An algorithmic approach to Chevalley's Theorem on images of rational morphisms between affine varieties

TL;DR

This paper presents an algorithmic geometric proof of Chevalley's Theorem for affine varieties, resulting in an efficient computational method for determining the images of rational maps.

Contribution

It introduces a constructive, algorithmic proof of the affine Chevalley's Theorem and provides an implementable code for computing constructible images of rational maps.

Findings

Developed an efficient algorithm for image computation of rational maps

Provided a constructive geometric proof of Chevalley's Theorem

Extended descriptions of uniform matrix product states to uMPS(2,2,5)

Abstract

The goal of this paper is to introduce a new constructive geometric proof of the affine version of Chevalley's Theorem. This proof is algorithmic and a verbatim implementation resulted in an efficient code for computing the constructible image of rational maps between affine varieties. Our approach extends the known descriptions of uniform matrix product states to $\operatorname{uMPS}(2,2,5)$