Elementary Invariants

Points(D) : IncGeom -> SetIndx

Elements(D) : IncGeom -> SetIndx

Given an incidence geometry D, return the set of elements of D. These elements are the points of the incidence graph of D.

Types(D) : IncGeom -> SetIndx

Given an incidence geometry D, return the set of types of D.

Types(C) : CosetGeom -> SetIndx

Given a coset geometry C, return the set of types of C.

Rank(D) : IncGeom -> RngIntElt

Given an incidence geometry D, return the rank of D, i.e. the cardinality of the set of types.

Rank(C) : CosetGeom -> RngIntElt

Given a coset geometry C, return the rank of C.

IncidenceGraph(D) : IncGeom -> GrphUnd, GrphVertSet, GrphEdgeSet

Given an incidence geometry D, return the incidence graph of D, its vertex set and its edge set.

We remark that this function is not implemented for coset geometries but we may convert a coset geometry into an incidence geometry using IncidenceGeometry and then compute its incidence graph.

MaxParabolics(C) : CosetGeom -> SetIndx

MaximalParabolics(C) : CosetGeom -> SetIndx

Given a coset geometry C, return an indexed set containing the maximal parabolics of D.

Borel(C) : CosetGeom -> GrpPerm

BorelSubgroup(C) : CosetGeom -> GrpPerm

Given a coset geometry C, return the Borel subgroup of C, i.e. the intersection of all maximal parabolic subgroups of C.