Advertisement

Computational aspects of Kummer theory

  • M. E. Pohst
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1122)

Abstract

New methods and algorithms for computations with pure relative extensions of algebraic number fields are discussed. The emphasis is on relative normal forms, relative bases, Hilbert class fields, subfield detection, and embedding of subfields.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [Ar]
    E. Artin, Questions de base minimale dans la théorie des nombres algébriques, The collected papers of Emil Artin, Addison-Wesley 1965, 229–231.Google Scholar
  2. [BoPo]
    W. Bosma and M. Pohst, Computations with finitely generated modules over Dedekind rings, Proc. ISSAC'91 (1991), 151–156.Google Scholar
  3. [Co]
    H. Cohen, Algorithms for modules over Dedekind domains and relative extensions of number fields, to appear in Math. Comp.Google Scholar
  4. [Dabe]
    M. Daberkow, Über die Bestimmung der ganzen Elemente in Radikalerweiterungen algebraischer Zahlkörper, Thesis, Berlin 1995.Google Scholar
  5. [DaPo1]
    M. Daberkow and M. Pohst, On Integral Bases in Relative Quadratic Extensions, to appear in Math. Comp.Google Scholar
  6. [DaPo2]
    M. Daberkow and M. Pohst, Computations with relative extensions of number fields with an application to the construction of Hilbert class fields, Proc. ISSAC'95, ACM Press, New York 1995, pp. 68–76.Google Scholar
  7. [DaPo3]
    M. Daberkow and M. Pohst, On Computing Hilbert Class Fields of Prime Degree, this volume.Google Scholar
  8. [DaPo4]
    M. Daberkow and M. Pohst, On the computation of Hilbert class fields, submitted for publication.Google Scholar
  9. [Dixo]
    J. Dixon, Computing Subfields in Algebraic Number Fields, J. Austral. Math. Soc. (Series A) 49 (1990), 434–448.Google Scholar
  10. [Has]
    H. Hasse, Über den Klassenkörper zum quadratischen Zahlkörper mit der Diskriminante-47, Acta Arithmetica 9 (1964), 419–434.Google Scholar
  11. [He]
    E. Hecke, Lectures on the Theory of Algebraic Numbers, Springer Verlag 1981.Google Scholar
  12. [Kant]
    Kant group, KANT V4, to appear in J. Symb. Comp.Google Scholar
  13. [Klun]
    J. Klüners, Über die Berechnung von Teilkörpern algebraischer Zahlkörper, Diplomarbeit, TU-Berlin 1995.Google Scholar
  14. [KlPo]
    J. Klüners and M. Pohst, On Computing subfields, to appear in J. Symb. Comp.Google Scholar
  15. [Lang]
    S. Lang, Algebraic number theory, Grad. Texts in Math. 110, Springer Verlag 1986.Google Scholar
  16. [OMea]
    O. T. O'Meara, Introduction to Quadratic Forms, Springer Verlag 1963.Google Scholar
  17. [PoZa]
    M. Pohst and H. Zassenhaus, Algorithmic Algebraic Number Theory, Cambridge University Press 1989.Google Scholar
  18. [Somm]
    J. Sommer, Einführung in Zahlentheorie, Teubner Verlag, Leipzig 1907.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • M. E. Pohst
    • 1
  1. 1.Fachbereich 3, Mathematik 8-1Technische Universität BerlinBerlinGermany

Personalised recommendations