[1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science (1991)

San Juan, Puerto Rico

Oct. 1, 1991 to Oct. 4, 1991

ISBN: 0-8186-2445-0

pp: 670-677

J. Blomer , Inst. fuer Inf., Fachbereich Math., Freie Univ., Berlin, Germany

ABSTRACT

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 ).

INDEX TERMS

positive rational integer, polynomial time algorithm, decidability, probabilistic checking, sums of radicals, Monte Carlo algorithm, coefficient representation, subalgorithm, real algebraic number field

CITATION

J. Blomer, "Computing sums of radicals in polynomial time,"

*[1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science(FOCS)*, San Juan, Puerto Rico, 1991, pp. 670-677.

doi:10.1109/SFCS.1991.185434

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