I ran into the following problem for elements of rings of integers: they inherit from FieldElement. That's a problem when, for instance you want to implement a method "canonical_associate" that tries to find a canonical representative modulo multiplication by units. For fields, such a thing is easily defined, but for rings of integers such a method isn't necessarily easy to implement. It's natural to implement this method on "FieldElement", but then elements of rings of integers inherit that method (and it does the wrong thing there!)
I'd be interested if someone has a coherent idea about how we can handle such issues. It seems to me we have a problem in our inheritance hierarchy. I suspect someone made this design decision (that superficially looks like an error) for a good reason and may have put some thought into how to easily work around the obvious draw-backs. The following mro illustrates the problem: sage: R.<x>=ZZ[] sage: K.<a>=NumberField(x^3+x+1) sage: OK=K.ring_of_integers() sage: type(OK.0).mro() [<class 'sage.rings.number_field.number_field_element.OrderElement_absolute'>, <class 'sage.rings.number_field.number_field_element.NumberFieldElement_absolute'>, <class 'sage.rings.number_field.number_field_element.NumberFieldElement'>, <class 'sage.rings.number_field.number_field_element_base.NumberFieldElement_base'>, <class 'sage.structure.element.FieldElement'>, <class 'sage.structure.element.CommutativeRingElement'>, <class 'sage.structure.element.RingElement'>, <class 'sage.structure.element.ModuleElement'>, <class 'sage.structure.element.Element'>, <class 'sage.structure.sage_object.SageObject'>, <class 'object'>] -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To view this discussion visit https://groups.google.com/d/msgid/sage-devel/358676a7-0542-4a4d-992e-30be9e1bde8cn%40googlegroups.com.
