as you might have noticed, I am trying to improve the syntax and semantics
for symbolic math in Python. Until now, I have to say, my ideas were not that well received, but I learned from the discussion and maybe this time I come up with something people like.
For about 10 years I've used PARI/gp for computer algebra, mainly for integer linear algebra and polynomials. One day I might use its number theory features. http://pari.math.u-bordeaux.fr/
Lately it's acquired good Python bindings, and most likely for my next project I'll start using them. https://pari.math.u-bordeaux.fr/Events/PARI2019/talks/jeroen.html https://pypi.org/project/cypari2/ https://cypari2.readthedocs.io/en/latest/
Regarding semantics, I'm very happy to go along with PARI/gp. This is in part because of its deep roots in computational number theory and the community it has around it.
See also: Integer Factorization Software: PARI/GP, Mathematica, and SymPy https://dzone.com/articles/integer-factorization-software-parigp-mathematica
Regarding syntax, I'd be pleased to see a paritools package that makes it easier to use the cypari2 bindings for common purposes. This perhaps could become part of sympy. It's also worth looking at sage. https://doc.sagemath.org/html/en/reference/libs/sage/libs/pari.html
This is what I would like. Other people will most likely have different wishes for improving symbolic math in Python.