References
Aho, A., Hopcroft, J., Ullman, J.: The design and analysis of computer algorithms. Reading, MA: Addison-Wesley 1974
Apostol, T.M.: Resultants of cyclotomic polynomials. Proc. Am. Math. Soc.24, 457–462 (1970)
Cantor, D.G.: On arithmetical algorithms over finite fields. J. Combinat. Theory A50, 285–300 (1989)
Chudnovsky, D.V., Chudnovsky, G.V.: Algebraic complexities and algebraic curves over finite fields. J. Complexity4, 285–316 (1988)
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
Kaltofen, E.: Greatest common divisors of polynomials given by straight-line programs. J. ACM35, 231–264 (1988)
Kaminski, M.: An algorithm for polynomial multiplication that does not depend on the ring of constants. J. Algorithms9, 137–147 (1988)
Knuth, D.E.: The art of computer programming, vol. 2. 2nd edn. Reading, MA: Addison-Wesley 1981
Lang, S.: Algebraic number theory. Reading, MA: Addison-Wesley 1970
Lempel, A., Seroussi, G., Winograd, S.: On the complexity of multiplication in finite fields. Theoret. Comput. Sci.22, 285–296 (1983)
Nussbaumer, H.J.: Fast polynomial transform algorithms for digital convolutions. IEEE Trans. ASSP28, 205–215 (1980)
Schönhage, A.: Schnelle Multiplikation von Polynomen über Körpern der Charakteristik 2. Acta Inf.7, 395–398 (1977)
Schönhage, A., Strassen, V.: Schnelle Multiplikation großer Zahlen. Computing7, 281–292 (1971)
Winograd, S.: Arithmetic complexity of computations. CBMS-NSF Regional Conference Series in Applied Math. 33. Philadelphia, PA: SIAM 1980
Author information
Authors and Affiliations
Additional information
The authors would like to acknowledge the partial support of NSA Grant MDA-904-II-2031 and NSF Grant Nr. CCR-87-05363
Rights and permissions
About this article
Cite this article
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
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01178683