On the existence of telescopers for rational functions in three variables

doi:10.1016/j.jsc.2020.08.006

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	On the existence of telescopers for rational functions in three variables
	Chen, Shaoshi 1,2; Du, Lixin 1,2,3; Wang, Rong-Hua 4; Zhu, Chaochao 1,2
	2021-05-01
发表期刊	JOURNAL OF SYMBOLIC COMPUTATION
ISSN	0747-7171
卷号	104 页码:494-522
摘要	Zeilberger's method of creative telescoping is crucial for the computer-generated proofs of combinatorial and special-function identities. Telescopers are linear differential or (q-)recurrence operators computed by algorithms for creative telescoping. Two fundamental problems related to creative telescoping are whether telescopers exist, and how to construct them efficiently when they do. In this paper, we solve the existence problem of telescopers for rational functions in three variables including 18 cases. We reduce the existence problem from the trivariate case to the bivariate case and some related problems. The existence criteria given in this paper enable us to determine the termination of algorithms for creative telescoping with trivariate rational inputs. (C) 2020 Elsevier Ltd. All rights reserved.
关键词	Creative telescoping Existence criterion Reduction Telescoper
DOI	10.1016/j.jsc.2020.08.006
收录类别	SCI
语种	英语
WOS研究方向	Computer Science ; Mathematics
WOS类目	Computer Science, Theory & Methods ; Mathematics, Applied
WOS记录号	WOS:000598670000025
出版者	ACADEMIC PRESS LTD- ELSEVIER SCIENCE LTD
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/57892
专题	中国科学院数学与系统科学研究院
通讯作者	Chen, Shaoshi
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, KLMM, Beijing 100190, Peoples R China 2.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China 3.Johannes Kepler Univ Linz, Inst Algebra, A-4040 Linz, Austria 4.Tiangong Univ, Sch Math Sci, Tianjin 300387, Peoples R China
推荐引用方式 GB/T 7714	Chen, Shaoshi,Du, Lixin,Wang, Rong-Hua,et al. On the existence of telescopers for rational functions in three variables[J]. JOURNAL OF SYMBOLIC COMPUTATION,2021,104:494-522.
APA	Chen, Shaoshi,Du, Lixin,Wang, Rong-Hua,&Zhu, Chaochao.(2021).On the existence of telescopers for rational functions in three variables.JOURNAL OF SYMBOLIC COMPUTATION,104,494-522.
MLA	Chen, Shaoshi,et al."On the existence of telescopers for rational functions in three variables".JOURNAL OF SYMBOLIC COMPUTATION 104(2021):494-522.