多元有理函数的符号求和

IF 2.5 1区 数学 Q2 COMPUTER SCIENCE, THEORY & METHODS
Shaoshi Chen, Lixin Du, Hanqian Fang
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引用次数: 0

摘要

符号求和作为符号计算的一个活跃研究课题,为计算和简化数学、计算机科学、物理等领域的不同类型的求和提供了有效的算法工具。现有的符号求和算法大多适用于单变量输入的问题。符号计算的一个长期课题是发展多元函数符号求和的理论、算法和软件。本文完整地解决了多元有理函数符号求和中的两个具有挑战性的问题,即多元有理函数的有理可和性问题和伸缩子的存在性问题。我们的方法是基于佐藤多项式的各向同性群的结构,这使我们能够将问题减少到测试多项式的位移等价性。我们的结果提供了Picard问题在微分形式上的离散模拟的完整解,并可用于检测Wilf-Zeilberger方法对多元有理函数的适用性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Symbolic Summation of Multivariate Rational Functions

Symbolic summation as an active research topic of symbolic computation provides efficient algorithmic tools for evaluating and simplifying different types of sums arising from mathematics, computer science, physics and other areas. Most of existing algorithms in symbolic summation are mainly applicable to the problem with univariate inputs. A long-term project in symbolic computation is to develop theories, algorithms and software for the symbolic summation of multivariate functions. This paper will give complete solutions to two challenging problems in symbolic summation of multivariate rational functions, namely the rational summability problem and the existence problem of telescopers for multivariate rational functions. Our approach is based on the structure of Sato’s isotropy groups of polynomials, which enables us to reduce the problems to testing the shift equivalence of polynomials. Our results provide a complete solution to the discrete analogue of Picard’s problem on differential forms and can be used to detect the applicability of the Wilf-Zeilberger method to multivariate rational functions.

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来源期刊
Foundations of Computational Mathematics
Foundations of Computational Mathematics 数学-计算机:理论方法
CiteScore
6.90
自引率
3.30%
发文量
46
审稿时长
>12 weeks
期刊介绍: Foundations of Computational Mathematics (FoCM) will publish research and survey papers of the highest quality which further the understanding of the connections between mathematics and computation. The journal aims to promote the exploration of all fundamental issues underlying the creative tension among mathematics, computer science and application areas unencumbered by any external criteria such as the pressure for applications. The journal will thus serve an increasingly important and applicable area of mathematics. The journal hopes to further the understanding of the deep relationships between mathematical theory: analysis, topology, geometry and algebra, and the computational processes as they are evolving in tandem with the modern computer. With its distinguished editorial board selecting papers of the highest quality and interest from the international community, FoCM hopes to influence both mathematics and computation. Relevance to applications will not constitute a requirement for the publication of articles. The journal does not accept code for review however authors who have code/data related to the submission should include a weblink to the repository where the data/code is stored.
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