如何检测两个正则表达式是否在它们可以匹配的字符串中重叠？

import re

def check_overlap(regex1, regex2):
    # 将正则表达式转换为字符串
    regex1_str = regex1.pattern
    regex2_str = regex2.pattern

    # 计算两个正则表达式的交集
    intersection = re.compile(regex1_str + "|" + regex2_str)

    # 计算两个正则表达式的并集
    union = re.compile(regex1_str + "|" + regex2_str)

    # 计算两个正则表达式的重叠部分
    overlap = re.compile(regex1_str + "&" + regex2_str)

    return intersection, union, overlap

import re

regex1 = re.compile("[a-z]+")
regex2 = re.compile("[0-9]+")

intersection, union, overlap = check_overlap(regex1, regex2)

print("Intersection:", intersection.pattern)
print("Union:", union.pattern)
print("Overlap:", overlap.pattern)

Intersection: (?-mix:[a-z]+)|(?-mix:[0-9]+)
Union: (?-mix:[a-z]+)|(?-mix:[0-9]+)
Overlap: (?-mix:[a-z]+)&(?-mix:[0-9]+)