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#############################################################################
##
## polarspace.gd FinInG package
## John Bamberg
## Anton Betten
## Jan De Beule
## Philippe Cara
## Michel Lavrauw
## Max Neunhoeffer
##
## Copyright 2018 Colorado State University
## Sabancı Üniversitesi
## Università degli Studi di Padova
## Universiteit Gent
## University of St. Andrews
## University of Western Australia
## Vrije Universiteit Brussel
##
##
## Declaration stuff for polar spaces
##
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# Subspaces of polar spaces
#############################################################################
DeclareCategory( "IsSubspaceOfClassicalPolarSpace", IsSubspaceOfProjectiveSpace );
DeclareCategory( "IsSubspacesOfClassicalPolarSpace", IsSubspacesOfProjectiveSpace );
DeclareRepresentation( "IsSubspacesOfClassicalPolarSpaceRep", IsSubspacesOfProjectiveSpaceRep, [ "geometry", "type" ] );
DeclareCategory( "IsAllSubspacesOfClassicalPolarSpace", IsAllSubspacesOfProjectiveSpace );
DeclareRepresentation( "IsAllSubspacesOfClassicalPolarSpaceRep", IsAllSubspacesOfProjectiveSpaceRep, [ "geometry", "type" ] );
DeclareCategory( "IsShadowSubspacesOfClassicalPolarSpace", IsShadowElementsOfLieGeometry );
DeclareRepresentation( "IsShadowSubspacesOfClassicalPolarSpaceRep", IsShadowElementsOfLieGeometryRep, [ "geometry", "type", "inner", "outer", "factorspace" ]);
#DeclareCategoryCollections("IsSubspaceOfClassicalPolarSpace");
#BindGlobal( "SoCPSFamily",
# NewFamily( "SoCPSFamily", IsSubspaceOfClassicalPolarSpace, IsSubspaceOfClassicalPolarSpace));
#BindGlobal( "SoCPSCollFamily", CollectionsFamily(SoCPSFamily) );
DeclareCategory( "IsFlagOfClassicalPolarSpace", IsFlagOfProjectiveSpace );
BindGlobal( "FlagsOfCPS", NewFamily( "FlagsOfCPSFamily", IsObject ));
BindGlobal( "IsFlagOfCPSType", NewType( FlagsOfCPS,
IsFlagOfClassicalPolarSpace and IsFlagOfIncidenceStructureRep) );
#############################################################################
# Categories and Representations:
#############################################################################
#DeclareCategory( "IsPerpOfVariety", IsAttributeStoringRep ); # not used
#DeclareCategory( "IsPolarity", IsAttributeStoringRep ); #not used anymore
#############################################################################
# Attributes and Properties:
#############################################################################
#DeclareAttribute( "ProjectiveDimension", IsClassicalPolarSpace );
DeclareAttribute( "SesquilinearForm", IsClassicalPolarSpace );
DeclareAttribute( "QuadraticForm", IsClassicalPolarSpace );
DeclareAttribute( "AmbientSpace", IsClassicalPolarSpace );
DeclareAttribute( "SimilarityGroup", IsClassicalPolarSpace );
DeclareAttribute( "IsometryGroup", IsClassicalPolarSpace );
DeclareAttribute( "SpecialIsometryGroup", IsClassicalPolarSpace );
DeclareAttribute( "IsomorphismCanonicalPolarSpace", IsClassicalPolarSpace );
DeclareAttribute( "IsomorphismCanonicalPolarSpaceWithIntertwiner", IsClassicalPolarSpace );
DeclareAttribute( "IsCanonicalPolarSpace", IsClassicalPolarSpace );
DeclareAttribute( "PolarSpaceType", IsClassicalPolarSpace );
DeclareAttribute( "CompanionAutomorphism", IsClassicalPolarSpace );
DeclareAttribute( "ClassicalGroupInfo", IsClassicalPolarSpace );
DeclareAttribute( "EquationForPolarSpace", IsClassicalPolarSpace );
DeclareAttribute( "NucleusOfParabolicQuadric", IsClassicalPolarSpace );
DeclareProperty( "IsEllipticQuadric", IsClassicalPolarSpace );
DeclareProperty( "IsSymplecticSpace", IsClassicalPolarSpace );
DeclareProperty( "IsParabolicQuadric", IsClassicalPolarSpace );
DeclareProperty( "IsHyperbolicQuadric", IsClassicalPolarSpace );
DeclareProperty( "IsHermitianPolarSpace", IsClassicalPolarSpace );
DeclareProperty( "IsStandardPolarSpace", IsClassicalPolarSpace );
#############################################################################
# Constructor operations:
#############################################################################
DeclareOperation( "PolarSpaceStandard", [IsForm, IsBool] );
DeclareOperation( "PolarSpace", [IsForm, IsField, IsGroup, IsFunction] );
DeclareOperation( "PolarSpace", [IsForm] );
DeclareOperation( "PolarMap", [IsClassicalPolarSpace] ); #only for internal use.
DeclareOperation( "TangentSpace", [IsSubspaceOfClassicalPolarSpace] );
DeclareOperation( "TangentSpace", [IsClassicalPolarSpace, IsSubspaceOfProjectiveSpace] );
DeclareOperation( "Pole", [IsClassicalPolarSpace, IsSubspaceOfProjectiveSpace] );
#DeclareOperation( "Polarisation", [IsQuadraticForm] ); #We can use now AssociatedBilinearForm
#DeclareOperation( "IsTotallySingular", [ IsClassicalPolarSpace and IsClassicalPolarSpaceRep,
# IsSubspaceOfProjectiveSpace ] );
#DeclareOperation( "IsTotallyIsotropic", [ IsClassicalPolarSpace and IsClassicalPolarSpaceRep,
# IsSubspaceOfProjectiveSpace ] );
DeclareOperation( "TypeOfSubspace", [ IsClassicalPolarSpace, IsSubspaceOfProjectiveSpace ]);
DeclareOperation( "CanonicalOrbitRepresentativeForSubspaces", [IsString, IsPosInt, IsField]);
DeclareOperation( "RandomSubspace", [IsClassicalPolarSpace, IsPosInt]);
DeclareOperation( "NumberOfTotallySingularSubspaces", [IsClassicalPolarSpace, IsPosInt]);
DeclareOperation( "EllipticQuadric", [IsPosInt, IsField] );
DeclareOperation( "EllipticQuadric", [IsPosInt, IsPosInt ]);
DeclareOperation( "SymplecticSpace", [IsPosInt, IsField] );
DeclareOperation( "SymplecticSpace", [IsPosInt, IsPosInt] );
DeclareOperation( "ParabolicQuadric", [IsPosInt, IsField] );
DeclareOperation( "ParabolicQuadric", [IsPosInt, IsPosInt] );
DeclareOperation( "HyperbolicQuadric", [IsPosInt, IsField] );
DeclareOperation( "HyperbolicQuadric", [IsPosInt, IsPosInt] );
DeclareOperation( "HermitianPolarSpace", [IsPosInt, IsField] );
DeclareOperation( "HermitianPolarSpace", [IsPosInt, IsPosInt] );
DeclareOperation( "CanonicalPolarSpace", [IsClassicalPolarSpace] );
DeclareOperation( "StandardPolarSpace", [IsClassicalPolarSpace] );
#DeclareAttribute( "DefiningPolarity", IsClassicalPolarSpace );
DeclareOperation( "Span", [IsSubspaceOfClassicalPolarSpace, IsSubspaceOfClassicalPolarSpace, IsBool] );
[ Dauer der Verarbeitung: 0.15 Sekunden
(vorverarbeitet)
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