Hi!

On 6 Nov., 10:57, luisfe <[email protected]> wrote:
> You could use resultants in this case to eliminate de u.

Or, more generally, you could use elimination:

sage: R.<x,y,u> = QQ[]
sage: I = [2*x -(2*u^2+2*u-1 ), -y^2- (u^4+2*u^3-2*u-1)]*R
sage: I.elimination_ideal([u])
Ideal (16*x^4 + 32*x^2*y^2 + 16*y^4 - 24*x^2 - 24*y^2 - 16*x - 3) of
Multivariate Polynomial Ring in x, y, u over Rational Field

This would also work if you have more than one variable to eliminate,
as you will find if you read the documentation by
  sage: I.elimination_ideal?

Cheers,
Simon

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