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<!-- %% --> <!-- %A wordass.xml GAP documentation Alexander Hulpke --> <!-- %% --> <!-- %% --> <!-- %Y (C) 1998 School Math and Comp. Sci., University of St Andrews, Scotland --> <!-- %Y Copyright (C) 2002 The GAP Group --> <!-- %% --> <Chapter Label="Associative Words"> <Heading>Associative Words</Heading> <!-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% --> <Section Label="Categories of Associative Words"> <Heading>Categories of Associative Words</Heading> <#Include Label="[1]{wordass}"> <#Include Label="IsAssocWord"> </Section> <!-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% --> <Section Label="Free Groups, Monoids and Semigroups"> <Heading>Free Groups, Monoids and Semigroups</Heading> Usually a family of associative words will be generated by constructing the free object generated by them. See <Ref Func="FreeMonoid" Label="for given rank"/>, <Ref Func="FreeSemigroup" Label="for given rank"/> for details. <#Include Label="FreeGroup"> <#Include Label="IsFreeGroup"> <#Include Label="AssignGeneratorVariables"> </Section> <!-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% --> <Section Label="Comparison of Associative Words"> <Heading>Comparison of Associative Words</Heading> <#Include Label="[2]{wordass}"> <#Include Label="IsShortLexLessThanOrEqual"> <#Include Label="IsBasicWreathLessThanOrEqual"> </Section> <!-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% --> <Section Label="Operations for Associative Words"> <Heading>Operations for Associative Words</Heading> <#Include Label="[3]{wordass}"> <P/> <#Include Label="Length:wordass"> <#Include Label="ExponentSumWord"> <#Include Label="Subword"> <#Include Label="PositionWord"> <#Include Label="SubstitutedWord"> <#Include Label="EliminatedWord"> </Section> <!-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% --> <Section Label="Operations for Associative Words by their Syllables"> <Heading>Operations for Associative Words by their Syllables</Heading> <#Include Label="[5]{wordass}"> <#Include Label="NumberSyllables"> <#Include Label="ExponentSyllable"> <#Include Label="GeneratorSyllable"> <#Include Label="SubSyllables"> </Section> <!-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% --> <Section Label="Representations for Associative Words"> <Heading>Representations for Associative Words</Heading> &GAP; provides two different internal kinds of representations of associative words. The first one are <Q>syllable representations</Q> in which words are stored in syllable (i.e. generator,exponent) form. (Older versions of &GAP; only used this representation.) The second kind are <Q>letter representations</Q> in which each letter in a word is represented by its index number. Negative numbers are used for inverses. Unless the syllable representation is specified explicitly when creating the free group/monoid or semigroup, a letter representation is used by default. <P/> Depending on the task in mind, either of these two representations will perform better in time or in memory use and algorithms that are syllable or letter based (for example <Ref Oper="GeneratorSyllable"/> and <Ref Oper="Subword"/>) perform substantially better in the corresponding representation. For example when creating pc groups (see <Ref Chap="Pc Groups"/>), it is advantageous to use a syllable representation while calculations in free groups usually benefit from using a letter representation. <#Include Label="IsLetterAssocWordRep"> <#Include Label="IsLetterWordsFamily"> <#Include Label="IsBLetterAssocWordRep"> <#Include Label="IsBLetterWordsFamily"> <#Include Label="IsSyllableAssocWordRep"> <#Include Label="IsSyllableWordsFamily"> <#Include Label="Is8BitsFamily"> <#Include Label="LetterRepAssocWord"> <#Include Label="AssocWordByLetterRep"> </Section> <!-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% --> <Section Label="The External Representation for Associative Words"> <Heading>The External Representation for Associative Words</Heading> <#Include Label="[6]{wordass}"> </Section> <!-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% --> <Section Label="Straight Line Programs"> <Heading>Straight Line Programs</Heading> <#Include Label="[1]{straight}"> <#Include Label="IsStraightLineProgram"> <#Include Label="StraightLineProgram"> <#Include Label="LinesOfStraightLineProgram"> <#Include Label="NrInputsOfStraightLineProgram"> <#Include Label="ResultOfStraightLineProgram"> <#Include Label="StringOfResultOfStraightLineProgram"> <#Include Label="CompositionOfStraightLinePrograms"> <#Include Label="IntegratedStraightLineProgram"> <#Include Label="RestrictOutputsOfSLP"> <#Include Label="IntermediateResultOfSLP"> <#Include Label="IntermediateResultOfSLPWithoutOverwrite"> <#Include Label="IntermediateResultsOfSLPWithoutOverwrite"> <#Include Label="ProductOfStraightLinePrograms"> <#Include Label="SlotUsagePattern"> </Section> <!-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% --> <Section Label="Straight Line Program Elements"> <Heading>Straight Line Program Elements</Heading> <#Include Label="[2]{straight}"> <#Include Label="IsStraightLineProgElm"> <#Include Label="StraightLineProgElm"> <#Include Label="StraightLineProgGens"> <#Include Label="EvalStraightLineProgElm"> <#Include Label="StretchImportantSLPElement"> </Section> </Chapter> <!-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% --> <!-- %% --> <!-- %E --> ¤ Dauer der Verarbeitung: 0.13 Sekunden (vorverarbeitet) ¤*© Formatika GbR, Deutschland |
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2026-03-28