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Elementary Symmetric Functions

  • Definition: The elementary symmetric functions are some special symmetric polynomials. When there are n variables, they are: s_1 = sum_(over i) [u_i]; s_2 = sum_(i<j) [(u_i)(u_j)]; s_3 = sum_(i<j<k) [(u_i)(u_j)(u_k)]; ... ; s_n = (u_1)(u_2)...(u_n).

    Source: Algebra, second edition by Michael Artin

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