Desingularization in the $q$-Weyl algebra

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.

References in corpus (8)

• The colored Jones function is q-holonomic
• Irreducibility of q-difference operators and the knot 7_4
• Computing solutions of linear Mahler equations
• The non-commutative A-polynomial of (-2,3,n) pretzel knots
• Desingularization Explains Order-Degree Curves for Ore Operators
• Univariate Contraction and Multivariate Desingularization of Ore Ideals
• Twisting q-holonomic sequences by complex roots of unity
• Apparent Singularities of D-finite Systems

Cited by in corpus (1)

• Computing differential Galois groups of second-order linear $q$-difference equations