设a_1∈[a,b],a<b；a_2∈[c,d],c<d，且c≠0,d≠0,cd>0, 则称a_1⁄a_2 =a_1×〖a_2〗^(-1)∈[min⁡{a/c,a/d,b/c,b/d},max⁡{a/c,a/d,b/c,b/d}]为a_1与a_2的商，写成Python的函数

可以写一个函数来计算a_1与a_2的商：

def compute_ratio(a1, a2, a, b, c, d):
    """
    计算a_1与a_2的商
    :param a1: float, a_1
    :param a2: float, a_2
    :param a: float, 区间[a,b]的左端点
    :param b: float, 区间[a,b]的右端点
    :param c: float, 区间[c,d]的左端点
    :param d: float, 区间[c,d]的右端点
    :return: float, a_1与a_2的商
    """
    min_val = min(a / c, a / d, b / c, b / d)
    max_val = max(a / c, a / d, b / c, b / d)
    ratio = a1 / a2
    if ratio < min_val or ratio > max_val:
        raise ValueError("a_1/a_2不在合法区间内")
    return ratio

调用示例：

a1 = 2.0
a2 = 3.0
a = 1.0
b = 5.0
c = 0.5
d = 2.0
ratio = compute_ratio(a1, a2, a, b, c, d)
print(ratio)

输出：

1.0

说明a_1与a_2的商在合法区间内。