Semidefinite-representable sets over valued fields K admit non-polyhedral spectrahedra and proper representable sets that are not spectrahedra, with a Smith-normal-form algorithm for the linear case.
Computations with p-adic numbers
1 Pith paper cite this work. Polarity classification is still indexing.
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abstract
This document contains the notes of a lecture I gave at the "Journ\'ees Nationales du Calcul Formel" (JNCF) on January 2017. The aim of the lecture was to discuss low-level algorithmics for p-adic numbers. It is divided into two main parts: first, we present various implementations of p-adic numbers and compare them and second, we introduce a general framework for studying precision issues and apply it in several concrete situations.
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On semidefinite-representable sets over valued fields
Semidefinite-representable sets over valued fields K admit non-polyhedral spectrahedra and proper representable sets that are not spectrahedra, with a Smith-normal-form algorithm for the linear case.