FinInG consists of the following components: geometry, liegeometry, group, projectivespace, correlations, polarspace/morphisms, enumerators, diagram, varieties, affinespace/affinegroup, gpolygons, and orbits-stabilisers. Each of these components corresponds with a component.gd and component.gi file. The file component.gi will be dependent on component.gd and all previously loaded .gd files, component1/component2 means that both component1.gi and component2.gi depend on the declarations in both component1.gd and component2.gd.
Operations geometry.gd: operations O: IncidenceStructure: [IsList, IsFunction, IsFunction, IsList] O: ResidueOfFlag: [IsFlagOfIncidenceStructure] O: ElementsOfIncidenceStructure: [IsIncidenceStructure] O: ElementsOfIncidenceStructure: [IsIncidenceStructure, IsPosInt] O: ElementsOfIncidenceStructure: [IsIncidenceStructure, IsString] O: NrElementsOfIncidenceStructure: [IsIncidenceStructure, IsPosInt] O: NrElementsOfIncidenceStructure: [IsIncidenceStructure, IsString] O: IncidenceGraph: [IsIncidenceStructure] O: Points: [IsIncidenceStructure] O: Lines: [IsIncidenceStructure] O: Planes: [IsIncidenceStructure] O: Solids: [IsIncidenceStructure] O: FlagOfIncidenceStructure: [IsIncidenceStructure, IsElementOfIncidenceStructureCollection] O: FlagOfIncidenceStructure: [IsIncidenceStructure, IsListandIsEmpty] O: ChamberOfIncidenceStructure: [IsElementOfIncidenceStructureCollection] O: ElementsOfFlag: [IsFlagOfIncidenceStructure] O: IsIncident: [IsElementOfIncidenceStructure, IsElementOfIncidenceStructure] O: IsIncident: [IsElementOfIncidenceStructure, IsFlagOfIncidenceStructure] O: IsIncident: [IsFlagOfIncidenceStructure, IsElementOfIncidenceStructure] O: ShadowOfElement: [IsElementOfIncidenceStructure, IsPosInt] O: IsCollinear: [IsIncidenceStructure, IsElementOfIncidenceStructure, IsElementOfIncidenceStructure] O: Span: [IsElementOfIncidenceStructure, IsElementOfIncidenceStructure] O: Meet: [IsElementOfIncidenceStructure, IsElementOfIncidenceStructure] O: Type: [IsElementOfIncidenceStructureandIsElementOfIncidenceStructureRep] O: Type: [IsElementsOfIncidenceStructureandIsElementsOfIncidenceStructureRep] O: Type: [IsFlagOfIncidenceStructureandIsFlagOfIncidenceStructureRep] O: Wrap: [IsIncidenceStructure, IsPosInt, IsObject] O: Unwrap: [IsElementOfIncidenceStructure] O: ObjectToElement: [IsIncidenceStructure, IsPosInt, IsObject] O: ObjectToElement: [IsIncidenceStructure, IsObject] O: UnderlyingObject: [IsElementOfIncidenceStructure] O: ShadowOfElement: [IsIncidenceStructure, IsElementOfIncidenceStructure, IsPosInt] O: ShadowOfElement: [IsIncidenceStructure, IsElementOfIncidenceStructure, IsString] O: ShadowOfFlag: [IsIncidenceStructure, IsFlagOfIncidenceStructure, IsPosInt] O: ShadowOfFlag: [IsIncidenceStructure, IsFlagOfIncidenceStructure, IsString] O: ShadowOfFlag: [IsIncidenceStructure, IsList, IsPosInt] O: ShadowOfFlag: [IsIncidenceStructure, IsList, IsString] O: ElementsIncidentWithElementOfIncidenceStructure: [IsElementOfIncidenceStructure, IsPosInt] O: Points: [IsElementOfIncidenceStructure] O: Lines: [IsElementOfIncidenceStructure] O: Planes: [IsElementOfIncidenceStructure] O: Solids: [IsElementOfIncidenceStructure] O: Hyperplanes: [IsElementOfIncidenceStructure] O: Points: [IsIncidenceStructure, IsElementOfIncidenceStructure] O: Lines: [IsIncidenceStructure, IsElementOfIncidenceStructure] O: Planes: [IsIncidenceStructure, IsElementOfIncidenceStructure] O: Solids: [IsIncidenceStructure, IsElementOfIncidenceStructure] O: Hyperplanes: [IsIncidenceStructure, IsElementOfIncidenceStructure] liegeometry.gd: operations O: UnderlyingVectorSpace: [IsLieGeometry] O: UnderlyingVectorSpace: [IsElementOfLieGeometry] O: UnderlyingVectorSpace: [IsFlagOfLieGeometry] O: VectorSpaceToElement: [IsLieGeometry, IsRowVector] O: VectorSpaceToElement: [IsLieGeometry, Is8BitVectorRep] O: VectorSpaceToElement: [IsLieGeometry, IsPlistRep] O: VectorSpaceToElement: [IsLieGeometry, Is8BitMatrixRep] O: VectorSpaceToElement: [IsLieGeometry, IsGF2MatrixRep] O: VectorSpaceToElement: [IsLieGeometry, IsCVecRep] O: VectorSpaceToElement: [IsLieGeometry, IsCMatRep] O: EmptySubspace: [IsLieGeometry] O: RandomSubspace: [IsVectorSpace, IsInt] O: IsIncident: [IsEmptySubspace, IsElementOfLieGeometry] O: IsIncident: [IsElementOfLieGeometry, IsEmptySubspace] O: IsIncident: [IsEmptySubspace, IsLieGeometry] O: IsIncident: [IsLieGeometry, IsEmptySubspace] O: IsIncident: [IsEmptySubspace, IsEmptySubspace] O: Span: [IsEmptySubspace, IsElementOfLieGeometry] O: Span: [IsElementOfLieGeometry, IsEmptySubspace] O: Span: [IsEmptySubspace, IsLieGeometry] O: Span: [IsLieGeometry, IsEmptySubspace] O: Span: [IsEmptySubspace, IsEmptySubspace] O: Span: [IsList] O: Meet: [IsEmptySubspace, IsElementOfLieGeometry] O: Meet: [IsElementOfLieGeometry, IsEmptySubspace] O: Meet: [IsEmptySubspace, IsLieGeometry] O: Meet: [IsLieGeometry, IsEmptySubspace] O: Meet: [IsEmptySubspace, IsEmptySubspace] O: ElementToElement: [IsLieGeometry, IsElementOfLieGeometry] O: ConvertElement: [IsLieGeometry, IsElementOfLieGeometry] O: ConvertElementNC: [IsLieGeometry, IsElementOfLieGeometry] group.gd: operations O: FindBasePointCandidates: [IsGroup, IsRecord, IsInt] O: FindBasePointCandidates: [IsGroup, IsRecord, IsInt, IsObject] O: ProjEl: [IsMatrixandIsFFECollColl] O: ProjEls: [IsList] O: Projectivity: [IsList, IsField] O: Projectivity: [IsProjectiveSpace, IsMatrix] O: ProjElWithFrob: [IsMatrixandIsFFECollColl, IsMapping] O: ProjElWithFrob: [IsMatrixandIsFFECollColl, IsMapping, IsField] O: ProjElsWithFrob: [IsList] O: ProjElsWithFrob: [IsList, IsField] O: CollineationOfProjectiveSpace: [IsList, IsField] O: CollineationOfProjectiveSpace: [IsList, IsMapping, IsField] O: CollineationOfProjectiveSpace: [IsProjectiveSpace, IsMatrix] O: CollineationOfProjectiveSpace: [IsProjectiveSpace, IsMatrix, IsMapping] O: CollineationOfProjectiveSpace: [IsProjectiveSpace, IsMapping] O: Collineation: [IsProjectiveSpace, IsMatrix] O: Collineation: [IsProjectiveSpace, IsMatrix, IsMapping] O: ProjectiveSemilinearMap: [IsList, IsMapping, IsField] O: ProjectivityByImageOfStandardFrameNC: [IsProjectiveSpace, IsList] O: MatrixOfCollineation: [IsProjGrpElWithFrobandIsProjGrpElWithFrobRep] O: MatrixOfCollineation: [IsProjGrpElandIsProjGrpElRep] O: FieldAutomorphism: [IsProjGrpElWithFrobandIsProjGrpElWithFrobRep] O: ActionOnAllProjPoints: [IsProjectiveGroupWithFrob] O: CanonicalGramMatrix: [IsString, IsPosInt, IsField] O: CanonicalQuadraticForm: [IsString, IsPosInt, IsField] O: SOdesargues: [IsInt, IsPosInt, IsFieldandIsFinite] O: GOdesargues: [IsInt, IsPosInt, IsFieldandIsFinite] O: SUdesargues: [IsPosInt, IsFieldandIsFinite] O: GUdesargues: [IsPosInt, IsFieldandIsFinite] O: Spdesargues: [IsPosInt, IsFieldandIsFinite] O: GeneralSymplecticGroup: [IsPosInt, IsFieldandIsFinite] O: GSpdesargues: [IsPosInt, IsFieldandIsFinite] O: DeltaOminus: [IsPosInt, IsFieldandIsFinite] O: DeltaOplus: [IsPosInt, IsFieldandIsFinite] O: GammaOminus: [IsPosInt, IsFieldandIsFinite] O: GammaO: [IsPosInt, IsFieldandIsFinite] O: GammaOplus: [IsPosInt, IsFieldandIsFinite] O: GammaU: [IsPosInt, IsFieldandIsFinite] O: GammaSp: [IsPosInt, IsFieldandIsFinite] projectivespace.gd: operations O: ProjectiveSpace: [IsInt, IsField] O: ProjectiveSpace: [IsInt, IsPosInt] O: IsIncident: [IsSubspaceOfProjectiveSpace, IsProjectiveSpace] O: IsIncident: [IsProjectiveSpace, IsSubspaceOfProjectiveSpace] O: IsIncident: [IsProjectiveSpace, IsProjectiveSpace] O: Hyperplanes: [IsProjectiveSpace] O: BaerSublineOnThreePoints: [ IsSubspaceOfProjectiveSpace, IsSubspaceOfProjectiveSpace, IsSubspaceOfProjectiveSpace] O: BaerSubplaneOnQuadrangle: [ IsSubspaceOfProjectiveSpace, IsSubspaceOfProjectiveSpace, IsSubspaceOfProjectiveSpace, IsSubspaceOfProjectiveSpace ] O: RandomSubspace: [IsProjectiveSpace, IsInt] O: RandomSubspace: [IsSubspaceOfProjectiveSpace, IsInt] O: RandomSubspace: [IsProjectiveSpace] O: Span: [IsProjectiveSpace, IsSubspaceOfProjectiveSpace] O: Span: [IsSubspaceOfProjectiveSpace, IsProjectiveSpace] O: Span: [IsSubspaceOfProjectiveSpace, IsSubspaceOfProjectiveSpace, IsBool] O: Span: [IsList, IsBool] O: Meet: [IsSubspaceOfProjectiveSpace, IsProjectiveSpace] O: Meet: [IsProjectiveSpace, IsSubspaceOfProjectiveSpace] O: Meet: [IsList] O: DualCoordinatesOfHyperplane: [IsSubspaceOfProjectiveSpace] O: HyperplaneByDualCoordinates: [IsProjectiveSpace, IsList] O: ComplementSpace: [IsVectorSpace, IsFFECollColl] O: ElationOfProjectiveSpace: [IsSubspaceOfProjectiveSpace, IsSubspaceOfProjectiveSpace, IsSubspaceOfProjectiveSpace] O: ProjectiveElationGroup: [IsSubspaceOfProjectiveSpace, IsSubspaceOfProjectiveSpace] O: ProjectiveElationGroup: [IsSubspaceOfProjectiveSpace] O: HomologyOfProjectiveSpace: [IsSubspaceOfProjectiveSpace, IsSubspaceOfProjectiveSpace, IsSubspaceOfProjectiveSpace, IsSubspaceOfProjectiveSpace ] O: ProjectiveHomologyGroup: [IsSubspaceOfProjectiveSpace, IsSubspaceOfProjectiveSpace] O: SingerCycleMat: [IsInt, IsInt] O: SingerCycleCollineation: [IsInt, IsInt] correlations.gd: operations O: StandardDualityOfProjectiveSpace: [IsProjectiveSpace] O: IdentityMappingOfElementsOfProjectiveSpace: [IsProjectiveSpace] O: ActionOnAllPointsHyperplanes: [IsProjGroupWithFrobWithPSIsom] O: ProjElWithFrobWithPSIsom: [IsMatrix and IsFFECollColl, IsMapping, IsField] O: ProjElWithFrobWithPSIsom: [IsMatrix and IsFFECollColl, IsMapping, IsField, IsStandardDualityOfProjectiveSpace] O: ProjElWithFrobWithPSIsom: [IsMatrix and IsFFECollColl, IsMapping, IsField, IsGeneralMapping and IsSPGeneralMapping and IsOne] O: ProjElsWithFrobWithPSIsom: [IsList, IsField] O: CorrelationOfProjectiveSpace: [IsList, IsField] O: CorrelationOfProjectiveSpace: [IsList, IsMapping, IsField] O: CorrelationOfProjectiveSpace: [IsList, IsField, IsStandardDualityOfProjectiveSpace] O: CorrelationOfProjectiveSpace: [IsList, IsField, IsIdentityMappingOfElementsOfProjectiveSpace] O: CorrelationOfProjectiveSpace: [IsList, IsMapping, IsField, IsStandardDualityOfProjectiveSpace] O: CorrelationOfProjectiveSpace: [IsList, IsMapping, IsField, IsIdentityMappingOfElementsOfProjectiveSpace] O: CorrelationOfProjectiveSpace: [IsProjectiveSpace, IsMatrix, IsMapping, IsStandardDualityOfProjectiveSpace] O: CorrelationOfProjectiveSpace: [IsProjectiveSpace, IsMatrix, IsMapping, IsIdentityMappingOfElementsOfProjectiveSpace] O: Correlation: [IsProjectiveSpace, IsMatrix, IsMapping, IsStandardDualityOfProjectiveSpace] O: Correlation: [IsProjectiveSpace, IsMatrix, IsMapping, IsIdentityMappingOfElementsOfProjectiveSpace] O: MatrixOfCorrelation: [IsProjGrpElWithFrobWithPSIsomandIsProjGrpElWithFrobWithPSIsomRep] O: FieldAutomorphism: [IsProjGrpElWithFrobWithPSIsomandIsProjGrpElWithFrobWithPSIsomRep] O: ProjectiveSpaceIsomorphism: [IsProjGrpElWithFrobWithPSIsomandIsProjGrpElWithFrobWithPSIsomRep] O: PolarityOfProjectiveSpaceOp: [IsForm] O: PolarityOfProjectiveSpace: [IsForm] O: PolarityOfProjectiveSpace: [IsMatrix, IsFieldandIsFinite] O: PolarityOfProjectiveSpace: [IsMatrix, IsFrobeniusAutomorphism, IsFieldandIsFinite] O: HermitianPolarityOfProjectiveSpace: [IsMatrix, IsFieldandIsFinite] O: PolarityOfProjectiveSpace: [IsClassicalPolarSpace] O: BaseField: [IsPolarityOfProjectiveSpace] O: IsAbsoluteElement: [IsElementOfIncidenceStructure, IsPolarityOfProjectiveSpace] O: GeometryOfAbsolutePoints: [IsPolarityOfProjectiveSpace] O: AbsolutePoints: [IsPolarityOfProjectiveSpace] O: PolarSpace: [IsPolarityOfProjectiveSpace] polarspace.gd: operations O: PolarSpaceStandard: [IsForm, IsBool] O: PolarSpace: [IsForm, IsField, IsGroup, IsFunction] O: PolarSpace: [IsForm] O: PolarMap: [IsClassicalPolarSpace] O: TangentSpace: [IsSubspaceOfClassicalPolarSpace] O: TangentSpace: [IsClassicalPolarSpace, IsSubspaceOfProjectiveSpace] O: Pole: [IsClassicalPolarSpace, IsSubspaceOfProjectiveSpace] O: TypeOfSubspace: [IsClassicalPolarSpace, IsSubspaceOfProjectiveSpace] O: CanonicalOrbitRepresentativeForSubspaces: [IsString, IsPosInt, IsField] O: RandomSubspace: [IsClassicalPolarSpace, IsPosInt] O: NumberOfTotallySingularSubspaces: [IsClassicalPolarSpace, IsPosInt] O: EllipticQuadric: [IsPosInt, IsField] O: EllipticQuadric: [IsPosInt, IsPosInt] O: SymplecticSpace: [IsPosInt, IsField] O: SymplecticSpace: [IsPosInt, IsPosInt] O: ParabolicQuadric: [IsPosInt, IsField] O: ParabolicQuadric: [IsPosInt, IsPosInt] O: HyperbolicQuadric: [IsPosInt, IsField] O: HyperbolicQuadric: [IsPosInt, IsPosInt] O: HermitianPolarSpace: [IsPosInt, IsField] O: HermitianPolarSpace: [IsPosInt, IsPosInt] O: CanonicalPolarSpace: [IsClassicalPolarSpace] O: StandardPolarSpace: [IsClassicalPolarSpace] O: Span: [IsSubspaceOfClassicalPolarSpace, IsSubspaceOfClassicalPolarSpace, IsBool] morphisms.gd: operations O: GeometryMorphismByFunction: [ IsAnyElementsOfIncidenceStructure, IsAnyElementsOfIncidenceStructure, IsFunction, IsBool, IsFunction ] O: GeometryMorphismByFunction: [ IsAnyElementsOfIncidenceStructure, IsAnyElementsOfIncidenceStructure, IsFunction, IsFunction ] O: GeometryMorphismByFunction: [ IsAnyElementsOfIncidenceStructure, IsAnyElementsOfIncidenceStructure, IsFunction ] O: IsomorphismPolarSpacesProjectionFromNucleus: [IsClassicalPolarSpace, IsClassicalPolarSpace, IsBool] O: IsomorphismPolarSpacesNC: [ IsClassicalPolarSpace, IsClassicalPolarSpace, IsBool ] O: IsomorphismPolarSpacesNC: [ IsClassicalPolarSpace, IsClassicalPolarSpace ] O: IsomorphismPolarSpaces: [ IsClassicalPolarSpace, IsClassicalPolarSpace, IsBool ] O: IsomorphismPolarSpaces: [ IsClassicalPolarSpace, IsClassicalPolarSpace ] O: NaturalEmbeddingBySubspace: [ IsLieGeometry, IsLieGeometry, IsSubspaceOfProjectiveSpace ] O: NaturalEmbeddingBySubspaceNC: [ IsLieGeometry, IsLieGeometry, IsSubspaceOfProjectiveSpace ] O: NaturalProjectionBySubspace: [ IsClassicalPolarSpace, IsSubspaceOfClassicalPolarSpace ] O: NaturalProjectionBySubspace: [ IsProjectiveSpace, IsSubspaceOfProjectiveSpace ] O: NaturalProjectionBySubspaceNC: [ IsClassicalPolarSpace, IsSubspaceOfClassicalPolarSpace ] O: NaturalProjectionBySubspaceNC: [ IsProjectiveSpace, IsSubspaceOfProjectiveSpace ] O: ShrinkMat: [IsBasis, IsMatrix] O: ShrinkMat: [IsField, IsField, IsVector] O: ShrinkVec: [IsField, IsField, IsVector] O: ShrinkVec: [IsField, IsField, IsVector, IsBasis] O: BlownUpProjectiveSpace: [IsBasis, IsProjectiveSpace] O: BlownUpProjectiveSpaceBySubfield: [IsField, IsProjectiveSpace] O: BlownUpSubspaceOfProjectiveSpace: [IsBasis, IsSubspaceOfProjectiveSpace] O: BlownUpSubspaceOfProjectiveSpaceBySubfield: [IsField, IsSubspaceOfProjectiveSpace] O: IsDesarguesianSpreadElement: [IsBasis, IsSubspaceOfProjectiveSpace] O: IsBlownUpSubspaceOfProjectiveSpace: [IsBasis, IsSubspaceOfProjectiveSpace] O: NaturalEmbeddingByFieldReduction: [ IsProjectiveSpace, IsField, IsBasis ] O: NaturalEmbeddingByFieldReduction: [ IsProjectiveSpace, IsField ] O: NaturalEmbeddingByFieldReduction: [ IsProjectiveSpace, IsProjectiveSpace ] O: NaturalEmbeddingByFieldReduction: [ IsProjectiveSpace, IsProjectiveSpace, IsBasis ] O: BilinearFormFieldReduction: [IsBilinearForm, IsField, IsFFE, IsBasis] O: QuadraticFormFieldReduction: [IsQuadraticForm, IsField, IsFFE, IsBasis] O: HermitianFormFieldReduction: [IsHermitianForm, IsField, IsFFE, IsBasis] O: BilinearFormFieldReduction: [IsBilinearForm, IsField, IsFFE] O: QuadraticFormFieldReduction: [IsQuadraticForm, IsField, IsFFE] O: HermitianFormFieldReduction: [IsHermitianForm, IsField, IsFFE] O: NaturalEmbeddingByFieldReduction: [IsClassicalPolarSpace, IsField, IsFFE, IsBasis, IsBool] O: NaturalEmbeddingByFieldReduction: [IsClassicalPolarSpace, IsField, IsFFE, IsBasis] O: NaturalEmbeddingByFieldReduction: [IsClassicalPolarSpace, IsField, IsFFE, IsBool] O: NaturalEmbeddingByFieldReduction: [IsClassicalPolarSpace, IsField, IsFFE] O: NaturalEmbeddingByFieldReduction: [IsClassicalPolarSpace, IsField, IsBool] O: NaturalEmbeddingByFieldReduction: [IsClassicalPolarSpace, IsField] O: NaturalEmbeddingByFieldReduction: [IsClassicalPolarSpace, IsClassicalPolarSpace, IsBool] O: NaturalEmbeddingByFieldReduction: [IsClassicalPolarSpace, IsClassicalPolarSpace] O: CanonicalEmbeddingByFieldReduction: [ IsClassicalPolarSpace, IsField, IsBool ] O: CanonicalEmbeddingByFieldReduction: [ IsClassicalPolarSpace, IsClassicalPolarSpace, IsBool ] O: NaturalEmbeddingBySubfield: [ IsProjectiveSpace, IsProjectiveSpace ] O: NaturalEmbeddingBySubfield: [ IsClassicalPolarSpace, IsClassicalPolarSpace, IsBool ] O: NaturalEmbeddingBySubfield: [ IsClassicalPolarSpace, IsClassicalPolarSpace ] O: PluckerCoordinates: [IsMatrix] O: InversePluckerCoordinates: [IsVector] O: PluckerCoordinates: [IsSubspaceOfProjectiveSpace] O: KleinCorrespondence: [IsField, IsBool] O: KleinCorrespondence: [IsField] O: KleinCorrespondence: [IsPosInt, IsBool] O: KleinCorrespondence: [IsPosInt] O: KleinCorrespondence: [IsClassicalPolarSpace, IsBool] O: KleinCorrespondence: [IsClassicalPolarSpace] O: KleinCorrespondenceExtended: [IsField, IsBool] O: KleinCorrespondenceExtended: [IsField] O: KleinCorrespondenceExtended: [IsPosInt, IsBool] O: KleinCorrespondenceExtended: [IsPosInt] O: KleinCorrespondenceExtended: [IsClassicalPolarSpace, IsBool] O: KleinCorrespondenceExtended: [IsClassicalPolarSpace] O: NaturalDualitySymplectic: [IsClassicalGQ, IsClassicalGQ, IsBool, IsBool] O: NaturalDualityHermitian: [IsClassicalGQ, IsClassicalGQ, IsBool, IsBool] O: SelfDualitySymplectic: [IsClassicalGQ, IsBool] O: SelfDualityParabolic: [IsClassicalGQ, IsBool] O: NaturalDuality: [IsClassicalGQ, IsClassicalGQ, IsBool] O: NaturalDuality: [IsClassicalGQ, IsClassicalGQ] O: NaturalDuality: [IsClassicalGQ, IsBool] O: NaturalDuality: [IsClassicalGQ] O: SelfDuality: [IsClassicalGQ, IsBool] O: SelfDuality: [IsClassicalGQ] O: ProjectiveCompletion: [IsAffineSpace] enumerators.gd: operations O: AntonEnumerator: [IsSubspacesOfClassicalPolarSpace] O: EnumeratorByOrbit: [IsSubspacesOfClassicalPolarSpace] diagram.gd: operations O: CosetGeometry: [IsGroup, IsHomogeneousList] O: ParabolicSubgroups: [IsCosetGeometry] O: AmbientGroup: [IsCosetGeometry] O: FlagToStandardFlag: [IsCosetGeometry, IsFlagOfCosetGeometry] O: ResidueOfFlag: [IsFlagOfCosetGeometry] O: CanonicalResidueOfFlag: [IsCosetGeometry, IsFlagOfCosetGeometry] O: RandomElement: [IsCosetGeometry] O: RandomFlag: [IsCosetGeometry] O: RandomChamber: [IsCosetGeometry] O: AutGroupIncidenceStructureWithNauty: [IsCosetGeometry] O: CorGroupIncidenceStructureWithNauty: [IsCosetGeometry] O: IsIsomorphicIncidenceStructureWithNauty: [IsCosetGeometry, IsCosetGeometry] O: Rk2GeoDiameter: [IsCosetGeometry, IsPosInt] O: Rk2GeoGonality: [IsCosetGeometry] O: GeometryOfRank2Residue: [IsRank2Residue] O: GeometryFromLabelledGraph: [IsObjectandIS_REC] O: Rank2Residues: [IsIncidenceGeometry] O: MakeRank2Residue: [IsRank2Residue] varieties.gd: operations O: AlgebraicVariety: [IsProjectiveSpace, IsList] O: AlgebraicVariety: [IsAffineSpace, IsList] O: AlgebraicVariety: [IsProjectiveSpace, IsPolynomialRing, IsList] O: AlgebraicVariety: [IsAffineSpace, IsPolynomialRing, IsList] O: PointsOfAlgebraicVariety: [IsAlgebraicVariety] O: Points: [IsAlgebraicVariety] O: ProjectiveVariety: [IsProjectiveSpace, IsPolynomialRing, IsList] O: ProjectiveVariety: [IsProjectiveSpace, IsList] O: HermitianVariety: [IsPosInt, IsField] O: HermitianVariety: [IsPosInt, IsPosInt] O: HermitianVariety: [IsProjectiveSpace, IsPolynomialRing, IsPolynomial] O: HermitianVariety: [IsProjectiveSpace, IsPolynomial] O: QuadraticVariety: [IsPosInt, IsField] O: QuadraticVariety: [IsPosInt, IsField, IsString] O: QuadraticVariety: [IsPosInt, IsPosInt] O: QuadraticVariety: [IsPosInt, IsPosInt, IsString] O: QuadraticVariety: [IsProjectiveSpace, IsPolynomialRing, IsPolynomial] O: QuadraticVariety: [IsProjectiveSpace, IsPolynomial] O: PolarSpace: [IsProjectiveVariety] O: AffineVariety: [IsAffineSpace, IsPolynomialRing, IsList] O: AffineVariety: [IsAffineSpace, IsList] O: SegreMap: [IsHomogeneousList] O: SegreMap: [IsHomogeneousList, IsField] O: SegreVariety: [IsHomogeneousList] O: SegreVariety: [IsHomogeneousList, IsField] O: PointsOfSegreVariety: [IsSegreVariety] O: SegreMap: [IsSegreVariety] O: SegreMap: [IsProjectiveSpace, IsProjectiveSpace] O: SegreMap: [IsPosInt, IsPosInt, IsField] O: SegreMap: [IsPosInt, IsPosInt, IsPosInt] O: SegreVariety: [IsProjectiveSpace, IsProjectiveSpace] O: SegreVariety: [IsPosInt, IsPosInt, IsField] O: SegreVariety: [IsPosInt, IsPosInt, IsPosInt] O: VeroneseMap: [IsProjectiveSpace] O: VeroneseMap: [IsPosInt, IsField] O: VeroneseMap: [IsPosInt, IsPosInt] O: VeroneseVariety: [IsProjectiveSpace] O: VeroneseVariety: [IsPosInt, IsField] O: VeroneseVariety: [IsPosInt, IsPosInt] O: PointsOfVeroneseVariety: [IsVeroneseVariety] O: VeroneseMap: [IsVeroneseVariety] O: GrassmannCoordinates: [IsSubspaceOfProjectiveSpace] O: GrassmannMap: [IsPosInt, IsProjectiveSpace] O: GrassmannMap: [IsPosInt, IsPosInt, IsPosInt] O: GrassmannMap: [IsSubspacesOfProjectiveSpace] O: GrassmannMap: [IsGrassmannVariety] O: GrassmannVariety: [IsPosInt, IsProjectiveSpace] O: GrassmannVariety: [IsPosInt, IsPosInt, IsField] O: GrassmannVariety: [IsPosInt, IsPosInt, IsPosInt] O: GrassmannVariety: [IsSubspacesOfProjectiveSpace] O: PointsOfGrassmannVariety: [IsGrassmannVariety] O: ConicOnFivePoints: [IsHomogeneousListand IsSubspaceOfProjectiveSpaceCollection ] affinespace.gd: operations O: VectorSpaceTransversal: [IsVectorSpace, IsFFECollColl] O: VectorSpaceTransversalElement: [IsVectorSpace, IsFFECollColl, IsVector] O: AffineSpace: [IsPosInt, IsField] O: AffineSpace: [IsPosInt, IsPosInt] O: Hyperplanes: [IsAffineSpace] O: AffineSubspace: [IsAffineSpace, IsRowVector] O: AffineSubspace: [IsAffineSpace, IsCVecRep] O: AffineSubspace: [IsAffineSpace, IsRowVector, IsPlistRep] O: AffineSubspace: [IsAffineSpace, IsRowVector, Is8BitMatrixRep] O: AffineSubspace: [IsAffineSpace, IsRowVector, IsGF2MatrixRep] O: AffineSubspace: [IsAffineSpace, IsCVecRep, IsCMatRep] O: RandomSubspace: [IsAffineSpace, IsInt] O: IsParallel: [IsSubspaceOfAffineSpace, IsSubspaceOfAffineSpace] O: UnderlyingVectorSpace: [IsAffineSpace] O: ParallelClass: [IsAffineSpace, IsSubspaceOfAffineSpace] O: ParallelClass: [IsSubspaceOfAffineSpace] affinegroup.gd: operations gpolygons.gd: operations O: GeneralisedPolygonByBlocks: [IsHomogeneousList] O: GeneralisedPolygonByIncidenceMatrix: [IsMatrix] O: GeneralisedPolygonByElements: [IsSet, IsSet, IsFunction] O: GeneralisedPolygonByElements: [IsSet, IsSet, IsFunction, IsGroup, IsFunction] O: DistanceBetweenElements: [IsElementOfGeneralisedPolygon, IsElementOfGeneralisedPolygon] O: DistanceBetweenElements: [IsSubspaceOfProjectiveSpace, IsSubspaceOfProjectiveSpace] O: BlockDesignOfGeneralisedPolygon: [IsGeneralisedPolygon] O: SplitCayleyHexagon: [IsFieldandIsFinite] O: SplitCayleyHexagon: [IsPosInt] O: SplitCayleyHexagon: [IsClassicalPolarSpace] O: TwistedTrialityHexagon: [IsFieldandIsFinite] O: TwistedTrialityHexagon: [IsPosInt] O: TwistedTrialityHexagon: [IsClassicalPolarSpace] O: G2fining: [IsPosInt, IsFieldandIsFinite] O: 3D4fining: [IsFieldandIsFinite] O: IsKantorFamily: [IsGroup, IsList, IsList] O: EGQByKantorFamily: [IsGroup, IsList, IsList] O: Wrap: [IsElationGQByKantorFamily, IsPosInt, IsPosInt, IsObject] O: IsAnisotropic: [IsFFECollColl, IsFieldandIsFinite] O: IsqClan: [IsFFECollCollColl, IsFieldandIsFinite] O: qClan: [IsFFECollCollColl, IsField] O: LinearqClan: [IsPosInt] O: FisherThasWalkerKantorBettenqClan: [IsPosInt] O: KantorMonomialqClan: [IsPosInt] O: KantorKnuthqClan: [IsPosInt] O: FisherqClan: [IsPosInt] O: BLTSetByqClan: [IsqClanObjandIsqClanRep] O: KantorFamilyByqClan: [IsqClanObjandIsqClanRep] O: EGQByqClan: [IsqClanObjandIsqClanRep] O: EGQByBLTSet: [IsList, IsSubspaceOfProjectiveSpace, IsSubspaceOfProjectiveSpace] O: EGQByBLTSet: [IsList] O: FlockGQByqClan: [IsqClanObj]
Attributes geometry.gd: attributes A: IsChamberOfIncidenceStructure: IsFlagOfIncidenceStructure A: IsEmptyFlag: IsFlagOfIncidenceStructure A: RankAttr: IsIncidenceStructure A: RankAttr: IsFlagOfIncidenceStructure A: TypesOfElementsOfIncidenceStructure: IsIncidenceStructure A: TypesOfElementsOfIncidenceStructurePlural: IsIncidenceStructure A: CollineationGroup: IsIncidenceStructure A: CorrelationCollineationGroup: IsIncidenceStructure A: CollineationAction: IsIncidenceStructure A: CorrelationAction: IsIncidenceStructure A: RepresentativesOfElements: IsIncidenceStructure A: AmbientGeometry: IsIncidenceStructure A: AmbientGeometry: IsFlagOfIncidenceStructure A: Size: IsFlagOfIncidenceStructure A: AmbientGeometry: IsElementOfIncidenceStructureandIsElementOfIncidenceStructureRep A: AmbientGeometry: IsElementsOfIncidenceStructureandIsElementsOfIncidenceStructureRep A: AmbientGeometry: IsAllElementsOfIncidenceStructure A: CollineationAction: IsGroup liegeometry.gd: attributes A: AmbientSpace: IsLieGeometry A: AmbientSpace: IsElementOfLieGeometry A: ProjectiveDimension: IsLieGeometry A: ProjectiveDimension: IsElementOfLieGeometry A: ProjectiveDimension: IsEmptySubspace A: Dimension: IsLieGeometry group.gd: attributes A: Dimension: IsProjectiveGroupWithFrob projectivespace.gd: attributes A: ProjectivityGroup: IsProjectiveSpace A: SpecialProjectivityGroup: IsProjectiveSpace A: Dimension: IsSubspaceOfProjectiveSpace A: Dimension: IsEmpty A: Coordinates: IsSubspaceOfProjectiveSpace A: CoordinatesOfHyperplane: IsSubspaceOfProjectiveSpace A: EquationOfHyperplane: IsSubspaceOfProjectiveSpace A: StandardFrame: IsProjectiveSpace A: StandardFrame: IsSubspaceOfProjectiveSpace correlations.gd: attributes A: Dimension: IsProjGroupWithFrobWithPSIsom A: GramMatrix: IsPolarityOfProjectiveSpace A: CompanionAutomorphism: IsPolarityOfProjectiveSpace A: SesquilinearForm: IsPolarityOfProjectiveSpace polarspace.gd: attributes A: SesquilinearForm: IsClassicalPolarSpace A: QuadraticForm: IsClassicalPolarSpace A: AmbientSpace: IsClassicalPolarSpace A: SimilarityGroup: IsClassicalPolarSpace A: IsometryGroup: IsClassicalPolarSpace A: SpecialIsometryGroup: IsClassicalPolarSpace A: IsomorphismCanonicalPolarSpace: IsClassicalPolarSpace A: IsomorphismCanonicalPolarSpaceWithIntertwiner: IsClassicalPolarSpace A: IsCanonicalPolarSpace: IsClassicalPolarSpace A: PolarSpaceType: IsClassicalPolarSpace A: CompanionAutomorphism: IsClassicalPolarSpace A: ClassicalGroupInfo: IsClassicalPolarSpace A: EquationForPolarSpace: IsClassicalPolarSpace A: NucleusOfParabolicQuadric: IsClassicalPolarSpace morphisms.gd: attributes A: Intertwiner: IsGeometryMorphism enumerators.gd: attributes diagram.gd: attributes A: DiagramOfGeometry: IsIncidenceGeometry A: IsFlagTransitiveGeometry: IsIncidenceGeometry A: IsResiduallyConnected: IsIncidenceGeometry A: IsConnected: IsIncidenceGeometry A: IsFirmGeometry: IsIncidenceGeometry A: IsThinGeometry: IsIncidenceGeometry A: IsThickGeometry: IsIncidenceGeometry A: BorelSubgroup: IsCosetGeometry A: StandardFlagOfCosetGeometry: IsCosetGeometry A: Rank2Parameters: IsCosetGeometry A: OrderVertex: IsVertexOfDiagram A: NrElementsVertex: IsVertexOfDiagram A: StabiliserVertex: IsVertexOfDiagram A: ResidueLabelForEdge: IsEdgeOfDiagram A: GirthEdge: IsEdgeOfDiagram A: PointDiamEdge: IsEdgeOfDiagram A: LineDiamEdge: IsEdgeOfDiagram A: ParametersEdge: IsEdgeOfDiagram A: GeometryOfDiagram: IsDiagram varieties.gd: attributes A: DefiningListOfPolynomials: IsAlgebraicVariety A: AmbientSpace: IsAlgebraicVariety A: SesquilinearForm: IsHermitianVariety A: QuadraticForm: IsQuadraticVariety A: Source: IsGeometryMap A: Range: IsGeometryMap affinespace.gd: attributes A: Dimension: IsAffineSpace A: AmbientSpace: IsAffineSpace A: AmbientSpace: IsSubspaceOfAffineSpace affinegroup.gd: attributes A: AffineGroup: IsAffineSpace gpolygons.gd: attributes A: Order: IsGeneralisedPolygon A: IncidenceMatrixOfGeneralisedPolygon: IsGeneralisedPolygon A: AmbientPolarSpace: IsGeneralisedHexagon A: ElationGroup: IsElationGQ A: BasePointOfEGQ: IsElationGQ A: IsLinearqClan: IsqClanObj A: DefiningPlanesOfEGQByBLTSet: IsElationGQByBLTSet A: CollineationSubgroup: IsElationGQByBLTSet
Properties geometry.gd: properties P: IsConfiguration: IsIncidenceStructure P: IsConstellation: IsIncidenceStructure liegeometry.gd: properties group.gd: properties P: IsProjectivity: IsProjGrpEl P: IsProjectivity: IsProjGrpElWithFrob P: IsStrictlySemilinear: IsProjGrpEl P: IsStrictlySemilinear: IsProjGrpElWithFrob P: IsCollineation: IsProjGrpEl P: IsCollineation: IsProjGrpElWithFrob P: IsProjectivityGroup: IsProjectiveGroupWithFrob P: IsCollineationGroup: IsProjectiveGroupWithFrob P: CanComputeActionOnPoints: IsProjectiveGroupWithFrob projectivespace.gd: properties correlations.gd: properties P: IsCorrelation: IsProjGrpElWithFrobWithPSIsom P: IsCorrelation: IsProjGrpElWithFrob P: IsCorrelation: IsProjGrpEl P: CanComputeActionOnPoints: IsProjGroupWithFrobWithPSIsom P: IsProjectivity: IsProjGrpElWithFrobWithPSIsom P: IsStrictlySemilinear: IsProjGrpElWithFrobWithPSIsom P: IsCollineation: IsProjGrpElWithFrobWithPSIsom P: IsProjectivityGroup: IsProjGroupWithFrobWithPSIsom P: IsCollineationGroup: IsProjGroupWithFrobWithPSIsom P: IsHermitianPolarityOfProjectiveSpace: IsPolarityOfProjectiveSpace P: IsSymplecticPolarityOfProjectiveSpace: IsPolarityOfProjectiveSpace P: IsOrthogonalPolarityOfProjectiveSpace: IsPolarityOfProjectiveSpace P: IsPseudoPolarityOfProjectiveSpace: IsPolarityOfProjectiveSpace polarspace.gd: properties P: IsEllipticQuadric: IsClassicalPolarSpace P: IsSymplecticSpace: IsClassicalPolarSpace P: IsParabolicQuadric: IsClassicalPolarSpace P: IsHyperbolicQuadric: IsClassicalPolarSpace P: IsHermitianPolarSpace: IsClassicalPolarSpace P: IsStandardPolarSpace: IsClassicalPolarSpace morphisms.gd: properties enumerators.gd: properties diagram.gd: properties varieties.gd: properties P: IsStandardHermitianVariety: IsHermitianVariety P: IsStandardQuadraticVariety: IsQuadraticVariety affinespace.gd: properties affinegroup.gd: properties gpolygons.gd: properties P: HasGraphWithUnderlyingObjectsAsVertices: IsGeneralisedPolygon
Functions geometry.gi: global functions F: HashFuncForElements F: HashFuncForSetElements liegeometry.gi: global functions group.gi: global functions F: MakeAllProjectivePoints F: IsFiningScalarMatrix F: OnProjPoints F: OnProjPointsWithFrob F: OnProjSubspacesNoFrob F: OnProjSubspacesWithFrob F: NiceMonomorphismByOrbit F: NiceMonomorphismByDomain projectivespace.gi: global functions F: OnProjSubspaces F: OnSetsProjSubspaces correlations.gi: global functions F: OnProjPointsWithFrobWithPSIsom F: OnProjSubspacesWithFrobWithPSIsom F: OnProjSubspacesExtended polarspace.gi: global functions morphisms.gi: global functions enumerators.gi: global functions F: PositionNonZeroFromRight F: FG_pos F: FG_ffenumber F: FG_alpha_power F: FG_log_alpha F: FG_beta_power F: FG_log_beta F: FG_norm_one_element F: FG_index_of_norm_one_element F: PG_element_normalize F: FG_evaluate_hyperbolic_quadratic_form F: FG_evaluate_hermitian_form F: FG_nb_pts_Nbar F: FG_nb_pts_S F: FG_nb_pts_N F: FG_nb_pts_N1 F: FG_nb_pts_Sbar F: FG_herm_nb_pts_N F: FG_herm_nb_pts_S F: FG_herm_nb_pts_N1 F: FG_herm_nb_pts_Sbar F: FG_N1_unrank F: FG_S_unrank F: FG_Sbar_unrank F: FG_Nbar_unrank F: FG_N_unrank F: FG_herm_N_unrank F: FG_herm_N_rank F: FG_herm_S_unrank F: FG_herm_S_rank F: FG_herm_N1_unrank F: FG_herm_N1_rank F: FG_herm_Sbar_unrank F: FG_herm_Sbar_rank F: FG_S_rank F: FG_N_rank F: FG_N1_rank F: FG_Sbar_rank F: FG_Nbar_rank F: QElementNumber F: QplusElementNumber F: QminusElementNumber F: QNumberElement F: QplusNumberElement F: QminusNumberElement F: HermElementNumber F: HermNumberElement F: FG_specialresidual F: FG_enum_orthogonal F: FG_enum_hermitian F: FG_enum_symplectic diagram.gi: global functions F: OnCosetGeometryElement F: DrawDiagram F: DrawDiagramWithNeato F: Drawing_Diagram varieties.gi: global functions affinespace.gi: global functions affinegroup.gi: global functions F: OnAffinePoints F: OnAffineNotPoints F: OnAffineSubspaces gpolygons.gi: global functions F: SplitCayleyPointToPlane5 F: SplitCayleyPointToPlane F: ZeroPointToOnePointsSpaceByTriality F: TwistedTrialityHexagonPointToPlaneByTwoTimesTriality F: OnKantorFamily orbits-stabilisers.gi: global functions
Methods geometry.gi: methods M: IncidenceStructure, [ IsList, IsFunction, IsFunction, IsList ], M: Rank, [IsIncidenceStructure], M: IncidenceGraph, [ IsIncidenceStructure ], M: ElementsOfIncidenceStructure, [IsIncidenceStructure, IsPosInt], M: ElementsOfIncidenceStructure, [IsIncidenceStructure, IsString], M: Iterator, [ IsElementsOfIncidenceStructure ], M: Enumerator, [ IsElementsOfIncidenceStructure ], M: NrElementsOfIncidenceStructure, [IsIncidenceStructure, IsString], M: NrElementsOfIncidenceStructure, [IsIncidenceStructure, IsPosInt], M: ChooseHashFunction, [ IsElementOfIncidenceStructure, IsPosInt ], M: ChooseHashFunction, [ CategoryCollections(IsElementOfIncidenceStructure), IsPosInt ], M: AmbientGeometry, [ IsElementsOfIncidenceStructure and IsElementsOfIncidenceStructureRep ], M: AmbientGeometry, [ IsAllElementsOfIncidenceStructure ], M: Type, [IsElementsOfIncidenceStructure and IsElementsOfIncidenceStructureRep], M: Wrap, [IsIncidenceStructure, IsPosInt, IsObject], M: Unwrap, [IsElementOfIncidenceStructure and IsElementOfIncidenceStructureRep], M: UnderlyingObject, [ IsElementOfIncidenceStructure and IsElementOfIncidenceStructureRep ], M: ObjectToElement, [ IsIncidenceStructure, IsPosInt, IsObject ], M: AmbientGeometry, [ IsElementOfIncidenceStructure and IsElementOfIncidenceStructureRep ], M: Intersection2, [IsElementOfIncidenceStructure, IsElementOfIncidenceStructure], M: Type, [ IsElementOfIncidenceStructure and IsElementOfIncidenceStructureRep ], M: \=, [IsElementOfIncidenceStructure, IsElementOfIncidenceStructure], M: \<, [IsElementOfIncidenceStructure, IsElementOfIncidenceStructure], M: \*, [IsElementOfIncidenceStructure, IsElementOfIncidenceStructure], M: IsIncident, [IsElementOfIncidenceStructure, IsElementOfIncidenceStructure], M: FlagOfIncidenceStructure, [ IsIncidenceStructure, IsElementOfIncidenceStructureCollection ], M: FlagOfIncidenceStructure, [ IsIncidenceStructure, IsList and IsEmpty ], M: IsChamberOfIncidenceStructure, [ IsFlagOfIncidenceStructure and IsFlagOfIncidenceStructureRep ], M: AmbientGeometry, [ IsFlagOfIncidenceStructure and IsFlagOfIncidenceStructureRep], M: ElementsOfFlag, [ IsFlagOfIncidenceStructure and IsFlagOfIncidenceStructureRep ], M: Size, [ IsFlagOfIncidenceStructure and IsFlagOfIncidenceStructureRep ], M: Rank, [ IsFlagOfIncidenceStructure ], M: Type, [ IsFlagOfIncidenceStructure and IsFlagOfIncidenceStructureRep ], M: ResidueOfFlag, [ IsFlagOfIncidenceStructure ], M: \=, [ IsFlagOfIncidenceStructure, IsFlagOfIncidenceStructure ], M: \<, [ IsFlagOfIncidenceStructure, IsFlagOfIncidenceStructure ], M: \<, [ IsFlagOfIncidenceStructure, IsElementOfIncidenceStructure ], M: \<, [ IsElementOfIncidenceStructure, IsFlagOfIncidenceStructure ], M: IsIncident, [ IsElementOfIncidenceStructure, IsFlagOfIncidenceStructure ], M: IsIncident, [IsFlagOfIncidenceStructure, IsElementOfIncidenceStructure], M: \in, [ IsElementOfIncidenceStructure, IsFlagOfIncidenceStructure ], M: ShadowOfElement, [IsIncidenceStructure, IsElementOfIncidenceStructure, IsPosInt], M: ShadowOfElement, [IsIncidenceStructure, IsElementOfIncidenceStructure, IsString], M: ElementsIncidentWithElementOfIncidenceStructure, [ IsElementOfIncidenceStructure, IsPosInt], M: ShadowOfFlag, [IsIncidenceStructure, IsFlagOfIncidenceStructure, IsPosInt], M: ShadowOfFlag, [IsIncidenceStructure, IsFlagOfIncidenceStructure, IsString], M: ShadowOfFlag, [IsIncidenceStructure, IsList, IsPosInt], M: ShadowOfFlag, [IsIncidenceStructure, IsList, IsString], M: Iterator, [ IsShadowElementsOfIncidenceStructure ], M: ViewObj, [ IsElementOfIncidenceStructure and IsElementOfIncidenceStructureRep ], M: ViewObj, [ IsFlagOfIncidenceStructure and IsFlagOfIncidenceStructureRep ], M: PrintObj, [ IsElementOfIncidenceStructure and IsElementOfIncidenceStructureRep ], M: Display, [ IsElementOfIncidenceStructure and IsElementOfIncidenceStructureRep ], M: ViewObj, [ IsAllElementsOfIncidenceStructure ], M: PrintObj, [ IsAllElementsOfIncidenceStructure ], M: ViewObj, [ IsShadowElementsOfIncidenceStructure ], M: ViewObj, [ IsElementsOfIncidenceStructure ], M: PrintObj, [ IsElementsOfIncidenceStructure ], M: ViewObj, [ IsIncidenceStructure ], M: PrintObj, [ IsIncidenceStructure ], M: Display, [ IsIncidenceStructure ], M: IsConfiguration, [ IsIncidenceStructure], M: IsConstellation, [ IsIncidenceStructure], liegeometry.gi: methods M: UnderlyingVectorSpace, [ IsLieGeometry], M: ProjectiveDimension, [ IsLieGeometry ], M: Dimension, [ IsLieGeometry ], M: BaseField, [ IsLieGeometry ], M: Wrap, [IsLieGeometry, IsPosInt, IsObject], M: UnderlyingObject, [IsElementOfLieGeometry], M: AmbientSpace, [IsElementOfLieGeometry], M: ViewObj, [ IsAllElementsOfLieGeometry and IsAllElementsOfLieGeometryRep ], M: PrintObj, [ IsAllElementsOfLieGeometry and IsAllElementsOfLieGeometryRep ], M: ViewObj, [ IsElementsOfLieGeometry and IsElementsOfLieGeometryRep ], M: PrintObj, [ IsElementsOfLieGeometry and IsElementsOfLieGeometryRep ], M: Points, [IsLieGeometry], M: Lines, [IsLieGeometry], M: Planes, [IsLieGeometry], M: Solids, [IsLieGeometry], M: EmptySubspace, [IsLieGeometry], M: BaseField, [IsEmptySubspace and IsEmptySubspaceRep], M: ViewObj, InstallMethod(ViewObj,[IsEmptySubspace], M: PrintObj, InstallMethod(PrintObj,[IsEmptySubspace], M: Display, InstallMethod(Display,[IsEmptySubspace], M: \=, [IsEmptySubspace, IsEmptySubspace], M: \in, [ IsEmptySubspace, IsEmptySubspace ], M: \in, [ IsEmptySubspace, IsElementOfLieGeometry ], M: \in, [ IsElementOfLieGeometry, IsEmptySubspace ], M: \in, [ IsEmptySubspace, IsLieGeometry ], M: Span, [ IsEmptySubspace, IsElementOfLieGeometry ], M: Span, [ IsElementOfLieGeometry, IsEmptySubspace ], M: Span, [IsEmptySubspace, IsEmptySubspace], M: Meet, [ IsEmptySubspace, IsElementOfLieGeometry ], M: Meet, [ IsElementOfLieGeometry, IsEmptySubspace ], M: Meet, [IsEmptySubspace, IsEmptySubspace], M: Points, [ IsElementOfLieGeometry ], M: Points, [ IsLieGeometry, IsElementOfLieGeometry ], M: Lines, [ IsElementOfLieGeometry ], M: Lines, [ IsLieGeometry, IsElementOfLieGeometry ], M: Planes, [ IsElementOfLieGeometry ], M: Planes, [ IsLieGeometry, IsElementOfLieGeometry ], M: Solids, InstallMethod(Solids,[IsElementOfLieGeometry], M: Solids, [ IsLieGeometry, IsElementOfLieGeometry ], M: Hyperplanes, [ IsElementOfLieGeometry ], M: Hyperplanes, [ IsLieGeometry, IsElementOfLieGeometry ], M: ViewObj, [ IsShadowElementsOfLieGeometry and IsShadowElementsOfLieGeometryRep ], M: \in, [IsElementOfLieGeometry, IsElementOfLieGeometry], M: Random, [ IsSubspacesVectorSpace ], M: RandomSubspace, [IsVectorSpace,IsInt], M: ElementToElement, [IsLieGeometry, IsElementOfLieGeometry], M: ObjectToElement, [IsLieGeometry, IsPosInt, IsObject], M: ObjectToElement, [IsLieGeometry, IsObject], group.gi: methods M: ProjEl, [IsMatrix and IsFFECollColl], M: ProjEls, [IsList], M: Projectivity, InstallMethod(Projectivity,[IsMatrixandIsFFECollColl,IsField], M: Projectivity, InstallMethod(Projectivity,[IsCMatRepandIsFFECollColl,IsField], M: Projectivity, InstallMethod(Projectivity,[IsProjectiveSpace,IsMatrix], M: Projectivity, InstallMethod(Projectivity,[IsProjectiveSpace,IsCMatRep], M: IsProjectivity, InstallMethod(IsProjectivity,[IsProjGrpEl], M: IsProjectivity, InstallMethod(IsProjectivity,[IsProjGrpElWithFrob], M: IsStrictlySemilinear, InstallMethod(IsStrictlySemilinear,[IsProjGrpEl], M: IsStrictlySemilinear, InstallMethod(IsStrictlySemilinear,[IsProjGrpElWithFrob], M: IsCollineation, InstallMethod(IsCollineation,[IsProjGrpEl], M: IsCollineation, InstallMethod(IsCollineation,[IsProjGrpElWithFrob], M: IsProjectivityGroup, InstallMethod(IsProjectivityGroup,[IsProjectiveGroupWithFrob], M: IsCollineationGroup, InstallMethod(IsCollineationGroup,[IsProjectiveGroupWithFrob], M: ProjElWithFrob, [IsCMatRep and IsFFECollColl, #changed 19/3/14 to cmat. IsRingHomomorphism and IsMultiplicativeElementWithInverse, IsField], M: ProjElWithFrob, [IsMatrix and IsFFECollColl, IsRingHomomorphism and IsMultiplicativeElementWithInverse, IsField], M: ProjElWithFrob, [IsCMatRep and IsFFECollColl, #changed 19/3/14. IsRingHomomorphism and IsMultiplicativeElementWithInverse], M: ProjElWithFrob, [IsCMatRep and IsFFECollColl, IsRingHomomorphism and IsMultiplicativeElementWithInverse], M: ProjElsWithFrob, [IsList, IsField], M: ProjElsWithFrob, [IsList], M: CollineationOfProjectiveSpace, [ IsMatrix and IsFFECollColl, IsField], M: CollineationOfProjectiveSpace, InstallMethod(CollineationOfProjectiveSpace,[IsProjectiveSpace,IsMatrix], M: CollineationOfProjectiveSpace, InstallMethod(CollineationOfProjectiveSpace,[IsProjectiveSpace,IsMapping], M: CollineationOfProjectiveSpace, InstallMethod(CollineationOfProjectiveSpace,[IsProjectiveSpace,IsMatrix,IsMapping], M: Collineation, InstallMethod(Collineation,[IsProjectiveSpace,IsMatrix], M: Collineation, InstallMethod(Collineation,[IsProjectiveSpace,IsMatrix,IsMapping], M: CollineationOfProjectiveSpace, [ IsMatrix and IsFFECollColl, IsRingHomomorphism and IsMultiplicativeElementWithInverse, IsField], M: ProjectiveSemilinearMap, [ IsMatrix and IsFFECollColl, IsRingHomomorphism and IsMultiplicativeElementWithInverse, IsField], M: ProjectivityByImageOfStandardFrameNC, InstallMethod(ProjectivityByImageOfStandardFrameNC,[IsProjectiveSpace,IsList], M: MatrixOfCollineation, InstallMethod(MatrixOfCollineation,[IsProjGrpElandIsProjGrpElRep], M: MatrixOfCollineation, InstallMethod(MatrixOfCollineation,[IsProjGrpElWithFrobandIsProjGrpElWithFrobRep], M: FieldAutomorphism, InstallMethod(FieldAutomorphism,[IsProjGrpElWithFrobandIsProjGrpElWithFrobRep], M: Representative, [IsProjGrpEl and IsProjGrpElRep], M: BaseField, [IsProjGrpEl and IsProjGrpElRep], M: Representative, [IsProjGrpElWithFrob and IsProjGrpElWithFrobRep], M: BaseField, [IsProjGrpElWithFrob and IsProjGrpElWithFrobRep], M: ViewObj, [IsProjGrpEl and IsProjGrpElRep], M: Display, [IsProjGrpEl and IsProjGrpElRep], M: PrintObj, [IsProjGrpEl and IsProjGrpElRep], M: ViewObj, [IsProjGrpElWithFrob and IsProjGrpElWithFrobRep], M: Display, [IsProjGrpElWithFrob and IsProjGrpElWithFrobRep], M: PrintObj, [IsProjGrpElWithFrob and IsProjGrpElWithFrobRep], M: \=, [IsProjGrpEl and IsProjGrpElRep, IsProjGrpEl and IsProjGrpElRep], M: \<, [IsProjGrpEl, IsProjGrpEl], M: \=, [IsProjGrpElWithFrob and IsProjGrpElWithFrobRep, IsProjGrpElWithFrob and IsProjGrpElWithFrobRep], M: \<, [IsProjGrpElWithFrob, IsProjGrpElWithFrob], M: Order, [IsProjGrpEl and IsProjGrpElRep], M: Order, [IsProjGrpElWithFrob and IsProjGrpElWithFrobRep], M: IsOne, [IsProjGrpEl and IsProjGrpElRep], M: IsOne, [IsProjGrpElWithFrob and IsProjGrpElWithFrobRep], M: DegreeFFE, [IsProjGrpEl and IsProjGrpElRep], M: DegreeFFE, [IsProjGrpElWithFrob and IsProjGrpElWithFrobRep], M: Characteristic, [IsProjGrpEl and IsProjGrpElRep], M: Characteristic, [IsProjGrpElWithFrob and IsProjGrpElWithFrobRep], M: \*, [IsProjGrpEl and IsProjGrpElRep, IsProjGrpEl and IsProjGrpElRep], M: InverseSameMutability, [IsProjGrpEl and IsProjGrpElRep], M: InverseMutable, [IsProjGrpEl and IsProjGrpElRep], M: OneImmutable, [IsProjGrpEl and IsProjGrpElRep], M: OneSameMutability, [IsProjGrpEl and IsProjGrpElRep], M: \^, [ IsVector and IsFFECollection and IsMutable, IsFrobeniusAutomorphism ], M: \^, [ IsCVecRep and IsFFECollection and IsMutable, IsFrobeniusAutomorphism ], M: \^, [ IsVector and IsFFECollection, IsFrobeniusAutomorphism ], M: \^, [ IsCVecRep and IsFFECollection, IsFrobeniusAutomorphism ], M: \^, [ IsVector and IsFFECollection and IsMutable, IsMapping and IsOne ], M: \^, [ IsCVecRep and IsFFECollection and IsMutable, IsMapping and IsOne ], M: \^, [ IsVector and IsFFECollection and IsGF2VectorRep, IsFrobeniusAutomorphism ], M: \^, [ IsVector and IsFFECollection and IsGF2VectorRep and IsMutable, IsFrobeniusAutomorphism ], M: \^, [ IsVector and IsFFECollection and IsGF2VectorRep, IsMapping and IsOne ], M: \^, [ IsVector and IsFFECollection and IsGF2VectorRep and IsMutable, IsMapping and IsOne ], M: \^, [ IsVector and IsFFECollection and Is8BitVectorRep, IsFrobeniusAutomorphism ], M: \^, [ IsVector and IsFFECollection and Is8BitVectorRep and IsMutable, IsFrobeniusAutomorphism ], M: \^, [ IsVector and IsFFECollection and Is8BitVectorRep, IsMapping and IsOne ], M: \^, [ IsVector and IsFFECollection and Is8BitVectorRep and IsMutable, IsMapping and IsOne ], M: \^, [ IsMatrix and IsFFECollColl, IsFrobeniusAutomorphism ], M: \^, [ IsCMatRep and IsFFECollColl, IsFrobeniusAutomorphism ], M: \^, [ IsMatrix and IsFFECollColl and IsMutable, IsFrobeniusAutomorphism ], M: \^, [ IsCMatRep and IsFFECollColl and IsMutable, IsFrobeniusAutomorphism ], M: \^, [ IsMatrix and IsFFECollColl, IsMapping and IsOne ], M: \^, [ IsCMatRep and IsFFECollColl and IsMutable, IsMapping and IsOne ], M: \^, [ IsMatrix and IsFFECollColl, IsMapping and IsOne ], M: \^, [ IsCMatRep and IsFFECollColl , IsMapping and IsOne ], M: \^, [ IsMatrix and IsFFECollColl and IsGF2MatrixRep, IsFrobeniusAutomorphism ], M: \^, [ IsMatrix and IsFFECollColl and IsGF2MatrixRep and IsMutable, IsFrobeniusAutomorphism ], M: \^, [ IsMatrix and IsFFECollColl and IsGF2MatrixRep, IsMapping and IsOne ], M: \^, [ IsMatrix and IsFFECollColl and IsGF2MatrixRep and IsMutable, IsMapping and IsOne ], M: \^, [ IsMatrix and IsFFECollColl and Is8BitMatrixRep, IsFrobeniusAutomorphism ], M: \^, [ IsMatrix and IsFFECollColl and Is8BitMatrixRep and IsMutable, IsFrobeniusAutomorphism ], M: \^, [ IsMatrix and IsFFECollColl and Is8BitMatrixRep, IsMapping and IsOne ], M: \^, [ IsMatrix and IsFFECollColl and Is8BitMatrixRep and IsMutable, IsMapping and IsOne ], M: \*, [IsProjGrpElWithFrob and IsProjGrpElWithFrobRep, IsProjGrpElWithFrob and IsProjGrpElWithFrobRep], M: InverseSameMutability, [IsProjGrpElWithFrob and IsProjGrpElWithFrobRep], M: InverseMutable, [IsProjGrpElWithFrob and IsProjGrpElWithFrobRep], M: OneImmutable, [IsProjGrpElWithFrob and IsProjGrpElWithFrobRep], M: OneSameMutability, [IsProjGrpElWithFrob and IsProjGrpElWithFrobRep], M: ViewObj, [IsProjectiveGroupWithFrob], M: ViewObj, [IsProjectiveGroupWithFrob and IsTrivial], M: ViewObj, [IsProjectiveGroupWithFrob and HasGeneratorsOfGroup], M: ViewObj, [IsProjectiveGroupWithFrob and HasSize], M: ViewObj, [IsProjectiveGroupWithFrob and HasGeneratorsOfGroup and HasSize], M: BaseField, [IsProjectiveGroupWithFrob], M: Dimension, [IsProjectiveGroupWithFrob], M: OneImmutable, # was [IsGroup and IsProjectiveGroupWithFrob], I think might be M: CanComputeActionOnPoints, [IsProjectiveGroupWithFrob], M: ActionOnAllProjPoints, [ IsProjectiveGroupWithFrob ], M: NiceMonomorphism, [IsProjectivityGroup and CanComputeActionOnPoints and IsHandledByNiceMonomorphism], M: NiceMonomorphism, [IsProjectiveGroupWithFrob and IsHandledByNiceMonomorphism], M: NiceMonomorphism, [IsProjectiveGroupWithFrob and CanComputeActionOnPoints and IsHandledByNiceMonomorphism], 1, M: NiceMonomorphism, [IsProjectiveGroupWithFrob and IsHandledByNiceMonomorphism], 50, M: FindBasePointCandidates, [IsProjectivityGroup,IsRecord,IsInt], M: FindBasePointCandidates, [IsProjectiveGroupWithFrob,IsRecord,IsInt], M: FindBasePointCandidates, [IsProjectiveGroupWithFrob,IsRecord,IsInt,IsObject], M: CanonicalGramMatrix, [IsString, IsPosInt, IsField], M: CanonicalQuadraticForm, [IsString, IsPosInt, IsField], M: SOdesargues, [IsInt, IsPosInt, IsField and IsFinite], M: GOdesargues, InstallMethod(GOdesargues,[IsInt,IsPosInt,IsFieldandIsFinite], M: SUdesargues, InstallMethod(SUdesargues,[IsPosInt,IsFieldandIsFinite], M: GUdesargues, InstallMethod(GUdesargues,[IsPosInt,IsFieldandIsFinite], M: Spdesargues, InstallMethod(Spdesargues,[IsPosInt,IsFieldandIsFinite], M: GeneralSymplecticGroup, InstallMethod(GeneralSymplecticGroup,[IsPosInt,IsFieldandIsFinite], M: GSpdesargues, InstallMethod(GSpdesargues,[IsPosInt,IsFieldandIsFinite], M: GammaSp, InstallMethod(GammaSp,[IsPosInt,IsFieldandIsFinite], M: DeltaOminus, InstallMethod(DeltaOminus,[IsPosInt,IsFieldandIsFinite], M: GammaOminus, InstallMethod(GammaOminus,[IsPosInt,IsFieldandIsFinite], M: GammaO, InstallMethod(GammaO,[IsPosInt,IsFieldandIsFinite], M: DeltaOplus, InstallMethod(DeltaOplus,[IsPosInt,IsFieldandIsFinite], M: GammaOplus, InstallMethod(GammaOplus,[IsPosInt,IsFieldandIsFinite], M: GammaU, InstallMethod(GammaU,[IsPosInt,IsFieldandIsFinite], projectivespace.gi: methods M: Wrap, [IsProjectiveSpace, IsPosInt, IsObject], M: ProjectiveSpace, [ IsInt, IsField ], M: ProjectiveSpace, [ IsInt, IsPosInt ], M: ViewObj, InstallMethod(ViewObj,[IsProjectiveSpaceandIsProjectiveSpaceRep], M: ViewString, [ IsProjectiveSpace and IsProjectiveSpaceRep ], M: PrintObj, InstallMethod(PrintObj,[IsProjectiveSpaceandIsProjectiveSpaceRep], M: Display, InstallMethod(Display,[IsProjectiveSpaceandIsProjectiveSpaceRep], M: \=, [IsProjectiveSpace, IsProjectiveSpace], M: Rank, [ IsProjectiveSpace and IsProjectiveSpaceRep ], M: BaseField, [IsSubspaceOfProjectiveSpace], M: StandardFrame, [IsProjectiveSpace], M: RepresentativesOfElements, "for a projective space", [IsProjectiveSpace], M: Hyperplanes, [ IsProjectiveSpace ], M: TypesOfElementsOfIncidenceStructure, "for a projective space", [IsProjectiveSpace], M: TypesOfElementsOfIncidenceStructurePlural, [IsProjectiveSpace], M: ElementsOfIncidenceStructure, [IsProjectiveSpace, IsPosInt], M: ElementsOfIncidenceStructure, [IsProjectiveSpace], M: \=, [ IsAllSubspacesOfProjectiveSpace, IsAllSubspacesOfProjectiveSpace ], M: Size, [IsSubspacesOfProjectiveSpace and IsSubspacesOfProjectiveSpaceRep], M: \in, [IsElementOfIncidenceStructure, IsElementsOfIncidenceStructure], 1*SUM_FLAGS+3, M: \in, [IsElementOfIncidenceStructure, IsAllElementsOfIncidenceStructure], 1*SUM_FLAGS+3, M: VectorSpaceToElement, [IsProjectiveSpace, IsCMatRep], M: VectorSpaceToElement, [IsProjectiveSpace, IsPlistRep and IsMatrix], M: VectorSpaceToElement, [IsProjectiveSpace, IsGF2MatrixRep], M: VectorSpaceToElement, [IsProjectiveSpace, Is8BitMatrixRep], M: VectorSpaceToElement, [IsProjectiveSpace, IsCVecRep], M: VectorSpaceToElement, [IsProjectiveSpace, IsRowVector], M: VectorSpaceToElement, [IsProjectiveSpace, Is8BitVectorRep], M: UnderlyingVectorSpace, [IsSubspaceOfProjectiveSpace], M: ProjectiveDimension, [ IsSubspaceOfProjectiveSpace ], M: Dimension, [ IsSubspaceOfProjectiveSpace ], M: StandardFrame, [IsSubspaceOfProjectiveSpace], M: Coordinates, [IsSubspaceOfProjectiveSpace], M: DualCoordinatesOfHyperplane, [IsSubspaceOfProjectiveSpace], M: HyperplaneByDualCoordinates, [IsProjectiveSpace,IsList], M: EquationOfHyperplane, [IsSubspaceOfProjectiveSpace], M: Span, [ IsEmptySubspace, IsProjectiveSpace ], M: Span, [ IsProjectiveSpace, IsEmptySubspace ], M: Meet, [ IsEmptySubspace, IsProjectiveSpace ], M: Meet, [ IsProjectiveSpace, IsEmptySubspace ], M: ShadowOfElement, [IsProjectiveSpace, IsSubspaceOfProjectiveSpace, IsPosInt], M: Size, [IsShadowSubspacesOfProjectiveSpace and IsShadowSubspacesOfProjectiveSpaceRep ], M: CollineationGroup, [ IsProjectiveSpace and IsProjectiveSpaceRep ], M: ProjectivityGroup, [ IsProjectiveSpace ], M: SpecialProjectivityGroup, [ IsProjectiveSpace ], M: \^, [IsElementOfIncidenceStructure, IsProjGrpElWithFrob], M: \^, [IsElementOfIncidenceStructure, IsProjGrpElWithFrobWithPSIsom], M: AsList, [IsSubspacesOfProjectiveSpace], M: Iterator, [IsSubspacesOfProjectiveSpace], M: FlagOfIncidenceStructure, [ IsProjectiveSpace, IsSubspaceOfProjectiveSpaceCollection ], M: FlagOfIncidenceStructure, [ IsProjectiveSpace, IsList and IsEmpty ], M: UnderlyingVectorSpace, [ IsFlagOfProjectiveSpace and IsFlagOfIncidenceStructureRep ], M: PrintObj, [ IsFlagOfProjectiveSpace and IsFlagOfIncidenceStructureRep ], M: Display, [ IsFlagOfProjectiveSpace and IsFlagOfIncidenceStructureRep ], M: ShadowOfFlag, [IsProjectiveSpace, IsFlagOfProjectiveSpace, IsPosInt], M: Iterator, [IsShadowSubspacesOfProjectiveSpace and IsShadowSubspacesOfProjectiveSpaceRep ], M: \in, [ IsProjectiveSpace, IsSubspaceOfProjectiveSpace ], M: \in, [ IsProjectiveSpace, IsEmptySubspace ], M: \in, [IsSubspaceOfProjectiveSpace, IsProjectiveSpace], M: \in, [IsProjectiveSpace, IsSubspaceOfProjectiveSpace], M: IsIncident, [IsSubspaceOfProjectiveSpace, IsSubspaceOfProjectiveSpace], M: Span, [IsProjectiveSpace, IsSubspaceOfProjectiveSpace], M: Span, [IsSubspaceOfProjectiveSpace, IsProjectiveSpace], M: Span, [IsSubspaceOfProjectiveSpace, IsSubspaceOfProjectiveSpace], M: Span, [IsSubspaceOfProjectiveSpace, IsSubspaceOfProjectiveSpace, IsBool], M: Span, [ IsHomogeneousList and IsSubspaceOfProjectiveSpaceCollection ], M: Span, [ IsList ], M: Span, [IsList, IsBool], M: Meet, [IsProjectiveSpace, IsSubspaceOfProjectiveSpace], M: Meet, [IsSubspaceOfProjectiveSpace, IsProjectiveSpace], M: Meet, [IsSubspaceOfProjectiveSpace, IsSubspaceOfProjectiveSpace], M: Meet, [ IsHomogeneousList and IsSubspaceOfProjectiveSpaceCollection], M: Meet, [ IsList ], M: RandomSubspace, [IsProjectiveSpace,IsInt], M: RandomSubspace, [IsSubspaceOfProjectiveSpace,IsInt], M: RandomSubspace, [IsProjectiveSpace], M: Random, [ IsSubspacesOfProjectiveSpace ], M: Random, [ IsAllSubspacesOfProjectiveSpace ], M: Random, [ IsShadowSubspacesOfProjectiveSpace ], M: BaerSublineOnThreePoints, [IsSubspaceOfProjectiveSpace, IsSubspaceOfProjectiveSpace, IsSubspaceOfProjectiveSpace], M: BaerSubplaneOnQuadrangle, InstallMethod(BaerSubplaneOnQuadrangle,[IsSubspaceOfProjectiveSpace, IsSubspaceOfProjectiveSpace, IsSubspaceOfProjectiveSpace, IsSubspaceOfProjectiveSpace], M: ComplementSpace, [IsVectorSpace, IsFFECollColl], M: ElationOfProjectiveSpace, [ IsSubspaceOfProjectiveSpace, IsSubspaceOfProjectiveSpace, IsSubspaceOfProjectiveSpace ], M: ProjectiveElationGroup, [ IsSubspaceOfProjectiveSpace, IsSubspaceOfProjectiveSpace ], M: ProjectiveElationGroup, [ IsSubspaceOfProjectiveSpace ], M: HomologyOfProjectiveSpace, [ IsSubspaceOfProjectiveSpace, IsSubspaceOfProjectiveSpace, IsSubspaceOfProjectiveSpace, IsSubspaceOfProjectiveSpace ], M: ProjectiveHomologyGroup, [ IsSubspaceOfProjectiveSpace, IsSubspaceOfProjectiveSpace ], M: SingerCycleMat, InstallMethod(SingerCycleMat,[IsInt,IsInt], M: SingerCycleCollineation, InstallMethod(SingerCycleCollineation,[IsInt,IsInt], M: IncidenceGraph, [ IsProjectiveSpace ], correlations.gi: methods M: IdentityMappingOfElementsOfProjectiveSpace, [IsProjectiveSpace], M: StandardDualityOfProjectiveSpace, [IsProjectiveSpace], M: IsCollineation, InstallMethod(IsCollineation,[IsProjGrpElWithFrobWithPSIsom], M: IsCorrelation, InstallMethod(IsCorrelation,[IsProjGrpElWithFrobWithPSIsom], M: IsCorrelation, InstallMethod(IsCorrelation,[IsProjGrpElWithFrob], M: IsCorrelation, InstallMethod(IsCorrelation,[IsProjGrpEl], M: IsProjectivity, [ IsProjGrpElWithFrobWithPSIsom and IsProjGrpElWithFrobWithPSIsomRep], M: IsStrictlySemilinear, [ IsProjGrpElWithFrobWithPSIsom and IsProjGrpElWithFrobWithPSIsomRep], M: IsProjectivityGroup, InstallMethod(IsProjectivityGroup,[IsProjGroupWithFrobWithPSIsom], M: IsCollineationGroup, InstallMethod(IsCollineationGroup,[IsProjGroupWithFrobWithPSIsom], M: ViewObj, [IsStandardDualityOfProjectiveSpace and IsSPMappingByFunctionWithInverseRep], M: Display, [IsStandardDualityOfProjectiveSpace and IsSPMappingByFunctionWithInverseRep], M: PrintObj, [IsStandardDualityOfProjectiveSpace and IsSPMappingByFunctionWithInverseRep], M: \*, [IsStandardDualityOfProjectiveSpace, IsStandardDualityOfProjectiveSpace], M: \*, [IsIdentityMappingOfElementsOfProjectiveSpace, IsStandardDualityOfProjectiveSpace], M: \*, [IsStandardDualityOfProjectiveSpace, IsIdentityMappingOfElementsOfProjectiveSpace], M: \*, [IsIdentityMappingOfElementsOfProjectiveSpace, IsIdentityMappingOfElementsOfProjectiveSpace], M: \^, [ IsProjectiveSpaceIsomorphism, IsZeroCyc ], M: \=, [IsStandardDualityOfProjectiveSpace, IsStandardDualityOfProjectiveSpace], M: \=, [IsStandardDualityOfProjectiveSpace, IsIdentityMappingOfElementsOfProjectiveSpace], M: \=, [IsIdentityMappingOfElementsOfProjectiveSpace, IsStandardDualityOfProjectiveSpace], M: \=, [IsIdentityMappingOfElementsOfProjectiveSpace, IsIdentityMappingOfElementsOfProjectiveSpace], M: ProjElWithFrobWithPSIsom, [IsCMatRep and IsFFECollColl, IsRingHomomorphism and IsMultiplicativeElementWithInverse, IsField, IsStandardDualityOfProjectiveSpace], M: ProjElWithFrobWithPSIsom, [IsMatrix and IsFFECollColl, IsRingHomomorphism and IsMultiplicativeElementWithInverse, IsField, IsStandardDualityOfProjectiveSpace], M: ProjElWithFrobWithPSIsom, [IsCMatRep and IsFFECollColl, IsRingHomomorphism and IsMultiplicativeElementWithInverse, IsField], M: ProjElWithFrobWithPSIsom, [IsMatrix and IsFFECollColl, IsRingHomomorphism and IsMultiplicativeElementWithInverse, IsField], M: ProjElWithFrobWithPSIsom, [IsCMatRep and IsFFECollColl, IsRingHomomorphism and IsMultiplicativeElementWithInverse, IsField, IsGeneralMappingand IsSPGeneralMapping and IsOne], M: ProjElWithFrobWithPSIsom, [IsMatrix and IsFFECollColl, IsRingHomomorphism and IsMultiplicativeElementWithInverse, IsField, IsGeneralMappingand IsSPGeneralMapping and IsOne], M: ViewObj, [IsProjGrpElWithFrobWithPSIsom and IsProjGrpElWithFrobWithPSIsomRep], M: Display, [IsProjGrpElWithFrobWithPSIsom and IsProjGrpElWithFrobWithPSIsomRep], M: PrintObj, [IsProjGrpElWithFrobWithPSIsom and IsProjGrpElWithFrobWithPSIsomRep], M: Representative, [IsProjGrpElWithFrobWithPSIsom and IsProjGrpElWithFrobWithPSIsomRep], M: BaseField, [IsProjGrpElWithFrobWithPSIsom and IsProjGrpElWithFrobWithPSIsomRep], M: BaseField, [IsProjGroupWithFrobWithPSIsom], M: \=, [IsProjGrpElWithFrobWithPSIsom and IsProjGrpElWithFrobWithPSIsomRep, IsProjGrpElWithFrobWithPSIsom and IsProjGrpElWithFrobWithPSIsomRep], M: IsOne, [IsProjGrpElWithFrobWithPSIsom and IsProjGrpElWithFrobWithPSIsomRep], M: OneImmutable, [IsProjGrpElWithFrobWithPSIsom and IsProjGrpElWithFrobWithPSIsomRep], M: OneImmutable, [IsGroup and IsProjGrpElWithFrobWithPSIsom], M: OneSameMutability, [IsProjGrpElWithFrobWithPSIsom and IsProjGrpElWithFrobWithPSIsomRep], M: \^, [ IsCVecRep and IsFFECollection, IsIdentityMappingOfElementsOfProjectiveSpace ], M: \^, [ IsVector and IsFFECollection, IsIdentityMappingOfElementsOfProjectiveSpace ], M: \^, [ IsVector and IsFFECollection and IsGF2VectorRep, IsIdentityMappingOfElementsOfProjectiveSpace ], M: \^, [ IsVector and IsFFECollection and Is8BitVectorRep, IsIdentityMappingOfElementsOfProjectiveSpace ], M: \^, [ IsCMatRep and IsFFECollColl, IsStandardDualityOfProjectiveSpace ], M: \^, [ IsMatrix and IsFFECollColl, IsStandardDualityOfProjectiveSpace ], M: \^, [ IsCMatRep and IsFFECollColl, IsIdentityMappingOfElementsOfProjectiveSpace ], M: \^, [ IsMatrix and IsFFECollColl, IsIdentityMappingOfElementsOfProjectiveSpace ], M: \^, [ IsSubspaceOfProjectiveSpace, IsIdentityMappingOfElementsOfProjectiveSpace ], M: \^, [ IsSubspaceOfProjectiveSpace, IsStandardDualityOfProjectiveSpace ], M: \*, [IsProjGrpElWithFrobWithPSIsom and IsProjGrpElWithFrobWithPSIsomRep, IsProjGrpElWithFrobWithPSIsom and IsProjGrpElWithFrobWithPSIsomRep], M: \<, [IsProjGrpElWithFrobWithPSIsom, IsProjGrpElWithFrobWithPSIsom], M: InverseSameMutability, [IsProjGrpElWithFrobWithPSIsom and IsProjGrpElWithFrobWithPSIsomRep], M: InverseMutable, [IsProjGrpElWithFrobWithPSIsom and IsProjGrpElWithFrobWithPSIsomRep], M: \*, [IsProjGrpElWithFrob and IsProjGrpElWithFrobRep, IsProjGrpElWithFrobWithPSIsom and IsProjGrpElWithFrobWithPSIsomRep], M: \*, [IsProjGrpElWithFrobWithPSIsom and IsProjGrpElWithFrobWithPSIsomRep, IsProjGrpElWithFrob and IsProjGrpElWithFrobRep], M: ProjElsWithFrobWithPSIsom, [IsList, IsField], M: CorrelationCollineationGroup, [ IsProjectiveSpace and IsProjectiveSpaceRep ], M: CorrelationOfProjectiveSpace, [ IsMatrix and IsFFECollColl, IsField], M: CorrelationOfProjectiveSpace, [ IsMatrix and IsFFECollColl, IsRingHomomorphism and IsMultiplicativeElementWithInverse, IsField], M: CorrelationOfProjectiveSpace, [ IsMatrix and IsFFECollColl, IsField, IsStandardDualityOfProjectiveSpace], M: CorrelationOfProjectiveSpace, [ IsMatrix and IsFFECollColl, IsField, IsIdentityMappingOfElementsOfProjectiveSpace], M: CorrelationOfProjectiveSpace, [ IsMatrix and IsFFECollColl, IsRingHomomorphism and IsMultiplicativeElementWithInverse, IsField, IsStandardDualityOfProjectiveSpace], M: CorrelationOfProjectiveSpace, [ IsMatrix and IsFFECollColl, IsRingHomomorphism and IsMultiplicativeElementWithInverse, IsField, IsIdentityMappingOfElementsOfProjectiveSpace], M: CorrelationOfProjectiveSpace, [ IsProjectiveSpace, IsMatrix and IsFFECollColl, IsRingHomomorphism and IsMultiplicativeElementWithInverse, IsStandardDualityOfProjectiveSpace], M: CorrelationOfProjectiveSpace, [ IsProjectiveSpace, IsMatrix and IsFFECollColl, IsRingHomomorphism and IsMultiplicativeElementWithInverse, IsIdentityMappingOfElementsOfProjectiveSpace], M: Correlation, [ IsProjectiveSpace, IsMatrix and IsFFECollColl, IsRingHomomorphism and IsMultiplicativeElementWithInverse, IsStandardDualityOfProjectiveSpace], M: Correlation, [ IsProjectiveSpace, IsMatrix and IsFFECollColl, IsRingHomomorphism and IsMultiplicativeElementWithInverse, IsIdentityMappingOfElementsOfProjectiveSpace], M: MatrixOfCorrelation, InstallMethod(MatrixOfCorrelation,[IsProjGrpElWithFrobWithPSIsomand IsProjGrpElWithFrobWithPSIsomRep], M: FieldAutomorphism, InstallMethod(FieldAutomorphism,[IsProjGrpElWithFrobWithPSIsomand IsProjGrpElWithFrobWithPSIsomRep], M: ProjectiveSpaceIsomorphism, InstallMethod(ProjectiveSpaceIsomorphism,[IsProjGrpElWithFrobWithPSIsomand IsProjGrpElWithFrobWithPSIsomRep], M: Embedding, [IsProjectiveGroupWithFrob, IsProjGroupWithFrobWithPSIsom], M: Dimension, [IsProjGroupWithFrobWithPSIsom], M: ActionOnAllPointsHyperplanes, [ IsProjGroupWithFrobWithPSIsom ], M: CanComputeActionOnPoints, [IsProjGroupWithFrobWithPSIsom], M: NiceMonomorphism, [IsProjGroupWithFrobWithPSIsom and CanComputeActionOnPoints and IsHandledByNiceMonomorphism], 50, M: NiceMonomorphism, [IsProjGroupWithFrobWithPSIsom and IsHandledByNiceMonomorphism], 50, M: ViewObj, [IsProjGroupWithFrobWithPSIsom], M: ViewObj, [IsProjGroupWithFrobWithPSIsom and IsTrivial], M: ViewObj, [IsProjGroupWithFrobWithPSIsom and HasGeneratorsOfGroup], M: ViewObj, [IsProjGroupWithFrobWithPSIsom and HasSize], M: ViewObj, [IsProjGroupWithFrobWithPSIsom and HasGeneratorsOfGroup and HasSize], M: PolarityOfProjectiveSpaceOp, [IsSesquilinearForm and IsFormRep], M: ViewObj, [IsPolarityOfProjectiveSpace and IsPolarityOfProjectiveSpaceRep], M: PrintObj, [IsPolarityOfProjectiveSpace and IsPolarityOfProjectiveSpaceRep], M: Display, [IsPolarityOfProjectiveSpace and IsPolarityOfProjectiveSpaceRep], M: PolarityOfProjectiveSpace, [IsSesquilinearForm and IsFormRep], M: PolarityOfProjectiveSpace, [IsMatrix,IsField and IsFinite], M: PolarityOfProjectiveSpace, [IsMatrix, IsFrobeniusAutomorphism, IsField and IsFinite], M: HermitianPolarityOfProjectiveSpace, [IsMatrix,IsField and IsFinite], M: GramMatrix, [IsPolarityOfProjectiveSpace and IsPolarityOfProjectiveSpaceRep], M: BaseField, [IsPolarityOfProjectiveSpace and IsPolarityOfProjectiveSpaceRep], M: CompanionAutomorphism, [IsPolarityOfProjectiveSpace and IsPolarityOfProjectiveSpaceRep], M: SesquilinearForm, [IsPolarityOfProjectiveSpace and IsPolarityOfProjectiveSpaceRep], M: IsHermitianPolarityOfProjectiveSpace, [IsPolarityOfProjectiveSpace and IsPolarityOfProjectiveSpaceRep], M: IsOrthogonalPolarityOfProjectiveSpace, [IsPolarityOfProjectiveSpace and IsPolarityOfProjectiveSpaceRep], M: IsSymplecticPolarityOfProjectiveSpace, [IsPolarityOfProjectiveSpace and IsPolarityOfProjectiveSpaceRep], M: IsPseudoPolarityOfProjectiveSpace, [IsPolarityOfProjectiveSpace and IsPolarityOfProjectiveSpaceRep], M: \^, [ IsSubspaceOfProjectiveSpace, IsPolarityOfProjectiveSpace], polarspace.gi: methods M: Wrap, [IsClassicalPolarSpace, IsPosInt, IsObject], M: PolarSpace, [ IsSesquilinearForm, IsField, IsGroup, IsFunction ], M: PolarSpaceStandard, [ IsSesquilinearForm, IsBool ], M: PolarSpaceStandard, [ IsQuadraticForm, IsBool ], M: PolarSpace, [ IsSesquilinearForm ], M: PolarSpace, [ IsQuadraticForm ], M: PolarSpace, [ IsHermitianForm ], M: CanonicalOrbitRepresentativeForSubspaces, [IsString, IsPosInt, IsField], M: EllipticQuadric, [ IsPosInt, IsField ], M: EllipticQuadric, [ IsPosInt, IsPosInt ], M: SymplecticSpace, [ IsPosInt, IsField ], M: SymplecticSpace, [ IsPosInt, IsPosInt ], M: ParabolicQuadric, [ IsPosInt, IsField ], M: ParabolicQuadric, [ IsPosInt, IsPosInt ], M: HyperbolicQuadric, [ IsPosInt, IsField ], M: HyperbolicQuadric, [ IsPosInt, IsPosInt ], M: HermitianPolarSpace, [ IsPosInt, IsField ], M: HermitianPolarSpace, [ IsPosInt, IsPosInt ], M: StandardPolarSpace, [ IsClassicalPolarSpace ], M: IsCanonicalPolarSpace, [ IsClassicalPolarSpace and IsClassicalPolarSpaceRep ], M: CanonicalPolarSpace, [ IsClassicalPolarSpace ], M: QuadraticForm, [ IsClassicalPolarSpace ], M: PolarSpaceType, [ IsClassicalPolarSpace and IsClassicalPolarSpaceRep ], M: CompanionAutomorphism, [ IsClassicalPolarSpace ], M: ViewObj, [ IsClassicalPolarSpace and IsClassicalPolarSpaceRep ], M: ViewString, [ IsClassicalPolarSpace and IsClassicalPolarSpaceRep ], M: ViewObj, [ IsClassicalPolarSpace and IsClassicalPolarSpaceRep and IsEllipticQuadric], M: ViewObj, [ IsClassicalPolarSpace and IsClassicalPolarSpaceRep and IsEllipticQuadric and IsStandardPolarSpace], M: ViewString, [ IsClassicalPolarSpace and IsClassicalPolarSpaceRep and IsEllipticQuadric and IsStandardPolarSpace], M: ViewString, [ IsClassicalPolarSpace and IsClassicalPolarSpaceRep and IsEllipticQuadric], M: ViewObj, [ IsClassicalPolarSpace and IsClassicalPolarSpaceRep and IsSymplecticSpace], M: ViewObj, [ IsClassicalPolarSpace and IsClassicalPolarSpaceRep and IsSymplecticSpace and IsStandardPolarSpace], M: ViewString, [ IsClassicalPolarSpace and IsClassicalPolarSpaceRep and IsSymplecticSpace and IsStandardPolarSpace], M: ViewString, [ IsClassicalPolarSpace and IsClassicalPolarSpaceRep and IsSymplecticSpace], M: ViewObj, [ IsClassicalPolarSpace and IsClassicalPolarSpaceRep and IsParabolicQuadric ], M: ViewObj, [ IsClassicalPolarSpace and IsClassicalPolarSpaceRep and IsParabolicQuadric and IsStandardPolarSpace ], M: ViewString, [ IsClassicalPolarSpace and IsClassicalPolarSpaceRep and IsParabolicQuadric and IsStandardPolarSpace ], M: ViewString, [ IsClassicalPolarSpace and IsClassicalPolarSpaceRep and IsParabolicQuadric ], M: ViewObj, [ IsClassicalPolarSpace and IsClassicalPolarSpaceRep and IsParabolicQuadric ], M: ViewObj, [ IsClassicalPolarSpace and IsClassicalPolarSpaceRep and IsHyperbolicQuadric ], M: ViewObj, [ IsClassicalPolarSpace and IsClassicalPolarSpaceRep and IsHyperbolicQuadric and IsStandardPolarSpace], M: ViewString, [ IsClassicalPolarSpace and IsClassicalPolarSpaceRep and IsHyperbolicQuadric and IsStandardPolarSpace], M: ViewString, [ IsClassicalPolarSpace and IsClassicalPolarSpaceRep and IsHyperbolicQuadric], M: ViewObj, [IsClassicalPolarSpace and IsClassicalPolarSpaceRep and IsHermitianPolarSpace ], M: ViewObj, [IsClassicalPolarSpace and IsClassicalPolarSpaceRep and IsHermitianPolarSpace and IsStandardPolarSpace], M: ViewString, [IsClassicalPolarSpace and IsClassicalPolarSpaceRep and IsHermitianPolarSpace and IsStandardPolarSpace], M: ViewString, [IsClassicalPolarSpace and IsClassicalPolarSpaceRep and IsHermitianPolarSpace], M: PrintObj, InstallMethod(PrintObj,[IsClassicalPolarSpaceandIsClassicalPolarSpaceRep], M: Display, InstallMethod(Display,[IsClassicalPolarSpaceandIsClassicalPolarSpaceRep], M: PrintObj, [ IsClassicalPolarSpace and IsClassicalPolarSpaceRep and IsEllipticQuadric ], M: Display, [ IsClassicalPolarSpace and IsClassicalPolarSpaceRep and IsEllipticQuadric ], M: PrintObj, [ IsClassicalPolarSpace and IsClassicalPolarSpaceRep and IsSymplecticSpace ], M: Display, [ IsClassicalPolarSpace and IsClassicalPolarSpaceRep and IsSymplecticSpace ], M: PrintObj, [ IsClassicalPolarSpace and IsClassicalPolarSpaceRep and IsParabolicQuadric ], M: Display, [ IsClassicalPolarSpace and IsClassicalPolarSpaceRep and IsParabolicQuadric ], M: PrintObj, [ IsClassicalPolarSpace and IsClassicalPolarSpaceRep and IsHyperbolicQuadric ], M: Display, [ IsClassicalPolarSpace and IsClassicalPolarSpaceRep and IsHyperbolicQuadric ], M: PrintObj, [IsClassicalPolarSpace and IsClassicalPolarSpaceRep and IsHermitianPolarSpace ], M: Display, [ IsClassicalPolarSpace and IsClassicalPolarSpaceRep and IsHermitianPolarSpace ], M: IsomorphismCanonicalPolarSpace, [ IsClassicalPolarSpace and IsClassicalPolarSpaceRep ], M: IsomorphismCanonicalPolarSpaceWithIntertwiner, [ IsClassicalPolarSpace and IsClassicalPolarSpaceRep ], M: RankAttr, [ IsClassicalPolarSpace and IsClassicalPolarSpaceRep ], M: TypesOfElementsOfIncidenceStructure, [ IsClassicalPolarSpace and IsClassicalPolarSpaceRep ], M: TypesOfElementsOfIncidenceStructurePlural, [IsClassicalPolarSpace], M: Order, [ IsClassicalPolarSpace and IsClassicalPolarSpaceRep ], M: RepresentativesOfElements, [ IsClassicalPolarSpace and IsClassicalPolarSpaceRep ], M: QUO, [ IsClassicalPolarSpace and IsClassicalPolarSpaceRep, IsSubspaceOfClassicalPolarSpace], M: Size, [IsSubspacesOfClassicalPolarSpace], M: VectorSpaceToElement, [IsClassicalPolarSpace, IsCMatRep], M: VectorSpaceToElement, [IsClassicalPolarSpace, IsCVecRep], M: VectorSpaceToElement, [IsClassicalPolarSpace, IsPlistRep and IsMatrix], M: VectorSpaceToElement, [IsClassicalPolarSpace, IsGF2MatrixRep], M: VectorSpaceToElement, [IsClassicalPolarSpace, Is8BitMatrixRep], M: VectorSpaceToElement, [IsClassicalPolarSpace, IsRowVector], M: VectorSpaceToElement, [IsClassicalPolarSpace, Is8BitVectorRep], M: \in, [IsElementOfIncidenceStructure, IsClassicalPolarSpace], M: Span, [IsSubspaceOfProjectiveSpace, IsSubspaceOfProjectiveSpace, IsBool], M: Meet, [IsSubspaceOfClassicalPolarSpace, IsSubspaceOfClassicalPolarSpace], M: ElementsOfIncidenceStructure, [IsClassicalPolarSpace and IsClassicalPolarSpaceRep, IsPosInt], M: ElementsOfIncidenceStructure, [IsClassicalPolarSpace and IsClassicalPolarSpaceRep], M: NumberOfTotallySingularSubspaces, [IsClassicalPolarSpace, IsPosInt], M: TypeOfSubspace, [ IsClassicalPolarSpace, IsSubspaceOfProjectiveSpace ], M: FlagOfIncidenceStructure, [ IsClassicalPolarSpace, IsSubspaceOfProjectiveSpaceCollection ], M: FlagOfIncidenceStructure, [ IsClassicalPolarSpace, IsList and IsEmpty ], M: ViewObj, [ IsFlagOfClassicalPolarSpace and IsFlagOfIncidenceStructureRep ], M: PrintObj, [ IsFlagOfClassicalPolarSpace and IsFlagOfIncidenceStructureRep ], M: Display, [ IsFlagOfClassicalPolarSpace and IsFlagOfIncidenceStructureRep ], M: RandomSubspace, [ IsClassicalPolarSpace, IsPosInt ], M: Random, [ IsSubspacesOfClassicalPolarSpace ], M: Iterator, [IsSubspacesOfClassicalPolarSpace], M: ShadowOfElement, [IsClassicalPolarSpace, IsSubspaceOfProjectiveSpace, IsPosInt], M: Iterator, [ IsShadowSubspacesOfClassicalPolarSpace ], M: Size, [IsShadowSubspacesOfClassicalPolarSpace andIsShadowSubspacesOfClassicalPolarSpaceRep ], M: IsCollinear, [IsClassicalPolarSpace and IsClassicalPolarSpaceRep, IsSubspaceOfProjectiveSpace, IsSubspaceOfProjectiveSpace], M: PolarityOfProjectiveSpace, [IsClassicalPolarSpace], M: PolarSpace, [ IsPolarityOfProjectiveSpace ], M: GeometryOfAbsolutePoints, [ IsPolarityOfProjectiveSpace ], M: AbsolutePoints, [ IsPolarityOfProjectiveSpace ], M: AbsolutePoints, [ IsPolarityOfProjectiveSpace ], M: PolarMap, [IsClassicalPolarSpace], M: CollineationGroup, [ IsClassicalPolarSpace and IsClassicalPolarSpaceRep ], M: SpecialIsometryGroup, [ IsClassicalPolarSpace and IsClassicalPolarSpaceRep ], M: IsometryGroup, [ IsClassicalPolarSpace and IsClassicalPolarSpaceRep ], M: SimilarityGroup, InstallMethod(SimilarityGroup,[IsClassicalPolarSpaceandIsClassicalPolarSpaceRep], M: IsParabolicQuadric, [IsClassicalPolarSpace], M: IsParabolicQuadric, [IsClassicalPolarSpace], M: IsHyperbolicQuadric, [IsClassicalPolarSpace], M: IsHyperbolicQuadric, [IsClassicalPolarSpace], M: IsEllipticQuadric, [IsClassicalPolarSpace], M: IsEllipticQuadric, [IsClassicalPolarSpace], M: IsSymplecticSpace, [IsClassicalPolarSpace], M: IsHermitianPolarSpace, [IsClassicalPolarSpace], M: DefiningListOfPolynomials, [IsProjectiveVariety and IsClassicalPolarSpace and IsClassicalPolarSpaceRep], M: NucleusOfParabolicQuadric, [ IsClassicalPolarSpace ], M: TangentSpace, [ IsSubspaceOfClassicalPolarSpace ], M: TangentSpace, [ IsClassicalPolarSpace, IsSubspaceOfProjectiveSpace ], M: Pole, [ IsClassicalPolarSpace, IsSubspaceOfProjectiveSpace ], M: IncidenceGraph, [ IsClassicalPolarSpace ], morphisms.gi: methods M: GeometryMorphismByFunction, [ IsAnyElementsOfIncidenceStructure, IsAnyElementsOfIncidenceStructure, IsFunction, IsBool, IsFunction ], M: GeometryMorphismByFunction, [ IsAnyElementsOfIncidenceStructure, IsAnyElementsOfIncidenceStructure, IsFunction, IsFunction ], M: GeometryMorphismByFunction, [ IsAnyElementsOfIncidenceStructure, IsAnyElementsOfIncidenceStructure, IsFunction ], M: ViewObj, [ IsGeometryMorphism ], M: PrintObj, [ IsGeometryMorphism ], M: Display, [ IsGeometryMorphism ], M: ViewObj, [ IsGeometryMorphism and IsMappingByFunctionWithInverseRep ], M: ViewObj, [ IsGeometryMorphism and IsMappingByFunctionRep ], M: PrintObj, [ IsGeometryMorphism and IsMappingByFunctionRep ], M: Display, [ IsGeometryMorphism and IsMappingByFunctionRep ], M: ImageElm, [IsGeometryMorphism, IsElementOfIncidenceStructure], M: \^, [IsElementOfIncidenceStructure, IsGeometryMorphism], M: ImagesSet, [IsGeometryMorphism, IsElementOfIncidenceStructureCollection], M: PreImageElm, [IsGeometryMorphism, IsElementOfIncidenceStructure], M: PreImagesSet, [IsGeometryMorphism, IsElementOfIncidenceStructureCollection], M: NaturalEmbeddingBySubspace, [ IsProjectiveSpace, IsProjectiveSpace, IsSubspaceOfProjectiveSpace ], M: NaturalEmbeddingBySubspaceNC, [ IsProjectiveSpace, IsProjectiveSpace, IsSubspaceOfProjectiveSpace ], M: NaturalEmbeddingBySubspace, [ IsClassicalPolarSpace, IsClassicalPolarSpace, IsSubspaceOfProjectiveSpace ], M: NaturalEmbeddingBySubspaceNC, [ IsClassicalPolarSpace, IsClassicalPolarSpace, IsSubspaceOfProjectiveSpace ], M: IsomorphismPolarSpaces, [ IsClassicalPolarSpace, IsClassicalPolarSpace, IsBool ], M: IsomorphismPolarSpaces, [ IsClassicalPolarSpace, IsClassicalPolarSpace ], M: IsomorphismPolarSpacesNC, [ IsClassicalPolarSpace, IsClassicalPolarSpace, IsBool ], M: IsomorphismPolarSpacesNC, [ IsClassicalPolarSpace, IsClassicalPolarSpace ], M: ShrinkMat, [ IsBasis, IsMatrix ], M: ShrinkMat, [ IsField,IsField, IsMatrix ], M: ShrinkVec, [ IsField, IsField, IsVector ], M: ShrinkVec, [ IsField, IsField, IsVector, IsBasis ], M: BlownUpProjectiveSpace, [ IsBasis, IsProjectiveSpace ], M: BlownUpProjectiveSpaceBySubfield, [ IsField, IsProjectiveSpace ], M: BlownUpSubspaceOfProjectiveSpace, [ IsBasis, IsSubspaceOfProjectiveSpace ], M: BlownUpSubspaceOfProjectiveSpaceBySubfield, [ IsField, IsSubspaceOfProjectiveSpace], M: IsDesarguesianSpreadElement, [ IsBasis, IsSubspaceOfProjectiveSpace ], M: IsBlownUpSubspaceOfProjectiveSpace, [ IsBasis, IsSubspaceOfProjectiveSpace ], M: NaturalEmbeddingByFieldReduction, [ IsProjectiveSpace, IsField, IsBasis ], M: NaturalEmbeddingByFieldReduction, [ IsProjectiveSpace, IsField ], M: NaturalEmbeddingByFieldReduction, [ IsProjectiveSpace, IsProjectiveSpace, IsBasis ], M: NaturalEmbeddingByFieldReduction, [ IsProjectiveSpace, IsProjectiveSpace ], M: BilinearFormFieldReduction, [ IsBilinearForm, IsField, IsFFE, IsBasis ], M: BilinearFormFieldReduction, [ IsBilinearForm, IsField, IsFFE ], M: QuadraticFormFieldReduction, [ IsQuadraticForm, IsField, IsFFE, IsBasis ], M: QuadraticFormFieldReduction, [ IsQuadraticForm, IsField, IsFFE ], M: HermitianFormFieldReduction, [ IsHermitianForm, IsField, IsFFE, IsBasis ], M: HermitianFormFieldReduction, [ IsHermitianForm, IsField, IsFFE ], M: NaturalEmbeddingByFieldReduction, [IsClassicalPolarSpace, IsField, IsFFE, IsBasis, IsBool], M: NaturalEmbeddingByFieldReduction, [IsClassicalPolarSpace, IsField, IsFFE, IsBasis], M: NaturalEmbeddingByFieldReduction, [IsClassicalPolarSpace, IsField, IsFFE, IsBool], M: NaturalEmbeddingByFieldReduction, [IsClassicalPolarSpace, IsField, IsFFE], M: NaturalEmbeddingByFieldReduction, [IsClassicalPolarSpace, IsField, IsBool], M: NaturalEmbeddingByFieldReduction, [IsClassicalPolarSpace, IsField], M: NaturalEmbeddingByFieldReduction, [ IsClassicalPolarSpace, IsClassicalPolarSpace ], M: NaturalEmbeddingByFieldReduction, [IsClassicalPolarSpace, IsClassicalPolarSpace, IsBool], M: NaturalEmbeddingByFieldReduction, [IsClassicalPolarSpace, IsClassicalPolarSpace], M: NaturalEmbeddingBySubfield, [ IsProjectiveSpace, IsProjectiveSpace ], M: NaturalEmbeddingBySubfield, [ IsClassicalPolarSpace, IsClassicalPolarSpace, IsBool ], M: NaturalEmbeddingBySubfield, [ IsClassicalPolarSpace, IsClassicalPolarSpace ], M: NaturalProjectionBySubspace, [ IsProjectiveSpace, IsSubspaceOfProjectiveSpace ], M: NaturalProjectionBySubspaceNC, [ IsProjectiveSpace, IsSubspaceOfProjectiveSpace ], M: QUO, [ IsProjectiveSpace and IsProjectiveSpaceRep, IsSubspaceOfProjectiveSpace], M: NaturalProjectionBySubspace, [ IsClassicalPolarSpace, IsSubspaceOfClassicalPolarSpace ], M: NaturalProjectionBySubspaceNC, [ IsClassicalPolarSpace, IsSubspaceOfClassicalPolarSpace ], M: PluckerCoordinates, [ IsMatrix ], M: InversePluckerCoordinates, [ IsVector ], M: PluckerCoordinates, [ IsSubspaceOfProjectiveSpace ], M: KleinCorrespondence, [ IsField, IsBool ], M: KleinCorrespondence, [ IsPosInt ], M: KleinCorrespondence, [ IsPosInt, IsBool ], M: KleinCorrespondence, [ IsField ], M: KleinCorrespondence, [ IsClassicalPolarSpace, IsBool ], M: KleinCorrespondence, [ IsClassicalPolarSpace ], M: KleinCorrespondenceExtended, [ IsField, IsBool ], M: KleinCorrespondenceExtended, [ IsPosInt ], M: KleinCorrespondenceExtended, [ IsClassicalPolarSpace, IsBool ], M: KleinCorrespondenceExtended, [ IsClassicalPolarSpace ], M: NaturalDualitySymplectic, [ IsClassicalGQ, IsClassicalGQ, IsBool, IsBool ], M: NaturalDualityHermitian, [ IsClassicalGQ, IsClassicalGQ, IsBool, IsBool ], M: NaturalDuality, [ IsClassicalGQ, IsClassicalGQ, IsBool ], M: NaturalDuality, [ IsClassicalGQ, IsClassicalGQ ], M: NaturalDuality, [ IsClassicalGQ, IsBool ], M: NaturalDuality, [ IsClassicalGQ ], M: IsomorphismPolarSpacesProjectionFromNucleus, [ IsClassicalPolarSpace, IsClassicalPolarSpace, IsBool ], M: SelfDualitySymplectic, [ IsClassicalGQ, IsBool ], M: SelfDualityParabolic, [ IsClassicalGQ, IsBool ], M: SelfDuality, [ IsClassicalGQ, IsBool ], M: SelfDuality, [ IsClassicalGQ ], enumerators.gi: methods M: AntonEnumerator, [IsSubspacesOfClassicalPolarSpace], M: EnumeratorByOrbit, [ IsSubspacesOfClassicalPolarSpace ], M: AsList, [IsSubspacesOfClassicalPolarSpace], M: AsSortedList, [IsSubspacesOfClassicalPolarSpace], M: AsSSortedList, [IsSubspacesOfClassicalPolarSpace], M: Enumerator, [ IsSubspacesOfClassicalPolarSpace ], M: Enumerator, [IsShadowSubspacesOfClassicalPolarSpace and IsShadowSubspacesOfClassicalPolarSpaceRep ], diagram.gi: methods M: CosetGeometry, InstallMethod(CosetGeometry,"forgroupsandlistofsubgroups",[IsGroup,IsHomogeneousList], M: Rank2Residues, InstallMethod(Rank2Residues,[IsIncidenceGeometry], M: MakeRank2Residue, InstallMethod(MakeRank2Residue,[IsRank2Residue], M: \^, [IsElementOfCosetGeometry, IsMultiplicativeElementWithInverse], M: \^, [IsFlagOfCosetGeometry, IsMultiplicativeElementWithInverse], M: FlagOfIncidenceStructure, [ IsCosetGeometry, IsElementOfIncidenceStructureCollection ], M: FlagOfIncidenceStructure, [ IsCosetGeometry, IsList and IsEmpty ], M: \=, InstallOtherMethod(\=,[IsCosetGeometry,IsCosetGeometry ], M: ElementsOfIncidenceStructure, InstallMethod(ElementsOfIncidenceStructure,[IsCosetGeometry,IsPosInt], M: ElementsOfIncidenceStructure, [IsCosetGeometry], M: RandomElement, [IsCosetGeometry], M: RandomChamber, [IsCosetGeometry], M: RandomFlag, [IsCosetGeometry], M: Random, [IsAllElementsOfCosetGeometry], M: Size, InstallMethod(Size,[IsElementsOfCosetGeometry], M: Wrap, [IsCosetGeometry, IsPosInt, IsObject], M: Iterator, [IsElementsOfCosetGeometry], M: IsIncident, [IsElementOfCosetGeometry, IsElementOfCosetGeometry], M: ParabolicSubgroups, [ IsCosetGeometry ], cg -> cg!.parabolics ); M: AmbientGroup, [ IsCosetGeometry ], cg -> cg!.group ); M: BorelSubgroup, [ IsCosetGeometry ], cg -> Intersection(cg!.parabolics) ); M: IsFlagTransitiveGeometry, [ IsCosetGeometry ], M: IsFirmGeometry, [ IsCosetGeometry ], M: IsThinGeometry, [ IsCosetGeometry ], M: IsThickGeometry, [ IsCosetGeometry ], M: IsConnected, [ IsCosetGeometry ], M: IsResiduallyConnected, [ IsCosetGeometry ], M: StandardFlagOfCosetGeometry, [ IsCosetGeometry ], M: FlagToStandardFlag, [ IsCosetGeometry, IsFlagOfCosetGeometry ], M: CanonicalResidueOfFlag, [ IsCosetGeometry, IsFlagOfCosetGeometry ], M: ResidueOfFlag, [ IsFlagOfCosetGeometry ], M: IncidenceGraph, InstallMethod(IncidenceGraph,[IsCosetGeometryandIsHandledByNiceMonomorphism], M: IncidenceGraph, InstallMethod(IncidenceGraph,[IsCosetGeometry], M: AutGroupIncidenceStructureWithNauty, [ IsCosetGeometry ], M: CorGroupIncidenceStructureWithNauty, [ IsCosetGeometry ], M: IsIsomorphicIncidenceStructureWithNauty, [ IsCosetGeometry, IsCosetGeometry ], M: ViewObj, [ IsDiagram and IsDiagramRep ], M: ViewObj, [ IsDiagram and IsDiagramRep and HasGeometryOfDiagram], M: ViewObj, [ IsCosetGeometry and IsCosetGeometryRep ], M: ViewObj, [ IsFlagOfCosetGeometry ], M: PrintObj, [ IsFlagOfCosetGeometry ], M: PrintObj, [ IsCosetGeometry and IsCosetGeometryRep ], M: ViewObj, [ IsElementsOfCosetGeometry and IsElementsOfCosetGeometryRep ], M: PrintObj, InstallMethod(PrintObj,"forcosetgeometry",[IsElementsOfCosetGeometryand IsElementsOfCosetGeometryRep ], M: ViewObj, InstallMethod(ViewObj,"forcosetgeometry",[IsElementOfCosetGeometry], M: PrintObj, InstallMethod(PrintObj,"forelementofcosetgeometry",[IsElementOfCosetGeometry], M: ViewObj, InstallMethod(ViewObj,"forvertexofdiagram",[IsVertexOfDiagramandIsVertexOfDiagramRep], M: PrintObj, InstallMethod(PrintObj,"forvertexofdiagram",[IsVertexOfDiagramandIsVertexOfDiagramRep], M: ViewObj, InstallMethod(ViewObj,"foredgeofdiagram",[IsEdgeOfDiagramandIsEdgeOfDiagramRep], M: PrintObj, InstallMethod(PrintObj,"foredgeofdiagram",[IsEdgeOfDiagramandIsEdgeOfDiagramRep], M: ViewObj, InstallMethod(ViewObj,"forrank2residue",[IsRank2ResidueandIsRank2ResidueRep], M: PrintObj, InstallMethod(PrintObj,"forrank2residue",[IsRank2ResidueandIsRank2ResidueRep], M: \=, InstallMethod(\=,[IsVertexOfDiagramandIsVertexOfDiagramRep, IsVertexOfDiagram and IsVertexOfDiagramRep ], M: \=, InstallMethod(\=,[IsEdgeOfDiagramandIsEdgeOfDiagramRep, IsEdgeOfDiagram and IsEdgeOfDiagramRep ], M: DiagramOfGeometry, InstallMethod(DiagramOfGeometry,"forflag-transitivecosetgeometry",[IsCosetGeometry], M: Display, InstallMethod(Display,[IsDiagramandIsDiagramRep], M: DiagramOfGeometry, InstallMethod(DiagramOfGeometry,"foraprojectivespace",[IsProjectiveSpace], M: Rk2GeoDiameter, InstallMethod(Rk2GeoDiameter,"foracosetgeometry",[IsCosetGeometry, IsPosInt], M: Rk2GeoGonality, InstallMethod(Rk2GeoGonality,"foracosetgeometry",[IsCosetGeometry], M: GeometryOfRank2Residue, InstallMethod(GeometryOfRank2Residue,"forarank2residue",[IsRank2Residue], M: Rank2Parameters, InstallMethod(Rank2Parameters,"foracosetgeometryofrank2",[IsCosetGeometry], M: \<, [ IsElementOfCosetGeometry and IsElementOfCosetGeometryRep, IsElementOfCosetGeometry and IsElementOfCosetGeometryRep ], M: DiagramOfGeometry, InstallMethod(DiagramOfGeometry,[IsClassicalPolarSpace], varieties.gi: methods M: AlgebraicVariety, [ IsProjectiveSpace, IsPolynomialRing, IsList ], M: AlgebraicVariety, [ IsProjectiveSpace, IsList ], M: AlgebraicVariety, [ IsAffineSpace, IsPolynomialRing, IsList ], M: AlgebraicVariety, [ IsAffineSpace, IsList ], M: ProjectiveVariety, [ IsProjectiveSpace, IsPolynomialRing, IsList ], M: ProjectiveVariety, [ IsProjectiveSpace, IsList ], M: ViewObj, [ IsProjectiveVariety and IsProjectiveVarietyRep ], M: PrintObj, [ IsProjectiveVariety and IsProjectiveVarietyRep ], M: Display, [ IsProjectiveVariety and IsProjectiveVarietyRep ], M: HermitianVariety, [IsPosInt, IsField], M: HermitianVariety, [IsPosInt, IsPosInt], M: HermitianVariety, [IsProjectiveSpace,IsPolynomialRing, IsPolynomial], M: HermitianVariety, [IsProjectiveSpace, IsPolynomial], M: ViewObj, [ IsHermitianVariety and IsHermitianVarietyRep ], M: PrintObj, [ IsHermitianVariety and IsHermitianVarietyRep ], M: Display, [ IsHermitianVariety and IsHermitianVarietyRep ], M: QuadraticVariety, [IsProjectiveSpace,IsPolynomialRing, IsPolynomial], M: QuadraticVariety, [IsProjectiveSpace, IsPolynomial], M: QuadraticVariety, [IsPosInt, IsField, IsString], M: QuadraticVariety, [IsPosInt, IsField], M: QuadraticVariety, [IsPosInt, IsPosInt], M: QuadraticVariety, [IsPosInt, IsPosInt, IsString], M: ViewObj, [ IsQuadraticVariety and IsQuadraticVarietyRep ], M: PrintObj, [ IsQuadraticVariety and IsQuadraticVarietyRep ], M: Display, [ IsQuadraticVariety and IsQuadraticVarietyRep ], M: PolarSpace, [IsProjectiveVariety and IsProjectiveVarietyRep], M: AffineVariety, [ IsAffineSpace, IsPolynomialRing, IsList ], M: AffineVariety, [ IsAffineSpace, IsList ], M: AlgebraicVariety, [ IsAffineSpace, IsList ], M: ViewObj, [ IsAffineVariety and IsAffineVarietyRep ], M: PrintObj, [ IsAffineVariety and IsAffineVarietyRep ], M: Display, [ IsAffineVariety and IsAffineVarietyRep ], M: \in, [IsElementOfIncidenceStructure, IsAlgebraicVariety], M: PointsOfAlgebraicVariety, [IsAlgebraicVariety and IsAlgebraicVarietyRep], M: ViewObj, [ IsPointsOfAlgebraicVariety and IsPointsOfAlgebraicVarietyRep ], M: PrintObj, [ IsPointsOfAlgebraicVariety and IsPointsOfAlgebraicVarietyRep ], M: Points, [IsAlgebraicVariety and IsAlgebraicVarietyRep], M: \in, [IsElementOfIncidenceStructure, IsPointsOfAlgebraicVariety], 1*SUM_FLAGS+3, M: Iterator, [IsPointsOfAlgebraicVariety], M: Enumerator, [IsPointsOfAlgebraicVariety], M: AmbientSpace, [IsAlgebraicVariety and IsAlgebraicVarietyRep], M: SegreMap, [ IsHomogeneousList ], M: SegreMap, [IsHomogeneousList, IsField ], M: SegreMap, [IsProjectiveSpace, IsProjectiveSpace ], M: SegreMap, [ IsPosInt, IsPosInt, IsField ], M: SegreMap, [ IsPosInt, IsPosInt, IsPosInt ], M: Source, [ IsSegreMap ], M: ViewObj, [ IsSegreMap and IsSegreMapRep ], M: PrintObj, [ IsSegreMap and IsSegreMapRep ], M: SegreVariety, [IsHomogeneousList], M: SegreVariety, [IsHomogeneousList, IsField ], M: SegreVariety, [IsProjectiveSpace, IsProjectiveSpace ], M: SegreVariety, [ IsPosInt, IsPosInt, IsField ], M: SegreVariety, [ IsPosInt, IsPosInt, IsPosInt ], M: ViewObj, [ IsSegreVariety and IsSegreVarietyRep ], M: PrintObj, [ IsSegreVariety and IsSegreVarietyRep ], M: SegreMap, [IsSegreVariety], M: PointsOfSegreVariety, [IsSegreVariety and IsSegreVarietyRep], M: ViewObj, [ IsPointsOfSegreVariety and IsPointsOfSegreVarietyRep ], M: Points, [IsSegreVariety and IsSegreVarietyRep], M: Iterator, [IsPointsOfSegreVariety], M: Enumerator, [IsPointsOfSegreVariety], M: Size, [IsPointsOfSegreVariety], M: ImageElm, [IsSegreMap, IsList], M: \^, [IsList, IsSegreMap], M: ImagesSet, [IsSegreMap, IsList], M: VeroneseMap, [IsProjectiveSpace], M: ViewObj, [ IsVeroneseMap and IsVeroneseMapRep ], M: PrintObj, [ IsVeroneseMap and IsVeroneseMapRep ], M: VeroneseVariety, [IsProjectiveSpace], M: VeroneseVariety, [ IsPosInt, IsField ], M: VeroneseVariety, [ IsPosInt, IsPosInt ], M: ViewObj, [ IsVeroneseVariety and IsVeroneseVarietyRep ], M: PrintObj, [ IsVeroneseVariety and IsVeroneseVarietyRep ], M: VeroneseMap, [IsVeroneseVariety], M: PointsOfVeroneseVariety, [IsVeroneseVariety and IsVeroneseVarietyRep], M: ViewObj, [ IsPointsOfVeroneseVariety and IsPointsOfVeroneseVarietyRep ], M: Points, [IsVeroneseVariety and IsVeroneseVarietyRep], M: Iterator, [IsPointsOfVeroneseVariety], M: Enumerator, [IsPointsOfVeroneseVariety], M: Size, [IsPointsOfVeroneseVariety], M: ImageElm, [IsGeometryMap, IsElementOfIncidenceStructure], M: \^, [IsElementOfIncidenceStructure, IsGeometryMap], M: ImagesSet, [IsGeometryMap, IsElementOfIncidenceStructureCollection], M: Source, [ IsGeometryMap ], M: Range, [ IsGeometryMap ], M: GrassmannCoordinates, [ IsSubspaceOfProjectiveSpace ], M: GrassmannMap, [ IsPosInt, IsProjectiveSpace ], M: GrassmannMap, [ IsPosInt, IsPosInt, IsPosInt ], M: GrassmannMap, [ IsSubspacesOfProjectiveSpace ], M: ViewObj, [ IsGrassmannMap and IsGrassmannMapRep ], M: PrintObj, [ IsGrassmannMap and IsGrassmannMapRep ], M: GrassmannVariety, [ IsPosInt, IsProjectiveSpace ], M: GrassmannVariety, [ IsSubspacesOfProjectiveSpace ], M: ViewObj, [ IsGrassmannVariety and IsGrassmannVarietyRep ], M: PrintObj, [ IsGrassmannVariety and IsGrassmannVarietyRep ], M: GrassmannMap, [IsGrassmannVariety], M: PointsOfGrassmannVariety, [IsGrassmannVariety and IsGrassmannVarietyRep], M: ViewObj, [ IsPointsOfGrassmannVariety and IsPointsOfGrassmannVarietyRep ], M: Points, [IsGrassmannVariety and IsGrassmannVarietyRep], M: Iterator, [IsPointsOfGrassmannVariety], M: Enumerator, [IsPointsOfGrassmannVariety], M: Size, [IsPointsOfGrassmannVariety], affinespace.gi: methods M: AffineSpace, [ IsPosInt, IsField ], M: AffineSpace, [ IsPosInt, IsPosInt ], M: ViewObj, InstallMethod(ViewObj,[IsAffineSpaceandIsAffineSpaceRep], M: PrintObj, InstallMethod(PrintObj,[IsAffineSpaceandIsAffineSpaceRep], M: \=, [IsAffineSpace, IsAffineSpace], M: Dimension, [ IsAffineSpace and IsAffineSpaceRep ], M: UnderlyingVectorSpace, [ IsAffineSpace and IsAffineSpaceRep ], M: AmbientSpace, [IsSubspaceOfAffineSpace], M: BaseField, [IsAffineSpace and IsAffineSpaceRep], M: BaseField, [IsSubspaceOfAffineSpace], M: TypesOfElementsOfIncidenceStructure, [IsAffineSpace], M: TypesOfElementsOfIncidenceStructurePlural, [IsAffineSpace], M: VectorSpaceTransversalElement, [IsVectorSpace, IsFFECollColl, IsVector], M: VectorSpaceTransversal, [IsVectorSpace, IsFFECollColl], M: ViewObj, [ IsVectorSpaceTransversal and IsVectorSpaceTransversalRep ], M: PrintObj, [ IsVectorSpaceTransversal and IsVectorSpaceTransversalRep ], M: Wrap, [IsAffineSpace, IsPosInt, IsObject], M: ViewObj, [ IsSubspacesOfAffineSpace and IsSubspacesOfAffineSpaceRep ], M: PrintObj, [ IsSubspacesOfAffineSpace and IsAllSubspacesOfProjectiveSpaceRep ], M: Display, [ IsSubspaceOfAffineSpace ], M: AffineSubspace, [IsAffineSpace, IsRowVector, IsPlistRep and IsMatrix], M: AffineSubspace, [IsAffineSpace, IsRowVector], M: AffineSubspace, [IsAffineSpace, IsCVecRep], M: AffineSubspace, [IsAffineSpace, IsRowVector, Is8BitMatrixRep], M: AffineSubspace, [IsAffineSpace, IsRowVector, IsGF2MatrixRep], M: AffineSubspace, [IsAffineSpace, IsCVecRep, IsCMatRep], M: ObjectToElement, [ IsAffineSpace, IsList], M: ObjectToElement, [ IsAffineSpace, IsPosInt, IsList], M: RandomSubspace, [ IsAffineSpace, IsInt ], M: Random, [ IsSubspacesOfAffineSpace ], M: ElementsOfIncidenceStructure, [IsAffineSpace], M: ElementsOfIncidenceStructure, [ IsAffineSpace, IsPosInt], M: Points, [IsAffineSpace], M: Lines, [IsAffineSpace], M: Planes, [IsAffineSpace], M: Solids, [IsAffineSpace], M: Hyperplanes, [IsAffineSpace], M: Size, [IsSubspacesOfAffineSpace], M: FlagOfIncidenceStructure, [ IsAffineSpace, IsSubspaceOfAffineSpaceCollection ], M: FlagOfIncidenceStructure, [ IsAffineSpace, IsList and IsEmpty ], M: ViewObj, [ IsFlagOfAffineSpace and IsFlagOfIncidenceStructureRep ], M: PrintObj, [ IsFlagOfAffineSpace and IsFlagOfIncidenceStructureRep ], M: Display, [ IsFlagOfAffineSpace and IsFlagOfIncidenceStructureRep ], M: Enumerator, [ IsVectorSpaceTransversal ], M: Enumerator, [ IsSubspacesOfAffineSpace ], M: Iterator, [IsSubspacesOfAffineSpace], M: \in, [IsSubspaceOfAffineSpace, IsAffineSpace], M: \in, [ IsAffineSpace, IsSubspaceOfAffineSpace ], M: \in, [IsSubspaceOfAffineSpace, IsSubspaceOfAffineSpace], M: IsIncident, [IsSubspaceOfAffineSpace, IsSubspaceOfAffineSpace], M: Span, [IsSubspaceOfAffineSpace, IsSubspaceOfAffineSpace], M: Meet, [IsSubspaceOfAffineSpace, IsSubspaceOfAffineSpace], M: IsParallel, [ IsSubspaceOfAffineSpace, IsSubspaceOfAffineSpace ], M: ProjectiveCompletion, [ IsAffineSpace ], M: ShadowOfElement, [IsAffineSpace, IsSubspaceOfAffineSpace, IsPosInt], M: ShadowOfFlag, [IsAffineSpace, IsFlagOfIncidenceStructure, IsPosInt], M: ParallelClass, [IsAffineSpace, IsSubspaceOfAffineSpace], M: ParallelClass, [ IsSubspaceOfAffineSpace ], M: Iterator, [IsParallelClassOfAffineSpace and IsParallelClassOfAffineSpaceRep ], M: Size, [IsShadowSubspacesOfAffineSpace and IsShadowSubspacesOfAffineSpaceRep ], M: Iterator, [IsShadowSubspacesOfAffineSpace and IsShadowSubspacesOfAffineSpaceRep ], M: ViewObj, [ IsShadowSubspacesOfAffineSpace and IsShadowSubspacesOfAffineSpaceRep ], M: ViewObj, [ IsParallelClassOfAffineSpace and IsParallelClassOfAffineSpaceRep ], M: Points, InstallMethod(Points,[IsSubspaceOfAffineSpace], M: Points, InstallMethod(Points,[IsAffineSpace,IsSubspaceOfAffineSpace], M: Lines, InstallMethod(Lines,[IsSubspaceOfAffineSpace], M: Lines, InstallMethod(Lines,[IsAffineSpace,IsSubspaceOfAffineSpace], M: Planes, InstallMethod(Planes,[IsSubspaceOfAffineSpace], M: Planes, InstallMethod(Planes,[IsAffineSpace,IsSubspaceOfAffineSpace], M: Solids, InstallMethod(Solids,[IsSubspaceOfAffineSpace], M: Solids, InstallMethod(Solids,[IsAffineSpace,IsSubspaceOfAffineSpace], M: IncidenceGraph, [ IsAffineSpace ], affinegroup.gi: methods M: AffineGroup, [ IsAffineSpace ], M: CollineationGroup, [ IsAffineSpace ], M: \^, [IsSubspaceOfAffineSpace, IsProjGrpElWithFrob], gpolygons.gi: methods M: GeneralisedPolygonByBlocks, [ IsHomogeneousList ], M: GeneralisedPolygonByIncidenceMatrix, [ IsMatrix ], M: GeneralisedPolygonByElements, [ IsSet, IsSet, IsFunction ], M: GeneralisedPolygonByElements, [ IsSet, IsSet, IsFunction, IsGroup, IsFunction ], M: ViewObj, [ IsProjectivePlaneCategory and IsGeneralisedPolygonRep], M: ViewObj, [ IsGeneralisedQuadrangle and IsGeneralisedPolygonRep], M: ViewObj, [ IsGeneralisedHexagon and IsGeneralisedPolygonRep], M: ViewObj, [ IsGeneralisedOctagon and IsGeneralisedPolygonRep], M: ViewObj, [ IsGeneralisedPolygon and IsGeneralisedPolygonRep], M: ViewObj, [ IsWeakGeneralisedPolygon and IsGeneralisedPolygonRep], M: Order, [ IsWeakGeneralisedPolygon ], M: UnderlyingObject, [ IsElementOfGeneralisedPolygon ], M: ObjectToElement, [ IsGeneralisedPolygon and IsGeneralisedPolygonRep, IsPosInt, IsObject], M: ObjectToElement, [ IsGeneralisedPolygon and IsGeneralisedPolygonRep, IsObject], M: ElementsOfIncidenceStructure, [IsGeneralisedPolygon and IsGeneralisedPolygonRep, IsPosInt], M: ElementsOfIncidenceStructure, [IsWeakGeneralisedPolygon and IsGeneralisedPolygonRep, IsPosInt], M: Points, [IsGeneralisedPolygon and IsGeneralisedPolygonRep], M: Lines, [IsGeneralisedPolygon and IsGeneralisedPolygonRep], M: ViewObj, [ IsElementsOfGeneralisedPolygon and IsElementsOfGeneralisedPolygonRep ], M: PrintObj, [ IsElementsOfGeneralisedPolygon and IsElementsOfGeneralisedPolygonRep ], M: Size, [IsElementsOfGeneralisedPolygon], M: Iterator, [ IsElementsOfGeneralisedPolygon and IsElementsOfGeneralisedPolygonRep], M: Iterator, [IsShadowElementsOfGeneralisedPolygon and IsShadowElementsOfGeneralisedPolygonRep ], M: Random, [ IsElementsOfGeneralisedPolygon and IsElementsOfGeneralisedPolygonRep ], M: IsIncident, [IsElementOfGeneralisedPolygon, IsElementOfGeneralisedPolygon], M: Span, [ IsElementOfGeneralisedPolygon, IsElementOfGeneralisedPolygon ], M: Meet, [ IsElementOfGeneralisedPolygon, IsElementOfGeneralisedPolygon ], M: Wrap, [IsGeneralisedPolygon, IsPosInt, IsObject], M: TypesOfElementsOfIncidenceStructurePlural, [ IsGeneralisedPolygon and IsGeneralisedPolygonRep ], M: ShadowOfElement, [IsGeneralisedPolygon and IsGeneralisedPolygonRep, IsElementOfGeneralisedPolygon, IsPosInt], M: ViewObj, [ IsShadowElementsOfGeneralisedPolygon and IsShadowElementsOfGeneralisedPolygonRep ], M: Points, [ IsElementOfGeneralisedPolygon ], M: Lines, [ IsElementOfGeneralisedPolygon ], M: DistanceBetweenElements, [ IsElementOfGeneralisedPolygon, IsElementOfGeneralisedPolygon], M: IncidenceGraph, [ IsGeneralisedPolygon ], M: IncidenceMatrixOfGeneralisedPolygon, [ IsGeneralisedPolygon ], M: CollineationGroup, [ IsGeneralisedPolygon and IsGeneralisedPolygonRep ], M: BlockDesignOfGeneralisedPolygon, [ IsGeneralisedPolygon and IsGeneralisedPolygonRep ], M: DistanceBetweenElements, [ IsSubspaceOfProjectiveSpace, IsSubspaceOfProjectiveSpace ], M: IncidenceGraph, [ IsDesarguesianPlane ], M: DistanceBetweenElements, [ IsSubspaceOfClassicalPolarSpace, IsSubspaceOfClassicalPolarSpace ], M: IncidenceGraph, [ IsClassicalGQ ], M: Wrap, [IsClassicalGeneralisedHexagon, IsPosInt, IsObject], M: SplitCayleyHexagon, [ IsField and IsFinite ], M: SplitCayleyHexagon, [ IsPosInt ], M: SplitCayleyHexagon, [ IsClassicalPolarSpace ], M: TwistedTrialityHexagon, [ IsField and IsFinite ], M: TwistedTrialityHexagon, [ IsPosInt ], M: TwistedTrialityHexagon, [ IsClassicalPolarSpace ], M: Display, [ IsGeneralisedHexagon and IsLieGeometry ], M: G2fining, [ IsPosInt, IsField and IsFinite ], M: 3D4fining, [ IsField and IsFinite ], M: CollineationGroup, [ IsClassicalGeneralisedHexagon], M: IncidenceGraph, [ IsClassicalGeneralisedHexagon and IsGeneralisedPolygonRep ], M: VectorSpaceToElement, [ IsClassicalGeneralisedHexagon, IsCVecRep], M: VectorSpaceToElement, [ IsClassicalGeneralisedHexagon, IsRowVector ], M: VectorSpaceToElement, [ IsClassicalGeneralisedHexagon, Is8BitVectorRep ], M: VectorSpaceToElement, [ IsClassicalGeneralisedHexagon, IsPlistRep and IsMatrix], M: VectorSpaceToElement, [ IsClassicalGeneralisedHexagon, IsGF2MatrixRep], M: VectorSpaceToElement, [ IsClassicalGeneralisedHexagon, Is8BitMatrixRep], M: VectorSpaceToElement, [ IsClassicalGeneralisedHexagon, IsCMatRep], M: \in, [ IsElementOfIncidenceStructure, IsClassicalGeneralisedHexagon ], M: ObjectToElement, [ IsClassicalGeneralisedHexagon, IsObject], M: ViewObj, [ IsElementOfKantorFamily ], M: PrintObj, [ IsElementOfKantorFamily ], M: Wrap, [IsElationGQByKantorFamily, IsPosInt, IsPosInt, IsObject], M: \=, [IsElementOfKantorFamily, IsElementOfKantorFamily], M: \<, [IsElementOfKantorFamily, IsElementOfKantorFamily], M: IsKantorFamily, [IsGroup, IsList, IsList], M: EGQByKantorFamily, [IsGroup, IsList, IsList], M: Display, [ IsElationGQByKantorFamily ], M: UnderlyingObject, [ IsElementOfKantorFamily ], M: ObjectToElement, [ IsElationGQByKantorFamily, IsPosInt, IsRightCoset ], M: ObjectToElement, [ IsElationGQByKantorFamily, IsRightCoset ], M: ObjectToElement, [ IsElationGQByKantorFamily, IsPosInt, IsMultiplicativeElementWithInverse ], M: ObjectToElement, [ IsElationGQByKantorFamily, IsMultiplicativeElementWithInverse ], M: ObjectToElement, [ IsElationGQByKantorFamily, IsPosInt, IsMagmaWithInverses ], M: ObjectToElement, [ IsElationGQByKantorFamily, IsMagmaWithInverses ], M: IsAnisotropic, [IsFFECollColl, IsField and IsFinite], M: IsqClan, [ IsFFECollCollColl, IsField and IsFinite], M: qClan, [ IsFFECollCollColl, IsField ], M: ViewObj, [ IsqClanObj and IsqClanRep ], M: PrintObj, [ IsqClanObj and IsqClanRep ], M: AsList, [IsqClanObj and IsqClanRep], M: AsSet, [IsqClanObj and IsqClanRep], M: BaseField, [IsqClanObj and IsqClanRep], M: IsLinearqClan, [ IsqClanObj ], M: LinearqClan, [ IsPosInt ], M: FisherThasWalkerKantorBettenqClan, [ IsPosInt ], M: KantorMonomialqClan, [ IsPosInt ], M: KantorKnuthqClan, [ IsPosInt ], M: FisherqClan, [ IsPosInt ], M: KantorFamilyByqClan, [ IsqClanObj and IsqClanRep ], M: EGQByqClan, [ IsqClanObj and IsqClanRep ], M: IncidenceGraph, [ IsElationGQ and IsGeneralisedPolygonRep ], M: BLTSetByqClan, [ IsqClanObj and IsqClanRep ], M: EGQByBLTSet, [IsList, IsSubspaceOfProjectiveSpace, IsSubspaceOfProjectiveSpace], M: EGQByBLTSet, [ IsList ], M: Display, [ IsElationGQByBLTSet ], M: DefiningPlanesOfEGQByBLTSet, [ IsElationGQByBLTSet ], M: ObjectToElement, [ IsElationGQByBLTSet, IsPosInt, IsSubspaceOfClassicalPolarSpace], M: ObjectToElement, [ IsElationGQByBLTSet, IsSubspaceOfClassicalPolarSpace], M: CollineationSubgroup, [ IsElationGQByBLTSet ], M: FlockGQByqClan, InstallMethod(FlockGQByqClan,[IsqClanObj], orbits-stabilisers.gi: methods M: FiningOrbit, [ IsProjectiveGroupWithFrob, IsElementOfIncidenceStructure, IsFunction], M: FiningOrbit, [ IsProjectiveGroupWithFrob, IsSubspaceOfProjectiveSpace ], M: FiningOrbit, [ IsProjectiveGroupWithFrob, IsSubspaceOfAffineSpace ], M: FiningOrbit, [ IsProjectiveGroupWithFrob, CategoryCollections(IsElementOfIncidenceStructure), IsFunction], M: FiningOrbit, [ IsProjectiveGroupWithFrob, CategoryCollections(IsElementOfIncidenceStructure) ], M: FiningOrbits, [ IsGroup, IsHomogeneousList, IsFunction], M: FiningOrbitsDomain, [ IsGroup, IsElementsOfIncidenceGeometry, IsFunction ], M: FiningOrbits, [ IsProjectiveGroupWithFrob, IsSubspaceOfProjectiveSpaceCollection and IsHomogeneousList ], M: FiningOrbits, [ IsProjectiveGroupWithFrob, IsSubspaceOfAffineSpaceCollection and IsHomogeneousList ], M: FiningOrbits, [ IsProjectiveGroupWithFrob, IsSubspacesOfProjectiveSpace ], M: FiningOrbits, [ IsProjectiveGroupWithFrob, IsSubspacesOfAffineSpace ], M: FiningOrbits, [ IsProjectiveGroupWithFrob, IsShadowSubspacesOfProjectiveSpace], M: FiningOrbits, [ IsProjectiveGroupWithFrob, IsShadowSubspacesOfAffineSpace], M: FiningOrbits, [ IsProjectiveGroupWithFrob, IsShadowSubspacesOfClassicalPolarSpace], M: FiningOrbits, [ IsProjectiveGroupWithFrob, IsParallelClassOfAffineSpace], M: FiningElementStabiliserOp, [ IsGroup, IsElementOfIncidenceStructure, IsFunction], M: FiningStabiliser, [ IsProjectiveGroupWithFrob, IsSubspaceOfProjectiveSpace], M: FiningStabiliser, [ IsProjectiveGroupWithFrob, IsSubspaceOfAffineSpace], M: FiningStabiliserOrb, [IsProjectiveGroupWithFrob, IsSubspaceOfProjectiveSpace], M: FiningStabiliserOrb, [IsProjectiveGroupWithFrob, IsSubspaceOfAffineSpace], M: FiningSetwiseStabiliser, [IsProjectiveGroupWithFrob, IsSubspaceOfProjectiveSpaceCollection and IsHomogeneousList], M: FiningSetwiseStabiliser, [IsProjectiveGroupWithFrob, IsSubspaceOfAffineSpaceCollection and IsHomogeneousList], M: FiningStabiliserPerm, InstallMethod(FiningStabiliserPerm,[IsProjectiveGroupWithFrob,IsElementOfIncidenceStructure], M: FiningStabiliserPerm2, [IsProjectiveGroupWithFrob, IsElementOfIncidenceStructure], M: FixedSubspaces, [IsProjectiveGroupWithFrob, IsProjectiveSpace], M: ProjectiveStabiliserGroupOfSubspace, [IsSubspaceOfProjectiveSpace], M: StabiliserGroupOfSubspace, [IsSubspaceOfProjectiveSpace], M: SpecialProjectiveStabiliserGroupOfSubspace, [IsSubspaceOfProjectiveSpace],
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