\begin{definition}[Definition:Elementary Symmetric Polynomial]
Let $K$ be a field.
Let $K \sqbrk {X_1, \ldots, X_n}$ be the ring of polynomial forms over $K$.
The '''elementary symmetric polynomials in $n$ variables''' are:
:$\ds \map {f_r} {X_1, \ldots, X_n} = \sum_{1 \mathop \le i_1 \mathop < \cdots \mathop < i_r \mathop \le n} x_{i_1} \cdots x_{i_r}: \quad r = 1, \ldots, n$
Category:Definitions/Polynomial Theory
\end{definition}