/* 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/Rational.h"
#include "polymake/TropicalNumber.h"
#include "polymake/Vector.h"
#include "polymake/Matrix.h"
#include "polymake/ListMatrix.h"
#include "polymake/IncidenceMatrix.h"
#include "polymake/Graph.h"
#include "polymake/common/incidence_tools.h"
#include "polymake/polytope/compress_incidence.h"
#include "polymake/tropical/arithmetic.h"
#include "polymake/tropical/thomog.h"

namespace polymake { namespace tropical {

template <typename Addition>
void hypersurface_dome(BigObject h)
{
  Matrix<Rational> monoms = h.give("MONOMIALS"); // cast coefficients Integer -> Rational
  const Vector< TropicalNumber<Addition> > coefs=h.give("COEFFICIENTS");
  const Int d = monoms.cols();
  const Int n = monoms.rows();

  if (n != coefs.size())
    throw std::runtime_error("Coefficient vector has the wrong dimension.");

  // We have to make all exponents positive, otherwise the below equations produce
  // a wrong result. We multiply the polynomial with a single monomial, which 
  // does not change the hypersurface.
  Vector<Rational> min_degrees(d);
  for (auto c = entire<indexed>(cols(monoms)); !c.at_end(); ++c) {
    accumulate_in(entire(*c),operations::min(),min_degrees[c.index()]);
  }
  // make sure we dont hit the zero vector which can only happen with exactly one term.
  if (n == 1)
    min_degrees -= ones_vector<Rational>(d);

  monoms -= repeat_row(min_degrees,n);

  // dual to extended Newton polyhedron
  ListMatrix<Vector<Rational>> ineq;
  const TropicalNumber<Addition> zero=TropicalNumber<Addition>::zero();
  for (Int i = 0; i < n; ++i) {
    if (coefs[i]==zero)
      ineq /= unit_vector<Rational>(d+1,0);
    else
      ineq /= Addition::orientation()*(Rational(coefs[i])|monoms[i]);
  }

  h.take("DOME.INEQUALITIES") << ineq;
  h.take("DOME.FEASIBLE") << true;
  h.take("DOME.BOUNDED") << false;
}

template <typename Addition>
void dome_regions(BigObject h)
{
  const Set<Int> far_vertices = h.give("FAR_VERTICES");
  BigObject dome = h.give("DOME");

  // here we explicitly want to take redundant MONOMIALS into account ...
  const SparseMatrix<Int> monoms = h.give("MONOMIALS");
  const IncidenceMatrix<> vii = dome.give("VERTICES_IN_INEQUALITIES");
  const Set<Int> redundant_monomials = polytope::compress_incidence(vii).first;

  // but we also need the irredundant version
  const IncidenceMatrix<> vif = dome.give("VERTICES_IN_FACETS");
  const Int f = common::find_row(vif, far_vertices);
  Graph<> dg = dome.give("DUAL_GRAPH.ADJACENCY");
  if (f >= 0)
    dg.out_edges(f).clear(); // deletes the 'cells at infinity'

  // We construct a map that computes for a row index in vif, what it's original row index in vii was
  // (i.e. what the corresponding monomial is)
  Map<Int, Int> old_index;
  Int count = 0;
  Set<Int> non_redundant_monomials = sequence(0,vii.rows()) - redundant_monomials;
  for (auto nrm = entire(non_redundant_monomials); !nrm.at_end(); ++nrm) {
    old_index[count] = *nrm;
    ++count;
  }

  const Int n_cells = dg.edges();
  Array<Set<Int>> cells(n_cells);
  Vector<Integer> weights(n_cells);
  Int i = 0;
  for (auto e = entire(edges(dg));  !e.at_end();  ++e, ++i) {
    cells[i]=vif.row(e.from_node())*vif.row(e.to_node());
    // Compute the weight of this cell
    Vector<Integer> lattice_diff(monoms.row(old_index[e.from_node()]) - monoms.row(old_index[e.to_node()]));
    weights[i] = 0;
    for (Int ld = 0; ld < lattice_diff.dim(); ++ld)
      weights[i] = gcd(weights[i],lattice_diff[ld]);
  }

  h.take("MAXIMAL_POLYTOPES") << cells;
  h.take("REDUNDANT_MONOMIALS") << redundant_monomials;
  // This takes care of constant polynomials - otherwise the regions would be empty
  IncidenceMatrix<> regions = vif.minor(~range(f,f),All);
  if (regions.rows() == 0) regions /= scalar2set(0);
  h.take("REGIONS") << regions; 
  h.take("WEIGHTS") << weights;
}

FunctionTemplate4perl("hypersurface_dome<Addition>(Hypersurface<Addition>)");
FunctionTemplate4perl("dome_regions<Addition>(Hypersurface<Addition>)");

} }

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