CAS: Computing homology of complex of non-free abelian groups

Question

Which computer algebra system allows me to compute the homology of a complex of finitely presented abelian groups which are not necessarily free?

Sage and Magma apparently don't: see here and here.

Edit: I should specify that the main obstacle for me of doing this by hand with a CAS is the lack of an algorithm for computing the kernel of a homomorphism between finitely generated abelian groups.

Answer 1

Magma can compute the kernel and the image of a homomorphism between abelian groups. For instance,

  A<[x]> := AbelianGroup([0]);
  B<[y]> := AbelianGroup([2,4]);
  C<[z]> := AbelianGroup([2]);
  g := hom< B -> C | [z[1],2*z[1]]>;
  K := Kernel(g);
  K;
  f := hom< A -> K | [4*y[1]-2*y[2]]>;
  I := Image(f);
  I;
  K/I;

gives the following result:

 Abelian Group isomorphic to Z/4
 Defined on 1 generator in supergroup B:
     K.1 = y[2]
 Relations:
     4*K.1 = 0
 Abelian Group isomorphic to Z/2
 Defined on 1 generator in supergroup K:
     I.1 = 2*K.1
 Relations:
2*I.1 = 0
 Abelian Group isomorphic to Z/2
 Defined on 1 generator
 Relations:
     2*$.1 = 0