Fields of Algebraic Numbers Computable in Polynomial Time. I

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3 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)447-469
Number of pages23
JournalAlgebra and Logic
Volume58
Issue number6
DOIs
Publication statusPublished - 1 Jan 2020

Keywords

  • field of complex algebraic numbers
  • ordered field of real algebraic numbers
  • polynomially computable presentation

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