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Lu Dong1; Sun Yao2; Wang Dingkang1
Source Publicationjournalofsystemssciencecomplexity
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.
Document Type期刊论文
Recommended Citation
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.
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