Quelle chapA.html Sprache: HTML

products/Sources/formale Sprachen/GAP/pkg/fining/doc/chapA.html

<?xml version="1.0" encoding="UTF-8"?>

<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN"
         "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">

<html xmlns="http://www.w3.org/1999/xhtml" xml:lang="en">
<head>
<title>GAP (FinInG) - Appendix A: The structure of FinInG </title>
<meta http-equiv="content-type" content="text/html; charset=UTF-8" />
<meta name="generator" content="GAPDoc2HTML" />
<link rel="stylesheet" type="text/css" href="manual.css" />
<script src="manual.js" type="text/javascript"></script>
<script type="text/javascript">overwriteStyle();</script>
</head>
<body class="chapA"  onload="jscontent()">

<div class="chlinktop"><span class="chlink1">Goto Chapter: </span><a href="chap0.html">Top</a>  <a href="chap1.html">1</a>  <a href="chap2.html">2</a>  <a href="chap3.html">3</a>  <a href="chap4.html">4</a>  <a href="chap5.html">5</a>  <a href="chap6.html">6</a>  <a href="chap7.html">7</a>  <a href="chap8.html">8</a>  <a href="chap9.html">9</a>  <a href="chap10.html">10</a>  <a href="chap11.html">11</a>  <a href="chap12.html">12</a>  <a href="chap13.html">13</a>  <a href="chap14.html">14</a>  <a href="chapA.html">A</a>  <a href="chapB.html">B</a>  <a href="chapC.html">C</a>  <a href="chapBib.html">Bib</a>  <a href="chapInd.html">Ind</a>  </div>

<div class="chlinkprevnexttop"> <a href="chap0.html">[Top of Book]</a>   <a href="chap0.html#contents">[Contents]</a>    <a href="chap14.html">[Previous Chapter]</a>    <a href="chapB.html">[Next Chapter]</a>   </div>

<p id="mathjaxlink" class="pcenter"><a href="chapA_mj.html">[MathJax on]</a></p>
<p><a id="X7F3345C884CD0268" name="X7F3345C884CD0268"></a></p>
<div class="ChapSects"><a href="chapA.html#X7F3345C884CD0268">A <span class="Heading">The structure of <strong class="pkg">FinInG</strong> </span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chapA.html#X84D6D0EC7989CF5E">A.1 <span class="Heading">The different components</span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chapA.html#X83E153B784E17E05">A.2 <span class="Heading">The complete inventory</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chapA.html#X844A8A1F85E6E038">A.2-1 <span class="Heading">Declarations</span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chapA.html#X81736D4378BF64FF">A.2-2 <span class="Heading">Functions/Methods</span></a>
</span>
</div></div>
</div>

<h3>A <span class="Heading">The structure of <strong class="pkg">FinInG</strong> </span></h3>

<p><a id="X84D6D0EC7989CF5E" name="X84D6D0EC7989CF5E"></a></p>

<h4>A.1 <span class="Heading">The different components</span></h4>

<p><strong class="pkg">FinInG</strong> 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 <em>component.gd</em> and <em>component.gi</em> file. The file <em>component.gi</em> will be dependent on <em>component.gd</em> and all previously loaded <em>.gd</em> files, <em>component1/component2</em> means that both <em>component1.gi</em> and <em>component2.gi</em> depend on the declarations in both <em>component1.gd</em> and <em>component2.gd</em>.</p>

<p><a id="X83E153B784E17E05" name="X83E153B784E17E05"></a></p>

<h4>A.2 <span class="Heading">The complete inventory</span></h4>

<p><a id="X844A8A1F85E6E038" name="X844A8A1F85E6E038"></a></p>

<h5>A.2-1 <span class="Heading">Declarations</span></h5>

<div class="example"><pre>
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]

</pre></div>

<div class="example"><pre>
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

</pre></div>

<div class="example"><pre>
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

</pre></div>

<p><a id="X81736D4378BF64FF" name="X81736D4378BF64FF"></a></p>

<h5>A.2-2 <span class="Heading">Functions/Methods</span></h5>

<div class="example"><pre>
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

</pre></div>

<div class="example"><pre>
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],
--> --------------------

--> maximum size reached

--> --------------------

quality100%

¤ Dauer der Verarbeitung: 0.19 Sekunden (vorverarbeitet) ¤

Wurzel

Suchen

Beweissystem der NASA

Beweissystem Isabelle

NIST Cobol Testsuite

Cephes Mathematical Library

Wiener Entwicklungsmethode

Haftungshinweis

Die Informationen auf dieser Webseite wurden nach bestem Wissen sorgfältig zusammengestellt. Es wird jedoch weder Vollständigkeit, noch Richtigkeit, noch Qualität der bereit gestellten Informationen zugesichert.

Bemerkung:

Die farbliche Syntaxdarstellung ist noch experimentell.