#5976: [with patch; needs work] Add an Elliptic Curve Isogeny object
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Reporter: shumow | Owner: shumow
Type: enhancement | Status: assigned
Priority: major | Milestone: sage-4.0
Component: number theory | Keywords: Elliptic Curves
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Comment(by shumow):
Replying to [comment:6 mabshoff]:
> All the private functions with leading double underscore aren't
doctested, so this is "needs work". Dan never intended to put this up for
review so quickly, but I guess once the coverage is at 100% it ought to go
in since John is happy.
>
Yup, mabshoff is one hundred percent correct. I just got done w/ the velu
/ kohel algorithms and figured I'd get thoughts from the real sage number
theory devs on how I was doing.
So far this feed back has been great, thanks everyone!
Replying to [comment:7 cremona]:
> When this is fixed it would be nice to make it easier to construct this
multiplication as an isgeny from E to itself (and not just from E to an
isomorphic curve). Which would suggest making the isogeny code work
alongside the weierstrass map code (since weierstrass isomorphisms
[u,r,s,t] are nothing other than isogenies of degree 1), for example by
allowing the construction of an isogeny from a urst and vice versa for
isogenies of degree 1.
Yes, I totally see what you are saying. And this is a point of
clarification that I need on some of the math here: All the algorithms
that I have been looking at for isogenies are for computing "normalized"
isogenies. It is my partial (possibly incorrect) understanding that the
multiplication by "m" map is not a normalized isogeny, and as such, these
algorithms don't work.
I was in fact planning on trying to rectify this when I figured out how to
do the correct inheritance.
Replying to [comment:8 AlexGhitza]:
> Replying to [comment:2 shumow]:
> I would think that SchemeMorphism or one of its descendants in
schemes/generic/morphism.py would be a natural choice. I'm working on
fixing a number of things in that file, so it might not be a good idea to
make your isogeny object inherit from it just yet. I'll try to be done
soon, though.
Cool, do you have an ETA on that?
Replying to [comment:4 cremona]:
> My reviewer's patch just does the following:
>
> 1. Corrects spelling of "separable" throughout
Ugh, embarrassing. I never was very good at spelling. It's why I liked
maths more in school...
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/5976#comment:9>
Sage <http://sagemath.org/>
Sage - Open Source Mathematical Software: Building the Car Instead of
Reinventing the Wheel
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