To do list
* from Alice's talk:
- Implement the algorithm (use Sage's pseudoprime function to check)
- What other primality tests does Pari have? Wrap these.
- Make things faster: implement as a python (maybe cython??) file
- How does GIMPS work?
- Ask Drew Sutherland what he's done?
- Implement Larry Washington's formulas for dealing with elliptic curves over integral domains
- Wrap E.reduction(prime)(P) so that we can also use P.reduction(prime)
- See what exactly is going on in E.global_minimal_model(), is it returning the unique restricted model? If so, update documentation
- Implement Singular Weierstrass Equations and functionality similar to Elliptic Curves
- make E.reduction(bad_prime) able to return this singular cubic object (maybe with a flag?)
- Compute lots of examples to find guesses for bounds on "C"
- p-adic Tate's algorithm
* Put Kate's EDS class into sage (document properly)?
* p-adics
#8685: evaluation of Monsky-Washnitzer objects (really about power series over p-adics)
#11319: Cannot create homomorphism from prime residue field to finite field
* wrapping of gauss composition (in pari: QuadClassUnit)
* #11697: Global minimal models over number fields with class number >= 1
- this is in Connell and probably wouldn't take to long to get at least a python toy version
- Sage already has this for class number 1 fields
* Reviewing number theory and elliptic curve tickets
* From William: For L-series lovers: Getting the doctest coverage to 100% on this might be a good project:
That may discover "issues" (bugs), which I would likely have to fix, but would also be fun because one gets to come up with lots of creative examples of L-series all over the place. Also, the top of that file has a todo list for new features to implement -- most would be bad projects, but one which would be good would be to make it so the Lseries object can use Lcalc (Rubinstein's program) to compute L-series instead of Dokchitser. This would be a good project, because it would mainly involve thinking about the annoying mathematics involved in going between normalizing L-series with the center of the critical strip at 1/2 versus not doing that. Also, it is all pure Python, so easier to get going.
Anyway, I'd say 1 could be a good project for people who know the basics of L-series, but want to get a much more concrete feel for them. In fact, instead of just trying to get coverage to 100%, writing a *tutorial* for computing with L-series using that package would be really nice. E.g., one could walk through how to find missing information, create new L-series classes, etc.