David Joyner wrote:
> On Fri, Feb 15, 2008 at 12:43 PM, John Cremona <[EMAIL PROTECTED]> wrote:
>> I think both/either of these are useful enough they should be
>> included. In David's code I noticed that he had to shift from
>> permutations starting at 1 to 0 and back, but Jason's code did not do
>> this. What magic is that? Either way, this particular issue needs to
>> be well documented...
>
> Done. The version below has a better docstring. It works not only
> for vectors and matrices but for sequences as well, so I renamed it
> simply perm_action:
>
> def perm_action(g,v):
> """
> Returns permutation of rows g*v; also works on vectors
> (permuting coordinates). The code requires switching from
> i to i+1 (and back again) since the SymmetricGroup is,
> by convention, the symmetric group on the "letters"
> {1, 2, ..., n} (not {0, 1, ..., n-1}).
>
> 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(g,v)
> (1, 2, 0, 0, 1)
> sage: g = G([()])
> sage: perm_action(g,v)
> (0, 1, 2, 0, 1)
> sage: g = G([(1,2,3,4,5)])
> sage: perm_action(g,v)
> (1, 2, 0, 1, 0)
> sage: L = Sequence([1,2,3,4,5])
> sage: perm_action(g,L)
> [2, 3, 1, 4, 5]
> sage: MS = MatrixSpace(GF(3),3,7)
> sage: A = 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: A; perm_action(g,A)
> <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)
>
> I still don't have any idea where it should go...
Can we merge it with the code for g(listable)? I'm not sure if I was
clear in my response before: my point was that we have a specific case
already in the code for permutation group elements (the special case of
permuting a list). Your code is more general (it works for any listable
object). Can you patch the current code that was incorporated from the
patch on #750?
If there is a 0-1 indexing issue, we could make it an option to g(listable).
In this case, your examples would look like the following (with possibly
a argument added to adjust for 0 or 1 indexing).
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: g(v)
(1, 2, 0, 0, 1)
sage: g = G([()])
sage: g(v)
(0, 1, 2, 0, 1)
sage: g = G([(1,2,3,4,5)])
sage: g(v)
(1, 2, 0, 1, 0)
sage: L = Sequence([1,2,3,4,5])
sage: g(L)
[2, 3, 1, 4, 5]
sage: MS = MatrixSpace(GF(3),3,7)
sage: A = 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: A; g(A)
<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]
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