Practically solving some problems expressed in the first order theory of real closed field

CSpace

	Practically solving some problems expressed in the first order theory of real closed field
	Ma, SL ; Ning, SC
	1998
发表期刊	INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS
ISSN	0020-7160
卷号	69 期号:3-4 页码:265-282
摘要	Many important mathematical and engineering problems can be expressed in the first order theory of real closed field Th(RLC), however any decision method for this theory needs exponential lime even using nondeterministic computation models. Therefore it is desirable to find practical and efficient methods (non-decision methods) of solving problems expressed in this theory. By combining Ritt-Wu' method with Budan-Fourier's theorem, we propose a method to practically solve some problems expressed in this theory. In our method Budan-Fourier's theorem is used to provide information on real roots of polynomial equations and to prove polynomial inequalities to hold, which is simpler and more efficient than Sturm theorem that is used in decision methods for Th(RLC). Our method has been found to efficiently work on many examples in practice though it is incomplete in general. Using our method, we have solved some problems, including deriving some new conditions on the existence of eight limit cycles for a cubic differential system which can not be dealt with using conventional methods because of the complexity of manipulating large polynomials. In this paper we describe our method by presenting some algorithms and examples. C. R. Category. I.1.
关键词	real closed field symbolic computation Ritt-Wu's method Budan-Fourier's theorem
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000084098600005
出版者	GORDON BREACH SCI PUBL LTD
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/13590
专题	中国科学院数学与系统科学研究院
通讯作者	Ning, SC
作者单位	1.Acad Sinica, Inst Math, Beijing 100080, Peoples R China 2.Beijing Univ Aeronaut & Astronaut, Dept Comp Sci, Beijing 100083, Peoples R China
推荐引用方式 GB/T 7714	Ma, SL,Ning, SC. Practically solving some problems expressed in the first order theory of real closed field[J]. INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS,1998,69(3-4):265-282.
APA	Ma, SL,&Ning, SC.(1998).Practically solving some problems expressed in the first order theory of real closed field.INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS,69(3-4),265-282.
MLA	Ma, SL,et al."Practically solving some problems expressed in the first order theory of real closed field".INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS 69.3-4(1998):265-282.