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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.

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 0.22.0 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

FAQ

Q: Does installing this asset automatically edit my global MCP configuration? A: No. TokRepo stages the supplied files. Review and merge .mcp.json in the client you use.

Q: Which version and Python runtime does this entry use? A: The supplied configuration pins Jacobian 0.22.0 and requests Python 3.12 through uvx. Upstream documents its tested platform contract and optional backends in the README.

Q: Has every operation been checked? A: No. The local check covered server initialization, tool discovery, and one exact extended-GCD result. Check each operation's typed contract and backend availability before relying on it.