#6021: [with new patch, needs review] Implement period lattices for elliptic
curves over CC
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Reporter: cremona | Owner: was
Type: enhancement | Status: new
Priority: major | Milestone: sage-4.0.1
Component: number theory | Keywords: elliptic curve periods
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Comment(by cremona):
Good question.
I knew we use pari for complex agm and had assumed we also did for real
agm. I suggest that first we implement complex agm in native Sage, to
remove that variable.
Here are the steps:
1. compute 2-division poly over the number field (exact)
2. embed the coeffs into RR or CC (depends on the embedding precision)
3. find its roots in RR or CC (depends on precision)
4. compute some square roots (ditto)
5. compute some AGMs
6. take reciprocals and multiply by pi
What should be done is to find out exactly at what point things differ.
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/6021#comment:12>
Sage <http://sagemath.org/>
Sage - Open Source Mathematical Software: Building the Car Instead of
Reinventing the Wheel
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