#18567: LatticePoset: add maximal_sublattices()
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Reporter: jmantysalo | Owner:
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-6.8
Component: combinatorics | Resolution:
Keywords: | Merged in:
Authors: Jori Mäntysalo | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
u/jmantysalo/latticeposet__add_maximal_sublattices_iterator__|
ef073c191be5c7e28967b11dd72c1072a2336336
Dependencies: | Stopgaps:
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Changes (by {'newvalue': u'Jori M\xe4ntysalo', 'oldvalue': ''}):
* status: new => needs_review
* milestone: sage-wishlist => sage-6.8
* author: => Jori Mäntysalo
Old description:
> How to add an iterator over maximal sublattices of a lattice? I think
> that the algorithm is not too complicated. Basically we from 1 to n on
> elements.
>
> Lets suppose that sublattice generated by elements 2,4,5 is not whole
> lattice. Now try to add 6. If it generates element 1 or 3, we will skip
> it. That's because if for example 1,2,4,6,8 is a maximal sublattice, then
> it had been generated already (we have tried all sublattices containing 1
> before going to those that does not contain 1).
>
> There might be a room for improvement by somehow arranging elements. But
> time for it is, I think, after we have some working code.
New description:
This adds a new function that computes maximal (proper) sublattices of the
lattice.
It could be faster to reverse thinking: instead of computing sublattice
try to get a minimal "remainder" of sublattice. For example the remainder
must be a connected poset and it's every minimal element may not have more
than one lower cover. However, this slow implementation at least works,
and can be used as a checkpoint when making faster implementations.
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Ticket URL: <http://trac.sagemath.org/ticket/18567#comment:5>
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