diff --git a/Segment_Delaunay_graph_2/demo/Segment_Delaunay_graph_2/pdg_typedefs.h b/Segment_Delaunay_graph_2/demo/Segment_Delaunay_graph_2/pdg_typedefs.h
index ca2a07665e4..3b82a97656c 100644
--- a/Segment_Delaunay_graph_2/demo/Segment_Delaunay_graph_2/pdg_typedefs.h
+++ b/Segment_Delaunay_graph_2/demo/Segment_Delaunay_graph_2/pdg_typedefs.h
@@ -48,11 +48,11 @@ namespace CGAL {
 }
 #endif
 
-typedef CGAL::Sqrt_field_tag  MTag;
+typedef CGAL::Field_with_sqrt_tag  MTag;
 #ifdef CGAL_USE_CORE
-typedef CGAL::Sqrt_field_tag  EMTag;
+typedef CGAL::Field_with_sqrt_tag  EMTag;
 #else
-typedef CGAL::Ring_tag        EMTag;
+typedef CGAL::Integral_domain_without_division_tag        EMTag;
 #endif
 
 typedef CGAL::Tag_false      ITag;
diff --git a/Segment_Delaunay_graph_2/demo/Segment_Delaunay_graph_2/typedefs.h b/Segment_Delaunay_graph_2/demo/Segment_Delaunay_graph_2/typedefs.h
index bc498ff9a84..600b6a86185 100644
--- a/Segment_Delaunay_graph_2/demo/Segment_Delaunay_graph_2/typedefs.h
+++ b/Segment_Delaunay_graph_2/demo/Segment_Delaunay_graph_2/typedefs.h
@@ -44,8 +44,8 @@ struct Rep : public CGAL::Simple_cartesian<CORE::Expr> {};
 
 #ifdef USE_FILTERED_TRAITS
 #ifdef CGAL_USE_CORE
-typedef CGAL::Sqrt_field_tag MTag;
-typedef CGAL::Sqrt_field_tag EMTag;
+typedef CGAL::Field_with_sqrt_tag MTag;
+typedef CGAL::Field_with_sqrt_tag EMTag;
 typedef CGAL::Simple_cartesian<CORE::Expr> ERep;
 struct Gt
   : public CGAL::Segment_Delaunay_graph_filtered_traits_2<Rep,
diff --git a/Segment_Delaunay_graph_2/examples/Segment_Delaunay_graph_2/sdg-count-sites.cpp b/Segment_Delaunay_graph_2/examples/Segment_Delaunay_graph_2/sdg-count-sites.cpp
index 04519dbb310..8e361b491c2 100644
--- a/Segment_Delaunay_graph_2/examples/Segment_Delaunay_graph_2/sdg-count-sites.cpp
+++ b/Segment_Delaunay_graph_2/examples/Segment_Delaunay_graph_2/sdg-count-sites.cpp
@@ -22,7 +22,7 @@ typedef CGAL::Simple_cartesian<ENT>        EK;
 #include <CGAL/Segment_Delaunay_graph_2.h>
 
 typedef CGAL::Segment_Delaunay_graph_filtered_traits_2<CK,
-/* The construction kernel allows for / and sqrt */    CGAL::Sqrt_field_tag,
+/* The construction kernel allows for / and sqrt */    CGAL::Field_with_sqrt_tag,
 						       EK,
 /* The exact kernel supports field ops exactly */      CGAL::Field_tag>  Gt;
 
diff --git a/Segment_Delaunay_graph_2/include/CGAL/Segment_Delaunay_graph_2.h b/Segment_Delaunay_graph_2/include/CGAL/Segment_Delaunay_graph_2.h
index 2f4a6fa0fd9..e6a77e39254 100644
--- a/Segment_Delaunay_graph_2/include/CGAL/Segment_Delaunay_graph_2.h
+++ b/Segment_Delaunay_graph_2/include/CGAL/Segment_Delaunay_graph_2.h
@@ -1239,20 +1239,20 @@ protected:
 
   // types
   typedef
-  CGAL_SEGMENT_DELAUNAY_GRAPH_2_NS::Construct_sdg_circle_2<Gt,Ring_tag>
+  CGAL_SEGMENT_DELAUNAY_GRAPH_2_NS::Construct_sdg_circle_2<Gt,Integral_domain_without_division_tag>
   Construct_sdg_circle_2;
 
   typedef
-  CGAL_SEGMENT_DELAUNAY_GRAPH_2_NS::Construct_sdg_bisector_2<Gt,Ring_tag>
+  CGAL_SEGMENT_DELAUNAY_GRAPH_2_NS::Construct_sdg_bisector_2<Gt,Integral_domain_without_division_tag>
   Construct_sdg_bisector_2;
 
   typedef
-  CGAL_SEGMENT_DELAUNAY_GRAPH_2_NS::Construct_sdg_bisector_ray_2<Gt,Ring_tag>
+  CGAL_SEGMENT_DELAUNAY_GRAPH_2_NS::Construct_sdg_bisector_ray_2<Gt,Integral_domain_without_division_tag>
   Construct_sdg_bisector_ray_2;
 
   typedef
   CGAL_SEGMENT_DELAUNAY_GRAPH_2_NS::
-  Construct_sdg_bisector_segment_2<Gt,Ring_tag>
+  Construct_sdg_bisector_segment_2<Gt,Integral_domain_without_division_tag>
   Construct_sdg_bisector_segment_2;
 
   // access
diff --git a/Segment_Delaunay_graph_2/include/CGAL/Segment_Delaunay_graph_2/Basic_predicates_C2.h b/Segment_Delaunay_graph_2/include/CGAL/Segment_Delaunay_graph_2/Basic_predicates_C2.h
index 75bc6477f62..0c3a0acd5d8 100644
--- a/Segment_Delaunay_graph_2/include/CGAL/Segment_Delaunay_graph_2/Basic_predicates_C2.h
+++ b/Segment_Delaunay_graph_2/include/CGAL/Segment_Delaunay_graph_2/Basic_predicates_C2.h
@@ -26,7 +26,6 @@
 
 #include <CGAL/Segment_Delaunay_graph_2/basic.h>
 #include <CGAL/enum.h>
-#include <CGAL/Number_type_traits.h>
 #include <CGAL/Segment_Delaunay_graph_2/Sqrt_extension_1.h>
 #include <CGAL/Segment_Delaunay_graph_2/Sqrt_extension_2.h>
 
@@ -58,8 +57,8 @@ public:
   typedef CGAL::Sqrt_extension_2<RT>       Sqrt_2;
   typedef CGAL::Sqrt_extension_2<Sqrt_1>   Sqrt_3;
 
-  typedef typename Number_type_traits<RT>::Has_sqrt  RT_Has_sqrt;
-  typedef typename Number_type_traits<FT>::Has_sqrt  FT_Has_sqrt;
+    typedef Boolean_tag<CGALi::Is_field_with_sqrt<RT>::value>  RT_Has_sqrt;
+    typedef Boolean_tag<CGALi::Is_field_with_sqrt<FT>::value>  FT_Has_sqrt;
 
   static const RT_Has_sqrt& rt_has_sqrt() {
     static RT_Has_sqrt has_sqrt;
diff --git a/Segment_Delaunay_graph_2/include/CGAL/Segment_Delaunay_graph_2/Constructions_C2.h b/Segment_Delaunay_graph_2/include/CGAL/Segment_Delaunay_graph_2/Constructions_C2.h
index 6694dd44ac6..bb5da79b372 100644
--- a/Segment_Delaunay_graph_2/include/CGAL/Segment_Delaunay_graph_2/Constructions_C2.h
+++ b/Segment_Delaunay_graph_2/include/CGAL/Segment_Delaunay_graph_2/Constructions_C2.h
@@ -186,8 +186,7 @@ private:
 
   static Point_2 midpoint(const Point_2& p, const Point_2& q) {
     typedef typename Gt::FT  FT;
-    static typename Number_type_traits<FT>::Has_division  has_division;
-    return midpoint(p, q, has_division);
+    return midpoint(p, q, Boolean_tag<CGALi::Is_field<FT>::value>());
   }
 
 public:
diff --git a/Segment_Delaunay_graph_2/include/CGAL/Segment_Delaunay_graph_2/Filtered_traits_base_2.h b/Segment_Delaunay_graph_2/include/CGAL/Segment_Delaunay_graph_2/Filtered_traits_base_2.h
index f9877221784..a8b05f3b752 100644
--- a/Segment_Delaunay_graph_2/include/CGAL/Segment_Delaunay_graph_2/Filtered_traits_base_2.h
+++ b/Segment_Delaunay_graph_2/include/CGAL/Segment_Delaunay_graph_2/Filtered_traits_base_2.h
@@ -22,8 +22,6 @@
 #ifndef CGAL_SEGMENT_DELAUNAY_GRAPH_2_FILTERED_TRAITS_BASE_2_H
 #define CGAL_SEGMENT_DELAUNAY_GRAPH_2_FILTERED_TRAITS_BASE_2_H
 
-#include <CGAL/Number_type_traits.h>
-
 #include <CGAL/Segment_Delaunay_graph_2/basic.h>
 #include <CGAL/Segment_Delaunay_graph_2/Traits_base_2.h>
 #include <CGAL/Segment_Delaunay_graph_2/Kernel_wrapper_2.h>
diff --git a/Segment_Delaunay_graph_2/include/CGAL/Segment_Delaunay_graph_2/Filtered_traits_concept_check_tags.h b/Segment_Delaunay_graph_2/include/CGAL/Segment_Delaunay_graph_2/Filtered_traits_concept_check_tags.h
index eb22d13a09e..b1615b6badd 100644
--- a/Segment_Delaunay_graph_2/include/CGAL/Segment_Delaunay_graph_2/Filtered_traits_concept_check_tags.h
+++ b/Segment_Delaunay_graph_2/include/CGAL/Segment_Delaunay_graph_2/Filtered_traits_concept_check_tags.h
@@ -34,26 +34,26 @@ namespace Internal {
   struct Concept_check_tags {};
 
   template<class D>
-  struct Concept_check_tags<D,Ring_tag,2>
+  struct Concept_check_tags<D,Integral_domain_without_division_tag,2>
   {
     Concept_check_tags() {
-      THE_2ND_TEMPLATE_PARAMETER_MUST_EITHER_BE_Field_tag_OR_Sqrt_field_tag
+      THE_2ND_TEMPLATE_PARAMETER_MUST_EITHER_BE_Field_tag_OR_Field_with_sqrt_tag
       ( D() );
     }
   };
 
   template<class D>
-  struct Concept_check_tags<D,Ring_tag,4> {
+  struct Concept_check_tags<D,Integral_domain_without_division_tag,4> {
     Concept_check_tags() {
-      THE_4TH_TEMPLATE_PARAMETER_MUST_EITHER_BE_Field_tag_OR_Sqrt_field_tag
+      THE_4TH_TEMPLATE_PARAMETER_MUST_EITHER_BE_Field_tag_OR_Field_with_sqrt_tag
       ( D() );
     }
   };
 
   template<class D>
-  struct Concept_check_tags<D,Ring_tag,6> {
+  struct Concept_check_tags<D,Integral_domain_without_division_tag,6> {
     Concept_check_tags() {
-      THE_6TH_TEMPLATE_PARAMETER_MUST_EITHER_BE_Field_tag_OR_Sqrt_field_tag
+      THE_6TH_TEMPLATE_PARAMETER_MUST_EITHER_BE_Field_tag_OR_Field_with_sqrt_tag
       ( D() );
     }
   };
@@ -64,7 +64,7 @@ namespace Internal {
   struct Concept_check_tags<D,Euclidean_ring_tag,2>
   {
     Concept_check_tags() {
-      THE_2ND_TEMPLATE_PARAMETER_MUST_EITHER_BE_Field_tag_OR_Sqrt_field_tag
+      THE_2ND_TEMPLATE_PARAMETER_MUST_EITHER_BE_Field_tag_OR_Field_with_sqrt_tag
       ( D() );
     }
   };
@@ -72,7 +72,7 @@ namespace Internal {
   template<class D>
   struct Concept_check_tags<D,Euclidean_ring_tag,4> {
     Concept_check_tags() {
-      THE_4TH_TEMPLATE_PARAMETER_MUST_EITHER_BE_Field_tag_OR_Sqrt_field_tag
+      THE_4TH_TEMPLATE_PARAMETER_MUST_EITHER_BE_Field_tag_OR_Field_with_sqrt_tag
       ( D() );
     }
   };
@@ -80,7 +80,7 @@ namespace Internal {
   template<class D>
   struct Concept_check_tags<D,Euclidean_ring_tag,6> {
     Concept_check_tags() {
-      THE_6TH_TEMPLATE_PARAMETER_MUST_EITHER_BE_Field_tag_OR_Sqrt_field_tag
+      THE_6TH_TEMPLATE_PARAMETER_MUST_EITHER_BE_Field_tag_OR_Field_with_sqrt_tag
       ( D() );
     }
   };
@@ -94,7 +94,7 @@ namespace Internal {
   struct Concept_check_tags_wi<D,Field_tag,2>
   {
     Concept_check_tags_wi() {
-      THE_2ND_TEMPLATE_PARAMETER_MUST_EITHER_BE_Ring_tag_OR_Sqrt_field_tag
+      THE_2ND_TEMPLATE_PARAMETER_MUST_EITHER_BE_Integral_domain_without_division_tag_OR_Field_with_sqrt_tag
       ( D() );
     }
   };
@@ -102,7 +102,7 @@ namespace Internal {
   template<class D>
   struct Concept_check_tags_wi<D,Field_tag,4> {
     Concept_check_tags_wi() {
-      THE_4TH_TEMPLATE_PARAMETER_MUST_EITHER_BE_Ring_tag_OR_Sqrt_field_tag
+      THE_4TH_TEMPLATE_PARAMETER_MUST_EITHER_BE_Integral_domain_without_division_tag_OR_Field_with_sqrt_tag
       ( D() );
     }
   };
@@ -110,7 +110,7 @@ namespace Internal {
   template<class D>
   struct Concept_check_tags_wi<D,Field_tag,6> {
     Concept_check_tags_wi() {
-      THE_6TH_TEMPLATE_PARAMETER_MUST_EITHER_BE_Ring_tag_OR_Sqrt_field_tag
+      THE_6TH_TEMPLATE_PARAMETER_MUST_EITHER_BE_Integral_domain_without_division_tag_OR_Field_with_sqrt_tag
       ( D() );
     }
   };
@@ -121,7 +121,7 @@ namespace Internal {
   struct Concept_check_tags_wi<D,Euclidean_ring_tag,2>
   {
     Concept_check_tags_wi() {
-      THE_2ND_TEMPLATE_PARAMETER_MUST_EITHER_BE_Ring_tag_OR_Sqrt_field_tag
+      THE_2ND_TEMPLATE_PARAMETER_MUST_EITHER_BE_Integral_domain_without_division_tag_OR_Field_with_sqrt_tag
       ( D() );
     }
   };
@@ -129,7 +129,7 @@ namespace Internal {
   template<class D>
   struct Concept_check_tags_wi<D,Euclidean_ring_tag,4> {
     Concept_check_tags_wi() {
-      THE_4TH_TEMPLATE_PARAMETER_MUST_EITHER_BE_Ring_tag_OR_Sqrt_field_tag
+      THE_4TH_TEMPLATE_PARAMETER_MUST_EITHER_BE_Integral_domain_without_division_tag_OR_Field_with_sqrt_tag
       ( D() );
     }
   };
@@ -137,7 +137,7 @@ namespace Internal {
   template<class D>
   struct Concept_check_tags_wi<D,Euclidean_ring_tag,6> {
     Concept_check_tags_wi() {
-      THE_6TH_TEMPLATE_PARAMETER_MUST_EITHER_BE_Ring_tag_OR_Sqrt_field_tag
+      THE_6TH_TEMPLATE_PARAMETER_MUST_EITHER_BE_Integral_domain_without_division_tag_OR_Field_with_sqrt_tag
       ( D() );
     }
   };
diff --git a/Segment_Delaunay_graph_2/include/CGAL/Segment_Delaunay_graph_2/Sqrt_extension_1.h b/Segment_Delaunay_graph_2/include/CGAL/Segment_Delaunay_graph_2/Sqrt_extension_1.h
index 09577aba854..a003c369576 100644
--- a/Segment_Delaunay_graph_2/include/CGAL/Segment_Delaunay_graph_2/Sqrt_extension_1.h
+++ b/Segment_Delaunay_graph_2/include/CGAL/Segment_Delaunay_graph_2/Sqrt_extension_1.h
@@ -286,127 +286,6 @@ public:
     };   
 };
 
-
-
-template<class NT>
-struct Number_type_traits< Sqrt_extension_1<NT> >
-{
-
-  static inline
-  std::pair<double,double> to_interval(const Sqrt_extension_1<NT>& x) {
-    return x.to_interval();
-  }
-
-  static inline bool is_positive(const Sqrt_extension_1<NT>& x) {
-    return x.sign() == POSITIVE;
-  }
-
-  static inline bool is_negative(const Sqrt_extension_1<NT>& x) {
-    return x.sign() == NEGATIVE;
-  }
-
-  static inline bool is_zero(const Sqrt_extension_1<NT>& x) {
-    return x.sign() == ZERO;
-  }
-
-  static inline Sign sign(const Sqrt_extension_1<NT>& x) {
-    return x.sign();
-  }
-
-  static inline Sqrt_extension_1<NT> square(const Sqrt_extension_1<NT>& x) {
-    return x.square();
-  }
-
-  static inline
-  Comparison_result compare(const Sqrt_extension_1<NT>& x,
-			    const Sqrt_extension_1<NT>& y) {
-    CGAL_exactness_precondition( CGAL::compare(x.c(), y.c()) == EQUAL );
-
-    //  Sign s = CGAL::sign(x - y);
-    Sign s = (x - y).sign();
-
-    if ( s == ZERO ) { return EQUAL; }
-    return (s == POSITIVE) ? LARGER : SMALLER;
-  }
-
-  static inline double to_double(const Sqrt_extension_1<NT>& x) {
-    return x.to_double();
-  }
-};
-
-
-
-
-
-
-
-
-template<class NT>
-inline
-std::pair<double,double>
-to_interval(const Sqrt_extension_1<NT>& x)
-{
-  return Number_type_traits< Sqrt_extension_1<NT> >::to_interval(x);
-}
-
-
-template<class NT>
-inline
-bool
-is_positive(const Sqrt_extension_1<NT>& x)
-{
-  return Number_type_traits< Sqrt_extension_1<NT> >::is_positive(x);
-}
-
-template<class NT>
-inline
-bool
-is_negative(const Sqrt_extension_1<NT>& x)
-{
-  return Number_type_traits< Sqrt_extension_1<NT> >::is_negative(x);
-}
-
-template<class NT>
-inline
-bool
-is_zero(const Sqrt_extension_1<NT>& x)
-{
-  return Number_type_traits< Sqrt_extension_1<NT> >::is_zero(x);
-}
-
-
-template<class NT>
-inline
-Sign
-sign(const Sqrt_extension_1<NT>& x)
-{
-  return Number_type_traits< Sqrt_extension_1<NT> >::sign(x);
-}
-
-template<class NT>
-inline
-Sqrt_extension_1<NT>
-square(const Sqrt_extension_1<NT>& x)
-{
-  return Number_type_traits< Sqrt_extension_1<NT> >::square(x);
-}
-
-template<class NT>
-inline
-Comparison_result
-compare(const Sqrt_extension_1<NT>& x, const Sqrt_extension_1<NT>& y)
-{
-  return Number_type_traits< Sqrt_extension_1<NT> >::compare(x, y);
-}
-
-template<class NT>
-inline
-double
-to_double(const Sqrt_extension_1<NT>& x)
-{
-  return Number_type_traits< Sqrt_extension_1<NT> >::to_double(x);
-}
-
 // operator <<
 template<class Stream, class NT>
 inline
diff --git a/Segment_Delaunay_graph_2/include/CGAL/Segment_Delaunay_graph_2/Sqrt_extension_2.h b/Segment_Delaunay_graph_2/include/CGAL/Segment_Delaunay_graph_2/Sqrt_extension_2.h
index 08b5650ba9f..e2941e69543 100644
--- a/Segment_Delaunay_graph_2/include/CGAL/Segment_Delaunay_graph_2/Sqrt_extension_2.h
+++ b/Segment_Delaunay_graph_2/include/CGAL/Segment_Delaunay_graph_2/Sqrt_extension_2.h
@@ -117,9 +117,9 @@ public:
     Sqrt_1 x(a0_, a1_, A_);
     Sqrt_1 y(a2_, a3_, A_);
 
-    Sign s_x = Number_type_traits<Sqrt_1>::sign(x);
-    Sign s_y = Number_type_traits<Sqrt_1>::sign(y);
-    Sign s_B = Number_type_traits<Sqrt_1>::sign(B_);
+    Sign s_x = CGAL_NTS sign(x);
+    Sign s_y = CGAL_NTS sign(y);
+    Sign s_B = CGAL_NTS sign(B_);
 
     if ( s_B == ZERO ) {
       return s_x;
@@ -131,7 +131,7 @@ public:
       return s_x;
     } else {
       Sqrt_1 Q = CGAL::square(x) - CGAL::square(y) * B_;
-      return Sign(s_x * Number_type_traits<Sqrt_1>::sign(Q));
+      return Sign(s_x * CGAL_NTS sign(Q));
     }
   }
 
@@ -282,7 +282,8 @@ public:
         CGAL::Comparison_result operator()(
                 const Real_embeddable& x, 
                 const Real_embeddable& y) const {
-            CGAL_exactness_precondition( CGAL::compare(x.c(), y.c()) == EQUAL );
+            CGAL_exactness_precondition( CGAL::compare(x.e(), y.e()) == EQUAL );
+            CGAL_exactness_precondition( CGAL::compare(x.f(), y.f()) == EQUAL );
             return (x - y).sign();
         }
     };
@@ -304,94 +305,6 @@ public:
     };   
 };
 
-template<class NT>
-struct Number_type_traits< Sqrt_extension_2<NT> >
-{
-  static inline bool is_positive(const Sqrt_extension_2<NT>& x) {
-    return x.sign() == POSITIVE;
-  }
-
-  static inline bool is_negative(const Sqrt_extension_2<NT>& x) {
-    return x.sign() == NEGATIVE;
-  }
-
-  static inline bool is_zero(const Sqrt_extension_2<NT>& x) {
-    return x.sign() == ZERO;
-  }
-
-  static inline Sign sign(const Sqrt_extension_2<NT>& x) {
-    return x.sign();
-  }
-
-  static inline Sqrt_extension_2<NT> square(const Sqrt_extension_2<NT>& x) {
-    return x.square();
-  }
-
-  static inline
-  Comparison_result compare(const Sqrt_extension_2<NT>& x,
-			    const Sqrt_extension_2<NT>& y)
-  {
-    CGAL_exactness_precondition( CGAL::compare(x.e(), y.e()) == EQUAL );
-    CGAL_exactness_precondition( CGAL::compare(x.f(), y.f()) == EQUAL );
-
-    //  Sign s = CGAL::sign(x - y);
-    Sign s = (x - y).sign();
-
-    if ( s == ZERO ) { return EQUAL; }
-    return (s == POSITIVE) ? LARGER : SMALLER;
-  }
-};
-
-template<class NT>
-inline
-bool
-is_positive(const Sqrt_extension_2<NT>& x)
-{
-  return Number_type_traits< Sqrt_extension_2<NT> >::is_positive(x);
-}
-
-template<class NT>
-inline
-bool
-is_negative(const Sqrt_extension_2<NT>& x)
-{
-  return Number_type_traits< Sqrt_extension_2<NT> >::is_negative(x);
-}
-
-template<class NT>
-inline
-bool
-is_zero(const Sqrt_extension_2<NT>& x)
-{
-  return Number_type_traits< Sqrt_extension_2<NT> >::is_zero(x);
-}
-
-
-template<class NT>
-inline
-Sign
-sign(const Sqrt_extension_2<NT>& x)
-{
-  return Number_type_traits< Sqrt_extension_2<NT> >::sign(x);
-}
-
-template<class NT>
-inline
-Sqrt_extension_2<NT>
-square(const Sqrt_extension_2<NT>& x)
-{
-  return Number_type_traits< Sqrt_extension_2<NT> >::square(x);
-}
-
-template<class NT>
-inline
-Comparison_result
-compare(const Sqrt_extension_2<NT>& x,
-	const Sqrt_extension_2<NT>& y)
-{
-  return Number_type_traits< Sqrt_extension_2<NT> >::compare(x, y);
-}
-
 // operator <<
 template<class Stream, class NT>
 inline
diff --git a/Segment_Delaunay_graph_2/include/CGAL/Segment_Delaunay_graph_2/Traits_base_2.h b/Segment_Delaunay_graph_2/include/CGAL/Segment_Delaunay_graph_2/Traits_base_2.h
index a311ef2b7fd..e19e2ea64c5 100644
--- a/Segment_Delaunay_graph_2/include/CGAL/Segment_Delaunay_graph_2/Traits_base_2.h
+++ b/Segment_Delaunay_graph_2/include/CGAL/Segment_Delaunay_graph_2/Traits_base_2.h
@@ -34,7 +34,6 @@
 #endif
 
 
-#include <CGAL/Number_type_traits.h>
 #include <CGAL/Segment_Delaunay_graph_2/Kernel_wrapper_2.h>
 
 
diff --git a/Segment_Delaunay_graph_2/include/CGAL/Segment_Delaunay_graph_2/Voronoi_vertex_C2.h b/Segment_Delaunay_graph_2/include/CGAL/Segment_Delaunay_graph_2/Voronoi_vertex_C2.h
index b1c51c2fd8f..70ab7ce173f 100644
--- a/Segment_Delaunay_graph_2/include/CGAL/Segment_Delaunay_graph_2/Voronoi_vertex_C2.h
+++ b/Segment_Delaunay_graph_2/include/CGAL/Segment_Delaunay_graph_2/Voronoi_vertex_C2.h
@@ -24,7 +24,6 @@
 
 
 #include <CGAL/Segment_Delaunay_graph_2/basic.h>
-#include <CGAL/Number_type_traits.h>
 #include <CGAL/Segment_Delaunay_graph_2/Voronoi_vertex_ring_C2.h>
 #include <CGAL/Segment_Delaunay_graph_2/Voronoi_vertex_sqrt_field_C2.h>
 
@@ -38,13 +37,13 @@ namespace Internal {
   template<class K,class M> struct Which_Voronoi_vertex_base_C2;
 
   template<class K>
-  struct Which_Voronoi_vertex_base_C2<K,Ring_tag>
+  struct Which_Voronoi_vertex_base_C2<K,Integral_domain_without_division_tag>
   {
     typedef Voronoi_vertex_ring_C2<K>          Base;
   };
 
   template<class K>
-  struct Which_Voronoi_vertex_base_C2<K,Sqrt_field_tag>
+  struct Which_Voronoi_vertex_base_C2<K,Field_with_sqrt_tag>
   {
     typedef Voronoi_vertex_sqrt_field_C2<K>    Base;
   };
diff --git a/Segment_Delaunay_graph_2/include/CGAL/Segment_Delaunay_graph_2/Voronoi_vertex_ring_C2.h b/Segment_Delaunay_graph_2/include/CGAL/Segment_Delaunay_graph_2/Voronoi_vertex_ring_C2.h
index dd6c25989b7..36b7479aa0e 100644
--- a/Segment_Delaunay_graph_2/include/CGAL/Segment_Delaunay_graph_2/Voronoi_vertex_ring_C2.h
+++ b/Segment_Delaunay_graph_2/include/CGAL/Segment_Delaunay_graph_2/Voronoi_vertex_ring_C2.h
@@ -1379,13 +1379,11 @@ public:
   inline FT y(const Tag_true&) const { return hy() / hw(); }
 
   inline FT x() const {
-    static typename Number_type_traits<FT>::Has_division has_division;
-    return x(has_division);
+    return x(Boolean_tag<CGALi::Is_field<FT>::value>());
   }
 
   inline FT y() const {
-    static typename Number_type_traits<FT>::Has_division has_division;
-    return y(has_division);
+    return y(Boolean_tag<CGALi::Is_field<FT>::value>());
   }
 
   FT hx() const {
diff --git a/Segment_Delaunay_graph_2/include/CGAL/Segment_Delaunay_graph_filtered_traits_2.h b/Segment_Delaunay_graph_2/include/CGAL/Segment_Delaunay_graph_filtered_traits_2.h
index 4d84ec80cf4..dd4f83116e9 100644
--- a/Segment_Delaunay_graph_2/include/CGAL/Segment_Delaunay_graph_filtered_traits_2.h
+++ b/Segment_Delaunay_graph_2/include/CGAL/Segment_Delaunay_graph_filtered_traits_2.h
@@ -58,7 +58,7 @@ CGAL_BEGIN_NAMESPACE
 
 // this traits class does support intersecting segments
 template<class CK,
-	 class CK_MTag = Sqrt_field_tag,
+	 class CK_MTag = Field_with_sqrt_tag,
 #ifdef CGAL_USE_GMP
 	 class EK      = Simple_cartesian< Gmpq >,
 #else
@@ -66,7 +66,7 @@ template<class CK,
 #endif
 	 class EK_MTag = Field_tag,
 	 class FK      = Simple_cartesian< Interval_nt<false> >,
-	 class FK_MTag = Sqrt_field_tag,
+	 class FK_MTag = Field_with_sqrt_tag,
 	 class C2E     = Cartesian_converter<CK, EK>,
 #if defined(__sun) && defined(__SUNPRO_CC)
          class C2F     = SDG2_INS::SUNPRO_CC_Interval_converter<CK, FK> >
@@ -83,9 +83,9 @@ struct Segment_Delaunay_graph_filtered_traits_2
 {
 public:
   Segment_Delaunay_graph_filtered_traits_2() {
-    SDG2_INS::Concept_check_tags<Ring_tag,CK_MTag,2>();
-    SDG2_INS::Concept_check_tags<Ring_tag,EK_MTag,4>();
-    SDG2_INS::Concept_check_tags<Ring_tag,FK_MTag,6>();
+    SDG2_INS::Concept_check_tags<Integral_domain_without_division_tag,CK_MTag,2>();
+    SDG2_INS::Concept_check_tags<Integral_domain_without_division_tag,EK_MTag,4>();
+    SDG2_INS::Concept_check_tags<Integral_domain_without_division_tag,FK_MTag,6>();
   }
 };
 
@@ -96,7 +96,7 @@ struct Segment_Delaunay_graph_filtered_traits_2<CK, Field_tag,
 						EK, EK_MTag,
 						FK, FK_MTag,
 						C2E, C2F>
-  : public Segment_Delaunay_graph_filtered_traits_base_2<CK, Ring_tag,
+  : public Segment_Delaunay_graph_filtered_traits_base_2<CK, Integral_domain_without_division_tag,
 							 EK, EK_MTag,
 							 FK, FK_MTag,
 							 C2E, C2F,
@@ -104,8 +104,8 @@ struct Segment_Delaunay_graph_filtered_traits_2<CK, Field_tag,
 {
 public:
   Segment_Delaunay_graph_filtered_traits_2() {
-    SDG2_INS::Concept_check_tags<Ring_tag,EK_MTag,4>();
-    SDG2_INS::Concept_check_tags<Ring_tag,FK_MTag,6>();
+    SDG2_INS::Concept_check_tags<Integral_domain_without_division_tag,EK_MTag,4>();
+    SDG2_INS::Concept_check_tags<Integral_domain_without_division_tag,FK_MTag,6>();
   }
 };
 
@@ -116,15 +116,15 @@ struct Segment_Delaunay_graph_filtered_traits_2<CK, CK_MTag,
 						FK, FK_MTag,
 						C2E, C2F>
   : public Segment_Delaunay_graph_filtered_traits_base_2<CK, CK_MTag,
-							 EK, Ring_tag,
+							 EK, Integral_domain_without_division_tag,
 							 FK, FK_MTag,
 							 C2E, C2F,
 							 Tag_true>
 {
 public:
   Segment_Delaunay_graph_filtered_traits_2() {
-    SDG2_INS::Concept_check_tags<Ring_tag,CK_MTag,2>();
-    SDG2_INS::Concept_check_tags<Ring_tag,FK_MTag,6>();
+    SDG2_INS::Concept_check_tags<Integral_domain_without_division_tag,CK_MTag,2>();
+    SDG2_INS::Concept_check_tags<Integral_domain_without_division_tag,FK_MTag,6>();
   }
 };
 
@@ -136,14 +136,14 @@ struct Segment_Delaunay_graph_filtered_traits_2<CK, CK_MTag,
 						C2E, C2F>
   : public Segment_Delaunay_graph_filtered_traits_base_2<CK, CK_MTag,
 							 EK, EK_MTag,
-							 FK, Ring_tag,
+							 FK, Integral_domain_without_division_tag,
 							 C2E, C2F,
 							 Tag_true>
 {
 public:
   Segment_Delaunay_graph_filtered_traits_2() {
-    SDG2_INS::Concept_check_tags<Ring_tag,CK_MTag,2>();
-    SDG2_INS::Concept_check_tags<Ring_tag,EK_MTag,4>();
+    SDG2_INS::Concept_check_tags<Integral_domain_without_division_tag,CK_MTag,2>();
+    SDG2_INS::Concept_check_tags<Integral_domain_without_division_tag,EK_MTag,4>();
   }
 };
 
@@ -154,14 +154,14 @@ struct Segment_Delaunay_graph_filtered_traits_2<CK, CK_MTag,
 						FK, Field_tag,
 						C2E, C2F>
   : public Segment_Delaunay_graph_filtered_traits_base_2<CK, CK_MTag,
-							 EK, Ring_tag,
-							 FK, Ring_tag,
+							 EK, Integral_domain_without_division_tag,
+							 FK, Integral_domain_without_division_tag,
 							 C2E, C2F,
 							 Tag_true>
 {
 public:
   Segment_Delaunay_graph_filtered_traits_2() {
-    SDG2_INS::Concept_check_tags<Ring_tag,CK_MTag,2>();
+    SDG2_INS::Concept_check_tags<Integral_domain_without_division_tag,CK_MTag,2>();
   }
 };
 
@@ -171,15 +171,15 @@ struct Segment_Delaunay_graph_filtered_traits_2<CK, Field_tag,
 						 EK, EK_MTag,
 						 FK, Field_tag,
 						 C2E, C2F>
-  : public Segment_Delaunay_graph_filtered_traits_base_2<CK, Ring_tag,
+  : public Segment_Delaunay_graph_filtered_traits_base_2<CK, Integral_domain_without_division_tag,
 							 EK, EK_MTag,
-							 FK, Ring_tag,
+							 FK, Integral_domain_without_division_tag,
 							 C2E, C2F,
 							 Tag_true>
 {
 public:
   Segment_Delaunay_graph_filtered_traits_2() {
-    SDG2_INS::Concept_check_tags<Ring_tag,EK_MTag,4>();
+    SDG2_INS::Concept_check_tags<Integral_domain_without_division_tag,EK_MTag,4>();
   }
 };
 
@@ -189,15 +189,15 @@ struct Segment_Delaunay_graph_filtered_traits_2<CK, Field_tag,
 						EK, Field_tag,
 						FK, FK_MTag,
 						C2E, C2F>
-  : public Segment_Delaunay_graph_filtered_traits_base_2<CK, Ring_tag,
-							 EK, Ring_tag,
+  : public Segment_Delaunay_graph_filtered_traits_base_2<CK, Integral_domain_without_division_tag,
+							 EK, Integral_domain_without_division_tag,
 							 FK, FK_MTag,
 							 C2E, C2F,
 							 Tag_true>
 {
 public:
   Segment_Delaunay_graph_filtered_traits_2() {
-    SDG2_INS::Concept_check_tags<Ring_tag,FK_MTag,6>();
+    SDG2_INS::Concept_check_tags<Integral_domain_without_division_tag,FK_MTag,6>();
   }
 };
 
@@ -206,9 +206,9 @@ struct Segment_Delaunay_graph_filtered_traits_2<CK, Field_tag,
 						EK, Field_tag,
 						FK, Field_tag,
 						C2E, C2F>
-  : public Segment_Delaunay_graph_filtered_traits_base_2<CK, Ring_tag,
-							 EK, Ring_tag,
-							 FK, Ring_tag,
+  : public Segment_Delaunay_graph_filtered_traits_base_2<CK, Integral_domain_without_division_tag,
+							 EK, Integral_domain_without_division_tag,
+							 FK, Integral_domain_without_division_tag,
 							 C2E, C2F,
 							 Tag_true>
 {};
@@ -218,15 +218,15 @@ struct Segment_Delaunay_graph_filtered_traits_2<CK, Field_tag,
 
 // this traits class does NOT support intersecting segments
 template<class CK,
-	 class CK_MTag = Sqrt_field_tag,
+	 class CK_MTag = Field_with_sqrt_tag,
 #ifdef CGAL_USE_GMP
 	 class EK      = Simple_cartesian< Gmpq >,
 #else
 	 class EK      = Simple_cartesian< MP_Float >,
 #endif
-	 class EK_MTag = Ring_tag,
+	 class EK_MTag = Integral_domain_without_division_tag,
 	 class FK      = Simple_cartesian< Interval_nt<false> >,
-	 class FK_MTag = Sqrt_field_tag,
+	 class FK_MTag = Field_with_sqrt_tag,
 	 class C2E     = Cartesian_converter<CK, EK>,
 #if defined(__sun) && defined(__SUNPRO_CC)
          class C2F     = SDG2_INS::SUNPRO_CC_Interval_converter<CK, FK> >
@@ -242,9 +242,9 @@ struct Segment_Delaunay_graph_filtered_traits_without_intersections_2
 							 Tag_false>
 {
   Segment_Delaunay_graph_filtered_traits_without_intersections_2() {
-    SDG2_INS::Concept_check_tags_wi<Ring_tag,CK_MTag,2>();
-    SDG2_INS::Concept_check_tags_wi<Ring_tag,EK_MTag,4>();
-    SDG2_INS::Concept_check_tags_wi<Ring_tag,FK_MTag,6>();
+    SDG2_INS::Concept_check_tags_wi<Integral_domain_without_division_tag,CK_MTag,2>();
+    SDG2_INS::Concept_check_tags_wi<Integral_domain_without_division_tag,EK_MTag,4>();
+    SDG2_INS::Concept_check_tags_wi<Integral_domain_without_division_tag,FK_MTag,6>();
   }
 };
 
diff --git a/Segment_Delaunay_graph_2/include/CGAL/Segment_Delaunay_graph_traits_2.h b/Segment_Delaunay_graph_2/include/CGAL/Segment_Delaunay_graph_traits_2.h
index 3694e5e5c71..985f86ee6d5 100644
--- a/Segment_Delaunay_graph_2/include/CGAL/Segment_Delaunay_graph_traits_2.h
+++ b/Segment_Delaunay_graph_2/include/CGAL/Segment_Delaunay_graph_traits_2.h
@@ -25,7 +25,6 @@
 
 #include <CGAL/Segment_Delaunay_graph_2/basic.h>
 
-#include <CGAL/Number_type_traits.h>
 #include <CGAL/Segment_Delaunay_graph_2/Traits_base_2.h>
 
 #include <CGAL/Filtered_kernel.h>
@@ -45,26 +44,26 @@ struct Segment_Delaunay_graph_traits_2
 
 template<class R>
 struct Segment_Delaunay_graph_traits_2<R,Field_tag>
-  : public Segment_Delaunay_graph_traits_base_2<R,Ring_tag,Tag_true> {};
+  : public Segment_Delaunay_graph_traits_base_2<R,Integral_domain_without_division_tag,Tag_true> {};
 
 
 // Concept checking
 template<class R>
-struct Segment_Delaunay_graph_traits_2<R,Ring_tag>
-  : public Segment_Delaunay_graph_traits_base_2<R,Ring_tag,Tag_true>
+struct Segment_Delaunay_graph_traits_2<R,Integral_domain_without_division_tag>
+  : public Segment_Delaunay_graph_traits_base_2<R,Integral_domain_without_division_tag,Tag_true>
 {
   Segment_Delaunay_graph_traits_2() {
-    THE_2ND_TEMPLATE_PARAMETER_MUST_EITHER_BE_Field_tag_OR_Sqrt_field_tag
+    THE_2ND_TEMPLATE_PARAMETER_MUST_EITHER_BE_Field_tag_OR_Field_with_sqrt_tag
     ( R() );
   }
 };
 
 template<class R>
 struct Segment_Delaunay_graph_traits_2<R,Euclidean_ring_tag>
-  : public Segment_Delaunay_graph_traits_base_2<R,Ring_tag,Tag_true>
+  : public Segment_Delaunay_graph_traits_base_2<R,Integral_domain_without_division_tag,Tag_true>
 {
   Segment_Delaunay_graph_traits_2() {
-    THE_2ND_TEMPLATE_PARAMETER_MUST_EITHER_BE_Field_tag_OR_Sqrt_field_tag
+    THE_2ND_TEMPLATE_PARAMETER_MUST_EITHER_BE_Field_tag_OR_Field_with_sqrt_tag
     ( R() );
   }
 };
@@ -77,32 +76,32 @@ struct Segment_Delaunay_graph_traits_2<Filtered_kernel<R>,Field_tag>
 					   typename Filtered_kernel<R>::EK,
 					   Field_tag,
 					   typename Filtered_kernel<R>::FK,
-					   Sqrt_field_tag>
+					   Field_with_sqrt_tag>
 {};
 
 template<class R>
-struct Segment_Delaunay_graph_traits_2<Filtered_kernel<R>,Sqrt_field_tag>
+struct Segment_Delaunay_graph_traits_2<Filtered_kernel<R>,Field_with_sqrt_tag>
   : public
-  Segment_Delaunay_graph_filtered_traits_2<R,Sqrt_field_tag,
+  Segment_Delaunay_graph_filtered_traits_2<R,Field_with_sqrt_tag,
 					   typename Filtered_kernel<R>::EK,
 					   Field_tag,
 					   typename Filtered_kernel<R>::FK,
-					   Sqrt_field_tag>
+					   Field_with_sqrt_tag>
 {};
 
 //=========================================================================
 
 // this traits class does NOT support intersecting segments
-template<class R, class MTag = Ring_tag>
+template<class R, class MTag = Integral_domain_without_division_tag>
 struct Segment_Delaunay_graph_traits_without_intersections_2
   : public Segment_Delaunay_graph_traits_base_2<R,MTag,Tag_false> {};
 
 template<class R>
 struct Segment_Delaunay_graph_traits_without_intersections_2<R,Field_tag>
-  : public Segment_Delaunay_graph_traits_base_2<R,Ring_tag,Tag_false>
+  : public Segment_Delaunay_graph_traits_base_2<R,Integral_domain_without_division_tag,Tag_false>
 {
   Segment_Delaunay_graph_traits_without_intersections_2() {
-    THE_2ND_TEMPLATE_PARAMETER_MUST_EITHER_BE_Ring_tag_OR_Sqrt_field_tag
+    THE_2ND_TEMPLATE_PARAMETER_MUST_EITHER_BE_Integral_domain_without_division_tag_OR_Field_with_sqrt_tag
     ( R() );
   }
 };
@@ -110,10 +109,10 @@ struct Segment_Delaunay_graph_traits_without_intersections_2<R,Field_tag>
 template<class R>
 struct
 Segment_Delaunay_graph_traits_without_intersections_2<R,Euclidean_ring_tag>
-  : public Segment_Delaunay_graph_traits_base_2<R,Ring_tag,Tag_false>
+  : public Segment_Delaunay_graph_traits_base_2<R,Integral_domain_without_division_tag,Tag_false>
 {
   Segment_Delaunay_graph_traits_without_intersections_2() {
-    THE_2ND_TEMPLATE_PARAMETER_MUST_EITHER_BE_Ring_tag_OR_Sqrt_field_tag
+    THE_2ND_TEMPLATE_PARAMETER_MUST_EITHER_BE_Integral_domain_without_division_tag_OR_Field_with_sqrt_tag
     ( R() );
   }
 };
@@ -123,26 +122,26 @@ Segment_Delaunay_graph_traits_without_intersections_2<R,Euclidean_ring_tag>
 template<class R>
 struct
 Segment_Delaunay_graph_traits_without_intersections_2<Filtered_kernel<R>,
-						      Ring_tag>
+						      Integral_domain_without_division_tag>
   : public
-  Segment_Delaunay_graph_filtered_traits_without_intersections_2<R,Ring_tag,
+  Segment_Delaunay_graph_filtered_traits_without_intersections_2<R,Integral_domain_without_division_tag,
 					    typename Filtered_kernel<R>::EK,
-					    Ring_tag,
+					    Integral_domain_without_division_tag,
 					    typename Filtered_kernel<R>::FK,
-					    Sqrt_field_tag>
+					    Field_with_sqrt_tag>
 {};
 
 template<class R>
 struct
 Segment_Delaunay_graph_traits_without_intersections_2<Filtered_kernel<R>,
-						      Sqrt_field_tag>
+						      Field_with_sqrt_tag>
   : public
   Segment_Delaunay_graph_filtered_traits_without_intersections_2<R,
-					    Sqrt_field_tag,
+					    Field_with_sqrt_tag,
 					    typename Filtered_kernel<R>::EK,
-					    Ring_tag,
+					    Integral_domain_without_division_tag,
 					    typename Filtered_kernel<R>::FK,
-					    Sqrt_field_tag>
+					    Field_with_sqrt_tag>
 {};
 
 CGAL_END_NAMESPACE
diff --git a/Segment_Delaunay_graph_2/test/Segment_Delaunay_graph_2/test_sdg_2_et.cpp b/Segment_Delaunay_graph_2/test/Segment_Delaunay_graph_2/test_sdg_2_et.cpp
index 700dfa12b7b..f9a86ea168f 100644
--- a/Segment_Delaunay_graph_2/test/Segment_Delaunay_graph_2/test_sdg_2_et.cpp
+++ b/Segment_Delaunay_graph_2/test/Segment_Delaunay_graph_2/test_sdg_2_et.cpp
@@ -31,7 +31,6 @@ typedef exact_ring_t   ring_number_t;
 typedef exact_field_t  field_number_t;
 
 #include <CGAL/Simple_cartesian.h>
-#include <CGAL/Number_type_traits.h>
 
 #include <CGAL/Segment_Delaunay_graph_2.h>
 #include <CGAL/Segment_Delaunay_graph_traits_2.h>
@@ -40,7 +39,7 @@ struct K_ring  : public CGAL::Simple_cartesian<ring_number_t> {};
 struct K_field : public CGAL::Simple_cartesian<field_number_t> {};
 
 typedef CGAL::Field_tag  MTag;
-typedef CGAL::Ring_tag   MTag_wi;
+typedef CGAL::Integral_domain_without_division_tag   MTag_wi;
 
 typedef CGAL::Segment_Delaunay_graph_traits_2<K_field,MTag> Gt;
 
diff --git a/Segment_Delaunay_graph_2/test/Segment_Delaunay_graph_2/test_sdg_2_ft.cpp b/Segment_Delaunay_graph_2/test/Segment_Delaunay_graph_2/test_sdg_2_ft.cpp
index d328d7f22a6..6e74a5d0290 100644
--- a/Segment_Delaunay_graph_2/test/Segment_Delaunay_graph_2/test_sdg_2_ft.cpp
+++ b/Segment_Delaunay_graph_2/test/Segment_Delaunay_graph_2/test_sdg_2_ft.cpp
@@ -17,7 +17,6 @@ typedef CGAL::Quotient<exact_ring_t>   exact_field_t;
 #endif
 
 #include <CGAL/Simple_cartesian.h>
-#include <CGAL/Number_type_traits.h>
 
 #include <CGAL/Segment_Delaunay_graph_2.h>
 #include <CGAL/Segment_Delaunay_graph_filtered_traits_2.h>
@@ -26,9 +25,9 @@ typedef CGAL::Simple_cartesian<double>          CK;
 typedef CGAL::Simple_cartesian<exact_ring_t>    EK_ring;
 typedef CGAL::Simple_cartesian<exact_field_t>   EK_field;
 
-typedef CGAL::Sqrt_field_tag  CK_MTag;
+typedef CGAL::Field_with_sqrt_tag  CK_MTag;
 typedef CGAL::Field_tag       EK_MTag;
-typedef CGAL::Ring_tag        EK_MTag_wi;
+typedef CGAL::Integral_domain_without_division_tag        EK_MTag_wi;
 
 typedef CGAL::Segment_Delaunay_graph_filtered_traits_2<CK,CK_MTag,
 						       EK_field,EK_MTag>
diff --git a/Segment_Delaunay_graph_2/test/Segment_Delaunay_graph_2/test_sdg_hierarchy_2_et.cpp b/Segment_Delaunay_graph_2/test/Segment_Delaunay_graph_2/test_sdg_hierarchy_2_et.cpp
index 8a43b2ef7b6..0b04a64faed 100644
--- a/Segment_Delaunay_graph_2/test/Segment_Delaunay_graph_2/test_sdg_hierarchy_2_et.cpp
+++ b/Segment_Delaunay_graph_2/test/Segment_Delaunay_graph_2/test_sdg_hierarchy_2_et.cpp
@@ -31,7 +31,6 @@ typedef exact_ring_t   ring_number_t;
 typedef exact_field_t  field_number_t;
 
 #include <CGAL/Simple_cartesian.h>
-#include <CGAL/Number_type_traits.h>
 
 #include <CGAL/Segment_Delaunay_graph_hierarchy_2.h>
 #include <CGAL/Segment_Delaunay_graph_traits_2.h>
@@ -40,7 +39,7 @@ struct K_ring  : public CGAL::Simple_cartesian<ring_number_t> {};
 struct K_field : public CGAL::Simple_cartesian<field_number_t> {};
 
 typedef CGAL::Field_tag  MTag;
-typedef CGAL::Ring_tag   MTag_wi;
+typedef CGAL::Integral_domain_without_division_tag   MTag_wi;
 
 typedef CGAL::Segment_Delaunay_graph_traits_2<K_field,MTag> Gt;
 
diff --git a/Segment_Delaunay_graph_2/test/Segment_Delaunay_graph_2/test_sdg_hierarchy_2_ft.cpp b/Segment_Delaunay_graph_2/test/Segment_Delaunay_graph_2/test_sdg_hierarchy_2_ft.cpp
index 923b9c804ef..d96c75cf825 100644
--- a/Segment_Delaunay_graph_2/test/Segment_Delaunay_graph_2/test_sdg_hierarchy_2_ft.cpp
+++ b/Segment_Delaunay_graph_2/test/Segment_Delaunay_graph_2/test_sdg_hierarchy_2_ft.cpp
@@ -17,7 +17,6 @@ typedef CGAL::Quotient<exact_ring_t>   exact_field_t;
 #endif
 
 #include <CGAL/Simple_cartesian.h>
-#include <CGAL/Number_type_traits.h>
 
 #include <CGAL/Segment_Delaunay_graph_hierarchy_2.h>
 #include <CGAL/Segment_Delaunay_graph_filtered_traits_2.h>
@@ -26,9 +25,9 @@ typedef CGAL::Simple_cartesian<double>          CK;
 typedef CGAL::Simple_cartesian<exact_ring_t>    EK_ring;
 typedef CGAL::Simple_cartesian<exact_field_t>   EK_field;
 
-typedef CGAL::Sqrt_field_tag  CK_MTag;
+typedef CGAL::Field_with_sqrt_tag  CK_MTag;
 typedef CGAL::Field_tag       EK_MTag;
-typedef CGAL::Ring_tag        EK_MTag_wi;
+typedef CGAL::Integral_domain_without_division_tag        EK_MTag_wi;
 
 typedef CGAL::Segment_Delaunay_graph_filtered_traits_2<CK,CK_MTag,
 						       EK_field,EK_MTag>
diff --git a/Segment_Delaunay_graph_2/test/Segment_Delaunay_graph_2/test_sdg_info_2.cpp b/Segment_Delaunay_graph_2/test/Segment_Delaunay_graph_2/test_sdg_info_2.cpp
index 4dad7e69b85..0d2c3926e85 100644
--- a/Segment_Delaunay_graph_2/test/Segment_Delaunay_graph_2/test_sdg_info_2.cpp
+++ b/Segment_Delaunay_graph_2/test/Segment_Delaunay_graph_2/test_sdg_info_2.cpp
@@ -5,7 +5,6 @@
 #include <iostream>
 #include <fstream>
 #include <cassert>
-
 // choose the kernel
 #include <CGAL/Simple_cartesian.h>
 
diff --git a/Segment_Delaunay_graph_2/test/Segment_Delaunay_graph_2/test_sdg_traits_2.cpp b/Segment_Delaunay_graph_2/test/Segment_Delaunay_graph_2/test_sdg_traits_2.cpp
index b5b1f432af1..70c2b4b0ae5 100644
--- a/Segment_Delaunay_graph_2/test/Segment_Delaunay_graph_2/test_sdg_traits_2.cpp
+++ b/Segment_Delaunay_graph_2/test/Segment_Delaunay_graph_2/test_sdg_traits_2.cpp
@@ -9,7 +9,6 @@
 #include <CGAL/Simple_cartesian.h>
 #include <CGAL/Segment_Delaunay_graph_traits_2.h>
 #include <CGAL/Segment_Delaunay_graph_filtered_traits_2.h>
-#include <CGAL/Number_type_traits.h>
 
 #ifdef CGAL_USE_CORE
 #include <CGAL/CORE_Expr.h>
@@ -32,9 +31,9 @@ typedef CGAL::Simple_cartesian<CGAL::Gmpq>  Gmpq_Kernel;
 typedef CGAL::Simple_cartesian<CGAL::Gmpz>  Gmpz_Kernel;
 #endif
 
-typedef CGAL::Ring_tag        Ring;
+typedef CGAL::Integral_domain_without_division_tag        Ring;
 typedef CGAL::Field_tag       Field;
-typedef CGAL::Sqrt_field_tag  Sqrt;
+typedef CGAL::Field_with_sqrt_tag  Sqrt;
 
 //----------------------------------------------------------------------
 //----------------------------------------------------------------------