Computation of differential Chow forms for ordinary prime differential ideals

doi:10.1016/j.aam.2015.09.004

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	Computation of differential Chow forms for ordinary prime differential ideals
	Li, Wei; Li, Ying-Hong
	2016
发表期刊	ADVANCES IN APPLIED MATHEMATICS
ISSN	0196-8858
卷号	72 页码:77-112
摘要	In this paper, we propose algorithms for computing differential Chow forms for ordinary prime differential ideals which are given by characteristic sets. The algorithms are based on an optimal bound for the order of a prime differential ideal in terms of a characteristic set under an arbitrary ranking, which shows the Jacobi bound conjecture holds in this case. Apart from the order bound, we also give a degree bound for the differential Chow form. In addition, for a prime differential ideal given by a characteristic set under an orderly ranking, a much simpler algorithm is given to compute its differential Chow form. The computational complexity of the algorithms is single exponential in terms of the Jacobi number, the maximal degree of the differential polynomials in a characteristic set, and the number of variables. (C) 2015 Elsevier Inc. All rights reserved.
关键词	Differential Chow form Jacobi bound Characteristic set Single exponential algorithm
DOI	10.1016/j.aam.2015.09.004
语种	英语
资助项目	National Key Basic Research Project of China[2011CB302400] ; NSFC[60821002] ; NSFC[11301519]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000366958300004
出版者	ACADEMIC PRESS INC ELSEVIER SCIENCE
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/21625
专题	系统科学研究所
通讯作者	Li, Wei
作者单位	Chinese Acad Sci, Acad Math & Syst Sci, KLMM, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Li, Wei,Li, Ying-Hong. Computation of differential Chow forms for ordinary prime differential ideals[J]. ADVANCES IN APPLIED MATHEMATICS,2016,72:77-112.
APA	Li, Wei,&Li, Ying-Hong.(2016).Computation of differential Chow forms for ordinary prime differential ideals.ADVANCES IN APPLIED MATHEMATICS,72,77-112.
MLA	Li, Wei,et al."Computation of differential Chow forms for ordinary prime differential ideals".ADVANCES IN APPLIED MATHEMATICS 72(2016):77-112.