#3416: Weierstrass form for cubics
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Reporter: moretti | Owner: was
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-4.6
Component: number theory | Keywords: nagell, weierstrass, cubic,
elliptic curves, editor_wstein
Author: | Upstream: N/A
Reviewer: | Merged:
Work_issues: |
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Comment(by Niels):
Replying to [comment:13 cremona]:
> I'm not sure we really want my old lecture notes attached to this
ticket! There is nothing you are using there that is not in standard
other sources. But if they are there, they should be attributed ;)
The problem is that most of the standard other sources contain incorrect
formulas. These lecture notes are the first source I found with correct
formulas. The main reason for including them is that it may help people in
reviewing the patch. If anyone finds the same transformations in a
standard source, please let me know.
> Secondly, you absolutely cannot have print statements giving part of the
output as a side-effect. Better to return a tuple consisting of the
elliptic curve and the morphisms. This will break backwards
compatibility, since the Magma version does not so this (though he
underlying Magma function surely does), but it could be controlled by an
extra parameter which defaults to False.
Ok, I can change that. Is there nice a way to represent such a morphism in
Sage? I have difficulty expressing a transformation like the following as
a single morphism (just an example from the top of my head):
x -> x^2^ - y
y -> x^2^ + y
z -> z^2^
Then multiply with 6/(x^2^ z)
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/3416#comment:14>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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