import numpy as np
import matplotlib.pyplot as plt
import math
from fractions import Fraction

def nextPair(x, y):
	a = x
	b = y
	if (a + b) % 2 == 0:
		a -= 1
		b += 1
		if a == 0:
			a = 1
	else:
		a += 1
		b -= 1
		if b == 0:
			b = 1
	return a, b

def nextRational(x):
	if x == 0:
		return Fraction(1, 1)
	n = x.numerator
	d = x.denominator
	n, d = nextPair(n, d)
	while math.gcd(n, d) != 1:
		n, d = nextPair(n, d)
	return Fraction(n, d)

def seriesFunction(center, x):
	return 0 if x == center else (x-center)*(x-center)*math.sin(1/(x-center))

def series(n, x):
	q = 1.1
	f = 1
	s = 0
	r = Fraction(0, 1)
	for i in range(n):
		s += (seriesFunction(r, x)) / f
		if (i > 0):
			s += (seriesFunction(-r, x)) / f
		f *= q
		r = nextRational(r)
	return s - 20*x

x = np.linspace(-2.1, 2.1, 5000)
y = [series(100, i) for i in x]


f, ax = plt.subplots()

ax.set_xlim(-2, 2)
plt.plot(x, y)

plt.savefig("The continuosly differentiably in irrational and discontinuosly differentiably in rational function.svg")