On 22 May 2017 at 13:01, Waldek Hebisch <[email protected]> wrote: > Bill Page wrote: >> >> Just to confirm in FriCAS the 'totalGroebner' routine which apparently >> uses degree reverse lexical ordering takes much less time: >> >> Time: 1718.35 (EV) + 0.53 (OT) = 1718.88 sec >> >> and finds a basis with 28 polynomials (although that is still a >> lot longer than Singular needs for this computation). > > There is a simple trick to make this about 10-20 time faster: > clear denominator and use coefficients in the ring. I profiled > the groebner basis computation and 95% of time goes into > gcd-s needed for fraction arithmetic. I also did computation > over a ring and then fraction of time spent computing gcd-s > went down to 5%. >
Thank you for this idea. By multiplying through by the parameter domain denominators and changing to a polynomial domain over the ring instead of the quotient field I can compute the 'totalGroebner' for this case in just 89 seconds - much better - still not the speed of Singular but quite useable. As you say it seems that FriCAS does spend a lot of time computing canonical representation for fractions when there is no immediate need to do so. >> But as you say, even with this result I am a bit stuck since there I >> could not find any convenient way to change the ordering of a given >> basis. >> >> In computing 'groebnerFactorize' is there some way to keep the basis >> in degree reverse lexical order? Maybe it I use some other polynomial >> type rather than 'Polynomial'? > > IIUC 'groebnerFactorize' uses order from the polynomial type: > > ++ The term ordering is determined by the polynomial type used. > > OTOH I am not sure how term order affects the result you will get... > I am only looking for some 'groebnerFactorize' result for any convenient term ordering. Still, by the documentation I am left wondering just which polynomial domain I should use to get degree reverse lexical order? -- You received this message because you are subscribed to the Google Groups "FriCAS - computer algebra system" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at https://groups.google.com/group/fricas-devel. For more options, visit https://groups.google.com/d/optout.
