use the finer new categories for some lattice posets in library

[fchapoton]

namely declare some known properties as categories, as allowed by #39554

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[fchapoton]

one question : should I add doctests for all these enhanced categories ?

[mantepse]

I think it might be good to have, for each of the categories, something like _test_congruence_uniform.

I realize that I don't understand something. I did

sage: P = posets.TamariLattice(3)
sage: P.category()
Category of facade finite enumerated trim congruence uniform lattice posets
sage: P.is_congruence_uniform
<bound method FiniteLatticePoset.is_congruence_uniform of Finite lattice containing 5 elements>

and indeed, trace confirms that this is not picking up the method from LatticePosets.CongruenceUniform.ParentMethods. Is this to be expected?

[fchapoton]

I was thinking of adding tests to check that each poset where we declare a specific category is in this category. This may seem superfluous, as there can be no failure, otherwise the init would fail.

yes, the category always have a very low priority.

moving the "is_congruence_uniform" and similar method to the category would be a possible next step in the future

[mantepse]

But then, why is there a method 'is_congruence_uniform' if it is not used?

[fchapoton]

It will become used once the method in "LatticePoset" will be moved to the general category of lattices. I plan to do that later.

[mantepse]

I think having a _test_congruence_uniform etc would be good idea.

Can we already iterate over the posets of given size in a given category? Then checking the number of posets against the Oeis is also an obvious candidate.

[fchapoton]

thanks for the suggestions, Martin. Maybe we can keep them for another PR ? Here the aim is just to put some existing examples in more refined categories.

[mantepse]

Bien sur !

[mantepse]

LGTM