Compatible rewriting of noncommutative polynomials for proving operator identities

Cyrille Chenavier, Clemens Hofstadler, Clemens Raab, Georg Regensburger

Research output: Working paper and reportsPreprint

Abstract

The goal of this paper is to prove operator identities using equalities between noncommutative polynomials. In general, a polynomial expression is not valid in terms of operators, since it may not be compatible with domains and codomains of the corresponding operators. Recently, some of the authors introduced a framework based on labelled quivers to rigorously translate polynomial identities to operator identities. In the present paper, we extend and adapt the framework to the context of rewriting and polynomial reduction. We give a sufficient condition on the polynomials used for rewriting to ensure that standard polynomial reduction automatically respects domains and codomains of operators. Finally, we adapt the noncommutative Buchberger procedure to compute additional compatible polynomials for rewriting. In the package OperatorGB, we also provide an implementation of the concepts developed.
Original languageEnglish
Number of pages17
DOIs
Publication statusPublished - Feb 2020

Publication series

NamearXiv.org
No.2002.03626
ISSN (Print)2331-8422

Fields of science

  • 101 Mathematics
  • 101001 Algebra
  • 101005 Computer algebra
  • 101013 Mathematical logic
  • 102031 Theoretical computer science

JKU Focus areas

  • Digital Transformation

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