To manipulate equations I use Derive, SymPy, Wolfram Alpha (tried pro, but it does not enable any longer equations than the free version), and Wolframscript from Wolfram Engine for Developers. I also use Octave (MATLAB clone) and mpmath for large-number stuff.
Please do not hesitate to edit my questions and answers.
I try to remember to write out every abbreviation and explain obscure mathematical symbols at the first mention. Also it is never bad to link to Wikipedia.
I vote also on answers that compete with mine.
I cross-license all of my code and images in Stack Exchange under CC0 1.0.