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On the Complexity of the Montes Ideal Factorization Algorithm

  • David Ford
  • Olga Veres
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6197)

Abstract

Let p be a rational prime and let Φ(X) be a monic irreducible polynomial in Z[X], with nΦ = degΦ and δΦ = v p (discΦ). In [13] Montes describes an algorithm for the decomposition of the ideal \(p\mathcal{O}K\) in the algebraic number field K generated by a root of Φ. A simplified version of the Montes algorithm, merely testing Φ(X) for irreducibility over Q p , is given in [19], together with a full Maple implementation and a demonstration that in the worst case, when Φ(X) is irreducible over Q p , the expected number of bit operations for termination is O(nΦ3 + ε δΦ2 + ε ). We now give a refined analysis that yields an improved estimate of O(nΦ3 + ε δΦ + nΦ2 + ε δΦ2 + ε ) bit operations. Since the worst case of the simplified algorithm coincides with the worst case of the original algorithm, this estimate applies as well to the complete Montes algorithm.

Keywords

Finite Field Monic Polynomial Newton Polygon Rational Integer Polynomial Factorization 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • David Ford
    • 1
  • Olga Veres
    • 1
  1. 1.Concordia UniversityMontréalCanada

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