Hi,

The ticket at

https://trac.sagemath.org/ticket/28096

makes cached methods with do_pickle=True work (get the content pickled) for 
UniqueRepresentation objects. This is not an issue at an obscure corner of 
Sage, but would affect most users when saving objects to disk.

Note that most parents in Sage are UniqueRepresentation objects. If you ran 
cached methods (coded with do_pickle=True) of a parent, then when you save 
the parent object, the computed contents of the methods would get pickled 
along with it. I guess this would be very convenient feature for most 
cases. 

Actually we should have had this already, but did not because of a bug in 
UniqueRepresentation class, which the ticket solves.

Thank you for attention.

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