It looks to me as though there are some crossed wires here. The
permutation is acting on *any* list of length 5 by permuting the
indices of the elements (taken as 1..5 rather than python-standard
0..4 but still). In the example you are using the entries in the
list happen to also be the numbers 0,1,2,3,4 and that is causing
confusion!
John
On 02/11/2007, William Stein <[EMAIL PROTECTED]> wrote:
>
> On Fri, 02 Nov 2007 00:08:40 -0700, <[EMAIL PROTECTED]> wrote:
> > On Thu, 1 Nov 2007, William Stein wrote:
> >> On 11/1/07, [EMAIL PROTECTED]
> >>> Under the way I've implemented this, the
> >>> action on the list [1,...,n] is trivially
> >>> isomorphic to the group structure. You
> >>> seem to be using a left-action which
> >> ^^^^^^^^^^^^^^^^^^^
> >>
> >> I am using a left action.
> >
> > ... failure to type ... I meant right action.
> >
>
> Now we are getting somewhere, maybe. I'm thinking of the
> natural (to me!) right action and you're thinking
> of the left action got by inverting the permutation and acting
> in the natural way :-).
>
> I guess I just don't think permutation (which are functions) should
> act on the left. It's repulsive to me. I guess there's just
> not much more to say than that.
>
> -- William
>
> >>
> >>> doesn't really go well with the notation g(l).
> >>
> >> If g and h are in a group and you use the
> >> notation g(x) to denote the action of g on
> >> x then you had better be talking about a left
> >> action, since
> >>
> >> g(h(x)) = (g*h)(x)
> >
> > ... yeah, that's what I was getting at.
> >
> > My way:
> >
> > sage: a = G([(1,2,3),(4,5)])
> > sage: b = G([(1,2,3,4,5)])
> > sage: a('abcde')
> > 'bcaed'
> > sage: b(a('abcde'))
> > 'caedb'
> > sage: (b*a)('abcde')
> > 'caedb'
> >
> >
> > Your way: (note -- I'm doing this part by hand, so it might be wrong -- the
> > above is output from Sage)
> >
> > sage: a = G([(1,2,3),(4,5)])
> > sage: b = G([(1,2,3,4,5)])
> > sage: c = b*a; c
> > (1,3,5,2)
> > sage: a('abcde')
> > 'cabed'
>
>
>
> > sage: b(a('abcde'))
> > 'dcabe'
> > sage: c('abcde')
> > 'beadc'
> >
> >
> >
> >
> >>
> >>> If you still disagree, I suggest backing out the patch and > waiting for
> >>> Jason Grout, who requested the feature, to
> >>> clarify his intent.
> >>
> >> That would be good. His intent is inclear, since
> >> he gives no unambiguous example.
> >>
> >>> (OTOH, backing it out isn't really
> >>> necessary -- the patch only adds functionality)
> >>
> >> Adding incorrect functionality isn't good.
> >> (Again, I'm not sure I'm right here -- I'm just
> >> very uncomfortable by instinct.)
> >>
> >> -- William
> >>
> >> >
> >>
> >
> >
> >
> > >
> >
>
>
>
> --
> William Stein
> Associate Professor of Mathematics
> University of Washington
> http://wstein.org
>
> >
>
--
John Cremona
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