Positive polynomials and hyperdeterminants
Let be a homogeneous real polynomial of even degree in any number of variables. We consider the problem of giving explicit conditions on the coefficients so that is positive definite or positive semi-definite. In this note we produce a necessary condition for positivity, and a sufficient condition for non-negativity, in terms of positivity or semi-positivity of a one-variable of . Also, we revisit the known sufficient condition in terms of Hankel matrices.