Changes between Version 13 and Version 18 of Ticket #727


Ignore:
Timestamp:
Dec 8, 2010, 5:34:03 PM (12 years ago)
Author:
Marco Streng
Comment:

Here's a version that uses hilbert symbols and rnfisnorm from resp. #9334 and #2329. This patch provides motivation and testcases for those two other tickets.

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  • Ticket #727

    • Property Status changed from needs_review to needs_work
    • Property Work issues changed from to needs serious retesting after #9334 and #2329
    • Property Summary changed from find rational points on plane conic curves [with patch, needs work] to find rational points on plane conic curves
  • Ticket #727 – Description

    v13 v18  
    44
    55 * given a conic with a point over a field, compute a parametrization.
    6 
    7 {{{
    8 John Cremona <john.cremona@gmail.com>            hide details    1:37 am (2 minutes ago)
    9         reply-to                sage-support@googlegroups.com   
    10         to              sage-support@googlegroups.com   
    11         date            Sep 21, 2007 1:37 AM     
    12         subject         [sage-support] Re: rational solutions to a bivariate polynomial 
    13         mailed-by               googlegroups.com         
    14 
    15 It *is* a ternary quadratic form once you homogenize with a 3rd variable z.
    16 
    17 Finding rational points on plane conics (which is what this is) has
    18 advanced substantially in the last few years.  My paper with Rusin
    19 (Mathematics of Computation, 72 (2003), no. 243, pages 1417-1441.)
    20 works well for diaginal ones and is behind Magma's first
    21 implementations for RationalPoint(Conic());  a different method by
    22 Denis Simon is better for non-diagonal ones and is (I believe) what
    23 Magma uses.
    24 
    25 My method is implemented in the C++ code which is already in Sage in
    26 the mwrank package, so all tat would be needed would be to write the
    27 appropriate wrappers!
    28 
    29 }}}