Polynomial Computability of Fields of Algebraic Numbers

Polynomial Computability of Fields of Algebraic Numbers Full article

Journal

Doklady Mathematics
ISSN: 1064-5624 , E-ISSN: 1531-8362

Output data

Year: 2018, Volume: 98, Number: 1, Pages: 341-343 Pages count : 3 DOI: 10.1134/S1064562418050137

Authors

Alaev P.E. ^1,2 , Selivanov V.L. ^3,4

Affiliations

1	Sobolev Institute of Mathematics of the Siberian Branch of the Russian Academy of Sciences, Novosibirsk, 630090, Russian Federation
2	Novosibirsk State University, Novosibirsk, 630090, Russian Federation
3	Ershov Institute of Informatics System of the Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russian Federation
4	Kazan Federal University, Kazan, Tatarstan, 420008, Russian Federation

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.

Alaev P.E. , Selivanov V.L.
Polynomial Computability of Fields of Algebraic Numbers
Doklady Mathematics. 2018. V.98. N1. P.341-343. DOI: 10.1134/S1064562418050137 WOS Scopus OpenAlex

Alaev P.E. , Селиванов В.Л.
Полиномиальная вычислимость полей алгебраических чисел
Доклады Академии наук. Серия: Математика, информатика, процессы управления. 2018. Т.481. №4. С.355-357. DOI: 10.31857/S086956520001685-6 OpenAlex

Web of science:	WOS:000443716900012
Scopus:	2-s2.0-85052881621
OpenAlex:	W2891212621

DB	Citing
Scopus	5
OpenAlex	5
Web of science	2