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