| 多变元Sylvester结式与多余因子 |
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| 引用本文： | 赵世忠,符红光. 多变元Sylvester结式与多余因子[J]. 中国科学:数学, 2010, 0(7): 649-660 |
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| 作者姓名： | 赵世忠 符红光 |
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| 作者单位： | [1]华东师范大学上海市高可信计算重点实验室,上海200062 [2]电子科技大学计算机科学与工程学院,成都610054 [3]中国科学院成都计算机应用研究所,成都610041 |
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| 基金项目： | 通信作者圈家重点基础研究发展计划（973计划）（批准号：2004CB318003）、国家自然科学基金（批准号：90718041）以及上海市重点学科建设（批准号：B412）资助项目 |
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| 摘 要： | 经典的Sylvester结式方法是代数几何的一种基本消元方法,但它一次只能处理1个变元2个方程的多项式系统.本文将Sylvester结式扩展到n个变元n+1个方程的多项式系统,并且证明了新的多变元的Sylvester结式包含在原多项式系统的理想中.同时,给出了一种去掉其部分多余因子的方法.
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| 关 键 词： | 多变元Sylvester矩阵 多变元Sylvester结式 多余因子 |
Multivariate Sylvester resultant and extraneous factors |
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| ZHAO ShiZhong ＆ FU HongGuang. Multivariate Sylvester resultant and extraneous factors[J]. Scientia Sinica Mathemation, 2010, 0(7): 649-660 |
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| Authors: | ZHAO ShiZhong ＆ FU HongGuang |
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| Affiliation: | ZHAO ShiZhong ＆ FU HongGuang |
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| Abstract: | Sylvester resultant technique is a basic elimination technique in algebraic geometry, but it can only be used in the system of two polynomial equations with one indeterminate at one time. In this paper, we extend the definition of the Sylvester resultant to a new system of n ＋ 1 polynomial equations with n indeterminates and prove that the new multivariate Sylvester resultant is in the ideal of the original polynomials. Meanwhile, a method of removing its partial extraneous factors is suggested. |
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| Keywords: | multivariate Sylvester matrix multivariate Sylvester resultant extraneous factors |
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