| 解仿射多项式系统的结式消元法 |
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| 引用本文： | 罗洪勇,刘卫江.解仿射多项式系统的结式消元法[J].吉林大学学报(理学版),1998(4). |
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| 作者姓名： | 罗洪勇 刘卫江 |
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| 作者单位： | 吉林大学数学研究所(罗洪勇)，锦州师范学院信息技术系(刘卫江) |
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| 摘 要： | 在仿射变换下给出一种结式消元法的充要条件，并由此给出解仿射多项式系统的变换消元法．利用变换消元法可以把代数簇分解成纯ｄ维的子簇，并把代数簇表示为ｄ＋１维子空间上的超曲面形式和一系列的消元多项式组，且能求出全部孤立解，同时给出了算法及其在多项式因式分解中的应用
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| 关 键 词： | 仿射多项式，结式组，含幺交换环，唯一分解环，代数闭域 |
The Resultant Elimination Mothod for Solving Affine Polynomials System |
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| Luo Hongyong.The Resultant Elimination Mothod for Solving Affine Polynomials System[J].Journal of Jilin University: Sci Ed,1998(4). |
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| Authors: | Luo Hongyong |
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| Abstract: | The present paper presents the necessary and sufficient condition of the resultant elimination method under affine change, on the basis of which a substitution elimination method is given for solving affine polynomials system. Using the substitution elimination method affine algebraic variety can be resolved to pure d dimensional subvariety and expressed by an algebraic hypersurface on d 1 dimensional space with a sequence of elimination polynomial systems. All 0 dimensional solution can be found, too. |
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| Keywords: | affine polynomial resultant system commutative ring with identity unique factorization domain algebraically closed field |
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