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