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<!-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -->
<!-- %% -->
<!-- %A orders.xml GAP documentation Isabel Araújo -->
<!-- %% -->
<!-- %% -->
<!-- %Y (C) 2000 School Math and Comp. Sci., University of St Andrews, Scotland -->
<!-- %Y Copyright (C) 2002 The GAP Group -->
<!-- %% -->
<Chapter Label="Orderings">
<Heading>Orderings</Heading>
<#Include Label="[1]{orders}">
<!-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -->
<Section Label="sect:IsOrdering">
<Heading>IsOrdering (Filter)</Heading>
<#Include Label="IsOrdering">
<#Include Label="OrderingsFamily">
</Section>
<!-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -->
<Section Label="Building new orderings">
<Heading>Building new orderings</Heading>
<#Include Label="OrderingByLessThanFunctionNC">
<#Include Label="OrderingByLessThanOrEqualFunctionNC">
</Section>
<!-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -->
<Section Label="Properties and basic functionality">
<Heading>Properties and basic functionality</Heading>
<#Include Label="IsWellFoundedOrdering">
<#Include Label="IsTotalOrdering">
<#Include Label="IsIncomparableUnder">
<#Include Label="FamilyForOrdering">
<#Include Label="LessThanFunction">
<#Include Label="LessThanOrEqualFunction">
<#Include Label="IsLessThanUnder">
<#Include Label="IsLessThanOrEqualUnder">
</Section>
<!-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -->
<Section Label="Orderings on families of associative words">
<Heading>Orderings on families of associative words</Heading>
<#Include Label="[2]{orders}">
<#Include Label="IsOrderingOnFamilyOfAssocWords">
<#Include Label="IsTranslationInvariantOrdering">
<#Include Label="IsReductionOrdering">
<#Include Label="OrderingOnGenerators">
<#Include Label="LexicographicOrdering">
<#Include Label="ShortLexOrdering">
<#Include Label="IsShortLexOrdering">
<#Include Label="WeightLexOrdering">
<#Include Label="IsWeightLexOrdering">
<#Include Label="WeightOfGenerators">
<#Include Label="BasicWreathProductOrdering">
<#Include Label="IsBasicWreathProductOrdering">
<#Include Label="WreathProductOrdering">
<#Include Label="IsWreathProductOrdering">
<#Include Label="LevelsOfGenerators">
</Section>
</Chapter>
<!-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -->
<!-- %% -->
<!-- %E -->
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