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Bivariate Factorization Using a Critical Fiber

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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Martin Weimann. Bivariate Factorization Using a Critical Fiber. Foundations of Computational Mathematics, Springer Verlag, 2017, 17 (5), pp.1219-1263. ⟨10.1007/s10208-016-9318-8⟩. ⟨hal-01645143⟩

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