#13615: Extend elliptic curve isogenies to arbitrary prime degrees
-------------------------------------+-------------------------------------
Reporter: cremona | Owner: John Cremona
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-5.12
Component: elliptic curves | Resolution:
Keywords: isogenies, sd51 | Merged in:
Authors: Kimi Tsukazaki, | Reviewers: John Cremona, Jenny
John Cremona | Cooley, Samuele Anni, Luca De Feo
Report Upstream: N/A | Work issues:
Branch: u/defeo/trac13615 | Commit:
Dependencies: | Stopgaps:
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Changes (by defeo):
* reviewer: John Cremona, Jenny Cooley, Samuele Anni => John Cremona,
Jenny Cooley, Samuele Anni, Luca De Feo
* branch: => u/defeo/trac13615
Old description:
> As of Sage 5.4, we can compute l-isogenies of elliptic curves only for
> l=2,3,5,7,13 (the ones for which X_0(l) has genus 0), together with some
> "sporadic" degrees which can occur over QQ.
>
> In this ticket we will add extra functionality to be able to compute
> l-isogenies for arbitrary prime degrees.
>
> Apply: ell_curve_isogeny_split.patch, isogeny_genus_0.patch,
> trac_13615_review.patch
New description:
As of Sage 5.4, we can compute l-isogenies of elliptic curves only for
l=2,3,5,7,13 (the ones for which X_0(l) has genus 0), together with some
"sporadic" degrees which can occur over QQ.
In this ticket we will add extra functionality to be able to compute
l-isogenies for arbitrary prime degrees.
--
Comment:
Thanks for the link, and congratulations to Kimi. I quickly read it
through. I obviously didn't check line by line, but no doubt that you got
the maths and the coding right. So, I'm ready to give a positive review.
> I agree that the filename is not wonderful, but we did want to split
off the general isogeny code now in ell_curve_isogeny from the special
cases. Perhaps you are right that the "general" one belongs in the other
file.
I agree, it is best to keep specific algorithms separate from the isogeny
class. On second thought, all the algorithms in that file have something
in common: they are generic algorithms only practical for small prime
degrees (as you suggest in the title of the doc page). Maybe it's just the
filename that needs to be changed. What about `isogenies_small_degree.py`?
> {{{least_semi_primitive}}} is indeed internal. If I thught there would
be other applications I might have suggested putting it with primitive
roots and similar functions.
I had the same feeling about the variable `isog_table` and the function
`hyperelliptic_isogeny_data`. Hence, I renamed all the three by adding an
underscore in front of them.
I also
- Edited the copyright banner by adding your names
- Fixed the docstring of `_least_semi_primitive()`
- Added `ALGORITHM::` sections to some functions, pointing to the relevant
chapter in Kimi's thesis.
I'm attaching my reviewer's patch. I'm working with the git repo, and I'm
confused by this directory renaming stuff, so I guess it'll be easier if I
link to my git branch on trac.
I'm not giving a positive review right away, so that you can review my
patch, and give your opinion on renaming the file. Enjoy vacation!
--
Ticket URL: <http://trac.sagemath.org/ticket/13615#comment:12>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
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