|
Dependency of units in number fields
Author(s):
Claus
Fieker;
Michael
E.
Pohst.
Journal:
Math. Comp.
75
(2006),
1507-1518.
MSC (2000):
Primary 11Y16, 11-04
Posted:
April 3, 2006
Retrieve article in:
PDF
Abstract |
References |
Similar articles |
Additional information
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.
References:
-
- 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
adis aw 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)
Similar Articles:
Retrieve articles in Mathematics of Computation
with MSC
(2000):
11Y16, 11-04
Retrieve articles in all Journals with MSC
(2000):
11Y16, 11-04
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:
10.1090/S0025-5718-06-01899-0
PII:
S 0025-5718(06)01899-0
Received by editor(s):
July 21, 2004
Posted:
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.
Copyright of article:
Copyright
2006,
American Mathematical Society
|