The Recovery of $\lambda$ from a Hilbert Polynomial

In the study of Hilbert schemes, the integer partition $\lambda$ helps researchers identify some geometric and combinatorial properties of the scheme in question. To aid researchers in extracting such information from a Hilbert polynomial, we describe an efficient algorithm which can identify if $p(x)\in \mathbb{Q}[x]$ is a Hilbert polynomial and if so, recover the integer partition $\lambda$ associated with it.