On tensor products of matrix factorizations
Yves Baudelaire Fomatati

TL;DR
This paper introduces a new multiplicative tensor product for matrix factorizations, enabling more efficient polynomial factorization algorithms with smaller matrix sizes.
Contribution
It proposes a novel bifunctorial tensor product for matrix factorizations that produces factorizations of the product of polynomials, improving existing algorithms.
Findings
Defined the multiplicative tensor product $ ilde{oxtimes}$ for matrix factorizations.
Proved properties of the new tensor product and its variants.
Developed an improved polynomial factorization algorithm with smaller matrix sizes.
Abstract
Let be a field. Let and be nonzero elements. If (resp. ) is a matrix factorization of (resp. ), Yoshino had constructed a tensor product (of matrix factorizations) such that is a matrix factorization of . In this paper, we propose a bifunctorial operation and its variant such that and are two different matrix factorizations of . We call the multiplicative tensor product of and . Several properties of are proved. Moreover, we find three functorial variants of Yoshino's tensor product . Then, (or its variant) is…
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Taxonomy
TopicsCoding theory and cryptography · Advanced Topics in Algebra · Polynomial and algebraic computation
