Thank you for keeping this sort of discussion on the mailing list. I think categories that take arguments such as
AbelianMonoidRing(R:Ring,E:OrderedAbelianMonoid) are quite distinct from category constants such as Ring Category with arguments really are "constructors" and are (usually) functorial in nature. They do not stand for a single category but rather for all the categories that can be constructed given the domain of the arguments. In fact as I understand it, FriCAS/Axiom treats constructor expressions as unevaluated (only references are replaced with values) and so one really should think of the whole expression as the "name" of a category. As such I do not find the new definitions AbelianMonoidRing(R : Join(SemiRng, AbelianMonoid), E : OrderedAbelianMonoid ) and FiniteAbelianMonoidRing(R : Join(SemiRng, AbelianMonoid), E : OrderedAbelianMonoid) particularly confusing. In the source we see category expressions such as: AbelianMonoidRing(D, NonNegativeInteger) ... where D: Join(IntegralDomain, GcdDomain) AbelianMonoidRing(Coef,Expon) FiniteAbelianMonoidRing(UPXS,EXPUPXS) etc. I think there is actually a much worse problem with these names since they are so close to the domain constructor "MonoidRing' and 'MonoidRingCategory' which are related but quite different. Regards, Bill Page. On Tue, Jul 26, 2011 at 12:00 PM, Waldek Hebisch <[email protected]> wrote: > In private mail Ralf Hemmecke wrote about commot 1119: >> > > > Support polynomial rings over semirings. >> > > >> > > You cannot really mean that. >> > > >> > > I don't question that the construction is useful, but I question the >> > > naming of things. >> > > >> > > Now we have that an AbelianMonoidRing is no longer a Ring or rather is >> > > only a ring under certain contitions. I think that is confusing. > > My reply: >> > My feeling is that this is within usual abuse of notation which is >> > common in mathematics (for example "simple Lie group" is not >> > necesserily a "simple group"). >> >> I'm more in favour of avoiding such abuse in the context of computer >> algebra as much as possible. >> >> > What do you propose? AbelianMonoidSemiRing is heavy and still >> > somewhat inaccurate >> > ... -- 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.
