Does anyone have a recommendation for software which can efficiently calculate the Baker-Campbell-Hausdorff series in classical Lie algebras?

Right now, I have a problem which boils down to understanding Baker-Campbell-Hausdorff with respect to a basis in su(2), and this seems like the kind of thing Sage or Mathematica should be able to handle. However, I haven't had to use computer algebra packages for Lie theory before, so I would love to be pointed in the right direction.

Many thanks,

Jesse