By the way, why would "G = AdditiveAbelianGroup([7,23])" 

> 1) expect input from Z/161
>> 2) give its output as pairs 7x23 ?
>>
>
> That must be an oversight (and hence a reportable bug). This is just too 
> confusing:
>
> sage: G1=AdditiveAbelianGroup([2,4]); G1
> Additive abelian group isomorphic to Z/2 + Z/4
> sage: G2=AdditiveAbelianGroup([4,2]); G2
> Additive abelian group isomorphic to Z/2 + Z/4
> sage: G2([1,0]).order()
> 2
> sage: G2(vector([1,0])).order()
> 4
>
> It is probably a matter of the implementer forgetting to support "list as 
> input" and then the underlying structure (with internal basis) taking over 
> to interpret the coefficient wrt. the internal basis.
>

I think it would be better to make these UniqueRepresentations by sorting 
the list of integer inputs, that way things like

sage: G1 is G2
False
sage: G1 == G2
False

would make sense. Going to point 1, this would allow us to define natural 
coercions and allow people could use whichever format they wanted.

Best,
Travis

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