多项式隐函数在一点邻域里的近似显式算法

The Algorithm of Approximated Explicit of Polynomial Implicit Mapping in A Neighborhood of A Given Point

利用隐函数定理和Ｗｕ－Ｒｉｔｔ方法给出了多项式隐函数在一点邻域内的一种近似显式算法，并给出了根据要求精度计算邻域半径和迭代次数的关系式．使得这种算法的误差具有可控性，计算量小，容易上机实现，在理想的近似参数化及近似定理证明中有进一步的应用．

Based on implicit mapping theorem and Wu Ritt method, an approximated explicit algorithm of polynomial implicit mapping is given in a neighborhood of a given point, and formulas of computing the radius of neighborhood and iterative times are presented according to the required precision. This makes the error of the algorithm controllable and implementation easy. It is useful in approximated parametrization of ideal and approximated theorem proving.