Add Euler's Totient Function and Visualization

pysnippets/Mathematics/Euler Function/euler.py

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+import matplotlib.pyplot as plt
+from math import gcd
+
+def euler_totient_function(n):
+    """
+    Calculate Euler's Totient Function φ(n), which is the count of integers 
+    from 1 to n that are coprime with n.
+    
+    Parameters:
+    n (int): Input number
+    
+    Returns:
+    tuple: (Value of φ(n), List of coprime numbers)
+    """
+    if n <= 0:
+        raise ValueError("Input must be a positive integer.")
+
+    original_n = n  # Save the original value of n for coprime calculation
+    result = n
+    coprimes = []
+
+    # Check divisors up to √n
+    p = 2
+    while p * p <= n:
+        if n % p == 0:
+            while n % p == 0:
+                n //= p
+            result -= result // p
+        p += 1
+
+    if n > 1:
+        result -= result // n
+
+    # Find coprimes using the original n
+    for i in range(1, original_n + 1):
+        if gcd(i, original_n) == 1:
+            coprimes.append(i)
+
+    return result, coprimes
+
+def visualize_coprimes(n, coprimes):
+    """
+    Visualize coprime numbers up to n using a bar chart.
+    
+    Parameters:
+    n (int): Input number
+    coprimes (list): List of coprime numbers
+    """
+    all_numbers = list(range(1, n + 1))
+    coprime_flags = [1 if num in coprimes else 0 for num in all_numbers]
+
+    plt.figure(figsize=(10, 6))
+    plt.bar(all_numbers, coprime_flags, color='skyblue', edgecolor='black', label='Coprime')
+    plt.title(f"Coprime Numbers Up to {n}", fontsize=16)
+    plt.xlabel("Numbers", fontsize=14)
+    plt.ylabel("Coprime (1 = Yes, 0 = No)", fontsize=14)
+    plt.xticks(range(1, n + 1, max(1, n // 10)))
+    plt.yticks([0, 1], labels=["Not Coprime", "Coprime"])
+    plt.grid(axis='y', linestyle='--', alpha=0.6)
+    plt.legend()
+    plt.show()
+
+# Example usage
+if __name__ == "__main__":
+    num = int(input("Enter a positive integer: "))
+    result, coprimes = euler_totient_function(num)
+    print(f"φ({num}) = {result}")
+    print(f"Coprime numbers up to {num}: {coprimes}")
+
+    visualize_coprimes(num, coprimes)

pysnippets/Mathematics/Euler Function/test_euler.py

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+import unittest
+from euler import euler_totient_function, visualize_coprimes
+
+class TestEulerFunction(unittest.TestCase):
+
+    def test_phi_value(self):
+        # Test the Euler's Totient function value
+        self.assertEqual(euler_totient_function(1)[0], 1)
+        self.assertEqual(euler_totient_function(6)[0], 2)
+        self.assertEqual(euler_totient_function(9)[0], 6)
+        self.assertEqual(euler_totient_function(10)[0], 4)
+
+    def test_coprimes_list(self):
+        # Test the list of coprimes
+        self.assertEqual(euler_totient_function(9)[1], [1, 2, 4, 5, 7, 8])
+        self.assertEqual(euler_totient_function(10)[1], [1, 3, 7, 9])
+        self.assertEqual(euler_totient_function(6)[1], [1, 5])
+        self.assertEqual(euler_totient_function(1)[1], [1])
+
+    def test_invalid_input(self):
+        # Test invalid input
+        with self.assertRaises(ValueError):
+            euler_totient_function(0)
+        with self.assertRaises(ValueError):
+            euler_totient_function(-5)
+
+    def test_visualize_coprimes(self):
+        # Test the visualize_coprimes function 
+        try:
+            visualize_coprimes(10, [1, 3, 7, 9])
+        except Exception as e:
+            self.fail(f"visualize_coprimes raised an exception: {e}")
+
+if __name__ == "__main__":
+    unittest.main()