import numpy as np
import matplotlib.pyplot as plt
import math

def seriesFunction(center, x):
	if x - center > 0:
		return (x - center) ** (1/3)
	else:
		return -((center - x) ** (1/3))

def series(n, x):
	q = 1.8
	f = 1
	s = 0
	for i in range(2, n+1):
		subs = 0
		for j in range(1, i):
			if math.gcd(i, j) == 1:
				subs += seriesFunction(j/i, x)
		s += subs / f
		f *= q
	return s

y = np.linspace(-0.1, 1.1, 5000)
x = [series(20, i) for i in y]


f, ax = plt.subplots()

ax.set_xlim(-4, 4)
ax.set_ylim(0, 1)
plt.plot(x, y)

plt.savefig("Pompeiu function.svg")