PlanetMath: symmetric polynomial

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symmetric polynomial

(Definition)

A polynomial $f \in R[x_1, \dots, x_n]$ in variables with coefficients in a ring is symmetric if $\sigma(f) = f$ for every permutation $\sigma$ of the set $\{x_1, \dots, x_n\}$ .

Every symmetric polynomial can be written as a polynomial expression in the elementary symmetric polynomials.

"symmetric polynomial" is owned by djao.

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Cross-references: elementary symmetric polynomials, expression, permutation, symmetric, ring, coefficients, variables, polynomial
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This is version 3 of symmetric polynomial, born on 2002-01-05, modified 2004-02-02.
Object id is 1337, canonical name is SymmetricPolynomial.
Accessed 4786 times total.

Classification:

AMS MSC:	13B25 (Commutative rings and algebras :: Ring extensions and related topics :: Polynomials over commutative rings)
	12F10 (Field theory and polynomials :: Field extensions :: Separable extensions, Galois theory)

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