[GAP Forum] Computation of the quotient of abelian groups

[mbg nimda]

Dear Forum members,

I would like to know if there is an easy way to calculate, using GAP, the
quotient of two Abelian groups. The groups I obtain are generated by vectors
in finite dimensional vectorspaces and have integer coefficients. For
example: V is the Z-module generated by the vectors
[ [   1,   0,   0,   0,   0,   0,   0,   0,   0,   1,   1,   0,  -1,   1,
0,   0 ],
  [   0,   1,   0,   0,   0,   0,   0,   0,   0,  -1,  -1,  -1,   0,  -1,
0,   1 ],
  [   0,   0,   1,   0,   0,   0,   0,   0,   0,   1,   0,   1,   0,   0,
1,  -1 ],
  [   0,   0,   0,   1,   0,   0,   0,   0,   0,  -1,   0,   0,   1,   0,
-1,   0 ],
  [   0,   0,   0,   0,   1,   0,   0,   0,   0,   0,  -1,   0,   0,  -1,
1,   0 ],
  [   0,   0,   0,   0,   0,   1,   0,   0,   0,   0,   0,  -1,  -1,   0,
0,   1 ],
  [   0,   0,   0,   0,   0,   0,   1,   0,   0,   1,   1,   0,   0,   0,
0,   0 ],
  [   0,   0,   0,   0,   0,   0,   0,   1,   0,  -1,  -1,  -1,   0,   0,
0,   0 ],
  [   0,   0,   0,   0,   0,   0,   0,   0,   1,   1,   0,   1,   0,   0,
0,   0 ] ]

and W is the submodule generated by the vectors
[ [   1,   1,   1,   1,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,
0,   0 ],
  [   1,   0,  -1,   0,   1,  -1,   0,   0,   0,   0,   0,   0,   0,   0,
0,   0 ],
  [   0,   0,   0,   0,   0,   0,   1,   1,   1,   1,   0,   0,   0,   0,
0,   0 ],
  [   0,   0,   0,   0,   0,   0,   1,   0,  -1,   0,   1,  -1,   0,   0,
0,   0 ],
  [   0,   1,   0,   0,   0,   0,   0,  -1,   0,   0,   0,   0,   0,  -1,
0,   1 ],
  [   0,   0,   0,   0,   1,   0,   0,   0,   0,   0,  -1,   0,   0,  -1,
1,   0 ],
  [   0,   0,   0,   1,   0,   0,   0,   0,   0,  -1,   0,   0,   1,   0,
-1,   0 ],
  [   0,   0,   0,   0,   0,   1,   0,   0,   0,   0,   0,  -1,  -1,   0,
0,   1 ] ]

Assuming I'm correct we have that V/W is the direct sum of Z and Z/2Z. Is
there an easy way to calculate this?

Mark.