Martin, There is not very much I could add to Ralf's and Bertfried's comments except that I also do not much like the current design of hom-sets. But I thought I should say something because I still feel rather strongly that category theory ought to play a much more important role than it currently does in FriCAS/OpenAxiom/Axiom (+ Aldor ... someday real soon now, I hope). Saul Youssef was at least in part, experimenting with the idea that the Axiom library (or rather Aldor libraries) as a whole could in principle be written to be "correct by design" with all domains and categories defined from the ground up as fully categorical constructions. Of course this would be a very ambitious task and the exercise is as much as test of the programming language as it is a library design strategy. But in my opinion something intermediate between what is done now and this higher goal could still be interesting and useful.
I hesitate to suggest this since I personally am not very fond of the results so far but you might also like to look at what the combinat project did in the design of a category framework for Sage. My main point is that they also felt that category theory could play a significant role. Martin, I am very encouraged that you are thinking of category theory in FriCAS and I am glad that you take the time to write code to illustrate your ideas. One thing that I would suggest is that you take more care to use terminology from category theory in a correct manner. Nothing turns off people with a mathematical orientation more than seemingly imprecise use of terms such as functor, natural transformation etc. There are now a number of very good books on beginning category theory and applications to various subjects. I think it would be a good idea to pick one of these as reference for the terms you use. Regards, Bill Page. -- You received this message because you are subscribed to the Google Groups "FriCAS - computer algebra system" group. To post to this group, send email to [email protected]. To unsubscribe from this group, send email to [email protected]. For more options, visit this group at http://groups.google.com/group/fricas-devel?hl=en.
