Abstract
We propose a general algorithmic approach to noncommutative operator algebras generated by linear operators using quotients of tensor algebras. In order to work with reduction systems in tensor algebras, Bergman’s setting provides a tensor analog of Gröbner bases. We discuss a modification of Bergman’s setting that allows for smaller reduction systems and tends to make computations more efficient. Verification of the confluence criterion based on S-polynomials has been implemented as a Mathematica package. Our implementation can also be used for computer-assisted construction of Gröbner bases starting from basic identities of operators. We illustrate our approach and the software using differential and integro-differential operators as examples.
All authors were supported by the Austrian Science Fund (FWF): P27229.
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Hossein Poor, J., Raab, C.G., Regensburger, G. (2016). Normal Forms for Operators via Gröbner Bases in Tensor Algebras. In: Greuel, GM., Koch, T., Paule, P., Sommese, A. (eds) Mathematical Software – ICMS 2016. ICMS 2016. Lecture Notes in Computer Science(), vol 9725. Springer, Cham. https://doi.org/10.1007/978-3-319-42432-3_65
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DOI: https://doi.org/10.1007/978-3-319-42432-3_65
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