Diff for "days33/kates"

Project Leader

Kate

Group Members

Aly, Jenn, Diane, Ekin

Project Description

Associated notebook file KateWishList.sws

Projects are listed by section below. No one is currently working on these ones:

• Compute lots of examples to find guesses for bounds on "C"
• Put Kate's EDS class into sage (document properly)?

Restricted global_minimal_model()

* ticket?

Wrapping E.reduction(prime)(P)

* Ticket needs review! #11822

p-adics

* Implement E.reduction(p) for E defined over a p-adic fields: reduction of elliptic curves over padics.sws

• This found a bug/needed enhancement which is now reported: #11826

* Tate's algorithm

Singular Cubics

Trac ticket 11823

* Currently the patch on the trac server will allow one to define singular cubics.

sage: E = WeierstrassCubic([0,0,0,0,0])
sage: E.is_singular()
True

* Stuff to do:

• Work through elliptic curve documentation, test functions that should work for singular curves, and update the following lists

• Document the WeierstrassCubic and SingularWeierstrass classes we've created

• Do the stuff on the list below
• make E.reduction(bad_prime) able to return this singular cubic object

• put the checks back in for EllipticCurve and SingularWeierstrass that it is actually (or is not) singular

* Functions that seem ok out of the box (so need only documentation adjustment/testing):

• a_invariants() etc. (b, c also)
• discriminant()
• base_ring()
• base_field()
• is_on_curve()
• coordinate_ring()
• division_polynomial()
• formal_group()
• multiplication_by_m()?

* Functions that should do something appropriate but don't (need coding):

• j_invariant() -- should probably return +infinity?
• change_weierstrass_model() -- the new curve needs to pass flag
• base_extend() -- the problem may be my patch didn't work
• change_ring() -- the problem may be my patch didn't work
• cardinality() -- for finite fields
• local stuff....??
• addition of points on a curve (seems to work, but needs to avoid singular point)

* Functions that we should write (new): done - see attached worksheet.

• singularcurves.sws

• is_singular() (done) -- this is also accessible as an internal flag: self._is_singular
• P.is_singular_point() -- for a point on the curve
• singularity_type() -- tells you if it's a node or a cusp
• singular_point() -- returns the node or cusp