Use S::=Q[x,y]; I1:=Ideal(2x^2+3xy+y^2-3x-3y, xy^2-x, y^3-y); I2:=Ideal(3x^2+ 4xy +y^2 -7x -5y +4, 3y^3+ 10xy +7y^2 -4x -20y +4, 3xy^2 -7xy -7y^2 -2x +11y+2); ----------------------- Use R::=Q[x,y,z]; I3:=Ideal(x^2-2xz+5, xy^2+yz+1, 3y^2-8xz); I4:=Ideal(x^2+2y^2-y-2z, x^2-8y^2+10z-1, x^2-7yz);