### Abstract

We display an existence of the short (polynomial size) proofs for nondivisibility of two sparse multivariate polynomials under the Extended Riemann Hyphothe-sis (ERH). The divisibility problem is closely related to the rational interpolation problem (whose complexity bounds were determined in [GKS 90] and [GK 91]). In this setting we assume that a rational function is given by a black box (see e.g. [KT 88, GKS 90, K 89]) for evaluating it. We prove also that, surprisingly, the problem of deciding whether a rational function given by a black box equals a polynomial belongs to the parallel class NC (see e.g. [KR 90]), provided we know the degree of some sparse representation of it.

Original language | English (US) |
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Title of host publication | Papers from the International Symposium on Symbolic and Algebraic Computation, ISSAC 1992 |

Editors | Paul S. Wang |

Publisher | Association for Computing Machinery |

Pages | 117-122 |

Number of pages | 6 |

ISBN (Electronic) | 0897914899 |

DOIs | |

State | Published - Aug 1 1992 |

Event | 1992 International Symposium on Symbolic and Algebraic Computation, ISSAC 1992 - Berkeley, United States Duration: Jul 27 1992 → Jul 29 1992 |

### Publication series

Name | Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC |
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Volume | Part F129620 |

### Other

Other | 1992 International Symposium on Symbolic and Algebraic Computation, ISSAC 1992 |
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Country | United States |

City | Berkeley |

Period | 7/27/92 → 7/29/92 |

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## Cite this

*Papers from the International Symposium on Symbolic and Algebraic Computation, ISSAC 1992*(pp. 117-122). (Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC; Vol. Part F129620). Association for Computing Machinery. https://doi.org/10.1145/143242.143287