Computing images of polynomial maps

Corey Harris; Mateusz Michałek; Emre Can Sertöz

doi:10.1007/s10444-019-09715-8

Computing images of polynomial maps

Corey Harris, Mateusz Michałek^*, Emre Can Sertöz

^*Corresponding author for this work

Department of Mathematics and Systems Analysis

Research output: Contribution to journal › Article › Scientific › peer-review

10 Citations (Scopus)

85 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 language	English
Pages (from-to)	2845–2865
Journal	Advances in Computational Mathematics
Volume	45
Issue number	5-6
Early online date	1 Jan 2019
DOIs	https://doi.org/10.1007/s10444-019-09715-8
Publication status	Published - Dec 2019
MoE publication type	A1 Journal article-refereed

Keywords

Constructible set
Matrix product states
Polynomial maps

Access to Document

10.1007/s10444-019-09715-8Licence: CC BY

Harris2019_Article_ComputingImagesOfPolynomialMapFinal published version, 1.18 MBLicence: CC BY

Cite this

@article{43ca9124951b4455b15a5318148f93f8,

title = "Computing images of polynomial maps",

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.",

keywords = "Constructible set, Matrix product states, Polynomial maps",

author = "Corey Harris and Mateusz Micha{\l}ek and Sert{\"o}z, {Emre Can}",

year = "2019",

month = dec,

doi = "10.1007/s10444-019-09715-8",

language = "English",

volume = "45",

pages = "2845–2865",

journal = "Advances in Computational Mathematics",

issn = "1019-7168",

publisher = "Springer",

number = "5-6",

}

TY - JOUR

T1 - Computing images of polynomial maps

AU - Harris, Corey

AU - Michałek, Mateusz

AU - Sertöz, Emre Can

PY - 2019/12

Y1 - 2019/12

N2 - 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.

AB - 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.

KW - Constructible set

KW - Matrix product states

KW - Polynomial maps

UR - http://www.scopus.com/inward/record.url?scp=85070315887&partnerID=8YFLogxK

U2 - 10.1007/s10444-019-09715-8

DO - 10.1007/s10444-019-09715-8

M3 - Article

AN - SCOPUS:85070315887

SN - 1019-7168

VL - 45

SP - 2845

EP - 2865

JO - Advances in Computational Mathematics

JF - Advances in Computational Mathematics

IS - 5-6

ER -

Computing images of polynomial maps

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this