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

DOI: 10.7523/j.issn.2095-6134.2016.01.004

Keywords: 判别式矩阵,判别式序列,数学归纳法
discriminant matrix,discriminant sequence,mathematical induction

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Abstract:

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.

References

[1]	Yang L. Recent advances on determining the number of real roots of parametric polynomials[J]. Journal of Symbolic Computation, 1999, 28(1): 225-242.
[2]	Dubé T W. The structure of polynomial ideals and Grobner bases[J]. SIAM Journal on Computing, 1990, 19(4): 750-773.
[3]	Tarski A. A decision method for elementary algebra and geometry[M]. 2nd ed. Berkeley: Univ of Calif Press Berkeley, 1951.
[4]	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.
[5]	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.
[6]	陈玉福. 计算机代数讲义[M].北京:高等教育出版社,2009.
[7]	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.
[8]	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.
[9]	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.
[10]	Wang D. Automated deduction in geometry[M]. Berlin: Springer-Verlag, 1998.
[11]	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.</p>
[12]	<p> Cox D A, Little J, O'Shea D. Ideals,varieties,and algorithms[M]. NewYork: Springer, 2007.

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