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arXiv · 1809.03350

Detecting tropical defects of polynomial equations

Paul Görlach·Yue Ren·Jeff Sommars
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Abstract

We introduce the notion of tropical defects, certificates that a system of polynomial equations is not a tropical basis, and provide two algorithms for finding them in affine spaces of complementary dimension to the zero set. We use these techniques to solve open problems regarding del Pezzo surfaces of degree 3 and realizability of valuated gaussoids on 4 elements.

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Paul Görlach, Yue Ren, Jeff Sommars. 2018-09-10. Detecting tropical defects of polynomial equations. https://doi.org/10.1007/s10801-019-00916-4

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