Effective membership problem and systems of polynomial equations with multiple roots

2024/08/20 by Ivan Nikitin, Nikitin, Ivan
Computer Science · Mathematics · #14H55 (Secondary) #14M25 (Primary) 14H50 #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #FOS: Mathematics #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.2408.10884

openalex publication_date 2024/08/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a tuple of k+1 convex polytopes (A, B,…, B) we solve the so-called effective membership problem, i.e. for a tuple f=(f₁,…, f_k) of polynomials satisfying some certain properties of generality and having Newton polytope B we provide a method to compute ℂ^A∩ I, where I is an ideal in the ring of Laurent polynomials generated by f. We connect this topic to the study of mixed discriminants and multiple solutions of systems of polynomial equations.

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