Thank you.
On 18 July 2013 16:09, William Stein <wst...@gmail.com> wrote: > On Thu, Jul 18, 2013 at 12:53 PM, Santanu Sarkar > <sarkar.santanu....@gmail.com> wrote: > > Over integer. > > I did > > R.<x> = QQ[x] > f = x*(x^3+1)*(x-17) > > then looked at f.roots?? which says it uses f.factor. So I looked at > f.factor?? and it uses Pari. (It probably helped that I wrote a lot > of this code.) > > So the answer appears to be the Sage completely factors the polynomial > using Pari, then pulls off the degree 1 factors to give the roots. > > I make no claim that this is in any way the best approach -- it really > can't be in general. For example, if you can factor the constant term > of the polynomial, then simply checking through divisors might be > dramatically faster (depending on how many divisors there are). > > William > > > > > > > On 18 July 2013 15:50, William Stein <wst...@gmail.com> wrote: > >> > >> On Thu, Jul 18, 2013 at 11:54 AM, Santanu Sarkar > >> <sarkar.santanu....@gmail.com> wrote: > >> > What algorithm is used in Sage to calculate the roots of a polynomial > >> > f(x)? > >> > Corresponding Sage function is f.roots() > >> > >> What is the base ring? There are a dozen answers, depending on the > >> ring in which the coefficients of f live... > >> > >> > > >> > -- > >> > You received this message because you are subscribed to the Google > >> > Groups > >> > "sage-support" group. > >> > To unsubscribe from this group and stop receiving emails from it, send > >> > an > >> > email to sage-support+unsubscr...@googlegroups.com. > >> > To post to this group, send email to sage-support@googlegroups.com. > >> > Visit this group at http://groups.google.com/group/sage-support. > >> > For more options, visit https://groups.google.com/groups/opt_out. > >> > > >> > > >> > >> > >> > >> -- > >> William Stein > >> Professor of Mathematics > >> University of Washington > >> http://wstein.org > >> > >> -- > >> You received this message because you are subscribed to the Google > Groups > >> "sage-support" group. > >> To unsubscribe from this group and stop receiving emails from it, send > an > >> email to sage-support+unsubscr...@googlegroups.com. > >> To post to this group, send email to sage-support@googlegroups.com. > >> Visit this group at http://groups.google.com/group/sage-support. > >> For more options, visit https://groups.google.com/groups/opt_out. > >> > >> > > > > -- > > You received this message because you are subscribed to the Google Groups > > "sage-support" group. > > To unsubscribe from this group and stop receiving emails from it, send an > > email to sage-support+unsubscr...@googlegroups.com. > > To post to this group, send email to sage-support@googlegroups.com. > > Visit this group at http://groups.google.com/group/sage-support. > > For more options, visit https://groups.google.com/groups/opt_out. > > > > > > > > -- > William Stein > Professor of Mathematics > University of Washington > http://wstein.org > > -- > You received this message because you are subscribed to the Google Groups > "sage-support" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to sage-support+unsubscr...@googlegroups.com. > To post to this group, send email to sage-support@googlegroups.com. > Visit this group at http://groups.google.com/group/sage-support. > For more options, visit https://groups.google.com/groups/opt_out. > > > -- You received this message because you are subscribed to the Google Groups "sage-support" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-support+unsubscr...@googlegroups.com. To post to this group, send email to sage-support@googlegroups.com. Visit this group at http://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/groups/opt_out.
