  In this paper, we formalize the notion of lambda-AT-model (where $\lambda$ is
a non-null integer) for a given chain complex, which allows the computation of
homological information in the integer domain avoiding using the Smith Normal
Form of the boundary matrices. We present an algorithm for computing such a
model, obtaining Betti numbers, the prime numbers p involved in the invariant
factors of the torsion subgroup of homology, the amount of invariant factors
that are a power of p and a set of representative cycles of generators of
homology mod p, for each p. Moreover, we establish the minimum valid lambda for
such a construction, what cuts down the computational costs related to the
torsion subgroup. The tools described here are useful to determine topological
information of nD structured objects such as simplicial, cubical or simploidal
complexes and are applicable to extract such an information from digital
pictures.
