Title | **Affine solution sets of sparse polynomial systems** |

Author(s) | María Isabel Herrero, Gabriela Jeronimo, Juan Sabia |

Type | Article in Journal |

Abstract | This paper focuses on the equidimensional decomposition of affine varieties defined by sparse polynomial systems. For generic systems with fixed supports, we give combinatorial conditions for the existence of positive dimensional components which characterize the equidimensional decomposition of the associated affine variety. This result is applied to design an equidimensional decomposition algorithm for generic sparse systems. For arbitrary sparse systems of n polynomials in n variables with fixed supports, we obtain an upper bound for the degree of the affine variety defined and we present an algorithm which computes finite sets of points representing its equidimensional components. |

Keywords | Sparse polynomial systems, Equidimensional decomposition of algebraic varieties, Degree of affine varieties, Algorithms and complexity |

ISSN | 0747-7171 |

URL |
http://www.sciencedirect.com/science/article/pii/S0747717112001149 |

Language | English |

Journal | Journal of Symbolic Computation |

Volume | 51 |

Number | 0 |

Pages | 34 - 54 |

Year | 2013 |

Note | Effective Methods in Algebraic Geometry |

Edition | 0 |

Translation |
No |

Refereed |
No |