多项式方程组符号求解的主项解耦消元法

提出多项式组符号求解的主项解耦消元法：视多项式为变元不同幂乘积的线性组合，以主项解耦三角型多项式组为引导，用逐项伪除法求余式，将原多项式组化为与其同解的主项解耦三角型多项式组。该法综合了Grobner基法、吴氏消元法和线性变换消元法等方法的长处，适用于求解一般多项式组，且计算效率较高；又易用于研究多项式组解的类型及其存在条件。文中给出两例，其一较详细地讨论了3个二元二次完全多项式组解的类型及其存在条件。

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 ascending polynomial set DTS with decoupling of leading terms and both are equivalent equation sets. This method synthesises the strong points of Grobner basis elimination, Wu elimination and linear elimination and so it is suitable for solving efficiently general polynomial set. And it can be used for determining types and existing conditions of solutions of a polynomial set.