[teho98]

Does anyone know how Gröbner bases compare to homotopy continuation methods for solving systems of polynomials?

https://www.juliahomotopycontinuation.org/

I haven’t been able to find much discussion about the specific trade offs in both, and how they compte from a practical perspective.

[zhamisen]

Roughly speaking, Gröbner bases is used for symbolic computations while homotopy continuation is used for numeric computation of roots