Symbolic mathematics is severely underexplored in undergraduate studies, and the little exposure I had was generally tied to proprietary software such as Mathematica and MATLAB. I learned to use it as an imperfect extension of pen-and-paper thinking, and source code for more advanced stuff gets shaky the deeper into abstraction one goes. For example, I work in a field of mathematics/engineering that requires heavy use of tensor calculations. My go-to tool for that is Maxima, however, it has limited and cumbersome packages for it (see [0]). Now for more sophisticated calculations I resort to SymPy, not necessarily because of better handling of symbolics but because of the abstractions that Python already has. Maybe someday I'll get to read the Principles by Norvig and fix Maxima to suit my needs (if anyone has better references to read Maxima's source code/implementation of tensor computations/symbolic (tensor, geometric) algebra I would be grateful to know).
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For great justice, does anyone know of any applications (other than Maple) that support WYSIWYG typeset input (not output) like Maple does?
As far as I know, Wolfram/Mathematica, LaTex, SymPy, Jupyter, Sage etc all rely on typewriter text for composing and inputting math. For this (and only this) reason, Maple is the only application that ever resonated with me, because input may be written in the same form it's written by hand, and it's baffling this capability isn't more commonplace. Is this a barrier to anyone else?
There's a lot of them. In principle every CAS that has a TeXmacs interface can do it (FriCAS, Maxima, Reduce ... oo). E.g. https://news.ycombinator.com/item?id=19465270.
MathCad works this way also, IIRC.
a close friend of mine used to tell me about these production Mathematica Notebooks he'd author at his company Coherence to do all these optical and thermal calculations with. It was a regular workhorse for him.
A very long time ago I used to play around with Derive5 in my youth. It was the most affordable Computer Algebra System (CAS) of the time and I learned to program in that funky one liner programming language where I had to strip all the white space from my editor and always be careful to balance parenthesis. I should dig up those old files and upload them to my github. I've been actually meaning to reimplement those operations in a more modern CAS system and see if I can more densely plot these curves I was studying with some iso-arc-length families of exponentials about the point (0,1).