continuedfractions#

A simple extension of the Python fractions standard library for working with continued fractions as Python objects.

The package is designed to:

make it easy to construct continued fractions as Python objects
explore their key continued fractions properties, such as elements/coefficients, convergents, remainders, and other numerical properties etc.
operate on them fully as rational numbers and instances of the standard library fractions.Fraction class
support approximations and experimental computations for irrational numbers

You can start here, or go straight to the API reference.

Prelude#

\[\pi = 3 + \cfrac{1}{7 + \cfrac{1}{15 + \cfrac{1}{1 + \cfrac{1}{292 + \ddots}}}}\]

>>> import decimal, math; from continuedfractions.continuedfraction import ContinuedFraction
>>> cf = ContinuedFraction(math.pi)
>>> cf
ContinuedFraction(884279719003555, 281474976710656)
>>> cf.elements
(3,7,15,1,292,1,1,1,2,1,3,1,14,4,2,3,1,12,5,1,5,20,1,11,1,1,1,2)
>>> cf.as_decimal()
Decimal('3.141592653589793115997963468544185161590576171875')
>>> cf.convergent(0), cf.convergent(1), cf.convergent(2), cf.convergent(10), cf.convergent(20), cf.convergent(27)
(ContinuedFraction(3, 1), ContinuedFraction(22, 7), ContinuedFraction(333, 106), ContinuedFraction(4272943, 1360120), ContinuedFraction(509453239292, 162164002615), ContinuedFraction(884279719003555, 281474976710656))
>>> cf.order
27
>>> pi_approx = ContinuedFraction.from_elements(3, 7, 15, 1, 292)
>>> pi_approx
ContinuedFraction(355, 113)
>>> pi_approx.as_float()
3.1415929203539825
>>> math.pi - pi_approx.as_float()
-2.667641894049666e-07
>>> import pytest
>>> pytest.approx(pi_approx.as_float(), abs=1e-6) == math.pi
True

Contents:

Indices and tables#