多项式组的结式理论

RESULTANT THEORY OF POLYNOMIAL SYSTEM

目前求解两个一元多项式最大公因式的典型方法是辗转相除法和张三元、汪国昭的方法．虽然张、汪的方法比起辗转相除法具有存储量和运算时间均较小等特点，但它的运算速度仍较低．这是由于它需计算许多行列式的缘故．本文引入了一元和二元多项式组的结多项式的概念并讨论了它们的性质．从而开辟了一条求解多项式最大公因式的新途径．

The current typical methods for finding the greatest common factors of two onevariable polynomials are division algorithm and Zhang Sanyuan and Wang Guozhao's Methods. Although the second method needs less storage capacity and computing time and so on than the first method. It is high time costing since it need to compute many determinant. In this paper, we introduce the concept of resultant polynomials on onevariable and twovariable polynomial systems and discuss their properties. Thereby we break a new path to find the greatest common factor of polynomials.