Michael,
> Did you check for the result being [1]?
Sort of. I did this:
sage: len(G)
<<< 1
Since the output G has length one, it's reasonable to conclude that it
ended with {1}; otherwise there should have been at least 6
polynomials. I didn't think to look at G until afterwards, partly
because I wanted to terminate Sage & look at the CPU time. Sorry...
> I was referring to "termination in reasonable time".
Do you consider 139 minutes to be reasonable time for a toy
implementation?
Similarly, do you have a "toy" implementation of slimgb we could run
for comparison? By this I mean an interpreted version that doesn't use
any of Singular's internal optimizations. I would love to run it on
the same system and get an idea of how much of the time is due to the
constant factor you mentioned from Singular's & Sage's interpreted
languages.
You might recall that, back in March, Chris & I built a "toy" Gebauer-
Moeller for Singular. It was so much slower than the toy F5 that I
believed that we had made a mistake in our implementation. Gert-Martin
(I think) told us of the "toy" G-M included with Singular, so I tried
that but it was just as bad, maybe worse.
> Would it be possible to modify the algorithm, in such a way, that it
> doesn't work incrementally (maybe
> affecting the theoretical "no reduction to zero"-property)?
I don't know myself, but it's worth consideration.
> As you might have seen in your protocol, the most computation should
> have been done in the penultimate step.
In my case it was the ultimate step, but only because the
implementation re-orders the polynomials from smallest to largest
degree, so the last two polynomials in the system you supplied were
swapped. The penultimate step generated polynomials of degree 22; the
ultimate step generated polynomials of degree 30. A lot of reductions
to zero occurred in the penultimate step; none in the ultimate step.
john
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