I need to solve a 12th degree polynomial with coefficients that are not numbers, but are made out of lots of algebra operations with letters. I could do them all by hand, but I counted them and it would take me around 7000 algebra operations do to so. Since this task can easily be automated I'm wondering what tools do professionals use to check their algebra?
Edit: And please dont tell me that 12 degree polynomials cant be solved, because I know all about Galois groups.
Wolfram Mathematica is really nice for stuff like that.