diff --git a/Kernel_d/include/CGAL/Filtered_kernel_d.h b/Kernel_d/include/CGAL/Filtered_kernel_d.h
index 8a8ff858b7d..9bf561a2c30 100644
--- a/Kernel_d/include/CGAL/Filtered_kernel_d.h
+++ b/Kernel_d/include/CGAL/Filtered_kernel_d.h
@@ -26,21 +26,21 @@ struct Filtered_kernel_d : public Cartesian_d<typename Kernel::FT>
     // the corresponding exact kernel
     //typedef Linear_algebraCd< Exact_nt, boost::pool_allocator<Exact_nt> > Exact_linalg;
     typedef Linear_algebraCd< Exact_nt > Exact_linalg;
-    typedef Cartesian_d<Exact_nt, Exact_linalg>		EK;
+    typedef Cartesian_d<Exact_nt, Exact_linalg>		Exact_kernel;
     
     // the kernel used for filtered predicates
     typedef Interval_nt<false> IA;
     //typedef Linear_algebraCd<IA, boost::pool_allocator<IA> > Interval_linalg;
-    typedef Linear_algebraCd<IA > Interval_linalg;
-    typedef Cartesian_d<IA, Interval_linalg >	FK;
+    typedef Linear_algebraCd<IA> Interval_linalg;
+    typedef Cartesian_d<IA, Interval_linalg >	Approximate_kernel;
     
     // the converter
-    typedef Cartesian_converter_d<Base, EK>	C2E;
-    typedef Cartesian_converter_d<Base, FK>	C2F;
+    typedef Cartesian_converter_d<Base, Exact_kernel>	C2E;
+    typedef Cartesian_converter_d<Base, Approximate_kernel>	C2F;
 
     // we change the predicates.
 #define CGAL_Kernel_pred(P, Pf) \
-    typedef Filtered_predicate<typename EK::P, typename FK::P, C2E, C2F> P; \
+    typedef Filtered_predicate<typename Exact_kernel::P, typename Approximate_kernel::P, C2E, C2F> P; \
     P Pf() const { return P(); }
 
     // we don't touch the constructions.
diff --git a/Kernel_d/include/CGAL/Kernel_d/Cartesian_converter_d.h b/Kernel_d/include/CGAL/Kernel_d/Cartesian_converter_d.h
index 5db508e73e2..7be84cf7637 100644
--- a/Kernel_d/include/CGAL/Kernel_d/Cartesian_converter_d.h
+++ b/Kernel_d/include/CGAL/Kernel_d/Cartesian_converter_d.h
@@ -44,18 +44,18 @@
 namespace CGAL {
 
 // Guess which compiler needs this work around ?
-namespace CGALi {
+namespace internal {
 template < typename K1, typename K2 >
 struct Default_converter_d {
   typedef typename K1::FT FT1;
   typedef typename K2::FT FT2;
   typedef ::CGAL::NT_converter<FT1, FT2> Type;
 };
-} // namespace CGALi
+} // namespace internal
 
 template < class K1, class K2,
           //class Converter = NT_converter<typename K1::FT, typename K2::FT> >
-           class Converter = typename CGALi::Default_converter_d<K1, K2>::Type >
+           class Converter = typename internal::Default_converter_d<K1, K2>::Type >
 class Cartesian_converter_d : public Enum_converter
 {
     typedef Enum_converter   Base;
diff --git a/Kernel_d/include/CGAL/Kernel_d/Interval_linear_algebra.h b/Kernel_d/include/CGAL/Kernel_d/Interval_linear_algebra.h
index a680a5c502e..ce01da61c83 100644
--- a/Kernel_d/include/CGAL/Kernel_d/Interval_linear_algebra.h
+++ b/Kernel_d/include/CGAL/Kernel_d/Interval_linear_algebra.h
@@ -12,6 +12,10 @@ namespace internal
 
 template<class Matrix>
 Sign // The matrix is row major: M[i] represents row i.
+/*
+FIXME : the function DOES MODIFY the matrix M, but calling functions
+assume M is not modified --> BUGS. (e.g. Side_of_oriented_subsphere)
+*/
 sign_of_determinantDxD_with_interval_arithmetic(Matrix & M)
 // attempts to compute the determinant using interval arithmetic
 {
diff --git a/Kernel_d/include/CGAL/Kernel_d/Linear_algebraCd_impl.h b/Kernel_d/include/CGAL/Kernel_d/Linear_algebraCd_impl.h
index 7a4237de8fd..95f4ba8a342 100644
--- a/Kernel_d/include/CGAL/Kernel_d/Linear_algebraCd_impl.h
+++ b/Kernel_d/include/CGAL/Kernel_d/Linear_algebraCd_impl.h
@@ -135,7 +135,10 @@ Triangular_system_solver(const Matrix &U, const Matrix& L, const Vector &b,
     CGAL_KD_TRACEN("Triangular_system_solver");CGAL_KD_TRACEV(U);CGAL_KD_TRACEV(b);
   D = FT(1); int i;
   for (i = rank; i < U.row_dimension(); ++i) 
-    if ( b[i] != FT(0) ) { x = L.row(i); return false; }
+      if ( b[i] != FT(0) ) {
+          x = L.row(i);
+          return false;
+      }
 
   x = Vector(U.column_dimension());
   for (i = rank-1; i>=0; --i) {
diff --git a/Kernel_d/include/CGAL/Kernel_d/PointCd.h b/Kernel_d/include/CGAL/Kernel_d/PointCd.h
index 52bfd682ac7..433f14fab93 100644
--- a/Kernel_d/include/CGAL/Kernel_d/PointCd.h
+++ b/Kernel_d/include/CGAL/Kernel_d/PointCd.h
@@ -74,14 +74,14 @@ PointCd(int d, InputIterator first, InputIterator last)
   // else first specifies common denominator:
   CGAL_assertion_msg(FT(*first)!=FT(0),
     "PointCd::constructor: denominator must be nonzero.");
-  for (int i=0; i<d; ++i) entry(i)/=FT(*first);
+  for (int i=0; i<d; ++i) entry(i)=entry(i)/FT(*first);
 }
 
 template <class InputIterator>
 PointCd (int d, InputIterator first, InputIterator last, 
   const FT& D) : Base( Tuple(d,first,last) )
 { CGAL_assertion_msg(D!=FT(0),"PointCd::constructor: D must be nonzero.");
-  for (int i=0; i<d; ++i) entry(i)/=D;
+  for (int i=0; i<d; ++i) entry(i)=entry(i)/D;
 }
 
 PointCd(int x, int y, int w = 1) : Base( Tuple((FT)x,(FT)y) )
diff --git a/Kernel_d/include/CGAL/Kernel_d/function_objectsCd.h b/Kernel_d/include/CGAL/Kernel_d/function_objectsCd.h
index 8b2820b5c96..6b11abebcbf 100644
--- a/Kernel_d/include/CGAL/Kernel_d/function_objectsCd.h
+++ b/Kernel_d/include/CGAL/Kernel_d/function_objectsCd.h
@@ -401,6 +401,7 @@ class Side_of_oriented_subsphereCd
 	typedef typename R::Oriented_side   Oriented_side;
 	typedef typename R::Side_of_oriented_sphere_d	Side_of_oriented_sphere;
 	typedef typename R::Coaffine_orientation_d		Coaffine_orientation;
+	typedef typename LA::Matrix	        Matrix;	
 	typedef typename Coaffine_orientation::Axes		Axes;
 	// DATA MEMBERS
 	mutable Coaffine_orientation ori_;
@@ -427,7 +428,7 @@ public:
 			return sos(first, last, q); // perhaps slap user on the back of the head here?
 		}
         if( M.row_dimension() < d+1 )
-            M = typename LA::Matrix(d+1);
+            M = Matrix(d+1);
 		if( ! ori_.state().axes_found_ )
 		{
             // the call to ori_(...) will compute a set of axes to complement our base.
diff --git a/Kernel_d/include/CGAL/Kernel_d/interface_macros_d.h b/Kernel_d/include/CGAL/Kernel_d/interface_macros_d.h
index 35e7318891f..926510a4567 100644
--- a/Kernel_d/include/CGAL/Kernel_d/interface_macros_d.h
+++ b/Kernel_d/include/CGAL/Kernel_d/interface_macros_d.h
@@ -53,56 +53,56 @@ CGAL_Kernel_obj(Line_d)
 
 
 CGAL_Kernel_pred(Affinely_independent_d,
-		 affinely_independent_d_object)
+                 affinely_independent_d_object)
 CGAL_Kernel_pred(Affine_rank_d,
-		 affine_rank_d_object)
+                 affine_rank_d_object)
 CGAL_Kernel_pred(Compare_lexicographically_d,
-		 compare_lexicographically_d_object)
+                 compare_lexicographically_d_object)
 CGAL_Kernel_pred(Contained_in_affine_hull_d,
-		 contained_in_affine_hull_d_object)
+                 contained_in_affine_hull_d_object)
 CGAL_Kernel_pred(Contained_in_linear_hull_d,
-		 contained_in_linear_hull_d_object)
+                 contained_in_linear_hull_d_object)
 CGAL_Kernel_pred(Contained_in_simplex_d,
-		 contained_in_simplex_d_object)
+                 contained_in_simplex_d_object)
 // TODO: create a Do_intersect_d functor
 //CGAL_Kernel_pred(Do_intersect_d,
-//		 do_intersect_d_object)
+//                 do_intersect_d_object)
 CGAL_Kernel_pred(Less_lexicographically_d,
-		 less_lexicographically_d_object)
+                 less_lexicographically_d_object)
 CGAL_Kernel_pred(Less_or_equal_lexicographically_d,
-		 less_or_equal_lexicographically_d_object)
+                 less_or_equal_lexicographically_d_object)
 CGAL_Kernel_pred(Linearly_independent_d,
-		 linearly_independent_d_object)
+                 linearly_independent_d_object)
 CGAL_Kernel_pred(Linear_rank_d,
-		 linear_rank_d_object)
+                 linear_rank_d_object)
 CGAL_Kernel_pred(Orientation_d,
-		 orientation_d_object)
+                 orientation_d_object)
 CGAL_Kernel_pred(Coaffine_orientation_d,
-		 coaffine_orientation_d_object)
+                 coaffine_orientation_d_object)
 CGAL_Kernel_pred(Side_of_bounded_sphere_d,
-		 side_of_bounded_sphere_d_object)
+                 side_of_bounded_sphere_d_object)
 CGAL_Kernel_pred(Side_of_oriented_sphere_d,
-		 side_of_oriented_sphere_d_object)
+                 side_of_oriented_sphere_d_object)
 CGAL_Kernel_pred(Side_of_oriented_subsphere_d,
-		 side_of_oriented_subsphere_d_object)
+                 side_of_oriented_subsphere_d_object)
 CGAL_Kernel_pred(Oriented_side_d,
-		 oriented_side_d_object)
+                 oriented_side_d_object)
 
 
 CGAL_Kernel_cons(Linear_base_d,
-		 linear_base_d_object)
+                 linear_base_d_object)
 CGAL_Kernel_cons(Center_of_sphere_d,
-		 center_of_sphere_d_object)
+                 center_of_sphere_d_object)
 CGAL_Kernel_cons(Intersection_d_,
-		 intersection_d_object)
+                 intersection_d_object)
 CGAL_Kernel_cons(Lift_to_paraboloid_d,
-		 lift_to_paraboloid_d_object)
+                 lift_to_paraboloid_d_object)
 CGAL_Kernel_cons(Midpoint_d,
-		 midpoint_d_object)
+                 midpoint_d_object)
 CGAL_Kernel_cons(Project_along_d_axis_d,
-		 project_along_d_axis_d_object)
+                 project_along_d_axis_d_object)
 CGAL_Kernel_cons(Squared_distance_d,
-		 squared_distance_d_object)
+                 squared_distance_d_object)
 
 #undef CGAL_Kernel_pred
 #undef CGAL_Kernel_cons
diff --git a/Kernel_d/include/CGAL/Linear_algebraCd.h b/Kernel_d/include/CGAL/Linear_algebraCd.h
index c8a1483f655..b22583c6aec 100644
--- a/Kernel_d/include/CGAL/Linear_algebraCd.h
+++ b/Kernel_d/include/CGAL/Linear_algebraCd.h
@@ -118,6 +118,6 @@ public:
 } //namespace CGAL
 
 #include <CGAL/Kernel_d/Linear_algebraCd_impl.h>
-#include <CGAL/Kernel_d/Interval_linear_algebra.h>
+//#include <CGAL/Kernel_d/Interval_linear_algebra.h>
 
 #endif // CGAL_LINEAR_ALGEBRACD_H