Factoring bivariate polynomials using adjoints - Archive ouverte HAL Access content directly
Journal Articles Journal of Symbolic Computation Year : 2013

Factoring bivariate polynomials using adjoints

(1, 2)
1
2

Abstract

We relate factorization of bivariate polynomials to singularities of projective plane curves. We prove that adjoint polynomials of a polynomial F ∈ k[x, y] with coefficients in a field k permit to recombinations of the factors of F (0, y) induced by both the absolute and rational factorizations of F , and so without using Hensel lifting. We show in such a way that a fast computation of adjoint polynomials leads to a fast factorization. Our results establish the relations between the algorithms of Duval-Ragot based on locally constant functions and the algorithms of Lecerf and Chèze-Lecerf based on lifting and recombinations. The proof is based on cohomological sequences and residue theory.
Fichier principal
Vignette du fichier
FactoAdjoint-Revised.pdf (432.28 Ko) Télécharger le fichier
Origin : Files produced by the author(s)
Loading...

Dates and versions

hal-02137322 , version 1 (22-05-2019)

Identifiers

Cite

Martin Weimann. Factoring bivariate polynomials using adjoints. Journal of Symbolic Computation, 2013, 58, pp.77-98. ⟨10.1016/j.jsc.2013.05.011⟩. ⟨hal-02137322⟩
29 View
61 Download

Altmetric

Share

Gmail Facebook Twitter LinkedIn More