x_R := PolynomialAlgebra( IntegerRing() ); x_x := Generator(x_R, 1); x_O := MaximalOrder( x_x^5-5*x_x^3+7*x_x^2-15*x_x+16 ); x_G := ClassGroup(x_O); x_f := x_G.ext1; x_I := Factorization( 7*x_O )[1][1]; x_g := Preimage(x_I, x_f); x_J := x_f(x_g); IsPrincipal(x_I / x_J);