We propose a cut-based algorithm for finding all vertices and all facets of the convex hull of all integer points of a polyhedron defined by a system of linear inequalities. Our algorithm, DDMCuts, is based on the Gomory cuts and the dynamic version of the double description method. We describe the computer implementation of the algorithm and present the results of computational experiments comparing our algorithm with a naive one and an algorithm implemented in Normaliz.

中文翻译：

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如何找到多面体中所有整数点的凸包？

我们提出一种基于割的算法，用于查找由线性不等式系统定义的多面体的所有整数点的所有顶点和凸包的所有小平面。我们的算法DDMCuts基于Gomory割和双重描述方法的动态版本。我们描述了该算法的计算机实现，并给出了将我们的算法与朴素算法和在Normaliz中实现的算法进行比较的计算实验结果。