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%W  introduc.msk          GAP 4 package `ctbllib'               Thomas Breuer
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%H  @(#)$Id: introduc.msk,v 1.2 2002/01/14 16:49:06 gap Exp $
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%Y  Copyright (C) 2001,  Lehrstuhl D fuer Mathematik,   RWTH Aachen,  Germany
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\Chapter{Introduction to the GAP Character Table Library}

The usefulness of {\GAP} for character theoretic tasks depends on the
availability of many known character tables,
and there is a lot of character tables in the {\GAP} table library.
Of course, this library is ``open'' in the sense that it shall be extended.
So we would be grateful for any further tables of interest
sent to us for inclusion into our library.
Please send interesting new character tables via e-mail
to~\Mailto{sam@math.rwth-aachen.de}.
% A cross-reference to this address is at the end of another chapter!

It depends on your {\GAP} installation whether the character table library
is available.
You can check this as follows.
\beginexample 
gap> IsBound( LOADED_PACKAGES.ctbllib );
true
\endexample
If the result is `false' then the library is not installed,
and you may ask your system administrator for installing it,
or install the library in your home directory
(see~"Installing the GAP Character Table Library").

For general information about character tables in {\GAP},
see Chapter~"ref:Character Tables" in the {\GAP} Reference Manual.

The `doc' directory of the {\GAP} Character Table Library contains several
files with demonstrations of computations with character tables.
Currently these are `ctbldeco.dvi', `ctblpope.dvi', and `multfree.dvi'.

If you use the {\GAP} Character Table Library to solve a problem then
please send a short email to~\Mailto{sam@math.rwth-aachen.de} about it.
The {\GAP} Character Table Library database should be referenced
with the entry~\cite{Bre01} in the bibliography of this manual.

For referencing the {\GAP} system in general,
use the entry~\cite{GAP4} in the bibliography of this manual.


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\Section{History of the GAP Character Table Library}

The first version of the {\GAP} Character Table Library was released with
{\GAP}~3.1 in March 1992.

It was the first aim of this library to continue the character table library
of the {\sf CAS} system (see~\cite{NPP84}) in {\GAP},
as a part of the process of reimplementing the algorithms of {\sf CAS}
in {\GAP} (see~"ref:History of Character Theory Stuff in GAP" in the
{\GAP} Reference Manual).
{\GAP}~3.1 provided only very restricted methods for computing character
tables from groups,
so its character theory part was concerned mainly with library tables.

A second aspect of the character table library was to make all character
tables shown in the {\ATLAS} of Finite Groups (\cite{CCN85})
available in {\GAP}.
In fact {\GAP} turned out to provide a very good environment for
systematic checks of these character tables.

To some extent, the access to the (ordinary) character tables in~\cite{CCN85}
was a prerequisite for storing also the corresponding Brauer character tables
in the {\GAP} character table library.
Already {\GAP}~3.1 contained many of these tables.
They have been computed mainly ``outside of {\GAP}'',
using the methods described in~\cite{HJLP92},
and part of the library has been published in the {\ATLAS} of Brauer
Characters (\cite{JLPW95}).
One of the roles of {\GAP} was again to perform systematic checks.

Besides these projects, many individual character tables have been added
to the {\GAP} Character Table Library since the times of {\GAP}~3.1.
They were computed from groups or with character theoretic methods
or using a combination of these two possibilities
(see, e.g., \cite{NPP84} and \cite{LP91}).
Section~"Contents of the GAP Character Table Library" lists some of the
sources.
The changes in the {\GAP} Character Table Library since the release of
{\GAP}~4.1 (in July 1999) are individually documented in the file
`ctbldiff.dvi' which is part of the distribution of the library.

In the meantime, a rudimentary interface between groups in {\GAP} and the
tables in the {\GAP} Character Table Library has been provided
(see~"ref:The Interface between Character Tables and Groups" in the {\GAP}
Reference Manual).
Similarly, there is an interface to the {\GAP} Libary of Tables of Marks
(see~"ref:The Interface between Tables of Marks and Character Tables"
in the {\GAP} Reference Manual).

Currently the main focus in the development of the {\GAP} Character Table
Library is --besides the addition of tables that appear to be interesting--
the better interaction with other databases, such as the {\ATLAS} of Group
Representations (see the {\GAP}~4 package AtlasRep),
and an improvement of the ``database'' aspect of the character table library
itself, for example by providing a ``WWW table of contents''.

Until the release of {\GAP}~4.3 in spring 2002,
the {\GAP} Character Table Library had been a part of the main {\GAP}
library.
With {\GAP}~4.3, it is ``split off'' as a {\GAP} package.


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\Section{Installing the GAP Character Table Library}

To install the {\GAP} package `ctbllib', unpack the archive file in a
directory in the `pkg' directory of your local copy of {\GAP}~4.
This might be the `pkg' directory of the {\GAP}~4 home directory,
see Section~"ref:Installing GAP Packages"
of the {\GAP}~4 Reference Manual for details.
It is however also possible to keep an additional `pkg' directory
in your private directories,
see~"ref:Installing a GAP Package in your home directory"
of the {\GAP}~4 Reference Manual.
The latter possibility *must* be chosen if you do not have write access
to the {\GAP} root directory.

The package consists entirely of {\GAP} code,
no external binaries need to be compiled.

Both dvi and PostScript versions of the manual for the {\GAP} Character Table
Library are available (as `manual.dvi' and `manual.ps' respectively) in the
`doc' directory of the `ctbllib' package,
and an HTML version can be found in the `htm' directory.


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\Section{Loading the GAP Character Table Library}

The {\GAP} Character Table Library may be loaded automatically when {\GAP}
is started,
or it has to be loaded within {\GAP} as follows.
\begintt
gap> RequirePackage( "ctbllib" );
\endtt
See~"ref:Loading a GAP Package" in the {\GAP} Reference Manual
for details about these alternatives;
also the possibility to disable automatic loading of the library
is described in this manual section.
The default is that the {\GAP} Character Table Library is loaded
automatically.


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\Section{Acknowledgements}

The functions for the conversion of {\sf CAS} tables to {\GAP} format have
been written by G{\accent127 o}tz Pfeiffer.
The functions for converting the ``Cambridge format'' (in which the original
data of the {\ATLAS} of Finite Groups had been stored) to {\GAP} format
have been written by Christoph Jansen.
The functions for checking library tables have been written by Thomas Breuer.

The development of the {\GAP} Character Table Library has been supported
by several DFG grants,
in particular the project ``Representation Theory of Finite Groups and Finite
Dimensional Algebras'' (until 1991),
and the Schwerpunkt ``Algorithmische Zahlentheorie und Algebra''
(from 1991 until 1997).


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