Ok, I think I understand how to check a root candidate. How do I obtain the set of possible integer roots to check, if not by the expanded resultant?
On Monday, January 23, 2017 at 5:22:05 PM UTC+1, Dima Pasechnik wrote: > > > > On Monday, January 23, 2017 at 4:15:39 PM UTC, Ralf Stephan wrote: >> >> You are quite right. I extract the roots from the (integer) constant >> coefficient by substitution of its divisors. I will have to think about >> your determinant method. At the moment it makes no sense. >> > > the resultant can be represented as a determinant, with coefficients being > polynomials > with all your variables, except the one you eliminate. I guess most > algorithms > will go about computing the resultant by expanding this determinant. > The latter is the most expensive part, and if it can be avoided, then it > should be avoided. > There is no need to expand the determinant if you just need to see if it's > identically 0 > at some point. > > >> >> On Monday, January 23, 2017 at 4:58:01 PM UTC+1, Dima Pasechnik wrote: >>> >>> >>> >>> On Monday, January 23, 2017 at 2:40:13 PM UTC, Ralf Stephan wrote: >>>> >>>> Hello, >>>> is there a faster way to compute resultants than >>>> what Singular provides? Is there software outside Sage >>>> that can do this faster? >>>> >>>> Resultants of big polynomials are needed by the Gosper >>>> algorithm of which the implementation in Pynac now needs >>>> some speedup. >>>> >>> >>> Are they really needed to be expanded? >>> I ask as IIRC Gosper checks whether a resultant has a particular >>> root - and this is about checking whether a determinant with polynomial >>> coefficients is non-0. >>> >>> Over a field of characteristic 0 this can be done by a randomised >>> algorithm very quickly (evaluate the determinant at few random enough >>> integer points). >>> >>> Does this make sense for you? >>> Dima >>> >>> >>> >>> >>>> >>>> A Sage example of two polynomials in 4 res. 5 variables >>>> is attached and does not finish within ten minutes here. >>>> >>>> Regards, >>>> >>> -- 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.
