= Sum of squares polynomial
{wiki=Polynomial_SOS}
= SOS polynomial
{c}
{synonym}
A real <polynomial> $p$ is a sum of squares polynomial if $p=\sum_\ell q_\ell^2$ for real <polynomials> $q_\ell$. Such a representation certifies global nonnegativity. If $m(z)$ is the vector of relevant <monomials>, the identity $p(z)=m(z)^TGm(z)$ with a <positive semidefinite matrix> $G$ encodes a sum of squares through a <Gram matrix>. Equating coefficients is linear in $G$, so finding a certificate is a <semidefinite program>.
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