Complexity and real computation
Complexity and real computation
Journal of Symbolic Computation - Special issue: validated numerical methods and computer algebra
A new constructive root bound for algebraic expressions
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
CCA '00 Selected Papers from the 4th International Workshop on Computability and Complexity in Analysis
Exact geometric computation: theory and applications
Exact geometric computation: theory and applications
Shortest path amidst disc obstacles is computable
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
Theory of Real Computation According to EGC
Reliable Implementation of Real Number Algorithms: Theory and Practice
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The Exact Geometric Computing approach requires a zero test for numbers which are built up using standard operations starting with the natural numbers. The uniformity conjecture, part of an 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.