Some algorithms related to the Jacobian Conjecture

2017/08/26 by Jorge A. Guccione, Juan J. Guccione, Guccione, Jorge A. +5
Mathematics · #14R15 (Primary) 13F20 (Secondary) #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1708.07936

openalex publication_date 2017/08/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We describe an algorithm that computes possible corners of hypothetical counterexamples to the Jacobian Conjecture up to a given bound. Using this algorithm we compute the possible families corresponding to gcd(deg(P),deg(Q))≤ 35, and all the pairs (deg(P),deg(Q)) with max(deg(P),deg(Q))≤ 150 for any hypothetical counterexample.

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