  Let $I$ be a homogeneous ideal in $R=\mathbb K[x_0,\ldots,x_n]$, such that
$R/I$ is an Artinian Gorenstein ring. A famous theorem of Macaulay says that in
this instance $I$ is the ideal of polynomial differential operators with
constant coefficients that cancel the same homogeneous polynomial $F$. A major
question related to this result is to be able to describe $F$ in terms of the
ideal $I$. In this note we give a partial answer to this question, by analyzing
the case when $I$ is the Artinian reduction of the ideal of a reduced
(arithmetically) Gorenstein zero-dimensional scheme $\Gamma\subset\mathbb P^n$.
We obtain $F$ from the coordinates of the points of $\Gamma$.
