On Wednesday, May 4, 2016 at 11:58:13 PM UTC-5, parisse wrote: > Le mercredi 4 mai 2016 23:00:23 UTC+2, john_perry_usm a écrit : >> >> Unfortunately Roman doesn't mention on that page whether he used >> Singular's std() or dstd(). The numbers look vaguely std()ish to me (i.e., >> when I compute the GB of Cyclic-8 using std(), it takes about 40 seconds; >> homogenized takes a few seconds longer, but my machine is slower than the >> 3.2GHz he advertised). If I'm right, the comparison is inaccurate. >> > The precise timings are inaccurate : giac timings have improved, mgb have > probably also, for singular I don't know. But this does not change the > global picture: singular is slow for "dense" computations compared to the 3 > others while being fast for very sparse problems, probably because the f4 > algorithm is not the best choice if there are few pairs to be reduced > simultaneously. >
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.) -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at https://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout.
