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 $\Delta^k p(x_1, \ldots x_n)$