diff --git a/Kernel_23/include/CGAL/determinant.h b/Kernel_23/include/CGAL/determinant.h
index c91ea8d32e5..a88d697894a 100644
--- a/Kernel_23/include/CGAL/determinant.h
+++ b/Kernel_23/include/CGAL/determinant.h
@@ -211,6 +211,83 @@ determinant(
   return m012345;
 }
 
+template <class RT>
+RT
+determinant(
+ const RT& a00, const RT& a01, const RT& a02, const RT& a03, const RT& a04,
+ const RT& a05, const RT& a06,
+ const RT& a10, const RT& a11, const RT& a12, const RT& a13, const RT& a14,
+ const RT& a15, const RT& a16,
+ const RT& a20, const RT& a21, const RT& a22, const RT& a23, const RT& a24,
+ const RT& a25, const RT& a26,
+ const RT& a30, const RT& a31, const RT& a32, const RT& a33, const RT& a34,
+ const RT& a35, const RT& a36,
+ const RT& a40, const RT& a41, const RT& a42, const RT& a43, const RT& a44,
+ const RT& a45, const RT& a46,
+ const RT& a50, const RT& a51, const RT& a52, const RT& a53, const RT& a54,
+ const RT& a55, const RT& a56,
+ const RT& a60, const RT& a61, const RT& a62, const RT& a63, const RT& a64,
+ const RT& a65, const RT& a66)
+{
+  return a00 * determinant(
+                           a11, a12, a13, a14, a15, a16,
+                           a21, a22, a23, a24, a25, a26,
+                           a31, a32, a33, a34, a35, a36,
+                           a41, a42, a43, a44, a45, a46,
+                           a51, a52, a53, a54, a55, a56,
+                           a61, a62, a63, a64, a65, a66)
+    
+    - a10 * determinant(a01, a02, a03, a04, a05, a06,
+
+                        a21, a22, a23, a24, a25, a26,
+                        a31, a32, a33, a34, a35, a36,
+                        a41, a42, a43, a44, a45, a46,
+                        a51, a52, a53, a54, a55, a56,
+                        a61, a62, a63, a64, a65, a66)
+    
+    + a20 * determinant(a01, a02, a03, a04, a05, a06,
+                        a11, a12, a13, a14, a15, a16,
+
+                        a31, a32, a33, a34, a35, a36,
+                        a41, a42, a43, a44, a45, a46,
+                        a51, a52, a53, a54, a55, a56,
+                        a61, a62, a63, a64, a65, a66)
+    
+    - a30 * determinant(a01, a02, a03, a04, a05, a06,
+                        a11, a12, a13, a14, a15, a16,
+                        a21, a22, a23, a24, a25, a26,
+
+                        a41, a42, a43, a44, a45, a46,
+                        a51, a52, a53, a54, a55, a56,
+                        a61, a62, a63, a64, a65, a66)
+    
+    + a40 * determinant(a01, a02, a03, a04, a05, a06,
+                        a11, a12, a13, a14, a15, a16,
+                        a21, a22, a23, a24, a25, a26,
+                        a31, a32, a33, a34, a35, a36,
+
+                        a51, a52, a53, a54, a55, a56,
+                        a61, a62, a63, a64, a65, a66)
+    
+    - a50 * determinant(a01, a02, a03, a04, a05, a06,
+                        a11, a12, a13, a14, a15, a16,
+                        a21, a22, a23, a24, a25, a26,
+                        a31, a32, a33, a34, a35, a36,
+                        a41, a42, a43, a44, a45, a46,
+                        
+                        a61, a62, a63, a64, a65, a66)
+    
+    + a60 * determinant(a01, a02, a03, a04, a05, a06,
+                        a11, a12, a13, a14, a15, a16,
+                        a21, a22, a23, a24, a25, a26,
+                        a31, a32, a33, a34, a35, a36,
+                        a41, a42, a43, a44, a45, a46,
+                        a51, a52, a53, a54, a55, a56
+
+                        );
+}
+
+  
 } //namespace CGAL
 
 #endif // CGAL_DETERMINANT_H
diff --git a/NewKernel_d/include/CGAL/NewKernel_d/Cartesian_filter_K.h b/NewKernel_d/include/CGAL/NewKernel_d/Cartesian_filter_K.h
index f931da3f15d..baff656bc69 100644
--- a/NewKernel_d/include/CGAL/NewKernel_d/Cartesian_filter_K.h
+++ b/NewKernel_d/include/CGAL/NewKernel_d/Cartesian_filter_K.h
@@ -49,7 +49,7 @@ template<> struct Functors_without_division<Dimension_tag<5> > {
 template<> struct Functors_without_division<Dimension_tag<6> > {
   typedef typeset<Orientation_of_points_tag> type;
 };
-
+  
 template < typename Base_, typename AK_, typename EK_, typename Pred_list = typeset_all >
 struct Cartesian_filter_K : public Base_,
   private Store_kernel<EK_>
diff --git a/NewKernel_d/include/CGAL/NewKernel_d/LA_eigen/LA.h b/NewKernel_d/include/CGAL/NewKernel_d/LA_eigen/LA.h
index 082e84263b5..9261ed89609 100644
--- a/NewKernel_d/include/CGAL/NewKernel_d/LA_eigen/LA.h
+++ b/NewKernel_d/include/CGAL/NewKernel_d/LA_eigen/LA.h
@@ -151,6 +151,15 @@ template<class NT_,class Dim_,class Max_dim_=Dim_> struct LA_eigen {
 		  m(3,0),m(3,1),m(3,2),m(3,3),m(3,4),m(3,5),
 		  m(4,0),m(4,1),m(4,2),m(4,3),m(4,4),m(4,5),
 		  m(5,0),m(5,1),m(5,2),m(5,3),m(5,4),m(5,5));
+	    case 7:
+	      return CGAL::determinant(
+		  m(0,0),m(0,1),m(0,2),m(0,3),m(0,4),m(0,5),m(0,6),
+		  m(1,0),m(1,1),m(1,2),m(1,3),m(1,4),m(1,5),m(1,6),
+		  m(2,0),m(2,1),m(2,2),m(2,3),m(2,4),m(2,5),m(2,6),
+		  m(3,0),m(3,1),m(3,2),m(3,3),m(3,4),m(3,5),m(3,6),
+		  m(4,0),m(4,1),m(4,2),m(4,3),m(4,4),m(4,5),m(4,6),
+		  m(5,0),m(5,1),m(5,2),m(5,3),m(5,4),m(5,5),m(5,6),
+		  m(6,0),m(6,1),m(6,2),m(6,3),m(6,4),m(6,5),m(6,6));
 	    default:
 #if _MSC_VER >= 1911 || __cpp_if_constexpr >= 201606L
 	      // Avoid compiling the LU decomposition for nothing