For some areas within algebraic geometry I think other CAS's work better than Mathematica and have functionality that it lacks. For example, in the past I used

For some areas within algebraic geometry I think other CAS's work better than Mathematica and have functionality that it lacks. For example, in the past I used https://www.singular.uni-kl.de/ https://www.singular.uni-kl.de/. It has been too long since I studied such things so I cannot give any specific examples.