多元差分域的符号求和

IF 0.8 2区数学 Q2 MATHEMATICS

Journal of Algebra Pub Date : 2025-09-17 DOI:10.1016/j.jalgebra.2025.08.043

Lixin Du , Yarong Wei

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引用次数: 0

摘要

二元差分域为满足二阶递归的序列提供了一个代数框架。在此基础上，重点研究了满足高阶常系数递推的序列，并考虑了多元差分域，将这些序列的求和问题转化为求解一阶差分方程。在一类特殊的多元差分域中，给出了判定差分方程是否有有理解的判据，并给出了计算该差分方程是否有有理解的算法。并且得到了该方程所有有理解的集合。

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Symbolic summation in multivariate difference fields

The bivariate difference fields provide an algebraic framework for sequences satisfying a recurrence of order two. Based on this, we focus on sequences satisfying a recurrence of higher order with constant coefficients, and consider the multivariate difference fields, in which the summation problem of these sequences could be transformed into solving the first order difference equations. In a special class of multivariate difference fields, we present a criterion for deciding whether the difference equation has a rational solution and present an algorithm for computing one rational solution of such a difference equation, if it exists. Moreover we get the set of all rational solutions of such an equation.

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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.