Polynomial Computability of Fields of Algebraic Numbers

Standard

Polynomial Computability of Fields of Algebraic Numbers. / Alaev, P. E.; Selivanov, V. L.

In: Doklady Mathematics, Vol. 98, No. 1, 01.07.2018, p. 341-343.

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

Harvard

Alaev, PE & Selivanov, VL 2018, 'Polynomial Computability of Fields of Algebraic Numbers', Doklady Mathematics, vol. 98, no. 1, pp. 341-343. https://doi.org/10.1134/S1064562418050137

APA

Alaev, P. E., & Selivanov, V. L. (2018). Polynomial Computability of Fields of Algebraic Numbers. Doklady Mathematics, 98(1), 341-343. https://doi.org/10.1134/S1064562418050137

Vancouver

Alaev PE, Selivanov VL. Polynomial Computability of Fields of Algebraic Numbers. Doklady Mathematics. 2018 Jul 1;98(1):341-343. doi: 10.1134/S1064562418050137

Author

Alaev, P. E. ; Selivanov, V. L. / Polynomial Computability of Fields of Algebraic Numbers. In: Doklady Mathematics. 2018 ; Vol. 98, No. 1. pp. 341-343.

BibTeX

@article{de9d87ba13854456af6230bbc3ce9dba,

title = "Polynomial Computability of Fields of Algebraic Numbers",

abstract = "We prove that the field of complex algebraic numbers and the ordered field of real algebraic numbers have isomorphic presentations computable in polynomial time. For these presentations, new algorithms are found for evaluation of polynomials and solving equations of one unknown. It is proved that all best known presentations for these fields produce polynomially computable structures or quotient-structures such that there exists an isomorphism between them polynomially computable in both directions.",

author = "Alaev, {P. E.} and Selivanov, {V. L.}",

note = "Publisher Copyright: {\textcopyright} 2018, Pleiades Publishing, Ltd.",

year = "2018",

month = jul,

day = "1",

doi = "10.1134/S1064562418050137",

language = "English",

volume = "98",

pages = "341--343",

journal = "Doklady Mathematics",

issn = "1064-5624",

publisher = "Maik Nauka-Interperiodica Publishing",

number = "1",

}

RIS

TY - JOUR

T1 - Polynomial Computability of Fields of Algebraic Numbers

AU - Alaev, P. E.

AU - Selivanov, V. L.

PY - 2018/7/1

Y1 - 2018/7/1

N2 - We prove that the field of complex algebraic numbers and the ordered field of real algebraic numbers have isomorphic presentations computable in polynomial time. For these presentations, new algorithms are found for evaluation of polynomials and solving equations of one unknown. It is proved that all best known presentations for these fields produce polynomially computable structures or quotient-structures such that there exists an isomorphism between them polynomially computable in both directions.

AB - We prove that the field of complex algebraic numbers and the ordered field of real algebraic numbers have isomorphic presentations computable in polynomial time. For these presentations, new algorithms are found for evaluation of polynomials and solving equations of one unknown. It is proved that all best known presentations for these fields produce polynomially computable structures or quotient-structures such that there exists an isomorphism between them polynomially computable in both directions.

UR - http://www.scopus.com/inward/record.url?scp=85052881621&partnerID=8YFLogxK

U2 - 10.1134/S1064562418050137

DO - 10.1134/S1064562418050137

M3 - Article

AN - SCOPUS:85052881621

VL - 98

SP - 341

EP - 343

JO - Doklady Mathematics

JF - Doklady Mathematics

SN - 1064-5624

IS - 1

ER -

ID: 16485768