On Mon, Aug 25, 2014 at 11:14:09AM +0300, Jori Mantysalo wrote:
> Posets(5)
>
> which internally does something like
>
> [x for x in GenerateAllDirectedGrapsh(5) if x.is_poset()]
Semantically, this is correct. Luckily the implementation is more
clever than this: it only runs through digraphs that are actually
Hasse diagrams. For details, see the section "Graphs up to
isomorphism" in sage.combinat.tutorial?
> To get lattices of size 5 one says
>
> [sage.combinat.posets.lattices.FiniteLatticePoset(x) for x in
> Posets(5) if x.is_lattice()]
>
> Because a) FiniteLatticePoset is not available on global namespace
> and b) there is no ready method to get lattices of given size.
>
> Am I right on this?
Alas, yes.
In theory, the orderly generation technique should be applicable for
lattices too, doing an augmentation by vertices (see also the
tutorial). However this would require some basic control on how
vertices are added (the meet-semi lattice property is stable upon
removing largest elements only). Tom Denton had given it a quick shot
back in 2010, but it seemed like the orderly generation code did not
make it easy to gain such control. I'd love to be proven wrong :-)
Cheers,
Nicolas
--
Nicolas M. Thiéry "Isil" <nthi...@users.sf.net>
http://Nicolas.Thiery.name/
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