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<li class="navelem"><a class="el" href="namespace_lin_box.html">LinBox</a> </li>
<li class="navelem"><a class="el" href="class_lin_box_1_1_smith_form_iliopoulos.html">SmithFormIliopoulos</a> </li>
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<a href="#pro-static-methods">Static Protected Member Functions</a> </div>
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<div class="title">SmithFormIliopoulos Class Reference</div> </div>
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<!-- doxytag: class="LinBox::SmithFormIliopoulos" -->
<p>This is Iliopoulos' algorithm do diagonalize.
<a href="class_lin_box_1_1_smith_form_iliopoulos.html#details">More...</a></p>
<p><code>#include <smith-form-iliopoulos.h></code></p>
<table class="memberdecls">
<tr><td colspan="2"><h2><a name="pro-static-methods"></a>
Static Protected Member Functions</h2></td></tr>
<tr><td class="memTemplParams" colspan="2">template<class Matrix , class Ring > </td></tr>
<tr><td class="memTemplItemLeft" align="right" valign="top">static <a class="el" href="class_lin_box_1_1_zero_one.html">Matrix</a> & </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="class_lin_box_1_1_smith_form_iliopoulos.html#a05223e776923ad354e8a367868271d9c">eliminationRow</a> (<a class="el" href="class_lin_box_1_1_zero_one.html">Matrix</a> &A, const Ring &r)</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">eliminationRow will make the first row (*, 0, ..., 0) by col operations. <a href="#a05223e776923ad354e8a367868271d9c"></a><br/></td></tr>
<tr><td class="memTemplParams" colspan="2">template<class Matrix , class Ring > </td></tr>
<tr><td class="memTemplItemLeft" align="right" valign="top">static <a class="el" href="class_lin_box_1_1_zero_one.html">Matrix</a> & </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="class_lin_box_1_1_smith_form_iliopoulos.html#a63aee05aeb307ee96f53f0fd31aa7239">eliminationCol</a> (<a class="el" href="class_lin_box_1_1_zero_one.html">Matrix</a> &A, const Ring &r)</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">eliminationCol will make the first col (*, 0, ..., 0) by elementary row operation. <a href="#a63aee05aeb307ee96f53f0fd31aa7239"></a><br/></td></tr>
<tr><td class="memTemplParams" colspan="2"><a class="anchor" id="a231b6336921347e4d7db57c857621be8"></a><!-- doxytag: member="LinBox::SmithFormIliopoulos::diagonalizationIn" ref="a231b6336921347e4d7db57c857621be8" args="(Matrix &A, const Ring &r)" -->
template<class Matrix , class Ring > </td></tr>
<tr><td class="memTemplItemLeft" align="right" valign="top">static <a class="el" href="class_lin_box_1_1_zero_one.html">Matrix</a> & </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="class_lin_box_1_1_smith_form_iliopoulos.html#a231b6336921347e4d7db57c857621be8">diagonalizationIn</a> (<a class="el" href="class_lin_box_1_1_zero_one.html">Matrix</a> &A, const Ring &r)</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Diagonalize the matrix A. <br/></td></tr>
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<hr/><a name="details" id="details"></a><h2>Detailed Description</h2>
<div class="textblock"><p>This is Iliopoulos' algorithm do diagonalize. </p>
<p>Compute Smith Form by elimination modulo m, for some modulus m such as S(n), the last invariant factor. The elimination method is originally described in </p>
<dl class="bib"><dt><b><a class="el" href="bib.html#_bib000016">Bibliography:</a></b></dt><dd><em>Worst Case Complexity Bounds on Algorithms for computing the Canonical Structure of Finite Abelian Groups and the Hermite and Smith Normal Forms of an Integer Matrix</em>, by Costas Iliopoulos. </dd></dl>
</div><hr/><h2>Member Function Documentation</h2>
<a class="anchor" id="a05223e776923ad354e8a367868271d9c"></a><!-- doxytag: member="LinBox::SmithFormIliopoulos::eliminationRow" ref="a05223e776923ad354e8a367868271d9c" args="(Matrix &A, const Ring &r)" -->
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<td class="memname">static <a class="el" href="class_lin_box_1_1_zero_one.html">Matrix</a>& eliminationRow </td>
<td>(</td>
<td class="paramtype"><a class="el" href="class_lin_box_1_1_zero_one.html">Matrix</a> & </td>
<td class="paramname"><em>A</em>, </td>
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<td class="paramkey"></td>
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<td class="paramtype">const Ring & </td>
<td class="paramname"><em>r</em> </td>
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<td></td>
<td>)</td>
<td></td><td><code> [inline, static, protected]</code></td>
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<p>eliminationRow will make the first row (*, 0, ..., 0) by col operations. </p>
<p>It is the implementation of Iliopoulos algorithm </p>
</div>
</div>
<a class="anchor" id="a63aee05aeb307ee96f53f0fd31aa7239"></a><!-- doxytag: member="LinBox::SmithFormIliopoulos::eliminationCol" ref="a63aee05aeb307ee96f53f0fd31aa7239" args="(Matrix &A, const Ring &r)" -->
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<td class="memname">static <a class="el" href="class_lin_box_1_1_zero_one.html">Matrix</a>& eliminationCol </td>
<td>(</td>
<td class="paramtype"><a class="el" href="class_lin_box_1_1_zero_one.html">Matrix</a> & </td>
<td class="paramname"><em>A</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">const Ring & </td>
<td class="paramname"><em>r</em> </td>
</tr>
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<td></td>
<td>)</td>
<td></td><td><code> [inline, static, protected]</code></td>
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<div class="memdoc">
<p>eliminationCol will make the first col (*, 0, ..., 0) by elementary row operation. </p>
<p>It is the implementation of Iliopoulos algorithm </p>
</div>
</div>
<hr/>The documentation for this class was generated from the following file:<ul>
<li>smith-form-iliopoulos.h</li>
</ul>
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