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. _______________________________________________ Forum mailing list Forum@mail.gap-system.org http://mail.gap-system.org/mailman/listinfo/forum
