PALP: A Package for Analyzing Lattice Polytopes with Applications to Toric Geometry
Maximilian Kreuzer, Harald Skarke
我们描述了我们的C程序PALP,用于计算格子多面和toric几何中的应用,这些图块在互联网上免费提供。 它包含顶点和面枚举的例程,事件和对称的计算,以及完成给定点的凸壳体中的一组晶格点。 此外,还有专门用于反射性聚表的程序,例如反射子聚位体的枚举,以及图层几何和弦理论的应用,例如计算Toric Calabi-Yau品种的Hodge数据和纤维化结构。 该包经过良好的测试和优化,因为它用于耗时的任务,例如4个维度的反射性多面体的分类以及创建和操纵非常大的5维多面体列表。 虽然最初用于低维应用,但算法可以在任何维度上工作,我们对顶点和面枚举的关键例程与现有软件包进行了很好的比较。
We describe our package PALP of C programs for calculations with lattice polytopes and applications to toric geometry, which is freely available on the internet. It contains routines for vertex and facet enumeration, computation of incidences and symmetries, as well as completion of the set of lattice points in the convex hull of a given set of points. In addition, there are procedures specialised to reflexive polytopes such as the enumeration of reflexive subpolytopes, and applications to toric...