Some algorithms related to the Jacobian Conjecture

TL;DR

This paper introduces an algorithm to identify potential counterexamples to the Jacobian Conjecture by analyzing polynomial degree pairs up to certain bounds, aiding in the conjecture's investigation.

Contribution

The paper presents a novel algorithm for computing potential counterexample structures to the Jacobian Conjecture based on degree bounds, expanding the search space.

Findings

Identified possible counterexample families with gcd of degrees ≤ 35

Enumerated degree pairs with maximum degree ≤ 150

Provided computational tools for Jacobian Conjecture analysis

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 $\gcd(deg(P),deg(Q))\le 35$, and all the pairs $(deg(P),deg(Q))$ with $\max(deg(P),deg(Q))\le 150$ for any hypothetical counterexample.