Title | **On the probability distribution of singular varieties of given corank** |

Author(s) | Carlos Beltrán, Luis Miguel Pardo |

Type | Article in Journal |

Abstract | We exhibit sharp upper bounds for the probability distribution of the distance from a system of multivariate polynomial equations to the strata of all systems having a critical zero of given corank. We also prove sharp upper bounds for the probability distribution of the condition number of singular systems of multivariate polynomial equations. We finally state a new and sharp technique of the Geometry of Numbers. Using this technique we show that rational systems of multivariate polynomial equations are equidistributed with respect to singular systems having a critical zero of given corank. |

Keywords | Polynomial equation solving, Condition number, Discrepancy bounds |

ISSN | 0747-7171 |

URL |
http://www.sciencedirect.com/science/article/pii/S0747717106000629 |

Language | English |

Journal | Journal of Symbolic Computation |

Volume | 42 |

Number | 1–2 |

Pages | 4 - 29 |

Year | 2007 |

Note | Effective Methods in Algebraic Geometry (MEGA 2005) |

Edition | 0 |

Translation |
No |

Refereed |
No |