# AI use cases for Jacobian (morluto/jacobian)

Repo: [morluto/jacobian](https://github.com/morluto/jacobian) | Use cases: 3 | Page: https://dedupedai.com/use-cases/morluto-jacobian/

Jacobian is an MCP server, CLI, and Python library that gives AI agents a searchable set of typed, exact mathematical operations they can inspect and run.

This file holds every use case of this repo. Each one starts with a "## " heading and ends with its URL.

- Have an agent compute an exact matrix determinant: https://dedupedai.com/use-cases/morluto-jacobian/agent-checks-exact-matrix-determinant/
- Compute a gcd and Bézout coefficients from the terminal: https://dedupedai.com/use-cases/morluto-jacobian/compute-gcd-and-bezout-from-terminal/
- Let an agent find and run a graph or SAT operation: https://dedupedai.com/use-cases/morluto-jacobian/agent-finds-solver-operation-for-graph-or-sat-question/

## How to have an agent compute an exact matrix determinant with Jacobian

Repo: [morluto/jacobian](https://github.com/morluto/jacobian) | Difficulty: Intermediate | Time: 30 minutes | Basis: From the README

Connect an MCP host to Jacobian so the agent computes exact determinants instead of estimating them.

**Who it is for:** A developer or analyst using an AI agent for linear algebra who needs exact rational results rather than approximate ones.

**The problem:** Language models often produce approximate or wrong arithmetic for determinants of rational matrices, and the answer cannot be checked.

**The outcome:** The agent finds the matrix.determinant.compute operation, reads its contract, and returns the exact determinant from a typed result.

### Steps

1. Run `npx jacobian@latest setup` and choose the agents you use, reviewing the changes before they are written.
2. Restart your agent host so it loads the Jacobian MCP server.
3. Ask the agent to use math.find in inspection mode on matrix.determinant.compute.
4. Ask the agent to call math.run once with an exact rational matrix of your choice.

### Prompt to paste into your agent

```text
Using the Jacobian MCP server from the repo morluto/jacobian, use math.find in inspection mode on matrix.determinant.compute, then call math.run once on the exact rational matrix <matrix>. Return the determinant as an exact value. Verify that the returned value is exact and not a decimal approximation.
```

### Caveat

Singular and QEPCAD are optional system runtimes for only a small subset of operations, so check the backend requirements before relying on a specific operation.

Disclaimer: Third-party repos we don't own or vouch for. AI-generated use cases can be wrong: review everything and run at your own risk. Full text: https://dedupedai.com/disclaimer/

URL: https://dedupedai.com/use-cases/morluto-jacobian/agent-checks-exact-matrix-determinant/

## How to compute a gcd and Bézout coefficients from the terminal with Jacobian

Repo: [morluto/jacobian](https://github.com/morluto/jacobian) | Difficulty: Intermediate | Time: 15 minutes | Basis: From the README

Install the Python package and get the gcd and Bézout coefficients of two integers as JSON.

**Who it is for:** A developer or student who wants a quick, exact check of an integer gcd without writing code, and who is comfortable with Python.

**The problem:** Hand calculations of extended gcd are slow and error-prone, and a quick exact check is needed.

**The outcome:** A JSON result with the gcd and the Bézout coefficients for the two inputs, produced by the installed Jacobian operation.

### Steps

1. Run `python -m pip install jacobian`.
2. Run `jacobian inspect integer.compute.extended_gcd` to read the exact contract.
3. Run `jacobian run integer.compute.extended_gcd --json '{"left":"84","right":"30"}'`.
4. Replace the left and right values in the JSON payload with your own integers and run the command again.

### Prompt to paste into your agent

```text
Install the repo morluto/jacobian with `python -m pip install jacobian`, then run `jacobian run integer.compute.extended_gcd` with the payload {"left":"<a>","right":"<b>"}. Report the gcd and Bézout coefficients as returned in JSON. Verify that a*x + b*y equals the gcd for the returned coefficients.
```

### Caveat

The tested binary install targets CPython 3.12 or 3.13 on glibc Linux x86-64, and other systems are not part of the tested release contract yet.

Disclaimer: Third-party repos we don't own or vouch for. AI-generated use cases can be wrong: review everything and run at your own risk. Full text: https://dedupedai.com/disclaimer/

URL: https://dedupedai.com/use-cases/morluto-jacobian/compute-gcd-and-bezout-from-terminal/

## How to let an agent find and run a graph or SAT operation with Jacobian

Repo: [morluto/jacobian](https://github.com/morluto/jacobian) | Difficulty: Advanced | Time: 30 minutes | Basis: From the README

Use math.find to match a graph or SAT question to a bounded operation, then run it once.

**Who it is for:** A researcher or engineer whose agent needs a bounded graph, coloring, or SAT or SMT answer and should not guess it from text.

**The problem:** Agents tend to reason informally about graph colorings or satisfiability, and the reasoning is hard to verify.

**The outcome:** The agent selects a matching typed operation, confirms its contract, and returns the solver result for your problem.

### Steps

1. Run `uvx --python 3.12 --from jacobian jacobian-mcp` or add the same command to your MCP host configuration.
2. Ask the agent to describe your problem and use math.find to search for a matching operation.
3. Ask the agent to use math.find in inspection mode on the most promising operation.
4. Ask the agent to call math.run once with your input and report the typed result.

### Prompt to paste into your agent

```text
Using the Jacobian MCP server from morluto/jacobian, use math.find to match this need: <problem description>. Inspect the best operation, call math.run once with <input>, and return the typed result. Verify that the result states whether it is exact, approximate, or incomplete.
```

### Caveat

Operations use the bundled Python backends, but some operations require the optional Singular or QEPCAD runtimes that the Python package does not provision.

Disclaimer: Third-party repos we don't own or vouch for. AI-generated use cases can be wrong: review everything and run at your own risk. Full text: https://dedupedai.com/disclaimer/

URL: https://dedupedai.com/use-cases/morluto-jacobian/agent-finds-solver-operation-for-graph-or-sat-question/