%
% Copyright (C) 1998-2019 Javier Bezos http://www.texnia.com
%
% This file may be distributed and/or modified under the conditions of
% the MIT License. A version can be found at the end of this file.
%

\def\fileversion{1.1}
\def\docdate{August 7, 2000}

\documentclass{ltxguide}
\usepackage{tensind}

\title{The \textsf{tensind} Package for
Tensorial Indexes\footnote{This 
package is currently at version 1.1.}}

\author{Javier Bezos\footnote{For bug reports, comments and
suggestions go to
\texttt{http://www.tex-tipografia.com}.
English is not my strong point, so contact me when you
find mistakes in the manual. Other packages by the same author:
\textsf{accents, titlesec, dotlessi}.}}

\date{\docdate}

\newenvironment{sample}{\begin{quote}\small\begin{tabbing}%
  \hskip12pc\=\hskip6pc\\}
  {\end{tabbing}\end{quote}}
  
\tensordelimiter{?}
\tensorformat{lrb}

\raggedright

\begin{document}

\maketitle
  
This package provides typographically fine tensorial notation, with the 
following features:
\begin{itemize}
\item Dots filling gaps.
\item Symbol subtitution to easy typing (if you are using greek letters, for 
example).
\item Corrected position of indexes: horizontally, to compensate the small 
displacement in letters
like $f$ (look carefully at $f_*^*$) and vertically, to avoid superscripts 
too raised.
\item Aditional minute corrections are also allowed.
\end{itemize}

\section{User Interface}

\begin{decl}
|\tensordelimiter{<tensor-delim>}|
\end{decl}

Defines |<tensor-delim>| to be a tensor delimiter. In subsequent examples we will 
assume
\begin{verbatim}
\tensordelimiter{?}
\end{verbatim}
and every instance of |?| will actually mean |<tensor-delim>|.

\begin{decl}
|?[<format>]{<nucleous>}{<special-index>}{<special-index>}...|\\
|                       <super-or-sub><super-or-sub>...?|
\end{decl}

Creates a tensor. |<super-or-sub>| is either |_{<index>}{<index>}...| or 
|^{<index>}{<index>}|.
|<nucleous>| is the symbol which indexes will be add to. |<special-index>| is a 
superscript which is neither covariant nor contravariant (dual, 
prime...). In 
one-letter |<index>|, |<special-index>| or |<nucleous>|, curly braces can be 
omitted.
For example:
\begin{sample}
|?R_ij^kl_\alpha^\beta?|     \>        $?R_ij^kl_\alpha^\beta?$\\[2pt]
|?R^ij_kl^\alpha_\beta?|     \>        $?R^ij_kl^\alpha_\beta?$\\[2pt]
|?R**_ij^kl_\alpha^\beta?|   \>        $?R**_ij^kl_\alpha^\beta?$\\[2pt] 
|?R**^ij_kl^\alpha_\beta?|   \>        $?R**^ij_kl^\alpha_\beta?$
\end{sample}

(\emph{Don't forget the closing |?|!})
Finally, |<format>| changes the format in a tensor. (See |\tensorformat| 
below.)

\begin{decl}
|\tensorformat{<format>}|
\end{decl}

The following letter may be used in format.
\begin{itemize}
\item[\texttt{l}] Gaps to the left of the last index are filled with dots.
\item[\texttt{r}] Gaps to the right of the first index are filled.
\item[\texttt{e}] If there is no index (empty), gaps are filled.
\item[\texttt{b}] Only gaps in subscripts are filled.
\end{itemize}

Sensible settings are: none (no dots), |l| and |lrb|.
Further options are:
\begin{itemize}
\item[\texttt{c}] Brings index lines closer.
\item[\texttt{o}] Opens index lines.
\item[\texttt{s}] Styled. |o| in display style and |c| otherwise.
\end{itemize}
These options are mutually exclusive. If none of them is
used, then indexes behave in a similar way to standard ones.
This document sets
\begin{verbatim}
\tensorformat{lrb}
\end{verbatim}

\begin{sample}
|?[]f\prime_ij^kl?|    \>  $?[]f\prime_ij^kl?$\\[2pt]
|?[e]f^ij?|            \>  $?[e]f^ij?$ \\[2pt] 
|?[l]f*_ij^kl?|        \>  $?[l]f*_ij^kl?$\\[2pt]
|?[c]R^ij_kl?|         \>  $?[c]R^ij_kl?$
\end{sample}

\begin{decl}
|\indexdot|
\end{decl}

This macro is the index dot. Defined to |\cdot|. You can
redefine it with |\renewcommand|.

\begin{decl}
|\whenindex{<index>}{<new-index>}{<commands>}|
\end{decl}

Automatically replaces |<index>| (if not enclosed in braces)
by |<new-index>| and the additional |<commands>| are
executed. For example, if you like to use greek indexes:
\begin{verbatim}
\whenindex{a}{\alpha}{}
\whenindex{b}{\beta}{}
\whenindex{g}{\gamma}{}
\end{verbatim}

\whenindex{a}{\alpha}{}
\whenindex{b}{\beta}{}
\whenindex{g}{\gamma}{
}
A |\whenindex{'}{\prime}{}| is performed by the package. For instance
\begin{sample}
|?R'_ijk^abg?|    \>  $?R'_ijk^abg?$
\end{sample}

In |<commands>|, two command for space fine-tuning are provided:
|\sbadjust{<index>}{<comma-space>}| adds |<comma-space>| times
|\,| before the current subscript index if the last superscript index
was |<index>|. Similarly, |\spadjust| adds the space before the current
superscript index if the last subscript index was |<index>|.
For instance, the normal result of |?[]R^ik_lm?| is $?[]R^ij_kl?$, but
with
\begin{verbatim}
\whenindex{k}{k}{\sbadjust{j}{-1}}
\end{verbatim}
\whenindex{k}{k}{\sbadjust{j}{-1}}
is $?[]R^ij_kl?$.
These commands will be ignored if dots are used.

Two further command allowed in |\whenindex|
are: |\omitdot| omits the dot for the current
index, and |\finishdots| omits as well all subsequent indexes.
For example
\begin{verbatim}
\whenindex{;}{\,;\,}{\finishdots}
\end{verbatim}
\whenindex{;}{\,;\,}{\finishdots}

\begin{sample}
|?[lr]A*_i^kl;i?|  \>   $?[lr]A*_i^kl;i?$
\end{sample}

\begin{decl}
|tensor|
\end{decl}

The environment called by |?...?|. Useful if for some reason you
don't want an equivalent defined with |\tensordelimiter| . Example:
\begin{verbatim}
\begin{tensor}[lr]A*_i^kl;i\end{tensor}
\end{verbatim}

\end{document}

MIT License
-----------

Permission is hereby granted, free of charge, to any person obtaining a
copy of this software and associated documentation files (the
"Software"), to deal in the Software without restriction, including
without limitation the rights to use, copy, modify, merge, publish,
distribute, sublicense, and/or sell copies of the Software, and to
permit persons to whom the Software is furnished to do so, subject to
the following conditions:

The above copyright notice and this permission notice shall be included
in all copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.
IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY
CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,
TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE
SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
