Implementations of the LMT heuristic for minimum weight triangulation
Proceedings of the fourteenth annual symposium on Computational geometry
Optimally cutting a surface into a disk
Proceedings of the eighteenth annual symposium on Computational geometry
A Probabilistic Zero-Test for Expressions Involving Root of Rational Numbers
ESA '98 Proceedings of the 6th Annual European Symposium on Algorithms
Computer algebra handbook
Splitting (complicated) surfaces is hard
Proceedings of the twenty-second annual symposium on Computational geometry
Minimum-weight triangulation is NP-hard
Journal of the ACM (JACM)
Splitting (complicated) surfaces is hard
Computational Geometry: Theory and Applications
On the Sum of Square Roots of Polynomials and Related Problems
ACM Transactions on Computation Theory (TOCT)
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For a certain sum of radicals the author presents a Monte Carlo algorithm that runs in polynomial time to decide whether the sum is contained in some number field Q( alpha ), and, if so, its coefficient representation in Q( alpha ) is computed. As a special case the algorithm decides whether the sum is zero. The main algorithm is based on a subalgorithm which is of interest in its own right. This algorithm uses probabilistic methods to check for an element beta of an arbitrary (not necessarily) real algebraic number field Q( alpha ) and some positive rational integer r whether there exists an rth root of beta in Q( alpha ).