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author | Karl Berry <karl@freefriends.org> | 2017-09-13 22:04:42 +0000 |
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committer | Karl Berry <karl@freefriends.org> | 2017-09-13 22:04:42 +0000 |
commit | e8c20bb0877f0c49076ba2768b4cc359d973ed58 (patch) | |
tree | 126468f9f8be7c3b95774ad08f9612fca1eb47e5 /Master/texmf-dist/doc/latex/dynkin-diagrams | |
parent | e93b2d183454ff002d8526083f8706347afd28cc (diff) |
dynkin-diagrams (14sep17)
git-svn-id: svn://tug.org/texlive/trunk@45287 c570f23f-e606-0410-a88d-b1316a301751
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-rw-r--r-- | Master/texmf-dist/doc/latex/dynkin-diagrams/README | 19 | ||||
-rw-r--r-- | Master/texmf-dist/doc/latex/dynkin-diagrams/dynkin-diagrams.pdf | bin | 0 -> 153870 bytes | |||
-rw-r--r-- | Master/texmf-dist/doc/latex/dynkin-diagrams/dynkin-diagrams.tex | 211 |
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diff --git a/Master/texmf-dist/doc/latex/dynkin-diagrams/README b/Master/texmf-dist/doc/latex/dynkin-diagrams/README new file mode 100644 index 00000000000..0a9ec82779f --- /dev/null +++ b/Master/texmf-dist/doc/latex/dynkin-diagrams/README @@ -0,0 +1,19 @@ +___________________________________ + + Dynkin diagrams + + v1.0 + + 8 September 2017 +___________________________________ + +Authors : Ben McKay +Maintainer: Ben McKay +E-mail : b.mckay@ucc.ie +Licence : Released under the LaTeX Project Public License v1.3c or + later, see http://www.latex-project.org/lppl.txt + +---------------------------------------------------------------------- + +Provides Dynkin diagrams drawn in TikZ. + diff --git a/Master/texmf-dist/doc/latex/dynkin-diagrams/dynkin-diagrams.pdf b/Master/texmf-dist/doc/latex/dynkin-diagrams/dynkin-diagrams.pdf Binary files differnew file mode 100644 index 00000000000..fa4ed5acbe9 --- /dev/null +++ b/Master/texmf-dist/doc/latex/dynkin-diagrams/dynkin-diagrams.pdf diff --git a/Master/texmf-dist/doc/latex/dynkin-diagrams/dynkin-diagrams.tex b/Master/texmf-dist/doc/latex/dynkin-diagrams/dynkin-diagrams.tex new file mode 100644 index 00000000000..7bc9eb0a18d --- /dev/null +++ b/Master/texmf-dist/doc/latex/dynkin-diagrams/dynkin-diagrams.tex @@ -0,0 +1,211 @@ +\documentclass{amsart} + +\title{The Dynkin diagrams package} +\author{Ben McKay} +\date{\today} + +\usepackage{dynkin-diagrams} +\usepackage{amsmath} +\usepackage{amsfonts} +\usepackage{array} +\usepackage{xstring} +\usepackage{etoolbox} +\usetikzlibrary{backgrounds} +\usetikzlibrary{decorations.markings} +\usepackage{longtable} +\usepackage{showexpl} + +\newcommand{\C}[1]{\mathbb{C}^{#1}} + + +\renewcommand*{\arraystretch}{1.5} + +\begin{document} +\maketitle +\tableofcontents + +\section{Quick introduction} + +This is a test of the Dynkin diagram package. +Load the package via +\begin{verbatim} +\usepackage{dynkin-diagrams} +\end{verbatim} +and invoke it directly: +\begin{LTXexample} +The flag variety of pointed lines in +projective 3-space is associated to +the Dykin diagram \dynk[parabolic=3]{A}{3}. +\end{LTXexample} +or use the long form inside a \verb!\tikz! statement or environment: +\begin{LTXexample} +\tikz \dynkin[parabolic=3]{A}{3}; +\end{LTXexample} +With labels for the roots: +\begin{LTXexample} +\tikz \dynkin[parabolic=3,label=true]{A}{3}; +\end{LTXexample} + +\bigskip + +Inside an environment: +\begin{LTXexample} +\begin{tikzpicture} +\dynkin[parabolic=3,label=true]{A}{3} +\end{tikzpicture} +\end{LTXexample} + +\bigskip + +Make up your own labels for the roots: + +\begin{LTXexample} +\begin{tikzpicture} +\dynkin[parabolic=3]{A}{3}; +\node at (root label 2) {\scalebox{.7}{\(\alpha_2\)}}; +\end{tikzpicture} +\end{LTXexample} + +\newpage + +Drawing curves between the roots: + +\begin{LTXexample} +\begin{tikzpicture} +\dynkin[parabolic=429]{E}{8} +\draw[brown,-latex] + (root 3.south) + to [out=-90, in=-90] + (root 6.south); +\end{tikzpicture} +\end{LTXexample} + +Various options: + +\begin{LTXexample} +\tikz \dynkin[color=brown]{G}{2}; +\end{LTXexample} + +\begin{LTXexample} +\tikz \dynkin[edgelength=1.2,parabolic=3]{A}{3}; +\end{LTXexample} + +\begin{LTXexample} +\tikz \dynkin[crosssize=.1cm,parabolic=3]{A}{3}; +\end{LTXexample} + +\begin{LTXexample} +\tikz \dynkin[dotradius=.08cm,parabolic=3]{A}{3}; +\end{LTXexample} + +\begin{LTXexample} +\begin{tikzpicture}[ + show background rectangle, + background rectangle/.style={fill=lightgray}] +\dynkin[parabolic=1,background color=lightgray]{G}{2} +\end{tikzpicture} +\end{LTXexample} + + +\section{Syntax} + +Inside a \verb!\tikz! environment, the syntax is \verb!\dynkin[<options>]{<letter>}{<rank>}! where \verb!<letter>! is \(A,B,C,D,E,F\) or \(G\), the family of root system for the Dynkin diagram, and \verb!<rank>! is an integer representing the rank, or is the symbol \verb!*! to represent an indefinite rank: + +\begin{LTXexample} +\begin{tikzpicture} +\dynkin[parabolic=5]{D}{*} +\end{tikzpicture} +\end{LTXexample} + +Outside a \verb!\tikz! environment, use \verb!\dynk! instead of \verb!\dynkin!. + + +\bigskip + +\newcommand*{\typ}[1]{\(\left<\texttt{#1}\right>\)} +\newcommand*{\optionLabel}[3]{%% +\multicolumn{2}{l}{\(\texttt{#1}=\texttt{#2}, \texttt{default}=\texttt{#3}\)} \\ +}%% + +\section{Options} +\par\noindent% +\begin{tabular}{p{1cm}p{10cm}} +\optionLabel{parabolic}{\typ{integer}}{0} +& A parabolic subgroup with specified integer, where the integer +is computed as \(n=\sum 2^i a_i\), \(a_i=0\) or \(1\), to say that root \(i\) is crossed, i.e. a noncompact root. \\ +\optionLabel{color}{\typ{color name}}{black} \\ +\optionLabel{background color}{\typ{color name}}{white} +& This only says what color you have already set for the background rectangle. It is needed precisely for the \(G_2\) root system, to draw the triple line correctly, and only when your background color is not white. \\ +\optionLabel{dotradius}{\typ{number}cm}{.04cm} +& size of the dots in the Dynkin diagram \\ +\optionLabel{edgelength}{\typ{number}cm}{.35cm} +& distance between nodes in the Dynkin diagram \\ +\optionLabel{crosssize}{\typ{number}}{1.5} +& size of the crosses, for parabolic subgroup diagrams. \\ +\optionLabel{label}{true or false}{false} +& whether to label the roots by their root numbers. \\ +\end{tabular} +%% All other options are passed to tikz. + +\section{Finding the roots} +The roots are labelled in the Bourbaki labelling, but from \(0\) to \(r-1\), where \(r\) is the rank. +The command sets up nodes \texttt{(root 0)}, \texttt{(root 1)}, and so on. +Use these tikz nodes to draw on the Dynkin diagram. +It also sets up nodes \texttt{(root label 0)}, \texttt{(root label 1)}, and so on for the labels. + + + +\section{Example: some parabolic subgroups} + +\newcommand{\drawparabolic}[3]%% +{#1_{#2,#3} & \tikz \dynkin[parabolic=#3]{#1}{#2}; \\} + +\begin{center} +\begin{longtable}{@{}>{$}r<{$}m{2cm}m{2cm}@{}} +\endfirsthead +\endhead +\endfoot +\endlastfoot +\drawparabolic{A}{1}{0} +\drawparabolic{A}{1}{1} +\drawparabolic{A}{2}{0} +\drawparabolic{A}{2}{2} +\drawparabolic{A}{2}{2} +\drawparabolic{B}{2}{3} +\drawparabolic{C}{3}{5} +\drawparabolic{D}{5}{4} +\drawparabolic{E}{6}{5} +\drawparabolic{E}{7}{101} +\drawparabolic{E}{8}{123} +\drawparabolic{F}{4}{13} +\drawparabolic{G}{2}{2} +\end{longtable} +\end{center} + + + +\section{Example: the Hermitian symmetric spaces} + + \renewcommand*{\arraystretch}{1.5} +\begin{center} +\begin{longtable}{@{}>{$}r<{$}m{2cm}m{5cm}@{}} +\endfirsthead +\endhead +\endfoot +\endlastfoot + A_n &\dynk[parabolic=8]{A}{*}& Grassmannian of $k$-planes in $\C{n+1}$ \\ + B_n &\dynk[parabolic=1]{B}{*}& $(2n-1)$-dimensional hyperquadric, i.e. the variety of null lines in $\C{2n+1}$ + \\ + C_n &\dynk[parabolic=16]{C}{*}& space of Lagrangian $n$-planes in $\C{2n}$ + \\ + D_n &\dynk[parabolic=1]{D}{*}&$(2n-2)$-dimensional hyperquadric, i.e. the variety of null lines in $\C{2n}$ +\\ + D_n&\dynk[parabolic=32]{D}{*}& one component of the variety of maximal dimension null subspaces of $\C{2n}$ \\ + D_n + &\dynk[parabolic=16]{D}{*}&the other component\\ + E_6&\dynk[parabolic=1]{E}{6}&complexified octave projective plane\\ + E_6&\dynk[parabolic=32]{E}{6}&its dual plane\\ + E_7 &\dynk[parabolic=64]{E}{7}& the space of null octave 3-planes in octave 6-space +\end{longtable} +\end{center} +\end{document} |