# Sums of squares in Macaulay2

## TL;DR

The paper introduces a Macaulay2 package that efficiently decomposes polynomials into sums of squares using advanced methods, supporting various optimization techniques and external solvers.

## Contribution

It presents a new Macaulay2 package with capabilities for sums-of-squares decomposition, integrating modern algorithms and solver support.

## Key findings

- Supports external semidefinite programming solvers
- Includes a data type for sums-of-squares polynomials
- Enables optimization over algebraic varieties

## Abstract

The Macaulay2 package SumsOfSquares decomposes polynomials as sums of squares. It is based on methods to rationalize sum-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.