Let K:=x:g(x)≤1 be the compact sub-level set of some homogeneous
polynomial g. Assume that the only knowledge about K is the degree of g
as well as the moments of the Lebesgue measure on K up to order 2d. Then the
vector of coefficients of g is solution of a simple linear system whose
associated matrix is nonsingular. In other words, the moments up to order 2d of
the Lebesgue measure on K encode all information on the homogeneous
polynomial g that defines K (in fact, only moments of order d and 2d are
needed)