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<div class="title">DiophantineSolver< QSolver > Class Template Reference</div> </div>
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<!-- doxytag: class="LinBox::DiophantineSolver" -->
<p>DiophantineSolver<QSolver> creates a diophantine solver using a QSolver to generate rational solutions.
<a href="class_lin_box_1_1_diophantine_solver.html#details">More...</a></p>
<p><code>#include <diophantine-solver.h></code></p>
<table class="memberdecls">
<tr><td colspan="2"><h2><a name="pub-methods"></a>
Public Member Functions</h2></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_lin_box_1_1_diophantine_solver.html#a9b6974839e76772aec40cf0de16e8417">DiophantineSolver</a> (QSolver &rs)</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Constructor from a rationalSolver. <a href="#a9b6974839e76772aec40cf0de16e8417"></a><br/></td></tr>
<tr><td class="memTemplParams" colspan="2">template<class IMatrix , class Vector1 , class Vector2 > </td></tr>
<tr><td class="memTemplItemLeft" align="right" valign="top"><a class="el" href="group__padic.html#gabf95d1fb4fcd12ca89717f0be14212a1">SolverReturnStatus</a> </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="class_lin_box_1_1_diophantine_solver.html#a5dfcab907a2c983cbd7d68bad5a1bbaf">solve</a> (Vector1 &x, Integer &den, const IMatrix &A, const Vector2 &b, const int maxPrimes=DEFAULT_MAXPRIMES, const <a class="el" href="group__padic.html#gaee2ff986111a9d28c71343fbdc651a9f">SolverLevel</a> level=SL_DEFAULT)</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Solve a linear system <code>Ax=b</code> over quotient field of a ring. <a href="#a5dfcab907a2c983cbd7d68bad5a1bbaf"></a><br/></td></tr>
<tr><td class="memTemplParams" colspan="2">template<class IMatrix , class Vector1 , class Vector2 > </td></tr>
<tr><td class="memTemplItemLeft" align="right" valign="top"><a class="el" href="group__padic.html#gabf95d1fb4fcd12ca89717f0be14212a1">SolverReturnStatus</a> </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="class_lin_box_1_1_diophantine_solver.html#a0800abd4fbb0a1acf2d3eb020dec152f">randomSolve</a> (Vector1 &x, Integer &den, const IMatrix &A, const Vector2 &b, const int maxPrimes=DEFAULT_MAXPRIMES, const <a class="el" href="group__padic.html#gaee2ff986111a9d28c71343fbdc651a9f">SolverLevel</a> level=SL_DEFAULT)</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Find a random solution of the general linear system <code>Ax=b</code> over quotient field of a ring. <a href="#a0800abd4fbb0a1acf2d3eb020dec152f"></a><br/></td></tr>
<tr><td class="memTemplParams" colspan="2">template<class IMatrix , class Vector1 , class Vector2 > </td></tr>
<tr><td class="memTemplItemLeft" align="right" valign="top"><a class="el" href="group__padic.html#gabf95d1fb4fcd12ca89717f0be14212a1">SolverReturnStatus</a> </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="class_lin_box_1_1_diophantine_solver.html#ae31dda79cd513fe2e2d5d9f461d5e441">diophantineSolve</a> (Vector1 &x, Integer &den, const IMatrix &A, const Vector2 &b, const int maxPrimes=DEFAULT_MAXPRIMES, const <a class="el" href="group__padic.html#gaee2ff986111a9d28c71343fbdc651a9f">SolverLevel</a> level=SL_DEFAULT)</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Find a solution of the linear system <code>Ax=b</code> whose denominator (when written as an integer vector over a single denom) is minimal. <a href="#ae31dda79cd513fe2e2d5d9f461d5e441"></a><br/></td></tr>
</table>
<hr/><a name="details" id="details"></a><h2>Detailed Description</h2>
<div class="textblock"><h3>template<class QSolver><br/>
class LinBox::DiophantineSolver< QSolver ></h3>
<p>DiophantineSolver<QSolver> creates a diophantine solver using a QSolver to generate rational solutions. </p>
<p>Methods solve, randomSolve just expose functions from underlying rational solver. <a class="el" href="struct_lin_box_1_1_method.html" title="Method specifiers for controlling algorithm choice.">Method</a> diophantineSolve creates a solution with minimal denominator, and can also create a certificate of minimality (described in 'Certified Dense Linear System Solving' by Mulders+Storjohann) which will be left in the public field lastCertificate. </p>
</div><hr/><h2>Constructor & Destructor Documentation</h2>
<a class="anchor" id="a9b6974839e76772aec40cf0de16e8417"></a><!-- doxytag: member="LinBox::DiophantineSolver::DiophantineSolver" ref="a9b6974839e76772aec40cf0de16e8417" args="(QSolver &rs)" -->
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<td class="memname"><a class="el" href="class_lin_box_1_1_diophantine_solver.html">DiophantineSolver</a> </td>
<td>(</td>
<td class="paramtype">QSolver & </td>
<td class="paramname"><em>rs</em></td><td>)</td>
<td><code> [inline]</code></td>
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<p>Constructor from a rationalSolver. </p>
<dl><dt><b>Parameters:</b></dt><dd>
<table class="params">
<tr><td class="paramname">rs</td><td>a rationalSolver </td></tr>
</table>
</dd>
</dl>
</div>
</div>
<hr/><h2>Member Function Documentation</h2>
<a class="anchor" id="a5dfcab907a2c983cbd7d68bad5a1bbaf"></a><!-- doxytag: member="LinBox::DiophantineSolver::solve" ref="a5dfcab907a2c983cbd7d68bad5a1bbaf" args="(Vector1 &x, Integer &den, const IMatrix &A, const Vector2 &b, const int maxPrimes=DEFAULT_MAXPRIMES, const SolverLevel level=SL_DEFAULT)" -->
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<td class="memname"><a class="el" href="group__padic.html#gabf95d1fb4fcd12ca89717f0be14212a1">SolverReturnStatus</a> solve </td>
<td>(</td>
<td class="paramtype">Vector1 & </td>
<td class="paramname"><em>x</em>, </td>
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<td class="paramkey"></td>
<td></td>
<td class="paramtype">Integer & </td>
<td class="paramname"><em>den</em>, </td>
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<td class="paramkey"></td>
<td></td>
<td class="paramtype">const IMatrix & </td>
<td class="paramname"><em>A</em>, </td>
</tr>
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<td class="paramkey"></td>
<td></td>
<td class="paramtype">const Vector2 & </td>
<td class="paramname"><em>b</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">const int </td>
<td class="paramname"><em>maxPrimes</em> = <code>DEFAULT_MAXPRIMES</code>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">const <a class="el" href="group__padic.html#gaee2ff986111a9d28c71343fbdc651a9f">SolverLevel</a> </td>
<td class="paramname"><em>level</em> = <code>SL_DEFAULT</code> </td>
</tr>
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<td></td>
<td>)</td>
<td></td><td></td>
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<div class="memdoc">
<p>Solve a linear system <code>Ax=b</code> over quotient field of a ring. </p>
<dl><dt><b>Parameters:</b></dt><dd>
<table class="params">
<tr><td class="paramname">A</td><td>Matrix of linear system </td></tr>
<tr><td class="paramname">x</td><td>Vector in which to store solution </td></tr>
<tr><td class="paramname">b</td><td>Right-hand side of system </td></tr>
<tr><td class="paramname">maxPrimes</td><td>maximum number of moduli to try </td></tr>
<tr><td class="paramname">level</td><td>level of certification to be used </td></tr>
<tr><td class="paramname">den</td><td></td></tr>
</table>
</dd>
</dl>
<dl class="return"><dt><b>Returns:</b></dt><dd>status of solution. if <code></code>(return != SS_FAILED), and <code></code>(level >= SL_LASVEGAS), solution is guaranteed correct. <code>SS_FAILED</code> - all primes used were bad <code>SS_OK</code> - solution found. <code>SS_INCONSISTENT</code> - system appreared inconsistent. certificate is in <code>lastCertificate</code> if <code></code>(level >= SL_CERTIFIED) </dd></dl>
</div>
</div>
<a class="anchor" id="a0800abd4fbb0a1acf2d3eb020dec152f"></a><!-- doxytag: member="LinBox::DiophantineSolver::randomSolve" ref="a0800abd4fbb0a1acf2d3eb020dec152f" args="(Vector1 &x, Integer &den, const IMatrix &A, const Vector2 &b, const int maxPrimes=DEFAULT_MAXPRIMES, const SolverLevel level=SL_DEFAULT)" -->
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<td class="memname"><a class="el" href="group__padic.html#gabf95d1fb4fcd12ca89717f0be14212a1">SolverReturnStatus</a> randomSolve </td>
<td>(</td>
<td class="paramtype">Vector1 & </td>
<td class="paramname"><em>x</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">Integer & </td>
<td class="paramname"><em>den</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">const IMatrix & </td>
<td class="paramname"><em>A</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">const Vector2 & </td>
<td class="paramname"><em>b</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">const int </td>
<td class="paramname"><em>maxPrimes</em> = <code>DEFAULT_MAXPRIMES</code>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">const <a class="el" href="group__padic.html#gaee2ff986111a9d28c71343fbdc651a9f">SolverLevel</a> </td>
<td class="paramname"><em>level</em> = <code>SL_DEFAULT</code> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div>
<div class="memdoc">
<p>Find a random solution of the general linear system <code>Ax=b</code> over quotient field of a ring. </p>
<dl><dt><b>Parameters:</b></dt><dd>
<table class="params">
<tr><td class="paramname">A</td><td>Matrix of linear system </td></tr>
<tr><td class="paramname">x</td><td>Vector in which to store solution </td></tr>
<tr><td class="paramname">b</td><td>Right-hand side of system </td></tr>
<tr><td class="paramname">maxPrimes</td><td>maximum number of moduli to try </td></tr>
<tr><td class="paramname">level</td><td>level of certification to be used </td></tr>
<tr><td class="paramname">den</td><td></td></tr>
</table>
</dd>
</dl>
<dl class="return"><dt><b>Returns:</b></dt><dd>status of solution. if <code></code>(return != SS_FAILED), and <code></code>(level >= SL_LASVEGAS), solution is guaranteed correct. <code>SS_FAILED</code> - all primes used were bad <code>SS_OK</code> - solution found. <code>SS_INCONSISTENT</code> - system appreared inconsistent. certificate is in <code>lastCertificate</code> if <code></code>(level >= SL_CERTIFIED) </dd></dl>
</div>
</div>
<a class="anchor" id="ae31dda79cd513fe2e2d5d9f461d5e441"></a><!-- doxytag: member="LinBox::DiophantineSolver::diophantineSolve" ref="ae31dda79cd513fe2e2d5d9f461d5e441" args="(Vector1 &x, Integer &den, const IMatrix &A, const Vector2 &b, const int maxPrimes=DEFAULT_MAXPRIMES, const SolverLevel level=SL_DEFAULT)" -->
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<td class="memname"><a class="el" href="group__padic.html#gabf95d1fb4fcd12ca89717f0be14212a1">SolverReturnStatus</a> diophantineSolve </td>
<td>(</td>
<td class="paramtype">Vector1 & </td>
<td class="paramname"><em>x</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">Integer & </td>
<td class="paramname"><em>den</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">const IMatrix & </td>
<td class="paramname"><em>A</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">const Vector2 & </td>
<td class="paramname"><em>b</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">const int </td>
<td class="paramname"><em>maxPrimes</em> = <code>DEFAULT_MAXPRIMES</code>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">const <a class="el" href="group__padic.html#gaee2ff986111a9d28c71343fbdc651a9f">SolverLevel</a> </td>
<td class="paramname"><em>level</em> = <code>SL_DEFAULT</code> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div>
<div class="memdoc">
<p>Find a solution of the linear system <code>Ax=b</code> whose denominator (when written as an integer vector over a single denom) is minimal. </p>
<dl><dt><b>Parameters:</b></dt><dd>
<table class="params">
<tr><td class="paramname">A</td><td>Matrix of linear system </td></tr>
<tr><td class="paramname">x</td><td>Vector in which to store solution </td></tr>
<tr><td class="paramname">b</td><td>Right-hand side of system </td></tr>
<tr><td class="paramname">maxPrimes</td><td>maximum number of moduli to try </td></tr>
<tr><td class="paramname">level</td><td>level of certification to be used </td></tr>
<tr><td class="paramname">den</td><td></td></tr>
</table>
</dd>
</dl>
<dl class="return"><dt><b>Returns:</b></dt><dd>status of solution. if <code></code>(return != SS_FAILED) and <code></code>(level >= SL_LASVEGAS), solution is guaranteed correct if <code></code>(return == SS_OK) and <code></code>(level >= SL_LASVEGAS), solution is guaranteed minimal. <code>SS_FAILED</code> - all primes used were bad <code>SS_OK</code> - solution found. certificate of minimality is in lastCertificate if <code></code>(level >= SL_CERTIFIED) <code>SS_INCONSISTENT</code> - system appreared inconsistent. certificate of inconsistency is in <code>lastCertificate</code> if <code></code>(level >= SL_CERTIFIED)</dd>
<dd>
status of solution - OK, FAILED, SINGULAR, INCONSISTENT, BAD_PRECONDITIONER </dd></dl>
</div>
</div>
<hr/>The documentation for this class was generated from the following files:<ul>
<li>diophantine-solver.h</li>
<li>diophantine-solver.inl</li>
</ul>
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