For operators f and g there exists an operator  such that the solution space of  is the intersection of the solution spaces of f and g. This procedure finds this operator . Like the gcd for polynomials, this  is a combination  for some operators a and b.

The argument domain describes the differential algebra. If this argument is the list  then the differential operators are notated with the symbols  and . They are viewed as elements of the differential algebra   where  is the field of constants.

If the argument domain is omitted then the differential specified by the environment variable _Envdiffopdomain will be used. If this environment variable is not set then the argument domain may not be omitted.