PD Dr. Andreas Paffenholz

polymake

I am a developer of the software system polymake. Besides general design tasks and maintanance I work mainly on the following aspects of the program

Polymake Viewer

PolyViewer is a Viewer for Mac OS for files created by polymake. It can also be used to view the properties currently defined for an object from inside the polymake shell.

Here is a screenshot.

The sources are at github.

Polymake Extensions

You have to install polymake to use these extensions. Installation instructions for extensions to polymake are here.
More information on polymake is here.

Contact me if you have problems or questions.

LLL, Hermite Normal Form and Integer Kernel via the NTL library of Victor Shoup

polymake version 2.14 NTLWrapper-0.2.tgz [version of August 19, 2015]

The latest version of this extension can be found at github. It provides

via an interface to NTL.

Hermite Normal Form and Smith Normal Form via the Flint library

polymake version 2.14 FlintWrapper-0.1.tgz [version of August 19, 2015]

The latest version of this extension can be found at github. It provides

via an interface to Flint.

Polyhedral Adjunction

polymake version 2.14 PolyhedralAdjunction-1.0.tgz [version of August 19, 2015]

The latest version of this extension can be found at github. This extensions offers computations for polyhedral adjunction theory, in particular of the nef value, the q-codegree, constructions of the core face and projections along the core face. For more explanations see [DiRocco, Haase, Nill, Paffenholz: Polyhedral Adjunction Theory, arxiv:1105:2415]

Lattice Normalization

polymake version 2.14 lattice_normalization-0.1.tgz [version of August 19, 2015]

The latest version of this extension can be found at github. This is an extension to the polymake system for the computation of lattice normal forms of lattice polytopes and for checking lattice isomorphism of lattice polytopes (based on the algorithm of Kreuzer and Skarke (see arxiv:math/0204356) with improvements by Grinis and Kasprzyk (see arxiv:1301.6641) This extension depends on the polymake extension polymake_flint_wrapper, so please install and import this first.

Defect Polytopes

polymake version 2.12 defect_polytopes-v0.1.tgz

This extensions offers the computations used in [Joswig, Paffenholz: Defect Polytopes and Counter-Examples with polymake, arxiv:1105.5027]

Push-Forward Projections

polymake version 2.12 projection_with_subdivision.tgz

The latest version of this extension can be found at github. This extension provides methods to do push-forward projections of polytopes. An application of this is described in my paper with Christian Haase On Fanos and Chimneys, where we construct regular unimodular triangulations for smooth reflexive polytopes. A more detailed paper will appear soon.

Polyhedral methods for Nash equilibria

polymake version 2.12 bimatrix_games.tgz

This extension is maintained on at github and provides an still experimental and limited extension that provides a new application bimatrix_games to polymake. It can compute Nash equilibria of bimatrix games.
The only new data type is BimatrixGame that can take a pair of matrices of equal dimensions as input in PAYOFF_MATRICES. It can compute the set of extrem Nash equilibria, their payoffs, and the connected components of the extreme equilibria for a degenerate game. Further, it defines the associated polyhedra for the game.
The employed algorithm is only mildly efficient, and it only works for polyhedra that have positive payoff (see comments in extension for more details). In all other cases the extension uses support enumeration.
You might need to restart polymake after you imported the extension.

Using barvinok with polymake

barvinok-extension-1.0.tar.bz2

barvinok by Sven Verdoolaege is a library to count integer points in parametric and non-parametric polytopes. The above extension makes counting and computing the Ehrhart polynomial accessible from within polymake
Note that you have to install barvinok to use the extension.