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extensions [2019/05/16 12:03]
paffenholz [Lattice Polytopes and Toric Geometry]
extensions [2021/03/15 08:39] (current)
paffenholz [Lattice Polytopes and Toric Geometry]
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 ===== Lattice Polytopes and Toric Geometry ===== ===== Lattice Polytopes and Toric Geometry =====
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-  * Lars Kastner/​Benjamin Lorenz: [[https://​github.com/​lkastner|Toric Varieties and Singular interface]] 
- 
-  * Benjamin Lorenz: [[http://​ehrhart.math.fu-berlin.de/​people/​benmuell/​classification.html|classification of smooth lattice polytopes with few lattice points]] 
  
   * Silke Horn/​Andreas Paffenholz:   * Silke Horn/​Andreas Paffenholz:
-    * //​[[https://​github.com/​apaffenholz/​lattice_normalization|lattice_normalization]]//​ Normal forms of lattice polytopes and lattice equivalence of lattice polytopes 
     * //​[[https://​github.com/​apaffenholz/​polymake_flint_wrapper|polymake_flint_wrapper]]//​ Computation of Hermite Normal Form, Smith Normal Form and LLL-reduced lattice bases using the [[http://​flintlib.org/​|flint]] library     * //​[[https://​github.com/​apaffenholz/​polymake_flint_wrapper|polymake_flint_wrapper]]//​ Computation of Hermite Normal Form, Smith Normal Form and LLL-reduced lattice bases using the [[http://​flintlib.org/​|flint]] library
  
   * Andreas Paffenholz:   * Andreas Paffenholz:
 +    * //​[[https://​github.com/​apaffenholz/​polymake_LatticeNormalForm|LatticeNormalForm]]//​ Normal forms of lattice polytopes and lattice equivalence of lattice polytopes
     * //​[[https://​github.com/​apaffenholz/​polymake_ntl_wrapper|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.     * //​[[https://​github.com/​apaffenholz/​polymake_ntl_wrapper|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.
     * //​[[https://​github.com/​apaffenholz/​polymake_polyhedral_adjunction|polyhedral_adjunction]]//:​ This extension provides properties and constructions used in [[http://​arxiv.org/​abs/​1105.2415|DiRocco,​ Haase, Nill, Paffenholz: Polyhedral Adjunction Theory, arxiv:​1105:​2415]]. In particular, it computes the nef value and the Q-codegree of a polytope.     * //​[[https://​github.com/​apaffenholz/​polymake_polyhedral_adjunction|polyhedral_adjunction]]//:​ This extension provides properties and constructions used in [[http://​arxiv.org/​abs/​1105.2415|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: [[http://​www.mathematik.tu-darmstadt.de/​~paffenholz/​software.html|ToricVarieties-v0.5]] 
-    * //defect polytopes//:​ This extension allows computations used in [[http://​arxiv.org/​abs/​1105.5027|Joswig,​ Paffenholz: Defect Polytopes and Counter-Examples with polymake, arxiv:​1105:​5027]] 
-       * polymake 2.12: [[http://​www.mathematik.tu-darmstadt.de/​~paffenholz/​software.html|DefectPolytopes-v0.1]] 
-    * //​[[https://​github.com/​apaffenholz/​polymake_projection_with_subdivision|projection_with_subdivision]]//:​ Projections of smooth polytopes together with the hyperplane subdivision implied by the facets. ​ 
-    * {{:​download:​barvinok-extension-1.0.tar.bz2}}\\ This extension lets you use [[http://​barvinok.gforge.inria.fr/​|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 ===== ===== Tropical Geometry =====
  
 +  * Michael Joswig, Marta Panizzut, Bernd Sturmfels: [[extensions:​tropicalcubics|Tropical Cubics]]
 +  * Ewgenij Gawrilow, Michael Joswig, Benjamin Schröter: [[extensions:​polytropes|polytropes]]
   * Simon Hampe: [[https://​github.com/​simonhampe/​atint|Algorithmic tropical intersection theory]] (now bundled with polymake)   * Simon Hampe: [[https://​github.com/​simonhampe/​atint|Algorithmic tropical intersection theory]] (now bundled with polymake)
   * Silke Horn: [[http://​solros.de/​polymake/​tropmat/​|Tropical Oriented Matroids]]   * Silke Horn: [[http://​solros.de/​polymake/​tropmat/​|Tropical Oriented Matroids]]
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   * Matthias Walter: [[https://​github.com/​xammy/​polymake-extended-formulations|This extension]] can compute nonnegative slack matrix factorizations from extended formulations of polytopes and vice versa. See [[https://​github.com/​xammy/​polymake-extended-formulations/​wiki|here]] for more information.   * Matthias Walter: [[https://​github.com/​xammy/​polymake-extended-formulations|This extension]] can compute nonnegative slack matrix factorizations from extended formulations of polytopes and vice versa. See [[https://​github.com/​xammy/​polymake-extended-formulations/​wiki|here]] for more information.
  
-===== Phylogentics ​=====+===== Phylogenetics ​=====
  
   * Sven Herrmann: [[http://​www.uea.ac.uk/​computing/​quasidec|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: [[http://​www.uea.ac.uk/​computing/​quasidec|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.
  • extensions.1558008202.txt.gz
  • Last modified: 2019/05/16 12:03
  • by paffenholz