| Quellcodebibliothek Statistik Leitseite products/sources/formale Sprachen/GAP/pkg/xmod/lib/ (Algebra von RWTH Aachen Version 4.15.1©) Datei vom 10.6.2025 mit Größe 15 kB |
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SSL gp2obj.gd Sprache: unbekannt |
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rahmenlose Ansicht.gd DruckansichtUnknown {[0] [0] [0]} [Methode: Schwerpunktbildung, einfache Gewichte, sechs Dimensionen] ############################################################################## ## #W gp2obj.gd GAP4 package `XMod' Chris Wensley #W & Murat Alp #Y Copyright (C) 2001-2023, Chris Wensley et al, ############################################################################# ## #P IsPreXModDomain( <obj> ) #P IsPreCat1Domain( <obj> ) ## ## these apply to groups, algebras, whatever ... ## DeclareProperty( "IsPreXModDomain", Is2DimensionalDomain ); DeclareProperty( "IsPreCat1Domain", Is2DimensionalDomain ); InstallTrueMethod( Is2DimensionalDomain, IsPreXModDomain ); InstallTrueMethod( Is2DimensionalDomain, IsPreCat1Domain ); ############################################################################# ## #A Size2d( <obj> ) ## DeclareAttribute( "Size2d", Is2DimensionalDomain ); ############################################################################# ## #R IsPreXModObj( <obj> ) ## A pre-crossed module is a group homomorphism which preserves an action #R IsPreCat1Obj( <obj> ) ## A pre-cat1-group is a pair of group endomorphisms with a common image ## DeclareRepresentation( "IsPreXModObj", Is2DimensionalGroup and IsAttributeStoringRep, [ "boundary", "action" ] ); DeclareRepresentation( "IsPreCat1Obj", Is2DimensionalGroup and IsAttributeStoringRep, [ "tailMap", "headMap", "rangeEmbedding" ] ); ############################################################################# ## #P IsPerm2DimensionalGroup( <obj> ) #P IsFp2DimensionalGroup( <obj> ) #P IsPc2DimensionalGroup( <obj> ) ## DeclareProperty( "IsPerm2DimensionalGroup", Is2DimensionalGroup ); DeclareProperty( "IsFp2DimensionalGroup", Is2DimensionalGroup ); DeclareProperty( "IsPc2DimensionalGroup", Is2DimensionalGroup ); InstallTrueMethod( Is2DimensionalGroup, IsPerm2DimensionalGroup ); InstallTrueMethod( Is2DimensionalGroup, IsFp2DimensionalGroup ); InstallTrueMethod( Is2DimensionalGroup, IsPc2DimensionalGroup ); ############################################################################# ## #T PreXModObjType . . . . . . . . . . . . . . . . . type for crossed modules #T PermPreXModObjType . . . . . . . . . . . . type for perm crossed modules #T PcPreXModObjType . . . . . . . . . . . . . . type for pc crossed modules #T PreCat1ObjType . . . . . . . . . . . . . . . . . . . type for cat1-groups #T PermPreCat1ObjType . . . . . . . . . . . . . . type for perm cat1-groups #T PcPreCat1ObjType . . . . . . . . . . . . . . . . type for pc cat1-groups ## BindGlobal( "PreXModObjType", NewType( Family2DimensionalGroup, IsPreXModObj ) ); BindGlobal( "PermPreXModObjType", NewType( Family2DimensionalGroup, IsPreXModObj and IsPerm2DimensionalGroup ) ); BindGlobal( "PcPreXModObjType", NewType( Family2DimensionalGroup, IsPreXModObj and IsPc2DimensionalGroup ) ); BindGlobal( "PreCat1ObjType", NewType( Family2DimensionalGroup, IsPreCat1Obj ) ); BindGlobal( "PermPreCat1ObjType", NewType( Family2DimensionalGroup, IsPreCat1Obj and IsPerm2DimensionalGroup ) ); BindGlobal( "PcPreCat1ObjType", NewType( Family2DimensionalGroup, IsPreCat1Obj and IsPc2DimensionalGroup ) ); ############################################################################# ## #P IsPreXMod( <PM> ) #P IsPermPreXMod( <PM> ) #P IsFpPreXMod( <PM> ) #P IsPcPreXMod( <PM> ) ## DeclareProperty( "IsPreXMod", Is2DimensionalGroup ); InstallTrueMethod( Is2DimensionalGroup, IsPreXMod ); DeclareSynonym( "IsPermPreXMod", IsPreXMod and IsPerm2DimensionalGroup ); DeclareSynonym( "IsFpPreXMod", IsPreXMod and IsFp2DimensionalGroup ); DeclareSynonym( "IsPcPreXMod", IsPreXMod and IsPc2DimensionalGroup ); ############################################################################# ## #P IsXMod( <PM> ) #P IsPermXMod( <XM> ) #P IsFpXMod( <XM> ) #P IsPcXMod( <XM> ) ## DeclareProperty( "IsXMod", IsPreXMod ); InstallTrueMethod( IsPreXMod, IsXMod ); DeclareSynonym( "IsPermXMod", IsXMod and IsPerm2DimensionalGroup ); DeclareSynonym( "IsFpXMod", IsXMod and IsFp2DimensionalGroup ); DeclareSynonym( "IsPcXMod", IsXMod and IsPc2DimensionalGroup ); ############################################################################# ## #P IsPreCat1Group( <PCG> ) #P IsPermPreCat1Group( <PCG> ) #P IsFpPreCat1Group( <PCG> ) #P IsPcPreCat1Group( <PCG> ) ## DeclareProperty( "IsPreCat1Group", Is2DimensionalGroup ); InstallTrueMethod( Is2DimensionalGroup, IsPreCat1Group ); DeclareSynonym( "IsPermPreCat1Group", IsPreCat1Group and IsPerm2DimensionalGroup ); DeclareSynonym( "IsFpPreCat1Group", IsPreCat1Group and IsFp2DimensionalGroup ); DeclareSynonym( "IsPcPreCat1Group", IsPreCat1Group and IsPc2DimensionalGroup ); ############################################################################# ## #P IsCat1Group( <C1G> ) #P IsPermCat1Group( <CG> ) #P IsFpCat1Group( <CG> ) #P IsPcCat1Group( <CG> ) ## DeclareProperty( "IsCat1Group", IsPreCat1Group ); InstallTrueMethod( IsPreCat1Group, IsCat1Group ); DeclareSynonym( "IsPermCat1Group", IsCat1Group and IsPerm2DimensionalGroup ); DeclareSynonym( "IsFpCat1Group", IsCat1Group and IsFp2DimensionalGroup ); DeclareSynonym( "IsPcCat1Group", IsCat1Group and IsPc2DimensionalGroup ); ############################################################################# ## #O PreXModObj( <bdy>, <act> ) #A Boundary( <PM> ) #A XModAction( <PM> ) #A ExternalSetXMod( <PM> ) #O ImageElmXModAction( <PM>, <srcobj>, <rngobj> ) ## DeclareOperation( "PreXModObj", [ IsGroupHomomorphism, IsGroupHomomorphism ] ); DeclareAttribute( "Boundary", IsPreXMod ); DeclareAttribute( "XModAction", IsPreXMod ); DeclareAttribute( "ExternalSetXMod", IsPreXMod ); DeclareOperation( "ImageElmXModAction", [ Is2DimensionalDomain, IsObject, IsObject ] ); ############################################################################# ## #A PeifferSubgroup( <obj> ) #A PeifferSub2DimensionalGroup( <obj> ) #O PeifferSubgroupPreXMod( <PM> ) #O PeifferSubgroupPreCat1Group( <P1C> ) ## DeclareAttribute( "PeifferSubgroup", Is2DimensionalGroup ); DeclareAttribute( "PeifferSub2DimensionalGroup", Is2DimensionalGroup ); DeclareOperation( "PeifferSubgroupPreXMod", [ IsPreXMod ] ); DeclareOperation( "PeifferSubgroupPreCat1Group", [ IsPreCat1Group ] ); ############################################################################# ## #O PreXModByBoundaryAndAction( <bdy>, <act> ) #O PreXModWithTrivialRange( <bdy>, <act> ) ## DeclareOperation( "PreXModByBoundaryAndAction", [ IsGroupHomomorphism, IsGroupHomomorphism ] ); DeclareOperation( "PreXModWithTrivialRange", [ IsGroup, IsGroup ] ); ############################################################################# ## #F XMod( <args> ) #O AsXMod( <arg> ) #O XModByBoundaryAndAction( <bdy>, <act> ) #O XModByTrivialAction( <f> ) #O XModByNormalSubgroup( <G>, <N> ) #O XModByCentralExtension( <hom> ) #O XModByGroupOfAutomorphisms( <G>, <A> ) #A XModByAutomorphismGroup( <G> ) #A XModByInnerAutomorphismGroup( <G> ) #O XModByAbelianModule( <R> ) #A XModByPeifferQuotient( <PM> ) #O XModByPullback( <PM>, <hom> ) ## DeclareGlobalFunction( "XMod" ); DeclareOperation( "AsXMod", [ IsDomain ] ); DeclareOperation( "XModByBoundaryAndAction", [ IsGroupHomomorphism, IsGroupHomomorphism ] ); DeclareOperation( "XModByTrivialAction", [ IsGroupHomomorphism ] ); DeclareOperation( "XModByNormalSubgroup", [ IsGroup, IsGroup ] ); DeclareOperation( "XModByCentralExtension", [ IsGroupHomomorphism ] ); DeclareOperation( "XModByGroupOfAutomorphisms", [ IsGroup, IsGroup ] ); DeclareAttribute( "XModByAutomorphismGroup", IsGroup ); DeclareAttribute( "XModByInnerAutomorphismGroup", IsGroup ); DeclareOperation( "XModByAbelianModule", [ IsAbelianModule ] ); DeclareAttribute( "XModByPeifferQuotient", IsPreXMod ); DeclareOperation( "XModByPullback", [ IsXMod, IsGroupHomomorphism ] ); ############################################################################# ## #A KernelCokernelXMod( <2dgp> ) ## DeclareAttribute( "KernelCokernelXMod", Is2DimensionalGroup ); ############################################################################# ## #P IsTrivialAction2DimensionalGroup( <obj> ) #P IsNormalSubgroup2DimensionalGroup( <obj> ) #P IsCentralExtension2DimensionalGroup( <obj> ) #P IsAutomorphismGroup2DimensionalGroup( <XM> ) #P IsAbelianModule2DimensionalGroup( <obj> ) #P IsFreeXMod( <XM> ) ## DeclareProperty( "IsTrivialAction2DimensionalGroup", Is2DimensionalGroup ); DeclareProperty( "IsNormalSubgroup2DimensionalGroup", Is2DimensionalGroup ); DeclareProperty( "IsCentralExtension2DimensionalGroup", Is2DimensionalGroup ); DeclareProperty( "IsAutomorphismGroup2DimensionalGroup", Is2DimensionalGroup ); DeclareProperty( "IsAbelianModule2DimensionalGroup", Is2DimensionalGroup ); DeclareProperty( "IsFreeXMod", IsPreXModObj ); ############################################################################# ## #O IsSub2DimensionalGroup( <obj>, <sub> ) #O IsSubPreXMod( <obj>, <subobj> ) #O IsSubXMod( <obj>, <subobj> ) #O IsSubPreCat1Group( <obj>, <subobj> ) #O IsSubCat1Group( <obj>, <subobj> ) #O IsNormalSub2DimensionalDomain( <obj>, <subobj> ) ## DeclareOperation( "IsSub2DimensionalGroup", [ Is2DimensionalGroup, Is2DimensionalGroup ] ); DeclareOperation( "IsSubPreXMod", [ Is2DimensionalGroup, Is2DimensionalGroup ] ); DeclareOperation( "IsSubXMod", [ Is2DimensionalGroup, Is2DimensionalGroup ] ); DeclareOperation( "IsSubPreCat1Group", [ Is2DimensionalGroup, Is2DimensionalGroup ] ); DeclareOperation( "IsSubCat1Group", [ Is2DimensionalGroup, Is2DimensionalGroup ] ); DeclareOperation( "IsNormalSub2DimensionalDomain", [ Is2DimensionalGroup, Is2DimensionalGroup ] ); ############################################################################## ## #O Sub2DimensionalGroup( <obj>, <src>, <rng> ) #O SubPreXMod( <PM, Ssrc, Srng> ) #O SubXMod( <PM, Ssrc, Srng> ) #O SubPreCat1Group( <C>, <H> ) #O SubCat1Group( <C>, <H> ) ## DeclareOperation( "Sub2DimensionalGroup", [ Is2DimensionalGroup, IsGroup, IsGroup ] ); DeclareOperation( "SubPreXMod", [ IsPreXMod, IsGroup, IsGroup ] ); DeclareOperation( "SubXMod", [ IsXMod, IsGroup, IsGroup ] ); DeclareOperation( "SubPreCat1Group", [ IsPreCat1Group, IsGroup, IsGroup ] ); DeclareOperation( "SubCat1Group", [ IsCat1Group, IsGroup, IsGroup ] ); ############################################################################# ## #O TrivialSub2DimensionalGroup( <obj> ) #A TrivialSubPreXMod( <obj> ) #A TrivialSubXMod( <obj> ) #A TrivialSubPreCat1Group( <obj> ) #A TrivialSubCat1Group( <obj> ) #P IsIdentityPreCat1Group( <obj> ) #P IsPreCat1GroupWithIdentityEmbedding( <obj> ) #P IsSymmetric2DimensionalGroup( <obj> ) ## DeclareOperation( "TrivialSub2DimensionalGroup", [ Is2DimensionalGroup ] ); DeclareAttribute( "TrivialSubPreXMod", IsPreXMod ); DeclareAttribute( "TrivialSubXMod", IsXMod ); DeclareAttribute( "TrivialSubPreCat1Group", IsPreCat1Group ); DeclareAttribute( "TrivialSubCat1Group", IsCat1Group ); DeclareProperty( "IsIdentityPreCat1Group", IsPreCat1Group ); DeclareProperty( "IsPreCat1GroupWithIdentityEmbedding", IsPreCat1Group ); DeclareProperty( "IsSymmetric2DimensionalGroup", Is2DimensionalGroup ); ############################################################################# ## #O PreCat1Obj( <arg> ) #A HeadMap( <PCG> ) #A TailMap( <PCG> ) #A RangeEmbedding( <PCG> ) #A KernelEmbedding( <C> ) ## DeclareOperation( "PreCat1Obj", [ IsGroupHomomorphism, IsGroupHomomorphism, IsGroupHomomorphism ] ); DeclareAttribute( "HeadMap", IsPreCat1Group ); DeclareAttribute( "TailMap", IsPreCat1Group ); DeclareAttribute( "RangeEmbedding", IsPreCat1Group ); DeclareAttribute( "KernelEmbedding", IsPreCat1Group ); ############################################################################# ## #F PreCat1Group( <arg> ) #O PreCat1GroupByTailHeadEmbedding( <t>, <h>, <e> ) #O PreCat1GroupWithIdentityEmbedding( <tail>, <head> ) #A IsomorphicPreCat1GroupWithIdentityEmbedding( <PCG> ) #A IsomorphismToPreCat1GroupWithIdentityEmbedding( <PCG> ) #A TransposeCat1Group( <PCG> ) ## DeclareGlobalFunction( "PreCat1Group" ); DeclareOperation( "PreCat1GroupByTailHeadEmbedding", [ IsGroupHomomorphism, IsGroupHomomorphism, IsGroupHomomorphism ] ); DeclareOperation( "PreCat1GroupWithIdentityEmbedding", [ IsGroupHomomorphism, IsGroupHomomorphism ] ); DeclareAttribute( "IsomorphicPreCat1GroupWithIdentityEmbedding", IsPreCat1Group ); DeclareAttribute( "IsomorphismToPreCat1GroupWithIdentityEmbedding", IsPreCat1Group ); DeclareAttribute( "TransposeCat1Group", IsPreCat1Group ); ############################################################################# ## #A PreXModRecordOfPreCat1Group( <PCG> ) #A PreCat1GroupRecordOfPreXMod( <PM> ) #A XModOfCat1Group( <C1G> ) #A Cat1GroupOfXMod( <XM> ) ## DeclareAttribute( "PreXModRecordOfPreCat1Group", IsPreCat1Group ); DeclareAttribute( "PreCat1GroupRecordOfPreXMod", IsPreXMod ); DeclareAttribute( "XModOfCat1Group", IsCat1Group ); DeclareAttribute( "Cat1GroupOfXMod", IsXMod ); ############################################################################# ## #F Cat1Group( <arg> ) #O Cat1Select( <size>, <gpnum>, <num> ) #O PermCat1Select( <size>, <gpnum>, <num> ) #O Cat1GroupByPeifferQuotient( <PM> ) #O DiagonalCat1Group( <list> ) ## DeclareGlobalFunction( "Cat1Group" ); DeclareOperation( "Cat1Select", [ IsInt, IsInt, IsInt ] ); DeclareOperation( "Cat1Select", [ IsInt, IsInt ] ); DeclareOperation( "Cat1Select", [ IsInt ] ); DeclareOperation( "PermCat1Select", [ IsInt, IsInt, IsInt ] ); DeclareOperation( "Cat1GroupByPeifferQuotient", [ IsPreCat1Group ] ); DeclareOperation( "DiagonalCat1Group", [ IsList ] ); ############################################################################# ## #O AllCat1GroupsWithImage( <gp>, <subgp> ) #O AllCat1GroupsWithImageIterator( <gp>, <subgp> ) #O AllCat1GroupsWithImageNumber( <gp>, <subgp> ) #F DoAllCat1GroupsWithImageIterator #O AllCat1GroupsWithImageUpToIsomorphism( <gp> ) ## DeclareOperation( "AllCat1GroupsWithImage", [ IsGroup, IsGroup ] ); DeclareOperation( "AllCat1GroupsWithImageIterator", [ IsGroup, IsGroup ] ); DeclareOperation( "AllCat1GroupsWithImageNumber", [ IsGroup, IsGroup ] ); DeclareGlobalFunction( "DoAllCat1GroupsWithImageIterator" ); DeclareOperation( "AllCat1GroupsWithImageUpToIsomorphism", [ IsGroup ] ); ############################################################################# ## #O AllCat1Groups( <gp> ) #O AllCat1GroupsIterator( <gp> ) #F DoAllCat1GroupsIterator #O AllCat1GroupsMatrix( <gp> ) #A AllCat1GroupsNumber( <gp> ) #O AllCat1GroupsUpToIsomorphism( <gp> ) #O AllCat1GroupFamilies( <gp> ) ## DeclareOperation( "AllCat1Groups", [ IsGroup ] ); DeclareOperation( "AllCat1GroupsIterator", [ IsGroup ] ); DeclareGlobalFunction( "DoAll DeclareOperation( "AllCat1GroupsMatrix", [ IsGroup ] ); DeclareAttribute( "AllCat1Group DeclareOperation( "AllCat1GroupsUpToIsomorphism", [ IsGroup ] ); DeclareOperation( "AllCat1GroupFamilies", [ IsGroup ] ); ############################################################################# ## #A DirectProduct2dInfo( <D> ) #A Coproduct2dInfo( <D> ) ## DeclareAttribute( "DirectProduct2dInfo", Is2DimensionalDomain, "mutable" ); DeclareAttribute( "Coproduct2dInfo", Is2DimensionalDomain, "mutable" ); ############################################################################# ## #A NormalSubXMods( <XM> ) #A NormalSubCat1Groups( <C1G> ) ## DeclareAttribute( "NormalSubXMods", IsXMod ); DeclareAttribute( "NormalSubCat1Groups", IsCat1Group ); ############################################################################# ## #A CatnGroupNumbers( <G> ) #A CatnGroupLists( <G> ) #A InitCatnGroupRecords( <G> ) ## DeclareAttribute( "CatnGroupNumbers", IsGroup, "mutable" ); DeclareAttribute( "CatnGroupLists", IsGroup, "mutable" ); DeclareOperation( "InitCatnGroupRecords", [ IsGroup ] ); [ Verzeichnis aufwärts0.99unsichere Verbindung ] |
2026-03-28