# your code goes here
""" base58 encoding / decoding functions """
import unittest
 
alphabet = '123456789ABCDEFGHJKLMNPQRSTUVWXYZabcdefghijkmnopqrstuvwxyz'
base_count = len(alphabet)
 
def encode(num):
	""" Returns num in a base58-encoded string """
	encode = ''
 
	if (num < 0):
		return ''
 
	while (num >= base_count):	
		mod = num % base_count
		encode = alphabet[mod] + encode
		num = num / base_count
 
	if (num):
		encode = alphabet[num] + encode
 
	return encode
 
def decode(s):
	""" Decodes the base58-encoded string s into an integer """
	decoded = 0
	multi = 1
	s = s[::-1]
	for char in s:
		decoded += multi * alphabet.index(char)
		multi = multi * base_count
 
	return decoded
 
class Base58Tests(unittest.TestCase):
 
  def test_alphabet_length(self):
    self.assertEqual(58, len(alphabet))
 
  def test_encode_10002343_returns_Tgmc(self):
    result = encode(10002343)
    self.assertEqual('Tgmc', result)
 
  def test_decode_Tgmc_returns_10002343(self):
    decoded = decode('Tgmc')
    self.assertEqual(10002343, decoded)
 
  def test_encode_1000_returns_if(self):
    result = encode(1000)
    self.assertEqual('if', result)
 
  def test_decode_if_returns_1000(self):
    decoded = decode('if')
    self.assertEqual(1000, decoded)
 
  def test_encode_zero_returns_empty_string(self):
    self.assertEqual('', encode(0))
 
  def test_encode_negative_number_returns_empty_string(self):
    self.assertEqual('', encode(-100))
 
if __name__ == '__main__':
  #print encode(int("00B94BA6C51B3D8372D82FDE5DC78773D960B5A82FCDAC8181",16))
  print hex(decode("Wh4bh"))

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import numpy as np
from scipy.optimize import fsolve

# Define parameters
alpha = 1.0
T0 = 300
g4 = -2.0
g6 = 1.0

# Define g2 as a function of T
def g2(T):
    return alpha * (T - T0)

# Define the free energy function
def F(P, T):
    return 0.5 * g2(T) * P**2 + 0.25 * g4 * P**4 + (1/6) * g6 * P**6

# Define the derivative of F with respect to P
def dF_dP(P, T):
    return g2(T) * P + g4 * P**3 + g6 * P**5

# Function to find P_s for a given T
def find_Ps(T):
    # Initial guess for P_s
    P_guess = 1.0
    # Solve dF/dP = 0
    P_s = fsolve(dF_dP, P_guess, args=(T))[0]
    return P_s

# Function to find T_c where F(P_s, T) = F(0, T)
def find_Tc():
    # Define a function for the difference in free energy
    def delta_F(T):
        P_s = find_Ps(T)
        return F(P_s, T) - F(0, T)
    # Initial guess for T_c
    T_guess = 310
    # Solve delta_F = 0
    T_c = fsolve(delta_F, T_guess)[0]
    return T_c

# Find T_c
Tc = find_Tc()
print(f"Curie Temperature T_c: {Tc}")

# Find P_s at T_c
P_s = find_Ps(Tc)
P5_squared = P_s**2
print(f"P_5^2(T_c): {P5_squared}")