Counterexamples to the uniformity conjecture

Daniel Richardson, Ahmed Elsonbaty

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

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.
Original languageEnglish
Pages (from-to)58-64
Number of pages7
JournalComputational Geometry-Theory and Applications
Volume33
Issue number1-2
DOIs
Publication statusPublished - 2006

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Syntactics
Uniformity
Counterexample
Natural number
Zero
Postulate
Complex number
Logarithm
Number field
Roots
Computing

Cite this

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

In: Computational Geometry-Theory and Applications, Vol. 33, No. 1-2, 2006, p. 58-64.

Research output: Contribution to journalArticle

Richardson, Daniel ; Elsonbaty, Ahmed. / Counterexamples to the uniformity conjecture. In: Computational Geometry-Theory and Applications. 2006 ; Vol. 33, No. 1-2. pp. 58-64.
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