Polynomial Computability of Fields of Algebraic Numbers

P. E. Alaev, V. L. Selivanov

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


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.

Original languageEnglish
Pages (from-to)341-343
Number of pages3
JournalDoklady Mathematics
Issue number1
Publication statusPublished - 1 Jul 2018

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