For a long time I have been puzzled by the apparent lack of a comprehensive Open Source computer algebra software, i.e. what Octave is to MatLab and what R is to S. In other words, where is the Open Source equivalent of Mathematica and Maple? For several years now I have been migrating towards Open Source for most of the software I use, with the notable exception of my computer algebra software (which currently is Mathematica). Most recently I took the leap from MatLab to R. Switching from a software I have been using for over a decade to a new software that I knew nothing about was (is) rather intimidating.

Although there are numerous Open Source symbolic math softwares available (see e.g. here for a list) most seem to be rather specialized, e.g. either polynomials, or matrix calculations, or general algebra, or symbolic manipulations. So far I have not found anything that is even close to being as mathematically capable as Mathematica and Maple. Have I overlooked something or is there really nothing out there?