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 f46e81a4c32..ddbdc37b8ae 100644
--- a/NewKernel_d/include/CGAL/NewKernel_d/LA_eigen/LA.h
+++ b/NewKernel_d/include/CGAL/NewKernel_d/LA_eigen/LA.h
@@ -135,7 +135,12 @@ template<class NT_,class Dim_,class Max_dim_=Dim_> struct LA_eigen {
 
 	// m*a==b
 	template<class DV, class DM, class V>
-	static bool solve(DV&a, DM const&m, V const& b){
+	static void solve(DV&a, DM const&m, V const& b){
+		//a = m.colPivHouseholderQr().solve(b);
+		a = m.fullPivLu().solve(b);
+	}
+	template<class DV, class DM, class V>
+	static bool solve_and_check(DV&a, DM const&m, V const& b){
 		//a = m.colPivHouseholderQr().solve(b);
 		a = m.fullPivLu().solve(b);
 		return b.isApprox(m*a);
diff --git a/NewKernel_d/include/CGAL/NewKernel_d/function_objects_cartesian.h b/NewKernel_d/include/CGAL/NewKernel_d/function_objects_cartesian.h
index e3acecc915b..aa073d8af29 100644
--- a/NewKernel_d/include/CGAL/NewKernel_d/function_objects_cartesian.h
+++ b/NewKernel_d/include/CGAL/NewKernel_d/function_objects_cartesian.h
@@ -425,7 +425,11 @@ template<class R_> struct Contained_in_simplex : private Store_kernel<R_> {
 		  }
 		  m(d,i)=1;
 		}
-		if (!LA::solve(a,CGAL_MOVE(m),CGAL_MOVE(b))) return false;
+		// If the simplex has full dimension, there must be a solution, only the signs need to be checked.
+		if (n == d+1)
+		  LA::solve(a,CGAL_MOVE(m),CGAL_MOVE(b));
+		else if (!LA::solve_and_check(a,CGAL_MOVE(m),CGAL_MOVE(b)))
+		  return false;
 		for(int i=0;i<n;++i){
 		  if (a[i]<0) return false;
 		}
@@ -683,7 +687,6 @@ template <class R_> struct Construct_circumcenter : Store_kernel<R_> {
       typedef typename LAd::Vector Vec;
       typename Get_functor<R_, Scalar_product_tag>::type sp(this->kernel());
       int k=static_cast<int>(std::distance(f,e));
-      int d=pd(p0);
       Matrix m(k,k);
       Vec b(k);
       Vec l(k);
diff --git a/Stream_support/include/CGAL/IO/io.h b/Stream_support/include/CGAL/IO/io.h
index 26e2ac5e00c..9f7be26865b 100644
--- a/Stream_support/include/CGAL/IO/io.h
+++ b/Stream_support/include/CGAL/IO/io.h
@@ -35,6 +35,7 @@
 #include <CGAL/tags.h>
 #include <CGAL/IO/io_tags.h>
 #include <CGAL/IO/Color.h>
+#include <CGAL/assertions.h>
 
 
 namespace CGAL {