In the special case when the vector
consists entirely of rational numbers and we are taking
ai=ai' for all i,
we of course know in advance that the rank of the lattice of integer
relations for a is equal to n-1 (assuming a non-zero).
If C is taken sufficiently large, then upon completion
of the lattice reduction algorithm, all numbers
will be equal to 0
for any vector w in the reduced basis,
since
are integers and, by the definition
of a reduced basis,
In Section 3.3 we present an application of finding integer relations for integer input vectors.