Creating beautiful Hasse diagrams with little effort
The Hasse diagram of a partially ordered set (poset) is an extremely useful graph to help understand the poset. It is also a pain in the keister to create them in \(\LaTeX\) using Tikz. Here’s how to do it painlessly using Sage.
Prerequisites
First, make sure that you have graphviz and dot2tex installed. (Thanks to this ask.sagemath post for pointing this out.)
You can do this by calling
sage --pip install graphviz
sage --pip install dot2tex
in your terminal.
Making the diagram
First, create your poset in Sage. For example
sage: P = posets.SetPartitions(4)
Of course, you could also make your own custom poset, but that is well-documented, so I won’t rehash that.
Now, calling view(P) will create a PDF of the Hasse diagram. For me, it automatically opens in my system viewer. I hope it does the same for you. From there I could “save-as” to put the PDF where I want it. I know I could probably choose a custom path yada yada yada… but my file-saving GUI is nice so I use it. If it looks funky and curvy, double check that you installed graphviz and dot2tex. Sometimes, a PDF is enough, and you can include it into your \(\LaTeX\) document using \includegraphics.
Getting the code
Sometimes, you might want to customize the image to call attention to a specific element (for me, I’d do this when localizing at a specific flat in a matroid). To get the Tikz code
that create the beautiful PDF, just run view(P, debug=True).
Edit: 3/20/24 It turns out to be easier to import the _latex_file_ function after running from sage.misc.latex import _latex_file_. Still set debug=True.
This will give you a long output. But the top part is what matters. Heres what I get
sage: view(P, debug=True)
\documentclass{article}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{amsfonts}
\usepackage{graphicx}
\usepackage{mathrsfs}
\pagestyle{empty}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\oddsidemargin 0.0in
\evensidemargin 0.0in
\textwidth 6.45in
\topmargin 0.0in
\headheight 0.0in
\headsep 0.0in
\textheight 9.0in
\usepackage{tikz}
\usepackage{tkz-graph}
\usepackage{tkz-berge}
\usetikzlibrary{arrows,shapes}
\newcommand{\ZZ}{\Bold{Z}}
\newcommand{\NN}{\Bold{N}}
\newcommand{\RR}{\Bold{R}}
\newcommand{\CC}{\Bold{C}}
\newcommand{\QQ}{\Bold{Q}}
\newcommand{\QQbar}{\overline{\QQ}}
\newcommand{\GF}[1]{\Bold{F}_{#1}}
\newcommand{\Zp}[1]{\Bold{Z}_{#1}}
\newcommand{\Qp}[1]{\Bold{Q}_{#1}}
\newcommand{\Zmod}[1]{\ZZ/#1\ZZ}
\newcommand{\CDF}{\Bold{C}}
\newcommand{\CIF}{\Bold{C}}
\newcommand{\CLF}{\Bold{C}}
\newcommand{\RDF}{\Bold{R}}
\newcommand{\RIF}{\Bold{I} \Bold{R}}
\newcommand{\RLF}{\Bold{R}}
\newcommand{\SL}{\mathrm{SL}}
\newcommand{\PSL}{\mathrm{PSL}}
\newcommand{\Bold}[1]{\mathbf{#1}}
\usepackage[tightpage,active]{preview}
\PreviewEnvironment{page}
\begin{document}\begin{page}$\begin{tikzpicture}[>=latex,line join=bevel,]
%%
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\node (node_12) at (485.0bp,114.5bp) [draw,draw=none] {$\{\{1, 3, 4\}, \{2\}\}$};
\node (node_8) at (133.0bp,114.5bp) [draw,draw=none] {$\{\{1, 2, 3\}, \{4\}\}$};
\node (node_13) at (397.0bp,114.5bp) [draw,draw=none] {$\{\{1, 4\}, \{2, 3\}\}$};
\node (node_9) at (573.0bp,114.5bp) [draw,draw=none] {$\{\{1, 3\}, \{2, 4\}\}$};
\node (node_11) at (309.0bp,114.5bp) [draw,draw=none] {$\{\{1, 2, 4\}, \{3\}\}$};
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\draw [black,->] (node_10) ..controls (422.28bp,76.666bp) and (414.64bp,87.79bp) .. (node_13);
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%
\end{tikzpicture}$\end{page}
\end{document}
['pdflatex', '\\nonstopmode', '\\input{sage.tex}']
This is pdfTeX, Version 3.141592653-2.6-1.40.25 (TeX Live 2023) (preloaded format=pdflatex)
restricted \write18 enabled.
entering extended mode
LaTeX2e <2022-11-01> patch level 1
...
(see the transcript file for additional information)</usr/local/texlive/2023/te
xmf-dist/fonts/type1/public/amsfonts/cm/cmmi10.pfb></usr/local/texlive/2023/tex
mf-dist/fonts/type1/public/amsfonts/cm/cmr10.pfb></usr/local/texlive/2023/texmf
-dist/fonts/type1/public/amsfonts/cm/cmsy10.pfb>
Output written on sage.pdf (1 page, 29017 bytes).
Transcript written on sage.log.
viewer: "open"
The ... eight lines from the bottom represents over a hundred lines of output. Don’t worry about those to get your Tikz output. All you need is
\begin{tikzpicture}[>=latex,line join=bevel,]
%%
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\node (node_5) at (40.0bp,61.5bp) [draw,draw=none] {$\{\{1, 2\}, \{3\}, \{4\}\}$};
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\node (node_10) at (432.0bp,61.5bp) [draw,draw=none] {$\{\{1, 4\}, \{2\}, \{3\}\}$};
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\node (node_6) at (45.0bp,114.5bp) [draw,draw=none] {$\{\{1, 2\}, \{3, 4\}\}$};
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\node (node_9) at (573.0bp,114.5bp) [draw,draw=none] {$\{\{1, 3\}, \{2, 4\}\}$};
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\node (node_14) at (309.0bp,167.5bp) [draw,draw=none] {$\{\{1, 2, 3, 4\}\}$};
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%
\end{tikzpicture}
Thats it. Thats the post.