Suppose I have a basis A=(a1,a2,...,an) for the nullspace of a matrix with integer coefficients (i.e. Q-linear combinations of A will give me the span of A). I want to find the integral basis for this (perhaps my terminology isn't correct... but what I mean is I want to find a basis B=(b1,b2,...,bn) where the bi's are integers, such that Z-linear combinations of B will give me the span of the A.)
I'm not sure how to do this. In algebra class, given a field Q(sqrt(d)) I remember finding integral basis' for this... but I can't figure out whether what I'm doing here is at all similar... or much easier... any suggestions would be appreciated!