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Diffstat (limited to 'Master/texmf-dist/doc/latex/dynkin-diagrams/dynkin-diagrams.tex')
-rw-r--r-- | Master/texmf-dist/doc/latex/dynkin-diagrams/dynkin-diagrams.tex | 114 |
1 files changed, 80 insertions, 34 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 6d84d1606d9..b11488ffdd8 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 3.141592} +\title{The Dynkin diagrams package \\ Version 3.1415926} \makeatletter \DeclareRobustCommand{\scotsMc}{\scotsMcx{c}} @@ -20,16 +20,18 @@ \author{Ben \scotsMc{}Kay} \address{School of Mathematical Sciences, University College Cork, Cork, Ireland} \email{b.mckay@ucc.ie} -\date{24 January 2019} +\date{25 November 2019} \usepackage{etex} \usepackage[T1]{fontenc} \usepackage[utf8]{inputenx} \usepackage{etoolbox} \usepackage{lmodern} +\RequirePackage[tt=lining]{cfr-lm} \usepackage[kerning=true,tracking=true]{microtype} \usepackage{amsmath} \usepackage{amsfonts} +\usepackage{mathtools} \usepackage{array} \usepackage{xstring} \usepackage{longtable} @@ -65,10 +67,10 @@ \newcommand{\C}[1]{\mathbb{C}^{#1}} \renewcommand*{\arraystretch}{1.5} -\NewDocumentCommand\wdtA{}{.7cm} -\NewDocumentCommand\wdtD{}{3cm} -\NewDocumentCommand\wdtE{}{6cm} -\NewDocumentCommand\wdtL{}{3cm} +\newcommand{\wdtA}{.7cm} +\newcommand{\wdtD}{3cm} +\newcommand{\wdtE}{6cm} +\newcommand{\wdtL}{3cm} \newcolumntype{A}{@{}>{\columncolor[gray]{.9}$}m{\wdtA}<{$}} \newcolumntype{B}{@{}>{\columncolor[gray]{.9}}m{\wdtA}} \newcolumntype{D}{>{\columncolor[gray]{.9}}m{\wdtD}} @@ -106,8 +108,8 @@ \NewDocumentEnvironment{dynkinTable}{mmm}% {% -\RenewDocumentCommand\wdtD{}{#2} -\RenewDocumentCommand\wdtL{}{#3} +\renewcommand{\wdtD}{#2} +\renewcommand{\wdtL}{#3} \begin{longtable}{ADM} \caption{#1}\\ \endfirsthead @@ -150,7 +152,6 @@ before upper={\widowpenalties=3 10000 10000 150}} \fvset{fontsize=\small} \begin{document} - \maketitle \begin{center} \begin{varwidth}{\textwidth} @@ -158,7 +159,6 @@ before upper={\widowpenalties=3 10000 10000 150}} \end{varwidth} \end{center} - \setlength{\arrayrulewidth}{1.5pt} \section{Quick introduction} @@ -185,7 +185,7 @@ The Dynkin diagram of \(B_3\) is \end{dynkinDiagram} \end{tcblisting} \begin{tcblisting}{title={Inside a \TikZ environment}} -The baseline controls the vertical alignment: +Baseline controls vertical alignment: the Dynkin diagram of \(B_3\) is \begin{tikzpicture}[baseline=(origin.base)] \dynkin{B}{3} @@ -208,6 +208,7 @@ the Dynkin diagram of \(B_3\) is \end{dynkinTable} + \section{Set options globally} \begin{tcolorbox}[title={Most options set globally \dots}] @@ -234,6 +235,7 @@ You can also pass options to the package in \verb!\usepackage!. + \section{Coxeter diagrams} \begin{tcblisting}{title={Coxeter diagram option}} @@ -259,6 +261,7 @@ You can also pass options to the package in \verb!\usepackage!. \dyn[Coxeter,gonality=n]{I}{} \end{dynkinTable} + \section{Satake diagrams}\label{section:Satake} \begin{tcblisting}{title={Satake diagrams use the standard name instead of a rank}} @@ -342,10 +345,10 @@ 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_{#1}},edge length=.75cm]{D}{5} +\dynkin[label,label macro/.code={\alpha_{\mathrlap{#1}}},edge length=.75cm]{D}{5} \end{tcblisting} \begin{tcblisting}{title={Labelling several roots}} -\dynkin[labels={,2,...,5,,7},label macro/.code={\alpha_{#1}}]{A}{7} +\dynkin[labels={,2,...,5,,7},label macro/.code={\alpha_{\mathrlap#1}}]{A}{7} \end{tcblisting} \begin{tcblisting}{title={The \texttt{foreach} notation I}} \dynkin[labels={1,3,...,7},]{A}{9} @@ -354,7 +357,7 @@ 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_{#1}},labels={,2,...,7},]{A}{7} +\dynkin[label macro/.code={\beta_{\mathrlap{#1}}},labels={,2,...,7},]{A}{7} \end{tcblisting} \begin{tcblisting}{title={Label the roots individually by root number}} \dynkin[label]{B}{3} @@ -364,14 +367,9 @@ segment length=1mm,amplitude=.6mm}}} \dynkinLabelRoot{2}{\alpha_2} \end{dynkinDiagram} \end{tcblisting} -\begin{tcblisting}{title={Use a text style}} -\begin{dynkinDiagram}[text/.style={scale=1.2}]{B}{3}; -\dynkinLabelRoot{2}{\alpha_2} -\end{dynkinDiagram} -\end{tcblisting} \begin{tcblisting}{title={Access root labels via TikZ}} \begin{dynkinDiagram}{B}{3} -\node[below] at (root 2) {\(\alpha_2\)}; +\node[below] at (root 2) {\(\alpha_{\mathrlap{2}}\)}; \end{dynkinDiagram} \end{tcblisting} \begin{tcblisting}{title={Commands to label several roots}} @@ -387,8 +385,8 @@ segment length=1mm,amplitude=.6mm}}} \end{tcblisting} \begin{tcblisting}{title={Labelling several roots and alternates}} \dynkin[% -label macro/.code={\alpha_{#1}}, -label macro*/.code={\gamma_{#1}}, +label macro/.code={\alpha_{\mathrlap{#1}}}, +label macro*/.code={\gamma_{\mathrlap{#1}}}, labels={,2,...,5,,7}, labels*={1,3,4,5,6}]{A}{7} \end{tcblisting} @@ -399,6 +397,50 @@ labels*={1,3,4,5,6}]{A}{7} \end{dynkinDiagram} \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} +\par\noindent{}% +\dynkin[label,label macro/.code={\alpha_{\mathrlap{#1}}},edge length=.75cm]{D}{15} +\end{tcblisting} + + +\section{Height and depth of labels} +Labels are set with default maximum height the height of the character \(b\), and default maximum depth the depth of the character \(g\). +To change these, set \verb!label height! and \verb!label depth!: +\begin{tcblisting}{title={Change height and dept of characters}} +\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 height=$\alpha_1$, +label depth=$\alpha_1$, +labels={,2,...,5,,7}, +labels*={1,3,4,5,6}]{A}{7} +\dynkin[labels={A,B,C,D},label height=$A$,label depth=$A$]{F}{4} +\dynkin[labels={a^1,b^2,c^3,d^4},label height=$X^X$]{F}{4} +\end{tcblisting} + +\section{Text style for the labels} +\begin{tcblisting}{title={Use a text style: big and blue}} +\begin{dynkinDiagram}[text style={scale=1.2,blue}, +edge length=.75cm, +labels={1,2,n-1,n}, +label macro/.code={\alpha_{\mathrlap{#1}}} +]{A}{} +\end{dynkinDiagram} +\end{tcblisting} +\begin{tcblisting}{title={Use a text style; font selection is in the label macro}} +\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}{} +\end{dynkinDiagram} +\end{tcblisting} + + \section{Bracing roots} \begin{tcblisting}{title={Bracing roots}} @@ -610,7 +652,7 @@ If you need to repeat a mark, you can give a \emph{single digit} positive intege \NewDocumentCommand\ClassicalLieSuperalgebras{om}% {% \IfValueT{#1}{\tikzset{/Dynkin diagram,root radius=#1}} -\RenewDocumentCommand\wdtE{}{10cm} +\renewcommand{\wdtE}{10cm} \begin{dynkinTable}{Classical Lie superalgebras \cite{Frappat/Sciarrino/Sorba:1989}. #2}{3.5cm}{6.5cm} \IfValueT{#1}{ & & \texttt{\textbackslash{}tikzset\{/Dynkin diagram,root radius=#1\}} \\ @@ -667,8 +709,8 @@ For such rare situations, there is an option: \begingroup -\RenewDocumentCommand\wdtA{}{.35cm} -\RenewDocumentCommand\wdtE{}{6.55cm} +\renewcommand{\wdtA}{.35cm} +\renewcommand{\wdtE}{6.55cm} \begin{dynkinTable}{Springer's table of indices \cite{Springer:2009}, pp. 320-321, with one form of \(E_7\) corrected}{2.5cm}{3.7cm} % 1 A_n & @@ -961,7 +1003,7 @@ We include a style called \verb!Kac! which tries to imitate the style of \cite{K \endgroup \section{Ceref style} -We include a style called \verb!ceref! which shapes the root markers more oblongly and with shadows. +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''. \begin{tcblisting}{title={Ceref style}} \dynkin[ceref]{F}{4} @@ -1045,9 +1087,9 @@ We have to be careful about the 4-ply foldings of \(D^{(1)}_{2\ell}\), for which \end{dynkinDiagram} \end{tcblisting} \begingroup -\RenewDocumentCommand\wdtA{}{.7cm} -\RenewDocumentCommand\wdtD{}{3.5cm} -\RenewDocumentCommand\wdtL{}{7cm} +\renewcommand{\wdtA}{.7cm} +\renewcommand{\wdtD}{3.5cm} +\renewcommand{\wdtL}{7cm} \NewDocumentCommand\seriesName{mmm}% {% \IfStrEq{#2}{0}{#1_{#3}}{#1^{#2}_{#3}}% @@ -1152,7 +1194,7 @@ We have to be careful about the 4-ply foldings of \(D^{(1)}_{2\ell}\), for which \end{longtable} \endgroup \begingroup -\RenewDocumentCommand\wdtA{}{.8cm} +\renewcommand{\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}{} @@ -1193,8 +1235,8 @@ Sources are Adams \cite{Adams:1996} p. 56--57, Bourbaki \cite{Bourbaki:2002} p. \dynkin[label,ordering=Kac]{#1}{#2}\\ }% \begin{center} -\RenewDocumentCommand\wdtA{}{.7cm} -\RenewDocumentCommand\wdtL{}{2.2cm} +\renewcommand{\wdtA}{.7cm} +\renewcommand{\wdtL}{2.2cm} \begin{longtable}{@{}ALLLLL@{}} \toprule & Adams & Bourbaki & Carter & Dynkin & Kac \\ \midrule @@ -1328,7 +1370,7 @@ Below we draw the Vogan diagrams of some affine Lie superalgebras \cite{Ransingh \begingroup \tikzset{/Dynkin diagram,label macro/.code=\labls{#1},label,root radius=.06cm} \tcbset{text width=10cm} -\RenewDocumentCommand\wdtA{}{2cm} +\renewcommand{\wdtA}{2cm} \NewDocumentEnvironment{Category}{m}% {% \begin{tcolorbox}[title={\(#1\)},breakable]{} @@ -1673,7 +1715,7 @@ The environment syntax is \verb!\begin{dynkinDiagram}! followed by the same para is computed as \(n=\sum 2^{i-1} a_i\), \(a_i=0\) or \(1\), to say that root \(i\) is crossed, i.e. a noncompact root. \\ \optionLabel{root radius}{\typ{number}cm}{.05cm} & size of the dots and of the crosses in the Dynkin diagram \\ -\optionLabel{text/.style}{\typ{TikZ style data}}{scale=.7} +\optionLabel{text style}{\typ{TikZ style data}}{scale=.7} & Style for any labels on the roots. \\ \optionLabel{mark}{\typ{o,O,t,x,X,*}}{*} & default root mark \\ @@ -1685,6 +1727,10 @@ is computed as \(n=\sum 2^{i-1} a_i\), \(a_i=0\) or \(1\), to say that root \(i\ & the current labelling scheme for roots. \\ \optionLabel{label macro*}{\typ{1-parameter \TeX{} macro}}{\texttt{\#1}} & the current labelling scheme for alternate roots. \\ +\optionLabel{label height}{\typ{1-parameter \TeX{} macro}}{b} +& the current maximal height of text labels for the roots, set by giving mathematics text of that height. \\ +\optionLabel{label depth}{\typ{1-parameter \TeX{} macro}}{g} +& the current maximal depth of text labels for the roots, set by giving mathematics text of that depth. \\ \optionLabel{make indefinite edge}{\typ{edge pair \(i\)-\(j\) or list of such}}{\{\}} & edge pair or list of edge pairs to treat as having indefinitely many roots on them. \\ \optionLabel{indefinite edge ratio}{\typ{float}}{1.6} |