Let p be a quadratic multivariate polynomial in Sage, for example
sage: R.<x,y,z> = QQ[]
sage: p = -x^2 - y^2 - z^2 + x*y + x*z + y*z
sage: q = -x^2 - y^2 - z^2 + 3/2 * (x*y + x*z + y*z)I want to test whether there exists a vector (a,b,c) with positive entries such that p(a,b,c)>0. With the above examples the answer is no for p and yes for q since q(1,1,1)=3/2. Is there a way to achieve that in SageMath? It is a very particular instance of non-linear optimization but did not find anything relevant.
