#20980: LatticePoset: certificate for non-modularity, part 1
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Reporter: jmantysalo | Owner:
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-7.3
Component: combinatorics | Resolution:
Keywords: | Merged in:
Authors: Jori Mäntysalo | Reviewers:
Report Upstream: N/A | Work issues: rebase over 7.3.beta7
Branch: | Commit:
public/test_branch_find_pentagon | 6043924acb37777cf7daa5f8a143d31d85bfd817
Dependencies: | Stopgaps:
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Comment (by jmantysalo):
True, minimal certificate for non-semimodularity would be two elements.
They can be extracted from this pentagon.
What about non-modular and non-distributive lattices? Should we return
elements `(a, b, x)` violating definition of modularity, and same with
distributivity?
After this we could think about best implementation. Maybe
`is_distributive(certificate=True)` should first call
`is_modular(certificate=True)` which could call `is_upper_semimodular()`
and `is_lower(semimodular)`. But if a non-distributive lattice is modular,
then `is_distributive()` runs it's own subprogram to find the three
elements of `M_3` sublattice.
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Ticket URL: <https://trac.sagemath.org/ticket/20980#comment:11>
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