MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV ( that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint

Computing images of polynomial maps

Corey Harris, Mateusz Michałek and Emre Sertöz


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.

MSC Codes:
14Q15, 68U05, 15A69
image of an algebraic variety, matrix product state

Related publications

2019 Journal Open Access
Corey Harris, Mateusz Michałek and Emre Can Sertöz

Computing images of polynomial maps

In: Advances in computational mathematics, 45 (2019) 5/6, pp. 2845-2865