I'm developing a method where the user has to define a problem-dependent function $p: \mathbb{R}^n \times \mathbb{R}^n \rightarrow \mathbb{R}$ that will later be used as a condition:
$p(a,b) = 0$
I now want to ensure that both $a$ and $b$ are contained in the function definition. How do I write this down? The way I'm doing it right now is:
$p: \mathbb{R}^{n} \times \mathbb{R}^{n} \rightarrow \mathbb{R} \qquad \nabla_{a} p \neq 0 \qquad \nabla_{b} p \neq 0$
Such that, for example $p(a,b) = b^T b$ is not allowed but $p(a,b) = a^T b$ is.
How would you write this? Is there anything wrong with my notation?