On Tuesday, 11 July 2017 12:20:15 UTC+2, Simon King wrote: > > Hi, > > On 2017-07-10, mmarco <mma...@unizar.es <javascript:>> wrote: > > It is surprising the difference between singular and Sage, considering > that > > Sage mostly relies on Singular for multivariate polynomial arithmetic. > > Note that Singular is optimised for Gröbner basis computations, but > certainly > not optimised for fast arithmetics. So, it is absolutely no surprise that > polynomial arithmetics can be improved by using a different backend. > However, > keep in mind that the other backend probably will be much slower than > Singular > in doing Gröbner basis computations. > > Best regards, > Simon > > That's absolutely correct, and a point I make in my blog. One heuristic is that GBs tend to have a large number of very small polynomials and so one can dispatch larger arithmetic operations to a different back end safely (converting to and from some other format on the fly). This is something Singular already does, I believe.
Of course there are also libraries that do GBs and still have basic arithmetic that is comparable to the timings I've given. This is definitely something we care about and will be working on in future. The main goal of the ODK work we are doing, as we see it, is to speed up Singular (by speeding up Factory). We are also independently looking at parallelising GBs (in a totally different way, of course). So once this project is done, we may get the best of both worlds! It's a very interesting project that a number of people are having input into. -- 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.
