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On fast multiplication of polynomials over arbitrary algebras

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References

  1. Aho, A., Hopcroft, J., Ullman, J.: The design and analysis of computer algorithms. Reading, MA: Addison-Wesley 1974

    Google Scholar 

  2. Apostol, T.M.: Resultants of cyclotomic polynomials. Proc. Am. Math. Soc.24, 457–462 (1970)

    Google Scholar 

  3. Cantor, D.G.: On arithmetical algorithms over finite fields. J. Combinat. Theory A50, 285–300 (1989)

    Google Scholar 

  4. Chudnovsky, D.V., Chudnovsky, G.V.: Algebraic complexities and algebraic curves over finite fields. J. Complexity4, 285–316 (1988)

    Google Scholar 

  5. Grigoriev, D.Yu.: Multiplicative complexity of a pair of bilinear forms and of the polynomial multiplication. Proc. 7th MFCS. (Lect. Notes Comput. Sci., vol. 64, pp. 250–256) Berlin, Heidelberg, New York: Springer 1978

    Google Scholar 

  6. Kaltofen, E.: Greatest common divisors of polynomials given by straight-line programs. J. ACM35, 231–264 (1988)

    Google Scholar 

  7. Kaminski, M.: An algorithm for polynomial multiplication that does not depend on the ring of constants. J. Algorithms9, 137–147 (1988)

    Google Scholar 

  8. Knuth, D.E.: The art of computer programming, vol. 2. 2nd edn. Reading, MA: Addison-Wesley 1981

    Google Scholar 

  9. Lang, S.: Algebraic number theory. Reading, MA: Addison-Wesley 1970

    Google Scholar 

  10. Lempel, A., Seroussi, G., Winograd, S.: On the complexity of multiplication in finite fields. Theoret. Comput. Sci.22, 285–296 (1983)

    Google Scholar 

  11. Nussbaumer, H.J.: Fast polynomial transform algorithms for digital convolutions. IEEE Trans. ASSP28, 205–215 (1980)

    Google Scholar 

  12. Schönhage, A.: Schnelle Multiplikation von Polynomen über Körpern der Charakteristik 2. Acta Inf.7, 395–398 (1977)

    Google Scholar 

  13. Schönhage, A., Strassen, V.: Schnelle Multiplikation großer Zahlen. Computing7, 281–292 (1971)

    Google Scholar 

  14. Winograd, S.: Arithmetic complexity of computations. CBMS-NSF Regional Conference Series in Applied Math. 33. Philadelphia, PA: SIAM 1980

    Google Scholar 

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The authors would like to acknowledge the partial support of NSA Grant MDA-904-II-2031 and NSF Grant Nr. CCR-87-05363

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Cantor, D.G., Kaltofen, E. On fast multiplication of polynomials over arbitrary algebras. Acta Informatica 28, 693–701 (1991). https://doi.org/10.1007/BF01178683

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