#19123: LatticePoset: add is_vertically_decomposable
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Reporter: jmantysalo | Owner:
Type: enhancement | Status: needs_work
Priority: major | Milestone: sage-6.9
Component: combinatorics | Resolution:
Keywords: | Merged in:
Authors: Jori Mäntysalo | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
u/jmantysalo/vertically_decomposable|
0d472a68c9edf4ddea1404ff0cb6d2f508de55d0
Dependencies: | Stopgaps:
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Changes (by jmantysalo):
* status: needs_review => needs_work
Comment:
Replying to [comment:3 ncohen]:
> Sounds good, but don't you think it may be useful to *know* where the
poset splits?
Yes, I think that will be usefull. For posets we have `is_connected()`,
`connected_components()` and `disjoint_union()`. I guess we should have
`is_vertically_decomposable()`, `vertically_indecomposable_parts()` and
`vertical_sum()` for lattices.
There are of course other options, like having a function (this one, with
an argument?) returning list of "decomposition elements". The user could
then run `interval()` on them to get parts.
> Also, why is it only defined for lattices? The algorithm works in all
cases.
How should it be defined on non-connected posets? And I am not sure if
this works with non-bounded posets; I thinked about bounded ones when
writing this.
> I did not test it, but from the code's look I am not sure that it works
for the chain of length 2, as the docstring indicates. Could you add a
doctest for that?
Arghs! You are right, of course. I forget the special case when writing
the code. I'll correct it.
(Btw, this would be nice exercise of (totally unneeded) optimization. One
should not need to look for all edged of Hasse diagram to see that a poset
is indecomposable.)
--
Ticket URL: <http://trac.sagemath.org/ticket/19123#comment:4>
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