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
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