Hello !

Nils mentionned in #17408 [1] that we may *not* need Posets to be parents. 
The facade Posets (i.e. the default ones) are parents, and it seems that 
this is the reason why they have been made UniqueRepresentation.

Could anybody confirm that ? Also, would anybody know how to make it change 
?

The goal would be to remove the dependency of facade FinitePoset objects on 
UniqueRepresentation. The non-facade posets returned by the Poset function 
could then inherit from both Poset and UniqueRepresentation.

The problem here is that inheriting from UniqueRepresentation wastes a 
*LOT* of time on some computations [2], and is actually the most costly 
part of the creation of some posets. Also, the current behaviour makes it 
impossible for Jori to enumerate posets up to isomorphism (because of the 
memory cost).

I am personally stuck, my psychoanalist advised me to not touch 
Parent/Category code ever again.

Nathann

[1] http://trac.sagemath.org/ticket/17408
[2] http://trac.sagemath.org/ticket/17408#comment:13

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