Find a continuous function , if exists , (explicitly in terms of known functions) $f: \mathbb{R}\times\mathbb{R} \to \mathbb{R}$, such that $f$ is not always positive , not even always negative and $f(u, v) > 0$ and $f(w, z) > 0$ implies $f(u+w, v+z) > 0$ and $f(uw - vz, uz+vw) > 0$.
Find a real-valued function of 2 variables satisfying certain positivity constraints
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3Let $f$ be the constant $-1$. – 2012-10-11