#727: find rational points on plane conic curves [with patch, needs work]
--------------------------------------------+-------------------------------
Reporter: was | Owner: mstreng
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-4.5.2
Component: geometry | Keywords: rational point
points conic quadratic form
Author: Nick Alexander, Marco Streng | Upstream: N/A
Reviewer: | Merged:
Work_issues: |
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Description changed by mstreng:
Old description:
> Implement a Conic class that is able to find rational points on plane
> conic curves over QQ, finite fields, RR, CC, and number fields.
>
> {{{
> John Cremona <[email protected]> hide details 1:37 am
> (2 minutes ago)
> reply-to [email protected]
> to [email protected]
> date Sep 21, 2007 1:37 AM
> subject [sage-support] Re: rational solutions to a
> bivariate polynomial
> mailed-by googlegroups.com
>
> It *is* a ternary quadratic form once you homogenize with a 3rd variable
> z.
>
> Finding rational points on plane conics (which is what this is) has
> advanced substantially in the last few years. My paper with Rusin
> (Mathematics of Computation, 72 (2003), no. 243, pages 1417-1441.)
> works well for diaginal ones and is behind Magma's first
> implementations for RationalPoint(Conic()); a different method by
> Denis Simon is better for non-diagonal ones and is (I believe) what
> Magma uses.
>
> My method is implemented in the C++ code which is already in Sage in
> the mwrank package, so all tat would be needed would be to write the
> appropriate wrappers!
>
> }}}
New description:
Implement a Conic class that is able to
* find rational points on plane conic curves over QQ, finite fields, RR,
CC, and number fields.
* given a conic with a point over a field, compute a parametrization.
{{{
John Cremona <[email protected]> hide details 1:37 am
(2 minutes ago)
reply-to [email protected]
to [email protected]
date Sep 21, 2007 1:37 AM
subject [sage-support] Re: rational solutions to a
bivariate polynomial
mailed-by googlegroups.com
It *is* a ternary quadratic form once you homogenize with a 3rd variable
z.
Finding rational points on plane conics (which is what this is) has
advanced substantially in the last few years. My paper with Rusin
(Mathematics of Computation, 72 (2003), no. 243, pages 1417-1441.)
works well for diaginal ones and is behind Magma's first
implementations for RationalPoint(Conic()); a different method by
Denis Simon is better for non-diagonal ones and is (I believe) what
Magma uses.
My method is implemented in the C++ code which is already in Sage in
the mwrank package, so all tat would be needed would be to write the
appropriate wrappers!
}}}
--
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/727#comment:13>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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