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Fix InvariantQuadraticForm
for Omega(-1, 2*d, 2^n)
#4327
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Thanks.
Is there anything one can say why the matrix of the quadratic form in OmegaMinus
can look like this? (The structure of the generators yields that one has to work only for d = 4.)
In CheckQuadraticForm
, checking the relation between the matrices of the bilinear and the quadratic form still makes sense, it is just not sufficient in even characteristic.
I believe the generators are taken from `Rylands, Taylor: Matrix generators for the Orthogonal Group, JSC 25 (1998), 351--360, and p. 359 (about the middle) gives the form for Omega- |
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@ThomasBreuer I restored the check for the relation between the matrices of the bilinear and the quadratic form -- I did not mean to disable it in the first place, thanks for spotting this! |
@hulpke Thanks for the hint. Yes, the Rylands/Taylor paper is mentioned in the GAP manual, and it describes the form. |
Also add proper tests to check that the quadratic forms are indeed correct (the existing tests were too weak).
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@ThomasBreuer ah that's of course much nicer. Pushed it. |
InvariantQuadraticForm
for Omega(-1, 2*d, 2^n)
Also add proper tests to check that the quadratic forms are indeed correct
(the existing tests were too weak).
Fixes #4323
Some background: We didn't even store the
InvariantQuadraticForm
for these groups up to GAP 4.9; it was only added in 4.10, via my PR #2577. In there, I also added tests to verify the quadratic form, but those tests were insufficient (rather obviously so, in retrospect sigh). This adds a test similar to what Thomas used to highlight the issue in his bug report.