Title | **Some constructions for real algebraic curves** |

Author(s) | Elisabetta Fortuna, Patrizia M. Gianni, P. Parenti |

Type | Article in Journal |

Abstract | We address two basic questions for real algebraic curves. The first one is how to decide whether a real algebraic curve in the n -projective space contains some real point. We present an algorithm that reduces the original question to deciding whether the zero-set of a zero-dimensional ideal contains real points. The second part of the paper is devoted to giving necessary and sufficient conditions for the existence of a real line disjoint from a given real plane algebraic curve. An algorithm for testing whether these conditions are fulfilled is given. |

Keywords | Real algebraic curves, Algorithms, Gröbner bases, Multi-tangents |

ISSN | 0747-7171 |

URL |
http://www.sciencedirect.com/science/article/pii/S0747717105001021 |

Language | English |

Journal | Journal of Symbolic Computation |

Volume | 40 |

Number | 4–5 |

Pages | 1169 - 1179 |

Year | 2005 |

Note | Applications of Computer Algebra (ACA) 2001 and 2002 ACA Applications of Computer Algebra (ACA) 2001 and 2002 |

Edition | 0 |

Translation |
No |

Refereed |
No |