#10998: Categories for posets
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   Reporter:  nthiery                                                           
  |          Owner:  sage-combinat                                        
       Type:  enhancement                                                       
  |         Status:  needs_work                                           
   Priority:  major                                                             
  |      Milestone:  sage-4.7.1                                           
  Component:  combinatorics                                                     
  |       Keywords:                                                       
Work_issues:                                                                    
  |       Upstream:  N/A                                                  
   Reviewer:  Franco Saliola, Christian Stump, Nicolas M. Thiéry, Florent 
Hivert  |         Author:  Frédéric Chapoton, Christian Stump, Nicolas M. Thiéry
     Merged:                                                                    
  |   Dependencies:                                                       
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Comment(by novoselt):

 Replying to [comment:20 nthiery]:
 > For the record: finite posets and their elements, now have
 UniqueRepresentation. This could have an influence if the same poset is
 created several times when constructing several fans.

 Yes, this is it. Repeating the failing code twice in the command line
 reproduced the error. This raises two questions:
 1) Out of curiosity: Why does it show up in doctests? Shouldn't the state
 of Sage be clean before running a new test?
 2) To the point: How to fix it?

 I really don't want to make fans unique at this point as I am planning
 some adjustments to them and related objects.

 Does uniqueness test rely on `==` test? Is there any way to change it?
 Currently `==` for fans checks that fans have the same rays and the same
 generating cones in the same order. Things relates to facets require even
 stronger `is`-equivalence. On the other hand, Volker votes for `==` being
 mathematical equivalence without taking order into account. Such
 equivalence definitely would not be acceptable deep inside implementation
 which relies on fixed order.

 So I guess my preferred solution for now would be to trick posets into
 creating different face lattices for fans and cones even if they are `==`.
 Can I somehow attach `id(fan)` to the poset without altering its
 structure?..

-- 
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/10998#comment:21>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, 
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