Hi Ferdinand,

On Sat, Apr 4, 2020 at 12:44 AM Ferdinand Ihringer
<ferdinand.ihrin...@gmail.com> wrote:
>
> My understanding is that I should ask for improvements here. Can one remove 
> the restriction on q in NonisotropicOrthogonalPolarGraph in 
> graphs/generators/classical_geometries.py? These graphs are nice for general 
> q, see [1] or [2].

IIRC this restriction is due to these graphs not being strongly
regular for the other values of q.
Certainly we can make that function more general, and test for the
strongly regular needs elsewhere.
(although functions with names starting from _ are not meant for general use...)

If you can open a trac ticket for this, please do and CC me on this
(incidentally I am working on https://trac.sagemath.org/ticket/26513
right now - and appear to have a fix :-))



>
> My current hack is to change
>
>     if m % 2 == 0:
>         if q in [2, 3]:
>             G = _orthogonal_polar_graph(m, q, sign=sign, point_type=[1])
>         else:
>             raise ValueError("for m even q must be 2 or 3")
>
> to
>
>     if m % 2 == 0:
>         if q in [2, 3]:
>             G = _orthogonal_polar_graph(m, q, sign=sign, point_type=[1])
>         elif q == 5:
>             G = _orthogonal_polar_graph(m, q, sign=sign, point_type=[1,4])
>         elif q == 7:
>             G = _orthogonal_polar_graph(m, q, sign=sign, point_type=[1,2,4])
>         else:
>             raise ValueError("for m even q must be 2 or 3")
>
> but maybe one can do this more properly in Sage itself? For q odd and m even, 
> point_type should simply be the set of all squares in GF(q). For q odd and m 
> odd (I did not copy this part in the code snippet above), it is either the 
> set of all squares or the set of all non-squares.
>
> For q even, one replaces square/non-square with the trace to distinguish.
>
> I never use Sage's GAP interface (usually, I use GAP directly), but I suspect 
> that anymore slightly more familiar can do this in a minute.
>
> All the best,
>
> Ferdinand
>
>
> [1] https://www.sciencedirect.com/science/article/pii/009731659090029V
> [2] https://arxiv.org/abs/1905.04677 or 
> https://link.springer.com/article/10.1007/s00493-020-4226-6
>
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