- methods for lattice polyhedra and toric geometry
- interfaces to software for computations in commutative algebra/algebraic geometry
- implementation/efficient algorithms for cones and fans
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.
The sources are at github.
Contact me if you have problems or questions.
|polymake version 2.12||lll-v0.6.tgz [version of April 11, 2012]|
|polymake svn version||ntl_wrapper.tgz|
The latest version of this extension can be found at github. It provides
- computation of a short lattice basis with the LLL algorithm,
- the computation of the integer kernel (Gale dual), and
- the Hermite normal form
|polymake version 2.12||polyhedral_adjunction.tgz|
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]Toric Varieties
|polymake version 2.12||toric_varieties-v0.5.tgz|
|polymake svn version||download from github|
This extensions extends polymake's capabilities with new properties and methods for toric varieties associated to a polyhedral fan, in particular:
- it can compute the cones of effective and nef divisors on a projective toric variety,
- you can define toric divisors, in particular it allows checks for ample, nef, effective, Cartier, Q-Cartier
- you can compute the polytope associated to a divisor
- you can check whether a complete polyhedral fan is projective
|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.
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
Note that you have to install barvinok to use the extension.