MixedSubdivisions.jl

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A Julia package for computing a (fine) mixed subdivision and the mixed volume of lattice polytopes. The mixed volume of lattice polytopes arising as Newton polytopes of a polynomial system gives an upper bound of the number of solutions of the system. This is the celebrated BKK-Theorem. A (fine) mixed subdivision can be used to efficiently solve sparse polynomial systems as first described in A Polyhedral Method for Solving Sparse Polynomial Systems by Huber and Sturmfels.

There are many algorithms for computing mixed volumes and mixed subdivisions. This implementation is based on the tropical homotopy continuation algorithm by Anders Jensen described in arXiv:1601.02818.

Installation

The package can be installed via the Julia package manager

pkg> add MixedSubdivisions