maths.numerical_analysis.proper_fractions
=========================================

.. py:module:: maths.numerical_analysis.proper_fractions


Functions
---------

.. autoapisummary::

   maths.numerical_analysis.proper_fractions.proper_fractions


Module Contents
---------------

.. py:function:: 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