Definition:Symmetric Polynomial
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Definition
Let $K$ be a field.
Let $K \sqbrk {X_1, \ldots, X_n}$ be the ring of polynomial forms over $K$.
A polynomial $f \in K \sqbrk {X_1, \ldots, X_n}$ is symmetric if and only if for every permutation $\pi$ of $\set {1, 2, \ldots, n}$:
- $\map f {X_1, \dotsc, X_n} = \map f {X_{\map \pi 1}, \dotsc, X_{\map \pi n} }$
Also see
- Results about symmetric polynomials can be found here.