我想要实现一个通过使用C#、Semantic Kernel库、OpenAI GPT 4的API和以下使用C#开源库MathNet实现通过中文自然语言提示词中包含LATEX代码输入到系统，通过以下符号和数值计算和其它符号和数值计算程序输出计算结果和必要步骤的应用，这样的数学计算使用程序直接产生结果，可以避免出现模型的幻觉，在AWS云上设计出这个应用系统的架构、详细设计、关键代码、实现及部署流程和测试用例。
建议部署时使用AWS CDK实现基础设施即代码，通过分阶段部署（蓝绿部署）确保业务连续性，并定期进行混沌工程测试验证系统韧性。
一、系统架构设计
- 前端层：
- API Gateway：接收用户中文自然语言请求
- S3：存储生成的LaTeX文件
- 计算服务层：
- Lambda：无状态计算服务（适合轻量级计算）
- ECS Fargate：运行C#核心计算服务（需要MathNet/SymPy等依赖）
- AI处理层：
- SageMaker：运行Semantic Kernel模型
- Lambda：处理OpenAI API调用
- 支持服务：
- Secrets Manager：存储API密钥
- CloudWatch：监控和日志
- CodeBuild/CodePipeline：CI/CD流水线
二、详细设计
- 请求处理流程：
用户请求 → API Gateway → Lambda路由 →
Semantic Kernel解析 → MathNet计算 →
Python计算(可选) → LaTeX生成 → S3存储 →
返回下载链接
- 核心模块划分：
- NLP解析模块
- 符号计算引擎
- LaTeX生成器
- Python集成桥接
- 错误处理模块
三、关键代码实现（增强版）
1. 增强的数学表达式处理器
public class MathExpressionProcessor
{private static readonly Dictionary<string, string> LatexReplacements = new(){{"sin(x)", @"\sin x"}, {"cos(x)", @"\cos x"},{"tan(x)", @"\tan x"}, {"ln(x)", @"\ln x"},{"π", @"\pi"}, {"*", ""}, {"^", @"^"}};public string ToLatex(string expression){return LatexReplacements.Aggregate(expression, (current, replacement) => current.Replace(replacement.Key, replacement.Value));}public SymbolicExpression SafeParse(string expr){try {return SymbolicExpression.Parse(expr);}catch (Exception ex) {throw new MathParseException($"解析失败: {expr}", ex);}}
}
2. AWS Lambda入口函数
public class Function
{[LambdaSerializer(typeof(Amazon.Lambda.Serialization.SystemTextJson.DefaultLambdaJsonSerializer))]public async Task<APIGatewayProxyResponse> FunctionHandler(APIGatewayProxyRequest request){var mathRequest = JsonConvert.DeserializeObject<MathRequest>(request.Body);var processor = new MathProcessor();var result = await processor.ProcessRequest(mathRequest);return new APIGatewayProxyResponse {StatusCode = 200,Body = JsonConvert.SerializeObject(result),Headers = new Dictionary<string, string> { {"Content-Type", "application/json"} }};}
}public class MathProcessor
{public async Task<MathResponse> ProcessRequest(MathRequest request){using var kernel = Kernel.Builder.Build();kernel.Config.AddOpenAITextCompletionService("gpt4", "text-davinci-003", Environment.GetEnvironmentVariable("OPENAI_KEY"));var semanticResult = await kernel.RunAsync(request.Question,kernel.CreateSemanticFunction("解析数学问题类型，返回JSON格式：{ operation: '导数|积分|微分方程', variables: [...] }"));var operation = JsonConvert.DeserializeObject<MathOperation>(semanticResult.Result);return operation.OperationType switch {"导数" => CalculateDerivative(operation),"积分" => CalculateIntegral(operation),"微分方程" => SolveDifferentialEquation(operation),_ => throw new NotSupportedException()};}
}
四、部署实施流程
- 基础设施准备：
# 使用CloudFormation部署基础架构
aws cloudformation create-stack \--stack-name MathCalcStack \--template-body file://infra-template.yaml \--capabilities CAPABILITY_NAMED_IAM
- CI/CD流水线配置：
# buildspec.yml
version: 0.2
phases:install:runtime-versions:dotnet: 6.0build:commands:- dotnet restore- dotnet publish -c Release -o outpost_build:commands:- aws ecr get-login-password | docker login --username AWS --password-stdin $ECR_URI- docker build -t $IMAGE_REPO_NAME .- docker tag $IMAGE_REPO_NAME:latest $ECR_URI/$IMAGE_REPO_NAME:latest- docker push $ECR_URI/$IMAGE_REPO_NAME:latest
- ECS任务定义关键配置：
{"containerDefinitions": [{"name": "math-container","image": "math-repo:latest","environment": [{"name": "PYTHONPATH", "value": "/usr/local/bin/python"},{"name": "LATEX_TEMP_DIR", "value": "/tmp/latex"}],"mountPoints": [{"sourceVolume": "latex-storage","containerPath": "/tmp/latex"}]}]
}
五、测试用例设计
- 正向测试用例：
测试ID,输入,预期输出
TC001,"求x²在x=2处的导数", "4x, 8"
TC002,"计算∫(x^2 + 3x)dx", "(1/3)x³ + (3/2)x² + C"
TC003,"验证y=e^x是y'' - y = 0的解", "验证通过"
- 边界测试用例：
[Test]
public void Test_Edge_Cases()
{var processor = new MathExpressionProcessor();Assert.AreEqual(@"\sin x", processor.ToLatex("sin(x)"));Assert.Throws<MathParseException>(() => processor.SafeParse("x^^2")