Newton iteration for lexicographic Gr\"obner bases in two variables
Commutative Algebra
2023-02-09 v1 Symbolic Computation
Algebraic Geometry
Abstract
We present an -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.
Keywords
Cite
@article{arxiv.2302.03766,
title = {Newton iteration for lexicographic Gr\"obner bases in two variables},
author = {Éric Schost and Catherine St-Pierre},
journal= {arXiv preprint arXiv:2302.03766},
year = {2023}
}