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sage: R.<x,y> = QQ[]
sage: I = Ideal( x^3-x+1 , y-x^6 )
sage: R
Multivariate Polynomial Ring in x, y over Rational Field
sage: I
Ideal (x^3 - x + 1, -x^6 + y) of Multivariate Polynomial Ring in x, y over Rational Field
sage: I.elimination_ideal( [x] )
Ideal (y^3 - 5*y^2 - 2*y - 1) of Multivariate Polynomial Ring in x, y over Rational Field