Detecting integral polyhedral functions
Abstract
We study the class of real-valued functions on convex subsets of Rn which are computed by the maximum of finitely many affine functionals with integer slopes. We prove several results to the effect that this property of a function can be detected by sampling on small subsets of the domain. In so doing, we recover in a unified way some prior results of the first author (some joint with Liang Xiao). We also prove that a function on R2 is a tropical polynomial if and only if its restriction to each translate of a generic tropical line is a tropical polynomial.
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