Free (rational) Derivation
arXiv:2012.07398 · doi:10.17398/2605-5686.36.1.25
Abstract
By representing elements in free fields (over a commutative field and a finite alphabet) using Cohn and Reutenauer's linear representations, we provide an algorithmic construction for the (partial) non-commutative (or Hausdorff-) derivative and show how it can be applied to the non-commutative version of the Newton iteration to find roots of matrix-valued rational equations.
22 pages, 1 figure; peer-reviewed version, accepted in Extracta Mathematicae