def METHOD_NAME(self, m):
    ##
    # Check the approximation of the transformation of the paraboloid
    ##
    z = m.pw_paraboloid.get_transformation_var(m.paraboloid_expr)
    self.assertIsInstance(z, Var)
    paraboloid_block = z.parent_block()
    ct.check_trans_block_structure(self, paraboloid_block)
    self.assertEqual(len(paraboloid_block.disjuncts), 4)
    disjuncts_dict = {
        # the normal vectors of the faces are normalized when we get
        # them from scipy:
        paraboloid_block.disjuncts[0]: (
            [
                [sqrt(2) / 2, -sqrt(2) / 2, sqrt(2) / 2],
                [-1.0, 0.0, 0.0],
                [0.0, 1.0, -4.0],
            ],
            m.g1,
        ),
        paraboloid_block.disjuncts[1]: (
            [
                [-sqrt(2) / 2, sqrt(2) / 2, -sqrt(2) / 2],
                [0.0, -1.0, 1.0],
                [1.0, 0.0, -3.0],
            ],
            m.g1,
        ),
        paraboloid_block.disjuncts[2]: (
            [
                [-sqrt(2) / 2, -sqrt(2) / 2, 7 * sqrt(2) / 2],
                [0.0, 1.0, -7.0],
                [1.0, 0.0, -3.0],
            ],
            m.g2,
        ),
        paraboloid_block.disjuncts[3]: (
            [
                [sqrt(2) / 2, sqrt(2) / 2, -7 * sqrt(2) / 2],
                [-1.0, 0.0, 0.0],
                [0.0, -1.0, 4.0],
            ],
            m.g2,
        ),
    }
    for d, (constraint_coefs, f) in disjuncts_dict.items():
        self.check_paraboloid_disjunct(
            d, constraint_coefs, f, paraboloid_block.substitute_var, m.x1, m.x2
        )
    # Check the Disjunction
    self.assertIsInstance(paraboloid_block.pick_a_piece, Disjunction)
    self.assertEqual(len(paraboloid_block.pick_a_piece.disjuncts), 4)
    for i in range(3):
        self.assertIs(
            paraboloid_block.pick_a_piece.disjuncts[i],
            paraboloid_block.disjuncts[i],
        )
    # And check the substitute Var is in the objective now.
    self.assertIs(m.indexed_c[0].body.args[0].expr, paraboloid_block.substitute_var)