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diff --git a/Master/texmf-dist/doc/latex/bezos/tensind.tex b/Master/texmf-dist/doc/latex/bezos/tensind.tex new file mode 100644 index 00000000000..d81a3577a73 --- /dev/null +++ b/Master/texmf-dist/doc/latex/bezos/tensind.tex @@ -0,0 +1,194 @@ +% +--------------------------------------------------+ +% | Typeset this file to get the documentation. | +% +--------------------------------------------------+ +% +% This file is copyrighted (c) 1998, 2000 by Javier Bezos. +% All Rights Reserved. +% +% This program can be redistributed and/or modified under the terms +% of the LaTeX Project Public License Distributed from CTAN +% archives in directory macros/latex/base/lppl.txt; either +% version 1 of the License, or any later version. + +\def\fileversion{1.0} +\def\docdate{August 7, 2000} + +\documentclass{ltxguide} +\usepackage{tensind} + +\title{The \textsf{tensind} Package for +Tensorial Indexes\footnote{This +package is currently at version 1.0.}} + +\author{Javier Bezos\footnote{Please, send your +comments and suggestions to \texttt{jbezos@wanadoo.es}, or +to my postal address: Apartado 116.035, E-28080 Madrid, Spain. +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} |