On the Factorization of Non-Commutative Polynomials (in Free Associative Algebras)
| Autor: | Schrempf, Konrad |
|---|---|
| Rok vydání: | 2017 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1016/j.jsc.2018.07.004 |
| Popis: | 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). Comment: 29 pages, extended (section 2.2 is new) and slightly updated version, accepted in JSC |
| Databáze: | arXiv |
| Externí odkaz: |
|