I'm confirming what Dima and Martin just said: a lot of us need to see
permutations as words. For most of what I do, a permutation of size 4 is
just a word on the letter 1234. And in this case, the fact that it is
1-based or 0-based matters. It mostly matters in terms of printing and
input.
2014-09-10 22:37 GMT+02:00 'Martin R' via sage-devel <
sage-devel@googlegroups.com>:
> 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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