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Algorithms for a multiple algebraic extension II

  • Lars Langemyr
Submitted Contributions
Part of the Lecture Notes in Computer Science book series (LNCS, volume 539)

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(d1+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.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Lars Langemyr
    • 1
  1. 1.Numerical Analysis and Computing ScienceRoyal Institute of TechnologyStockholmSweden

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