Looking at Mark van Hoeij's website, he has a (maple) implementation of his algorithm: http://www.math.fsu.edu/~hoeij/knapsack.html
he also mentions "My implementation is not tuned in the best possible way. A much better way (more efficient, more robust and simpler) to tune the algorithm is given by Karim Belabas in section 2 of his paper "A relative van Hoeij algorithm over number fields", to appear in J. Symbolic Computation" that paper is available at Belabas' website: http://www.ufr-mi.u-bordeaux.fr/~belabas/research/vanhoeij.pdf and the end of the introduction reads "Our implementations are part of the PARI library [23]. All timings were obtained with PARI-2.2.6 configured to use GMP-4.1 as its multiprecision kernel, on a 1GHz Athlon under Linux (lucrezia.medicis.polytechnique.fr), and are given in seconds." so it seems PARI already contains an algorithm similar to what you are looking for. Alternatively, since it seems that van Hoeijs algorithm reduces to a knapsack problem, so maybe it could be easily built upon the brand new fast graphs methods that we got? Cheers J On Jan 12, 2:08 pm, YannLC <yannlaiglecha...@gmail.com> wrote: > 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/stab... > > > 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.
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