Diff for "days33/kates"

Project Leader

Kate

Group Members

Aly, Jenn, Diane, Ekin

Project Description

* KateWishList.sws

• Wrap E.reduction(prime)(P) so that we can also use P.reduction(prime) #11822

• Implement E.reduction(p) for E defined over a p-adic fields

  • This found a bug: #11826

• 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 #11823

  • change weierstrass model, addition of points, P.is_singular() to check if point is node/cusp, etc
• 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)?

Singular Cubics

Trac ticket 11823

* 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()?
• addition of points on a curve

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

• j_invariant() -- should probably return +infinity?
• change_weierstrass_model() -- the problem may be my patch didn't work
• 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....??

* Functions that we should write (new):

• is_singular() (done)
• 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