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#############################################################################
##
## gp4obj.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 cubes and
## (pre-)cat3-groups.
#############################################################################
##
#A Front3DimensionalGroup( <PS> )
#A Left3DimensionalGroup( <PS> )
#A Up3DimensionalGroup( <PS> )
#A Right3DimensionalGroup( <PS> )
#A Down3DimensionalGroup ( <PS> )
#A Back3DimensionalGroup( <PS> )
##
DeclareAttribute( "Front3DimensionalGroup", IsHigherDimensionalGroup );
DeclareAttribute( "Left3DimensionalGroup", IsHigherDimensionalGroup );
DeclareAttribute( "Up3DimensionalGroup", IsHigherDimensionalGroup );
DeclareAttribute( "Right3DimensionalGroup", IsHigherDimensionalGroup );
DeclareAttribute( "Down3DimensionalGroup", IsHigherDimensionalGroup );
DeclareAttribute( "Back3DimensionalGroup", IsHigherDimensionalGroup );
#############################################################################
##
#A Size4d( <obj> )
##
DeclareAttribute( "Size4d", IsHigherDimensionalDomain );
#############################################################################
##
#R IsPreCat3GroupObj ( <obj> )
#T PreCat3GroupObjType
#O PreCat3GroupObj( <cat2gp>, <cat2 gp> )
## A pre-cat3-group is a cube of commuting pre-cat1-groups
##
DeclareRepresentation( "IsPreCat3GroupObj",
IsHigherDimensionalGroup and IsAttributeStoringRep,
[ "front3d", "left3d", "up3d", "right3d", "down3d", "back3d" ] );
BindGlobal( "PreCat3GroupObjType",
NewType( FamilyHigherDimensionalGroup, IsPreCat3GroupObj ) );
DeclareOperation( "PreCat3GroupObj", [ IsList] );
#############################################################################
##
#P IsPreCat3Group( <PCG> )
#P IsCat3Group( <C1G> )
##
DeclareProperty( "IsPreCat3Group", IsHigherDimensionalGroup );
DeclareProperty( "IsCat3Group", IsHigherDimensionalGroup );
InstallTrueMethod( IsPreCat3Group, IsCat3Group );
#############################################################################
##
#F PreCat3Group( <arg> )
#F Cat3Group( <arg> }
#F DetermineRemainingFaces( <arg> )
#O DetermineRemainingCat2Groups( <front> <left> )
#O PreCat3GroupByPreCat2Groups( <front>,<left>,<up>,<right>,<down>,<back> )
##
DeclareGlobalFunction( "PreCat3Group" );
DeclareGlobalFunction( "Cat3Group" );
DeclareGlobalFunction( "DetermineRemainingFaces" );
DeclareOperation( "DetermineRemainingCat2Groups",
[ IsPreCat2Group, IsPreCat2Group ] );
DeclareOperation( "PreCat3GroupByPreCat2Groups",
[ IsPreCat2Group, IsPreCat2Group, IsPreCat2Group,
IsPreCat2Group, IsPreCat2Group, IsPreCat2Group ] );
#############################################################################
##
#O AllCat3Groups( <G> )
#O AllCat3GroupsIterator( <gp> )
#A AllCat3GroupsNumber( <gp> )
#O AllCat3GroupsUpToIsomorphism( <G> )
#O AllCat3GroupTriples( <G> )
##
DeclareOperation( "AllCat3Groups", [ IsGroup ] );
DeclareOperation( "AllCat3GroupsIterator", [ IsGroup ] ); DeclareAttribute( "AllCat3GroupsNumber", IsGroup );
DeclareOperation( "AllCat3GroupsUpToIsomorphism", [ IsGroup ] );
DeclareOperation( "AllCat3GroupTriples", [ IsGroup ] );
[ Dauer der Verarbeitung: 0.15 Sekunden
(vorverarbeitet)
]
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