Pari will find complex roots and to whatever precision you request it. I don't know what it guarantees though with regards to error bounds. Probably only that the last binary digit is rounded correctly.
Actually, someone sent me some very good code for doing complex root approximation in FLINT. But I've been too damned lazy to properly incorporate it in FLINT. I will get around to it soon. Carl if you can give me a specific interface that you'd like, I can put some thought into implementing it and it will eventually get done. It's got to be a priority since we need root finding for polynomial GCD. It will probably be one of the first things I will implement after finishing the FLINT Z_poly wrapper, polynomial pseudo-division and my quadratic sieve. Though I reserve the right to work on polynomials over Z/pZ and polynomial irreducibility tests (which is already a feature request for SAGE) at the same time. In short don't expect this by next week. If you email me, I can give you a FLINT trac account and you can just add a ticket with all the details of your wishlist if you like. Bill. On 25 Sep, 17:28, "John Cremona" <[EMAIL PROTECTED]> wrote: > I thought this had been solved some time ago, and was implemented in > pari. Or is that only for real roots of real polynomials? > > John > > On 9/25/07, cwitty <[EMAIL PROTECTED]> wrote: > > > > > > > On Sep 25, 8:02 am, Bill Hart <[EMAIL PROTECTED]> wrote: > > > Well that answered my next question, which is whether this method > > > could be used for Qbar. > > > The biggest obstacle to handling Qbar directly is that I haven't found > > a good way of isolating the roots of a complex polynomial (that is, > > finding the roots with a GUARANTEED error bound) and then refining a > > root to arbitrary precision. (The other annoying part is that SAGE > > does not yet have complex interval arithmetic.) > > > And the third obstacle is that at the moment, I only care about real > > numbers; so I'm not very motivated to work on the extension to > > Qbar. :-) (Although I'd be happy to answer questions, if anybody else > > wanted to work on it!) > > > > Carl, what language is your code in. I would be interested in taking a > > > look. > > > The part I wrote is just Python (although it makes heavy use of the > > rest of SAGE); it's in .../sage/rings/algebraic_real.py . > > > > Bill. > > > Carl > > -- > John Cremona --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-devel@googlegroups.com 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/ -~----------~----~----~----~------~----~------~--~---
