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

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