Newton iteration for lexicographic Gr\"obner bases in two variables

DOI10.1016/J.JALGEBRA.2024.04.018arXiv2302.03766OpenAlexW4396218073MaRDI QIDQ6425775

Catherine st-Pierre, Éric Schost

Publication date: 7 February 2023

Abstract: We present an $m$-adic Newton iteration with quadratic convergence for lexicographic Gr"obner basis of zero dimensional ideals in two variables. We rely on a structural result about the syzygies in such a basis due to Conca and Valla, that allowed them to explicitly describe these Gr"obner bases by affine parameters; our Newton iteration works directly with these parameters.

Full work available at URL: https://doi.org/10.1016/j.jalgebra.2024.04.018

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