Continued fraction expansion

[stla]

Hello,

I 've done that, if you're interested in including it in the package:

from gmpy2 import mpz, mpq
from math import floor


def contfrac(x, n=10):
    """
    Continued fraction expansion.
    
    Parameters
    ----------
    x : rational
        A rational (mpq) number.
    n : int
        A positive integer, the desired number of terms of the continued 
        fraction expansion of `x`.

    Returns
    -------
    list
        A list of `mpz` integers, the `n` first terms of the continued 
        fraction expansion of `x` (or all the terms if there are less than `n`).
    
    Examples
    --------
    >>> from gmpy2 import mpq
    >>> cf = contfrac(mpq(10,7))
    >>> print(cf)
    [mpz(1), mpz(2), mpz(3)]

    """
    floor_x = floor(x)
    frac_x = x - floor_x
    cf = [floor_x]
    i = 1
    while i < n and frac_x != 0:
        x = 1 / frac_x
        floor_x = floor(x)
        cf.append(floor_x)
        frac_x = x - floor_x
        i += 1
    return cf


def contfrac2mpq(cf):
    """
    Evaluate a continued fraction.
    
    Parameters
    ----------
    cf : list
        A list of `mpz` integers.

    Returns
    -------
    ratinoal
        A `mpq` rational number, obtained by evaluating the continued fraction 
        represented by `cf`.
    
    Examples
    --------
    >>> from gmpy2 import mpq
    >>> cf = contfrac(mpq(10,7))
    >>> print(cf)
    [mpz(1), mpz(2), mpz(3)]
    >>> contfrac2mpq(cf)
    10/7
    """
    cf.reverse()
    x = cf[1] + 1 / mpq(cf[0])
    for i in range(len(cf))[2:]:
        x = cf[i] + 1 / x
    return x


# test
x = mpq(10, 7)
cf = contfrac(x)
print(contfrac2mpq(cf)) # x
print("***********************")
print(contfrac(mpq(10,7)))