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D.13.3.17 groupActionOnQImage
Procedure from library gitfan.lib (see gitfan_lib).
- Usage:
- groupActionOnQImage(G,Q); G: list of permutations, Q: intmat
- Purpose:
- Given the group G of permutations acting on the simplex on ncols(Q) objects, computes the corresponding group action on the image of Q. We assume that the basering has characteristic 0.
- Return:
- list of matrices
Example:
| | LIB "gitfan.lib";
ring R = 0,(x),dp;
intmat Q[5][10] =
1, 1, 1, 1, 0, 0, 0, 0, 0, 0,
1, 0, 0, 0, 1, 1, 1, 0, 0, 0,
0, 1, 1, 0, 0, 0, -1, 1, 0, 0,
0, 1, 0, 1, 0, -1, 0, 0, 1, 0,
0, 0, 1, 1, -1, 0, 0, 0, 0, 1;
list generatorsG = permutationFromIntvec(intvec( 1, 3, 2, 4, 6, 5, 7, 8, 10, 9 )),
permutationFromIntvec(intvec( 5, 7, 1, 6, 9, 2, 8, 4, 10, 3 ));
groupActionOnQImage(generatorsG,Q);
==> [1]:
==> 1,0,0,0,0,
==> 0,1,0,0,0,
==> 0,0,1,0,0,
==> 0,0,0,0,1,
==> 0,0,0,1,0
==> [2]:
==> -1,1,1,0,1,
==> 1,0,0,0,0,
==> -1,1,0,0,1,
==> -1,1,1,0,0,
==> -2,1,1,1,1
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