source: git/factory/cf_hnf.h @ 9c0b20a

/* emacs edit mode for this file is -*- C++ -*- */
#ifndef CF_HNF_H
#define CF_HNF_H

/*BEGINPUBLIC*/

/* $Id$ */

//{{{ docu
//
// The input matrix A is square matrix of integers
// output: the Hermite Normal Form of A; that is,
// the unique m x m matrix whose rows span L, such that
//
// - 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.
//
// via NTL:HNF
//
//}}}

CFMatrix* cf_HNF(CFMatrix& A);

// performs LLL reduction.

// B is an m x n matrix, viewed as m rows of n-vectors.  m may be less
// than, equal to, or greater than n, and the rows need not be
// linearly independent.  B is transformed into an LLL-reduced basis,
// and the return value is the rank r of B.  The first m-r rows of B
// are zero.  

// More specifically, elementary row transformations are performed on
// B so that the non-zero rows of new-B form an LLL-reduced basis
// for the lattice spanned by the rows of old-B.
// The default reduction parameter is delta=3/4, which means
// that the squared length of the first non-zero basis vector
// is no more than 2^{r-1} times that of the shortest vector in
// the lattice.

CFMatrix* cf_LLL(CFMatrix& A);

/*ENDPUBLIC*/

#endif