Refined multiplicative tensor product of matrix factorizations

Abstract

An algorithm for matrix factorization of polynomials was proposed in [11] and it was shown that this algorithm produces better results than the standard method for factoring polynomials on the class of summand-reducible polynomials. In this paper, we improve this algorithm by refining the construction of one of its two main ingredients, namely the multiplicative tensor product ⊗˜ of matrix factorizations to obtain another different bifunctorial operation denoted by ⊗‾. We refer to ⊗‾ as the refined multiplicative tensor product of matrix factorizations. In fact, we observe that in the algorithm for matrix factorization of polynomials developed in [11], if we replace ⊗˜ by ⊗‾, we obtain better results on the class of summand-reducible polynomials in the sense that the refined algorithm produces matrix factors which are of smaller sizes.