diff --git a/Convex_hull_3/test/Convex_hull_3/degeneracy_test.cpp b/Convex_hull_3/test/Convex_hull_3/degeneracy_test.cpp
index d57fd12eede..4c0a7f93b5b 100644
--- a/Convex_hull_3/test/Convex_hull_3/degeneracy_test.cpp
+++ b/Convex_hull_3/test/Convex_hull_3/degeneracy_test.cpp
@@ -20,7 +20,7 @@
 // ============================================================================
  
 
-#include <CGAL/Cartesian.h>
+#include <CGAL/Simple_cartesian.h>
 #include <CGAL/Polyhedron_3.h>
 #include <CGAL/Convex_hull_2/ch_assertions.h>
 #include <CGAL/convex_hull_3.h>
@@ -28,7 +28,7 @@
 #include <fstream>
 
 typedef double                                     NumberType;
-typedef CGAL::Cartesian<NumberType>                Kernel;
+typedef CGAL::Simple_cartesian<NumberType>         Kernel;
 typedef CGAL::Polyhedron_3<Kernel>                 Polyhedron;
 typedef Kernel::Point_3                            Point_3;
 
diff --git a/Convex_hull_3/test/Convex_hull_3/quickhull_degenerate_test_3.cpp b/Convex_hull_3/test/Convex_hull_3/quickhull_degenerate_test_3.cpp
index aa9042ff279..2f51b0ac7f3 100644
--- a/Convex_hull_3/test/Convex_hull_3/quickhull_degenerate_test_3.cpp
+++ b/Convex_hull_3/test/Convex_hull_3/quickhull_degenerate_test_3.cpp
@@ -1,5 +1,5 @@
 #include <CGAL/Exact_rational.h>
-#include <CGAL/Cartesian.h>
+#include <CGAL/Simple_cartesian.h>
 #include <CGAL/Polyhedron_3.h>
 
 #include <fstream>
@@ -12,7 +12,7 @@
 
 
 typedef CGAL::Exact_rational Exact_rational;
-typedef CGAL::Cartesian< Exact_rational >     R;
+typedef CGAL::Simple_cartesian<Exact_rational>  R;
 typedef CGAL::Convex_hull_traits_3<R>           Traits;
 typedef Traits::Polygon_mesh                    Polyhedron_3;
 
diff --git a/Distance_2/test/Distance_2/test_distance_2.cpp b/Distance_2/test/Distance_2/test_distance_2.cpp
index 54849f91469..ccf57a20b78 100644
--- a/Distance_2/test/Distance_2/test_distance_2.cpp
+++ b/Distance_2/test/Distance_2/test_distance_2.cpp
@@ -4,14 +4,8 @@
 #undef NDEBUG //this testsuite requires NDEBUG to be not defined
 #endif
 
-#include <CGAL/Line_2.h>
-#include <CGAL/Point_2.h>
-#include <CGAL/Segment_2.h>
-#include <CGAL/Ray_2.h>
-#include <CGAL/Triangle_2.h>
-#include <CGAL/Iso_rectangle_2.h>
 
-#include <CGAL/Cartesian.h>
+#include <CGAL/Simple_cartesian.h>
 #include <CGAL/Homogeneous.h>
 
 #include <vector>
@@ -296,7 +290,7 @@ struct Test {
 
 int main()
 {
-	Test< CGAL::Cartesian<double>   >().run();
+	Test< CGAL::Simple_cartesian<double>   >().run();
 	Test< CGAL::Homogeneous<double> >().run();
 	// TODO : test more kernels.
 }
diff --git a/Distance_3/test/Distance_3/test_distance_3.cpp b/Distance_3/test/Distance_3/test_distance_3.cpp
index 1df77add0b0..32656ef5314 100644
--- a/Distance_3/test/Distance_3/test_distance_3.cpp
+++ b/Distance_3/test/Distance_3/test_distance_3.cpp
@@ -4,15 +4,7 @@
 #undef NDEBUG //this testsuite requires NDEBUG to be not defined
 #endif
 
-#include <CGAL/Object.h>
-#include <CGAL/Line_3.h>
-#include <CGAL/Point_3.h>
-#include <CGAL/Segment_3.h>
-#include <CGAL/Ray_3.h>
-#include <CGAL/Triangle_3.h>
-#include <CGAL/Iso_cuboid_3.h>
-
-#include <CGAL/Cartesian.h>
+#include <CGAL/Simple_cartesian.h>
 #include <CGAL/Homogeneous.h>
 
 #include <vector>
@@ -253,7 +245,7 @@ struct Test {
 
 int main()
 {
-	Test< CGAL::Cartesian<double>   >().run();
+	Test< CGAL::Simple_cartesian<double>   >().run();
 	Test< CGAL::Homogeneous<double> >().run();
 	// TODO : test more kernels.
 }
diff --git a/Generator/test/Generator/generic_random_test.cpp b/Generator/test/Generator/generic_random_test.cpp
index 3090ddbfc80..6f09f8c6ac3 100644
--- a/Generator/test/Generator/generic_random_test.cpp
+++ b/Generator/test/Generator/generic_random_test.cpp
@@ -1,5 +1,4 @@
 #include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
-#include <CGAL/Simple_cartesian.h>
 
 #include <CGAL/Mesh_complex_3_in_triangulation_3.h>
 #include <CGAL/Mesh_criteria_3.h>
diff --git a/Generator/test/Generator/random_poly_test.cpp b/Generator/test/Generator/random_poly_test.cpp
index c121d2c843a..074fe49ba5a 100644
--- a/Generator/test/Generator/random_poly_test.cpp
+++ b/Generator/test/Generator/random_poly_test.cpp
@@ -22,14 +22,14 @@
 // Random Simple Polygons: Test Program
 // ============================================================================
 
-#include <CGAL/Cartesian.h>
+#include <CGAL/Simple_cartesian.h>
 #include <CGAL/Homogeneous.h>
 #include <CGAL/point_generators_2.h>
 #include <CGAL/random_polygon_2.h>
 #include <CGAL/Polygon_2.h>
 #include <list>
 
-typedef CGAL::Cartesian< double >                           CR;
+typedef CGAL::Simple_cartesian< double >                    CR;
 typedef CGAL::Point_2< CR >                                 CPoint_2;
 typedef std::list<CPoint_2>                                 CContainer;
 typedef CGAL::Polygon_2<CR, CContainer>                     CPolygon_2;
diff --git a/Generator/test/Generator/rcs_test.cpp b/Generator/test/Generator/rcs_test.cpp
index 4bde453151c..ae8bf3315d0 100644
--- a/Generator/test/Generator/rcs_test.cpp
+++ b/Generator/test/Generator/rcs_test.cpp
@@ -23,7 +23,7 @@
 // Random Convex Point Sets: Test Program
 // ============================================================================
 
-#include <CGAL/Cartesian.h>
+#include <CGAL/Simple_cartesian.h>
 #include <CGAL/Point_2.h>
 #include <CGAL/Polygon_2.h>
 #include <CGAL/point_generators_2.h>
@@ -34,7 +34,7 @@
 
 using std::vector;
 using std::back_inserter;
-using CGAL::Cartesian;
+using CGAL::Simple_cartesian;
 using CGAL::Creator_uniform_2;
 using CGAL::Random_points_in_square_2;
 using CGAL::set_pretty_mode;
@@ -44,7 +44,7 @@ using CGAL::random_convex_set_2;
 int
 main( )
 {
-  typedef Cartesian< double >                            R;
+  typedef Simple_cartesian< double >                     R;
   typedef CGAL::Point_2< R >                             Point_2;
   typedef vector< Point_2 >                              Cont;
   typedef CGAL::Polygon_2< R, Cont >                     Polygon_2;
diff --git a/Generator/test/Generator/test_generators.cpp b/Generator/test/Generator/test_generators.cpp
index 6bf865e0933..40e792875ea 100644
--- a/Generator/test/Generator/test_generators.cpp
+++ b/Generator/test/Generator/test_generators.cpp
@@ -29,10 +29,8 @@
 #include <cstddef>
 #include <vector>
 #include <algorithm>
-#include <CGAL/Cartesian.h>
+#include <CGAL/Simple_cartesian.h>
 #include <CGAL/Cartesian_d.h>
-#include <CGAL/Point_2.h>
-#include <CGAL/Point_3.h>
 #include <CGAL/point_generators_2.h>
 #include <CGAL/point_generators_3.h>
 #include <CGAL/point_generators_d.h>
@@ -42,7 +40,7 @@
 
 using namespace CGAL;
 
-typedef Cartesian<double>                R;
+typedef Simple_cartesian<double>         R;
 typedef CGAL::Cartesian_d<double>        Kd;
 
 
diff --git a/Generator/test/Generator/test_tetrahedron_3.cpp b/Generator/test/Generator/test_tetrahedron_3.cpp
index 610d85e3f06..56656a07783 100644
--- a/Generator/test/Generator/test_tetrahedron_3.cpp
+++ b/Generator/test/Generator/test_tetrahedron_3.cpp
@@ -3,12 +3,11 @@
 #include <CGAL/Random.h>
 #include <CGAL/algorithm.h>
 #include <CGAL/double.h>
-#include <CGAL/Triangle_3.h>
-#include <CGAL/Cartesian.h>
+#include <CGAL/Simple_cartesian.h>
 #include <cassert>
 typedef double RT;
 
-typedef CGAL::Cartesian<RT>					K;
+typedef CGAL::Simple_cartesian<RT>				K;
 typedef K::Point_3 						Point_3;
 typedef K::Vector_3 						Vector_3;
 typedef K::Tetrahedron_3 					Tetrahedron_3;
diff --git a/Generator/test/Generator/test_triangle_3.cpp b/Generator/test/Generator/test_triangle_3.cpp
index e4648d7f4da..750d047e94e 100644
--- a/Generator/test/Generator/test_triangle_3.cpp
+++ b/Generator/test/Generator/test_triangle_3.cpp
@@ -3,7 +3,6 @@
 #include <CGAL/Random.h>
 #include <CGAL/algorithm.h>
 #include <CGAL/double.h>
-#include <CGAL/Triangle_3.h>
 #include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
 #include <cassert>
 
diff --git a/HalfedgeDS/test/HalfedgeDS/test_hds.cpp b/HalfedgeDS/test/HalfedgeDS/test_hds.cpp
index e07f491f74a..e65351e18a1 100644
--- a/HalfedgeDS/test/HalfedgeDS/test_hds.cpp
+++ b/HalfedgeDS/test/HalfedgeDS/test_hds.cpp
@@ -26,7 +26,7 @@
 // ============================================================================
 
 
-#include <CGAL/Cartesian.h>
+#include <CGAL/Simple_cartesian.h>
 #include <CGAL/HalfedgeDS_default.h>
 #include <CGAL/HalfedgeDS_min_items.h>
 #include <CGAL/Polyhedron_items_3.h>
@@ -34,7 +34,7 @@
 #include <cstddef>
 #include <cassert>
 
-typedef CGAL::Cartesian<double>   Kernel;
+typedef CGAL::Simple_cartesian<double>   Kernel;
 struct Dummy_traits_3 {
     typedef Kernel::Point_3    Point_3;
     typedef Kernel::Plane_3    Plane_3;
diff --git a/HalfedgeDS/test/HalfedgeDS/test_hds_decorator.cpp b/HalfedgeDS/test/HalfedgeDS/test_hds_decorator.cpp
index 1cc3d7bf9a5..fd9d9d2d746 100644
--- a/HalfedgeDS/test/HalfedgeDS/test_hds_decorator.cpp
+++ b/HalfedgeDS/test/HalfedgeDS/test_hds_decorator.cpp
@@ -26,14 +26,14 @@
 // ============================================================================
 
 
-#include <CGAL/Cartesian.h>
+#include <CGAL/Simple_cartesian.h>
 #include <CGAL/HalfedgeDS_default.h>
 #include <CGAL/Polyhedron_items_3.h>
 #include <CGAL/HalfedgeDS_decorator.h>
 
 #include <cassert>
 
-typedef CGAL::Cartesian<double> Kernel;
+typedef CGAL::Simple_cartesian<double> Kernel;
 struct Dummy_traits_2 {
     typedef Kernel::Point_2 Point_2;
 };
diff --git a/Hash_map/test/Hash_map/Unique_hash_map_test.cpp b/Hash_map/test/Hash_map/Unique_hash_map_test.cpp
index 4980a550334..7f83cc81528 100644
--- a/Hash_map/test/Hash_map/Unique_hash_map_test.cpp
+++ b/Hash_map/test/Hash_map/Unique_hash_map_test.cpp
@@ -1,4 +1,3 @@
-#include <CGAL/Cartesian.h>
 #include <list>
 #include <CGAL/Unique_hash_map.h>
 #include <CGAL/test_macros.h>
diff --git a/Polyhedron/test/Polyhedron/test_polyhedron.cpp b/Polyhedron/test/Polyhedron/test_polyhedron.cpp
index 3a90a99dcc3..ebc6beab112 100644
--- a/Polyhedron/test/Polyhedron/test_polyhedron.cpp
+++ b/Polyhedron/test/Polyhedron/test_polyhedron.cpp
@@ -26,7 +26,7 @@
 // ============================================================================
 
 
-#include <CGAL/Cartesian.h>
+#include <CGAL/Simple_cartesian.h>
 #include <CGAL/Polyhedron_3.h>
 #include <CGAL/HalfedgeDS_vector.h>
 #include <CGAL/HalfedgeDS_list.h>
@@ -276,8 +276,8 @@ struct Test_facet_modifier : public CGAL::Modifier_base<HDS>
 };
 
 void test_Polyhedron() {
-    typedef CGAL::Cartesian<double>                     Kernel;
-    typedef CGAL::Cartesian<int>                        KernelI;
+    typedef CGAL::Simple_cartesian<double>                     Kernel;
+    typedef CGAL::Simple_cartesian<int>                        KernelI;
     typedef CGAL::Point_3<Kernel>                       Point;
     typedef CGAL::Plane_3<Kernel>                       Plane;
     typedef CGAL::Polyhedron_traits_3<Kernel>           Traits;
@@ -1116,7 +1116,7 @@ void test_Polyhedron() {
 }
 
 void test_min_Polyhedron() {
-    typedef CGAL::Cartesian<double>                     Kernel;
+    typedef CGAL::Simple_cartesian<double>              Kernel;
     typedef CGAL::Point_3<Kernel>                       Point;
     typedef CGAL::Polyhedron_traits_3<Kernel>           Traits;
     typedef CGAL::Polyhedron_3<Traits,
diff --git a/Polyhedron_IO/test/Polyhedron_IO/test_polyhedron_io.cpp b/Polyhedron_IO/test/Polyhedron_IO/test_polyhedron_io.cpp
index f737d11d10f..581a77019bd 100644
--- a/Polyhedron_IO/test/Polyhedron_IO/test_polyhedron_io.cpp
+++ b/Polyhedron_IO/test/Polyhedron_IO/test_polyhedron_io.cpp
@@ -25,7 +25,7 @@
 // ============================================================================
 
 
-#include <CGAL/Cartesian.h>
+#include <CGAL/Simple_cartesian.h>
 #include <CGAL/Polyhedron_3.h>
 
 // This is the test file for the new design. Skip new design test for 
@@ -66,8 +66,8 @@ const char* tetra =    "OFF\n"
 
 
 void test_file_IO_OFF() {
-    typedef Cartesian<double>     Kernel;
-    typedef Polyhedron_3<Kernel>  Polyhedron;
+    typedef Simple_cartesian<double> Kernel;
+    typedef Polyhedron_3<Kernel>     Polyhedron;
     {
         Polyhedron P;
         std::istringstream in( triangle);
diff --git a/Principal_component_analysis/test/Principal_component_analysis/test_barycenter.cpp b/Principal_component_analysis/test/Principal_component_analysis/test_barycenter.cpp
index b55a30248e7..22174db3bc4 100644
--- a/Principal_component_analysis/test/Principal_component_analysis/test_barycenter.cpp
+++ b/Principal_component_analysis/test/Principal_component_analysis/test_barycenter.cpp
@@ -4,15 +4,15 @@
 #include <vector>
 #include <cassert>
 
-#include <CGAL/Cartesian.h>
+#include <CGAL/Simple_cartesian.h>
 
 #include <CGAL/barycenter.h>
 #include <CGAL/centroid.h>
 
-typedef double               FT;
-typedef CGAL::Cartesian<FT>  K;
-typedef K::Point_2           Point_2;
-typedef K::Point_3           Point_3;
+typedef double                      FT;
+typedef CGAL::Simple_cartesian<FT>  K;
+typedef K::Point_2                  Point_2;
+typedef K::Point_3                  Point_3;
 
 void test_2()
 {
diff --git a/Principal_component_analysis/test/Principal_component_analysis/test_bounding_box.cpp b/Principal_component_analysis/test/Principal_component_analysis/test_bounding_box.cpp
index 582aa0a3c69..1c1870db817 100644
--- a/Principal_component_analysis/test/Principal_component_analysis/test_bounding_box.cpp
+++ b/Principal_component_analysis/test/Principal_component_analysis/test_bounding_box.cpp
@@ -4,15 +4,15 @@
 #include <vector>
 #include <cassert>
 
-#include <CGAL/Cartesian.h>
+#include <CGAL/Simple_cartesian.h>
 #include <CGAL/bounding_box.h>
 
-typedef double               FT;
-typedef CGAL::Cartesian<FT>  K;
-typedef K::Point_2           Point_2;
-typedef K::Point_3           Point_3;
-typedef K::Segment_2         Segment_2;
-typedef K::Triangle_3        Triangle_3;
+typedef double                      FT;
+typedef CGAL::Simple_cartesian<FT>  K;
+typedef K::Point_2                  Point_2;
+typedef K::Point_3                  Point_3;
+typedef K::Segment_2                Segment_2;
+typedef K::Triangle_3               Triangle_3;
 
 void test_2()
 {
diff --git a/Principal_component_analysis/test/Principal_component_analysis/test_linear_least_squares_fitting_circles_2.cpp b/Principal_component_analysis/test/Principal_component_analysis/test_linear_least_squares_fitting_circles_2.cpp
index 4f5bac3277d..007d8e82939 100644
--- a/Principal_component_analysis/test/Principal_component_analysis/test_linear_least_squares_fitting_circles_2.cpp
+++ b/Principal_component_analysis/test/Principal_component_analysis/test_linear_least_squares_fitting_circles_2.cpp
@@ -2,16 +2,16 @@
 
 // Example program for the linear_least_square_fitting function on a set of circles in 2D
 
-#include <CGAL/Cartesian.h>
+#include <CGAL/Simple_cartesian.h>
 #include <CGAL/linear_least_squares_fitting_2.h>
 
 #include <list>
 
-typedef double               FT;
-typedef CGAL::Cartesian<FT>  K;
-typedef K::Line_2            Line;
-typedef K::Point_2           Point;
-typedef K::Circle_2          Circle;
+typedef double                      FT;
+typedef CGAL::Simple_cartesian<FT>  K;
+typedef K::Line_2                   Line;
+typedef K::Point_2                  Point;
+typedef K::Circle_2                 Circle;
 
 int main()
 {
diff --git a/Principal_component_analysis/test/Principal_component_analysis/test_linear_least_squares_fitting_cuboids_3.cpp b/Principal_component_analysis/test/Principal_component_analysis/test_linear_least_squares_fitting_cuboids_3.cpp
index da09885b0f0..d66d6f7df7c 100644
--- a/Principal_component_analysis/test/Principal_component_analysis/test_linear_least_squares_fitting_cuboids_3.cpp
+++ b/Principal_component_analysis/test/Principal_component_analysis/test_linear_least_squares_fitting_cuboids_3.cpp
@@ -1,7 +1,7 @@
 #include <CGAL/internal/disable_deprecation_warnings_and_errors.h>
 
 // Example program for the linear_least_square_fitting function on set of cuboids in 3D
-#include <CGAL/Cartesian.h>
+#include <CGAL/Simple_cartesian.h>
 #include <CGAL/linear_least_squares_fitting_3.h>
 #include <list>
 
@@ -9,12 +9,12 @@
 #include <CGAL/Diagonalize_traits.h>
 #endif
 
-typedef double               FT;
-typedef CGAL::Cartesian<FT>  Kernel;
-typedef Kernel::Line_3       Line;
-typedef Kernel::Plane_3      Plane;
-typedef Kernel::Point_3      Point;
-typedef Kernel::Iso_cuboid_3 Iso_cuboid;
+typedef double                      FT;
+typedef CGAL::Simple_cartesian<FT>  Kernel;
+typedef Kernel::Line_3              Line;
+typedef Kernel::Plane_3             Plane;
+typedef Kernel::Point_3             Point;
+typedef Kernel::Iso_cuboid_3        Iso_cuboid;
 
 int main()
 {
diff --git a/Principal_component_analysis/test/Principal_component_analysis/test_linear_least_squares_fitting_points_2.cpp b/Principal_component_analysis/test/Principal_component_analysis/test_linear_least_squares_fitting_points_2.cpp
index bd063d67ed5..96985afecb6 100644
--- a/Principal_component_analysis/test/Principal_component_analysis/test_linear_least_squares_fitting_points_2.cpp
+++ b/Principal_component_analysis/test/Principal_component_analysis/test_linear_least_squares_fitting_points_2.cpp
@@ -1,7 +1,7 @@
 #include <CGAL/internal/disable_deprecation_warnings_and_errors.h>
 
 // test for the linear_least_square_fitting() functions.
-#include <CGAL/Cartesian.h>
+#include <CGAL/Simple_cartesian.h>
 #include <CGAL/algorithm.h>
 #include <CGAL/linear_least_squares_fitting_2.h>
 #include <CGAL/point_generators_2.h>
@@ -93,11 +93,11 @@ int main()
 {
   std::cout << "Test 2D linear least squares fitting of points"  << std::endl;
 
-	typedef CGAL::Cartesian<double> Kernel_double;
+	typedef CGAL::Simple_cartesian<double> Kernel_double;
   test_2D<Kernel_double>();
   test_2D_point_set<Kernel_double>(100);
 
-	typedef CGAL::Cartesian<float> Kernel_float;
+	typedef CGAL::Simple_cartesian<float> Kernel_float;
   test_2D<Kernel_float>();
   test_2D_point_set<Kernel_float>(100);
 
diff --git a/Principal_component_analysis/test/Principal_component_analysis/test_linear_least_squares_fitting_points_3.cpp b/Principal_component_analysis/test/Principal_component_analysis/test_linear_least_squares_fitting_points_3.cpp
index 6308207c8b9..1f18f88e592 100644
--- a/Principal_component_analysis/test/Principal_component_analysis/test_linear_least_squares_fitting_points_3.cpp
+++ b/Principal_component_analysis/test/Principal_component_analysis/test_linear_least_squares_fitting_points_3.cpp
@@ -3,7 +3,7 @@
 // test for the linear_least_square_fitting() functions.
 
 
-#include <CGAL/Cartesian.h>
+#include <CGAL/Simple_cartesian.h>
 #include <CGAL/linear_least_squares_fitting_3.h>
 #include <CGAL/Default_diagonalize_traits.h>
 
@@ -13,7 +13,7 @@
 #include <list>
 
 // types
-typedef CGAL::Cartesian<float> Kernel;
+typedef CGAL::Simple_cartesian<float> Kernel;
 typedef Kernel::FT FT;
 typedef Kernel::Line_3 Line;
 typedef Kernel::Point_3 Point;
diff --git a/Principal_component_analysis/test/Principal_component_analysis/test_linear_least_squares_fitting_rectangles_2.cpp b/Principal_component_analysis/test/Principal_component_analysis/test_linear_least_squares_fitting_rectangles_2.cpp
index 22fbdc53fa0..42a812ba3e0 100644
--- a/Principal_component_analysis/test/Principal_component_analysis/test_linear_least_squares_fitting_rectangles_2.cpp
+++ b/Principal_component_analysis/test/Principal_component_analysis/test_linear_least_squares_fitting_rectangles_2.cpp
@@ -3,7 +3,7 @@
 // test for the linear_least_square_fitting() functions.
 
 
-#include <CGAL/Cartesian.h>
+#include <CGAL/Simple_cartesian.h>
 #include <CGAL/algorithm.h>
 #include <CGAL/linear_least_squares_fitting_2.h>
 #include <CGAL/point_generators_2.h>
@@ -14,7 +14,7 @@
 #define THRESHOLD 0.001
 // types
 
-typedef CGAL::Cartesian<double> Kernel;
+typedef CGAL::Simple_cartesian<double> Kernel;
 typedef Kernel::FT FT;
 
 typedef Kernel::Line_2 Line_2;
diff --git a/Principal_component_analysis/test/Principal_component_analysis/test_linear_least_squares_fitting_segments_2.cpp b/Principal_component_analysis/test/Principal_component_analysis/test_linear_least_squares_fitting_segments_2.cpp
index bee7a607098..d666452a1d2 100644
--- a/Principal_component_analysis/test/Principal_component_analysis/test_linear_least_squares_fitting_segments_2.cpp
+++ b/Principal_component_analysis/test/Principal_component_analysis/test_linear_least_squares_fitting_segments_2.cpp
@@ -3,7 +3,7 @@
 // test for the linear_least_square_fitting() functions.
 
 
-#include <CGAL/Cartesian.h>
+#include <CGAL/Simple_cartesian.h>
 #include <CGAL/algorithm.h>
 #include <CGAL/linear_least_squares_fitting_2.h>
 #include <CGAL/point_generators_2.h>
@@ -14,7 +14,7 @@
 #define THRESHOLD 0.001
 // types
 
-typedef CGAL::Cartesian<double> Kernel;
+typedef CGAL::Simple_cartesian<double> Kernel;
 typedef Kernel::FT FT;
 
 typedef Kernel::Line_2 Line_2;
diff --git a/Principal_component_analysis/test/Principal_component_analysis/test_linear_least_squares_fitting_segments_3.cpp b/Principal_component_analysis/test/Principal_component_analysis/test_linear_least_squares_fitting_segments_3.cpp
index 6f148de7cd2..952453d0c44 100644
--- a/Principal_component_analysis/test/Principal_component_analysis/test_linear_least_squares_fitting_segments_3.cpp
+++ b/Principal_component_analysis/test/Principal_component_analysis/test_linear_least_squares_fitting_segments_3.cpp
@@ -3,7 +3,7 @@
 // test for the linear_least_square_fitting() functions.
 
 
-#include <CGAL/Cartesian.h>
+#include <CGAL/Simple_cartesian.h>
 #include <CGAL/algorithm.h>
 #include <CGAL/linear_least_squares_fitting_3.h>
 #include <CGAL/point_generators_3.h>
@@ -18,7 +18,7 @@
 #define THRESHOLD 0.001
 // types
 
-typedef CGAL::Cartesian<double> Kernel;
+typedef CGAL::Simple_cartesian<double> Kernel;
 typedef Kernel::FT FT;
 
 typedef Kernel::Line_3 Line;
diff --git a/Principal_component_analysis/test/Principal_component_analysis/test_linear_least_squares_fitting_spheres_3.cpp b/Principal_component_analysis/test/Principal_component_analysis/test_linear_least_squares_fitting_spheres_3.cpp
index 4a8a8b4251d..64b77f83ceb 100644
--- a/Principal_component_analysis/test/Principal_component_analysis/test_linear_least_squares_fitting_spheres_3.cpp
+++ b/Principal_component_analysis/test/Principal_component_analysis/test_linear_least_squares_fitting_spheres_3.cpp
@@ -2,7 +2,7 @@
 
 #include <CGAL/internal/disable_deprecation_warnings_and_errors.h>
 
-#include <CGAL/Cartesian.h>
+#include <CGAL/Simple_cartesian.h>
 #include <CGAL/linear_least_squares_fitting_3.h>
 #ifdef CGAL_EIGEN3_ENABLED
 #include <CGAL/Eigen_diagonalize_traits.h>
@@ -11,12 +11,12 @@
 
 #include <list>
 
-typedef double               FT;
-typedef CGAL::Cartesian<FT>  Kernel;
-typedef Kernel::Line_3       Line;
-typedef Kernel::Plane_3      Plane;
-typedef Kernel::Point_3      Point;
-typedef Kernel::Sphere_3     Sphere;
+typedef double                      FT;
+typedef CGAL::Simple_cartesian<FT>  Kernel;
+typedef Kernel::Line_3              Line;
+typedef Kernel::Plane_3             Plane;
+typedef Kernel::Point_3             Point;
+typedef Kernel::Sphere_3            Sphere;
 
 int main(void)
 {
diff --git a/Principal_component_analysis/test/Principal_component_analysis/test_linear_least_squares_fitting_tetrahedra_3.cpp b/Principal_component_analysis/test/Principal_component_analysis/test_linear_least_squares_fitting_tetrahedra_3.cpp
index cc56701293a..e764671b1ae 100644
--- a/Principal_component_analysis/test/Principal_component_analysis/test_linear_least_squares_fitting_tetrahedra_3.cpp
+++ b/Principal_component_analysis/test/Principal_component_analysis/test_linear_least_squares_fitting_tetrahedra_3.cpp
@@ -3,7 +3,7 @@
 // Example program for the linear_least_square_fitting function
 // on a set of tetrahedra in 3D
 
-#include <CGAL/Cartesian.h>
+#include <CGAL/Simple_cartesian.h>
 #include <CGAL/linear_least_squares_fitting_3.h>
 #include <list>
 
@@ -11,12 +11,12 @@
 #include <CGAL/Diagonalize_traits.h>
 #endif
 
-typedef double                FT;
-typedef CGAL::Cartesian<FT>   Kernel;
-typedef Kernel::Line_3        Line;
-typedef Kernel::Plane_3       Plane;
-typedef Kernel::Point_3       Point;
-typedef Kernel::Tetrahedron_3 Tetrahedron;
+typedef double                       FT;
+typedef CGAL::Simple_cartesian<FT>   Kernel;
+typedef Kernel::Line_3               Line;
+typedef Kernel::Plane_3              Plane;
+typedef Kernel::Point_3              Point;
+typedef Kernel::Tetrahedron_3        Tetrahedron;
 
 int main()
 {
diff --git a/Principal_component_analysis/test/Principal_component_analysis/test_linear_least_squares_fitting_triangles_2.cpp b/Principal_component_analysis/test/Principal_component_analysis/test_linear_least_squares_fitting_triangles_2.cpp
index 83941382425..cc9471be8c3 100644
--- a/Principal_component_analysis/test/Principal_component_analysis/test_linear_least_squares_fitting_triangles_2.cpp
+++ b/Principal_component_analysis/test/Principal_component_analysis/test_linear_least_squares_fitting_triangles_2.cpp
@@ -1,7 +1,7 @@
 #include <CGAL/internal/disable_deprecation_warnings_and_errors.h>
 
 // test for the linear_least_square_fitting() functions.
-#include <CGAL/Cartesian.h>
+#include <CGAL/Simple_cartesian.h>
 #include <CGAL/algorithm.h>
 #include <CGAL/linear_least_squares_fitting_2.h>
 #include <CGAL/point_generators_2.h>
@@ -12,8 +12,8 @@
 
 #define THRESHOLD 0.001
 
-typedef CGAL::Cartesian<double> Kernel;
-typedef Kernel::FT FT;
+typedef CGAL::Simple_cartesian<double> Kernel;
+typedef Kernel::FT              FT;
 typedef Kernel::Line_2          Line_2;
 typedef Kernel::Point_2         Point_2;
 typedef Kernel::Vector_2        Vector_2;
diff --git a/Principal_component_analysis/test/Principal_component_analysis/test_linear_least_squares_fitting_triangles_3.cpp b/Principal_component_analysis/test/Principal_component_analysis/test_linear_least_squares_fitting_triangles_3.cpp
index 20fba3fb597..0507c09fce3 100644
--- a/Principal_component_analysis/test/Principal_component_analysis/test_linear_least_squares_fitting_triangles_3.cpp
+++ b/Principal_component_analysis/test/Principal_component_analysis/test_linear_least_squares_fitting_triangles_3.cpp
@@ -1,7 +1,7 @@
 #include <CGAL/internal/disable_deprecation_warnings_and_errors.h>
 
 // Example program for the linear_least_square_fitting function on set of triangles in 3D
-#include <CGAL/Cartesian.h>
+#include <CGAL/Simple_cartesian.h>
 #include <CGAL/linear_least_squares_fitting_3.h>
 #ifdef CGAL_EIGEN3_ENABLED
 #include <CGAL/Diagonalize_traits.h>
@@ -9,12 +9,12 @@
 
 #include <list>
 
-typedef double               FT;
-typedef CGAL::Cartesian<FT>  Kernel;
-typedef Kernel::Line_3       Line;
-typedef Kernel::Plane_3      Plane;
-typedef Kernel::Point_3      Point;
-typedef Kernel::Triangle_3   Triangle;
+typedef double                      FT;
+typedef CGAL::Simple_cartesian<FT>  Kernel;
+typedef Kernel::Line_3              Line;
+typedef Kernel::Plane_3             Plane;
+typedef Kernel::Point_3             Point;
+typedef Kernel::Triangle_3          Triangle;
 
 int main()
 {