anewalgorithmforcomputingtheextendedhenselconstructionofmultivariatepolynomials

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	anewalgorithmforcomputingtheextendedhenselconstructionofmultivariatepolynomials
	Lu Dong 1; Sun Yao 2; Wang Dingkang1
	2018
发表期刊	journalofsystemssciencecomplexity
ISSN	1009-6124
卷号	31 期号:6 页码:1633
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.
语种	英语
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/37099
专题	系统科学研究所
作者单位	1.中国科学院数学与系统科学研究院 2.中国科学院信息工程研究所
推荐引用方式 GB/T 7714	Lu Dong,Sun Yao,Wang Dingkang. anewalgorithmforcomputingtheextendedhenselconstructionofmultivariatepolynomials[J]. journalofsystemssciencecomplexity,2018,31(6):1633.
APA	Lu Dong,Sun Yao,&Wang Dingkang.(2018).anewalgorithmforcomputingtheextendedhenselconstructionofmultivariatepolynomials.journalofsystemssciencecomplexity,31(6),1633.
MLA	Lu Dong,et al."anewalgorithmforcomputingtheextendedhenselconstructionofmultivariatepolynomials".journalofsystemssciencecomplexity 31.6(2018):1633.