| 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")
|
|
|
|
|
| symbol_expr = self._generate_symbolic_expression(sequence)
|
|
|
|
|
| general_expr = self._generate_general_expression(symbol_expr)
|
|
|
|
|
| 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"""
|
|
|
| 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)
|
|
|
| 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"""
|
|
|
| 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)"
|
|
|
|
|
| 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],
|
| [1, 3, 5, 7, 9],
|
| [1, 2, 4, 8, 16, 31]
|
| ]
|
|
|
| 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()
|
|
|
