Computing images of polynomial maps

  • Corey Harris
  • Mateusz MichałekEmail author
  • Emre Can Sertöz
Open Access


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.


Polynomial maps Constructible set Matrix product states 

Mathematics Subject Classification (2010)

Primary 14Q15 Secondary 68U05 15A69 



Open access funding provided by Max Planck Society. We thank Wolfgang Hackbusch for posing the question which motivated this work and for the stimulating discussions. We are grateful to Bernd Sturmfels and Michael Joswig for many suggestions and encouraging remarks.

Funding information

MM was supported by Polish National Science Center project 2013/08/A/ST1/00804 affiliated at the University of Warsaw.


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© The Author(s) 2019

Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.Max Planck Institute for Mathematics in the SciencesLeipzigGermany
  2. 2.Institute of Mathematics of the Polish Academy of SciencesWarsawPoland
  3. 3.Aalto UniversityEspooFinland

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