Short Representation of Quadratic Integers

  • Johannes Buchmann
  • Christoph Thiel
  • Hugh Williams
Part of the Mathematics and Its Applications book series (MAIA, volume 325)


Let O be a real quadratic order of discriminant Δ. For elements α in O we develop a compact representation whose binary length is polynomially bounded in log log H(α), log N(α) and log Δ where H(α) is the height of α and N(α) is the norm of α. We show that using compact representations we can in polynomial time compute norms, signs, products, and inverses of numbers in O and principal ideals generated by numbers in O. We also show how to compare numbers given in compact representation in polynomial time.


Polynomial Time Polynomial Time Algorithm Standard Representation Class Number Compact Representation 
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Copyright information

© Springer Science+Business Media Dordrecht 1995

Authors and Affiliations

  • Johannes Buchmann
    • 1
  • Christoph Thiel
    • 1
  • Hugh Williams
    • 2
  1. 1.Fachbereich InformatikUniversität des SaarlandesSaarbrückenGermany
  2. 2.Department of Computer ScienceUniversity of ManitobaWinnipegCanada

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