替换不推荐的`fractions.gcd()函数？

Question

我想计算两个作为fractions.Fraction实例实现的有理数的最大公共因子。虽然输出了弃用警告，但它仍按预期工作：

In [1]: gcd(Fraction(2, 3), Fraction(2, 3))
/usr/local/bin/ipython:1: DeprecationWarning: fractions.gcd() is deprecated. Use math.gcd() instead.
  #!/usr/local/opt/python3/bin/python3.6
Out[1]: Fraction(1, 6)

查看文档，我可以看到，fractions.gcd()确实是不受欢迎的，并且邀请用户使用math.gcd()。问题是后者不支持有理数：

In [2]: gcd(Fraction(2, 3), Fraction(2, 3))
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
<ipython-input-2-c3ad2389f290> in <module>()
----> 1 gcd(Fraction(2, 3), Fraction(2, 3))

TypeError: 'Fraction' object cannot be interpreted as an integer

我可以用哪种功能来代替fractions.gcd()？我不是在寻找这里使用的实际算法，而是替代不推荐的函数。

Answer 1

你可能得写一个。gcd(a/b, c/d) = gcd(a, c)/lcm(b, d)，所以这不算太糟。math不提供lcm，所以我使用的是编写的这里。

from fractions import Fraction
from math import gcd

def lcm(a, b):
    """Return lowest common multiple."""
    return a * b // gcd(a, b)

def fraction_gcd(x, y):
    a = x.numerator
    b = x.denominator
    c = y.numerator
    d = y.denominator
    return Fraction(gcd(a, c), lcm(b, d))

print(fraction_gcd(Fraction(2, 3), Fraction(2, 3)))
# 2/3

Answer 2

注:以下内容最初由原海报编辑成问题正文。我把它移到了另一个答案。

正如@glibdud在他的评论中所提到的，使用带有有理数的fractions.gcd()并不是一种预期的行为，当然也没有文档化.它可以很容易地通过以下方式实现：

def gcd(numbers):
"""Compute Greastest Common Divisor of rational numbers.

Args:
    numbers: list of rational numbers.

Returns:
    Greatest Common Divisor of rational numbers.
"""
# Treat the two-number case and reduce
def _gcd(a, b):
    if b == 0:
        return a
    if isinstance(a, int) and isinstance(b, int):
        _gcd(b, a % b)
    a = Fraction(a)
    b = Fraction(b)
    return Fraction(gcd([a.numerator, b.numerator]), lcm([a.denominator, b.denominator]))

return reduce(_gcd, numbers)

def lcm(numbers):
    """Compute Least Common Multiple of rational numbers.

    Args:
        numbers: list of rational numbers.

    Returns:
        Least Common Multiple of rational numbers.
    """
    # Treat the two-number case and reduce
    def _lcm(a, b):
        if b == 0:
            return a
        if isinstance(a, int) and isinstance(b, int):
            return a * b // gcd([a, b])
        a = Fraction(a)
        b = Fraction(b)
        return Fraction(lcm([a.numerator, b.numerator]), gcd([a.denominator, b.denominator]))

    return reduce(_lcm, numbers)

推导并解释了这个公式：https://math.stackexchange.com/questions/44836/rational-numbers-lcm-and-hcf。