I'm sorry. I got the name mixed up; the function you want to look at is
sba(), not dstd() (which is something experimental of mine that never saw
the light of day).
http://www.singular.uni-kl.de/Manual/latest/sing_391.htm#SEC430
Because my copy of Singular is a little... "tinkered with" I'd have to
redownload and recompile Singular, but replace std() with sba() in your
example and see how the timings compare, but for example when I run your
example the timing my version reports falls from 169 to 114. -- Again, I
tinkered with mine, so the timings won't be reflective of actual
performance.
john perry
On Friday, May 6, 2016 at 1:06:05 PM UTC-5, parisse wrote:
>
>
>
> 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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