Diff for "days33/kates" - Sagemath Wiki

Differences between revisions 1 and 29 (spanning 28 versions)

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 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

-  ⇤ ← Revision 1 as of 2011-09-20 21:15:43 → 
  Size: 14
  Editor: lola
  Comment:
+   ← Revision 29 as of 2011-09-23 05:38:14 → ⇥
  Size: 2763
  Editor: jmypark
  Comment:
-Deletions are marked like this.
+Additions are marked like this.
 Line 1:
-Kate's Group
+=== Project Leader ===

Kate

=== Group Members ===

Aly, Jenn, Diane, Ekin

=== Project Description ===

Associated notebook file [[attachment: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! [[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 [[attachment:Tate.sws]]

=== Singular Cubics ===

[[http://trac.sagemath.org/sage_trac/ticket/11823 | 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.

  [[attachment: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