60 citations · 106 across the 16 of their papers we have counts for
19 papers
Automorphisms and canonical forms of integer lattices
Simon Brandhorst, Tommy Hofmann
We improve the Plesken--Souvignier algorithm for computing automorphism groups and isometries of positive definite integer quadratic lattices by exploiting characteristic sublattic…
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…
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
Computation of lattice isomorphisms and the integral matrix similarity problem
Werner Bley, Tommy Hofmann, Henri Johnston
Let be a number field, let be a finite-dimensional -algebra, let denote the Jacobson radical of , and let be an -order in . Su…
Finite subgroups of automorphisms of K3 surfaces
Simon Brandhorst, Tommy Hofmann
We give a complete classification of finite subgroups of automorphisms of K3 surfaces up to deformation. The classification is in terms of Hodge theoretic data associated to certai…
Generation of Local Unitary Groups
Simon Brandhorst, Tommy Hofmann, Sven Manthe
Let be a two-dimensional étale algebra over a non-Archimedean local field of characteristic zero. We show that the unitary group of a non-degenerate hermitian lattice over…
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…
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 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…
On Integral Forms of Specht Modules Labelled by Hook Partitions
Susanne Danz, Tommy Hofmann
We investigate integral forms of simple modules of symmetric groups over fields of characteristic labelled by hook partitions. Building on work of Plesken and Craig, for every…
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…
Valuations of -adic regulators of cyclic cubic fields
Tommy Hofmann, Yinan Zhang
We compute the -adic regulator of cyclic cubic extensions of with discriminant up to for , and observe the distribution of the -adic valuation…
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…
Zeta Functions of Lattices of the Symmetric Group
Tommy Hofmann
The symmetric group of degree admits an -dimensional irreducible -module corresponding to the hook partition …
Computing tropical points and tropical links
Tommy Hofmann, Yue Ren
We present an algorithm for computing zero-dimensional tropical varieties based on triangular decomposition and Newton polygon methods. From it, we derive algorithms for computing…