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<div class="chlinktop"><span class="chlink1">Goto Chapter: </span><a href="chap0.html">Top</a>  <a href="chap1.html">1</a>  <a href="chapBib.html">Bib</a>  <a href="chapInd.html">Ind</a>  </div>

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<h1><strong class="pkg">EDIM</strong></h1>


<h2>Elementary Divisors and Integer Matrices</h2>

<p>
      Version 1.3.8</p>

<p>February 2024</p>

</div>
<p><b>Frank Lübeck

    
    
    </b>
<br />Email: <span class="URL"><a href="mailto:Frank.Luebeck@Math.RWTH-Aachen.De">Frank.Luebeck@Math.RWTH-Aachen.De</a></span>
<br />Homepage: <span class="URL"><a href="https://www.math.rwth-aachen.de/~Frank.Luebeck">https://www.math.rwth-aachen.de/~Frank.Luebeck</a></span>
<br />Address: <br />Lehrstuhl D für Mathematik RWTH Aachen Pontdriesch 14/16 52062 Aachen Germany
</p>

<p><a id="X81488B807F2A1CF1" name="X81488B807F2A1CF1"></a></p>
<h3>Copyright</h3>
<p>© 2000-2024 by Frank Lübeck</p>

<p><strong class="pkg">EDIM</strong> is free software; you can redistribute it and/or modify it under the terms of the <span class="URL"><a href="https://www.fsf.org/licenses/gpl.html">GNU General Public License</a></span> as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version.</p>

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<h3>Contents<a id="contents" name="contents"></a></h3>

<div class="ContChap"><a href="chap1.html#X7AA826067CC8C395">1 <span class="Heading">The <strong class="pkg">EDIM</strong>-Package</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap1.html#X84D3F5E77E3BF046">1.1 <span class="Heading">Installation of the <strong class="pkg">EDIM</strong> package</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7AF83FEC7CD0311C">1.1-1 InfoEDIM</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap1.html#X818BE04687230849">1.2 <span class="Heading"><span class="SimpleMath">p</span>-Parts of Elementary Divisors</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X813B0D73868CD751">1.2-1 ElementaryDivisorsPPartRk</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X82EC4724865F4DF9">1.2-2 ElementaryDivisorsPPartHavasSterling</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap1.html#X80FF39C07E03D7EF">1.3 <span class="Heading">Inverse of Rational Matrices</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7A9656D47C4D2D16">1.3-1 InverseRatMat</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X8302B31E86B3AFDB">1.3-2 RationalSolutionIntMat</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X86DA61D978D2D889">1.3-3 ExponentSquareIntMatFullRank</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap1.html#X7A6548FA7C837D27">1.4 <span class="Heading">All Elementary Divisors Using p-adic Method</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7B6A3B8486872B0C">1.4-1 ElementaryDivisorsSquareIntMatFullRank</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X821E30477A5DCE68">1.4-2 ElementaryDivisorsIntMatDeterminant</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap1.html#X788047737FA04422">1.5 <span class="Heading">Gcd and Normal Forms Using LLL</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X799B1A5285D00859">1.5-1 GcdexIntLLL</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7C6AE6777B72F9D2">1.5-2 HermiteIntMatLLL</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X862962B7878A284F">1.5-3 HermiteIntMatLLLTrans</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X8626F15179C09798">1.5-4 SmithIntMatLLL</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X86094B1B7C87EBF6">1.5-5 SmithIntMatLLLTrans</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap1.html#X832582857EB36B23">1.6 <span class="Heading">Utility Functions from the <strong class="pkg">EDIM</strong>-package</span></a>
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<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7EC844F97C469C03">1.6-1 RatNumberFromModular</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X78518E1D81435762">1.6-2 InverseIntMatMod</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7CDF3D2081207080">1.6-3 HadamardBoundIntMat</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7BAB977C7EB05067">1.6-4 CheapFactorsInt</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X8312EDA78209B4EA">1.6-5 RankMod</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap1.html#X83FD1AAB7EB2E934">1.7 <span class="Heading">InverseRatMat - the Algorithm</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X791ED7D97F87FDFD">1.7-1 <span class="Heading">Rank of Integer Matrix</span></a>
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</div></div>
</div>
<div class="ContChap"><a href="chapBib.html"><span class="Heading">References</span></a></div>
<div class="ContChap"><a href="chapInd.html"><span class="Heading">Index</span></a></div>
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