#3416: Weierstrass form for cubics
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Reporter: moretti |
Owner: was
Type: enhancement |
Status: needs_work
Priority: major |
Milestone: sage-5.6
Component: elliptic curves |
Resolution:
Keywords: nagell, weierstrass, cubic, elliptic curves, editor_wstein |
Work issues:
Report Upstream: N/A |
Reviewers: John Cremona, Marco Streng, Nils Bruin
Authors: Niels Duif |
Merged in:
Dependencies: |
Stopgaps:
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Comment (by cremona):
Replying to [comment:38 novoselt]:
> And what is done by Maple in
>
http://www.maplesoft.com/support/help/Maple/view.aspx?path=algcurves/Weierstrassform
> ?
>
> It does return the maps in both directions without using any points.
I have no idea. The definition there is wrong: an elliptic curve is not
just a genus 1 curve, it is a genus one curve with a specified point.
Perhaps Maple tries to find a point (it does say that the function can be
speeded up by providing one), and perhaps if there is no rational point it
uses something generic, or a point defined over an extension. Without a
notion of field of definition, you could do anything. Note that Magma's
function does not require a point to be specified; if none is given it
tries to find one, uses it if it finds one and otherwise raises a run-time
error.
Someone with Maple could try the Selmer curve (of my previous post) to see
what it does.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/3416#comment:39>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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