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A New Algorithm for Computing the Extended Hensel Construction of Multivariate Polynomials

文献类型：期刊论文

作者Lu Dong1,2; Sun Yao3; Wang Dingkang1,2
刊名JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY
出版日期2018-12-01
卷号31期号:6页码:1633-1646
关键词Extended Hensel construction multivariate polynomial resultant sylvester matrix
ISSN号1009-6124
DOI10.1007/s11424-018-6445-0
英文摘要This 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.
WOS研究方向Mathematics
语种英语
WOS记录号WOS:000452723900015
出版者SPRINGER HEIDELBERG
源URL[http://ir.amss.ac.cn/handle/2S8OKBNM/31875]  
专题系统科学研究所
通讯作者Lu Dong
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.Chinese Acad Sci, Inst Informat Engn, SKLOIS, Beijing 100093, Peoples R China
推荐引用方式
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.

入库方式： OAI收割

来源：数学与系统科学研究院

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