Apparent singularities of D-finite systems

doi:10.1016/j.jsc.2019.02.009

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	Apparent singularities of D-finite systems
	Chen, Shaoshi2,3 ; Kauers, Manuel 4; Li, Ziming2,3 ; Zhang, Yi 1,5
刊名	JOURNAL OF SYMBOLIC COMPUTATION
	2019-11-01
卷号	95 页码:217-237
关键词	D-finite system Grobner basis Ordinary point Formal power series Apparent singularity Desingularization
ISSN号	0747-7171
DOI	10.1016/j.jsc.2019.02.009
英文摘要	We generalize the notions of ordinary points and singularities from linear ordinary differential equations to D-finite systems. Ordinary points and apparent singularities of a D-finite system are characterized in terms of its formal power series solutions. We also show that apparent singularities can be removed like in the univariate case by adding suitable additional solutions to the system at hand. Several algorithms are presented for removing and detecting apparent singularities. In addition, an algorithm is given for computing formal power series solutions of a D-finite system at apparent singularities. (C) 2019 Elsevier Ltd. All rights reserved.
资助项目	NSFC[11771433] ; NSFC[11871067] ; NSFC[11501552] ; NSFC[11688101] ; Frontier Key Project[QYZDJ-SSW-SYS022] ; Fund of the Youth Innovation Promotion Association, CAS ; Austrian Science Fund (FWF)[F50-04] ; Austrian Science Fund (FWF)[Y464-N18] ; Austrian Science Fund (FWF)[P29467-N32]
WOS研究方向	Computer Science ; Mathematics
语种	英语
出版者	ACADEMIC PRESS LTD- ELSEVIER SCIENCE LTD
WOS记录号	WOS:000470955400013
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/34971]
专题	系统科学研究所
通讯作者	Chen, Shaoshi
作者单位	1.Austrian Acad Sci, RICAM, Linz, Austria 2.Chinese Acad Sci, Acad Math & Syst Sci, KLMM, Beijing 100190, Peoples R China 3.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China 4.Johannes Kepler Univ Linz, Inst Algebra, Linz, Austria 5.Univ Texas Dallas, Dept Math Sci, Richardson, TX 75083 USA
推荐引用方式 GB/T 7714	Chen, Shaoshi,Kauers, Manuel,Li, Ziming,et al. Apparent singularities of D-finite systems[J]. JOURNAL OF SYMBOLIC COMPUTATION,2019,95:217-237.
APA	Chen, Shaoshi,Kauers, Manuel,Li, Ziming,&Zhang, Yi.(2019).Apparent singularities of D-finite systems.JOURNAL OF SYMBOLIC COMPUTATION,95,217-237.
MLA	Chen, Shaoshi,et al."Apparent singularities of D-finite systems".JOURNAL OF SYMBOLIC COMPUTATION 95(2019):217-237.