多项式方程组的主项解耦消元法

本文提出多项式组符号求解的主项解耦 (主项只含主元 )消元法 :视多项式为变元不同幂积的线性组合 ,以主项解耦三角型多项式组 DTS为引导 ,用逐项伪除求余式 ,将多项式组 PS化为与其同解的 DTS.内容涉及 :消元算法、DTS的存在性与结构特性、零点集结构公式等 .亦对 Grobner基法、吴文俊消元法与本文方法之间的相互联系、区别以及特点进行了比较 .研究表明主项解耦消元法适用于一般多项式组且效率较高

An Elimination Method With Decoupling of Leading Terms for Polynomial Set

This paper presents an elimination method with decoupling of leading terms for polynomial set. A polynomial is considered to be a linear combination of power products of variables. Using the term by term Euclidean Algorithm for polynomials, an original polynomial set PS could be translated into an triangular polynomial set DTS with decoupling of leading terms and both are equivalent eguation sets.;This method synthesises the strong points of Grobner basis elimination, Wu elimsnation and linear elimination and so that is suitable to solve efficiently general polynomial set. and it can be used for determining types and exiting conditions of solutions of a polynomial set.