>   * Hyperelliptic curves -- Sage has nothing really for jacobian over
>     number fields, effective Chabauty.  Sage also doesn't implement  
> the
>     analytic Jacobians package from Magma.
>
> PROJECT: Make the group law on hyperelliptic Jacobians very fast.

Two comments: the patch at http://trac.sagemath.org/sage_trac/ticket/6218 
  makes arithmetic in hyperelliptic Jacobians a constant factor, about  
4-5 times faster for me.  It's just a few simple changes that really  
help.

Second, I have code that should be merged in the next few iterations  
for computing theta functions (and their derivatives) which is the  
easy half Magma's analytic Jacobians package.  I will eventually  
implement the other half (finding a homology basis and period matrix,  
etc) but not until much later -- if you're interested, please let me  
know (and preferably do it for me!).

Nick

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