Open Access
2002 Algorithms for function fields
Jürgen Klüners
Experiment. Math. 11(2): 171-181 (2002).


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 \!}).


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Jürgen Klüners. "Algorithms for function fields." Experiment. Math. 11 (2) 171 - 181, 2002.


Published: 2002
First available in Project Euclid: 3 September 2003

zbMATH: 1116.11325
MathSciNet: MR1959261

Primary: 11R58
Secondary: 11Y40 , 12F10

Keywords: algorithms , decompositions , Galois groups , subfields

Rights: Copyright © 2002 A K Peters, Ltd.

Vol.11 • No. 2 • 2002
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