Quelle functions.xml Sprache: XML

<Chapter Label="Functions">
<Heading>Functions</Heading>

Here we include a list of all functions that are provided to the User.<P/>

The following functions are designed to improve the User experience
when working or experimenting with wreath products of finite groups and their elements.
Most functions are about presenting elements in an intuitive way
and giving access to useful information. <P/>

<Section Label="Isomorphism Functions">
<Heading>Generic Wreath Product Representation</Heading>

The main way for the User to look at a wreath product in a "human-readable" way
is by using an isomorphism from a specialised wreath product representation
to a generic representation.

<#Include Label="IsomorphismWreathProduct">

</Section>

<Section Label="Component Functions">
<Heading>Accessing Components</Heading>

The following functions give access to components of wreath products and their elements.

<#Include Label="ComponentsOfWreathProduct">
<#Include Label="TopGroupOfWreathProduct">
<#Include Label="BaseGroupOfWreathProduct">

<#Include Label="TopComponentOfWreathProductElement">
<#Include Label="BaseComponentOfWreathProductElement">

</Section>

<Section Label="Wreath Product Element Functions">
<Heading>Properties of Wreath Product Elements</Heading>

The following functions give access to important properties of wreath product elements.

<#Include Label="Territory">
<#Include Label="IsWreathCycle">
<#Include Label="IsSparseWreathCycle">
<#Include Label="WreathCycleDecomposition">
<#Include Label="Yade">

</Section>

<Section Label="Display Functions">
<Heading>Printing, Viewing and Displaying</Heading>

<ManSection>
<Meth Name="ViewObj" Arg="x" Label="for a wreath product element"/>
<Meth Name="PrintObj" Arg="x" Label="for a wreath product element"/>
<Meth Name="Display" Arg="x[, optrec]" Label="for a wreath product element"/>

<Description>
Wreath product elements are viewed, printed and displayed (see
Section <Ref BookName="Reference" Sect="View and Print"/> for the distinctions between these
operations) as generic wreath product elements (see Section <Ref Sect="Wreath Product"/>).
For an example of the distinctions and outputs see <Ref Sect="Tutorial Display Wreath Product Elements"/>. <P/>

The method <C>Display</C> allows an optional argument <A>optrec</A> which must be a record
and modifies the display output for the execution of a single instance of the command. <P/>

For modifying the display output globally for all subsequent executions of <C>Display</C> see <Ref Func="SetDisplayOptionsForWreathProductElements"/>. <P/>

The following components of <A>optrec</A> are supported.
Note, that in the following <E>labels</E> refer to the the printing output <Q><M>1, /ldots, m</M></Q> and <Q>top</Q> as seen in the tutorials.

<List>
<Mark><C>horizontal</C></Mark>
<Item>
<K>true</K> to use the horizontal printer. <E>DEFAULT</E> <P/>
<K>false</K> to use the vertical printer. <P/>
</Item>
<Mark><C>labels</C></Mark>
<Item>
<K>true</K> to print labels. <E>DEFAULT</E> <P/>
<K>false</K> to suppress labels. <P/>
</Item>
<Mark><C>labelStyle</C></Mark>
<Item>
<K>"none"</K> for labels in normal intensity. <E>DEFAULT</E> <P/>
<K>"bold"</K> for labels in increased intensity. <P/>
<K>"faint"</K> for labels in decreased intensity. <P/>
</Item>
<Mark><C>labelColor</C></Mark>
<Item>
<K>"default"</K> for labels in the default GAP output color. <E>DEFAULT</E> <P/>
<K>"red"</K> for labels in red color. <P/>
<K>"blue"</K> for labels in blue color. <P/>
</Item>
</List>
</Description>

</ManSection>

<#Include Label="DisplayOptionsForWreathProductElements">
<#Include Label="SetDisplayOptionsForWreathProductElements">
<#Include Label="ResetDisplayOptionsForWreathProductElements">

</Section>

<Section Label="Cycle Index">
<Heading>Cycle Index of Wreath Products</Heading>

The following functions construct the cycle index polynomial of wreath products in certain actions.

<#Include Label="CycleIndexWreathProductImprimitiveAction">
<#Include Label="CycleIndexWreathProductProductAction">

</Section>

</Chapter>

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