Software for Computing Baker-Campbell-Hausdorff 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
 A: You don't need any packages to be able to do that in Mathematica for small Lie algebras such as su(2), probably not in SAGE either (I'm familiar with Mathematica). Anyway, Basically you just need to use the MatrixExp function and solve some equations. E.g. define
$M_1 = \text{MatrixExp}\left[\sum\limits_i \alpha^i X_i\right]$ and $M_2 =\prod\limits_i\text{MatrixExp}\left[\beta^i X_i\right]$
You may get transcendental equations, but you can simplify things by hand. Here's $M_2$ explicitly (just pick a basis $X_i$):
$\text{M2}=\text{MatrixExp}[X[1]\alpha [1]].\text{MatrixExp}[X[2]\alpha [2]].\text{MatrixExp}[X[3]\alpha [3]]\text{//}\text{FullSimplify}$
A: There is a quite comprehensive package for Lie algebras in Maple. It is developed by Ian Anderson (from Utah State not Jethro Tull). 
A: I don't have a  first-hand experience, but   hope this is  helpful anyway. K.Engo, A.Marthinsen and H.Munthe-Kaas have done a lot of work on numerical methods for solving ODE on manifolds  (and Lie groups in particular). See for example their paper ''DiffMan: an object-oriented Matlab toolbox for solving differential equations on manifolds'', Appl. Numerical Mathematics, 39 (2001), p.323 where they discuss a particular package.
