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.
Type de document :
Pré-publication, Document de travail
arXiv:1610.06746. 2016
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https://hal.inria.fr/hal-01422639
Contributeur : Stephane Gaubert <>
Soumis le : lundi 26 décembre 2016 - 15:21:39
Dernière modification le : jeudi 10 mai 2018 - 02:05:39

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  • HAL Id : hal-01422639, version 1
  • ARXIV : 1610.06746

Citation

Xavier Allamigeon, Stéphane Gaubert, Mateusz Skomra. Tropical spectrahedra. arXiv:1610.06746. 2016. 〈hal-01422639〉

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