x_gf3 := FiniteField(3);; x_gf3x := PolynomialAlgebra(x_gf3);; x_gf3xy := PolynomialAlgebra(x_gf3x);; x_f := x_gf3xy.1^2+1;; x_F := FunctionField(x_f);; x_O := MaximalOrderFinite(x_F);; x_I := Element(x_O,[3,1])*x_O; IsIntegral(x_I); IsIntegral(1/x_I);