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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 matches a mathematical need or inspects one exact contract, and math.run executes it 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 20.17+, 22.13+, or 23.5+ 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.

To refresh an existing registration explicitly, run npx jacobian@latest upgrade and select the agents to update. The generated launcher pins the exact release resolved by npm.

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.

Singular and QEPCAD are optional system runtimes for a small subset of operations. The Python installation does not provision them, and ordinary operations do not require Docker. Python callers can use jacobian.backends.check_backend; MCP inspection reports availability in the server environment. See backend requirements for exact coverage and setup.

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.

For a local terminal workflow, inspect the exact installed contract and run one of its examples with the CLI:

jacobian inspect integer.compute.extended_gcd
jacobian run integer.compute.extended_gcd --json '{"left":"84","right":"30"}'

The second command returns the gcd and Bézout coefficients as JSON. In an MCP host, use math.find in inspection mode to read the same contract and math.run with the same payload shape. See Discover and invoke operations for that agent workflow.

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.

SAT and SMT operations use the maintained Z3 Python binding directly. Use math.find to match the mathematical result needed, then use its inspection mode on a promising operation before calling math.run once.

See the domain operation library for the maintained operation portfolio and backend requirements.

Status

Jacobian 0.20.0 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
• Remote deployment: HTTP deployment and authentication

Contributing

Jacobian uses Python 3.12, uv, and a small Makefile:

make setup
make affected AFFECTED_BASE=origin/main

Read CONTRIBUTING.md before changing code. It documents focused test commands, verification rules, documentation placement, and pull-request expectations.

License

MIT