I recently reinstalled my python environment and a code that used to work very quickly now creeps at best (usually just hangs taking up more and more memory).
The point
The rational=False flag was introduced for such cases as this.
>>> q=14.7296138519
>>> solve(exp(-alpha * q**2) - 0.01, alpha, rational=False)
[0.0212257459123917]
(The explanation is given in the issue cited above.)
Rolling back from version 0.7.2 to 0.7.1 solved this problem.
easy_install sympy==0.7.1
I've reported this as a bug to sympy's google code.