#16598: Useless new classes and a replacement for _check_pbd
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Reporter: ncohen | Owner:
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-6.3
Component: combinatorial | Resolution:
designs | Merged in:
Keywords: | Reviewers:
Authors: Nathann Cohen | Work issues:
Report Upstream: N/A | Commit:
Branch: u/ncohen/16598 | fa3c715732a965786f86a2a0ce7087c63294519a
Dependencies: #16553 | Stopgaps:
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Comment (by vdelecroix):
Replying to [comment:16 ncohen]:
> > All right, add the extra assumption that each point is covered by at
least one block! If not `.groups()` raises an exception.
>
> It's unrelated. What are the blocks of
`IncidenceStructure(4,[[0,1],[1,2],[2,3]])` ? I am just telling you that
{"u~v" if the pair `u,v` is not covered by a block} is not an equivalence
relation unless you are in a GDD.
For GDD you have an extra assumption of the existence of a lambda:
{{{
blocks = [[0,1],[0,2]]
groups = [[0],[1,2]]
}}}
is not a GDD (0 is covered by two blocks, but 1 and 2 are covered by one
block). But "not being in a block" for pairs is an equivalence relation...
I definitely agree that "not being in the same block" is not an
equivalence relation for many incidence structures (lack of
transitivity)... but it is well defined and symmetric.
Vincent
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Ticket URL: <http://trac.sagemath.org/ticket/16598#comment:17>
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