| 判断有理系数多项式方程是否存在实数解的初等方法 |
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| 作者姓名： | 王蒙 陈玉福 |
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| 作者单位： | 中国科学院大学数学科学学院, 北京 100049 |
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| 基金项目： | 国家自然科学基金(11271363)资助 |
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| 摘 要： | 给出判断有理系数多元多项式方程组是否存在实数解的初等方法,从而证明多元多项式方程组的实解存在性可在有限步内自动判定.基于此,给出判定有理系数多元多项式方程组是否存在实数解的算法.
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| 关 键 词： | 判别式矩阵 判别式序列 数学归纳法 |
| 收稿时间： | 2015-03-18 |
| 修稿时间： | 2015-04-14 |
An elementary method for verifying the existence of real roots of rational polynomial equations |
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| Authors: | WANG Meng CHEN Yufu |
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| Institution: | School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China |
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| Abstract: | In this paper we present an elementary method to decide whether a system of multivariate polynomials with rational coefficients has a real solution. Based on our discussion of the method, an algorithm is shown, which implies that verifying a system of multivariate polynomials with rational coefficients has a real solution can be completed in finite steps. |
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| Keywords: | discriminant matrix discriminant sequence mathematical induction |
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