Rename the following functions:

det2x2_by_formula
  det3x3_by_formula
  det4x4_by_formula
  det5x5_by_formula
  det6x6_by_formula
to:
  determinant

How cute...  a name independent of the dimension, and even readable !

Alpha_shapes_2/include/CGAL/constructions/squared_radius_smallest_orthogonalcircle_ftC2.h

@@ -44,11 +44,11 @@ squared_radius_orthogonalcircleC2(
   FT dpp = CGAL_NTS square(dpx)+CGAL_NTS square(dpy)-pw+rw;
   FT dqq = CGAL_NTS square(dqx)+CGAL_NTS square(dqy)-qw+rw;
 
-  FT det0 = det2x2_by_formula(dpx, dpy, dqx, dqy);
+  FT det0 = determinant(dpx, dpy, dqx, dqy);
   
-  FT det1 = det2x2_by_formula(dpp, dpy, dqq, dqy);
+  FT det1 = determinant(dpp, dpy, dqq, dqy);
 
-  FT det2 = det2x2_by_formula(dpx, dpp, dqx, dqq);
+  FT det2 = determinant(dpx, dpp, dqx, dqq);
 
   return 
     (CGAL_NTS square(det1)+CGAL_NTS square(det2))/

Apollonius_graph_2/include/CGAL/Apollonius_graph_2/Constructions_ftC2.h

@@ -65,9 +65,9 @@ w_plane_tangent_line_2(const FT &x1, const FT &y1, const FT &w1,
   FT Dv = v2 - v3;
   FT Dr = r2 - r3;
 
-  FT Duv = det2x2_by_formula(u2, v2, u3, v3);
+  FT Duv = determinant(u2, v2, u3, v3);
-  FT Dur = det2x2_by_formula(u2, r2, u3, r3);
+  FT Dur = determinant(u2, r2, u3, r3);
-  FT Dvr = det2x2_by_formula(v2, r2, v3, r3);
+  FT Dvr = determinant(v2, r2, v3, r3);
 
   FT D1 = CGAL::square(Du) + CGAL::square(Dv);
   FT D1inv = FT(1) / D1;
@@ -162,9 +162,9 @@ ad_left_bitangent_lineC2(const FT &x1, const FT &y1, const FT &w1,
   FT dy = y1 - y2;
   FT dw = w1 - w2;
 
-  FT dxw = det2x2_by_formula(x1, w1, x2, w2);
+  FT dxw = determinant(x1, w1, x2, w2);
-  FT dyw = det2x2_by_formula(y1, w1, y2, w2);
+  FT dyw = determinant(y1, w1, y2, w2);
-  FT dxy = det2x2_by_formula(x1, y1, x2, y2);
+  FT dxy = determinant(x1, y1, x2, y2);
 
   FT D1 = CGAL::square(dx) + CGAL::square(dy);
   FT invD1 = FT(1) / D1;

Apollonius_graph_2/include/CGAL/Apollonius_graph_2/Incircle8_C2.h

@@ -101,13 +101,13 @@ public:
     FT pk = CGAL::square(xk) + CGAL::square(yk) - CGAL::square(rk);
     FT pl = CGAL::square(xl) + CGAL::square(yl) - CGAL::square(rl);
 
-    FT Exp = det2x2_by_formula(xj, pj, xk, pk);
+    FT Exp = determinant(xj, pj, xk, pk);
-    FT Eyp = det2x2_by_formula(yj, pj, yk, pk);
+    FT Eyp = determinant(yj, pj, yk, pk);
-    FT Erp = det2x2_by_formula(rj, pj, rk, pk);
+    FT Erp = determinant(rj, pj, rk, pk);
 
-    FT Exy = det2x2_by_formula(xj, yj, xk, yk);
+    FT Exy = determinant(xj, yj, xk, yk);
-    FT Exr = det2x2_by_formula(xj, rj, xk, rk);
+    FT Exr = determinant(xj, rj, xk, rk);
-    FT Eyr = det2x2_by_formula(yj, rj, yk, rk);
+    FT Eyr = determinant(yj, rj, yk, rk);
 
     FT Exyp = xl * Eyp - yl * Exp + pl * Exy;
     FT Exrp = xl * Erp - rl * Exp + pl * Exr;

Apollonius_graph_2/include/CGAL/Apollonius_graph_2/Infinite_edge_test_C2.h

@@ -155,7 +155,7 @@ public:
 	    const FT& D, const FT& P) const
     {
       FT sigma = a * A + b * B;
-      FT delta = det2x2_by_formula(a, b, A, B);
+      FT delta = determinant(a, b, A, B);
 
       Sign sign_sigma = CGAL::sign(sigma);
       Sign sign_delta = CGAL::sign(delta);

Apollonius_graph_2/include/CGAL/Apollonius_graph_2/Orientation8_C2.h

@@ -118,15 +118,15 @@ public:
     FT pj = CGAL::square(xj) + CGAL::square(yj) - CGAL::square(rj);
     FT pk = CGAL::square(xk) + CGAL::square(yk) - CGAL::square(rk);
 
-    FT Exp = det2x2_by_formula(xj, pj, xk, pk);
+    FT Exp = determinant(xj, pj, xk, pk);
-    FT Eyp = det2x2_by_formula(yj, pj, yk, pk);
+    FT Eyp = determinant(yj, pj, yk, pk);
-    FT Erp = det2x2_by_formula(rj, pj, rk, pk);
+    FT Erp = determinant(rj, pj, rk, pk);
 
-    FT Exy = det2x2_by_formula(xj, yj, xk, yk);
+    FT Exy = determinant(xj, yj, xk, yk);
-    FT Exr = det2x2_by_formula(xj, rj, xk, rk);
+    FT Exr = determinant(xj, rj, xk, rk);
-    FT Eyr = det2x2_by_formula(yj, rj, yk, rk);
+    FT Eyr = determinant(yj, rj, yk, rk);
 
-    FT Exy2 = 2 * det2x2_by_formula(xl, yl, xm, ym);
+    FT Exy2 = 2 * determinant(xl, yl, xm, ym);
 
     FT A = (Exp * Exr + Eyp * Eyr) * Exy2 + (Eyp * dx - Exp * dy) * Erp;
     FT B = Exy * Exy2 - Exp * dx - Eyp * dy;
@@ -194,13 +194,13 @@ public:
     pj = nj - CGAL::square(rj);
     pk = nk - CGAL::square(rk);
 
-    Exp = det2x2_by_formula(xj, pj, xk, pk);
+    Exp = determinant(xj, pj, xk, pk);
-    Eyp = det2x2_by_formula(yj, pj, yk, pk);
+    Eyp = determinant(yj, pj, yk, pk);
-    Erp = det2x2_by_formula(rj, pj, rk, pk);
+    Erp = determinant(rj, pj, rk, pk);
 
-    Exy = det2x2_by_formula(xj, yj, xk, yk);
+    Exy = determinant(xj, yj, xk, yk);
-    Exr = det2x2_by_formula(xj, rj, xk, rk);
+    Exr = determinant(xj, rj, xk, rk);
-    Eyr = det2x2_by_formula(yj, rj, yk, rk);
+    Eyr = determinant(yj, rj, yk, rk);
 
     A1 = Exp * Exr + Eyp * Eyr;
 
@@ -284,7 +284,7 @@ private:
     FT dx = xl - xm;
     FT dy = yl - ym;
 
-    FT Exy2 = 2 * det2x2_by_formula(xl, yl, xm, ym);
+    FT Exy2 = 2 * determinant(xl, yl, xm, ym);
 
     FT A = A1 * Exy2 + (Eyp * dx - Exp * dy) * Erp;
     FT B = Exy * Exy2 - Exp * dx - Eyp * dy;

Apollonius_graph_2/include/CGAL/Apollonius_graph_2/Orientation_2.h

@@ -62,7 +62,7 @@ private:
     FT b = vc.b1() + vc.b2() * CGAL::sqrt(vc.delta());
     FT det1 = a * (p2.y() - p1.y()) - b * (p2.x() - p1.x());
     FT c = vc.c1() + vc.c2() * CGAL::sqrt(vc.delta());
-    FT det2 = det2x2_by_formula(p1.x() - sp1.x(), p1.y() - sp1.y(),
+    FT det2 = determinant(p1.x() - sp1.x(), p1.y() - sp1.y(),
 				p2.x() - sp1.x(), p2.y() - sp1.y());
     return CGAL::sign(det1 + FT(2) * c * det2);
   }
@@ -73,7 +73,7 @@ private:
   {
     FT dx = p2.x() - p1.x();
     FT dy = p2.y() - p1.y();
-    FT det1 = det2x2_by_formula(p1.x() - sp1.x(), p1.y() - sp1.y(),
+    FT det1 = determinant(p1.x() - sp1.x(), p1.y() - sp1.y(),
 				p2.x() - sp1.x(), p2.y() - sp1.y());
     FT A = vc.a1() * dy - vc.b1() * dx + FT(2) * vc.c1() * det1;
     FT B = vc.a2() * dy - vc.b2() * dx + FT(2) * vc.c2() * det1;

Apollonius_graph_2/include/CGAL/Apollonius_graph_2/Predicate_constructions_C2.h

@@ -100,12 +100,12 @@ public:
   Voronoi_radius_2(const Inverted_weighted_point& u1,
 		   const Inverted_weighted_point& u2)
     {
-      FT dxp = det2x2_by_formula(u1.x(), u1.p(), u2.x(), u2.p());
+      FT dxp = determinant(u1.x(), u1.p(), u2.x(), u2.p());
-      FT dyp = det2x2_by_formula(u1.y(), u1.p(), u2.y(), u2.p());
+      FT dyp = determinant(u1.y(), u1.p(), u2.y(), u2.p());
-      FT dwp = det2x2_by_formula(u1.weight(), u1.p(), u2.weight(), u2.p());
+      FT dwp = determinant(u1.weight(), u1.p(), u2.weight(), u2.p());
-      FT dxy = det2x2_by_formula(u1.x(), u1.y(), u2.x(), u2.y());
+      FT dxy = determinant(u1.x(), u1.y(), u2.x(), u2.y());
-      FT dxw = det2x2_by_formula(u1.x(), u1.weight(), u2.x(), u2.weight());
+      FT dxw = determinant(u1.x(), u1.weight(), u2.x(), u2.weight());
-      FT dyw = det2x2_by_formula(u1.y(), u1.weight(), u2.y(), u2.weight());
+      FT dyw = determinant(u1.y(), u1.weight(), u2.y(), u2.weight());
 
       _a = CGAL::square(dxp) + CGAL::square(dyp);
       _b = dxp * dxw + dyp * dyw;
@@ -193,9 +193,9 @@ public:
       FT dx = p1.x() - p2.x();
       FT dy = p1.y() - p2.y();
       FT dw = p1.weight() - p2.weight();
-      FT dxy = det2x2_by_formula(p1.x(), p1.y(), p2.x(), p2.y());
+      FT dxy = determinant(p1.x(), p1.y(), p2.x(), p2.y());
-      FT dxw = det2x2_by_formula(p1.x(), p1.weight(), p2.x(), p2.weight());
+      FT dxw = determinant(p1.x(), p1.weight(), p2.x(), p2.weight());
-      FT dyw = det2x2_by_formula(p1.y(), p1.weight(), p2.y(), p2.weight());
+      FT dyw = determinant(p1.y(), p1.weight(), p2.y(), p2.weight());
 
       store(dx, dy, dw, dxy, dxw, dyw);
     }
@@ -204,12 +204,12 @@ public:
   Bitangent_line_2(const Inverted_weighted_point& u1,
 		   const Inverted_weighted_point& u2)
     {
-      FT dxp = det2x2_by_formula(u1.x(), u1.p(), u2.x(), u2.p());
+      FT dxp = determinant(u1.x(), u1.p(), u2.x(), u2.p());
-      FT dyp = det2x2_by_formula(u1.y(), u1.p(), u2.y(), u2.p());
+      FT dyp = determinant(u1.y(), u1.p(), u2.y(), u2.p());
-      FT dwp = det2x2_by_formula(u1.weight(), u1.p(), u2.weight(), u2.p());
+      FT dwp = determinant(u1.weight(), u1.p(), u2.weight(), u2.p());
-      FT dxy = det2x2_by_formula(u1.x(), u1.y(), u2.x(), u2.y());
+      FT dxy = determinant(u1.x(), u1.y(), u2.x(), u2.y());
-      FT dxw = det2x2_by_formula(u1.x(), u1.weight(), u2.x(), u2.weight());
+      FT dxw = determinant(u1.x(), u1.weight(), u2.x(), u2.weight());
-      FT dyw = det2x2_by_formula(u1.y(), u1.weight(), u2.y(), u2.weight());
+      FT dyw = determinant(u1.y(), u1.weight(), u2.y(), u2.weight());
 
       store(dxp, dyp, dwp, dxy, dxw, dyw);
     }
@@ -315,13 +315,13 @@ public:
 		const Inverted_weighted_point& u2,
 		const Inverted_weighted_point& u3) const
     {
-      FT dx1 = det2x2_by_formula(u2.x(), u2.p(), u1.x(), u1.p());
+      FT dx1 = determinant(u2.x(), u2.p(), u1.x(), u1.p());
-      FT dy1 = det2x2_by_formula(u2.y(), u2.p(), u1.y(), u1.p());
+      FT dy1 = determinant(u2.y(), u2.p(), u1.y(), u1.p());
-      FT dw1 = det2x2_by_formula(u2.weight(), u2.p(), u1.weight(), u1.p());
+      FT dw1 = determinant(u2.weight(), u2.p(), u1.weight(), u1.p());
 
-      FT dx3 = det2x2_by_formula(u3.x(), u3.p(), u2.x(), u2.p());
+      FT dx3 = determinant(u3.x(), u3.p(), u2.x(), u2.p());
-      FT dy3 = det2x2_by_formula(u3.y(), u3.p(), u2.y(), u2.p());
+      FT dy3 = determinant(u3.y(), u3.p(), u2.y(), u2.p());
-      FT dw3 = det2x2_by_formula(u3.weight(), u3.p(), u2.weight(), u2.p());
+      FT dw3 = determinant(u3.weight(), u3.p(), u2.weight(), u2.p());
 
       FT u2Pv2 = CGAL::square(u2.x()) + CGAL::square(u2.y());
       FT u2Mv2 = CGAL::square(u2.x()) - CGAL::square(u2.y());

Apollonius_graph_2/include/CGAL/Apollonius_graph_2/new_traits/Conflict_2.h

@@ -58,15 +58,15 @@ protected:
                               const Inverted_weighted_point &p3, int i) const
     {
         Sign s =  CGAL::sign(
-		CGAL::square(det3x3_by_formula<RT>(
+		CGAL::square(determinant<RT>(
                         p1.p(), p1.weight(), p1.y(),
                         p2.p(), p2.weight(), p2.y(),
                         p3.p(), p3.weight(), p3.y()))
-                + CGAL::square(det3x3_by_formula<RT>(
+                + CGAL::square(determinant<RT>(
                         p1.p(), p1.x(), p1.weight(),
                         p2.p(), p2.x(), p2.weight(),
                         p3.p(), p3.x(), p3.weight()))
-                - CGAL::square(det3x3_by_formula<RT>(
+                - CGAL::square(determinant<RT>(
                         p1.p(), p1.x(), p1.y(),
                         p2.p(), p2.x(), p2.y(),
                         p3.p(), p3.x(), p3.y())));
@@ -91,17 +91,17 @@ protected:
         CGAL_assertion(i == -1 || i == 1 || i == 2 || i == 3);
 
         Sign s =  -CGAL::sign(
-                  det2x2_by_formula<RT>(
+                  determinant<RT>(
                       p1.p(), p1.x(), 
                       p2.p(), p2.x()) 
-                  * det3x3_by_formula<RT>(
+                  * determinant<RT>(
                       p1.p(), p1.weight(), p1.x(),
                       p2.p(), p2.weight(), p2.x(),
                       p3.p(), p3.weight(), p3.x())
-                  + det2x2_by_formula<RT>(
+                  + determinant<RT>(
                       p1.p(), p1.y(),
                       p2.p(), p2.y())
-                  * det3x3_by_formula<RT>(
+                  * determinant<RT>(
                       p1.p(), p1.weight(), p1.y(),
                       p2.p(), p2.weight(), p2.y(),
                       p3.p(), p3.weight(), p3.y()));

Apollonius_graph_2/include/CGAL/Hyperbola_2.h

@@ -159,7 +159,7 @@ protected:
   bool right(const Point_2& p) const
   {
     return
-      CGAL::is_negative( det3x3_by_formula<FT>(f1.x(), f1.y(), 1,
+      CGAL::is_negative( determinant<FT>(f1.x(), f1.y(), 1,
 					       f2.x(), f2.y(), 1,
 					       p.x(),   p.y(), 1) );
   }

Apollonius_graph_2/include/CGAL/Parabola_2.h

@@ -191,7 +191,7 @@ protected:
   bool right(const Point_2& p) const
   {
     return
-      CGAL::is_positive( det3x3_by_formula<FT>(c.x(), c.y(), FT(1),
+      CGAL::is_positive( determinant<FT>(c.x(), c.y(), FT(1),
 					       o.x(), o.y(), FT(1),
 					       p.x(), p.y(), FT(1)) );
   }

Cartesian_kernel/include/CGAL/Cartesian/Aff_transformation_rep_3.h

@@ -206,22 +206,22 @@ typename Aff_transformation_repC3<R>::Aff_transformation_3
 Aff_transformation_repC3<R>::inverse() const // FIXME : construction
 {
   return Aff_transformation_3(
-      det2x2_by_formula( t22, t23, t32, t33),         // i 11
+      determinant( t22, t23, t32, t33),         // i 11
-     -det2x2_by_formula( t12, t13, t32, t33),         // i 12
+     -determinant( t12, t13, t32, t33),         // i 12
-      det2x2_by_formula( t12, t13, t22, t23),         // i 13
+      determinant( t12, t13, t22, t23),         // i 13
-     -det3x3_by_formula( t12, t13, t14, t22, t23, t24, t32, t33, t34 ),
+     -determinant( t12, t13, t14, t22, t23, t24, t32, t33, t34 ),
 
-     -det2x2_by_formula( t21, t23, t31, t33),         // i 21 
+     -determinant( t21, t23, t31, t33),         // i 21 
-      det2x2_by_formula( t11, t13, t31, t33),         // i 22
+      determinant( t11, t13, t31, t33),         // i 22
-     -det2x2_by_formula( t11, t13, t21, t23),         // i 23
+     -determinant( t11, t13, t21, t23),         // i 23
-      det3x3_by_formula( t11, t13, t14, t21, t23, t24, t31, t33, t34 ),
+      determinant( t11, t13, t14, t21, t23, t24, t31, t33, t34 ),
 
-      det2x2_by_formula( t21, t22, t31, t32),         // i 31
+      determinant( t21, t22, t31, t32),         // i 31
-     -det2x2_by_formula( t11, t12, t31, t32),         // i 32
+     -determinant( t11, t12, t31, t32),         // i 32
-      det2x2_by_formula( t11, t12, t21, t22),         // i 33
+      determinant( t11, t12, t21, t22),         // i 33
-     -det3x3_by_formula( t11, t12, t14, t21, t22, t24, t31, t32, t34 ),
+     -determinant( t11, t12, t14, t21, t22, t24, t31, t32, t34 ),
 
-      det3x3_by_formula( t11, t12, t13, t21, t22, t23, t31, t32, t33 ));
+      determinant( t11, t12, t13, t21, t22, t23, t31, t32, t33 ));
 }
 
 template < class R >

Cartesian_kernel/include/CGAL/Cartesian/function_objects.h

@@ -769,7 +769,7 @@ namespace CartesianKernelFunctors {
       FT v1y = q.y() - p.y();
       FT v2x = r.x() - p.x();
       FT v2y = r.y() - p.y();
-      return det2x2_by_formula(v1x, v1y, v2x, v2y)/2;
+      return determinant(v1x, v1y, v2x, v2y)/2;
     }
 
     result_type
@@ -793,7 +793,7 @@ namespace CartesianKernelFunctors {
     result_type
     operator()(const Vector_2& v, const Vector_2& w) const
     {
-	return det2x2_by_formula(v.x(), v.y(), w.x(), w.y());
+	return determinant(v.x(), v.y(), w.x(), w.y());
     }
   };
 
@@ -809,7 +809,7 @@ namespace CartesianKernelFunctors {
     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(),
+	return determinant(v.x(), v.y(), v.z(),
                                  w.x(), w.y(), w.z(),
                                  t.x(), t.y(), t.z());
     }
@@ -984,7 +984,7 @@ namespace CartesianKernelFunctors {
     operator()(const Point_3& p0, const Point_3& p1,
 	       const Point_3& p2, const Point_3& p3) const
     {
-      return det3x3_by_formula<FT>(p1.x()-p0.x(), p1.y()-p0.y(), p1.z()-p0.z(),
+      return determinant<FT>(p1.x()-p0.x(), p1.y()-p0.y(), p1.z()-p0.z(),
                                    p2.x()-p0.x(), p2.y()-p0.y(), p2.z()-p0.z(),
                                    p3.x()-p0.x(), p3.y()-p0.y(), p3.z()-p0.z())/6;
     }
@@ -1846,24 +1846,24 @@ namespace CartesianKernelFunctors {
 
       // The following determinants can be developped and simplified.
       //
-      // FT num_x = det3x3_by_formula(psy,psz,ps2,
+      // FT num_x = determinant(psy,psz,ps2,
       //                              qsy,qsz,qs2,
       //                              rsy,rsz,0);
-      // FT num_y = det3x3_by_formula(psx,psz,ps2,
+      // FT num_y = determinant(psx,psz,ps2,
       //                              qsx,qsz,qs2,
       //                              rsx,rsz,0);
-      // FT num_z = det3x3_by_formula(psx,psy,ps2,
+      // FT num_z = determinant(psx,psy,ps2,
       //                              qsx,qsy,qs2,
       //                              rsx,rsy,0);
 
-      FT num_x = ps2 * det2x2_by_formula(qsy,qsz,rsy,rsz)
+      FT num_x = ps2 * determinant(qsy,qsz,rsy,rsz)
-	       - qs2 * det2x2_by_formula(psy,psz,rsy,rsz);
+	       - qs2 * determinant(psy,psz,rsy,rsz);
-      FT num_y = ps2 * det2x2_by_formula(qsx,qsz,rsx,rsz)
+      FT num_y = ps2 * determinant(qsx,qsz,rsx,rsz)
-	       - qs2 * det2x2_by_formula(psx,psz,rsx,rsz);
+	       - qs2 * determinant(psx,psz,rsx,rsz);
-      FT num_z = ps2 * det2x2_by_formula(qsx,qsy,rsx,rsy)
+      FT num_z = ps2 * determinant(qsx,qsy,rsx,rsy)
-	       - qs2 * det2x2_by_formula(psx,psy,rsx,rsy);
+	       - qs2 * determinant(psx,psy,rsx,rsy);
 
-      FT den   = det3x3_by_formula(psx,psy,psz,
+      FT den   = determinant(psx,psy,psz,
                                    qsx,qsy,qsz,
                                    rsx,rsy,rsz);
 
@@ -1901,16 +1901,16 @@ namespace CartesianKernelFunctors {
       FT spz = s.z()-p.z();
       FT sp2 = CGAL_NTS square(spx) + CGAL_NTS square(spy) + CGAL_NTS square(spz);
 
-      FT num_x = det3x3_by_formula(qpy,qpz,qp2,
+      FT num_x = determinant(qpy,qpz,qp2,
                                    rpy,rpz,rp2,
                                    spy,spz,sp2);
-      FT num_y = det3x3_by_formula(qpx,qpz,qp2,
+      FT num_y = determinant(qpx,qpz,qp2,
                                    rpx,rpz,rp2,
                                    spx,spz,sp2);
-      FT num_z = det3x3_by_formula(qpx,qpy,qp2,
+      FT num_z = determinant(qpx,qpy,qp2,
                                    rpx,rpy,rp2,
                                    spx,spy,sp2);
-      FT den   = det3x3_by_formula(qpx,qpy,qpz,
+      FT den   = determinant(qpx,qpy,qpz,
                                    rpx,rpy,rpz,
                                    spx,spy,spz);
       CGAL_kernel_assertion( ! CGAL_NTS is_zero(den) );
@@ -2149,24 +2149,24 @@ namespace CartesianKernelFunctors {
 
       // The following determinants can be developped and simplified.
       //
-      // FT num_x = det3x3_by_formula(psy,psz,ps2,
+      // FT num_x = determinant(psy,psz,ps2,
       //                              qsy,qsz,qs2,
       //                              rsy,rsz,0);
-      // FT num_y = det3x3_by_formula(psx,psz,ps2,
+      // FT num_y = determinant(psx,psz,ps2,
       //                              qsx,qsz,qs2,
       //                              rsx,rsz,0);
-      // FT num_z = det3x3_by_formula(psx,psy,ps2,
+      // FT num_z = determinant(psx,psy,ps2,
       //                              qsx,qsy,qs2,
       //                              rsx,rsy,0);
 
-      FT num_x = ps2 * det2x2_by_formula(qsy,qsz,rsy,rsz)
+      FT num_x = ps2 * determinant(qsy,qsz,rsy,rsz)
-	       - qs2 * det2x2_by_formula(psy,psz,rsy,rsz);
+	       - qs2 * determinant(psy,psz,rsy,rsz);
-      FT num_y = ps2 * det2x2_by_formula(qsx,qsz,rsx,rsz)
+      FT num_y = ps2 * determinant(qsx,qsz,rsx,rsz)
-	       - qs2 * det2x2_by_formula(psx,psz,rsx,rsz);
+	       - qs2 * determinant(psx,psz,rsx,rsz);
-      FT num_z = ps2 * det2x2_by_formula(qsx,qsy,rsx,rsy)
+      FT num_z = ps2 * determinant(qsx,qsy,rsx,rsy)
-	       - qs2 * det2x2_by_formula(psx,psy,rsx,rsy);
+	       - qs2 * determinant(psx,psy,rsx,rsy);
 
-      FT den   = det3x3_by_formula(psx,psy,psz,
+      FT den   = determinant(psx,psy,psz,
                                    qsx,qsy,qsz,
                                    rsx,rsy,rsz);
 

Cartesian_kernel/include/CGAL/constructions/kernel_ftC2.h

@@ -53,7 +53,7 @@ circumcenter_translateC2(const FT &dqx, const FT &dqy,
   // What we do is intersect the bisectors.
   FT r2 = CGAL_NTS square(drx) + CGAL_NTS square(dry);
   FT q2 = CGAL_NTS square(dqx) + CGAL_NTS square(dqy);
-  FT den = 2 * det2x2_by_formula(dqx, dqy, drx, dry);
+  FT den = 2 * determinant(dqx, dqy, drx, dry);
 
   // The 3 points aren't collinear.
   // Hopefully, this is already checked at the upper level.
@@ -61,8 +61,8 @@ circumcenter_translateC2(const FT &dqx, const FT &dqy,
 
   // One possible optimization here is to precompute 1/den, to avoid one
   // division.  However, we loose precision, and it's maybe not worth it (?).
-  dcx =   det2x2_by_formula (dry, dqy, r2, q2) / den;
+  dcx =   determinant (dry, dqy, r2, q2) / den;
-  dcy = - det2x2_by_formula (drx, dqx, r2, q2) / den;
+  dcy = - determinant (drx, dqx, r2, q2) / den;
 }
 
 template < class FT >
@@ -338,7 +338,7 @@ scaled_distance_to_lineC2( const FT &px, const FT &py,
                            const FT &qx, const FT &qy,
                            const FT &rx, const FT &ry)
 {
-  return det2x2_by_formula<FT>(px-rx, py-ry, qx-rx, qy-ry);
+  return determinant<FT>(px-rx, py-ry, qx-rx, qy-ry);
 }
 
 CGAL_END_NAMESPACE

Cartesian_kernel/include/CGAL/constructions/kernel_ftC3.h

@@ -87,16 +87,16 @@ squared_radiusC3(const FT &px, const FT &py, const FT &pz,
   FT spz = sz-pz;
   FT sp2 = CGAL_NTS square(spx) + CGAL_NTS square(spy) + CGAL_NTS square(spz);
 
-  FT num_x = det3x3_by_formula(qpy,qpz,qp2,
+  FT num_x = determinant(qpy,qpz,qp2,
                                rpy,rpz,rp2,
                                spy,spz,sp2);
-  FT num_y = det3x3_by_formula(qpx,qpz,qp2,
+  FT num_y = determinant(qpx,qpz,qp2,
                                rpx,rpz,rp2,
                                spx,spz,sp2);
-  FT num_z = det3x3_by_formula(qpx,qpy,qp2,
+  FT num_z = determinant(qpx,qpy,qp2,
                                rpx,rpy,rp2,
                                spx,spy,sp2);
-  FT den   = det3x3_by_formula(qpx,qpy,qpz,
+  FT den   = determinant(qpx,qpy,qpz,
                                rpx,rpy,rpz,
                                spx,spy,spz);
   CGAL_kernel_assertion( ! CGAL_NTS is_zero(den) );
@@ -125,14 +125,14 @@ squared_radiusC3(const FT &px, const FT &py, const FT &pz,
   FT rsy = psz*qsx-psx*qsz;
   FT rsz = psx*qsy-psy*qsx;
 
-  FT num_x = ps2 * det2x2_by_formula(qsy,qsz,rsy,rsz)
+  FT num_x = ps2 * determinant(qsy,qsz,rsy,rsz)
-	   - qs2 * det2x2_by_formula(psy,psz,rsy,rsz);
+	   - qs2 * determinant(psy,psz,rsy,rsz);
-  FT num_y = ps2 * det2x2_by_formula(qsx,qsz,rsx,rsz)
+  FT num_y = ps2 * determinant(qsx,qsz,rsx,rsz)
-	   - qs2 * det2x2_by_formula(psx,psz,rsx,rsz);
+	   - qs2 * determinant(psx,psz,rsx,rsz);
-  FT num_z = ps2 * det2x2_by_formula(qsx,qsy,rsx,rsy)
+  FT num_z = ps2 * determinant(qsx,qsy,rsx,rsy)
-	   - qs2 * det2x2_by_formula(psx,psy,rsx,rsy);
+	   - qs2 * determinant(psx,psy,rsx,rsy);
 
-  FT den   = det3x3_by_formula(psx,psy,psz,
+  FT den   = determinant(psx,psy,psz,
                                qsx,qsy,qsz,
                                rsx,rsy,rsz);
 
@@ -254,7 +254,7 @@ scaled_distance_to_planeC3(
      const FT &prx, const FT &pry, const FT &prz,
      const FT &px,  const FT &py,  const FT &pz)
 {
-  return det3x3_by_formula(ppx-px,ppy-py,ppz-pz,
+  return determinant(ppx-px,ppy-py,ppz-pz,
                            pqx-px,pqy-py,pqz-pz,
                            prx-px,pry-py,prz-pz);
 }

Cartesian_kernel/include/CGAL/predicates/kernel_ftC2.h

@@ -75,8 +75,8 @@ compare_xC2(const FT &px,
             const FT &ha, const FT &hb, const FT &hc)
 {
   // The abscissa of the intersection point is num/den.
-  FT num = det2x2_by_formula( lb, lc, hb, hc);
+  FT num = determinant( lb, lc, hb, hc);
-  FT den = det2x2_by_formula( la, lb, ha, hb);
+  FT den = determinant( la, lb, ha, hb);
   typename Sgn<FT>::result_type s = CGAL_NTS sign(den);
   CGAL_kernel_assertion( s != ZERO );
   return s * CGAL_NTS compare(px * den, num);
@@ -90,20 +90,20 @@ compare_xC2(const FT &la, const FT &lb, const FT &lc,
             const FT &h2a, const FT &h2b, const FT &h2c)
 {
   /*
-  FT num1 = det2x2_by_formula( lb, lc, h1b, h1c);
+  FT num1 = determinant( lb, lc, h1b, h1c);
-  FT den1 = det2x2_by_formula( la, lb, h1a, h1b);
+  FT den1 = determinant( la, lb, h1a, h1b);
-  FT num2 = det2x2_by_formula( lb, lc, h2b, h2c);
+  FT num2 = determinant( lb, lc, h2b, h2c);
-  FT den2 = det2x2_by_formula( la, lb, h2a, h2b);
+  FT den2 = determinant( la, lb, h2a, h2b);
   Sign s = Sign (CGAL_NTS sign(den1) * CGAL_NTS sign(den2));
   CGAL_kernel_assertion( s != ZERO );
   return s * sign_of_determinant(num1, num2, den1, den2);
   */
-  FT num1 = det2x2_by_formula( la, lc, h1a, h1c);
+  FT num1 = determinant( la, lc, h1a, h1c);
-  FT num2 = det2x2_by_formula( la, lc, h2a, h2c);
+  FT num2 = determinant( la, lc, h2a, h2c);
-  FT num  = det2x2_by_formula(h1a,h1c,h2a,h2c)*lb
+  FT num  = determinant(h1a,h1c,h2a,h2c)*lb
-            + det2x2_by_formula(num1,num2,h1b,h2b);
+            + determinant(num1,num2,h1b,h2b);
-  FT den1 = det2x2_by_formula( la, lb, h1a, h1b);
+  FT den1 = determinant( la, lb, h1a, h1b);
-  FT den2 = det2x2_by_formula( la, lb, h2a, h2b);
+  FT den2 = determinant( la, lb, h2a, h2b);
   return CGAL_NTS sign(lb) *
          CGAL_NTS sign(num) *
          CGAL_NTS sign(den1) *
@@ -118,10 +118,10 @@ compare_xC2(const FT &l1a, const FT &l1b, const FT &l1c,
             const FT &l2a, const FT &l2b, const FT &l2c,
             const FT &h2a, const FT &h2b, const FT &h2c)
 {
-  FT num1 = det2x2_by_formula( l1b, l1c, h1b, h1c);
+  FT num1 = determinant( l1b, l1c, h1b, h1c);
-  FT den1 = det2x2_by_formula( l1a, l1b, h1a, h1b);
+  FT den1 = determinant( l1a, l1b, h1a, h1b);
-  FT num2 = det2x2_by_formula( l2b, l2c, h2b, h2c);
+  FT num2 = determinant( l2b, l2c, h2b, h2c);
-  FT den2 = det2x2_by_formula( l2a, l2b, h2a, h2b);
+  FT den2 = determinant( l2a, l2b, h2a, h2b);
   typename Sgn<FT>::result_type s = CGAL_NTS sign(den1) * CGAL_NTS sign(den2);
   CGAL_kernel_assertion( s != ZERO );
   return s * sign_of_determinant(num1, num2, den1, den2);
@@ -175,8 +175,8 @@ compare_y_at_xC2(const FT &l1a, const FT &l1b, const FT &l1c,
                  const FT &h2a, const FT &h2b, const FT &h2c)
 {
   // The abscissa of the intersection point is num/den.
-  FT num = det2x2_by_formula( l1b, l1c, l2b, l2c);
+  FT num = determinant( l1b, l1c, l2b, l2c);
-  FT den = det2x2_by_formula( l1a, l1b, l2a, l2b);
+  FT den = determinant( l1a, l1b, l2a, l2b);
   typename Sgn<FT>::result_type s = CGAL_NTS sign(h1b) *
                                     CGAL_NTS sign(h2b) *
                                     CGAL_NTS sign(den);

Cartesian_kernel/include/CGAL/predicates/kernel_ftC3.h

@@ -417,14 +417,14 @@ side_of_bounded_sphereC3(const FT &px, const FT &py, const FT &pz,
   FT tsy = ty-sy;
   FT tsz = tz-sz;
 
-  FT num_x = ps2 * det2x2_by_formula(qsy,qsz,rsy,rsz)
+  FT num_x = ps2 * determinant(qsy,qsz,rsy,rsz)
-	   - qs2 * det2x2_by_formula(psy,psz,rsy,rsz);
+	   - qs2 * determinant(psy,psz,rsy,rsz);
-  FT num_y = ps2 * det2x2_by_formula(qsx,qsz,rsx,rsz)
+  FT num_y = ps2 * determinant(qsx,qsz,rsx,rsz)
-	   - qs2 * det2x2_by_formula(psx,psz,rsx,rsz);
+	   - qs2 * determinant(psx,psz,rsx,rsz);
-  FT num_z = ps2 * det2x2_by_formula(qsx,qsy,rsx,rsy)
+  FT num_z = ps2 * determinant(qsx,qsy,rsx,rsy)
-	   - qs2 * det2x2_by_formula(psx,psy,rsx,rsy);
+	   - qs2 * determinant(psx,psy,rsx,rsy);
 
-  FT den2  = 2 * det3x3_by_formula(psx,psy,psz,
+  FT den2  = 2 * determinant(psx,psy,psz,
                                    qsx,qsy,qsz,
                                    rsx,rsy,rsz);
 

Cartesian_kernel/package_info/Cartesian_kernel/changes.txt

@@ -21,7 +21,7 @@
 - Remove <FT> qualification for functions part of the NT interface
   (sign, compare...), for efficiency.
 - Add <FT> qualification for functions which are not part of the
-  NT interface (det3x3_by_formula...) to support GMP++ like types.
+  NT interface (determinant...) to support GMP++ like types.
 
 1 August 2005 Sylvain Pion
 - Cartesian_converter : specialize when same_type<K1, K2>.

Distance_2/include/CGAL/squared_distance_utils.h

@@ -110,7 +110,7 @@ wcross_tag(const typename K::Point_2 &p,
 	   const K&,
 	   const Homogeneous_tag&)
 {
-    return det3x3_by_formula(
+    return determinant(
         p.hx(), q.hx(), r.hx(),
         p.hy(), q.hy(), r.hy(),
         p.hw(), q.hw(), r.hw());

Filtered_kernel/include/CGAL/Static_filters/Coplanar_orientation_3.h

@@ -143,7 +143,7 @@ private:
     double prx = rx-px;
     double pry = ry-py;
 
-    double det = det2x2_by_formula(pqx, pqy,
+    double det = determinant(pqx, pqy,
                                    prx, pry);
 
     // Then semi-static filter.

Filtered_kernel/include/CGAL/Static_filters/Coplanar_side_of_bounded_circle_3.h

@@ -42,7 +42,7 @@ class SF_Side_of_bounded_circle_3
     F sq = t1*t1+t1*t1+t1*t1; // squares
     F n1 = t1*t1 - t1*t1;     // normal vector
     F sq_n1 = n1*n1 + n1*n1 + n1*n1;
-    F det = det4x4_by_formula(t1, t1, t1, sq,
+    F det = determinant(t1, t1, t1, sq,
                               t1, t1, t1, sq,
                               t1, t1, t1, sq,
                               n1, n1, n1, sq_n1); // Full det
@@ -99,7 +99,7 @@ public:
     double v2 = CGAL_NTS square(vx) + CGAL_NTS square(vy) +
 	        CGAL_NTS square(vz);
 
-    double det = det4x4_by_formula(ptx,pty,ptz,pt2,
+    double det = determinant(ptx,pty,ptz,pt2,
                                    rtx,rty,rtz,rt2,
                                    qtx,qty,qtz,qt2,
                                    vx,vy,vz,v2);

Filtered_kernel/include/CGAL/Static_filters/Orientation_2.h

@@ -76,7 +76,7 @@ public:
           double prx = rx - px;
           double pry = ry - py;
 
-          double det = det2x2_by_formula(pqx, pqy,
+          double det = determinant(pqx, pqy,
                                          prx, pry);
 
           // Then semi-static filter.
@@ -111,7 +111,7 @@ public:
   {
     typedef Static_filter_error F;
     F t1 = F(1, F::ulp()/2);         // First translation
-    F det = det2x2_by_formula(t1, t1,
+    F det = determinant(t1, t1,
                               t1, t1); // Full det
     double err = det.error();
     err += err * 2 * F::ulp(); // Correction due to "epsilon * maxx * maxy".

Filtered_kernel/include/CGAL/Static_filters/Orientation_3.h

@@ -97,7 +97,7 @@ public:
           if (maxz < fabs(prz)) maxz = fabs(prz);
           if (maxz < fabs(psz)) maxz = fabs(psz);
           double eps = 5.1107127829973299e-15 * maxx * maxy * maxz;
-          double det = det3x3_by_formula(pqx, pqy, pqz,
+          double det = determinant(pqx, pqy, pqz,
                                          prx, pry, prz,
                                          psx, psy, psz);
 
@@ -131,7 +131,7 @@ public:
   {
     typedef Static_filter_error F;
     F t1 = F(1, F::ulp()/2);         // First translation
-    F det = det3x3_by_formula(t1, t1, t1,
+    F det = determinant(t1, t1, t1,
                               t1, t1, t1,
                               t1, t1, t1); // Full det
     double err = det.error();

Filtered_kernel/include/CGAL/Static_filters/Side_of_oriented_circle_2.h

@@ -64,7 +64,7 @@ public:
 	  double rqx = rx-qx;
 	  double rqy = ry-qy;
 
-          double det = det2x2_by_formula(qpx*tpy - qpy*tpx, tpx*tqx + tpy*tqy,
+          double det = determinant(qpx*tpy - qpy*tpx, tpx*tqx + tpy*tqy,
                                          qpx*rpy - qpy*rpx, rpx*rqx + rpy*rqy);
 
           // We compute the semi-static bound.
@@ -106,7 +106,7 @@ public:
     F t1 = F(1, F::ulp()/2);         // First translation
     F a = t1*t1 - t1*t1;
     F b = t1*t1 + t1*t1;
-    F det = det2x2_by_formula(a, b, a, b);
+    F det = determinant(a, b, a, b);
     double err = det.error();
     err += err * 3 * F::ulp(); // Correction due to "eps * maxx * maxy...".
 

Filtered_kernel/include/CGAL/Static_filters/Side_of_oriented_sphere_3.h

@@ -104,7 +104,7 @@ public:
           double eps = 1.2466136531027298e-13 * maxx * maxy * maxz
                      * (maxz * maxz);
 
-          double det = det4x4_by_formula(ptx,pty,ptz,pt2,
+          double det = determinant(ptx,pty,ptz,pt2,
                                          rtx,rty,rtz,rt2,
                                          qtx,qty,qtz,qt2,
                                          stx,sty,stz,st2);
@@ -131,7 +131,7 @@ public:
     typedef CGAL::Static_filter_error F;
     F t1 = F(1,F::ulp()/2);         // First translation
     F sq = t1*t1+t1*t1+t1*t1; // squares
-    F det = det4x4_by_formula(t1, t1, t1, sq,
+    F det = determinant(t1, t1, t1, sq,
                               t1, t1, t1, sq,
                               t1, t1, t1, sq,
                               t1, t1, t1, sq); // Full det

Homogeneous_kernel/include/CGAL/Homogeneous/Aff_transformationH3.h

@@ -441,58 +441,58 @@ Aff_transformation_repH3<R>::inverse() const
   typedef typename R::RT RT;
   const RT  RT0(0);
   return Aff_transformation_3(
-                           det3x3_by_formula( t11, t12, t13,
+                           determinant( t11, t12, t13,
                                                    t21, t22, t23,     // i 00
                                                    RT0, RT0, t33 ),
 
-                        -  det3x3_by_formula( t01, t02, t03,
+                        -  determinant( t01, t02, t03,
                                                    t21, t22, t23,     // i 01
                                                    RT0, RT0, t33 ),
 
-                           det3x3_by_formula( t01, t02, t03,
+                           determinant( t01, t02, t03,
                                                    t11, t12, t13,     // i 02
                                                    RT0, RT0, t33 ),
 
-                        -  det3x3_by_formula( t01, t02, t03,
+                        -  determinant( t01, t02, t03,
                                                    t11, t12, t13,     // i 03
                                                    t21, t22, t23 ),
 
 
-                        -  det3x3_by_formula( t10, t12, t13,
+                        -  determinant( t10, t12, t13,
                                                    t20, t22, t23,     // i 10
                                                    RT0, RT0, t33 ),
 
-                           det3x3_by_formula( t00, t02, t03,
+                           determinant( t00, t02, t03,
                                                    t20, t22, t23,     // i 11
                                                    RT0, RT0, t33 ),
 
-                        -  det3x3_by_formula( t00, t02, t03,
+                        -  determinant( t00, t02, t03,
                                                    t10, t12, t13,     // i 12
                                                    RT0, RT0, t33 ),
 
-                           det3x3_by_formula( t00, t02, t03,
+                           determinant( t00, t02, t03,
                                                    t10, t12, t13,     // i 13
                                                    t20, t22, t23 ),
 
 
-                           det3x3_by_formula( t10, t11, t13,
+                           determinant( t10, t11, t13,
                                                    t20, t21, t23,     // i 20
                                                    RT0, RT0, t33 ),
 
-                        -  det3x3_by_formula( t00, t01, t03,
+                        -  determinant( t00, t01, t03,
                                                    t20, t21, t23,     // i 21
                                                    RT0, RT0, t33 ),
 
-                           det3x3_by_formula( t00, t01, t03,
+                           determinant( t00, t01, t03,
                                                    t10, t11, t13,     // i 22
                                                    RT0, RT0, t33 ),
 
-                        -  det3x3_by_formula( t00, t01, t03,
+                        -  determinant( t00, t01, t03,
                                                    t10, t11, t13,     // i 23
                                                    t20, t21, t23 ),
 
 
-                           det3x3_by_formula( t00, t01, t02,
+                           determinant( t00, t01, t02,
                                                    t10, t11, t12,     // i 33
                                                    t20, t21, t22 )
                                                        ) ;
@@ -523,7 +523,7 @@ bool
 Aff_transformation_repH3<R>::is_even() const
 {
   return (CGAL_NTS sign<RT>( t33 *
-	                    det3x3_by_formula(t00, t01, t02,
+	                    determinant(t00, t01, t02,
                                               t10, t11, t12,
                                               t20, t21, t22 ) ) == POSITIVE );
 }

Homogeneous_kernel/include/CGAL/Homogeneous/PlaneH3.h

@@ -495,7 +495,7 @@ PlaneH3<R>::transform_to_2d() const
   RT t32 =  -( e1phx*e2phz - e1phz*e2phx );
   RT t33 =   ( e1phx*e2phy - e1phy*e2phx );
 
-  RT scale = det3x3_by_formula( orthohx, orthohy, orthohz,
+  RT scale = determinant( orthohx, orthohy, orthohz,
                                      e1phx,   e1phy,   e1phz,
                                      e2phx,   e2phy,   e2phz );
 

Homogeneous_kernel/include/CGAL/Homogeneous/basic_constructionsH3.h

@@ -60,16 +60,16 @@ gp_linear_intersection(const PlaneH3<R> &f,
 {
   typedef typename R::RT RT;
   return typename R::Point_3(
-                  det3x3_by_formula<RT>(-f.d(), f.b(), f.c(),
+                  determinant<RT>(-f.d(), f.b(), f.c(),
                                         -g.d(), g.b(), g.c(),
                                         -h.d(), h.b(), h.c()),
-                  det3x3_by_formula<RT>( f.a(),-f.d(), f.c(),
+                  determinant<RT>( f.a(),-f.d(), f.c(),
                                          g.a(),-g.d(), g.c(),
                                          h.a(),-h.d(), h.c()),
-                  det3x3_by_formula<RT>( f.a(), f.b(),-f.d(),
+                  determinant<RT>( f.a(), f.b(),-f.d(),
                                          g.a(), g.b(),-g.d(),
                                          h.a(), h.b(),-h.d()),
-                  det3x3_by_formula<RT>( f.a(), f.b(), f.c(),
+                  determinant<RT>( f.a(), f.b(), f.c(),
                                          g.a(), g.b(), g.c(),
                                          h.a(), h.b(), h.c()));
 }

Homogeneous_kernel/include/CGAL/Homogeneous/function_objects.h

@@ -178,16 +178,16 @@ namespace HomogeneousKernelFunctors {
       const RT & vpy = vp.hy();
       const RT & vpz = vp.hz();
 
-      RT alpha = det3x3_by_formula( vpx, v2x, v3x,
+      RT alpha = determinant( vpx, v2x, v3x,
                                     vpy, v2y, v3y,
                                     vpz, v2z, v3z );
-      RT beta  = det3x3_by_formula( v1x, vpx, v3x,
+      RT beta  = determinant( v1x, vpx, v3x,
                                     v1y, vpy, v3y,
                                     v1z, vpz, v3z );
-      RT gamma = det3x3_by_formula( v1x, v2x, vpx,
+      RT gamma = determinant( v1x, v2x, vpx,
                                     v1y, v2y, vpy,
                                     v1z, v2z, vpz );
-      RT det = det3x3_by_formula( v1x, v2x, v3x,
+      RT det = determinant( v1x, v2x, v3x,
                                   v1y, v2y, v3y,
                                   v1z, v2z, v3z );
 
@@ -1277,7 +1277,7 @@ namespace HomogeneousKernelFunctors {
     result_type
     operator()(const Vector_2& v, const Vector_2& w) const
     {
-	return det2x2_by_formula(v.hx(), v.hy(),
+	return determinant(v.hx(), v.hy(),
                                  w.hx(), w.hy()) / FT(v.hw() * w.hw());
     }
   };
@@ -1294,7 +1294,7 @@ namespace HomogeneousKernelFunctors {
     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(),
+	return determinant(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());
@@ -2385,19 +2385,19 @@ namespace HomogeneousKernelFunctors {
       shz *= shw;
       shw *= shw;
 
-      RT chx =  det4x4_by_formula(phy, phz, pssq, phw,
+      RT chx =  determinant(phy, phz, pssq, phw,
 				  qhy, qhz, qssq, qhw,
 				  rhy, rhz, rssq, rhw,
 				  shy, shz, sssq, shw );
-      RT chy =  det4x4_by_formula(phx, phz, pssq, phw,
+      RT chy =  determinant(phx, phz, pssq, phw,
 				  qhx, qhz, qssq, qhw,
 				  rhx, rhz, rssq, rhw,
 				  shx, shz, sssq, shw );
-      RT chz =  det4x4_by_formula(phx, phy, pssq, phw,
+      RT chz =  determinant(phx, phy, pssq, phw,
 				  qhx, qhy, qssq, qhw,
 				  rhx, rhy, rssq, rhw,
 				  shx, shy, sssq, shw );
-      RT chw =  det4x4_by_formula(phx, phy, phz, phw,
+      RT chw =  determinant(phx, phy, phz, phw,
 				  qhx, qhy, qhz, qhw,
 				  rhx, rhy, rhz, rhw,
 				  shx, shy, shz, shw );
@@ -4657,7 +4657,7 @@ namespace HomogeneousKernelFunctors {
       const RT & thw = t.hw();
       const RT thw2 = thw*thw;
 
-      const RT det = det5x5_by_formula<RT>(
+      const RT det = determinant<RT>(
 	   phx*phw, phy*phw, phz*phw, phx*phx + phy*phy + phz*phz, phw2,
 	   qhx*qhw, qhy*qhw, qhz*qhw, qhx*qhx + qhy*qhy + qhz*qhz, qhw2,
 	   rhx*rhw, rhy*rhw, rhz*rhw, rhx*rhx + rhy*rhy + rhz*rhz, rhw2,

Interpolation/include/CGAL/constructions/constructions_for_voronoi_intersection_cartesian_2_3.h

@@ -34,7 +34,7 @@ plane_centered_circumcenter_translateC3(const RT &ax, const RT &ay,
 					const RT &rz,
 					RT &x, RT &y, RT &z)
 {
-  RT den = RT(2) * det3x3_by_formula(nx,qx,rx,
+  RT den = RT(2) * determinant(nx,qx,rx,
 				     ny,qy,ry,
 				     nz,qz,rz);
   // The 3 points aren't collinear.
@@ -48,15 +48,15 @@ plane_centered_circumcenter_translateC3(const RT &ax, const RT &ay,
   RT na = nx*ax + ny*ay + nz*az;
   na *= RT(2.0);
 
-  x =   det3x3_by_formula(ny,nz,na,
+  x =   determinant(ny,nz,na,
 			  qy,qz,q2,
 			  ry,rz,r2)/ den ;
 
-  y = - det3x3_by_formula(nx,nz,na,
+  y = - determinant(nx,nz,na,
 			  qx,qz,q2,
 			  rx,rz,r2)/ den ;
 
-  z =   det3x3_by_formula(nx,ny,na,
+  z =   determinant(nx,ny,na,
 			  qx,qy,q2,
 			  rx,ry,r2)/ den ;
 }
@@ -106,18 +106,18 @@ bisector_plane_intersection_translateC3(const RT &ax, const RT &ay,
   // the line is defined by p1 and p2 with
   //=> p1: z1 =0, p2: z2=1
   // precondition: (nx!=0 || ny!=0) && (qx!=0 && qy!=0) && den!=0
-  // where RT den = RT(2.0) * det2x2_by_formula(qx,qy,nx, ny);
+  // where RT den = RT(2.0) * determinant(qx,qy,nx, ny);
 
   RT q2 = CGAL_NTS square(qx) + CGAL_NTS square(qy)
     + CGAL_NTS square(qz);
   RT na = nx*ax + ny*ay + nz*az;
   na *= RT(2.0);
 
-  x1 = det2x2_by_formula(ny, na, qy, q2);
+  x1 = determinant(ny, na, qy, q2);
-  y1 = - det2x2_by_formula(nx, na, qx, q2);
+  y1 = - determinant(nx, na, qx, q2);
 
-  x2 = x1 +  RT(2.0) * det2x2_by_formula(qy,qz,ny, nz);
+  x2 = x1 +  RT(2.0) * determinant(qy,qz,ny, nz);
-  y2 = y1 -  RT(2.0) * det2x2_by_formula(qx,qz,nx, nz);
+  y2 = y1 -  RT(2.0) * determinant(qx,qz,nx, nz);
 
   x1 /= den;
   x2 /= den;
@@ -199,7 +199,7 @@ bisector_plane_intersectionC3(const RT &ax, const RT &ay, const RT &az,
   //    2) the projection of n and (p-q) onto the plane is not
   //    identical
   //    computation for (z=0) with adequate permutations
-  RT den = RT(2.0) * det2x2_by_formula(qx-px,qy-py,nx, ny);
+  RT den = RT(2.0) * determinant(qx-px,qy-py,nx, ny);
   if ((nx!=0 ||  ny!=0) && (qx!=px || qy!=py) && den!=RT(0))
     //den==0 <=> projections of (qx,qy) and (nx,ny) are identical
     //intersection with z=0/z=1
@@ -207,14 +207,14 @@ bisector_plane_intersectionC3(const RT &ax, const RT &ay, const RT &az,
 					  qx,qy,qz,den,
 					  x1,y1,z1,x2,y2,z2);
   else{
-    den = RT(2.0) * det2x2_by_formula(qy-py,qz-pz,ny,nz);
+    den = RT(2.0) * determinant(qy-py,qz-pz,ny,nz);
     if ((ny!=0 ||  nz!=0) && (qy!=py || qz!=pz) && den!=RT(0))
       //intersection with x=0/x=1 => permutations
       bisector_plane_intersection_permuteC3(ay,az,ax,ny,nz,nx,py,pz,px,
 					    qy,qz,qx,den,
 					    y1,z1,x1,y2,z2,x2);
     else{
-      den = RT(2.0) * det2x2_by_formula(qz-pz,qx-px,nz,nx);
+      den = RT(2.0) * determinant(qz-pz,qx-px,nz,nx);
       CGAL_assertion((nx!=0 ||  nz!=0) && (qx!=px || qz!=pz) && den!=RT(0));
       //intersection with y=0/y=1 => permutations
       bisector_plane_intersection_permuteC3(az,ax,ay,nz,nx,ny,pz,px,py,

Kernel_23/include/CGAL/Kernel/Wutils.h

@@ -156,7 +156,7 @@ struct wcross_tag_2<Homogeneous_tag>
                                      const Point_2 &q,
                                      const Point_2 &r) const
   {
-    return det3x3_by_formula(p.hx(), q.hx(), r.hx(),
+    return determinant(p.hx(), q.hx(), r.hx(),
                              p.hy(), q.hy(), r.hy(),
                              p.hw(), q.hw(), r.hw());
   }

Kernel_23/include/CGAL/determinant.h

@@ -30,7 +30,7 @@ CGAL_BEGIN_NAMESPACE
 template <class RT>
 inline
 RT
-det2x2_by_formula(
+determinant(
  const RT& a00,  const RT& a01,
  const RT& a10,  const RT& a11)
 {
@@ -42,7 +42,7 @@ det2x2_by_formula(
 template <class RT>
 CGAL_KERNEL_MEDIUM_INLINE
 RT
-det3x3_by_formula(
+determinant(
  const RT& a00,  const RT& a01,  const RT& a02,
  const RT& a10,  const RT& a11,  const RT& a12,
  const RT& a20,  const RT& a21,  const RT& a22)
@@ -59,7 +59,7 @@ det3x3_by_formula(
 template <class RT>
 CGAL_KERNEL_LARGE_INLINE
 RT
-det4x4_by_formula(
+determinant(
  const RT& a00,  const RT& a01,  const RT& a02,  const RT& a03,
  const RT& a10,  const RT& a11,  const RT& a12,  const RT& a13,
  const RT& a20,  const RT& a21,  const RT& a22,  const RT& a23,
@@ -85,7 +85,7 @@ det4x4_by_formula(
 template <class RT>
 CGAL_KERNEL_LARGE_INLINE
 RT
-det5x5_by_formula(
+determinant(
  const RT& a00,  const RT& a01,  const RT& a02,  const RT& a03,  const RT& a04,
  const RT& a10,  const RT& a11,  const RT& a12,  const RT& a13,  const RT& a14,
  const RT& a20,  const RT& a21,  const RT& a22,  const RT& a23,  const RT& a24,
@@ -127,7 +127,7 @@ det5x5_by_formula(
 
 template <class RT>
 RT
-det6x6_by_formula(
+determinant(
  const RT& a00, const RT& a01, const RT& a02, const RT& a03, const RT& a04,
  const RT& a05,
  const RT& a10, const RT& a11, const RT& a12, const RT& a13, const RT& a14,

Kernel_23/include/CGAL/predicates/sign_of_determinant.h

@@ -45,7 +45,7 @@ sign_of_determinant( const RT& a00,  const RT& a01,  const RT& a02,
                         const RT& a10,  const RT& a11,  const RT& a12,
                         const RT& a20,  const RT& a21,  const RT& a22)
 {
-  return CGAL_NTS sign(det3x3_by_formula(a00, a01, a02,
+  return CGAL_NTS sign(determinant(a00, a01, a02,
                                          a10, a11, a12,
                                          a20, a21, a22));
 }
@@ -59,7 +59,7 @@ sign_of_determinant(
  const RT& a20,  const RT& a21,  const RT& a22,  const RT& a23,
  const RT& a30,  const RT& a31,  const RT& a32,  const RT& a33)
 {
-  return CGAL_NTS sign(det4x4_by_formula(a00, a01, a02, a03,
+  return CGAL_NTS sign(determinant(a00, a01, a02, a03,
                                          a10, a11, a12, a13,
                                          a20, a21, a22, a23,
                                          a30, a31, a32, a33));
@@ -75,7 +75,7 @@ sign_of_determinant(
  const RT& a30,  const RT& a31,  const RT& a32,  const RT& a33,  const RT& a34,
  const RT& a40,  const RT& a41,  const RT& a42,  const RT& a43,  const RT& a44)
 {
-  return CGAL_NTS sign(det5x5_by_formula(a00, a01, a02, a03, a04,
+  return CGAL_NTS sign(determinant(a00, a01, a02, a03, a04,
                                          a10, a11, a12, a13, a14,
                                          a20, a21, a22, a23, a24,
                                          a30, a31, a32, a33, a34,
@@ -99,7 +99,7 @@ sign_of_determinant(
  const RT& a50, const RT& a51, const RT& a52, const RT& a53, const RT& a54,
  const RT& a55)
 {
-  return CGAL_NTS sign(det6x6_by_formula(a00, a01, a02, a03, a04, a05,
+  return CGAL_NTS sign(determinant(a00, a01, a02, a03, a04, a05,
                                          a10, a11, a12, a13, a14, a15,
                                          a20, a21, a22, a23, a24, a25,
                                          a30, a31, a32, a33, a34, a35,

Kernel_23/package_info/Kernel_23/changes.txt

@@ -2086,7 +2086,7 @@ Version 1.106 (09 February 2004) [rursu]
 - authors for determinant.h updated
 
 1.2.8 -> 1.2.9
-- det4x4_by_formula improved as suggested by Sylvain and Olivier
+- determinant improved as suggested by Sylvain and Olivier
 
 1.2.7 -> 1.2.8
 - #define CGAL_KERNEL_INLINE inline   added again

Kernel_23/test/Kernel_23/include/CGAL/_test_fct_determinant.h

@@ -33,54 +33,54 @@ _test_fct_determinant(const NT&)
   NT one = NT(1);
   NT two = NT(2);
 
-  // detDxD_by_formula
+  // determinant()
 
-  assert( CGAL::det2x2_by_formula<NT>( zero, one, \
+  assert( CGAL::determinant<NT>( zero, one, \
                                    one,  zero) == - one );
 
-  assert( CGAL::det2x2_by_formula<NT>( one,  one, \
+  assert( CGAL::determinant<NT>( one,  one, \
                                    zero, -one) == - one );
 
-  assert( CGAL::det3x3_by_formula<NT>( one,  zero, one, \
+  assert( CGAL::determinant<NT>( one,  zero, one, \
                                    zero, one,  one, \
                                   -one,  -one, zero ) == \
-          one * CGAL::det2x2_by_formula<NT>( one, one, \
+          one * CGAL::determinant<NT>( one, one, \
                                         -one, zero ) \
-        - one * CGAL::det2x2_by_formula<NT>( zero, one, \
+        - one * CGAL::determinant<NT>( zero, one, \
                                          one, one ) );
 
-  assert( CGAL::det4x4_by_formula<NT>( one,  zero, one, -one, \
+  assert( CGAL::determinant<NT>( one,  zero, one, -one, \
                                    zero, one,  one, -one, \
                                    one,  two,  zero, one, \
                                   -one,  -one, zero, zero ) == \
-          one * CGAL::det3x3_by_formula<NT>( zero, one, -one, \
+          one * CGAL::determinant<NT>( zero, one, -one, \
                                          one, one, -one, \
                                          two, zero, one ) \
-        - one * CGAL::det3x3_by_formula<NT>( one, one, -one, \
+        - one * CGAL::determinant<NT>( one, one, -one, \
                                          zero, one, -one, \
                                          one, zero, one ) );
 
-  assert( CGAL::det5x5_by_formula<NT>( one,  zero, one, -one, zero, \
+  assert( CGAL::determinant<NT>( one,  zero, one, -one, zero, \
                                    zero, one,  one, -one, zero, \
                                    one,  two,  zero, one, two, \
                                    one, one,  zero, -one, zero, \
                                   -one,  -one, zero, zero, one ) == \
-          two * CGAL::det4x4_by_formula<NT>( one,  zero, one,  -one, \
+          two * CGAL::determinant<NT>( one,  zero, one,  -one, \
                                          zero, one,  one,  -one, \
                                          one,  one,  zero, -one, \
                                         -one, -one,  zero, zero) \
-        + one * CGAL::det4x4_by_formula<NT>( one,  zero, one,  -one, \
+        + one * CGAL::determinant<NT>( one,  zero, one,  -one, \
                                          zero, one,  one,  -one, \
                                          one,  two,  zero,  one, \
                                          one,  one,  zero, -one) );
 
-  assert( CGAL::det6x6_by_formula<NT>( one,  zero, zero, zero, zero, zero, \
+  assert( CGAL::determinant<NT>( one,  zero, zero, zero, zero, zero, \
                                    zero, one,  zero, one,  -one, zero, \
                                    zero, zero, one,  one, -one, zero, \
                                    zero, one,  two,  zero, one, two, \
                                    zero, one, one,  zero, -one, zero, \
                                    zero, -one,  -one, zero, zero, one ) == \
-          CGAL::det5x5_by_formula<NT>( one,  zero, one, -one, zero, \
+          CGAL::determinant<NT>( one,  zero, one, -one, zero, \
                                    zero, one,  one, -one, zero, \
                                    one,  two,  zero, one, two, \
                                    one, one,  zero, -one, zero, \

Kinetic_data_structures/hidden/example/Kinetic_data_structures/update_Delaunay_triangulation_2.cpp

@@ -145,7 +145,7 @@ CNT  incircle(CNT ax, CNT ay, CNT bx, CNT by,
   CNT rpy = cy - ay;
   CNT tpx = dx - ax;
   CNT tpy = dy - ay;
-  CNT det=CGAL::det2x2_by_formula(qpx*tpy - qpy*tpx, tpx*(dx - bx) 
+  CNT det=CGAL::determinant(qpx*tpy - qpy*tpx, tpx*(dx - bx) 
 				  + tpy*(dy - by),
 				  qpx*rpy - qpy*rpx, rpx*(cx - bx) 
 				  + rpy*(cy - by));

Kinetic_data_structures/hidden/include/CGAL/Updatable_Delaunay_triangulation_table_2.h

@@ -1015,7 +1015,7 @@ public:
     CNT rpy = cy;
     CNT tpx = dx;
     CNT tpy = dy;
-    CNT det=CGAL::det2x2_by_formula(qpx*tpy - qpy*tpx, 
+    CNT det=CGAL::determinant(qpx*tpy - qpy*tpx, 
 				    tpx*(dx - bx) + tpy*(dy - by),
 				    qpx*rpy - qpy*rpx, 
 				    rpx*(cx - bx) + rpy*(cy - by));
@@ -1032,7 +1032,7 @@ public:
     CNT rpy = cy - ay;
     CNT tpx = dx - ax;
     CNT tpy = dy - ay;
-    CNT det=CGAL::det2x2_by_formula(qpx*tpy - qpy*tpx,
+    CNT det=CGAL::determinant(qpx*tpy - qpy*tpx,
 				    tpx*(dx - bx) + tpy*(dy - by),
 				    qpx*rpy - qpy*rpx,
 				    rpx*(cx - bx) + rpy*(cy - by));

Kinetic_data_structures/include/CGAL/Kinetic/internal/Kernel/cartesian_predicates_3.h

@@ -64,7 +64,7 @@ struct Cartesian_side_of_oriented_sphere_3
     FT dsy = (d.y()) - (e.y());
     FT dsz = (d.z()) - (e.z());
     FT dst = dsx*dsx + dsy*dsy + dsz*dsz;
-    FT ret= CGAL::det4x4_by_formula(dpx, dpy, dpz, dpt,
+    FT ret= CGAL::determinant(dpx, dpy, dpz, dpt,
 				    dqx, dqy, dqz, dqt,
 				    drx, dry, drz, drt,
 				    dsx, dsy, dsz, dst);
@@ -127,7 +127,7 @@ struct Cartesian_power_test_3
     FT dst = dsx*dsx + dsy*dsy
       + dsz*dsz - (d.weight()) + (e.weight());
 
-    return ::CGAL::det4x4_by_formula(dpx, dpy, dpz, dpt,
+    return ::CGAL::determinant(dpx, dpy, dpz, dpt,
 				     dqx, dqy, dqz, dqt,
 				     drx, dry, drz, drt,
 				     dsx, dsy, dsz, dst);
@@ -192,7 +192,7 @@ struct Cartesian_lifted_power_test_3
     FT dsz = (d.point().z()) - (e.point().z());
     FT dst = (d.lifted()) - (e.lifted());
 
-    return CGAL::det4x4_by_formula(dpx, dpy, dpz, dpt,
+    return CGAL::determinant(dpx, dpy, dpz, dpt,
 				   dqx, dqy, dqz, dqt,
 				   drx, dry, drz, drt,
 				   dsx, dsy, dsz, dst);
@@ -244,7 +244,7 @@ struct Cartesian_linear_lifted_power_test_3
       FT dsz = (d.point().z()) - (e.point().z());
       FT dst = (d.lifted()) - (e.lifted());
 
-      safe_ret = CGAL::det4x4_by_formula(dpx, dpy, dpz, dpt,
+      safe_ret = CGAL::determinant(dpx, dpy, dpz, dpt,
 					 dqx, dqy, dqz, dqt,
 					 drx, dry, drz, drt,
 					 dsx, dsy, dsz, dst);
@@ -354,7 +354,7 @@ typename Pt::Coordinate co3(const Pt &a, const Pt &b, const Pt &c, const Pt &d)
   RT a20= qz-pz;
   RT a21= rz-pz;
   RT a22= sz-pz;
-  RT ret= CGAL::det3x3_by_formula(a00, a01, a02,
+  RT ret= CGAL::determinant(a00, a01, a02,
 				  a10, a11, a12,
 				  a20, a21, a22);
   /*CGAL_LOG_MAPLE(std::endl << std::endl);
@@ -554,7 +554,7 @@ typename CC::result_type co3(const Pt &a, const Pt &b, const Pt &c, const Pt &d,
   RT a20= qz-pz;
   RT a21= rz-pz;
   RT a22= sz-pz;
-  RT ret= CGAL::det3x3_by_formula(a00, a01, a02,
+  RT ret= CGAL::determinant(a00, a01, a02,
 				  a10, a11, a12,
 				  a20, a21, a22);
   CGAL::Kinetic::log()->stream(CGAL::KDS::Log::MAPLE) << std::endl << std::endl;
@@ -600,7 +600,7 @@ typename CC::result_type pt3(const Pt &a, const Pt &b, const Pt &c, const Pt &d,
   FT dst = dsx*dsx + dsy*dsy
     + dsz*dsz - cc(d.weight()) + cc(e.weight());
 
-  return CGAL::det4x4_by_formula(dpx, dpy, dpz, dpt,
+  return CGAL::determinant(dpx, dpy, dpz, dpt,
 				 dqx, dqy, dqz, dqt,
 				 drx, dry, drz, drt,
 				 dsx, dsy, dsz, dst);
@@ -633,7 +633,7 @@ typename CC::result_type pt3(const Cartesian_moving_point_3<C>  &a,
   FT dsy = cc(d.y()) - cc(e.y());
   FT dsz = cc(d.z()) - cc(e.z());
   FT dst = dsx*dsx + dsy*dsy + dsz*dsz;
-  FT ret= CGAL::det4x4_by_formula(dpx, dpy, dpz, dpt,
+  FT ret= CGAL::determinant(dpx, dpy, dpz, dpt,
 				  dqx, dqy, dqz, dqt,
 				  drx, dry, drz, drt,
 				  dsx, dsy, dsz, dst);
@@ -728,7 +728,7 @@ typename CC::result_type pt3(Cartesian_moving_lifted_point_3<CGAL::Polynomial::L
     ret= m0123;
   }
   if (flip) ret=-ret;
-  /*FT ret = CGAL::det4x4_by_formula(dpx, dpy, dpz, dpt,
+  /*FT ret = CGAL::determinant(dpx, dpy, dpz, dpt,
     dqx, dqy, dqz, dqt,
     drx, dry, drz, drt,
     dsx, dsy, dsz, dst);*/
@@ -788,7 +788,7 @@ typename CC::result_type pt3(Cartesian_moving_lifted_point_3<C> a,
   FT dsz = cc(d.point().z()) - cc(e.point().z());
   FT dst = cc(d.lifted()) - cc(e.lifted());
 
-  FT ret = CGAL::det4x4_by_formula(dpx, dpy, dpz, dpt,
+  FT ret = CGAL::determinant(dpx, dpy, dpz, dpt,
 				   dqx, dqy, dqz, dqt,
 				   drx, dry, drz, drt,
 				   dsx, dsy, dsz, dst);

Segment_Delaunay_graph_2/include/CGAL/Segment_Delaunay_graph_2/Are_parallel_C2.h

@@ -61,7 +61,7 @@ private:
       x4 = s2.target().x(),
       y4 = s2.target().y();
 
-    FT det = det2x2_by_formula(x2 - x1, x4 - x3,
+    FT det = determinant(x2 - x1, x4 - x3,
 			       y2 - y1, y4 - y3);
 
     return ( CGAL::sign(det) == CGAL::ZERO );

Segment_Delaunay_graph_2/include/CGAL/Segment_Delaunay_graph_2/Arrangement_type_C2.h

@@ -79,7 +79,7 @@ private:
 			      const RT& x3, const RT& y3,
 			      const RT& x4, const RT& y4) const
   {
-    RT delta = -det2x2_by_formula(x2 - x1, x4 - x3, y2 - y1, y4 - y3);
+    RT delta = -determinant(x2 - x1, x4 - x3, y2 - y1, y4 - y3);
 
     Sign s = CGAL::sign( delta );
     if ( s != CGAL::ZERO ) {
@@ -94,8 +94,8 @@ private:
 		  const RT& x3, const RT& y3, const RT& x4, const RT& y4,
 		  const RT& D) const
   {
-    RT Dt = -det2x2_by_formula(x3 - x1, x4 - x3, y3 - y1, y4 - y3);
+    RT Dt = -determinant(x3 - x1, x4 - x3, y3 - y1, y4 - y3);
-    RT Ds = det2x2_by_formula(x2 - x1, x3 - x1, y2 - y1, y3 - y1);
+    RT Ds = determinant(x2 - x1, x3 - x1, y2 - y1, y3 - y1);
 
     Sign s_D = CGAL::sign( D );
     Sign s_Dt = CGAL::sign( Dt );
@@ -164,7 +164,7 @@ private:
   parallel_C2(const RT& x1, const RT& y1, const RT& x2, const RT& y2,
 	      const RT& x3, const RT& y3, const RT& x4, const RT& y4) const
   {
-    RT D1 = det2x2_by_formula(x2 - x1, x3 - x1,	y2 - y1, y3 - y1);
+    RT D1 = determinant(x2 - x1, x3 - x1,	y2 - y1, y3 - y1);
 
     if ( CGAL::sign( D1 ) != CGAL::ZERO ) {
       return Enum::DISJOINT;

Segment_Delaunay_graph_2/include/CGAL/Segment_Delaunay_graph_site_2.h

@@ -284,8 +284,8 @@ protected:
     RT x3 = p3.x(), y3 = p3.y();
     RT x4 = p4.x(), y4 = p4.y();
 
-    RT D = det2x2_by_formula(x2 - x1, x4 - x3, y2 - y1, y4 - y3);
+    RT D = determinant(x2 - x1, x4 - x3, y2 - y1, y4 - y3);
-    RT Dt = det2x2_by_formula(x3 - x1, x4 - x3, y3 - y1, y4 - y3);
+    RT Dt = determinant(x3 - x1, x4 - x3, y3 - y1, y4 - y3);
 
     RT t = Dt / D;
 

Surface_mesh_simplification/include/CGAL/Cartesian/MatrixC33.h

@@ -145,7 +145,7 @@ public:
  
   RT determinant() const
   {
-    return det3x3_by_formula(r0().x(),r0().y(),r0().z()
+    return determinant(r0().x(),r0().y(),r0().z()
                             ,r1().x(),r1().y(),r1().z()
                             ,r2().x(),r2().y(),r2().z()
                             );
@@ -189,17 +189,17 @@ MatrixC33<R> cofactors_matrix ( MatrixC33<R> const& m )
 {
   typedef typename R::RT RT ;
   
-  RT c00 =  det2x2_by_formula(m.r1().y(),m.r1().z(),m.r2().y(),m.r2().z());
+  RT c00 =  determinant(m.r1().y(),m.r1().z(),m.r2().y(),m.r2().z());
-  RT c01 = -det2x2_by_formula(m.r1().x(),m.r1().z(),m.r2().x(),m.r2().z());
+  RT c01 = -determinant(m.r1().x(),m.r1().z(),m.r2().x(),m.r2().z());
-  RT c02 =  det2x2_by_formula(m.r1().x(),m.r1().y(),m.r2().x(),m.r2().y());
+  RT c02 =  determinant(m.r1().x(),m.r1().y(),m.r2().x(),m.r2().y());
   
-  RT c10 = -det2x2_by_formula(m.r0().y(),m.r0().z(),m.r2().y(),m.r2().z());
+  RT c10 = -determinant(m.r0().y(),m.r0().z(),m.r2().y(),m.r2().z());
-  RT c11 =  det2x2_by_formula(m.r0().x(),m.r0().z(),m.r2().x(),m.r2().z());
+  RT c11 =  determinant(m.r0().x(),m.r0().z(),m.r2().x(),m.r2().z());
-  RT c12 = -det2x2_by_formula(m.r0().x(),m.r0().y(),m.r2().x(),m.r2().y());
+  RT c12 = -determinant(m.r0().x(),m.r0().y(),m.r2().x(),m.r2().y());
   
-  RT c20 =  det2x2_by_formula(m.r0().y(),m.r0().z(),m.r1().y(),m.r1().z());
+  RT c20 =  determinant(m.r0().y(),m.r0().z(),m.r1().y(),m.r1().z());
-  RT c21 = -det2x2_by_formula(m.r0().x(),m.r0().z(),m.r1().x(),m.r1().z());
+  RT c21 = -determinant(m.r0().x(),m.r0().z(),m.r1().x(),m.r1().z());
-  RT c22 =  det2x2_by_formula(m.r0().x(),m.r0().y(),m.r1().x(),m.r1().y());
+  RT c22 =  determinant(m.r0().x(),m.r0().y(),m.r1().x(),m.r1().y());
   
   return MatrixC33<R>(c00,c01,c02
                      ,c10,c11,c12

Triangulation_2/include/CGAL/constructions_on_weighted_points_cartesian_2.h

@@ -39,7 +39,7 @@ weighted_circumcenter_translateC2(const RT &dqx, const RT &dqy, const RT &dqw,
   RT r2 = CGAL_NTS square(drx) + CGAL_NTS square(dry) - drw;
   RT q2 = CGAL_NTS square(dqx) + CGAL_NTS square(dqy) - dqw;
 
-  RT den = RT(2) * det2x2_by_formula(dqx, dqy, drx, dry);
+  RT den = RT(2) * determinant(dqx, dqy, drx, dry);
 
   // The 3 points aren't collinear.
   // Hopefully, this is already checked at the upper level.
@@ -47,8 +47,8 @@ weighted_circumcenter_translateC2(const RT &dqx, const RT &dqy, const RT &dqw,
 
   // One possible optimization here is to precompute 1/den, to avoid one
   // division.  However, we loose precision, and it's maybe not worth it (?).
-  dcx =   det2x2_by_formula (dry, dqy, r2, q2) / den;
+  dcx =   determinant (dry, dqy, r2, q2) / den;
-  dcy = - det2x2_by_formula (drx, dqx, r2, q2) / den;
+  dcy = - determinant (drx, dqx, r2, q2) / den;
 }
 
 //template < class RT >

Triangulation_2/test/Triangulation_2/include/CGAL/_test_traits.h

@@ -222,7 +222,7 @@ public:
       RT RT0(0);
       RT RT1(1);
 
-      RT det = CGAL::det4x4_by_formula(px, py, px*px + py*py, RT1,
+      RT det = CGAL::determinant(px, py, px*px + py*py, RT1,
 				       qx, qy, qx*qx + qy*qy, RT1,
 				       rx, ry, rx*rx + ry*ry, RT1,
 				       tx, ty, tx*tx + ty*ty, RT1);

Triangulation_3/include/CGAL/constructions/constructions_on_weighted_points_cartesian_3.h

@@ -50,16 +50,16 @@ determinants_for_weighted_circumcenterC3(
   FT sp2 = CGAL_NTS square(spx) + CGAL_NTS square(spy) + 
            CGAL_NTS square(spz) - sw + pw;
 
-  num_x = det3x3_by_formula(qpy,qpz,qp2,
+  num_x = determinant(qpy,qpz,qp2,
 			    rpy,rpz,rp2,
 			    spy,spz,sp2);
-  num_y = det3x3_by_formula(qpx,qpz,qp2,
+  num_y = determinant(qpx,qpz,qp2,
 			    rpx,rpz,rp2,
 			    spx,spz,sp2);
-  num_z = det3x3_by_formula(qpx,qpy,qp2,
+  num_z = determinant(qpx,qpy,qp2,
 			    rpx,rpy,rp2,
 			    spx,spy,sp2);
-  den   = det3x3_by_formula(qpx,qpy,qpz,
+  den   = determinant(qpx,qpy,qpz,
 			    rpx,rpy,rpz,
 			    spx,spy,spz);
 }
@@ -182,26 +182,26 @@ determinants_for_weighted_circumcenterC3(
 
   // The following determinants can be developped and simplified.
   //
-  // FT num_x = det3x3_by_formula(qpy,qpz,qp2,
+  // FT num_x = determinant(qpy,qpz,qp2,
   //                              rpy,rpz,rp2,
   //                              sy,sz,FT(0));
-  // FT num_y = det3x3_by_formula(qpx,qpz,qp2,
+  // FT num_y = determinant(qpx,qpz,qp2,
   //                              rpx,rpz,rp2,
   //                              sx,sz,FT(0));
-  // FT num_z = det3x3_by_formula(qpx,qpy,qp2,
+  // FT num_z = determinant(qpx,qpy,qp2,
   //                              rpx,rpy,rp2,
   //                              sx,sy,FT(0));
 
-  num_x = qp2 * det2x2_by_formula(rpy,rpz,sy,sz)
+  num_x = qp2 * determinant(rpy,rpz,sy,sz)
-        - rp2 * det2x2_by_formula(qpy,qpz,sy,sz);
+        - rp2 * determinant(qpy,qpz,sy,sz);
 
-  num_y = qp2 * det2x2_by_formula(rpx,rpz,sx,sz)
+  num_y = qp2 * determinant(rpx,rpz,sx,sz)
-	- rp2 * det2x2_by_formula(qpx,qpz,sx,sz);
+	- rp2 * determinant(qpx,qpz,sx,sz);
 
-  num_z = qp2 * det2x2_by_formula(rpx,rpy,sx,sy)
+  num_z = qp2 * determinant(rpx,rpy,sx,sy)
-	- rp2 * det2x2_by_formula(qpx,qpy,sx,sy);
+	- rp2 * determinant(qpx,qpy,sx,sy);
 
-  den   = det3x3_by_formula(qpx,qpy,qpz,
+  den   = determinant(qpx,qpy,qpz,
 			    rpx,rpy,rpz,
 			    sx,sy,sz);
 }
@@ -383,9 +383,9 @@ radical_axisC3(const RT &px, const RT &py, const RT &pz, const We &pw,
 
   //il manque des tests...
 
-  a= RT(1)*det2x2_by_formula(dqy, dqz, dry, drz);
+  a= RT(1)*determinant(dqy, dqz, dry, drz);
-  b= - RT(1)*det2x2_by_formula(dqx, dqz, drx, drz);
+  b= - RT(1)*determinant(dqx, dqz, drx, drz);
-  c= RT(1)*det2x2_by_formula(dqx, dqy, drx, dry);
+  c= RT(1)*determinant(dqx, dqy, drx, dry);
 }
 
 // function used in critical_squared_radiusC3
@@ -423,7 +423,7 @@ power_to_orthogonal_sphereC3(
     FT dst = CGAL_NTS square(dsx) + CGAL_NTS square(dsy) + 
              CGAL_NTS square(dsz) - sw + tw;
 
-    return det4x4_by_formula(dpx, dpy, dpz, dpt,
+    return determinant(dpx, dpy, dpz, dpt,
 			     dqx, dqy, dqz, dqt,
 			     drx, dry, drz, drt,
 			     dsx, dsy, dsz, dst);

Triangulation_3/include/CGAL/predicates/predicates_on_weighted_points_cartesian_3.h

@@ -72,11 +72,11 @@ in_smallest_orthogonal_sphereC3(
   FT qpw = qq - qw + pw ;
   FT rpw = rr - rw + pw ;
   
-  FT den = det2x2_by_formula(qq,qr,
+  FT den = determinant(qq,qr,
 			     qr,rr);
-  FT detq = det2x2_by_formula(qpw,qr,
+  FT detq = determinant(qpw,qr,
 			      rpw,rr);
-  FT detr = det2x2_by_formula(qq,qpw,
+  FT detr = determinant(qq,qpw,
 			      qr,rpw);
 
   // Smallest  smallest orthogonal sphere center
@@ -159,16 +159,16 @@ does_simplex_intersect_weighted_dual_supportC3(
   FT rpw = rr - rw + pw ;
   FT spw = ss - sw + pw ;
  
-  FT den = det3x3_by_formula(qq,qr,qs,
+  FT den = determinant(qq,qr,qs,
 			     qr,rr,rs,
 			     qs,rs,ss);
-  FT detq = det3x3_by_formula(qpw,qr,qs,
+  FT detq = determinant(qpw,qr,qs,
 			      rpw,rr,rs,
 			      spw,rs,ss);
-  FT detr = det3x3_by_formula(qq,qpw,qs,
+  FT detr = determinant(qq,qpw,qs,
 			      qr,rpw,rs,
 			      qs,spw,ss);
-  FT dets = det3x3_by_formula(qq,qr,qpw,
+  FT dets = determinant(qq,qr,qpw,
 			      qr,rr,rpw,
 			      qs,rs,spw);
   CGAL_kernel_assertion( ! CGAL_NTS is_zero(den) );
@@ -222,11 +222,11 @@ does_simplex_intersect_weighted_dual_supportC3(
   FT qpw = qq - qw + pw ;
   FT rpw = rr - rw + pw ;
   
-  FT den = det2x2_by_formula(qq,qr,
+  FT den = determinant(qq,qr,
 			     qr,rr);
-  FT detq = det2x2_by_formula(qpw,qr,
+  FT detq = determinant(qpw,qr,
 			      rpw,rr);
-  FT detr = det2x2_by_formula(qq,qpw,
+  FT detr = determinant(qq,qpw,
 			      qr,rpw);
 
   CGAL_kernel_assertion( ! CGAL_NTS is_zero(den) );