Journal of University of Chinese Academy of Sciences >
An elementary method for verifying the existence of real roots of rational polynomial equations
Received date: 2015-03-18
Revised date: 2015-04-14
Online published: 2016-01-15
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.
WANG Meng , CHEN Yufu . An elementary method for verifying the existence of real roots of rational polynomial equations[J]. Journal of University of Chinese Academy of Sciences, 2016 , 33(1) : 23 -30 . DOI: 10.7523/j.issn.2095-6134.2016.01.004
[1] Cox D A, Little J, O'Shea D. Ideals,varieties,and algorithms[M]. NewYork: Springer, 2007.
[2] 陈玉福. 计算机代数讲义[M].北京:高等教育出版社,2009.
[3] 王东明,夏壁灿,李子明.计算机代数[M].北京:清华大学出版社,2007.
[4] Yang L. Recent advances on determining the number of real roots of parametric polynomials[J]. Journal of Symbolic Computation, 1999, 28(1): 225-242.
[5] Dubé T W. The structure of polynomial ideals and Grobner bases[J]. SIAM Journal on Computing, 1990, 19(4): 750-773.
[6] Tarski A. A decision method for elementary algebra and geometry[M]. 2nd ed. Berkeley: Univ of Calif Press Berkeley, 1951.
[7] Ben-Or M, Kozen D, Reif J. The complexity of elementary algebra and geometry[J]. Journal of Computer and System Sciences, 1984, 32(2): 251-264.
[8] Yang L, Hou X, Xia B. A complete algorithm for automated discovering of a class of inequality-type theorems[J]. Science in China Series F Information Sciences, 2001, 44(1): 33-49.
[9] Mehlhorn K, Sagraloff M. A deterministic algorithm for isolating real roots of a real polynomial[J]. Journal of Symbolic Computation, 2011, 46(1): 70-90.
[10] Cheng J S, Gao X S, Guo L. Root isolation of zero-dimensional polynomial systems with linear univariate representation[J]. Journal of Symbolic Computation, 2012, 47(7): 843-858.
[11] Wang D. Automated deduction in geometry[M]. Berlin: Springer-Verlag, 1998.
[12] Yang L, Hou X R, Zeng Z B. A complete discrimination system for polynomials[J]. 中国科学 E 辑 (英文版), 1996, 6: 8.
/
| 〈 |
|
〉 |