Math Computation Reproducible

Contract

• Input: mathematical computation (symbolic / numeric) and target CAS.
• Output: versioned script + container + manifest.
• Side effects: none.
• Dependencies: none.
• Stop condition: container builds; manifest complete.
• Risk: low.
• Boundary: produces reproducible artifacts; no system-wide install beyond declared environment.

Reproducible Math Computation

Run a mathematical computation that another researcher can rerun bit-for-bit — same inputs, same library versions, same outputs — and ship the artifacts.

When to use

• A paper's result depends on a non-trivial computation.
• A computational number (e.g. counterexample, zeta value) needs to be cited.
• A reviewer wants to verify the calculation.

Process

1. Pick the tool

• SymPy / SymEngine — symbolic, Python, free.
• Mathematica — broad coverage; commercial.
• Magma — number theory, algebra, finite groups.
• SageMath — open umbrella; bridges many libraries.
• Julia (Nemo, Hecke, AbstractAlgebra) — performance + algebra.

State the choice; pin version.

Completion criterion: tool and version fixed.

2. Script the computation

• One script per question (not a notebook cell dump).
• Inputs declared at the top.
• Random seeds explicit.
• Outputs written to files with content-hash filenames.

Completion criterion: script runs end-to-end from a clean checkout.

3. Pin the environment

• Python: requirements.txt with hashes, or pixi.lock / uv.lock.
• Conda: environment.yml with channel + version.
• Mathematica: $Version and $SystemID recorded.
• Magma: release version + OS.
• OS: declare base image (Ubuntu 22.04, etc.).

Completion criterion: env manifest saved with exact versions.

4. Containerise

• Docker: minimal image with the tool + dependencies.
• Apptainer (Singularity): for HPC clusters.
• Nix: for reproducible Linux builds.

The container must run the script and produce the declared outputs.

Completion criterion: container builds; produces identical outputs on a fresh host.

5. Archive and document

• Push code to a versioned repo (Git tag the result).
• Upload inputs / outputs to Zenodo with a DOI.
• Markdown report links: code repo, container image, Zenodo bundle, paper section.

Completion criterion: all artifacts reachable via DOI or Git tag.

Notes

• Pair with cs-formal-methods for verification and scientific-reproducibility for broader framing.
• A reproducible computation earns a footnote in the paper.