【摘要】 获得了如下齐次对称多项式的分解原理:设f(x)为m次齐次对称多项式,且m≥2,n≥2,如果当x1=…=xn时,有f(x)≡0,那么存在m-2次齐次多项式pi,j(x)(1≤i<j≤n),使得f(x)≡∑1≤i<j≤npi,j(x).(xi-xj)2.利用这个结果并借助于计算机可以给出一大批齐次对称多项式不等式的可读性机器证明.由此结果的证明方法证明了方差平均不等式猜想.更多还原

【Abstract】 In this paper the following factoring principle of homogeneous and symmetric polynomials are obtained.Let f（x） be a homogeneous and symmetric polynomial of degree m,and let m≥2,n≥2,if x₁=…=x_n,we have f（x）≡0,then there exists a homogeneous polynomial p_i,j（x）（1≤i<j≤n） of degree m-2 such that f（x）≡∑1≤i<j≤np_i,j（x）·（x_i-x_j）²is holds.By means of this result and computer,the readable machine proofs for a lot of the inequalities of homogeneous and symmetric polynomials can be obtained.And using the proof of proving this result,a conjecture for inequality of variance mean is proved.更多还原