variety X
i1 : X = PP_QQ^(2,2); o1 : ProjectiveVariety, surface in PP^5
i2 : class X o2 = EmbeddedProjectiveVariety o2 : Type
i3 : X' = variety X;
i4 : class X' o4 = ProjectiveVariety o4 : Type
i5 : assert(ring X === ring X')