#14532: Symplectic graphs
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Reporter: ncohen | Owner: jason, ncohen, rlm
Type: enhancement | Status: closed
Priority: major | Milestone: sage-5.10
Component: graph theory | Resolution: fixed
Keywords: strongly regular graphs | Work issues:
Report Upstream: N/A | Reviewers: Frédéric Chapoton
Authors: Nathann Cohen | Merged in: sage-5.10.beta4
Dependencies: #14217 | Stopgaps:
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Comment (by dimpase):
Replying to [comment:18 ncohen]:
> Helloooooooo !
>
> > maybe Sage should have "polar space" graphs in general, not, only
symplectic ones?
>
> Well, yes it would be nice indeed, but I do not know how to build them.
I guess that it only takes 5~6 lines, like for the symplectic ones, but I
don't know which ones. Actually, I have no idea on earth what these graphs
are, except what I could read (and understand, which is even less) from
Brouwer's website.
>
> http://www.win.tue.nl/~aeb/graphs/srg/srgtab.html
>
> I believe I created what he calls a `VO^-` graph
(`graphs.BrouwerHaemersGraph`), and the same code worked for different
parameters but I was not able to make it work in characteristic two, and
so I did not write this more general patch.
no, these are different species. I mean classical polar spaces as
introduced by J.Tits (or even long before him). See e.g. Sect 6.5 of
http://www.maths.qmul.ac.uk/~pjc/pps/pps6.pdf
To construct these, you need to be able to create the corresponding forms,
which are well-studied by group theory, as they lead to finite classical
groups. GAP has code to create these forms; it's not completely trivial in
characteristic two. You can actually just call GAP!
E.g.
{{{
gap> Display(InvariantQuadraticForm(GO(1,6,2)).matrix);
. 1 . . . .
. . . . . .
. . . 1 . .
. . . . . .
. . . . . 1
. . . . . .
gap> Display(InvariantQuadraticForm(GO(-1,6,2)).matrix);
. 1 . . . .
. . . . . .
. . 1 1 . .
. . . 1 . .
. . . . . 1
. . . . . .
gap> Display(InvariantSesquilinearForm(GU(6,2)).matrix);
. . . . . 1
. . . . 1 .
. . . 1 . .
. . 1 . . .
. 1 . . . .
1 . . . . .
}}}
etc...
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/14532#comment:19>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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