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 | | ~~}}}~~ |