Methods mimicking function calls and iterables

Using a class instance together with parentheses or brackets, () or [], invokes a call to one of the special methods __call__ or __getitem__, giving the instance the behavior of a function or of an iterable; see also Table 8.1.

class Polynomial:
    ...
    def __call__(self, x):
        return self.eval(x)

Which now may be used as follows:

p = Polynomial(...)    # Creating a polynomial object
p(3.) # value of p at 3.

The special method __getitem__ makes sense if the class provides an iterator (it is recommended that you review Section 9.2.1: Generators before you consider the following example).

The recursion is called a three-term recursion. It plays an important role in applied mathematics, in particular in the construction of orthogonal polynomials. We can set up a three-term recursion as a class in the following way:

import itertools

class  Recursion3Term:
    def __init__(self, a0, a1, u0, u1):
        self.coeff = [a1, a0]
     ...