# polarization by differential operators

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

Title polarization by differential operators PolarizationByDifferentialOperators 2013-03-22 17:37:26 2013-03-22 17:37:26 rspuzio (6075) rspuzio (6075) 6 rspuzio (6075) Definition msc 16R99 msc 15A69 msc 15A63 msc 17A99