I believe I understood now:

sage: ?parent
Type:           function
<snip>
        Return x.parent() if defined, or type(x) if not.

I wonder why this is a function, and not a method of Parent?  (Am I right that
all Sage parents inherit from Parent?  Would be great to know this)

Set_object inherits from Set_generic, and does not define a parent method, for
whatever reason, maybe because the elements of the set need not have a common
type.

I just saw on
http://trac.sagemath.org/sage_trac/attachment/ticket/2314/coerce_2_sets.patch

a patch to primes.py, which, in particular, makes Primes inherit from a new
class Subset instead of Set_generic.  I guess this adresses the issue.

It would be wonderful to hear either of "yes, correct", or "no, you are
mistaken".

Many thanks,

Martin


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