<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
<html xmlns="http://www.w3.org/1999/xhtml">
<head>
<meta http-equiv="Content-Type" content="text/xhtml;charset=UTF-8"/>
<title>linbox: p-adic lifting for linear system solutions.</title>
<link href="tabs.css" rel="stylesheet" type="text/css"/>
<link href="doxygen.css" rel="stylesheet" type="text/css"/>
</head>
<body>
<!-- Generated by Doxygen 1.7.4 -->
<script type="text/javascript">
function hasClass(ele,cls) {
return ele.className.match(new RegExp('(\\s|^)'+cls+'(\\s|$)'));
}
function addClass(ele,cls) {
if (!this.hasClass(ele,cls)) ele.className += " "+cls;
}
function removeClass(ele,cls) {
if (hasClass(ele,cls)) {
var reg = new RegExp('(\\s|^)'+cls+'(\\s|$)');
ele.className=ele.className.replace(reg,' ');
}
}
function toggleVisibility(linkObj) {
var base = linkObj.getAttribute('id');
var summary = document.getElementById(base + '-summary');
var content = document.getElementById(base + '-content');
var trigger = document.getElementById(base + '-trigger');
if ( hasClass(linkObj,'closed') ) {
summary.style.display = 'none';
content.style.display = 'block';
trigger.src = 'open.png';
removeClass(linkObj,'closed');
addClass(linkObj,'opened');
} else if ( hasClass(linkObj,'opened') ) {
summary.style.display = 'block';
content.style.display = 'none';
trigger.src = 'closed.png';
removeClass(linkObj,'opened');
addClass(linkObj,'closed');
}
return false;
}
</script>
<div id="top">
<div id="titlearea">
<table cellspacing="0" cellpadding="0">
<tbody>
<tr style="height: 56px;">
<td style="padding-left: 0.5em;">
<div id="projectname">linbox</div>
</td>
</tr>
</tbody>
</table>
</div>
<div id="navrow1" class="tabs">
<ul class="tablist">
<li><a href="index.html"><span>Main Page</span></a></li>
<li><a href="pages.html"><span>Related Pages</span></a></li>
<li><a href="modules.html"><span>Modules</span></a></li>
<li><a href="namespaces.html"><span>Namespaces</span></a></li>
<li><a href="annotated.html"><span>Data Structures</span></a></li>
<li><a href="files.html"><span>Files</span></a></li>
<li><a href="dirs.html"><span>Directories</span></a></li>
<li><a href="examples.html"><span>Examples</span></a></li>
</ul>
</div>
</div>
<div class="header">
<div class="summary">
<a href="#nested-classes">Data Structures</a> |
<a href="#enum-members">Enumerations</a> </div>
<div class="headertitle">
<div class="title">p-adic lifting for linear system solutions.</div> </div>
<div class="ingroups"><a class="el" href="group__algorithms.html">algorithms</a></div></div>
<div class="contents">
<p>interface for solving linear system by p-adic lifting technique over the quotient field of a ring.
<a href="#details">More...</a></p>
<table class="memberdecls">
<tr><td colspan="2"><h2><a name="nested-classes"></a>
Data Structures</h2></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">class  </td><td class="memItemRight" valign="bottom"><a class="el" href="class_lin_box_1_1_rational_solver.html">RationalSolver< Ring, Field, RandomPrime, MethodTraits ></a></td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Interface for the different specialization of p-adic lifting based solvers. <a href="class_lin_box_1_1_rational_solver.html#details">More...</a><br/></td></tr>
<tr><td colspan="2"><h2><a name="enum-members"></a>
Enumerations</h2></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">enum  </td><td class="memItemRight" valign="bottom"><a class="el" href="group__padic.html#gabf95d1fb4fcd12ca89717f0be14212a1">SolverReturnStatus</a> </td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">define the different return status of the p-adic based solver's computation. <br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">enum  </td><td class="memItemRight" valign="bottom"><a class="el" href="group__padic.html#gaee2ff986111a9d28c71343fbdc651a9f">SolverLevel</a> </td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Define the different strategy which can be used in the p-adic based solver. <a href="group__padic.html#gaee2ff986111a9d28c71343fbdc651a9f">More...</a><br/></td></tr>
</table>
<hr/><a name="details" id="details"></a><h2>Detailed Description</h2>
<p>interface for solving linear system by p-adic lifting technique over the quotient field of a ring. </p>
<p>i.e. solution over the rational for an integer linear system.</p>
<dl class="user"><dt><b>Headers</b></dt><dd><code>#include <<a class="el" href="rational-solver_8h.html" title="Rational solving (Dixon, Wiedemann,...)">linbox/algorithms/rational-solver.h</a>></code></dd></dl>
<p>See the following reference for details on this algorithm: </p>
<dl class="bib"><dt><b><a class="el" href="bib.html#_bib000008">Bibliography:</a></b></dt><dd></dd></dl>
<p>- Robert T. Moenck and John H. Carter <em>Approximate algorithms to derive exact solutions to system of linear equations.</em> In Proc. EUROSAM'79, volume 72 of Lectures Note in Computer Science, pages 65-72, Berlin-Heidelberger-New York, 1979. Springer-Verlag.</p>
<ul>
<li>John D. Dixon <em>Exact Solution of linear equations using p-adic expansions.</em> Numerische Mathematik, volume 40, pages 137-141, 1982.</li>
</ul>
<hr/><h2>Enumeration Type Documentation</h2>
<a class="anchor" id="gaee2ff986111a9d28c71343fbdc651a9f"></a><!-- doxytag: member="LinBox::SolverLevel" ref="gaee2ff986111a9d28c71343fbdc651a9f" args="" -->
<div class="memitem">
<div class="memproto">
<table class="memname">
<tr>
<td class="memname">enum SolverLevel</td>
</tr>
</table>
</div>
<div class="memdoc">
<p>Define the different strategy which can be used in the p-adic based solver. </p>
<p>Used to determine what level of solving should be done:</p>
<ul>
<li>Monte Carlo: Try to solve if possible, but result is not guaranteed. In any case a 0 denominator should not be returned.</li>
<li>Las Vegas : Result should be guaranteed correct.</li>
<li>Certified : Additionally, provide certificates that the result returned is correct.<ul>
<li>if the return value is <code>SS_INCONSISTENT</code>, this means <code>lastCertificate</code> satisfies <img class="formulaInl" alt="$lC \cdot A = 0$" src="form_15.png"/> and <img class="formulaInl" alt="$lC \cdot b \neq 0 $" src="form_16.png"/></li>
<li>if diophantine solving was called and the return value is <code>SS_OK</code>, this means <code>lastCertificate</code> satisfies <img class="formulaInl" alt="$ \mathrm{den}(lC \cdot A) = 1, \mathrm{den}(lC \cdot b) = \mathrm{den}(answer) $" src="form_17.png"/></li>
</ul>
</li>
</ul>
</div>
</div>
</div>
<hr class="footer"/><address class="footer"><small>Generated on Tue Aug 30 2011 for linbox by 
<a href="http://www.doxygen.org/index.html">
<img class="footer" src="doxygen.png" alt="doxygen"/></a> 1.7.4 </small></address>
</body>
</html>
