TPLib

TPLib (Tropical Polyhedra Library) is a library written in OCaml which allows to manipulate tropical polyhedra.

You can download it here and build it from source:

./configure
make
make install

You can also install it with the package manager OPAM:

opam install tplib

The main operations which TPLib provides are:

• conversion between external representations (with half-spaces) and internal representations (with vertices/rays), see (Allamigeon, Gaubert, & Goubault, 2013)
• computing the minimal external representation, see (Allamigeon & Katz, 2013)
• computing the polyhedral complex associated with the polytope, see (Develin & Sturmfels, 2004)

You can call these operations by using TPLib as a library, or directly from the command-line.

Example

To compute the extreme rays of a tropical cone from a list of inequalities, call:

compute_ext_rays <dim> < my_inequalities

where <dim> stands for the dimension of the ambiant space, and my_inequalities is a file containing a set of inequalities. For instance, the list

[-oo,2,-1,4,-oo,2,2,-oo,4,2]
[1,-oo,4,5,4,-oo,4,-oo,5,4] 

encode the following two inequalities over $(\mathbb{R} \cup \{–\infty\})^5$:

References

• Allamigeon, X., Gaubert, S. & Goubault, E. (2013). Computing the Vertices of Tropical Polyhedra using Directed Hypergraphs. Discrete & Computational Geometry, 49(2), 247–279.
  • arXiv
  • Publisher
• Allamigeon, X. & Katz, R. D. (2013). Minimal external representations of tropical polyhedra. Journal of Combinatorial Theory, Series A, 120(4), 907–940.
  • arXiv
  • Publisher
• Develin, M. & Sturmfels, B. (2004). Tropical convexity. Documenta Mathematica, 9, 1–27.