#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: days30, sd31
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: #11289, #10938, #9065
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Comment(by novoselt):
As I understand the uniqueness framework, it is based on checking that the
input to the constructor is the same as was already used before. So if
posets are unique, the constructor input is somehow normalized (using
Hasse diagram, perhaps?) and then compared with those that were already
constructed.
In this cases fans and cones report that "==" is true for all the elements
and therefore the posets are considered to be the same and become a unique
object.
However for implementation purposes there is a big difference between
treating two cones as cones of the same fan and as two arbitrary cones. In
the first case the intersection is internally computed as the intersection
of two ordered sets of integers. In the second one it involves
constructing a new polyhedral object and determining its minimal generator
set. With old PALP/cdd interfaces this takes forever (compared to
intersection two short lists of integers). With Volker's new PPL interface
it is much better, yet still it requires many more operations.
I agree that we have here more structure than poset itself but it is
basically the question of "the same" and "isomorphic". We have a similar
issue with toric lattices: if M = ZZ^n^, then the dual space is also
ZZ^n^, yet they are isomorphic but not equal. It would be great actually
to have some standard way in Sage to tag objects. Maybe ZZ is unique as a
ring, but it is possible that one wants to consider several modules which
are isomorphic to ZZ and treat them as different ones.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/10998#comment:38>
Sage <http://www.sagemath.org>
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