[Tex/LaTex] the best way to typeset spectral sequences

diagramsmath-mode

While writing articles about algebraic topology, I have had to typeset spectral sequences. These are tools for calculating homology and cohomology. Examples appear on page 10 of this book by Hatcher.

So far I've typeset these using xypic, but I'm not completely satisfied with this. It doesn't produce the best-looking spectral sequences, I have difficulty creating arrows leaving or entering the visible part of the page and I haven't figured out yet how to shade the background in a checkerboard style (or any other style), which is sometimes useful if your page contains many zeroes. An alternative is Tilman Bauer's package, but I don't really like the "turtle"-approach, moving a cursor between entries and dropping characters.

My questions are: Are there other methods for typesetting spectral sequences? What is, in your opinion, the "best" one? Do you have any tips for typesetting spectral sequences?

Best Answer

As long as there's no good package specialized in spectral sequences I would use

TikZ with its nodes and arrows,
its matrix library and a matrix of math nodes,
also shapes and colors are no problem with TikZ.

Here's a very simple demo example which you could extend:

\documentclass{article}
\usepackage{tikz}
\usepackage{dsfont}
\usetikzlibrary{matrix}
\newcommand*\Z{\mathds{Z}}
\newcommand*\ZZ{|[draw,circle]| \Z_2}
\begin{document}
\begin{tikzpicture}
  \matrix (m) [matrix of math nodes,
    nodes in empty cells,nodes={minimum width=5ex,
    minimum height=5ex,outer sep=-5pt},
    column sep=1ex,row sep=1ex]{
                &      &     &     & \\
          1     &  \ZZ &  0  & \ZZ & \\
          0     &  \Z  & \ZZ &  0  & \\
    \quad\strut &   0  &  1  &  2  & \strut \\};
  \draw[-stealth] (m-3-3.north west) -- (m-2-2.south east);
\draw[thick] (m-1-1.east) -- (m-4-1.east) ;
\draw[thick] (m-4-1.north) -- (m-4-5.north) ;
\end{tikzpicture}
\end{document}

Output:

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enter image description here

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Best Answer

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