I'd be interested in doing some computations in quantum groups $ U\_q(\mathfrak g)$ that are conceptually simple (``is this element 0"?, and $\mathfrak g = sl\_5$), but are somewhat lengthy to do by hand. Is there software available that can do this? (I.e. take an element of the quantum group and reduce it to a PBW basis.) I've done some Googling and asked a couple people who I thought might know, but haven't found an answer. (In particular, the QuantumGroups package by Scott Morrison on KnotAtlas doesn't seem to do reductions to a PBW basis.)



Computing in quantum groups
There is the package QuaGroup by de Graaf for both GAP and Magma: see [QuaGroup](http://www.science.unitn.it/~degraaf/quagroup.html). I've used it in both systems and found it to be extremely helpful. Since there's a GAP package, you also have the option of using it inside Sage.


You will potentially want to be careful about exactly which PBW basis you and the computer are working with, of course.


