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Available Extensions
polymake
supports an extension system for writing and maintaining outside the distribution. Please contact the extensions authors if you have questions.
Lattice Polytopes and Toric Geometry
- Lars Kastner/Benjamin Lorenz: Toric Varieties and Singular interface
- Benjamin Lorenz: classification of smooth lattice polytopes with few lattice points
- Andreas Paffenholz:
- ntl_wrapper: This extension provides a small interface to lll and lets you compute an lll-reduced lattice basis and a basis of the integer relations of the rows of a matrix.
- for polymake version 2.12:lll-v0.6
- for polymake svn version:ntl_wrapper.tgz
- latest:github
- polyhedral_adjunction: This extension provides properties and constructions used in DiRocco, Haase, Nill, Paffenholz: Polyhedral Adjunction Theory, arxiv:1105:2415. In particular, it computes the nef value and the Q-codegree of a polytope.
- polymake 2.12: polyhedral_adjunction.tgz
- latest:github
- Toric Varieties: Defines a new property for toric varieties associated to a fan and divisors on that variety. Computes properties of the variety and the divisors, and the cone of nef and effective divisors. To use this extension you need the short lattice basis extension above.
- polymake 2.12: ToricVarieties-v0.5
- defect polytopes: This extension allows computations used in Joswig, Paffenholz: Defect Polytopes and Counter-Examples with polymake, arxiv:1105:5027
- polymake 2.12: DefectPolytopes-v0.1
- projection_with_subdivision: Projections of smooth polytopes together with the hyperplane subdivision implied by the facets.
- polymake 2.12: projection_with_subdivision.tgz
- latest: github
- barvinok-extension-1.0.tar.bz2
This extension lets you use barvinok by Sven Verdolaege for the computation of the number of lattice points in a rational polytope and the coefficients of the Ehrhart polynomial of a lattice polytope.
Tropical Geometry
- Simon Hampe: Algorithmic tropical intersection theory
Integer Programming
- Matthias Walter: With this extension you can test an integer matrix for total unimodularity. If the answer is “no”, it can return the row/column indices of a submatrix with |det| >= 2. It can also test for the related properties (strong) unimodularity, (strong) k-modularity and the Dantzig property.
Metric Spaces
- Sven Herrmann and Andreas Spillner: metrics-1.0.tar.bz2
This extensions contains a new application metric introducing finite metric spaces as objects. The core feature is an algorithm to compute a realisation of a finite metric space using the tight-span, as described in Herrmann, Moulton, Spillner: Computing Realizations of Finite Metric Spaces.