SymKit

Mathematica-style symbolic computation, powered by LLMs.

🌐 English | 简体中文

What if you had Mathematica's symbolic engine, driven by natural language?

Mathematica gave us precise symbolic math. LLMs gave us natural-language reasoning. SymKit combines both.

It is an MCP server that lets AI agents perform step-by-step symbolic derivations: calculate, transform, verify, and store formulas with full provenance — all through conversation.

┌────────────────────────────────────────────────────────────────────┐
│                                                                    │
│  You describe the math in plain English                              │
│        ↓                                                           │
│  SymKit executes, verifies, and records every step                 │
│        ↓                                                           │
│  You get an exact, reusable formula with an audit trail            │
│                                                                    │
└────────────────────────────────────────────────────────────────────┘

Why SymKit?

Traditional LLM	SymKit
❌ "The answer is approximately..."	✅ "The exact expression is..."
❌ "Let me calculate that again"	✅ Every step is recorded and verifiable
❌ "I think these units work out"	✅ Dimensional analysis checks every result
❌ "Where did this formula come from?"	✅ Full provenance: base formulas + derivation steps
❌ Calculation is lost in chat history	✅ Stored as reusable Markdown + YAML

What it does

SymKit is not a formula database. It is a symbolic derivation engine that creates new formulas from existing ones.

Known formulas                      New formula
┌─────────────────┐                 ┌────────────────────────────┐
│ F = -kx         │                 │                            │
│ F = ma          │  ──compose──▶   │  ω = √(k/m)                │
│ d²x/dt² = a     │                 │  (simple harmonic oscillator) │
└─────────────────┘                 └────────────────────────────┘

Use it for physics, engineering, chemistry, biology, economics — any domain where you need to combine and transform mathematical relationships.

⚡ Four superpowers

Capability	What it means	Tools
Derive	Combine base formulas into new ones	derive, intent_execute, math
Control	Review, annotate, and rollback every step	session_*, *_step
Verify	Check correctness symbolically and dimensionally	session_verify_*, assume*
Ship	Turn results into Python, LaTeX, Markdown, or SymPy	generate_*

🚀 See it in action

Derive a physical law from first principles:

User: Derive the angular frequency of a simple harmonic oscillator.

SymKit:
  1. Load F = -kx  and  F = m·d²x/dt²
  2. Substitute → m·d²x/dt² = -kx
  3. Solve ODE → x(t) = A·cos(ωt + φ),  ω = √(k/m)
  4. Verify by substitution: d²x/dt² = -ω²x  ✓
  5. Store result with full derivation history

Build a custom engineering model:

User: Find the cutoff frequency of an RC high-pass filter.

SymKit:
  1. Load Q = CV and V = IR
  2. Derive capacitive reactance X_c = 1/(2πfC)
  3. Set X_c = R at cutoff
  4. Solve for f → f_c = 1 / (2πRC)  ✓

Verify a calculus result:

User: Calculate and verify ∫(x² + 3x) dx.

→ Result: x³/3 + 3x²/2 + C
→ Verify: d/dx(x³/3 + 3x²/2) = x² + 3x  ✓

🛠️ 41 MCP tools, one coherent workflow

SymKit exposes 41 MCP tools across 8 categories. Everything routes through a few high-level tools while power users can drop down to individual steps.

Category	Tools	Count
Unified Math	math	1
Session Management	session_start, session_show, session_rollback, session_complete, ...	17
Assumptions	assume, show_assumptions, assume_for_step, list_assumptions, check_assumption_conflicts, clear_step_assumptions	6
Formula Search	formula_search, formula_get, formula_add, formula_categories	4
Symbol Registry	register_symbol, lookup_symbol, list_domain_symbols, check_symbol_conflicts	4
Code Generation	generate_python_function, generate_latex_derivation, generate_derivation_report, generate_sympy_script	4
Derivation & Orchestration	derive, intent_execute, list_patterns	3
Tool Discovery	tool_categories, tool_recommend	2

The math() tool alone covers ~25 symbolic operations — calculus, ODEs, matrices, vector analysis, integral transforms — and can write its result directly into a derivation session.

🔍 Formula search workflow

SymKit can pull authoritative formulas from Wikidata and physical constants from SciPy, normalize LLM queries automatically, and load the chosen formula straight into a derivation session.

Recommended workflow:

1. Search
   formula_search("Navier-Stokes equations", domain="fluid_dynamics")

2. Get and load
   formula_get("Q201321", source="wikidata", load_into_session=True)

3. Derive
   math("simplify", "...", session=True)

4. Complete
   session_complete(description="Incompressible NS momentum equation")

Query normalization: you can write queries naturally — fluid_dynamics, fluid mechanics, and cfd all resolve to the same domain; Navier–Stokes (en dash) and Navier-Stokes (hyphen) match the same Wikidata item.

MathML handling: Wikidata sometimes returns rendered MathML for search previews. Call formula_get on the result ID to retrieve the original LaTeX and a SymPy-ready string.

🎛️ You own every step

A derivation in SymKit is a chain of immutable, verifiable steps. You can:

• Create — session_record_step
• Read — session_get_steps, session_show
• Annotate — session_add_note
• Rollback — session_rollback
• Verify — session_verify_step, session_verify_session

Expressions are never edited in place. If something goes wrong, roll back to the last good state and continue. This keeps the entire derivation reproducible.

🌍 Works with the MCP ecosystem

SymKit is designed to extend, not replace, your scientific computing stack. It handles derivation, verification, and provenance; raw symbolic computation and base formulas are delegated to SymPy-MCP.

When to use SymKit:

• ✅ Deriving new formulas from existing ones
• ✅ Building temperature/pressure/parameter-corrected models
• ✅ Creating custom models for any quantitative domain
• ✅ Producing verified, citable derivation results

When to use something else:

• ❌ Looking up basic physics formulas → use sympy-mcp
• ❌ Fetching physical constants → use sympy-mcp or SciPy
• ❌ Clinical scoring → use medical-calc-mcp
• ❌ Reading textbook formulas → use the reference directly

📦 Get started in 60 seconds

Requirements

• Python 3.10+
• uv (recommended)

# Install
uv add symkit-mcp

# Or use pip
pip install symkit-mcp

Where data lives

After install, SymKit stores runtime data in a per-user directory (resolved via platformdirs): derived formulas and session JSONs persist under ~/.local/share/symkit/ (Linux), %LOCALAPPDATA%\symkit (Windows), or ~/Library/Application Support/symkit (macOS). Set the SYMKIT_DATA_DIR environment variable to override this location. Seed formulas (Reynolds number, Navier-Stokes, …) ship read-only inside the package; user-added formulas via formula_add are written to the writable overlay and override seeds by id.

Connect to Claude Desktop / Cherry Studio

The same JSON works in any MCP-compatible client (Claude Desktop, Cherry Studio, etc.).

If you installed from PyPI:

{
  "mcpServers": {
    "symkit": {
      "command": "uvx",
      "args": ["symkit-mcp"]
    }
  }
}

If you are running from the local source directory (no install needed):

{
  "mcpServers": {
    "symkit": {
      "command": "uv",
        "args": [
        "run",
        "--no-sync",
        "--directory",
        "<your-local-symkit-mcp-path>",
        "python",
        "-m",
        "symkit_mcp.server"
      ]
    }
  }
}

Replace --directory with the absolute path to your local symkit-mcp clone. --no-sync skips dependency resolution on every launch; run uv sync manually when dependencies change.

From source

git clone https://github.com/LBurny/symkit-mcp.git
cd symkit-mcp
uv sync --all-extras
uv run symkit-mcp

🏗️ Clean architecture, built to extend

symkit-mcp/
├── src/
│   ├── symkit/               # Pure domain logic (no MCP dependency)
│   │   ├── domain/          # Entities, value objects, derivation engine
│   │   ├── application/     # Use cases
│   │   └── infrastructure/  # SymPy engine, adapters, persistence
│   └── symkit_mcp/          # MCP server layer
│       ├── server.py
│       └── tools/           # 41 MCP tools
├── formulas/                # Seed formula library (source tree)
├── tests/                   # 295 tests
└── pyproject.toml

• Domain-driven design — core logic is independent of MCP and SymPy.
• Pluggable engines — swap the symbolic engine or verifier via protocols.
• File-based persistence — formulas and sessions live in readable Markdown/YAML/JSON.

🧪 Development

# Run the full test suite
uv run pytest

# Lint and type check
uv run ruff check src/ tests/
uv run mypy src/

# Start the dev server
uv run symkit-mcp

📖 Learn more

• Architecture — DDD layering and responsibilities
• SymKit Design — In-depth technical design (English)
• SymKit Design (中文) — 中文设计文档
• SymKit vs SymPy-MCP — Capability comparison
• Roadmap — What's coming next

🙏 Acknowledgments

SymKit is built on the foundation of nsforge-mcp, which pioneered the neurosymbolic formula-derivation approach. The original Chinese README of nsforge-mcp can be found here.

SymKit works alongside sympy-mcp, which provides the underlying SymPy-based symbolic computation and base formula lookup that SymKit builds upon.

📄 License

Apache 2.0 — see LICENSE.

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<p align="center"> <strong>Stop answering math questions. Start deriving new knowledge.</strong> </p>