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<h1>NormalForms.h File Reference</h1>
<p><a href="NormalForms_8h_source.html">Go to the source code of this file.</a></p>
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<tr><td colspan="2"><h2>Functions</h2></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="NormalForms_8h.html#a1d5c5fdbd71ebc1eb2ce3f11ce9fbd5f">Smith</a> (<a class="el" href="structmatrix.html">Matrix</a> *A, <a class="el" href="structmatrix.html">Matrix</a> **U, <a class="el" href="structmatrix.html">Matrix</a> **V, <a class="el" href="structmatrix.html">Matrix</a> **Product)</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Smith : This function takes a Matrix A of dim n * l as its input and returns the three matrices U, V and Product such that A = U * Product * V, where U is an unimodular <a class="el" href="structmatrix.html">matrix</a> of dimension n * n and V is an unimodular <a class="el" href="structmatrix.html">matrix</a> of dimension l * l. <a href="#a1d5c5fdbd71ebc1eb2ce3f11ce9fbd5f"></a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="NormalForms_8h.html#acd4e00bd353920b83e3f27a76909b2ed">Hermite</a> (<a class="el" href="structmatrix.html">Matrix</a> *A, <a class="el" href="structmatrix.html">Matrix</a> **H, <a class="el" href="structmatrix.html">Matrix</a> **U)</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Hermite : This function takes a Matrix as its input and finds its HNF ( Left form ). <a href="#acd4e00bd353920b83e3f27a76909b2ed"></a><br/></td></tr>
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<hr/><h2>Function Documentation</h2>
<a class="anchor" id="acd4e00bd353920b83e3f27a76909b2ed"></a><!-- doxytag: member="NormalForms.h::Hermite" ref="acd4e00bd353920b83e3f27a76909b2ed" args="(Matrix *A, Matrix **H, Matrix **U)" -->
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<td class="memname">void Hermite </td>
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<td class="paramtype"><a class="el" href="structmatrix.html">Matrix</a> ** </td>
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<td class="paramtype"><a class="el" href="structmatrix.html">Matrix</a> ** </td>
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<p>Hermite : This function takes a Matrix as its input and finds its HNF ( Left form ). </p>
<p>Input : A Matrix A (The Matrix A is not necessarily a Polylib <a class="el" href="structmatrix.html">matrix</a>. It is just a <a class="el" href="structmatrix.html">matrix</a> as far as Hermite is concerned. It does not even check if the <a class="el" href="structmatrix.html">matrix</a> is a Polylib <a class="el" href="structmatrix.html">matrix</a> or not) Output : The Hnf <a class="el" href="structmatrix.html">matrix</a> H and the Unimodular <a class="el" href="structmatrix.html">matrix</a> U such that A = H * U.</p>
<p>We use Alan Darte's implementation of Hermite to compute the HNF. Alan Darte's implementation computes the Upper Triangular HNF. So We work on the fact that if A = H * U then A (transpose) = U(transpose) * H (transpose) There are a set of interface functions written in Interface.c which convert a <a class="el" href="structmatrix.html">matrix</a> from Polylib representationt to that of Alan Darte's and vice versa.</p>
<p>This Function Does the Following Step 1 : Given the <a class="el" href="structmatrix.html">matrix</a> A it finds its Transpose. Step 2 : Finds the HNF (Right Form) using Alan Darte's Algorithm. Step 3 : The H1 and U1 obtained in Step2 are both Transposed to get the actual H and U such that A = HU. </p>
<p>Definition at line <a class="el" href="NormalForms_8c_source.html#l00670">670</a> of file <a class="el" href="NormalForms_8c_source.html">NormalForms.c</a>.</p>
<p>References <a class="el" href="NormalForms_8c_source.html#l00604">ConvertDarMattoPolMat()</a>, <a class="el" href="NormalForms_8c_source.html#l00580">ConvertPolMattoDarMat()</a>, <a class="el" href="NormalForms_8c_source.html#l00492">hermite()</a>, <a class="el" href="NormalForms_8c_source.html#l00272">identite()</a>, <a class="el" href="Matop_8c_source.html#l00118">Matrix_Copy()</a>, <a class="el" href="matrix_8c_source.html#l00092">Matrix_Free()</a>, <a class="el" href="types_8h_source.html#l00092">matrix::NbColumns</a>, <a class="el" href="types_8h_source.html#l00092">matrix::NbRows</a>, <a class="el" href="Matop_8c_source.html#l00103">Transpose()</a>, <a class="el" href="NormalForms_8c_source.html#l00297">transpose()</a>, <a class="el" href="source_2arith_2arithmetique_8h_source.html#l00462">value_clear</a>, and <a class="el" href="source_2arith_2arithmetique_8h_source.html#l00458">value_init</a>.</p>
<p>Referenced by <a class="el" href="Lattice_8c_source.html#l00176">AffineHermite()</a>, <a class="el" href="Matop_8c_source.html#l00361">findHermiteBasis()</a>, <a class="el" href="Lattice_8c_source.html#l01267">isfulldim()</a>, <a class="el" href="SolveDio_8c_source.html#l00248">RearrangeMatforSolveDio()</a>, and <a class="el" href="SolveDio_8c_source.html#l00081">SolveDiophantine()</a>.</p>
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<a class="anchor" id="a1d5c5fdbd71ebc1eb2ce3f11ce9fbd5f"></a><!-- doxytag: member="NormalForms.h::Smith" ref="a1d5c5fdbd71ebc1eb2ce3f11ce9fbd5f" args="(Matrix *A, Matrix **U, Matrix **V, Matrix **Product)" -->
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<td class="memname">void Smith </td>
<td>(</td>
<td class="paramtype"><a class="el" href="structmatrix.html">Matrix</a> * </td>
<td class="paramname"> <em>A</em>, </td>
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<td class="paramtype"><a class="el" href="structmatrix.html">Matrix</a> ** </td>
<td class="paramname"> <em>U</em>, </td>
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<td class="paramtype"><a class="el" href="structmatrix.html">Matrix</a> ** </td>
<td class="paramname"> <em>V</em>, </td>
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<td class="paramtype"><a class="el" href="structmatrix.html">Matrix</a> ** </td>
<td class="paramname"> <em>Product</em></td><td> </td>
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<p>Smith : This function takes a Matrix A of dim n * l as its input and returns the three matrices U, V and Product such that A = U * Product * V, where U is an unimodular <a class="el" href="structmatrix.html">matrix</a> of dimension n * n and V is an unimodular <a class="el" href="structmatrix.html">matrix</a> of dimension l * l. </p>
<p>Product is a diagonal <a class="el" href="structmatrix.html">matrix</a> of dimension n * l.</p>
<p>We use Alan Darte's implementation of Smith for computing the Smith Normal Form </p>
<p>Definition at line <a class="el" href="NormalForms_8c_source.html#l00627">627</a> of file <a class="el" href="NormalForms_8c_source.html">NormalForms.c</a>.</p>
<p>References <a class="el" href="Matop_8c_source.html#l00058">Identity()</a>, <a class="el" href="Matop_8c_source.html#l00118">Matrix_Copy()</a>, <a class="el" href="matrix_8c_source.html#l00092">Matrix_Free()</a>, <a class="el" href="types_8h_source.html#l00092">matrix::NbColumns</a>, <a class="el" href="types_8h_source.html#l00092">matrix::NbRows</a>, <a class="el" href="types_8h_source.html#l00094">matrix::p_Init</a>, and <a class="el" href="NormalForms_8c_source.html#l00383">smith()</a>.</p>
<p>Referenced by <a class="el" href="Lattice_8c_source.html#l00221">AffineSmith()</a>, and <a class="el" href="Lattice_8c_source.html#l00674">Lattice2LatticeUnion()</a>.</p>
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