#8829: Saturation for MW-groups of elliptic curves over number fields.
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Reporter: robertwb | Owner: cremona
Type: enhancement | Status: needs_work
Priority: major | Milestone: sage-6.4
Component: elliptic curves | Resolution:
Keywords: saturation | Merged in:
Authors: Robert Bradshaw, | Reviewers:
John Cremona | Work issues:
Report Upstream: N/A | Commit:
Branch: u/cremona/8829 | 8686677fa5cdf4359fd6f6b8d8e25925f6893a4c
Dependencies: #8828 | Stopgaps:
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Comment (by cremona):
The latest branch I just pushed has some merges in it which were not
intended but I hope that will not cause any problems -- as well as merging
6.9.beta6 I also merged by branch 'isogs' which has been merged into
beta7.
One bug fix addresses the previous comment -- after re-reading my own 2006
paper I found that the original implementer from #8828 had missed one
point (when mu is halved one must increment n_max in order to guarantee
termination). A small additional improvement in the same place (the
method min_gr() in height.py) now gives a small improvement in the bound,
which is why one doctest there has been changed.
The second bug was to do with mutability of lists giving unwanted side
effects, and is commented at the point in the source which has changed.
It is likely that users who call the saturation() method will also want to
lll_reduce() the output but I have not made that automatic.
I will set this to needs_review once my own full test has completed.
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Ticket URL: <http://trac.sagemath.org/ticket/8829#comment:34>
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