替换已弃用的 `fractions.gcd()` 函数？

Question

我想计算实现为 fractions.Fraction 个实例的两个有理数的最大公约数。尽管打印了弃用警告，但它按预期工作：

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 documentation 我可以看到 fractions.gcd() 确实已弃用，邀请用户改用 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

我可以用哪个函数来代替fractions.gcd()？我不是在寻找此处使用的实际算法，而是在寻找已弃用函数的替代品。

Answer 1

您可能需要写一个。 gcd(a/b, c/d) = gcd(a, c)/lcm(b, d)，所以这还不错。 math 没有提供 lcm，所以我使用 here.

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：以下内容由楼主原创编辑入正文。我已将其移至单独的答案中。

正如@glibdud 在他的评论中提到的，将 fractions.gcd() 与有理数一起使用不是预期的行为，当然也没有记录......并且可以使用以下方法轻松实现：

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)

公式推导和解释在这里：https://math.stackexchange.com/questions/44836/rational-numbers-lcm-and-hcf.

替换已弃用的 `fractions.gcd()` 函数？

Replacement for deprecated `fractions.gcd()` function?

python

fractions

python-3.x