#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 chapoton):
Oh, I have not seen your answer, for some reason.
I will take care of the header question soon.
Concerning terminology, it seems that confusion is everywhere, see for
instance
http://en.wikipedia.org/wiki/Order_ideal
saying "The terms order ideal, order filter, semi-ideal, down-set and
decreasing subset are sometimes used for arbitrary lower or upper sets"
So far, in sage, we have the following definition (in P.order_ideal?)
I is an order ideal if, for any x in I and y such that y <= x, then y is
in I.
So I have tried to stick at this convention and not to introduce two
competing notations in sage. I do not like upper set and lower set because
of the word set, which does not has the idea of closure. I do not like
order ideal and order filter because I never remember which one is which.
I would like to use upper ideal and lower ideal, but nobody seems to use
that. This is rather boring.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/12848#comment:15>
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