Set Partitions, either a bug or something is unclear.

[startakovsky]

Consider the following code. The first is an example of not being able to verify the type Set Partition, the second is an analogous example with Permutations. Please advise on this discrepancy and how to get around it.

sage: sp = SetPartitions(5).random_element()
sage: sp
{{5}, {2, 3}, {1, 4}}
sage: type(sp)
<class 'sage.sets.set.Set_object_enumerated_with_category'>
sage: type(sp) == Set_object_enumerated_with_category
----------------------------------------------- NameError                             
   Traceback (most recent call last)
   /home/sage-admin/<ipython console> in <module>()
   NameError: name  'Set_object_enumerated_with_category' is not defined

sage: p = Permutations(5).random_element()
sage: p
(1,4,3,5,2)
sage: type(p)
<class 'sage.combinat.permutation.Permutation_class'>
sage: type(p) == Permutation_class  
True

[tscrim]

This is taken care of by #14140:

sage: sp = SetPartitions(5).random_element(); sp
{{1, 4}, {2, 5}, {3}}
sage: type(sp)
sage.combinat.set_partition.SetPartitions_set_with_category.element_class
sage: sp.parent()
Set partitions of {1, 2, 3, 4, 5}

There were two problems:

1. The underlying/central problem was that there was no specified element class before #14140.

2. The Set_object_enumerated class (which is a subclass of Parent) is changed by the category framework into the with_category class which doesn't exist as code. There's also the fact that permutations are not yet in the category framework.

Hope that clarifies some things.

[ncohen]

(cc me)