# Identity and Isomorphism

Two planes are considered equal if their point sets are equal and they have the same lines.

## `P eq Q: Plane, Plane -> BoolElt`

Return `true` if the planes $P$ and $Q$ are equal, otherwise `false`.

## `P ne Q: Plane, Plane -> BoolElt`

Return `true` if the planes $P$ and $Q$ are not equal, otherwise `false`.

## `IsIsomorphic(P, Q: parameters): Plane, Plane -> BoolElt, Map`

```magma
AutomorphismGroups: MonStgElt                    Default: "None"
```

Return `true` if the planes $P$ and $Q$ are isomorphic, otherwise `false`. If the planes are isomorphic, an isomorphism $f$ from $P$ onto $Q$ is also returned. The function first computes none, one, or both of the automorphism groups of the left and right planes. This may assist the isomorphism testing. The parameter `AutomorphismGroups`, with valid string values `"Both"`, `"Left"`, `"Right"`, `"None"`, may be used to specify which of the automorphism groups should be constructed first if not already known. The default is `"None"`.

## `P subset Q: Plane, Plane -> BoolElt`

Returns `true` if $P$ is a subplane of $Q$, otherwise `false`.