a.py

from math import *
from fractions import Fraction
from sys import *

def twice(x, y):
    x2 = (x*x*x*x-16*x)/(4*x*x*x+8)
    y2 = sqrt_frac(x2*x2*x2+2)
    return x2, y2

def sqrt_frac(x):
    n = x.numerator
    d = x.denominator
    r_n = 0
    r_d = 1
    found = False 
    for i in range(100000000):
        if i*i == n:
            r_n = i
            found = True
            break
        if i*i > n:
            break
    if not found:
        sys.exit()

    found = False
    for i in range(100000000):
        if i*i == d:
            r_d = i
            found = True
            break
        if i*i > d:
            break
    if not found:
        sys.exit()

    return Fraction(r_n, r_d)

r1x, r1y = twice(Fraction(-1), Fraction(1)) 
print(r1x, r1y)
r2x, r2y = twice(r1x, r1y)
print(r2x, r2y)
r3x, r3y = twice(r2x, r2y)
print(r3x, r3y)