= Solution
For canonical coordinates $(q_i,p_i)$, the <Poisson bracket> is
$$
\boxed{\{F,G\}=\sum_i\left(
\frac{\partial F}{\partial q_i}\frac{\partial G}{\partial p_i}
-\frac{\partial F}{\partial p_i}\frac{\partial G}{\partial q_i}\right).}
$$
It is bilinear and antisymmetric, obeys the <Leibniz rule> in either argument, and satisfies the <Jacobi identity>. These properties encode the symplectic structure of <phase space>. The two printed inline applications are treated separately below.
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