<!-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -->
<!-- %% -->
<!-- %W  tom.xml                     GAP documentation              Götz Pfeiffer -->
<!-- %W                                                            Thomas Merkwitz -->
<!-- %% -->
<!-- %% -->
<!-- %Y  (C) 1999 School Math and Comp. Sci., University of St Andrews, Scotland -->
<!-- %Y  Copyright (C) 2002 The GAP Group -->
<!-- %% -->
<!-- %%  This file describes the functions dealing with tables of marks. -->
<!-- %%  The corresponding &GAP; code is contained in the files <C>lib/tom.g[di]</C>. -->
<!-- %% -->
<Chapter Label="Tables of Marks">
<Heading>Tables of Marks</Heading>

<#Include Label="[1]{tom}">

<!-- %%  The code for tables of marks has been designed and implemented by G{\"o}tz -->
<!-- %%  Pfeiffer and Thomas Merkwitz. -->


<!-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -->
<Section Label="More about Tables of Marks">
<Heading>More about Tables of Marks</Heading>

<#Include Label="[2]{tom}">

</Section>


<!-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -->
<Section Label="Table of Marks Objects in GAP">
<Heading>Table of Marks Objects in GAP</Heading>

<#Include Label="[3]{tom}">
<P/>
Several examples in this chapter require
the &GAP; package <Package>TomLib</Package>
(the &GAP; Library of Tables of Marks) to be available.
If it is not yet loaded then we load it now.
<P/>
<Example><![CDATA[
gap> LoadPackage( "tomlib" );
true
]]></Example>

</Section>


<!-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -->
<Section Label="Constructing Tables of Marks">
<Heading>Constructing Tables of Marks</Heading>

<#Include Label="TableOfMarks">
<#Include Label="TableOfMarksByLattice">
<#Include Label="LatticeSubgroupsByTom">

</Section>


<!-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -->
<Section Label="Printing Tables of Marks">
<Heading>Printing Tables of Marks</Heading>

<#Include Label="[5]{tom}">

</Section>


<!-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -->
<Section Label="Sorting Tables of Marks">
<Heading>Sorting Tables of Marks</Heading>

<#Include Label="SortedTom">
<#Include Label="PermutationTom">

</Section>


<!-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -->
<Section Label="Technical Details about Tables of Marks">
<Heading>Technical Details about Tables of Marks</Heading>

<#Include Label="InfoTom">
<#Include Label="IsTableOfMarks">
<#Include Label="TableOfMarksFamily">
<#Include Label="TableOfMarksComponents">
<#Include Label="ConvertToTableOfMarks">

</Section>


<!-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -->
<Section Label="Attributes of Tables of Marks">
<Heading>Attributes of Tables of Marks</Heading>

<#Include Label="MarksTom">
<#Include Label="NrSubsTom">
<#Include Label="LengthsTom">
<#Include Label="ClassTypesTom">
<#Include Label="ClassNamesTom">
<#Include Label="FusionsTom">
<#Include Label="UnderlyingGroup:tom">
<#Include Label="IdempotentsTom">
<#Include Label="Identifier:tom">
<#Include Label="MatTom">
<#Include Label="MoebiusTom">
<#Include Label="WeightsTom">

</Section>


<!-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -->
<Section Label="Properties of Tables of Marks">
<Heading>Properties of Tables of Marks</Heading>

<#Include Label="[6]{tom}">

</Section>


<!-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -->
<Section Label="Other Operations for Tables of Marks">
<Heading>Other Operations for Tables of Marks</Heading>

<#Include Label="[7]{tom}">
<#Include Label="DerivedSubgroupTom">
<#Include Label="DerivedSubgroupsTomPossible">
<#Include Label="NormalizerTom">
<#Include Label="ContainedTom">
<#Include Label="ContainingTom">
<#Include Label="CyclicExtensionsTom">
<#Include Label="DecomposedFixedPointVector">
<#Include Label="EulerianFunctionByTom">
<#Include Label="IntersectionsTom">
<#Include Label="FactorGroupTom">
<#Include Label="MaximalSubgroupsTom">
<#Include Label="MinimalSupergroupsTom">

</Section>


<!-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -->
<Section Label="Accessing Subgroups via Tables of Marks">
<Heading>Accessing Subgroups via Tables of Marks</Heading>

<#Include Label="[8]{tom}">
<#Include Label="GeneratorsSubgroupsTom">
<#Include Label="StraightLineProgramsTom">
<#Include Label="IsTableOfMarksWithGens">
<#Include Label="RepresentativeTom">

</Section>


<!-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -->
<Section Label="The Interface between Tables of Marks and Character Tables">
<Heading>The Interface between Tables of Marks and Character Tables</Heading>

The following examples require the &GAP; Character Table Library
to be available.
If it is not yet loaded then we load it now.
<P/>
<Example><![CDATA[
gap> LoadPackage( "ctbllib" );
true
]]></Example>
<P/>
<#Include Label="FusionCharTableTom">
<#Include Label="PermCharsTom">

</Section>


<!-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -->
<Section Label="Generic Construction of Tables of Marks">
<Heading>Generic Construction of Tables of Marks</Heading>

<#Include Label="[9]{tom}">
<#Include Label="TableOfMarksCyclic">
<#Include Label="TableOfMarksDihedral">
<#Include Label="TableOfMarksFrobenius">

</Section>


<!-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -->
<Section Label="The Library of Tables of Marks">
<Heading>The Library of Tables of Marks</Heading>

The &GAP; package <Package>TomLib</Package> provides access to several
hundred tables of marks of almost simple groups and their maximal subgroups.
If this package is installed then the tables from this database can be
accessed via <Ref Attr="TableOfMarks" Label="for a string"/> with argument
a string.
If also the &GAP; Character Table Library is installed and contains the
ordinary character table of the group for which one wants to fetch the table
of marks then one can also call
<Ref Attr="TableOfMarks" Label="for a string"/>
<!-- This reference is not correct.
     The Character Table Library or the ``Interface'' section above
     should document this method,
     and then an external reference should be created. -->
with argument the character table.
<P/>
A list of all names of tables of marks that are provided by the
<Package>TomLib</Package> package can be obtained via
<Ref Func="AllLibTomNames" BookName="tomlib"/>.
<P/>
<Example><![CDATA[
gap> names:= AllLibTomNames();;
gap> "A5" in names;
true
]]></Example>

</Section>
</Chapter>


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<!-- %% -->
<!-- %E -->

