局部对称多项式线性空间初探

The Primary Exploration into the Linear Space of the Local Symmetric Polynomial

对4元-2元对称多项式和4元-3元对称多项式线性空间进行了初步探讨;给出了3元和4元轮换对称多项式线性空间维数的计算公式;讨论了实数范围内多项式半正定分拆证明问题;提出了两个待解决的问题.

In this paper, we make a primary exploration into symmetrical polynomial in quaternarybinary form as well as linear space of symmetrical polynomial in quaternary-ternary form, and give a count formation about the dimensions of linear space of cycle symmetrical polynomial in ternary-quaternary form. Besides, we also discuss the proof about the semi-definite partition of a polynomial in real space and pose two open problems.