DeterminantalRepresentations swMATH ID: 33866 Software Authors: Chen, Justin; Dey, Papri Description: Computing symmetric determinantal representations. 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. Homepage: http://www2.macaulay2.com/Macaulay2/doc/Macaulay2-1.14/share/doc/Macaulay2/DeterminantalRepresentations/html/index.html Dependencies: Macaulay2 Keywords: determinantal representations; linear matrix inequalities; plane curves; hyperbolic polynomials Related Software: Macaulay2; Bertini Cited in: 6 Documents Standard Articles 1 Publication describing the Software, including 1 Publication in zbMATH Year Computing symmetric determinantal representations. Zbl 1436.11006Chen, Justin; Dey, Papri 2020 Cited by 5 Authors 6 Dey, Papri 2 Chen, Justin 1 Görlach, Paul 1 Kaihnsa, Nidhi 1 Plaumann, Daniel all top 5 Cited in 6 Serials 1 Beiträge zur Algebra und Geometrie 1 Journal of Symbolic Computation 1 Experimental Mathematics 1 Journal of Algebra and its Applications 1 Mathematics in Computer Science 1 The Journal of Software for Algebra and Geometry all top 5 Cited in 10 Fields 4 Algebraic geometry (14-XX) 4 Linear and multilinear algebra; matrix theory (15-XX) 2 Numerical analysis (65-XX) 2 Computer science (68-XX) 2 Operations research, mathematical programming (90-XX) 1 Number theory (11-XX) 1 Commutative algebra (13-XX) 1 Real functions (26-XX) 1 Ordinary differential equations (34-XX) 1 Geometry (51-XX) Citations by Year