The Groebner basis and solution set of a polynomial system related to the Jacobian conjecture

TL;DR

This paper computes the Groebner basis for a polynomial system connected to the Jacobian conjecture and fully characterizes its solution set, providing insights into this longstanding mathematical problem.

Contribution

It introduces a method to explicitly compute the Groebner basis and describe the solution set for a polynomial system related to the Jacobian conjecture, advancing understanding of this problem.

Findings

Complete description of the solution set for the polynomial system.

Explicit computation of the Groebner basis for the system.

Insights into the structure of solutions related to the Jacobian conjecture.

Abstract

We compute the Groebner basis of a system of polynomial equations related to the Jacobian conjecture, and describe completely the solution set.