I have a homogenous degree 8 polynomial in 14 variables. I know it is possible to express it as a sum of 8 squares, but it's a very complicated polynomial and it's infeasible to manipulate it by hand. To be clear, by square I mean a square of a polynomial. I can share the polynomial if it helps. Any advice is much appreciated.
2026-03-25 06:10:33.1774419033
Is there an algorithm to factor a many variable polynomial into a sum of squares?
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There are a number of properties of polynomials that can be used to obtain this decomposition when possible. There are software tools that help in this purpose such as SOSTOOLS that uses LMI solvers and the properties of Newton polytope to reach this purpose. Check out this page.