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| * [[attachment:KateWishList.sws]] * Wrap E.reduction(prime)(P) so that we can also use P.reduction(prime) [[http://trac.sagemath.org/sage_trac/ticket/11822|#11822]] * Implement E.reduction(p) for E defined over a p-adic fields * This found a bug: [[http://trac.sagemath.org/sage_trac/ticket/11826|#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 [[http://trac.sagemath.org/sage_trac/ticket/11823|#11823]] * change weierstrass model, addition of points, P.is_singular() to check if point is node/cusp, etc |
Associated notebook file [[attachment:KateWishList.sws]] Projects are listed by section below. No one is currently working on these ones: |
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| * p-adic Tate's algorithm | * Put Kate's EDS class into sage (document properly)? |
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| * Put Kate's EDS class into sage (document properly)? | === Restricted global_minimal_model() === * ticket? === Wrapping E.reduction(prime)(P) === * Ticket needs review! [[http://trac.sagemath.org/sage_trac/ticket/11822|#11822]] === p-adics === * Implement E.reduction(p) for E defined over a p-adic fields: [[attachment:reduction of elliptic curves over padics.sws]] * This found a bug/needed enhancement which is now reported: [[http://trac.sagemath.org/sage_trac/ticket/11826|#11826]] * Tate's algorithm |
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* 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 |
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| * Functions that we should write (new): | * Functions that we should write (new): done - see attached worksheet. |
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| [[attachment:singularcurves.sws]] |
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
* 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
* 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.
- 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