On Wednesday, March 30, 2016 at 7:46:29 AM UTC-7, Pierre wrote:
>
> Come to think of it, I just spotted a little bug in libgap:
>
> sage: p= Permutation([ (1, 2, 3), (4, 5) ])
> sage: pp= libgap( p ); pp
>
> [ 2, 3, 1, 5, 4 ]
>
> Here pp is a list, not a permutation ! GAP should respond (1,2,3)(4,5), 
> regardless of Sage's default behaviour of printing permutations as lists.
>
>
It looks like the best solution would be to equip 
"sage.combinat.permutation.StandardPermutations_n_with_category.element_class" 
with a `_libgap_()` method. It would probably mean implementing an 
efficient interface routine to create permutations in libgap, and call that 
from the _libgap_ method.

Mind you,

sage: s=SymmetricGroup(3)([2,3,1])
sage: type(s)
<type 'sage.groups.perm_gps.permgroup_element.PermutationGroupElement'>

is an entirely different beast. I don't think that the two concepts 
"permutation-as-a-combinatorial-object" and 
"permutation-as-a-group-element" are entirely unified in sage.

It also seems that "SymmetricGoup" has its elements live in a pexpect gap, 
not in libgap. It might be attractive to move that too.

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