import tkinter as tk from tkinter import ttk, messagebox import random import sys # 尝试导入 matplotlib + Pillow 用于渲染 LaTeX 到图片（可选） USE_MATPLOTLIB = False try: import matplotlib matplotlib.use("Agg") import matplotlib.pyplot as plt from PIL import Image, ImageTk USE_MATPLOTLIB = True except Exception: USE_MATPLOTLIB = False # 示例公式库：每项包含 id/title/latex/description/example formulas = [ { "id": "pythagoras", "title": "勾股定理 (Pythagorean theorem)", "latex": r"c^2 = a^2 + b^2", "description": "直角三角形斜边的平方等于两直角边的平方和。", "example": "如果 a=3, b=4，则 c=5。" }, { "id": "quadratic", "title": "二次方程求根公式 (Quadratic formula)", "latex": r"x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}", "description": "求解 ax^2 + bx + c = 0 的根（a ≠ 0）。", "example": "例如 x^2 - 3x + 2 = 0 的根为 x=1,2。" }, { "id": "euler", "title": "欧拉公式 (Euler's identity)", "latex": r"e^{i\pi} + 1 = 0", "description": "复分析中的优美恒等式，将 e,i,π,1,0 联系在一起。", "example": "" }, { "id": "derivative_product", "title": "乘积法则 (Product rule)", "latex": r"\frac{d}{dx}[u(x)v(x)] = u'(x)v(x) + u(x)v'(x)", "description": "求导的乘积法则。", "example": "" }, { "id": "integral_def", "title": "定积分定义（黎曼）", "latex": r"\int_a^b f(x)\,dx = \lim_{n\to\infty} \sum_{i=1}^n f(x_i^*)\Delta x_i", "description": "定积分的黎曼和定义（简略）。", "example": "" } ] class FormulaApp(tk.Tk): def __init__(self, formulas): super().__init__() self.title("数学公式查询") self.geometry("900x600") self.formulas = formulas self.filtered = list(range(len(formulas))) self.current_idx = 0 self.create_widgets() self.populate_list() if self.filtered: self.select_by_filtered_pos(0) def create_widgets(self): top = ttk.Frame(self) top.pack(side="top", fill="x", padx=8, pady=6) ttk.Label(top, text="搜索：").pack(side="left") self.search_var = tk.StringVar() search_entry = ttk.Entry(top, textvariable=self.search_var, width=40) search_entry.pack(side="left", padx=(4,6)) search_entry.bind("", lambda e: self.do_search()) ttk.Button(top, text="搜索", command=self.do_search).pack(side="left") ttk.Button(top, text="显示全部", command=self.show_all).pack(side="left", padx=6) ttk.Button(top, text="随机一条", command=self.random_formula).pack(side="left") main = ttk.PanedWindow(self, orient="horizontal") main.pack(fill="both", expand=True, padx=8, pady=6) left = ttk.Frame(main, width=280) main.add(left, weight=1) right = ttk.Frame(main) main.add(right, weight=3) self.listbox = tk.Listbox(left, exportselection=False) self.listbox.pack(side="left", fill="both", expand=True) self.listbox.bind("<>", self.on_list_select) sb = ttk.Scrollbar(left, orient="vertical", command=self.listbox.yview) sb.pack(side="right", fill="y") self.listbox.config(yscrollcommand=sb.set) # 右侧顶部：标题与按钮 title_frame = ttk.Frame(right) title_frame.pack(fill="x") self.title_label = ttk.Label(title_frame, text="", font=("Helvetica", 16, "bold")) self.title_label.pack(anchor="w") btn_frame = ttk.Frame(title_frame) btn_frame.pack(anchor="e") ttk.Button(btn_frame, text="复制 LaTeX", command=self.copy_latex).pack(side="left", padx=4) ttk.Button(btn_frame, text="渲染 (matplotlib)", command=self.render_latex).pack(side="left", padx=4) # 公式渲染区（图片）和 LaTeX 源 display_frame = ttk.Frame(right) display_frame.pack(fill="both", expand=True) # image label for rendered formula self.image_label = ttk.Label(display_frame) self.image_label.pack(fill="both", expand=False, pady=(6,4)) # LaTeX source text (readonly) ttk.Label(display_frame, text="LaTeX 源：").pack(anchor="w") self.latex_text = tk.Text(display_frame, height=3, wrap="none") self.latex_text.pack(fill="x", padx=2, pady=(0,6)) self.latex_text.config(state="disabled") # description and example ttk.Label(display_frame, text="说明：").pack(anchor="w") self.desc_var = tk.StringVar() ttk.Label(display_frame, textvariable=self.desc_var, wraplength=500, foreground="black").pack(anchor="w", pady=(0,6)) ttk.Label(display_frame, text="示例/备注：").pack(anchor="w") self.example_var = tk.StringVar() ttk.Label(display_frame, textvariable=self.example_var, wraplength=500, foreground="gray").pack(anchor="w") bottom = ttk.Frame(right) bottom.pack(fill="x", pady=6) ttk.Button(bottom, text="上一条", command=self.prev).pack(side="left", padx=6) ttk.Button(bottom, text="下一条", command=self.next).pack(side="left", padx=6) def populate_list(self): self.listbox.delete(0, "end") for i in self.filtered: item = self.formulas[i] self.listbox.insert("end", f"{item['title']}") def select_by_filtered_pos(self, pos): if not self.filtered: return pos = max(0, min(pos, len(self.filtered)-1)) self.current_idx = self.filtered[pos] self.listbox.select_clear(0, "end") self.listbox.select_set(pos) self.listbox.activate(pos) self.listbox.see(pos) self.show_formula(self.current_idx) def on_list_select(self, evt): sel = self.listbox.curselection() if not sel: return pos = sel[0] self.current_idx = self.filtered[pos] self.show_formula(self.current_idx) def show_formula(self, idx): f = self.formulas[idx] self.title_label.config(text=f.get("title","")) # LaTeX 源 self.latex_text.config(state="normal") self.latex_text.delete("1.0", "end") self.latex_text.insert("end", f.get("latex","")) self.latex_text.config(state="disabled") # description/example self.desc_var.set(f.get("description","")) self.example_var.set(f.get("example","")) # clear rendered image self.image_label.config(image="", text="") self._photo = None def do_search(self): kw = self.search_var.get().strip().lower() if not kw: self.show_all() return self.filtered = [] for i, f in enumerate(self.formulas): hay = " ".join([f.get("title",""), f.get("latex",""), f.get("description",""), f.get("example","")]) if kw in hay.lower(): self.filtered.append(i) if not self.filtered: messagebox.showinfo("搜索", f"未找到包含“{kw}”的公式。") return self.populate_list() self.select_by_filtered_pos(0) def show_all(self): self.filtered = list(range(len(self.formulas))) self.populate_list() if self.filtered: self.select_by_filtered_pos(0) def random_formula(self): if not self.formulas: return idx = random.randrange(len(self.formulas)) # 若在 filtered 中则在当前列表中选择，否则切换为全量 if idx in self.filtered: pos = self.filtered.index(idx) self.select_by_filtered_pos(pos) else: self.filtered = list(range(len(self.formulas))) self.populate_list() pos = self.filtered.index(idx) self.select_by_filtered_pos(pos) def prev(self): if not self.filtered: return try: pos = self.filtered.index(self.current_idx) except ValueError: pos = 0 pos = (pos - 1) % len(self.filtered) self.select_by_filtered_pos(pos) def next(self): if not self.filtered: return try: pos = self.filtered.index(self.current_idx) except ValueError: pos = 0 pos = (pos + 1) % len(self.filtered) self.select_by_filtered_pos(pos) def copy_latex(self): f = self.formulas[self.current_idx] latex = f.get("latex","") if not latex: return self.clipboard_clear() self.clipboard_append(latex) messagebox.showinfo("复制", "LaTeX 源已复制到剪贴板。") def render_latex(self): if not USE_MATPLOTLIB: messagebox.showwarning("渲染不可用", "未安装 matplotlib/Pillow，无法渲染 LaTeX。\n可通过 pip install matplotlib pillow 安装。") return f = self.formulas[self.current_idx] latex = f.get("latex","") if not latex: return # 使用 matplotlib 渲染 LaTeX 到图片 try: fig = plt.figure(figsize=(0.01,0.01)) fig.text(0, 0, f"${latex}$", fontsize=20) fig.patch.set_alpha(0) buf = None from io import BytesIO buf = BytesIO() plt.axis("off") plt.savefig(buf, format="png", bbox_inches="tight", dpi=150, pad_inches=0.1, transparent=True) plt.close(fig) buf.seek(0) img = Image.open(buf) # 可选调整图像大小以适应界面 maxw, maxh = 700, 200 w, h = img.size scale = min(1.0, maxw / w, maxh / h) if scale < 1.0: img = img.resize((int(w*scale), int(h*scale)), Image.ANTIALIAS) photo = ImageTk.PhotoImage(img) self._photo = photo # 保持引用避免被回收 self.image_label.config(image=photo) except Exception as e: messagebox.showerror("渲染失败", f"渲染 LaTeX 失败：{e}") if __name__ == "__main__": app = FormulaApp(formulas) app.mainloop()