# A polynomial reduction algorithm

Henri Cohen; Francisco Diaz Y Diaz

Journal de théorie des nombres de Bordeaux (1991)

- Volume: 3, Issue: 2, page 351-360
- ISSN: 1246-7405

## Access Full Article

top## Abstract

top## How to cite

topCohen, Henri, and Diaz Y Diaz, Francisco. "A polynomial reduction algorithm." Journal de théorie des nombres de Bordeaux 3.2 (1991): 351-360. <http://eudml.org/doc/93544>.

@article{Cohen1991,

abstract = {The algorithm described in this paper is a practical approach to the problem of giving, for each number field $K$ a polynomial, as canonical as possible, a root of which is a primitive element of the extension $K/ \mathbb \{Q\}$. Our algorithm uses the $LLL$ algorithm to find a basis of minimal vectors for the lattice of $\mathbb \{R\}^n$ determined by the integers of $K$ under the canonical map.},

author = {Cohen, Henri, Diaz Y Diaz, Francisco},

journal = {Journal de théorie des nombres de Bordeaux},

keywords = {polynomial reduction algorithm; canonical elements for generating number fields; basis of minimal vectors; lattices; LLL-reduction},

language = {eng},

number = {2},

pages = {351-360},

publisher = {Université Bordeaux I},

title = {A polynomial reduction algorithm},

url = {http://eudml.org/doc/93544},

volume = {3},

year = {1991},

}

TY - JOUR

AU - Cohen, Henri

AU - Diaz Y Diaz, Francisco

TI - A polynomial reduction algorithm

JO - Journal de théorie des nombres de Bordeaux

PY - 1991

PB - Université Bordeaux I

VL - 3

IS - 2

SP - 351

EP - 360

AB - The algorithm described in this paper is a practical approach to the problem of giving, for each number field $K$ a polynomial, as canonical as possible, a root of which is a primitive element of the extension $K/ \mathbb {Q}$. Our algorithm uses the $LLL$ algorithm to find a basis of minimal vectors for the lattice of $\mathbb {R}^n$ determined by the integers of $K$ under the canonical map.

LA - eng

KW - polynomial reduction algorithm; canonical elements for generating number fields; basis of minimal vectors; lattices; LLL-reduction

UR - http://eudml.org/doc/93544

ER -

## References

top- [Ford] D.J. Ford, The construction of maximal orders over a Dedekind domain, J. Symbolic Computation4 (1987), 69-75. Zbl0632.13003MR908413
- [Kwon-Mart] S.-H. Kwon and J. Martinet, Sur les corps resolubles de degré premier, J. Reine Angew. Math.375/376 (1987), 12-23. Zbl0601.12013MR882288
- [LLL] A.K. Lenstra, H.W. Lenstra, Jr. and L. Lovász, Factoring polynomials with rational coefficients, Math. Annalen61 (1982), 515-534. Zbl0488.12001MR682664
- [Oliv] M. Olivier, Corps sextiques primitifs, Ann. Institut Fourier40 (1990), 757-767. Zbl0734.11054MR1096589
- [PMD] M. Pohst, J. Martinet and F. Diaz y Diaz, The minimum discriminant of totally real octic fields, J. Number Theory36 (1990), 145-159. Zbl0719.11079MR1072461
- [Stau] R.P. Stauduhar, The determination of Galois groups, Math. Comp.27 (1973), 981-996. Zbl0282.12004MR327712

## Citations in EuDML Documents

top## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.