catena

catena is a Python library for exact computation with simple continued fractions (SCFs).

A simple continued fraction is an expression of the form

\[ x = a_0 + \cfrac{1}{a_1 + \cfrac{1}{a_2 + \cfrac{1}{\ddots}}} \]

written compactly as \([a_0;\, a_1, a_2, \ldots]\). Every rational number has a finite SCF expansion; every quadratic irrational has a periodic one.

Three types

Class	Represents	Example
FiniteSimpleContinuedFraction	A rational number	\(22/7 = [3;\,7]\)
SimpleContinuedFraction	An infinite SCF given by a generator	\(e, \pi, \ldots\)
PeriodicSimpleContinuedFraction	A quadratic irrational	\(\sqrt{2} = [1;\,\overline{2}]\)

Quick start

from catena import FiniteSimpleContinuedFraction, PeriodicSimpleContinuedFraction

# 22/7 as a continued fraction
x = FiniteSimpleContinuedFraction.from_rational((22, 7))
x.partial_quotients   # (7,)
x.integer_part        # 3

# Exact rational value
x.terminal_convergent # (22, 7)

# Inversion  →  7/22
x.inverse().terminal_convergent  # (7, 22)

# √2 = [1; 2, 2, 2, …]
sqrt2 = PeriodicSimpleContinuedFraction(period=[2], integer_part=1)
float(sqrt2)  # 1.4142135623730951

Installation

pip install catena-scf