"""
Exercise 7.12 from "A primer on...
Implement a class for computing
a sum, where each term in the 
sum is given by a function passed 
as an argument to the constructor. 
A call method should compute and 
return the sum for a given argument x.
"""

from math import factorial, pi

#a) Implementation of the class 
class Sum:
    def __init__(self, term, M, N):
        self.term = term
        self.M = M
        self.N = N

    def __call__(self, x):
        s = 0
        for k in range(self.M, self.N+1):
            s += self.term(k, x)
        return s
        
#test code from the question text:
def term(k, x):
    return (-x)**k

S = Sum(term, M=0, N=3)
x = 0.5
print(S(x))
print(S.term(k=4, x=x)) # (-0.5)**4

#b) A test function for the class 
# (using the example above as the test case):
def test_Sum():
    S = Sum(term, M=0, N=3)
    x = 0.5
    tol = 1e-8
    expected_sum = 0.625
    expected_term = 0.0625
    assert abs(S(x)-expected_sum) < tol
    assert abs(S.term(4, x) - expected_term) < tol

test_Sum()

#c) Calculate the Taylor series approximation to sin(x),
# for x = pi and a given N

def term_sin(k, x):
    return (-1)**k / factorial(2 * k + 1) * x**(2 * k + 1) 

#test the approximation with N=6:
sin_taylor = Sum(term_sin, M=0, N = 6)
print(sin_taylor(pi))