Algorithms for function fields. (English) Zbl 1116.11325

Summary: Let \(K/\mathbb Q(t)\) be a finite extension. We describe algorithms for computing subfields and automorphisms of \(K/\mathbb Q(t)\). As an application we give an algorithm for finding decompositions of rational functions in \(\mathbb Q(\alpha)\). We also present an algorithm which decides if an extension \(L/\mathbb Q(t)\) is a subfield of \(K\). In case \([K:\mathbb Q(t)] = [L/\mathbb Q(t)]\) we obtain a \(\mathbb Q(t)\)-isomorphism test. Furthermore, we describe an algorithm which computes subfields of the normal closure of \(K/\mathbb Q(t)\).


11Y40 Algebraic number theory computations
11R58 Arithmetic theory of algebraic function fields
12E05 Polynomials in general fields (irreducibility, etc.)
12F10 Separable extensions, Galois theory
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