#6386: [with patch, needs work] Implement elliptic exponential
---------------------------+------------------------------------------------
Reporter: cremona | Owner: was
Type: enhancement | Status: new
Priority: major | Milestone: sage-4.1
Component: number theory | Keywords: elliptic curve
Reviewer: | Author: John Cremona
Merged: |
---------------------------+------------------------------------------------
Comment(by cremona):
Replying to [comment:2 robertwb]:
> For the most part this looks good, and specifically I wasn't able to
find any precision issues.
>
> * I think the elliptic exponential should actually return a point on
E(C), not just a tuple (x,y)
OK, I'll do that. I literally had not tried that!
>
> * The docstring in elliptic exponential about to_Weierstrass is wrong.
(Maybe it could be to_curve, default True to give something on E(C), false
returning the raw {{{(wp(z), wp'(z))}}}.
I'll check that out.
>
> * The {{{antilogarithm}}} shouldn't simply discard the imaginary part:
>
> {{{
> sage: E = EllipticCurve('389a')
> sage: z0 = CC(1.76776906963, 0.303020775118)
> sage: E.elliptic_exponential(z0)
> (1.00012725137998 + 1.00002216580174*I,
> 0.000229106700941339 + 2.00010160734906*I)
> sage: E.antilogarithm(z0, 10)
> (1 : 0 : 1)
> }}}
My reasoning is that you only use this function when you have reason to
believe that the result is actually a rational point, so in particular it
is real. Can I just clarify the docstring? Note that this function is
never going to be able to give a provable result, at best it will retrun a
rational point whose elliptic log is close to the input value, but it is
still a useful thing to have.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/6386#comment:3>
Sage <http://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
-~----------~----~----~----~------~----~------~--~---
