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›› 2016, Vol. 33 ›› Issue (1): 23-30.DOI: 10.7523/j.issn.2095-6134.2016.01.004

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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 Online:2016-01-15

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

CLC Number: