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Mathematics of Computation

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Dependency of units in number fields

Authors: Claus Fieker and Michael E. Pohst
Journal: Math. Comp. 75 (2006), 1507-1518
MSC (2000): Primary 11Y16, 11-04
Published electronically: April 3, 2006
MathSciNet review: 2219041
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Abstract: We develop a method for validating the indepencence of units in algebraic number fields. In case that a given system of units has a dependency, we compute a certificate for this.

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  • 1. Karim Belabas, Topics in computational algebraic number theory, J. Théor. Nombres Bordeaux 16 (2004), no. 1, 19–63 (English, with English and French summaries). MR 2145572
  • 2. John J. Cannon, MAGMA,, 2003.
  • 3. Henri Cohen, A course in computational algebraic number theory, Graduate Texts in Mathematics, vol. 138, Springer-Verlag, Berlin, 1993. MR 1228206
  • 4. Edward Dobrowolski, On the maximal modulus of conjugates of an algebraic integer, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 26 (1978), no. 4, 291–292 (English, with Russian summary). MR 0491585
  • 5. Nicholas J. Higham, Analysis of the Cholesky decomposition of a semi-definite matrix, Reliable numerical computation, Oxford Sci. Publ., Oxford Univ. Press, New York, 1990, pp. 161–185. MR 1098323
  • 6. L. Kronecker, Zwei Sätze über Gleichungen mit ganzahlingen Coeffizienten, J. Reine Angew. Math 53 (1857), 173-175.
  • 7. Władysław Narkiewicz, Elementary and analytic theory of algebraic numbers, 3rd ed., Springer Monographs in Mathematics, Springer-Verlag, Berlin, 2004. MR 2078267
  • 8. Michael E. Pohst, A modification of the LLL reduction algorithm, J. Symb. Comput. 4 (1987), 123-127. MR 0908420 (89c:11183)
  • 9. Michael E. Pohst, On computing isomorphisms of equation orders, Math.Comp. 48 (1987), no. 177. MR 0908420 (89c:11183)
  • 10. Michael E. Pohst, Computational algebraic number theory, DMV Seminar, vol. 21, Birkhäuser Verlag, Basel, 1993. MR 1243639
  • 11. M. Pohst and H. Zassenhaus, Algorithmic algebraic number theory, Encyclopedia of Mathematics and its Applications, vol. 30, Cambridge University Press, Cambridge, 1989. MR 1033013
  • 12. A. Schinzel and H. Zassenhaus, A refinement of two theorems of Kronecker, Michigan Math. J. 12 (1965), 81–85. MR 0175882
  • 13. J. Stoer and R. Bulirsch, Introduction to numerical analysis, 3rd ed., Texts in Applied Mathematics, vol. 12, Springer-Verlag, New York, 2002. Translated from the German by R. Bartels, W. Gautschi and C. Witzgall. MR 1923481

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Additional Information

Claus Fieker
Affiliation: School of Mathematics and Statistics, University of Sydney, NSW 2006, Australia.

Michael E. Pohst
Affiliation: Institut für Mathematik, Technische Universität Berlin, Straße des 17.Juni 136, 10623 Berlin, Germany.
Email: pohst@math.TU-Berlin.DE

Received by editor(s): July 21, 2004
Published electronically: April 3, 2006
Additional Notes: This article was written while the second author visited the Computational Algebra Group at the University of Sydney in October, 2003.
Article copyright: © Copyright 2006 American Mathematical Society