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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
DOI: https://doi.org/10.1090/S0025-5718-06-01899-0
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. Theor. Nombres Bordeaux, 16 (2004), 19-63. MR 2145572 (2006a:11174)
  • 2. John J. Cannon, MAGMA, http://magma.maths.usyd.edu.au, 2003.
  • 3. Henri Cohen, A course in computational algebraic number theory, erste ed., Graduate Texts in Mathematics, vol. 138, Springer, 1993. MR 1228206 (94i:11105)
  • 4. Edward Dobrowolski, On the maximal modulus of conjugates of an algebraic integer, Bul. Acad. Pol. Sci. 26 (1978), no. 4, 291-292. MR 0491585 (58:10811)
  • 5. Nicholas J. Higham, Analysis of the Cholesky decomposition of a semi-definite matrix., Reliable numerical computation, Proc. Conf. in Honour of J. H. Wilkinson, Teddington/UK, 161-185 , 1990. MR 1098323 (92c:65036)
  • 6. L. Kronecker, Zwei Sätze über Gleichungen mit ganzahlingen Coeffizienten, J. Reine Angew. Math 53 (1857), 173-175.
  • 7. W\ladis\law Narkiewicz, Elementary and analytic theory of algebraic numbers, 2nd ed., Springer, 1989. MR 2078267 (2005c:11131)
  • 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. 21. Basel: Birkhäuser, 1993. MR 1243639 (94j:11132)
  • 11. Michael E. Pohst and Hans Zassenhaus, Algorithmic algebraic number theory, Encyclopaedia of mathematics and its applications, Cambridge University Press, 1989. MR 1033013 (92b:11074)
  • 12. Andrzej Schinzel and Hans Zassenhaus, A refinement of two theorems of Kronecker, Mich. Math. J. 12 (1965), 81-85. MR 0175882 (31:158)
  • 13. J. Stoer and R. Bulirsch, Introduction to numerical analysis. Transl. from the German by R. Bartels, W. Gautschi, and C. Witzgall. 3rd ed., Texts in Applied Mathematics. 12. New York, NY: Springer., 2002 (English). MR 1923481 (2003d:65001)

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Additional Information

Claus Fieker
Affiliation: School of Mathematics and Statistics, University of Sydney, NSW 2006, Australia.
Email: claus@maths.usyd.edu.au

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

DOI: https://doi.org/10.1090/S0025-5718-06-01899-0
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

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