SymmetricPolynomial

SymmetricPolynomial[k,{x1,,xn}]

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

Details

  • 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.

Examples

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Basic Examples  (1)

The elementary symmetric polynomial of degree 3 in variables x1,x2,x3,x4:

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Scope  (1)

Applications  (1)

Properties & Relations  (4)

Neat Examples  (1)

See Also

SymmetricReduction  PolynomialReduce  Subsets

Tutorials

Introduced in 2007
(6.0)