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Computation of relative quadratic class groups

  • Henri Cohen
  • Francisco Diaz y Diaz
  • Michel Olivier
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1423)

Abstract

Using the theory of binary pseudo-quadratic forms over Z developed in [5], we sketch an algorithm for computing the relative class group of quadratic extensions. We end by a striking example which can be treated orders of magnitude faster using the relative method than using the absolute one.

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References

  1. 1.
    A.-M. Bergé and J. Martinet: Notions relatives de regulateurs et de hauteurs. Acta Arith. 54, No. 2, (1989) 155–170MATHMathSciNetGoogle Scholar
  2. 2.
    H. Cohen: A Course in Computational Algebraic Number Theory. GTM 138, (1993) Springer-VerlagGoogle Scholar
  3. 3.
    H. Cohen, F. Diaz y Diaz and M. Olivier: Subexponential Algorithms for Class and Unit Group Computations. J. Symb. Comp. 24 (1997) 433–441MATHMathSciNetCrossRefGoogle Scholar
  4. 4.
    H. Cohen, F. Diaz y Diaz and M. Olivier: Algorithms for Finite Abelian Groups. Submitted to J. Symb. Comp. (1997)Google Scholar
  5. 5.
    H. Cohen, F. Diaz y Diaz and M. Olivier: Pseudo-quadratic forms and their applications. Preprint (1998)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Henri Cohen
    • 1
  • Francisco Diaz y Diaz
    • 1
  • Michel Olivier
    • 1
  1. 1.Laboratoire A2XUniversité Bordeaux ITalenceFrance

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