Hi Ben!

On Feb 28, 11:28 pm, Ben Goodrich <[email protected]> wrote:
> sage: R.<x,y,z> = QQ[]
> sage: ideal(sqrt(x) - 2, y - 2*x, x - z**2).groebner_basis()
> ---------------------------------------------------------------------------
> ...
> AttributeError: 'Ideal_generic' object has no attribute
> 'groebner_basis'

You may introduce an additional variable r, and add one polynomial to
your ideal such that r becomes square root of x:
  sage: R.<x,y,z,r> = QQ[]
  sage: ideal(r**2 - x, r - 2, y - 2*x, x - z**2).groebner_basis()
  [z^2 - 4, x - 4, y - 8, r - 2]

I guess this easily yields the solution to your equations, which is in
fact the same as the one obtained with "solve" (see Yann's post).

Best regards,
Simon

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