基于还原的 D 有限函数定和创造性伸缩

IF 0.6 4区数学 Q4 COMPUTER SCIENCE, THEORY & METHODS

Journal of Symbolic Computation Pub Date : 2024-04-29 DOI:10.1016/j.jsc.2024.102329

Hadrien Brochet, Bruno Salvy

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引用次数: 0

摘要

创造性伸缩是蔡尔伯格（Zeilberger）提出的一种算法方法，它通过合成能伸缩的和来计算定和，这些和被称为证书。我们描述了一种创造性的伸缩算法，它能以紧凑的形式计算 D 有限函数定和的伸缩器以及相关的证书。该算法依赖于广义赫米特还原法的离散类比，或者等价于阿布拉莫夫-佩特科夫舍克还原法的广义化。我们提供了一个 Maple 实现，在各种示例上都有很好的时效性。

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Reduction-based creative telescoping for definite summation of D-finite functions

Creative telescoping is an algorithmic method initiated by Zeilberger to compute definite sums by synthesizing summands that telescope, called certificates. We describe a creative telescoping algorithm that computes telescopers for definite sums of D-finite functions as well as the associated certificates in a compact form. The algorithm relies on a discrete analogue of the generalized Hermite reduction, or equivalently, a generalization of the Abramov-Petkovšek reduction. We provide a Maple implementation with good timings on a variety of examples.

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来源期刊

Journal of Symbolic Computation 工程技术-计算机：理论方法

CiteScore

2.10

自引率

14.30%

发文量

审稿时长

142 days

期刊介绍： An international journal, the Journal of Symbolic Computation, founded by Bruno Buchberger in 1985, is directed to mathematicians and computer scientists who have a particular interest in symbolic computation. The journal provides a forum for research in the algorithmic treatment of all types of symbolic objects: objects in formal languages (terms, formulas, programs); algebraic objects (elements in basic number domains, polynomials, residue classes, etc.); and geometrical objects. It is the explicit goal of the journal to promote the integration of symbolic computation by establishing one common avenue of communication for researchers working in the different subareas. It is also important that the algorithmic achievements of these areas should be made available to the human problem-solver in integrated software systems for symbolic computation. To help this integration, the journal publishes invited tutorial surveys as well as Applications Letters and System Descriptions.