2007/9/19, Joel B. Mohler <[EMAIL PROTECTED]>: > > On Wednesday 19 September 2007 16:22, William Stein wrote: > > I think those timings are way out of date, since Singular 3 seems > > to be *very* fast at mod p multivariate GCD computation, even > > though it sucks over QQ. Check out this paper: > > > > http://www.cecm.sfu.ca/CAG/papers/brown.ps > > > > It on exactly the problem of GCD over QQ (or equiv ZZ), > > and section 2 has a complete description of a gcd algorithm > > that reduces gcd over ZZ to doing gcd's mod p. > > I'll be looking into implementing that. It makes me disgruntled to be at the > mercy of mathematica (or pick your favorite big commercial m). :D.
FYI, I plan on implementing a multivariate gcd algorithm for Sage over RR and CC some time next year. The algorithm is by Kaltofen et al. Here's the abstract: " Abstract. We consider the problem of computing minimal real or complex deformations to the coefficients in a list of relatively prime real or complex multivariate polynomials such that the deformed polynomials have a greatest common divisor (GCD) of at least a given degree k. In addition,we restrict the deformed coefficients by a given set of linear constraints, thus introducing the linearly constrained approximate GCD problem. We present an algorithm based on a version of the structured " There is already an implementation of the algorithm written in maple available here if anyone is interested: http://www4.ncsu.edu/~kaltofen/software/manystln/ didier > > -- > Joel > > > > --~--~---------~--~----~------------~-------~--~----~ 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/ -~----------~----~----~----~------~----~------~--~---
