×

A polynomial reduction algorithm. (English) Zbl 0758.11053

The authors develop a normal form for generating elements of algebraic number fields. It bases on LLL-reduction and is therefore not necessarily unique. (It might not even exist in rare cases.) Its usefulness is demonstrated by several illustrative examples.

MSC:

11Y40 Algebraic number theory computations
PDFBibTeX XMLCite
Full Text: DOI Numdam EuDML

References:

[1] Ford, D.J., The construction of maximal orders over a Dedekind domain, J. Symbolic Computation4 (1987), 69-75. · Zbl 0632.13003
[2] Kwon, S.-H. and Martinet, J., Sur les corps resolubles de degré premier, J. Reine Angew. Math.375/376 (1987), 12-23. · Zbl 0601.12013
[3] Lenstra, A.K., Lenstra, H.W. and Lovász, L., Factoring polynomials with rational coefficients, Math. Annalen61 (1982), 515-534. · Zbl 0488.12001
[4] Olivier, M., Corps sextiques primitifs, Ann. Institut Fourier40 (1990), 757-767. · Zbl 0734.11054
[5] Pohst, M., Martinet, J. and Diaz y Diaz, F., The minimum discriminant of totally real octic fields, J. Number Theory36 (1990), 145-159. · Zbl 0719.11079
[6] Stauduhar, R.P., The determination of Galois groups, Math. Comp.27 (1973), 981-996. · Zbl 0282.12004
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.