Hi Andrey,
On Sun, Feb 13, 2011 at 01:30:03PM -0800, Andrey Novoseltsev wrote:
> While writing an enhancement proposal on
> http://trac.sagemath.org/sage_trac/ticket/10777
> I thought that it could be convenient to create a (finite) poset
> without specifying its elements but perhaps adding them one-by-one as/
> if they are created later.
>
> It seems to me that it is not possible to create such posets in Sage
> now, is it?
Nope.
> Is it actually of any interest to anyone or my situation was too
> specific? (I want to create polytopes which are faces of other
> polytopes without necessarily constructing the whole face lattice.)
We definitely have interest for lazy posets, where the list of
vertices/edges is not necessarily constructed explicitly at the
creation of the poset. For example, many of us would like to
manipulate infinite posets, like Bruhat order on an infinite Coxeter
group. A first step in this direction would be to create the category
of posets, and progressively factor out there the code from Poset.
Then one could create other concrete classes for posets, such as
LazyPoset, ..
Just a note: one should assume that a given LazyPoset P always model
the the same (large/infinite/not yet completely calculated)
mathematical poset. In other words P is semantically immutable. Does
this indeed cover your needs?
Speaking about posets: one indeed cannot yet create "facade posets"
whose elements are not wrapped. That's also a feature desired by many
of us!
For more about "facades" see also (with the Sage-Combinat patches applied):
sage: F = Sets().Facades()
sage: F?
Cheers,
Nicolas
--
Nicolas M. Thiéry "Isil" <nthi...@users.sf.net>
http://Nicolas.Thiery.name/
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