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

Barakat, Mohamed; Lange-Hegermann, Markus

doi:10.1090/mcom/3632

An algorithmic approach to Chevalley’s Theorem on images of rational morphisms between affine varieties
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by Mohamed Barakat and Markus Lange-Hegermann HTML | PDF

Math. Comp. 91 (2022), 451-490 Request permission

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 $\operatorname {uMPS}(2,2,5)$.

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