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arXiv · 1801.04160

Desingularization in the $q$-Weyl algebra

Christoph Koutschan·Yi Zhang
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Abstract

In this paper, we study the desingularization problem in the first $q$-Weyl algebra. We give an order bound for desingularized operators, and thus derive an algorithm for computing desingularized operators in the first $q$-Weyl algebra. Moreover, an algorithm is presented for computing a generating set of the first $q$-Weyl closure of a given $q$-difference operator. As an application, we certify that several instances of the colored Jones polynomial are Laurent polynomial sequences by computing the corresponding desingularized operator.

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BibTeXRIS

Christoph Koutschan, Yi Zhang. 2018-01-12. Desingularization in the $q$-Weyl algebra. https://doi.org/10.1016/j.aam.2018.02.005

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