Computing subfields : Reverse of the primitive element problem

Abstract : We describe an algorithm which computes all subfields of an effectively given finite algebraic extension. Although the base field can be arbitrary, we focus our attention on the rationals. This appears to be a fundamental tool for the simplification of algebraic numbers.
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Daniel Lazard, Annick Valibouze. Computing subfields : Reverse of the primitive element problem. Frédéric Eyssette, and André Galligo. Computational Algebraic Geometry (MEGA, Nice, 1992), ⟨Birkhäuser Boston⟩, pp.63--176, 1993, Progress in Mathematics 109, 978-1-4612-2752-6. ⟨10.1007/978-1-4612-2752-6_11⟩. ⟨hal-01672218⟩

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