[AI学习笔记]数学解题系统：DeepSeek符号计算集成方案深度解析

class SymbolParser:
    def __init__(self):
        self.lexer = Lexer()
        self.parser = Parser()
    
    def parse_expression(self, expression):
        """解析数学表达式"""
        tokens = self.lexer.tokenize(expression)
        ast = self.parser.build_ast(tokens)
        return self._convert_to_internal_representation(ast)
    
    def _convert_to_internal_representation(self, ast):
        """将语法树转换为内部表示"""
        internal_repr = {}
        for node in ast.nodes:
            if node.type == "integral":
                internal_repr["type"] = "integral"
                internal_repr["integrand"] = self._process_integrand(node.integrand)
                internal_repr["limits"] = (node.lower_limit, node.upper_limit)
        return internal_repr
    
    def _process_integrand(self, integrand):
        """处理被积函数"""
        if integrand.type == "polynomial":
            return {
                "type": "polynomial",
                "terms": integrand.terms
            }

class InferenceEngine:
    def __init__(self):
        self.method_selector = IntegrationMethodSelector()
        self.validator = ResultValidator()
    
    def solve_integral(self, integral_expr):
        """求解积分"""
        method = self.method_selector.select_method(integral_expr)
        intermediate_results = []
        
        # 应用积分方法
        if method == "polynomial":
            result = self._apply_polynomial_integration(integral_expr)
        elif method == "substitution":
            result = self._apply_substitution(integral_expr)
        
        # 验证结果
        if self.validator.validate(result, integral_expr):
            return result
        else:
            raise ValueError("Integration result validation failed")
    
    def _apply_polynomial_integration(self, expr):
        """应用多项式积分方法"""
        integrated_terms = []
        for term in expr["integrand"]["terms"]:
            coefficient = term["coefficient"]
            exponent = term["exponent"] + 1
            integrated_terms.append({
                "coefficient": coefficient / exponent,
                "exponent": exponent
            })
        return integrated_terms

# 创建虚拟环境
python -m venv deepseek-math
source deepseek-math/bin/activate

# 安装依赖
pip install torch==1.12.0
pip install sympy==1.9
pip install transformers==4.20.0
pip install flask==2.0.1

from deepseek.parser import SymbolParser

# 初始化符号解析器
parser = SymbolParser()

# 解析示例表达式
expression = "∫(x² + 3x + 2) dx from 1 to 3"
internal_repr = parser.parse_expression(expression)
print("内部表示:", internal_repr)

from deepseek.inference import InferenceEngine

# 初始化推理引擎
engine = InferenceEngine()

# 求解积分
result = engine.solve_integral(internal_repr)
print("积分结果:", result)

from deepseek.validator import ResultValidator

# 初始化结果验证器
validator = ResultValidator()

# 验证结果
is_valid = validator.validate(result, internal_repr)
print("结果验证:", "有效" if is_valid else "无效")

from deepseek.api import MathSolverAPI

# 初始化API服务
api = MathSolverAPI()

# 启动服务
api.run(host="0.0.0.0", port=5000)

# 部署示例
python scripts/init_parser.py
python scripts/train_model.py
python api.py

import unittest
from deepseek.inference import InferenceEngine

class TestInferenceEngine(unittest.TestCase):
    def setUp(self):
        self.engine = InferenceEngine()
    
    def test_polynomial_integration(self):
        # 构建多项式积分表达式
        integral_expr = {
            "type": "integral",
            "integrand": {
                "type": "polynomial",
                "terms": [
                    {"coefficient": 1, "exponent": 2},
                    {"coefficient": 3, "exponent": 1},
                    {"coefficient": 2, "exponent": 0}
                ]
            },
            "limits": (1, 3)
        }
        
        # 执行积分
        result = self.engine.solve_integral(integral_expr)
        
        # 验证结果
        expected_terms = [
            {"coefficient": 1/3, "exponent": 3},
            {"coefficient": 3/2, "exponent": 2},
            {"coefficient": 2, "exponent": 1}
        ]
        self.assertEqual(result, expected_terms)

def test_end_to_end():
    # 初始化组件
    parser = SymbolParser()
    engine = InferenceEngine()
    validator = ResultValidator()
    
    # 输入表达式
    expression = "∫(x² + 3x + 2) dx from 1 to 3"
    
    # 完整流程测试
    internal_repr = parser.parse_expression(expression)
    result = engine.solve_integral(internal_repr)
    is_valid = validator.validate(result, internal_repr)
    
    # 验证结果
    assert is_valid == True
    assert len(result) == 3
    assert result[0]["coefficient"] == 1/3