Pólya’s theorem

Pólya’s theorem provides a way to determine if a multivariate polynomial with certain symmetric properties can be expressed as a sum of squares, which means it can be written as a sum of non-negative parts. In simpler terms, it helps mathematicians verify if a polynomial never takes negative values over a specific domain by checking if it can be broken down into simpler, always non-negative pieces. This is useful in optimization and control theory, where ensuring non-negativity of functions is crucial for system stability and performance.