The Computation of Polynomial Greatest Common Divisors Over an Algebraic Number Field

Abstract We present a modular algorithm for computing the greatest common divisor of two polynomials over an algebraic number field. Our algorithm is an application of ideas of Brown and Collins. We use the Weinberger-Rothschild homomorphic scheme with the important change that we avoid factoring the modular image of the minimal polynomial. We perform a computing time analysis and report some empirical computing times.

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