On the Direct Sum Conjecture in the Straight Line Model

We prove that if a quadratic system satisfies the direct sum conjecture strongly in the quadratic algorithm model, then it satisfies the direct sum conjecture strongly in the straight line algorithm model. Therefore, if the strong direct sum conjecture is true for the quadratic algorithm model then it is also true for the straight line algorithm model. We use this to classify all the minimal programs that compute the product of two polynomials modulo a squarefree polynomial.

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