- To: mathgroup at yoda.physics.unc.edu
- Subject: Re: LatticeReduce
- From: Brian Evans <evans at gauss.eedsp.gatech.edu>
- Date: Wed, 11 Mar 1992 16:53:30 GMT
In response to Shiv Gupta's question about reducing rectangular integer matrices (that represent lattices), Mr. Grayson of Wolfram Research Inc. correctly pointed out that he can reduce the integer matrix to column Hermite form and discard the zero rows. This kind of operation is very common in linear systems and signal processing. In linear systems, coupled systems represented as matrices have Laplace transforms that are matrices of polynomials. These are often reduced using gcd and modulo operations with polynomials into a column Hermite form. In signal processing, lattice theory forms the basis for many multidimensional operations on non-rectangular sampling grids (FFT, etc.). Lattice theory also forms the basis for multidimensional multirate signal processing (filter banks, wavelets, etc.). Since lattice operations are commonly performed in signal processing, I encoded a comprehensive set of lattice operations for the signal processing packages, including row and column Hermite forms, left and right least common multiples, left and right greatest common divisors, and various Smith form decompositions. The routines can show intermediate calculations. They are defined by the file "SignalProcessing/Support/Multirate.m". These have only been a part of the signal processing packages for the last two months or so. The signal processing packages are available via anonymous ftp to gauss.eedsp.gatech.edu (IP #22.214.171.124) in the compressed tar file "Mathematica/SigProc2.0.tar.Z". I hope that his helps. Brian Evans evans at eedsp.gatech.edu P.S. Although I am not a fan of Maple, Maple does provide many lattice operations in its standard library.