#19884: LatticePosets: Add is_relatively_complemented()
-------------------------------------+-------------------------------------
Reporter: jmantysalo | Owner:
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-7.1
Component: combinatorics | Resolution:
Keywords: latticeposet | Merged in:
Authors: Jori Mäntysalo | Reviewers: Travis Scrimshaw
Report Upstream: N/A | Work issues:
Branch: | Commit:
u/jmantysalo/relatively_complemented|
26725ab54e1c090b2a2d64d711f19c6e6dece105
Dependencies: | Stopgaps:
-------------------------------------+-------------------------------------
Changes (by tscrim):
* reviewer: => Travis Scrimshaw
Comment:
For the reverse implication counterexample, could you also have it display
that `L` is (co)atomic.
Also, could you make the following changes:
{{{#!diff
sage: [Posets.ChainPoset(i).is_relatively_complemented() for
- ....: i in range(5)]
+ ....: i in range(5)]
[True, True, True, False, False]
}}}
{{{#!diff
Usually a lattice that is not relatively complemented contains
elements
- `l`, `m`, and `u` such that rank(`l`)+1 == rank(`m`) ==
rank(`u`)-1
- and `m` is the only element in the interval `[l, u]`. We make an
+ `l`, `m`, and `u` such that `r(l) + 1 = r(m) = r(u) - 1`, where
`r` is
+ the rank function and `m` is the only element in the interval
`[l, u]`.
+ We construct an example where this does not hold::
}}}
{{{#!diff
C = Counter(flatten([H.neighbors_out(e2) for e2 in
H.neighbors_out(e1)]))
- for e3, c in C.iteritems():
- if c == 1:
- if len(H.closed_interval(e1, e3)) == 3:
- return False
+ if any(c == 1 and len(H.closed_interval(e1, e3)) == 3 for e3,
c in C.iteritems()):
+ return False
return True
}}}
Otherwise it is a positive review.
--
Ticket URL: <http://trac.sagemath.org/ticket/19884#comment:7>
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