def arithmeticalOperationX(self, i2, alpha, operation):
		""" Wrapper class for performing Fuzzy Arithmetic on X-mu Functions using SymPy/MPI. Primarily used as a private class, but could be used publicly.
		@param	i2	the target sympy formula.
		@param	alpha	the level on which to perform the operation.
		@param	operation	One of the following: +, -, *, /, **
		"""
		res = self.get_xequals().subs(ALPHA, float(alpha))
		res2 = i2.get_xequals().subs(ALPHA, float(alpha))
		if (not res.is_EmptySet) and (not res2.is_EmptySet):
			if (type(res) != FiniteSet) and (type(res2) != FiniteSet):
				result = eval("res.to_mpi() " + operation + " res2.to_mpi()")
			else:
				res_mpi = mpmath.mpi(res.inf, res.sup)
				res2_mpi = mpmath.mpi(res2.inf, res2.sup)
				result = eval("res_mpi " + operation + " res2_mpi")
			
			return BasicXmu(self.u, Interval(float(mpmath.mpf(result.a)), float(mpmath.mpf(result.b))))
		else:
			return None

def test_special_printers():
    class IntervalPrinter(LambdaPrinter):
        """Use ``lambda`` printer but print numbers as ``mpi`` intervals. """

        def _print_Integer(self, expr):
            return "mpi('%s')" % super(IntervalPrinter, self)._print_Integer(expr)

        def _print_Rational(self, expr):
            return "mpi('%s')" % super(IntervalPrinter, self)._print_Rational(expr)

    def intervalrepr(expr):
        return IntervalPrinter().doprint(expr)

    expr = sympy.sqrt(sympy.sqrt(2) + sympy.sqrt(3)) + sympy.S(1)/2

    func0 = lambdify((), expr, modules="mpmath", printer=intervalrepr)
    func1 = lambdify((), expr, modules="mpmath", printer=IntervalPrinter)
    func2 = lambdify((), expr, modules="mpmath", printer=IntervalPrinter())

    mpi = type(mpmath.mpi(1, 2))

    assert isinstance(func0(), mpi)
    assert isinstance(func1(), mpi)
    assert isinstance(func2(), mpi)

 def to_mpi(self, prec=53):
     return mpi(mpf(self.start.evalf(prec)), mpf(self.end.evalf(prec)))

def test_interval_to_mpi():
    assert Interval(0, 1).to_mpi() == mpi(0, 1)
    assert Interval(0, 1, True, False).to_mpi() == mpi(0, 1)
    assert type(Interval(0, 1).to_mpi()) == type(mpi(0, 1))

def test_D12():
    assert (mpi(-4, 2) * x + mpi(1, 3)) ** 2 == mpi(-8, 16)*x**2 + mpi(-24, 12)*x + mpi(1, 9)

 def _eval_evalf(self, prec):
     return mpi(self.start.evalf(prec), self.end.evalf(prec))

def test_interval_evalf():
    assert Interval(0, 1).evalf() == mpi(0, 1)
    assert Interval(0, 1, True, False).evalf() == mpi(0, 1)

def test_interval_to_mpi():
    raises(SymPyDeprecationWarning, "Interval(0, 1).to_mpi()")
    assert Interval(0, 1).to_mpi() == mpi(0, 1)
    assert Interval(0, 1, True, False).to_mpi() == mpi(0, 1)
    assert type(Interval(0, 1).to_mpi()) == type(mpi(0, 1))