diff --git a/Number_types/include/CGAL/CORE_BigFloat.h b/Number_types/include/CGAL/CORE_BigFloat.h
index 2488af7d00d..09302bcdfa3 100644
--- a/Number_types/include/CGAL/CORE_BigFloat.h
+++ b/Number_types/include/CGAL/CORE_BigFloat.h
@@ -531,6 +531,7 @@ namespace Eigen {
     typedef CORE::BigFloat Real;
     typedef CORE::BigFloat NonInteger;
     typedef CORE::BigFloat Nested;
+    typedef CORE::BigFloat Literal;
 
     static inline Real epsilon() { return 0; }
     static inline Real dummy_precision() { return 0; }
diff --git a/Number_types/include/CGAL/CORE_BigInt.h b/Number_types/include/CGAL/CORE_BigInt.h
index 288ebedbd0b..a3c18b16101 100644
--- a/Number_types/include/CGAL/CORE_BigInt.h
+++ b/Number_types/include/CGAL/CORE_BigInt.h
@@ -207,6 +207,7 @@ namespace Eigen {
     typedef CORE::BigInt Real;
     typedef CORE::BigRat NonInteger;
     typedef CORE::BigInt Nested;
+    typedef CORE::BigInt Literal;
 
     static inline Real epsilon() { return 0; }
     static inline Real dummy_precision() { return 0; }
diff --git a/Number_types/include/CGAL/CORE_BigRat.h b/Number_types/include/CGAL/CORE_BigRat.h
index 6afc12f1fd7..8f5f7260185 100644
--- a/Number_types/include/CGAL/CORE_BigRat.h
+++ b/Number_types/include/CGAL/CORE_BigRat.h
@@ -243,6 +243,7 @@ namespace Eigen {
     typedef CORE::BigRat Real;
     typedef CORE::BigRat NonInteger;
     typedef CORE::BigRat Nested;
+    typedef CORE::BigRat Literal;
 
     static inline Real epsilon() { return 0; }
     static inline Real dummy_precision() { return 0; }
diff --git a/Number_types/include/CGAL/CORE_Expr.h b/Number_types/include/CGAL/CORE_Expr.h
index 579a2090e5a..4bd38945006 100644
--- a/Number_types/include/CGAL/CORE_Expr.h
+++ b/Number_types/include/CGAL/CORE_Expr.h
@@ -196,6 +196,7 @@ namespace Eigen {
     typedef CORE::Expr Real;
     typedef CORE::Expr NonInteger;
     typedef CORE::Expr Nested;
+    typedef CORE::Expr Literal;
 
     static inline Real epsilon() { return 0; }
     static inline Real dummy_precision() { return 0; }
diff --git a/Number_types/include/CGAL/Gmpfi.h b/Number_types/include/CGAL/Gmpfi.h
index 97bb80d8647..479f1608a4b 100644
--- a/Number_types/include/CGAL/Gmpfi.h
+++ b/Number_types/include/CGAL/Gmpfi.h
@@ -342,6 +342,7 @@ namespace Eigen {
     typedef CGAL::Gmpfi Real;
     typedef CGAL::Gmpfi NonInteger;
     typedef CGAL::Gmpfi Nested;
+    typedef CGAL::Gmpfi Literal;
 
     static inline Real epsilon() { return 0; }
     static inline Real dummy_precision() { return 0; }
diff --git a/Number_types/include/CGAL/Gmpfr.h b/Number_types/include/CGAL/Gmpfr.h
index 5179425ff19..94bb613b61e 100644
--- a/Number_types/include/CGAL/Gmpfr.h
+++ b/Number_types/include/CGAL/Gmpfr.h
@@ -162,6 +162,7 @@ namespace Eigen {
     typedef CGAL::Gmpfr Real;
     typedef CGAL::Gmpfr NonInteger;
     typedef CGAL::Gmpfr Nested;
+    typedef CGAL::Gmpfr Literal;
 
     static inline Real epsilon() { return 0; }
     static inline Real dummy_precision() { return 0; }
diff --git a/Number_types/include/CGAL/Gmpq.h b/Number_types/include/CGAL/Gmpq.h
index 38fd09242c4..2fde983a7b3 100644
--- a/Number_types/include/CGAL/Gmpq.h
+++ b/Number_types/include/CGAL/Gmpq.h
@@ -141,6 +141,7 @@ namespace Eigen {
     typedef CGAL::Gmpq Real;
     typedef CGAL::Gmpq NonInteger;
     typedef CGAL::Gmpq Nested;
+    typedef CGAL::Gmpq Literal;
 
     static inline Real epsilon() { return 0; }
     static inline Real dummy_precision() { return 0; }
diff --git a/Number_types/include/CGAL/Gmpz.h b/Number_types/include/CGAL/Gmpz.h
index b196789c267..5a1b15dbb35 100644
--- a/Number_types/include/CGAL/Gmpz.h
+++ b/Number_types/include/CGAL/Gmpz.h
@@ -215,6 +215,7 @@ namespace Eigen {
     typedef CGAL::Gmpz Real;
     typedef CGAL::Gmpq NonInteger;
     typedef CGAL::Gmpz Nested;
+    typedef CGAL::Gmpz Literal;
 
     static inline Real epsilon() { return 0; }
     static inline Real dummy_precision() { return 0; }
diff --git a/Number_types/include/CGAL/Interval_nt.h b/Number_types/include/CGAL/Interval_nt.h
index e725e74621e..5dfa8b33bc4 100644
--- a/Number_types/include/CGAL/Interval_nt.h
+++ b/Number_types/include/CGAL/Interval_nt.h
@@ -1268,6 +1268,7 @@ namespace Eigen {
     typedef CGAL::Interval_nt<b> Real;
     typedef CGAL::Interval_nt<b> NonInteger;
     typedef CGAL::Interval_nt<b> Nested;
+    typedef double Literal;
 
     static inline Real epsilon() { return 0; }
     static inline Real dummy_precision() { return 0; }
diff --git a/Number_types/include/CGAL/Lazy_exact_nt.h b/Number_types/include/CGAL/Lazy_exact_nt.h
index 4c0678a7976..77350845ba6 100644
--- a/Number_types/include/CGAL/Lazy_exact_nt.h
+++ b/Number_types/include/CGAL/Lazy_exact_nt.h
@@ -1428,6 +1428,7 @@ namespace Eigen {
     // typedef CGAL::Lazy_exact_nt<ET> NonInteger;
     typedef CGAL::Lazy_exact_nt<typename NumTraits<ET>::NonInteger> NonInteger;
     typedef CGAL::Lazy_exact_nt<ET> Nested;
+    typedef CGAL::Lazy_exact_nt<ET> Literal;
 
     static inline Real epsilon() { return 0; }
     static inline Real dummy_precision() { return 0; }
diff --git a/Number_types/include/CGAL/MP_Float.h b/Number_types/include/CGAL/MP_Float.h
index 96687997387..0b55d55f692 100644
--- a/Number_types/include/CGAL/MP_Float.h
+++ b/Number_types/include/CGAL/MP_Float.h
@@ -888,6 +888,7 @@ namespace Eigen {
     typedef CGAL::MP_Float Real;
     typedef CGAL::Quotient<CGAL::MP_Float> NonInteger;
     typedef CGAL::MP_Float Nested;
+    typedef CGAL::MP_Float Literal;
 
     static inline Real epsilon() { return 0; }
     static inline Real dummy_precision() { return 0; }
diff --git a/Number_types/include/CGAL/Mpzf.h b/Number_types/include/CGAL/Mpzf.h
index 57707666d69..8d645478283 100644
--- a/Number_types/include/CGAL/Mpzf.h
+++ b/Number_types/include/CGAL/Mpzf.h
@@ -1137,6 +1137,7 @@ namespace Eigen {
     /* Should this be Quotient<Mpzf>? Gmpq?  */
     typedef CGAL::Mpzf NonInteger;
     typedef CGAL::Mpzf Nested;
+    typedef CGAL::Mpzf Literal;
 
     static inline Real epsilon() { return 0; }
     static inline Real dummy_precision() { return 0; }
diff --git a/Number_types/include/CGAL/Quotient.h b/Number_types/include/CGAL/Quotient.h
index a1934fc12ee..2617ac92dd8 100644
--- a/Number_types/include/CGAL/Quotient.h
+++ b/Number_types/include/CGAL/Quotient.h
@@ -859,6 +859,7 @@ namespace Eigen {
     typedef CGAL::Quotient<NT> Real;
     typedef CGAL::Quotient<NT> NonInteger;
     typedef CGAL::Quotient<NT> Nested;
+    typedef CGAL::Quotient<NT> Literal;
 
     static inline Real epsilon() { return NumTraits<NT>::epsilon(); }
     static inline Real dummy_precision() { return NumTraits<NT>::dummy_precision(); }
diff --git a/Number_types/include/CGAL/Sqrt_extension/Eigen_NumTraits.h b/Number_types/include/CGAL/Sqrt_extension/Eigen_NumTraits.h
index c9d28d8a993..725e8b177e2 100644
--- a/Number_types/include/CGAL/Sqrt_extension/Eigen_NumTraits.h
+++ b/Number_types/include/CGAL/Sqrt_extension/Eigen_NumTraits.h
@@ -30,6 +30,7 @@ namespace Eigen {
     typedef CGAL::Sqrt_extension<NT, ROOT, ACDE_TAG, FP_TAG> Real;
     typedef Real NonInteger;
     typedef Real Nested;
+    typedef Real Literal;
 
     static inline Real epsilon() { return NumTraits<NT>::epsilon(); }
 
diff --git a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/polygon_soup_to_polygon_mesh.h b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/polygon_soup_to_polygon_mesh.h
index 4406c5c2b1f..016abfcfaf6 100644
--- a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/polygon_soup_to_polygon_mesh.h
+++ b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/polygon_soup_to_polygon_mesh.h
@@ -26,6 +26,7 @@
 #include <CGAL/boost/graph/Euler_operations.h>
 #include <CGAL/property_map.h>
 #include <CGAL/Polygon_mesh_processing/orient_polygon_soup.h>
+#include <CGAL/algorithm.h>
 #include <set>
 
 #include <boost/range/size.hpp>
diff --git a/Polyline_simplification_2/include/CGAL/Polyline_simplification_2/simplify.h b/Polyline_simplification_2/include/CGAL/Polyline_simplification_2/simplify.h
index 9f0f46f38e5..9b6a4002b39 100644
--- a/Polyline_simplification_2/include/CGAL/Polyline_simplification_2/simplify.h
+++ b/Polyline_simplification_2/include/CGAL/Polyline_simplification_2/simplify.h
@@ -339,7 +339,7 @@ template <class Traits, class Container, class CostFunction, class StopFunction>
   typedef Vertex_base_2< K > Vb;
   typedef CGAL::Constrained_triangulation_face_base_2<K> Fb;
   typedef CGAL::Triangulation_data_structure_2<Vb,Fb> TDS;
-  typedef CGAL::Constrained_Delaunay_triangulation_2<K, TDS, CGAL::Exact_predicates_tag> CDT;
+  typedef CGAL::Constrained_Delaunay_triangulation_2<K, TDS,typename internal::Itag<K>::type>  CDT;
   typedef CGAL::Constrained_triangulation_plus_2<CDT>       PCT;
   typedef typename PCT::Constraint_id Constraint_id;
   typedef typename PCT::Vertices_in_constraint_iterator Vertices_in_constraint_iterator;
@@ -387,7 +387,7 @@ Simplifies an open or closed polyline given as an iterator range of 2D \cgal poi
   typedef Vertex_base_2< K > Vb;
   typedef CGAL::Constrained_triangulation_face_base_2<K> Fb;
   typedef CGAL::Triangulation_data_structure_2<Vb,Fb> TDS;
-  typedef CGAL::Constrained_Delaunay_triangulation_2<K, TDS, CGAL::Exact_predicates_tag> CDT;
+  typedef CGAL::Constrained_Delaunay_triangulation_2<K, TDS,typename internal::Itag<K>::type > CDT;
   typedef CGAL::Constrained_triangulation_plus_2<CDT>       PCT;
   typedef typename PCT::Constraint_id Constraint_id;
   typedef typename PCT::Vertices_in_constraint_iterator Vertices_in_constraint_iterator;
diff --git a/Triangulation_2/include/CGAL/Constrained_triangulation_2.h b/Triangulation_2/include/CGAL/Constrained_triangulation_2.h
index 56f3149513e..6a14a41a77a 100644
--- a/Triangulation_2/include/CGAL/Constrained_triangulation_2.h
+++ b/Triangulation_2/include/CGAL/Constrained_triangulation_2.h
@@ -32,12 +32,24 @@
 #include <CGAL/intersections.h>
 #include <CGAL/squared_distance_2.h>
 
+#include <boost/mpl/if.hpp>
+
 namespace CGAL {
 
 struct No_intersection_tag{};
 struct Exact_intersections_tag{}; // to be used with an exact number type
 struct Exact_predicates_tag{}; // to be used with filtered exact number
 
+namespace internal {
+
+template <typename K>
+struct Itag {
+  typedef typename boost::mpl::if_<typename Algebraic_structure_traits<typename K::FT>::Is_exact,
+                                   Exact_intersections_tag,
+                                   Exact_predicates_tag>::type type;
+};
+
+} // namespace internal
 
 template < class Gt, 
            class Tds_ = Default ,