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Project Leader
Kate
Group Members
Aly, Jenn, Diane, Ekin
Project Description
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
- 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
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