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

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.