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Sum of squares optimization built on top of picos. Easy access to pseudoexpectation operators for both formulating problems and extracting solutions via rounding algorithms.
To install from pypi:
pip install SumOfSquares
To compute the sum of squares decomposition of a polynomial:
>>> import sympy as sp
>>> x, y = sp.symbols('x y')
>>> p = 2*x**4 + 2*x**3*y - x**2*y**2 + 5*y**4
>>> prob = SOSProblem()
>>> c = prob.add_sos_constraint(p, [x, y])
>>> prob.solve()
>>> c.get_sos_decomp()
Matrix([
[5.0*(-0.306*x**2 + y**2)**2],
[2.057*(0.486*x**2 + x*y)**2],
[ 1.047*x**4]])If you use this library in your work, please consider citing:
@software{Yuan_SumOfSquares_py,
author = {Yuan, Chenyang},
license = {MIT},
title = {{SumOfSquares.py}},
url = {https://github.com/yuanchenyang/SumOfSquares.py}
}