60 citations · 61 across the 4 of their papers we have counts for
7 papers
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
Normal CM-fields with class number one
Tommy Hofmann, Carlo Sircana
We show that assuming the generalized Riemann hypothesis there are no normal CM-fields with class number one of degree 64 and 96. This is done by constructing complete tables of no…
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…
On the computation of overorders
Tommy Hofmann, Carlo Sircana
The computation of a maximal order of an order in a semisimple algebra over a global field is a classical well-studied problem in algorithmic number theory. In this paper we consid…
Efficient Gröbner Bases Computation over Principal Ideal Rings
Christian Eder, Tommy Hofmann
In this paper we present a new efficient variant to compute strong Gröbner basis over quotients of principal ideal domains. We show an easy lifting process which allows us to reduc…
On Gröbner bases over Dedekind domains
Tommy Hofmann
Gröbner bases are a fundamental tool when studying ideals in multivariate polynomial rings. More recently there has been a growing interest in transferring techniques from the fiel…