# Operations on Elements

## Equality and Comparison

### `u eq v: GrpSLPElt, GrpSLPElt -> BoolElt`

Returns `true` if and only if the straight-line programs $u$ and $v$ are identical. Identical here means they are identical as expression trees, not that they will always evaluate to the same word in the generators.

### `u ne v: GrpSLPElt, GrpSLPElt -> BoolElt`

Returns `true` if and only if the straight-line programs $u$ and $v$ are not identical. Identical here means they are identical as expression trees, not that they will always evaluate to the same word in the generators.