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Jacobian
An executable mathematical vocabulary for agents: discover one typed operation, run it, and compose its result.
Jacobian is an MCP server that gives AI agents a searchable vocabulary of typed
mathematical operations. math.find discovers an operation, and math.run
executes exactly one bounded mathematical contract and returns its typed
result. The same mathematical library is also available through a CLI and
native Python API.
Each operation establishes one stable, reusable mathematical postcondition rather than prescribing a workflow or proof strategy. Results are exact where claimed and make approximation, incompleteness, or uncertainty explicit.
Jacobian's hypothesis is that mathematical reasoning benefits from an executable vocabulary of semantically scoped, bounded operations. Rather than exposing large domain solvers or precomposed workflows, Jacobian exposes mathematical primitives that agents can search for and compose into solutions beyond what any individual operation was designed to solve. The library supplies trustworthy mathematical moves; the reasoning model decides which moves to make, how to combine their results, and when to stop. Keeping the operations semantically narrow and domain-owned preserves that search space instead of baking one proof strategy or workflow into the tools themselves.
See Executable mathematical vocabulary for what semantic atomicity means and how the operation vocabulary grows.
Quickstart
Set up Jacobian for your agents with a single command. The setup command
requires Node.js 18 or newer and uvx on your PATH.
npx jacobian@latest setup
Choose detected agents and review the changes before they are written. Setup
does not install Node.js, Python, uv, or an agent. For automation, preview
an explicit plan with npx jacobian@latest setup --codex --dry-run; use
--yes only with explicit agent flags or --all.
Run the canonical Python MCP command without installing Jacobian globally:
uvx --from jacobian jacobian-mcp
Where an MCP host requires an npm command, the npm package is a deterministic carrier for that same command:
npx jacobian mcp
For a persistent installation:
python -m pip install jacobian
jacobian-mcp
That package includes Jacobian's exact maintained Python backend stack: SymPy, NetworkX, Z3, and Python-FLINT. A normal Python or npm installation therefore exposes the same built-in Python-backed operation portfolio. The tested binary-install contract is CPython 3.12 or 3.13 on glibc Linux x86-64; the release gate installs the built wheel and starts Jacobian on both Python versions. Other systems may have compatible upstream wheels, but are not part of the tested release contract yet. In particular, Alpine/musl cannot install the complete mandatory stack from PyPI.
The Python distribution contains the mathematical kernel, CLI, and MCP server.
The npm package deterministically maps its exact package version to the
corresponding uvx invocation.
Compute one bounded result
An ordinary operation returns mathematics first. For example,
matrix.determinant.compute accepts one exact rational matrix and returns its
determinant directly. Callers compose results by passing their typed values to a
subsequent operation.
Available mathematics
The built-in portfolio covers work in:
- polynomial maps and polynomial algebra;
- exact linear algebra;
- graphs, paths, colorings, and isomorphism;
- bounded SAT and SMT solving;
- finite algebra, probability, geometry, and topology; and
- Lean source elaboration.
SAT and SMT operations use the maintained Z3 Python binding directly. The
optional lean.check operation runs one bounded source snippet in the fixed
Lean service environment, using a request-scoped temporary directory and
returning typed diagnostics. Use math.find to search for an operation, browse
an unfamiliar domain, and inspect one operation before calling math.run once.
See the domain operation library for the maintained operation portfolio and backend requirements.
Status
Jacobian 0.13.0 is pre-stable. Its published package and operation contracts describe the supported surface; experimental operation contracts may change between releases.
Documentation
- Documentation home: tutorials, how-to guides, reference, and explanations
- Architecture: runtime structure and trust boundaries
- Product model: operation contracts, ownership, and project boundaries
- Tool reference: MCP resources and invocation contracts
- Backend requirements: maintained Python backends and optional Lean
- Remote deployment: HTTP deployment and authentication
Contributing
Jacobian uses Python 3.12, uv, and a small Makefile:
make setup
make test-math
make check
Read CONTRIBUTING.md before changing code. It documents focused test commands, verification rules, documentation placement, and pull-request expectations.