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Efficient enumeration of extensions of local fields with bounded discriminant

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Efficient enumeration of extensions of local fields with bounded discriminant

Pauli, Sebastian (2001) Efficient enumeration of extensions of local fields with bounded discriminant. PhD thesis, Concordia University.

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Abstract

Let k be a p -adic field. It is well-known that k has only finitely many extensions of a given finite degree. Krasner [1966] gives 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 K / k of a given degree and discriminant. We also present canonical sets of generating polynomials of extensions of degree p m . Some methods from the proof of the number of extensions of a given degree and discriminant can also be used for the determination of a bound that gives a considerably improved estimate of the complexity of polynomial factorization over local fields. We use this bound in an efficient new algorithm for factoring a polynomial Z over a local field k . For every irreducible factor [varphi]( x ) of Z ( x ) our algorithm return an integral basis for k [ x ]/[varphi]( x ) k [ x ] over k .

Divisions:Concordia University > Faculty of Arts and Science > Mathematics and Statistics
Item Type:Thesis (PhD)
Authors:Pauli, Sebastian
Pagination:viii, 96 leaves ; 29 cm.
Institution:Concordia University
Degree Name:Theses (Ph.D.)
Program:Mathematics and Statistics
Date:2001
Thesis Supervisor(s):Ford, David
ID Code:1533
Deposited By:Concordia University Libraries
Deposited On:27 Aug 2009 13:20
Last Modified:08 Dec 2010 10:21
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