# fundamental theorem of symmetric polynomials

Every symmetric polynomial$P(x_{1},\,x_{2},\,\ldots,\,x_{n})$  in the indeterminates $x_{1},\,x_{2},\,\ldots,\,x_{n}$ can be expressed as a polynomial$Q(p_{1},\,p_{2},\,\ldots,\,p_{n})$  in the elementary symmetric polynomials $p_{1},\,p_{2},\,\ldots,\,p_{n}$ of $x_{1},\,x_{2},\,\ldots,\,x_{n}$.  The polynomial $Q$ is unique, its coefficients are elements of the ring determined by the coefficients of $P$ and its degree with respect to $p_{1},\,p_{2},\,\ldots,\,p_{n}$ is same as the degree of $P$ with respect to $x_{1}$.

Title fundamental theorem of symmetric polynomials FundamentalTheoremOfSymmetricPolynomials 2013-03-22 19:07:40 2013-03-22 19:07:40 pahio (2872) pahio (2872) 7 pahio (2872) Theorem msc 13B25 msc 12F10 fundamental theorem of symmetric functions