The list of moduli m must be pairwise relatively prime positive integers. Both lists u and m must be the same length . The list of images u need not be reduced modulo m on input. In the following,  denotes the product of the moduli.

If u is a list of integers, chrem(u, m) computes the unique positive integer a such that  , and .

If the global variable mod has been assigned to mods then the result  is returned in the symmetric range for the integers modulo . For example, the symmetric range for the integers modulo  is .

If u is a list of polynomials, chrem is applied across the polynomials so that the output  is a polynomial satisfying  , ..., .

If u is a list of lists, chrem is applied across the lists so that the output will be a list  satisfying , ...,  .

For a definition, see Chinese remainder theorem.