#6750: [with spkg, needs review] New version of optional Group Cohomology spkg
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Reporter: SimonKing | Owner: Simon King
Type: enhancement | Status: new
Priority: major | Milestone:
Component: optional packages | Keywords: cohomology ring p-group
Reviewer: | Author: Simon King
Merged: |
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Comment(by SimonKing):
Dear David,
thank you that you found the time (despite of teaching) to look into it!
Replying to [comment:4 wdj]:
> This applies fine to an intel macbook running 10.4.11 and sage
4.1.1.rc2. Positive test form me as an optional package.
>
> I cannot vouch for the mathematics though (however, I believe some
functions on the older version were checked against some other programs
for an independent.
Yes. Of course, it is hardly possible to test different ring presentations
for being isomorphic. So, what I did was to see if I get the same number
of generators resp. of relations (sorted by degree), and the same Poincaré
series. This was mainly done for 2-groups: All groups of order 64, checked
against the independent results of David Green and of Jon F. Carlson, and
the Sylow 2-subgroup of the Higman-Sims group (order 512), whose
cohomology ring was previously computed by Jon F. Carlson et al. There are
only few cohomology computations for p-groups with p>2 available, but the
results are consistent as well.
> Does this need further testing or can this be changed to "positive
review".
The main part of the programs, namely the computation of the ring
structure, wasn't touched, and was carefully tested in the past. William
did extensive installation tests on a multitude of platforms with the
first package version, and I don't think that the new code can be critical
for certain machines.
So, the only part that ''really'' needs review is the computation of
Massey products.
I tried to be careful in my implementation, of course, and to the best of
my knowledge the results agree with what I found in the literature. But I
find independent tests and peer reviewing quite important. So, I would not
feel comfortable with a positive review before some experts assert that
some non-trivial computational results involving Massey products are at
least plausible.
One might try systematic cross verifications with the CRIME package, which
computes Massey products as well. It would be quite difficult though to do
it in detail, because one would have to deal with different ring
presentations, and there might also be some different sign conventions
around.
At least, CRIME agrees that the cohomology rings of C_3 and C_9 can be
distinguished using Massey products.
I should certainly ask Marcus Bishop, the author of CRIME, but I haven't
seen him recently.
Best regards,
Simon
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/6750#comment:5>
Sage <http://sagemath.org/>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
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