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+\documentclass{amsart}
+\usepackage{etex}
+\usepackage[T1]{fontenc}
+\usepackage[utf8]{inputenx}
+
+\title{The Rank 2 Roots Package \\ Version 1.0}
+\author{Ben McKay}
+\date{30 August 2018}
+
+\usepackage{etoolbox} 
+\usepackage{lmodern}
+\usepackage[kerning=true,tracking=true]{microtype}
+\usepackage{amsmath}
+\usepackage{amsfonts}
+\usepackage{array}
+\usepackage{xparse}
+\usepackage{xstring}
+\usepackage{longtable}
+\usepackage{rank-2-roots}
+\usepackage{tikz}
+\usepackage[listings]{tcolorbox} 
+\tcbuselibrary{breakable}
+\tcbuselibrary{skins}
+\definecolor{example-color}{gray}{.85}
+\definecolor{example-border-color}{gray}{.7} 
+\tcbset{coltitle=black,colback=white,colframe=example-border-color,enhanced,breakable,pad at break*=1mm,
+toprule=1.2mm,bottomrule=1.2mm,leftrule=1mm,rightrule=1mm,toprule at break=-1mm,bottomrule at break=-1mm,
+before upper={\widowpenalties=3 10000 10000 150}}
+\usepackage[pdftex]{hyperref}
+\hypersetup{
+  colorlinks   = true,  %Colours links instead of ugly boxes
+  urlcolor     = black, %Colour for external hyperlinks
+  linkcolor    = black, %Colour of internal links
+  citecolor    = black  %Colour of citations
+}
+\usepackage{booktabs}
+\usepackage{colortbl}
+\usepackage{varwidth}
+\usepackage{dynkin-diagrams}
+\usepackage{fancyvrb}
+\usepackage{xspace}
+\newcommand{\TikZ}{Ti\textit{k}Z\xspace}
+\usepackage{filecontents}
+\usetikzlibrary{decorations.markings}
+\usetikzlibrary{arrows,decorations.pathmorphing,backgrounds,positioning,fit}
+\arrayrulecolor{white}
+\makeatletter
+    \def\rulecolor#1#{\CT@arc{#1}}
+    \def\CT@arc#1#2{%
+      \ifdim\baselineskip=\z@\noalign\fi
+      {\gdef\CT@arc@{\color#1{#2}}}}
+    \let\CT@arc@\relax
+\rulecolor{white}
+\makeatother
+
+
+
+
+
+\NewDocumentCommand\todo{m}%
+{%
+\textcolor{blue}{\textit{#1}}
+}%
+
+\begin{document}
+\maketitle
+\tableofcontents
+
+\section{Introduction}
+This package concerns mathematical drawings arising in representation theory.
+The purpose of this package is to ease drawing of rank 2 root systems, with Weyl chambers, weight lattices, and parabolic subgroups, mostly imitating the drawings of Fulton and Harris \cite{Fulton.Harris:1991}.
+We use definitions of root systems and weight lattices as in Carter \cite{Carter:2005} p. 540--609.
+
+
+\section{Root systems}
+\NewDocumentCommand\drawroots{m}%
+{%
+\begin{tikzpicture}[baseline=-.5]
+\begin{rootSystem}{#1}
+\roots
+\end{rootSystem}
+\end{tikzpicture}
+}%
+
+\NewDocumentCommand\csdrawroots{m}%
+{%
+\texttt{\detokenize{\begin{tikzpicture}[baseline=-.5]}}%
+\par\noindent%
+\texttt{\detokenize{\begin{rootSystem}}\{#1\}}%
+\par\noindent%
+\texttt{\detokenize{\roots}}%
+\par\noindent%
+\texttt{\detokenize{\end{rootSystem}}}%
+\par\noindent%
+\texttt{\detokenize{\end{tikzpicture}}}%
+}%
+
+\newcommand*\mytablecontents{}
+\foreach \i in {A,B,C,G}{
+    \xappto\mytablecontents{$\i_2$ & \drawroots{\i} & \csdrawroots{\i}
+}
+  \gappto\mytablecontents{\\ \\}
+}
+
+\begin{longtable}{rcm{8cm}}
+\caption{The root systems}\\
+\endfirsthead
+\caption{\dots continued}\\
+\endhead
+\multicolumn{3}{c}{continued \dots}\\
+\endfoot
+\endlastfoot
+\mytablecontents
+\end{longtable}
+
+
+\section{Weights}
+Type \verb!\wt{x}{y}! to get a weight at position \((x,y)\) (as measured in a basis of \emph{fundamental weights}).
+Type \verb!\wt[multiplicity=n]{x}{y}! to get multiplicity \(m\).
+Add an option: \verb!\wt[Z]{x}{y}{m}! to get \verb!Z! passed to TikZ.
+
+
+\RenewDocumentCommand\drawroots{m}%
+{%
+\begin{tikzpicture}[baseline=-.5]
+\begin{rootSystem}{#1}
+\roots
+\wt[brown]{1}{0}
+\wt[red]{0}{1}
+\wt[multiplicity=4,blue]{1}{3}
+\wt[blue,multiplicity=2]{2}{2}
+\wt[blue]{-1}{3}
+\end{rootSystem}
+\end{tikzpicture}
+}%
+
+\RenewDocumentCommand\csdrawroots{m}%
+{%
+\texttt{\detokenize{\begin{tikzpicture}[baseline=-.5]}}%
+\par\noindent%
+\texttt{\detokenize{\begin{rootSystem}}\{#1\}}%
+\par\noindent%
+\texttt{\detokenize{\roots}}%
+\par\noindent%
+\texttt{\detokenize{\wt[brown]{1}{0}}}%
+\par\noindent%
+\texttt{\detokenize{\wt[red]{0}{1}}}%
+\par\noindent%
+\texttt{\detokenize{\wt[multiplicity=4,blue]{1}{3}}}%
+\par\noindent%
+\texttt{\detokenize{\wt[blue,multiplicity=2]{2}{2}}}%
+\par\noindent%
+\texttt{\detokenize{\wt[blue]{-1}{3}}}%
+\par\noindent%
+\texttt{\detokenize{\end{rootSystem}}}%
+\par\noindent%
+\texttt{\detokenize{\end{tikzpicture}}}%
+}%
+
+\renewcommand*\mytablecontents{}
+\foreach \i in {A,B,C,G}{
+    \xappto\mytablecontents{$\i_2$ & \drawroots{\i} & \csdrawroots{\i}
+}
+  \gappto\mytablecontents{\\ \\}
+}
+
+\begin{longtable}{rcm{8cm}}
+\caption{Some weights drawn with multiplicities}\\
+\endfirsthead
+\caption{\dots continued}\\
+\endhead
+\multicolumn{3}{c}{continued \dots}\\
+\endfoot
+\endlastfoot
+\mytablecontents
+\end{longtable}
+
+
+
+
+\RenewDocumentCommand\drawroots{m}%
+{%
+\begin{tikzpicture}[baseline=-.5]
+\begin{rootSystem}{#1}
+\roots
+\wt[multiplicity=2,root]{0}{0}
+\end{rootSystem}
+\end{tikzpicture}
+}%
+
+\RenewDocumentCommand\csdrawroots{m}%
+{%
+\texttt{\detokenize{\begin{tikzpicture}[baseline=-.5]}}%
+\par\noindent%
+\texttt{\detokenize{\begin{rootSystem}}\{#1\}}%
+\par\noindent%
+\texttt{\detokenize{\roots}}%
+\par\noindent%
+\texttt{\detokenize{\wt[multiplicity=2,root]{0}{0}}}%
+\par\noindent%
+\texttt{\detokenize{\end{rootSystem}}}%
+\par\noindent%
+\texttt{\detokenize{\end{tikzpicture}}}%
+}%
+
+\renewcommand*\mytablecontents{}
+\foreach \i in {A,B,C,G}{
+    \xappto\mytablecontents{$\i_2$ & \drawroots{\i} & \csdrawroots{\i}
+}
+  \gappto\mytablecontents{\\ \\}
+}
+
+\begin{longtable}{rcm{8cm}}
+\caption{The root systems with all multiplicities of the adjoint representation, like Fulton and Harris}\\
+\endfirsthead
+\caption{\dots continued}\\
+\endhead
+\multicolumn{3}{c}{continued \dots}\\
+\endfoot
+\endlastfoot
+\mytablecontents
+\end{longtable}
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+\RenewDocumentCommand\drawroots{m}%
+{%
+\begin{tikzpicture}[baseline=-.5]
+\begin{rootSystem}{#1}
+\roots
+\WeylChamber
+\end{rootSystem}
+\end{tikzpicture}
+}%
+
+\RenewDocumentCommand\csdrawroots{m}%
+{%
+\texttt{\detokenize{\begin{tikzpicture}[baseline=-.5]}}%
+\par\noindent%
+\texttt{\detokenize{\begin{rootSystem}}\{#1\}}%
+\par\noindent%
+\texttt{\detokenize{\roots}}%
+\par\noindent%
+\texttt{\detokenize{\WeylChamber}}%
+\par\noindent%
+\texttt{\detokenize{\end{rootSystem}}}%
+\par\noindent%
+\texttt{\detokenize{\end{tikzpicture}}}%
+}%
+
+\renewcommand*\mytablecontents{}
+\foreach \i in {A,B,C,G}{
+    \xappto\mytablecontents{$\i_2$ & \drawroots{\i} & \csdrawroots{\i}
+}
+  \gappto\mytablecontents{\\ \\}
+}
+
+\begin{longtable}{rcm{8cm}}
+\caption{Weyl chambers}\\
+\endfirsthead
+\caption{\dots continued}\\
+\endhead
+\multicolumn{3}{c}{continued \dots}\\
+\endfoot
+\endlastfoot
+\mytablecontents
+\end{longtable}
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+\section{Parabolic subgroups}
+
+\RenewDocumentCommand\drawroots{m}%
+{%
+\begin{tikzpicture}[baseline=-.5]
+\begin{rootSystem}{#1}
+\roots
+\positiveRootHyperplane
+\end{rootSystem}
+\end{tikzpicture}
+}%
+
+\RenewDocumentCommand\csdrawroots{m}%
+{%
+\texttt{\detokenize{\begin{tikzpicture}[baseline=-.5]}}%
+\par\noindent%
+\texttt{\detokenize{\begin{rootSystem}}\{#1\}}%
+\par\noindent%
+\texttt{\detokenize{\roots}}%
+\par\noindent%
+\texttt{\detokenize{\positiveRootHyperplane}}%
+\par\noindent%
+\texttt{\detokenize{\end{rootSystem}}}%
+\par\noindent%
+\texttt{\detokenize{\end{tikzpicture}}}%
+}%
+
+\renewcommand*\mytablecontents{}
+\foreach \i in {A,B,C,G}{
+    \xappto\mytablecontents{$\i_2$ & \drawroots{\i} & \csdrawroots{\i}
+}
+  \gappto\mytablecontents{\\ \\}
+}
+
+\begin{longtable}{rcm{8cm}}
+\caption{The positive root hyperplane}\\
+\endfirsthead
+\caption{\dots continued}\\
+\endhead
+\multicolumn{3}{c}{continued \dots}\\
+\endfoot
+\endlastfoot
+\mytablecontents
+\end{longtable}
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+\RenewDocumentCommand\drawroots{mm}%
+{%
+\begin{tikzpicture}[baseline=-.5]
+\begin{rootSystem}{#1}
+\roots
+\parabolic{#2}
+\end{rootSystem}
+\end{tikzpicture}
+}%
+
+\RenewDocumentCommand\csdrawroots{mm}%
+{%
+\texttt{\detokenize{\begin{tikzpicture}[baseline=-.5]}}%
+\par\noindent%
+\texttt{\detokenize{\begin{rootSystem}}\{#1\}}%
+\par\noindent%
+\texttt{\detokenize{\roots}}%
+\par\noindent%
+\texttt{\detokenize{\parabolic}\{#2\}}%
+\par\noindent%
+\texttt{\detokenize{\end{rootSystem}}}%
+\par\noindent%
+\texttt{\detokenize{\end{tikzpicture}}}%
+}%
+
+\renewcommand*\mytablecontents{}
+\foreach \i in {A,B,C,G}{
+	\foreach \j in {1,2,3}{
+	    \xappto\mytablecontents{$\i_{2,\j}$ & \drawroots{\i}{\j} & \csdrawroots{\i}{\j}
+	}
+  \gappto\mytablecontents{\\ \\}
+}
+}
+
+\begin{longtable}{rcm{8cm}}
+\caption{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: \(A_{5,37}\) means the parabolic subgroup of \(A_5\) so that the binary digits of \(37=2^5+2^2+2^0\) give us roots \(0,2,5\) in Bourbaki ordering being compact roots, i.e. having the root vectors of both that root and its negative inside the parabolic subgroup. }\\
+\endfirsthead
+\caption{\dots continued}\\
+\endhead
+\multicolumn{3}{c}{continued \dots}\\
+\endfoot
+\endlastfoot
+\mytablecontents
+\end{longtable}
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+\RenewDocumentCommand\drawroots{mm}%
+{%
+\begin{tikzpicture}[baseline=-.5]
+\begin{rootSystem}{#1}
+\roots
+\parabolic{#2}
+\parabolicgrading
+\end{rootSystem}
+\end{tikzpicture}
+}%
+
+\RenewDocumentCommand\csdrawroots{mm}%
+{%
+\texttt{\detokenize{\begin{tikzpicture}[baseline=-.5]}}%
+\par\noindent%
+\texttt{\detokenize{\begin{rootSystem}}\{#1\}}%
+\par\noindent%
+\texttt{\detokenize{\roots}}%
+\par\noindent%
+\texttt{\detokenize{\parabolic}\{#2\}}%
+\par\noindent%
+\texttt{\detokenize{\parabolicgrading}}%
+\par\noindent%
+\texttt{\detokenize{\end{rootSystem}}}%
+\par\noindent%
+\texttt{\detokenize{\end{tikzpicture}}}%
+}%
+
+\renewcommand*\mytablecontents{}
+\foreach \i in {A,B,C,G}{
+	\foreach \j in {1,2,3}{
+	    \xappto\mytablecontents{$\i_{2,\j}$ & \drawroots{\i}{\j} & \csdrawroots{\i}{\j}
+	}
+  \gappto\mytablecontents{\\ \\}
+}
+}
+
+\begin{longtable}{rcm{8cm}}
+\caption{Parabolic subgroups with grading of the positive roots}\\
+\endfirsthead
+\caption{\dots continued}\\
+\endhead
+\multicolumn{3}{c}{continued \dots}\\
+\endfoot
+\endlastfoot
+\mytablecontents
+\end{longtable}
+
+
+
+
+\NewDocumentCommand{\labelWt}{mmmm}%
+{%
+\node[#1,black] at \weight{#2}{#3} {\(#4\)};
+}%
+
+
+{
+\NewDocumentCommand\labelRoots{}%
+{%
+\labelWt{above right}{0}{0}{0}%
+\labelWt{right}{1}{1}{e_1-e_3}%
+\labelWt{right}{2}{-1}{e_1-e_2}%
+\labelWt{below}{1}{-2}{e_3-e_2}%
+\labelWt{left}{-1}{-1}{e_3-e_1}%
+\labelWt{left}{-2}{1}{e_2-e_1}%
+\labelWt{above}{-1}{2}{e_2-e_3}%
+}%
+\setlength{\weightLength}{1cm}
+\begin{tikzpicture}
+\begin{rootSystem}{A}
+\roots
+\wt{0}{0}
+\labelRoots
+\end{rootSystem}
+\end{tikzpicture}
+}
+
+
+\tikzstyle{weight arrow}=[black,-stealth,shorten <=.25cm,shorten >=.25cm]
+
+{
+\NewDocumentCommand\wa{O{}mm}%
+{%
+\IfStrEq{#1}{0}%
+{%
+\draw[weight arrow]  \weight{#2}{#3} -- \weight{#2+1}{#3+1} node[right=-4pt]{\(0\)};%
+}%
+{%
+\draw[weight arrow]  \weight{#2}{#3} -- \weight{#2+1}{#3+1};%
+}%
+}%
+\setlength{\weightLength}{.75cm}
+\begin{tikzpicture}
+\begin{rootSystem}{A}
+\setlength{\weightRadius}{1.5pt}
+\roots
+\wt{0}{0}
+\labelWt{above left}{0}{0}{0}
+\labelWt{right}{1}{1}{e_1-e_3}
+\labelWt{right}{2}{-1}{e_1-e_2}
+\labelWt{below}{1}{-2}{e_3-e_2}
+\labelWt{left}{-1}{-1}{e_3-e_1}
+\labelWt{left}{-2}{1}{e_2-e_1}
+\labelWt{above left}{-1}{2}{e_2-e_3}
+\wa{0}{0}
+\wa[0]{1}{1}
+\wa[0]{2}{-1}
+\wa[0]{-1}{2}
+\wa{1}{-2}
+\wa{-1}{-1}
+\wa{-2}{1}
+\end{rootSystem}
+\end{tikzpicture}
+}
+
+
+
+\begin{tcblisting}{title={Drawing the \(A_2\) root system and a weight at the origin. The option \texttt{root} indicates that this weight is to be coloured like a root.}}
+\begin{tikzpicture}
+\begin{rootSystem}{A}
+\roots
+\wt[root]{0}{0}
+\end{rootSystem}
+\end{tikzpicture}
+\end{tcblisting}
+
+
+\begin{tcblisting}{title={Drawing the \(A_2\) root system and a weight at the origin and the positive root hyperplane}}
+\begin{tikzpicture}
+\begin{rootSystem}{A}
+\roots
+\wt[root]{0}{0}
+\positiveRootHyperplane
+\end{rootSystem}
+\end{tikzpicture}
+\end{tcblisting}
+
+
+
+
+\section{Coordinate systems}
+
+The package provides three coordinate systems: hex, square and weight.
+Above we have seen the weight coordinates: a basis of fundamental weights.
+We can also use weight coordinates like
+\[
+\verb!\draw \weight{0}{1} -- \weight{1}{0};!
+\]
+The square system, used like \verb!\draw (square cs:x=1,y=2) circle (2pt);!, is simply the standard Cartesian coordinate system measured so that the minimum distance between weights is one unit.
+The hex coordinate system has basis precisely the fundamental weights of the \(A_2\) lattice.
+We can use the hex system in drawing on the \(A_2\) or \(G_2\) weight lattices, as below, as they are the same lattices.
+
+\begin{tcblisting}{title={Automatic sizing of the weight lattice (the default) \dots}}
+\begin{tikzpicture}
+\begin{rootSystem}{A}
+\wt{0}{0}
+\fill[gray!50,opacity=.2]  (hex cs:x=5,y=-7) -- (hex cs:x=1,y=1) -- (hex cs:x=-7,y=5) arc (150:270:{7*\weightLength});
+\draw[black,very thick] (hex cs:x=5,y=-7) -- (hex cs:x=1,y=1) -- (hex cs:x=-7,y=5);
+\node[above right=-2pt] at (hex cs:x=1,y=1) {\small\(\alpha\)};
+\end{rootSystem}
+\end{tikzpicture}
+\end{tcblisting}
+
+\begin{tcblisting}{title={\dots and here with manual sizing, setting the weight lattice to include 3 steps to the right of the origin}}
+\begin{tikzpicture}
+\AutoSizeWeightLatticefalse
+\begin{rootSystem}{A}
+\wt{0}{0}
+\weightLattice{3}
+\fill[gray!50,opacity=.2]  (hex cs:x=5,y=-7) -- (hex cs:x=1,y=1) -- (hex cs:x=-7,y=5) arc (150:270:{7*\weightLength});
+\draw[black,very thick] (hex cs:x=5,y=-7) -- (hex cs:x=1,y=1) -- (hex cs:x=-7,y=5);
+\node[above right=-2pt] at (hex cs:x=1,y=1) {\small\(\alpha\)};
+\end{rootSystem}
+\end{tikzpicture}
+\end{tcblisting}
+
+\begin{tcblisting}{title={Fulton and Harris p. 170}}
+\begin{tikzpicture}
+\begin{rootSystem}{A}
+\draw \weight{3}{1} -- \weight{-4}{4.5};
+\foreach \i in {1,...,4}{\wt{5-2*\i}{\i}}
+\node[above right=-2pt] at (hex cs:x=3,y=1){\small\(\alpha\)};
+\end{rootSystem}
+\end{tikzpicture}
+\end{tcblisting}
+
+
+
+
+
+\begin{tcblisting}{title={Automatic sizing of the weight lattice (the default) \dots}}
+\begin{tikzpicture}
+\begin{rootSystem}{A}
+\setlength{\weightRadius}{2pt}
+\draw \weight{3}{1} -- \weight{-3}{4};
+\draw \weight{3}{1} -- \weight{4}{-1};
+\wt{4}{-1}
+\foreach \i in {1,...,4}{\wt{5-2*\i}{\i}}
+\node[above right=-2pt] at (hex cs:x=3,y=1){\small\(\alpha\)};
+\draw[very thick] \weight{0}{-4} -- \weight{0}{4.5} node[above]{\small\(\left<H_{12},L\right>=0\)};
+\draw[very thick] \weight{-4}{0} -- \weight{4.5}{0} node[right]{\small\(\left<H_{23},L\right>=0\)};
+\end{rootSystem}
+\end{tikzpicture}
+\end{tcblisting}
+
+
+\begin{tcblisting}{title={\dots and manual sizing}}
+\begin{tikzpicture}
+\AutoSizeWeightLatticefalse
+\begin{rootSystem}{A}
+\setlength{\weightRadius}{2pt}
+\weightLattice{4}
+\draw \weight{3}{1} -- \weight{-3}{4};
+\draw \weight{3}{1} -- \weight{4}{-1};
+\wt{4}{-1}
+\foreach \i in {1,...,4}{\wt{5-2*\i}{\i}}
+\node[above right=-2pt] at (hex cs:x=3,y=1){\small\(\alpha\)};
+\draw[very thick] \weight{0}{-4} -- \weight{0}{4.5} node[above]{\small\(\left<H_{12},L\right>=0\)};
+\draw[very thick] \weight{-4}{0} -- \weight{4.5}{0} node[right]{\small\(\left<H_{23},L\right>=0\)};
+\end{rootSystem}
+\end{tikzpicture}
+\end{tcblisting}
+
+\begin{tcblisting}{}
+\begin{tikzpicture}
+\AutoSizeWeightLatticefalse
+\begin{rootSystem}{A}
+\setlength{\weightRadius}{2pt}
+\weightLattice{4}
+\draw \weight{3}{1} -- \weight{-3}{4};
+\draw \weight{3}{1} -- \weight{4}{-1};
+\draw \weight{-3}{4} -- \weight{-4}{3};
+\wt{4}{-1}
+\wt{-4}{3}
+\foreach \i in {1,...,4}{\wt{5-2*\i}{\i}}
+\node[above right=-2pt] at (hex cs:x=3,y=1){\small\(\alpha\)};
+\draw[very thick] \weight{0}{-4} -- \weight{0}{4.5} node[above]{\small\(\left<H_{12},L\right>=0\)};
+\draw[very thick] \weight{-4}{0} -- \weight{4.5}{0} node[right]{\small\(\left<H_{23},L\right>=0\)};
+\draw[very thick] \weight{4}{-4} -- \weight{-4.5}{4.5} node[above]{\small\(\left<H_{13},L\right>=0\)};
+\end{rootSystem}
+\end{tikzpicture}
+\end{tcblisting}
+
+
+\begin{tcblisting}{}
+\setlength{\weightRadius}{2pt}
+\setlength\weightLength{.75cm}
+\begin{tikzpicture}
+\begin{rootSystem}{A}
+\foreach \x/\y in {1/0, -1/1, 0/-1, -2/0, 0/2, 2/-2}{\wt{\x}{\y}}
+\node[above] at \weight{1}{0} {\small\(L_1\)};
+\node[above] at \weight{-1}{1} {\small\(L_2\)};
+\node[above] at \weight{0}{-1} {\small\(L_3\)};
+\end{rootSystem}
+\end{tikzpicture}
+\end{tcblisting}
+
+\begin{tcblisting}{title={Changing the weight length rescales}}
+\begin{tikzpicture}
+\setlength\weightLength{.3cm}
+\begin{rootSystem}{A}
+\wt[multiplicity=2]{0}{0}
+\foreach \x/\y in {1/1, 2/-1, 1/-2, -1/-1, -2/1, -1/2}{\wt{\x}{\y}}
+\end{rootSystem}
+\end{tikzpicture}
+\end{tcblisting}
+
+\begin{tcblisting}{}
+\begin{tikzpicture}
+\setlength\weightLength{.3cm}
+\begin{rootSystem}{A}
+\foreach \x/\y in {0/0, 3/0, 2/-1, 1/-2, 0/-3, 1/1, -1/-1, -1/2, -2/1, -3/3}{\wt{\x}{\y}}
+\end{rootSystem}
+\end{tikzpicture}
+\end{tcblisting}
+
+\begin{tcblisting}{}
+\begin{tikzpicture}
+\setlength\weightLength{.3cm}
+\begin{rootSystem}{A}
+\foreach \x/\y in {0/0, -3/0, 2/-1, 1/-2, 3/-3, 1/1, -1/-1, -1/2, -2/1, 0/3}{\wt{\x}{\y}}
+\end{rootSystem}
+\end{tikzpicture}
+\end{tcblisting}
+
+\begin{tcblisting}{title={We use a basis of fundamental weights, as given in Carter's book \cite{Carter:2005} p. 540--609}}
+\begin{tikzpicture}
+\begin{rootSystem}{B}
+\roots
+\draw[green!50!black,very thick] \weight{0}{1} -- \weight{1}{0};
+\weightLattice{3}
+\wt[blue]{1}{0}{1}
+\wt[red]{0}{1}{1}
+\end{rootSystem}
+\end{tikzpicture}
+\end{tcblisting}
+
+
+
+
+
+
+Without automatic stretching of the weight lattice to fit the picture, you won't see the weight lattice at all unless you ask for it.
+
+\AutoSizeWeightLatticefalse
+
+
+
+
+
+
+\RenewDocumentCommand\drawroots{m}%
+{%
+\begin{tikzpicture}[baseline=-.5]
+\begin{rootSystem}{#1}
+\roots
+\end{rootSystem}
+\end{tikzpicture}
+}%
+
+\RenewDocumentCommand\csdrawroots{m}%
+{%
+\texttt{\detokenize{\begin{tikzpicture}[baseline=-.5]}}%
+\par\noindent%
+\texttt{\detokenize{\begin{rootSystem}}\{#1\}}%
+\par\noindent%
+\texttt{\detokenize{\roots}}%
+\par\noindent%
+\texttt{\detokenize{\end{rootSystem}}}%
+\par\noindent%
+\texttt{\detokenize{\end{tikzpicture}}}%
+}%
+
+\renewcommand*\mytablecontents{}
+\foreach \i in {A,B,C,G}{
+    \xappto\mytablecontents{$\i_2$ & \drawroots{\i} & \csdrawroots{\i}
+}
+  \gappto\mytablecontents{\\ \\}
+}
+
+\begin{longtable}{rcm{8cm}}
+\caption{The root systems}\\
+\endfirsthead
+\caption{\dots continued}\\
+\endhead
+\multicolumn{3}{c}{continued \dots}\\
+\endfoot
+\endlastfoot
+\mytablecontents
+\end{longtable}
+
+
+
+
+Type \verb!\wt{x}{y}{m}! to get a weight at position \((x,y)\) (as measured in a basis of \emph{fundamental weights}) with multiplicity \(m\).
+Add an option: \verb!\wt[Z]{x}{y}{m}! to get \verb!Z! passed to TikZ.
+
+
+\RenewDocumentCommand\drawroots{m}%
+{%
+\begin{tikzpicture}[baseline=-.5]
+\begin{rootSystem}{#1}
+\roots
+\wt[brown]{1}{0}{1}
+\wt[red]{0}{1}{1}
+\wt[blue]{1}{3}{4}
+\wt[blue]{2}{2}{2}
+\wt[blue]{-1}{3}{1}
+\end{rootSystem}
+\end{tikzpicture}
+}%
+
+\RenewDocumentCommand\csdrawroots{m}%
+{%
+\texttt{\detokenize{\begin{tikzpicture}[baseline=-.5]}}%
+\par\noindent%
+\texttt{\detokenize{\begin{rootSystem}}\{#1\}}%
+\par\noindent%
+\texttt{\detokenize{\roots}}%
+\par\noindent%
+\texttt{\detokenize{\wt[brown]{1}{0}{1}}}%
+\par\noindent%
+\texttt{\detokenize{\wt[red]{0}{1}{1}}}%
+\par\noindent%
+\texttt{\detokenize{\wt[blue]{1}{3}{4}}}%
+\par\noindent%
+\texttt{\detokenize{\wt[blue]{2}{2}{2}}}%
+\par\noindent%
+\texttt{\detokenize{\wt[blue]{-1}{3}{1}}}%
+\par\noindent%
+\texttt{\detokenize{\end{rootSystem}}}%
+\par\noindent%
+\texttt{\detokenize{\end{tikzpicture}}}%
+}%
+
+\renewcommand*\mytablecontents{}
+\foreach \i in {A,B,C,G}{
+    \xappto\mytablecontents{$\i_2$ & \drawroots{\i} & \csdrawroots{\i}
+}
+  \gappto\mytablecontents{\\ \\}
+}
+
+\begin{longtable}{rcm{8cm}}
+\caption{Some weights drawn with multiplicities}\\
+\endfirsthead
+\caption{\dots continued}\\
+\endhead
+\multicolumn{3}{c}{continued \dots}\\
+\endfoot
+\endlastfoot
+\mytablecontents
+\end{longtable}
+
+
+
+
+\RenewDocumentCommand\drawroots{m}%
+{%
+\begin{tikzpicture}[baseline=-.5]
+\begin{rootSystem}{#1}
+\roots
+\wt[multiplicity=2]{0}{0}
+\end{rootSystem}
+\end{tikzpicture}
+}%
+
+\RenewDocumentCommand\csdrawroots{m}%
+{%
+\texttt{\detokenize{\begin{tikzpicture}[baseline=-.5]}}%
+\par\noindent%
+\texttt{\detokenize{\begin{rootSystem}}\{#1\}}%
+\par\noindent%
+\texttt{\detokenize{\roots}}%
+\par\noindent%
+\texttt{\detokenize{\wt[multiplicity=2]{0}{0}}}%
+\par\noindent%
+\texttt{\detokenize{\end{rootSystem}}}%
+\par\noindent%
+\texttt{\detokenize{\end{tikzpicture}}}%
+}%
+
+\renewcommand*\mytablecontents{}
+\foreach \i in {A,B,C,G}{
+    \xappto\mytablecontents{$\i_2$ & \drawroots{\i} & \csdrawroots{\i}
+}
+  \gappto\mytablecontents{\\ \\}
+}
+
+\begin{longtable}{rcm{8cm}}
+\caption{The root systems with all multiplicities of the adjoint representation, like Fulton and Harris}\\
+\endfirsthead
+\caption{\dots continued}\\
+\endhead
+\multicolumn{3}{c}{continued \dots}\\
+\endfoot
+\endlastfoot
+\mytablecontents
+\end{longtable}
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+\RenewDocumentCommand\drawroots{m}%
+{%
+\begin{tikzpicture}[baseline=-.5]
+\begin{rootSystem}{#1}
+\roots
+\WeylChamber
+\end{rootSystem}
+\end{tikzpicture}
+}%
+
+\RenewDocumentCommand\csdrawroots{m}%
+{%
+\texttt{\detokenize{\begin{tikzpicture}[baseline=-.5]}}%
+\par\noindent%
+\texttt{\detokenize{\begin{rootSystem}}\{#1\}}%
+\par\noindent%
+\texttt{\detokenize{\roots}}%
+\par\noindent%
+\texttt{\detokenize{\WeylChamber}}%
+\par\noindent%
+\texttt{\detokenize{\end{rootSystem}}}%
+\par\noindent%
+\texttt{\detokenize{\end{tikzpicture}}}%
+}%
+
+\renewcommand*\mytablecontents{}
+\foreach \i in {A,B,C,G}{
+    \xappto\mytablecontents{$\i_2$ & \drawroots{\i} & \csdrawroots{\i}
+}
+  \gappto\mytablecontents{\\ \\}
+}
+
+\begin{longtable}{rcm{8cm}}
+\caption{Weyl chambers}\\
+\endfirsthead
+\caption{\dots continued}\\
+\endhead
+\multicolumn{3}{c}{continued \dots}\\
+\endfoot
+\endlastfoot
+\mytablecontents
+\end{longtable}
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+\RenewDocumentCommand\drawroots{m}%
+{%
+\begin{tikzpicture}[baseline=-.5]
+\begin{rootSystem}{#1}
+\roots
+\positiveRootHyperplane
+\end{rootSystem}
+\end{tikzpicture}
+}%
+
+\RenewDocumentCommand\csdrawroots{m}%
+{%
+\texttt{\detokenize{\begin{tikzpicture}[baseline=-.5]}}%
+\par\noindent%
+\texttt{\detokenize{\begin{rootSystem}}\{#1\}}%
+\par\noindent%
+\texttt{\detokenize{\roots}}%
+\par\noindent%
+\texttt{\detokenize{\positiveRootHyperplane}}%
+\par\noindent%
+\texttt{\detokenize{\end{rootSystem}}}%
+\par\noindent%
+\texttt{\detokenize{\end{tikzpicture}}}%
+}%
+
+\renewcommand*\mytablecontents{}
+\foreach \i in {A,B,C,G}{
+    \xappto\mytablecontents{$\i_2$ & \drawroots{\i} & \csdrawroots{\i}
+}
+  \gappto\mytablecontents{\\ \\}
+}
+
+\begin{longtable}{rcm{8cm}}
+\caption{The positive root hyperplane}\\
+\endfirsthead
+\caption{\dots continued}\\
+\endhead
+\multicolumn{3}{c}{continued \dots}\\
+\endfoot
+\endlastfoot
+\mytablecontents
+\end{longtable}
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+\RenewDocumentCommand\drawroots{mm}%
+{%
+\begin{tikzpicture}[baseline=-.5]
+\begin{rootSystem}{#1}
+\roots
+\parabolic{#2}
+\end{rootSystem}
+\end{tikzpicture}
+}%
+
+\RenewDocumentCommand\csdrawroots{mm}%
+{%
+\texttt{\detokenize{\begin{tikzpicture}[baseline=-.5]}}%
+\par\noindent%
+\texttt{\detokenize{\begin{rootSystem}}\{#1\}}%
+\par\noindent%
+\texttt{\detokenize{\roots}}%
+\par\noindent%
+\texttt{\detokenize{\parabolic}\{#2\}}%
+\par\noindent%
+\texttt{\detokenize{\end{rootSystem}}}%
+\par\noindent%
+\texttt{\detokenize{\end{tikzpicture}}}%
+}%
+
+\renewcommand*\mytablecontents{}
+\foreach \i in {A,B,C,G}{
+	\foreach \j in {1,2,3}{
+	    \xappto\mytablecontents{$\i_{2,\j}$ & \drawroots{\i}{\j} & \csdrawroots{\i}{\j}
+	}
+  \gappto\mytablecontents{\\ \\}
+}
+}
+
+\begin{longtable}{rcm{8cm}}
+\caption{Parabolic subgroups}\\
+\endfirsthead
+\caption{\dots continued}\\
+\endhead
+\multicolumn{3}{c}{continued \dots}\\
+\endfoot
+\endlastfoot
+\mytablecontents
+\end{longtable}
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+\RenewDocumentCommand\drawroots{mm}%
+{%
+\begin{tikzpicture}[baseline=-.5]
+\begin{rootSystem}{#1}
+\roots
+\parabolic{#2}
+\parabolicgrading
+\end{rootSystem}
+\end{tikzpicture}
+}%
+
+\RenewDocumentCommand\csdrawroots{mm}%
+{%
+\texttt{\detokenize{\begin{tikzpicture}[baseline=-.5]}}%
+\par\noindent%
+\texttt{\detokenize{\begin{rootSystem}}\{#1\}}%
+\par\noindent%
+\texttt{\detokenize{\roots}}%
+\par\noindent%
+\texttt{\detokenize{\parabolic}\{#2\}}%
+\par\noindent%
+\texttt{\detokenize{\parabolicgrading}}%
+\par\noindent%
+\texttt{\detokenize{\end{rootSystem}}}%
+\par\noindent%
+\texttt{\detokenize{\end{tikzpicture}}}%
+}%
+
+\renewcommand*\mytablecontents{}
+\foreach \i in {A,B,C,G}{
+	\foreach \j in {1,2,3}{
+	    \xappto\mytablecontents{$\i_{2,\j}$ & \drawroots{\i}{\j} & \csdrawroots{\i}{\j}
+	}
+  \gappto\mytablecontents{\\ \\}
+}
+}
+
+\begin{longtable}{rcm{8cm}}
+\caption{Parabolic subgroups with grading of the positive roots}\\
+\endfirsthead
+\caption{\dots continued}\\
+\endhead
+\multicolumn{3}{c}{continued \dots}\\
+\endfoot
+\endlastfoot
+\mytablecontents
+\end{longtable}
+
+
+
+
+
+\section{Examples of weights of various representations}
+
+Henceforth assume \verb!\AutoSizeWeightLatticetrue! (the default).
+
+\AutoSizeWeightLatticetrue
+
+
+\begin{tcblisting}{title={Fulton and Harris, p. 186}}
+\begin{tikzpicture}
+\begin{rootSystem}{A}
+\foreach \x/\y/\m in 
+{0/ 1/5,  -1/0/5,  1/-1/5,  2/ 0/4, -2/ 2/4,  0/-2/4, 
+ 1/ 2/2,  -1/3/2,  3/-2/2,  2/-3/2, -2/-1/2, -3/ 1/2,
+ 4/-1/1,   3/1/1, -3/ 4/1, -4/ 3/1, -1/-3/1,  1/-4/1}
+{\wt[multiplicity=\m]{\x}{\y}}
+\end{rootSystem}
+\end{tikzpicture}
+\end{tcblisting}
+
+
+\begin{tcblisting}{title={A representation of \(G_2\)}}
+\setlength\weightLength{1cm}
+\begin{tikzpicture}
+\begin{rootSystem}{G}
+\roots
+\foreach \m/\x/\y in {
+1/1/1, 1/4/-1, 1/-1/2, 2/2/0, 1/5/-2,
+2/0/1, 2/3/-1, 2/-2/2, 4/1/0, 1/-4/3,
+2/4/-2, 4/-1/1, 4/2/-1,  2/-3/2, 1/5/-3,
+4/0/0, 1/-5/3, 2/3/-2, 4/-2/1, 4/1/-1,
+2/-4/2, 1/4/-3, 4/-1/0, 2/2/-2, 2/-3/1, 
+2/0/-1, 1/-5/2, 2/-2/0, 1/1/-2, 1/-4/1,
+1/-1/-1}{\wt[multiplicity=\m]{\x}{\y}}
+\positiveRootHyperplane
+\WeylChamber
+\end{rootSystem}
+\end{tikzpicture}
+\end{tcblisting}
+
+
+\begin{tcblisting}{title={Dimensions of representations of \(G_2\), parameterized by highest weight}}
+\setlength\weightLength{1cm}
+\begin{tikzpicture}
+\begin{rootSystem}{G}
+\roots
+\foreach \x/\y/\d in {
+0/1/14, 0/2/77, 0/3/273, 1/0/7, 1/1/64,
+1/2/286, 2/0/27, 2/1/189, 2/2/729, 3/0/77,
+4/0/182, 5/0/318, 6/0/714, 3/1/448, 4/1/924}
+{\wt{\x}{\y}\node[black,above] at \weight{\x}{\y} {\(\d\)};}
+\positiveRootHyperplane
+\WeylChamber
+\end{rootSystem}
+\end{tikzpicture}
+\end{tcblisting}
+
+
+\bibliographystyle{amsplain}
+\bibliography{rank-2-roots}
+
+\end{document}