spielwiese
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| 1 | |
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| 2 | /**************************************************************************\ |
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| 3 | |
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| 4 | MODULE: HNF |
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| 5 | |
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| 6 | SUMMARY: |
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| 7 | |
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| 8 | A routine for computing Hermite Normal Forms |
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| 9 | |
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| 10 | \**************************************************************************/ |
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| 11 | |
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| 12 | |
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| 13 | #include <NTL/mat_ZZ.h> |
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| 14 | |
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| 15 | void HNF(mat_ZZ& W, const mat_ZZ& A, const ZZ& D); |
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| 16 | |
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| 17 | // The input matrix A is an n x m matrix of rank m (so n >= m), and D |
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| 18 | // is a multiple of the determinant of the lattice L spanned by the |
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| 19 | // rows of A. W is computed as the Hermite Normal Form of A; that is, |
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| 20 | // W is the unique m x m matrix whose rows span L, such that |
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| 21 | |
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| 22 | // - W is lower triangular, |
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| 23 | // - the diagonal entries are positive, |
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| 24 | // - any entry below the diagonal is a non-negative number |
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| 25 | // strictly less than the diagonal entry in its column. |
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| 26 | |
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| 27 | // Currently, this is implemented using the algorithm of [P. Domich, |
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| 28 | // R. Kannan and L. Trotter, Math. Oper. Research 12:50-59, 1987]. |
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| 29 | |
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