36 citations · 90 across the 10 of their papers we have counts for
5 papers · 1 filter
Commensurability of automorphism groups
Alex Bartel, Hendrik W. Lenstra
We develop a theory of commensurability of groups, of rings, and of modules. It allows us, in certain cases, to compare sizes of automorphism groups of modules, even when those are…
Algorithms for commutative algebras over the rational numbers
H. W. Lenstra, A. Silverberg
The algebras considered in this paper are commutative rings of which the additive group is a finite-dimensional vector space over the field of rational numbers. We present determin…
Roots of unity in orders
H. W. Lenstra, A. Silverberg
We give deterministic polynomial-time algorithms that, given an order, compute the primitive idempotents and determine a set of generators for the group of roots of unity in the or…
Determining cyclicity of finite modules
H. W. Lenstra, A. Silverberg
We present a deterministic polynomial-time algorithm that determines whether a finite module over a finite commutative ring is cyclic, and if it is, outputs a generator.
Lattices with Symmetry
H. W. Lenstra, A. Silverberg
For large ranks, there is no good algorithm that decides whether a given lattice has an orthonormal basis. But when the lattice is given with enough symmetry, we can construct a pr…