Fast separable factorization and applications

  • Authors:

  • Grégoire Lecerf

  • Affiliations:

  • Université de Versailles Saint-Quentin-en-Yvelines, Laboratoire de Mathématiques (UMR 8100 CNRS), 45 Avenue des États-Unis, 78035, Versailles, France

  • Venue:
  • Applicable Algebra in Engineering, Communication and Computing
  • Year:
  • 2008

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Abstract

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.