Numerical Software to Compute Newton polytopes and Tropical Membership

We present our implementation of an algorithm which functions as a numerical oracle for the Newton polytope of a hypersurface. Additionally, we propose an algorithm which functions as a tropical membership test for higher codimension varieties based on ideas from Hept and Theobald. This tropical membership algorithm relies on a numerical oracle and we analyze some of the convergence rates involved. Our implementation is written as a Macaulay2 package called NumericalNP.m2. To showcase this package, we investigate the Newton polytope of both a hypersurface coming from algebraic vision and the Lüroth invariant.