Having used early versions of Mathematica in university, I'm actually a huge fan of Maxima (a fork of Macsyma, the latter having been the principle inspiration behind Mathematica). I have it installed on several systems and use it now for all the things I used to use Mathematica. In fact, the CL source code for rational numbers in Maxima formed the basis of similar work in LFE (the horatio project).

I was very sad to find out that Xlisp-Stat had not been ported and maintained in CL :-/ ... perhaps a good project for a motivated, if fringe, *SoC project :-)