On Oct 14, 2008, at 2:02 PM, Martin Rubey wrote: > Robert Bradshaw <[EMAIL PROTECTED]> writes: > >> On Oct 14, 2008, at 1:33 PM, Martin Rubey wrote: >> >>> >>> 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? >> >> Typically one uses the parent() function when one has an element >> (such as an integer) and wants it's Parent. This is why it's not an >> element of the Parent. > > Hm, I do not understand that. Why wouldn't one want to use 5.parent > (), for > example? (The method notation together with tab completion is > really nice...) > Well, I suppose that some people prefer usual functional notation.
Yes, the method notation + tab completion is very nice and usually prefered. The reason one would want to use parent() however is because not everything has a parent method. For example, int(1).parent () would fail with an attribute error. The parent function always succeeds, giving something reasonable if the object in question doesn't have such a method. Often functional notation is just handier for really common things, e.g. writing sin(pi/5) rather than (pi/5).sin(). >> The docstring should have some better examples, e.g. >> >> sage: parent(5) >> Integer Ring >> sage: parent(1/2) >> Rational Field >> sage: parent(1.5) >> Real Field with 53 bits of precision > > Well, actually, I find the current docstring OK, it answered my > question, at > least partially. OK, maybe some more examples wouldn't hurt. > > But what I really do not understand is why Parent doesn't implement > a parent > method... >>> (Am I right that all Sage parents inherit from Parent? Would be >>> great to >>> know this) >> >> Yes, that is correct. > > OK, great. > >>> 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". > >> I'm not sure exactly what your question is, > > The question was, why does > > parent(Primes()) give an answer, while Primes().parent() yields an > error. > >> but sets don't really have a parent, > > well, they do: > > sage: parent(Set([1,2,3])) <class > 'sage.sets.set.Set_object_enumerated'> > > ;-) > > I think it's ok to have things without parent, but I do not > understand yet, why > x.f() and f(x) are designed differently in some cases. One case I > stepped into > was parent, the other was Mod. Here it's a question of context. The method mod(a,b) is a constructor for an element of Z/mZ, a.mod(b) means "divide and take the remainder (as an integer)" >> as the set of all sets is not a category. > > Äh? You don't mean category in the mathematical sense here, do you? > http://en.wikipedia.org/wiki/Category_of_sets Yes, I meant in the sense that the class of all sets can't be an object in a category. I think the confusion here is as to what a parent actually is. A parent is an Object in a concrete category, i.e. it contains Elements. This is why the notion of the "parent of a Parent" is a bit strange. Because Python (justifiably) doesn't force all objects to have categorically-theoretical underpinnings, we use the type (or, internally "the set of all objects of type X") as a pseudo-parent to be able to reason with (e.g. for coercion). > Does Sage have it's own notion of category, just as FriCAS? Yes, though it's not as heavily used (yet, it's becoming more so). - Robert --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
