On Tue, Jul 26, 2011 at 6:33 PM, Ralf Hemmecke <[email protected]> wrote: >> I am not quite sure what you mean by "inherit" in >> this context, but at least in one sense you are not correct when you >> say that AbelianMonoidRing does not inherit from Ring anymore. > >> 58 + if R has Ring then Ring > > Well you know what I meant. If a (Abelian)MonoidRing is only a ring > under certain conditions, then I find that confusing. > >>> 2) Up to minor details AbelianMonoidRing is in fact a specialization of >>> MonoidRingCategory, i.e. AbelianMonoidRing could inherit from >>> MonoidRingCategory. >> >> Perhaps. But as mathematical abstractions I think these FriCAS >> categories remain quite different in intention. > > What do you think is the different intention? > > In AbelianMonoidRing(R,E) the E is an additively written monoid. In > MonoidRingCategory(R,M), M is multiplicatively written and not > necessarily commutative. So what is the big difference? >
That difference is not big enough? :) A "monoid ring is a new ring constructed from some other ring and a monoid.". Or as it says in the documentation: "the algebra of all maps from the monoid M to the commutative ring R with finite support". "MonoidRingCategory(R,M)" is the (FriCAS) category of all such rings constructed in this manner. Contrast this with the description of AbelianMonoidRing. (I suppose that you already did this.) There is the issue of finite support but of course we also have FiniteAbelianMonoidRing. My interpretation is that the fact that these two abstractions are essentially equivalent is more properly a theorem and not something necessarily true by design. Anyway, I think we all agree that there is some room for improvement in the design of the category "heterarchy" (It seems to me intentional that it is not strictly a hierarchy). I am quite pleased that Waldek is undertaking these kinds of changes. 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.
