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/* Copyright (c) 1997-2024
Ewgenij Gawrilow, Michael Joswig, and the polymake team
Technische Universität Berlin, Germany
https://polymake.org
This program is free software; you can redistribute it and/or modify it
under the terms of the GNU General Public License as published by the
Free Software Foundation; either version 2, or (at your option) any
later version: http://www.gnu.org/licenses/gpl.txt.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
--------------------------------------------------------------------------------
*/
#pragma once
#include "polymake/client.h"
#include "polymake/SparseMatrix.h"
#include "polymake/linalg.h"
#include "polymake/numerical_functions.h"
#include "polymake/GenericStruct.h"
namespace pm {
template<typename E>
class HermiteNormalForm
: public GenericStruct<HermiteNormalForm<E> > {
public:
DeclSTRUCT( DeclTemplFIELD(hnf, Matrix<E>)
DeclTemplFIELD(companion, SparseMatrix<E>)
DeclTemplFIELD(rank, Int) );
};
template <typename TMatrix, typename E>
Int ranked_hermite_normal_form(const GenericMatrix<TMatrix, E>& M, Matrix<E>& hnf, SparseMatrix<E>& companion, bool reduced = true)
{
SparseMatrix2x2<E> U;
SparseMatrix<E> R, S;
Matrix<E> N(M);
const Int rows = M.rows();
const Int cols = M.cols();
R = unit_matrix<E>(cols);
Int current_col = 0;
Int rank = -1;
for (Int i = 0; i < rows; ++i) {
bool nonzero = true;
// Find a non-zero entry and move it to here.
if (N(i,current_col) == 0) {
nonzero = false;
for (Int j = current_col; j < cols; ++j) {
if (!is_zero(N(i,j))) {
nonzero = true;
U.i = current_col;
U.j = j;
U.a_ii = zero_value<E>();
U.a_ij = one_value<E>();
U.a_ji = one_value<E>();
U.a_jj = zero_value<E>();
R.multiply_from_right(U);
N.multiply_from_right(U);
}
}
}
if (!nonzero) {
continue;
} else {
rank = current_col;
}
// GCD part of algorithm.
for (Int j = current_col+1; j < cols; ++j) {
if (!is_zero(N(i,j))) {
U.i = current_col;
U.j = j;
ExtGCD<E> egcd = ext_gcd(N(i,current_col), N(i,j));
U.a_ii = egcd.p;
U.a_ji = egcd.q;
U.a_ij = egcd.k2;
U.a_jj = -egcd.k1;
R.multiply_from_right(U);
N.multiply_from_right(U);
}
}
if (N(i,current_col)<0) {
S = unit_matrix<E>(cols);
S(current_col,current_col) = -1;
R = R*S;
N = N*S;
}
if (reduced) {
for (Int j = 0; j < current_col; ++j) {
U.i = j;
U.j = current_col;
E factor = N(i,j) % N(i,current_col);
if (factor < 0) factor += N(i,current_col);
factor = (N(i,j) - factor)/N(i,current_col);
U.a_ii = 1;
U.a_ji = -factor;
U.a_ij = 0;
U.a_jj = 1;
R.multiply_from_right(U);
N.multiply_from_right(U);
}
}
++current_col;
if (current_col == cols) {
break;
}
}
++rank;
hnf = N;
companion = R;
return rank;
}
template <typename TMatrix, typename E>
HermiteNormalForm<E> hermite_normal_form(const GenericMatrix<TMatrix, E>& M, bool reduced = true)
{
HermiteNormalForm<E> res;
res.rank = ranked_hermite_normal_form(M, res.hnf, res.companion, reduced);
return res;
}
//returns as rows a basis of the null space in an euclidean ring
template <typename TMatrix, typename E>
SparseMatrix<E> null_space_integer(const GenericMatrix<TMatrix, E>& M)
{
Matrix<E> H;
SparseMatrix<E> R;
Int r = ranked_hermite_normal_form(M, H, R);
return T(R.minor(All, range(r, R.cols()-1)));
}
} // namespace pm
namespace polymake {
using pm::HermiteNormalForm;
using pm::null_space_integer;
}
// Local Variables:
// mode:C++
// c-basic-offset:3
// indent-tabs-mode:nil
// End:
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