---
_id: '35954'
abstract:
- lang: eng
  text: 'Let {\ASIE K}\,/{\small \ℚ}({\ASIE t \!}) be a finite extension. We describe
    algorithms for computing subfields and automorphisms of {\ASIE K}\,/{\small \ℚ}({\ASIE
    t }\!). As an application we give an algorithm for finding decompositions of rational
    functions in {\small \ℚ(α)}. We also present an algorithm which decides if an
    extension {\ASIE L}\,/{\small \ℚ}({\ASIE t \!}) is a subfield of {\ASIE K}. In
    case [{\ASIE K : \;}{\small\ℚ}({\ASIE t \!})] = [{\ASIE L : \;}{\small \ℚ}({\ASIE
    t \!})] we obtain a {\small \ℚ}({\ASIE t \!})-isomorphism test. Furthermore, we
    describe an algorithm which computes subfields of the normal closure of {\ASIE
    K}\,/{\small \ℚ}({\ASIE t \!}).'
author:
- first_name: Jürgen
  full_name: Klüners, Jürgen
  id: '21202'
  last_name: Klüners
citation:
  ama: Klüners J. Algorithms for function fields. <i>Experiment Math </i>. 2002;11(2):171-181.
  apa: Klüners, J. (2002). Algorithms for function fields. <i>Experiment. Math. </i>,
    <i>11</i>(2), 171–181.
  bibtex: '@article{Klüners_2002, title={Algorithms for function fields}, volume={11},
    number={2}, journal={Experiment. Math. }, publisher={Elsevier BV}, author={Klüners,
    Jürgen}, year={2002}, pages={171–181} }'
  chicago: 'Klüners, Jürgen. “Algorithms for Function Fields.” <i>Experiment. Math.
    </i> 11, no. 2 (2002): 171–81.'
  ieee: J. Klüners, “Algorithms for function fields,” <i>Experiment. Math. </i>, vol.
    11, no. 2, pp. 171–181, 2002.
  mla: Klüners, Jürgen. “Algorithms for Function Fields.” <i>Experiment. Math. </i>,
    vol. 11, no. 2, Elsevier BV, 2002, pp. 171–81.
  short: J. Klüners, Experiment. Math.  11 (2002) 171–181.
date_created: 2023-01-11T09:45:40Z
date_updated: 2023-03-06T10:26:58Z
department:
- _id: '102'
intvolume: '        11'
issue: '2'
keyword:
- algorithms
- decompositions
- Galois groups
- subfields
language:
- iso: eng
page: 171-181
publication: 'Experiment. Math. '
publication_status: published
publisher: Elsevier BV
related_material:
  link:
  - relation: confirmation
    url: https://projecteuclid.org/journals/experimental-mathematics/volume-11/issue-2/Algorithms-for-function-fields/em/1062621213.full
status: public
title: Algorithms for function fields
type: journal_article
user_id: '93826'
volume: 11
year: '2002'
...