Definition:Symmetric Polynomial

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

A polynomial $f \in K[X_1,\ldots,X_n]$ is symmetric if for every permutation $\pi$ of $\{1,\ldots,n\}$:


 * $f(X_1,\ldots,X_n) = f(X_{\pi(1)},\ldots,X_{\pi(n)})$