Elsevier Science Home
Computer Physics Communications Program Library
Full text online from Science Direct
Programs in Physics & Physical Chemistry
CPC Home

Manuscript Title: PALP: a package for analysing lattice polytopes with applications to toric geometry.
Authors: M. Kreuzer, H. Skarke
Program title: PALP
Catalogue identifier: ADSQ
Journal reference: Comput. Phys. Commun. 157(2004)87
Programming language: C.
Computer: Any computer featuring C.
Operating system: Linux, IRIX, AIX, OSF1.
Keywords: Lattice polytopes, Facet enumeration, Reflexive polytopes, Toric geometry, Calabi-Yau manifolds, String Theory, Conformal filed theory, Computer algebra.
Classification: 5.

Nature of problem:
Certain lattice polytopes called reflective 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, the package also handles standard questions (facet enumeration and similar problems) about arbitrary lattice polytopes very efficiently.

Solution method:
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 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.

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.

Running time:
Most tasks (typically: analysis of a four dimensional reflexive polytope) can be performed interactively within milliseconds. The classification of all reflexive polytopes in four dimensions takes several processor years. The facet enumeration problem for higher (eg. 12-20) dimensional polytopes varies strongly with the dimension and structure of the polytope; here PALP's performamce is similar to that of existing packages.