Dear Sage Developers,
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].
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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