An Implementation of Exact Mixed Volume Computation

Abstract

Mixed volumes of lattice polytopes play a central role in numerical and tropical algebraic geometry. We present an implementation of a new algorithm for their computation based on tropical homotopy continuation, which is a combinatorial procedure using ideas from numerical algebraic geometry. While the mathematical aspects of the algorithm are presented elsewhere, here we mainly address technical details of the implementation, in particular how it was made fast and reliable. The implementation is distributed as part of the library gfanlib.