Vol. 10, No. 1, 2020

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Sums of squares in Macaulay2

Diego Cifuentes, Thomas Kahle and Pablo Parrilo

Vol. 10 (2020), 17–24
DOI: 10.2140/jsag.2020.10.17
Abstract

The Macaulay2 package SumsOfSquares decomposes polynomials as sums of squares. It is based on methods to rationalize sums-of-squares decompositions due to Parrilo and Peyrl. The package features a data type for sums-of-squares polynomials, support for external semidefinite programming solvers, and optimization over varieties.

Keywords
sums of squares, semidefinite programming
Mathematical Subject Classification 2010
Primary: 13J30
Secondary: 13P25, 90C22
Supplementary material

A Macaulay2 package for sums of squares calculations

Milestones
Received: 13 December 2018
Revised: 7 December 2019
Accepted: 6 January 2020
Published: 7 March 2020
Authors
Diego Cifuentes
Department of Mathematics
Massachusetts Institute of Technology
Cambridge, MA
United States
Thomas Kahle
Fakultät für Mathematik
Otto-von-Guericke Universität Magdeburg
Institut Algebra und Geometrie
Universitätsplatz 2
Magdeburg
Germany
Pablo Parrilo
Laboratory for Information and Decision Systems
Massachusetts Institute of Technology
Cambridge, MA
United States