Construction of Incidence and Coset Geometries
Construction of an Incidence Geometry
IncidenceGeometry(G) : GrphUnd -> IncGeom
IncidenceGeometry(C) : CosetGeom -> IncGeom
Example IncidenceGeometry_Constructors (H96E1)
Example IncidenceGeometry_Constructors (H96E2)
Example IncidenceGeometry_Constructors (H96E3)
Example IncidenceGeometry_Constructors (H96E4)
Construction of a Coset Geometry
CosetGeometry(G, S, I) : GrpPerm, Set, Set -> CosetGeom
CosetGeometry(G, S) : GrpPerm, Set -> CosetGeom
CosetGeometry(D) : IncGeom -> BoolElt, CosetGeom
Example IncidenceGeometry_Constructors (H96E5)
Example IncidenceGeometry_Constructors (H96E6)
Example IncidenceGeometry_Constructors (H96E7)
Example IncidenceGeometry_Constructors (H96E8)
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
MaxParabolics(C) : CosetGeom -> SetIndx
Borel(C) : CosetGeom -> GrpPerm
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
Automorphism Group and Correlation Group
AutomorphismGroup(D) : IncGeom -> GrpPerm
AutomorphismGroupNew(D) : IncGeom -> GrpPerm
CorrelationGroup(D) : IncGeom -> GrpPerm
Properties of Incidence Geometries and Coset Geometries
IsFTGeometry(D) : IncGeom -> BoolElt
IsFTGeometry(C) : CosetGeom -> BoolElt
IsFirm(D) : IncGeom -> BoolElt
IsFirm(C) : CosetGeom -> BoolElt
IsThin(D) : IncGeom -> BoolElt
IsThin(C) : CosetGeom -> BoolElt
IsThick(D) : IncGeom -> BoolElt
IsThick(C) : CosetGeom -> BoolElt
IsResiduallyConnected(D) : IncGeom -> BoolElt
IsResiduallyConnected(C) : CosetGeom -> BoolElt
Diagram of an Incidence Geometry
Diagram(D) : IncGeom -> GrphUnd, GrphVertSet, GrphEdgeSet
Example IncidenceGeometry_diagram (H96E9)
Example IncidenceGeometry_diagram (H96E10)
Example IncidenceGeometry_diagram (H96E11)