Re: [Axiom-developer] MonoidWithZero

[Bill Page]

On 7/20/07, Franz Lehner wrote:
> here is an algebra question for a change.
> I need a version of MonoidRing for MonoidWithZero.
> That is, the monoid has a "zero" element which also becomes the zero
> element of its monoid ring and thus needs special treatment.
> For this I need (so I think) both a Category MonoidWithZero, which is
> easy, and a special version of MonoidRing which knows how to treat the zero
> element. I would like to reuse as much as possible from MonoidRing,
> however I realized that MonoidRingCategory is only locally defined in
> mring.spad:
>
> MonoidRing(R: Ring, M: Monoid): MRcategory == MRdefinition where
>      Term ==> Record(coef: R, monom: M)
>
>      MRcategory ==> Join(Ring, RetractableTo M, RetractableTo R) with
>      ...
>
> Is there a smart way to reuse this without completely rewriting it?

I think the short answer is "no". But if you do re-write it, I can see
no reason why this should not be written as a normal category
definition and used in MonoidRing instead of the local macro
definition.

On the other hand perhaps the category "AbelianMonoidRing" in
'src/algebra/polycat.spad.pamphlet' is what you need?

Regards,
Bill Page.