> In part. But more importantly because LinearExtensionsOfPoset accepts
> a list as input, and lists are not hashable. So class call needs to
> transform it into a tuple before passing it down to
> UniqueRepresentation. See the documentation of UniqueRepresentation
> for details.
Ok, thank you!
> Ok. Then don't we want instead to be able to specify a linear
> extension to the Poset constructor?
>
> Say:
>
> sage: P = Poset(...., linear_extension = [1,2,3,4,5,6,7])
>
> Which could be used as well to change the default linear extension:
>
> sage: Q = Poset(P, linear_extension = [1,3,2,5,4,6,7])
>
> Also we might want to have Poset be clever enough to test if the list
> of vertices provided by the user is a linear extension, and if it is
> to use it as default linear extension rather than looking for some
> random one?
Having this as an input in Poset was my very first suggestion.
But now my inclination is actual different. I think the real culprit
that throws me off in the applications I have in mind are the methods
def _vertex_to_element(self,vertex):
and
def _element_to_vertex(self,element):
in /combinat/posets/posets.py, which assign the integers 0,1,2,....,n-1 to the
elements in the poset. The linear extension of a given poset is in fact set to
the
identity (which is what I really want)
sage: P = Poset(([1,2,3,4,5,6,7], [[1,2],[1,4],[2,3],[2,5],[3,6],[4,7],[5,6]]),
cover_relations = True)
sage: P._hasse_diagram.linear_extension()
[0, 1, 2, 3, 4, 5, 6]
sage: P.linear_extension()
[1, 2, 3, 5, 6, 4, 7]
So if I use ._hasse_diagram.linear_extension() and linear_extensions() and not
use the assignment
to the element of the poset, this would work much better. Also, I tend to think
of linear extensions
as permutations rather than lists of poset elements.
In this light ...
> I am a bit confused now. I guess part of the question is whether we
> want to have a double use for P.linear_extension:
>
> sage: P.linear_extension()
> returns the default linear extension of P (as a list or as a linear
> extension?)
>
> sage: P.linear_extension([1,5,3])
> returns the linear extension [1,5,3]
... we could leave P.linear_extension() and P.linear_extensions() as is and
have them return lists of
elements of the poset, and then the new class LinearExtensionOfPoset represents
its elements
as permutations (in one line notation) of {1,2,...,n} for a poset of size n.
Then I can get rid of
the "order" input.
What do you think?
Best,
Anne
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