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The square of a real-valued polynomial is clearly non-negative, and so the sum of the squares of polynomials is non-negative. What about the converse? Is a non-negative polynomial the sum of the squares of polynomials? For polynomials in one variable, yes. For polynomials in several variables, no. However, Emil Artin proved nearly a century ago […] The post Positive polynomials revisited first appeared on John D. Cook....