diff --git a/Cartesian_kernel/include/CGAL/Cartesian/function_objects.h b/Cartesian_kernel/include/CGAL/Cartesian/function_objects.h
index 85f198f3af1..e87523f9281 100644
--- a/Cartesian_kernel/include/CGAL/Cartesian/function_objects.h
+++ b/Cartesian_kernel/include/CGAL/Cartesian/function_objects.h
@@ -804,6 +804,40 @@ namespace CartesianKernelFunctors {
     { return t.area(); }
   };
 
+  template <typename K>
+  class Compute_determinant_2
+  {
+    typedef typename K::FT                FT;
+    typedef typename K::Vector_2          Vector_2;
+  public:
+    typedef FT               result_type;
+    typedef Arity_tag< 2 >   Arity;
+
+    result_type
+    operator()(const Vector_2& v, const Vector_2& w) const
+    {
+	return det2x2_by_formula(v.x(), v.y(), w.x(), w.y());
+    }
+  };
+
+  template <typename K>
+  class Compute_determinant_3
+  {
+    typedef typename K::FT                FT;
+    typedef typename K::Vector_3          Vector_3;
+  public:
+    typedef FT               result_type;
+    typedef Arity_tag< 3 >   Arity;
+
+    result_type
+    operator()(const Vector_3& v, const Vector_3& w, const Vector_3& t) const
+    {
+	return det3x3_by_formula(v.x(), v.y(), v.z(),
+                                 w.x(), w.y(), w.z(),
+                                 t.x(), t.y(), t.z());
+    }
+  };
+
   template <typename K>
   class Compute_scalar_product_2
   {
diff --git a/Homogeneous_kernel/include/CGAL/Homogeneous/function_objects.h b/Homogeneous_kernel/include/CGAL/Homogeneous/function_objects.h
index 130dd846efc..7f6252e356c 100644
--- a/Homogeneous_kernel/include/CGAL/Homogeneous/function_objects.h
+++ b/Homogeneous_kernel/include/CGAL/Homogeneous/function_objects.h
@@ -1235,6 +1235,42 @@ namespace HomogeneousKernelFunctors {
     { return t.area(); }
   };
 
+  template <typename K>
+  class Compute_determinant_2
+  {
+    typedef typename K::FT                FT;
+    typedef typename K::Vector_2          Vector_2;
+  public:
+    typedef FT               result_type;
+    typedef Arity_tag< 2 >   Arity;
+
+    result_type
+    operator()(const Vector_2& v, const Vector_2& w) const
+    {
+	return det2x2_by_formula(v.hx(), v.hy(),
+                                 w.hx(), w.hy()) / FT(v.hw() * w.hw());
+    }
+  };
+
+  template <typename K>
+  class Compute_determinant_3
+  {
+    typedef typename K::FT                FT;
+    typedef typename K::Vector_3          Vector_3;
+  public:
+    typedef FT               result_type;
+    typedef Arity_tag< 3 >   Arity;
+
+    result_type
+    operator()(const Vector_3& v, const Vector_3& w, const Vector_3& t) const
+    {
+	return det3x3_by_formula(v.hx(), v.hy(), v.hz(),
+                                 w.hx(), w.hy(), w.hz(),
+                                 t.hx(), t.hy(), t.hz())
+                              / FT(v.hw() * w.hw() * t.hw());
+    }
+  };
+
   template <typename K>
   class Compute_scalar_product_2
   {
diff --git a/Kernel_23/doc_tex/Kernel_23_ref/Kernel_ComputeDeterminant_2.tex b/Kernel_23/doc_tex/Kernel_23_ref/Kernel_ComputeDeterminant_2.tex
new file mode 100644
index 00000000000..849672ae161
--- /dev/null
+++ b/Kernel_23/doc_tex/Kernel_23_ref/Kernel_ComputeDeterminant_2.tex
@@ -0,0 +1,17 @@
+\begin{ccRefFunctionObjectConcept}{Kernel::ComputeDeterminant_2}
+A model for this must provide:
+
+\ccCreationVariable{fo}
+
+\ccMemberFunction{Kernel::FT operator()(const Kernel::Vector_2& v,
+					const Kernel::Vector_2& w);}
+       {returns the determinant of the two vectors $v$ and $w$. }
+
+\ccRefines
+AdaptableFunctor (with two arguments)
+
+\ccSeeAlso
+\ccRefIdfierPage{CGAL::Vector_2<Kernel>} \\
+\ccRefIdfierPage{CGAL::determinant}  \\
+
+\end{ccRefFunctionObjectConcept}
diff --git a/Kernel_23/doc_tex/Kernel_23_ref/Kernel_ComputeDeterminant_3.tex b/Kernel_23/doc_tex/Kernel_23_ref/Kernel_ComputeDeterminant_3.tex
new file mode 100644
index 00000000000..51706c70dfc
--- /dev/null
+++ b/Kernel_23/doc_tex/Kernel_23_ref/Kernel_ComputeDeterminant_3.tex
@@ -0,0 +1,18 @@
+\begin{ccRefFunctionObjectConcept}{Kernel::ComputeDeterminant_3}
+A model for this must provide:
+
+\ccCreationVariable{fo}
+
+\ccMemberFunction{Kernel::FT operator()(const Kernel::Vector_2& u,
+					const Kernel::Vector_2& v,
+					const Kernel::Vector_2& w);}
+       {returns the determinant of the three vectors $u$, $v$ and $w$. }
+
+\ccRefines
+AdaptableFunctor (with three arguments)
+
+\ccSeeAlso
+\ccRefIdfierPage{CGAL::Vector_3<Kernel>} \\
+\ccRefIdfierPage{CGAL::determinant}  \\
+
+\end{ccRefFunctionObjectConcept}
diff --git a/Kernel_23/doc_tex/Kernel_23_ref/Kernel_ConstructCrossProductVector_3.tex b/Kernel_23/doc_tex/Kernel_23_ref/Kernel_ConstructCrossProductVector_3.tex
index 6fd9417dda4..1bd9ee2fe9f 100644
--- a/Kernel_23/doc_tex/Kernel_23_ref/Kernel_ConstructCrossProductVector_3.tex
+++ b/Kernel_23/doc_tex/Kernel_23_ref/Kernel_ConstructCrossProductVector_3.tex
@@ -14,5 +14,6 @@ AdaptableFunctor (with two arguments)
 \ccSeeAlso
 
 \ccRefIdfierPage{CGAL::cross_product}\\
+\ccRefIdfierPage{CGAL::determinant}\\
 
 \end{ccRefFunctionObjectConcept}
diff --git a/Kernel_23/doc_tex/Kernel_23_ref/Kernel_ConstructDifferenceOfVectors_2.tex b/Kernel_23/doc_tex/Kernel_23_ref/Kernel_ConstructDifferenceOfVectors_2.tex
index 0265ebc1c33..1b7f2aac70a 100644
--- a/Kernel_23/doc_tex/Kernel_23_ref/Kernel_ConstructDifferenceOfVectors_2.tex
+++ b/Kernel_23/doc_tex/Kernel_23_ref/Kernel_ConstructDifferenceOfVectors_2.tex
@@ -3,13 +3,10 @@ A model for this must provide:
 
 \ccCreationVariable{fo}
 
-
-
 \ccMemberFunction{Kernel::Vector_2 operator()(const Kernel::Vector_2 &v1,
 	                                      const Kernel::Vector_2 &v2);}
             {introduces the vector $v1 - v2$.}
 
-
 \ccRefines
 AdaptableFunctor (with two arguments)
 
diff --git a/Kernel_23/doc_tex/Kernel_23_ref/Kernel_ConstructDividedVector_2.tex b/Kernel_23/doc_tex/Kernel_23_ref/Kernel_ConstructDividedVector_2.tex
index e0ca89eeccb..485dddc1226 100644
--- a/Kernel_23/doc_tex/Kernel_23_ref/Kernel_ConstructDividedVector_2.tex
+++ b/Kernel_23/doc_tex/Kernel_23_ref/Kernel_ConstructDividedVector_2.tex
@@ -3,8 +3,6 @@ A model for this must provide:
 
 \ccCreationVariable{fo}
 
-
-
 \ccMemberFunction{Kernel::Vector_2 operator()(const Kernel::Vector_2 &v,
 	                                      const Kernel::RT s);}
             {introduces the vector $v/s$.}
diff --git a/Kernel_23/doc_tex/Kernel_23_ref/Kernel_ConstructOrthogonalVector_3.tex b/Kernel_23/doc_tex/Kernel_23_ref/Kernel_ConstructOrthogonalVector_3.tex
index 7531b229e45..0b41b8ec887 100644
--- a/Kernel_23/doc_tex/Kernel_23_ref/Kernel_ConstructOrthogonalVector_3.tex
+++ b/Kernel_23/doc_tex/Kernel_23_ref/Kernel_ConstructOrthogonalVector_3.tex
@@ -19,4 +19,5 @@ AdaptableFunctor (with one argument)
 \ccSeeAlso
 \ccRefIdfierPage{CGAL::Plane_3<Kernel>} \\
 \ccRefIdfierPage{Kernel::ConstructCrossProductVector_3}\\
+
 \end{ccRefFunctionObjectConcept}
diff --git a/Kernel_23/doc_tex/Kernel_23_ref/Kernel_ConstructScaledVector_2.tex b/Kernel_23/doc_tex/Kernel_23_ref/Kernel_ConstructScaledVector_2.tex
index 734e51c7dee..1876ff96886 100644
--- a/Kernel_23/doc_tex/Kernel_23_ref/Kernel_ConstructScaledVector_2.tex
+++ b/Kernel_23/doc_tex/Kernel_23_ref/Kernel_ConstructScaledVector_2.tex
@@ -3,7 +3,6 @@ A model for this must provide:
 
 \ccCreationVariable{fo}
 
-
 \ccMemberFunction{
 Kernel::Vector_2 operator()(const Kernel::Vector_2 &v,
                             const Kernel::RT& scale);}
@@ -14,7 +13,6 @@ Kernel::Vector_2 operator()(const Kernel::Vector_2 &v,
                             const Kernel::FT& scale);}
             {produces the vector \ccc{v} scaled by a factor \ccc{scale}.}
 
-
 \ccRefines
 AdaptableFunctor (with two arguments)
 
diff --git a/Kernel_23/doc_tex/Kernel_23_ref/Kernel_ConstructScaledVector_3.tex b/Kernel_23/doc_tex/Kernel_23_ref/Kernel_ConstructScaledVector_3.tex
index e3f8535b134..d96554ab420 100644
--- a/Kernel_23/doc_tex/Kernel_23_ref/Kernel_ConstructScaledVector_3.tex
+++ b/Kernel_23/doc_tex/Kernel_23_ref/Kernel_ConstructScaledVector_3.tex
@@ -3,7 +3,6 @@ A model for this must provide:
 
 \ccCreationVariable{fo}
 
-
 \ccMemberFunction{
 Kernel::Vector_3 operator()(const Kernel::Vector_3 &v,
                             const Kernel::RT& scale);}
diff --git a/Kernel_23/doc_tex/Kernel_23_ref/Kernel_ConstructSumOfVectors_2.tex b/Kernel_23/doc_tex/Kernel_23_ref/Kernel_ConstructSumOfVectors_2.tex
index 2015e875334..62bc43aaab9 100644
--- a/Kernel_23/doc_tex/Kernel_23_ref/Kernel_ConstructSumOfVectors_2.tex
+++ b/Kernel_23/doc_tex/Kernel_23_ref/Kernel_ConstructSumOfVectors_2.tex
@@ -3,8 +3,6 @@ A model for this must provide:
 
 \ccCreationVariable{fo}
 
-
-
 \ccMemberFunction{Kernel::Vector_2 operator()(const Kernel::Vector_2 &v1,
 	                                      const Kernel::Vector_2 &v2);}
             {introduces the vector $v1 + v2$.}
diff --git a/Kernel_23/doc_tex/Kernel_23_ref/Kernel_Vector_2.tex b/Kernel_23/doc_tex/Kernel_23_ref/Kernel_Vector_2.tex
index ae2eba13353..9d23b2ab3aa 100644
--- a/Kernel_23/doc_tex/Kernel_23_ref/Kernel_Vector_2.tex
+++ b/Kernel_23/doc_tex/Kernel_23_ref/Kernel_Vector_2.tex
@@ -7,6 +7,7 @@ CopyConstructible, Assignable, DefaultConstructible
 
 \ccSeeAlso 
 \ccRefIdfierPage{CGAL::Vector_2<Kernel>} \\
+\ccRefConceptPage{Kernel::ComputeDeterminant_2} \\
 \ccRefConceptPage{Kernel::ComputeX_2} \\
 \ccRefConceptPage{Kernel::ComputeY_2} \\
 \ccRefConceptPage{Kernel::ComputeHx_2} \\
diff --git a/Kernel_23/doc_tex/Kernel_23_ref/Kernel_Vector_3.tex b/Kernel_23/doc_tex/Kernel_23_ref/Kernel_Vector_3.tex
index e404bfa66b9..c4bde6e9c9a 100644
--- a/Kernel_23/doc_tex/Kernel_23_ref/Kernel_Vector_3.tex
+++ b/Kernel_23/doc_tex/Kernel_23_ref/Kernel_Vector_3.tex
@@ -7,6 +7,7 @@ CopyConstructible, Assignable, DefaultConstructible
 
 \ccSeeAlso
 \ccRefIdfierPage{CGAL::Vector_3<Kernel>} \\
+\ccRefConceptPage{Kernel::ComputeDeterminant_3} \\
 \ccRefConceptPage{Kernel::ConstructCrossProductVector_3} \\
 \ccRefConceptPage{Kernel::ConstructDirection_3} \\
 \ccRefConceptPage{Kernel::ConstructOppositeVector_3} \\
diff --git a/Kernel_23/doc_tex/Kernel_23_ref/Vector_3.tex b/Kernel_23/doc_tex/Kernel_23_ref/Vector_3.tex
index 580d3ff5fb2..ed20471d30b 100644
--- a/Kernel_23/doc_tex/Kernel_23_ref/Vector_3.tex
+++ b/Kernel_23/doc_tex/Kernel_23_ref/Vector_3.tex
@@ -147,5 +147,6 @@ The following operations can be applied on vectors:
 \ccSeeAlso
 \ccRefConceptPage{Kernel::Vector_3} \\
 \ccRefIdfierPage{CGAL::cross_product} \\
+\ccRefIdfierPage{CGAL::determinant} \\
 
 \end{ccRefClass} 
diff --git a/Kernel_23/doc_tex/Kernel_23_ref/determinant.tex b/Kernel_23/doc_tex/Kernel_23_ref/determinant.tex
new file mode 100644
index 00000000000..934ed5d2421
--- /dev/null
+++ b/Kernel_23/doc_tex/Kernel_23_ref/determinant.tex
@@ -0,0 +1,22 @@
+%\ccHtmlNoRefLinks
+\begin{ccRefFunction}{determinant}
+
+\ccHtmlNoLinks
+\ccFunction{Kernel::FT determinant(const Vector_2<Kernel>& v,
+                                   const Vector_2<Kernel>& w);}
+{returns the determinant of $v$ and $w$.}
+
+\ccHtmlNoLinks
+\ccFunction{Kernel::FT determinant(const Vector_3<Kernel>& u,
+                                   const Vector_3<Kernel>& v,
+                                   const Vector_3<Kernel>& w);}
+{returns the determinant of $u$, $v$ and $w$.}
+
+\ccSeeAlso
+\ccRefIdfierPage{CGAL::orientation}
+\ccRefIdfierPage{CGAL::collinear}
+\ccRefIdfierPage{CGAL::left_turn}
+\ccRefIdfierPage{CGAL::right_turn}
+
+\end{ccRefFunction}
+
diff --git a/Kernel_23/doc_tex/Kernel_23_ref/main.tex b/Kernel_23/doc_tex/Kernel_23_ref/main.tex
index 851923b15e4..961c1d0348a 100644
--- a/Kernel_23/doc_tex/Kernel_23_ref/main.tex
+++ b/Kernel_23/doc_tex/Kernel_23_ref/main.tex
@@ -176,6 +176,7 @@ in the kernel.
 \input{Kernel_23_ref/coplanar_orientation.tex}
 \input{Kernel_23_ref/coplanar_side_of_bounded_circle.tex}
 \input{Kernel_23_ref/cross_product.tex}
+\input{Kernel_23_ref/determinant.tex}
 \input{Kernel_23_ref/do_intersect.tex}
 \input{Kernel_23_ref/do_overlap.tex}
 \input{Kernel_23_ref/enum_cast.tex}
@@ -259,6 +260,8 @@ in the kernel.
 \input{Kernel_23_ref/Kernel_ComputeC_2.tex}
 \input{Kernel_23_ref/Kernel_ComputeArea_2.tex}
 \input{Kernel_23_ref/Kernel_ComputeArea_3.tex}
+\input{Kernel_23_ref/Kernel_ComputeDeterminant_2.tex}
+\input{Kernel_23_ref/Kernel_ComputeDeterminant_3.tex}
 \input{Kernel_23_ref/Kernel_ComputeScalarProduct_2.tex}
 \input{Kernel_23_ref/Kernel_ComputeScalarProduct_3.tex}
 \input{Kernel_23_ref/Kernel_ComputeSquaredArea_3.tex}
diff --git a/Kernel_23/include/CGAL/Kernel/global_functions_2.h b/Kernel_23/include/CGAL/Kernel/global_functions_2.h
index 8f7cafba5e9..226a3f8c7d0 100644
--- a/Kernel_23/include/CGAL/Kernel/global_functions_2.h
+++ b/Kernel_23/include/CGAL/Kernel/global_functions_2.h
@@ -445,6 +445,14 @@ compare_yx(const Point_2<K> &p, const Point_2<K> &q)
   return CGALi::compare_yx(p, q, K());
 }
 
+template < class K >
+inline
+typename K::FT
+determinant(const Vector_2<K> &v0, const Vector_2<K> &v1)
+{
+  return CGALi::determinant(v0, v1, K());
+}
+
 template <class K>
 inline
 bool
diff --git a/Kernel_23/include/CGAL/Kernel/global_functions_3.h b/Kernel_23/include/CGAL/Kernel/global_functions_3.h
index a3d7dfe9c0b..7f7191204d7 100644
--- a/Kernel_23/include/CGAL/Kernel/global_functions_3.h
+++ b/Kernel_23/include/CGAL/Kernel/global_functions_3.h
@@ -314,6 +314,15 @@ cross_product(const Vector_3<K> &v, const Vector_3<K> &w)
   return CGALi::cross_product(v, w, K());
 }
 
+template < class K >
+inline
+typename K::FT
+determinant(const Vector_3<K> &v0, const Vector_3<K> &v1,
+            const Vector_3<K> &v2)
+{
+  return CGALi::determinant(v0, v1, v2, K());
+}
+
 template < class K >
 inline
 bool
diff --git a/Kernel_23/include/CGAL/Kernel/global_functions_internal_2.h b/Kernel_23/include/CGAL/Kernel/global_functions_internal_2.h
index eb16a7331c9..0eb83b35df2 100644
--- a/Kernel_23/include/CGAL/Kernel/global_functions_internal_2.h
+++ b/Kernel_23/include/CGAL/Kernel/global_functions_internal_2.h
@@ -447,6 +447,15 @@ compare_y_at_x(const typename CGAL_WRAP(K)::Line_2 &l1,
   return k.compare_y_at_x_2_object()(l1, l2, h1, h2);
 }
 
+template < class K >
+inline
+typename K::FT
+determinant(const typename CGAL_WRAP(K)::Vector_2 &v0,
+            const typename CGAL_WRAP(K)::Vector_2 &v1, const K &k)
+{
+  return k.compute_determinant_2_object()(v0, v1);
+}
+
 template <class K>
 inline
 bool
diff --git a/Kernel_23/include/CGAL/Kernel/global_functions_internal_3.h b/Kernel_23/include/CGAL/Kernel/global_functions_internal_3.h
index 578b921e709..91bc1348aad 100644
--- a/Kernel_23/include/CGAL/Kernel/global_functions_internal_3.h
+++ b/Kernel_23/include/CGAL/Kernel/global_functions_internal_3.h
@@ -333,6 +333,16 @@ cross_product(const typename CGAL_WRAP(K)::Vector_3 &v,
   return k.construct_cross_product_vector_3_object()(v, w);
 }
 
+template < class K >
+inline
+typename K::FT
+determinant(const typename CGAL_WRAP(K)::Vector_3 &v0,
+            const typename CGAL_WRAP(K)::Vector_3 &v1,
+            const typename CGAL_WRAP(K)::Vector_3 &v2, const K &k)
+{
+  return k.compute_determinant_3_object()(v0, v1, v2);
+}
+
 template < class K >
 inline
 bool
diff --git a/Kernel_23/include/CGAL/Kernel/interface_macros.h b/Kernel_23/include/CGAL/Kernel/interface_macros.h
index 2ad8e783974..a6d764c60bd 100644
--- a/Kernel_23/include/CGAL/Kernel/interface_macros.h
+++ b/Kernel_23/include/CGAL/Kernel/interface_macros.h
@@ -151,6 +151,10 @@ CGAL_Kernel_cons(Compute_area_2,
 		 compute_area_2_object)
 CGAL_Kernel_cons(Compute_area_3,
 		 compute_area_3_object)
+CGAL_Kernel_cons(Compute_determinant_2,
+		 compute_determinant_2_object)
+CGAL_Kernel_cons(Compute_determinant_3,
+		 compute_determinant_3_object)
 CGAL_Kernel_cons(Compute_scalar_product_2,
 		 compute_scalar_product_2_object)
 CGAL_Kernel_cons(Compute_scalar_product_3,
diff --git a/Kernel_23/test/Kernel_23/include/CGAL/_test_fct_vector_2.h b/Kernel_23/test/Kernel_23/include/CGAL/_test_fct_vector_2.h
index a1311fae04d..06155150b56 100644
--- a/Kernel_23/test/Kernel_23/include/CGAL/_test_fct_vector_2.h
+++ b/Kernel_23/test/Kernel_23/include/CGAL/_test_fct_vector_2.h
@@ -60,6 +60,12 @@ _test_fct_vector_2(const R& )
  assert( orientation(v1, v2) == CGAL::RIGHT_TURN );
  assert( orientation(v2, v1) == CGAL::LEFT_TURN );
 
+ assert( determinant(v0, v0) == 0 );
+ assert( determinant(v1, v1) == 0 );
+ assert( determinant(v1, v0) == 0 );
+ assert( determinant(v1, v2) == -30 );
+ assert( determinant(v2, v1) == 30 );
+
  assert( v1 + v2 == v3 );
  assert( v1 - v2 == v4 );
  assert( v3 - v1 == v2 );
diff --git a/Kernel_23/test/Kernel_23/include/CGAL/_test_fct_vector_3.h b/Kernel_23/test/Kernel_23/include/CGAL/_test_fct_vector_3.h
index 672e2c4a46f..b1131602164 100644
--- a/Kernel_23/test/Kernel_23/include/CGAL/_test_fct_vector_3.h
+++ b/Kernel_23/test/Kernel_23/include/CGAL/_test_fct_vector_3.h
@@ -66,6 +66,15 @@ _test_fct_vector_3(const R& )
  assert( orientation(v1, v2, v12) == CGAL::POSITIVE );
  assert( orientation(v1, v12, v2) == CGAL::NEGATIVE );
 
+ assert( determinant(v0, v0, v0) == 0 );
+ assert( determinant(v1, v1, v1) == 0 );
+ assert( determinant(v1, v1, v2) == 0 );
+ assert( determinant(v1, v2, v1) == 0 );
+ assert( determinant(v2, v1, v1) == 0 );
+ assert( determinant(v1, v2, v3) == 0 );
+ assert( determinant(v1, v2, v12) == 180 );
+ assert( determinant(v1, v12, v2) == -180 );
+
  assert( v1 + v2 == v3 );
  assert( v1 - v2 == v4 );
  assert( v3 - v1 == v2 );
diff --git a/Kernel_23/test/Kernel_23/include/CGAL/_test_new_2.h b/Kernel_23/test/Kernel_23/include/CGAL/_test_new_2.h
index 1360718461d..ad6cb0a806c 100644
--- a/Kernel_23/test/Kernel_23/include/CGAL/_test_new_2.h
+++ b/Kernel_23/test/Kernel_23/include/CGAL/_test_new_2.h
@@ -343,15 +343,19 @@ test_new_2(const R& rep)
      tmp22a = compute_area_2(rec2);
      tmp22a = compute_area_2(p3, p4, p5);
 
+  typename R::Compute_determinant_2 compute_determinant_2
+        = rep.compute_determinant_2_object();
+  FT tmp22b = compute_determinant_2(v3, v4);
+
   typename R::Compute_scalar_product_2 Compute_scalar_product
         = rep.compute_scalar_product_2_object();
-  FT tmp22b = Compute_scalar_product(v3, v4);
+  FT tmp22c = Compute_scalar_product(v3, v4);
 
   typename R::Compute_squared_distance_2 Compute_squared_distance
         = rep.compute_squared_distance_2_object();
-  FT tmp22c = Compute_squared_distance(p1, p2);
-     tmp22c = Compute_squared_distance(p1, r2);
-     tmp22c = Compute_squared_distance(p1, t2);
+  FT tmp22d = Compute_squared_distance(p1, p2);
+     tmp22d = Compute_squared_distance(p1, r2);
+     tmp22d = Compute_squared_distance(p1, t2);
 
   typename R::Compute_squared_length_2 Compute_squared_length
         = rep.compute_squared_length_2_object();
diff --git a/Kernel_23/test/Kernel_23/include/CGAL/_test_new_3.h b/Kernel_23/test/Kernel_23/include/CGAL/_test_new_3.h
index 6db617abf83..7b590919460 100644
--- a/Kernel_23/test/Kernel_23/include/CGAL/_test_new_3.h
+++ b/Kernel_23/test/Kernel_23/include/CGAL/_test_new_3.h
@@ -391,6 +391,10 @@ test_new_3(const R& rep)
   (void) tmp12a;
   (void) tmp12b;
 
+  typename R::Compute_determinant_3 compute_determinant_3
+        = rep.compute_determinant_3_object();
+  FT tmp12aa = compute_determinant_3(v3, v4, v5);
+
   typename R::Compute_scalar_product_3 Compute_scalar_product
         = rep.compute_scalar_product_3_object();
   FT tmp12bb = Compute_scalar_product(v3, v4);
@@ -708,7 +712,7 @@ test_new_3(const R& rep)
   use(tmp3); use(tmp3a);
   use(tmp9); use(tmp14a); use(tmp5); use(tmp6);
   use(tmp7); use(tmp71); use(sp1a); use(tmp72);
-  use(tmp12a); use(tmp12b);
+  use(tmp12a); use(tmp12aa); use(tmp12b);
   use(bb1); use(bb2); use(bb3); use(bb4); use(bb5); use(bb6); 
   use(r4); use(r5); use(l7); use(l8); use(v7); use(v8); use(v9); use(h8);
   use(cccit);