Abstract
We give fast algorithms for computing product and inverse in a multiple algebraic extension of the rational numbers. The algorithms are almost linear in terms of the output length, i.e. they work 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 algorithms are close to optimal. The algorithm for inverse uses a technique referred to as dynamic evaluation for computing in algebraic extensions defined by reducible polynomials.
Supported by ESPRIT BRA 3012 CompuLog and Fakultetsnämnden KTH. Formerly with: The Royal Institute of Technology, 100 44 Stockholm, Sweden.
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Langemyr, L. (1991). Algorithms for a Multiple Algebraic Extension. In: Mora, T., Traverso, C. (eds) Effective Methods in Algebraic Geometry. Progress in Mathematics, vol 94. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0441-1_16
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DOI: https://doi.org/10.1007/978-1-4612-0441-1_16
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