
/**************************************************************************\

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].

