GAPLink

GAPLink connects Wolfram Language to GAP. Use GAP's groups, characters, finite fields, and packages from a Wolfram Language session.

Documentation · Paclet resource · Releases

Install

GAPLink requires Wolfram Language 15.0 or later on Linux x86-64, macOS (Intel or Apple silicon), or Windows x86-64. Release paclets include GAP and its required packages; a separate GAP installation is not needed.

Install the latest release for your system:

PacletInstall[
    ResourceObject[
        "https://www.wolframcloud.com/obj/wolframinstitute/DeployedResources/Paclet/WolframInstitute/GAPLink"
    ]["PacletFile"],
    ForceVersionInstall -> True,
    "ShowProgress" -> True
];

The resource selects your platform automatically. The command shows download progress and allows reinstalling the same version. Versioned .paclet files and checksums are also on GitHub Releases.

Quick start

Load GAPLink, start GAP, and count the permutations of five objects:

Needs["WolframInstitute`GAPLink`"];
session = StartGAPSession[];
group = GAPCall[session, "SymmetricGroup", 5];
GAPCall[session, "Size", group]

120

Keep this session open for the examples below. Loading GAPLink alone does not start GAP.

Examples

Characters

Find the dimensions of the irreducible representations of the group above:

characters = GAPCall[session, "Irr", group];
Sort[GAPCall[session, "DegreeOfCharacter", #] & /@ characters]

{1, 1, 4, 4, 5, 5, 6}

Matrices over a finite field

Count the invertible 2-by-2 matrices over the field with three elements:

matrices = GAPEvaluate[session, "GL(2,3);"];
GAPCall[session, "Size", matrices]

48

GAP functions as values

Use a function returned by GAP:

square = GAPEvaluate[session, "x -> x^2;"];
GAPCall[session, "List", {1, 2, 3, 4}, square]

{1, 4, 9, 16}

Close the session

Close GAP when finished:

DeleteObject[session];

Functions and values

Function	Purpose
StartGAPSession	Start GAP and return a GAPSession.
GAPCall	Call a GAP function with Wolfram Language arguments.
GAPEvaluate	Evaluate complete GAP source code.
GAPPackageAvailableQ	Check whether a package is installed.
LoadGAPPackage	Load an installed package.

GAPCall accepts GAP function names, record paths such as "MTX.Dimension", and functions held in a GAPObject. Use "GAPOptions" -> <|"name" -> value|> for GAP's named options. GAPEvaluate accepts complete GAP source code.

Groups, characters, finite fields, and other values that cannot be copied remain in GAP as GAPObject values. Pass them to further calls in the same session. Use "ReturnType" -> "Object" to retain a complete result, and Normal[object] to copy a supported value. Large, cyclic, or sparse containers stay in GAP.

LoadGAPPackage makes an installed package's functions available through the same interface. It does not download packages. The coverage report describes what is checked and what requires a separate package or interactive GAP.

Use another GAP

An explicit path takes priority over the GAP included in the paclet:

session = StartGAPSession["Executable" -> "/path/to/gap"];

Development

Development needs wolframscript, Git, make, Python 3, and GAP 4.14–4.16. Load a source checkout before evaluating the quick start:

PacletDirectoryLoad["/path/to/GAPLink/GAPLink"];

Source checkouts need a separate GAP installation. Check the source, run tests, and build the documentation and paclet with:

GAPLINK_GAP=/path/to/gap make all test-gap

make all fetches pinned PacletPage tools and evaluates the documentation examples. See CONTRIBUTING.md for platform builds and releases, and docs/architecture.md for the main design rules.

License

GAPLink code uses the MIT License. Release paclets also contain GAP, GMP, and GAP packages under their own licenses. Their license files are included with the runtime. Matching GAP source archives are available with each GitHub release.