Bivariate factorization using a critical fiber

2015/01/13 by Martin Weimann, Weimann, Martin
Computer Science · Mathematics · #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry and Number Theory #Polynomial and algebraic computation #math.AG #msc:12Y05 #msc:14H20 #msc:14H50 #msc:14Q05 #msc:14Q20 #msc:68W30

paper · pdf · doi:10.48550/arxiv.1501.03011

39 pages

arxiv created 2015/01/13 · arxiv updated 2015/01/14

Abstract

We generalize the classical lifting and recombination scheme for rational and absolute factorization of bivariate polynomials to the case of a critical fiber. We explore different strategies for recombinations of the analytic factors, depending on the complexity of the ramification. We show that working along a critical fiber leads in some cases to a good theoretical complexity, due to the smaller number of analytic factors to recombine. We pay a particular attention to the case of polynomials that are non degenerate with respect to their P-adic Newton polytopes.

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