Remove restriction on q in NonisotropicOrthogonalPolarGraph

[ferihr]

The restriction in the function NonisotropicOrthogonalPolarGraph in graphs/generators/classical_geometries.py to some specific small values in q is not necessary. The current code is as follows:

    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")
    elif not perp is None:
        if q == 5:
            G = _orthogonal_polar_graph(m, q, point_type=\
                [-1,1] if sign=='+' else [2,3] if sign=='-' else [])
            dec = ",perp"
        else:
            raise ValueError("for perp not None q must be 5")

One can easily make this work for general q. For q odd and m even, the point_type should be the set of nonzero squares in GF(q). For q odd and m odd, the two point types are either the set of all squares (so [-1,1] for q=5) and all non-squares (so [2, 3] for q=5). For q even, one can use the trace to do determine the point_type in a similar way.

Note that in the general case the graphs are no longer strongly regular.

CC: @dimpase @slel

Component: graph theory

Issue created by migration from https://trac.sagemath.org/ticket/29459

[slel]

comment:1

Note: discussion on sage-devel, 2020-04:

• https://groups.google.com/d/topic/sage-devel/qQBTC1qoUiA/discussion

[mkoeppe]

comment:3

Batch modifying tickets that will likely not be ready for 9.1, based on a review of the ticket title, branch/review status, and last modification date.

[mkoeppe]

comment:5

Setting new milestone based on a cursory review of ticket status, priority, and last modification date.