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<font color="#0000ed"><i>/*</i></font><font color="#0000ed"><i>*************************************************************************\</i></font><br>
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<font color="#0000ed"><i>MODULE: HNF</i></font><br>
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<font color="#0000ed"><i>SUMMARY:</i></font><br>
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<font color="#0000ed"><i>A routine for computing Hermite Normal Forms</i></font><br>
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<font color="#0000ed"><i>\*************************************************************************</i></font><font color="#0000ed"><i>*/</i></font><br>
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<font color="#1773cc">#include </font><font color="#4a6f8b"><NTL/mat_ZZ.h></font><br>
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<font color="#008b00"><b>void</b></font> HNF(mat_ZZ& W, <font color="#008b00"><b>const</b></font> mat_ZZ& A, <font color="#008b00"><b>const</b></font> ZZ& D);<br>
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<font color="#0000ed"><i>// The input matrix A is an n x m matrix of rank m (so n >= m), and D</i></font><br>
<font color="#0000ed"><i>// is a multiple of the determinant of the lattice L spanned by the</i></font><br>
<font color="#0000ed"><i>// rows of A. W is computed as the Hermite Normal Form of A; that is,</i></font><br>
<font color="#0000ed"><i>// W is the unique m x m matrix whose rows span L, such that</i></font><br>
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<font color="#0000ed"><i>// - W is lower triangular,</i></font><br>
<font color="#0000ed"><i>// - the diagonal entries are positive,</i></font><br>
<font color="#0000ed"><i>// - any entry below the diagonal is a non-negative number</i></font><br>
<font color="#0000ed"><i>// strictly less than the diagonal entry in its column.</i></font><br>
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<font color="#0000ed"><i>// Currently, this is implemented using the algorithm of [P. Domich,</i></font><br>
<font color="#0000ed"><i>// R. Kannan and L. Trotter, Math. Oper. Research 12:50-59, 1987].</i></font><br>
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