Preprint 2/2018

Computing images of polynomial maps

Corey Harris, Mateusz Michałek, and Emre Sertöz

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Submission date: 04. Jan. 2018
published in: Advances in computational mathematics, 45 (2019) 5/6, p. 2845-2865 
DOI number (of the published article): 10.1007/s10444-019-09715-8
MSC-Numbers: 14Q15, 68U05, 15A69
Keywords and phrases: image of an algebraic variety, matrix product state
Link to arXiv: See the arXiv entry of this preprint.

The image of a polynomial map is a constructible set. While computing its closure is standard in computer algebra systems, a procedure for computing the constructible set itself is not. We provide a new algorithm, based on algebro-geometric techniques, addressing this problem. We also apply these methods to answer a question of W. Hackbusch on the non-closedness of site-independent cyclic matrix product states for infinitely many parameters.

06.03.2023, 02:19