Journal of Symbolic Computation - Special issue: validated numerical methods and computer algebra
The Parallel Evaluation of General Arithmetic Expressions
Journal of the ACM (JACM)
CCA '00 Selected Papers from the 4th International Workshop on Computability and Complexity in Analysis
Some observations on familiar numbers
Proceedings of the 2002 international symposium on Symbolic and algebraic computation
Counterexamples to the uniformity conjecture
Computational Geometry: Theory and Applications - Special issue on robust geometric algorithms and their implementations
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A polynomial term is a tree with operators *,+,- on the interior nodes and natural numbers and variables on the frontier.We attempt to decide whether or not such a tree represents the zero polynomial by substituting algebraically independent real numbers for the variables and attempting to decide whether or not the resulting constant is zero.From this we get a probabilistic zero recognition test which is somewhat more expensive computationally than the usual method of choosing random integers in a large interval and evaluating, but which depends on the ability to choose a random point in the unit cube and to approximate a polynomial at that point.We also state a conjecture about algebraic independence measure which would give us a deterministic test with a uniformly chosen test point. The result is that if a polynomial term has s(T) nodes, then the bit complexity of deterministic zero recognition is bounded by O(s(T)M(s(T) length(T))), where length(T) measures the length of the term T, and M(n) is the bit complexity of multiplication of two n-digit natural numbers.