Add ConformalOrthogonalPlus

[ssiccha]

The GO in GAP creates the group of invertible matrices which leave the corresponding quadratic form invariant. In the book "The subgroup structure of the finite classical groups" Kleidman and Liebeck GAP's GO is the I(V, F, kappa). We also want generators for Delta(V, F, kappa) which is the group GO (the isometries) together with all similarities. In Magma this is called e.g. the ConformalOrthogonalPlus.

If we have these groups, we could submit them to the gap-system/gap repository, that is move them upstream.

[ssiccha]

I guess there's more conformal groups we don't have the generators for. All of those would be nice to have. I guess that applies to all orthogonal, symplectic and unitary groups.

[fingolfin]

@ThomasBreuer has been working on adding conformal symplectic groups to GAP and also the forms package.

I hope he can later extend this to also cover the unitary and orthogonal case, too.

[ThomasBreuer]

Yes, as soon as the symplectic case is merged, it is clear how to provide the conformal groups for the other classical groups: Generalize the setup for the classical groups themselves in the GAP library and in the Forms package, add the constructors, the documentation, and the methods not depending on forms to the GAP library, add the methods depending on forms to the Forms package.