PALP: A Package for Analysing Lattice Polytopes with applications to toric geometry☆
PALP: A Package for Analysing Lattice Polytopes with applications to toric geometry☆
复制标题
PALP：用于分析晶格多面体及其在复曲面几何中的应用☆
DOI：
10.1016/s0010-4655(03)00491-0
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发表时间：
2002
影响因子：
6.3
通讯作者：
H. Skarke
中科院分区：
文献类型：
--
作者：
M. Kreuzer;H. Skarke
我们描述了我们的包PALP的C程序计算与晶格多面体和应用程序复曲面几何，这是免费的互联网上。它包含顶点和小平面枚举，计算的发病率和对称性，以及完成一组点的凸船体的晶格点的例程。此外，还有专门针对自反多面体的程序，如自反子多面体的枚举，以及在复曲面几何和弦理论中的应用，如计算霍奇数据和复曲面卡-丘簇的纤维化结构。该软件包在速度上经过了很好的测试和优化，因为它被用于耗时的任务，例如4维自反多面体的分类以及非常大的5维多面体列表的创建和操作。虽然最初是为低维应用程序，该算法的工作在任何维度和我们的顶点和面枚举的关键例程与现有的软件包相比。课程获取形式：CPC Program Library，Queen's University of贝尔法斯特，N。爱尔兰程序名称：PALP目录标识符：ADSQ程序摘要URL：http://cpc.cs.qub.ac.uk/summaries/ADSQ设计该程序的计算机：任何具有C语言的计算机测试过的计算机：PC、SGI Origin 2000、IBM RS/6000、COMPAQ GS 140测试过的程序操作系统：Linux、IRIX、AIX、OSF 1使用的编程语言：C语言执行典型数据所需的内存：对大多数应用程序可忽略不计;对大型多面体分析变化很大;没有最小值，但对某些任务的计算时间有很大影响一个字中的位数：任意使用的处理器数量：1代码是否已矢量化或并行化？：否分布式程序中的字节数，包括测试数据等：138098 Distribution format：tar gzip file关键词：格多面体，面枚举，自反多面体，复曲面几何，卡-丘流形，弦理论，共形场论问题的性质：某些称为自反多面体的格多面体提供了一个非常大的一类卡-丘流形在复曲面几何方面的组合描述。这些流形在弦理论的紧化中扮演着重要的角色。虽然最初的设计是为了处理和分类自反多面体，特别强调与弦理论应用有关的问题[M。Kreuzer和H. Skarke，Rev.Math.Phys.14（2002）343]，该包还非常有效地处理关于任意晶格多面体的标准问题（面枚举和类似问题）。解决方法：大部分代码都是直接编程，但某些关键例程在计算时间和处理大量数据方面进行了优化。双重描述方法（参见，例如，[D. Avis等人，Comput.几何学7（1997）265]）用于面枚举问题、用于扩展的GCD的格基约简以及用于涉及大量多面体的任务（诸如分类问题）的二进制数据库结构。对程序复杂性的限制：唯一的硬限制来自于使用固定整数运算（32位或64位），允许输入数据（多面体坐标）大约高达109。其他参数（尺寸、点数和顶点数等）可以在编译前设置。典型的运行时间：大多数任务（典型的：分析一个四维自反多面体）可以在几毫秒内交互式执行。所有四维自反多面体的分类需要几年的处理时间。那个...
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 specialized to reflexive polytopes such as the enumeration of reflexive subpolytopes, and applications to toric geometry and string theory, like the computation of Hodge data and fibration structures for toric Calabi–Yau varieties. The package is well tested and optimized in speed as it was used for time consuming tasks such as the classification of reflexive polyhedra in 4 dimensions and the creation and manipulation of very large lists of 5-dimensional polyhedra. While originally intended for low-dimensional applications, the algorithms work in any dimension and our key routine for vertex and facet enumeration compares well with existing packages. PROGRAM SUMMARY: Program obtainable form: CPC Program Library, Queen's University of Belfast, N. Ireland Title of program: PALP Catalogue identifier: ADSQ Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADSQ Computer for which the program is designed: Any computer featuring C Computers on which it has been tested: PCs, SGI Origin 2000, IBM RS/6000, COMPAQ GS140 Operating systems under which the program has been tested: Linux, IRIX, AIX, OSF1 Programming language used: C Memory required to execute with typical data: Negligible for most applications; highly variable for analysis of large polytopes; no minimum but strong effects on calculation time for some tasks Number of bits in a word: arbitrary Number of processors used: 1 Has the code been vectorised or parallelized?: No Number of bytes in distributed program, including test data, etc.: 138098 Distribution format: tar gzip file Keywords: Lattice polytopes, facet enumeration, reflexive polytopes, toric geometry, Calabi–Yau manifolds, string theory, conformal field theory Nature of problem: Certain lattice polytopes called reflexive polytopes afford a combinatorial description of a very large class of Calabi–Yau manifolds in terms of toric geometry. These manifolds play an essential role for compactifications of string theory. While originally designed to handle and classify reflexive polytopes, with particular emphasis on problems relevant to string theory applications [M. Kreuzer and H. Skarke, Rev. Math. Phys. 14 (2002) 343], the package also handles standard questions (facet enumeration and similar problems) about arbitrary lattice polytopes very efficiently. Method of solution: Much of the code is straightforward programming, but certain key routines are optimized with respect to calculation time and the handling of large sets of data. A double description method (see, e.g., [D. Avis et al., Comput. Geometry 7 (1997) 265]) is used for the facet enumeration problem, lattice basis reduction for extended gcd and a binary database structure for tasks involving large numbers of polytopes, such as classification problems. Restrictions on the complexity of the program: The only hard limitation comes from the fact that fixed integer arithmetic (32 or 64 bit) is used, allowing for input data (polytope coordinates) of roughly up to 109. Other parameters (dimension, numbers of points and vertices, etc.) can be set before compilation. Typical running time: Most tasks (typically: analysis of a four dimensional reflexive polytope) can be perfomed interactively within milliseconds. The classification of all reflexive polytopes in four dimensions takes several processor years. The …