The computation of polynomial greatest common divisors over an algebraic number field
We present an algorithm for computing the greatest common divisor of two polynomials over an algebraic number field. We obtain a better computing time bound for this algorithm than for previously published algorithms solving the same problem. We have also performed empirical run time tests which have confirmed this. Our motivation for seeking the algorithm of the present paper stems from our interest in the cylindrical algebraic decomposition (cad) algorithm (Collins , Arnon et al. ). The cad algorithm makes essential use of algebraic polynomial gcd computations, which often dominate the cost of the algorithm.
Our algorithm is a generalization of the modular algorithm developed by Brown
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