Desingularization in the q-Weyl algebra

Christoph Koutschan and Yi Zhang
support of q-recurrences


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.


Here is the full text (preprint) of our paper Desingularization in the q-Weyl algebra.

Supplementary electronic material

Examples: twist knots

   p    original recurrence linear combination bimonic recurrence
 ord  deg file  ord  deg file  ord  deg file
-3 623 rec.twist.knot.-3.m  616 lincomb.twist.-3.m  1218 bmrec.twist.-3.m 
-2 415rec.twist.knot.-2.m 49lincomb.twist.-2.m 811bmrec.twist.-2.m
-1 27rec.twist.knot.-1.m 23lincomb.twist.-1.m 45bmrec.twist.-1.m
2 312rec.twist.knot.2.m 24lincomb.twist.2.m 59bmrec.twist.2.m
3 520rec.twist.knot.3.m 410lincomb.twist.3.m 915bmrec.twist.3.m
4 728rec.twist.knot.4.m 616lincomb.twist.4.m 1321bmrec.twist.4.m

Examples: pretzel knots