修改曲线曲面积分

curvilinear_and_surface_integaration.py

@@ -14,6 +14,9 @@ def first_kind_curve_integration(r, t_range, function):
     :return: 第一类曲线积分的值
     """
     t = sp.symbols('t')
+    r_tuple = eval(r)  # 将输入的字符串转换为元组
+    # 将元组中每个元素转换为sympy表达式（类似处理function的方式）
+    r = tuple(sp.sympify(convert_formula(elem)) for elem in r_tuple)
     if len(r) == 2:
         x, y = r
         dx_dt = sp.diff(x, t)
@@ -25,8 +28,10 @@ def first_kind_curve_integration(r, t_range, function):
         dy_dt = sp.diff(y, t)
         dz_dt = sp.diff(z, t)
         ds = sp.sqrt(dx_dt**2 + dy_dt**2 + dz_dt**2)
+    else:
+        raise ValueError("参数方程长度必须为2（二维曲线）或3（三维曲线）")
     function = sp.sympify(convert_formula(function))
-    lower, upper = t_range
+    lower, upper = eval(t_range)
     result = sp.integrate(function * ds, (t, lower, upper))
     return result
 
@@ -40,13 +45,17 @@ def second_kind_curve_integration(P, Q, r, t_range):
     :return: 第二类曲线积分的值
     """
     t = sp.symbols('t')
+    # 转换r为sympy表达式元组
+    r_tuple = eval(r)
+    r = tuple(sp.sympify(convert_formula(elem)) for elem in r_tuple)
     x, y = r
     dx_dt = sp.diff(x, t)
     dy_dt = sp.diff(y, t)
-    P = sp.sympify(convert_formula(P))
-    Q = sp.sympify(convert_formula(Q))
-    lower, upper = t_range
-    result = sp.integrate(P * dx_dt + Q * dy_dt, (t, lower, upper))
+    # 将 P 和 Q 中的 x、y 替换为 t 的函数
+    P_expr = sp.sympify(convert_formula(P)).subs({sp.symbols('x'): x, sp.symbols('y'): y})
+    Q_expr = sp.sympify(convert_formula(Q)).subs({sp.symbols('x'): x, sp.symbols('y'): y})
+    lower, upper = eval(t_range)
+    result = sp.integrate(P_expr * dx_dt + Q_expr * dy_dt, (t, lower, upper))
     return result
 
 def first_kind_surface_integration(r, u_range, v_range, function):
@@ -59,14 +68,18 @@ def first_kind_surface_integration(r, u_range, v_range, function):
     :return: 第一类曲面积分的值
     """
     u, v = sp.symbols('u v')
+    # 转换r为sympy表达式元组
+    r_tuple = eval(r)
+    r = tuple(sp.sympify(convert_formula(elem)) for elem in r_tuple)
     x, y, z = r
     ru = (sp.diff(x, u), sp.diff(y, u), sp.diff(z, u))
     rv = (sp.diff(x, v), sp.diff(y, v), sp.diff(z, v))
     cross_product = (ru[1]*rv[2] - ru[2]*rv[1], ru[2]*rv[0] - ru[0]*rv[2], ru[0]*rv[1] - ru[1]*rv[0])
     E = sp.sqrt(cross_product[0]**2 + cross_product[1]**2 + cross_product[2]**2)
+    # 转换function为sympy表达式
     function = sp.sympify(convert_formula(function))
-    u1, u2 = u_range
-    v1, v2 = v_range
+    u1, u2 = eval(u_range)
+    v1, v2 = eval(v_range)
     integration1 = sp.integrate(function * E, (u, u1, u2))
     result = sp.integrate(integration1, (v, v1, v2))
     return result
@@ -84,16 +97,23 @@ def second_kind_surface_integration(P, Q, R, r, u_range, v_range):
     :return: 第二类曲面积分的值
     """
     u, v = sp.symbols('u v')
+    # 转换r为sympy表达式元组
+    r_tuple = eval(r)
+    r = tuple(sp.sympify(convert_formula(elem)) for elem in r_tuple)
     x, y, z = r
     ru = (sp.diff(x, u), sp.diff(y, u), sp.diff(z, u))
     rv = (sp.diff(x, v), sp.diff(y, v), sp.diff(z, v))
+    # 计算叉乘 cross_product（原方向指向内部，取反后指向外侧）
     cross_product = (ru[1]*rv[2] - ru[2]*rv[1], ru[2]*rv[0] - ru[0]*rv[2], ru[0]*rv[1] - ru[1]*rv[0])
-    P = sp.sympify(convert_formula(P))
-    Q = sp.sympify(convert_formula(Q))
-    R = sp.sympify(convert_formula(R))
-    u1, u2 = u_range
-    v1, v2 = v_range
-    integration1 = sp.integrate(P * cross_product[0] + Q * cross_product[1] + R * cross_product[2], (u, u1, u2))
+    # 取反叉乘结果以匹配外侧法向量
+    cross_product = (-cross_product[0], -cross_product[1], -cross_product[2])
+    # 将 P、Q、R 中的 x、y、z 替换为 u、v 的函数
+    P_expr = sp.sympify(convert_formula(P)).subs({sp.symbols('x'): x, sp.symbols('y'): y, sp.symbols('z'): z})
+    Q_expr = sp.sympify(convert_formula(Q)).subs({sp.symbols('x'): x, sp.symbols('y'): y, sp.symbols('z'): z})
+    R_expr = sp.sympify(convert_formula(R)).subs({sp.symbols('x'): x, sp.symbols('y'): y, sp.symbols('z'): z})
+    u1, u2 = eval(u_range)
+    v1, v2 = eval(v_range)
+    integration1 = sp.integrate(P_expr * cross_product[0] + Q_expr * cross_product[1] + R_expr * cross_product[2], (u, u1, u2))
     result = sp.integrate(integration1, (v, v1, v2))
     return result
 
@@ -280,11 +300,4 @@ def UI():
 
 if __name__ == "__main__":
     UI()
-    unittest.main(exit=False)
-
-
-
-
-
-
-
+    unittest.main(exit=False)