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Comment: implemented all the new functions for singular cubics from Kate's wishlist
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=== Project Leader === |
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Kate === Group Members === Aly, Jenn, Diane, Ekin === Project Description === * [[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 * 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 === [[http://trac.sagemath.org/sage_trac/ticket/11823 | 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()? * 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): [[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 |
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
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
* 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):
- 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