Computing sum of squares decompositions with rational coefficients
Theoretical Computer Science
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A geometric inequality among three triangles, originating in circle packing problems, is introduced. In order to prove it, we reduce the original formulation to the nonnegativity of a polynomial in four real indeterminates. Techniques based on sum of squares decompositions, semidefinite programming and symmetry reduction are then applied to provide an easily verifiable nonnegativity certificate.