determine degree of boolean polynomial given as black box

Question

I searched a lot but couldn't find a good resource that addresses this question. Given a boolean polynomial with $n$ boolean variables as a black box, what is the most efficient way to compute its degree? Can you please provide references for both classical and quantum algorithms? What happens if we can compute polynomial in any $\mathbb{Z}_p$ through the black box. What happens if we have access to polynomial at real $\mathbb{R}$ points.