onfunctionaldecompositionofmultivariatepolynomialswithdifferentiationandhomogenization

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	onfunctionaldecompositionofmultivariatepolynomialswithdifferentiationandhomogenization
	Zhao Shangwei 1; Feng Ruyong2 ; Gao Xiaoshan2
	2012
发表期刊	journalofsystemsscienceandcomplexity
ISSN	1009-6124
卷号	025 期号:002 页码:329
摘要	This paper gives a theoretical analysis for the algorithms to compute functional decomposition for multivariate polynomials based on differentiation and homogenization which were proposed by Ye, Dai, and Lam （1999） and were developed by Faugere, Perret （2006, 2008, 2009）. The authors show that a degree proper functional decomposition for a set of randomly decomposable quartic homoge- nous polynomials can be computed using the algorithm with high probability. This solves a conjecture proposed by Ye, Dal, and Lam （1999）. The authors also propose a conjecture which asserts that the decomposition for a set of polynomials can be computed from that of its homogenization and show that the conjecture is valid with high probability for quartic polynomials. Finally, the authors prove that the right decomposition factors for a set of polynomials can be computed from its right decomposition factor space.
语种	英语
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/46230
专题	系统科学研究所
作者单位	1.北京电子科技学院 2.中国科学院数学与系统科学研究院
推荐引用方式 GB/T 7714	Zhao Shangwei,Feng Ruyong,Gao Xiaoshan. onfunctionaldecompositionofmultivariatepolynomialswithdifferentiationandhomogenization[J]. journalofsystemsscienceandcomplexity,2012,025(002):329.
APA	Zhao Shangwei,Feng Ruyong,&Gao Xiaoshan.(2012).onfunctionaldecompositionofmultivariatepolynomialswithdifferentiationandhomogenization.journalofsystemsscienceandcomplexity,025(002),329.
MLA	Zhao Shangwei,et al."onfunctionaldecompositionofmultivariatepolynomialswithdifferentiationandhomogenization".journalofsystemsscienceandcomplexity 025.002(2012):329.