adding a proper fractions algorithm (#11224)

* adding a proper fractions algorithm

* Implementing suggestions in maths/numerical_analysis/proper_fractions.py

Co-authored-by: Christian Clauss <cclauss@me.com>

* [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci

* Implementing suggestions to proper_fractions.py

* Fixing ruff errors in proper_fractions.py

* Apply suggestions from code review

* ruff check --output-format=github .

* Update maths/numerical_analysis/proper_fractions.py

* Update proper_fractions.py

---------

Co-authored-by: Christian Clauss <cclauss@me.com>
Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>

.github/workflows/ruff.yml

@@ -13,4 +13,4 @@ jobs:
     steps:
       - uses: actions/checkout@v4
       - run: pip install --user ruff
-      - run: ruff --output-format=github .
+      - run: ruff check --output-format=github .

maths/numerical_analysis/proper_fractions.py

@@ -0,0 +1,40 @@
+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
+    https://en.wikipedia.org/wiki/Fraction#Proper_and_improper_fractions
+
+    >>> 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 must be an integer
+    """
+
+    if denominator < 0:
+        raise ValueError("The Denominator Cannot be less than 0")
+    elif isinstance(denominator, float):
+        raise ValueError("The Denominator must be an integer")
+    return [
+        f"{numerator}/{denominator}"
+        for numerator in range(1, denominator)
+        if gcd(numerator, denominator) == 1
+    ]
+
+
+if __name__ == "__main__":
+    from doctest import testmod
+
+    testmod()