Definition:Elementary Symmetric Polynomial

Definition
Let $K$ be a field and $K[X_1,\ldots,X_n]$ the ring of polynomial forms over $K$.

The elementary symmetric polynomials in $n$ variables are:


 * $\displaystyle f_r(X_1,\ldots,X_n) = \sum_{1 \leq i_1 < \cdots < i_r \leq n}x_{i_1} \cdots x_{i_r},\quad r = 1,\ldots, n$