#12848: Bug in order_ideal_complement_generators: 'down'
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Reporter: nthiery | Owner:
sage-combinat
Type: defect | Status:
needs_review
Priority: major | Milestone:
sage-5.10
Component: combinatorics | Resolution:
Keywords: posets | Work issues:
Report Upstream: N/A | Reviewers:
Authors: Nicolas M. Thiéry, Frédéric Chapoton | Merged in:
Dependencies: | Stopgaps:
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Comment (by nthiery):
Replying to [comment:17 chapoton]:
> The other definition of "order filter" is not quite that: it says "an
upper set such that any two elements have a common lowest bound in the
upper set"
Oops, you are right; I formulated this to fast.
> It seems to imply (for finite posets) that it has a unique minimal
element, and that this other definition could be called a "principal upper
ideal" or "principal upper set".
Indeed.
> There are subtle issues for infinite posets, but should we be concerned
about that ?
Not right now. But that will come! So it would be good to know that there
exist a plan, even if we don't know right away which plan it should be.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/12848#comment:18>
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