/* Copyright (c) 1997-2021
   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/topaz/FiniteFields.h"
#include "polymake/topaz/complex_tools.h"
#include "polymake/topaz/SimplicialComplex_as_FaceMap.h"
#include "polymake/PowerSet.h"
#include "polymake/Array.h"
#include "polymake/linalg.h"
#include <cassert>

namespace polymake { namespace topaz {
  
namespace {

bool regular(const Set<Int>& s, const Set<Int>& t)
{
   auto i = entire(s);
   assert(!i.at_end());
   Set<Int>::const_iterator j = t.begin();
   assert(!j.at_end());

   // check B_{-1}
   if (*j<*i) return false;
   assert(*j==*i);
   ++i;                      // now index odd

   // check B_m
   while (!i.at_end()) {
      while (*j<*i) ++j;     // terminates since s subset of t
      assert(*j==*i);

      ++i; ++j;              // now index even
      if (i.at_end()) {
         // check B_p, if p is odd
         if (!j.at_end()) return false;
         else return true;
      }

      assert(!j.at_end());
      if (*i!=*j) return false;
      
      ++i;                    // now index odd
   }

   return true;
}

} // end unnamed namespace

Array<PowerSet<Int>> stiefel_whitney(const Array<Set<Int>>& facets, OptionSet options)
{
   const bool verbose = options["verbose"];

   typedef SimplicialComplex_as_FaceMap<> sc_type;
   sc_type SC (facets);
   
   const Int d = SC.dim();
   Int high_d;
   if (!(options["high_d"]>>high_d))
      high_d = d;
   Int low_d;
   if (!(options["low_d"]>>low_d))
      low_d = 0;
   
   if (low_d < 0)
      low_d += d+1;
   if (high_d < 0)
      high_d += d+1;
   
   if (high_d < low_d || high_d > d)
      throw std::runtime_error("stiefel_whitney: dim_low(" + std::to_string(low_d) + "), dim_high(" + std::to_string(high_d) + ") out of bounds");
   
   Array<PowerSet<Int>> omega_cycle(high_d-low_d+1);
   auto omega_cycle_k = omega_cycle.begin();
   SC.complete_faces(d, low_d);
   
   for (Int k = low_d; k <= high_d; ++k, ++omega_cycle_k) {
      const Int size_k = SC.size_of_dim(k);
      Array<Set<Int>> face(size_k);
      if (verbose)
         cout << "f_" << k << "=" << size_k << ", regular pairs:" << std::endl;
      SparseVector<GF2_old> omega(size_k);
      for (Int l = k; l <= d; ++l)
         for (auto t = entire(SC.faces_of_dim(l)); !t.at_end(); ++t) {
            for (auto s = entire(all_subsets_of_k(*t,k+1)); !s.at_end(); ++s) {
               if (regular(*s,*t)) {
                  if (verbose)
                     cout << " " << *s << *t << endl;
                  const Int s_idx = SC[*s];
                  if (face[s_idx].empty()) face[s_idx]=*s;
                  omega[s_idx]+=GF2_old(1);
               }
            }
         }
      if (k!=d) {
         SparseMatrix<GF2_old> delta_kk(SC.boundary_matrix<GF2_old>(k+1));
         omega = reduce(delta_kk,omega);
      }
      
      accumulate_in(entire(select(face,indices(omega))), operations::add(), *omega_cycle_k);
      if (verbose)
         cout << "omega_" << k << ":\n" << *omega_cycle_k << endl;
   }
   
   return omega_cycle;
}

UserFunction4perl("# @category Other"
                  "# Computes __Stiefel-Whitney homology classes__ of mod 2 Euler space (in particular, closed manifold).\n"
                  "# See Richard Z. Goldstein and Edward C. Turner, Proc. Amer. Math. Soc., 58:339-342 (1976)"
                  "# Use option //verbose// to show regular pairs and cycles.\n"
                  "# A narrower dimension range of interest can be specified.\n"
                  "# Negative values are treated as co-dimension - 1\n"
                  "# @param Array<Set<Int>> facets the facets of the simplicial complex"
                  "# @option Int high_dim"
                  "# @option Int low_dim"
                  "# @option Bool verbose"
                  "# @return Array<Set<Set<Int>>>",
                  &stiefel_whitney,"stiefel_whitney(Array<Set<Int>> { high_dim => undef, low_dim => undef, verbose => 0} )");
   
} }

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