diff --git a/.gitattributes b/.gitattributes
index f8a72e6b758..d89d207cabd 100644
--- a/.gitattributes
+++ b/.gitattributes
@@ -1762,6 +1762,7 @@ Number_types/include/CGAL/Sqrt_extension/Algebraic_extension_traits.h -text
 Number_types/include/CGAL/Sqrt_extension/Algebraic_structure_traits.h -text
 Number_types/include/CGAL/Sqrt_extension/Coercion_traits.h -text
 Number_types/include/CGAL/Sqrt_extension/Fraction_traits.h -text
+Number_types/include/CGAL/Sqrt_extension/Modular_traits.h -text
 Number_types/include/CGAL/Sqrt_extension/Real_embeddable_traits.h -text
 Number_types/include/CGAL/Sqrt_extension/Scalar_factor_traits.h -text
 Number_types/include/CGAL/Sqrt_extension/Sqrt_extension_type.h -text
diff --git a/Modular_arithmetic/include/CGAL/Modular_traits.h b/Modular_arithmetic/include/CGAL/Modular_traits.h
index 9ff297f3a52..43ee5a634db 100644
--- a/Modular_arithmetic/include/CGAL/Modular_traits.h
+++ b/Modular_arithmetic/include/CGAL/Modular_traits.h
@@ -5,17 +5,8 @@
 
 #include <CGAL/basic.h>
 #include <CGAL/Modular.h>
-#include <CGAL/Sqrt_extension.h>
 #include <vector>
 
-#ifdef CGAL_USE_LEDA
-#include <CGAL/leda_integer.h>
-#endif// CGAL_USE_LEDA
-
-#ifdef CGAL_USE_CORE
-#include <CGAL/CORE_BigInt.h>
-#endif// CGAL_USE_CORE
-
 
 namespace CGAL { 
 
@@ -26,7 +17,7 @@ namespace CGAL {
     for unsupported types. Note that this support is optional. 
     \see CGAL_Modular_traits_spec for supported types. 
  */
-
+ 
 template<class NT_>
 class Modular_traits{
 public: 
@@ -88,153 +79,6 @@ public:
     };    
 };
 
-#ifdef CGAL_USE_LEDA
-// TODO: mv to leda_integer.h 
-template<>
-class Modular_traits< ::leda::integer > {
-    typedef Modular MOD;
- public:
-    typedef ::leda::integer NT;
-    typedef ::CGAL::Tag_true Is_modularizable;
-    typedef MOD Modular_NT;
-
-    struct Modular_image{
-        Modular_NT operator()(const NT& a){
-            return Modular_NT ((a%NT(MOD::get_current_prime())).to_long());
-        }
-    };
-    struct Modular_image_inv{
-        NT operator()(const Modular& x){
-            return NT(x.get_value());
-        }
-    };    
-};
-#endif // CGAL_USE_LEDA
-
-#ifdef CGAL_USE_CORE
-// ---------------------------------
-// TODO: mv to CORE_BigInt.h
-
-/*! \ingroup NiX_Modular_traits_spec
- *  \brief a model of concept ModularTraits, 
- *  specialization of NiX::Modular_traits. 
- */
-template<>
-class Modular_traits< ::CORE::BigInt > {
-    typedef Modular MOD;
- public:
-    typedef ::CORE::BigInt NT;
-    typedef CGAL::Tag_true Is_modularizable;
-    typedef MOD Modular_NT;
-
-    struct Modular_image{
-        Modular_NT operator()(const NT& a){
-            NT tmp = a % NT(MOD::get_current_prime());
-// TODO: reactivate this assertion
-// it fails with core_v1.6x_20040329
-//            NiX_assert(tmp.isInt());
-            int mi(tmp.longValue());
-            if (mi < 0) mi += MOD::get_current_prime();
-            return Modular_NT(mi);
-        }
-    };
-    struct Modular_image_inv{
-        NT operator()(const Modular& x){
-            return NT(x.get_value());
-        }
-    };    
-};
-#endif //  CGAL_USE_CORE
-
-
-//--------------------------------
-// TODO : mv to Sqrt_extension.h
-
-template< class COEFF, class ROOT>
-class Modular_traits< Sqrt_extension<COEFF,ROOT> > {
-    
-private:
-    typedef Sqrt_extension<COEFF,ROOT> EXT; 
-    typedef Modular_traits<COEFF> MT_COEFF;
-    typedef Modular_traits<ROOT>  MT_ROOT;
-    typedef typename MT_COEFF::Modular_NT Modular_NT_coeff;
-    typedef typename MT_ROOT::Modular_NT  Modular_NT_root;
-public:
-    typedef Sqrt_extension<COEFF, ROOT > NT;
-    typedef typename MT_COEFF::Is_modularizable Is_modularizable;
-    typedef Sqrt_extension<Modular_NT_coeff, Modular_NT_root> Modular_NT;
-    
-    struct Modular_image{
-        Modular_NT operator()(const EXT& a){
-            typename MT_ROOT::Modular_image mod_image_root;
-            typename MT_COEFF::Modular_image mod_image_coeff;
-            Modular_NT_root  root_mod = mod_image_root(a.root());
-            if(root_mod != Modular_NT_root(0)){
-                return Modular_NT(mod_image_coeff(a.a0()),
-                                  mod_image_coeff(a.a1()),
-                                  root_mod);
-            }else{
-                return Modular_NT(mod_image_coeff(a.a0()));
-            }
-        }
-    };
-
-    struct Modular_image_inv{
-        NT operator()(const Modular_NT& a){
-            typename MT_ROOT::Modular_image_inv mod_image_inv_root;
-            typename MT_COEFF::Modular_image_inv mod_image_inv_coeff;
-            
-            if(a.is_extended()){
-                return NT(
-                        mod_image_inv_coeff(a.a0()),
-                        mod_image_inv_coeff(a.a1()),
-                        mod_image_inv_root(a.root()));
-            }else{
-                return NT(mod_image_inv_coeff(a.a0()));
-            }
-        }
-    };
-};
-
-//template < typename  Coeffcient > class Polynomial; 
-/*! \ingroup NiX_Polynomial
- *  \ingroup NiX_Modular_traits_spec
- *  \brief Specialization of Modular_traits for NiX::Polynomial.
- * 
- *  NiX::Modular_traits::Modular_image maps the coefficients of a polynomial
- *  to their Modular_image and returns the resulting polynomial.  
- */
-/*template< class COEFF >
-class Modular_traits< Polynomial<COEFF> > {
-    
-private:
-    typedef Modular_traits<COEFF> Mtr;
-public:
-    typedef Polynomial<COEFF> NT;
-    typedef Modular_traits<NT> Self;
-    typedef typename Mtr::Is_modularizable Is_modularizable;
-    typedef Polynomial<typename Mtr::Modular_NT> Modular_NT;
-    
-    struct Modular_image{ 
-        Modular_NT operator()(const NT& p){  
-            std::vector<typename Mtr::Modular_NT> V;
-            typename Mtr::Modular_image modular_image;
-            for(int i=0; i<=p.degree();i++)
-                V.push_back(modular_image(p[i]));
-            return Modular_NT(V.begin(),V.end());           
-        }
-    };
-    struct Modular_image_inv{ 
-        NT operator()(const Modular_NT& p){  
-            std::vector<COEFF> V;
-            typename Mtr::Modular_image_inv modular_image_inv;
-            for(int i=0; i<=p.degree();i++)
-                V.push_back(modular_image_inv(p[i]));
-            return NT(V.begin(),V.end());           
-        }
-    };
-};*/
-
 // TODO: put this into Modular_arithmetic/src/ 
 int primes[64] = {
     67089287,67089299,67089329,67089377,67089461,67089469,67089479,67089511, 
diff --git a/Number_types/include/CGAL/CORE_BigInt.h b/Number_types/include/CGAL/CORE_BigInt.h
index ddea0fdf10e..0e057bcc856 100644
--- a/Number_types/include/CGAL/CORE_BigInt.h
+++ b/Number_types/include/CGAL/CORE_BigInt.h
@@ -25,6 +25,9 @@
 #include <CGAL/number_type_basic.h>
 #include <CGAL/CORE_coercion_traits.h>
 
+#include <CGAL/Modular.h>
+#include <CGAL/Modular_traits.h>
+
 CGAL_BEGIN_NAMESPACE
 
 //
@@ -129,6 +132,37 @@ template <> class Real_embeddable_traits< CORE::BigInt >
     };
 };
 
+/*! \ingroup NiX_Modular_traits_spec
+ *  \brief a model of concept ModularTraits, 
+ *  specialization of NiX::Modular_traits. 
+ */
+template<>
+class Modular_traits< ::CORE::BigInt > {
+    typedef Modular MOD;
+ public:
+    typedef ::CORE::BigInt NT;
+    typedef CGAL::Tag_true Is_modularizable;
+    typedef MOD Modular_NT;
+
+    struct Modular_image{
+        Modular_NT operator()(const NT& a){
+            NT tmp = a % NT(MOD::get_current_prime());
+// TODO: reactivate this assertion
+// it fails with core_v1.6x_20040329
+//            NiX_assert(tmp.isInt());
+            int mi(tmp.longValue());
+            if (mi < 0) mi += MOD::get_current_prime();
+            return Modular_NT(mi);
+        }
+    };
+    struct Modular_image_inv{
+        NT operator()(const Modular& x){
+            return NT(x.get_value());
+        }
+    };    
+};
+
+
 template<>
 struct Needs_parens_as_product<CORE::BigInt>{
     bool operator()(const CORE::BigInt& x){
diff --git a/Number_types/include/CGAL/CORE_BigRat.h b/Number_types/include/CGAL/CORE_BigRat.h
index c5a7d48ab1e..d1a9872ab8a 100644
--- a/Number_types/include/CGAL/CORE_BigRat.h
+++ b/Number_types/include/CGAL/CORE_BigRat.h
@@ -26,6 +26,9 @@
 #include <CGAL/CORE_coercion_traits.h>
 #include <CGAL/CORE_Expr.h> // used for To_interval-functor
 
+#include <CGAL/Modular.h>
+#include <CGAL/Modular_traits.h>
+
 //#if defined(CGAL_CORE_BIGRAT_NUMER_DENOM_ARE_MEMBERS)
 //  #define CGAL_CORE_NUMERATOR(X) ((X).numerator())
 //  #define CGAL_CORE_DENOMINATOR(X) ((X).denominator())
@@ -152,6 +155,29 @@ public:
     };
 };
 
+/*! \ingroup NiX_Modular_traits_spec
+ *  \brief a model of concept ModularTraits, 
+ *  specialization of NiX::Modular_traits. 
+ */
+template<>
+class Modular_traits< ::CORE::BigRat > {
+    typedef ::CORE::BigInt Integer;
+    typedef Modular_traits<Integer> MT_int;
+public:
+    typedef ::CORE::BigRat NT;
+    typedef ::CGAL::Tag_true Is_modularizable;
+    typedef CGAL::Modular Modular_NT;
+    struct Modular_image{
+        Modular_NT operator()(const NT& rat){
+            MT_int::Modular_image int_mod;
+            Modular_NT num = int_mod(CGAL_CORE_NUMERATOR(rat));
+            Modular_NT den = int_mod(CGAL_CORE_DENOMINATOR(rat));
+            return num/den;
+        }
+    };  
+};
+
+
 template <class F>
 class Output_rep< ::CORE::BigRat, F> {
     const ::CORE::BigRat& t;
diff --git a/Number_types/include/CGAL/Sqrt_extension.h b/Number_types/include/CGAL/Sqrt_extension.h
index 290be85e0af..50aa353b512 100644
--- a/Number_types/include/CGAL/Sqrt_extension.h
+++ b/Number_types/include/CGAL/Sqrt_extension.h
@@ -57,6 +57,7 @@ factorization property.
 #include <CGAL/Sqrt_extension/Real_embeddable_traits.h>
 #include <CGAL/Sqrt_extension/Fraction_traits.h>
 #include <CGAL/Sqrt_extension/Coercion_traits.h>
+#include <CGAL/Sqrt_extension/Modular_traits.h>
 #include <CGAL/Sqrt_extension/io.h>
 
 #endif  // CGAL_SQRT_EXTENSION_H
diff --git a/Number_types/include/CGAL/Sqrt_extension/Modular_traits.h b/Number_types/include/CGAL/Sqrt_extension/Modular_traits.h
new file mode 100644
index 00000000000..fc72d60af1b
--- /dev/null
+++ b/Number_types/include/CGAL/Sqrt_extension/Modular_traits.h
@@ -0,0 +1,83 @@
+// Copyright (c) 2006-2007 Max-Planck-Institute Saarbruecken (Germany).
+// All rights reserved.
+//
+// This file is part of CGAL (www.cgal.org); you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public License as
+// published by the Free Software Foundation; version 2.1 of the License.
+// See the file LICENSE.LGPL distributed with CGAL.
+//
+// Licensees holding a valid commercial license may use this file in
+// accordance with the commercial license agreement provided with the software.
+//
+// This file is provided AS IS with NO WARRANTY OF ANY KIND, INCLUDING THE
+// WARRANTY OF DESIGN, MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
+//
+// $URL: $
+// $Id: $
+//
+//
+// Author(s)     : Michael Hemmer   <hemmer@mpi-inf.mpg.de>
+
+
+#ifndef CGAL_SQRT_EXTENSION_MODULAR_TRAITS_H
+#define CGAL_SQRT_EXTENSION_MODULAR_TRAITS_H
+
+#include <CGAL/basic.h>
+#include <CGAL/Modular.h>
+#include <CGAL/Modular_traits.h>
+
+CGAL_BEGIN_NAMESPACE
+
+/////////// MODULAR_TRAITS BEGIN
+
+template< class COEFF, class ROOT>
+class Modular_traits< Sqrt_extension<COEFF,ROOT> > {
+    
+private:
+    typedef Sqrt_extension<COEFF,ROOT> EXT; 
+    typedef Modular_traits<COEFF> MT_COEFF;
+    typedef Modular_traits<ROOT>  MT_ROOT;
+    typedef typename MT_COEFF::Modular_NT Modular_NT_coeff;
+    typedef typename MT_ROOT::Modular_NT  Modular_NT_root;
+public:
+    typedef Sqrt_extension<COEFF, ROOT > NT;
+    typedef typename MT_COEFF::Is_modularizable Is_modularizable;
+    typedef Sqrt_extension<Modular_NT_coeff, Modular_NT_root> Modular_NT;
+    
+    struct Modular_image{
+        Modular_NT operator()(const EXT& a){
+            typename MT_ROOT::Modular_image mod_image_root;
+            typename MT_COEFF::Modular_image mod_image_coeff;
+            Modular_NT_root  root_mod = mod_image_root(a.root());
+            if(root_mod != Modular_NT_root(0)){
+                return Modular_NT(mod_image_coeff(a.a0()),
+                                  mod_image_coeff(a.a1()),
+                                  root_mod);
+            }else{
+                return Modular_NT(mod_image_coeff(a.a0()));
+            }
+        }
+    };
+
+    struct Modular_image_inv{
+        NT operator()(const Modular_NT& a){
+            typename MT_ROOT::Modular_image_inv mod_image_inv_root;
+            typename MT_COEFF::Modular_image_inv mod_image_inv_coeff;
+            
+            if(a.is_extended()){
+                return NT(
+                        mod_image_inv_coeff(a.a0()),
+                        mod_image_inv_coeff(a.a1()),
+                        mod_image_inv_root(a.root()));
+            }else{
+                return NT(mod_image_inv_coeff(a.a0()));
+            }
+        }
+    };
+};
+
+/////////// MODULAR_TRAITS END
+
+CGAL_END_NAMESPACE
+
+#endif
diff --git a/Number_types/include/CGAL/leda_integer.h b/Number_types/include/CGAL/leda_integer.h
index b0fe4ab32d1..4631b06ec36 100644
--- a/Number_types/include/CGAL/leda_integer.h
+++ b/Number_types/include/CGAL/leda_integer.h
@@ -40,6 +40,9 @@
 #include <LEDA/numbers/bigfloat.h>// for To_interval
 #endif
 
+#include <CGAL/Modular.h>
+#include <CGAL/Modular_traits.h>
+
 CGAL_BEGIN_NAMESPACE
 
 template <> class Algebraic_structure_traits< leda_integer >
@@ -170,6 +173,26 @@ template <> class Real_embeddable_traits< leda_integer >
     };
 };
 
+template<>
+class Modular_traits< ::leda::integer > {
+    typedef Modular MOD;
+ public:
+    typedef ::leda::integer NT;
+    typedef ::CGAL::Tag_true Is_modularizable;
+    typedef MOD Modular_NT;
+
+    struct Modular_image{
+        Modular_NT operator()(const NT& a){
+            return Modular_NT ((a%NT(MOD::get_current_prime())).to_long());
+        }
+    };
+    struct Modular_image_inv{
+        NT operator()(const Modular& x){
+            return NT(x.get_value());
+        }
+    };    
+};
+
 //
 // Needs_parens_as_product
 //
diff --git a/Number_types/include/CGAL/leda_rational.h b/Number_types/include/CGAL/leda_rational.h
index ee83042eb60..1c2def22bb8 100644
--- a/Number_types/include/CGAL/leda_rational.h
+++ b/Number_types/include/CGAL/leda_rational.h
@@ -29,6 +29,9 @@
 #include <CGAL/leda_coercion_traits.h>
 #include <CGAL/Interval_nt.h>
 
+#include <CGAL/Modular.h>
+#include <CGAL/Modular_traits.h>
+
 #include <CGAL/Needs_parens_as_product.h>
 
 #include <utility>
@@ -197,6 +200,27 @@ public:
     };
 };
 
+// Modular_traits
+template<>
+class Modular_traits< ::leda::rational > {
+    typedef ::leda::integer Integer;
+    typedef CGAL::Modular_traits<Integer> MT_int;
+public:
+    typedef ::leda::rational NT;
+    typedef ::CGAL::Tag_true Is_modularizable;
+    typedef CGAL::Modular Modular_NT;
+
+    struct Modular_image{
+        Modular_NT operator()(const NT& rat){
+            MT_int::Modular_image int_mod;
+            Modular_NT num = int_mod(rat.numerator());
+            Modular_NT den = int_mod(rat.denominator());
+            return num/den;
+        }
+    };
+};
+
+
 template <class F>
 class Output_rep< leda_rational, F> {
     const leda_rational& t;