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-rw-r--r--Master/texmf-dist/doc/latex/lie-hasse/README4
-rw-r--r--Master/texmf-dist/doc/latex/lie-hasse/lie-hasse.pdfbin573306 -> 631928 bytes
-rw-r--r--Master/texmf-dist/doc/latex/lie-hasse/lie-hasse.tex123
3 files changed, 66 insertions, 61 deletions
diff --git a/Master/texmf-dist/doc/latex/lie-hasse/README b/Master/texmf-dist/doc/latex/lie-hasse/README
index e63a82cc605..1bd63c4cba2 100644
--- a/Master/texmf-dist/doc/latex/lie-hasse/README
+++ b/Master/texmf-dist/doc/latex/lie-hasse/README
@@ -2,9 +2,9 @@ ___________________________________
Lie Hasse
- v1.0
+ v1.01
- 3 February 2020
+ 9 July 2024
___________________________________
Authors : Ben McKay
diff --git a/Master/texmf-dist/doc/latex/lie-hasse/lie-hasse.pdf b/Master/texmf-dist/doc/latex/lie-hasse/lie-hasse.pdf
index 5be5791e7ff..ed444cc7d17 100644
--- a/Master/texmf-dist/doc/latex/lie-hasse/lie-hasse.pdf
+++ b/Master/texmf-dist/doc/latex/lie-hasse/lie-hasse.pdf
Binary files differ
diff --git a/Master/texmf-dist/doc/latex/lie-hasse/lie-hasse.tex b/Master/texmf-dist/doc/latex/lie-hasse/lie-hasse.tex
index 82643fee141..762639c6038 100644
--- a/Master/texmf-dist/doc/latex/lie-hasse/lie-hasse.tex
+++ b/Master/texmf-dist/doc/latex/lie-hasse/lie-hasse.tex
@@ -1,5 +1,5 @@
\documentclass{amsart}
-\title[The Lie Hasse package]{The Lie Hasse package \\ Version 1.0}
+\title[The Lie Hasse package]{The Lie Hasse package \\ Version 1.01}
%% My name:
\makeatletter
\DeclareRobustCommand{\scotsMc}{\scotsMcx{c}}
@@ -19,8 +19,7 @@
\author{\authorsname}
\address{School of Mathematical Sciences, University College Cork, Cork, Ireland}
\email{b.mckay@ucc.ie}
-\date{3 February 2020}
-\usepackage{etex}
+\date{9 July 2024}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenx}
\usepackage{etoolbox}
@@ -87,7 +86,7 @@
root radius=.02cm,
edge length=.5cm,
edge quotes/.style={opacity=0}%
- ]{E}{8}%
+ ]E8%
\end{tikzpicture}%
\end{center}%
\begin{center}
@@ -106,26 +105,26 @@ This package draws the Hasse diagram of the poset of the positive simple roots o
\begin{document}
The Hasse diagram of \(F_4\) is
\begin{center}
-\hasse[edge length=1cm]{F}{4}
+\hasse F4
\end{center}
\end{document}
\end{Verbatim}
\end{tcolorbox}
\par\noindent{}The Hasse diagram of \(F_4\) is
\begin{center}
-\hasse[edge length=1cm]{F}{4}
+\hasse[edge length=1cm]F4
\end{center}
Each edge is labelled with the simple root by which vertices differ.
\begin{tcblisting}{title={Inside a \TikZ statement}}
-\(B_4\) has Dynkin diagram \tikz \dynkin[edge length=.35cm]{B}{4};, Hasse diagram
+\(B_4\) has Dynkin diagram \tikz \dynkin{B}{4};, Hasse diagram
\begin{center}
-\hasse[edge length=1cm]{B}{4}
+\hasse[edge length=1cm]B4
\end{center}
\end{tcblisting}
\begin{tcblisting}{title={Inside a Dynkin diagram environment, diagrams fit together}}
The Hasse diagram of \(B_4\) is
\begin{dynkinDiagram}[vertical shift=0,edge length=1cm]{B}{4}
-\hasse{B}{4}
+\hasse[edge length=1cm]B4
\end{dynkinDiagram}
\end{tcblisting}
We shut off the default vertical shift of the Dynkin diagram, so that it starts at the origin.
@@ -133,35 +132,26 @@ There is an option to \verb!\hasse! for this:
\begin{tcblisting}{title={Attaching the Dynkin diagram}}
The Hasse diagram of \(B_4\) is
\begin{center}
-\hasse[attach Dynkin diagram=true]{B}{4}
+\hasse[attach Dynkin diagram=true]B4
\end{center}
\end{tcblisting}
Unfortunately, attaching a Dynkin diagram looks terrible for \(D\) or \(E\) series, so a Dynkin diagram appears below.
\begin{tcblisting}{title={Attaching the Dynkin diagram}}
The Hasse diagram of \(D_5\) is
\begin{center}
-\hasse[attach Dynkin diagram=true]{D}{5}
+\hasse[attach Dynkin diagram=true]D5
\end{center}
\end{tcblisting}
\begin{tcblisting}{title={Inside a \TikZ environment}}
\begin{tikzpicture}
-\hasse{A}{4}
+\hasse A4
\draw (4;1) circle (5pt);
\draw[red] (2;3) circle (5pt);
\end{tikzpicture}
\end{tcblisting}
In this example, we see that the roots of the Hasse diagram are \TikZ{} nodes labelled \(g;i\) for grade \(g\) (i.e. \(g\) units up the page) and index \(i\) (i.e. \(i^{\text{th}}\) root of grade \(g\) drawn on the page, starting from the left).
-\section{Inherited options}
-The Lie Hasse package inherits options from the Dynkin diagrams package: the edge lengths are set with
-\begin{Verbatim}
-\tikzset{/Dynkin diagram/edge lengths=1.2cm}
-\end{Verbatim}
-and similarly the ordering of roots with
-\begin{Verbatim}
-\tikzset{/Dynkin diagram/ordering=Bourbaki}
-\end{Verbatim}
-
+\newpage
\section{Prettier}
The package includes a more elaborate \verb!\hasseDiagrams! command, taking a list of semicolon separated Dynkin diagram identfiers.
\begin{tcolorbox}[title={With some global options to make prettier diagrams}]
@@ -198,11 +188,20 @@ The package includes a more elaborate \verb!\hasseDiagrams! command, taking a li
\endgroup
Global options:
\begin{verbatim}
- edge/.style={ultra thick},
- edge quotes/.style={/Dynkin diagram/text style,auto,inner sep=2pt},
+\tikzset{/Lie Hasse,
+ edge/.style={ultra thick},
+ edge quotes/.style={
+ /Dynkin diagram/text style,
+ auto,
+ inner sep=2pt},
\end{verbatim}
allow to change the edges, and to change the way that labels are printed, and how close labels are to the edges.
-
+To give even greater control, the user can define a command \verb!\edgeQuote! of one argument, which is applied to the label placed on every edge of the Hasse diagram.
+The default is
+\begin{verbatim}
+\NewDocumentCommand\edgeQuote{m}{\contour{white}{#1}}
+\end{verbatim}
+which ensures that every label, which is black text by default, has a slight white outline to make it easier to read against a coloured background.
\section{Root order}
@@ -222,6 +221,10 @@ We can use this like:
\hasseDiagrams{[ordering=Carter]E6;[ordering=Dynkin]E6}
\hasseDiagrams{[ordering=Kac]E6}
\endgroup
+The Lie Hasse package inherits the ordering of roots from the Dynkin diagrams package, so we can set it with
+\begin{Verbatim}
+\tikzset{/Dynkin diagram/ordering=Bourbaki}
+\end{Verbatim}
\section{Graph height and width}
The \emph{height} of a Hasse diagram is the number of grades.
@@ -238,7 +241,7 @@ to store the height of \(G_2\) in a counter called \verb!\h!, and
\end{Verbatim}
to store the width of \(G_2\) at grade \(3\) in a counter called \verb!\w!.
-Once you use \verb!\dynkin{G}{2}! or \verb!\hasse{G}{2}! or the other commands, like
+Once you use \verb!\dynkin G2! or \verb!\hasse G2! or the other commands, like
\begin{Verbatim}
\rootSystemHeight[G][2]{\h}
\end{Verbatim}
@@ -260,7 +263,8 @@ The \verb!show height! option:
\hasseDiagrams{G2}
\end{Verbatim}
\tikzset{/Lie Hasse diagram,show name=true,show height=true}
-\hasseDiagrams{G2}
+\hasse G2
+
The \verb!show widths! option:
\begin{Verbatim}
\tikzset{/Lie Hasse diagram/show widths=true}
@@ -293,11 +297,11 @@ Here is the Dynkin diagram of \(E_8\), indicating the order of the roots in Cart
Here is the same Dynkin diagram, except showing, at each simple root, the coefficient of that simple root in the highest root.
\begin{Verbatim}
\rootSum[E][8]{29}{1}{\rs}
-\dynkin[labels=\rs,ordering=Carter,edge length=.35cm]{E}{8}
+\dynkin[expand labels=\rs,ordering=Carter,edge length=.35cm]{E}{8}
\end{Verbatim}
\rootSum[E][8]{29}{1}{\rs}
\begin{center}
-\dynkin[labels=\rs,ordering=Carter,edge length=.35cm]{E}{8}
+\dynkin[expand labels=\rs,ordering=Carter,edge length=.35cm]{E}{8}
\end{center}
The option \verb!for all roots! allows execution of code once on every root.
@@ -312,7 +316,7 @@ The option \verb!for all roots! allows execution of code once on every root.
root radius=.05cm
},
for all roots/.code 2 args={\drawRootAsDynkinSum{#1}{#2}}}
-\hasseDiagrams{D5}
+\hasse D5
\end{Verbatim}
\begingroup
\tikzset{/Lie Hasse diagram,
@@ -341,23 +345,23 @@ A simple example:
\end{Verbatim}
\newcommand{\foo}[2]%
{%
- \node[below,scale=.75] at (#1;#2) {\(#1,#2\)};%
+ \node[below,scale=.5] at (#1;#2) {\(#1,#2\)};%
}%
Inside a \TikZ{} or \verb!dynkinDiagram! environment:
\begin{Verbatim}
\tikzset{/Lie Hasse diagram/edge quotes/.style={opacity=0},
/Dynkin diagram/edge length=1.5cm}
\begin{tikzpicture}
- \hasse{D}{6}%
- \forAllPositiveRootsInHasseDiagram{\foo}%
+ \hasse D6%
+ \forAllPositiveRoots{\foo}%
\end{tikzpicture}
\end{Verbatim}
\begingroup
\tikzset{/Lie Hasse diagram/edge quotes/.style={opacity=0},
/Dynkin diagram/edge length=1.5cm}
\begin{tikzpicture}
- \hasse{D}{6}%
- \forAllPositiveRootsInHasseDiagram{\foo}%
+ \hasse D6%
+ \forAllPositiveRoots{\foo}%
\end{tikzpicture}
If you put this into the \verb!for all roots! option, it executes on its own:
@@ -378,19 +382,19 @@ Opposite sides of any square have the same edge label, by commutativity of addit
Hence we don't need to see every edge perfectly.
The three dimensional effect is the default:
\begin{Verbatim}
-\hasse{D}{4}\hasse{E}{6}
+\hasse D4\hasse E6
\end{Verbatim}
\begin{center}
-\hasse{D}{4}\hasse{E}{6}
+\hasse D4\hasse E6
\end{center}
We can turn it off:
\begin{Verbatim}
-\hasse[three D=false]{D}{4}
-\hasse[three D=false]{E}{6}
+\hasse[three D=false] D4
+\hasse[three D=false] E6
\end{Verbatim}
\begin{center}
-\hasse[three D=false]{D}{4}
-\hasse[three D=false]{E}{6}
+\hasse[three D=false] D4
+\hasse[three D=false] E6
\end{center}
or globally with \verb!\tikzset{/Lie Hasse diagram/three D=false}!.
@@ -430,9 +434,9 @@ You can change these:
\section{Label the simple roots}
Ringel \cite{Ringel:2013} labels his edges like
\begin{Verbatim}
-\hasseDiagrams{[labels={f,e,d,c,u,b,a}]E7}
+\hasse[labels={f,e,d,c,u,b,a}]E7
\end{Verbatim}
-\hasseDiagrams{[labels={f,e,d,c,u,b,a}]E7}
+\hasse[labels={f,e,d,c,u,b,a}]E7
\section{Parabolic subgroups}
This package offers nothing over Ringel's original pictures, except that the user can pick some simple roots whose associated edges are drawn differently.
@@ -440,47 +444,48 @@ The chosen simple roots are called \emph{compact}, following terminology from th
We let the reader explore the notation for parabolic subgroups in the Dynkin diagrams package, and use this to declare various roots compact.
\begin{Verbatim}
\tikzset{/Lie Hasse diagram,attach Dynkin diagram=true,three D=false}
-\hasseDiagrams{D{**x*x*x*}}
+\hasse D{**x*x*x*}
\end{Verbatim}
\begingroup
\tikzset{/Lie Hasse diagram,attach Dynkin diagram=true,three D=false}
-\hasseDiagrams{D{**x*x*x*}}
+\hasse D{**x*x*x*}
\endgroup
+
Our motivation comes from trying to identify the invariant vector subbundles of the tangent bundle of a rational homogeneous variety \cite{MathOverflow:123801}.
Such diagrams are often unreadable if we don't turn off the three dimensional graphics.
By default, noncompact root edges are not drawn.
\begingroup
\tikzset{/Lie Hasse diagram,attach Dynkin diagram=true,show name=false,three D=false}
\begin{Verbatim}
-\hasseDiagrams{E{*xx*x*}}
+\hasse E{*xx*x*}
\end{Verbatim}
-\hasseDiagrams{E{*xx*x*}}
+\hasse E{*xx*x*}
\begin{Verbatim}
-\hasseDiagrams{A{x*x*}}
+\hasse A{x*x*}
\end{Verbatim}
-\hasseDiagrams{A{x*x*}}
+\hasse A{x*x*}
\begin{Verbatim}
-\hasseDiagrams{[parabolic=113]B8}
+\hasse[parabolic=113]B8
\end{Verbatim}
-\hasseDiagrams{[parabolic=113]B8}
+\hasse[parabolic=113]B8
\begin{Verbatim}
-\hasseDiagrams{C{**xx*x**}}
+\hasse C{**xx*x**}
\end{Verbatim}
-\hasseDiagrams{C{**xx*x**}}
+\hasse C{**xx*x**}
\newpage
\begin{Verbatim}
-\hasseDiagrams{E{*x*x*x**}}
+\hasse E{*x*x*x**}
\end{Verbatim}
-\hasseDiagrams{E{*x*x*x**}}
+\hasse E{*x*x*x**}
\newpage
\begin{Verbatim}
-\hasseDiagrams{F{**xx}}
+\hasse F{**xx}
\end{Verbatim}
-\hasseDiagrams{F{**xx}}
+\hasse F{**xx}
\begin{Verbatim}
-\hasseDiagrams{G{*x}}
+\hasse G{*x}
\end{Verbatim}
-\hasseDiagrams{G{*x}}
+\hasse G{*x}
\endgroup
\section{Examples}