fix: enforce simple form uniqueness of element sequences in `Continue…

…dFraction.extend` op + update tests

src/continuedfractions/continuedfraction.py

@@ -321,7 +321,17 @@ def extend(self, *new_elements: int) -> None:
             )
 
         elements = self._elements + new_elements
+
+        # A step to ensure uniqueness of the simple form of the continued
+        # fraction - if the last of the new elements is ``1`` it can be
+        # "absorbed" by adding it to the second last element, thereby
+        # shortening the sequence by one element. The resulting simple
+        # continued fraction becomes unique for the number that is represented.
+        if len(elements) > 1 and elements[-1] == 1:
+            elements = elements[:-2] + (elements[-2] + 1,)
+
         fraction = fraction_from_elements(*elements)
+
         self._numerator, self._denominator = fraction.as_integer_ratio()
         self._elements = elements
 

tests/units/test_continuedfraction.py

@@ -561,8 +561,13 @@ def test_ContinuedFraction__extend__invalid_elements__value_error_raised(self, i
     @pytest.mark.parametrize(
         "instance, new_elements, expected_comparative_instance",
         [
+            (ContinuedFraction(0, 1), (1,), ContinuedFraction(1, 1)),
             (ContinuedFraction(0, 1), (2,), ContinuedFraction(1, 2)),
+            (ContinuedFraction(0, 1), (2, 1,), ContinuedFraction(1, 3)),
+            (ContinuedFraction(0, 1), (3,), ContinuedFraction(1, 3)),
             (ContinuedFraction(1, 1), (2,), ContinuedFraction(3, 2)),
+            (ContinuedFraction(1, 1), (2, 1), ContinuedFraction(4, 3)),
+            (ContinuedFraction(1, 1), (3,), ContinuedFraction(4, 3)),
             (ContinuedFraction(3, 2), (3,), ContinuedFraction(10, 7)),
             (ContinuedFraction(649, 200), (5, 2), ContinuedFraction(7457, 2298)),
             (ContinuedFraction(-415, 93), (2, 1, 5), ContinuedFraction(-7403, 1659))