On Sunday, December 27, 2015 at 9:19:31 AM UTC-8, Daniel Lännström wrote:
>
> # BUT THIS FAILS
> assert J2(0) == J1(0) 
>

Equality of elements of point sests of different jacobians is indeed 
inconsistent, but with something else than what you note:

sage: J1(x,1)+J2(x,1)
(x^2, y + 6)

Apparently we allow coercion discovery between different jacobians, which 
we really shouldn't. This is probably a knock-on effect of J1 == J2.

I think the correct behavior would be J2(0) == J1(0). 
>

If we insist on keeping support for coercion then yes, we should do that. 
But I think we should have J1 != J2 (which is most naturally attained by H1 
!= H2 and that's hard to establish)


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