Jacobian README
The full upstream README, mirrored here for reference. Install config, tool schemas, adoption signals, and an original overview live on the Jacobian listing page.
English · 简体中文
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.
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:
Where an MCP host requires an npm command, the npm package is a deterministic carrier for that same command:
For a persistent installation:
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:
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:
Read CONTRIBUTING.md before changing code. It documents focused test commands, verification rules, documentation placement, and pull-request expectations.