Polynomial Computability of Fields of Algebraic Numbers

被引：2
|
作者：
Alaev, P. E. [1 ,2 ]
Selivanov, V. L. [3 ,4 ]
机构：
[1] Russian Acad Sci, Siberian Branch, Sobolev Inst Math, Novosibirsk 630090, Russia
[2] Novosibirsk State Univ, Novosibirsk 630090, Russia
[3] Russian Acad Sci, Siberian Branch, Ershov Inst Informat Syst, Novosibirsk, Russia
[4] Kazan Fed Univ, Kazan 420008, Republic Of Tat, Russia
来源：
DOKLADY MATHEMATICS | 2018年 / 98卷 / 01期
关键词：
D O I：
10.1134/S1064562418050137
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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.
引用
收藏
页码：341 / 343
页数：3
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