diff --git a/Kernel_23/doc/Kernel_23/CGAL/Aff_transformation_2.h b/Kernel_23/doc/Kernel_23/CGAL/Aff_transformation_2.h
index ae9adff736a..a8d6d43f269 100644
--- a/Kernel_23/doc/Kernel_23/CGAL/Aff_transformation_2.h
+++ b/Kernel_23/doc/Kernel_23/CGAL/Aff_transformation_2.h
@@ -34,7 +34,7 @@ translation vector \f$ (v_0,\,v_1,\,1)\f$ appears in the last column of the
 matrix. The entries \f$ m_{20}\f$ and \f$ m_{21}\f$ are always zero and 
 therefore do not appear in the constructors. 
 
-\cgalModels `Hashable` if `Kernel::FT` is a floating-point number
+\cgalModels `Hashable` if `Kernel` is a cartesian kernel and if `Kernel::FT` is `Hashable`
 
 \sa `Identity_transformation`
 \sa `Rotation`
diff --git a/Kernel_23/doc/Kernel_23/CGAL/Aff_transformation_3.h b/Kernel_23/doc/Kernel_23/CGAL/Aff_transformation_3.h
index 40803c6186c..e23674bbc6b 100644
--- a/Kernel_23/doc/Kernel_23/CGAL/Aff_transformation_3.h
+++ b/Kernel_23/doc/Kernel_23/CGAL/Aff_transformation_3.h
@@ -29,7 +29,7 @@ In three-dimensional space we have a \f$ 4\times 4\f$ matrix
 \f$ m_{32}\f$ are always zero and therefore do not appear in the 
 constructors. 
 
-\cgalModels `Hashable` if `Kernel::FT` is a floating-point number
+\cgalModels `Hashable` if `Kernel` is a cartesian kernel and if `Kernel::FT` is `Hashable`
 
 \sa `CGAL::Aff_transformation_2<Kernel>` 
 \sa `CGAL::Identity_transformation` 
diff --git a/Kernel_23/doc/Kernel_23/CGAL/Circle_2.h b/Kernel_23/doc/Kernel_23/CGAL/Circle_2.h
index a75cd35afc2..be4a2b7424f 100644
--- a/Kernel_23/doc/Kernel_23/CGAL/Circle_2.h
+++ b/Kernel_23/doc/Kernel_23/CGAL/Circle_2.h
@@ -12,7 +12,7 @@ splits \f$ \E^2\f$ into a bounded and an unbounded side. Note that the
 circle can be degenerated, i.e.\ the squared radius may be zero. 
 
 \cgalModels `Kernel::Circle_2`
-\cgalModels `Hashable` if `Kernel::FT` is a floating-point number
+\cgalModels `Hashable` if `Kernel` is a cartesian kernel and if `Kernel::FT` is `Hashable`
 
 */
 template< typename Kernel >
diff --git a/Kernel_23/doc/Kernel_23/CGAL/Iso_cuboid_3.h b/Kernel_23/doc/Kernel_23/CGAL/Iso_cuboid_3.h
index b63d2e8db02..72471b06f6e 100644
--- a/Kernel_23/doc/Kernel_23/CGAL/Iso_cuboid_3.h
+++ b/Kernel_23/doc/Kernel_23/CGAL/Iso_cuboid_3.h
@@ -17,7 +17,7 @@ whereas the coordinate type of an iso-oriented cuboid is chosen by
 the user. 
 
 \cgalModels `Kernel::IsoCuboid_3`
-\cgalModels `Hashable` if `Kernel::FT` is a floating-point number
+\cgalModels `Hashable` if `Kernel` is a cartesian kernel and if `Kernel::FT` is `Hashable`
 
 */
 template< typename Kernel >
diff --git a/Kernel_23/doc/Kernel_23/CGAL/Iso_rectangle_2.h b/Kernel_23/doc/Kernel_23/CGAL/Iso_rectangle_2.h
index c89fd390e9e..7a725ce421b 100644
--- a/Kernel_23/doc/Kernel_23/CGAL/Iso_rectangle_2.h
+++ b/Kernel_23/doc/Kernel_23/CGAL/Iso_rectangle_2.h
@@ -18,7 +18,7 @@ whereas the coordinate type of an iso-oriented rectangle is chosen by
 the user. 
 
 \cgalModels `Kernel::IsoRectangle_2`
-\cgalModels `Hashable` if `Kernel::FT` is a floating-point number
+\cgalModels `Hashable` if `Kernel` is a cartesian kernel and if `Kernel::FT` is `Hashable`
 
 */
 template< typename Kernel >
diff --git a/Kernel_23/doc/Kernel_23/CGAL/Point_2.h b/Kernel_23/doc/Kernel_23/CGAL/Point_2.h
index 4c59f467f71..8ac3eff82d6 100644
--- a/Kernel_23/doc/Kernel_23/CGAL/Point_2.h
+++ b/Kernel_23/doc/Kernel_23/CGAL/Point_2.h
@@ -31,7 +31,7 @@ std::cout << p.x() << " " << p.y() << std::endl;
 \endcode
 
 \cgalModels `Kernel::Point_2`
-\cgalModels `Hashable` if `Kernel::FT` is a floating-point number
+\cgalModels `Hashable` if `Kernel` is a cartesian kernel and if `Kernel::FT` is `Hashable`
 
 */
 template< typename Kernel >
diff --git a/Kernel_23/doc/Kernel_23/CGAL/Point_3.h b/Kernel_23/doc/Kernel_23/CGAL/Point_3.h
index 9f86642f5ec..deed3e522d7 100644
--- a/Kernel_23/doc/Kernel_23/CGAL/Point_3.h
+++ b/Kernel_23/doc/Kernel_23/CGAL/Point_3.h
@@ -17,7 +17,7 @@ to `NT`, and `Kernel::FT` is equal to `Quotient<NT>`.
 The following operations can be applied on points:
 
 \cgalModels `Kernel::Point_3`
-\cgalModels `Hashable` if `Kernel::FT` is a floating-point number
+\cgalModels `Hashable` if `Kernel` is a cartesian kernel and if `Kernel::FT` is `Hashable`
 
 */
 template< typename Kernel >
diff --git a/Kernel_23/doc/Kernel_23/CGAL/Segment_2.h b/Kernel_23/doc/Kernel_23/CGAL/Segment_2.h
index 1d8a370d9eb..391e3aa80a2 100644
--- a/Kernel_23/doc/Kernel_23/CGAL/Segment_2.h
+++ b/Kernel_23/doc/Kernel_23/CGAL/Segment_2.h
@@ -15,7 +15,7 @@ perform a square root operation which is not defined for all
 number types, which is expensive, and may not be exact. 
 
 \cgalModels `Kernel::Segment_2`
-\cgalModels `Hashable` if `Kernel::FT` is a floating-point number
+\cgalModels `Hashable` if `Kernel` is a cartesian kernel and if `Kernel::FT` is `Hashable`
 
 */
 template< typename Kernel >
diff --git a/Kernel_23/doc/Kernel_23/CGAL/Segment_3.h b/Kernel_23/doc/Kernel_23/CGAL/Segment_3.h
index 151c86778e2..454e31cc848 100644
--- a/Kernel_23/doc/Kernel_23/CGAL/Segment_3.h
+++ b/Kernel_23/doc/Kernel_23/CGAL/Segment_3.h
@@ -15,7 +15,7 @@ perform a square root operation which is not defined for all
 number types, which is expensive, and may not be exact. 
 
 \cgalModels `Kernel::Segment_3`
-\cgalModels `Hashable` if `Kernel::FT` is a floating-point number
+\cgalModels `Hashable` if `Kernel` is a cartesian kernel and if `Kernel::FT` is `Hashable`
 
 */
 template< typename Kernel >
diff --git a/Kernel_23/doc/Kernel_23/CGAL/Sphere_3.h b/Kernel_23/doc/Kernel_23/CGAL/Sphere_3.h
index 93b97a78ac3..94947d291f4 100644
--- a/Kernel_23/doc/Kernel_23/CGAL/Sphere_3.h
+++ b/Kernel_23/doc/Kernel_23/CGAL/Sphere_3.h
@@ -12,6 +12,7 @@ splits \f$ \E^3\f$ into a bounded and an unbounded side. Note that the
 sphere can be degenerated, i.e.\ the squared radius may be zero. 
 
 \cgalModels `Kernel::Sphere_3`
+\cgalModels `Hashable` if `Kernel` is a cartesian kernel and if `Kernel::FT` is `Hashable`
 
 */
 template< typename Kernel >
diff --git a/Kernel_23/doc/Kernel_23/CGAL/Vector_2.h b/Kernel_23/doc/Kernel_23/CGAL/Vector_2.h
index 0328accda34..6fb8d5b0ea9 100644
--- a/Kernel_23/doc/Kernel_23/CGAL/Vector_2.h
+++ b/Kernel_23/doc/Kernel_23/CGAL/Vector_2.h
@@ -13,7 +13,7 @@ will explicitly state where you can pass this constant as an argument
 instead of a vector initialized with zeros. 
 
 \cgalModels `Kernel::Vector_2`
-\cgalModels `Hashable` if `Kernel::FT` is a floating-point number
+\cgalModels `Hashable` if `Kernel` is a cartesian kernel and if `Kernel::FT` is `Hashable`
 
 */
 template< typename Kernel >
diff --git a/Kernel_23/doc/Kernel_23/CGAL/Vector_3.h b/Kernel_23/doc/Kernel_23/CGAL/Vector_3.h
index 9a80105c33f..924b35f04d1 100644
--- a/Kernel_23/doc/Kernel_23/CGAL/Vector_3.h
+++ b/Kernel_23/doc/Kernel_23/CGAL/Vector_3.h
@@ -13,7 +13,7 @@ will explicitly state where you can pass this constant as an argument
 instead of a vector initialized with zeros. 
 
 \cgalModels `Kernel::Vector_3`
-\cgalModels `Hashable` if `Kernel::FT` is a floating-point number
+\cgalModels `Hashable` if `Kernel` is a cartesian kernel and if `Kernel::FT` is `Hashable`
 
 \sa `cross_product_grp` 
 \sa `determinant_grp` 
diff --git a/Kernel_23/doc/Kernel_23/CGAL/Weighted_point_2.h b/Kernel_23/doc/Kernel_23/CGAL/Weighted_point_2.h
index 74e41bacee3..4c2d0a15cbc 100644
--- a/Kernel_23/doc/Kernel_23/CGAL/Weighted_point_2.h
+++ b/Kernel_23/doc/Kernel_23/CGAL/Weighted_point_2.h
@@ -14,7 +14,7 @@ to `NT`, and `Kernel::FT` is equal to `Quotient<NT>`.
 \sa `Point_2<Kernel>`
 
 \cgalModels `Kernel::WeightedPoint_2`
-\cgalModels `Hashable` if `Kernel::FT` is a floating-point number
+\cgalModels `Hashable` if `Kernel` is a cartesian kernel and if `Kernel::FT` is `Hashable`
 
 */
 template< typename Kernel >
diff --git a/Kernel_23/doc/Kernel_23/CGAL/Weighted_point_3.h b/Kernel_23/doc/Kernel_23/CGAL/Weighted_point_3.h
index 8717bc187c8..e652a47049d 100644
--- a/Kernel_23/doc/Kernel_23/CGAL/Weighted_point_3.h
+++ b/Kernel_23/doc/Kernel_23/CGAL/Weighted_point_3.h
@@ -14,7 +14,7 @@ to `NT`, and `Kernel::FT` is equal to `Quotient<NT>`.
 \sa `Point_3<Kernel>`
 
 \cgalModels `Kernel::WeightedPoint_3`
-\cgalModels `Hashable` if `Kernel::FT` is a floating-point number
+\cgalModels `Hashable` if `Kernel` is a cartesian kernel and if `Kernel::FT` is `Hashable`
 
 */
 template< typename Kernel >
diff --git a/Kernel_23/include/CGAL/Kernel/hash_functions.h b/Kernel_23/include/CGAL/Kernel/hash_functions.h
index 3559828cce2..c1c1631516d 100644
--- a/Kernel_23/include/CGAL/Kernel/hash_functions.h
+++ b/Kernel_23/include/CGAL/Kernel/hash_functions.h
@@ -31,7 +31,7 @@ namespace CGAL
 using boost::hash_value;
 
 template <typename K>
-inline std::enable_if_t<std::is_floating_point<typename K::FT>::value, std::size_t>
+inline std::enable_if_t<std::is_same<typename K::Rep_tag, Cartesian_tag>::value, std::size_t>
 hash_value (const Aff_transformation_2<K>& transform)
 {
   std::size_t result = hash_value(transform.cartesian(0,0));
@@ -53,7 +53,7 @@ hash_value (const Bbox_2& bbox)
 }
 
 template <typename K>
-inline std::enable_if_t<std::is_floating_point<typename K::FT>::value, std::size_t>
+inline std::enable_if_t<std::is_same<typename K::Rep_tag, Cartesian_tag>::value, std::size_t>
 hash_value (const Circle_2<K>& circle)
 {
   std::size_t result = hash_value(circle.center());
@@ -63,7 +63,7 @@ hash_value (const Circle_2<K>& circle)
 }
 
 template <typename K>
-inline std::enable_if_t<std::is_floating_point<typename K::FT>::value, std::size_t>
+inline std::enable_if_t<std::is_same<typename K::Rep_tag, Cartesian_tag>::value, std::size_t>
 hash_value (const Iso_rectangle_2<K>& iso_rectangle)
 {
   std::size_t result = hash_value(iso_rectangle.min());
@@ -72,7 +72,7 @@ hash_value (const Iso_rectangle_2<K>& iso_rectangle)
 }
 
 template <typename K>
-inline std::enable_if_t<std::is_floating_point<typename K::FT>::value, std::size_t>
+inline std::enable_if_t<std::is_same<typename K::Rep_tag, Cartesian_tag>::value, std::size_t>
 hash_value (const Point_2<K>& point)
 {
   std::size_t result = hash_value(point.x());
@@ -81,7 +81,7 @@ hash_value (const Point_2<K>& point)
 }
 
 template <typename K>
-inline std::enable_if_t<std::is_floating_point<typename K::FT>::value, std::size_t>
+inline std::enable_if_t<std::is_same<typename K::Rep_tag, Cartesian_tag>::value, std::size_t>
 hash_value (const Segment_2<K>& segment)
 {
   std::size_t result = hash_value(segment.source());
@@ -90,7 +90,7 @@ hash_value (const Segment_2<K>& segment)
 }
 
 template <typename K>
-inline std::enable_if_t<std::is_floating_point<typename K::FT>::value, std::size_t>
+inline std::enable_if_t<std::is_same<typename K::Rep_tag, Cartesian_tag>::value, std::size_t>
 hash_value (const Vector_2<K>& vector)
 {
   std::size_t result = hash_value(vector.x());
@@ -99,7 +99,7 @@ hash_value (const Vector_2<K>& vector)
 }
 
 template <typename K>
-inline std::enable_if_t<std::is_floating_point<typename K::FT>::value, std::size_t>
+inline std::enable_if_t<std::is_same<typename K::Rep_tag, Cartesian_tag>::value, std::size_t>
 hash_value (const Weighted_point_2<K>& weighed_point)
 {
   std::size_t result = hash_value(weighed_point.point());
@@ -108,7 +108,7 @@ hash_value (const Weighted_point_2<K>& weighed_point)
 }
 
 template <typename K>
-inline std::enable_if_t<std::is_floating_point<typename K::FT>::value, std::size_t>
+inline std::enable_if_t<std::is_same<typename K::Rep_tag, Cartesian_tag>::value, std::size_t>
 hash_value (const Aff_transformation_3<K>& transform)
 {
   std::size_t result = hash_value(transform.cartesian(0,0));
@@ -132,7 +132,7 @@ hash_value (const Bbox_3& bbox)
 }
 
 template <typename K>
-inline std::enable_if_t<std::is_floating_point<typename K::FT>::value, std::size_t>
+inline std::enable_if_t<std::is_same<typename K::Rep_tag, Cartesian_tag>::value, std::size_t>
 hash_value (const Iso_cuboid_3<K>& iso_cuboid)
 {
   std::size_t result = hash_value(iso_cuboid.min());
@@ -141,7 +141,7 @@ hash_value (const Iso_cuboid_3<K>& iso_cuboid)
 }
 
 template <typename K>
-inline std::enable_if_t<std::is_floating_point<typename K::FT>::value, std::size_t>
+inline std::enable_if_t<std::is_same<typename K::Rep_tag, Cartesian_tag>::value, std::size_t>
 hash_value (const Point_3<K>& point)
 {
   std::size_t result = hash_value(point.x());
@@ -151,7 +151,7 @@ hash_value (const Point_3<K>& point)
 }
 
 template <typename K>
-inline std::enable_if_t<std::is_floating_point<typename K::FT>::value, std::size_t>
+inline std::enable_if_t<std::is_same<typename K::Rep_tag, Cartesian_tag>::value, std::size_t>
 hash_value (const Segment_3<K>& segment)
 {
   std::size_t result = hash_value(segment.source());
@@ -160,7 +160,7 @@ hash_value (const Segment_3<K>& segment)
 }
 
 template <typename K>
-inline std::enable_if_t<std::is_floating_point<typename K::FT>::value, std::size_t>
+inline std::enable_if_t<std::is_same<typename K::Rep_tag, Cartesian_tag>::value, std::size_t>
 hash_value (const Sphere_3<K>& sphere)
 {
   std::size_t result = hash_value(sphere.center());
@@ -170,7 +170,7 @@ hash_value (const Sphere_3<K>& sphere)
 }
 
 template <typename K>
-inline std::enable_if_t<std::is_floating_point<typename K::FT>::value, std::size_t>
+inline std::enable_if_t<std::is_same<typename K::Rep_tag, Cartesian_tag>::value, std::size_t>
 hash_value (const Vector_3<K>& vector)
 {
   std::size_t result = hash_value(vector.x());
@@ -180,7 +180,7 @@ hash_value (const Vector_3<K>& vector)
 }
 
 template <typename K>
-inline std::enable_if_t<std::is_floating_point<typename K::FT>::value, std::size_t>
+inline std::enable_if_t<std::is_same<typename K::Rep_tag, Cartesian_tag>::value, std::size_t>
 hash_value (const Weighted_point_3<K>& weighed_point)
 {
   std::size_t result = hash_value(weighed_point.point());