### Abstract

Original language | English |
---|---|

Pages (from-to) | 58-64 |

Number of pages | 7 |

Journal | Computational Geometry-Theory and Applications |

Volume | 33 |

Issue number | 1-2 |

DOIs | |

Publication status | Published - 2006 |

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### Cite this

*Computational Geometry-Theory and Applications*,

*33*(1-2), 58-64. https://doi.org/10.1016/j.comgeo.2004.02.005

**Counterexamples to the uniformity conjecture.** / Richardson, Daniel; Elsonbaty, Ahmed.

Research output: Contribution to journal › Article

*Computational Geometry-Theory and Applications*, vol. 33, no. 1-2, pp. 58-64. https://doi.org/10.1016/j.comgeo.2004.02.005

}

TY - JOUR

T1 - Counterexamples to the uniformity conjecture

AU - Richardson, Daniel

AU - Elsonbaty, Ahmed

N1 - ID number: ISI:000233471000004

PY - 2006

Y1 - 2006

N2 - The Exact Geometric Computing approach requires a zero test for numbers which are built Lip using standard operations starting with the natural numbers. The uniformity conjecture, pan of ail attempt to solve this problem, Postulates a simple linear relationship between the syntactic length of expressions built up from the natural numbers using field operations, radicals and exponentials and logarithms. and the smallness of non zero complex numbers defined by such expressions. It is shown in this article that this conjecture is incorrect, and a technique is given for generating counterexamples. The technique may be useful to check other conjectured constructive root bounds of this kind. A revised form of the uniformity conjecture is proposed which avoids all the known counterexamples. (c) 2005 Elsevier B.V. All rights reserved.

AB - The Exact Geometric Computing approach requires a zero test for numbers which are built Lip using standard operations starting with the natural numbers. The uniformity conjecture, pan of ail attempt to solve this problem, Postulates a simple linear relationship between the syntactic length of expressions built up from the natural numbers using field operations, radicals and exponentials and logarithms. and the smallness of non zero complex numbers defined by such expressions. It is shown in this article that this conjecture is incorrect, and a technique is given for generating counterexamples. The technique may be useful to check other conjectured constructive root bounds of this kind. A revised form of the uniformity conjecture is proposed which avoids all the known counterexamples. (c) 2005 Elsevier B.V. All rights reserved.

UR - http://dx.doi.org/10.1016/j.comgeo.2004.02.005

U2 - 10.1016/j.comgeo.2004.02.005

DO - 10.1016/j.comgeo.2004.02.005

M3 - Article

VL - 33

SP - 58

EP - 64

JO - Computational Geometry-Theory and Applications

JF - Computational Geometry-Theory and Applications

SN - 0925-7721

IS - 1-2

ER -