TY - JOUR

T1 - Desingularization in the q-Weyl algebra

AU - Koutschan, Christoph

AU - Zhang, Yi

N1 - Publisher Copyright:
© 2018 Elsevier Inc.

PY - 2018/6

Y1 - 2018/6

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85043397924&partnerID=8YFLogxK

U2 - 10.1016/j.aam.2018.02.005

DO - 10.1016/j.aam.2018.02.005

M3 - Article

AN - SCOPUS:85043397924

SN - 0196-8858

VL - 97

SP - 80

EP - 101

JO - Advances in Applied Mathematics

JF - Advances in Applied Mathematics

ER -