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Maxima enabled me to make my color space [HSLuv](https://www.hsluv.org/). I encoded CIELUV <-> RGB transformation functions into Maxima, ran `solve` and converted the output back into code. It's great to be able to commit [Maxima code](https://github.com/hsluv/hsluv/tree/master/math) into your repository and not leave the math as an "exercise to the reader".
An alternative is to run maxima from jupyter: https://github.com/robert-dodier/maxima-jupyter.
Except when it doesn't work. I tried using it a few months ago on both Windows and WSL, but I had to give up. Surprisingly, EIN¹ running a Maxima kernel worked.
I was going to try again before commenting, but I broke my WSL setup last week and didn't have time to fix it yet, but I sure will try it again next month.
¹ http://millejoh.github.io/emacs-ipython-notebook/
If you need programmability or interoperability, Sympy is way nicer. If you just want an interactive symbolic calculator, Maxima is fine but sometimes quirky (has odd conventions due mainly to its age). As heisig points out, Maxima can be quite a bit faster (but I run into slow things with it too). Using Maxima via Sage is in some ways the best of both worlds.
You may also be interested in SymEngine: https://github.com/symengine/symengine
Reduce is another lisp based computer algebra system from the prehistoric times, now open sourced.
https://en.wikipedia.org/wiki/Reduce_(computer_algebra_syste...
https://reduce-algebra.sourceforge.io/
I paid money for a Reduce release for RISCOS back in the last ice age. I recollect having to register my licence with the Rand Corporation for some reason.
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