| 实闭域计算的一个实用有效方法 |
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| 引用本文： | 马世龙.实闭域计算的一个实用有效方法[J].北京航空航天大学学报,2003,29(10):847-851. |
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| 作者姓名： | 马世龙 |
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| 作者单位： | 北京航空航天大学 计算机学院, 北京 100083 |
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| 基金项目： | 国家重点基础研究发展计划(973计划);G1999032701; |
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| 摘 要： | 在计算实践中,处理大型多项式时,由于复杂性原因,实闭域一阶理论判定方法实际上无效.因此寻找求解多项式方程与不等式组的有效方法(未必是判定方法)是符号计算中的重要问题.为解决这一问题,将Budan-Fourier 定理与Ritt-Wu 方法结合提出确定多项式方程实根和证明不等式的简单有效方法.尽管该方法不完备,但是在计算实践中发现这一方法对许多例子在计算上很有效.
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| 关 键 词： | 符号计算 多项式方程 多项式不等式 |
| 文章编号： | 1001-5965(2003)10-0847-05 |
| 收稿时间： | 2003-06-05 |
| 修稿时间： | 2003年6月5日 |
Practical and efficient method for computations over real closed fields |
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| Ma Shilong.Practical and efficient method for computations over real closed fields[J].Journal of Beijing University of Aeronautics and Astronautics,2003,29(10):847-851. |
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| Authors: | Ma Shilong |
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| Institution: | School of Computer Science and Technology, Beijing University of Aeronautics and Astronautics, Beijing 100083, China |
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| Abstract: | The conventional methods do not work in practice when dealing with large polynomials because of their high complexity. Thus, finding practical and efficient methods (not necessary to be decision method) to solve systems of large polynomial equations and inequalities is very important in symbolic computation. Ritt Wu's method was combined with Budan Fourier's theorem to do such task. Though incomplete for the problems in general, the proposed method was found to be computationally more efficient in practice on many examples. |
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| Keywords: | symbolic computation polynomial equation polynomial inequality |
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