有理数域上多项式因子分解的一个注记

A Note on Decomposition of Multivariate Polynomial over Rational Number Field

本文推广了Kronecker一元多项式因子分解的构造性证明，给出了有理数域上多元多项式因子分解的一个构造性证明．把多元多项式因子分解这个非线性问题转化为系列线性问题和多项式的可除性判定，由此给出了有理数域上多元多项式因子分解的一个算法．

In this paper,a constructive proof of decomposition of multivariate polynomial over rational number field,which generalizes Kronecker's result on univariate polynomial,is given. Baed on this result,the nonlinear problem of decomposition of multivariate polynomial is converted into series of linear problem and dedsion of divisibility of polynomial. An algorithm on decomposition of multivariate polynomial over rational number field is found.