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<div class="title">algorithms</div> </div>
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<p>The core linear algebra algorithms of <a class="el" href="namespace_lin_box.html" title="Namespace in which all linbox code resides.">LinBox</a>.
<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_blackbox_container_symmetrize.html">BlackboxContainerSymmetrize< Field, _Blackbox, RandIter ></a></td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Symmetrizing iterator (for rank computations). <a href="class_lin_box_1_1_blackbox_container_symmetrize.html#details">More...</a><br/></td></tr>
<tr><td colspan="2"><h2><a name="groups"></a>
Modules</h2></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"> </td><td class="memItemRight" valign="bottom"><a class="el" href="group___c_r_a.html">Chinese Remaindering Algorithm</a></td></tr>
<p><tr><td class="mdescLeft"> </td><td class="mdescRight"><p>Chinese Remaindering (<code>cra</code>) in <a class="el" href="namespace_lin_box.html" title="Namespace in which all linbox code resides.">LinBox</a>. </p>
<br/></td></tr>
</p>
<tr><td class="memItemLeft" align="right" valign="top"> </td><td class="memItemRight" valign="bottom"><a class="el" href="group__diophant.html">Diophantine solvers</a></td></tr>
<p><tr><td class="mdescLeft"> </td><td class="mdescRight"><p>NO DOC YET. </p>
<br/></td></tr>
</p>
<tr><td class="memItemLeft" align="right" valign="top"> </td><td class="memItemRight" valign="bottom"><a class="el" href="group__elim.html">Elimination</a></td></tr>
<p><tr><td class="mdescLeft"> </td><td class="mdescRight"><p>NO DOC YET. </p>
<br/></td></tr>
</p>
<tr><td class="memItemLeft" align="right" valign="top"> </td><td class="memItemRight" valign="bottom"><a class="el" href="group__lanczos.html">Lanczos</a></td></tr>
<p><tr><td class="mdescLeft"> </td><td class="mdescRight"><p>NO DOC YET. </p>
<br/></td></tr>
</p>
<tr><td class="memItemLeft" align="right" valign="top"> </td><td class="memItemRight" valign="bottom"><a class="el" href="group__padic.html">p-adic lifting for linear system solutions.</a></td></tr>
<p><tr><td class="mdescLeft"> </td><td class="mdescRight"><p>interface for solving linear system by p-adic lifting technique over the quotient field of a ring. </p>
<br/></td></tr>
</p>
<tr><td class="memItemLeft" align="right" valign="top"> </td><td class="memItemRight" valign="bottom"><a class="el" href="group__sigmabase.html">Sigma-basis</a></td></tr>
<p><tr><td class="mdescLeft"> </td><td class="mdescRight"><p>NO DOC YET. </p>
<br/></td></tr>
</p>
<tr><td class="memItemLeft" align="right" valign="top"> </td><td class="memItemRight" valign="bottom"><a class="el" href="group__wiedemann.html">Wiedemann</a></td></tr>
<p><tr><td class="mdescLeft"> </td><td class="mdescRight"><p>NO DOC YET. </p>
<br/></td></tr>
</p>
<tr><td class="memItemLeft" align="right" valign="top"> </td><td class="memItemRight" valign="bottom"><a class="el" href="group___solvers.html">Solvers</a></td></tr>
<tr><td colspan="2"><h2><a name="files"></a>
Files</h2></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">file  </td><td class="memItemRight" valign="bottom"><a class="el" href="bbcharpoly_8h.html">bbcharpoly.h</a></td></tr>
<p><tr><td class="mdescLeft"> </td><td class="mdescRight"><p>no doc. </p>
<br/></td></tr>
</p>
<tr><td class="memItemLeft" align="right" valign="top">file  </td><td class="memItemRight" valign="bottom"><a class="el" href="blackbox-block-container-base_8h.html">blackbox-block-container-base.h</a></td></tr>
<p><tr><td class="mdescLeft"> </td><td class="mdescRight"><p>NO DOC. </p>
<br/></td></tr>
</p>
<tr><td class="memItemLeft" align="right" valign="top">file  </td><td class="memItemRight" valign="bottom"><a class="el" href="blackbox-block-container_8h.html">blackbox-block-container.h</a></td></tr>
<p><tr><td class="mdescLeft"> </td><td class="mdescRight"><p>no doc. </p>
<br/></td></tr>
</p>
<tr><td class="memItemLeft" align="right" valign="top">file  </td><td class="memItemRight" valign="bottom"><a class="el" href="blas-domain_8h.html">blas-domain.h</a></td></tr>
<p><tr><td class="mdescLeft"> </td><td class="mdescRight"><p>NO DOC. </p>
<br/></td></tr>
</p>
<tr><td class="memItemLeft" align="right" valign="top">file  </td><td class="memItemRight" valign="bottom"><a class="el" href="cra-domain_8h.html">cra-domain.h</a></td></tr>
<p><tr><td class="mdescLeft"> </td><td class="mdescRight"><p>Wrapper around OMP/SEQ version of ChineseRemainder. </p>
<br/></td></tr>
</p>
<tr><td class="memItemLeft" align="right" valign="top">file  </td><td class="memItemRight" valign="bottom"><a class="el" href="cra-early-multip_8h.html">cra-early-multip.h</a></td></tr>
<p><tr><td class="mdescLeft"> </td><td class="mdescRight"><p>NO DOC. </p>
<br/></td></tr>
</p>
<tr><td class="memItemLeft" align="right" valign="top">file  </td><td class="memItemRight" valign="bottom"><a class="el" href="cra-early-single_8h.html">cra-early-single.h</a></td></tr>
<p><tr><td class="mdescLeft"> </td><td class="mdescRight"><p>NO DOC. </p>
<br/></td></tr>
</p>
<tr><td class="memItemLeft" align="right" valign="top">file  </td><td class="memItemRight" valign="bottom"><a class="el" href="cra-full-multip-fixed_8h.html">cra-full-multip-fixed.h</a></td></tr>
<p><tr><td class="mdescLeft"> </td><td class="mdescRight"><p>CRA for multi-residues. </p>
<br/></td></tr>
</p>
<tr><td class="memItemLeft" align="right" valign="top">file  </td><td class="memItemRight" valign="bottom"><a class="el" href="cra-full-multip_8h.html">cra-full-multip.h</a></td></tr>
<p><tr><td class="mdescLeft"> </td><td class="mdescRight"><p>NO DOC. </p>
<br/></td></tr>
</p>
<tr><td class="memItemLeft" align="right" valign="top">file  </td><td class="memItemRight" valign="bottom"><a class="el" href="cra-givrnsfixed_8h.html">cra-givrnsfixed.h</a></td></tr>
<p><tr><td class="mdescLeft"> </td><td class="mdescRight"><p>NO DOC. </p>
<br/></td></tr>
</p>
<tr><td class="memItemLeft" align="right" valign="top">file  </td><td class="memItemRight" valign="bottom"><a class="el" href="cra-kaapi_8h.html">cra-kaapi.h</a></td></tr>
<p><tr><td class="mdescLeft"> </td><td class="mdescRight"><p>NO DOC. </p>
<br/></td></tr>
</p>
<tr><td class="memItemLeft" align="right" valign="top">file  </td><td class="memItemRight" valign="bottom"><a class="el" href="lifting-container_8h.html">lifting-container.h</a></td></tr>
<p><tr><td class="mdescLeft"> </td><td class="mdescRight"><p>Lifting from <code>mod p^n</code> to rationals NO DOC. </p>
<br/></td></tr>
</p>
<tr><td class="memItemLeft" align="right" valign="top">file  </td><td class="memItemRight" valign="bottom"><a class="el" href="matrix-hom_8h.html">matrix-hom.h</a></td></tr>
<p><tr><td class="mdescLeft"> </td><td class="mdescRight"><p>Matrix Homomorphism A map function converts a matrix on a field/ring to its natural image in another field/ring. </p>
<br/></td></tr>
</p>
<tr><td class="memItemLeft" align="right" valign="top">file  </td><td class="memItemRight" valign="bottom"><a class="el" href="rational-reconstruction_8h.html">rational-reconstruction.h</a></td></tr>
<p><tr><td class="mdescLeft"> </td><td class="mdescRight"><p>NO DOC. </p>
<br/></td></tr>
</p>
<tr><td class="memItemLeft" align="right" valign="top">file  </td><td class="memItemRight" valign="bottom"><a class="el" href="rational-solver_8h.html">rational-solver.h</a></td></tr>
<p><tr><td class="mdescLeft"> </td><td class="mdescRight"><p>Rational solving (Dixon, Wiedemann,...) </p>
<br/></td></tr>
</p>
<tr><td class="memItemLeft" align="right" valign="top">file  </td><td class="memItemRight" valign="bottom"><a class="el" href="rns_8h.html">rns.h</a></td></tr>
<p><tr><td class="mdescLeft"> </td><td class="mdescRight"><p><b>R</b>esidue <b>N</b>umber <b>S</b>ystem tools. </p>
<br/></td></tr>
</p>
<tr><td class="memItemLeft" align="right" valign="top">file  </td><td class="memItemRight" valign="bottom"><a class="el" href="rns_8inl.html">rns.inl</a></td></tr>
<p><tr><td class="mdescLeft"> </td><td class="mdescRight"><p><b>R</b>esidue <b>N</b>umber <b>S</b>ystem implementation. </p>
<br/></td></tr>
</p>
<tr><td class="memItemLeft" align="right" valign="top">file  </td><td class="memItemRight" valign="bottom"><a class="el" href="smith-form-adaptive_8h.html">smith-form-adaptive.h</a></td></tr>
<p><tr><td class="mdescLeft"> </td><td class="mdescRight"><p>Implement the adaptive algorithm for Smith form computation. </p>
<br/></td></tr>
</p>
<tr><td class="memItemLeft" align="right" valign="top">file  </td><td class="memItemRight" valign="bottom"><a class="el" href="wiedemann_8h.html">wiedemann.h</a></td></tr>
<p><tr><td class="mdescLeft"> </td><td class="mdescRight"><p>minpoly computation and Wiedeman solvers. </p>
<br/></td></tr>
</p>
<tr><td colspan="2"><h2><a name="func-members"></a>
Functions</h2></td></tr>
<tr><td class="memTemplParams" colspan="2">template<class Polynomial , class Blackbox > </td></tr>
<tr><td class="memTemplItemLeft" align="right" valign="top">Polynomial & </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="group__algorithms.html#ga1ef0e9d69b30d9e2db5e3c52a6bf0839">cia</a> (Polynomial &P, const Blackbox &A, const Method::BlasElimination &M)</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Algorithm computing the integer characteristic polynomial of a dense matrix. <a href="#ga1ef0e9d69b30d9e2db5e3c52a6bf0839"></a><br/></td></tr>
</table>
<hr/><a name="details" id="details"></a><h2>Detailed Description</h2>
<p>The core linear algebra algorithms of <a class="el" href="namespace_lin_box.html" title="Namespace in which all linbox code resides.">LinBox</a>. </p>
<p>The codes here implement algorithms for linear algebra problems. The names often reflect the authorship of the central algorithm (Lanczos, Wiedemann, ...). In contrast, the "drivers" in the <a class="el" href="group__solutions.html">solutions</a> directory are named for the problem solved (rank, det, ...). Those are generally wrappers of algorithms from this directory. Their purpose is to give a simple and direct user interface and sometimes to provide a solution strategy which is a hybrid of algorithms from this directory.</p>
<p>Algorithm classes and functions generally have the field class as a template parameter. Blackbox algorithms may have a BlackboxMatrix parameter or allow a Blackbox class as template parameter. Elimination codes work over DenseMatrix or SparseMatrix types with varying degrees of substitution among the types possible. </p>
<hr/><h2>Function Documentation</h2>
<a class="anchor" id="ga1ef0e9d69b30d9e2db5e3c52a6bf0839"></a><!-- doxytag: member="LinBox::cia" ref="ga1ef0e9d69b30d9e2db5e3c52a6bf0839" args="(Polynomial &P, const Blackbox &A, const Method::BlasElimination &M)" -->
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<td class="memname">Polynomial& LinBox::cia </td>
<td>(</td>
<td class="paramtype">Polynomial & </td>
<td class="paramname"><em>P</em>, </td>
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<td class="paramkey"></td>
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<td class="paramtype">const Blackbox & </td>
<td class="paramname"><em>A</em>, </td>
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<td class="paramtype">const Method::BlasElimination & </td>
<td class="paramname"><em>M</em> </td>
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<td>)</td>
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<div class="memdoc">
<p>Algorithm computing the integer characteristic polynomial of a dense matrix. </p>
<dl class="bib"><dt><b><a class="el" href="bib.html#_bib000003">Bibliography:</a></b></dt><dd>[Dumas-Pernet-Wan ISSAC05]</dd></dl>
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