On tensor products of matrix factorizations

Reduced multiplicative tensor product of matrix factorizations

“…In [7], this standard technique was improved on a subclass of polynomials that are sums of squares. This technique has recently been improved in [12] on the class of summand-reducible polynomials (cf. definition 4.2).…”

“…definition 4.2). Our main objective in this paper is to refine the algorithm proposed in [12] for the foregoing class of polynomials. Since a polynomial is made up of sums and products of monomials, the procedure developed in [12] uses two main ingredients which are functorial operations: The Yoshino tensor product of matrix factorizations (cf.…”

“…Our main objective in this paper is to refine the algorithm proposed in [12] for the foregoing class of polynomials. Since a polynomial is made up of sums and products of monomials, the procedure developed in [12] uses two main ingredients which are functorial operations: The Yoshino tensor product of matrix factorizations (cf. subsection 2.1) with the ability to produce a matrix factorization of the sum of two polynomials from their respective matrix factorizations and the multiplicative tensor product of matrix factorizations (cf.…”

“…

An algorithm for matrix factorization of polynomials was proposed in [12] 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 that we call the reduced multiplicative tensor product of matrix factorizations denoted by ⊗.

…”

“…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 that we call the reduced multiplicative tensor product of matrix factorizations denoted by ⊗. In fact, we observe that in the algorithm for matrix factorization of polynomials developed in [12], 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.…”