Pauli, Sebastian (2001) Efficient enumeration of extensions of local fields with bounded discriminant. PhD thesis, Concordia University.
Let k be a p -adic field. It is well-known that k has only finitely many extensions of a given finite degree. Krasner  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)|
|Pagination:||viii, 96 leaves ; 29 cm.|
|Degree Name:||Theses (Ph.D.)|
|Program:||Mathematics and Statistics|
|Thesis Supervisor(s):||Ford, David|
|Deposited By:||Concordia University Libraries|
|Deposited On:||27 Aug 2009 13:20|
|Last Modified:||08 Dec 2010 10:21|
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