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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… Click to show full abstract
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.
Journal Title: Mathematics in Computer Science
Year Published: 2020
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