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Journal Articles Discrete and Computational Geometry Year : 2020

Tropical spectrahedra

Abstract

We introduce tropical spectrahedra, defined as the images by the nonarchimedean valuation of spectrahedra over the field of real Puiseux series. We provide an explicit characterization of generic tropical spectrahedra, involving principal tropical minors of size at most 2. To do so, we show that the nonarchimedean valuation maps semialgebraic sets to semilinear sets that are closed. We also prove that, under a regularity assumption, the image by the valuation of a basic semialgebraic set is obtained by tropicalizing the inequalities which define it.

Dates and versions

hal-01422639 , version 1 (26-12-2016)

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Xavier Allamigeon, Stéphane Gaubert, Mateusz Skomra. Tropical spectrahedra. Discrete and Computational Geometry, 2020, 63, pp.507-548. ⟨10.1007/s00454-020-00176-1⟩. ⟨hal-01422639⟩
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