v1.0

.idea/.gitignore

@@ -0,0 +1,3 @@
+# 默认忽略的文件
+/shelf/
+/workspace.xml

.idea/.name

@@ -0,0 +1 @@
+FunctionDisplay_X5.py

.idea/ijf6mgr5.iml

@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<module type="PYTHON_MODULE" version="4">
+  <component name="NewModuleRootManager">
+    <content url="file://$MODULE_DIR$" />
+    <orderEntry type="jdk" jdkName="Python 3.9" jdkType="Python SDK" />
+    <orderEntry type="sourceFolder" forTests="false" />
+  </component>
+</module>

.idea/inspectionProfiles/profiles_settings.xml

@@ -0,0 +1,6 @@
+<component name="InspectionProjectProfileManager">
+  <settings>
+    <option name="USE_PROJECT_PROFILE" value="false" />
+    <version value="1.0" />
+  </settings>
+</component>

.idea/misc.xml

@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<project version="4">
+  <component name="Black">
+    <option name="sdkName" value="Python 3.8" />
+  </component>
+  <component name="ProjectRootManager" version="2" project-jdk-name="Python 3.9" project-jdk-type="Python SDK" />
+</project>

.idea/modules.xml

@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<project version="4">
+  <component name="ProjectModuleManager">
+    <modules>
+      <module fileurl="file://$PROJECT_DIR$/.idea/ijf6mgr5.iml" filepath="$PROJECT_DIR$/.idea/ijf6mgr5.iml" />
+    </modules>
+  </component>
+</project>

.idea/vcs.xml

@@ -0,0 +1,6 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<project version="4">
+  <component name="VcsDirectoryMappings">
+    <mapping directory="" vcs="Git" />
+  </component>
+</project>

step1/function.json

@@ -0,0 +1 @@
+{"sin(x)":"sin(x)","cos(x)":"cos(x)","tan(x)":"tan(x)"}

step1/step.py

@@ -0,0 +1 @@
+############### 请在右侧图形化界面，全屏展示界面，完成本关卡 ###################

step1/step1.sh

@@ -0,0 +1,6 @@
+xrandr --addmode VNC-0 "1920x1080"
+xrandr --output VNC-0 --mode "1920x1080"
+nohup python3 x5/FunctionDisplay_X5.py &
+echo "编译成功"
+echo "运行成功"
+echo "测评成功"

x1/x1_1.py

@@ -0,0 +1,11 @@
+import numpy as np
+
+def x1_1():  # 随机给出1000个点坐标,赋值给xyMap,<class 'numpy.ndarray'>
+    shape = [1000, 2]
+    xyMap = np.random.randint(-200, 200, size=shape)
+    return xyMap
+
+
+
+if __name__ == '__main__':
+    print(x1_1())

x1/x1_2.py

@@ -0,0 +1,27 @@
+import numpy as np
+def x1_2(problemIndex):  # 程序给出任一函数 y=f(x)计算x=1到1000的y值，赋值给xyMap
+    # shape = [1000,2]                                #x值为1到1000，y为其对应函数值
+    xyMap = np.random.rand(1000, 2)
+    if problemIndex == 1:
+        for x in range(1, 1001):
+            xyMap[x - 1][0] = x  # xyMap序号为0-999
+            xyMap[x - 1][1] = np.sin(x)
+        return xyMap
+    elif problemIndex == 2:
+        for x in range(1, 1001):
+            xyMap[x - 1][0] = x
+            xyMap[x - 1][1] = np.cos(x)
+        return xyMap
+    elif problemIndex == 3:
+        for x in range(1, 1001):
+            xyMap[x - 1][0] = x
+            xyMap[x - 1][1] = np.tan(x)
+        return xyMap
+    elif problemIndex == 4:
+        for x in range(1, 1001):
+            xyMap[x - 1][0] = x
+            xyMap[x - 1][1] = x * 2 + 2
+        return xyMap
+
+if __name__ == '__main__':
+    print(x1_2(4)[:50])

x1/x1_3.py

@@ -0,0 +1,43 @@
+import numpy as np
+import math
+
+def x1_3(problemIndex):  # 程序给出任一函数y=f(x)计算x=-500到+500的y值赋值给xyMap
+    c = 0  # 此处x赋值为-500到-1到，1到500到1000个
+    shape = [1000, 2]  # y赋值为其对应的函数
+    xyMap = np.random.rand(1000, 2)
+    if problemIndex == 1:
+        for x in range(-500, 500):
+            if (x == 0):
+                continue
+            xyMap[c][0] = x
+            xyMap[c][1] = math.sin(x)
+            c += 1
+        return xyMap
+    elif problemIndex == 2:
+        for x in range(-500, 500):
+            if (x == 0):
+                continue
+            xyMap[c][0] = x
+            xyMap[c][1] = math.cos(x)
+            c += 1
+        return xyMap
+    elif problemIndex == 3:
+        for x in range(-500, 500):
+            if (x == 0):
+                continue
+            xyMap[c][0] = x
+            xyMap[c][1] = math.tan(x)
+            c += 1
+        return xyMap
+    elif problemIndex == 4:
+        for x in range(-500, 501):
+            if (x == 0):
+                continue
+            xyMap[c][0] = x
+            xyMap[c][1] = x * 2 + 2
+            c += 1
+        return xyMap
+
+
+if __name__ == '__main__':
+    print(x1_3(1))

x1/x1_4.py

@@ -0,0 +1,31 @@
+import numpy as np
+import math
+
+def x1_4(ProblemIndex):
+    step = 3  # 步长
+    y = []
+    i, c = 0, 0
+    number = 1000  # 个数
+    while (True):
+        if (c == number):
+            break
+        else:
+            y.append(i)
+            i += step
+            c += 1
+    y = np.array(y)
+    xyMap = np.random.rand(1000, 2)
+    if (ProblemIndex == 1):
+        for i in range(len(y)):
+            xyMap[i][0] = y[i]
+            xyMap[i][1] = 2 * y[i] + 1
+        return xyMap
+    elif (ProblemIndex == 2):
+        for i in range(len(y)):
+            xyMap[i][0] = y[i]
+            xyMap[i][1] = y[i] / 3
+        return xyMap
+
+
+if __name__ == '__main__':
+    print(x1_4(1))

x3/FunctionDisplay_X3.py

@@ -0,0 +1,362 @@
+import math
+from collections import OrderedDict
+from time import sleep
+from ttkbootstrap import *
+import tkinter.font as tkFont
+from tkinter import messagebox
+from tkinter.ttk import Treeview
+
+import sympy
+from numpy import arange
+from functionUtil import FunctionUtil
+
+
+# 获取文本的宽度和高度
+def get_text_dimensions(canvas, text, font):
+    text_id = canvas.create_text(0, 0, text=text, font=font, anchor="center")
+    bbox = canvas.bbox(text_id)
+    width = bbox[2] - bbox[0]
+    height = bbox[3] - bbox[1]
+    canvas.delete(text_id)
+    return width, height
+
+
+# 在画布中央绘制文本
+def center_text(canvas, text, font):
+    canvas_width = int(canvas.cget("width"))
+    text_width, text_height = get_text_dimensions(canvas, text, font)
+    x = canvas_width // 2
+    y = 200
+    canvas.create_text(x, y, text=text, font=font, anchor="center")
+
+
+class Graph(Canvas):
+    def __init__(self, master=None, **kwargs):
+        super().__init__(master, **kwargs)
+        self.width = int(self.cget('width'))
+        self.height = int(self.cget('height'))
+        self.origin = (self.width / 2, self.height / 2)
+        self.bili_x = 20
+        self.bili_y = 20
+        self.draw_axis()
+        self.draw_scale()
+
+    def draw_axis(self):
+        """
+        绘制坐标轴
+        """
+        self.delete("all")
+        self.create_line(0, self.origin[1], self.width, self.origin[1], fill='black', arrow=LAST)  # 一象限xy轴
+        self.create_line(self.origin[0], 0, self.origin[0], self.height, fill='black', arrow=FIRST)
+
+    def draw_scale(self):
+        """
+        绘制刻度值
+        """
+        for i in range(-math.ceil((self.origin[0] / self.bili_x)) + 1, math.ceil((self.width - self.origin[0]) / self.bili_x)):
+            j = i * self.bili_x
+            if (i % 10 == 0):
+                self.create_line(j + self.origin[0], self.origin[1], j + self.origin[0], self.origin[1] - 5, fill='black')
+                self.create_text(j + self.origin[0], self.origin[1] + 10, text=i)
+        for i in range(-math.ceil((self.height - self.origin[1]) / self.bili_y) + 1, math.ceil((self.origin[1] / self.bili_y))):
+            j = -(i * self.bili_y)
+            if (i == 0):
+                continue
+            elif (i % 2 == 0):
+                self.create_line(self.origin[0], j + self.origin[1], self.origin[0] + 5, j + self.origin[1], fill='black')
+                self.create_text(self.origin[0] - 10, j + self.origin[1], text=i)
+
+    def switch_quadrant(self, quadrant):
+        """
+        切换象限
+        """
+        if quadrant == 1:
+            self.origin = (50, self.height - 50)
+        else:
+            self.origin = (self.width / 2, self.height / 2)
+        self.draw_axis()
+        self.draw_scale()
+
+    def draw_graph(self, func, draw_precision=0.1, count=100,  bili_x=20, bili_y=40, c='blue'):
+        'xmin,xmax 自变量的取值范围； c 图像颜色'
+        'x0,y0 原点坐标  w,h 横纵轴半长 draw_precision 步进'
+        self.bili_x, self.bili_y = int(bili_x), int(bili_y)
+        self.draw_axis()
+        self.draw_scale()
+        w1, w2 = self.bili_x, self.bili_y  # w1,w2为自变量和函数值在横纵轴上的放大倍数
+        xmin, xmax = -math.ceil((self.origin[0] / self.bili_x)) + 1, math.ceil((self.width - self.origin[0]) / self.bili_x)
+        co2 = []
+        try:
+            for x in arange(xmin, xmax, draw_precision):  # draw_precision----画图精度
+                y = sympy.sympify(func).subs("x", x).evalf()
+                coord = self.origin[0] + w1 * x, self.origin[1] - w2 * y, self.origin[0] + w1 * x + 1, self.origin[1] - w2 * y + 1
+                if abs(coord[1]) < self.height:  # 超过w,h就截断
+                    co2.append((self.origin[0] + w1 * x, self.origin[1] - w2 * y))
+            if count is None:
+                length = len(co2)
+            else:
+                length = len(co2[:int(count)])
+            for i in range(length):
+                if (draw_precision >= 1):
+                    self.create_line(co2, fill=c, width=1)
+                if (i + 1 == len(co2)):
+                    break
+                if (abs(co2[i][1] - co2[i + 1][1]) > 100):
+                    continue
+                else:
+                    self.create_line(co2[i], co2[i + 1], fill=c, width=1)
+                sleep(0.01)
+                self.update()
+        except Exception as E:
+            messagebox.showerror("错误", message=f"函数有误!\n{E}")
+
+
+class ExpressionCanvas(Canvas):
+    def __init__(self, master, *args, **kwargs):
+        super().__init__(master, *args, **kwargs)
+        self.node_width = 60
+        self.node_height = 30
+        self.x_spacing = 10
+        self.y_spacing = 70
+        self.level = {}
+
+    def add_node(self, text, x, y, parent=None):
+        node_width = len(text) * 5 + 20
+        if node_width < 40:
+            node_width = 50
+        # 创建节点
+        coords = [x - node_width / 2, y, x + node_width / 2, y + self.node_height]
+        if coords[1] in self.level:
+            max_x = max(self.level[coords[1]])
+            if coords[0] <= max_x:
+                x = max_x + node_width / 2 + self.x_spacing
+            node_id = self.create_rectangle(x - node_width / 2, y, x + node_width / 2, y + self.node_height,
+                                            fill="white")
+            sleep(0.2)
+            self.update()
+        elif text == "x":
+            x = self.coords(parent)[0] + node_width / 2
+            node_id = self.create_rectangle(x - node_width / 2, y, x + node_width / 2, y + self.node_height,
+                                            fill="white")
+            sleep(0.2)
+            self.update()
+        else:
+            node_id = self.create_rectangle(x - node_width / 2, y, x + node_width / 2, y + self.node_height, fill="white")
+            sleep(0.2)
+            self.update()
+        coords = [x - node_width / 2, y, x + node_width / 2, y + self.node_height]
+        if coords[1] in self.level:
+            self.level[coords[1]].append(coords[2])
+        else:
+            self.level[coords[1]] = [coords[2]]
+        text_id = self.create_text(x + 5, y + self.node_height // 2, text=text, anchor="center")
+        sleep(0.2)
+        self.update()
+        # 绘制父节点和当前节点的连线
+        if parent:
+            parent_coords = self.coords(parent)
+            parent_x = parent_coords[0] + (parent_coords[2] - parent_coords[0]) // 2
+            parent_y = parent_coords[1] + (parent_coords[3] - parent_coords[1]) // 2
+            self.create_line(parent_x, parent_y + self.node_height // 2, x, y, fill="black")
+            self.update()
+        return node_id
+
+    def draw_expression(self, expression, x, y, parent=None, sibling_width=0):
+        # 创建节点并绘制表达式文本
+        node = self.add_node(str(expression), x, y, parent=parent)
+        if expression.is_Atom:
+            return node
+        # 处理子表达式
+        num_children = len(expression.args)
+        total_width = num_children * self.node_width + (num_children - 1) * self.x_spacing
+        start_x = x - total_width // 2
+        for subexpr in expression.args:
+            subnode = self.draw_expression(subexpr, start_x, y + self.y_spacing, parent=node, sibling_width=total_width)
+            start_x += self.node_width + self.x_spacing
+        return node
+
+
+class FunctionDisplay(Frame):
+    def __init__(self, master, attr):
+        super().__init__(master)
+        self.attr = attr
+        self.font_style = tkFont.Font(family="Lucida Grande", size=30)
+        self.functions = FunctionUtil()
+        self.master = master
+        self.create_window()
+
+    def add_function(self):
+        """
+        用户添加函数
+        """
+        input_func = self.func_input.get()
+        if input_func == "":
+            messagebox.showwarning("注意", message="请输入函数！")
+            return
+        elif input_func.find("=") < 0:
+            messagebox.showerror("注意", message="添加函数的格式为：\nSinPlusCos(x)=sin(x)+cos(x)")
+            return
+        left_var = input_func.split("=")[0]
+        right_var = input_func.split("=")[1]
+        try:
+            function = self.functions.get_function_by_iter(right_var)
+            sympy.sympify(function, evaluate=False)
+        except Exception as E:
+            messagebox.showerror("注意", message="函数解析错误，请仔细检查函数是否正确！")
+            self.func_input.delete(0, END)
+            return
+        if self.functions.check_function_exit(left_var):
+            result = messagebox.askokcancel(title='标题~', message=f'函数{left_var}已经存在，是否需要覆盖！')
+            if result:
+                self.functions.add_function(left_var, right_var)
+                messagebox.showinfo(title="提示", message="覆盖成功！")
+                self.func_input.delete(0, END)
+            return
+        self.functions.add_function(left_var, right_var)
+        messagebox.showinfo(title="提示", message="添加成功！")
+        self.func_input.delete(0, END)
+
+    def update_quadrant(self):
+        """
+        更换象限
+        """
+        self.axis_canvas.switch_quadrant(self.quadrant.get())
+        self.print_function()
+
+    def print_function(self):
+        """
+        输出
+        """
+        input_func = self.func_input.get()
+        if input_func == "":
+            messagebox.showwarning("注意", message="请输入函数！")
+            return
+        step = eval(self.x_step.get()) if not self.x_step.get() == "" else 0.1
+        count = self.x_count.get() if not self.x_count.get() == "" else None
+        x_scale = self.x_scale.get() if not self.x_scale.get() == "" else 20
+        y_scale = self.y_scale.get() if not self.y_scale.get() == "" else 40
+        if input_func.find("=") >= 0:
+            left_var = input_func.split("=")[0]
+            right_var = input_func.split("=")[1]
+            if self.functions.check_function_exit(right_var):
+                func = self.functions.get_function_by_iter(right_var)
+                self.axis_canvas.draw_graph(func, step, count,
+                                            x_scale, y_scale)
+            else:
+                self.axis_canvas.draw_graph(input_func, step, count,
+                                            x_scale, y_scale)
+        else:
+            if self.functions.check_function_exit(input_func):
+                func = self.functions.get_function_by_iter(input_func)
+                self.axis_canvas.draw_graph(func, step, count,
+                                            x_scale, y_scale)
+            else:
+                self.axis_canvas.draw_graph(input_func, step, count,
+                                        x_scale, y_scale)
+
+    def create_form(self):
+        bottom_frame = Frame(self.master, width=self.attr["width"], height=self.attr["height"] * 0.3)
+        self.func_input = Entry(bottom_frame, font=self.font_style, width=40)
+        self.func_input.grid(row=0, column=0, columnspan=4, padx=30)
+        self.add_func_button = Button(bottom_frame, text="用户命名并新增基本函数", command=self.add_function)
+        self.add_func_button.grid(row=0, column=4, padx=10)
+        Label(bottom_frame, text="x步长", font=("Lucida Grande", 20)).grid(row=1, column=0, padx=30)
+        self.x_step = Entry(bottom_frame, font=self.font_style, width=10)
+        self.x_step.grid(row=1, column=1, padx=10, pady=10)
+        Label(bottom_frame, text="x个数", font=("Lucida Grande", 20)).grid(row=1, column=2, padx=30)
+        self.x_count = Entry(bottom_frame, font=self.font_style, width=10)
+        self.x_count.grid(row=1, column=3, padx=10, pady=10)
+
+        Label(bottom_frame, text="坐标轴", font=("Lucida Grande", 20)).grid(row=2, column=0, padx=30)
+        self.quadrant = IntVar()
+        self.quadrant.set(4)
+        Radiobutton(bottom_frame, text="四象限",  command=self.update_quadrant, value=4, variable=self.quadrant).grid(row=2, column=1, padx=10, pady=10)
+        Radiobutton(bottom_frame, text="一象限",  command=self.update_quadrant, value=1, variable=self.quadrant).grid(row=2, column=2, padx=10, pady=10)
+
+        Label(bottom_frame, text="x放大倍数", font=("Lucida Grande", 20)).grid(row=3, column=0, padx=30)
+        self.x_scale = Entry(bottom_frame, font=self.font_style,  width=10)
+        self.x_scale.grid(row=3, column=1, padx=10, pady=10)
+        Label(bottom_frame, text="y放大倍数", font=("Lucida Grande", 20)).grid(row=3, column=2, padx=30)
+        self.y_scale = Entry(bottom_frame, font=self.font_style,  width=10)
+        self.y_scale.grid(row=3, column=3, padx=10, pady=10)
+
+        Button(bottom_frame, text="输出",
+               command=self.print_function, width=5).grid(row=1, rowspan=3, column=4, sticky="w")
+        bottom_frame.place(x=0, y=self.attr["height"] * 0.65 + 20)
+
+    def show_user_function(self):
+        children_window = Toplevel(root)
+        children_window.title("用户自定义函数")
+        children_window.geometry('350x260+450+200')
+        packet_frame = Frame(children_window)
+        packet_frame.grid(row=0, column=0, columnspan=3, padx=10, pady=5)
+        function_treeview = Treeview(packet_frame, columns=("function_name", "function"), show="headings")
+        function_treeview.heading("function_name", text="函数名称")
+        function_treeview.column("function_name", width=100, anchor=CENTER)
+        function_treeview.heading("function", text="函数体")
+        function_treeview.column("function", width=200, anchor=CENTER)
+        function_treeview.pack(side="left", fill="both")
+        scrollbar = Scrollbar(packet_frame, orient="vertical", command=function_treeview.yview)
+        scrollbar.pack(side="right", fill="y")
+        function_treeview.configure(yscrollcommand=scrollbar.set)
+
+        def delete_item():
+            selected_item = function_treeview.selection()
+            for item in selected_item:
+                item_data = function_treeview.item(item)
+                function_treeview.delete(item)
+                self.functions.data.pop(item_data["values"][0])
+                self.functions.save()
+
+        context_menu = Menu(root, tearoff=False)
+        context_menu.add_command(label="删除", command=delete_item)
+
+        def popup_menu(event):
+            if function_treeview.identify_region(event.x, event.y) == "cell":
+                function_treeview.selection_set(function_treeview.identify_row(event.y))
+                context_menu.post(event.x_root, event.y_root)
+
+        function_treeview.bind("<Button-3>", popup_menu)
+        for function_name, function in self.functions.data.items():
+            function_treeview.insert("", "end", values=(function_name, function))
+
+
+    def create_window(self):
+        self.axis_canvas = Graph(self.master, width=self.attr["width"] * 0.65, height=self.attr["height"] * 0.65, bg="#cdcdcd")
+        self.axis_canvas.place(x=0, y=0)
+        self.text_canvas = ExpressionCanvas(self.master, width=self.attr["width"] * 0.35, height=self.attr["height"] * 0.65, bg="#cdcdcd")
+        self.text_canvas.create_text(20 + 180, 35, text='可识别基本函数', fill='red', font=("Purisa", 25, "bold"))
+        menubar = Menu(root)
+        menubar.add_command(label='查看自定义函数', command=self.show_user_function)
+        root.config(menu=menubar)
+        text = "可支持下列函数的加减乘除组合运算\n" \
+               "\ty=sin(x)\n" \
+               "\tcos(x)\n" \
+               "\ttan(x)\n" \
+               "\tcot(x)\n" \
+               "\tx^n\n" \
+               "\tP1(x)=x^3+x^2+x+5\n" \
+               "---将括号内的表达式命名为P1,P1可\n" \
+               "出现于用户构造中"
+        self.text_canvas.create_text(20 + 180, 35, text='可识别基本函数', fill='red', font=("Purisa", 25, "bold"))
+        center_text(self.text_canvas, text, ("Lucida Grande", 17))
+        self.text_canvas.place(x=int(self.attr["width"] * 0.65), y=0)
+        self.create_form()
+
+
+if __name__ == '__main__':
+    root = Window()
+    screenwidth = root.winfo_screenwidth()
+    screenheight = root.winfo_screenheight()
+    root_attr = {
+        "width": 1200,
+        "height": 800,
+    }
+    alignstr = '%dx%d+%d+%d' % (root_attr['width'], root_attr['height'], (screenwidth - root_attr['width']) / 2,
+                                (screenheight - root_attr['height']) / 2)
+    root.geometry(alignstr)
+    root.resizable(width=False, height=False)
+    app = FunctionDisplay(root, root_attr)
+    ttk.Style().configure("TButton", font="-size 18")
+    ttk.Style().configure("TRadiobutton", font="-size 18")
+    root.mainloop()

x3/function.json

@@ -0,0 +1 @@
+{"f1": "x**2 + 2*x + 1", "f3": "x**2", "f2": "(x/100)**2+2*(x/100)+1", "sinpluscos(x)": "cos(x) + sin(x)"}

x3/functionUtil.py

@@ -0,0 +1,57 @@
+import json
+import re
+
+
+class FunctionUtil:
+    def __init__(self):
+        self.filename = "./function.json"
+        self.data = {}
+        self.load()
+
+    def load(self):
+        """
+        加载文件数据
+        """
+        try:
+            with open(self.filename, 'r', encoding="utf-8") as f:
+                self.data = json.load(f)
+        except FileNotFoundError:
+            pass
+
+    def save(self):
+        """
+        将函数保存至json文件当中
+        """
+        with open(self.filename, "w", encoding="utf-8") as f:
+            json.dump(self.data, f)
+
+    def check_function_exit(self, function):
+        """
+        检查用户输入的函数是否包含用户自定义函数
+        """
+        for key in self.data.keys():
+            if function.find(key) >=0:
+                return True
+        return False
+
+    def add_function(self, key, value):
+        """
+        添加函数
+        """
+        self.data[key.strip()] = value.strip()
+        self.save()
+
+    def get_function_by_iter(self, key):
+        result = key
+        for dict_key in self.data.keys():
+            if result.find(dict_key) >= 0:
+                value = result.replace(dict_key, self.data[dict_key])
+                result = self.replace_values_recursive(value)
+        return result
+
+    def replace_values_recursive(self, value):
+        for key in self.data:
+            if key in value:
+                replacement = self.data[key]
+                value = value.replace(key, replacement)
+        return value

x3/test.py

@@ -0,0 +1,9 @@
+import sympy
+
+from functionUtil import FunctionUtil
+
+
+# f = FunctionUtil()
+# print(f.get_function_by_iter("f1 + f3"))
+
+print(sympy.sympify("(x/100)**2+2*(x/100)+1"))

x3/x3_210.py

@@ -0,0 +1,25 @@
+def trapezoidal_rule(a, b, n):
+    """
+    梯形法进行数值积分
+
+    参数:
+        - f: 要积分的函数
+        - a: 积分区间的起始点
+        - b: 积分区间的结束点
+        - n: 划分的子区间数
+
+    返回:
+        - 积分近似值
+    """
+    h = (b - a) / n  # 子区间宽度
+    x = [a + i * h for i in range(n+1)]  # 子区间的节点
+    y = [x_i ** 2 for x_i in x]  # 子区间节点对应的函数值
+    integral = (h / 2) * (y[0] + 2 * sum(y[1:n]) + y[n])  # 梯形法计算积分值
+    return integral
+
+if __name__ == '__main__':
+    a = 0  # 积分区间的起始点
+    b = 1  # 积分区间的结束点
+    n = 100  # 划分的子区间数
+    integral = trapezoidal_rule(a, b, n)
+    print("数值积分的近似值:", integral)

x3/x3_211.py

@@ -0,0 +1,25 @@
+def central_difference(f, x, h):
+    """
+    中心差分法进行数值微分（计算导数）
+
+    参数:
+        - f: 要求导数的函数
+        - x: 求导点的横坐标
+        - h: 步长
+
+    返回:
+        - 导数的近似值
+    """
+    df = (f(x + h) - f(x - h)) / (2 * h)  # 中心差分法计算导数
+
+    return df
+
+def f(x):
+    return x**2
+
+if __name__ == '__main__':
+    x = 2  # 求导点的横坐标
+    h = 0.01  # 步长
+
+    df = central_difference(f, x, h)
+    print("导数的近似值:", df)

x3/x3_212.py

@@ -0,0 +1,39 @@
+def newton_method(f, f_prime, x0, tol=1e-6, max_iter=100):
+    """
+    牛顿迭代法计算函数值为0的解
+
+    参数:
+        - f: 要求解的函数
+        - f_prime: 函数的导数
+        - x0: 初始猜测值
+        - tol: 容差（迭代停止的条件，可选，默认为1e-6）
+        - max_iter: 最大迭代次数（可选，默认为100）
+
+    返回:
+        - 解的近似值
+    """
+    x = x0  # 初始猜测值
+    for _ in range(max_iter):
+        fx = f(x)  # 函数值
+        if abs(fx) < tol:
+            # 已达到容差要求，返回解的近似值
+            return x
+        fpx = f_prime(x)  # 函数的导数值
+        if abs(fpx) < tol:
+            # 导数值过小，无法继续迭代
+            break
+        x -= fx / fpx  # 牛顿迭代公式
+    # 迭代未收敛或超过最大迭代次数，返回None表示未找到解
+    return None
+
+def f(x):
+    return x**2 - 4
+
+def f_prime(x):
+    return 2 * x
+
+
+if __name__ == '__main__':
+    x0 = 1  # 初始猜测值
+    solution = newton_method(f, f_prime, x0)
+    print("解的近似值:", solution)

x4/FunctionDisplay_X4.py

@@ -0,0 +1,400 @@
+import math
+from collections import OrderedDict
+from time import sleep
+from ttkbootstrap import *
+import tkinter.font as tkFont
+from tkinter import messagebox
+from tkinter.ttk import Treeview
+
+import sympy
+from numpy import arange
+from functionUtil import FunctionUtil
+
+
+# 获取文本的宽度和高度
+def get_text_dimensions(canvas, text, font):
+    text_id = canvas.create_text(0, 0, text=text, font=font, anchor="center")
+    bbox = canvas.bbox(text_id)
+    width = bbox[2] - bbox[0]
+    height = bbox[3] - bbox[1]
+    canvas.delete(text_id)
+    return width, height
+
+
+# 在画布中央绘制文本
+def center_text(canvas, text, font):
+    canvas_width = int(canvas.cget("width"))
+    text_width, text_height = get_text_dimensions(canvas, text, font)
+    x = canvas_width // 2
+    y = 200
+    canvas.create_text(x, y, text=text, font=font, anchor="center")
+
+
+class Graph(Canvas):
+    def __init__(self, master=None, **kwargs):
+        super().__init__(master, **kwargs)
+        self.width = int(self.cget('width'))
+        self.height = int(self.cget('height'))
+        self.origin = (self.width / 2, self.height / 2)
+        self.bili_x = 20
+        self.bili_y = 20
+        self.draw_axis()
+        self.draw_scale()
+
+    def draw_axis(self):
+        """
+        绘制坐标轴
+        """
+        self.delete("all")
+        self.create_line(0, self.origin[1], self.width, self.origin[1], fill='black', arrow=LAST)  # 一象限xy轴
+        self.create_line(self.origin[0], 0, self.origin[0], self.height, fill='black', arrow=FIRST)
+
+    def draw_scale(self):
+        """
+        绘制刻度值
+        """
+        for i in range(-math.ceil((self.origin[0] / self.bili_x)) + 1, math.ceil((self.width - self.origin[0]) / self.bili_x)):#将画布x轴每20个像素点作为一个刻度，i向上取整代表刻度值
+            j = i * self.bili_x #j代表的是i刻度值这一点的像素值
+            if (i % 10 == 0):#如果刻度值是十的倍数
+                self.create_line(j + self.origin[0], self.origin[1], j + self.origin[0], self.origin[1] - 5, fill='black')
+                self.create_text(j + self.origin[0], self.origin[1] + 10, text=i)
+        for i in range(-math.ceil((self.height - self.origin[1]) / self.bili_y) + 1, math.ceil((self.origin[1] / self.bili_y))):#将画布y轴每20个像素点作为一个刻度，i向上取整代表刻度值
+            j = -(i * self.bili_y)
+            if (i == 0):#不重复写零点
+                continue
+            elif (i % 2 == 0):
+                self.create_line(self.origin[0], j + self.origin[1], self.origin[0] + 5, j + self.origin[1], fill='black')
+                self.create_text(self.origin[0] - 10, j + self.origin[1], text=i)
+
+    def switch_quadrant(self, quadrant):
+        """
+        切换象限
+        """
+        if quadrant == 1:
+            self.origin = (50, self.height - 50)
+        else:
+            self.origin = (self.width / 2, self.height / 2)
+        self.draw_axis()
+        self.draw_scale()
+
+    def get_xy(self):
+        return -math.ceil((self.origin[0] / self.bili_x)) + 1, math.ceil((self.width - self.origin[0]) / self.bili_x)
+        
+    def draw_graph(self, func, draw_precision=0.1, count=1000,  bili_x=20, bili_y=40, c='blue'):
+        'xmin,xmax 自变量的取值范围； c 图像颜色'
+        'x0,y0 原点坐标  w,h 横纵轴半长 draw_precision 步进'
+        self.bili_x, self.bili_y = int(bili_x), int(bili_y)
+        self.draw_axis()
+        self.draw_scale()
+        w1, w2 = self.bili_x, self.bili_y  # w1,w2为自变量和函数值在横纵轴上的放大倍数
+        xmin, xmax = self.get_xy()
+        co2 = []
+        try:
+            for x in arange(xmin, xmax, draw_precision):  # draw_precision----画图精度
+                y = sympy.sympify(func, convert_xor=True).subs("x", x).evalf()
+                coord = self.origin[0] + w1 * x, self.origin[1] - w2 * y, self.origin[0] + w1 * x + 1, self.origin[1] - w2 * y + 1
+                if abs(coord[1]) < self.height:  # 超过w,h就截断
+                    co2.append((self.origin[0] + w1 * x, self.origin[1] - w2 * y))
+            if count is None:
+                length = len(co2)
+            else:
+                length = len(co2[:int(count)])
+            for i in range(length):
+                if (draw_precision >= 1):
+                    self.create_line(co2, fill=c, width=1)
+                if (i + 1 == len(co2)):
+                    break
+                if (abs(co2[i][1] - co2[i + 1][1]) > 100):
+                    continue
+                else:
+                    self.create_line(co2[i], co2[i + 1], fill=c, width=1)
+                sleep(0.01)
+                self.update()
+        except Exception as E:
+            messagebox.showerror("错误", message=f"函数有误!\n{E}")
+
+
+class ExpressionCanvas(Canvas):
+    def __init__(self, master, *args, **kwargs):
+        super().__init__(master, *args, **kwargs)
+        self.node_width = 60
+        self.node_height = 30
+        self.x_spacing = 10
+        self.y_spacing = 70
+        self.level = {}
+
+    def add_node(self, text, x, y, parent=None):
+        node_width = len(text) * 5 + 20
+        if node_width < 40:
+            node_width = 50
+        # 创建节点
+        coords = [x - node_width / 2, y, x + node_width / 2, y + self.node_height]
+        if coords[1] in self.level:
+            max_x = max(self.level[coords[1]])
+            if coords[0] <= max_x:
+                x = max_x + node_width / 2 + self.x_spacing
+            node_id = self.create_rectangle(x - node_width / 2, y, x + node_width / 2, y + self.node_height,
+                                            fill="white")
+            sleep(0.2)
+            self.update()
+        elif text == "x":
+            x = self.coords(parent)[0] + node_width / 2
+            node_id = self.create_rectangle(x - node_width / 2, y, x + node_width / 2, y + self.node_height,
+                                            fill="white")
+            sleep(0.2)
+            self.update()
+        else:
+            node_id = self.create_rectangle(x - node_width / 2, y, x + node_width / 2, y + self.node_height, fill="white")
+            sleep(0.2)
+            self.update()
+        coords = [x - node_width / 2, y, x + node_width / 2, y + self.node_height]
+        if coords[1] in self.level:
+            self.level[coords[1]].append(coords[2])
+        else:
+            self.level[coords[1]] = [coords[2]]
+        text_id = self.create_text(x + 5, y + self.node_height // 2, text=text, anchor="center")
+        sleep(0.2)
+        self.update()
+        # 绘制父节点和当前节点的连线
+        if parent:
+            parent_coords = self.coords(parent)
+            parent_x = parent_coords[0] + (parent_coords[2] - parent_coords[0]) // 2
+            parent_y = parent_coords[1] + (parent_coords[3] - parent_coords[1]) // 2
+            self.create_line(parent_x, parent_y + self.node_height // 2, x, y, fill="black")
+            self.update()
+        return node_id
+
+    def draw_expression(self, expression, x, y, parent=None, sibling_width=0):
+        # 创建节点并绘制表达式文本
+        node = self.add_node(str(expression), x, y, parent=parent)
+        if expression.is_Atom:
+            return node
+        # 处理子表达式
+        num_children = len(expression.args)
+        total_width = num_children * self.node_width + (num_children - 1) * self.x_spacing
+        start_x = x - total_width // 2
+        for subexpr in expression.args:
+            subnode = self.draw_expression(subexpr, start_x, y + self.y_spacing, parent=node, sibling_width=total_width)
+            start_x += self.node_width + self.x_spacing
+        return node
+
+
+class FunctionDisplay(Frame):
+    def __init__(self, master, attr):
+        super().__init__(master)
+        self.attr = attr
+        self.font_style = tkFont.Font(family="Lucida Grande", size=30)
+        self.functions = FunctionUtil()
+        self.master = master
+        self.create_window()
+
+    def clear_text_canvas(self, event):
+        def clear_text():
+            self.text_canvas.delete("all")
+            self.text_canvas.create_text(20 + 180, 20, text='可识别基本函数', fill='red', font=("Purisa", 25, "bold"))
+            center_text(self.text_canvas, self.text, ("Lucida Grande", 15))
+        self.menu = Menu(self, tearoff=False)
+        self.menu.add_command(label="重置", command=clear_text)
+        self.menu.post(event.x_root, event.y_root)
+
+    def add_function(self):
+        """
+        用户添加函数
+        """
+        input_func = self.func_input.get()
+        if input_func == "":
+            messagebox.showwarning("注意", message="请输入函数！")
+            return
+        elif input_func.find("=") < 0:
+            messagebox.showerror("注意", message="添加函数的格式为：\nSinPlusCos(x)=sin(x)+cos(x)")
+            return
+        left_var = input_func.split("=")[0]
+        right_var = input_func.split("=")[1]
+        try:
+            function = self.functions.get_function_by_iter(right_var)
+            sympy.sympify(function, evaluate=False)
+        except Exception as E:
+            messagebox.showerror("注意", message="函数解析错误，请仔细检查函数是否正确！")
+            self.func_input.delete(0, END)
+            return
+        if self.functions.check_function_exit(left_var):
+            result = messagebox.askokcancel(title='标题~', message=f'函数{left_var}已经存在，是否需要覆盖！')
+            if result:
+                self.functions.add_function(left_var, right_var)
+                messagebox.showinfo(title="提示", message="覆盖成功！")
+                self.func_input.delete(0, END)
+            return
+        self.functions.add_function(left_var, right_var)
+        messagebox.showinfo(title="提示", message="添加成功！")
+        self.func_input.delete(0, END)
+
+    def update_quadrant(self):
+        """
+        更换象限
+        """
+        self.axis_canvas.switch_quadrant(self.quadrant.get())
+        self.print_function()
+
+    def print_function(self):
+        """
+        输出
+        """
+        self.text_canvas.delete("all")
+        self.text_canvas.level.clear()
+        input_func = self.func_input.get()
+        if input_func == "":
+            messagebox.showwarning("注意", message="请输入函数！")
+            return
+        step = eval(self.x_step.get()) if not self.x_step.get() == "" else 0.1
+        count = self.x_count.get() if not self.x_count.get() == "" else None
+        x_scale = self.x_scale.get() if not self.x_scale.get() == "" else 20
+        y_scale = self.y_scale.get() if not self.y_scale.get() == "" else 40
+        if input_func.find("=") >= 0:
+            left_var = input_func.split("=")[0]
+            right_var = input_func.split("=")[1]
+            if self.functions.check_function_exit(right_var):
+                func = self.functions.get_function_by_iter(right_var)
+                self.axis_canvas.draw_graph(func, step, count,
+                                            x_scale, y_scale)
+                self.text_canvas.draw_expression(sympy.sympify(func, evaluate=False, convert_xor=True), int(self.text_canvas.cget("width")) // 2, self.text_canvas.y_spacing)
+            else:
+                self.axis_canvas.draw_graph(right_var, step, count,
+                                            x_scale, y_scale)
+                self.text_canvas.draw_expression(sympy.sympify(right_var, evaluate=False, convert_xor=True), int(self.text_canvas.cget("width")) // 2, self.text_canvas.y_spacing)
+        else:
+            if self.functions.check_function_exit(input_func):
+                func = self.functions.get_function_by_iter(input_func)
+                self.axis_canvas.draw_graph(func, step, count,
+                                            x_scale, y_scale)
+                self.text_canvas.draw_expression(sympy.sympify(func, evaluate=False, convert_xor=True), int(self.text_canvas.cget("width")) // 2, self.text_canvas.y_spacing)
+            else:
+                self.axis_canvas.draw_graph(input_func, step, count,
+                                        x_scale, y_scale)
+                self.text_canvas.draw_expression(sympy.sympify(input_func, evaluate=False, convert_xor=True), int(self.text_canvas.cget("width")) // 2, self.text_canvas.y_spacing)
+
+    def create_form(self):
+        bottom_frame = Frame(self.master, width=self.attr["width"], height=self.attr["height"] * 0.3)
+        self.func_input = Entry(bottom_frame, font=self.font_style, width=40)
+        self.func_input.grid(row=0, column=0, columnspan=4, padx=30)
+        self.add_func_button = Button(bottom_frame, text="用户命名并新增基本函数", command=self.add_function)
+        self.add_func_button.grid(row=0, column=4, padx=10)
+        Label(bottom_frame, text="x步长", font=("Lucida Grande", 20)).grid(row=1, column=0, padx=30)
+        self.x_step = Entry(bottom_frame, font=self.font_style, width=10)
+        self.x_step.grid(row=1, column=1, padx=10, pady=10)
+        Label(bottom_frame, text="x个数", font=("Lucida Grande", 20)).grid(row=1, column=2, padx=30)
+        self.x_count = Entry(bottom_frame, font=self.font_style, width=10)
+        self.x_count.grid(row=1, column=3, padx=10, pady=10)
+
+        Label(bottom_frame, text="坐标轴", font=("Lucida Grande", 20)).grid(row=2, column=0, padx=30)
+        self.quadrant = IntVar()
+        self.quadrant.set(4)
+        Radiobutton(bottom_frame, text="四象限", command=self.update_quadrant, value=4, variable=self.quadrant).grid(row=2, column=1, padx=10, pady=10)
+        Radiobutton(bottom_frame, text="一象限", command=self.update_quadrant, value=1, variable=self.quadrant).grid(row=2, column=2, padx=10, pady=10)
+
+        Label(bottom_frame, text="x放大倍数", font=("Lucida Grande", 20)).grid(row=3, column=0, padx=30)
+        self.x_scale = Entry(bottom_frame, font=self.font_style, width=10)
+        self.x_scale.grid(row=3, column=1, padx=10, pady=10)
+        Label(bottom_frame, text="y放大倍数", font=("Lucida Grande", 20)).grid(row=3, column=2, padx=30)
+        self.y_scale = Entry(bottom_frame, font=self.font_style, width=10)
+        self.y_scale.grid(row=3, column=3, padx=10, pady=10)
+
+        Button(bottom_frame, text="输出",
+               command=self.print_function, width=5).grid(row=1, rowspan=3, column=4, sticky="w")
+        bottom_frame.place(x=0, y=self.attr["height"] * 0.65 + 20)
+
+    def show_user_function(self):
+        children_window = Toplevel(root)
+        children_window.title("用户自定义函数")
+        children_window.geometry('350x260+450+200')
+        packet_frame = Frame(children_window)
+        packet_frame.grid(row=0, column=0, columnspan=3, padx=10, pady=5)
+        function_treeview = Treeview(packet_frame, columns=("function_name", "function"), show="headings")
+        function_treeview.heading("function_name", text="函数名称")
+        function_treeview.column("function_name", width=100, anchor=CENTER)
+        function_treeview.heading("function", text="函数体")
+        function_treeview.column("function", width=200, anchor=CENTER)
+        function_treeview.pack(side="left", fill="both")
+        scrollbar = Scrollbar(packet_frame, orient="vertical", command=function_treeview.yview)
+        scrollbar.pack(side="right", fill="y")
+        function_treeview.configure(yscrollcommand=scrollbar.set)
+
+        def delete_item():
+            selected_item = function_treeview.selection()
+            for item in selected_item:
+                item_data = function_treeview.item(item)
+                function_treeview.delete(item)
+                self.functions.data.pop(item_data["values"][0])
+                self.functions.save()
+
+        context_menu = Menu(root, tearoff=False)
+        context_menu.add_command(label="删除", command=delete_item)
+
+        def popup_menu(event):
+            if function_treeview.identify_region(event.x, event.y) == "cell":
+                function_treeview.selection_set(function_treeview.identify_row(event.y))
+                context_menu.post(event.x_root, event.y_root)
+
+        function_treeview.bind("<Button-3>", popup_menu)
+        for function_name, function in self.functions.data.items():
+            function_treeview.insert("", "end", values=(function_name, function))
+
+    def create_window(self):
+        self.axis_canvas = Graph(self.master, width=self.attr["width"] * 0.65, height=self.attr["height"] * 0.65, bg="#cdcdcd")
+        self.axis_canvas.place(x=0, y=0)
+        self.text_canvas = ExpressionCanvas(self.master, width=self.attr["width"] * 0.35, height=self.attr["height"] * 0.65, bg="#cdcdcd")
+        menubar = Menu(root)
+        menubar.add_command(label='查看自定义函数', command=self.show_user_function)
+        root.config(menu=menubar)
+        # self.text = "可支持下列函数的加减乘除组合运算\n" \
+        #             "常用运算符：+,-,*,/,**,//,%\n" \
+        #             "常用函数：\n" \
+        #             "  sqrt(x)：求平方根\n" \
+        #             "数学常数：\n" \
+        #             "  虚数单位：I\n" \
+        #             "  自然对数的底：E\n" \
+        #             "  无穷大：oo\n" \
+        #             "  圆周率：pi\n" \
+        #             "三角函数：sin(x),cos(x),tan(x)\n" \
+        #             "  sec(x),csc(x),cot(x),sinc(x)\n" \
+        #             "  及其反函数：sinh(),cosh()等\n" \
+        #             "复杂函数：\n" \
+        #             "  伽马函数：gamma(x)\n" \
+        #             "  贝塔函数：beta()\n" \
+        #             "  误差函数：erf(x)\n" \
+        #             "指数运算：\n" \
+        #             "  指数运算：exp()\n" \
+        #             "  自然对数：log()\n" \
+        #             "  以十为底的对数：log(var, 10)\n" \
+        #             "  自然对数：ln()或log()\n"
+        self.text = "可支持下列函数的加减乘除组合运算\n" \
+               "\ty=sin(x)\n" \
+               "\tcos(x)\n" \
+               "\ttan(x)\n" \
+               "\tcot(x)\n" \
+               "\tx^n\n" \
+               "\tP1(x)=x^3+x^2+x+5\n" \
+               "---将括号内的表达式命名为P1,P1可\n" \
+               "出现于用户构造中"
+        self.text_canvas.create_text(20 + 180, 20, text='可识别基本函数', fill='red', font=("Purisa", 25, "bold"))
+        center_text(self.text_canvas, self.text, ("Lucida Grande", 15))
+        self.text_canvas.bind("<ButtonPress-3>", func=self.clear_text_canvas)
+        self.text_canvas.place(x=int(self.attr["width"] * 0.65), y=0)
+        self.create_form()
+
+
+if __name__ == '__main__':
+    root = Window()
+    screenwidth = root.winfo_screenwidth()
+    screenheight = root.winfo_screenheight()
+    root_attr = {
+        "width": 1200,
+        "height": 800,
+    }
+    alignstr = '%dx%d+%d+%d' % (root_attr['width'], root_attr['height'], (screenwidth - root_attr['width']) / 2,
+                                (screenheight - root_attr['height']) / 2)
+    root.geometry(alignstr)
+    root.resizable(width=False, height=False)
+    app = FunctionDisplay(root, root_attr)
+    ttk.Style().configure("TButton", font="-size 18")
+    ttk.Style().configure("TRadiobutton", font="-size 18")
+    root.mainloop()

x4/function.json

@@ -0,0 +1,8 @@
+{
+  "f1": "sin(x)+cos(x)+p3(x)",
+  "f3": "x**2",
+  "f2": "(x/100)**2+2*(x/100)+1",
+  "SinPlusCos(x)": "sin(x) + cos(x)",
+  "superFunc": "(x/100)**2 + 2*(x/100) + 1",
+  "func": "3 * x + sin(x) * cos(x)"
+}

x4/functionUtil.py

@@ -0,0 +1,57 @@
+import json
+import re
+
+
+class FunctionUtil:
+    def __init__(self):
+        self.filename = "./function.json"
+        self.data = {}
+        self.load()
+
+    def load(self):
+        """
+        加载文件数据
+        """
+        try:
+            with open(self.filename, 'r', encoding="utf-8") as f:
+                self.data = json.load(f)
+        except FileNotFoundError:
+            pass
+
+    def save(self):
+        """
+        将函数保存至json文件当中
+        """
+        with open(self.filename, "w", encoding="utf-8") as f:
+            json.dump(self.data, f)
+
+    def check_function_exit(self, function):
+        """
+        检查用户输入的函数是否包含用户自定义函数
+        """
+        for key in self.data.keys():
+            if function.find(key) >=0:
+                return True
+        return False
+
+    def add_function(self, key, value):
+        """
+        添加函数
+        """
+        self.data[key.strip()] = value.strip()
+        self.save()
+
+    def get_function_by_iter(self, key):
+        result = key
+        for dict_key in self.data.keys():
+            if result.find(dict_key) >= 0:
+                value = result.replace(dict_key, self.data[dict_key])
+                result = self.replace_values_recursive(value)
+        return result
+
+    def replace_values_recursive(self, value):
+        for key in self.data:
+            if key in value:
+                replacement = self.data[key]
+                value = value.replace(key, replacement)
+        return value

x4/test.py

@@ -0,0 +1,9 @@
+import sympy
+
+from functionUtil import FunctionUtil
+
+
+# f = FunctionUtil()
+# print(f.get_function_by_iter("f1 + f3"))
+
+print(sympy.sympify("(x/100)**2+2*(x/100)+1"))

x5/FunctionDisplay_X5.py

@@ -0,0 +1,447 @@
+# -*- coding: utf-8 -*-
+from time import sleep
+from tkinter import *
+import tkinter.font as tkFont
+from tkinter import messagebox
+
+import numpy as np
+from matplotlib.figure import Figure
+from matplotlib.backends.backend_tkagg import FigureCanvasTkAgg
+
+import sympy
+from numpy import arange
+from sympy import symbols, lambdify
+from functionUtil import FunctionUtil
+import math
+from PIL import ImageTk, Image
+import sys
+
+# 在画布中央绘制文本
+def center_text(canvas, text, font):
+    canvas_width = int(canvas.cget("width"))
+    x = canvas_width // 2
+    y = 200
+    canvas.create_text(x, y, text=text, font=font, anchor="center")
+
+
+class Graph(Canvas):
+    """
+    绘制函数图形
+    """
+
+    def __init__(self, master=None, **kwargs):
+        super().__init__(master, **kwargs)
+        self.width = int(self.cget('width'))
+        self.height = int(self.cget('height'))
+        self.origin = (self.width / 2, self.height / 2)
+        self.config(bg="white")
+        self.bili_x = 20
+        self.bili_y = 20
+        self.draw_axis()
+        self.draw_scale()
+        self.fig = FigureCanvasTkAgg()
+        self.y_scale = 1.0
+
+
+    def draw_axis(self):
+        """
+        绘制坐标轴
+        """
+        self.delete("all")
+        self.create_line(0, self.origin[1], self.width, self.origin[1], fill='black', arrow=LAST)  # 一象限xy轴
+        self.create_line(self.origin[0], 0, self.origin[0], self.height, fill='black', arrow=FIRST)
+
+    def draw_scale(self):
+        """
+        绘制刻度值
+        """
+        for i in range(-math.ceil((self.origin[0] / self.bili_x)) + 1,
+                       math.ceil((self.width - self.origin[0]) / self.bili_x)):
+            j = i * self.bili_x
+            if (i % 10 == 0):
+                self.create_line(j + self.origin[0], self.origin[1], j + self.origin[0], self.origin[1] - 5,
+                                 fill='black')
+                self.create_text(j + self.origin[0], self.origin[1] + 10, text=i)
+        for i in range(-math.ceil((self.height - self.origin[1]) / self.bili_y) + 1,
+                       math.ceil((self.origin[1] / self.bili_y))):
+            j = -(i * self.bili_y)
+            if i == 0:
+                continue
+            elif i % 2 == 0:
+                self.create_line(self.origin[0], j + self.origin[1], self.origin[0] + 5, j + self.origin[1],
+                                 fill='black')
+                self.create_text(self.origin[0] - 10, j + self.origin[1], text=i)
+
+    def switch_quadrant(self, quadrant):
+        """
+        切换象限
+        """
+        if quadrant == 1:
+            self.origin = (50, self.height - 50)
+        else:
+            self.origin = (self.width / 2, self.height / 2)
+        self.draw_axis()
+        self.draw_scale()
+
+
+    def draw_graph_3d(self, func, draw_precision=0.1, count=1000, bili_x=20, bili_y=40, ):
+        self.fig.get_tk_widget().destroy()
+        self.delete("all")
+        # 创建 sympy 符号
+        x, y = symbols('x y')
+        self.bili_x, self.bili_y = int(bili_x), int(bili_y)
+        # 将表达式转换为可计算的函数
+        expr = lambdify((x, y), func, modules=['numpy'])
+        xmin, xmax = -math.ceil((self.origin[0] / self.bili_x)) + 1, math.ceil(
+            (self.width - self.origin[0]) / self.bili_x)
+        # 创建数据网格
+        X = np.linspace(xmin, xmax, int(draw_precision * 100))
+        Y = np.linspace(xmin, xmax, int(draw_precision * 100))
+        X, Y = np.meshgrid(X, Y)
+        Z = expr(X, Y)
+        # 创建一个 Figure 对象
+        fig = Figure(figsize=(7, 5.5), dpi=120)
+        # 在 Figure 上创建一个 3D 子图
+        ax = fig.add_subplot(111, projection='3d')
+        ax.auto_scale_xyz(X, Y, Z)
+        # 绘制三维图形
+        ax.plot_surface(X, Y, Z, cmap='viridis')
+        self.fig = FigureCanvasTkAgg(fig, master=self)
+        self.fig.draw()
+        self.fig.get_tk_widget().pack(fill=BOTH, ipadx=0, ipady=0, pady=0, padx=0, expand=True)
+
+
+
+
+    def draw_graph_2d(self, func, draw_precision=0.1, count=1000, bili_x=20, bili_y=40, c='blue'):
+        'xmin,xmax 自变量的取值范围； c 图像颜色'
+        'x0,y0 原点坐标  w,h 横纵轴半长 draw_precision 步进'
+        self.fig.get_tk_widget().destroy()
+        self.bili_x, self.bili_y = int(bili_x), int(bili_y)
+        self.draw_axis()
+        self.draw_scale()
+        w1, w2 = self.bili_x, self.bili_y  # w1,w2为自变量和函数值在横纵轴上的放大倍数
+        xmin, xmax = -math.ceil((self.origin[0] / self.bili_x)) + 1, math.ceil(
+            (self.width - self.origin[0]) / self.bili_x)
+        co2 = []
+        try:
+            for x in arange(xmin, xmax, draw_precision):  # draw_precision----画图精度
+                y = sympy.sympify(func, convert_xor=True).subs("x", x).evalf()
+                coord = self.origin[0] + w1 * x, self.origin[1] - w2 * y, self.origin[0] + w1 * x + 1, self.origin[
+                    1] - w2 * y + 1
+                # if abs(coord[1]) < int(self.height):  # 超过w,h就截断  #已经将截断注释
+                co2.append((self.origin[0] + w1 * x, self.origin[1] - w2 * y))
+            if count is None:
+                length = len(co2)
+            else:
+                length = len(co2[:int(count)])
+            for i in range(length):
+                if (draw_precision >= 1):
+                    self.create_line(co2, fill=c, width=1)
+                if (i + 1 == len(co2)):
+                    break
+                if (abs(co2[i][1] - co2[i + 1][1]) > 100):
+                    continue
+                else:
+                    self.create_line(co2[i], co2[i + 1], fill=c, width=1)
+                # sleep(0.01)
+                self.update()
+        except Exception as E:
+            messagebox.showerror("错误", message=f"函数有误，错误信息如下!\n{E}")
+
+
+    def draw_graph(self,dimension,func, draw_precision=0.1, count=1000, bili_x=20, bili_y=40, ):
+        if dimension==1:
+            self.draw_graph_3d(func, draw_precision, count, bili_x, bili_y,)
+        else:
+            self.draw_graph_2d(func, draw_precision, count, bili_x, bili_y,c='blue')
+
+class ExpressionCanvas(Canvas):
+    def __init__(self, master, *args, **kwargs):
+        super().__init__(master, *args, **kwargs)
+        self.node_width = 100
+        self.node_height = 40
+        self.x_spacing = 15
+        self.y_spacing = 70
+        self.level = {}
+
+    def add_node(self, text, x, y, parent=None):
+        node_width = len(text) * 15 + 20
+        if node_width < 40:
+            node_width = 50
+        # 创建节点
+        coords = [x - node_width / 2, y, x + node_width / 2, y + self.node_height]
+        if coords[1] in self.level:
+            max_x = max(self.level[coords[1]])
+            if coords[0] <= max_x:
+                x = max_x + node_width / 2 + self.x_spacing
+            node_id = self.create_rectangle(x - node_width / 2, y, x + node_width / 2, y + self.node_height,
+                                            fill="white")
+            sleep(0.2)
+            self.update()
+        elif text == "x":
+            x = self.coords(parent)[0] + node_width / 2
+            node_id = self.create_rectangle(x - node_width / 2, y, x + node_width / 2, y + self.node_height,
+                                            fill="white")
+            sleep(0.2)
+            self.update()
+        else:
+            node_id = self.create_rectangle(x - node_width / 2, y, x + node_width / 2, y + self.node_height,
+                                            fill="white")
+            sleep(0.2)
+            self.update()
+        coords = [x - node_width / 2, y, x + node_width / 2, y + self.node_height]
+        if coords[1] in self.level:
+            self.level[coords[1]].append(coords[2])
+        else:
+            self.level[coords[1]] = [coords[2]]
+        text_id = self.create_text(x + 5, y + self.node_height // 2, text=text, anchor="center", font=("", 15))
+        sleep(0.2)
+        self.update()
+        # 绘制父节点和当前节点的连线
+        if parent:
+            try:
+                parent_coords = self.coords(parent)
+                parent_x = parent_coords[0] + (parent_coords[2] - parent_coords[0]) // 2
+                parent_y = parent_coords[1] + (parent_coords[3] - parent_coords[1]) // 2
+                self.create_line(parent_x, parent_y + self.node_height // 2, x, y, fill="black")
+                self.update()
+            except Exception as E:
+                pass
+        return node_id
+
+    def draw_expression(self, expression, x, y, parent=None, sibling_width=0):
+        # 创建节点并绘制表达式文本
+        node = self.add_node(str(expression), x, y, parent=parent)
+        if expression.is_Atom:
+            return node
+        # 处理子表达式
+        num_children = len(expression.args)
+        total_width = num_children * self.node_width + (num_children - 1) * self.x_spacing
+        start_x = x - total_width // 2
+        for subexpr in expression.args:
+            subnode = self.draw_expression(subexpr, start_x, y + self.y_spacing, parent=node, sibling_width=total_width)
+            start_x += self.node_width + self.x_spacing
+        return node
+
+
+class FunctionDisplay(Canvas):
+    def __init__(self, master, *args, **kwargs):
+        super().__init__(master, *args, **kwargs)
+        self.font_style = tkFont.Font(family="Lucida Grande", size=30)
+        self.functions = FunctionUtil()
+        self.width = int(self.cget("width"))
+        self.height = int(self.cget("height"))
+        self.background_img = ImageTk.PhotoImage(Image.open(sys.path[0]+"/./image/背景@3x.jpg").resize((self.width, self.height)))
+        self.create_image(0, 0, image=self.background_img, anchor=NW)
+        self.master = master
+        self.init_window()
+        self.load_user_function()
+
+    def add_function(self):
+        """
+        用户添加函数
+        """
+        input_func = self.func_input.get()
+        if input_func == "":
+            messagebox.showwarning("注意", message="请输入函数！")
+            return
+        elif input_func.find("=") < 0:
+            messagebox.showerror("注意", message="添加函数的格式为：\nSinPlusCos(x)=sin(x)+cos(x)")
+            return
+        left_var = input_func.split("=")[0]
+        right_var = input_func.split("=")[1]
+        try:
+            function = self.functions.get_function_by_iter(right_var)
+            sympy.sympify(function, evaluate=False)
+        except Exception as E:
+            messagebox.showerror("注意", message="函数解析错误，请仔细检查函数是否正确！")
+            self.func_input.delete(0, END)
+            return
+        if self.functions.check_function_exit(left_var):
+            result = messagebox.askokcancel(title='提示', message=f'函数{left_var}已经存在，是否需要覆盖！')
+            if result:
+                self.functions.add_function(left_var, right_var)
+                messagebox.showinfo(title="提示", message="覆盖成功！")
+                self.func_input.delete(0, END)
+                self.load_user_function()
+            return
+        self.functions.add_function(left_var, right_var)
+        messagebox.showinfo(title="提示", message="添加成功！")
+        self.func_input.delete(0, END)
+        self.load_user_function()
+
+    def update_dimension(self):
+        """
+        更换维度
+        """
+        dimension=self.dimension.get()
+        self.print_function()
+
+    def update_quadrant(self):
+        """
+        更换象限
+        """
+        self.axis_canvas.switch_quadrant(self.quadrant.get())
+        self.print_function()
+
+    def print_function(self):
+        """
+        输出
+        """
+        dimension=self.dimension.get()
+        self.text_canvas.delete("all")
+        self.text_canvas.level.clear()
+        input_func = self.func_input.get()
+        if input_func == "":
+            messagebox.showwarning("注意", message="请输入函数！")
+            return
+        step = eval(self.x_step.get()) if not self.x_step.get() == "" else 0.1
+        count = self.x_count.get() if not self.x_count.get() == "" else None
+        x_scale = int(self.x_scale.get())*20 if not self.x_scale.get() == "" else 20
+        y_scale = int(self.y_scale.get())*40 if not self.y_scale.get() == "" else 40
+        if input_func.find("=") >= 0:
+            input_func = input_func.split("=")[1]
+        if self.functions.check_function_exit(input_func):
+            func = self.functions.get_function_by_iter(input_func)
+            self.axis_canvas.draw_graph(dimension,func, step, count, x_scale, y_scale)
+            self.text_canvas.draw_expression(sympy.sympify(func, evaluate=False, convert_xor=True),
+                                             int(self.text_canvas.cget("width")) // 2, self.text_canvas.y_spacing)
+        else:
+            self.axis_canvas.draw_graph(dimension,input_func, step, count, x_scale, y_scale)
+            self.text_canvas.draw_expression(sympy.sympify(input_func, evaluate=False, convert_xor=True),
+                                             int(self.text_canvas.cget("width")) // 2, self.text_canvas.y_spacing)
+
+    def load_user_function(self):
+        self.user_function_canvas.delete(ALL)
+        self.user_function_canvas.create_text(20 + 90, 35, text='可识别基本函数', fill='red',
+                                              font=("Purisa", 20, "bold"))
+        num = 2
+        self.user_function_canvas.create_text(0, 70, anchor="nw", text="函数名", font=("", 15))
+        self.user_function_canvas.create_text(150, 70, anchor="nw", text="函数体", font=("", 15))
+        for function, function_body in self.functions.data.items():
+            self.user_function_canvas.create_text(0, 20 * num + 50, anchor="nw", text=function, font=("", 15))
+            self.user_function_canvas.create_text(150, 20 * num + 50, anchor="nw", text=function_body, font=("", 15))
+            num += 1
+        self.user_function_canvas.update()
+        self.user_function_canvas.configure(scrollregion=self.user_function_canvas.bbox("all"))
+
+    def create_form(self):
+        bottom_frame = Canvas(self, width=self.width, height=self.height * 0.3, highlightthickness=0)
+        self.back_image = ImageTk.PhotoImage(Image.open(sys.path[0]+"/./image/下部背景@3x.png").resize((self.width, int(self.height * 0.3))))
+        bottom_frame.create_image(0, 0, image=self.back_image, anchor=NW)
+        label_width, entry_width, label_margin_left, margin_left, height, margin_top = 100, 215, 120 + 50, 120, 42, 20
+        self.func_input = Entry(bottom_frame, font=self.font_style)
+        self.func_input.place(x=margin_left, y=margin_top, anchor=NW, width=1000, height=height)
+        self.add_func_image = ImageTk.PhotoImage(Image.open(sys.path[0]+"/./image/用户命名并新增基本函数@3x.png").resize((180, 62)))
+        self.add_func_button = Button(bottom_frame, image=self.add_func_image, bd=0, relief="solid", bg="#f7f7f7",
+                     highlightthickness=0, command=self.add_function)
+        self.add_func_button.place(x=1140, y=10, anchor=NW)
+
+        self.label_img = ImageTk.PhotoImage(Image.open(sys.path[0]+"/./image/文字背景@3x.png").resize((100, 42)))
+        bottom_frame.create_image(label_margin_left-100, 112, image=self.label_img)
+        bottom_frame.create_text(label_margin_left-100, 112, text="x步长", fill="white", font=("", 20))
+        self.x_step = Entry(bottom_frame, font=self.font_style)
+        self.x_step.place(x=margin_left + label_width-100, y=112 - 21, width=215, height=42)
+
+        self.label1_img = ImageTk.PhotoImage(Image.open(sys.path[0]+"/./image/文字背景@3x.png").resize((100, 42)))
+        bottom_frame.create_image(label_margin_left-100, 171, image=self.label1_img)
+        bottom_frame.create_text(label_margin_left-100, 170, text="x个数", fill="white", font=("", 20))
+        self.x_count = Entry(bottom_frame, font=self.font_style)
+        self.x_count.place(x=margin_left + label_width-100, y=112 + 39, width=215, height=42)
+
+        self.big_label_img = ImageTk.PhotoImage(Image.open(sys.path[0]+"/./image/文字背景2@3x.png").resize((label_width+5, height * 2 + margin_top)))
+        bottom_frame.create_image(label_margin_left + label_width + entry_width - 80, 112 + 31, image=self.big_label_img)
+        bottom_frame.create_text(label_margin_left + label_width + entry_width - 80, 112 + 31, text="坐标轴", fill="white", font=("", 25))
+        self.quadrant = IntVar()
+        self.quadrant.set(4)
+        Radiobutton(bottom_frame, text="四象限", command=self.update_quadrant, font=("", 17),
+                    bg="#b9b9f7",highlightthickness=0, highlightcolor="#aaaaf2",
+                    value=4, variable=self.quadrant).place(x=label_margin_left + label_width * 2 + entry_width -128, y=90,
+                                                           height=(height * 2 + margin_top) / 2, width=entry_width, anchor=NW)
+        Radiobutton(bottom_frame, text="一象限", command=self.update_quadrant, font=("", 17), bg="#b9b9f7",
+                    highlightthickness=0, highlightcolor="#aaaaf2",
+                    value=1, variable=self.quadrant).place(x=label_margin_left + label_width * 2 + entry_width -128, y=90 + (height * 2 + margin_top) / 2,
+                                                           height=(height * 2 + margin_top) / 2, width=entry_width, anchor=NW)
+
+
+        self.big_label_img1 = ImageTk.PhotoImage(Image.open(sys.path[0]+"/./image/文字背景2@3x.png").resize((label_width+5, height * 2 + margin_top)))
+        bottom_frame.create_image(label_margin_left + label_width + entry_width+278, 112 + 31, image=self.big_label_img1)
+        bottom_frame.create_text(label_margin_left + label_width + entry_width+278, 112 + 31, text="维度", fill="white", font=("", 25))
+        self.dimension = IntVar()
+        self.dimension.set(4)
+        Radiobutton(bottom_frame, text="二维", command=self.update_dimension, font=("", 17),
+                    bg="#b9b9f7",highlightthickness=0, highlightcolor="#aaaaf2",
+                    value=4, variable=self.dimension).place(x=label_margin_left + label_width * 2 + entry_width+230, y=90,
+                                                           height=(height * 2 + margin_top) / 2, width=entry_width, anchor=NW)
+        Radiobutton(bottom_frame, text="三维", command=self.update_dimension, font=("", 17), bg="#b9b9f7",
+                    highlightthickness=0, highlightcolor="#aaaaf2",
+                    value=1, variable=self.dimension).place(x=label_margin_left + label_width * 2 + entry_width+230, y=90 + (height * 2 + margin_top) / 2,
+                                                           height=(height * 2 + margin_top) / 2, width=entry_width, anchor=NW)
+
+
+        self.x_scale = Entry(bottom_frame, font=self.font_style)
+        self.x_scale.place(x=margin_left + label_width+100, y=112 - 21, width=215, height=42)
+        label_x = label_margin_left + 840
+        label_y = 112
+        self.label_img1 = ImageTk.PhotoImage(Image.open(sys.path[0]+"/./image/文字背景@3x.png").resize((130, 42)))
+        bottom_frame.create_image(label_x+100, label_y, image=self.label_img1)
+        bottom_frame.create_text(label_x+100, label_y, text="x放大倍数", fill="white", font=("", 20))
+        entry_x = margin_left + label_width + 855
+        entry_y = 112 - 21
+        self.x_scale.place(x=entry_x+100, y=entry_y, width=215, height=42)
+
+
+        self.y_scale = Entry(bottom_frame, font=self.font_style)
+        self.y_scale.place(x=margin_left + label_width+100, y=112 - 21, width=215, height=42)
+        label_x = label_margin_left + 840
+        label_y = 170
+        bottom_frame.create_image(label_x+100, label_y, image=self.label_img1)
+        bottom_frame.create_text(label_x+100, label_y, text="y放大倍数", fill="white", font=("", 20))
+        entry_x = margin_left + label_width + 855
+        entry_y = 170 - 21
+        self.y_scale.place(x=entry_x+100, y=entry_y, width=215, height=42)
+
+        self.print_function_image = ImageTk.PhotoImage(Image.open(sys.path[0]+"/./image/输出-点击@3x.png").resize((120, 60)))
+        self.print_function_button = Button(bottom_frame, image=self.print_function_image, bd=0, relief="solid", bg="#f7f7f7",
+                     highlightthickness=0, command=self.print_function)
+        self.print_function_button.place(x=1350, y=10, anchor=NW)
+        # Button(bottom_frame, text="输出", command=self.print_function, width=5) \
+        #     .place(x=1350, y=95, anchor=NW)
+        bottom_frame.place(x=0, y=self.height * 0.65 + 40, anchor=NW)
+
+    def init_window(self):
+        self.axis_canvas = Graph(self, width=self.width * 0.45, height=self.height * 0.65,highlightthickness=0)
+        self.axis_canvas.place(x=0, y=0, anchor=NW)
+        self.text_canvas = ExpressionCanvas(self, width=self.width * 0.35,
+                                            height=self.height * 0.65, bg="white",highlightthickness=0)
+        self.text_canvas.place(x=int(self.width * 0.45), y=0)
+        user_function = Frame(self, width=self.width * 0.2, height=self.height * 0.65)
+        user_function.place(x=int(self.width * 0.8), y=0)
+        self.user_function_canvas = Canvas(user_function, width=self.width * 0.19,
+                                           height=self.height * 0.65, bg="white",highlightthickness=0)
+        y_scrollbar = Scrollbar(user_function, orient="vertical", command=self.user_function_canvas.yview)
+        x_scrollbar = Scrollbar(user_function, orient="horizontal", command=self.user_function_canvas.xview)
+        x_scrollbar.pack(side=BOTTOM, fill=BOTH)
+        y_scrollbar.pack(side=RIGHT, fill=BOTH)
+        self.user_function_canvas.pack(side=TOP, fill=BOTH)
+        self.user_function_canvas.config(yscrollcommand=y_scrollbar.set, xscrollcommand=x_scrollbar.set)
+        self.user_function_canvas.config(scrollregion=self.user_function_canvas.bbox("all"))
+        self.create_form()
+
+
+if __name__ == '__main__':
+    root = Tk()
+    screenwidth = root.winfo_screenwidth()
+    screenheight = root.winfo_screenheight()
+    root_attr = {
+        "width": int(screenwidth * 1),
+        "height": int(screenheight * 1),
+    }
+    alignstr = '%dx%d+%d+%d' % (root_attr['width'], root_attr['height'], (screenwidth - root_attr['width']) / 2,
+                                (screenheight - root_attr['height']) / 2)
+    root.geometry(alignstr)
+    root.resizable(width=False, height=False)
+    app = FunctionDisplay(root, width=root_attr["width"], height=root_attr["height"])
+    app.place(x=0, y=0, anchor=NW)
+    root.mainloop()

x5/function.json

@@ -0,0 +1 @@
+{"sin(x)": "sin(x)", "cos(x)": "cos(x)", "tan(x)": "tan(x)"}

x5/functionUtil.py

@@ -0,0 +1,63 @@
+import json
+import re
+import sys
+
+class FunctionUtil:
+    def __init__(self):
+        self.filename = sys.path[0]+"/./function.json"
+        self.data = {}
+        self.load()
+
+    def load(self):
+        """
+        加载文件数据
+        """
+        try:
+            with open(self.filename, 'r', encoding="utf-8") as f:
+                self.data = json.load(f)
+        except FileNotFoundError:
+            pass
+
+    def save(self):
+        """
+        将函数保存至json文件当中
+        """
+        with open(self.filename, "w", encoding="utf-8") as f:
+            json.dump(self.data, f)
+
+    def check_function_exit(self, function):
+        """
+        检查用户输入的函数是否包含用户自定义函数
+        """
+        for key in self.data.keys():
+            if function.find(key) >=0:
+                return True
+        return False
+
+    def add_function(self, key, value):
+        """
+        添加函数
+        """
+        self.data[key.strip()] = value.strip()
+        self.save()
+
+    def get_function_by_iter(self, key):
+        """
+        遍历找出函数名所对应的函数体
+        """
+        result = key
+        for dict_key in self.data.keys():
+            if result.find(dict_key) >= 0:
+                value = result.replace(dict_key, "("+self.data[dict_key]+")")
+                result = self.replace_values_recursive(value)
+        return result
+
+    def replace_values_recursive(self, value):
+        """
+        将键值对应的数学函数替换为实际函数
+        """
+        for key in self.data:
+            if key in value:
+                replacement = self.data[key]
+                value = "("+value.replace(key, replacement)+")"
+        return value