Hi:
The following function is useful for me and maybe for
others. What is amusing is that I wrote it for vectors
by it works equally well for matrices (and maybe
other structures) unchanged.
I'm happy to make a patch for it, if others are interested,
but am not sure where it should go. Comments or criticisms?
def perm_action_on_matrix(g,v):
"""
Returns permutation of rows g*v; also works on vectors
(permuting coordinates).
EXAMPLES:
sage: V = VectorSpace(GF(3),5)
sage: v = V([0,1,2,0,1])
sage: G = SymmetricGroup(5)
sage: g = G([(1,2,3)])
sage: perm_action_on_vector(g,v)
(1, 2, 0, 0, 1)
sage: MS = MatrixSpace(GF(3),3,7)
sage: G = MS([[1,0,0,0,1,1,0],[0,1,0,1,0,1,0],[0,0,0,0,0,0,1]])
sage: S5 = SymmetricGroup(5)
sage: g = S5([(1,2,3)])
sage: G; perm_action_on_vector(g,G)
<BLANKLINE>
[1 0 0 0 1 1 0]
[0 1 0 1 0 1 0]
[0 0 0 0 0 0 1]
<BLANKLINE>
[0 1 0 1 0 1 0]
[0 0 0 0 0 0 1]
[1 0 0 0 1 1 0]
AUTHOR: David Joyner, licensed under the GPL v2 or greater.
"""
V = v.parent()
n = len(list(v))
gv = []
for i in range(n):
gv.append(v[g(i+1)-1])
return V(gv)
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