Diff for "days33/todo"

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

* KateWishList.sws

• 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
• Compute lots of examples to find guesses for bounds on "C"

* p-adics

• #7926: Bring coverage of Monsky-Washnitzer up to 50%

• #8241: p-adic fields should have Witt Frobenius

• #8685: evaluation of Monsky-Washnitzer objects (really about power series over p-adics)

• #9887: Slow coercion from integer ring to integer mod ring

• #11319: Cannot create homomorphism from prime residue field to finite field

• #11777: Coercion/printing problem with p-adics

* 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

* Open beginner tickets

* 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:

• http://code.google.com/p/purplesage/source/browse/psage/lseries/eulerprod.py

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.