#11474: Elliptic curves should be unique parent structures
-----------------------------------+--------------------------
Reporter: SimonKing | Owner: cremona
Type: defect | Status: needs_info
Priority: major | Milestone: sage-6.2
Component: elliptic curves | Resolution:
Keywords: unique parent | Merged in:
Authors: Simon King | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
Dependencies: | Stopgaps:
-----------------------------------+--------------------------
Comment (by cremona):
I agree with Peter here (we have been discussing these issues in our
common room in Warwick).
I particularly want to emphasize that what you have in mind is quite a
large project, which needs to be done step by step, with plenty of input
from other experienced Sage users who will be greatly affected by such
changes (e.g. me!). Also, be careful that the improved design will not be
accompanied by a decrease in efficiency.
Some of what is being proposed here would have been done a lot earlier,
but Sage's support for f.g. abelian groups was not good enough in the
early days. As soon as it became good enough it was applied to the
simplest of these cases, namely the group of points of an e.c. over a
finite field.
We want to keep separate the abstract abelian group from the concrete
realization of it as a set of points, so that we can use generaic abelian
group functionality to (for example) compute kernels. And as well as the
easy map from the abstract group to the concrete point set (using known
generators) we must also provide the harder map in the reverse direction,
which is a form of elliptic logarithm. This is actually easier in the
number field case since we can use canonical heights to express a point as
a linear combination of the generators.
--
Ticket URL: <http://trac.sagemath.org/ticket/11474#comment:17>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
--
You received this message because you are subscribed to the Google Groups
"sage-trac" group.
To unsubscribe from this group and stop receiving emails from it, send an email
to [email protected].
To post to this group, send email to [email protected].
Visit this group at http://groups.google.com/group/sage-trac.
For more options, visit https://groups.google.com/d/optout.
