adding a proper fractions algorithm

maths/numerical_analysis/proper_fractions.py

@@ -0,0 +1,42 @@
+def gcd(numerator: int, denominator: int) -> int:
+    """
+    >>> gcd(12, 18)
+    6
+    >>> gcd(20, 25)
+    5
+    >>> gcd(20, 0)
+    Traceback (most recent call last):
+    ValueError: The Denominator cannot be 0
+    """
+    if denominator == 0:
+        raise ValueError("The Denominator cannot be 0")
+    while denominator:
+        numerator, denominator = denominator, numerator % denominator
+    return numerator
+
+
+def proper_fractions(denominator: int) -> list[str]:
+    """
+    this algorithm returns a list of proper fractions, in the
+    range between 0 and 1, which can be formed with the given denominator
+    >>> proper_fractions(10)
+    ['1/10', '3/10', '7/10', '9/10']
+    >>> proper_fractions(5)
+    ['1/5', '2/5', '3/5', '4/5']
+    >>> proper_fractions(-15)
+    Traceback (most recent call last):
+    ValueError: The Denominator Cannot be less than 0
+    >>>
+    """
+
+    if denominator < 0:
+        raise ValueError("The Denominator Cannot be less than 0")
+    fractions: list[str] = []
+    for numerator in range(1, denominator):
+        if gcd(numerator, denominator) == 1:
+            fractions.append(f"{numerator}/{denominator}")
+    return fractions
+
+
+if __name__ == "__main__":
+    __import__("doctest").testmod()