On 14 May 2017 at 13:02, Waldek Hebisch <[email protected]> wrote:
>
> There were several bugs, I have now commited fixes for all that
> I have found.  I still could not finish the calculation, it
> takes a lot of time.  But it run for several hours without
> finding new errors.
>

Thank you very much Waldek. I greatly appreciate the effort you have
made to correct these problems.

I can now compute a Groebner basis for this problem where as before it
would produce either one or the other of the library error messages
that I previously reported. Unfortunately it took FriCAS "Time:
10263.20 (EV) + 1.13 (OT) = 10264.33 sec" (2.85 hours) to find this
basis while the groebnerFactorize command still did not complete after
more than 24 hours.  In contrast I can compute a Groebner basis for
this problem with Sage (which I believe uses the Singular library) in
about 10 seconds, albeit a different basis containing 28 polynomials
instead of the 34 polynomials returned by FriCAS. I do not yet have a
procedure in Sage that produces a Groebner factorization as such in
the same sense as returned by FriCAS but I suspect that this is
possible in considerably less time than what FriCAS would require.

I think the factor of 1000 in the difference in the time required to
compute the Groebner basis suggests that Singular is probably using a
different algorithm to produce this result - maybe something like
choosing a more favorable term order and then walking the solution,
but my first attempts to do this have not been able to improve on the
timing. It is hard to imagine that the FriCAS could be that much
slower simply due to manipulation of data.

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