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Computation of differential Chow forms for ordinary prime differential ideals
Li, Wei; Li, Ying-Hong
2016
Source PublicationADVANCES IN APPLIED MATHEMATICS
ISSN0196-8858
Volume72Pages:77-112
AbstractIn 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.
KeywordDifferential Chow form Jacobi bound Characteristic set Single exponential algorithm
DOI10.1016/j.aam.2015.09.004
Language英语
Funding ProjectNational Key Basic Research Project of China[2011CB302400] ; NSFC[60821002] ; NSFC[11301519]
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000366958300004
PublisherACADEMIC PRESS INC ELSEVIER SCIENCE
Citation statistics
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/21625
Collection系统科学研究所
Corresponding AuthorLi, Wei
AffiliationChinese Acad Sci, Acad Math & Syst Sci, KLMM, Beijing 100190, Peoples R China
Recommended Citation
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.
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