"""
Exercise 7.12 in "A Primer on..."

Implement a class for a sum:
- user provides function for each term
Attributes:
- function for each term
- lower and higher index of summation
"""

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



print('a:')
#following code should 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



print('b:')
def test_Sum():
    def f(k,x):
        return (-x)**k

    S = Sum(term = f, M=0, N=3)

    x = 0.5
    expected = 1 - x + x**2 - x**3
    computed = S(x)
    tol = 1e-10
    assert abs(computed-expected) < tol

test_Sum()

print('c:')
"""
Terms in Taylor approximation of sin(x):
(-1)**k*(x**(2*k+1))/factorial(2*k+1)
"""

from math import *
def taylor_sin(k,x):
    return (-1)**k*(x**(2*k+1))/factorial(2*k+1)

S = Sum(taylor_sin,0,5)

print(S(pi/4),S(pi/2),S(pi))

"""
Terminal> python Sum.py
a:
0.625
0.0625
b:
c:
0.7071067811796194 0.999999943741051 -0.00044516023820921277
"""