Systems

FriCAS Axiom

https://twitter.com/jjcarett2/status/1598627244292935681?s=20&t=5JLrAKIKjXwiuDermxDT0g Schwartz-Zippel and polynomial identity testing https://arxiv.org/abs/2211.09691

https://www.philipzucker.com/a-smattering-of-physics-in-sympy/

sympy makes math fun agan

from sympy import *
init_printing()
t,a,d,vf,vi = symbols("t a d vf vi")
e1 = Eq(d , vi * t + 1/2 * a * t ** 2)
tsub = solve(Eq(vf , vi + a * t),t)[0]
print(tsub) # This is assuming a is nonzero though.
expand(simplify(e1.subs(t,tsub)))

Integration

https://en.wikipedia.org/wiki/Symbolic_integration

Risch algorithm https://en.wikipedia.org/wiki/Risch_algorithm

https://groups.google.com/g/sci.math.symbolic