Update basic_maths.py (#1517)

* Update basic_maths.py

Add Doctests.

* Update basic_maths.py

* Add a space to fix the doctest

maths/basic_maths.py

@@ -2,55 +2,56 @@
 import math
 
 
-def prime_factors(n):
+def prime_factors(n: int) -> list:
-    """Find Prime Factors."""
+    """Find Prime Factors.
+    >>> prime_factors(100)
+    [2, 2, 5, 5]
+    """
     pf = []
     while n % 2 == 0:
         pf.append(2)
         n = int(n / 2)
-
     for i in range(3, int(math.sqrt(n)) + 1, 2):
         while n % i == 0:
             pf.append(i)
             n = int(n / i)
-
     if n > 2:
         pf.append(n)
-
     return pf
 
 
-def number_of_divisors(n):
+def number_of_divisors(n: int) -> int:
-    """Calculate Number of Divisors of an Integer."""
+    """Calculate Number of Divisors of an Integer.
+    >>> number_of_divisors(100)
+    9
+    """
     div = 1
-
     temp = 1
     while n % 2 == 0:
         temp += 1
         n = int(n / 2)
-    div = div * (temp)
+    div *= temp
-
     for i in range(3, int(math.sqrt(n)) + 1, 2):
         temp = 1
         while n % i == 0:
             temp += 1
             n = int(n / i)
-        div = div * (temp)
+        div *= temp
-
     return div
 
 
-def sum_of_divisors(n):
+def sum_of_divisors(n: int) -> int:
-    """Calculate Sum of Divisors."""
+    """Calculate Sum of Divisors.
+    >>> sum_of_divisors(100)
+    217
+    """
     s = 1
-
     temp = 1
     while n % 2 == 0:
         temp += 1
         n = int(n / 2)
     if temp > 1:
         s *= (2 ** temp - 1) / (2 - 1)
-
     for i in range(3, int(math.sqrt(n)) + 1, 2):
         temp = 1
         while n % i == 0:
@@ -58,27 +59,24 @@ def sum_of_divisors(n):
             n = int(n / i)
         if temp > 1:
             s *= (i ** temp - 1) / (i - 1)
-
+    return int(s)
-    return s
 
 
-def euler_phi(n):
+def euler_phi(n: int) -> int:
-    """Calculte Euler's Phi Function."""
+    """Calculte Euler's Phi Function.
+    >>> euler_phi(100)
+    40
+    """
     l = prime_factors(n)
     l = set(l)
     s = n
     for x in l:
         s *= (x - 1) / x
-    return s
+    return int(s)
 
 
-def main():
+if __name__ == "__main__":
-    """Print the Results of Basic Math Operations."""
     print(prime_factors(100))
     print(number_of_divisors(100))
     print(sum_of_divisors(100))
     print(euler_phi(100))
-
-
-if __name__ == "__main__":
-    main()