Programmatically create arithmetic special methods in Python, (aka factory function HOWTO)

My idea is to create specific function objects that can be added / subtracted / ... together, returning a new function object that has the same properties. This sample code hopefully demonstrates the idea:

from FuncObj import Func

# create some functions
quad = Func(lambda x: x**2)
cube = Func(lambda x: x**3)

# now combine functions as you like
plus = quad + cube
minus = quad - cube
other = quad * quad / cube

# and these can be called
plus(1) + minus(32) * other(5)

I wrote the following code, which I hope will be commented and documented to explain what I want to achieve.

import operator

class GenericFunction(object):
    """ Base class providing arithmetic special methods. 
        Use derived class which must implement the 
        __call__ method.
    """

    # this way of defining special methods works well
    def __add__(self, operand):
        """ This is an example of a special method i want to implement. """
        obj = GenericFunction()
        # this is a trick from Alex Martelli at
        # http://stackoverflow.com/questions/1705928/problem-with-making-object-callable-in-python
        # to allow per-instance __call__ methods
        obj.__class__ = type(obj.__class__.__name__, (obj.__class__,), {})
        obj.__class__.__call__ = lambda s, ti: self(ti) + operand(ti)
        return obj

    # on the other hand this factory function seems buggy 
    def _method_factory(operation, name):
        """ Method factory.
        Parameters
        ----------
        op : callable
            an arithmetic operator from the operator module
        name : str
            the name of the special method that will be created
        Returns
        -------
        method : callable
            the __***__ special method
        """
        def method(s, operand):
            obj = GenericFunction()
            obj.__class__ = type(obj.__class__.__name__, (obj.__class__,), {})
            obj.__class__.__call__ = lambda s, ti: operation(s(ti), operand(ti))
            return obj
        return method

    __sub__ = _method_factory(operator.__sub__, '__sub__')
    __mul__ = _method_factory(operator.__mul__, '__mul__')
    __truediv__ = _method_factory(operator.__truediv__, '__div__')


class Func(GenericFunction):
    """ A customizable callable object. 
        Parameters
        ----------
        func : callable
    """
    def __init__(self, func):
        self.func = func

    def __call__(self, *args):
        return self.func(*args)


if __name__ == '__main__':

    # create some functions
    quad = Func(lambda x: x**2)
    cube = Func(lambda x: x**3)

    # now combine functions
    poly_plus = quad + cube
    poly_minus = quad - cube

    # this is the expected behaviour, and it works well
    # since the __add__ method is defined correctly.
    assert quad(1) + cube(1) == poly_plus(1)

    # this, and the others with * and / result in a "maximum recursion depth exceeded"
    assert quad(1) - cube(1) == poly_minus(1)

I think something is missing from me, but I do not see it.

EDIT

After Dietrich’s answer, I forgot to mention the corner case. Suppose I want to subclass GenericInput, and I need to set up a method call without passing to the called constructor. I have examples (actually this is the code for which I originally posted this question).

class NoiseInput(GenericInput):
    def __init__(self, sigma, a, b, t):
        """ A band-pass noisy input. """
        self._noise = lfilter(b, a, np.random.normal(0, 1, len(t)))
        self._noise *= sigma/self._noise.std()
        self._spline = InterpolatedUnivariateSpline(t, self._noise, k=2)

    def __call__(self, ti):
        """ Compute value of the input at a given time. """
        return self._spline(ti)

class SineInput(GenericInput):
    def __init__(self, A, fc):
        self.A = A
        self.fc = fc

    def __call__(self, ti):
        return self.A*np.sin(2*np.pi*ti*self.fc)

In this case, remains to be done.