> Do you consider 139 minutes to be reasonable time for a toy
> implementation?
>

Absolutely, we are in the double exponential case, where differences
are quite big and
benchmarking is doomed.

> 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.

Your toy implementation was good.
But (don't misunderstand me), comparing toy implementations, which can
be improved by a few very simple
tricks by a factor of 1000 (I also played with toy implementations) is
quite ridiculous.
I have seen the code in teachstd.lib.

I never suggested the provided example as real benchmark (while a fast
time would of course have been a positive suprise), but just as a more
interesting example about studying the incremental behaviour, as you
did.
I think, I was misunderstood: I never wanted to benchmark these toy
implementations.
My general position with respect to benchmarks should be known.

>
> > 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.

This is in fact a question, I am more interested in.
Michael

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