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

^*Tämän työn vastaava kirjoittaja

Matematiikan ja systeemianalyysin laitos

Tutkimustuotos: Lehtiartikkeli › Article › Scientific › vertaisarvioitu

9 Sitaatiot (Scopus)

89 Lataukset (Pure)

Abstrakti

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.

Alkuperäiskieli	Englanti
Sivut	2845–2865
Julkaisu	Advances in Computational Mathematics
Vuosikerta	45
Numero	5-6
Varhainen verkossa julkaisun päivämäärä	1 tammik. 2019
DOI - pysyväislinkit	https://doi.org/10.1007/s10444-019-09715-8
Tila	Julkaistu - jouluk. 2019
OKM-julkaisutyyppi	A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä

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

Harris2019_Article_ComputingImagesOfPolynomialMapFinal published version, 1,18 MBLisenssi: CC BY

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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}",

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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

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U2 - 10.1007/s10444-019-09715-8

DO - 10.1007/s10444-019-09715-8

M3 - Article

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JO - Advances in Computational Mathematics

JF - Advances in Computational Mathematics

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Computing images of polynomial maps

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