| 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 12 kB |
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Quelle gp3obj.gd Sprache: unbekannt |
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## ## gp3obj.gd GAP4 package `XMod' Chris Wensley ## Alper Odabas #Y Copyright (C) 2001-2025, Chris Wensley et al, ## ## This file declares generic methods for (pre-)crossed squares and ## (pre-)cat2-groups. ############################################################################# ## #P IsPerm3DimensionalGroup( <obj> ) #P IsFp3DimensionalGroup( <obj> ) #P IsPc3DimensionalGroup( <obj> ) ## DeclareProperty( "IsPerm3DimensionalGroup", IsHigherDimensionalGroup ); DeclareProperty( "IsFp3DimensionalGroup", IsHigherDimensionalGroup ); DeclareProperty( "IsPc3DimensionalGroup", IsHigherDimensionalGroup ); ############################################################################# ## #A Size3d( <obj> ) #A CrossedPairing( <3dgp> ) ## DeclareAttribute( "Size3d", Is3DimensionalDomain ); DeclareAttribute( "CrossedPairing", Is3DimensionalDomain ); ############################################################################# ## #O CrossedPairingByCommutators #O CrossedPairingByDerivation #O CrossedPairingBySingleXModAction #A PrincipalCrossedPairing #O CrossedPairingByConjugators #O CrossedPairingByPreImages ## DeclareOperation( "CrossedPairingByCommutators", [ IsGroup, IsGroup, IsGroup ] ); DeclareOperation( "CrossedPairingByDerivations", [ IsXMod ] ); DeclareOperation( "CrossedPairingBySingleXModAction", [ IsXMod, IsXMod ] ); DeclareAttribute( "PrincipalCrossedPairing", IsXMod ); DeclareOperation( "CrossedPairingByConjugators", [ IsGroup ] ); DeclareOperation( "CrossedPairingByPreImages", [ IsXMod, IsXMod ] ); ############################################################################# ## #P IsSymmetric3DimensionalGroup( <obj> ) DeclareProperty( "IsSymmetric3DimensionalGroup", IsHigherDimensionalGroup ); ############################################################################# ## #A Up2DimensionalGroup( <PS> ) #A Down2DimensionalGroup ( <PS> ) #A Left2DimensionalGroup( <PS> ) #A Right2DimensionalGroup( <PS> ) #A Diagonal2DimensionalGroup( <PS> ) #A Subdiagonal2DimensionalGroup( <PS> ) #A CrossDiagonalActions( <PS> ) #A CrossedPairing( <PS> ) #A Transpose3DimensionalGroup( <PS> ) #A LeftRightMorphism( <PS> ) #A UpDownMorphism( <PS> ) ## DeclareAttribute( "Up2DimensionalGroup", IsHigherDimensionalGroup ); DeclareAttribute( "Left2DimensionalGroup", IsHigherDimensionalGroup ); DeclareAttribute( "Down2DimensionalGroup", IsHigherDimensionalGroup ); DeclareAttribute( "Right2DimensionalGroup", IsHigherDimensionalGroup ); DeclareAttribute( "Diagonal2DimensionalGroup", IsHigherDimensionalGroup ); DeclareAttribute( "Subdiagonal2DimensionalGroup", IsHigherDimensionalGroup ); DeclareAttribute( "CrossDiagonalActions", IsHigherDimensionalGroup ); DeclareAttribute( "CrossedPairing", IsHigherDimensionalGroup ); DeclareAttribute( "Transpose3DimensionalGroup", IsHigherDimensionalGroup ); DeclareAttribute( "LeftRightMorphism", IsHigherDimensionalGroup ); DeclareAttribute( "UpDownMorphism", IsHigherDimensionalGroup ); ############################################################################# ## #R IsPreCrossedSquareObj ( <obj> ) #T PreCrossedSquareObjType . . . . . . . . . . . . type for crossed squares #O PreCrossedSquareObj( <bdy>, <act> ) ## A pre-crossed square is a square of pre-crossed modules ## DeclareRepresentation( "IsPreCrossedSquareObj", IsHigherDimensionalGroup and IsAttributeStoringRep, [ "up2d", "left2d", "right2d", "down2d", "action", "pairing" ] ); BindGlobal( "PreCrossedSquareObjType", NewType( FamilyHigherDimensionalGroup, IsPreCrossedSquareObj ) ); DeclareOperation( "PreCrossedSquareObj", [ IsPreXMod, IsPreXMod, IsPreXMod, IsPreXMod, IsObject, IsObject] ); ############################################################################# ## #P IsPreCrossedSquare( <PM> } #P IsCrossedSquare( <PM> ) ## DeclareProperty( "IsPreCrossedSquare", IsHigherDimensionalGroup ); DeclareProperty( "IsCrossedSquare", IsHigherDimensionalGroup ); InstallTrueMethod( IsHigherDimensionalGroup, IsPreCrossedSquare ); InstallTrueMethod( IsPreCrossedSquare, IsCrossedSquare ); ############################################################################# ## #F PreCrossedSquare( <args> ) #F CrossedSquare( <args> ) #O PreCrossedSquareByPreXMods( <up>, <left>, <down>, <right>, <diag>, <xpair> ) #O CrossedSquareByXMods( <up>, <left>, <down>, <right>, <diag>, <xpair> ) #O CrossedSquareByNormalSubgroups( <L>, <M>, <N>, <P> ) #O CrossedSquareByNormalSubXMod( <xmod>, <subxmod> ) #O CrossedSquareByPullback( <xmod>, <xmod> ) #A CrossedSquareByAutomorphismGroup( <gp> ) #A ActorCrossedSquare( <xmod> ) #A CrossedSquareByXModSplitting( <xmod> ) ## DeclareGlobalFunction( "PreCrossedSquare" ); DeclareGlobalFunction( "CrossedSquare" ); DeclareOperation( "PreCrossedSquareByPreXMods", [ IsPreXMod, IsPreXMod, IsPreXMod, IsPreXMod, IsPreXMod, IsFunction ] ); DeclareOperation( "CrossedSquareByXMods", [ IsXMod, IsXMod, IsXMod, IsXMod, IsXMod, IsFunction ] ); DeclareOperation( "CrossedSquareByNormalSubgroups", [ IsGroup, IsGroup, IsGroup, IsGroup ] ); DeclareOperation( "CrossedSquareByNormalSubgroups", [ IsGroup, IsGroup, IsGroup ] ); DeclareOperation( "CrossedSquareByNormalSubXMod", [ IsXMod, IsXMod ] ); DeclareOperation( "CrossedSquareByPullback", [ IsXMod, IsXMod ] ); DeclareAttribute( "CrossedSquareByAutomorphismGroup", IsGroup ); DeclareAttribute( "ActorCrossedSquare", IsXMod ); DeclareAttribute( "CrossedSquareByXModSplitting", IsXMod ); ############################################################################# ## #R IsPreCat2GroupObj ( <obj> ) #T PreCat2GroupObjType #O PreCat2GroupObj( <cat1gp>, <cat1gp> ) ## A pre-cat2-group is a square of commuting pre-cat1-groups ## DeclareRepresentation( "IsPreCat2GroupObj", IsHigherDimensionalGroup and Is3DimensionalDomain and IsAttributeStoringRep, [ "up", "left", "right", "down", "diag" ] ); BindGlobal( "PreCat2GroupObjType", NewType( FamilyHigherDimensionalGroup, IsPreCat2GroupObj ) ); DeclareOperation( "PreCat2GroupObj", [ IsList ] ); ############################################################################# ## #P IsPreCat2Group( <PCG> ) #P IsCat2Group( <C1G> ) ## DeclareProperty( "IsPreCat2Group", IsHigherDimensionalGroup ); DeclareProperty( "IsCat2Group", IsHigherDimensionalGroup ); InstallTrueMethod( IsPreCat2Group, IsCat2Group ); ############################################################################# ## #F PreCat2Group( <arg> ) #F Cat2Group( <arg> } #O DetermineRemainingCat1Groups( <up>, <left> ) #O PreCat2GroupByPreCat1Groups( <up>, <left>, <right>, <down>, <diag> ) ## DeclareGlobalFunction( "PreCat2Group" ); DeclareGlobalFunction( "Cat2Group" ); DeclareOperation( "DetermineRemainingCat1Groups", [ IsPreCat1Group, IsPreCat1Group ] ); DeclareOperation( "PreCat2GroupByPreCat1Groups", [ IsPreCat1Group, IsPreCat1Group, IsPreCat1Group, IsPreCat1Group, IsPreCat1Group ] ); ############################################################################# ## ## functions for the paper "Computing 3-Dimensional Groups ..." ## #O AllCat2GroupsWithImages( <G> <R> <Q> ) #O AllCat2GroupsWithImagesIterator( <G> <R> <Q> ) #F DoAllCat2GroupsWithImagesIterator #O AllCat2GroupsWithFixedUp( <G> <C> ) #O AllCat2GroupsWithFixedUpIterator( <G> <C> ) #F DoAllCat2GroupsWithFixedUpIterator #O AllCat2GroupsWithImagesNumber( <G> <R> <Q> ) #O AllCat2GroupsWithImagesUpToIsomorphism( <G> <R> <Q> ) ## DeclareOperation( "AllCat2GroupsWithImages", [ IsGroup, IsGroup, IsGroup ] ); DeclareOperation( "AllCat2GroupsWithImagesIterator", [ IsGroup, IsGroup, IsGroup ] ); DeclareGlobalFunction( "DoAllCat2GroupsWithImagesIterator" ); DeclareOperation( "AllCat2GroupsWithImagesNumber", [ IsGroup, IsGroup, IsGroup ] ); DeclareOperation( "AllCat2GroupsWithImagesUpToIsomorphism", [ IsGroup, IsGroup, IsGroup ] ); DeclareOperation( "AllCat2GroupsWithFixedUpAndLeftRange", [ IsPreCat1Group, IsGroup ] ); DeclareOperation( "AllCat2GroupsWithFixedUp", [ IsPreCat1Group ] ); ############################################################################# ## ## more functions for the paper "Computing 3-Dimensional Groups ..." ## #O AllCat2Groups( <G> ) #O AllCat2GroupsIterator( <gp> ) #O AllCat2GroupsMatrix( <G> ) #A AllCat2GroupsNumber( <gp> ) #O AllCat2GroupsUpToIsomorphism( <G> ) #O TableRowForCat1Groups( <G> ) #O TableRowForCat2Groups( <G> ) ## DeclareOperation( "AllCat2Groups", [ IsGroup ] ); DeclareOperation( "AllCat2GroupsIterator", [ IsGroup ] ); DeclareOperation( "AllCat2Gro DeclareAttribute( "AllCat2GroupsNumber", IsGroup ); DeclareOperation( "AllCat2GroupsUpToIsomorphism", [ IsGroup ] ); DeclareOperation( "AllCat2GroupFamilies", [ IsGroup ] ); DeclareOperation( "TableRowForCat1Groups", [ IsGroup ] ); DeclareOperation( "TableRowForCat2Groups", [ IsGroup ] ); ############################################################################# ## #O ConjugationActionForCrossedSquare( <G>, <N> ) #A PreCrossedSquareOfPreCat2Group( <PCG> ) #A PreCat2GroupOfPreCrossedSquare( <PS> } #A CrossedSquareOfCat2Group( <C1G> } #A Cat2GroupOfCrossedSquare( <XS> ) ## DeclareOperation( "ConjugationActionForCrossedSquare", [ IsGroup, IsGroup ] ); DeclareAttribute( "PreCrossedSquareOfPreCat2Group", IsPreCat2Group ); DeclareAttribute( "PreCat2GroupOfPreCrossedSquare", IsPreCrossedSquare ); DeclareAttribute( "CrossedSquareOfCat2Group", IsCat2Group ); DeclareAttribute( "Cat2GroupOfCrossedSquare", IsCrossedSquare ); ############################################################################# ## The following subfunctions were implemented in April 2025 for version 2.93 ############################################################################# ############################################################################# ## #O IsSubPreCrossedSquare( <pxs> <subpxs> ) #O IsSubCrossedSquare( <xs> <subxs> ) #O IsSubPreCat2Group( <pc1> <subpc1> ) #O IsSubCat2Group( <cat1> <subcat1 ) ## DeclareOperation( "IsSubPreCrossedSquare", [ IsHigherDimensionalGroup, IsHigherDimensionalGroup ] ); DeclareOperation( "IsSubCrossedSquare", [ IsHigherDimensionalGroup, IsHigherDimensionalGroup ] ); DeclareOperation( "IsSubPreCat2Group", [ IsHigherDimensionalGroup, IsHigherDimensionalGroup ] ); DeclareOperation( "IsSubCat2Group", [ IsHigherDimensionalGroup, IsHigherDimensionalGroup ] ); ############################################################################# ## #O SubPreCrossedSquare( <PXS>, <ul>, <ur>, <dl>, <dr> ) #O SubCrossedSquare( <XS>, <ul>, <ur>, <dl>, <dr> ) #O SubPreCat2Group( <PC2>, <ul>, <ur>, <dl> ) #O SubCat2Group( <C2>, <ul>, <ur>, <dl> ) ## DeclareOperation( "SubPreCrossedSquare", [ IsPreCrossedSquare, IsGroup, IsGroup, IsGroup, IsGroup ] ); DeclareOperation( "SubCrossedSquare", [ IsCrossedSquare, IsGroup, IsGroup, IsGroup, IsGroup ] ); DeclareOperation( "SubPreCat2Group", [ IsPreCat2Group, IsGroup, IsGroup, IsGroup ] ); DeclareOperation( "SubCat2Group", [ IsCat2Group, IsGroup, IsGroup, IsGroup ] ); ############################################################################# ## #O TrivialSub3DimensionalGroup( <obj> ) #A TrivialSubPreCrossedSquare( <obj> ) #A TrivialSubCrossedSquare( <obj> ) #A TrivialSubPreCat2Group( <obj> ) #A TrivialSubCat2Group( <obj> ) #P IsIdentityCat2Group( <C1G> ) ## DeclareOperation( "TrivialSub3DimensionalGroup", [ Is3DimensionalDomain ] ); DeclareAttribute( "TrivialSubPreCrossedSquare", IsPreCrossedSquare ); DeclareAttribute( "TrivialSubCrossedSquare", IsCrossedSquare ); DeclareAttribute( "TrivialSubPreCat2Group", IsPreCat2Group ); DeclareAttribute( "TrivialSubCat2Group", IsCat2Group ); DeclareProperty( "IsIdentityCat2Group", IsCat2Group ); ############################################################################# ## #A NormalSubCrossedSquares( <XS> } #A NormalSubXCat2Groups( <C1G> } ## DeclareAttribute( "NormalSubCrossedSquares", IsCrossedSquare ); DeclareAttribute( "NormalSubCat2Groups", IsCat2Group ); [ Dauer der Verarbeitung: 0.17 Sekunden (vorverarbeitet) ] |
2026-03-28