<!-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% --> <!-- %% --> <!-- %A ctblfuns.xml GAP documentation Thomas Breuer --> <!-- %% --> <!-- %% --> <!-- %Y (C) 1999 School Math and Comp. Sci., University of St Andrews, Scotland --> <!-- %Y Copyright (C) 2002 The GAP Group --> <!-- %% --> <!-- %% The documentation in this chapter corresponds to the declarations in the --> <!-- %% library files ctblfuns.gd, ctbllatt.gd, ctblmoli.gd, ctblpope.gd. --> <!-- %% -->
<Chapter Label="Class Functions">
<Heading>Class Functions</Heading>
This chapter describes operations for <E>class functions of finite groups</E>.
For operations concerning <E>character tables</E>,
see Chapter <Ref Chap="Character Tables"/>.
<P/>
Several examples in this chapter 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>
<!-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -->
<Section Label="Why Class Functions?">
<Heading>Why Class Functions?</Heading>
<!-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -->
<Section Label="Basic Operations for Class Functions">
<Heading>Basic Operations for Class Functions</Heading>
<!-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -->
<Section Label="Comparison of Class Functions">
<Heading>Comparison of Class Functions</Heading>
<#Include Label="[3]{ctblfuns}">
</Section>
<!-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -->
<Section Label="Arithmetic Operations for Class Functions">
<Heading>Arithmetic Operations for Class Functions</Heading>
<#Include Label="[4]{ctblfuns}">
</Section>
<!-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -->
<Section Label="Printing Class Functions">
<Heading>Printing Class Functions</Heading>
<#Include Label="[5]{ctblfuns}">
</Section>
<!-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -->
<Section Label="Creating Class Functions from Values Lists">
<Heading>Creating Class Functions from Values Lists</Heading>
<!-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -->
<Section Label="Creating Class Functions using Groups">
<Heading>Creating Class Functions using Groups</Heading>
<!-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -->
<Section Label="Operations for Class Functions">
<Heading>Operations for Class Functions</Heading>
<!-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -->
<Section Label="Restricted and Induced Class Functions">
<Heading>Restricted and Induced Class Functions</Heading>
<!-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -->
<Section Label="Symmetrizations of Class Functions">
<Heading>Symmetrizations of Class Functions</Heading>
<!-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -->
<Section Label="Domains Generated by Class Functions">
<Heading>Domains Generated by Class Functions</Heading>
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