math-agent-framework 0.2.0

A reusable mathematical derivation and verification framework with 12 engines, supporting ODEs, PDEs, analysis, optimization, and formal proofs.

Math Agent Framework ·

Give LLMs mathematical rigor. Give computation conceptual understanding. 让 LLM 的数学推理接受严格检验，让符号计算获得概念理解。

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The Problem / 问题

LLMs understand mathematical concepts — they can plan derivations, explain theorems, and reason about structure. But they hallucinate calculations. An LLM may confidently claim ∫x·eˣdx = eˣ + C, and you won't know it's wrong until you check.

LLM 理解数学概念——能规划推导路径、解释定理、推理结构。 但它会幻觉计算。它可能自信地说 ∫x·eˣdx = eˣ + C，不亲手验证就不会发现错误。

Symbolic engines (SymPy, NumPy) compute faithfully — every derivative, integral, and solution is deterministic and correct. But they have zero conceptual understanding. They can't explain why a result matters or choose the right approach for a problem.

符号引擎（SymPy, NumPy）忠实计算——每次求导、积分、求解都是确定且正确的。 但它零概念理解，不能解释结果的意义，也无法为问题选择正确的方法。

The Solution / 解决方案

Math Agent Framework bridges this gap. It creates a controlled partnership:

Math Agent Framework 填补了这个鸿沟。 它建立了一个受控的协作关系：

LLM understands the problem   →   plans the derivation path
    (概念理解 / conceptual)         (规划推导路径 / plans)

Framework executes faithfully  →   computes every step deterministically
    (忠实执行 / execution)          (确定性计算 / computes)

Verification pipeline           →   catches every hallucination
    (验证流水线 / verification)     (扼杀幻觉 / kills hallucinations)

The LLM provides conceptual oversight — choosing which ODE method to apply, interpreting results, explaining significance. The framework provides computational fidelity — SymPy derives, NumPy verifies with 10,000 Monte Carlo samples, SageMath cross-checks, and a 5-level pipeline issues the final verdict.

LLM 提供概念监督——选择ODE解法、解释结果、说明意义。 框架提供计算保真——SymPy 推导、NumPy 万组蒙特卡洛验证、SageMath 交叉检验、五层流水线给出最终裁决。

The result: an LLM whose mathematical output is no longer trust-based. It is verified. 结果：LLM 的数学输出不再基于信任，而是经过验证。

pip install math-agent-framework
math-agent list
math-agent derive ode_solver

Above: deriving a damped harmonic oscillator — classify → solve → verify → report. One command. 上图: 阻尼谐振子推导——分类→求解→验证→报告。一条命令。

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30秒快速开始 / 30-Second Quick Start

为什么不用 SymPy？ / Why not just SymPy?

Capability / 能力	SymPy	Math Agent Framework
Symbolic derivation / 符号推导	✅	✅
Numerical verification / 数值验证	Partial	✅ (10K-sample Monte Carlo)
Reusable pipelines / 可复用流水线	❌	✅ (model-driven, ~50 lines)
Document generation / 文档生成 (MD/LaTeX/DOCX)	❌	✅
MCP tool auto-registration / MCP工具自动注册	❌	✅ (60+ tools)
LLM agent orchestration / LLM编排 (Harness)	❌	✅ (skills + prompts + routing)
ODE classify + solve + verify / ODE分类求解验证	❌	✅ (5 types)
PDE analytical + numerical / PDE解析+数值	❌	✅ (Heat/Wave/Laplace/Poisson/Transport)
5-level verification pipeline / 五层验证流水线	❌	✅
Cross-engine validation / 跨引擎交叉验证	❌	✅ (SymPy vs SageMath)

SymPy computes. This framework verifies, documents, and orchestrates. SymPy 负责计算，本框架负责验证、文档和编排。

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30秒快速开始 / 30-Second Quick Start

pip install math-agent-framework      # 安装 / Install
math-agent list                       # 列出所有可用模型 / List models
math-agent derive ode_solver          # 求解ODE并验证 / Solve ODE + verify
math-agent derive pde_solver          # 求解PDE并验证 / Solve PDE + verify
math-agent doc ode_solver --format md # 生成Markdown报告 / Generate report

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应用场景 / Use Cases

Domain / 领域	Capability / 能力
Optics / Photonics / 光学	Waveguide derivation, coupled-mode theory, dispersion
Physics / 物理	Harmonic oscillator, resonance, energy conservation
Engineering / 工程	ODE/PDE solving, stability, parameter sensitivity
Mathematics / 数学	Limits, series convergence, integrals, continuity
Research / 科研	Reproducible pipelines, verified appendices
LLM Agents / 智能体	MCP-native math tooling for Claude Code / GPT

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Harness: 多智能体编排 / Multi-Agent Orchestration

User: "solve y'' + 3y' + 2y = 0"   / 用户输入
  -> Orchestrator detects: ODE (2nd order)   / 编排器检测领域
  -> matched skill: derive_ode                / 匹配技能
  -> tool sequence: [classify -> solve_2nd_order -> verify]
  -> LLM follows plan, engines execute locally / LLM按计划调用本地引擎

Skill / 技能	Trigger / 触发词	Tool Sequence / 工具序列	Verification / 验证
derive_ode	ode, y', dy/dx	classify → solve → verify	checkodesol
solve_pde	pde, heat, wave	classify → analytical/numerical	CFL / L2 error
solve_analysis	limit, series, integral	limits → series → integrals	dual verification
verify_mathematical	verify, prove	5-level pipeline	multi-engine
full_pipeline	complete derivation	derive → verify → document	full stack
analyze_oscillator	oscillator, resonance	classify → solve → energy	conservation

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验证流水线 / Verification Pipeline

Every derivation passes through 5 levels of verification. 每次推导都经过五层验证：

Level 1: SymPy symbolic   — identity checks, FOC/SOC, Hessian / 符号恒等式检验
Level 2: Monte Carlo      — 10,000 random parameter sets / 万组随机参数
Level 3: SageMath CAS      — independent engine cross-check / 独立引擎交叉验证
Level 4: Lean 4            — formal proof template generation / 形式化证明模板
Level 5: QED Multi-Agent   — Proposer + Critic + Judge / 多Agent对抗验证

架构 / Architecture

┌─────────────────────────────────────────┐
│  LLM Agent (Claude / GPT)               │
│  负责规划推导、选择工具、解释结果           │
│  Requires: API Key                       │
└──────────────┬──────────────────────────┘
               │ MCP Protocol
               ▼
┌─────────────────────────────────────────┐
│  Math Agent Framework (this repo)        │
│  Zero API keys — all local computation   │
│  零 API Key，全部本地计算                  │
│                                          │
│  ┌──────────┐ ┌──────────┐ ┌──────────┐ │
│  │Derivation│ │Verification│ │Output    │ │
│  │SymPy     │ │5-level    │ │MD/LaTeX  │ │
│  │NumPy     │ │MonteCarlo │ │DOCX/JSON │ │
│  │QuantEcon │ │SageMath   │ │Lean4     │ │
│  │Analysis  │ │MultiAgent │ │Visual    │ │
│  │PDE       │ │           │ │          │ │
│  └──────────┘ └──────────┘ └──────────┘ │
│                                          │
│  Harness: Skills + Prompts + ToolRouter  │
│  CLI · MCP Server · Python SDK           │
└──────────────────────────────────────────┘

12 engines · 60+ MCP tools · 6 skills · 5 builtin models 12个引擎 · 60+个MCP工具 · 6个技能 · 5个内置模型

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自定义模型 (~50行) / Custom Model

from models.base_model import BaseModel, derivation_step

class WaveguideModel(BaseModel):
    name = "waveguide"
    description = "Optical waveguide mode derivation / 光波导模式推导"

    def define_symbols(self, engine):
        engine.declare_symbols({"x": None, "n1": {"positive": True},
                                 "k0": {"positive": True}, "beta": {"real": True}})

    def define_equations(self, engine):
        return {"helmholtz": "diff(E(x),x,2) + (n1**2*k0**2 - beta**2)*E(x)"}

    @derivation_step(1, "Solve waveguide mode / 求解波导模式", tools=["SymPy"])
    def step1_solve(self, engine, params):
        pass  # ~3 lines of derivation code / ~3行推导代码

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可靠性 / Reliability

Test Suite / 测试套件	Count / 数量	Status / 状态
Engine unit tests / 引擎单元测试	7	✅ All pass / 全部通过
Model system tests / 模型系统测试	6	✅ All pass / 全部通过
Analysis tests / 分析学测试	20+	✅ All pass / 全部通过
PDE tests / 偏微分方程测试	8	✅ All pass / 全部通过
Harness tests / 编排系统测试	6	✅ All pass / 全部通过

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Roadmap / 路线图

• SymPy symbolic engine + Builder API / 符号引擎
• Numerical verification (Monte Carlo, grid search) / 数值验证
• 5-level verification pipeline / 五层验证流水线
• ODE/PDE solving (analytical + numerical) / 常微分/偏微分求解
• Analysis engine (limits, series, integrals) / 分析学引擎
• SageMath cross-validation / SageMath交叉验证
• QuantEcon dynamic optimization / 动态优化
• Multi-agent adversarial verification (QED) / 多Agent验证
• Lean 4 formal proof templates / 形式化证明
• MCP server (60+ auto-registered tools) / MCP服务器
• Harness system (skills, prompts, routing) / 编排系统
• Wolfram Engine backend
• Jupyter notebook widgets
• Graph-based mathematical reasoning / 图数学推理
• Multi-step proof planning / 多步证明规划
• PyPI publication / PyPI发布

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MCP 集成 / MCP Integration

claude mcp add-json math-agent-framework '{
  "command": "python",
  "args": ["-m", "mcp.mcp_server"],
  "env": {}
}' -s local

Automatically registered tools include: model derivation, verification, analysis, unified pipeline, and harness orchestration. 自动注册工具包括：模型推导、验证、分析、统一流水线、编排调度。

License / 许可证

MIT — see LICENSE.

Citation / 引用

@software{math_agent_framework,
  title = {Math Agent Framework: Agent-native Mathematical Derivation and Verification},
  year = {2026},
  url = {https://github.com/symmetryseeker/math-agent-framework}
}