@inbook{f793b5b059434216b5b3dceb5f65a6d5,
title = "Fast decomposition of polynomials with known Galois group",
abstract = "Let f(X) be a separable polynomial with coefficients in a field K, generating a field extension M/K. If this extension is Galois with a solvable automorphism group, then the equation f(X) = 0 can be solved by radicals. The first step of the solution consists of splitting the extension M/K into intermediate fields. Such computations are classical, and we explain how fast polynomial arithmetic can be used to speed up the process. Moreover, we extend the algorithms to a more general case of extensions that are no longer Galois. Numerical examples are provided, including results obtained with our implementation for Hilbert class fields of imaginary quadratic fields.",
author = "Andreas Enge and Fran{\c c}ois Morain",
year = "2003",
month = jan,
day = "1",
doi = "10.1007/3-540-44828-4\_27",
language = "English",
isbn = "3540401113",
series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
publisher = "Springer Verlag",
pages = "254--264",
editor = "Marc Fossorier and Tom Hoholdt and Alain Poli",
booktitle = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
}