Speed up AsList, AsSet and ElementsStabChain for permutation groups, by not sorting the list returned by ElementsStabChain (in accordance with its documentation which never promised this)

[fingolfin]

The documentation for ElementsStabChain never claimed that the result it returns is sorted. So we change it to not do that, by using Append instead of UniteSet. Then we use that to provide a faster version of AsList. As a side effect, this actually even speeds up AsSet, as sorting only at the end is cheaper then sorting repeatedly during creation of the list.

Some timings:

Before:

gap> AsList(SymmetricGroup(10));; time;
1507

gap> AsSet(SymmetricGroup(10));; time;
1492

After:

gap> AsList(SymmetricGroup(10)); time;
611

gap> AsSet(SymmetricGroup(10)); time;
1120

As another side effect, the output of AsList(G) and
List(Iterator(G)) now seem to coincide if G is a permutation group.

Of course in practice it's usually a bad idea to enumerate all group elements to start with... but for some applications this is still needed.

[ThomasBreuer]

Changing the behaviour of a function w.r.t. sortedness of its result usually has the effect that some examples will have different outputs, thus tests have to be adjusted.
(I expect this effect in some package manuals or in files that document GAP computations.)

Nevertheless, the proposed change is a nice performance improvement.
Perhaps the fact that ElementsStabChain does no longer return a sorted result should be mentioned in the release notes.

[ChrisJefferson]

I approve this, but I agree this should be in the release notes

[fingolfin]

Another option would be to rename the modified ElementsStabChain to say ListStabChain, and then add a new ElementsStabChain which calls ListStabChain , sorts the result, and orders it. Though I think all calls in the library to ElementsStabChain would be removed in the end... Presumably I then should document ListStabChain...

Since no package calls ElementsStabChain, it should indeed also be sufficient to simply document the behavior change of ElementsStabChain and perhaps stress in its docstring that the result may not be sorted... (right now sorting is just not mentioned; but since Elements is a synonym for AsSet, people may infer based on that name that the result should be sorted...)

[ThomasBreuer]

ElementsStabChain is used only in those places in lib that get changed in this pull request. I think it is not a problem to change its behaviour, to mention this in the release notes, and perhaps to state in the documentation that the result is not necessarily sorted.

(The function looks like a utility that had been introduced only in order to use it in methods for AsSSortedList and AsSSortedListNonstored. If the idea would have been to provide functionality for stabilizer chains then the version that returns a list that is ordered w.r.t. the given chain would have been more natural. Thus is had been a mistake to document ElementsStabChain.)

[fingolfin]

@ThomasBreuer I've adjusted the docstring to mention that the result may be unsorted, and adjusted the title of this PR (which will be used for the release notes). Better now?

[ThomasBreuer]

@fingolfin Yes, thanks.