#19190: LatticePoset: add atoms, coatoms, doubly irreducibles etc.
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       Reporter:  jmantysalo      |        Owner:
           Type:  enhancement     |       Status:  new
       Priority:  minor           |    Milestone:  sage-wishlist
      Component:  combinatorics   |   Resolution:
       Keywords:  poset           |    Merged in:
        Authors:  Jori Mäntysalo  |    Reviewers:
Report Upstream:  N/A             |  Work issues:
         Branch:                  |       Commit:
   Dependencies:                  |     Stopgaps:
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Description changed by jmantysalo:

Old description:

> Add `atoms()`, `coatoms()`, and `doubly_irreducibles()` to
> `LatticePoset`. Add missing functions, like `join_irreducibles()`, to
> index of functions. Do this after #19123 gets positive review and gets
> into beta.
>
> Other things:
>
> - Check documentation of `breadth()`, stupid way to express
> `BooleanLattice(4)`.

New description:

 To a normal user viewpoint:

 - Add  `atoms()`, `coatoms()`, and `doubly_irreducibles()` to finite
 lattices.
 - Add missing functions, like `breadth()`, to index of functions. (Wait
 #19123 to get into beta.)

 Internal changes:

 - Put `meet_irreducibles()` and `join_irreducibles()` to
 `hasse_diagram.py`. Add wrappers to `lattices.py`. This can help some
 optimization later.

 Other things:

 - Check documentation of `breadth()`, stupid way to express
 `BooleanLattice(4)`.

 Maybe:

 - Think about `is_modular_element()` vs. `is_modular()` with argument.

--

--
Ticket URL: <http://trac.sagemath.org/ticket/19190#comment:2>
Sage <http://www.sagemath.org>
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