Changes between Initial Version and Version 4 of Ticket #6881

Jul 20, 2010, 9:13:37 PM (12 years ago)
Marco Streng

I changed the description to better fit what is already in #727. Besides things that are already in #727, all that I removed from the original description were the following two requests.

  1. Use John Cremona's algorithms for finding points on conics over QQ.

It seems that Simon's algorithms (in #727) are better, but that doesn't have to stop us from giving Cremona's code as an option. It is inside mwrank, which is part of Sage. If someone wants to do it, then it can be made into a separate ticket.

  1. Getting primes of bad reduction of conics.

This is as good as in #727: make a Conic C. Then do C.determinant().factor()


  • Ticket #6881

    • Property Cc Marco Streng added
    • Property Summary changed from Conics to Solving conics over polynomial rings.
    • Property Component changed from algebra to algebraic geometry
    • Property Report Upstream changed from to N/A
  • Ticket #6881 – Description

    initial v4  
    1 We should have a class (or classes) for conic curves, and, more specially diagonal conics.  In particular, one of the methods should be John Cremona's algorithms for finding points on solvable conics, both over Q and over fraction fields of polynomial rings.  Other methods might include getting discriminants, primes of bad reduction, producing parametrized solutions, etc.
     1Implement the algorithm of John Cremona and Mark van Hoeij for finding conics over fraction fields of polynomial rings.
     3The article [] contains references to implementations in Maple (van Hoeij) and Magma (Cremona-Roberts). All one needs to do is ask the authors if it can be GPL'ed and to translate the code into sage.
     5#727 provides classes for conic curves that this code should build upon