60 citations · 141 across the 17 of their papers we have counts for
7 papers · 1 filter
Number Theory in OSCAR
Claus Fieker, Tommy Hofmann
We give a brief introduction to computational algebraic number theory in OSCAR. Our main focus is on number fields, rings of integers and their invariants. After recalling some cla…
Constructions using Galois Theory
Claus Fieker, Nicole Sutherland
We describe algorithms to compute fixed fields, splitting fields and towers of radical extensions without using polynomial factorisation in towers or constructing any field contain…
Norm relations and computational problems in number fields
Jean-François Biasse, Claus Fieker, Tommy Hofmann +1
For a finite group , we introduce a generalization of norm relations in the group algebra . We give necessary and sufficient criteria for the existence of such rel…
On the computation of the HNF of a module over the ring of integers of a number field
Jean-François Biasse, Claus Fieker, Tommy Hofmann
We present a variation of the modular algorithm for computing the Hermite normal form of an -module presented by Cohen, where is the ring of integers o…
Computing in quotients of rings of integers
Tommy Hofmann, Claus Fieker
We develop algorithms to turn quotients of rings of rings of integers into effective Euclidean rings by giving polynomial algorithms for all fundamental ring operations. In additio…
Computation of Galois groups of rational polynomials
Claus Fieker, Jürgen Klüners
Computational Galois theory, in particular the problem of computing the Galois group of a given polynomial is a very old problem. Currently, the best algorithmic solution is Staudu…
New techniques for computing the ideal class group and a system of fundamental units in number fields
Jean-François Biasse, Claus Fieker
We describe a new algorithm for computing the ideal class group, the regulator and a system of fundamental units in number fields under the generalized Riemann hypothesis. We use s…