# Operations on Group Representations

## `Intersection(V, W): ModRed, ModRed -> ModRed`

## `V meet W: ModRed, ModRed -> ModRed`

If $V, W \subseteq U$ are both subrepresentations of $U$, return the intersection $V \cap W \subseteq U$.

## `V eq W: ModRed, ModRed -> BoolElt`

## `V eq W: CombFreeMod, CombFreeMod -> BoolElt`

Returns `true` if the representations $V$ and $W$ are equal; otherwise `false`

## Base Change

### `ChangeRing(V, S): ModRed, Rng -> ModRed`

The group representation $V_S = V \otimes_R S$ with base ring changed to $S$.

### `ChangeRing(M, S): CombFreeMod, Rng -> CombFreeMod`

The module $M_S = M \otimes_R S$ with base ring changed to $S$.

## Other Operations

### `FixedSubspace(H, V): GrpMat, ModRed -> ModRed`

Given a subgroup $H \subseteq G$, returns the subspace $V^H$, the vectors of $V$ fixed by $H$.