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A symmetric polynomial is a polynomial in several variables which is not changed after any permutation of variables. An important result about symmetric polynomials is the possibility to express any symmetric polynomial using elementary symmetric polynomials. Symmetric polynomials are useful, e.g., in connection with roots of polynomials (Vieta formulae). Another useful result concerns the Newton-Girard formulae, which expresses power sums in terms of elementary symmetric polynomials.

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