1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
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{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}
|
