The Newton-Puiseux algorithm and effective algebraic series

IF 0.8 2区数学 Q2 MATHEMATICS

Journal of Algebra Pub Date : 2025-10-10 DOI:10.1016/j.jalgebra.2025.09.027

Manfred Buchacher

引用次数: 0

Abstract

We explain how to encode an algebraic series by finite data and how to do effective arithmetic on the level of these encodings. The reasoning is based on the Newton-Puiseux algorithm and an effective equality test for algebraic series. Furthermore, we discuss how to derive information about the support of an algebraic series. Based thereon, we show how to identify the polynomial and rational solutions of a polynomial equation.

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牛顿-普塞算法和有效代数级数

我们解释了如何用有限数据编码代数级数，以及如何在这些编码的层次上进行有效的算术运算。该推理基于牛顿-普塞算法和一个有效的代数级数等式检验。此外，我们还讨论了如何推导代数级数的支持性信息。在此基础上，给出了多项式方程的多项式解和有理解的辨识方法。

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

Journal of Algebra 数学-数学

CiteScore

1.50

自引率

22.20%

发文量

414

审稿时长

2-4 weeks

期刊介绍： The Journal of Algebra is a leading international journal and publishes papers that demonstrate high quality research results in algebra and related computational aspects. Only the very best and most interesting papers are to be considered for publication in the journal. With this in mind, it is important that the contribution offer a substantial result that will have a lasting effect upon the field. The journal also seeks work that presents innovative techniques that offer promising results for future research.