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Routines to Implement Concepts from Lattice Theory

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
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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.

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

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