English

Free (rational) Derivation

Rings and Algebras 2021-06-24 v2

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.

Keywords

Cite

@article{arxiv.2012.07398,
  title  = {Free (rational) Derivation},
  author = {Konrad Schrempf},
  journal= {arXiv preprint arXiv:2012.07398},
  year   = {2021}
}

Comments

22 pages, 1 figure; peer-reviewed version, accepted in Extracta Mathematicae