Journal of Symbolic Computation - Special issue on computational algebra and number theory: proceedings of the first MAGMA conference
Modern computer algebra
Solvability by radicals from an algorithmic point of view
Proceedings of the 2001 international symposium on Symbolic and algebraic computation
Comparing Invariants for Class Fields of Imaginary Quadratic Fields
ANTS-V Proceedings of the 5th International Symposium on Algorithmic Number Theory
Fast arithmetics in artin-schreier towers over finite fields
Proceedings of the 2009 international symposium on Symbolic and algebraic computation
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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.