/* Copyright (c) 1997-2020
   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.
--------------------------------------------------------------------------------
*/

namespace polymake { namespace topaz {

template <typename Complex>
PowerSet<Int> k_skeleton(const Complex& C, const Int k)
{
   PowerSet<Int> SK;
  
   for (auto f_it = entire(C); !f_it.at_end(); ++f_it) {
      // the k skeleton are all faces of dimension <= k.
      if (f_it->size()<=k) {
         // facets are either equal or none contains the other.
         SK+=*f_it;
         continue;
      }

      // the k skeleton a facet are all subsets of size k+1
      for (auto s_it=entire(all_subsets_of_k(*f_it, k+1)); !s_it.at_end(); ++s_it) {
        // facets are either equal or none contains the other.
        SK+=*s_it;
      }
   }
   if (SK.empty())  // the empty complex is represented as a single empty set
      SK += Set<Int>();
   
   return SK;
}

} }

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