60 citations · 141 across the 17 of their papers we have counts for
17 papers
Group theory in OSCAR
Claus Fieker, Max Horn
OSCAR is an innovative new computer algebra system which combines and extends the power of its four cornerstone systems - GAP (group theory), Singular (algebra and algebraic geomet…
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…
Feynman integral reduction using Gröbner bases
Mohamed Barakat, Robin Brüser, Claus Fieker +2
We investigate the reduction of Feynman integrals to master integrals using Gröbner bases in a rational double-shift algebra Y in which the integration-by-parts (IBP) relations for…
Computing Galois groups of Ehrhart polynomials in OSCAR
Claus Fieker, Tommy Hofmann, Michael Joswig
We report on an implementation of Galois groups in the new computer algebra system OSCAR. As an application we compute Galois groups of Ehrhart polynomials of lattice polytope
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…
Resultants over principal Artinian rings
Claus Fieker, Tommy Hofmann, Carlo Sircana
The resultant of two univariate polynomials is an invariant of great importance in commutative algebra and vastly used in computer algebra systems. Here we present an algorithm to…
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…
Nemo/Hecke: Computer Algebra and Number Theory Packages for the Julia Programming Language
Claus Fieker, William Hart, Tommy Hofmann +1
We introduce two new packages, Nemo and Hecke, written in the Julia programming language for computer algebra and number theory. We demonstrate that high performance generic algori…
Bad Primes in Computational Algebraic Geometry
Janko Boehm, Wolfram Decker, Claus Fieker +2
Computations over the rational numbers often suffer from intermediate coefficient swell. One solution to this problem is to apply the given algorithm modulo a number of primes and…
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…
Gröbner Bases over Algebraic Number Fields
Dereje Kifle Boku, Claus Fieker, Wolfram Decker +1
Although Buchberger's algorithm, in theory, allows us to compute Gröbner bases over any field, in practice, however, the computational efficiency depends on the arithmetic of the g…
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…
The use of Bad Primes in Rational Reconstruction
Janko Boehm, Wolfram Decker, Claus Fieker +1
A standard method for finding a rational number from its values modulo a collection of primes is to determine its value modulo the product of the primes via Chinese remaindering, a…
A polynomial time algorithm for computing the HNF of a module over the integers of a number field
Jean-François Biasse, Claus Fieker
We present a variation of the modular algorithm for computing the Hermite Normal Form of an $\OK$-module presented by Cohen, where $\OK$ is the ring of integers of a number field K…
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…
Constructing algebraic Lie algebras
Claus Fieker, Willem de Graaf
We give an algorithm for constructing the algebraic hull of a given matrix Lie algebra in characteristic zero. It is based on an algorithm for finding integral linear dependencies…