Wolfram Language & System 11.0 (2016)|Legacy Documentation

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gives the k^(th) elementary symmetric polynomial in the variables x1,,xn.


  • A symmetric polynomial of n variables {x1,,xn} is invariant under any permutation of its variables. The k^(th) elementary symmetric polynomial is the sum of all square-free monomials of degree k.
  • The degree k must satisfy 0kn.
  • The elementary symmetric polynomials form a basis for the symmetric polynomials.
  • Expressing a general symmetric polynomial in terms of elementary symmetric polynomials is accomplished by using SymmetricReduction.
Introduced in 2007