111

159-1.py

@@ -2,7 +2,7 @@ def fx(x):
     return x**4-3*x+1
 
 
-def SolveByDivTwo(x1,x2,err):
+def erfen(x1,x2,err):
     while abs(x2-x1) >= err:
         x = (x1+x2)/2
         if fx(x) * fx(x1) < 0:
@@ -15,6 +15,5 @@ def SolveByDivTwo(x1,x2,err):
 if __name__ == "__main__":
     x1 = 0.3
     x2 = 0.4
-    err = 0.5e-5
-    root = SolveByDivTwo(x1, x2, err)
-    print(f"Root: {root:.5f}")
+    root = erfen(x1, x2, 0.5e-5)
+    print(f"解为: {root}")

159-2.py

@@ -4,21 +4,14 @@ import matplotlib.pyplot as plt
 def fx(x):
     return math.exp(x)-math.sin(x)
 
-def DrawGraph(a, b, stepper):
-    x = [a + (b-a)*i*stepper for i in range(int(1/stepper+1))]
+def huatu(a, b, buchang):
+    x = [a + (b-a)*i*buchang for i in range(int(1/buchang+1))]
     y = [fx(i) for i in x]
-    plt.xlim(a-abs(b-a)*0.1, b+abs(b-a)*0.1)
     plt.plot(x, y)
-    plt.axhline(0, color='black', lw=0.5, ls='-')
-    plt.axvline(a, color='red', lw=0.5, ls='--')
-    plt.axvline(b, color='red', lw=0.5, ls='--')
-    plt.text(a, y[0], f'({a:.5f},{y[0]:.5f})', fontsize=8, ha='left')
-    plt.text(b, y[-1], f'({b:.5f},{y[-1]:.5f})', fontsize=8, ha='right')
+    plt.axhline(0, color='black', lw=1)
     for i in range(len(x)-1):
         if y[i] * y[i+1] < 0:
-            print(f"可能存在零点: ({x[i]:.5f},{y[i]:.5f})和({x[i+1]:.5f},{y[i+1]:.5f})之间")
-            plt.plot((x[i]+x[i+1])/2, (y[i]+y[i+1])/2, 'ro', markersize=3)
-    plt.title("Graph of f(x)")
+            print(f"({x[i]},{y[i]}),({x[i+1]},{y[i+1]})")
     plt.xlabel("x")
     plt.ylabel("f(x)")
     plt.show()
@@ -28,7 +21,4 @@ def DrawGraph(a, b, stepper):
 if __name__ == "__main__":
     a = -2*math.pi
     b = math.pi
-    step = 0.00001
-    print(f"边界点: {a}, {b}")
-    print(f"步长: {step}")
-    x, y = DrawGraph(a, b, step)
+    huatu(a, b, 0.00001)

159-3.py

@@ -1,43 +1,40 @@
-def fd1(x):
+def f1(x):
     return 1+1/x**2
 
-def fd2(x):
-    return 1/(x-1)**0.5
+def f2(x):
+    return 1/((x-1)**0.5)
 
-def Renew(x,fd,err):
+def diedai(x,fd,err):
     count=0
     i = 0
-    try:
-        while True:
-            xk = fd(x)
-            if abs(i) < (xk-x):
-                count += 1
-            else:
-                count = 0
-            if count > 10:
-                print("不收敛")
-                break
-            if abs(xk-x) < err:
-                return xk
-            i = xk-x
-            x = xk
-    except Exception as e:
-        print(f"发生错误: {e}")
-        return None
+    while True:
+        xk = fd(x)
+        if complex(xk).imag != 0:
+            break
+        if (i) < abs(xk-x):
+            count += 1
+        else:
+            count = 0
+        if count > 10:
+            break
+        if abs(xk-x) < err:
+            return xk
+        i = abs(xk-x)
+        x = xk
     return None
 
 
 if __name__ == "__main__":
     x0 = 1.5
 
-    result = Renew(x0, fd1, 1e-5)
+    result = diedai(x0, f1, 1e-5)
     if result is not None:
-        print(f"1式收敛 解为: {result:.5f}")
+        print(f"(1)收敛 解为: {result:.5f}")
     else:
-        print("1式不收敛")
+        print("(1)不收敛")
 
-    result = Renew(x0, fd2, 1e-5)
+    result = diedai(x0, f2, 1e-5)
     if result is not None:
-        print(f"2式收敛 解为: {result:.5f}")
+        print(f"(2)收敛 解为: {result:.5f}")
     else:
-        print("2式不收敛")
+        print("(2)不收敛")