Computing images of polynomial maps

Corey Harris, Mateusz Michałek*, Emre Can Sertöz

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

2 Citations (Scopus)
46 Downloads (Pure)

Abstract

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.

Original languageEnglish
Pages (from-to)2845–2865
JournalADVANCES IN COMPUTATIONAL MATHEMATICS
Volume45
Issue number5-6
Early online date1 Jan 2019
DOIs
Publication statusPublished - Dec 2019
MoE publication typeA1 Journal article-refereed

Keywords

  • Constructible set
  • Matrix product states
  • Polynomial maps

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    Harris, C., Michałek, M., & Sertöz, E. C. (2019). Computing images of polynomial maps. ADVANCES IN COMPUTATIONAL MATHEMATICS, 45(5-6), 2845–2865. https://doi.org/10.1007/s10444-019-09715-8