On 2012-10-25, Florent Hivert wrote:
> Hi,
>
> With Nathann, we just got the following behavior:
>
> sage: p = Poset(((0,1,2),[(0,1),(0,2)]), facade=True)
> sage: pp = p.relabel({0:0, 1:2, 2:1})
> sage: p == pp
> False
>
> so relabeling by an automorphism doesn't return the same poset ! Note however
> that:
Note further that you still get
sage: p.is_isomorphic(pp)
True
sage: pp.is_isomorphic(p)
True
Also,
sage: p.hasse_diagram()==pp.hasse_diagram()
True
>
> sage: Poset(((0,1,2),[(0,1),(0,2)])) == Poset(((0,2,1),[(0,2),(0,1)]))
> True
> sage: Poset(((0,1,2),[(0,1),(0,2)]), facade=True) ==
> Poset(((0,2,1),[(0,2),(0,1)]), facade=True)
> True
>
> So during construction Sage is able to recognize equal Posets. I'm not
it probably treats collections of elements as sets, that's why you get
identical things.
That '==' returns False on p==pp above seems like a bug, not sure where.
> sure how to deal with this and the following remark of the documentation:
>
> .. note::
>
> As can be seen in the above examples, the default linear
> extension of ``Q`` is that of ``P`` after relabelling. In
> particular, ``P`` and ``Q`` share the same internal Hasse
> diagram.
>
> Adding uniqueness and this means that all isomorphic posets must share the
> same underlying hasse_diagram. I don't think this is a good idea.
Why? Isomorphic posets do have the same Hasse diagram. Why not share it
then?
>
> So I'm not sure what to do here.
>
> Cheers,
>
> Florent
>
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