判断有理系数多项式方程是否存在实数解的初等方法  

An elementary method for verifying the existence of real roots of rational polynomial equations

作　　者：王蒙[1] 陈玉福[1] 

机构地区：[1]中国科学院大学数学科学学院,北京100049

出　　处：《中国科学院大学学报（中英文）》2016年第1期23-30,共8页Journal of University of Chinese Academy of Sciences

基　　金：国家自然科学基金(11271363)资助

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.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.

关 键 词：判别式矩阵 判别式序列 数学归纳法 

分 类 号：O151.1[理学—数学] O141.2[理学—基础数学]