实闭域计算的一个实用有效方法

Practical and efficient method for computations over real closed fields

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 。

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.