Abstract
© 2014 Elsevier Inc. Let A be a Dedekind domain whose field of fractions K is a global field. Let p be a non-zero prime ideal of A, and Kp the completion of K at p. The Montes algorithm factorizes a monic irreducible polynomial f∈. A[. x] over Kp, and provides essential arithmetic information about the finite extensions of Kp determined by the different irreducible factors. In particular, it can be used to compute a p-integral basis of the extension of K determined by f. In this paper we present a new and faster method to compute p-integral bases, based on the use of the quotients of certain divisions with remainder of f that occur along the flow of the Montes algorithm.
Original language | English |
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Pages (from-to) | 549-589 |
Journal | Journal of Number Theory |
Volume | 147 |
DOIs | |
Publication status | Published - 1 Feb 2015 |
Keywords
- Dedekind domain
- Global field
- Local field
- Montes algorithm
- Newton polygon
- P-integral bases
- Reduced bases