import { Server } from "@modelcontextprotocol/sdk/server/index.js";
import { db } from "../database.js";
import * as math from "mathjs";
type Input = { text: string; paper_path?: string };
export const mathExplainer = {
definition: {
name: "math_explainer",
description: "深度数学智能：提取公式、构建 AST、推导关系并存入数据库",
inputSchema: {
type: "object",
properties: {
text: { type: "string" },
paper_path: { type: "string", description: "可选，用于关联数据库" }
},
required: ["text"],
additionalProperties: false,
},
},
handler: async (input: any) => {
const text = input.text || "";
// 1. 提取 LaTeX (增强版正则)
const inlineMathRegex = /\$([^$]+)\$/g;
const blockMathRegex = /\\\[([\s\S]*?)\\\]/g;
const formulas: string[] = [];
let match;
while ((match = inlineMathRegex.exec(text)) !== null) formulas.push(match[1]);
while ((match = blockMathRegex.exec(text)) !== null) formulas.push(match[1]);
// 2. 符号挖掘
const symbolRegex = /(?:where|let)\s+\$([^$]+)\$\s+(?:is|denotes|stands for|represents)\s+([^,.;]+)/gi;
const symbolMap: Record<string, string> = {};
const dbSymbols: any[] = [];
while ((match = symbolRegex.exec(text)) !== null) {
const symbol = match[1].trim();
const definition = match[2].trim();
if (symbol.length < 10) {
symbolMap[symbol] = definition;
dbSymbols.push({ symbol, definition, latex: symbol });
}
}
// 3. AST 解析与结构化 (使用 mathjs 尝试解析简单公式)
const astAnalysis: any[] = [];
for (const f of formulas.slice(0, 10)) { // 仅分析前 10 个，避免超时
try {
// 尝试将 LaTeX 转为 mathjs 可读格式（非常简化的 heuristic）
// 注意：mathjs 不直接支持 LaTeX，这里做简单替换演示原理
const simplified = f.replace(/\\frac\{([^}]+)\}\{([^}]+)\}/g, "($1)/($2)")
.replace(/\\sum/g, "sum")
.replace(/[\\][a-zA-Z]+/g, ""); // 去除其他 LaTeX 命令
const node = math.parse(simplified);
const variables = node.filter((n: any) => n.isSymbolNode).map((n: any) => n.name);
astAnalysis.push({
original: f,
variables: [...new Set(variables)],
structure: node.toString()
});
} catch (e) {
// 忽略解析失败的复杂 LaTeX
}
}
// 4. 存入数据库 (如果有 path)
if (input.paper_path) {
const paper = db.getPaperByPath(input.paper_path);
if (paper) {
db.saveSymbols(paper.id, dbSymbols);
}
}
return {
content: [
{ type: "text", text: JSON.stringify({
formulas_count: formulas.length,
symbols: symbolMap,
ast_analysis: astAnalysis,
derivation_hint: "提示：AST 分析已识别部分变量依赖，可用于推导链构建。"
})
}
]
};
},
};
