近似定理证明中的退化条件

Catagenesis Condition for Approximate Theorem-proving

复数域上近似定理证明的方法 :首先将一个初等命题转变为多项式的零点问题 ,然后在一个更大的域上将此理想分解为一些正规分支的交 .算法可快速判定命题在忽略一个低维部分的真假 .分析了此算法的复杂度 ,对相伴多项式 (退化条件 )的次数进行估计并与已有结果进行比较 .

The procedure of approximate theorem-proving over complex number system is as follows.Firstly,an elementary sentence is transformed to zero problem of ideal of polynomials.Then the ideal is decomposed,over a bigger field,into the intersection of some ideals which have a simpler form and are called normal components.This algorithm provides an efficient way to decide if a sentence over complex number system is true except a lower dimension part.The authors achieved the algorithm for the approximate theorem-proving over complex number system,analysed its complexity, estimated the degree of the associate polynomials(catagenesis condition),and compared the results with that of the Wu-method.