Le vendredi 6 mai 2016 15:07:48 UTC+2, john_perry_usm a écrit :
>
>
> One of us misunderstands the other. Here's what I'm saying:
>
> - Singular's std() is neither an F4- nor F5-style algorithm; it is a
> traditional, Buchberger algorithm that uses a modified Gebauer-Möller pair
> selection strategy.
> - Singular's dstd() is an F5-style algorithm, without F4-style
> reduction.
>
> Roman's webpage seems to be comparing Singular's Buchberger algorithm to
> several F4- or F5-style algorithms. So it's inaccurate to the point that
> one can't use it as a comparison between mgb and Singular, unless one is
> explicit that the comparison is of different algorithms based on completely
> different ideas.
>
> (To be fair to Roman, I'm not sure Singular-4.0.2 had implemented dstd()
> yet, but that is certainly a consideration now.)
>
The released version of singular seems to be 4.0.2, and I can not find dstd
in the online manual of singular, my own copy of singular does not
recognize dstd. for example cyclic7 modular with std works, but not with
dstd
// timer=1;
system("--ticks-per-sec",100);
//option(prot);
// 1.5s
ring r=16777213,(x1,x2,x3,x4,x5,x6,x7),dp;
ideal
k=x1+x2+x3+x4+x5+x6+x7,x1*x2+x1*x7+x2*x3+x3*x4+x4*x5+x5*x6+x6*x7,x1*x2*x3+x1*x2*x7+x1*x6*x7+x2*x3*x4+x3*x4*x5+x4*x5*x6+x5*x6*x7,x1*x2*x3*x4+x1*x2*x3*x7+x1*x2*x6*x7+x1*x5*x6*x7+x2*x3*x4*x5+x3*x4*x5*x6+x4*x5*x6*x7,x1*x2*x3*x4*x5+x1*x2*x3*x4*x7+x1*x2*x3*x6*x7+x1*x2*x5*x6*x7+x1*x4*x5*x6*x7+x2*x3*x4*x5*x6+x3*x4*x5*x6*x7,x1*x2*x3*x4*x5*x6+x1*x2*x3*x4*x5*x7+x1*x2*x3*x4*x6*x7+x1*x2*x3*x5*x6*x7+x1*x2*x4*x5*x6*x7+x1*x3*x4*x5*x6*x7+x2*x3*x4*x5*x6*x7,x1*x2*x3*x4*x5*x6*x7-1;
//size(groebner(k));
int RT = rtimer; int T=timer; ideal G = std(k); rtimer-RT; timer-T;
Where can I get a version of singular with dstd? Can you give us the
timings for dstd compared to std for the example of Roman?
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