Practically solving some problems expressed in the first order theory of real closed field
文献类型：期刊论文
| 作者 | Ma, SL; Ning, SC |
| 刊名 | INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS
 |
| 出版日期 | 1998 |
| 卷号 | 69期号:3-4页码:265-282 |
| 关键词 | real closed field symbolic computation Ritt-Wu's method Budan-Fourier's theorem |
| ISSN号 | 0020-7160 |
| 英文摘要 | 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. |
| WOS研究方向 | Mathematics |
| 语种 | 英语 |
| WOS记录号 | WOS:000084098600005 |
| 出版者 | GORDON BREACH SCI PUBL LTD |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/13589]  |
| 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. |
入库方式： OAI收割
来源：数学与系统科学研究院
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