- 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,
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 #220.127.116.11) in the compressed
tar file "Mathematica/SigProc2.0.tar.Z".
I hope that his helps.
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.
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