#7575: EllipticCurve.gens: height bounds not handled well in two_descent
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Reporter: rlm | Owner: cremona
Type: defect | Status: needs_info
Priority: major | Milestone: sage-4.3.1
Component: elliptic curves | Keywords:
Work_issues: | Author:
Upstream: N/A | Reviewer:
Merged: |
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Comment(by cremona):
In the original example (in this ticket's description), note that calling
E.two_descent() produces output to the screen but returns nothing and
stores nothing in E which was not there before. E.gens() by default uses
mwrank_shell, which does not allow any passing of parameters (see the TODO
block in the docstring), not because it cannot be done but because we have
not implemented it. The non-default option mwrank_lib goes via creation
of the associated mwrank_curve which also does not allow changing of the
parameters.
What I suggest is that we use mwrank_lib by default; that we allow
passing of all the parameters which the two_descent function of an mwrank
elliptic curve allows from all higher level functions which call mwrank
(e.g. gens()) and that we use the enquiry functions provided by mwrank to
find out how successful it has been: it can give you a lower and upper
bound for the rank, so all is well if they are equal and in any case can
give you a number of gens equal to the lower bound. The only difficulty
would be with caching rank and gens -- probably best not to do so at all
unless we have certainly found them.
Does this all make sense? I think it would be much more helpful to have
sample curves where things do not work well and sample code which does not
go via a call to the (presumably complicated) function prove_BSD()!
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/7575#comment:2>
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