# symmetric polynomial

A polynomial^{} $f\in R[{x}_{1},\mathrm{\dots},{x}_{n}]$ in $n$ variables^{} with coefficients in a ring $R$ is symmetric^{} if $\sigma (f)=f$ for every permutation^{} $\sigma $ of the set $\{{x}_{1},\mathrm{\dots},{x}_{n}\}$.

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

Title | symmetric polynomial |
---|---|

Canonical name | SymmetricPolynomial |

Date of creation | 2013-03-22 12:08:55 |

Last modified on | 2013-03-22 12:08:55 |

Owner | djao (24) |

Last modified by | djao (24) |

Numerical id | 7 |

Author | djao (24) |

Entry type | Definition |

Classification | msc 13B25 |

Classification | msc 12F10 |