Don't forget Octave ( www.octave.org ), which belongs on any list of open-source analysis suites.
https://www.gnu.org/philosophy/open-source-misses-the-point....
Doing linear algebra -> Matlab/octave
Twiddling data tables around and making plots -> R
twiddling data tables making plots -> python/numpy/matplotlib
abstract math/calculus -> python/sympy
statistics/quick data analysis -> R