Helloooooooooooooooooooooo !!!
> Well, unfortunately I don't know under which Seine bridge mathematicians
> are most
> welcome :-)
Ahahahah. I felt so shocked when I first learnt that Paris did not have the
only one O_O
> Mind you, when this part of GAP was developed, you were in primary
> school;-),
And I had more important things to do, like looking for sweets. I will not
be held responsible.
> computers were slow and weak, everything needed to be coded
> in C or Fortran (or one would need to use Lisp, which wasn't very
> popular in that part of computational algebra --- unfortunately);
> naturally, some features remain hugely underdeveloped due to this. IMHO
> a part of the GAP framework of actions which deals with tuples, subsets,
> etc.
> is at present more of a burden than of an advantage. (Whereas actions
> say on cosets of a subgroup which GAP has are hugely important and hard to
> beat)
Hmmm... But then, should we patch Sage to add features or patch GAP and use
it in Sage ? :-P
> Coding more generic orbit algorithms for permutation groups
> in a language like Python is, moreover, quite easy.
> (By more generic---than tuples, tuples of tuples, etc---
> I mean the action on trees with leafs labeled by
> elements of the group domain, and with some (fixed) non-terminal node
> might
> carry out the structure of a set, i.e. have unordered rathen than
> ordered neighbourhoods. E.g. you can get an action on gadgets like
> (1,{2,3},((4,5),2,{1,6,7})); here the domain elements are numbers, but
> this need not be a restriction.)
> Just get yourself a queue, put there the starting element, and add the
> new images to the other end of the queue, while computing the images of
> the 1st in order element in the queue.
> One is done when everything in the queue is processed
Yep yep. In my world that's called a depth-first-search. But we are shy
guys, especially when surrounded by real mathematicians.
> All the orbit algorithm needs to know, apart from the group generators,
> is how to compute the image is the tree "shape", i.e. no labels on the
> nodes.
> E.g. for the example above the shape is encoded by
> (,{,},((,),,{,,})).
>
> And this can be made modular etc, as there are more actions around than
> these which fit this pattern; so how to compute the action can be
> specified by a function passed as a parameter. (Not sure if one also
> needs a function to compare orbit elements for equality.)
Oh. You'd give "(,{,},((,),,{,,}))" as a string parameter, parse it and use
it to define the tree ? Ahahaha. Funny and efficient ! A bit ....
"home-made", but I like that :-P
Actually, what would have prevented me from dirtying beautiful groups with
my out-of-place graph approach (i.e. the DFS above) is that I would have
thought the group guys were too smart to use such things. Is that how GAP
computes orbits ? Just a BFS ? A "set" object, hash functions for the
group's elements, and that's all we need for a "state of the art" orbit
method ?
> I wrote above how I'd see this done.
> I think it's better to encode the "usual" types of action by such a
> pattern like above (e.g. (,{,},((,),,{,,}))).
> Such a pattern can either be guessed/computed by Volker's rules, or
> specified as a parameter. (And a user function to compute the action
> can also be a parameter).
> They could be translated into GAP actions and GAP calls, for which such
> actions exist.
Ok good point. But now I have a more pratical question : can we get #14291
after just replacing this "action" parameter with your funny string, and
return a "notimplementederror" when the value of action cannot be forwarded
to GAP ?
As it is, it is already a nice feature for humble graph theoreticians to
compute the orbit of a pair of elements :-)
Nathann
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