x_R := PolynomialAlgebra( IntegerRing() ); x_x := Generator(x_R, 1); x_O := MaximalOrder(x_x^2 - 18); x_a := Element(x_O, [0,1] ); x_I := Factorization( 3*x_O )[1][1]; x_Ox := PolynomialAlgebra( x_O ); x_x := Generator(x_Ox, 1); x_OO := MaximalOrder( x_x^3 - 27*x_a ); x_II := CoerceIdeal(x_OO, x_I);