Hi, I would like to implement it (or see it implemented) in the most generic case. I.e. assume R is a domain with a gcd algorithm and an algorithm for computing a/b if b divides a. Then we get gcd and division for R[x].
By iterating you get it for multivariate polynomials. Knuths seems to be fairly enthousiastic about this algorithm. I think that for p-adics there might be more efficient specialized algorithms though. Michel On May 17, 11:22 pm, "David Roe" <[EMAIL PROTECTED]> wrote: > I may be implementing something like this for p-adics soon. It's one of the > options for doing gcds meaningfully. If anyone else is interested in > working on this, get in touch with me. > David > > On 5/17/07, Michel <[EMAIL PROTECTED]> wrote: > > > > > It is rather frustrating that sage does not a have a gcd algorithm > > for > > multivariate polynomials over generic fields. > > > There is such an algorithm. It is called the "subresultant" algorithm. > > It is for example described > > in Knuth's book "Semi-numerical algorithms" in section 4.6.1. > > > Does anybody have experience with this algorithm? Does it perform > > acceptably? I think Magma > > uses it as a fallback if more specialized algorithms fail. > > > Michel --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to [email protected] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://sage.scipy.org/sage/ and http://modular.math.washington.edu/sage/ -~----------~----~----~----~------~----~------~--~---
