2017/06/06 by Konrad Schrempf · 1 voice
Mathematics · #math.RA #msc:16G99 #msc:16K40 #msc:16S10 #msc:16Z05
paper · pdf · doi:10.1016/j.jsc.2018.07.004
29 pages, extended (section 2.2 is new) and slightly updated version, accepted in JSC
arxiv published 2017/06/06 · arxiv created 2018/08/08 · arxiv updated 2018/08/09
We describe a simple approach to factorize non-commutative (nc) polynomials, that is, elements in free associative algebras (over a commutative field), into atoms (irreducible elements) based on (a special form of) their minimal linear representations. To be more specific, a correspondence between factorizations of an element and upper right blocks of zeros in the system matrix (of its representation) is established. The problem is then reduced to solving a system of polynomial equations (with at most quadratic terms) with commuting unknowns to compute appropriate transformation matrices (if possible).