Yes, in fact, this method is definitely able to handle these cases. There is a subtlety in the implementation which I had not paid attention to.
So yes, it precisely retrieves the answer to this problem. Next challenge? Bill. On May 2, 2:45 pm, Bill Hart <goodwillh...@googlemail.com> wrote: > Hmm, very interestingly, the new method *can* be made to output the > correct answer for this problem. > > I'll have to think about whether doing this will screw anything else > up. I think, in the class of problems it is designed to solve, the > answer is no, it won't screw others up. > > Bill. > > On May 2, 2:15 pm, Bill Hart <goodwillh...@googlemail.com> wrote: > > > > > > > It doesn't quite handle this case. But as I'm sure you are aware, > > neither does the classical algorithm: > > > sage: def rel_prec(approx, actual): > > return [oo if a==b else -log(abs(a-b)/abs(b), 2) for (a,b) in > > zip(approx, actual)] > > > sage: R.<x> = QQ[] > > sage: f = R((x^100-10^100)/(x-10)) > > sage: g = x-10 > > sage: ff=f.change_ring(RR) > > sage: gg=g.change_ring(RR) > > > sage: sorted(rel_prec(ff*gg, f*g)) > > [-infinity, -infinity, -infinity, -infinity, -infinity, -infinity, - > > infinity, -infinity, -infinity, -infinity, -infinity, -infinity, - > > infinity, -infinity, -infinity, -infinity, -infinity, -infinity, - > > infinity, -infinity, +Infinity, +Infinity, +Infinity, +Infinity, > > +Infinity, +Infinity, +Infinity, +Infinity, +Infinity, +Infinity, > > +Infinity, +Infinity, +Infinity, +Infinity, +Infinity, +Infinity, > > +Infinity, +Infinity, +Infinity, +Infinity, +Infinity, +Infinity, > > +Infinity, +Infinity, +Infinity, +Infinity, +Infinity, +Infinity, > > +Infinity, +Infinity, +Infinity, +Infinity, +Infinity, +Infinity, > > +Infinity, +Infinity, +Infinity, +Infinity, +Infinity, +Infinity, > > +Infinity, +Infinity, +Infinity, +Infinity, +Infinity, +Infinity, > > +Infinity, +Infinity, +Infinity, +Infinity, +Infinity, +Infinity, > > +Infinity, +Infinity, +Infinity, +Infinity, +Infinity, +Infinity, > > +Infinity, +Infinity, +Infinity, +Infinity, +Infinity, +Infinity, > > +Infinity, +Infinity, +Infinity, +Infinity, +Infinity, +Infinity, > > +Infinity, +Infinity, +Infinity, +Infinity, +Infinity, +Infinity, > > +Infinity, +Infinity, +Infinity, +Infinity, +Infinity] > > > Bill. > > > On May 2, 2:58 am, rjf <fate...@gmail.com> wrote: > > > > On May 1, 5:42 pm, Bill Hart <goodwillh...@googlemail.com> wrote: > > > > ... > > > > > So now anything that grows regularly can be multiplied with basically > > > > zero loss, asymptotically fast. That probably covers most of the > > > > interesting cases anyhow. > > > > The interesting cases are obvious those which are not covered. They > > > include the > > > cases where, as one multiples two polynomials, the coefficients in the > > > result are > > > zero. In which case any non-zero result is wrong in ALL places. > > > > I suggest testing > > > P*Q where P= (x^10-10^10)/(x-10) > > > and Q=x-10. > > > > replace 10 with a larger integer if you wish to make the test more > > > challenging. > > > Or compute (P^2*Q^2) etc. > > > > Will your suggestion get these polynomials exactly right? > > > > -- > > > To post to this group, send an email to sage-devel@googlegroups.com > > > To unsubscribe from this group, send an email to > > > sage-devel+unsubscr...@googlegroups.com > > > For more options, visit this group > > > athttp://groups.google.com/group/sage-devel > > > URL:http://www.sagemath.org > > > -- > > To post to this group, send an email to sage-devel@googlegroups.com > > To unsubscribe from this group, send an email to > > sage-devel+unsubscr...@googlegroups.com > > For more options, visit this group > > athttp://groups.google.com/group/sage-devel > > URL:http://www.sagemath.org > > -- > To post to this group, send an email to sage-devel@googlegroups.com > To unsubscribe from this group, send an email to > sage-devel+unsubscr...@googlegroups.com > For more options, visit this group athttp://groups.google.com/group/sage-devel > URL:http://www.sagemath.org -- To post to this group, send an email to sage-devel@googlegroups.com To unsubscribe from this group, send an email to sage-devel+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URL: http://www.sagemath.org
