: the labels are centered on the middle of the letter \(\alpha\), ignoring the space taken up by the subscripts. -\begin{tcblisting}{title={Label spacing improvement}} -\dynkin[label,label macro/.code={\alpha_{#1}},edge length=.75cm]{D}{15} +Note the slight improvement that \verb!\drlap! makes: the labels are centered on the middle of the letter \(\alpha\), ignoring the space taken up by the subscripts, using the \verb!mathtools! command \verb!\mathrlap!, but only for labels which are \emph{not} placed to the left or right of a root. +\begin{tcblisting}{title={Label subscript spacing}} +\dynkin[label,label macro/.code={\alpha_{#1}}, + edge length=.75cm]{D}{15} +\par\noindent{}% +\dynkin[label,label macro/.code={\alpha_{\drlap{#1}}}, + edge length=.75cm]{D}{15} +\end{tcblisting} +\begin{tcblisting}{title={Label subscript spacing}} +\dynkin[label,label macro/.code={\alpha_{#1}}, + edge length=.75cm]{E}{8} +\dynkin[label,label macro/.code={\alpha_{#1}},backwards, + edge length=.75cm]{E}{8} \par\noindent{}% -\dynkin[label,label macro/.code={\alpha_{\mathrlap{#1}}},edge length=.75cm]{D}{15} +\dynkin[label,label macro/.code={\alpha_{\mathrlap{#1}}}, + edge length=.75cm]{E}{8} +\dynkin[label,label macro/.code={\alpha_{\mathrlap{#1}}},backwards, + edge length=.75cm]{E}{8} +\par\noindent{}% +\dynkin[label,label macro/.code={\alpha_{\drlap{#1}}}, + edge length=.75cm]{E}{8} +\dynkin[label,label macro/.code={\alpha_{\drlap{#1}}},backwards, + edge length=.75cm]{E}{8} \end{tcblisting} \newpage @@ -420,8 +429,8 @@ To change these, set \verb!label height! and \verb!label depth!: \dynkin[labels={a,b,c,d}]{F}{4} \dynkin[labels*={a,b,c,d}]{F}{4} \dynkin[% -label macro/.code={\alpha_{\mathrlap{#1}}}, -label macro*/.code={\gamma_{\mathrlap{#1}}}, +label macro/.code={\alpha_{\drlap{#1}}}, +label macro*/.code={\gamma_{\drlap{#1}}}, label height=$\alpha_1$, label depth=$\alpha_1$, labels={,2,...,5,,7}, @@ -435,7 +444,7 @@ labels*={1,3,4,5,6}]{A}{7} \begin{dynkinDiagram}[text style={scale=1.2,blue}, edge length=.75cm, labels={1,2,n-1,n}, -label macro/.code={\alpha_{\mathrlap{#1}}} +label macro/.code={\alpha_{\drlap{#1}}} ]{A}{} \end{dynkinDiagram} \end{tcblisting} @@ -443,7 +452,7 @@ label macro/.code={\alpha_{\mathrlap{#1}}} \begin{dynkinDiagram}[text style={scale=1.2,blue}, edge length=.75cm, labels={1,2,n-1,n}, -label macro/.code={\mathbb{A}_{\mathrlap{#1}}}]{A}{} +label macro/.code={\mathbb{A}_{\drlap{#1}}}]{A}{} \end{dynkinDiagram} \end{tcblisting} @@ -474,7 +483,7 @@ label macro/.code={\mathbb{A}_{\mathrlap{#1}}}]{A}{} \end{tcblisting} \begin{filecontents*}{EulerProducts.tex} -\tikzset{/Dynkin diagram,ordering=Dynkin,label macro/.code={\alpha_{#1}}} +\tikzset{/Dynkin diagram,ordering=Dynkin,label macro/.code={\alpha_{\drlap{#1}}}} \newcounter{EPNo} \setcounter{EPNo}{0} \NewDocumentCommand\EP{smmmm}% @@ -820,11 +829,7 @@ D_4 & \end{longtable} \endgroup - - -\newpage \section{Parabolic subgroups} - Each set of roots is assigned a number, with each binary digit zero or one to say whether the corresponding root is crossed or not: \begin{tcblisting}{} The flag variety of pointed lines in @@ -858,29 +863,15 @@ the Dynkin diagram \dynkin[parabolic=3]{A}{3}. \endgroup \VerbatimInput{hermitian-symmetric-spaces.tex} -\begin{tcblisting}{title={Folded parabolics look bad (zoom in on a root)}} -\dynkin[fold,parabolic=3]{C}{2} -\dynkin[fold,parabolic=3]{G}{2} -\end{tcblisting} -\begin{tcblisting}{title={Folded parabolics: you can try using thicker crosses}} -\dynkin[fold,x/.style={very thick,line cap=round},parabolic=3]{C}{2} -\dynkin[fold,x/.style={ultra thick,line cap=round},parabolic=3]{G}{2} -\end{tcblisting} - \section{Extended Dynkin diagrams} - \begin{tcblisting}{title={Extended Dynkin diagrams}} \dynkin[extended]{A}{7} \end{tcblisting} - - The extended Dynkin diagrams are also described in the notation of Kac \cite{Kac:1990} p. 55 as affine untwisted Dynkin diagrams: we extend \verb!\dynkin{A}{7}! to become \verb!\dynkin{A}[1]{7}!: \begin{tcblisting}{title={Extended Dynkin diagrams}} \dynkin{A}[1]{7} \end{tcblisting} - - \renewcommand*{\arraystretch}{1.5} \begin{dynkinTable}{The Dynkin diagrams of the extended simple root systems}{3cm}{5cm} \dyn[extended]{A}{1} @@ -895,21 +886,15 @@ The extended Dynkin diagrams are also described in the notation of Kac \cite{Kac \dyn[extended]{G}{2} \end{dynkinTable} - - - +\newpage \section{Affine twisted and untwisted Dynkin diagrams} - The affine Dynkin diagrams are described in the notation of Kac \cite{Kac:1990} p. 55: \begin{tcblisting}{title={Affine Dynkin diagrams}} \(A^{(1)}_7=\dynkin{A}[1]{7}, \ E^{(2)}_6=\dynkin{E}[2]{6}, \ D^{(3)}_4=\dynkin{D}[3]{4}\) \end{tcblisting} - - - \begin{dynkinTable}{The affine Dynkin diagrams}{3cm}{3.75cm} \dyn{A}[1]{1} \dyn{A}[1]{} @@ -988,6 +973,7 @@ We include a style called \verb!Kac! which tries to imitate the style of \cite{K \dyn{F}{4} \dyn{G}{2} \end{dynkinTable} +\newpage \begin{dynkinTable}{The Dynkin diagrams of the extended simple root systems in Kac style}{5cm}{4.5cm} \dyn[extended]{A}{1} \dyn[extended]{A}{} @@ -1000,7 +986,6 @@ We include a style called \verb!Kac! which tries to imitate the style of \cite{K \dyn[extended]{F}{4} \dyn[extended]{G}{2} \end{dynkinTable} -\newpage \begin{dynkinTable}{The Dynkin diagrams of the twisted simple root systems in Kac style}{6cm}{4.5cm} \dyn{A}[2]{2} \dyn{A}[2]{even} @@ -1010,7 +995,7 @@ We include a style called \verb!Kac! which tries to imitate the style of \cite{K \dyn{D}[3]{4} \end{dynkinTable} \endgroup - +\newpage \section{Ceref style} We include a style called \verb!ceref! which paints oblong root markers with shadows. The word ``ceref'' is an old form of the word ``serif''. @@ -1267,6 +1252,17 @@ The marks are set down in order according to the current root ordering: \dynkin[label,ordering=Kac]{E}{*otxXOt*} \end{tcblisting} +\section{Typesetting mathematical names of Dynkin diagrams} +The \verb!\dynkinName! command, with the same syntax as \verb!\dynkin!, typesets a default name of your diagram in \LaTeX. +It is perhaps only useful when automatically generating a large collection of Dynkin diagrams in a computer program. +\begin{tcblisting}{title={Name of a diagram}} +\dynkinName[label,extended]{B}{7} +\dynkinName{A}[2]{even} +\dynkinName[Coxeter]{B}{7} +\dynkinName[label,extended]{B}{*} +\dynkinName{D}[3]{4} +\end{tcblisting} + \section{Connecting Dynkin diagrams}\label{section:name} We can make some sophisticated folded diagrams by drawing multiple diagrams, each with a name: \begin{tcblisting}{title={Name a diagram}} @@ -1669,8 +1665,6 @@ labels*={0,1,2,3,\ell-3,\ell-2,\ell-1,\ell}]{D}[1]{} \end{center} \endgroup \VerbatimInput{borovoi.tex} -\newpage - \section{Syntax} The syntax is \verb!\dynkin[<options>]{<letter>}[<twisted rank>]{<rank>}! where \verb!<letter>! is \verb!A!, \verb!B!, \verb!C!, \verb!D!, \verb!E!, \verb!F! or \verb!G!, the family of root system for the Dynkin diagram, \verb!<twisted rank>! is \verb!0!, \verb!1!, \verb!2!, \verb!3! (default is \verb!0!) representing: @@ -1715,6 +1709,8 @@ The environment syntax is \verb!\begin{dynkinDiagram}! followed by the same para & distance between nodes in the Dynkin diagram \\ \optionLabel{edge/.style}{TikZ style data}{solid,draw=black,fill=white,thin} & style of edges in the Dynkin diagram \\ +\optionLabel{edge label/.style}{TikZ style data}{text height=0,text depth=0,label distance=-2pt} +& style of edge labels in the Dynkin diagram, as found, for example, on some Coxeter diagrams \\ \optionLabel{Kac}{\typ{true or false}}{false} & whether to draw in the style of \cite{Kac:1990} \\ \optionLabel{name}{\typ{string}}{anonymous} |