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Algebra Logika, 2019, Volume 58, Number 6, Pages 673–705 (Mi al923)  

This article is cited in 2 scientific papers (total in 2 papers)

Fields of algebraic numbers computable in polynomial time. I

P. E. Alaevab, V. L. Selivanovcd

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
b Novosibirsk State University
c A.P. Ershov Institute of Informatics Systems, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
d Kazan (Volga Region) Federal University

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 via 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.

Funding Agency Grant Number
Russian Foundation for Basic Research 17-01-00247_а
Ministry of Science and Higher Education of the Russian Federation 0314-2019-0002
1.13556.2019/13.1
Supported by RFBR (project No. 17-01-00247) and by the RF Ministry of Science and Higher Education (state assignment to Sobolev Institute of Mathematics, SB RAS, project No. 0314-2019-0002). The work was carried out at the expense of the subsidy allocated to Kazan (Volga Region) Federal University for the fulfillment of the state assignment in the sphere of scientific activity, project No. 1.13556.2019/13.1.


DOI: https://doi.org/10.33048/alglog.2019.58.601

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English version:
Algebra and Logic, 2020, 58:6, 447–469

Bibliographic databases:

UDC: 510.52+512.62+510.67
Received: 15.07.2018
Revised: 12.02.2020

Citation: P. E. Alaev, V. L. Selivanov, “Fields of algebraic numbers computable in polynomial time. I”, Algebra Logika, 58:6 (2019), 673–705; Algebra and Logic, 58:6 (2020), 447–469

Citation in format AMSBIB
\Bibitem{AlaSel19}
\by P.~E.~Alaev, V.~L.~Selivanov
\paper Fields of algebraic numbers computable in polynomial time. I
\jour Algebra Logika
\yr 2019
\vol 58
\issue 6
\pages 673--705
\mathnet{http://mi.mathnet.ru/al923}
\crossref{https://doi.org/10.33048/alglog.2019.58.601}
\transl
\jour Algebra and Logic
\yr 2020
\vol 58
\issue 6
\pages 447--469
\crossref{https://doi.org/10.1007/s10469-020-09565-0}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85081549779}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. P. E. Alaev, “Polynomially computable structures with finitely many generators”, Algebra and Logic, 59:3 (2020), 266–272  mathnet  crossref  crossref  isi
    2. A. V. Seliverstov, “Dvoichnye resheniya dlya bolshikh sistem lineinykh uravnenii”, PDM, 2021, no. 52, 5–15  mathnet  crossref
  • Алгебра и логика Algebra and Logic
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