Abstract: Making use of the flexibility of the combination resultant method, rapid elimination and the diversity of combination resultant derived polynomial, the author proposed an improved algorithm of constructing Bezout matrix, and the combination resultant method was applied in solving the nonlinear equations, inferring unknown relationship, parametric curve and surface implicitization, structural triangular column, etc. Compared with the original method to solve the problems by examples, combination resultant method is more simple and feasible.

Key words: combination resultant, Dixon resultant, Bezout resultant, Dixon polynomial, combination resultant method

摘要： 利用组合结式方法的灵活性、快速消元和组合结式导出多项式的多样性等特点,提出了构造Bezout矩阵的改进算法,并把组合结式方法应用在求解非线性方程组、推导未知关系、参数曲线与曲面的隐式化、构造三角列等方面。通过实例验证,组合结式方法比原方法简单。

关键词: 组合结式, Dixon结式, Bezout结式, Dixon多项式, 组合结式方法