Newton iteration for lexicographic Gröbner bases in two variables

02/07/2023

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by   Eric Schost, et al.

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We present an m-adic Newton iteration with quadratic convergence for lexicographic Gröbner 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 Gröbner bases by affine parameters; our Newton iteration works directly with these parameters.