Release v0.18.1 (#128)

* chore: bump version refs to `0.18.0`

* ci: add Python 3.13 to the CI matrix strategy + update all docs refs to supported Python versions

* chore(deps): PDM update + update all dev + docs deps

* chore: TOML tweak to add Python 3.13 classifier

* chore: bump Read The Docs build Python version to 3.13

* docs: small improvements to the creating continued fractions docs

* docs: small improvements to the exploring continued fractions docs

* docs: small improvements to the sequences docs

* fix: enforce simple form uniqueness of element sequences in `ContinuedFraction.extend` op + update tests

* docs: tweak docs for creating continued fractions

* chore(deps): update dev. & docs deps

* chore: bump version refs to `0.18.1`

.readthedocs.yaml

@@ -9,7 +9,7 @@ version: 2
 build:
   os: ubuntu-22.04
   tools:
-    python: "3.11"
+    python: "3.13"
 
     # You can also specify other tool versions:
     # nodejs: "20"

CITATION.cff

@@ -24,5 +24,5 @@ keywords:
   - real numbers
 
 license: MPL-2.0
-version: 0.18.0
+version: 0.18.1
 date-released: 2024-10-25

CONTRIBUTING.md

@@ -227,7 +227,7 @@ includes Ruff linting, unit tests, Python doctests, and in that order.
 ## Versioning and Releases
 
 The [PyPI package](https://pypi.org/project/continuedfractions/) is
-currently at version `0.18.0` - the goal is to use [semantic
+currently at version `0.18.1` - the goal is to use [semantic
 versioning](https://semver.org/) consistently for all future releases,
 but some earlier releases do not comply with strict semantic versioning.
 

docs/requirements.txt

@@ -52,9 +52,9 @@ backports-tarfile==1.2.0; python_version < "3.12" \
 beautifulsoup4==4.12.3 \
     --hash=sha256:74e3d1928edc070d21748185c46e3fb33490f22f52a3addee9aee0f4f7781051 \
     --hash=sha256:b80878c9f40111313e55da8ba20bdba06d8fa3969fc68304167741bbf9e082ed
-bleach==6.1.0 \
-    --hash=sha256:0a31f1837963c41d46bbf1331b8778e1308ea0791db03cc4e7357b97cf42a8fe \
-    --hash=sha256:3225f354cfc436b9789c66c4ee030194bee0568fbf9cbdad3bc8b5c26c5f12b6
+bleach==6.2.0 \
+    --hash=sha256:117d9c6097a7c3d22fd578fcd8d35ff1e125df6736f554da4e432fdd63f31e5e \
+    --hash=sha256:123e894118b8a599fd80d3ec1a6d4cc7ce4e5882b1317a7e1ba69b56e95f991f
 certifi==2024.8.30 \
     --hash=sha256:922820b53db7a7257ffbda3f597266d435245903d80737e34f8a45ff3e3230d8 \
     --hash=sha256:bec941d2aa8195e248a60b31ff9f0558284cf01a52591ceda73ea9afffd69fd9
@@ -498,9 +498,9 @@ jupyterlab-server==2.27.3 \
 jupyterlab-widgets==3.0.13 \
     --hash=sha256:a2966d385328c1942b683a8cd96b89b8dd82c8b8f81dda902bb2bc06d46f5bed \
     --hash=sha256:e3cda2c233ce144192f1e29914ad522b2f4c40e77214b0cc97377ca3d323db54
-keyring==25.4.1 \
-    --hash=sha256:5426f817cf7f6f007ba5ec722b1bcad95a75b27d780343772ad76b17cb47b0bf \
-    --hash=sha256:b07ebc55f3e8ed86ac81dd31ef14e81ace9dd9c3d4b5d77a6e9a2016d0d71a1b
+keyring==25.5.0 \
+    --hash=sha256:4c753b3ec91717fe713c4edd522d625889d8973a349b0e582622f49766de58e6 \
+    --hash=sha256:e67f8ac32b04be4714b42fe84ce7dad9c40985b9ca827c592cc303e7c26d9741
 kiwisolver==1.4.7 \
     --hash=sha256:073a36c8273647592ea332e816e75ef8da5c303236ec0167196793eb1e34657a \
     --hash=sha256:0c18ec74c0472de033e1bebb2911c3c310eef5649133dd0bedf2a169a1b269e5 \
@@ -853,9 +853,9 @@ pillow==11.0.0 \
     --hash=sha256:fba162b8872d30fea8c52b258a542c5dfd7b235fb5cb352240c8d63b414013eb \
     --hash=sha256:fbbcb7b57dc9c794843e3d1258c0fbf0f48656d46ffe9e09b63bbd6e8cd5d0a2 \
     --hash=sha256:fcb4621042ac4b7865c179bb972ed0da0218a076dc1820ffc48b1d74c1e37fe9
-pip==24.2 \
-    --hash=sha256:2cd581cf58ab7fcfca4ce8efa6dcacd0de5bf8d0a3eb9ec927e07405f4d9e2a2 \
-    --hash=sha256:5b5e490b5e9cb275c879595064adce9ebd31b854e3e803740b72f9ccf34a45b8
+pip==24.3.1 \
+    --hash=sha256:3790624780082365f47549d032f3770eeb2b1e8bd1f7b2e02dace1afa361b4ed \
+    --hash=sha256:ebcb60557f2aefabc2e0f918751cd24ea0d56d8ec5445fe1807f1d2109660b99
 pkginfo==1.10.0 \
     --hash=sha256:5df73835398d10db79f8eecd5cd86b1f6d29317589ea70796994d49399af6297 \
     --hash=sha256:889a6da2ed7ffc58ab5b900d888ddce90bce912f2d2de1dc1c26f4cb9fe65097
@@ -904,9 +904,9 @@ pyparsing==3.2.0 \
 pytest==8.3.3 \
     --hash=sha256:70b98107bd648308a7952b06e6ca9a50bc660be218d53c257cc1fc94fda10181 \
     --hash=sha256:a6853c7375b2663155079443d2e45de913a911a11d669df02a50814944db57b2
-pytest-cov==5.0.0 \
-    --hash=sha256:4f0764a1219df53214206bf1feea4633c3b558a2925c8b59f144f682861ce652 \
-    --hash=sha256:5837b58e9f6ebd335b0f8060eecce69b662415b16dc503883a02f45dfeb14857
+pytest-cov==6.0.0 \
+    --hash=sha256:eee6f1b9e61008bd34975a4d5bab25801eb31898b032dd55addc93e96fcaaa35 \
+    --hash=sha256:fde0b595ca248bb8e2d76f020b465f3b107c9632e6a1d1705f17834c89dcadc0
 pytest-xdist==3.6.1 \
     --hash=sha256:9ed4adfb68a016610848639bb7e02c9352d5d9f03d04809919e2dafc3be4cca7 \
     --hash=sha256:ead156a4db231eec769737f57668ef58a2084a34b2e55c4a8fa20d861107300d
@@ -1155,9 +1155,9 @@ secretstorage==3.3.3; sys_platform == "linux" \
 send2trash==1.8.3 \
     --hash=sha256:0c31227e0bd08961c7665474a3d1ef7193929fedda4233843689baa056be46c9 \
     --hash=sha256:b18e7a3966d99871aefeb00cfbcfdced55ce4871194810fc71f4aa484b953abf
-setuptools==75.2.0 \
-    --hash=sha256:753bb6ebf1f465a1912e19ed1d41f403a79173a9acf66a42e7e6aec45c3c16ec \
-    --hash=sha256:a7fcb66f68b4d9e8e66b42f9876150a3371558f98fa32222ffaa5bced76406f8
+setuptools==75.3.0 \
+    --hash=sha256:f2504966861356aa38616760c0f66568e535562374995367b4e69c7143cf6bcd \
+    --hash=sha256:fba5dd4d766e97be1b1681d98712680ae8f2f26d7881245f2ce9e40714f1a686
 six==1.16.0 \
     --hash=sha256:1e61c37477a1626458e36f7b1d82aa5c9b094fa4802892072e49de9c60c4c926 \
     --hash=sha256:8abb2f1d86890a2dfb989f9a77cfcfd3e47c2a354b01111771326f8aa26e0254
@@ -1208,9 +1208,9 @@ sphinxtesters==0.2.3 \
 stack-data==0.6.3 \
     --hash=sha256:836a778de4fec4dcd1dcd89ed8abff8a221f58308462e1c4aa2a3cf30148f0b9 \
     --hash=sha256:d5558e0c25a4cb0853cddad3d77da9891a08cb85dd9f9f91b9f8cd66e511e695
-starlette==0.41.0 \
-    --hash=sha256:39cbd8768b107d68bfe1ff1672b38a2c38b49777de46d2a592841d58e3bf7c2a \
-    --hash=sha256:a0193a3c413ebc9c78bff1c3546a45bb8c8bcb4a84cae8747d650a65bd37210a
+starlette==0.41.2 \
+    --hash=sha256:9834fd799d1a87fd346deb76158668cfa0b0d56f85caefe8268e2d97c3468b62 \
+    --hash=sha256:fbc189474b4731cf30fcef52f18a8d070e3f3b46c6a04c97579e85e6ffca942d
 sympy==1.13.3 \
     --hash=sha256:54612cf55a62755ee71824ce692986f23c88ffa77207b30c1368eda4a7060f73 \
     --hash=sha256:b27fd2c6530e0ab39e275fc9b683895367e51d5da91baa8d3d64db2565fec4d9
@@ -1264,9 +1264,9 @@ urllib3==2.2.3 \
 uvicorn==0.32.0 \
     --hash=sha256:60b8f3a5ac027dcd31448f411ced12b5ef452c646f76f02f8cc3f25d8d26fd82 \
     --hash=sha256:f78b36b143c16f54ccdb8190d0a26b5f1901fe5a3c777e1ab29f26391af8551e
-virtualenv==20.27.0 \
-    --hash=sha256:2ca56a68ed615b8fe4326d11a0dca5dfbe8fd68510fb6c6349163bed3c15f2b2 \
-    --hash=sha256:44a72c29cceb0ee08f300b314848c86e57bf8d1f13107a5e671fb9274138d655
+virtualenv==20.27.1 \
+    --hash=sha256:142c6be10212543b32c6c45d3d3893dff89112cc588b7d0879ae5a1ec03a47ba \
+    --hash=sha256:f11f1b8a29525562925f745563bfd48b189450f61fb34c4f9cc79dd5aa32a1f4
 watchfiles==0.24.0 \
     --hash=sha256:01550ccf1d0aed6ea375ef259706af76ad009ef5b0203a3a4cce0f6024f9b68a \
     --hash=sha256:083dc77dbdeef09fa44bb0f4d1df571d2e12d8a8f985dccde71ac3ac9ac067a0 \

docs/sources/contributing.rst

@@ -178,7 +178,7 @@ The CI pipelines are defined in the `CI YML <https://github.com/sr-murthy/contin
 Versioning and Releases :fas:`upload`
 =====================================
 
-The `PyPI package <https://pypi.org/project/continuedfractions/>`_ is currently at version ``0.18.0`` - the goal is to use `semantic versioning <https://semver.org/>`_ consistently for all future releases, but some earlier releases do not comply with strict semantic versioning.
+The `PyPI package <https://pypi.org/project/continuedfractions/>`_ is currently at version ``0.18.1`` - the goal is to use `semantic versioning <https://semver.org/>`_ consistently for all future releases, but some earlier releases do not comply with strict semantic versioning.
 
 There is currently no dedicated pipeline for releases - both `GitHub releases <https://github.com/sr-murthy/continuedfractions/releases>`_ and `PyPI packages <https://pypi.org/project/continuedfractions>`_ are published manually, but both have the same version tag.
 

docs/sources/creating-continued-fractions.rst

@@ -24,32 +24,33 @@ This is derived by repeatedly applying `Euclid's division lemma <https://en.wiki
 .. math::
 
    \begin{align}
-   \frac{649}{200} &= 3 + \cfrac{49}{200} \\
+   \frac{649}{200} &= \cfrac{3 \times 200 + 49}{200} \\
+                   &= 3 + \cfrac{49}{200} \\
                    &= 3 + \cfrac{1}{\cfrac{200}{49}} \\
+                   &= 3 + \cfrac{1}{\cfrac{4 \times 49 + 4}{49}} \\
                    &= 3 + \cfrac{1}{4 + \cfrac{4}{49}} \\
                    &= 3 + \cfrac{1}{4 + \cfrac{1}{\cfrac{49}{4}}} \\
+                   &= 3 + \cfrac{1}{4 + \cfrac{1}{\cfrac{4 \times 12 + 1}{4}}} \\
                    &= 3 + \cfrac{1}{4 + \cfrac{1}{12 + \cfrac{1}{4}}}
    \end{align}
 
-The numbers :math:`3, 4, 12, 4` are called **elements** (or **coefficients**) of the continued fraction :math:`[3; 4, 12, 4]`, and the number of elements after the first - in this case :math:`3` - is defined to be its **order**.
+The numbers :math:`3, 4, 12, 4` are called **elements** (or **coefficients**) of the continued fraction :math:`[3; 4, 12, 4]`, and the number of elements after the first - in this case :math:`3` - is defined to be its **order**. The order can be finite or infinite depending on whether the number represented is rational or irrational, as will be discussed later.
 
 The representation :math:`[3; 4, 12, 4]` is called **simple** (or **regular**) because all of the numerators in the fractional terms are equal to :math:`1`, which makes the fractions irreducible (cannot be simplified further). Mathematically, the continued fraction is written as :math:`[3; 4, 12, 4]`. The representation is also unique - the only other representation is :math:`[3; 4, 12, 3, 1]`, which can be rewritten as :math:`[3; 4, 12, 4]`.
 
 .. note::
 
-   All references to continued fractions are to the simple forms where the last element :math:`> 1`.
-
-   Support for non-simple, generalised continued fractions is planned to be included in future releases.
+   All references to "continued fraction" are to the simple forms. Support for non-simple, generalised continued fractions is planned to be included in future releases.
 
 We can think of :math:`3`, which is the integer part of :math:`\frac{649}{200} = 3.245`, as the "head" of the continued fraction, and the integers :math:`4, 12, 4`, which determine the fractional part :math:`\cfrac{1}{4 + \cfrac{1}{12 + \cfrac{1}{4}}} = \frac{49}{200} = 0.245` of the continued fraction, as its "tail".
 
-In general, a simple continued fraction is denoted by a tuple of integers, enclosed in square brackets:
+The generally used notation for a simple continued fraction is a tuple of integers :math:`[a_0; a_1, a_2, \ldots, a_n, \ldots]`, which stands for the fraction:
 
 .. math::
 
-   [a_0; a_1, a_2, \ldots, a_n, \ldots] = a_0 + \cfrac{1}{a_1 + \cfrac{1}{a_2 + \ddots \cfrac{1}{a_n + \ddots}}}
+   a_0 + \cfrac{1}{a_1 + \cfrac{1}{a_2 + \ddots \cfrac{1}{a_n + \ddots}}}
 
-where :math:`a_0` is the integer part, and :math:`a_1,a_2,\ldots` are (positive) integers defining the fractional part, in the representation.
+where :math:`a_0` is the integer part, and :math:`a_1,a_2,\ldots` are (positive) integers defining the fractional part, in the representation. If the order is finite, i.e. :math:`n < \infty`, then we may assume the last element :math:`a_n > 1` because :math:`[a_0; a_1, a_2, \ldots a_{n - 1}, a_n = 1] = [a_0; a_1, a_2, \ldots a_{n - 1} + 1]`.
 
 .. _creating-continued-fractions.from-numeric-types:
 
@@ -260,6 +261,21 @@ A :py:class:`ValueError` is raised if the tail elements provided are invalid, e.
    ...
    ValueError: The elements/coefficients to be added to the tail must be positive integers.
 
+.. note::
+
+   If the last of the new elements passed to :py:meth:`~continuedfractions.continuedfraction.ContinuedFraction.extend` happens to be :math:`1` then it is added to the previous element to ensure uniqueness of the new sequence of elements of the resulting continued fraction, e.g.:
+
+   .. code:: python
+
+   >>> cf = ContinuedFraction.from_elements(3, 4, 12, 3)
+   >>> cf
+   ContinuedFraction(490, 151)
+   >>> cf.extend(1)
+   >>> cf
+   ContinuedFraction(649, 200)
+   >>> cf.elements
+   (3, 4, 12, 4)
+
 .. _creating-continued-fractions.inplace-truncation:
 
 In-place Truncation of Tail Elements

docs/sources/exploring-continued-fractions.rst

@@ -171,23 +171,23 @@ Convergents have a stronger version of this property: namely a rational number :
 
 The current implementation of :py:class:`~continuedfractions.continuedfraction.ContinuedFraction` can only represent finite (simple) continued fractions, which means that the convergents in its instances will always be finite in number, regardless of whether the real numbers they approximate are rational or irrational. Support for infinite, generalised continued fractions will be added in future releases.
 
-We know, for example, that the square root :math:`\sqrt{n}` of any non-square (positive) integer :math:`n` is irrational. This can be seen by writing :math:`n = a^2 + r`, for integers :math:`a, r > 0`, from which we have:
+We can show, for example, that the square root :math:`\sqrt{n}` of any non-square (positive) integer :math:`n` is irrational by considering positive integers of the form :math:`n = (ka)^2 + r`, for integers :math:`k, a, r > 0` and :math:`(k, a) = 1`. From this we have:
 
 .. math::
    :nowrap:
 
    \begin{alignat*}{1}
-   & r &&= n - a^2 = \left(\sqrt{n} + a\right)\left(\sqrt{n} - a\right) \\
-   & \sqrt{n} &&= a + \frac{r}{a + \sqrt{n}}
+   & r &&= n - (ka)^2 = \left(\sqrt{n} + ka\right)\left(\sqrt{n} - ka\right) \\
+   & \sqrt{n} &&= ka + \frac{r}{2ka + \sqrt{n}}
    \end{alignat*}
 
 Expanding the expression for :math:`\sqrt{n}` recursively we have the following infinite periodic continued fraction for :math:`\sqrt{n}`:
 
 .. math::
 
-   \sqrt{n} = a + \cfrac{r}{2a + \cfrac{r}{2a + \cfrac{r}{2a + \ddots}}}
+   \sqrt{n} = ka + \cfrac{r}{2ka + \cfrac{r}{2ka + \cfrac{r}{2ka + \ddots}}}
 
-With :math:`a = r = 1` we can represent :math:`\sqrt{2}` as the continued fraction:
+With :math:`k = a = r = 1` we can represent :math:`\sqrt{2}` as the continued fraction:
 
 .. math::
 

docs/sources/sequences.rst

@@ -108,7 +108,7 @@ Here are some examples of constructing left-mediants:
    >>> cf1 = ContinuedFraction('1/2')
    >>> cf2 = ContinuedFraction(3, 5)
    # The default `k = 1` gives you the common, simple mediant of the two rationals
-   >>> cf1.left_mediant(c2)
+   >>> cf1.left_mediant(cf2)
    ContinuedFraction(4, 7)
    >>> cf1.left_mediant(cf2, k=2)
    ContinuedFraction(5, 9)
@@ -124,7 +124,7 @@ and right-mediants:
    >>> cf1 = ContinuedFraction('1/2')
    >>> cf2 = ContinuedFraction(3, 5)
    # The default `k = 1` gives you the common, simple mediant of the two rationals
-   >>> cf1.right_mediant(c2)
+   >>> cf1.right_mediant(cf2)
    ContinuedFraction(4, 7)
    >>> cf1.right_mediant(cf2, k=2)
    ContinuedFraction(7, 12)