I highly recommend you look into SymPy, which offers symbolic math computations on top of standard Python programming capabilities. I checks all the boxes excep

I highly recommend you look into SymPy, which offers symbolic math computations on top of standard Python programming capabilities. I checks all the boxes except for speed—since it is Python after all... What makes SymPy great for learning is the API it provides closely matches the math verbs: expand, factor, simplify, etc. so it feel very similar to what doing math on paper would be like. There is an online shell[1] you can use to try out some commands, and I've written a tutorial[2] that showcases some of the most useful commands. [1] https://live.sympy.org/ https://live.sympy.org/ [2] https://minireference.com/static/tutorials/sympy_tutorial.pdf https://minireference.com/static/tutorials/sympy_tutorial.pd...