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

doi:10.1007/s11424-018-6445-0

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	A New Algorithm for Computing the Extended Hensel Construction of Multivariate Polynomials
	Lu Dong 1,2; Sun Yao 3; Wang Dingkang1,2
	2018-12-01
发表期刊	JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY
ISSN	1009-6124
卷号	31 期号:6 页码:1633-1646
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.
关键词	Extended Hensel construction multivariate polynomial resultant sylvester matrix
DOI	10.1007/s11424-018-6445-0
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Interdisciplinary Applications
WOS记录号	WOS:000452723900015
出版者	SPRINGER HEIDELBERG
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/31876
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.