SymmetricPolynomial 2002-01-05 04:42:59 2004-02-02 17:33:05 Definition \usepackage{amssymb} \usepackage{amsmath} \usepackage{amsfonts} \usepackage{graphicx} \usepackage{xypic} A polynomial $f \in R[x_1, \dots, x_n]$ in $n$ variables with coefficients in a ring $R$ is {\em symmetric} if $\sigma(f) = f$ for every permutation $\sigma$ of the set $\{x_1, \dots, x_n\}$. Every symmetric polynomial can be written as a polynomial expression in the elementary symmetric polynomials.