# polarization by differential operators

One can construct the polars of a polynomial^{} by means of a differential
operator. Suppose we have a homogeneous polynomial^{} $p({x}_{1},\mathrm{\dots},{x}_{n})$.
To compute the polars of $p$ we act on it with the operator
$\mathrm{\Delta}={y}_{1}\partial /\partial {x}_{1}+\mathrm{\cdots}+{y}_{n}\partial /\partial {x}_{n}$; the $k$-th polar of $p$ equals ${\mathrm{\Delta}}^{k}p({x}_{1},\mathrm{\dots}{x}_{n})$.

Title | polarization by differential operators |
---|---|

Canonical name | PolarizationByDifferentialOperators |

Date of creation | 2013-03-22 17:37:26 |

Last modified on | 2013-03-22 17:37:26 |

Owner | rspuzio (6075) |

Last modified by | rspuzio (6075) |

Numerical id | 6 |

Author | rspuzio (6075) |

Entry type | Definition |

Classification | msc 16R99 |

Classification | msc 15A69 |

Classification | msc 15A63 |

Classification | msc 17A99 |