Am Mittwoch, 10. September 2014 21:03:36 UTC+2 schrieb Nils Bruin:
>
> On Wednesday, September 10, 2014 11:51:55 AM UTC-7, Martin R wrote:
>>
>> I think that's what PermutationGroup and PermutationGroupElement do.
>
> No:
>
> sage: PermutationGroupElement((2,3,4)).parent()
> Symmetric group of order 4! as a permutation group
> sage: PermutationGroupElement([1,2,3]).parent()
> Symmetric group of order 3! as a permutation group
>
> They live in Sym({1,...,n}) (where n is somehow divined from the input),
> not in the injective limit of those things.
>
You are right. What I had in mind was:
sage: S3 = PermutationGroup([['b','c','a'],['a','c','b']],
domain=['a','b','c'])
sage: S3.list()
[(), ('b','c'), ('a','b'), ('a','b','c'), ('a','c','b'), ('a','c')]
I agree with you that a permutation should be a set of cycles. There are
two natural options then: anything that does not appear in a cycle is a
fixed point, or the domain is the set of elements appearing in the cycles.
It's important though to be able to regard "standard" permutations as
words, too...
Martin
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