# libtropicon

The computation of intersection points of generic tropical hyper-surfaces is a
fundamental problem in computational algebraic geometry.
An efficient algorithm for solving this problem will be a basic building block
in many higher level algorithms for studying tropical varieties,
computing mixed volume, enumerating mixed cells, constructing polyhedral homotopies, etc.
*libtropicon* is a library for computing intersection points of
generic tropical hyper-surfaces.
The core algorithm is designed to be naturally parallel and highly scalable.

## Downloads

*libtropicon* is still a work in progress.
As the implementation matures, stable versions will be released.
For now, following experimental versions (“alpha” versions) are available:

**v0.30** (April 2018)
This version relies on Intel TBB (not the open sourced TBB) for
carrying out parallel computation.
It will still run on systems without Intel TBB,
but it will only run in serial mode in that case.

## What does it compute?

A tropical polynomial is a piecewise linear function given by the
minimum of several linear polynomials in several real variables.
The set of points where the minimum is attained simultaneously by
two or more linear polynomials is called the tropical hypersurface
defined by that polynomial.
*libtropicon* computes the
**intersection points of several generic tropical hypersurfaces**.
In the case where the number of polynomials match the dimension,
this problem is equivalent to the problem of finding all
**mixed cells** of several polytopes.
In this case, it also computes, as a byproduct,
the **mixed volume** of these polytopes.

## How does it work?

- Mathematical theory
- Algorithms
- Parallel computation
- Shared-memory systems
- Computer clusters
- GPU devices