#8451: improve galois representation for elliptic curves
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Reporter: wuthrich | Owner: cremona
Type: defect | Status: needs_review
Priority: major | Milestone: sage-4.5.3
Component: elliptic curves | Keywords: elliptic curves, galois
representation, is_surjective
Author: Chris Wuthrich | Upstream: N/A
Reviewer: | Merged:
Work_issues: |
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Changes (by wuthrich):
* status: needs_work => needs_review
Comment:
Six months later I took the time to revise this patch completely. I have
rewritten the function image_type. It now never gives a probabilistic
answer, but only proven results. The package by Andrew Sutherland #8617
will add a much better probabilistic algorithm anyway.
One couls go on and implement things better so that a actually group is
returned, but I do not want to waste more time on this.
The above counter-examples now work. (I had programmed it quite badly).
See the doctest. Also I added more documentation in the source code.
There might still be bugs in it. It would be best though to put it in as
such and then once #8451 is in and has a good interface, we could run test
against it. That would be the best test.
By now it already improves a lot (and removes some bugs in is_surjective
that have implications to bsd stuff.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/8451#comment:13>
Sage <http://www.sagemath.org>
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