Hi all,

Sorry for jumping in late into the discussion. Been crazy those last
days (see my upcoming e-mail for one of the reasons).

Even though I do not yet have convincing arguments, I must say I don't
feel so good with not implementing maps as methods of the domain (in
the parent or element class) or of the codomain (in the parent
class). Weak arguments include:

- It introduces more (too much) complexity; in particular when it
  comes to inheriting maps from super classes.

  Granted: with all the category tricks, I am not in such a great
  position to defend the KISS principle :-)

- One can't use:

        sage: W.*tableau*?

  to find all methods on W that relate to tableaux (note: this feature
  currently only work on the terminal, but it really should also exist
  in the notebook)

That being said:

- I would very much favor adding tab completion, in the terminal and
  the notebook, on function options (this should be doable). And then
  one could have:

        sage: p.to_permutation(bijection=<tab>

  if not just:

        sage: p.to_permutation(<tab>

  The bijections themselves could be implemented as:

        sage: p._to_permutation_foo()
        sage: p._to_permutation_bar()

  either in the class or p, or in super class, or some mix thereof.

- I love the idea of having a framework to retrieve and manipulate
  (composition, ...)  maps between parents. And experiments in that
  direction are very welcome.

Cheers,
                                Nicolas
--
Nicolas M. ThiƩry "Isil" <nthi...@users.sf.net>
http://Nicolas.Thiery.name/

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