Robert Bradshaw <[EMAIL PROTECTED]> writes: > >> 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().
Yes, I agree here. Personally I would have done this only for "mathematical" functions, to reduce confusion. > > 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)" Oh, I saw this, but spelling it out made me understand. Thank you! (I'd rather call this method "remainder", however, then. Currently it's just very confusing. > >> 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. Hmm... > 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. Yes, that's why I would have thought that a set should have a parent: the class of all sets. Oh, I see, Set([1,2,3]) is a Parent. > This is why the notion of the "parent of a Parent" is a bit strange. I don't understand, I'd think that it is OK to have a Parent have elements, that are Parents in turn. For example, the set of combinatorial species is a ring (in various ways), but it's very natural to think of a particular species (eg. BinaryTree) as parent of it's structures. > > Does Sage have it's own notion of category, just as FriCAS? (I should have been more precise: FriCAS has it's own notion of category -- which is *different* from the usual mathematical notion of category. But now I understand that Sage - fortunately - does *not* introduce a concept "category", that differs from the usual one.) Martin --~--~---------~--~----~------------~-------~--~----~ 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 -~----------~----~----~----~------~----~------~--~---
