Algorithms for quantifying the differences between two lattices are used for Bravais lattice determination, database lookup for unit cells to select candidates for molecular replacement, and recently for clustering to group together images from serial crystallography. It is particularly desirable for the differences between lattices to be computed as a perturbation-stable metric, i.e. as distances that satisfy the triangle inequality, so that standard tree-based nearest-neighbor algorithms can be used, and for which small changes in the lattices involved produce small changes in the distances computed. A perturbation-stable metric space related to the reduction algorithm of Selling and to the Bravais lattice determination methods of Delone is described. Two ways of representing the space, as six-dimensional real vectors or equivalently as three-dimensional complex vectors, are presented and applications of these metrics are discussed. (Note: in his later publications, Boris Delaunay used the Russian version of his surname, Delone.)

中文翻译：

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格表示和聚类的空间

用于量化两个晶格之间差异的算法用于布拉维晶格测定、晶胞数据库查找以选择分子替换的候选者，以及最近用于聚类以将连续晶体学图像分组在一起。特别希望将晶格之间的差异计算为扰动稳定度量，IE作为满足三角不等式的距离，因此可以使用标准的基于树的最近邻算法，并且所涉及的晶格的微小变化会导致计算的距离产生微小的变化。描述了与Selling 的约简算法和Delone 的Bravais 格确定方法相关的扰动稳定度量空间。提出了两种表示空间的方法，即六维实向量或等效的三维复向量，并讨论了这些度量的应用。（注：鲍里斯·德劳内（Boris Delaunay）在其后来的出版物中使用了他的姓氏德隆（Delone）的俄语版本。）