import sys import json import os from PyQt5.QtWidgets import * from PyQt5.QtCore import * from PyQt5.QtGui import * import math class FormulaDatabase: """数学公式数据库管理类""" def __init__(self, data_file="formulas.json"): self.data_file = data_file self.formulas = self._load_formulas() def _load_formulas(self): """加载公式数据""" default_data = { "代数": { "一元二次方程求根公式": { "公式": "x = [-b ± √(b² - 4ac)] / 2a", "说明": "解 ax² + bx + c = 0 的公式，其中a≠0", "示例": "对于 2x² + 5x - 3 = 0，a=2, b=5, c=-3，\n解为 x=0.5 或 x=-3" }, "平方差公式": { "公式": "a² - b² = (a+b)(a-b)", "说明": "平方差因式分解公式", "示例": "x² - 9 = (x+3)(x-3)" }, "完全平方公式": { "公式": "(a ± b)² = a² ± 2ab + b²", "说明": "完全平方展开公式", "示例": "(x+2)² = x² + 4x + 4" } }, "几何": { "勾股定理": { "公式": "c² = a² + b²", "说明": "直角三角形斜边平方等于两直角边平方和", "示例": "a=3, b=4, 则 c=√(3²+4²)=5" }, "圆面积公式": { "公式": "S = πr²", "说明": "圆的面积公式，r为半径", "示例": "r=2, 则 S=4π≈12.57" }, "球体积公式": { "公式": "V = (4/3)πr³", "说明": "球的体积公式", "示例": "r=3, 则 V=36π≈113.1" } }, "微积分": { "幂函数导数": { "公式": "(xⁿ)' = nxⁿ⁻¹", "说明": "幂函数的导数公式", "示例": "(x³)' = 3x²" }, "指数函数导数": { "公式": "(eˣ)' = eˣ", "说明": "自然指数函数的导数", "示例": "(e²ˣ)' = 2e²ˣ" }, "幂函数积分": { "公式": "∫xⁿ dx = xⁿ⁺¹/(n+1) + C (n≠-1)", "说明": "幂函数的不定积分公式", "示例": "∫x² dx = x³/3 + C" } }, "三角函数": { "正弦定理": { "公式": "a/sinA = b/sinB = c/sinC = 2R", "说明": "三角形边与对角正弦值之比等于外接圆直径", "示例": "已知a=5, A=30°, B=60°, 则b=a*sinB/sinA≈8.66" }, "余弦定理": { "公式": "c² = a² + b² - 2ab·cosC", "说明": "三角形边长与夹角的关系", "示例": "已知a=3, b=4, C=60°, 则c=√(9+16-24 * 0.5)=√13≈3.606" } }, "概率统计": { "期望公式": { "公式": "E(X) = Σ[x * P(x)]", "说明": "离散随机变量的数学期望", "示例": "掷骰子期望值 = (1+2+3+4+5+6)/6=3.5" }, "方差公式": { "公式": "Var(X) = E[(X-μ)²] = E(X²) - [E(X)]²", "说明": "随机变量的方差公式", "示例": "" } } } if os.path.exists(self.data_file): try: with open(self.data_file, 'r', encoding='utf-8') as f: return json.load(f) except: return default_data else: self._save_formulas(default_data) return default_data def _save_formulas(self, data): """保存公式数据""" with open(self.data_file, 'w', encoding='utf-8') as f: json.dump(data, f, ensure_ascii=False, indent=2) def get_categories(self): """获取所有类别""" return list(self.formulas.keys()) def get_formulas_by_category(self, category): """获取指定类别的所有公式""" return self.formulas.get(category, {}) def search_formulas(self, keyword): """搜索公式""" results = [] keyword = keyword.lower() for category, formulas in self.formulas.items(): for name, info in formulas.items(): search_text = f"{category} {name} {info.get('公式', '')} {info.get('说明', '')} {info.get('示例', '')}".lower() if keyword in search_text: results.append({ 'category': category, 'name': name, 'formula': info.get('公式', ''), 'description': info.get('说明', ''), 'example': info.get('示例', '') }) return results def add_formula(self, category, name, formula, description="", example=""): """添加公式""" if category not in self.formulas: self.formulas[category] = {} if name in self.formulas[category]: return False self.formulas[category][name] = { "公式": formula, "说明": description, "示例": example } self._save_formulas(self.formulas) return True def delete_formula(self, category, name): """删除公式""" if category in self.formulas and name in self.formulas[category]: del self.formulas[category][name] if not self.formulas[category]: del self.formulas[category] self._save_formulas(self.formulas) return True return False class CalculatorWidget(QWidget): """公式计算器部件""" def __init__(self): super().__init__() self.init_ui() def init_ui(self): layout = QVBoxLayout() # 标题 title = QLabel("🧮 公式计算器") title.setStyleSheet("font-size: 18px; font-weight: bold; color: #2c3e50;") layout.addWidget(title) # 公式选择 form_layout = QFormLayout() self.category_combo = QComboBox() self.category_combo.addItems(["几何", "代数", "微积分", "三角函数", "概率统计"]) self.formula_combo = QComboBox() self.formula_combo.addItems(["勾股定理", "圆面积公式", "球体积公式"]) form_layout.addRow("公式类别:", self.category_combo) form_layout.addRow("选择公式:", self.formula_combo) layout.addLayout(form_layout) # 输入参数 self.param_widget = QWidget() param_layout = QVBoxLayout(self.param_widget) self.param_a = QLineEdit() self.param_b = QLineEdit() self.param_c = QLineEdit() param_layout.addWidget(QLabel("参数 a:")) param_layout.addWidget(self.param_a) param_layout.addWidget(QLabel("参数 b:")) param_layout.addWidget(self.param_b) param_layout.addWidget(QLabel("参数 c:")) param_layout.addWidget(self.param_c) layout.addWidget(self.param_widget) # 计算按钮 calc_btn = QPushButton("计算") calc_btn.clicked.connect(self.calculate) calc_btn.setStyleSheet(""" QPushButton { background-color: #3498db; color: white; border: none; padding: 8px; border-radius: 4px; font-weight: bold; } QPushButton:hover { background-color: #2980b9; } """) layout.addWidget(calc_btn) # 结果显示 self.result_label = QLabel("结果将在这里显示") self.result_label.setStyleSheet(""" background-color: #f8f9fa; border: 1px solid #dee2e6; border-radius: 4px; padding: 10px; font-family: 'Courier New', monospace; """) self.result_label.setWordWrap(True) layout.addWidget(self.result_label) self.setLayout(layout) def calculate(self): """执行计算""" try: formula = self.formula_combo.currentText() if formula == "勾股定理": a = float(self.param_a.text()) if self.param_a.text() else 0 b = float(self.param_b.text()) if self.param_b.text() else 0 c = math.sqrt(a*a + b*b) self.result_label.setText(f"c = √({a}² + {b}²) = {c:.4f}") elif formula == "圆面积公式": r = float(self.param_a.text()) if self.param_a.text() else 0 area = math.pi * r * r self.result_label.setText(f"S = π × {r}² = {area:.4f} ≈ {area}") elif formula == "球体积公式": r = float(self.param_a.text()) if self.param_a.text() else 0 volume = (4/3) * math.pi * r**3 self.result_label.setText(f"V = (4/3)π × {r}³ = {volume:.4f}") else: self.result_label.setText("该公式计算功能开发中...") except Exception as e: self.result_label.setText(f"计算错误: {str(e)}") class FormulaBrowser(QWidget): """公式浏览器""" def __init__(self, db): super().__init__() self.db = db self.init_ui() def init_ui(self): main_layout = QHBoxLayout() # 左侧类别列表 left_widget = QWidget() left_layout = QVBoxLayout(left_widget) # 类别列表 self.category_list = QListWidget() self.category_list.itemClicked.connect(self.on_category_selected) left_layout.addWidget(QLabel("📁 公式类别")) left_layout.addWidget(self.category_list) # 搜索框 search_layout = QHBoxLayout() self.search_input = QLineEdit() self.search_input.setPlaceholderText("搜索公式...") self.search_input.textChanged.connect(self.on_search) search_btn = QPushButton("🔍") search_btn.clicked.connect(self.on_search) search_layout.addWidget(self.search_input) search_layout.addWidget(search_btn) left_layout.addLayout(search_layout) # 中间公式列表 middle_widget = QWidget() middle_layout = QVBoxLayout(middle_widget) self.formula_list = QListWidget() self.formula_list.itemClicked.connect(self.on_formula_selected) middle_layout.addWidget(QLabel("📝 公式列表")) middle_layout.addWidget(self.formula_list) # 右侧详情显示 right_widget = QWidget() right_layout = QVBoxLayout(right_widget) self.detail_text = QTextEdit() self.detail_text.setReadOnly(True) self.detail_text.setStyleSheet(""" QTextEdit { background-color: #f8f9fa; border: 1px solid #dee2e6; border-radius: 4px; padding: 10px; font-family: 'Microsoft YaHei'; } """) right_layout.addWidget(QLabel("📄 公式详情")) right_layout.addWidget(self.detail_text) # 添加到主布局 main_layout.addWidget(left_widget, 1) main_layout.addWidget(middle_widget, 2) main_layout.addWidget(right_widget, 3) self.setLayout(main_layout) # 加载类别 self.load_categories() def load_categories(self): """加载所有类别""" self.category_list.clear() categories = self.db.get_categories() for category in categories: formulas = self.db.get_formulas_by_category(category) count = len(formulas) item = QListWidgetItem(f"{category} ({count}个)") item.setData(Qt.UserRole, category) self.category_list.addItem(item) def on_category_selected(self, item): """类别选择事件""" category = item.data(Qt.UserRole) self.load_formulas(category) def load_formulas(self, category): """加载指定类别的公式""" self.formula_list.clear() self.detail_text.clear() formulas = self.db.get_formulas_by_category(category) for name in formulas.keys(): item = QListWidgetItem(name) item.setData(Qt.UserRole, (category, name)) self.formula_list.addItem(item) def on_formula_selected(self, item): """公式选择事件""" category, name = item.data(Qt.UserRole) formula_info = self.db.get_formulas_by_category(category)[name] # 显示详细信息 text = f"""

{name}

📁 类别: {category}

📐 公式:

{formula_info.get('公式', '')}

📋 说明:

{formula_info.get('说明', '')}

""" if formula_info.get('示例'): text += f"""

🔍 示例:

{formula_info.get('示例', '')}

""" self.detail_text.setHtml(text) def on_search(self): """搜索公式""" keyword = self.search_input.text().strip() if not keyword: self.load_categories() if self.category_list.count() > 0: self.category_list.setCurrentRow(0) self.category_list.item(0).setSelected(True) self.on_category_selected(self.category_list.item(0)) return self.formula_list.clear() self.detail_text.clear() results = self.db.search_formulas(keyword) for result in results: item = QListWidgetItem(f"[{result['category']}] {result['name']}") item.setData(Qt.UserRole, (result['category'], result['name'])) self.formula_list.addItem(item) class AddFormulaDialog(QDialog): """添加公式对话框""" def __init__(self, db, parent=None): super().__init__(parent) self.db = db self.setWindowTitle("➕ 添加新公式") self.setModal(True) self.init_ui() def init_ui(self): layout = QVBoxLayout() form_layout = QFormLayout() # 类别输入 self.category_combo = QComboBox() self.category_combo.setEditable(True) self.category_combo.addItems(self.db.get_categories()) form_layout.addRow("类别:", self.category_combo) # 公式名称 self.name_input = QLineEdit() form_layout.addRow("公式名称:", self.name_input) # 公式表达式 self.formula_input = QLineEdit() form_layout.addRow("公式表达式:", self.formula_input) # 公式说明 self.description_input = QTextEdit() self.description_input.setMaximumHeight(60) form_layout.addRow("公式说明:", self.description_input) # 示例 self.example_input = QTextEdit() self.example_input.setMaximumHeight(60) form_layout.addRow("使用示例:", self.example_input) layout.addLayout(form_layout) # 按钮 button_layout = QHBoxLayout() add_btn = QPushButton("添加") add_btn.clicked.connect(self.accept) cancel_btn = QPushButton("取消") cancel_btn.clicked.connect(self.reject) button_layout.addWidget(add_btn) button_layout.addWidget(cancel_btn) layout.addLayout(button_layout) self.setLayout(layout) self.setFixedSize(400, 300) def get_data(self): """获取输入的数据""" return { 'category': self.category_combo.currentText(), 'name': self.name_input.text(), 'formula': self.formula_input.text(), 'description': self.description_input.toPlainText(), 'example': self.example_input.toPlainText() } class MainWindow(QMainWindow): """主窗口""" def __init__(self): super().__init__() self.db = FormulaDatabase() self.init_ui() def init_ui(self): self.setWindowTitle("🧮 数学公式查询系统") self.setGeometry(100, 100, 1200, 700) # 设置图标 self.setWindowIcon(QIcon(self.create_icon())) # 创建中心部件 central_widget = QWidget() self.setCentralWidget(central_widget) # 主布局 main_layout = QVBoxLayout(central_widget) # 标题 title_label = QLabel("📐 数学公式查询系统") title_label.setStyleSheet(""" QLabel { font-size: 24px; font-weight: bold; color: #2c3e50; padding: 20px; qproperty-alignment: AlignCenter; } """) main_layout.addWidget(title_label) # 创建标签页 self.tabs = QTabWidget() self.tabs.setStyleSheet(""" QTabWidget::pane { border: 1px solid #bdc3c7; border-radius: 4px; } QTabBar::tab { background: #ecf0f1; padding: 8px 16px; margin-right: 2px; border: 1px solid #bdc3c7; border-bottom: none; border-top-left-radius: 4px; border-top-right-radius: 4px; } QTabBar::tab:selected { background: #3498db; color: white; } QTabBar::tab:hover { background: #d6dbdf; } """) # 公式浏览器标签页 self.browser = FormulaBrowser(self.db) self.tabs.addTab(self.browser, "🔍 浏览查询") # 计算器标签页 self.calculator = CalculatorWidget() self.tabs.addTab(self.calculator, "🧮 公式计算") main_layout.addWidget(self.tabs) # 工具栏 self.create_toolbar() # 状态栏 self.statusBar().showMessage("就绪") def create_icon(self): """创建应用图标""" pixmap = QPixmap(32, 32) pixmap.fill(Qt.transparent) painter = QPainter(pixmap) painter.setRenderHint(QPainter.Antialiasing) # 绘制一个简单的数学图标 painter.setBrush(QColor("#3498db")) painter.setPen(QPen(QColor("#2980b9"), 2)) painter.drawEllipse(4, 4, 24, 24) painter.setPen(QPen(Qt.white, 3)) painter.drawText(QRect(4, 4, 24, 24), Qt.AlignCenter, "∑") painter.end() return QIcon(pixmap) def create_toolbar(self): """创建工具栏""" toolbar = self.addToolBar("工具") # 添加公式动作 add_action = QAction("➕ 添加公式", self) add_action.triggered.connect(self.add_formula) toolbar.addAction(add_action) # 刷新动作 refresh_action = QAction("🔄 刷新", self) refresh_action.triggered.connect(self.refresh) toolbar.addAction(refresh_action) toolbar.addSeparator() # 统计信息动作 stats_action = QAction("📊 统计", self) stats_action.triggered.connect(self.show_stats) toolbar.addAction(stats_action) # 关于动作 about_action = QAction("ℹ️ 关于", self) about_action.triggered.connect(self.show_about) toolbar.addAction(about_action) def add_formula(self): """添加公式""" dialog = AddFormulaDialog(self.db, self) if dialog.exec_(): data = dialog.get_data() if not all([data['category'], data['name'], data['formula']]): QMessageBox.warning(self, "警告", "请填写必填字段！") return if self.db.add_formula(data['category'], data['name'], data['formula'], data['description'], data['example']): QMessageBox.information(self, "成功", "公式添加成功！") self.browser.load_categories() self.statusBar().showMessage("公式添加成功") else: QMessageBox.warning(self, "警告", "公式已存在！") def refresh(self): """刷新数据""" self.db.formulas = self.db._load_formulas() self.browser.load_categories() self.statusBar().showMessage("数据已刷新") def show_stats(self): """显示统计信息""" categories = self.db.get_categories() total_formulas = 0 stats_text = "📊 数据库统计信息\n" stats_text += "=" * 30 + "\n" for category in categories: formulas = self.db.get_formulas_by_category(category) count = len(formulas) total_formulas += count stats_text += f"📁 {category}: {count} 个公式\n" stats_text += "=" * 30 + "\n" stats_text += f"📈 总计: {len(categories)} 个类别, {total_formulas} 个公式" QMessageBox.information(self, "统计信息", stats_text) def show_about(self): """显示关于信息""" about_text = """

数学公式查询系统

版本: 2.0 (GUI版)

功能:

欢迎使用数学公式查询系统！

""" QMessageBox.about(self, "关于", about_text) def main(): app = QApplication(sys.argv) # 设置应用样式 app.setStyle("Fusion") # 设置调色板 palette = QPalette() palette.setColor(QPalette.Window, QColor(240, 245, 248)) palette.setColor(QPalette.WindowText, QColor(44, 62, 80)) palette.setColor(QPalette.Base, QColor(255, 255, 255)) palette.setColor(QPalette.AlternateBase, QColor(233, 236, 239)) palette.setColor(QPalette.ToolTipBase, QColor(255, 255, 255)) palette.setColor(QPalette.ToolTipText, QColor(44, 62, 80)) palette.setColor(QPalette.Text, QColor(44, 62, 80)) palette.setColor(QPalette.Button, QColor(52, 152, 219)) palette.setColor(QPalette.ButtonText, QColor(255, 255, 255)) palette.setColor(QPalette.BrightText, Qt.red) palette.setColor(QPalette.Highlight, QColor(41, 128, 185)) palette.setColor(QPalette.HighlightedText, Qt.white) app.setPalette(palette) # 创建主窗口 window = MainWindow() window.show() sys.exit(app.exec_()) if __name__ == "__main__": main()