fundamental theorem of symmetric polynomials

Every symmetric polynomial  $P(x_1,x_2,\mathrm{\dots },x_n)$  in the indeterminates $x_1,x_2,\mathrm{\dots },x_n$ can be expressed as a polynomial  $Q(p_1,p_2,\mathrm{\dots },p_n)$  in the elementary symmetric polynomials $p_1,p_2,\mathrm{\dots },p_n$ of $x_1,x_2,\mathrm{\dots },x_n$.  The polynomial $Q$ is unique, its coefficients are elements of the ring determined by the coefficients of $P$ and its degree with respect to $p_1,p_2,\mathrm{\dots },p_n$ is same as the degree of $P$ with respect to $x_1$.

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