pyoculus.utils.continued_fraction

This module provides functions related to the continued fraction expansion. Reference in Ivan Niven, Irrational Numbers (Cambridge University Press, 2005).

authors:

Functions

expandcf(realnumber[, n, thres])

Expands a positive real number in its continued fraction.

fromcf(ai)

Obtains the fraction \(n/m\) from the coefficients \([a_0, a_1, ..., a_m]\) of the continued fraction.
pyoculus.utils.continued_fraction.expandcf(realnumber, n=100, thres=1e-12)

Expands a positive real number in its continued fraction.

Parameters:

  • realnumber (float) – The positive real number to expand. An absolute value will be taken if negative.

  • n (int, optional) – The maximum number of terms in the expansion. Default to 100.

  • thres (float, optional) – The threshold to stop the expansion. Default to 1e-6.

Returns:

A NumPy array containing the continued fraction expansion of the real number up to the nth term or until the threshold is met.

Return type:

np.ndarray

pyoculus.utils.continued_fraction.fromcf(ai)

Obtains the fraction \(n/m\) from the coefficients \([a_0, a_1, ..., a_m]\) of the continued fraction.

Parameters:

ai (list of int) – An integer list containing ai for the continued fraction expansion.

Returns:

A tuple \((n, m)\), representing the fraction.

Return type:

tuple