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.
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:
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.