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BUILT-IN MATHEMATICA SYMBOL
SymmetricReduction
SymmetricReduction[f, {x1, ..., xn}]
gives a pair of polynomials 
in 
such that 
, where 
is the symmetric part and 
is the remainder.
SymmetricReduction[f, {x1, ..., xn}, {s1, ..., sn}]
gives the pair 
with the elementary symmetric polynomials in 
replaced by 
.
Details
- If
is a symmetric polynomial, then 
is the unique polynomial in elementary symmetric polynomials equal to 
, and 
is zero. - If
is not a symmetric polynomial, then the output 
is not unique, but depends on the ordering of its variables. - For a given ordering, a nonsymmetric polynomial
can be expressed uniquely as a sum of its symmetric part 
and a remainder 
that does not contain descending monomials. A monomial 
is called descending if 
. - Changing the ordering of the variables may produce different pairs
. - SymmetricReduction does not check to see that
is a polynomial, and will attempt to symmetrize the polynomial part of 
.
New in 6
