Dynamic Decomposition of Tropical Prevarieties for Celestial Mechanics

Every tropical hypersurface is the union of finitely many polyhedra. By the distributive law, intersecting a list of tropical hypersurfaces amounts to doing a huge computation of intersections of polyhedra that may be naturally organised in an enumeration tree. The idea of dynamic enumeration proposed by Mizutani, Takeda and Kojima (2007) is extended to dynamic decomposition where tropical hypersurfaces are not just chosen dynamically but also split dynamically into disjoint half-open polyhedra. This has the advantage of making the enumeration tree even thinner. We present an implementation of this enumeration algorithm in the C++ library gfanlib and do a comparison against an implementation of an existing algorithm. Finally we give an example of how the software has been used in a celestial mechanics problem.