Thanks for your reply, my thesis deals with group isomorphisms. The smith form is used to decide the isomorphism problem for abelian groups. I describe how that works and try to include maple into our program to solve this problem. What I am looking for is the complexity (in O-notation) of maple's routine. In this case I use the deterministic function (the smith form is unique for a given matrix). I use integers only. Garbage collection is not taken into account.