This application concentrates on tropical hypersurfaces and tropical polytopes. It provides the functionality for the computation of basic properties. Visualization and various constructions are possible.
imports from: common, graph
uses: fan, group, polytope, topaz
A tropical hypersurface is the set of points in the tropical (d-1)-torus for which the minimum of a tropical polynomial is attained at least twice. It is given as a list of MONOMIALS and COEFFICIENTS. Currently polymake supports tropical hypersurfaces given by a homogeneous polynomial only!
Throughout this hypersurface is seen as a polyhedral complex in Rd-1.
Properties of TropicalHypersurface
User Methods of TropicalHypersurface
Permutations of TropicalHypersurface
Tropical convex hull of finitely many points in the tropical (d-1)-torus, as introduced by Develin and Sturmfels. One construction is via the bounded subcomplex of an unbounded ordinary convex polyhedron.
Properties of TropicalPolytope
User Methods of TropicalPolytope
- VISUAL () → Visual::TropicalPolytope
Visualize the tropical polytope.
option list: Visual::Polygons::decorations
Permutations of TropicalPolytope
- check_minimality (T, I, n) → Set
Checks the three criteria of Gaubert and Katz to be the type T of an apex of a minimal tropical halfspace. It is assumed that the points that the type refers to are given by 0,...,n-1 and that the index set I is a subset of 0,...,d-1 where d is the AMBIENT_DIM of the tropical polytope. If the input fulfills all criteria, the output set is empty. If the input doesn't fulfill the first criterion the whole set 0,...,d-1 is given back. If the input doesn't fulfill the second and third criterion, then the violating indices are stored.
- coarse_types (points, generators) → Array< Array<int>>
- trop2poly (T) → Polytope
Given points in the tropical projective space, compute an ordinary unbounded polyhedron such that the tropical convex hull of the input is the bounded subcomplex of the latter. Cf. Develin & Sturmfels math.MG/0308254v2, Lemma 22.
Warning: This client does not implement the reverse transformation to poly2trop.
- types (points, generators) → Array<Array<Set>>
- tropical_matroid_polytope (m, v) → TropicalPolytope
- dualize (points, generators) → Matrix
- ch2d_3phases (n, Types, G) → Array<int>