Computing sums of radicals in polynomial time
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
Simplification of nested radicals
SIAM Journal on Computing
Journal of Algorithms
Reducing randomness via irrational numbers
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
A strong and easily computable separation bound for arithmetic expressions involving square roots
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
Fast Multiple-Precision Evaluation of Elementary Functions
Journal of the ACM (JACM)
How to Compute the Voronoi Diagram of Line Segments: Theoretical and Experimental Results
ESA '94 Proceedings of the Second Annual European Symposium on Algorithms
Denesting by Bounded Degree Radicals
ESA '97 Proceedings of the 5th Annual European Symposium on Algorithms
Robust Proximity Queries in Implicit Voronoi Diagrams
Robust Proximity Queries in Implicit Voronoi Diagrams
Simplifying nested radicals and solving polynomials by radicals in minimum depth
SFCS '90 Proceedings of the 31st Annual Symposium on Foundations of Computer Science
How to denest Ramanujan's nested radicals
SFCS '92 Proceedings of the 33rd Annual Symposium on Foundations of Computer Science
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Given an expression E using +,-, *,/, with operands from Z and from the set of real roots of integers, we describe a probabilistic algorithm that decides whether E = 0. The algorithms has a one-sided error. If E = 0, then the algorithm will give the correct answer. If E ≠ 0, then the error probability can be made arbitrarily small. The algorithm has been implemented and is expected to be practical.