"""
Ex. 7.12 from "A primer on..."
Write a class for calculating a sum.
The constructor should take the
following parameters:
- A function representing each term in the sum 
- The upper and lower bounds in the sum
"""
from math import factorial, pi


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

#a) make sure the following lines work: 
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) write a test function test_Sum:
"""
(Not done in lecture, but added here for completeness)
We can use the case above for the test function, 
for which:
expected = 1 - x + x**2 - x**3 
= 1 - 0.5 + 0.25 - 0.125 = 0.625   
"""
def test_Sum():
    tol = 1e-8
    term = lambda k, x: (-x)**k
    s = Sum(term, M = 0, N = 3)
    computed = s(x = 0.5)
    expected = 0.625
    assert abs(computed - expected) < tol

test_Sum()

#c) Taylor series for sin(x):
def sin_term(k, x):
    return (-1)**k * x**(2 * k + 1) / factorial(2 * k + 1 )

#Taylor series with 11 terms:
sin_approx = Sum(sin_term, 0, 10)
print(sin_approx(pi))

"""
Terminal> python Sum.py 
0.625
0.0625
1.0348185903053497e-11
"""