The multiplicative complexity of the direct product of algebras Aₚ of polynomials modulo a polynomial P is studied. In particular, we show that if P and Q are irreducible polynomials then the multiplicative complexity of AP × AQ is 2 (P) (Q) - k, where k is the number of factors of P in the field extended by a root of Q.
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S. Winograd (1980) studied this question.
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