If you permit only for sake of discussion the proposed syntax: >>> Integer::Ring >>> >>> could be equivalent to your AsRing(Integer).
then it might be useful to be able to write for example: Integer::Join(AbelianMonoid,Monoid) Probably we would not want to write different library routines for each interesting parameter to Join. Join operates on the the category lattice. This reminds me also about an undocumented operator in Aldor called Meet: http://axiom-wiki.newsynthesis.org/SandBoxAldorJoinAndMeet Perhaps with your example there could be a good reason to want this sort of lattice operation on categories? Regards, Bill Page. On Tue, Nov 29, 2011 at 4:49 PM, Bill Page <[email protected]> wrote: >> ... >>> Forgetful functors look like a form of type coercion. We could say >>> that Axiom automatically applies such coercions. If there is a good >>> reason to want to force such coercions when they would not necessarily >>> occur automatically, I wonder if it would not make good sense to >>> support this syntactically rather than just in the library. E.g. >>> >>> Integer::Ring >>> >>> could be equivalent to your AsRing(Integer). >> > On Tue, Nov 29, 2011 at 4:37 PM, Waldek Hebisch > <[email protected]> wrote: >> No, Integer is a Ring, so the coercion (if supported) would be >> no-op. > > You may call this something other than "coercion" if you wish. > >> The point is that given a Ring you can test if say, R has GcdDomain. >> Forgetful functor makes sure that answer for such question is false. >> > > Yes, that is clear. My point was only that perhaps it should be > supported through some simply syntax rather than having to explicitly > add such functors to the library for every possible thing we might > want to forget. > -- 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.
