关于对称多项式的构造及其应用

On Constructions and Applications of Symmetric Polynomials

通过构造对称式和轮换对称式的一般表示式,借助于Maple应用程序,研究了3元到15元的对称多项式的缺项多项式、轮换对称代换缺项多项式、Si类对称多项式及Si类差分代换缺项多项式的通式构造,并对多元多项式的平方分拆进行了探讨.

General expressions for constructing symmetric polynomials are proposed. In Maple, 3 to 15-term symmetric polynomials, permute symmetric polynomials, Si symmetric polynomials and Si differential substitution polynomials with sparse terms have been constructed. Multiple-term polynomials have been studied in square decomposition.