Algorithms for function fields
Klüners, Jürgen
Experiment. Math., Tome 11 (2002) no. 3, p. 171-181 / Harvested from Project Euclid
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 $\Q(\alpha)$}. 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 \!}).
Publié le : 2002-05-14
Classification:  Galois groups,  subfields,  decompositions,  algorithms,  11R58,  11Y40,  12F10
@article{1062621213,
     author = {Kl\"uners, J\"urgen},
     title = {Algorithms for function fields},
     journal = {Experiment. Math.},
     volume = {11},
     number = {3},
     year = {2002},
     pages = { 171-181},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1062621213}
}
Klüners, Jürgen. Algorithms for function fields. Experiment. Math., Tome 11 (2002) no. 3, pp.  171-181. http://gdmltest.u-ga.fr/item/1062621213/