Practical and efficient method for computations over real closed fields
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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.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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Key words:
- symbolic computation /
- polynomial equation /
- polynomial inequality
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