[GAP Forum] Computation of the quotient of abelian groups
mbg nimda
mbg.nimda at gmail.com
Sun Apr 18 16:32:55 BST 2010
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.
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