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

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

  • Research
  • Intermediate
  • 15 minutes
  • From the README
  • Any agent

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

The problemHand calculations of extended gcd are slow and error-prone, and a quick exact check is needed.

The outcomeA JSON result with the gcd and the Bézout coefficients for the two inputs, produced by the installed Jacobian operation.

What you need first

  • Python 3.12 or 3.13 on glibc Linux x86-64 for the tested binary install, or another supported Python environment
  • uv with uvx on PATH for the canonical MCP command
  • Node.js 20.17+, 22.13+, or 23.5+ if you use the npm setup command
  • An MCP-capable agent host or a terminal for the CLI

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 for your agent

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.

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