#6583: Implement two descent over QQ natively in Sage using ratpoints
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Reporter: rlm | Owner: rlm
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-4.2.1
Component: elliptic curves | Keywords:
Work_issues: | Author: Robert Miller
Reviewer: | Merged:
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Comment(by wuthrich):
Ok. I tested the patches and they all go through. Also the -coverage gives
6 out of 6 despite the fact that many functions in descent_two_isogeny.pyx
lack a good documentation and especially examples are missing often. I
guess this is because cdefs are not tested. (I admit I never reviewed a
cython file.)
Currently the main function gives back four integers, like mwrank does.
They are useful to compute an upper bound on the rank of the Mordell-Weil
group and should (in the future) be called from {{{rank()}}} and also from
{{{sha()}}}.
Personnally I would like more, namely I would like to have a phi-Selmer
group. Ideally we should give back a abelian group associated to the
elliptic curve, or even better to the isogeny. But isogenies are not there
yet, though 2-isogenies should be. The Selmer groups would contain more
information than just these four integers and I believe this extra-
information is already computed in this algorithm.
Right now the functions are not callable without an extra import and so
they do not pollute the name-space and we are still flexible in how to do
this later; like {{{.selmer_group()}}} etc. That is very good. Yet it does
not really look like a finished patch.
It is work in progress (and it is very good work in the right direction),
but I am incapable of saying whether this sort of work should already be
included in sage or not. So before giving a positive review to this patch,
I would like to ask the author's and other's opinion on this. Maybe I
could also ask for more examples, especially in the header of the file,
despite the fact that it is not included in the documentation right now.
Chris.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/6583#comment:9>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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