Abstract
We give a probabilistic algorithm for computing the greatest common divisor (GCD) of two polynomials over an algebraic number field. We can compute the GCD using O(llog5(l)) expected binary operations where l is the size of the GCD given by standard estimations. Since we require time Ω(l) just to write down the GCD, the algorithm is close to optimal.
Supported by STU, ESPRIT BRA 3012 CompuLog and Fakultetsnämnden KTH. Present address: Numerical Analysis and Computing Science, The Royal Institute of Technology, S-100 44 Stockholm, Sweden. The material was improved and extracted from the author's PhD thesis
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© 1991 Springer-Verlag Berlin Heidelberg
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Langemyr, L. (1991). An asymptotically fast probabilistic algorithm for computing polynomial GCD's over an algebraic number field. In: Sakata, S. (eds) Applied Algebra, Algebraic Algorithms and Error-Correcting Codes. AAECC 1990. Lecture Notes in Computer Science, vol 508. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-54195-0_53
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DOI: https://doi.org/10.1007/3-540-54195-0_53
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