On 2013-03-21, Nils Bruin <nbr...@sfu.ca> wrote:
> On Mar 21, 9:05 am, Benjamin Jones <benjaminfjo...@gmail.com> wrote:
>> It seems to me that the ambiguity arises from the original statement,
>
> Systems like magma (and I assume gap as well) solve this by having a
> "GSet" type. If you have S3 acting on the GSet V={1,2,3} then, one can
> construct the powerset W of V as a GSet as well. In that context there
> is a natural distinction between the subset {1,2,3} of V (which is a
> sub-GSet) and the element {1,2,3} of W.
On GAP there is nothing like GSet.
As far as I know, one needs to do that "boxing" trick
I explained there, too, if one needs to "mix" things in the domain of the
group.
>
> One can talk about the orbit of the element {1,2} in W under S3 but
> obviously, {1,2} is not a sub-GSet of V.
>
> How these things coerce between each other is another matter, but I
> suspect making such distinctions internally is unavoidable.
Many years ago I abandoned Magma's predecessor, Cayley, for GAP, as
Cayley's lack of proper coersions/conversions drove me insane all the time.
Dima
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