Vol. 10, No. 1, 2020

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Computing symmetric determinantal representations

Justin Chen and Papri Dey

Vol. 10 (2020), 9–15
Abstract

We introduce the DeterminantalRepresentations package for Macaulay2, which computes definite symmetric determinantal representations of real polynomials. We focus on quadrics and plane curves of low degree (i.e., cubics and quartics). Our algorithms are geared towards speed and robustness, employing linear algebra and numerical algebraic geometry, without genericity assumptions on the polynomials.

Keywords
determinantal representations, linear matrix inequalities, plane curves, hyperbolic polynomials
Mathematical Subject Classification 2010
Primary: 11C20
Secondary: 15A15, 15B99, 65F40
Supplementary material

A package for computing determinantal representations

Milestones
Received: 16 May 2019
Revised: 28 October 2019
Accepted: 5 December 2019
Published: 6 February 2020
Authors
Justin Chen
School of Mathematics
Georgia Institute of Technology
Atlanta, GA
United States
Papri Dey
Department of Mathematics
University of Missouri
Columbia, MO
United States