Add to ORKGWe discuss three algorithms to find small norm elements in number fields. One of these algorithms is a continued fraction-like algorithm based on the LLL-reduction of positive definite quadratic forms as suggested by Beukers. The other two algorithms are adaptations of that algorithm. We discuss how to find units from these small norm elements and how to extract a system of independent units from that. We discuss properties of these algorithms and compare them to algorithms by Cohen, Diaz y Diaz, Olivier, by Buchmann, Peth\H{o} and by Pohst, Zassenhaus. We run tests on an implementation of these algorithms in Mathematica
This thesis focuses on additively indecomposable integers in totally real number fields and their ap...
The first part of this paper classifies all purely cubic function fields over a finite field of char...
An algorithm is discussed to compute the exponential representation of principal units in a finite e...
AbstractBased on a number geometric interpretation of the continued fraction algorithm in real quadr...
Dirichlet's theorem describes the structure of the group of units of the ring of algebraic integers ...
Minor corrections and new numerical resultsWe use the polynomials m_s(t) = t^2 − 4s, s ∈ {−1, 1}, in...
Multidimensional continued fraction algorithms associated with GLn(ZK), where Zk is the ring of inte...
Multidimensional continued fraction algorithms associated with GLn(ZK), where Zk is the ring of inte...
In real quadratic number field Q (root d), integral basis element is denoted by w(d) = [a(0); a(1), ...
The current state of the art algorithm for computing a system of fundamental units in a number field...
International audienceFor a finite group $G$, we introduce a generalization of norm relations in the...
26 pages. Elementary subject about real quadratic fields with new algorithms using given PARI progra...
26 pages. Elementary subject about real quadratic fields with new algorithms using given PARI progra...
For a finite group $G$, we introduce a generalization of norm relations in the group algebra $\mathb...
The objective of this book is to provide tools for solving problems which involve cubic number field...
This thesis focuses on additively indecomposable integers in totally real number fields and their ap...
The first part of this paper classifies all purely cubic function fields over a finite field of char...
An algorithm is discussed to compute the exponential representation of principal units in a finite e...
AbstractBased on a number geometric interpretation of the continued fraction algorithm in real quadr...
Dirichlet's theorem describes the structure of the group of units of the ring of algebraic integers ...
Minor corrections and new numerical resultsWe use the polynomials m_s(t) = t^2 − 4s, s ∈ {−1, 1}, in...
Multidimensional continued fraction algorithms associated with GLn(ZK), where Zk is the ring of inte...
Multidimensional continued fraction algorithms associated with GLn(ZK), where Zk is the ring of inte...
In real quadratic number field Q (root d), integral basis element is denoted by w(d) = [a(0); a(1), ...
The current state of the art algorithm for computing a system of fundamental units in a number field...
International audienceFor a finite group $G$, we introduce a generalization of norm relations in the...
26 pages. Elementary subject about real quadratic fields with new algorithms using given PARI progra...
26 pages. Elementary subject about real quadratic fields with new algorithms using given PARI progra...
For a finite group $G$, we introduce a generalization of norm relations in the group algebra $\mathb...
The objective of this book is to provide tools for solving problems which involve cubic number field...
This thesis focuses on additively indecomposable integers in totally real number fields and their ap...
The first part of this paper classifies all purely cubic function fields over a finite field of char...
An algorithm is discussed to compute the exponential representation of principal units in a finite e...