Free (rational) derivation

• K. Schrempf ^[1]
  1. [1] Austrian Academy of Sciences

     Austrian Academy of Sciences

     Innere Stadt, Austria

     
• Localización: Extracta mathematicae, ISSN-e 0213-8743, Vol. 36, Nº 1, 2021, págs. 25-50
• Idioma: inglés
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• Resumen

  • 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.