> > > Also, to Joel Mohler: > > You need "Algorithms for Computer Algebra" by Geddes, Czapor, and > > Labahn: > > Chapter 5: Chinese Remainder Theorem > > Chapter 6: Newton's Iteration and Hensel Lifting > > Chapter 7: Polynomial GCD > > Chapter 8: Polynomial Factorization > > > > What you are trying to do is not a "weeks long" project, it is one > > of the central achievements of the entire field. It took a > > decade > > to do the first time, so don't expect to have "industrial strength" > > routines soon. It will realistically take months of full time work. > > There's about 100 pages of material in that book, when you take out > > the exercises, etc. You need it all. > > We'll see. By the way, who "did it"? Does *any* program doing > multivariate polynomial gcd and factorization well except Magma? > I'm not being rhetorical -- I just don't know the answer. If only > Magma does well, we should just find out what algorithms they > use, and if they aren't just copying from the above book, then we > *need* to be more clever than whatever is in that book. Allan > Steel did it -- by himself -- and so can we. > > By the way, the book you suggest above was published in 1992. > Allan Steel implemented all the fast gcd/factoring code in Magma > many years later. It's perhaps highly likely he made great progress over > what's in that book. Maybe we can appeal to his vanity and > ask him.
Wait, actually Allan says what Magma does on this page: http://magma.maths.usyd.edu.au/magma/htmlhelp/text314.htm#1994 And he says in each case that he uses algorithms that he made that are based on those from the book you cite. For example he writes: "... (3) a recursive multivariate evaluation-interpolation algorithm (similar to that in [GCL92, section 7.4]), which in fact works generically over {Z} or most fields." William --~--~---------~--~----~------------~-------~--~----~ 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://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
