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Computing Sparse Multiples of Polynomials

  • Mark Giesbrecht
  • Daniel S. Roche
  • Hrushikesh Tilak
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6506)

Abstract

We consider the problem of finding a sparse multiple of a polynomial. Given f ∈ F[x] of degree d, and a desired sparsity t, our goal is to determine if there exists a multiple h ∈ F[x] of f such that h has at most t non-zero terms, and if so, to find such an h. When F=ℚ and t is constant, we give a polynomial-time algorithm in d and the size of coefficients in h. When F is a finite field, we show that the problem is at least as hard as determining the multiplicative order of elements in an extension field of F (a problem thought to have complexity similar to that of factoring integers), and this lower bound is tight when t = 2.

Keywords

Linear Code Irreducible Polynomial Irreducible Factor Integer Lattice Rational Polynomial 
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

  • Mark Giesbrecht
    • 1
  • Daniel S. Roche
    • 1
  • Hrushikesh Tilak
    • 1
  1. 1.Cheriton School of Computer ScienceUniversity of WaterlooCanada

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