Using multirow with smallmatrix

Question

I'd like to typeset a bunch of small 3x3 matrices to describe generators of certain ideals, as in this paper, p7.

Using smallmatrix works beautifully as long as I only want circles and bullets, but when I try to use multirow to merge cells and put a square across four entries of the matrix, it simply doesn't work. It works in the standard matrix or array environments, but they're far too large for what I need.

I've also tried How to model {smallmatrix} with {array}? but the squares get shrunk and it doesn't quite look right. Since I don't really understand the code in that thread, I don't know how to edit it to make it do what I want. I think it would be fine if I could make the squares a bit bigger.

Here is the code that hopefully illustrates what I'm trying to do. The smallarray environment comes directly from the thread I linked to above.

\documentclass{article}

\usepackage{amssymb}
\usepackage{amsmath}
\usepackage{multirow}


\newcommand{\ZZ}{\multicolumn{2}{c}{\multirow{2}{*}{$\square$}}}

\newenvironment{smallarray}[1]
 {\null\,\vcenter\bgroup\scriptsize
  \renewcommand{\arraystretch}{0.7}%
  \arraycolsep=.13885em
  \hbox\bgroup$\array{@{}#1@{}}}
 {\endarray$\egroup\egroup\,\null}


\begin{document}
When there's no cells to merge, both smallmatrix (left) and smallarray (right) work fine.
\begin{equation}
 \begin{smallmatrix}
   \circ & \circ & \bullet \\
   \circ  & \circ &\bullet \\
   \circ & \circ & \circ  
 \end{smallmatrix}
\qquad
\begin{smallarray}{ccc}
   \circ & \circ & \bullet \\
   \circ  & \circ &\bullet \\
   \circ & \circ & \circ  
  \end{smallarray}
\end{equation}
But when we try to merge some cells...
\begin{equation}
 \begin{smallmatrix}
   \circ & \ZZ \\
   \circ &  &  \\
   \circ & \circ & \circ  
 \end{smallmatrix}
\qquad
\begin{smallarray}{ccc}
   \circ & \ZZ \\
   \circ  & & \\
   \circ & \circ & \circ  
  \end{smallarray}
\end{equation}
...smallmatrix just doesn't work.  The second one is almost right and I'd happily just use that, but I also need a matrix of this form:
\[\begin{smallarray}{ccc}
   \circ & \ZZ \\
   \ZZ  &\\
    &  & \circ  
  \end{smallarray}
\]

and that's really not quite right.


\end{document}

Any hints or suggestions would be appreciated.

Answer 1

One option using TikZ and a matrix of math nodes:

\documentclass{article}
\usepackage{amssymb}
\usepackage{amsmath}
\usepackage{tikz}
\usetikzlibrary{matrix,calc}

\newenvironment{smallarray}[1]
  {\gdef\MatName{#1}\begin{tikzpicture}
    \matrix[
    matrix of math nodes,
    row sep=-\pgflinewidth,
    column sep=-\pgflinewidth,
    nodes={inner sep=1pt,rectangle,text width=2mm,align=center},
    text depth=0mm,
    text height=2mm,
    nodes in empty cells
    ]  (#1)}
  {\end{tikzpicture}}
\def\MyZ(#1,#2){%
  \draw ([xshift=-3.6pt,yshift=3.6pt] $ (\MatName-#1-#2)!0.5!(\MatName-\the\numexpr#1+1\relax-\the\numexpr#2+1\relax) $ ) rectangle ([xshift=3.6pt,yshift=-3.6pt] $ (\MatName-#1-#2)!0.5!(\MatName-\the\numexpr#1+1\relax-\the\numexpr#2+1\relax) $ );
}

\begin{document}

\begin{smallarray}{mat1}
{
\circ & \circ & \circ \\
\circ & \circ & \circ \\
\circ & \circ & \circ \\
};
\end{smallarray}
\begin{smallarray}{mat2}
{
\circ & \circ & \bullet \\
\circ & \circ & \bullet \\
\circ & \circ & \circ \\
};
\end{smallarray}

\begin{smallarray}{mat3}
{
\circ & & \\
\circ & & \\
\circ & \circ & \circ \\
};
\MyZ(1,2)
\end{smallarray}
\begin{smallarray}{mat4}
{
\circ & & \\
 & & \\
 & & \circ \\
};
\MyZ(1,2)
\MyZ(2,1)
\end{smallarray}

\end{document}

The smallarray environment has one mandatory argument that will be used as the name of the matrix; the second matrix in the image was produced with:

\begin{smallarray}{mat2}
{
\circ & \circ & \bullet \\
\circ & \circ & \bullet \\
\circ & \circ & \circ \\
};
\end{smallarray}

\MyZ allows to draw the squares; the syntax is

\MyZ(x,y)

where x,y is the entry of the upper left corner of the square.