#6193: [with patch, needs review] implement elliptic logarithm
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Reporter: robertwb | Owner: was
Type: defect | Status: new
Priority: major | Milestone: sage-4.0.1
Component: number theory | Keywords:
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Comment(by robertwb):
Replying to [comment:3 cremona]:
> Replying to [comment:2 robertwb]:
> > The code looks good after my first reading.
> >
> > * I assume by {{{on_egg}}} you're implying the non-identity component
of an elliptic curve over R?
>
> That is right. Some people call this (the compact component in
{{{R^2}}}) the "egg". Perhaps a comment should be included to explain
this, but the name has the advantage of being short.
I think it's fine, the terminology is very evocative of what it is :)
> > * Where does the terminology {{{ei}}} come from for the x-coordinates
of the 2-torsion? (I may just not be familiar with the notation, if so,
just let me know.)
>
> I thought it was standard to call the real roots e1, e2, e3 (i.e. these
are the x-coords of the points of order 2). Less standard is the ordering
(for curves over R): when they are all real then either e1<e2<e3 or the
other way round; and when only one is real, it is e1 for some people and
e3 for others. Hence I do make this explicit.
Oh, of course. I wasn't thinking of the i as an index, now ei makes total
sense with the e1, e2, and e3 conventions.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/6193#comment:4>
Sage <http://sagemath.org/>
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