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# EDIM

## Elementary Divisors and Integer Matrices

Version 1.3.6

September 2022

Frank Lübeck
Email: Frank.Luebeck@Math.RWTH-Aachen.De
Homepage: https://www.math.rwth-aachen.de/~Frank.Luebeck
Address:
Lehrstuhl D für Mathematik RWTH Aachen Pontdriesch 14/16 52062 Aachen Germany

### Copyright

© 2000-2018 by Frank Lübeck

EDIM is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version.

### Contents

1 The EDIM-Package
1.1 Installation of the EDIM package
1.1-1 InfoEDIM
1.2 \(p\)-Parts of Elementary Divisors
1.2-1 ElementaryDivisorsPPartRk
1.2-2 ElementaryDivisorsPPartHavasSterling
1.3 Inverse of Rational Matrices
1.3-1 InverseRatMat
1.3-2 RationalSolutionIntMat
1.3-3 ExponentSquareIntMatFullRank
1.4 All Elementary Divisors Using p-adic Method
1.4-1 ElementaryDivisorsSquareIntMatFullRank
1.4-2 ElementaryDivisorsIntMatDeterminant
1.5 Gcd and Normal Forms Using LLL
1.5-1 GcdexIntLLL
1.5-2 HermiteIntMatLLL
1.5-3 HermiteIntMatLLLTrans
1.5-4 SmithIntMatLLL
1.5-5 SmithIntMatLLLTrans
1.6 Utility Functions from the EDIM-package
1.6-1 RatNumberFromModular
1.6-2 InverseIntMatMod
1.6-3 HadamardBoundIntMat
1.6-4 CheapFactorsInt
1.6-5 RankMod
1.7 InverseRatMat - the Algorithm
1.7-1 Rank of Integer Matrix
References
Index
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