#12880: Inconsistent domain, codomain and parent in EllipticCurveIsogeny
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Reporter: nthiery | Owner: cremona
Type: defect | Status: needs_work
Priority: minor | Milestone: sage-6.2
Component: elliptic curves | Resolution:
Keywords: | Merged in:
Authors: Sébastien Besnier | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
u/sbesnier/ticket/12880 | b486f244b98a16b144cd45399eee3112ed5f824b
Dependencies: #11474 | Stopgaps:
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Comment (by defeo):
> This looks good to me overall. The main thing I am wondering about is
if it wouldn't make sense to keep the current version of `_composition_`
(raise a `NotImplementedError`) until we have real composition of
isogenies. What I mean is that with your change, we just get a "formal"
composition of two isogenies. Although this may be good enough for some
applications, what we really want is to compute the actual polynomials
defining the composed isogeny. From that perspective I wouldn't say that
removing the method "makes composition work".
I'd rather say the opposite. There are applications where formal
composition is the desired result.
Formal composition is essentially free, while "flesh-and-blood"
composition may be expensive (exponential in the length of the chain).
There are cryptosystems that exploit this fact, Sage should make it easy
to implement them in a few lines of code.
I'm more in favour of using formal composition by default, and having a
method (`.normalize()`, maybe?) to compute the "flesh-and-blood" version.
Subsidiary question : what should equality do in this case?
> I think we should open a separate ticket for composition, since we are
obviously not going to do all of #7368 at the same time.
Agreed. It would be a better place to continue this discussion.
--
Ticket URL: <http://trac.sagemath.org/ticket/12880#comment:21>
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