#3416: Weierstrass form for cubics
----------------------------------------+-----------------------------------
Reporter: moretti | Owner: was
Type: enhancement | Status: needs_work
Priority: major | Milestone: sage-4.7.1
Component: elliptic curves | Keywords: nagell, weierstrass,
cubic, elliptic curves, editor_wstein
Work_issues: | Upstream: N/A
Reviewer: Marco Streng, Nils Bruin | Author: Niels Duif
Merged: | Dependencies:
----------------------------------------+-----------------------------------
Changes (by mstreng):
* reviewer: Marco Streng => Marco Streng, Nils Bruin
Comment:
Replying to [comment:31 nbruin]:
> If you are implementing your algorithm "bare bones" (internally, you
just work with polynomials and you don't use any of the scheme machinery
and your input consists of a homogeneous poly rather than a plane curve)
there could be some value of also making your output available "bare
bones", i.e., just return the list [a1,a2,a3,a4,a6] and a list of
polynomials describing the map.
>
> There is a cost to using schemes, ambient spaces etc., so there may be a
benefit in having the raw functionality available in a form that avoids
it. Once you have a routine that does the heavy lifting, it's
straightforward to write a wrapper that provides an interface in scheme
language.
I like this idea. So Niels's code could simply output three lists: the
[a1,a2,a3,a4,a6] and 2 lists of 3 polynomials each. Outputting instead of
printing should be an easy enough change.
And then a new member function of {{{ProjectiveCurve_generic}}} could call
it (or an analogous "{{{y^2}}}=quartic" function) and convert the output
to an {{{EllipticCurve...}}} and two {{{SchemeMorphism...}}} objects.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/3416#comment:32>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
--
You received this message because you are subscribed to the Google Groups
"sage-trac" group.
To post to this group, send email to [email protected].
To unsubscribe from this group, send email to
[email protected].
For more options, visit this group at
http://groups.google.com/group/sage-trac?hl=en.
