Contrary to popular belief, #mathematician s and theoretical #physicist s don't just discuss their theories on blackboards all day, but much of the research in practice involves #software and coding. Recently, I started using #PariGP , which is an #opensource algebra system that has existed since the 1980s but is still being actively developed today. It has amazing abilities in the realm of number theory, all sorts of modulus and p-adic computations, etc. I use it because it is very fast in handling power series and polynomials. Of course, it can deal with big rational numbers and arbitrary precision float.
I recommend reading the "GP tutorial" pdf. It is one of the most entertaining tutorials I have done in a long time, written in a subtle funny way . https://pari.math.u-bordeaux.fr/doc.html