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.