Sage Days 16 Project Idea Page
Create a Cython class for points on elliptic curves and optimize basic arithmetic
PEOPLE: William Stein
- Right now basic arithmetic on elliptic curves is way too slow. It could be sped up by moving the point class to Cython, and possibly by using better formulas for arithmetic, e.g., using projective coordinates.
Create elliptic curve classes for elliptic curve models in the Explicit-Formulas Database
PEOPLE: David Kohel
- In order to optimize and compare arithmetic, we should first implement alternative models and verify relative performance. The isomorphisms between different models should also be implemented, and classes for isogenies of these models developed, making use first of the new isogenies code, and eventually putting in place special optimized code for specific models.
See the EFD: http://www.hyperelliptic.org/EFD/
Rewrite abelian groups
PEOPLE: William Stein
It would be possible to use trac 5882 to rewrite abelian groups natively in Sage (not using GAP), in a way that is much more flexible than the current implementation. This could be useful for many number theory applications.