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

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 uMPS⁡(2,2,5).