adaLovelaceDay2020.py

#!/usr/bin/env python

# Find cube roots. In honour of Pandrosion of Alexandria on Ada Lovelace day 2020

# from https://en.wikipedia.org/wiki/Cube_root#Numerical_methods

# see also https://docs.python.org/3/tutorial/floatingpoint.html

def cubeRoot(a, epislon = 0.001):
    ''' Approximate cube roots using Halley's method

    Examples
    --------
    >>> cubeRoot(27)[0]
    3.0

    >>> cubeRoot(19683, 0.00001)[0]
    27.0


    >>> cubeRoot(1)
    (1.0, 3)
    '''

    from decimal import Decimal
    n=0
    result = a/2
    while abs(result**3 - a) > epislon:
        n += 1
        cube = result**3
        result *= ((cube+2*a)/(2*cube+a))

    # print (f"cube of {a} is {result} after {n} iterations")
    digits = abs(Decimal(repr(epislon)).as_tuple().exponent)
    return round(result, digits), n

if __name__ == "__main__":
    import doctest
    doctest.testmod()