Boris Hemkemeier

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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)
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)
We have adopted the incremental construction algorithm paradigm which is a standard technique in computational geometry for lattice problems. The considered lattice problems are: lattice basis, successive minima, orthogonal decomposition. For these problems we give algorithms which are reasonable fast. Using a classical theorem of MINKOWSKI we prove a(More)
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