灵数求解器 · Lingshu Solver

≤6-dimensional deterministic real equation system solving engine · MCP tool for AI agents and everyday users

Lingshu Solver (codename Epsilon, V4.1) is an offline, deterministic, zero-data real equation system solver covering ≤6 variables, real solutions, and lightweight numerical localization. It does not require initial values from the user; it uses interval arithmetic for conservative contraction + the Krawczyk operator for solution certification, and does its best to exhaust multiple solutions.

🚀 Quick start (30 seconds)

If you know nothing about tech — just use the web version

Just open this link and it works — no installation needed: 👉 https://genesis-plan.github.io/lingshu-solver/

Type equations in the input box (e.g. x^2 + y^2 = 25 and x + y = 7), then click Solve. The page has 6 example buttons — click one to see what it can solve.

If you're an AI user (Claude / Cursor / Cline, etc.)

Copy the following configuration into your MCP client config file and restart the client:

{
  "mcpServers": {
    "lingshu-solver": {
      "command": "npx",
      "args": ["-y", "lingshu-solver"]
    }
  }
}

No need to download code or fill in paths. npx will fetch and run it automatically. If Node.js isn't installed on your machine, go to https://nodejs.org and install the LTS version (just click Next all the way through).

If you're a developer

git clone https://github.com/genesis-plan/lingshu-solver.git
cd lingshu-solver
node mcp-server.js        # 启动 MCP 服务端
node test/regression.js   # 跑回归测试（28 用例）

This repository contains:

• index.html — single-file product (in-browser UI + verified core script <script id="solver-core">)

• solver-core.js — Node engine loader (reads the index.html core script, zero dependencies, reused by MCP/tests)

• mcp-server.js — zero-dependency MCP stdio server (hand-rolled JSON-RPC 2.0 + Content-Length framing)

• package.json — standard metadata, one-line integration via npx lingshu-solver

• test/ — regression suite + smoke tests + three resident exam sets

Capability boundaries (honest statement)

Not guaranteed: 100% exhaustiveness for all inputs; guaranteed convergence within budget for highly ill-conditioned systems. These are honest boundaries, not defects.

Using as an MCP tool

1. Run the server

node mcp-server.js

2. Configure in an MCP client (Claude Desktop / Cursor / Cline / VS Code, etc.)

Recommended · one-line command (requires npm publication, not yet published; for now use the clone version below):

{
  "mcpServers": {
    "lingshu-solver": {
      "command": "npx",
      "args": ["-y", "lingshu-solver"]
    }
  }
}

Note: npx lingshu-solver will only work once this package is published to npm; we're working on it. Until then, use the "manually specify local path" version below (clone the repo first).

Alternative · manually specify local path (when the repo is already cloned):

{
  "mcpServers": {
    "lingshu-solver": {
      "command": "node",
      "args": ["把这里替换成你本地的绝对路径/灵数求解器/mcp-server.js"]
    }
  }
}

For the manual version, replace the path in args with the absolute path to your local mcp-server.js (e.g. C:/Users/你的用户名/Desktop/灵数求解器/mcp-server.js). The npx version doesn't need this step.

Tool 1: solve

Input:

{
  "equations": ["x^2 + y^2 = 25", "x + y = 7"],
  "variables": ["x", "y"],
  "domain": { "x": [-30, 30], "y": [-30, 30] }
}

• equations: array of equation strings (required), supports + - * / ^ sqrt log sin cos tan exp abs, plus in-text domain constraints like "x ∈ [-30,30]".

• variables: array of variable names (optional; if omitted, auto-detected in order of appearance, up to 6).

• domain: explicit search domain (optional). Recommended for the "finite solutions · partial" demo or fast-growing functions; otherwise the default ±1e6 may fail to prune and trigger truncated.

Output precision is fixed at 6 decimal places (product spec "6-decimal finite grid"); no precision switching is provided; solution points values are grid-snapped, with actual residuals typically ≤ 1e-9.

Output (excerpt):

{
  "resultType": 2,
  "resultTypeName": "finite",
  "certified": true,
  "truncated": false,
  "precisionDecimals": 6,
  "solutionCount": 2,
  "recommended": { "values": [3, 4], "tier": "proven", "residual": 0 },
  "solutions": [ { "values": [3, 4], "tier": "proven", "residual": 0 }, ... ],
  "warnings": []
}

• resultType: 1=empty(no solution) / 2=finite(finite solutions) / 3=infinite(infinite solution set; only the recommended solution nearest the origin is given).

• tier: proven (Krawczyk-certified) / candidate (unproven but possibly a solution) / structural (derived structurally).

Tool 2: give_feedback

AI agents proactively report when they hit a blocker/error/suspected issue; it only lands in the local feedback.log and is never sent out:

{ "name": "give_feedback", "arguments": { "message": "x^2=4 期望2解", "context": "批量求解场景" } }

Local verification

node verify_core.js        # 引擎加载 + 6 个代表性用例
node mcp_smoke.js          # MCP 字节级冒烟（initialize/tools/list/tools/call）
node mcp_smoke2.js         # give_feedback + 错误结构化（不泄露堆栈）
node test/regression.js    # 三套常驻考卷回归（28 用例，known 命中率统计）

Examples (covering 6 result categories)

Documentation

• 《灵数求解器_代码流程中文说明.md》 — complete internal flow from parsing to output (for readers with a math background)

• 《灵数求解器商业化战略白皮书.md》 — positioning, capability boundaries, risks

• Invention patent application series (submitted)

License

Apache License 2.0 — see LICENSE.