论文信息 - On the decomposition of lattices

On the decomposition of lattices

A lattice in euclidean space which is an orthogonal sum of no ntrivial sublattices is called decomposable. We present an algorithm to construct a lattice’s decomposition into indecomposable sublattices. Similar method s are used to prove a covering theorem for generating systems of lattices and to speed up va riations of the LLL algorithm for the computation of lattice bases from large generating s ystems.

Boris Hemkemeier | Frank Vallentin | F. Vallentin | Boris Hemkemeier

[1] Gene H. Golub,et al. Matrix computations , 1983 .

[2] M. V. Wilkes,et al. The Art of Computer Programming, Volume 3, Sorting and Searching , 1974 .

[3] László Lovász,et al. Factoring polynomials with rational coefficients , 1982 .

[4] M. Kneser. Zur Theorie der Kristallgitter , 1954 .

[5] Claus-Peter Schnorr,et al. Lattice basis reduction: Improved practical algorithms and solving subset sum problems , 1991, FCT.

[6] N. J. A. Sloane,et al. A LATTICE WITHOUT A BASIS OF MINIMAL VECTORS , 1995 .

[7] H. Minkowski,et al. Geometrie der Zahlen , 1896 .

[8] Michael E. Pohst,et al. A Modification of the LLL Reduction Algorithm , 1987, J. Symb. Comput..

[9] Donald E. Knuth,et al. The Art of Computer Programming: Volume 3: Sorting and Searching , 1998 .

[10] Michael E. Pohst,et al. Computing a lattice basis from a system of generating vectors , 1987, EUROCAL.

[11] M. Eichler. Note zur Theorie der Kristallgitter , 1952 .