Merge trunk + alpha complex fixes

git-svn-id: svn+ssh://scm.gforge.inria.fr/svnroot/gudhi/branches/alphashapes@753 636b058d-ea47-450e-bf9e-a15bfbe3eedb

Former-commit-id: a0a1f71420736a0a702e6dbc76bc010b36bf5e13

13 files changed, 265 insertions, 649 deletions

diff --git a/CMakeLists.txt b/CMakeLists.txt
index 066c63e2..bf01caeb 100644
--- a/CMakeLists.txt
+++ b/CMakeLists.txt
@@ -23,7 +23,6 @@ set(Boost_USE_STATIC_LIBS        ON)
 set(Boost_USE_MULTITHREADED      ON)
 set(Boost_USE_STATIC_RUNTIME    OFF)
 
-find_package(Boost)
 find_package(GMP)
 if(GMP_FOUND)
 	find_package(GMPXX)
diff --git a/src/Alpha_complex/example/Alpha_complex_from_off.cpp b/src/Alpha_complex/example/Alpha_complex_from_off.cpp
index 3ce4c7f4..b698d6d7 100644
--- a/src/Alpha_complex/example/Alpha_complex_from_off.cpp
+++ b/src/Alpha_complex/example/Alpha_complex_from_off.cpp
@@ -10,7 +10,7 @@
 void usage(char * const progName) {
   std::cerr << "Usage: " << progName << " filename.off alpha_square_max_value" << std::endl;
   std::cerr << "       i.e.: " << progName << " ../../data/points/alphacomplexdoc.off 60.0" << std::endl;
-  exit(-1);  // ----- >>
+  exit(-1); // ----- >>
 }
 
 int main(int argc, char **argv) {
@@ -37,12 +37,14 @@ int main(int argc, char **argv) {
 
   std::cout << "Iterator on alpha complex simplices in the filtration order, with [filtration value]:" << std::endl;
   for (auto f_simplex : alpha_complex_from_file.filtration_simplex_range()) {
-    std::cout << "   ( ";
-    for (auto vertex : alpha_complex_from_file.simplex_vertex_range(f_simplex)) {
-      std::cout << vertex << " ";
+    if (alpha_complex_from_file.filtration(f_simplex) <= alpha_complex_from_file.filtration()) {
+      std::cout << "   ( ";
+      for (auto vertex : alpha_complex_from_file.simplex_vertex_range(f_simplex)) {
+        std::cout << vertex << " ";
+      }
+      std::cout << ") -> " << "[" << alpha_complex_from_file.filtration(f_simplex) << "] ";
+      std::cout << std::endl;
     }
-    std::cout << ") -> " << "[" << alpha_complex_from_file.filtration(f_simplex) << "] ";
-    std::cout << std::endl;
   }
   return 0;
 }
diff --git a/src/Alpha_complex/example/alphaoffreader_for_doc.txt b/src/Alpha_complex/example/alphaoffreader_for_doc.txt
index 1153f097..71f29a00 100644
--- a/src/Alpha_complex/example/alphaoffreader_for_doc.txt
+++ b/src/Alpha_complex/example/alphaoffreader_for_doc.txt
@@ -1,27 +1,27 @@
 Alpha complex is of dimension 2 - 25 simplices - 7 vertices.
 Iterator on alpha complex simplices in the filtration order, with [filtration value]:
+   ( 0 ) -> [0] 
    ( 1 ) -> [0] 
    ( 2 ) -> [0] 
    ( 3 ) -> [0] 
    ( 4 ) -> [0] 
    ( 5 ) -> [0] 
    ( 6 ) -> [0] 
-   ( 7 ) -> [0] 
-   ( 4 3 ) -> [6.25] 
-   ( 6 5 ) -> [7.25] 
-   ( 3 1 ) -> [8.5] 
-   ( 2 1 ) -> [9.25] 
-   ( 4 2 ) -> [10] 
-   ( 3 2 ) -> [11.25] 
-   ( 4 3 2 ) -> [12.5] 
-   ( 3 2 1 ) -> [12.9959] 
-   ( 7 6 ) -> [13.25] 
-   ( 5 3 ) -> [20] 
-   ( 7 5 ) -> [22.7367] 
-   ( 7 6 5 ) -> [22.7367] 
-   ( 7 4 ) -> [30.25] 
-   ( 7 3 ) -> [36.5] 
-   ( 7 4 3 ) -> [36.5] 
-   ( 7 5 3 ) -> [37.2449] 
-   ( 5 1 ) -> [59.7107] 
-   ( 5 3 1 ) -> [59.7107] 
+   ( 3 2 ) -> [6.25] 
+   ( 5 4 ) -> [7.25] 
+   ( 2 0 ) -> [8.5] 
+   ( 1 0 ) -> [9.25] 
+   ( 3 1 ) -> [10] 
+   ( 2 1 ) -> [11.25] 
+   ( 3 2 1 ) -> [12.5] 
+   ( 2 1 0 ) -> [12.9959] 
+   ( 6 5 ) -> [13.25] 
+   ( 4 2 ) -> [20] 
+   ( 6 4 ) -> [22.7367] 
+   ( 6 5 4 ) -> [22.7367] 
+   ( 6 3 ) -> [30.25] 
+   ( 6 2 ) -> [36.5] 
+   ( 6 3 2 ) -> [36.5] 
+   ( 6 4 2 ) -> [37.2449] 
+   ( 4 0 ) -> [59.7107] 
+   ( 4 2 0 ) -> [59.7107] 
diff --git a/src/Alpha_complex/include/gudhi/Alpha_complex.h b/src/Alpha_complex/include/gudhi/Alpha_complex.h
index 213436e0..518d1792 100644
--- a/src/Alpha_complex/include/gudhi/Alpha_complex.h
+++ b/src/Alpha_complex/include/gudhi/Alpha_complex.h
@@ -99,8 +99,6 @@ class Alpha_complex : public Simplex_tree<> {
   Delaunay_triangulation* triangulation_;
   /** \brief Kernel for triangulation_ functions access.*/
   Kernel kernel_;
-  /** \brief Maximum value for alpha square.*/
-  Filtration_value max_alpha_square_;
 
  public:
   /** \brief Alpha_complex constructor from an OFF file name.
@@ -110,14 +108,14 @@ class Alpha_complex : public Simplex_tree<> {
    * @param[in] off_file_name OFF file [path and] name.
    */
   Alpha_complex(const std::string& off_file_name, Filtration_value max_alpha_square)
-      : triangulation_(nullptr),
-      max_alpha_square_(max_alpha_square) {
+      : triangulation_(nullptr) {
     Gudhi::Delaunay_triangulation_off_reader<Delaunay_triangulation> off_reader(off_file_name);
     if (!off_reader.is_valid()) {
       std::cerr << "Alpha_complex - Unable to read file " << off_file_name << std::endl;
       exit(-1);  // ----- >>
     }
     triangulation_ = off_reader.get_complex();
+    set_filtration(max_alpha_square);
     init();
   }
 
@@ -126,9 +124,9 @@ class Alpha_complex : public Simplex_tree<> {
    * @param[in] triangulation_ptr Pointer on a Delaunay triangulation.
    */
   Alpha_complex(Delaunay_triangulation* triangulation_ptr, Filtration_value max_alpha_square)
-      : triangulation_(triangulation_ptr),
-      max_alpha_square_(max_alpha_square) {
-    init();
+      : triangulation_(triangulation_ptr) {
+   set_filtration(max_alpha_square);
+   init();
   }
 
   /** \brief Alpha_complex constructor from a list of points.
@@ -143,14 +141,14 @@ class Alpha_complex : public Simplex_tree<> {
   template<typename ForwardIterator >
   Alpha_complex(int dimension, size_type size, ForwardIterator firstPoint, ForwardIterator lastPoint,
                 Filtration_value max_alpha_square)
-      : triangulation_(nullptr),
-      max_alpha_square_(max_alpha_square) {
+      : triangulation_(nullptr) {
     triangulation_ = new Delaunay_triangulation(dimension);
     size_type inserted = triangulation_->insert(firstPoint, lastPoint);
     if (inserted != size) {
       std::cerr << "Alpha_complex - insertion failed " << inserted << " != " << size << std::endl;
       exit(-1);  // ----- >>
     }
+    set_filtration(max_alpha_square);
     init();
   }
 
@@ -169,8 +167,9 @@ class Alpha_complex : public Simplex_tree<> {
    * @warning Exception std::out_of_range is thrown in case vertex is not in the map vertex_handle_to_iterator_.
    */
   Point_d get_point(Vertex_handle vertex) {
-    if (vertex_handle_to_iterator_[vertex] != nullptr) {
-      return vertex_handle_to_iterator_[vertex]->point();
+    auto found_it = vertex_handle_to_iterator_.find(vertex);
+    if (found_it != vertex_handle_to_iterator_.end()) {
+      return found_it->second->point();
     } else {
       throw std::out_of_range("Vertex out of vector range");
     }
@@ -210,20 +209,21 @@ class Alpha_complex : public Simplex_tree<> {
     Vertex_handle vertex_handle = Vertex_handle();
     // Loop on triangulation vertices list
     for (CGAL_vertex_iterator vit = triangulation_->vertices_begin(); vit != triangulation_->vertices_end(); ++vit) {
+      if (!triangulation_->is_infinite(*vit)) {
 #ifdef DEBUG_TRACES
-      std::cout << "Vertex insertion - " << vertex_handle << " -> " << vit->point() << std::endl;
+        std::cout << "Vertex insertion - " << vertex_handle << " -> " << vit->point() << std::endl;
 #endif  // DEBUG_TRACES
-      vertex_iterator_to_handle_[vit] = vertex_handle;
-      vertex_handle_to_iterator_[vertex_handle] = vit;
-      vertex_handle++;
+        vertex_iterator_to_handle_.emplace(vit, vertex_handle);
+        vertex_handle_to_iterator_.emplace(vertex_handle, vit);
+        vertex_handle++;
+      }
     }
     // --------------------------------------------------------------------------------------------
 
-    Filtration_value filtration_max = 0.0;
     // --------------------------------------------------------------------------------------------
     // Simplex_tree construction from loop on triangulation finite full cells list
     for (auto cit = triangulation_->finite_full_cells_begin(); cit != triangulation_->finite_full_cells_end(); ++cit) {
-      Vector_vertex vertex_full_cell;
+      Vector_vertex vertexVector;
 #ifdef DEBUG_TRACES
       std::cout << "Simplex_tree insertion ";
 #endif  // DEBUG_TRACES
@@ -233,149 +233,98 @@ class Alpha_complex : public Simplex_tree<> {
           std::cout << " " << vertex_iterator_to_handle_[*vit];
 #endif  // DEBUG_TRACES
           // Vector of vertex construction for simplex_tree structure
-          vertex_full_cell.push_back(vertex_iterator_to_handle_[*vit]);
+          vertexVector.push_back(vertex_iterator_to_handle_[*vit]);
         }
       }
 #ifdef DEBUG_TRACES
       std::cout << std::endl;
 #endif  // DEBUG_TRACES
-
-      Simplex_tree<> full_cell;
-      full_cell.set_dimension(triangulation_->maximal_dimension());
-      // Create a simplex tree containing only one of the full cells
-      Simplex_result insert_result = full_cell.insert_simplex_and_subfaces(vertex_full_cell);
+      // Insert each simplex and its subfaces in the simplex tree - filtration is NaN
+      Simplex_result insert_result = insert_simplex_and_subfaces(vertexVector,
+                                                                 std::numeric_limits<double>::quiet_NaN());
       if (!insert_result.second) {
         std::cerr << "Alpha_complex::init insert_simplex_and_subfaces failed" << std::endl;
         exit(-1);  // ----->>
       }
-      // +++ For i : d -> 0
-      for (int fc_decr_dim = full_cell.dimension(); (fc_decr_dim >= 0); fc_decr_dim--) {
-        // +++ Foreach Sigma of dim i
-        // No need to skip this loop in case alpha²(Sigma) > max_alpha_square_ because of
-        // if (fc_decr_dim == f_simplex_dim) which means "only for a full cell"
-        for (auto fc_simplex : full_cell.skeleton_simplex_range(fc_decr_dim)) {
-          int f_simplex_dim = full_cell.dimension(fc_simplex);
-          if (fc_decr_dim == f_simplex_dim) {
-            Vector_of_CGAL_points pointVector;
-            Vector_vertex current_vertex;
-#ifdef DEBUG_TRACES
-            std::cout << "Sigma of dim " << fc_decr_dim << " is";
-#endif  // DEBUG_TRACES
-            for (auto vertex : full_cell.simplex_vertex_range(fc_simplex)) {
-              pointVector.push_back(get_point(vertex));
-              current_vertex.push_back(vertex);
-#ifdef DEBUG_TRACES
-              std::cout << " " << vertex;
-#endif  // DEBUG_TRACES
-            }
+    }
+    // --------------------------------------------------------------------------------------------
+
+    // --------------------------------------------------------------------------------------------
+    // ### For i : d -> 0
+    for (int decr_dim = dimension(); decr_dim >= 0; decr_dim--) {
+      // ### Foreach Sigma of dim i
+      for (auto f_simplex : skeleton_simplex_range(decr_dim)) {
+        int f_simplex_dim = dimension(f_simplex);
+        if (decr_dim == f_simplex_dim) {
+          Vector_of_CGAL_points pointVector;
 #ifdef DEBUG_TRACES
-            std::cout << std::endl;
+          std::cout << "Sigma of dim " << decr_dim << " is";
 #endif  // DEBUG_TRACES
-            Simplex_handle sigma_handle = find(current_vertex);
-            bool skip_propagation = false;
-            // +++ If filt(Sigma) is NaN : filt(Sigma) = alpha²(Sigma)
-            if ((sigma_handle == null_simplex()) || isnan(filtration(sigma_handle))) {
-              Filtration_value alpha_complex_filtration = compute_alpha_square(pointVector.begin(), pointVector.end(),
-                                                                               f_simplex_dim);
-              if (alpha_complex_filtration <= max_alpha_square_) {
-                // Only insert Sigma in Simplex tree if alpha²(Sigma) <= max_alpha_square_
-                if (sigma_handle == null_simplex()) {
+          for (auto vertex : simplex_vertex_range(f_simplex)) {
+            pointVector.push_back(get_point(vertex));
 #ifdef DEBUG_TRACES
-                  std::cout << "Alpha_complex::init Sigma not found" << std::endl;
+            std::cout << " " << vertex;
 #endif  // DEBUG_TRACES
-                  insert_result = insert_simplex(current_vertex, std::numeric_limits<double>::quiet_NaN());
-                  if (!insert_result.second) {
-                    std::cerr << "Alpha_complex::init insert_simplex failed" << std::endl;
-                    exit(-1);  // ----->>
-                  }
-                  // Sigma is the new inserted simplex handle
-                  sigma_handle = insert_result.first;
-                }
+          }
 #ifdef DEBUG_TRACES
-                std::cout << "Alpha_complex::init filtration = " << alpha_complex_filtration << std::endl;
+          std::cout << std::endl;
 #endif  // DEBUG_TRACES
-                assign_filtration(sigma_handle, alpha_complex_filtration);
-                filtration_max = fmax(filtration_max, alpha_complex_filtration);
-              } else {
-                // if alpha²(Sigma) > max_alpha_square_ skip propagation
-                skip_propagation = true;
+          // ### If filt(Sigma) is NaN : filt(Sigma) = alpha(Sigma)
+          if (isnan(filtration(f_simplex))) {
+            Filtration_value alpha_complex_filtration = 0.0;
+            // No need to compute squared_radius on a single point - alpha is 0.0
+            if (f_simplex_dim > 0) {
+              // squared_radius function initialization
+              Squared_Radius squared_radius = kernel_.compute_squared_radius_d_object();
+
+              alpha_complex_filtration = squared_radius(pointVector.begin(), pointVector.end());
+            }
+            assign_filtration(f_simplex, alpha_complex_filtration);
 #ifdef DEBUG_TRACES
-                std::cout << "Alpha_complex::init skip propagation on this full cell" << std::endl;
+            std::cout << "filt(Sigma) is NaN : filt(Sigma) =" << filtration(f_simplex) << std::endl;
 #endif  // DEBUG_TRACES
-              }
-            }  // --- If filt(Sigma) is NaN : filt(Sigma) = alpha(Sigma)
-            if ((filtration(sigma_handle) <= max_alpha_square_) && !skip_propagation) {
-              // Propagate alpha filtration value in Simplex tree if alpha²(Sigma) <= max_alpha_square_
-              // in case Sigma is not found AND not inserted (alpha_complex_filtration > max_alpha_square_),
-              // filtration(null_simplex()) returns INFINITY => no propagation
-              propagate_alpha_filtration(full_cell, fc_simplex, fc_decr_dim, sigma_handle);
-            }
           }
-        }  // --- Foreach Sigma of dim i
-      }  // --- For i : d -> 0
+          propagate_alpha_filtration(f_simplex, decr_dim);
+        }
+      }
     }
     // --------------------------------------------------------------------------------------------
-
-#ifdef DEBUG_TRACES
-    std::cout << "filtration_max=" << filtration_max << std::endl;
-#endif  // DEBUG_TRACES
-    set_filtration(filtration_max);
-  }
-
-  template<typename ForwardIterator >
-  Filtration_value compute_alpha_square(ForwardIterator firstPoint, ForwardIterator lastPoint, int f_simplex_dim) {
-    Filtration_value alpha_square_value = 0.0;
-    // No need to compute squared_radius on a single point - alpha is 0.0
-    if (f_simplex_dim > 0) {
-      // squared_radius function initialization
-      Squared_Radius squared_radius = kernel_.compute_squared_radius_d_object();
-
-      alpha_square_value = squared_radius(firstPoint, lastPoint);
-    }
-    return alpha_square_value;
   }
 
-  void propagate_alpha_filtration(Simplex_tree& full_cell, Simplex_handle fc_simplex, int fc_decr_dim,
-                                  Simplex_handle sigma_handle) {
+  template<typename Simplex_handle>
+  void propagate_alpha_filtration(Simplex_handle f_simplex, int decr_dim) {
     // ### Foreach Tau face of Sigma
-    for (auto f_boundary : full_cell.boundary_simplex_range(fc_simplex)) {
+    for (auto f_boundary : boundary_simplex_range(f_simplex)) {
 #ifdef DEBUG_TRACES
       std::cout << " | --------------------------------------------------" << std::endl;
       std::cout << " | Tau ";
-#endif  // DEBUG_TRACES
-      Vector_vertex tau_vertex;
-      for (auto vertex : full_cell.simplex_vertex_range(f_boundary)) {
-        tau_vertex.push_back(vertex);
-#ifdef DEBUG_TRACES
+      for (auto vertex : simplex_vertex_range(f_boundary)) {
         std::cout << vertex << " ";
-#endif  // DEBUG_TRACES
       }
-#ifdef DEBUG_TRACES
       std::cout << "is a face of Sigma" << std::endl;
+      std::cout << " | isnan(filtration(Tau)=" << isnan(filtration(f_boundary)) << std::endl;
 #endif  // DEBUG_TRACES
-      Simplex_handle tau_handle = find(tau_vertex);
       // ### If filt(Tau) is not NaN
-
-      if ((tau_handle != null_simplex()) && (!isnan(filtration(tau_handle)))) {
+      if (!isnan(filtration(f_boundary))) {
         // ### filt(Tau) = fmin(filt(Tau), filt(Sigma))
-        Filtration_value alpha_complex_filtration = fmin(filtration(tau_handle), filtration(sigma_handle));
-        assign_filtration(tau_handle, alpha_complex_filtration);
-        // No need to check for filtration_max, alpha_complex_filtration is a min of an existing filtration value
+        Filtration_value alpha_complex_filtration = fmin(filtration(f_boundary), filtration(f_simplex));
+        assign_filtration(f_boundary, alpha_complex_filtration);
 #ifdef DEBUG_TRACES
-        std::cout << " | filt(Tau) = fmin(filt(Tau), filt(Sigma)) = " << alpha_complex_filtration << std::endl;
+        std::cout << " | filt(Tau) = fmin(filt(Tau), filt(Sigma)) = " << filtration(f_boundary) << std::endl;
 #endif  // DEBUG_TRACES
+        // ### Else
       } else {
         // No need to compute is_gabriel for dimension <= 2
         // i.e. : Sigma = (3,1) => Tau = 1
-        if (fc_decr_dim > 1) {
+        if (decr_dim > 1) {
           // insert the Tau points in a vector for is_gabriel function
           Vector_of_CGAL_points pointVector;
           Vertex_handle vertexForGabriel = Vertex_handle();
-          for (auto vertex : full_cell.simplex_vertex_range(f_boundary)) {
+          for (auto vertex : simplex_vertex_range(f_boundary)) {
             pointVector.push_back(get_point(vertex));
           }
           // Retrieve the Sigma point that is not part of Tau - parameter for is_gabriel function
-          for (auto vertex : simplex_vertex_range(sigma_handle)) {
+          for (auto vertex : simplex_vertex_range(f_simplex)) {
             if (std::find(pointVector.begin(), pointVector.end(), get_point(vertex)) == pointVector.end()) {
               // vertex is not found in Tau
               vertexForGabriel = vertex;
@@ -392,24 +341,11 @@ class Alpha_complex : public Simplex_tree<> {
 #endif  // DEBUG_TRACES
           // ### If Tau is not Gabriel of Sigma
           if (false == is_gab) {
-            if (tau_handle == null_simplex()) {
-#ifdef DEBUG_TRACES
-              std::cout << " | Tau not found" << std::endl;
-#endif  // DEBUG_TRACES
-              // in case Tau is not yet created
-              Simplex_result insert_result = insert_simplex(tau_vertex, std::numeric_limits<double>::quiet_NaN());
-              if (!insert_result.second) {
-                std::cerr << "Alpha_complex::propagate_alpha_filtration insert_simplex failed" << std::endl;
-                exit(-1);  // ----->>
-              }
-              // Sigma is the new inserted simplex handle
-              tau_handle = insert_result.first;
-            }
             // ### filt(Tau) = filt(Sigma)
-            assign_filtration(tau_handle, filtration(sigma_handle));
-            // No need to check for filtration_max, alpha_complex_filtration is an existing filtration value
+            Filtration_value alpha_complex_filtration = filtration(f_simplex);
+            assign_filtration(f_boundary, alpha_complex_filtration);
 #ifdef DEBUG_TRACES
-            std::cout << " | filt(Tau) = filt(Sigma) = " << filtration(sigma_handle) << std::endl;
+            std::cout << " | filt(Tau) = filt(Sigma) = " << filtration(f_boundary) << std::endl;
 #endif  // DEBUG_TRACES
           }
         }
diff --git a/src/Alpha_complex/test/Alpha_complex_unit_test.cpp b/src/Alpha_complex/test/Alpha_complex_unit_test.cpp
index c15f07e1..b2597eff 100644
--- a/src/Alpha_complex/test/Alpha_complex_unit_test.cpp
+++ b/src/Alpha_complex/test/Alpha_complex_unit_test.cpp
@@ -40,144 +40,68 @@
 typedef CGAL::Epick_d< CGAL::Dynamic_dimension_tag > Kernel_d;
 // The triangulation uses the default instantiation of the TriangulationDataStructure template parameter
 
-BOOST_AUTO_TEST_CASE(S4_100_OFF_file) {
+BOOST_AUTO_TEST_CASE(ALPHA_DOC_OFF_file) {
   // ----------------------------------------------------------------------------
   //
   // Init of an alpha-complex from a OFF file
   //
   // ----------------------------------------------------------------------------
-  std::string off_file_name("S4_100.off");
-  double max_alpha_square_value = 1e10;
-  std::cout << "========== OFF FILE NAME = " << off_file_name << " - alpha²=" <<
-      max_alpha_square_value << "==========" << std::endl;
-
-  Gudhi::alphacomplex::Alpha_complex<Kernel_d> alpha_complex_from_file(off_file_name, max_alpha_square_value);
-
-  const int DIMENSION = 4;
-  std::cout << "alpha_complex_from_file.dimension()=" << alpha_complex_from_file.dimension() << std::endl;
-  BOOST_CHECK(alpha_complex_from_file.dimension() == DIMENSION);
-
-  const int NUMBER_OF_VERTICES = 100;
-  std::cout << "alpha_complex_from_file.num_vertices()=" << alpha_complex_from_file.num_vertices() << std::endl;
-  BOOST_CHECK(alpha_complex_from_file.num_vertices() == NUMBER_OF_VERTICES);
-
-  const int NUMBER_OF_SIMPLICES = 6879;
-  std::cout << "alpha_complex_from_file.num_simplices()=" << alpha_complex_from_file.num_simplices() << std::endl;
-  // TODO(VR) : BOOST_CHECK(alpha_complex_from_file.num_simplices() == NUMBER_OF_SIMPLICES);
-
-  // + TODO(VR) : in wait of num_simplices fix in Simplex_tree [
-  int num_simplices = 0;
-  for (auto f_simplex : alpha_complex_from_file.filtration_simplex_range()) {
-    num_simplices++;
-  }
-  std::cout << "num_simplices=" << num_simplices << std::endl;
-  BOOST_CHECK(num_simplices == NUMBER_OF_SIMPLICES);
-  // - TODO(VR) : in wait of num_simplices fix in Simplex_tree ]
-}
-
-BOOST_AUTO_TEST_CASE(S4_100_OFF_file_filtered) {
-  // ----------------------------------------------------------------------------
-  //
-  // Init of an alpha-complex from a OFF file
-  //
-  // ----------------------------------------------------------------------------
-  std::string off_file_name("S4_100.off");
-  double max_alpha_square_value = 0.999;
+  std::string off_file_name("../../../data/points/alphacomplexdoc.off");
+  double max_alpha_square_value = 60.0;
   std::cout << "========== OFF FILE NAME = " << off_file_name << " - alpha²=" <<
       max_alpha_square_value << "==========" << std::endl;
 
   Gudhi::alphacomplex::Alpha_complex<Kernel_d> alpha_complex_from_file(off_file_name, max_alpha_square_value);
 
-  const int DIMENSION = 4;
+  const int DIMENSION = 2;
   std::cout << "alpha_complex_from_file.dimension()=" << alpha_complex_from_file.dimension() << std::endl;
   BOOST_CHECK(alpha_complex_from_file.dimension() == DIMENSION);
 
-  const int NUMBER_OF_VERTICES = 100;
+  const int NUMBER_OF_VERTICES = 7;
   std::cout << "alpha_complex_from_file.num_vertices()=" << alpha_complex_from_file.num_vertices() << std::endl;
   BOOST_CHECK(alpha_complex_from_file.num_vertices() == NUMBER_OF_VERTICES);
 
-  const int NUMBER_OF_SIMPLICES = 5966;  // Versus 6879, because of filtered alpha value
+  const int NUMBER_OF_SIMPLICES = 25;
   std::cout << "alpha_complex_from_file.num_simplices()=" << alpha_complex_from_file.num_simplices() << std::endl;
-  // TODO(VR) : BOOST_CHECK(alpha_complex_from_file.num_simplices() == NUMBER_OF_SIMPLICES);
+  BOOST_CHECK(alpha_complex_from_file.num_simplices() == NUMBER_OF_SIMPLICES);
 
-  // + TODO(VR) : in wait of num_simplices fix in Simplex_tree [
-  int num_simplices = 0;
-  for (auto f_simplex : alpha_complex_from_file.filtration_simplex_range()) {
-    num_simplices++;
-  }
-  std::cout << "num_simplices=" << num_simplices << std::endl;
-  BOOST_CHECK(num_simplices == NUMBER_OF_SIMPLICES);
-  // - TODO(VR) : in wait of num_simplices fix in Simplex_tree ]
 }
 
-BOOST_AUTO_TEST_CASE(S8_10_OFF_file) {
+BOOST_AUTO_TEST_CASE(ALPHA_DOC_OFF_file_filtered) {
   // ----------------------------------------------------------------------------
   //
   // Init of an alpha-complex from a OFF file
   //
   // ----------------------------------------------------------------------------
-  std::string off_file_name("S8_10.off");
-  double max_alpha_square_value = 1e10;
+  std::string off_file_name("../../../data/points/alphacomplexdoc.off");
+  double max_alpha_square_value = 59.0;
   std::cout << "========== OFF FILE NAME = " << off_file_name << " - alpha²=" <<
       max_alpha_square_value << "==========" << std::endl;
 
   Gudhi::alphacomplex::Alpha_complex<Kernel_d> alpha_complex_from_file(off_file_name, max_alpha_square_value);
 
-  const int DIMENSION = 8;
+  const int DIMENSION = 2;
   std::cout << "alpha_complex_from_file.dimension()=" << alpha_complex_from_file.dimension() << std::endl;
   BOOST_CHECK(alpha_complex_from_file.dimension() == DIMENSION);
 
-  const int NUMBER_OF_VERTICES = 10;
+  const int NUMBER_OF_VERTICES = 7;
   std::cout << "alpha_complex_from_file.num_vertices()=" << alpha_complex_from_file.num_vertices() << std::endl;
   BOOST_CHECK(alpha_complex_from_file.num_vertices() == NUMBER_OF_VERTICES);
 
-  const int NUMBER_OF_SIMPLICES = 1007;
+  const int NUMBER_OF_SIMPLICES = 25;
   std::cout << "alpha_complex_from_file.num_simplices()=" << alpha_complex_from_file.num_simplices() << std::endl;
-  // TODO(VR) : BOOST_CHECK(alpha_complex_from_file.num_simplices() == NUMBER_OF_SIMPLICES);
+  BOOST_CHECK(alpha_complex_from_file.num_simplices() == NUMBER_OF_SIMPLICES);
 
-  // + TODO(VR) : in wait of num_simplices fix in Simplex_tree [
-  int num_simplices = 0;
+  int num_filtered_simplices = 0;
   for (auto f_simplex : alpha_complex_from_file.filtration_simplex_range()) {
-    num_simplices++;
+    if (alpha_complex_from_file.filtration(f_simplex) <= alpha_complex_from_file.filtration()) {
+      num_filtered_simplices++;
+    }
   }
-  std::cout << "num_simplices=" << num_simplices << std::endl;
-  BOOST_CHECK(num_simplices == NUMBER_OF_SIMPLICES);
-  // - TODO(VR) : in wait of num_simplices fix in Simplex_tree ]
-}
-
-BOOST_AUTO_TEST_CASE(S8_10_OFF_file_filtered) {
-  // ----------------------------------------------------------------------------
-  //
-  // Init of an alpha-complex from a OFF file
-  //
-  // ----------------------------------------------------------------------------
-  std::string off_file_name("S8_10.off");
-  double max_alpha_square_value = 1.0;
-  std::cout << "========== OFF FILE NAME = " << off_file_name << " - alpha²=" <<
-      max_alpha_square_value << "==========" << std::endl;
-
-  Gudhi::alphacomplex::Alpha_complex<Kernel_d> alpha_complex_from_file(off_file_name, max_alpha_square_value);
-
-  const int DIMENSION = 8;
-  std::cout << "alpha_complex_from_file.dimension()=" << alpha_complex_from_file.dimension() << std::endl;
-  BOOST_CHECK(alpha_complex_from_file.dimension() == DIMENSION);
-
-  const int NUMBER_OF_VERTICES = 10;
-  std::cout << "alpha_complex_from_file.num_vertices()=" << alpha_complex_from_file.num_vertices() << std::endl;
-  BOOST_CHECK(alpha_complex_from_file.num_vertices() == NUMBER_OF_VERTICES);
-
-  const int NUMBER_OF_SIMPLICES = 1004;  // Versus 1007, because of filtered alpha value
-  std::cout << "alpha_complex_from_file.num_simplices()=" << alpha_complex_from_file.num_simplices() << std::endl;
-  // TODO(VR) : BOOST_CHECK(alpha_complex_from_file.num_simplices() == NUMBER_OF_SIMPLICES);
+  const int NUMBER_OF_FILTERED_SIMPLICES = 23;
+  std::cout << "num_filtered_simplices=" << num_filtered_simplices << std::endl;
+  BOOST_CHECK(num_filtered_simplices == NUMBER_OF_FILTERED_SIMPLICES);
 
-  // + TODO(VR) : in wait of num_simplices fix in Simplex_tree [
-  int num_simplices = 0;
-  for (auto f_simplex : alpha_complex_from_file.filtration_simplex_range()) {
-    num_simplices++;
-  }
-  std::cout << "num_simplices=" << num_simplices << std::endl;
-  BOOST_CHECK(num_simplices == NUMBER_OF_SIMPLICES);
-  // - TODO(VR) : in wait of num_simplices fix in Simplex_tree ]
 }
 
 bool are_almost_the_same(float a, float b) {
@@ -222,10 +146,11 @@ BOOST_AUTO_TEST_CASE(Alpha_complex_from_points) {
 
   std::cout << "========== Alpha_complex_from_points ==========" << std::endl;
 
+  // Another way to check num_simplices
   std::cout << "Iterator on alpha complex simplices in the filtration order, with [filtration value]:" << std::endl;
-  int num_simplices = 0;  // TODO(VR) : in wait of num_simplices fix in Simplex_tree
+  int num_simplices = 0;
   for (auto f_simplex : alpha_complex_from_points.filtration_simplex_range()) {
-    num_simplices++;  // TODO(VR) : in wait of num_simplices fix in Simplex_tree
+    num_simplices++;
     std::cout << "   ( ";
     for (auto vertex : alpha_complex_from_points.simplex_vertex_range(f_simplex)) {
       std::cout << vertex << " ";
@@ -233,13 +158,12 @@ BOOST_AUTO_TEST_CASE(Alpha_complex_from_points) {
     std::cout << ") -> " << "[" << alpha_complex_from_points.filtration(f_simplex) << "] ";
     std::cout << std::endl;
   }
+  BOOST_CHECK(num_simplices == 15);
+  std::cout << "alpha_complex_from_points.num_simplices()=" << alpha_complex_from_points.num_simplices() << std::endl;
+  BOOST_CHECK(alpha_complex_from_points.num_simplices() == 15);
 
   std::cout << "alpha_complex_from_points.dimension()=" << alpha_complex_from_points.dimension() << std::endl;
   BOOST_CHECK(alpha_complex_from_points.dimension() == 4);
-  // TODO(VR) : std::cout << "alpha_complex_from_points.num_simplices()=" << alpha_complex_from_points.num_simplices()
-  // << std::endl;
-  // TODO(VR) : BOOST_CHECK(alpha_complex_from_points.num_simplices() == 15);
-  BOOST_CHECK(num_simplices == 15);  // TODO(VR) : in wait of num_simplices fix in Simplex_tree
   std::cout << "alpha_complex_from_points.num_vertices()=" << alpha_complex_from_points.num_vertices() << std::endl;
   BOOST_CHECK(alpha_complex_from_points.num_vertices() == 4);
 
@@ -263,6 +187,11 @@ BOOST_AUTO_TEST_CASE(Alpha_complex_from_points) {
     }
   }
 
+  Point p0 = alpha_complex_from_points.get_point(0);
+  std::cout << "alpha_complex_from_points.get_point(0)=" << p0 << std::endl;
+  BOOST_CHECK(4 == p0.dimension());
+  BOOST_CHECK(is_point_in_list(points, p0));
+
   Point p1 = alpha_complex_from_points.get_point(1);
   std::cout << "alpha_complex_from_points.get_point(1)=" << p1 << std::endl;
   BOOST_CHECK(4 == p1.dimension());
@@ -278,12 +207,8 @@ BOOST_AUTO_TEST_CASE(Alpha_complex_from_points) {
   BOOST_CHECK(4 == p3.dimension());
   BOOST_CHECK(is_point_in_list(points, p3));
 
-  Point p4 = alpha_complex_from_points.get_point(4);
-  std::cout << "alpha_complex_from_points.get_point(4)=" << p4 << std::endl;
-  BOOST_CHECK(4 == p4.dimension());
-  BOOST_CHECK(is_point_in_list(points, p4));
-
-  BOOST_CHECK_THROW (alpha_complex_from_points.get_point(5), std::out_of_range);
-  BOOST_CHECK_THROW (alpha_complex_from_points.get_point(0), std::out_of_range);
+  // Test to the limit
+  BOOST_CHECK_THROW (alpha_complex_from_points.get_point(4), std::out_of_range);
+  BOOST_CHECK_THROW (alpha_complex_from_points.get_point(-1), std::out_of_range);
   BOOST_CHECK_THROW (alpha_complex_from_points.get_point(1234), std::out_of_range);
 }
diff --git a/src/Alpha_complex/test/S4_100.off b/src/Alpha_complex/test/S4_100.off
deleted file mode 100644
index cd017e12..00000000
--- a/src/Alpha_complex/test/S4_100.off
+++ /dev/null
@@ -1,102 +0,0 @@
-nOFF
-4 100 0 0
-0.562921 -0.735261 -0.256472 0.277007
--0.803733 -0.0527915 -0.315125 0.501918
--0.24946 -0.354982 -0.410773 -0.801887
-0.916381 -0.0512295 0.371049 0.141223
-0.182222 0.940836 -0.171362 -0.228599
--0.787145 -0.129213 0.568102 -0.202402
-0.0187866 -0.22093 -0.832882 -0.507095
--0.4702 -0.533814 0.353776 0.607286
--0.159798 -0.504771 0.263586 0.806346
-0.295546 0.162541 0.452931 0.825279
-0.242043 -0.107437 -0.913612 -0.308521
-0.875759 -0.113035 -0.469189 -0.0114505
-0.547877 -0.762247 -0.256972 -0.229729
--0.172302 0.521057 0.412013 -0.727363
--0.724729 -0.0574074 -0.0290602 0.686023
-0.700434 -0.102636 0.687285 0.162779
--0.681386 0.0946893 0.610047 0.393178
--0.847553 -0.357132 0.383743 0.0827718
-0.72297 -0.161631 -0.608517 0.284424
-0.757394 0.141549 0.196065 -0.606528
-0.78094 0.00901997 0.434536 0.448586
-0.14166 -0.619339 0.614589 -0.467582
-0.473105 -0.537832 -0.0103746 0.697711
--0.208004 0.536218 0.818027 0.00605288
-0.743694 -0.628926 0.188072 0.126488
--0.462228 -0.278147 0.35514 -0.76345
--0.17361 0.249211 0.758567 -0.57648
-0.416958 -0.254924 -0.576373 -0.654946
--0.590751 -0.286089 -0.424896 0.623402
--0.639538 -0.739693 -0.203745 0.0482932
-0.0731787 0.132121 0.864022 0.480266
--0.149644 -0.164724 -0.249746 -0.94239
--0.348592 0.0120379 -0.928656 -0.126239
-0.395328 -0.54513 0.149976 -0.723917
--0.974164 0.14707 0.157191 0.068302
--0.166425 0.119943 -0.627304 -0.751269
-0.031947 -0.358518 -0.708301 -0.607251
-0.93781 -0.155368 -0.30951 0.0240237
-0.276094 -0.753155 -0.597088 -0.00387459
--0.642876 -0.200551 -0.263517 -0.690687
-0.178711 0.604987 -0.262989 0.729993
--0.520347 0.497922 -0.676144 0.155374
--0.703999 0.500219 -0.484381 0.139789
--0.131013 0.835735 0.506779 0.166004
--0.536116 -0.566557 0.229226 0.582279
--0.334105 0.158252 0.926091 0.0754059
--0.0362677 0.296076 0.897108 0.325915
--0.57486 0.798575 0.15324 -0.0912754
-0.498602 0.0186805 0.72824 0.469801
--0.960329 0.0473356 0.261005 -0.0860505
-0.899134 -0.381392 -0.214508 0.00921711
-0.570576 0.567224 0.393019 -0.445237
--0.761763 -0.614589 -0.0546476 -0.197513
-0.188584 0.289531 0.174031 0.922129
--0.458506 -0.583876 0.639297 -0.2004
-0.785343 -0.21571 0.0794082 -0.574804
-0.0819036 0.65961 -0.247426 0.704973
-0.573125 0.49706 0.373026 0.534145
--0.513286 -0.626226 0.208535 -0.548536
-0.460558 0.468686 0.507832 -0.55707
-0.716158 -0.488201 0.388209 -0.313164
-0.881074 0.152441 0.380128 -0.236589
-0.885793 0.0386389 0.161009 -0.433537
--0.365162 0.298384 0.292846 0.831784
-0.364934 0.632269 -0.197205 -0.654346
--0.31469 -0.429991 0.665304 -0.522923
--0.734198 0.462914 -0.135691 -0.477756
--0.422885 0.674444 -0.364143 -0.483419
-0.829218 -0.154622 -0.381147 0.378439
-0.887881 0.310479 -0.109528 0.321363
--0.354398 -0.693974 0.456019 -0.429941
--0.492045 -0.160008 0.044387 0.854587
-0.0595532 0.158421 0.412577 -0.895062
--0.211441 0.491794 -0.153521 0.83058
--0.33558 -0.504711 0.353831 -0.71236
--0.735211 -0.197714 0.525626 0.379593
-0.465818 -0.424245 0.769469 -0.104627
--0.641071 -0.286339 -0.704442 -0.103923
--0.00446569 0.0249849 -0.194417 -0.980591
--0.610081 -0.252448 0.176698 -0.729966
--0.0859217 -0.154471 0.715027 0.676382
-0.091315 0.0723382 -0.855023 -0.505337
-0.165362 0.200983 -0.428242 -0.865373
--0.587465 0.303019 -0.152442 0.734729
-0.454946 -0.319828 0.437063 -0.706902
--0.384368 0.277509 0.879225 -0.0470385
-0.523335 -0.330233 -0.208592 0.757335
-0.895086 0.0448492 0.268089 -0.353466
--0.0272491 -0.567336 -0.72254 -0.39411
--0.0745014 -0.121818 -0.882466 0.448179
-0.382304 -0.240135 0.851109 -0.267941
--0.418057 -0.852847 -0.3128 0.00606452
--0.554046 0.304237 0.272381 -0.725453
-0.155115 -0.0894732 -0.245017 -0.952838
-0.114459 -0.130722 0.953669 0.245614
-0.0913002 -0.462466 0.244433 0.847374
--0.198849 0.0785111 0.131441 -0.967997
--0.303154 -0.686484 0.639333 0.167604
-0.521455 0.256835 -0.0584503 -0.811606
--0.109787 0.870544 0.161523 0.451676
diff --git a/src/Alpha_complex/test/S8_10.off b/src/Alpha_complex/test/S8_10.off
deleted file mode 100644
index 4e147c44..00000000
--- a/src/Alpha_complex/test/S8_10.off
+++ /dev/null
@@ -1,12 +0,0 @@
-nOFF
-8 10 0 0
-0.440036 -0.574754 -0.200485 0.216537 -0.501251 -0.0329236 -0.196529 0.313023
--0.129367 -0.184089 -0.213021 -0.415848 0.783529 -0.0438025 0.317256 0.120749
-0.132429 0.683748 -0.124536 -0.166133 -0.540695 -0.0887576 0.390234 -0.139031
-0.0137399 -0.161581 -0.609142 -0.370872 -0.320669 -0.364053 0.24127 0.41416
--0.115313 -0.36425 0.190208 0.581871 0.204605 0.112527 0.313562 0.571337
-0.168272 -0.0746917 -0.635156 -0.214488 0.629498 -0.0812499 -0.337255 -0.00823068
-0.369896 -0.514626 -0.173493 -0.1551 -0.127105 0.384377 0.303936 -0.536566
--0.49013 -0.0388242 -0.0196532 0.463953 0.515962 -0.0756047 0.506276 0.119908
--0.434258 0.060347 0.388793 0.250579 -0.653127 -0.275207 0.295714 0.0637842
-0.596172 -0.133284 -0.501793 0.234541 0.428452 0.0800735 0.110912 -0.343109
diff --git a/src/CMakeLists.txt b/src/CMakeLists.txt
index 7b30f77a..172f9128 100644
--- a/src/CMakeLists.txt
+++ b/src/CMakeLists.txt
@@ -19,7 +19,6 @@ set(Boost_USE_STATIC_LIBS        ON)
 set(Boost_USE_MULTITHREADED      ON)
 set(Boost_USE_STATIC_RUNTIME    OFF)
 
-find_package(Boost)
 find_package(GMP)
 if(GMP_FOUND)
   find_package(GMPXX)
diff --git a/src/Persistent_cohomology/example/alpha_shapes_persistence.cpp b/src/Persistent_cohomology/example/alpha_shapes_persistence.cpp
index 3a50c84c..1e907040 100644
--- a/src/Persistent_cohomology/example/alpha_shapes_persistence.cpp
+++ b/src/Persistent_cohomology/example/alpha_shapes_persistence.cpp
@@ -263,7 +263,6 @@ int main (int argc, char * const argv[])
       std::cout << "This shall not happen" << std::endl;
   }
   simplex_tree.set_filtration(filtration_max);
-  simplex_tree.set_num_simplices(count_vertices + count_edges + count_facets + count_cells);
   simplex_tree.set_dimension(dim_max);
 
 #ifdef DEBUG_TRACES
diff --git a/src/Persistent_cohomology/include/gudhi/Persistent_cohomology.h b/src/Persistent_cohomology/include/gudhi/Persistent_cohomology.h
index 896a7a9f..4c818ffa 100644
--- a/src/Persistent_cohomology/include/gudhi/Persistent_cohomology.h
+++ b/src/Persistent_cohomology/include/gudhi/Persistent_cohomology.h
@@ -230,9 +230,10 @@ class Persistent_cohomology {
       : cpx_(&cpx),
         dim_max_(cpx.dimension()),                       // upper bound on the dimension of the simplices
         coeff_field_(),                                  // initialize the field coefficient structure.
-        ds_rank_(cpx_->num_simplices()),                 // union-find
-        ds_parent_(cpx_->num_simplices()),               // union-find
-        ds_repr_(cpx_->num_simplices(), NULL),           // union-find -> annotation vectors
+        num_simplices_(cpx_->num_simplices()),           // num_simplices save to avoid to call thrice the function
+        ds_rank_(num_simplices_),                        // union-find
+        ds_parent_(num_simplices_),                      // union-find
+        ds_repr_(num_simplices_, NULL),                  // union-find -> annotation vectors
         dsets_(&ds_rank_[0], &ds_parent_[0]),            // union-find
         cam_(),                                          // collection of annotation vectors
         zero_cocycles_(),                                // union-find -> Simplex_key of creator for 0-homology
@@ -743,6 +744,7 @@ class Persistent_cohomology {
   Complex_ds * cpx_;
   int dim_max_;
   CoefficientField coeff_field_;
+  size_t num_simplices_;
 
   /*  Disjoint sets data structure to link the model of FilteredComplex
    * with the compressed annotation matrix.
diff --git a/src/Simplex_tree/example/simple_simplex_tree.cpp b/src/Simplex_tree/example/simple_simplex_tree.cpp
index 6d20e43e..a2e1f0e9 100644
--- a/src/Simplex_tree/example/simple_simplex_tree.cpp
+++ b/src/Simplex_tree/example/simple_simplex_tree.cpp
@@ -21,7 +21,6 @@
  */
 
 #include <iostream>
-#include <ctime>
 #include "gudhi/graph_simplicial_complex.h"
 #include "gudhi/Simplex_tree.h"
 
@@ -35,10 +34,6 @@ int main(int argc, char * const argv[]) {
   const Filtration_value SECOND_FILTRATION_VALUE = 0.2;
   const Filtration_value THIRD_FILTRATION_VALUE = 0.3;
   const Filtration_value FOURTH_FILTRATION_VALUE = 0.4;
-  Vertex_handle FIRST_VERTEX_HANDLE = (Vertex_handle) 0;
-  Vertex_handle SECOND_VERTEX_HANDLE = (Vertex_handle) 1;
-  Vertex_handle THIRD_VERTEX_HANDLE = (Vertex_handle) 2;
-  Vertex_handle FOURTH_VERTEX_HANDLE = (Vertex_handle) 3;
 
   // TEST OF INSERTION
   std::cout << "********************************************************************" << std::endl;
@@ -55,173 +50,132 @@ int main(int argc, char * const argv[]) {
 
   // ++ FIRST
   std::cout << "   * INSERT 0" << std::endl;
-  typeVectorVertex firstSimplexVector;
-  firstSimplexVector.push_back(FIRST_VERTEX_HANDLE);
+  typeVectorVertex firstSimplexVector = { 0 };
   typePairSimplexBool returnValue =
       simplexTree.insert_simplex(firstSimplexVector, Filtration_value(FIRST_FILTRATION_VALUE));
 
   if (returnValue.second == true) {
     std::cout << "   + 0 INSERTED" << std::endl;
-    int nb_simplices = simplexTree.num_simplices() + 1;
-    simplexTree.set_num_simplices(nb_simplices);
   } else {
     std::cout << "   - 0 NOT INSERTED" << std::endl;
   }
 
   // ++ SECOND
   std::cout << "   * INSERT 1" << std::endl;
-  typeVectorVertex secondSimplexVector;
-  secondSimplexVector.push_back(SECOND_VERTEX_HANDLE);
+  typeVectorVertex secondSimplexVector = { 1 };
   returnValue =
       simplexTree.insert_simplex(secondSimplexVector, Filtration_value(FIRST_FILTRATION_VALUE));
 
   if (returnValue.second == true) {
     std::cout << "   + 1 INSERTED" << std::endl;
-    int nb_simplices = simplexTree.num_simplices() + 1;
-    simplexTree.set_num_simplices(nb_simplices);
   } else {
     std::cout << "   - 1 NOT INSERTED" << std::endl;
   }
 
   // ++ THIRD
   std::cout << "   * INSERT (0,1)" << std::endl;
-  typeVectorVertex thirdSimplexVector;
-  thirdSimplexVector.push_back(FIRST_VERTEX_HANDLE);
-  thirdSimplexVector.push_back(SECOND_VERTEX_HANDLE);
+  typeVectorVertex thirdSimplexVector = { 0, 1 };
   returnValue =
       simplexTree.insert_simplex(thirdSimplexVector, Filtration_value(SECOND_FILTRATION_VALUE));
 
   if (returnValue.second == true) {
     std::cout << "   + (0,1) INSERTED" << std::endl;
-    int nb_simplices = simplexTree.num_simplices() + 1;
-    simplexTree.set_num_simplices(nb_simplices);
   } else {
     std::cout << "   - (0,1) NOT INSERTED" << std::endl;
   }
 
   // ++ FOURTH
   std::cout << "   * INSERT 2" << std::endl;
-  typeVectorVertex fourthSimplexVector;
-  fourthSimplexVector.push_back(THIRD_VERTEX_HANDLE);
+  typeVectorVertex fourthSimplexVector = { 2 };
   returnValue =
       simplexTree.insert_simplex(fourthSimplexVector, Filtration_value(FIRST_FILTRATION_VALUE));
 
   if (returnValue.second == true) {
     std::cout << "   + 2 INSERTED" << std::endl;
-    int nb_simplices = simplexTree.num_simplices() + 1;
-    simplexTree.set_num_simplices(nb_simplices);
   } else {
     std::cout << "   - 2 NOT INSERTED" << std::endl;
   }
 
   // ++ FIFTH
   std::cout << "   * INSERT (2,0)" << std::endl;
-  typeVectorVertex fifthSimplexVector;
-  fifthSimplexVector.push_back(THIRD_VERTEX_HANDLE);
-  fifthSimplexVector.push_back(FIRST_VERTEX_HANDLE);
+  typeVectorVertex fifthSimplexVector = { 2, 0 };
   returnValue =
       simplexTree.insert_simplex(fifthSimplexVector, Filtration_value(SECOND_FILTRATION_VALUE));
 
   if (returnValue.second == true) {
     std::cout << "   + (2,0) INSERTED" << std::endl;
-    int nb_simplices = simplexTree.num_simplices() + 1;
-    simplexTree.set_num_simplices(nb_simplices);
   } else {
     std::cout << "   - (2,0) NOT INSERTED" << std::endl;
   }
 
   // ++ SIXTH
   std::cout << "   * INSERT (2,1)" << std::endl;
-  typeVectorVertex sixthSimplexVector;
-  sixthSimplexVector.push_back(THIRD_VERTEX_HANDLE);
-  sixthSimplexVector.push_back(SECOND_VERTEX_HANDLE);
+  typeVectorVertex sixthSimplexVector = { 2, 1 };
   returnValue =
       simplexTree.insert_simplex(sixthSimplexVector, Filtration_value(SECOND_FILTRATION_VALUE));
 
   if (returnValue.second == true) {
     std::cout << "   + (2,1) INSERTED" << std::endl;
-    int nb_simplices = simplexTree.num_simplices() + 1;
-    simplexTree.set_num_simplices(nb_simplices);
   } else {
     std::cout << "   - (2,1) NOT INSERTED" << std::endl;
   }
 
   // ++ SEVENTH
   std::cout << "   * INSERT (2,1,0)" << std::endl;
-  typeVectorVertex seventhSimplexVector;
-  seventhSimplexVector.push_back(THIRD_VERTEX_HANDLE);
-  seventhSimplexVector.push_back(SECOND_VERTEX_HANDLE);
-  seventhSimplexVector.push_back(FIRST_VERTEX_HANDLE);
+  typeVectorVertex seventhSimplexVector = { 2, 1, 0 };
   returnValue =
       simplexTree.insert_simplex(seventhSimplexVector, Filtration_value(THIRD_FILTRATION_VALUE));
 
   if (returnValue.second == true) {
     std::cout << "   + (2,1,0) INSERTED" << std::endl;
-    int nb_simplices = simplexTree.num_simplices() + 1;
-    simplexTree.set_num_simplices(nb_simplices);
   } else {
     std::cout << "   - (2,1,0) NOT INSERTED" << std::endl;
   }
 
   // ++ EIGHTH
   std::cout << "   * INSERT 3" << std::endl;
-  typeVectorVertex eighthSimplexVector;
-  eighthSimplexVector.push_back(FOURTH_VERTEX_HANDLE);
+  typeVectorVertex eighthSimplexVector = { 3 };
   returnValue =
       simplexTree.insert_simplex(eighthSimplexVector, Filtration_value(FIRST_FILTRATION_VALUE));
 
   if (returnValue.second == true) {
     std::cout << "   + 3 INSERTED" << std::endl;
-    int nb_simplices = simplexTree.num_simplices() + 1;
-    simplexTree.set_num_simplices(nb_simplices);
   } else {
     std::cout << "   - 3 NOT INSERTED" << std::endl;
   }
 
   // ++ NINETH
   std::cout << "   * INSERT (3,0)" << std::endl;
-  typeVectorVertex ninethSimplexVector;
-  ninethSimplexVector.push_back(FOURTH_VERTEX_HANDLE);
-  ninethSimplexVector.push_back(FIRST_VERTEX_HANDLE);
+  typeVectorVertex ninethSimplexVector = { 3, 0 };
   returnValue =
       simplexTree.insert_simplex(ninethSimplexVector, Filtration_value(SECOND_FILTRATION_VALUE));
 
   if (returnValue.second == true) {
     std::cout << "   + (3,0) INSERTED" << std::endl;
-    int nb_simplices = simplexTree.num_simplices() + 1;
-    simplexTree.set_num_simplices(nb_simplices);
   } else {
     std::cout << "   - (3,0) NOT INSERTED" << std::endl;
   }
 
   // ++ TENTH
   std::cout << "   * INSERT 0 (already inserted)" << std::endl;
-  typeVectorVertex tenthSimplexVector;
-  tenthSimplexVector.push_back(FIRST_VERTEX_HANDLE);
+  typeVectorVertex tenthSimplexVector = { 0 };
   returnValue =
       simplexTree.insert_simplex(tenthSimplexVector, Filtration_value(FOURTH_FILTRATION_VALUE)); // With a different filtration value
 
   if (returnValue.second == true) {
     std::cout << "   + 0 INSERTED" << std::endl;
-    int nb_simplices = simplexTree.num_simplices() + 1;
-    simplexTree.set_num_simplices(nb_simplices);
   } else {
     std::cout << "   - 0 NOT INSERTED" << std::endl;
   }
 
   // ++ ELEVENTH
   std::cout << "   * INSERT (2,1,0) (already inserted)" << std::endl;
-  typeVectorVertex eleventhSimplexVector;
-  eleventhSimplexVector.push_back(THIRD_VERTEX_HANDLE);
-  eleventhSimplexVector.push_back(SECOND_VERTEX_HANDLE);
-  eleventhSimplexVector.push_back(FIRST_VERTEX_HANDLE);
+  typeVectorVertex eleventhSimplexVector = { 2, 1, 0 };
   returnValue =
       simplexTree.insert_simplex(eleventhSimplexVector, Filtration_value(FOURTH_FILTRATION_VALUE));
 
   if (returnValue.second == true) {
     std::cout << "   + (2,1,0) INSERTED" << std::endl;
-    int nb_simplices = simplexTree.num_simplices() + 1;
-    simplexTree.set_num_simplices(nb_simplices);
   } else {
     std::cout << "   - (2,1,0) NOT INSERTED" << std::endl;
   }
@@ -262,9 +216,7 @@ int main(int argc, char * const argv[]) {
   else
     std::cout << "***- NO IT ISN'T\n";
 
-  Vertex_handle UNKNOWN_VERTEX_HANDLE = (Vertex_handle) 15;
-  typeVectorVertex unknownSimplexVector;
-  unknownSimplexVector.push_back(UNKNOWN_VERTEX_HANDLE);
+  typeVectorVertex unknownSimplexVector = { 15 };
   simplexFound = simplexTree.find(unknownSimplexVector);
   std::cout << "**************IS THE SIMPLEX {15} IN THE SIMPLEX TREE ?\n";
   if (simplexFound != simplexTree.null_simplex())
@@ -279,9 +231,7 @@ int main(int argc, char * const argv[]) {
   else
     std::cout << "***- NO IT ISN'T\n";
 
-  typeVectorVertex otherSimplexVector;
-  otherSimplexVector.push_back(UNKNOWN_VERTEX_HANDLE);
-  otherSimplexVector.push_back(SECOND_VERTEX_HANDLE);
+  typeVectorVertex otherSimplexVector = { 1, 15 };
   simplexFound = simplexTree.find(otherSimplexVector);
   std::cout << "**************IS THE SIMPLEX {15,1} IN THE SIMPLEX TREE ?\n";
   if (simplexFound != simplexTree.null_simplex())
@@ -289,10 +239,7 @@ int main(int argc, char * const argv[]) {
   else
     std::cout << "***- NO IT ISN'T\n";
 
-  typeVectorVertex invSimplexVector;
-  invSimplexVector.push_back(SECOND_VERTEX_HANDLE);
-  invSimplexVector.push_back(THIRD_VERTEX_HANDLE);
-  invSimplexVector.push_back(FIRST_VERTEX_HANDLE);
+  typeVectorVertex invSimplexVector = { 1, 2, 0 };
   simplexFound = simplexTree.find(invSimplexVector);
   std::cout << "**************IS THE SIMPLEX {1,2,0} IN THE SIMPLEX TREE ?\n";
   if (simplexFound != simplexTree.null_simplex())
diff --git a/src/Simplex_tree/include/gudhi/Simplex_tree.h b/src/Simplex_tree/include/gudhi/Simplex_tree.h
index 247630cc..fe2faf90 100644
--- a/src/Simplex_tree/include/gudhi/Simplex_tree.h
+++ b/src/Simplex_tree/include/gudhi/Simplex_tree.h
@@ -108,13 +108,6 @@ class Simplex_tree {
   /* Type of dictionary Vertex_handle -> Node for traversing the simplex tree. */
   typedef typename boost::container::flat_map<Vertex_handle, Node> Dictionary;
 
-  friend class Simplex_tree_node_explicit_storage< Simplex_tree<FiltrationValue, SimplexKey, VertexHandle> >;
-  friend class Simplex_tree_siblings< Simplex_tree<FiltrationValue, SimplexKey, VertexHandle>, Dictionary>;
-  friend class Simplex_tree_simplex_vertex_iterator< Simplex_tree<FiltrationValue, SimplexKey, VertexHandle> >;
-  friend class Simplex_tree_boundary_simplex_iterator< Simplex_tree<FiltrationValue, SimplexKey, VertexHandle> >;
-  friend class Simplex_tree_complex_simplex_iterator< Simplex_tree<FiltrationValue, SimplexKey, VertexHandle> >;
-  friend class Simplex_tree_skeleton_simplex_iterator< Simplex_tree<FiltrationValue, SimplexKey, VertexHandle> >;
-
   /* \brief Set of nodes sharing a same parent in the simplex tree. */
   /* \brief Set of nodes sharing a same parent in the simplex tree. */
   typedef Simplex_tree_siblings<Simplex_tree, Dictionary> Siblings;
@@ -188,12 +181,12 @@ class Simplex_tree {
   /** \name Range and iterator methods
    * @{ */
 
-  /** \brief Returns a range over the vertices of the simplicial complex.
+  /** \brief Returns a range over the vertices of the simplicial complex. 
    * The order is increasing according to < on Vertex_handles.*/
   Complex_vertex_range complex_vertex_range() {
     return Complex_vertex_range(
-        boost::make_transform_iterator(root_.members_.begin(), return_first()),
-        boost::make_transform_iterator(root_.members_.end(), return_first()));
+                                boost::make_transform_iterator(root_.members_.begin(), return_first()),
+                                boost::make_transform_iterator(root_.members_.end(), return_first()));
   }
 
   /** \brief Returns a range over the simplices of the simplicial complex.
@@ -284,11 +277,10 @@ class Simplex_tree {
   /** \brief Constructs an empty simplex tree. */
   Simplex_tree()
       : null_vertex_(-1),
-        threshold_(0),
-        num_simplices_(0),
-        root_(NULL, null_vertex_),
-        filtration_vect_(),
-        dimension_(-1) {
+      threshold_(0),
+      root_(NULL, null_vertex_),
+      filtration_vect_(),
+      dimension_(-1) {
   }
 
   /** \brief Destructor; deallocates the whole tree structure. */
@@ -376,13 +368,27 @@ class Simplex_tree {
     return root_.members_.size();
   }
 
-  /** \brief Returns the number of simplices in the complex.
-   *
-   * Does not count the empty simplex. */
-  unsigned int num_simplices() const {
-    return num_simplices_;
+ public:
+  /** \brief returns the number of simplices in the simplex_tree. */
+  size_t num_simplices() {
+    return num_simplices(&root_);
   }
 
+ private:
+  /** \brief returns the number of simplices in the simplex_tree. */
+  size_t num_simplices(Siblings * sib) {
+    auto sib_begin = sib->members().begin();
+    auto sib_end = sib->members().end();
+    size_t simplices_number = sib_end - sib_begin;
+    for (auto sh = sib_begin; sh != sib_end; ++sh) {
+      if (has_children(sh)) {
+        simplices_number += num_simplices(sh->second.children());
+      }
+    }
+    return simplices_number;
+  }
+
+ public:
   /** \brief Returns the dimension of a simplex.
    *
    * Must be different from null_simplex().*/
@@ -407,6 +413,7 @@ class Simplex_tree {
     return (sh->second.children()->parent() == sh->first);
   }
 
+ public:
   /** \brief Given a range of Vertex_handles, returns the Simplex_handle
    * of the simplex in the simplicial complex containing the corresponding
    * vertices. Return null_simplex() if the simplex is not in the complex.
@@ -443,7 +450,7 @@ class Simplex_tree {
   Simplex_handle find_vertex(Vertex_handle v) {
     return root_.members_.begin() + v;
   }
-
+  
   /** \brief Insert a simplex, represented by a range of Vertex_handles, in the simplicial complex.
    *
    * @param[in]  simplex    range of Vertex_handles, representing the vertices of the new simplex
@@ -469,7 +476,7 @@ class Simplex_tree {
    * .end() return random access iterators, with 'value_type' Vertex_handle. */
   template<class RandomAccessVertexRange>
   std::pair<Simplex_handle, bool> insert_simplex(RandomAccessVertexRange & simplex,
-                                         Filtration_value filtration) {
+                                                 Filtration_value filtration) {
     if (simplex.empty()) {
       return std::pair<Simplex_handle, bool>(null_simplex(), true);
     }
@@ -506,7 +513,7 @@ class Simplex_tree {
    *
    * @param[in]  Nsimplex   range of Vertex_handles, representing the vertices of the new N-simplex
    * @param[in]  filtration the filtration value assigned to the new N-simplex.
-  */
+   */
   template<class RandomAccessVertexRange>
   std::pair<Simplex_handle, bool> insert_simplex_and_subfaces(RandomAccessVertexRange& Nsimplex,
                                                               Filtration_value filtration = 0.0) {
@@ -525,13 +532,11 @@ class Simplex_tree {
       // N-Simplex insert
       returned = insert_simplex(Nsimplex, filtration);
       if (returned.second == true) {
-        num_simplices_++;
       }
     } else if (Nsimplex.size() == 1) {
       // 1-Simplex insert - End of recursivity
       returned = insert_simplex(Nsimplex, filtration);
       if (returned.second == true) {
-        num_simplices_++;
       }
     } else {
       // Nothing to insert - empty vector
@@ -539,20 +544,13 @@ class Simplex_tree {
     return returned;
   }
 
-  /** \brief Assign a value 'key' to the key of the simplex
-   * represented by the Simplex_handle 'sh'. */
-  void assign_key(Simplex_handle sh, Simplex_key key) {
-    sh->second.assign_key(key);
-  }
-
  public:
   /** Returns the two Simplex_handle corresponding to the endpoints of
    * and edge. sh must point to a 1-dimensional simplex. This is an
    * optimized version of the boundary computation. */
   std::pair<Simplex_handle, Simplex_handle> endpoints(Simplex_handle sh) {
-    return std::pair<Simplex_handle, Simplex_handle>(
-        root_.members_.find(sh->first),
-        root_.members_.find(self_siblings(sh)->parent()));
+    assert(dimension(sh) == 1);
+    return { find_vertex(sh->first), find_vertex(self_siblings(sh)->parent()) };
   }
 
   /** Returns the Siblings containing a simplex.*/
@@ -563,23 +561,28 @@ class Simplex_tree {
       return sh->second.children();
   }
 
+  // void display_simplex(Simplex_handle sh)
+  // {
+  //   std::cout << "   " << "[" << filtration(sh) << "] ";
+  //   for( auto vertex : simplex_vertex_range(sh) )
+  //     { std::cout << vertex << " "; }
+  // }
+
+  // void print(Simplex_handle sh, std::ostream& os = std::cout)
+  // {  for(auto v : simplex_vertex_range(sh)) {os << v << " ";}
+  //    os << std::endl; }
+
  public:
   /** Returns a pointer to the root nodes of the simplex tree. */
   Siblings * root() {
     return &root_;
   }
 
- public:
   /** Set an upper bound for the filtration values. */
   void set_filtration(Filtration_value fil) {
     threshold_ = fil;
   }
 
-  /** Set a number of simplices for the simplicial complex. */
-  void set_num_simplices(unsigned int num_simplices) {
-    num_simplices_ = num_simplices;
-  }
-
   /** Set a dimension for the simplicial complex. */
   void set_dimension(int dimension) {
     dimension_ = dimension;
@@ -776,22 +779,20 @@ class Simplex_tree {
       dimension_ = 1;
     }
 
-    num_simplices_ = boost::num_vertices(skel_graph)
-        + boost::num_edges(skel_graph);
     root_.members_.reserve(boost::num_vertices(skel_graph));
 
     typename boost::graph_traits<OneSkeletonGraph>::vertex_iterator v_it,
         v_it_end;
     for (std::tie(v_it, v_it_end) = boost::vertices(skel_graph); v_it != v_it_end;
-        ++v_it) {
+         ++v_it) {
       root_.members_.emplace_hint(
-          root_.members_.end(), *v_it,
-          Node(&root_, boost::get(vertex_filtration_t(), skel_graph, *v_it)));
+                                  root_.members_.end(), *v_it,
+                                  Node(&root_, boost::get(vertex_filtration_t(), skel_graph, *v_it)));
     }
     typename boost::graph_traits<OneSkeletonGraph>::edge_iterator e_it,
         e_it_end;
     for (std::tie(e_it, e_it_end) = boost::edges(skel_graph); e_it != e_it_end;
-        ++e_it) {
+         ++e_it) {
       auto u = source(*e_it, skel_graph);
       auto v = target(*e_it, skel_graph);
       if (u < v) {
@@ -802,9 +803,9 @@ class Simplex_tree {
         }
 
         sh->second.children()->members().emplace(
-            v,
-            Node(sh->second.children(),
-                 boost::get(edge_filtration_t(), skel_graph, *e_it)));
+                                                 v,
+                                                 Node(sh->second.children(),
+                                                      boost::get(edge_filtration_t(), skel_graph, *e_it)));
       }
     }
   }
@@ -823,7 +824,7 @@ class Simplex_tree {
   void expansion(int max_dim) {
     dimension_ = max_dim;
     for (Dictionary_it root_it = root_.members_.begin();
-        root_it != root_.members_.end(); ++root_it) {
+         root_it != root_.members_.end(); ++root_it) {
       if (has_children(root_it)) {
         siblings_expansion(root_it->second.children(), max_dim - 1);
       }
@@ -832,10 +833,9 @@ class Simplex_tree {
   }
 
  private:
-
   /** \brief Recursive expansion of the simplex tree.*/
   void siblings_expansion(Siblings * siblings,  // must contain elements
-      int k) {
+                          int k) {
     if (dimension_ > k) {
       dimension_ = k;
     }
@@ -857,10 +857,9 @@ class Simplex_tree {
                      root_sh->second.children()->members().end(),
                      s_h->second.filtration());
         if (inter.size() != 0) {
-          this->num_simplices_ += inter.size();
           Siblings * new_sib = new Siblings(siblings,  // oncles
-              s_h->first,  // parent
-              inter);      // boost::container::ordered_unique_range_t
+                                            s_h->first,  // parent
+                                            inter);  // boost::container::ordered_unique_range_t
           inter.clear();
           s_h->second.assign_children(new_sib);
           siblings_expansion(new_sib, k - 1);
@@ -920,7 +919,6 @@ class Simplex_tree {
   /** \brief Upper bound on the filtration values of the simplices.*/
   Filtration_value threshold_;
   /** \brief Total number of simplices in the complex, without the empty simplex.*/
-  unsigned int num_simplices_;
   /** \brief Set of simplex tree Nodes representing the vertices.*/
   Siblings root_;
   /** \brief Simplices ordered according to a filtration.*/
@@ -930,8 +928,8 @@ class Simplex_tree {
 };
 
 // Print a Simplex_tree in os.
-template<typename T1, typename T2, typename T3>
-std::ostream& operator<<(std::ostream & os, Simplex_tree<T1, T2, T3> & st) {
+template<typename...T>
+std::ostream& operator<<(std::ostream & os, Simplex_tree<T...> & st) {
   for (auto sh : st.filtration_simplex_range()) {
     os << st.dimension(sh) << " ";
     for (auto v : st.simplex_vertex_range(sh)) {
@@ -942,18 +940,15 @@ std::ostream& operator<<(std::ostream & os, Simplex_tree<T1, T2, T3> & st) {
   return os;
 }
 
-template<typename T1, typename T2, typename T3>
-std::istream& operator>>(std::istream & is, Simplex_tree<T1, T2, T3> & st) {
-  // assert(st.num_simplices() == 0);
-
-  std::vector<typename Simplex_tree<T1, T2, T3>::Vertex_handle> simplex;
-  typename Simplex_tree<T1, T2, T3>::Filtration_value fil;
-  typename Simplex_tree<T1, T2, T3>::Filtration_value max_fil = 0;
+template<typename...T>
+std::istream& operator>>(std::istream & is, Simplex_tree<T...> & st) {
+  typedef Simplex_tree<T...> ST;
+  std::vector<typename ST::Vertex_handle> simplex;
+  typename ST::Filtration_value fil;
+  typename ST::Filtration_value max_fil = 0;
   int max_dim = -1;
-  size_t num_simplices = 0;
   while (read_simplex(is, simplex, fil)) {
     // read all simplices in the file as a list of vertices
-    ++num_simplices;
     // Warning : simplex_size needs to be casted in int - Can be 0
     int dim = static_cast<int> (simplex.size() - 1);
     if (max_dim < dim) {
@@ -966,7 +961,6 @@ std::istream& operator>>(std::istream & is, Simplex_tree<T1, T2, T3> & st) {
     st.insert_simplex(simplex, fil);
     simplex.clear();
   }
-  st.set_num_simplices(num_simplices);
   st.set_dimension(max_dim);
   st.set_filtration(max_fil);
 
diff --git a/src/Simplex_tree/test/simplex_tree_unit_test.cpp b/src/Simplex_tree/test/simplex_tree_unit_test.cpp
index 566d6d90..20403e2a 100644
--- a/src/Simplex_tree/test/simplex_tree_unit_test.cpp
+++ b/src/Simplex_tree/test/simplex_tree_unit_test.cpp
@@ -157,12 +157,17 @@ void set_and_test_simplex_tree_dim_fil(typeST& simplexTree, int vectorSize, cons
     std::cout << "   set_and_test_simplex_tree_dim_fil - max_fil=" << max_fil
         << std::endl;
   }
-  unsigned int nb_simplices = simplexTree.num_simplices() + 1;
-  simplexTree.set_num_simplices(nb_simplices);
-
+  
   BOOST_CHECK(simplexTree.dimension() == dim_max);
   BOOST_CHECK(AreAlmostTheSame(simplexTree.filtration(), max_fil));
-  BOOST_CHECK(simplexTree.num_simplices() == nb_simplices);
+
+  // Another way to count simplices:
+  long long int num_simp = 0;
+  for (auto f_simplex : simplexTree.complex_simplex_range()) {
+    num_simp++;
+  }
+  
+  BOOST_CHECK(simplexTree.num_simplices() == num_simp);
 }
 
 void test_cofaces(typeST& st, std::vector<Vertex_handle> v, int dim, std::vector<typeST::Simplex_handle> res) {
@@ -186,10 +191,6 @@ BOOST_AUTO_TEST_CASE(simplex_tree_insertion) {
   const Filtration_value SECOND_FILTRATION_VALUE = 0.2;
   const Filtration_value THIRD_FILTRATION_VALUE = 0.3;
   const Filtration_value FOURTH_FILTRATION_VALUE = 0.4;
-  Vertex_handle FIRST_VERTEX_HANDLE = (Vertex_handle) 0;
-  Vertex_handle SECOND_VERTEX_HANDLE = (Vertex_handle) 1;
-  Vertex_handle THIRD_VERTEX_HANDLE = (Vertex_handle) 2;
-  Vertex_handle FOURTH_VERTEX_HANDLE = (Vertex_handle) 3;
 
   // TEST OF INSERTION
   std::cout << "********************************************************************" << std::endl;
@@ -198,13 +199,10 @@ BOOST_AUTO_TEST_CASE(simplex_tree_insertion) {
 
   // ++ FIRST
   std::cout << "   - INSERT 0" << std::endl;
-  typeVectorVertex firstSimplexVector;
-  firstSimplexVector.push_back(FIRST_VERTEX_HANDLE);
+  typeVectorVertex firstSimplexVector { 0 };
   BOOST_CHECK(firstSimplexVector.size() == 1);
-  typeSimplex firstSimplex = std::make_pair(
-                                            firstSimplexVector, Filtration_value(FIRST_FILTRATION_VALUE));
-  typePairSimplexBool returnValue = st.insert_simplex(firstSimplex.first,
-                                                      firstSimplex.second);
+  typeSimplex firstSimplex = std::make_pair(firstSimplexVector, Filtration_value(FIRST_FILTRATION_VALUE));
+  typePairSimplexBool returnValue = st.insert_simplex(firstSimplex.first, firstSimplex.second);
 
   test_simplex_tree_insert_returns_true(returnValue);
   set_and_test_simplex_tree_dim_fil(st, firstSimplexVector.size(), firstSimplex.second);
@@ -212,13 +210,10 @@ BOOST_AUTO_TEST_CASE(simplex_tree_insertion) {
 
   // ++ SECOND
   std::cout << "   - INSERT 1" << std::endl;
-  typeVectorVertex secondSimplexVector;
-  secondSimplexVector.push_back(SECOND_VERTEX_HANDLE);
+  typeVectorVertex secondSimplexVector { 1 };
   BOOST_CHECK(secondSimplexVector.size() == 1);
-  typeSimplex secondSimplex = std::make_pair(
-                                             secondSimplexVector, Filtration_value(FIRST_FILTRATION_VALUE));
-  returnValue =
-      st.insert_simplex(secondSimplex.first, secondSimplex.second);
+  typeSimplex secondSimplex = std::make_pair(secondSimplexVector, Filtration_value(FIRST_FILTRATION_VALUE));
+  returnValue = st.insert_simplex(secondSimplex.first, secondSimplex.second);
 
   test_simplex_tree_insert_returns_true(returnValue);
   set_and_test_simplex_tree_dim_fil(st, secondSimplexVector.size(), secondSimplex.second);
@@ -226,14 +221,10 @@ BOOST_AUTO_TEST_CASE(simplex_tree_insertion) {
 
   // ++ THIRD
   std::cout << "   - INSERT (0,1)" << std::endl;
-  typeVectorVertex thirdSimplexVector;
-  thirdSimplexVector.push_back(FIRST_VERTEX_HANDLE);
-  thirdSimplexVector.push_back(SECOND_VERTEX_HANDLE);
+  typeVectorVertex thirdSimplexVector { 0, 1 };
   BOOST_CHECK(thirdSimplexVector.size() == 2);
-  typeSimplex thirdSimplex = std::make_pair(
-                                            thirdSimplexVector, Filtration_value(SECOND_FILTRATION_VALUE));
-  returnValue =
-      st.insert_simplex(thirdSimplex.first, thirdSimplex.second);
+  typeSimplex thirdSimplex = std::make_pair(thirdSimplexVector, Filtration_value(SECOND_FILTRATION_VALUE));
+  returnValue = st.insert_simplex(thirdSimplex.first, thirdSimplex.second);
 
   test_simplex_tree_insert_returns_true(returnValue);
   set_and_test_simplex_tree_dim_fil(st, thirdSimplexVector.size(), thirdSimplex.second);
@@ -241,13 +232,10 @@ BOOST_AUTO_TEST_CASE(simplex_tree_insertion) {
 
   // ++ FOURTH
   std::cout << "   - INSERT 2" << std::endl;
-  typeVectorVertex fourthSimplexVector;
-  fourthSimplexVector.push_back(THIRD_VERTEX_HANDLE);
+  typeVectorVertex fourthSimplexVector { 2 };
   BOOST_CHECK(fourthSimplexVector.size() == 1);
-  typeSimplex fourthSimplex = std::make_pair(
-                                             fourthSimplexVector, Filtration_value(FIRST_FILTRATION_VALUE));
-  returnValue =
-      st.insert_simplex(fourthSimplex.first, fourthSimplex.second);
+  typeSimplex fourthSimplex = std::make_pair(fourthSimplexVector, Filtration_value(FIRST_FILTRATION_VALUE));
+  returnValue = st.insert_simplex(fourthSimplex.first, fourthSimplex.second);
 
   test_simplex_tree_insert_returns_true(returnValue);
   set_and_test_simplex_tree_dim_fil(st, fourthSimplexVector.size(), fourthSimplex.second);
@@ -255,14 +243,10 @@ BOOST_AUTO_TEST_CASE(simplex_tree_insertion) {
 
   // ++ FIFTH
   std::cout << "   - INSERT (2,0)" << std::endl;
-  typeVectorVertex fifthSimplexVector;
-  fifthSimplexVector.push_back(THIRD_VERTEX_HANDLE);
-  fifthSimplexVector.push_back(FIRST_VERTEX_HANDLE);
+  typeVectorVertex fifthSimplexVector { 2, 0 };
   BOOST_CHECK(fifthSimplexVector.size() == 2);
-  typeSimplex fifthSimplex = std::make_pair(
-                                            fifthSimplexVector, Filtration_value(SECOND_FILTRATION_VALUE));
-  returnValue =
-      st.insert_simplex(fifthSimplex.first, fifthSimplex.second);
+  typeSimplex fifthSimplex = std::make_pair(fifthSimplexVector, Filtration_value(SECOND_FILTRATION_VALUE));
+  returnValue = st.insert_simplex(fifthSimplex.first, fifthSimplex.second);
 
   test_simplex_tree_insert_returns_true(returnValue);
   set_and_test_simplex_tree_dim_fil(st, fifthSimplexVector.size(), fifthSimplex.second);
@@ -270,14 +254,10 @@ BOOST_AUTO_TEST_CASE(simplex_tree_insertion) {
 
   // ++ SIXTH
   std::cout << "   - INSERT (2,1)" << std::endl;
-  typeVectorVertex sixthSimplexVector;
-  sixthSimplexVector.push_back(THIRD_VERTEX_HANDLE);
-  sixthSimplexVector.push_back(SECOND_VERTEX_HANDLE);
+  typeVectorVertex sixthSimplexVector { 2, 1 };
   BOOST_CHECK(sixthSimplexVector.size() == 2);
-  typeSimplex sixthSimplex = std::make_pair(
-                                            sixthSimplexVector, Filtration_value(SECOND_FILTRATION_VALUE));
-  returnValue =
-      st.insert_simplex(sixthSimplex.first, sixthSimplex.second);
+  typeSimplex sixthSimplex = std::make_pair(sixthSimplexVector, Filtration_value(SECOND_FILTRATION_VALUE));
+  returnValue = st.insert_simplex(sixthSimplex.first, sixthSimplex.second);
 
   test_simplex_tree_insert_returns_true(returnValue);
   set_and_test_simplex_tree_dim_fil(st, sixthSimplexVector.size(), sixthSimplex.second);
@@ -285,15 +265,10 @@ BOOST_AUTO_TEST_CASE(simplex_tree_insertion) {
 
   // ++ SEVENTH
   std::cout << "   - INSERT (2,1,0)" << std::endl;
-  typeVectorVertex seventhSimplexVector;
-  seventhSimplexVector.push_back(THIRD_VERTEX_HANDLE);
-  seventhSimplexVector.push_back(SECOND_VERTEX_HANDLE);
-  seventhSimplexVector.push_back(FIRST_VERTEX_HANDLE);
+  typeVectorVertex seventhSimplexVector { 2, 1, 0 };
   BOOST_CHECK(seventhSimplexVector.size() == 3);
-  typeSimplex seventhSimplex = std::make_pair(
-                                              seventhSimplexVector, Filtration_value(THIRD_FILTRATION_VALUE));
-  returnValue =
-      st.insert_simplex(seventhSimplex.first, seventhSimplex.second);
+  typeSimplex seventhSimplex = std::make_pair(seventhSimplexVector, Filtration_value(THIRD_FILTRATION_VALUE));
+  returnValue = st.insert_simplex(seventhSimplex.first, seventhSimplex.second);
 
   test_simplex_tree_insert_returns_true(returnValue);
   set_and_test_simplex_tree_dim_fil(st, seventhSimplexVector.size(), seventhSimplex.second);
@@ -301,13 +276,10 @@ BOOST_AUTO_TEST_CASE(simplex_tree_insertion) {
 
   // ++ EIGHTH
   std::cout << "   - INSERT 3" << std::endl;
-  typeVectorVertex eighthSimplexVector;
-  eighthSimplexVector.push_back(FOURTH_VERTEX_HANDLE);
+  typeVectorVertex eighthSimplexVector { 3 };
   BOOST_CHECK(eighthSimplexVector.size() == 1);
-  typeSimplex eighthSimplex = std::make_pair(
-                                             eighthSimplexVector, Filtration_value(FIRST_FILTRATION_VALUE));
-  returnValue =
-      st.insert_simplex(eighthSimplex.first, eighthSimplex.second);
+  typeSimplex eighthSimplex = std::make_pair(eighthSimplexVector, Filtration_value(FIRST_FILTRATION_VALUE));
+  returnValue = st.insert_simplex(eighthSimplex.first, eighthSimplex.second);
 
   test_simplex_tree_insert_returns_true(returnValue);
   set_and_test_simplex_tree_dim_fil(st, eighthSimplexVector.size(), eighthSimplex.second);
@@ -315,14 +287,10 @@ BOOST_AUTO_TEST_CASE(simplex_tree_insertion) {
 
   // ++ NINETH
   std::cout << "   - INSERT (3,0)" << std::endl;
-  typeVectorVertex ninethSimplexVector;
-  ninethSimplexVector.push_back(FOURTH_VERTEX_HANDLE);
-  ninethSimplexVector.push_back(FIRST_VERTEX_HANDLE);
+  typeVectorVertex ninethSimplexVector { 3, 0 };
   BOOST_CHECK(ninethSimplexVector.size() == 2);
-  typeSimplex ninethSimplex = std::make_pair(
-                                             ninethSimplexVector, Filtration_value(SECOND_FILTRATION_VALUE));
-  returnValue =
-      st.insert_simplex(ninethSimplex.first, ninethSimplex.second);
+  typeSimplex ninethSimplex = std::make_pair(ninethSimplexVector, Filtration_value(SECOND_FILTRATION_VALUE));
+  returnValue = st.insert_simplex(ninethSimplex.first, ninethSimplex.second);
 
   test_simplex_tree_insert_returns_true(returnValue);
   set_and_test_simplex_tree_dim_fil(st, ninethSimplexVector.size(), ninethSimplex.second);
@@ -330,13 +298,11 @@ BOOST_AUTO_TEST_CASE(simplex_tree_insertion) {
 
   // ++ TENTH
   std::cout << "   - INSERT 0 (already inserted)" << std::endl;
-  typeVectorVertex tenthSimplexVector;
-  tenthSimplexVector.push_back(FIRST_VERTEX_HANDLE);
+  typeVectorVertex tenthSimplexVector { 0 };
   BOOST_CHECK(tenthSimplexVector.size() == 1);
-  typeSimplex tenthSimplex = std::make_pair(
-                                            tenthSimplexVector, Filtration_value(FOURTH_FILTRATION_VALUE)); // With a different filtration value
-  returnValue =
-      st.insert_simplex(tenthSimplex.first, tenthSimplex.second);
+  // With a different filtration value
+  typeSimplex tenthSimplex = std::make_pair(tenthSimplexVector, Filtration_value(FOURTH_FILTRATION_VALUE));
+  returnValue = st.insert_simplex(tenthSimplex.first, tenthSimplex.second);
 
   BOOST_CHECK(returnValue.second == false);
   typeST::Simplex_handle shReturned = returnValue.first; // Simplex_handle = boost::container::flat_map< Vertex_handle, Node >::iterator
@@ -347,15 +313,10 @@ BOOST_AUTO_TEST_CASE(simplex_tree_insertion) {
 
   // ++ ELEVENTH
   std::cout << "   - INSERT (2,1,0) (already inserted)" << std::endl;
-  typeVectorVertex eleventhSimplexVector;
-  eleventhSimplexVector.push_back(THIRD_VERTEX_HANDLE);
-  eleventhSimplexVector.push_back(SECOND_VERTEX_HANDLE);
-  eleventhSimplexVector.push_back(FIRST_VERTEX_HANDLE);
+  typeVectorVertex eleventhSimplexVector { 2, 1, 0 };
   BOOST_CHECK(eleventhSimplexVector.size() == 3);
-  typeSimplex eleventhSimplex = std::make_pair(
-                                               eleventhSimplexVector, Filtration_value(FOURTH_FILTRATION_VALUE));
-  returnValue =
-      st.insert_simplex(eleventhSimplex.first, eleventhSimplex.second);
+  typeSimplex eleventhSimplex = std::make_pair(eleventhSimplexVector, Filtration_value(FOURTH_FILTRATION_VALUE));
+  returnValue = st.insert_simplex(eleventhSimplex.first, eleventhSimplex.second);
 
   BOOST_CHECK(returnValue.second == false);
   shReturned = returnValue.first; // Simplex_handle = boost::container::flat_map< Vertex_handle, Node >::iterator
@@ -415,15 +376,6 @@ BOOST_AUTO_TEST_CASE(simplex_tree_insertion) {
 }
 
 BOOST_AUTO_TEST_CASE(NSimplexAndSubfaces_tree_insertion) {
-  Vertex_handle FIRST_VERTEX_HANDLE = (Vertex_handle) 0;
-  Vertex_handle SECOND_VERTEX_HANDLE = (Vertex_handle) 1;
-  Vertex_handle THIRD_VERTEX_HANDLE = (Vertex_handle) 2;
-  Vertex_handle FOURTH_VERTEX_HANDLE = (Vertex_handle) 3;
-  Vertex_handle FIFTH_VERTEX_HANDLE = (Vertex_handle) 4;
-  Vertex_handle SIXTH_VERTEX_HANDLE = (Vertex_handle) 5;
-  Vertex_handle SEVENTH_VERTEX_HANDLE = (Vertex_handle) 6;
-  Vertex_handle EIGHTH_VERTEX_HANDLE = (Vertex_handle) 7;
-
   // TEST OF INSERTION
   std::cout << "********************************************************************" << std::endl;
   std::cout << "TEST OF INSERTION" << std::endl;
@@ -431,10 +383,7 @@ BOOST_AUTO_TEST_CASE(NSimplexAndSubfaces_tree_insertion) {
 
   // ++ FIRST
   std::cout << "   - INSERT (2,1,0)" << std::endl;
-  typeVectorVertex SimplexVector1;
-  SimplexVector1.push_back(THIRD_VERTEX_HANDLE);
-  SimplexVector1.push_back(SECOND_VERTEX_HANDLE);
-  SimplexVector1.push_back(FIRST_VERTEX_HANDLE);
+  typeVectorVertex SimplexVector1 { 2, 1, 0 };
   BOOST_CHECK(SimplexVector1.size() == 3);
   st.insert_simplex_and_subfaces(SimplexVector1);
 
@@ -442,8 +391,7 @@ BOOST_AUTO_TEST_CASE(NSimplexAndSubfaces_tree_insertion) {
 
   // ++ SECOND
   std::cout << "   - INSERT 3" << std::endl;
-  typeVectorVertex SimplexVector2;
-  SimplexVector2.push_back(FOURTH_VERTEX_HANDLE);
+  typeVectorVertex SimplexVector2 { 3 };
   BOOST_CHECK(SimplexVector2.size() == 1);
   st.insert_simplex_and_subfaces(SimplexVector2);
 
@@ -451,9 +399,7 @@ BOOST_AUTO_TEST_CASE(NSimplexAndSubfaces_tree_insertion) {
 
   // ++ THIRD
   std::cout << "   - INSERT (0,3)" << std::endl;
-  typeVectorVertex SimplexVector3;
-  SimplexVector3.push_back(FOURTH_VERTEX_HANDLE);
-  SimplexVector3.push_back(FIRST_VERTEX_HANDLE);
+  typeVectorVertex SimplexVector3 { 3, 0 };
   BOOST_CHECK(SimplexVector3.size() == 2);
   st.insert_simplex_and_subfaces(SimplexVector3);
 
@@ -461,9 +407,7 @@ BOOST_AUTO_TEST_CASE(NSimplexAndSubfaces_tree_insertion) {
 
   // ++ FOURTH
   std::cout << "   - INSERT (1,0) (already inserted)" << std::endl;
-  typeVectorVertex SimplexVector4;
-  SimplexVector4.push_back(SECOND_VERTEX_HANDLE);
-  SimplexVector4.push_back(FIRST_VERTEX_HANDLE);
+  typeVectorVertex SimplexVector4 { 1, 0 };
   BOOST_CHECK(SimplexVector4.size() == 2);
   st.insert_simplex_and_subfaces(SimplexVector4);
 
@@ -471,10 +415,7 @@ BOOST_AUTO_TEST_CASE(NSimplexAndSubfaces_tree_insertion) {
 
   // ++ FIFTH
   std::cout << "   - INSERT (3,4,5)" << std::endl;
-  typeVectorVertex SimplexVector5;
-  SimplexVector5.push_back(FOURTH_VERTEX_HANDLE);
-  SimplexVector5.push_back(FIFTH_VERTEX_HANDLE);
-  SimplexVector5.push_back(SIXTH_VERTEX_HANDLE);
+  typeVectorVertex SimplexVector5 { 3, 4, 5 };
   BOOST_CHECK(SimplexVector5.size() == 3);
   st.insert_simplex_and_subfaces(SimplexVector5);
 
@@ -482,11 +423,7 @@ BOOST_AUTO_TEST_CASE(NSimplexAndSubfaces_tree_insertion) {
 
   // ++ SIXTH
   std::cout << "   - INSERT (0,1,6,7)" << std::endl;
-  typeVectorVertex SimplexVector6;
-  SimplexVector6.push_back(FIRST_VERTEX_HANDLE);
-  SimplexVector6.push_back(SECOND_VERTEX_HANDLE);
-  SimplexVector6.push_back(SEVENTH_VERTEX_HANDLE);
-  SimplexVector6.push_back(EIGHTH_VERTEX_HANDLE);
+  typeVectorVertex SimplexVector6 { 0, 1, 6, 7 };
   BOOST_CHECK(SimplexVector6.size() == 4);
   st.insert_simplex_and_subfaces(SimplexVector6);
 
@@ -523,8 +460,7 @@ BOOST_AUTO_TEST_CASE(NSimplexAndSubfaces_tree_insertion) {
   // ------------------------------------------------------------------------------------------------------------------
   // Find in the simplex_tree
   // ------------------------------------------------------------------------------------------------------------------
-  typeVectorVertex simpleSimplexVector;
-  simpleSimplexVector.push_back(SECOND_VERTEX_HANDLE);
+  typeVectorVertex simpleSimplexVector { 1 };
   Simplex_tree<>::Simplex_handle simplexFound = st.find(simpleSimplexVector);
   std::cout << "**************IS THE SIMPLEX {1} IN THE SIMPLEX TREE ?\n";
   if (simplexFound != st.null_simplex())
@@ -534,9 +470,7 @@ BOOST_AUTO_TEST_CASE(NSimplexAndSubfaces_tree_insertion) {
   // Check it is found
   BOOST_CHECK(simplexFound != st.null_simplex());
 
-  Vertex_handle UNKNOWN_VERTEX_HANDLE = (Vertex_handle) 15;
-  typeVectorVertex unknownSimplexVector;
-  unknownSimplexVector.push_back(UNKNOWN_VERTEX_HANDLE);
+  typeVectorVertex unknownSimplexVector { 15 };
   simplexFound = st.find(unknownSimplexVector);
   std::cout << "**************IS THE SIMPLEX {15} IN THE SIMPLEX TREE ?\n";
   if (simplexFound != st.null_simplex())
@@ -555,9 +489,7 @@ BOOST_AUTO_TEST_CASE(NSimplexAndSubfaces_tree_insertion) {
   // Check it is found
   BOOST_CHECK(simplexFound != st.null_simplex());
 
-  typeVectorVertex otherSimplexVector;
-  otherSimplexVector.push_back(UNKNOWN_VERTEX_HANDLE);
-  otherSimplexVector.push_back(SECOND_VERTEX_HANDLE);
+  typeVectorVertex otherSimplexVector { 1, 15 };
   simplexFound = st.find(otherSimplexVector);
   std::cout << "**************IS THE SIMPLEX {15,1} IN THE SIMPLEX TREE ?\n";
   if (simplexFound != st.null_simplex())
@@ -567,10 +499,7 @@ BOOST_AUTO_TEST_CASE(NSimplexAndSubfaces_tree_insertion) {
   // Check it is NOT found
   BOOST_CHECK(simplexFound == st.null_simplex());
 
-  typeVectorVertex invSimplexVector;
-  invSimplexVector.push_back(SECOND_VERTEX_HANDLE);
-  invSimplexVector.push_back(THIRD_VERTEX_HANDLE);
-  invSimplexVector.push_back(FIRST_VERTEX_HANDLE);
+  typeVectorVertex invSimplexVector { 1, 2, 0 };
   simplexFound = st.find(invSimplexVector);
   std::cout << "**************IS THE SIMPLEX {1,2,0} IN THE SIMPLEX TREE ?\n";
   if (simplexFound != st.null_simplex())
@@ -580,8 +509,6 @@ BOOST_AUTO_TEST_CASE(NSimplexAndSubfaces_tree_insertion) {
   // Check it is found
   BOOST_CHECK(simplexFound != st.null_simplex());
 
-
-
   // Display the Simplex_tree - Can not be done in the middle of 2 inserts
   std::cout << "The complex contains " << st.num_simplices() << " simplices" << std::endl;
   std::cout << "   - dimension " << st.dimension() << "   - filtration " << st.filtration() << std::endl;