On Thursday, September 1, 2016 at 4:53:00 PM UTC+2, Daniel Krenn wrote: > > On 2016-09-01 01:47, Kwankyu Lee wrote: > > I am playing with an experimental implementation of "enumerated" axiom. > > From what I guess is, that this axiom implies an implementation of > __getitem__, correct? >
If you see the code for the enumerated sets category, it means that the object in the category is iterable and has ".list()" method basically. > Does it also imply something on the index set (e.g. natural numbers) of > this object? Or does it only mean an enumeration is possible by some > index set? > You know what it means mathematically (indexed by a countable set). Technically it means what I said above. > > This is rather ugly. I guess that this is caused partially by that the > > "finite" axiom does not imply "enumerated" axiom > > Side-question: Would it be SageMath-technically possible that one axiom > implies another? > I don't think so, but I am not sure about this. I just meant that in Sage, the finite sets category and the enumerated sets category are two distinct categories and that none of them is a subcategory of the other. I think that all this is reasonable. > > which is legitimate. > > Why? (I understand the following: From a mathematical point of view, > there is no need to print the "enumerated" when already a "finite" is > there. From a more technical point of view, "finite" does not mean > SageMath provides a way to enumerate it, i.e., that __getitem__ is > implemented) > It is legitimate from the technical point of view as you said. In Sage, "finite" and "finite enumerated" are distinct. If a category is of finite enumerated sets, then the objects in the category has ".list()" method while if it is only of finite sets, then not. On the other hand, some may prefer that "finite enumerated" is just printed as "finite" from esthetic point of view. So for example, a finite field belongs to the "Category of finite fields" rather than "Category of finite enumerated fields". I am inclined to living with "finite enumerated fields" :-) I now think we should have "enumerated" axiom in Sage. But I want to hear opinions of Sage-category experts. -- 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 post to this group, send email to sage-devel@googlegroups.com. Visit this group at https://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout.
