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* ticket? * Ticket needs review! [[http://trac.sagemath.org/sage_trac/ticket/11827|#11827]]

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 needs review! #11827

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 Tate.sws

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

days33/kates (last edited 2011-10-01 17:59:47 by ekin)