# Hiermee bereken je de parameters in het geval dat D = 0 en q'' > 0

import numpy as np

J = 1.7321
Rs = 1

E2 = 2 * (9 * Rs**2 * J + J**3 + (J**2 - 3 * Rs**2) * np.sqrt (J**2 - 3 * Rs**2)) / (27 * Rs**2 * J)
E = np.sqrt (E2)

K = E
U = 1 - K**2

a = Rs
b = -1
c = Rs / J**2
d = - U / J**2

D = 18 * a * b * c * d - 4 * a * c**3 - 27 * a**2 * d**2 + b**2 * c**2 - 4 * b**3 * d

q = (1 / (9 * Rs**2) - 1 / (3 * J**2)) * np.sqrt (1 / (9 * Rs**2) - 1 / (3 * J**2))

h1 = 1 - 3 * Rs**2 / J**2
h2 = np.sqrt (h1)
h3 = np.sqrt (h2)

n1 = (1 - 2 * h2) / (3 * Rs)
n2 = (1 + h2) / (3 * Rs)

r1 = 1 / n1
r2 = 1 / n2

print ("J = ", J)
print ("Rs = ", Rs)
print ("E2 = ", E2)
print ("E = ", E)
print ("K = ", K)
print ("U = ", U)
print ("a = ", a)
print ("b = ", b)
print ("c = ", c)
print ("d = ", d)
print ("D = ", D)
print ("q = ", q)
print ("n1 = ", n1)
print ("n2 = ", n2)
print ("r1 = ", r1)
print ("r2 = ", r2)