Singular

Is the radical easier or harder to calculate than Groebner basis? Is the basis given after radical calculation a Groebner basis? Is it better to calculate radical first or Groebner?

Now I know the answer myself. In practice it is much, much harder to calculate the radical of an ideal than its Gröbner basis. But the radical is a bliss. The basis in the calculation of the radical is not Gröbner, but from there Gröbner basis seems easy to calculate.