Grbner基的一个应用

An Application of Grbner Bases

固定一个项序,利用Buchberger算法求多项式环S=C[x1,x2,…,xn]上的理想I的Grbner基.根据S上任意多项式f(x1,x2,…,xn)用Grbner基表示时其余项唯一的特点,将其应用到求解多项式方程组问题.实例展示用Grbner基可证明一个联立方程式是无解的.

With a fixed monomial ordering,using Buchberger algorithm,we can find the Grobner bases of ideal I of polynomial ring S = C[x1,x2,…,xn ].Since the reminder of any polynomial f（x1,x2,…,xn）on Sis unique when expressed by Grbner bases,we can apply Grobner bases to problems related to polynomial equations.A system of polynomial equations which has no solution is shown as an example.