import math as m

class Sum(object):

	def __init__(self, term, M, N):
		#self.term = term
		self.f_k = term
		self.M = M
		self.N = N

	def __call__(self, x):
		# calculate Taylor polynomial approximation
		s = 0
		for k in range(self.M, self.N+1):
			s += self.f_k(k, x)
		return s

	def term(self, k, x):
		return self.f_k(k, x)


def term(k, x):
	return (-x)**k


def f_sin(j, x):
	return (-1)**j * (x**(2*j+1))/m.factorial(2*j + 1)


def test_Sum():
	def f(k, x):
		return x**k

	M = 0
	N = 2
	x = 0.5
	expected = x**0 + x**1 + x**2
	S = Sum(term=f, M=M, N=N)
	computed = S(x)

	tol = 1e-20

	assert abs(expected - computed) < tol


if __name__ == '__main__':
	print('a)')
	S = Sum(term, M=0, N=3)
	x = 0.5
	print(S(x)) # calculate sum over f_k(x) for various k
	print(S.term(k=4, x=x)) # caluclate f_k(x) for specific k
	
	print('b)')
	a = test_Sum()
	if a is None: # or a == None, *almost* the same
		print('Test succeeded!')

	print('c)')
	N = 5
	Taylor_sin = Sum(f_sin, M=0, N=N)
	x = m.pi # sin(x) = 0
	expected = 0
	result = Taylor_sin(x)
	print(result)