Could this be related ?

http://trac.sagemath.org/ticket/16384

I do not understand much about categories, but if we implement 
multiplication by a positive integer for semigroups and multiplication by a 
negative integer for semigroup with inverse, won't this automatically give 
a ZZ-Module structure to any additive abelian group ? And more technically, 
isn't it the case that every additive abelian parent in Sage will be 
detected as a ZZ-Module ?

Nathann

On Tuesday, May 27, 2014 9:14:06 PM UTC+2, vdelecroix wrote:
>
> Hi, 
>
> A module over ZZ is the same thing as an Abelian group. Why do we have 
> two distinct categories ? 
>
> More concretely, I want to implement a function that takes any finite 
> Abelian group as input ? So my test would looks like 
>
> def f(A): 
>     assert A in CommutativeAdditiveGroups().Finite() 
>
> or 
>
> def f(A): 
>     assert A in Modules(ZZ).Finite() 
>
> Is there a preference ? Is there a way to merge Modules(ZZ) and 
> CommutativeAdditiveGroups() ? 
>
> Vincent 
>

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