2012/01/27 by Martin Weimann, Weimann, Martin
Computer Science · Mathematics · #Algebraic Geometry and Number Theory #Coding theory and cryptography #Polynomial and algebraic computation #math.AC #math.AG #msc:13P05 #msc:14Q05 #msc:68W30
paper · pdf · doi:10.48550/arxiv.1201.5787
22 pages, 2 figures. Extended version of arXiv.1201.5787
arxiv created 2012/02/17 · arxiv updated 2012/02/20
One relates factorization of bivariate polynomials to singularities of projective plane curves. One proves that adjoint polynomials permit to solve the recombinations of the modular factors induced by the absolute and rational factorizations, and so without using Hensel's lifting. One establishes in such a way the relations between the algorithm of Duval-Ragot (locally constant functions) and of Chèze-Lecerf (lifting and recombinations), and one shows that a fast computation of adjoint polynomials leads to a fast factorization. The proof is based on cohomological sequences and residue theory.