Create a Fraction class and overload the comparison operators ( < , > , == , >= , <= ) to allow direct comparison between Fraction objects

为了创建一个`Fraction`类，我们首先需要定义类的基本结构，包括分子（numerator）和分母（denominator），以及相关的比较方法。这里是一个简单的实现示例：

class Fraction:
    def __init__(self, numerator, denominator):
        if denominator == 0:
            raise ValueError("Denominator cannot be zero.")
        self.numerator = numerator
        self.denominator = abs(denominator)

    def __str__(self):
        return f"{self.numerator}/{self.denominator}"

    def reduce(self):
        gcd = math.gcd(self.numerator, self.denominator)
        self.numerator //= gcd
        self.denominator //= gcd

    # Overload comparison operators
    def __lt__(self, other):
        return self.numerator * other.denominator < other.numerator * self.denominator

    def __gt__(self, other):
        return self.numerator * other.denominator > other.numerator * self.denominator

    def __eq__(self, other):
        return self.numerator * other.denominator == other.numerator * self.denominator

    def __ge__(self, other):
        return not self.__lt__(other)

    def __le__(self, other):
        return not self.__gt__(other)

    def __add__(self, other):
        # ... implement addition here

    def __sub__(self, other):
        # ... implement subtraction here

    # Add more methods as needed, like __mul__, __truediv__

在这个例子中，`__lt__`, `__gt__`, `__eq__`, `__ge__`, 和 `__le__` 方法分别实现了小于、大于、等于、大于等于和小于等于的比较。注意，这只是一个基础版本，实际的`__add__` 和 `__sub__` 方法还需要实现加法和减法操作。

使用这个`Fraction`类时，可以直接对两个分数对象进行比较，例如：

frac1 = Fraction(3, 4)
frac2 = Fraction(7, 8)
print(frac1 < frac2)  # True or False depending on the values