[SPACECADET3D]

It depends on what you want to do. It should be much faster than Sympy and it is often much faster than Mathematica, for example if you do pattern matching or are manipulating rational polynomials.

The idea of Symbolica is that you can use it as a library inside your existing projects, which is harder to do with MM since it is its own ecosystem.

Moreover, for personal projects Symbolica is free.

[jjtheblunt]

Can Symbolica compute Gröbner bases over user specified coefficient rings? I don't see, in the docs, how one would specify such.