# Set-Theoretic Operations

## Membership and Equality

### `g in G: GrpBBElt, GrpBB -> BoolElt`

Return `true` if and only if $G$ is the parent group of $g$ or the parent group of $g$ is a subgroup of $G$.

## Set Operations

### `PseudoRandom(G): GrpBB -> GrpBBElt`

Return a pseudo-random element of the BB-group $G$. The method used is product-replacement with accumulator.

### `Rep(G): GrpBB -> GrpBBElt`

A representative element of $G$.

## Coercions Between Related Groups

### `G ! g: GrpBB, GrpBBElt -> GrpBBElt`

Given an element $g$ belonging to a subgroup of the BB-group $G$, rewrite $g$ as an element of $G$.