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Routines to Implement Concepts from Lattice Theory
Authors

Brian L. Evans
Organization: University of Texas
Department: Department of Electrical and Computer Engineering
URL: http://www.ece.utexas.edu/~bevans/
James H. McClellan
Organization: Georgia Tech
Old MathSource #

0204-556
Revision date

1992-09-01
Description

This package provides some of the functions that are common in lattice theory (such as computing distinct coset vectors) and the geometry of numbers (such as the Bézout identity and generalized Euclid factors) that are not implemented in Mathematica. These routines form the basis for multirate signal processing.
Subjects

*Engineering > Signal Processing
*Mathematica Technology > Programming
*Mathematics > Algebra > Linear Algebra
*Mathematics > Foundations of Mathematics > Set Theory
*Mathematics > Number Theory
Keywords

Pure Mathematics, Signal Processing, Engineering, Communications Engineering, Electrical Engineering, multirate signal processing, lattice theory, coset vector, Bezout identity, Euclid factors, downsampling, sampling matrix, upsampling, BezoutNumbers, ColumnHermiteForm, CommutableResamplingMatricesQ, DiagonalMatrixQ, DistinctCosetVectors, GCLD, GCRD, IncList, ImpulseTrain, IntegerVectorQ, LCLM, LCRM, NormalizeSamplingMatrix, RegUnimodularResMatrixQ, RelativelyPrime, ReorderResampling, ResamplingMatrix, ResamplingMatrixMod, RowHermiteForm, SmithFormPivot, SmithFormSameU, SmithFormSameV, SmithLLLForm, SmithNormalForm, SmithOrderedForm, SmithReducedForm, UpsampledSystem
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LatticeTheory.m (52 KB) - Mathematica package