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.
