# Identity and Isomorphism

Incidence structures $D_1 = (P_1, B_1, I_1)$ and $D_2 = (P_2, B_2, I_2)$ are *identical* if $P_1 = P_2$, $B_1 = B_2$ and $I_1 = I_2$.

## `D eq E: Inc, Inc -> BoolElt`

Return `true` if the incidence structures $D$ and $E$ are identical, otherwise `false`.

## `D ne E: Inc, Inc -> BoolElt`

Return `true` if the incidence structures $D$ and $E$ are not identical, otherwise `false`.

## `IsIsomorphic(D, E: parameters): Inc, Inc -> BoolElt, Map`

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

Return `true` if the incidence structures $D$ and $E$ are isomorphic, otherwise `false`. If they are isomorphic, then an isomorphism is returned as the second value. The function first computes none, one, or both of the automorphism groups of the left and right incidence structures. In difficult examples, this may significantly speed up testing for isomorphism. The parameter `AutomorphismGroups`, with valid string values `"Both"`, `"Left"`, `"Right"`, `"None"`, may be used to specify which of the automorphism groups should be constructed if not already known. The default is `"None"`.