Ralf Hemmecke wrote:
> Thanks for pointing out MonoidRing.
>
> There are at least two problems.
> 1) The category ends in "...Category" while for quite a lot of other
> mathematical categories like Ring, Field, Group, AbelianMonoidRing, it
> does not.
> I quite like the convention that mathematical structures (i.e. FriCAS
> categories) don't have "...Category" in their names.
We have a few cases when we need both domain and category for which
we would like to use the same name. Then "...Category" suffix
allows to resolve clash. Polynomial domain and PolynomialCategory
is a prime example.
>
> 2) Up to minor details AbelianMonoidRing is in fact a specialization of
> MonoidRingCategory, i.e. AbelianMonoidRing could inherit from
> MonoidRingCategory.
>
> **Abelian**MonoidRing means that the underlying monoid is commutative.
> That's rather restrictive for modelling non-commutative polynomials. But
> I agree that it is a rather important special case that deserves its own
> category.
>
Actually, the only reason to separate MonoidRing and AbelianMonoidRing
is "monoid problem": AbelianMonoidRing ring assumes that underlying
monoid operation is denoted by '+'. MonoidRing ring assumes that underlying
monoid operation is denoted by '*'. There are reasonable mathematical
structures where '+' is noncommutative. If we decide to support
such structures then it would be natural to generalize AbelianMonoidRing
to support noncommutative '+'. I admit that in this case I would
be for rename since 'Abelian...' in then name of noncommutative
thing sounds too confusing...
--
Waldek Hebisch
[email protected]
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