An inversion algorithm for polynomial maps

TL;DR

This paper introduces an algorithmic approach to determine invertibility of polynomial maps and construct their inverses, offering a new classification method for polynomial automorphisms in affine spaces.

Contribution

It presents an algorithm that constructs polynomial sequences to test invertibility and compute inverses, linking to the Jacobian conjecture.

Findings

Algorithm successfully determines invertibility of polynomial maps.

Provides a constructive method for finding polynomial map inverses.

Classifies polynomial automorphisms of affine spaces.

Abstract

We present an algorithmic equivalent statement to the Jacobian conjecture. Given a polynomial map F on an affine space of dimension n, our algorithm constructs n sequences of polynomials such that F is invertible if and only if the zero polynomial appears in all n sequences and moreover computes the inverse map of F. This algorithm provides a classification of polynomial automorphisms of affine spaces.