Compatible rewriting of noncommutative polynomials for proving operator identities

Chenavier, Cyrille; Hofstadler, Clemens; Raab, Clemens G.; Regensburger, Georg

doi:10.1145/3373207.3404047

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Has a Finite Right Gröbner Basis1

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2020

2024

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Cited by 5 publications

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“…Remark 3.11 It has been observed that the noncommutative version of Buchberger's algorithm preserves compatibility of polynomials with a quiver [4,7,20]. This means that, if all polynomials that are given as input to this algorithm are compatible with a quiver, then so are all polynomials in the output.…”

Section: Has a Finite Right Gröbner Basismentioning

confidence: 99%

Computing Elements of Certain Form in Ideals to Prove Properties of Operators

2022

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Proving statements about linear operators expressed in terms of identities often leads to finding elements of certain form in noncommutative polynomial ideals. We illustrate this by examples coming from actual operator statements and discuss relevant algorithmic methods for finding such polynomials based on noncommutative Gröbner bases. In particular, we present algorithms for computing the intersection of a two-sided ideal with a one-sided ideal as well as for computing homogeneous polynomials in two-sided ideals and monomials in one-sided ideals. All methods presented in this work are implemented in the Mathematica package .

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Section: Has a Finite Right Gröbner Basismentioning

confidence: 99%