In accordance with the work of David Eisenbud cited under, it’s attainable to factorize nearly any polynomial with matrices (exclusions ~ no linear phrases), and this has apparently been of nice to make use of to string theorists, amongst others, and I understood him high say (Numberphile YouTube Video) that the end result will not be merely an existence theorem, there may be an algorithm for doing it.
(The paper is a proof of a generalisation of the approach invented by Paul Dirac that resulted in Dirac Matrices)
A cursory examination of the unique paper means that although the end result could also be merely acknowledged, the algorithm will not be essentially easy (I’ve not even discovered an outline of it) and it might most likely require each superior mathematical and superior Mathematica information.
Does anybody know of an current implementation of the algorithm in Mathematica?
A fast examine of the present on-line documentation for Issue doesn’t point out that matrix factorisation is an choice.
Eisenbud, David. ‘Homological Algebra on a Full Intersection, with
an Utility to Group Representations’. Transactions of the American
Mathematical Society 260, no. 1 (1980): 35–64.