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...
>
> John
>
>
>
> On 15/02/2008, Jason Grout <[EMAIL PROTECTED]> wrote:
> >
> > David Joyner wrote:
> > > 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)
> > >
> > > >
> > >
> >
> >
> > I think this is naturally related to #750, which added this functionality:
> >
> >
> > 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: V(g(v.list()))
> >
> > (1, 2, 0, 0, 1)
> >
> >
> > (g(list) does what your function does, but just takes and returns a
> > list; maybe it would be best to make g(list) really take g(listable) and
> > return the same type of object that it received).
> >
> > The corresponding functionality for your matrices is:
> >
> >
> > sage: MS = MatrixSpace(GF(3),3,7)
> > sage: m = MS([[1,0,0,0,1,1,0],[0,1,0,1,0,1,0],[0,0,0,0,0,0,1]])
> >
> > sage: G = SymmetricGroup(5)
> > sage: G = SymmetricGroup(3)
> >
> > sage: g = G([(1,2,3)])
> >
> > sage: m; MS(g(m.rows()))
> >
> >
> > [1 0 0 0 1 1 0]
> > [0 1 0 1 0 1 0]
> > [0 0 0 0 0 0 1]
> >
> >
> > [0 1 0 1 0 1 0]
> > [0 0 0 0 0 0 1]
> > [1 0 0 0 1 1 0]
> >
> >
> >
> > However, if m has more than three rows, we get an error. In your
> > example, you have a permutation living in S5 acting on something with
> > only 3 rows by thinking of the permutation as living in S3 (and fixing 4
> > and 5). Should we do that automatic coercion?
> >
> > Thanks,
> >
> >
> > Jason
> >
> >
> >
> >
> >
> >
> > >
> >
>
>
> --
> John Cremona
>
>
>
> >
>
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