Upload 3 files

app.py

@@ -0,0 +1,66 @@
+import gradio as gr
+from function_generator import FunctionGenerator
+
+def generate_function(sequence_str):
+    try:
+        sequence = [float(x.strip()) for x in sequence_str.split(',')]
+        generator = FunctionGenerator()
+        symbol_expr, general_expr, latex_expr = generator.generate(sequence)
+        
+        return (
+            f"y = {str(symbol_expr)}",
+            general_expr,
+            f"$$\\Large {latex_expr}$$"
+        )
+    except Exception as err:
+        return f"错误: {str(err)}", "", ""
+
+# 创建Gradio界面
+with gr.Blocks() as demo:
+    gr.Markdown("## 数学函数生成器")
+    
+    with gr.Row():
+        with gr.Column():
+            # 使用文本框输入
+            sequence_input = gr.Textbox(
+                label="输入数列（用逗号分隔）",
+                placeholder="例如: 1, 2, 4, 8, 16",
+                lines=1
+            )
+            
+            # 示例按钮
+            with gr.Row():
+                example_btn1 = gr.Button("示例1: 1, 2, 4, 8, 16")
+                example_btn2 = gr.Button("示例2: 1, 3, 5, 7, 9")
+                example_btn3 = gr.Button("示例3: 1, 4, 9, 16, 25")
+                
+            # 示例按钮点击事件
+            example_btn1.click(lambda: "1,2,4,8,16", outputs=sequence_input)
+            example_btn2.click(lambda: "1,3,5,7,9", outputs=sequence_input)
+            example_btn3.click(lambda: "1,4,9,16,25", outputs=sequence_input)
+    
+    with gr.Row():
+        generate_btn = gr.Button("生成函数", variant="primary")
+    
+    with gr.Row():
+        with gr.Column():
+            symbol_expr_output = gr.Textbox(label="符号表达式", interactive=False)
+            general_expr_output = gr.Textbox(label="一般数学表达式", interactive=False)
+            latex_expr_output = gr.Markdown(label="渲染的数学公式")
+    
+    # 实时更新
+    sequence_input.change(
+        fn=generate_function,
+        inputs=sequence_input,
+        outputs=[symbol_expr_output, general_expr_output, latex_expr_output]
+    )
+    
+    # 生成按钮点击事件
+    generate_btn.click(
+        fn=generate_function,
+        inputs=sequence_input,
+        outputs=[symbol_expr_output, general_expr_output, latex_expr_output]
+    )
+
+if __name__ == "__main__":
+    demo.launch()

function_generator.py

@@ -0,0 +1,99 @@
+import sympy as sp
+
+class FunctionGenerator:
+    def __init__(self):
+        self.x = sp.Symbol('x')
+        
+    def generate(self, sequence):
+        """生成函数表达式
+        
+        参数:
+            sequence (list): 输入数列
+            
+        返回:
+            tuple: (符号表达式, 一般数学表达式, LaTeX表达式)
+        """
+        try:
+            sequence = [float(x) for x in sequence]
+            if len(sequence) < 2:
+                raise ValueError("至少需要两个数来生成函数")
+                
+            # 生成符号表达式
+            symbol_expr = self._generate_symbolic_expression(sequence)
+            
+            # 生成一般数学表达式
+            general_expr = self._generate_general_expression(symbol_expr)
+            
+            # 生成LaTeX表达式
+            latex_expr = self._generate_latex_expression(symbol_expr)
+            
+            return symbol_expr, general_expr, latex_expr
+            
+        except Exception as e:
+            raise ValueError(f"生成函数时出错: {str(e)}")
+            
+    def _generate_symbolic_expression(self, sequence):
+        """生成符号表达式"""
+        # 使用拉格朗日插值
+        terms = []
+        for i in range(len(sequence)):
+            numerator = 1
+            denominator = 1
+            for j in range(len(sequence)):
+                if j != i:
+                    numerator *= (self.x - (j + 1))
+                    denominator *= ((i + 1) - (j + 1))
+            term = sp.Rational(sequence[i]) * numerator / denominator
+            terms.append(term)
+            
+        return sp.simplify(sum(terms))
+        
+    def _generate_general_expression(self, symbol_expr):
+        """生成一般数学表达式"""
+        expr_str = str(symbol_expr)
+        # 仅替换非符号表达式中的 ** 为 ^
+        expr_str = expr_str.replace('**', '^')
+        return f"y = {expr_str}"
+        
+    def _generate_latex_expression(self, symbol_expr):
+        """生成LaTeX表达式"""
+        return f"y = {sp.latex(symbol_expr)}"
+        
+    def _identify_pattern(self, sequence):
+        """识别数列模式"""
+        # 检查指数增长
+        if len(sequence) > 1:
+            ratios = [sequence[i+1]/sequence[i] for i in range(len(sequence)-1)]
+            if all(abs(r - ratios[0]) < 1e-10 for r in ratios):
+                base = sp.Rational(sequence[1]) / sp.Rational(sequence[0])
+                return f"{base}**(x)"
+                
+        # 检查线性增长
+        differences = [sequence[i+1] - sequence[i] for i in range(len(sequence)-1)]
+        if len(set(round(d, 10) for d in differences)) == 1:
+            diff = differences[0]
+            return f"{sp.Rational(sequence[0])} + {sp.Rational(diff)}*(x)"
+            
+        return None
+
+def test_function_generator(test_sequences=None):
+    """测试函数生成器"""
+    generator = FunctionGenerator()
+    test_sequences = test_sequences or [
+        [1, 2, 4, 8, 16],  # 指数增长
+        [1, 3, 5, 7, 9],   # 线性增长
+        [1, 2, 4, 8, 16, 31]  # 复杂序列
+    ]
+    
+    for seq in test_sequences:
+        print(f"\n测试序列: {seq}")
+        try:
+            symbol_expr, general_expr, latex_expr = generator.generate(seq)
+            print("符号表达式: y =", symbol_expr)
+            print("一般数学表达式:", general_expr)
+            print("LaTeX表达式:", latex_expr)
+        except Exception as e:
+            print(f"错误: {str(e)}")
+
+if __name__ == "__main__":
+    test_function_generator()

requirements.txt

@@ -0,0 +1,2 @@
+sympy
+gradio