# 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:
*polymake_flint_wrapper*Computation of Hermite Normal Form, Smith Normal Form and LLL-reduced lattice bases using the flint library

- Andreas Paffenholz:
*LatticeNormalForm*Normal forms of lattice polytopes and lattice equivalence of lattice polytopes*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.

## Tropical Geometry

- Ewgenij Gawrilow, Michael Joswig, Benjamin Schröter: polytropes
- Alheydis Geiger and Marta Panizzut: TropicalQuarticCurves
- Michael Joswig, Marta Panizzut, Bernd Sturmfels: Tropical Cubics
- 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.