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On the computation of all extensions of a |
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| Authors: | Sebastian Pauli Xavier-Franç ois Roblot. |
| Affiliation: | Centre Interuniversitaire en Calcul Mathématique Algébrique, Concordia University, 1455 de Maisonneuve Blvd. W., Montréal, Québec, H3G 1M8, CANADA ; Institut Girard Desargues, Université Claude Bernard (Lyon 1), 43, boulevard du 11 Novembre 1918, 69622 Villeurbanne cedex, France |
| Abstract: | Let |
| Keywords: | $p$-adic fields wildly ramified extensions Eisenstein polynomials |
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be a 
-adic field. It is well-known that 
has only finitely many extensions of a given finite degree. Krasner has given formulae for the number of extensions of a given degree and discriminant. Following his work, we present an algorithm for the computation of generating polynomials for all extensions 
of a given degree and discriminant.