Hello, A discussion was just started at http://trac.sagemath.org/ticket/15192about the reason why categories in Sage have a class ElementMethods. In this ticket, Julian Rüth moved the method is_unit from RingElement to Rings().ElementMethods to fix a certain bug. I thought this wasn't the only possible fix and wondered why the latter existed in the first place. We thought it would be a good idea to move the discussion here.
For now let me just quote myself out of context (see the ticket for context): Parents describe relations between elements; e.g. a ring is a set whose elements satisfy certain axioms. Categories are on a higher level; they describe relations between objects, and it shouldn't matter too much what the elements of these objects are, or even if the objects are sets at all. Whether an element is unit depends on relations satisfied *within* its parent, not on relations between the parent and *other* parents. In other words, the category its parent is in should not play any role. It is true that some categories (like the category of rings) *are* in a sense defined by relations between the *elements* of objects, but exploiting this to influence the behaviour of elements is confusing two different levels of abstraction, in my opinion. Hence, I don't see a good mathematical reason for putting methods in Ring.ElementMethods instead of RingElement. I can see why one would want a Category to have ObjectMethods (which are now called ParentMethods) and perhaps MorphismMethods (which only exist in a doctest). With ElementMethods, however, I somehow get the feeling that the authors of the category framework are aiming for world domination! (Last sentence is tongue-in-cheek, of course.) Can someone more familiar with the category framework motivate the reason for ElementMethods? Are there methods that cannot or should not be put in the relevant element classes (such as RingElement above)? Thanks, Peter -- 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 [email protected]. To post to this group, send email to [email protected]. Visit this group at http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/groups/opt_out.
