#11095: Add BMSS algorithm for isogenies of elliptic curves
-------------------------------+--------------------------------------------
Reporter: defeo | Owner: cremona
Type: enhancement | Status: needs_work
Priority: minor | Milestone: sage-4.7.1
Component: elliptic curves | Keywords: isogenies
Work_issues: | Upstream: N/A
Reviewer: John Cremona | Author: Luca De Feo
Merged: | Dependencies:
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Changes (by mstreng):
* status: needs_review => needs_work
Comment:
1. I'm confused by the {{{ValueErrors}}} raised by {{{isogeny_kernel}}}.
{{{
ValueError, "The two curves are not linked by a normalized isogeny of
degree %s"%ell
}}}
First of all, the comment "or a non-sense polynomial if no such isogeny
exists" (line 110) is inconsistent with the documentation of
{{{isogeny_BMSS}}}. Which of the two is correct?
Second, the test "{{{ker_poly.degree() != ell-1}}}" (line 113) implicitly
assumes that there is only one possible degree for a normalized isogeny.
It would help future developers to have a comment explaining that this is
always the case (it is, isn't it?)
Third, why is the test "{{{not check}}}" there in the Stark case (line
100)? Could {{{isogeny_Stark}}} return non-sense polynomials just like you
say {{{isogeny_BMSS}}} does? Does a non-sense polynomial always imply that
no normalized isogeny exist?
2. The word "separable" seems to be missing from the {{{ValueErrors}}}
3. I noticed that (with the default options) the function
{{{isogeny_kernel}}} will first test if algorithm equals "Stark", "stark",
"Starks", or "starks", before detecting that it actually equals "BMSS". It
may speed things up by epsilon to put the most-used case first. (this is
not the reason for "needs work")
ps. The patch bot seems to have understood that you only want the second
patch.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/11095#comment:13>
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