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 -