Let $p$ be a quadratic multivariate polynomial in Sage, for example
sage: R.<x,y,z> = QQ[]

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.