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中国科学院大学学报 ›› 2016, Vol. 33 ›› Issue (1): 23-30.DOI: 10.7523/j.issn.2095-6134.2016.01.004

• 数学与物理学 • 上一篇    下一篇

判断有理系数多项式方程是否存在实数解的初等方法

王蒙, 陈玉福   

  1. 中国科学院大学数学科学学院, 北京 100049
  • 收稿日期:2015-03-18 修回日期:2015-04-14 发布日期:2016-01-15
  • 通讯作者: 王蒙
  • 基金资助:

    国家自然科学基金(11271363)资助

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

WANG Meng, CHEN Yufu   

  1. School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
  • Received:2015-03-18 Revised:2015-04-14 Published:2016-01-15

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.

关键词: 判别式矩阵, 判别式序列, 数学归纳法

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.

Key words: discriminant matrix, discriminant sequence, mathematical induction

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