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Un polynôme symétrique est un [[polynomial|polynôme]] $P\in k[X_{1},\ldots,X_{n}]$ tel que, pour tout [[permutation|permutation]] $\sigma \in S_{n}$:
$$P(X_{\sigma(1)},\ldots,X_{\sigma(n)})=P(X_{1},\ldots,X_{n}).$$