連分数の計算

import math
from fractions import Fraction

def get_continued_fraction(n):
    """入力は素数と仮定して、循環の最初の周期を返却する"""
    r = 0
    s = 1
    a = int(math.floor(math.sqrt(n)))
    a0 = a
    lst_a = [a]
    cnt = 100
    while 0 < cnt:
        _s = (n-(r-a*s)**2) / s
        _r = -(r-a*s)
        a = int(math.floor( (math.sqrt(n) + _r) / _s))
        r = _r
        s = _s
        cnt -= 1
        lst_a.append(a)
        if a == 2*a0:
            break
    return lst_a

def get_approx_fraction(cfrac):
    assert 0 < len(cfrac)

    if 1 == len(cfrac):
        return Fraction(cfrac[0], 1)
    elif 2 == len(cfrac):
        return Fraction(cfrac[0] * cfrac[1] + 1, cfrac[1])
    else:
        pi_1 = cfrac[0] * cfrac[1] + 1
        pi = cfrac[2] * pi_1 + cfrac[0]
        qi_1 = cfrac[1]
        qi = cfrac[2] * qi_1 + 1
        for ai in cfrac[3:]:
            pi, pi_1 = ai * pi + pi_1, pi
            qi, qi_1 = ai * qi + qi_1, qi
        return Fraction(pi, qi)