Introduction
Construction of Incidence and Coset Geometries
Construction of an Incidence Geometry IncidenceGeometry(G) : GrphUnd -> IncGeom Example IncidenceGeometry_Constructors (H131E1) Example IncidenceGeometry_Constructors (H131E2) Example IncidenceGeometry_Constructors (H131E3) Example IncidenceGeometry_Constructors (H131E4)
Construction of a Coset Geometry CosetGeometry(G, S, I) : GrpPerm, Set, Set -> CosetGeom CosetGeometry(G, S) : GrpPerm, Set -> CosetGeom Example IncidenceGeometry_Constructors (H131E5) Example IncidenceGeometry_Constructors (H131E6) Example IncidenceGeometry_Constructors (H131E7)
Elementary Invariants Points(D) : IncGeom -> SetIndx Types(D) : IncGeom -> SetIndx Types(C) : CosetGeom -> SetIndx Rank(D) : IncGeom -> RngIntElt Rank(C) : CosetGeom -> RngIntElt IncidenceGraph(D) : IncGeom -> GrphUnd, GrphVertSet, GrphEdgeSet Group(C) : CosetGeom -> GrpPerm MaxParabolics(C) : CosetGeom -> SetIndx MinParabolics(C) : CosetGeom -> SetIndx Borel(C) : CosetGeom -> GrpPerm Kernel(C) : CosetGeom -> GrpPerm Kernels(C) : CosetGeom -> SeqEnum Quotient(C, K) : CosetGeom, GrpPerm -> CosetGeom
Conversion Functions IncidenceGeometry(C) : CosetGeom -> IncGeom CosetGeometry(D) : IncGeom -> BoolElt, CosetGeom Graph(D) : IncGeom -> GrphUnd Graph(C) : CosetGeom -> GrphUnd Example IncidenceGeometry_Constructors (H131E8)
Residues Residue(D, f) : IncGeom, Set -> IncGeom Residue(C, f) : CosetGeom, Set -> CosetGeom
Truncations Truncation(D, t) : IncGeom, Set -> IncGeom Truncation(C, t) : CosetGeom, Set -> CosetGeom
Shadows Shadow(D, I, F) : IncGeom, Set, Set -> SetIndx
Shadow Spaces ShadowSpace(D,I) : IncGeom, Set -> Inc
Automorphism Group and Correlation Group AutomorphismGroup(D) : IncGeom -> GrpPerm CorrelationGroup(D) : IncGeom -> GrpPerm
Properties of Incidence Geometries and Coset Geometries IsFTGeometry(D) : IncGeom -> BoolElt IsFTGeometry(C) : CosetGeom -> BoolElt IsFirm(X) : IncGeom -> BoolElt IsThin(X) : CosetGeom -> BoolElt IsThick(X) : CosetGeom -> BoolElt IsResiduallyConnected(X) : IncGeom -> BoolElt IsGraph(D) : IncGeom -> GrphUnd IsGraph(C) : CosetGeom -> GrphUnd
Intersection Properties of Coset Geometries HasIntersectionPropertyN(C,n) : CosetGeom, RngIntElt -> BoolElt, BoolElt HasIntersectionProperty(C) : CosetGeom -> BoolElt HasWeakIntersectionProperty(C) : CosetGeom -> BoolElt
Primitivity Properties on Coset Geometries IsPrimitive(C) : CosetGeom -> BoolElt IsWeaklyPrimitive(C) : CosetGeom -> BoolElt IsResiduallyPrimitive(C) : CosetGeom -> BoolElt IsResiduallyWealyPrimitive(C) : CosetGeom -> BoolElt IsLocallyTwoTransitive(C) : CosetGeom -> BoolElt
Diagram of an Incidence Geometry Diagram(D) : IncGeom -> GrphUnd, GrphVertSet, GrphEdgeSet Example IncidenceGeometry_diagram (H131E9) Example IncidenceGeometry_diagram (H131E10) Example IncidenceGeometry_diagram (H131E11)
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