This looks like a Sage bug.
Indeed, in src/sage/groups/matrix_gps/orthogonal.py one sees
if invariant_form is not None:
if is_FiniteField(ring):
raise NotImplementedError("invariant_form for finite
groups is fixed by GAP")
And it should be triggerred for your input, but it does not happen.
I've opened https://trac.sagemath.org/ticket/28054 to deal with it.
On Tue, Jun 25, 2019 at 12:55 PM Ayan Mahalanobis
<ayan.mahalano...@gmail.com> wrote:
>
> Hello,
>
> I was trying to compute with the general orthogonal group. If I am not wrong,
> I think that one can specify the bilinear form for the general orthogonal
> group.
>
> I did the following:
> sage: b
> [0 0 0 1 0 0]
> [0 0 0 0 1 0]
> [0 0 0 0 0 1]
> [1 0 0 0 0 0]
> [0 1 0 0 0 0]
> [0 0 1 0 0 0]
>
> This defines the bilinear form.
>
> Then the following:
>
> sage: G=GO(6,11,1,b)
> sage: G.invariant_bilinear_form()
> [0 1 0 0 0 0]
> [1 0 0 0 0 0]
> [0 0 2 0 0 0]
> [0 0 0 2 0 0]
> [0 0 0 0 2 0]
> [0 0 0 0 0 2]
>
>
> I thought that I would gent back my bilinear form. However, sage puts its own
> bilinear form.
>
> Is there something I am missing?
>
>
> Thanks and Regards,
> Ayan
>
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