我对模块化域有一组约束，例如 for all$\exists a \in A_i : x \equiv a \pmod{n_i}$$i=0,\ldots,k$

问题是，这样的存在吗？我已经指出了连续替换的方法，最终我实现了以下 python 代码。$x$

import fractions
def exist(ruleList, acc = [0,1]): # currentCandidate , currentDomain
  if len(ruleList) == 0:
    return True
  else:
    rule = ruleList[0]
    n = rule[1]/fractions.gcd(rule[1], acc[1])
    newDomain = acc[1] * n  
    for candidate in (acc[0] + acc[1] * i for i in xrange(n)): 
      if candidate % rule[1] in rule[0]:
        if exist(ruleList[1:], [candidate, newDomain]):
          return True
    return False

rules = [([0,1,2],5),   # A_1,n_1
         ([4,5,6],9),   # A_2,n_2
         ([0,3,6],10)]  # A_3,n_3

print (exists(rules),)  # True

rules = [([0,2,3],5),   # A_1,n_1
         ([1,2,8],9),   # A_2,n_2
         ([4,6,9],10)]  # A_3,n_3

print (exist(rules),)   # False

他们是实现这种更好的方法还是更好的算法方法？