gap

name	gap
description	Use when a proof step involves finite groups, character tables, conjugacy data, finite fields, or other exact discrete-algebra computations that can be checked or explored with a local GAP3/GAP4 CLI.

GAP

GAP is a system for computational discrete algebra. It is especially useful for finite groups, permutation groups, character tables, conjugacy classes, finite fields, and related exact algebra calculations.

Use GAP as a computational aid when a proof would benefit from exact finite algebra experiments, counterexample searches, or regression checks. The examples above are common uses, not an exhaustive boundary.

Availability

GAP is optional in this workspace. Users may have installed neither GAP CLI, only GAP4, only GAP3, or both. Treat the two command-line tools independently:

• gap is the expected GAP4 launcher. Do not assume a specific GAP4 version.
• gap3 is the expected GAP3 launcher. Do not assume a specific GAP3 version.

From the workspace root, check GAP4 availability with:

command -v gap
gap -q -c 'Print(Size(SymmetricGroup(3)),"\n"); QUIT;'

Optionally inspect the GAP4 version:

gap --version

Check GAP3 availability separately. GAP3 does not support the GAP4 -c or --version command-line options, so use stdin or a script file:

command -v gap3
printf 'Print(Size(SymmetricGroup(3)),"\\n"); quit;\n' | gap3 -q

If a launcher is missing or its smoke check fails, treat that GAP version as unavailable and do not claim evidence from it.

When To Use

Use GAP to check finite examples, search for counterexamples, compute small character tables, verify conjugacy-class counts, test explicit formulas for small parameters, or run other exact discrete-algebra computations that GAP is well suited for.

Prefer GAP4 (gap) for ordinary modern GAP computations. Use GAP3 (gap3) when the calculation depends on GAP3-only libraries, syntax, or historical behavior. If both are installed and the distinction matters, state which CLI was used.

Do not use GAP output as a substitute for a mathematical proof. Use it to find mistakes, guide conjectures, and support symbolic arguments that are written in the proof.

How To Use

For any nontrivial or multi-line calculation, write a .g script file and run it with the appropriate GAP CLI instead of packing the whole calculation into a shell one-liner:

# GAP4
gap -q path/to/check.g

# GAP3
gap3 -q path/to/check.g

This makes the computation easier to inspect, rerun, and move into solver/proof/ when it supports a submitted proof claim.

Artifact Policy

Scratch experiments may live under logs/optimize/.

If a GAP computation supports a submitted proof claim, put the GAP script, input data, generated table, or summarized output under solver/proof/, then cite the solver/proof/... path from the proof text. Do not rely on a claim whose only evidence is under logs/optimize/.