diff --git a/algorithm/optimization/gradient.py b/algorithm/optimization/gradient.py
index 793a60a..89abec4 100644
--- a/algorithm/optimization/gradient.py
+++ b/algorithm/optimization/gradient.py
@@ -346,6 +346,30 @@ class gd2d_compete(object):
         display(self.compute_output)
         self.button_plot.on_click(self.plot)
         display(self.plot_output)
+
+    def compute_default(self, *args):
+        with self.compute_output:
+            x0 = np.array(self.wg_x0.value.split(","), dtype=float)
+            xn = x0
+            x1 = symbols("x1")
+            x2 = symbols("x2")
+            expr = sympify(self.wg_expr.value)
+            self.xn_list, self.df_list = [], []
+
+            for n in tqdm(range(0, self.wg_max_iter.value)):
+                gradient = np.array([diff(expr, x1).subs(x1, xn[0]).subs(x2, xn[1]), 
+                                     diff(expr, x2).subs(x1, xn[0]).subs(x2, xn[1])], dtype=float)
+                self.xn_list.append(xn)
+                self.df_list.append(gradient)
+                if np.linalg.norm(gradient, ord=2) < self.wg_epsilon.value:
+                    clear_output(wait=True)
+                    print("Found solution of {} after".format(expr), n, "iterations")
+                    print("x* = [{}, {}]".format(xn[0], xn[1]))
+                    return None
+                xn = xn - self.wg_lr.value * gradient
+            clear_output(wait=True)
+            display("Exceeded maximum iterations. No solution found.")
+            return None
         
     def compute(self, *args):
         with self.compute_output:
@@ -358,16 +382,28 @@ class gd2d_compete(object):
                 self.xn_p1_list.append(x0)
             direction_p0 = np.array(self.wg_direction_p0.value.split(","), dtype=float)
             direction_p1 = np.array(self.wg_direction_p1.value.split(","), dtype=float)
+            
             self.timer = self.timer + 1
             # calcualte next point position
             x0_p0 = self.xn_p0_list[self.timer-1] + self.wg_lr.value * direction_p0
             x0_p1 = self.xn_p1_list[self.timer-1] + self.wg_lr.value * direction_p1
             self.xn_p0_list.append(x0_p0)
-            self.xn_p1_list.append(x0_p1)
+            self.xn_p1_list.append(x0_p1)            
             f = lambdify((x1, x2), expr, "numpy")
+            
             f_xn = f(np.array([x0_p0, x0_p1])[:, 0], np.array([x0_p0, x0_p1])[:, 1])
+            
+            self.expr = expr
+            self.x0_p0 = x0_p0
+            self.x0_p1 = x0_p1
+            gradient_p0 = np.array([diff(expr, x1).subs(x1, x0_p0[0]).subs(x2, x0_p0[1]), 
+                                    diff(expr, x2).subs(x1, x0_p0[0]).subs(x2, x0_p0[1])], dtype=float)
+            gradient_p1 = np.array([diff(expr, x1).subs(x1, x0_p1[0]).subs(x2, x0_p1[1]), 
+                                    diff(expr, x2).subs(x1, x0_p1[0]).subs(x2, x0_p1[1])], dtype=float)
+            
             clear_output(wait=True)
-            print("a1({}): {}, a2({}): {}".format(self.timer, np.append(x0_p0, f_xn[0]), self.timer,np.append(x0_p1, f_xn[1])))
+            print("coordinate： a1({}): {}, a2({}): {}".format(self.timer, np.append(x0_p0, f_xn[0]), self.timer,np.append(x0_p1, f_xn[1])))
+            print("gradient: a1({}): {}, a2({}): {}".format(self.timer, gradient_p0, self.timer,gradient_p1))
             
     def plot(self, *args):
         with self.plot_output: