move methods on general set partitions into AbstractSetPartition

[mantepse]

Several methods currently in SetPartition only make sense for set partitions of {1,...,n}.

As a first step towards resolving this, this tickets moves all the other methods into AbstractSetPartition.

It is not clear to me yet, however, how to proceed beyond that.

[tscrim]

New commits:

​29518ce

move methods into AbstractSetPartition class

[zabrocki]

For every method in AbstractSetPartition I think that there should be a doc test for elements of PartitionDiagram (since PartitionDiagram inherits from AbstractSetPartition). In particular, strict_coarsenings raises an error, but I've been meaning to go through each of the methods and add a doc test because I know that there are others and making changes to this class will inadvertently introduce additional bugs.

[mantepse]

Replying to zabrocki:

In particular, strict_coarsenings raises an error

The problem is simply that this (and other methods) of AbstractSetPartition expect self to be a ClonableArray of Sets. This is enforced in SetPartition.__init__.

I think one question is what the purpose of AbstractSetPartition really is. It now seems to me that it was intended as a class that allows a different representation of set partitions (eg., as a list of tuples, as in PartitionDiagram).

I think it would make sense to have one class for set partitions of {1,...,n}, and another one for general set partitions. The same goes for perfect matchings, permutations, etc. But maybe that's not really useful.

[zabrocki]

I think one question is what the purpose of AbstractSetPartition really is. It now seems to me that it was intended as a class that allows a different representation of set partitions (eg., as a list of tuples, as in PartitionDiagram).

AbstractSetPartition is supposed to contain methods that are common to SetPartition and diagrams from diagram algebras (e.g. PartitionDiagrams, BrauerDiagrams, etc.) so that we are not copy/pasting code. Before #25146, diagrams were inheriting all the methods from SetPartition and some of them were not appropriate.