On Tue, Nov 11, 2008 at 12:50 AM, Mike Hansen wrote: > > On Mon, Nov 10, 2008 at 9:31 PM, Bill Page wrote: >> ... >> It seems to me that of all the existing computer algebra systems, >> because of it's strong and often pedantic type system, Axiom >> seems most compatible with taking category theory as a foundation. >> Unfortunately in most respects Axiom does not do nearly enough to >> exploit this. Magma apparently also takes a formal approach that is >> at least in part motivated by category theory but I was rather >> disappointed to see how little of this remains in the approach now >> implemented in Sage. > > Just a quick note. Categories in Sage are modeled after the > mathematical categories rather than Ralf's universal algebra notion. > That is, you have objects, morphisms, functors, homsets, etc. They > just happen to be a convenient place to put generic methods for their > objects. >
Although I am vaguely aware that Sage does implement these notions, even after working with Sage now for the last two years I still know very little about what is actually implemented and what is planned. Unless I missed it, it seems to me that there is an extreme lack of documentation on all of this in Sage. Also, I have some trouble reconciling your comments with the comments of Nicolas Thiery at the start of this thread. Is Nicolas talking about mathematical categories in Sage or something more like categories in Axiom/MuPAD? Finally, I should note that I do not agree with Ralf's views (quoting Doye's article on Aldor) on the importance of universal algebra notions to categories in Axiom. But I do think that this article is very relevant to the subject of coercions in computer algebra and so also important in Sage. Regards, Bill Page. --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-devel@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-devel URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
