diff --git a/Arrangement_on_surface_2/include/CGAL/Arr_conic_traits_2.h b/Arrangement_on_surface_2/include/CGAL/Arr_conic_traits_2.h
index c9aec291440b..4f2071c4f736 100644
--- a/Arrangement_on_surface_2/include/CGAL/Arr_conic_traits_2.h
+++ b/Arrangement_on_surface_2/include/CGAL/Arr_conic_traits_2.h
@@ -3904,10 +3904,11 @@ class Arr_conic_traits_2 {
     auto u = cv.u();
     auto v = cv.v();
     auto w = cv.w();
-    Algebraic* ys_end = m_nt_traits->solve_quadratic_equation(t*t - four*r*s,
-                                                              two*t*u - four*r*v,
-                                                              u*u - four*r*w,
-                                                              ys);
+    Algebraic* ys_end = m_nt_traits->template
+      solve_quadratic_equation<Integer>(t*t - four*r*s,
+                                        two*t*u - four*r*v,
+                                        u*u - four*r*w,
+                                        ys);
     auto n = static_cast<int>(ys_end - ys);
 
     // Compute the x coordinates and construct the horizontal tangency points.
@@ -3915,7 +3916,7 @@ class Arr_conic_traits_2 {
       // Having computed y, x is the single solution to the quadratic equation
       // above, and since its discriminant is 0, x is simply given by:
       Algebraic x = -(m_nt_traits->convert(t)*ys[i] + m_nt_traits->convert(u)) /
-        m_nt_traits->convert(two*r);
+        m_nt_traits->convert(Integer(two*r));
       ps[i] = Point_2(x, ys[i]);
     }
 
diff --git a/Arrangement_on_surface_2/include/CGAL/Curved_kernel_via_analysis_2/gfx/Curve_renderer_traits.h b/Arrangement_on_surface_2/include/CGAL/Curved_kernel_via_analysis_2/gfx/Curve_renderer_traits.h
index 63e31f8ad504..7520f9cfad29 100644
--- a/Arrangement_on_surface_2/include/CGAL/Curved_kernel_via_analysis_2/gfx/Curve_renderer_traits.h
+++ b/Arrangement_on_surface_2/include/CGAL/Curved_kernel_via_analysis_2/gfx/Curve_renderer_traits.h
@@ -336,7 +336,7 @@ struct Curve_renderer_traits<CGAL::Interval_nt<true>, CORE::BigRat > :
 
 //! Specialization for \c CORE::BigFloat
 template <>
-struct Curve_renderer_traits<CORE::BigFloat, class CORE::BigRat>
+struct Curve_renderer_traits<CORE::BigFloat, CORE::BigRat>
          : public Curve_renderer_traits_base<CORE::BigFloat, CORE::BigInt,
                 CORE::BigRat> {
 
diff --git a/Envelope_3/include/CGAL/Env_sphere_traits_3.h b/Envelope_3/include/CGAL/Env_sphere_traits_3.h
index 3d272f81b29f..9c1eed123ff5 100644
--- a/Envelope_3/include/CGAL/Env_sphere_traits_3.h
+++ b/Envelope_3/include/CGAL/Env_sphere_traits_3.h
@@ -265,7 +265,7 @@ class Env_sphere_traits_3 : public ConicTraits_2 {
           if (n_ys == 0) return o; // no intersection
 
           // the x coordinate of the solution points
-          Algebraic xs = m / (2*a_diff);
+          Algebraic xs = m / (Rational(2)*a_diff);
 
           if (n_ys == 1) {
             // intersection is a point
@@ -340,7 +340,7 @@ class Env_sphere_traits_3 : public ConicTraits_2 {
           }
           if (n_xs == 1) {
             // intersection is a point
-            Point_2 inter_point(xs[0], (-2*a_diff*xs[0] + m)/(2*b_diff) );
+            Point_2 inter_point(xs[0], (-Rational(2)*a_diff*xs[0] + m)/(Rational(2)*b_diff) );
             *o++ = inter_point;
             return o;
           }
@@ -350,8 +350,8 @@ class Env_sphere_traits_3 : public ConicTraits_2 {
           // so we construct a COLLINEAR conic (with equation as in (1))
           // with 2 endpoints
           Algebraic ys[2];
-          ys[0] = (-2*a_diff*xs[0] + m)/(2*b_diff);
-          ys[1] = (-2*a_diff*xs[1] + m)/(2*b_diff);
+          ys[0] = (-Rational(2)*a_diff*xs[0] + m)/(Rational(2)*b_diff);
+          ys[1] = (-Rational(2)*a_diff*xs[1] + m)/(Rational(2)*b_diff);
 
           Alg_point_2 end1(xs[0], ys[0]);
           Alg_point_2 end2(xs[1], ys[1]);
@@ -977,10 +977,10 @@ class Env_sphere_traits_3 : public ConicTraits_2 {
     const Rational& u = cv.u();
     const Rational& v = cv.v();
     // const Rational& w = cv.w();      // unused
-    Algebraic m = -1 * (2*r*x0 + t*y0 + u);
-    Algebraic n = 2*s*y0 + t*x0 + v;
+    Algebraic m = -1 * (Rational(2)*r*x0 + t*y0 + u);
+    Algebraic n = Rational(2)*s*y0 + t*x0 + v;
     // line coefficients: A3, B3, C3
-    Algebraic A3 = -1*m, B3 = n, C3 = m*x0 - n*y0;
+    Algebraic A3 = -m, B3 = n, C3 = m*x0 - n*y0;
 
     // the tangences of the spheres (in point (x0,y0,z0)):
     Algebraic z0 = compute_envelope_z_in_point(cv_point, s1);
@@ -1077,8 +1077,8 @@ class Env_sphere_traits_3 : public ConicTraits_2 {
     Algebraic x_diff = x1 - a, y_diff = y1 - b;
     // the coefficients are:
     Algebraic A = 1;
-    Algebraic B = -2*c;
-    Algebraic C = x_diff*x_diff + y_diff*y_diff + c*c - sqr_r;
+    Algebraic B = -Rational(2)*c;
+    Algebraic C = x_diff*x_diff + y_diff*y_diff + Algebraic(c*c - sqr_r);
 
     Algebraic zs[2];
     Algebraic* zs_end;
diff --git a/Number_types/test/Number_types/ioformat.cpp b/Number_types/test/Number_types/ioformat.cpp
index 54eaa26bf227..457f1be15b11 100644
--- a/Number_types/test/Number_types/ioformat.cpp
+++ b/Number_types/test/Number_types/ioformat.cpp
@@ -106,7 +106,6 @@ int main()
 
   // CORE
 #ifdef CGAL_USE_CORE
-  static_assert(CGAL::Output_rep<CORE::BigRat>::is_specialized == true);
   //bug in io for CORE.
   test_it<CORE::BigInt>("CORE::BigInt");
   test_it<CORE::BigRat>("CORE::BigRat");