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Algebra i logika, 2019, Volume 58, Number 6, Pages 673–705
DOI: https://doi.org/10.33048/alglog.2019.58.601 (Mi al923) 		 
This article is cited in 18 scientific papers (total in 18 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
Full-text PDF (377 kB) Citations (18)
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DOI: https://doi.org/10.33048/alglog.2019.58.601
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.
Received: 15.07.2018
Revised: 12.02.2020
English version:
Algebra and Logic, 2020, Volume 58, Issue 6, Pages 447–469
DOI: https://doi.org/10.1007/s10469-020-09565-0
Bibliographic databases:
Document Type: Article
UDC: 510.52+512.62+510.67
Language: Russian
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
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\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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  • https://www.mathnet.ru/eng/al/v58/i6/p673
    Cycle of papers
    This publication is cited in the following 18 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Алгебра и логика Algebra and Logic
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