Abstract
We explore the concept of real tropical basis of an ideal in the field of real Puiseux series. We explicitly construct tropical bases of zero-dimensional real radical ideals, linear ideals and hypersurfaces coming from combinatorial patchworking. But we also show that there exist real radical ideals that do not admit a tropical basis. As an application, we show how to compute the set of singular points of a real tropical hypersurface, i.e. we compute the real tropical discriminant.
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The author is supported by the Spanish “Ministerio de Economía y Competitividad” and “European Regional Development Fund” (FEDER) under the Project MTM2011-25816-C02-02.
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Tabera, L.F. On real tropical bases and real tropical discriminants. Collect. Math. 66, 77–92 (2015). https://doi.org/10.1007/s13348-014-0119-6
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DOI: https://doi.org/10.1007/s13348-014-0119-6