On 22 Aug., 23:53, "Dr. David Kirkby" <david.kir...@onetel.net> wrote:
[...]
> > sage: R.<x,y,z> = PolynomialRing(GF(13))
> > sage: time _ = expand((x+y+z+1)**100)
> > CPU times: user 0.07 s, sys: 0.00 s, total: 0.08 s
> > Wall time: 0.08 s
>
> > In[1]:= Timing[Expand[(x+y+z+1)^100, Modulus -> 13]][[1]]
> > Out[1]= 4.20826

So, over QQ, MMA is slightly faster, but over finite fields Sage
clearly wins? That is already something worth pointing out.

> IMHO, it would be good to have one exactly as Karl has. By all means
> have others.

I know almost nothing about MMA, but from the discussion here I get
the impression that you believe that MMA is playing on its strengths
(= prefering benchmarks that MMA make look good) and tries to tune it
so that well-known commonly used benchmarks work well.

So, why shouldn't Sage do benchmarks in a similar spirit? Having only
the *same* benchmarks as MMA is weakness, IMHO. So, we should
definitely think of adding genuine "SAGE" benchmarks to the test
bench. Several good examples have been mentioned already.

Sorry for the self-promotion, but I doubt that any other software is
currently able to compute the complete ring structure + Poincaré
series + a-invariants of H^*(G;GF(2)) for all groups G of order 64 in
less than a day. Sage can do in less than an hour.

Best regards,
Simon

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