Dear All,
i hope it is ok if i reply to all of you in one mail.
In reply to Michael:
> Sage has so far only optimized the large case, but 2.8.6 (out in a day or
> so) should contain a patch that improves the small case also. There is
> active work going to improve the small case even further.
Good! I'm looking forward!
In reply to David:
> This is separate from your question, but in SAGE some wrappers
> for Graham Ellis' HAP package have been written.
That's interesting!
Our aim is to get a minimal set of generators for the cohomology RING
and a minimal set of algebraic relations between the generators.
Computation of cohomology GROUPS is of course part of the problem.
However, the isomorphism type of the cohomology groups wouldn't
suffice. Is there something in Sage that provides a minimal free
resolution? Or something that computes cup products of cocycles?
In reply to Martin:
> Do you need such small matrices for your project? If not it would be
> interesting to test bigger dimensions.
My question was not directly related with the project -- only in the
sense that at some point we need linear algebra over finite fields,
and of course we would like to use good algorithms. But first it makes
more sense to improve other parts of the computation. E.g., we need to
compute Gröbner bases in graded commutative rings. In one of our
examples, Singular/Plural improves the computation time from one month
to 50 minutes.
So, waiting for Sage 2.8.6 is no problem at all.
Yours sincerely
Simon
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