Abstract
We give a fast algorithm for computing the greatest common divisor of two univariate polynomials over a multiple algebraic extension of the rational numbers. The algorithm is almost linear in terms of the output length, i.e., it works in time O(d 1+δ, for all δ>0, where d is an a priori bound on the length of the output. Since we require time Ω(d) just to write down the output the algorithm is close to optimal. The algorithm uses a technique referred to as dynamic evaluation for computing in algebraic extensions defined by reducible polynomials.
Supported by Swedish National Board for Technical Development, ESPRIT BRA 3012 CompuLog and Fakultetsnämnden KTH. The work was initiated while the author was affiliated with Wilhelm-Schickard-Institut für Informatik, Universität Tübingen, Auf dem Sand 13, W-7400 Tübingen, Germany.
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Langemyr, L. (1991). Algorithms for a multiple algebraic extension II. In: Mattson, H.F., Mora, T., Rao, T.R.N. (eds) Applied Algebra, Algebraic Algorithms and Error-Correcting Codes. AAECC 1991. Lecture Notes in Computer Science, vol 539. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-54522-0_111
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DOI: https://doi.org/10.1007/3-540-54522-0_111
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