#6616: [with patch] refactor heegner points code out of ell_rational_field and
support computing higher heegner points
---------------------------+------------------------------------------------
Reporter: robertwb | Owner: was
Type: enhancement | Status: new
Priority: major | Milestone: sage-4.1.2
Component: number theory | Keywords:
Reviewer: | Author:
Merged: |
---------------------------+------------------------------------------------
Description changed by was:
Old description:
> You can apply http://sage.math.washington.edu/home/wstein/tmp/heegner.hg
> or apply patches in this order:
> {{{
> 6616-higher-heegner.patch
> trac_6616-part2.patch
> trac_6616-part3.patch
> trac_6616-part4.patch
> trac_6616-part5.patch
> trac_6616-part6.patch
> trac_6616-part7.patch
> trac_6616-part8.patch
> trac_6616-part9.patch
> trac_6616-part10.patch
> ...
> }}}
>
> PLAN:
>
> 1. Refactor ell_rational_field, so the Heegner points code (nearly 1000
> lines!) is in a new file heegner.py.
>
> 2. Extend the heegner point code to compute y_lambda for lambda > 1.
>
> I'm doing 1 and 2 together, since 2 is a fairly small change, but to do
> it right and make it at all fast requires restructuring the code a lot,
> otherwise one ends up fighting a lot with badly structured code instead
> of focusing on optimizing algorithms.
>
> Also, this refactoring is a long time coming!
>
> (NOTE: Code after part 7 might end up depending on #6745, #6751.)
New description:
You can apply http://sage.math.washington.edu/home/wstein/pat/heegner.hg
or apply patches in this order:
{{{
6616-higher-heegner.patch
trac_6616-part2.patch
trac_6616-part3.patch
trac_6616-part4.patch
trac_6616-part5.patch
trac_6616-part6.patch
trac_6616-part7.patch
trac_6616-part8.patch
trac_6616-part9.patch
trac_6616-part10.patch
...
}}}
NOTE: Code after part 7 depends on #6745, #6751, so make sure you apply
those patches!
PLAN:
1. Refactor ell_rational_field, so the Heegner points code (nearly 1000
lines!) is in a new file heegner.py.
2. Extend the heegner point code to compute y_lambda for lambda > 1.
3. Implement first ever algorithm for provable verification of Kolyvagin's
conjecture for specific rank 2 curves.
I'm doing 1 and 2 together, since 2 is a fairly small change, but to do it
right and make it at all fast requires restructuring the code a lot,
otherwise one ends up fighting a lot with badly structured code instead of
focusing on optimizing algorithms.
Also, this refactoring is a long time coming!
--
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/6616#comment:11>
Sage <http://sagemath.org/>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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