Ah, OK, now I understand. It would truly be interesting to do a profile of a complex interval approach against a purely algebraic approach. It sounds like a question begging to be answered.
I notice that in the example William gave, defining complex intervals as AA[x]/(x^2+1) he was able to find minimum polynomials. I'm curious as to how SAGE does that and whether the result is always reliable. I daresay over the coming months as the algebraic number theory package gets fleshed out, one way or another, you me, Robert, William, John and whoever else is interested, will figure this stuff out. I look forward to it. It sounds like a challenge to work on this stuff, and SAGE badly needs something, since at present Magma is the only place to get this stuff. Thanks for the answers to my (fairly dumb) questions. Bill. On 26 Sep, 17:47, cwitty <[EMAIL PROTECTED]> wrote: > On Sep 25, 6:40 pm, Bill Hart <[EMAIL PROTECTED]> wrote: > > > I still have a question about how one computes an approximate > > polynomial for a + b for algebraic a and b, given approximate > > polynomials for a and b, using interval arithmetic. > > I don't. :-) > > There are several possible representations for an algebraic real in my > code. An algebraic real can be a rational number, it can be a > particular root (selected by giving an interval containing the root) > of a polynomial with algebraic coefficients, or it can be the sum, > difference, product, or quotient of algebraic reals. So the > representation for a+b, with algebraic a and b, is a+b. > > Carl --~--~---------~--~----~------------~-------~--~----~ 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/ -~----------~----~----~----~------~----~------~--~---
