Refined multiplicative tensor product of matrix factorizations

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 circle times($) over tilde of matrix factorizations to obtain another different bifunctorial operation denoted by circle times($) over bar. We refer to circle times($) over bar as the refined multiplicative tensor product of matrix factorizations. In fact, we observe that in the algorithm for matrix factorization of polynomials developed in [11], if we replace circle times($) over tilde by circle times($) over bar, 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. (c) 2023 Elsevier B.V. All rights reserved.

Automated summary

This paper improves the algorithm for matrix factorization of polynomials, obtaining better results by refining the construction of one of the main ingredients of the algorithm.