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PALP: a package for analysing lattice polytopes with applications to toric geometry. (English) Zbl 1196.14007
Summary: 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.

14-04 Software, source code, etc. for problems pertaining to algebraic geometry
52B20 Lattice polytopes in convex geometry (including relations with commutative algebra and algebraic geometry)
14M25 Toric varieties, Newton polyhedra, Okounkov bodies
cdd; lrs; PALP; PORTA; Qhull
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