Construction of Incidence and Coset Geometries
Construction of an Incidence Geometry
IncidenceGeometry(G) : GrphUnd -> IncGeom
Example IncidenceGeometry_Constructors (H142E1)
Example IncidenceGeometry_Constructors (H142E2)
Example IncidenceGeometry_Constructors (H142E3)
Example IncidenceGeometry_Constructors (H142E4)
Construction of a Coset Geometry
CosetGeometry(G, S, I) : GrpPerm, Set, Set -> CosetGeom
CosetGeometry(G, S) : GrpPerm, Set -> CosetGeom
Example IncidenceGeometry_Constructors (H142E5)
Example IncidenceGeometry_Constructors (H142E6)
Example IncidenceGeometry_Constructors (H142E7)
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 (H142E8)
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 (H142E9)
Example IncidenceGeometry_diagram (H142E10)
Example IncidenceGeometry_diagram (H142E11)
Example IncidenceGeometry_diagram (H142E12)
Bibliography
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Version: V2.19 of
Mon Dec 17 14:40:36 EST 2012