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.

翻译：在希尔伯特概形的研究中，整数划分$\lambda$有助于研究者识别所考察概形的若干几何与组合性质。为帮助研究者从希尔伯特多项式中提取此类信息，我们描述了一种高效算法，该算法能够判定$p(x)\in\mathbb{Q}[x]$是否为希尔伯特多项式，若是，则恢复与之关联的整数划分$\lambda$。