Salut Nathann!
> I would personnally expect this to be the default behaviour,
That's arguable indeed. However I introduced this feature last year
only, whereas the poset library is four years old. So making this the
default would break backward compatibility. Beside, with a facade
poset, you can't do x<y for x and y two elements of your poset, and
that's a feature many expect.
> especially when the documentation of Poset says nothing about
> what the facade argument means nor that it could have any effect
> on such problems ^^;;;
Taken from ``Poset?'':
------------------------------------------------------------------------------
-[ Facade posets ]-
By default, the elements of a poset are wrapped so as to make them
aware that they belong to that poset:
sage: P = Poset(DiGraph({'d':['c','b'],'c':['a'],'b':['a']}))
sage: d,c,b,a = list(P)
sage: a.parent() is P
True
This allows for comparing elements according to P:
sage: c < a
True
As an experimental feature, one can construct instead facade
posets:
sage: P = Poset(DiGraph({'d':['c','b'],'c':['a'],'b':['a']}),
... facade = True)
In this example, the elements of the poset remain plain strings:
sage: d,c,b,a = list(P)
sage: type(a)
<type 'str'>
Of course, those strings are not aware of P. So to compare two such
strings, one needs to query P:
sage: a < b
True
sage: P.lt(a,b)
False
which models the usual mathematical notation a <_P b.
Most operations seem to still work, but at this point there is no
guarantee whatsoever:
sage: P.list()
['d', 'b', 'c', 'a']
sage: P.principal_order_ideal('a')
['d', 'b', 'c', 'a']
sage: P.principal_order_ideal('b')
['d', 'b']
sage: P.principal_order_ideal('d')
['d']
sage: TestSuite(P).run()
------------------------------------------------------------------------------
By the way, please have a look at the comment in ``Poset?'' about
DiGraph, int's and Integer's (just below the above piece of
documentation)
Cheers,
Nicolas
--
Nicolas M. Thiéry "Isil" <nthi...@users.sf.net>
http://Nicolas.Thiery.name/
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