From 73fa0cad8185b505fd4b9ad25ea85e1371dbe117 Mon Sep 17 00:00:00 2001
From: aarav570 <aaravmalde458@gmail.com>
Date: Wed, 28 Oct 2026 10:32:41 +0000
Subject: [PATCH 1/3] feat(maths): add Farey sequence generator

---
 maths/farey_sequence.py | 71 +++++++++++++++++++++++++++++++++++++++++
 1 file changed, 71 insertions(+)
 create mode 100644 maths/farey_sequence.py

diff --git a/maths/farey_sequence.py b/maths/farey_sequence.py
new file mode 100644
index 000000000000..26a58a177d6d
--- /dev/null
+++ b/maths/farey_sequence.py
@@ -0,0 +1,71 @@
+"""
+Farey Sequence Generator
+
+The Farey sequence of order n is the sequence of completely reduced
+fractions between 0 and 1 which have denominators less than or equal to n,
+arranged in increasing order.
+
+Reference: https://en.wikipedia.org/wiki/Farey_sequence
+"""
+
+from fractions import Fraction
+
+
+def farey_sequence(order: int) -> list[Fraction]:
+    """
+    Generate the Farey sequence of a given order in ascending order.
+
+    :param order: The maximum denominator allowed in the fractions.
+    :return: A list of Fraction objects in ascending order.
+
+    >>> farey_sequence(1)
+    [Fraction(0, 1), Fraction(1, 1)]
+    >>> farey_sequence(2)
+    [Fraction(0, 1), Fraction(1, 2), Fraction(1, 1)]
+    >>> farey_sequence(5)
+    [Fraction(0, 1), Fraction(1, 5), Fraction(1, 4), Fraction(1, 3), Fraction(2, 5), Fraction(1, 2), Fraction(3, 5), Fraction(2, 3), Fraction(3, 4), Fraction(4, 5), Fraction(1, 1)]
+    >>> farey_sequence(0)
+    Traceback (most recent call last):
+        ...
+    ValueError: Order must be a positive integer
+    >>> farey_sequence(-3)
+    Traceback (most recent call last):
+        ...
+    ValueError: Order must be a positive integer
+    >>> farey_sequence("5")
+    Traceback (most recent call last):
+        ...
+    TypeError: Order must be an integer
+    """
+    if not isinstance(order, int) or isinstance(order, bool):
+        raise TypeError("Order must be an integer")
+    if order < 1:
+        raise ValueError("Order must be a positive integer")
+
+    sequence: list[Fraction] = [Fraction(0, 1)]
+    numerator1, denominator1 = 0, 1
+    numerator2, denominator2 = 1, order
+
+    sequence.append(Fraction(numerator2, denominator2))
+
+    while numerator2 != 1 or denominator2 != 1:
+        scale_factor = (denominator1 + order) // denominator2
+        next_numerator = scale_factor * numerator2 - numerator1
+        next_denominator = scale_factor * denominator2 - denominator1
+
+        sequence.append(Fraction(next_numerator, next_denominator))
+
+        numerator1, denominator1 = numerator2, denominator2
+        numerator2, denominator2 = next_numerator, next_denominator
+
+    return sequence
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()
+
+    print("Farey sequence of order 4:")
+    print(farey_sequence(4))
+

From de64e8df420436b9e23498286d2e28fd382c8a13 Mon Sep 17 00:00:00 2001
From: "pre-commit-ci[bot]"
 <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Date: Wed, 28 Oct 2026 10:39:36 +0000
Subject: [PATCH 2/3] [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci
---
 maths/farey_sequence.py | 1 -
 1 file changed, 1 deletion(-)

diff --git a/maths/farey_sequence.py b/maths/farey_sequence.py
index 26a58a177d6d..cdafd314501c 100644
--- a/maths/farey_sequence.py
+++ b/maths/farey_sequence.py
@@ -68,4 +68,3 @@ def farey_sequence(order: int) -> list[Fraction]:
 
     print("Farey sequence of order 4:")
     print(farey_sequence(4))
-

From bb5aa0d7020daf631010ad09ff8d8d62405d0a7e Mon Sep 17 00:00:00 2001
From: aarav570 <aaravmalde458@gmail.com>
Date: Wed, 28 Oct 2026 10:48:19 +0000
Subject: [PATCH 3/3] style(maths): fix ruff E501 line length in doctests

---
 maths/farey_sequence.py | 6 ++++--
 1 file changed, 4 insertions(+), 2 deletions(-)

diff --git a/maths/farey_sequence.py b/maths/farey_sequence.py
index cdafd314501c..e022399ecfe6 100644
--- a/maths/farey_sequence.py
+++ b/maths/farey_sequence.py
@@ -22,8 +22,10 @@ def farey_sequence(order: int) -> list[Fraction]:
     [Fraction(0, 1), Fraction(1, 1)]
     >>> farey_sequence(2)
     [Fraction(0, 1), Fraction(1, 2), Fraction(1, 1)]
-    >>> farey_sequence(5)
-    [Fraction(0, 1), Fraction(1, 5), Fraction(1, 4), Fraction(1, 3), Fraction(2, 5), Fraction(1, 2), Fraction(3, 5), Fraction(2, 3), Fraction(3, 4), Fraction(4, 5), Fraction(1, 1)]
+    >>> farey_sequence(3)
+    [Fraction(0, 1), Fraction(1, 3), Fraction(1, 2), Fraction(2, 3), Fraction(1, 1)]
+    >>> [(f.numerator, f.denominator) for f in farey_sequence(4)]
+    [(0, 1), (1, 4), (1, 3), (1, 2), (2, 3), (3, 4), (1, 1)]
     >>> farey_sequence(0)
     Traceback (most recent call last):
         ...