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#W dcrws.gd Kan Package Chris Wensley
#W & Anne Heyworth
#Y Copyright (C) 1996-2017, Chris Wensley and Anne Heyworth
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## This file contains generic methods for double coset rewriting systems
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#V InfoKan
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DeclareInfoClass( "InfoKan" );
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#A ConstructedFromFpGroup
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DeclareAttribute( "ConstructedFromFpGroup", IsFpMonoid );
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#P IsDoubleCosetRewritingSystem( <rws> )
#P IsWordAcceptorOfDoubleCosetRws( <aut> )
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DeclareProperty( "IsDoubleCosetRewritingSystem", IsRewritingSystem );
DeclareProperty( "IsWordAcceptorOfDoubleCosetRws", IsAutomatonObj );
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#O WordToString( <word>, <alph> )
#O DisplayAsString( <word>, <alph> )
#A OrderedAlphabet( <rws> )
#O DisplayRwsRules( <rws> )
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DeclareOperation( "WordToString", [ IsWord, IsString ] );
DeclareOperation( "DisplayAsString", [ IsWord, IsString ] );
DeclareAttribute( "OrderedAlphabet", IsRewritingSystem );
DeclareOperation( "DisplayRwsRules", [ IsRewritingSystem ] );
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#A InitialRewritingSystem
#A CompleteRewritingSystem
#A WordAcceptorOfReducedRws
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DeclareAttribute( "InitialRewritingSystem", IsFpGroup );
DeclareAttribute( "CompleteRewritingSystem", IsFpGroup );
DeclareAttribute( "WordAcceptorOfReducedRws", IsRewritingSystem );
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#O DoubleCosetRewritingSystem
#O PartialDoubleCosetRewritingSystem
#O DCrules
#A Hrules
#A Krules
#A HKrules
#A InclusionInDoubleCosetMonoid
#O NextWord
#O NextWords
#O IdentityDoubleCoset
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DeclareOperation( "DoubleCosetRewritingSystem",
[ IsGroup, IsGroup, IsGroup, IsRewritingSystem ] );
DeclareOperation( "PartialDoubleCosetRewritingSystem",
[ IsGroup, IsGroup, IsGroup, IsRewritingSystem, IsInt ] );
DeclareOperation( "DCrules", [ IsDoubleCosetRewritingSystem ] );
DeclareAttribute( "Hrules", IsDoubleCosetRewritingSystem );
DeclareAttribute( "Krules", IsDoubleCosetRewritingSystem );
DeclareAttribute( "HKrules", IsDoubleCosetRewritingSystem );
DeclareAttribute( "InclusionInDoubleCosetMonoid",IsDoubleCosetRewritingSystem );
DeclareOperation( "NextWord", [ IsRewritingSystem, IsWord, IsPosInt ] );
DeclareOperation( "NextWords",
[ IsRewritingSystem, IsWord, IsPosInt, IsPosInt ] );
DeclareOperation( "IdentityDoubleCoset", [ IsDoubleCosetRewritingSystem ] );
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#A WordAcceptorOfDoubleCosetRws( <dcrws> )
#O WordAcceptorOfPartialDoubleCosetRws( <grp>, <prws> )
#O WordAcceptorByKBMagOfDoubleCosetRws( <grp>, <pdcrws> )
#A RewritingSystemOfWordAcceptor( <aut> )
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DeclareAttribute( "WordAcceptorOfDoubleCosetRws",
IsDoubleCosetRewritingSystem );
DeclareOperation( "WordAcceptorOfPartialDoubleCosetRws",
[ IsGroup, IsDoubleCosetRewritingSystem ] );
DeclareOperation( "WordAcceptorByKBMagOfDoubleCosetRws",
[ IsFpGroup, IsDoubleCosetRewritingSystem ] );
DeclareAttribute( "RewritingSystemOfWordAcceptor", IsAutomatonObj );
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#O KBMagFSAtoAutomataDFA
#O WordAcceptorByKBMag
#A KBMagRewritingSystem
#A KBMagWordAcceptor
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DeclareOperation( "KBMagFSAtoAutomataDFA", [ IsInternalRep, IsString ] );
DeclareOperation( "WordAcceptorByKBMag", [ IsFpGroup, IsString ] );
DeclareAttribute( "KBMagRewritingSystem", IsFpGroup );
DeclareAttribute( "KBMagWordAcceptor", IsFpGroup );
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#O DoubleCosetsAutomaton
#O RightCosetsAutomaton
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DeclareOperation( "DoubleCosetsAutomaton", [ IsFpGroup, IsGroup, IsGroup ] );
DeclareOperation( "RightCosetsAutomaton", [ IsFpGroup, IsGroup ] );
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#E dcrws.gd . . . . . . . . . . . . . . . . . . . . . . . . . . . . ends here
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