I'd like to give an alternative perspective on SymPy. Whilst I'm not familiar with Mathematica, and therefore cannot draw parallels between the two, I've used S

I'd like to give an alternative perspective on SymPy. Whilst I'm not familiar with Mathematica, and therefore cannot draw parallels between the two, I've used SymPy for a number of years and found it to be really useful. I was initially introduced to it as part of a first year programming module in a Physics degree, and it was more than sufficient for that use-case; for that use-case, it absolutely wasn't worth paying for something like Mathematica. When combined with a graphical REPL (some may use Spyder, I personally use jupyter-qtconsole) or a Jupyter Notebook, it becomes really quite useful as it incorporates LaTeX rendering to make its outputs more readable and a little less daunting. Whilst the syntax may not be optimal for the mathematical way of working, for many problems like simple rearrangements, automatic simplification, checking equivalences, etc. it is almost always the first tool I reach for. The syntax is just cosmetic, and I use Python enough that the syntax doesn't even bother me, either. It does its job well, and it's helped me solve and verify solutions for a number of mathematical problems during my degree. Admittedly, I do run into the occasional problem here and there where there are obviously better tools available, but that's the same with any gratis vs paid solution. In most cases, SymPy does a sufficiently good job.