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Upgrading from:

Algebra`SymmetricPolynomials`

New functions SymmetricPolynomial and SymmetricReduction have been added to the built-in Mathematica kernel.

The degree of the polynomial is now given as the first argument for SymmetricPolynomial:

Version 5.2 << Algebra`SymmetricPolynomials`; SymmetricPolynomial[{x, y, z, t}, 3]
Wolfram Language code: SymmetricPolynomial[3, {x, y, z, t}]

SymmetricReduction is now a built-in function:

Version 5.2 SymmetricReduction[(x + y)^2 + (x + z)^2 + (z + y)^2, {x, y, z}]
Wolfram Language code: SymmetricReduction[(x + y) ^ 2 + (x + z) ^ 2 + (z + y) ^ 2, {x, y, z}]