Fields of Algebraic Numbers Computable in Polynomial Time. II

IF 0.4 3区数学 Q4 LOGIC

Algebra and Logic Pub Date : 2022-05-06 DOI:10.1007/s10469-022-09661-3

P. E. Alaev, V. L. Selivanov

引用次数: 2

Abstract

This paper is a continuation of [Algebra and Logic, 58, No. 6, 447-469 (2019)] where we constructed polynomial-time presentations for the field of complex algebraic numbers and for the ordered field of real algebraic numbers. Here we discuss other known natural presentations of such structures. It is shown that all these presentations are equivalent to each other and prove a theorem which explains why this is so. While analyzing the presentations mentioned, we introduce the notion of a quotient structure. It is shown that the question whether a polynomial-time computable quotient structure is equivalent to an ordinary one is almost equivalent to the P = NP problem. Conditions are found under which the answer is positive.

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多项式时间可计算代数数的域。二、

本文是[代数与逻辑，58，No.6447-469（2019）]的延续，其中我们构造了复代数数域和实数代数数有序域的多项式时间表示。在这里，我们讨论其他已知的这种结构的自然表现。结果表明，所有这些表示都是等价的，并证明了一个定理来解释为什么会这样。在分析这些表示的同时，我们引入了商结构的概念。证明了多项式时间可计算商结构是否等价于普通商结构的问题几乎等价于P=NP问题。找到了答案为肯定的条件。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Algebra and Logic 数学-数学

CiteScore

1.10

自引率

20.00%

发文量

审稿时长

>12 weeks

期刊介绍： This bimonthly journal publishes results of the latest research in the areas of modern general algebra and of logic considered primarily from an algebraic viewpoint. The algebraic papers, constituting the major part of the contents, are concerned with studies in such fields as ordered, almost torsion-free, nilpotent, and metabelian groups; isomorphism rings; Lie algebras; Frattini subgroups; and clusters of algebras. In the area of logic, the periodical covers such topics as hierarchical sets, logical automata, and recursive functions. Algebra and Logic is a translation of ALGEBRA I LOGIKA, a publication of the Siberian Fund for Algebra and Logic and the Institute of Mathematics of the Siberian Branch of the Russian Academy of Sciences. All articles are peer-reviewed.