\documentclass[a4paper,twoside]{article}
\usepackage{easytitle}
\usepackage[definevectors]{easyvector}

\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{easyvector}}
\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{easyvector} package is a simple
macro package that provides a C-like syntax for writing vectors or matrices.
\end{abstract}

\tableofcontents

\newpage


\section{Some examples with \package{easyvector}}
Load the package in the usual way:
\begin{BOX}
\begin{verbatim}
   \documentclass{article}
   .
   .
   \usepackage[spacesep,definevectors]{easyvector}
   .
   .
\end{verbatim}
\end{BOX}
The package option \texttt{spacesep} means that the separator for 
the indices is \verb+\smallspace+ instead of ``$,$''~(comma).

The package option \texttt{definevectors} means that the command
\verb+\aa+\ldots\verb+\zz+ and \verb+\AA+\ldots\verb+\ZZ+
are predefined as vectors. It also define the commands
\verb+\Balpha+, \verb+\Bbeta+ and so on, as bold greek vectors.
The latex commands \verb+\aa+, \verb+\AA+, \verb+\gg+,
\verb+\l+, \verb+\ss+, \verb+\SS+\, \verb+\tt+ are saved in the 
commands \verb+\oldxx+ where \verb+xx+ is the name of
the old command.

\section{Use of the \texttt{\char`\\newvector} command}
The general syntax of \verb+\newvector+ command is
\begin{verbatim}
    \newvector[\cmda,\cmdb]{cmd}
\end{verbatim}
or 
\begin{verbatim}
    \newvector(a)[cmd]
\end{verbatim}
In the first case,
it creates the new command (macro) \verb+\cmd+ which executes
\verb+\cmda+ when in scalar mode, and \verb+\cmdb+ when in vector mode.
In the second case 
it creates a new command \verb+\cmd+ which substitutes the letter
\verb+\mathit{a}+ when in scalar, mode and \verb+\mathbf{a}+ when
in vector mode.
Scalar mode is activated when \verb+\cmd+ is immediately followed
by~$[$. In scalar mode everything between $[$~and~$]$ (with
balancing) is assumed to be indices. For example
the commands
\begin{BOX}
\begin{verbatim}
\newvector[\alpha,\beta]{W}
\newvector[X,\mathbf{X}]{X}
\[ \W = (\W[i,j]), \qquad \X = (\X[i,j;k])\]
\end{verbatim}
generate
\newvector[\alpha,\beta]{W}
\newvector[X,\mathbf{X}]{X}
\[ \W = (\W[i,j]), \qquad \X = (\X[i,j;k])\]
\end{BOX}
The structure of the $[\ldots]$ command is the following
\begin{verbatim}
   [i,j,...,k;x,y,...,z]
\end{verbatim}
where \verb+i,j,...,k+ are subscripts and
\verb+x,y,...,z+ are superscripts.
The character $,$~is used as a separator between different indices, and
the character $;$~separates subscripts and superscripts.
There are no limits on the number of indices, and the code is reentrant,
as the following example illustrates
\begin{BOX}
\begin{verbatim}
\newvector(a)[av]
\newvector(b)[bv]
\[ \av = \pmatrix{ \av[1,1] & \av[1,2] \cr
                   \av[2,1] & \av[2,2] \cr}, \qquad
   \bv = \left\{ \bv[\gamma,\bv[i,j;k];a] \right\}
\]
\end{verbatim}
produces
\newvector(a)[av]
\newvector(b)[bv]
\[ \av = \pmatrix{ \av[1,1] & \av[1,2] \cr
                   \av[2,1] & \av[2,2] \cr}, \qquad
   \bv = \left\{ \bv[\gamma,\bv[i,j;k];a] \right\}
\]
\end{BOX}

\section{Use of the \texttt! command}
In some circumstances it is useful to force vector
mode also when using indices. It is possible by using the character~\verb+!+
before~\verb+[+
\begin{BOX}
\begin{verbatim}
\newvector(z)[zzz]
\[ \zzz[1,2,3] \neq \zzz![1,2,3] \]
\end{verbatim}
produces the following output:
\newvector(z)[zzz]
\[ \zzz[1,2,3] \neq \zzz![1,2,3] \]
\end{BOX}

\section{Use of the \texttt{\char`\\newcustomvector} command}
In some circumstances the command \verb+\newcustomvector+ can be useful.
Is is essentially the \verb+\newvector+ command with an extra argument that
is a macro for manage the index part.
\begin{BOX}
\begin{verbatim}
\def\myindex[#1,#2,#3]{_{#1_{#2}}^{#3}}
\newcustomvector[\mathtt{a},\mathbf{a}]{aaa}\myindex
\[ \aaa[1,2,3], \qquad \aaa[3,2,1], \qquad \aaa \]
\end{verbatim}
produces
\def\myindex[#1,#2,#3]{_{#1_{#2}}^{#3}}
\newcustomvector[\mathtt{a},\mathbf{a}]{aaa}\myindex
\[ \aaa[1,2,3], \qquad \aaa[3,2,1], \qquad \aaa \]
\end{BOX}

\textbf{Important:} For the old user (version $< 0.6$) 
the command \verb+\customindex+ 
is suppressed and the \verb+\newcustomvector+ is used instead.

\section{The ``definevectors'' option}
This option define the following vectors for you:
\begin{BOX}
\begin{verbatim}
   \aa,\bb,...,\zz    \AA,\BB,...,\ZZ
   \Balpha, \Bbeta, ..., \Bomega
   
   example
   .
   .
   \usepackage[definevectors]{easyvector}
   .
   .
   .
   \[ \Balpha[i,j], \quad \Balpha,
      \quad \BB[i,j], \quad \BB, \]
\end{verbatim}
   \[ \Balpha[i,j], \quad \Balpha,
      \quad \BB[i,j], \quad \BB, \]
\end{BOX}


\section{The ``@'' convention}
In linear algebra sometimes with the notation $\AA[@,j]$ we denote the 
vector formed by the $j^{th}$ column of $\AA$. Notice that $\AA$ is in 
vector format not in scalar format ($\AA[]$). We can use a ``$\bullet$'' 
as a index in a vector forcing the vector mode by using @ as follows 
index 
\begin{BOX}
\begin{verbatim}
   \[ \AA[@,j], \qquad \Balpha[i,j;@] \]
\end{verbatim}
   \[ \AA[@,j], \qquad \Balpha[i,j;@] \]
\end{BOX}

\end{document}