/* 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.
--------------------------------------------------------------------------------
*/

#include "polymake/client.h"
#include "polymake/Matrix.h"
#include "polymake/Rational.h"
#include "polymake/PowerSet.h"
#include "polymake/linalg.h"
#include "polymake/list"
#include "polymake/common/finiteFieldLA.h"


namespace polymake { namespace matroid {

void bases_from_points_finite_char(BigObject m, const Int p)
{
   if (p != 2 && p != 3) throw std::runtime_error("the characteristic of the field has to be 2 or 3");
   const Matrix<Int> points= p==2 ? m.give("BINARY_VECTORS") : m.give("TERNARY_VECTORS");
   const Int n_elements = points.rows();
   const long int r = polymake::common::rank_mod_p(points, p);

   std::list<Set<Int>> bases;
   Int n_bases = 0;

   //test for each subset of size r
   for (auto i = entire(all_subsets_of_k(sequence(0, n_elements), r)); !i.at_end(); ++i) {
      const Matrix<Int> b = points.minor(*i, All);
      if (polymake::common::rank_mod_p(b, p) == r) {
         bases.push_back(*i);
         ++n_bases;
      }
   }

   m.take("BASES") << bases;
   m.take("N_BASES") << n_bases;
   m.take("RANK") << r;
   m.take("N_ELEMENTS") << n_elements;
}

Function4perl(&bases_from_points_finite_char, "bases_from_points(Matroid,$)");

} }

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