On 16 May 2017 at 16:13, Waldek Hebisch <[email protected]> wrote: > ... > One trick is to substitute integers for some parameters. > After > > oV := OrderedVariableList([mp,mq,mr,yqp,yrp,yrq]) > evl := enumerate()$oV > ideq2a := [map(c +-> eval(c, evl, [3, 5, 7, 9, 11, 13]), p) for p in ideq2]; > > I was able to compute groebner basis of the evaluated ideal > in about 5 seconds.
Wow, that is remarkable. I would not have expected this magnitude of speed up. > For almost all possible values the evaluated ideal > has Groebner basis with the same structure as the > orignal one. OK, interesting but not so immediately useful. > It is possible to reconstruct (and verify) Groebner basis > for the full ideal from Groebner basis for evaluated ideal, > but ATM FriCAS contains no such code. > Surely such reconstruction is likely to require a lot of computation, no? Do you have a reference to any publications on this subject? Is there already an implementation in some other system? > groebnerFactorize for evaluated ideal takes 224.17 sec. > I was also able to do groebnerFactorize after evaluating > IIRC only 3 variables. I am not sure if it possible to > reconstruct full result of groebnerFactorize from evaluated > result, but at least you should be able to get some > quantitative data like number of subsystems (1086) and > degrees. > There seems to be quite a lot of literature on algorithms for triangular decomposition. Reconstruction sounds interesting but I am skeptical if it can be made efficient. > BTW: After evaluating variables one could retract coefficients > to rational numbers and then reduce modulo a prime. For > Groebner basis this should give additianal speedup. For > groebnerFactorize reducing modulo prime is dangerous, > because then a lot of univariate polynomials will be reducible, > so it may change structure of basis quite a lot. > Thank you for these ideas. Bill. -- 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.
