adding a proper fractions algorithm

maths/numerical_analysis/proper_fractions.py

@@ -0,0 +1,37 @@
+import doctest
+from math import gcd
+
+
+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: https://en.wikipedia.org/wiki/Fraction#:~:text=Proper%20and%20improper,and%203/3.
+
+    >>> 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
+    >>> proper_fractions(0)
+    []
+    >>> proper_fractions(1.2)
+    Traceback (most recent call last):
+    ValueError: The Denominator has to be an integer
+    """
+
+    if denominator < 0:
+        raise ValueError("The Denominator Cannot be less than 0")
+    elif isinstance(denominator, float):
+        raise ValueError("The Denominator has to be an integer")
+    return [
+        f"{numerator}/{denominator}"
+        for numerator in range(1, denominator)
+        if gcd(numerator, denominator) == 1
+    ]
+
+
+if __name__ == "__main__":
+    doctest.testmod()