On Friday, November 8, 2013 12:09:24 AM UTC-8, Nathann Cohen wrote:

> 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.

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