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Fields of Algebraic Numbers Computable in Polynomial Time. I. / Alaev, P. E.; Selivanov, V. L.

In: Algebra and Logic, Vol. 58, No. 6, 01.01.2020, p. 447-469.

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

Harvard

Alaev, PE & Selivanov, VL 2020, 'Fields of Algebraic Numbers Computable in Polynomial Time. I', Algebra and Logic, vol. 58, no. 6, pp. 447-469. https://doi.org/10.1007/s10469-020-09565-0

APA

Alaev, P. E., & Selivanov, V. L. (2020). Fields of Algebraic Numbers Computable in Polynomial Time. I. Algebra and Logic, 58(6), 447-469. https://doi.org/10.1007/s10469-020-09565-0

Vancouver

Alaev PE, Selivanov VL. Fields of Algebraic Numbers Computable in Polynomial Time. I. Algebra and Logic. 2020 Jan 1;58(6):447-469. doi: 10.1007/s10469-020-09565-0

Author

Alaev, P. E. ; Selivanov, V. L. / Fields of Algebraic Numbers Computable in Polynomial Time. I. In: Algebra and Logic. 2020 ; Vol. 58, No. 6. pp. 447-469.

BibTeX

@article{546e5f68902741b094b8b84e978faea9,
title = "Fields of Algebraic Numbers Computable in Polynomial Time. I",
abstract = "It is proved that the field of complex algebraic numbers has an isomorphic presentation computable in polynomial time. A similar fact is proved for the ordered field of real algebraic numbers. The constructed polynomially computable presentations are based on a natural presentation of algebraic numbers by rational polynomials. Also new algorithms for computing values of polynomials on algebraic numbers and for solving equations in one variable with algebraic coefficients are presented.",
keywords = "field of complex algebraic numbers, ordered field of real algebraic numbers, polynomially computable presentation",
author = "Alaev, {P. E.} and Selivanov, {V. L.}",
year = "2020",
month = jan,
day = "1",
doi = "10.1007/s10469-020-09565-0",
language = "English",
volume = "58",
pages = "447--469",
journal = "Algebra and Logic",
issn = "0002-5232",
publisher = "Springer US",
number = "6",

}

RIS

TY - JOUR

T1 - Fields of Algebraic Numbers Computable in Polynomial Time. I

AU - Alaev, P. E.

AU - Selivanov, V. L.

PY - 2020/1/1

Y1 - 2020/1/1

N2 - It is proved that the field of complex algebraic numbers has an isomorphic presentation computable in polynomial time. A similar fact is proved for the ordered field of real algebraic numbers. The constructed polynomially computable presentations are based on a natural presentation of algebraic numbers by rational polynomials. Also new algorithms for computing values of polynomials on algebraic numbers and for solving equations in one variable with algebraic coefficients are presented.

AB - It is proved that the field of complex algebraic numbers has an isomorphic presentation computable in polynomial time. A similar fact is proved for the ordered field of real algebraic numbers. The constructed polynomially computable presentations are based on a natural presentation of algebraic numbers by rational polynomials. Also new algorithms for computing values of polynomials on algebraic numbers and for solving equations in one variable with algebraic coefficients are presented.

KW - field of complex algebraic numbers

KW - ordered field of real algebraic numbers

KW - polynomially computable presentation

UR - http://www.scopus.com/inward/record.url?scp=85081549779&partnerID=8YFLogxK

U2 - 10.1007/s10469-020-09565-0

DO - 10.1007/s10469-020-09565-0

M3 - Article

AN - SCOPUS:85081549779

VL - 58

SP - 447

EP - 469

JO - Algebra and Logic

JF - Algebra and Logic

SN - 0002-5232

IS - 6

ER -

ID: 23804346