Basis reduction for layered lattices
Promotor: H.W. Lenstra
- E.L. Torreão Dassen
- 20 December 2011
- Thesis in Leiden Repository
We develop the theory of layered Euclidean spaces and layered lattices. We present algorithms to compute both Gram-Schmidt and reduced bases in this generalized setting. A layered lattice can be seen as lattices where certain directions have infinite weight. It can also be interpreted as the natural objects to be identified with the cusps of de moduli spaces of lattices. In this thesis the theory of layered lattices is put forward together with algorithm to compute with them and applications.