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Apparent singularities of D-finite systems
Chen, Shaoshi1,2; Kauers, Manuel3; Li, Ziming1,2; Zhang, Yi4,5
2019-11-01
发表期刊JOURNAL OF SYMBOLIC COMPUTATION
ISSN0747-7171
卷号95页码:217-237
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.
关键词D-finite system Grobner basis Ordinary point Formal power series Apparent singularity Desingularization
DOI10.1016/j.jsc.2019.02.009
语种英语
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
WOS类目Computer Science, Theory & Methods ; Mathematics, Applied
WOS记录号WOS:000470955400013
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/34972
专题系统科学研究所
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, Linz, Austria
4.Austrian Acad Sci, RICAM, 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.
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