>>   1) iteration of couples "(vector, stabilizer of the vector)"
>
> It depend on what kind of information you want in `stabilizer of the
> vector`. If you want it to be a sage or gap permutation group, it can be
> very very painful (especially for speed...). The orbit is `very easy` to
> get, for more, there is some work to be done.
>

More precisely, before processing, I make the list of subgroups up to
conjugation. Then I want to be able to sort the vectors depending on
the conjugacy class of the stabilizer (I do not care about the class
of the group).

>>   2) iteration through vectors such that the stabilizer is trivial
>
> As Florent wanted in the design of SearchForest a post_processing, 2) is
> relatively simple to do:
>
> First apply the patch in the combinat queue..
> and test :
>
> [...]

Ok. This is exactly what I'm looking for ! Thank you.

A new question : is this the faster option ? Do we need to compute the
orbit explicitely to get the answer to "is the stabilizer trivial ?" ?
The typical input that i will give to the iterator corresponds to
vectors of length around 20 and sum around 30... I need fast
generation.

Thank you again,
Vincent

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