# Available Extensions

`polymake`

supports an extension system for writing and maintaining outside the distribution. Please contact the extension's authors if you have questions.

## Lattice Polytopes and Toric Geometry

- Silke Horn/Andreas Paffenholz:
*lattice_normalization*Normal forms of lattice polytopes and lattice equivalence of lattice polytopes*polymake_flint_wrapper*Computation of Hermite Normal Form, Smith Normal Form and LLL-reduced lattice bases using the flint library

- 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.*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.*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.- 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

- Michael Joswig, Marta Panizzut, Bernd Sturmfels: Tropical Cubics
- Ewgenij Gawrilow, Michael Joswig, Benjamin Schröter: polytropes
- Simon Hampe: Algorithmic tropical intersection theory (now bundled with polymake)
- Silke Horn: Tropical Oriented Matroids

## 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. See here for more information on implementation and theory.

## Extended Formulations

- Matthias Walter: This extension can compute nonnegative slack matrix factorizations from extended formulations of polytopes and vice versa. See here for more information.

## Phylogenetics

- Sven Herrmann: QuasiDec. This extension contains an algorithm for computing the block decomposition of a quasi-median graph obtained from a set of partitions or a sequence alignment.
- Sven Herrmann and Andreas Spillner: CoMRiT. 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.