Basic Properties

Accessing Representation Information

Rank(V): ModRed -> RngIntElt

Dimension(V): ModRed -> RngIntElt

Ngens(V): ModRed -> RngIntElt

The rank of the free module underlying the representation \(V\).

Basis(V): ModRed -> [ ModRedElt ]

A basis for the free module underlying the representation \(V\).

BaseRing(V): ModRed -> Rng

The coefficient ring, the ring over which \(V\) is defined.

Group(V): ModRed -> Grp

The group \(G\) that acts on \(V\).

CFM(V): ModRed -> CombFreeMod

The combinatorial free module underlying \(V\).

Accessing Combinatorial Free Module Information

Rank(M): CombFreeMod -> RngIntElt

Dimension(M): CombFreeMod -> RngIntElt

Ngens(M): CombFreeMod -> RngIntElt

The rank of \(M\).

Basis(M): CombFreeMod -> [ CombFreeModElt ]

A basis for \(M\).

BaseRing(M): CombFreeMod -> Rng

The ring \(R\) over which \(M\) is a module.

Names(M): CombFreeMod -> SetIndx

Names(M): CombFreeMod -> [ MonStgElt ]

The names of the basis elements.

Predicates

IsTrivial(V): ModRed -> BoolElt

Returns true iff \(V\) is the trivial representation.