thanks for both replies! OK, so there are various fast algorithms and Magma has implemented at least one of them. Sage is using Singular. I wonder why Singular has not got a fast algorithm for this?
For this application of mine, I need to do a number of one-off factorizations like this in order to implement some cases of elliptic curve isogenies (specifically in characteristics 2 and 3) which were not already done. So of course I can use Magma for those, and the resulting factors are then hard-wired into the Sage code. But it would be more satisfying to have the whole thing done in Sage! John 2010/1/12 YannLC <yannlaiglecha...@gmail.com>: > > > On Jan 12, 2:46 pm, javier <vengor...@gmail.com> wrote: >> There are indeed well known (sort of) fast algorithms for >> factorization of multivariable polynomials over finite >> fields:http://portal.acm.org/citation.cfm?id=808748http://www.jstor.org/stable/2008063?seq=1 >> >> In the second paper there is a particular (probabilistic) algorithm >> for bivariate polynomials. Maybe magma has something like that? >> > > Citing Magma's help (http://magma.maths.usyd.edu.au/magma/htmlhelp/ > text315.htm): > > For bivariate polynomials, a polynomial-time algorithm in the same > spirit as van Hoeij's Knapsack factoring algorithm [vH02] is used. > > -- > To post to this group, send an email to sage-devel@googlegroups.com > To unsubscribe from this group, send an email to > sage-devel+unsubscr...@googlegroups.com > For more options, visit this group at > http://groups.google.com/group/sage-devel > URL: http://www.sagemath.org > >
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