Random failure in diagram algebras

[vbraun]

I've seen this more than once on the buildbot...

sage -t --long src/sage/combinat/diagram_algebras.py
**********************************************************************
File "src/sage/combinat/diagram_algebras.py", line 696, in sage.combinat.diagram_algebras.SubPartitionAlgebra.__init__
Failed example:
    BA.ambient().has_coerce_map_from(BA)
Expected:
    True
Got:
    False
**********************************************************************

[vbraun]

Something related to the coercion is getting garbage collected during the execution of the command. On my desktop (a fast computer with gobs of RAM) I always get the right answer. But if I use the trace hook to force run a garbage collection between each Python command:

def trace_gc(frame, event, arg):
    import gc
    gc.collect()

then a) everything gets dog slow, about 5 mins for the lines below, and b) I get the wrong answer:

sage: sys.settrace(trace_gc)
sage: R.<x> = QQ[]
sage: BA = BrauerAlgebra(2, x, R)
sage: BA.ambient().has_coerce_map_from(BA)
False

[SimonKing]

I suppose the problem comes from __init_extra__, which for algebras is supposed to register the coercion from the base ring.

[SimonKing]

I found that we are in a rare case. This

            try:
                has_custom_conversion = self.category().parent_class.from_base_ring.__func__ is not self.from_base_ring.__func__
            except AttributeError:
                # Sometimes from_base_ring is a lazy attribute
                has_custom_conversion = True

ends up in "except AttributeError". So, the question is if it is really the case here that from_base_ring exists as lazy attribute, or the attribute error came from a different reason.

[SimonKing]

Yes, it is a lazy attribute of the parent class.

[tscrim]

I'm thinking the problem is coming from line 700-1:

self.module_morphism(self.lift, codomain=amb,
                     category=self.category()).register_as_coercion()

and is similar to what I posted on #16532, as a reference to the ambient partition algebra is not held by the subpartition algebra.

I'm thinking the easiest fix would be to actually just store a reference to the ambient algebra in the subpartition algebra. The best fix would probably be to add a _coerce_map_from_ in PartitionAlgebra which checks if the parent is an instance of SubPartitionAlgebra and returns the lift module morphism. Both fixes are easy, which do you think we should do?

[vbraun]

I don't see how storing a reference to ambient is going to help, the call to has_coerce_map_from in the ticket description already holds a reference to ambient (== self)