fundamental theorem of symmetric polynomials

Every symmetric polynomialMathworldPlanetmathP(x1,x2,,xn)  in the indeterminates x1,x2,,xn can be expressed as a polynomialMathworldPlanetmathPlanetmathPlanetmathQ(p1,p2,,pn)  in the elementary symmetric polynomials p1,p2,,pn of x1,x2,,xn.  The polynomial Q is unique, its coefficients are elements of the ring determined by the coefficients of P and its degree with respect to p1,p2,,pn is same as the degree of P with respect to x1.

Title fundamental theorem of symmetric polynomials
Canonical name FundamentalTheoremOfSymmetricPolynomials
Date of creation 2013-03-22 19:07:40
Last modified on 2013-03-22 19:07:40
Owner pahio (2872)
Last modified by pahio (2872)
Numerical id 7
Author pahio (2872)
Entry type Theorem
Classification msc 13B25
Classification msc 12F10
Synonym fundamental theorem of symmetric functions