Computing Hermite normal form

http://www-cse.ucsd.edu/users/daniele/papers/HNFalg.html

www.scg.uwaterloo.ca/~glabahn/Papers/arne2.pdf

Probably implementing one of these is more work than necessary; the
modified Gaussian elimination method should be fine for the small
problems likely to arise in music theory. However, they discuss what
Hermite normal form is and explain how to compute it, and give references.