Fast separable factorization and applications



In this paper we show that the separable decomposition of a univariate polynomial can be computed in softly optimal time, in terms of the number of arithmetic operations in the coefficient field. We also adapt the classical multi-modular strategy that speeds up the computations for many coefficient fields, and we analyze consequences of the new results to the squarefree and the irreducible factorizations.


Polynomial factorization Separable factorization Squarefree factorization Irreducible factorization 

Mathematics Subject Classification (2000)

Primary 12Y05 68W30 Secondary 11Y16 12D05 13P05 


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Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  1. 1.Laboratoire de Mathématiques (UMR 8100 CNRS)Université de Versailles Saint-Quentin-en-YvelinesVersaillesFrance

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