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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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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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Additional Information
  • Mohamed Barakat
  • Affiliation: Department of mathematics, University of Siegen, 57068 Siegen, Germany
  • MR Author ID: 706483
  • ORCID: 0000-0003-3642-4190
  • Email: mohamed.barakat@uni-siegen.de
  • Markus Lange-Hegermann
  • Affiliation: Department of electrical engineering and computer science, Ostwestfalen-Lippe University of Applied Sciences and Arts, 32657 Lemgo, Germany
  • MR Author ID: 937506
  • Email: markus.lange-hegermann@th-owl.de
  • Received by editor(s): December 4, 2019
  • Received by editor(s) in revised form: November 16, 2020
  • Published electronically: September 22, 2021
  • Additional Notes: This work was a contribution to Project II.1 of SFB-TRR 195 ‘Symbolic Tools in Mathematics and their Application’ funded by Deutsche Forschungsgemeinschaft (DFG)
  • © Copyright 2021 American Mathematical Society
  • Journal: Math. Comp. 91 (2022), 451-490
  • MSC (2020): Primary 13P10, 13P15, 68W30, 14Q20, 14R20
  • DOI: https://doi.org/10.1090/mcom/3632
  • MathSciNet review: 4350545