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A New Algorithm for Computing the Extended Hensel Construction of Multivariate Polynomials
Lu Dong1,2; Sun Yao3; Wang Dingkang1,2
2018-12-01
Source PublicationJOURNAL OF SYSTEMS SCIENCE & COMPLEXITY
ISSN1009-6124
Volume31Issue:6Pages:1633-1646
AbstractThis paper presents a new algorithm for computing the extended Hensel construction (EHC) of multivariate polynomials in main variable x and sub-variables u1, u2, center dot center dot center dot, um over a number field K. This algorithm first constructs a set by using the resultant of two initial coprime factors w. r. t. x, and then obtains the Hensel factors by comparing the coefficients of x i on both sides of an equation. Since the Hensel factors are polynomials of the main variable with coefficients in fraction field K(u1, u2, center dot center dot center dot, um), the computation cost of handling rational functions can be high. Therefore, the authors use a method which multiplies resultant and removes the denominators of the rational functions. Unlike previously-developed algorithms that use interpolation functions or Gr obner basis, the algorithm relies little on polynomial division, and avoids multiplying by different factors when removing the denominators of Hensel factors. All algorithms are implemented using Magma, a computational algebra system and experiments indicate that our algorithm is more efficient.
KeywordExtended Hensel construction multivariate polynomial resultant sylvester matrix
DOI10.1007/s11424-018-6445-0
Language英语
WOS Research AreaMathematics
WOS SubjectMathematics, Interdisciplinary Applications
WOS IDWOS:000452723900015
PublisherSPRINGER HEIDELBERG
Citation statistics
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/31876
Collection系统科学研究所
Affiliation1.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.Chinese Acad Sci, Inst Informat Engn, SKLOIS, Beijing 100093, Peoples R China
Recommended Citation
GB/T 7714
Lu Dong,Sun Yao,Wang Dingkang. A New Algorithm for Computing the Extended Hensel Construction of Multivariate Polynomials[J]. JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY,2018,31(6):1633-1646.
APA Lu Dong,Sun Yao,&Wang Dingkang.(2018).A New Algorithm for Computing the Extended Hensel Construction of Multivariate Polynomials.JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY,31(6),1633-1646.
MLA Lu Dong,et al."A New Algorithm for Computing the Extended Hensel Construction of Multivariate Polynomials".JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY 31.6(2018):1633-1646.
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