Projects per year
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 language | English |
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Number of pages | 17 |
DOIs | |
Publication status | Published - Feb 2020 |
Publication series
Name | arXiv.org |
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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
Projects
- 3 Finished
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Symbolic computations for identities of linear operators
Regensburger, G. (PI)
01.09.2019 → 29.02.2024
Project: Funded research › FWF - Austrian Science Fund
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Algorithmic integro-differential algebra
Raab, C. (PI)
01.01.2019 → 31.07.2023
Project: Funded research › FWF - Austrian Science Fund
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Algebra and algorithms for integro-differential equations
Hossein Poor, J. (Researcher), Raab, C. (Researcher) & Regensburger, G. (PI)
01.01.2015 → 31.12.2019
Project: Funded research › FWF - Austrian Science Fund