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
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