\documentclass[a4paper]{article}
% \usepackage{times}
\usepackage{easytitle}%
\usepackage{easymat}%

\let\package\texttt % so \package{foo} comes out in \tt
\let\envname\textsf % so \envname{foo} comes out as \sf

\newbox\tempbox

\def\BOX{%
    \setbox\tempbox\hbox\bgroup
    \begin{minipage}{0.9\textwidth}
}
\def\endBOX{%
    \end{minipage}
    \egroup
    \par\bigskip
    \begin{center}
        \fboxsep=10pt\fbox{\box\tempbox}
    \end{center}
    \bigskip\par
}

\title{The package \package{easymat}}
\author[E. Bertolazzi]{Enrico Bertolazzi}
\address{
  Laboratorio di Matematica Applicata e Meccanica Computazionale\\
  Dipartimento di Ingegneria Meccanica e Strutturale\\
  Universit\`a degli Studi di Trento\\
  Mesiano, Trento, Italy}

\mailto{enrico.bertolazzi@ing.unitn.it}

\begin{document}
\maketitle
\begin{abstract}
The \package{easymat} package is 
a macro package for writing block matrices, with equal column widths 
or equal rows heights or both, with various
kinds of rules~(lines) between rows and columns. It
uses an array/ta\-bular-like syntax. 
\end{abstract}

\tableofcontents

\vfill

{\bfseries Important} The package \package{easymat} was improved a lot
between version 0.1 to version 0.2. Unfortunately, due to some technical
choice, matrices written for version 0.2 are incompatible
(because of few modification) with matrices written for version 
0.1. If you prefer the old style you can find \verb+easymat.sty+ in the
directory \verb+``old''+. 

\newpage


\section{Some examples with \package{easymat}}
Load the package in the usual way:
\begin{BOX}
\begin{verbatim}
   \documentclass{article}
   .
   .
   \usepackage[thinlines,thiklines]{easymat}
   .
   .
\end{verbatim}
\end{BOX}
The options \texttt{thinlines}, and \texttt{thiklines} are self explanatory.
\package{easymat} provides the \envname{MAT}~environment which is a
simple re-implementation of the
array/tabular environment, with some limitation and some additional features.
The syntax is
\begin{BOX}
\begin{verbatim}
   \begin{MAT}`(eq)'`[ex]'`{cc...c}'
      a & b & ... & n \\
   .
   \end{MAT}
   
   or 
   
   \begin{MAT}`(eq,mx,my)'`[ex,MX,MY]'`{cc...c}'
      a & b & ... & n \\
   .
   \end{MAT}
\end{verbatim}
\end{BOX}
\begin{itemize}
\item \verb+(eq)+ or \verb+(eq,mx,my)+. By \verb+eq+ you can balance the rows or
the column or both, as shown in this table:
\begin{center}
\textbf{Table 1.} \\[1em]
\begin{tabular}{|l|l|}
\hline
value of $x$ & effect \\
\hline
\verb+@+ & no balancing \\
\verb+r+ & equal rows heights \\
\verb+c+ & equal column widths  \\
\verb+b+ & equal rows heights and equal column widths \\
\verb+e+ & equal rows heights and column widths \\
\hline
\end{tabular}
\end{center}
By \verb+mx+ and \verb+my+ you can modify the minimum size of the box in the 
MAT environment. This must be a valid measure e.g. 2pt.
This is  useful in writing matrices an vectors.

\item \verb+[ex]+ or \verb+[ex,MX,MY]+. By ``\verb+ex+'' you can specify
the amount of extra space around the item 
in the \envname{MAT} environment. The default is \verb+2pt+.
By \verb+MX+ and \verb+MY+ you can modify the minimum size of the whole 
table in the \envname{TAB} environment. This must be a valid measure e.g.10cm.

\item The \verb+`{cc...c}'+ is the definition of the columns
and their alignment. The possible alignment for
the columns are:
\begin{center}
\textbf{Table 2.} \\[1em]
\begin{tabular}{|l|l|}
\hline
\verb+c+ & centering \\
\verb+l+ & flush left \\
\verb+r+ & flush right \\
\hline
\end{tabular}
\end{center}
\end{itemize}
\textbf{IMPORTANT:} The package can manage matrices with a maximum 
of $30$ rows by $30$ columns.

It is possible to produce rules between columns or rows as this 
example shows:
\begin{BOX}
\begin{verbatim}
\[ \begin{MAT}(b){|l:cr|}
     \first-
     \aligntop
     1 & 1 & 1 \\;
     1 & \frac{111}{222} & 1 \\
     \alignbottom
     1 & 1 & 1 \\-
   \end{MAT}
   \qquad
   \begin{MAT}(b){|r:cl|}
     \first-
     \alignbottom
     1 & 1 & 1 \\;
     1 & \frac{111}{222} & 1 \\
     \aligntop
     1 & 1 & 1 \\-
   \end{MAT}
\]
\end{verbatim}
\[ \begin{MAT}(b){|l:cr|}
     \first-
     \aligntop
     1 & 1 & 1 \\;
     1 & \frac{111}{222} & 1 \\
     \alignbottom
     1 & 1 & 1 \\-
   \end{MAT}
   \qquad
   \begin{MAT}(b){|r:cl|}
     \first-
     \alignbottom
     1 & 1 & 1 \\;
     1 & \frac{111}{222} & 1 \\
     \aligntop
     1 & 1 & 1 \\-
   \end{MAT}
\]
\end{BOX}
The command \verb+\first+ is used to produce the first top rule. The 
various separation rules are defined by a character code immediately 
after the command \verb+\\+.
The available rules for the rows and columns are
\begin{center}
\textbf{Table 3.} \\[1em]
\begin{tabular}{|l|l|}
\hline
nothing  & no rule \\
\verb+|+ & solid line (or \verb+-+ for the rows) \\
\verb+:+ & dash line \\
\verb+;+ & dot-dash line \\
\verb+.+ & dotted line \\
\verb+0+ & solid line with size $1/5$ of normal line \\
\verb+1+ & solid line with size $1/4$ of normal line \\
\verb+2+ & solid line with size $1/3$ of normal line \\
\verb+3+ & solid line with size $1/2$ of normal line \\
\verb+4+ & equivalent to \verb+|+ \\
\verb+5+ & solid line with size $2$ times of normal line \\
\verb+6+ & solid line with size $3$ times of normal line \\
\verb+7+ & solid line with size $4$ times of normal line \\
\verb+8+ & solid line with size $5$ times of normal line \\
\verb+9+ & solid line with size $6$ times of normal line \\
\hline
\end{tabular}
\end{center}

\textbf{IMPORTANT:} each row \textbf{must} be ended by a \verb+\\+ 
unless an error is produced.

The main feature of the \envname{MAT}~environment
is that it is reentrant as shown it the following:
\begin{BOX}
\begin{verbatim}
\[ \begin{MAT}{0c.c9}
     \first-
     1 & 2 \\. 3 &
     \begin{MAT}{c:c}
          a & b \\.
          c & d \\
     \end{MAT} \\-
   \end{MAT}
\]
\end{verbatim}
\[ \begin{MAT}{0c.c9}
     \first-
     1 & 2 \\. 3 &
     \begin{MAT}{c:c}
          a & b \\.
          c & d \\
     \end{MAT} \\-
   \end{MAT}
\]
\end{BOX}

\textbf{IMPORTANT:} The package can manage a reentrance of a maximum 
of $8$ levels.


\section{Some example with balancing}
Here it is showed the effect of various balancing:
\begin{BOX}
\begin{verbatim}
\[
   \begin{MAT}{|c|c|c|}
       \first-
       1 & 22 & 333 \\-
       \frac{1}{2} & 1 & 1 \\-
       \frac{1}{\frac{1}{2}} & 1 & 1 \\-
   \end{MAT}
   \quad
   \begin{MAT}(r){|c|c|c|}
       \first-
       1 & 22 & 333 \\-
       \frac{1}{2} & 1 & 1 \\-
       \frac{1}{\frac{1}{2}} & 1 & 1 \\-
   \end{MAT}
   \quad
   \begin{MAT}(c){|c|c|c|}
       \first-
       1 & 22 & 333 \\-
       \frac{1}{2} & 1 & 1 \\-
       \frac{1}{\frac{1}{2}} & 1 & 1 \\-
   \end{MAT}
\]
\[
   \begin{MAT}(b){|c|c|c|}
       \first-
       1 & 22 & 333 \\-
       \frac{1}{2} & 1 & 1 \\-
       \frac{1}{\frac{1}{2}} & 1 & 1 \\-
   \end{MAT}
   \quad
   \begin{MAT}(e){|c|c|c|}
       \first-
       1 & 22 & 333 \\-
       \frac{1}{2} & 1 & 1 \\-
       \frac{1}{\frac{1}{2}} & 1 & 1 \\-
   \end{MAT}
\]
\end{verbatim}
\end{BOX}
which produce:
\begin{BOX}
\[
   \begin{MAT}{|c|c|c|}
       \first-
       1 & 22 & 333 \\-
       \frac{1}{2} & 1 & 1 \\-
       \frac{1}{\frac{1}{2}} & 1 & 1 \\-
   \end{MAT}
   \quad
   \begin{MAT}(r){|c|c|c|}
       \first-
       1 & 22 & 333 \\-
       \frac{1}{2} & 1 & 1 \\-
       \frac{1}{\frac{1}{2}} & 1 & 1 \\-
   \end{MAT}
   \quad
   \begin{MAT}(c){|c|c|c|}
       \first-
       1 & 22 & 333 \\-
       \frac{1}{2} & 1 & 1 \\-
       \frac{1}{\frac{1}{2}} & 1 & 1 \\-
   \end{MAT}
\]
\[
   \begin{MAT}(b){|c|c|c|}
       \first-
       1 & 22 & 333 \\-
       \frac{1}{2} & 1 & 1 \\-
       \frac{1}{\frac{1}{2}} & 1 & 1 \\-
   \end{MAT}
   \quad
   \begin{MAT}(e){|c|c|c|}
       \first-
       1 & 22 & 333 \\-
       \frac{1}{2} & 1 & 1 \\-
       \frac{1}{\frac{1}{2}} & 1 & 1 \\-
   \end{MAT}
\]
\end{BOX}


\section{An example with minimal size setting}
It is possible to specify the minimal size of the item inside a ``MAT''
environment, as shown here
\begin{BOX}
\begin{verbatim}
   \[ \left[
     \begin{MAT}(@,50pt,20pt){c.c}
         1 & 22 \\.
         \frac{1}{2} & 1 \\
     \end{MAT}
   \right] \]
\end{verbatim}
   \[ \left[
     \begin{MAT}(@,50pt,20pt){c.c}
         1 & 22 \\.
         \frac{1}{2} & 1 \\
     \end{MAT}
   \right] \]
\end{BOX}

It is possible to specify the total minimal size of a \envname{MAT}
environment, as shown here
\begin{BOX}
\begin{verbatim}
   \[ \left[
     \begin{MAT}(e)[2pt,3cm,3cm]{c.c}
        1 & 22 \\.
        \frac{1}{2} & 1 \\
     \end{MAT}
   \right] \times \left[
     \begin{MAT}(e)[2pt,0pt,3cm]{c}
          x \\. y \\
     \end{MAT}
   \right] = \left[
     \begin{MAT}(e)[2pt,1cm,3cm]{c}
          2 \\. \frac{3}{2} \\
     \end{MAT}
   \right] \]
\end{verbatim}
   \[ \left[
     \begin{MAT}(e)[2pt,3cm,3cm]{c.c}
        1 & 22 \\.
        \frac{1}{2} & 1 \\
     \end{MAT}
   \right] \times \left[
     \begin{MAT}(e)[2pt,0pt,3cm]{c}
          x \\. y \\
     \end{MAT}
   \right] = \left[
     \begin{MAT}(e)[2pt,1cm,3cm]{c}
          2 \\. \frac{3}{2} \\
     \end{MAT}
   \right] \]
\end{BOX}


\section{An example with various size rules}
This example shows the use of various size rule in \envname{MAT} 
environment:
\begin{BOX}
\begin{verbatim}
\[ \begin{MAT}(e,10pt,10pt){0c1c2c3c4c5c6c7c8c9}
   \first0
   * & * & * & * & * & * & * & * & * \\1
   * & * & * & * & * & * & * & * & * \\2
   * & * & * & * & * & * & * & * & * \\3
   * & * & * & * & * & * & * & * & * \\4
   * & * & * & * & * & * & * & * & * \\5
   * & * & * & * & * & * & * & * & * \\6
   * & * & * & * & * & * & * & * & * \\7
   * & * & * & * & * & * & * & * & * \\8
   * & * & * & * & * & * & * & * & * \\9 \end{MAT} \]
\end{BOX}
\end{verbatim}
\[ \begin{MAT}(e,10pt,10pt){0c1c2c3c4c5c6c7c8c9}
   \first0
   * & * & * & * & * & * & * & * & * \\1
   * & * & * & * & * & * & * & * & * \\2
   * & * & * & * & * & * & * & * & * \\3
   * & * & * & * & * & * & * & * & * \\4
   * & * & * & * & * & * & * & * & * \\5
   * & * & * & * & * & * & * & * & * \\6
   * & * & * & * & * & * & * & * & * \\7
   * & * & * & * & * & * & * & * & * \\8
   * & * & * & * & * & * & * & * & * \\9 \end{MAT} \]
\end{BOX}

\section{The \texttt{\char`\\addpath} command}
Is is possible to add paths to the ``MAT'' environment. The sintax 
is the following
\begin{verbatim}
   \begin{MAT} ...... {...}
      ...... \\
      ...... \\
      ...... \\
      \addpath{(`x',`y',`rule')`path'}
      .
      .
      \addpath{(`x',`y',`rule')`path'}
   \end{MAT}
\end{verbatim}
where
\begin{itemize}
   \item \verb+x+ and \verb+y+ are the integer coordinate of the 
   starting corner. The left down corner is at coordinate $x=0$, $y=0$.
   \item \verb+rule+ is the code of a valud rule as described in
   table 3.
   \item \verb+path+ is a string describing the path. Each letter of 
   the string is a movement coded as follows:
\begin{center}
\textbf{Table 4.} \\[1em]
\begin{tabular}{|l|l|}
\hline
letter & direction \\
\hline
\verb+l+ & left movement and drawing \\
\verb+r+ & right movement and drawing \\
\verb+u+ & up movement and drawing \\
\verb+d+ & down movement and drawing \\
\hline
\end{tabular}
\end{center}
\end{itemize}
The following example shows the use of \verb+\addpath+,
\begin{BOX}
\begin{verbatim}
\[ \begin{MAT}[5pt]{|ccccc|}
      \first-
      * & * & * & * & * \\
      * & * & * & * & * \\
      * & * & * & * & * \\
      * & * & * & * & *
      \addpath{(1,1,0)ruld}
      \addpath{(4,3,;)lldrrdll} \\-
   \end{MAT} \]
\end{verbatim}
\[ \begin{MAT}[5pt]{|ccccc|}
      \first-
      * & * & * & * & * \\
      * & * & * & * & * \\
      * & * & * & * & * \\
      * & * & * & * & *
      \addpath{(1,1,0)ruld}
      \addpath{(4,3,;)lldrrdll} \\-
   \end{MAT} \]
\end{BOX}
\textbf{IMPORTANT:} The commands \verb+\addpath+ can be putted anymere 
\textbf{before} the last \verb+\\+ command.

This is another example
\begin{BOX}
\begin{verbatim}
\[ \left(\begin{MAT}[5pt]{cccccc}
      1 & *  & *   & *    & *     & * \\
      0 & 11 & *   & *    & *     & * \\
      0 & 0  & 111 & *    & *     & * \\
      0 & 0  & 0   & 1111 & *     & * \\
      0 & 0  & 0   & 0    & 11111 & * \\
      0 & 0  & 0   & 0    & 0     & 11111
      \addpath{(0,5,.)rdrdrdrdrd} \\
   \end{MAT}\right) \]
\end{verbatim}
\[ \left(\begin{MAT}[5pt]{cccccc}
      1 & *  & *   & *    & *     & * \\
      0 & 11 & *   & *    & *     & * \\
      0 & 0  & 111 & *    & *     & * \\
      0 & 0  & 0   & 1111 & *     & * \\
      0 & 0  & 0   & 0    & 11111 & * \\
      0 & 0  & 0   & 0    & 0     & 11111
      \addpath{(0,5,.)rdrdrdrdrd} \\
   \end{MAT}\right) \]
\end{BOX}


\section{An example with reentrance}
This final example shows a slightly more complex (reentrant)
definition in 
which the \envname{MAT}~environment is used:
\begin{BOX}
\begin{verbatim}
\def\rec(#1){\expandafter\recurse#1-\end}
\def\recurse#1#2\end{%
 \if\noexpand#1-\def\next##1##2{}%
 \else\let\next=\recursea\fi%
 \expandafter\next{#1}{#2}%
}%
\def\recursea#1#2{%
  \bgroup
    \begin{MAT}[0pt]{l:c:r}
       \aligntop
       \rec(#2) &      #1  & \rec(#2) \\;
             #1 & \rec(#2) & #1       \\;
       \alignbottom
       \rec(#2) &      #1  & \rec(#2) \\
    \end{MAT}
  \egroup
}
\[ \recurse\clubsuit\diamondsuit\heartsuit\end \]
\end{verbatim}
\end{BOX}
It produces the following output:
\typeout{This example can take a while to compile on small machine, please wait...}
\def\rec(#1){\expandafter\recurse#1-\end}
\def\recurse#1#2\end{%
 \if\noexpand#1-\def\next##1##2{}%
 \else\let\next=\recursea\fi%
 \expandafter\next{#1}{#2}%
}%
\def\recursea#1#2{%
  \bgroup
    \begin{MAT}[0pt]{l:c:r}
       \aligntop
       \rec(#2) &      #1  & \rec(#2) \\;
             #1 & \rec(#2) & #1       \\;
       \alignbottom
       \rec(#2) &      #1  & \rec(#2) \\
    \end{MAT}
  \egroup
}
\small
\[ \recurse\clubsuit\diamondsuit\heartsuit\end \]
\typeout{...thanks, I have done}

\end{document}