# 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.