A detailed exposition of Kneser's neighbour method for quadratic lattices over totally real number fields, and of the sub-procedures needed for its implementation, is given. Using an actual computer program which automatically generates representatives for all isomorphism classes in one genus of rational lattices, various results about genera of`-elementary… (More)
I have a great suspicion that for example Euler today would spend much more of his time on writing software because he spent so much of his time e.g., in efforts of calculating tables of moon positions. And I believe that Gauß as well would spend much more time sitting in front of the screen.
A lattice in euclidean space which is an orthogonal sum of nontrivial sub-lattices is called decomposable. We present an algorithm to construct a lattice's decomposition into indecomposable sublattices. Similar methods are used to prove a covering theorem for generating systems of lattices and to speed up variations of the LLL algorithm for the computation… (More)